LMFDB - Embedded newform 737.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [737,2,Mod(1,737)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(737, 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("737.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 737 = 11 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	737.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:	$5.88497462897$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 26 x^{15} + 25 x^{14} + 272 x^{13} - 244 x^{12} - 1472 x^{11} + 1186 x^{10} + 4406 x^{9} + \cdots - 2 $ x^17 - x^16 - 26x^15 + 25x^14 + 272x^13 - 244x^12 - 1472x^11 + 1186x^10 + 4406x^9 - 3042x^8 - 7180x^7 + 4055x^6 + 5665x^5 - 2655x^4 - 1418x^3 + 810x^2 - 76*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.19652$ of defining polynomial
Character	$\chi$	$=$	737.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19652 q^{2} +0.987185 q^{3} -0.568334 q^{4} -0.744253 q^{5} -1.18119 q^{6} +4.07489 q^{7} +3.07307 q^{8} -2.02547 q^{9} +O(q^{10})$	\(q-1.19652 q^{2} +0.987185 q^{3} -0.568334 q^{4} -0.744253 q^{5} -1.18119 q^{6} +4.07489 q^{7} +3.07307 q^{8} -2.02547 q^{9} +0.890515 q^{10} +1.00000 q^{11} -0.561050 q^{12} -1.12199 q^{13} -4.87570 q^{14} -0.734715 q^{15} -2.54033 q^{16} +5.26387 q^{17} +2.42352 q^{18} -1.09401 q^{19} +0.422984 q^{20} +4.02267 q^{21} -1.19652 q^{22} -0.724154 q^{23} +3.03369 q^{24} -4.44609 q^{25} +1.34249 q^{26} -4.96106 q^{27} -2.31590 q^{28} +0.375376 q^{29} +0.879103 q^{30} +9.00211 q^{31} -3.10658 q^{32} +0.987185 q^{33} -6.29834 q^{34} -3.03275 q^{35} +1.15114 q^{36} +11.2851 q^{37} +1.30900 q^{38} -1.10761 q^{39} -2.28714 q^{40} +6.79208 q^{41} -4.81322 q^{42} +11.2636 q^{43} -0.568334 q^{44} +1.50746 q^{45} +0.866467 q^{46} -10.2318 q^{47} -2.50777 q^{48} +9.60475 q^{49} +5.31984 q^{50} +5.19641 q^{51} +0.637664 q^{52} -6.24245 q^{53} +5.93602 q^{54} -0.744253 q^{55} +12.5224 q^{56} -1.07999 q^{57} -0.449145 q^{58} +11.2509 q^{59} +0.417563 q^{60} +9.85237 q^{61} -10.7712 q^{62} -8.25356 q^{63} +8.79775 q^{64} +0.835044 q^{65} -1.18119 q^{66} -1.00000 q^{67} -2.99163 q^{68} -0.714874 q^{69} +3.62875 q^{70} +0.951027 q^{71} -6.22440 q^{72} -2.36454 q^{73} -13.5029 q^{74} -4.38911 q^{75} +0.621760 q^{76} +4.07489 q^{77} +1.32528 q^{78} -3.24116 q^{79} +1.89065 q^{80} +1.17891 q^{81} -8.12688 q^{82} -4.53797 q^{83} -2.28622 q^{84} -3.91765 q^{85} -13.4771 q^{86} +0.370565 q^{87} +3.07307 q^{88} -5.18671 q^{89} -1.80371 q^{90} -4.57199 q^{91} +0.411561 q^{92} +8.88674 q^{93} +12.2426 q^{94} +0.814216 q^{95} -3.06676 q^{96} +18.5902 q^{97} -11.4923 q^{98} -2.02547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9}+O(q^{10}) $ 17 * q + q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 - 6 * q^6 + 20 * q^7 + 25 * q^9	\( 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9} + 10 q^{10} + 17 q^{11} + 18 q^{12} + q^{13} - 11 q^{14} + 7 q^{15} + 19 q^{16} + 2 q^{17} - 24 q^{18} + 13 q^{19} + 3 q^{20} + 5 q^{21} + q^{22} + 16 q^{23} - 36 q^{24} + 33 q^{25} + 12 q^{26} + 19 q^{27} + 44 q^{28} - 5 q^{29} + 3 q^{30} + 16 q^{31} - 24 q^{32} + 10 q^{33} + 4 q^{34} - 2 q^{35} + 25 q^{36} + 29 q^{37} - 19 q^{38} + 2 q^{39} + 31 q^{40} - 6 q^{41} - 26 q^{42} + 19 q^{43} + 19 q^{44} + 20 q^{45} - 33 q^{46} + 40 q^{47} + 81 q^{48} + 23 q^{49} - 3 q^{50} - q^{51} - 28 q^{52} + 15 q^{53} - 27 q^{54} + 10 q^{55} - 38 q^{56} - 27 q^{57} - 12 q^{58} - 2 q^{59} - 59 q^{60} - 6 q^{61} + 3 q^{62} + 32 q^{63} - 4 q^{64} - 30 q^{65} - 6 q^{66} - 17 q^{67} - 13 q^{68} + 5 q^{69} + 71 q^{70} + 2 q^{71} - 47 q^{72} + 41 q^{73} - 13 q^{74} - 6 q^{75} + 21 q^{76} + 20 q^{77} + 31 q^{78} + 41 q^{79} - 23 q^{80} + 37 q^{81} - 8 q^{82} + 2 q^{83} - 16 q^{84} - 36 q^{85} - 54 q^{86} + 32 q^{87} + q^{89} - 44 q^{90} + 16 q^{91} + 36 q^{92} + 26 q^{93} + 12 q^{94} - 31 q^{95} - 72 q^{96} + 3 q^{97} - 64 q^{98} + 25 q^{99}+O(q^{100}) \) 17 * q + q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 - 6 * q^6 + 20 * q^7 + 25 * q^9 + 10 * q^10 + 17 * q^11 + 18 * q^12 + q^13 - 11 * q^14 + 7 * q^15 + 19 * q^16 + 2 * q^17 - 24 * q^18 + 13 * q^19 + 3 * q^20 + 5 * q^21 + q^22 + 16 * q^23 - 36 * q^24 + 33 * q^25 + 12 * q^26 + 19 * q^27 + 44 * q^28 - 5 * q^29 + 3 * q^30 + 16 * q^31 - 24 * q^32 + 10 * q^33 + 4 * q^34 - 2 * q^35 + 25 * q^36 + 29 * q^37 - 19 * q^38 + 2 * q^39 + 31 * q^40 - 6 * q^41 - 26 * q^42 + 19 * q^43 + 19 * q^44 + 20 * q^45 - 33 * q^46 + 40 * q^47 + 81 * q^48 + 23 * q^49 - 3 * q^50 - q^51 - 28 * q^52 + 15 * q^53 - 27 * q^54 + 10 * q^55 - 38 * q^56 - 27 * q^57 - 12 * q^58 - 2 * q^59 - 59 * q^60 - 6 * q^61 + 3 * q^62 + 32 * q^63 - 4 * q^64 - 30 * q^65 - 6 * q^66 - 17 * q^67 - 13 * q^68 + 5 * q^69 + 71 * q^70 + 2 * q^71 - 47 * q^72 + 41 * q^73 - 13 * q^74 - 6 * q^75 + 21 * q^76 + 20 * q^77 + 31 * q^78 + 41 * q^79 - 23 * q^80 + 37 * q^81 - 8 * q^82 + 2 * q^83 - 16 * q^84 - 36 * q^85 - 54 * q^86 + 32 * q^87 + q^89 - 44 * q^90 + 16 * q^91 + 36 * q^92 + 26 * q^93 + 12 * q^94 - 31 * q^95 - 72 * q^96 + 3 * q^97 - 64 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.19652	−0.846069	−0.423035	−	0.906114i	$-0.639035\pi$
$2$	−1.19652	−0.846069	−0.423035	+	0.906114i	$0.639035\pi$
$3$	0.987185	0.569951	0.284976	−	0.958535i	$-0.408014\pi$
$3$	0.987185	0.569951	0.284976	+	0.958535i	$0.408014\pi$
$4$	−0.568334	−0.284167
$5$	−0.744253	−0.332840	−0.166420	−	0.986055i	$-0.553221\pi$
$5$	−0.744253	−0.332840	−0.166420	+	0.986055i	$0.553221\pi$
$6$	−1.18119	−0.482218
$7$	4.07489	1.54016	0.770082	−	0.637944i	$-0.220215\pi$
$7$	4.07489	1.54016	0.770082	+	0.637944i	$0.220215\pi$
$8$	3.07307	1.08649
$9$	−2.02547	−0.675155
$10$	0.890515	0.281606
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.561050	−0.161961
$13$	−1.12199	−0.311184	−0.155592	−	0.987821i	$-0.549728\pi$
$13$	−1.12199	−0.311184	−0.155592	+	0.987821i	$0.549728\pi$
$14$	−4.87570	−1.30309
$15$	−0.734715	−0.189703
$16$	−2.54033	−0.635082
$17$	5.26387	1.27668	0.638338	−	0.769756i	$-0.279622\pi$
$17$	5.26387	1.27668	0.638338	+	0.769756i	$0.279622\pi$
$18$	2.42352	0.571228
$19$	−1.09401	−0.250982	−0.125491	−	0.992095i	$-0.540051\pi$
$19$	−1.09401	−0.250982	−0.125491	+	0.992095i	$0.540051\pi$
$20$	0.422984	0.0945821
$21$	4.02267	0.877819
$22$	−1.19652	−0.255099
$23$	−0.724154	−0.150997	−0.0754983	−	0.997146i	$-0.524055\pi$
$23$	−0.724154	−0.150997	−0.0754983	+	0.997146i	$0.524055\pi$
$24$	3.03369	0.619249
$25$	−4.44609	−0.889218
$26$	1.34249	0.263283
$27$	−4.96106	−0.954757
$28$	−2.31590	−0.437664
$29$	0.375376	0.0697055	0.0348528	−	0.999392i	$-0.488904\pi$
$29$	0.375376	0.0697055	0.0348528	+	0.999392i	$0.488904\pi$
$30$	0.879103	0.160502
$31$	9.00211	1.61683	0.808413	−	0.588615i	$-0.200327\pi$
$31$	9.00211	1.61683	0.808413	+	0.588615i	$0.200327\pi$
$32$	−3.10658	−0.549170
$33$	0.987185	0.171847
$34$	−6.29834	−1.08016
$35$	−3.03275	−0.512628
$36$	1.15114	0.191857
$37$	11.2851	1.85526	0.927630	−	0.373502i	$-0.121843\pi$
$37$	11.2851	1.85526	0.927630	+	0.373502i	$0.121843\pi$
$38$	1.30900	0.212348
$39$	−1.10761	−0.177360
$40$	−2.28714	−0.361629
$41$	6.79208	1.06074	0.530372	−	0.847765i	$-0.322052\pi$
$41$	6.79208	1.06074	0.530372	+	0.847765i	$0.322052\pi$
$42$	−4.81322	−0.742696
$43$	11.2636	1.71768	0.858838	−	0.512247i	$-0.171187\pi$
$43$	11.2636	1.71768	0.858838	+	0.512247i	$0.171187\pi$
$44$	−0.568334	−0.0856795
$45$	1.50746	0.224719
$46$	0.866467	0.127754
$47$	−10.2318	−1.49247	−0.746234	−	0.665684i	$-0.768140\pi$
$47$	−10.2318	−1.49247	−0.746234	+	0.665684i	$0.768140\pi$
$48$	−2.50777	−0.361966
$49$	9.60475	1.37211
$50$	5.31984	0.752340
$51$	5.19641	0.727643
$52$	0.637664	0.0884281
$53$	−6.24245	−0.857466	−0.428733	−	0.903431i	$-0.641040\pi$
$53$	−6.24245	−0.857466	−0.428733	+	0.903431i	$0.641040\pi$
$54$	5.93602	0.807791
$55$	−0.744253	−0.100355
$56$	12.5224	1.67338
$57$	−1.07999	−0.143048
$58$	−0.449145	−0.0589757
$59$	11.2509	1.46474	0.732372	−	0.680904i	$-0.238413\pi$
$59$	11.2509	1.46474	0.732372	+	0.680904i	$0.238413\pi$
$60$	0.417563	0.0539072
$61$	9.85237	1.26147	0.630733	−	0.776000i	$-0.282754\pi$
$61$	9.85237	1.26147	0.630733	+	0.776000i	$0.282754\pi$
$62$	−10.7712	−1.36795
$63$	−8.25356	−1.03985
$64$	8.79775	1.09972
$65$	0.835044	0.103574
$66$	−1.18119	−0.145394
$67$	−1.00000	−0.122169
$67$	−1.00000	−0.122169
$68$	−2.99163	−0.362789
$69$	−0.714874	−0.0860607
$70$	3.62875	0.433719
$71$	0.951027	0.112866	0.0564330	−	0.998406i	$-0.482027\pi$
$71$	0.951027	0.112866	0.0564330	+	0.998406i	$0.482027\pi$
$72$	−6.22440	−0.733552
$73$	−2.36454	−0.276748	−0.138374	−	0.990380i	$-0.544188\pi$
$73$	−2.36454	−0.276748	−0.138374	+	0.990380i	$0.544188\pi$
$74$	−13.5029	−1.56968
$75$	−4.38911	−0.506811
$76$	0.621760	0.0713208
$77$	4.07489	0.464377
$78$	1.32528	0.150059
$79$	−3.24116	−0.364659	−0.182329	−	0.983238i	$-0.558364\pi$
$79$	−3.24116	−0.364659	−0.182329	+	0.983238i	$0.558364\pi$
$80$	1.89065	0.211381
$81$	1.17891	0.130990
$82$	−8.12688	−0.897463
$83$	−4.53797	−0.498107	−0.249053	−	0.968490i	$-0.580119\pi$
$83$	−4.53797	−0.498107	−0.249053	+	0.968490i	$0.580119\pi$
$84$	−2.28622	−0.249447
$85$	−3.91765	−0.424929
$86$	−13.4771	−1.45327
$87$	0.370565	0.0397288
$88$	3.07307	0.327590
$89$	−5.18671	−0.549790	−0.274895	−	0.961474i	$-0.588643\pi$
$89$	−5.18671	−0.549790	−0.274895	+	0.961474i	$0.588643\pi$
$90$	−1.80371	−0.190128
$91$	−4.57199	−0.479274
$92$	0.411561	0.0429082
$93$	8.88674	0.921512
$94$	12.2426	1.26273
$95$	0.814216	0.0835368
$96$	−3.06676	−0.313000
$97$	18.5902	1.88755	0.943774	−	0.330590i	$-0.107248\pi$
$97$	18.5902	1.88755	0.943774	+	0.330590i	$0.107248\pi$
$98$	−11.4923	−1.16090
$99$	−2.02547	−0.203567
$100$	2.52686	0.252686
$101$	−8.94178	−0.889740	−0.444870	−	0.895595i	$-0.646750\pi$
$101$	−8.94178	−0.889740	−0.444870	+	0.895595i	$0.646750\pi$
$102$	−6.21762	−0.615636
$103$	−3.32967	−0.328082	−0.164041	−	0.986454i	$-0.552453\pi$
$103$	−3.32967	−0.328082	−0.164041	+	0.986454i	$0.552453\pi$
$104$	−3.44795	−0.338099
$105$	−2.99388	−0.292173
$106$	7.46923	0.725476
$107$	−3.44807	−0.333338	−0.166669	−	0.986013i	$-0.553301\pi$
$107$	−3.44807	−0.333338	−0.166669	+	0.986013i	$0.553301\pi$
$108$	2.81954	0.271310
$109$	18.5179	1.77369	0.886845	−	0.462067i	$-0.152892\pi$
$109$	18.5179	1.77369	0.886845	+	0.462067i	$0.152892\pi$
$110$	0.890515	0.0849073
$111$	11.1405	1.05741
$112$	−10.3516	−0.978132
$113$	−2.67935	−0.252052	−0.126026	−	0.992027i	$-0.540222\pi$
$113$	−2.67935	−0.252052	−0.126026	+	0.992027i	$0.540222\pi$
$114$	1.29223	0.121028
$115$	0.538954	0.0502577
$116$	−0.213339	−0.0198080
$117$	2.27255	0.210098
$118$	−13.4620	−1.23928
$119$	21.4497	1.96629
$120$	−2.25783	−0.206111
$121$	1.00000	0.0909091
$122$	−11.7886	−1.06729
$123$	6.70504	0.604573
$124$	−5.11620	−0.459448
$125$	7.03028	0.628807
$126$	9.87557	0.879786
$127$	−8.65780	−0.768256	−0.384128	−	0.923280i	$-0.625498\pi$
$127$	−8.65780	−0.768256	−0.384128	+	0.923280i	$0.625498\pi$
$128$	−4.31355	−0.381268
$129$	11.1192	0.978992
$130$	−0.999149	−0.0876311
$131$	−17.3709	−1.51771	−0.758853	−	0.651262i	$-0.774240\pi$
$131$	−17.3709	−1.51771	−0.758853	+	0.651262i	$0.774240\pi$
$132$	−0.561050	−0.0488332
$133$	−4.45795	−0.386554
$134$	1.19652	0.103364
$135$	3.69229	0.317781
$136$	16.1762	1.38710
$137$	21.4281	1.83072	0.915361	−	0.402634i	$-0.131905\pi$
$137$	21.4281	1.83072	0.915361	+	0.402634i	$0.131905\pi$
$138$	0.855363	0.0728133
$139$	−17.0333	−1.44474	−0.722371	−	0.691506i	$-0.756948\pi$
$139$	−17.0333	−1.44474	−0.722371	+	0.691506i	$0.756948\pi$
$140$	1.72361	0.145672
$141$	−10.1007	−0.850634
$142$	−1.13792	−0.0954925
$143$	−1.12199	−0.0938255
$144$	5.14535	0.428779
$145$	−0.279374	−0.0232008
$146$	2.82922	0.234148
$147$	9.48167	0.782035
$148$	−6.41370	−0.527203
$149$	−20.6676	−1.69316	−0.846579	−	0.532263i	$-0.821342\pi$
$149$	−20.6676	−1.69316	−0.846579	+	0.532263i	$0.821342\pi$
$150$	5.25167	0.428797
$151$	2.71367	0.220835	0.110418	−	0.993885i	$-0.464781\pi$
$151$	2.71367	0.220835	0.110418	+	0.993885i	$0.464781\pi$
$152$	−3.36195	−0.272691
$153$	−10.6618	−0.861955
$154$	−4.87570	−0.392895
$155$	−6.69984	−0.538144
$156$	0.629492	0.0503997
$157$	−19.7580	−1.57686	−0.788428	−	0.615127i	$-0.789105\pi$
$157$	−19.7580	−1.57686	−0.788428	+	0.615127i	$0.789105\pi$
$158$	3.87812	0.308527
$159$	−6.16245	−0.488714
$160$	2.31208	0.182786
$161$	−2.95085	−0.232560
$162$	−1.41060	−0.110827
$163$	1.47742	0.115720	0.0578601	−	0.998325i	$-0.481572\pi$
$163$	1.47742	0.115720	0.0578601	+	0.998325i	$0.481572\pi$
$164$	−3.86017	−0.301428
$165$	−0.734715	−0.0571975
$166$	5.42978	0.421433
$167$	0.728612	0.0563817	0.0281909	−	0.999603i	$-0.491025\pi$
$167$	0.728612	0.0563817	0.0281909	+	0.999603i	$0.491025\pi$
$168$	12.3619	0.953745
$169$	−11.7411	−0.903165
$170$	4.68756	0.359519
$171$	2.21587	0.169452
$172$	−6.40146	−0.488107
$173$	−11.0768	−0.842152	−0.421076	−	0.907025i	$-0.638348\pi$
$173$	−11.0768	−0.842152	−0.421076	+	0.907025i	$0.638348\pi$
$174$	−0.443390	−0.0336133
$175$	−18.1173	−1.36954
$176$	−2.54033	−0.191485
$177$	11.1067	0.834833
$178$	6.20602	0.465161
$179$	6.12132	0.457529	0.228765	−	0.973482i	$-0.426531\pi$
$179$	6.12132	0.457529	0.228765	+	0.973482i	$0.426531\pi$
$180$	−0.856740	−0.0638576
$181$	16.1112	1.19754	0.598769	−	0.800922i	$-0.295657\pi$
$181$	16.1112	1.19754	0.598769	+	0.800922i	$0.295657\pi$
$182$	5.47049	0.405499
$183$	9.72610	0.718974
$184$	−2.22538	−0.164057
$185$	−8.39897	−0.617504
$186$	−10.6332	−0.779663
$187$	5.26387	0.384932
$188$	5.81510	0.424110
$189$	−20.2158	−1.47048
$190$	−0.974228	−0.0706780
$191$	−3.72993	−0.269889	−0.134944	−	0.990853i	$-0.543086\pi$
$191$	−3.72993	−0.269889	−0.134944	+	0.990853i	$0.543086\pi$
$192$	8.68500	0.626786
$193$	−7.25204	−0.522013	−0.261007	−	0.965337i	$-0.584054\pi$
$193$	−7.25204	−0.522013	−0.261007	+	0.965337i	$0.584054\pi$
$194$	−22.2436	−1.59700
$195$	0.824342	0.0590324
$196$	−5.45870	−0.389907
$197$	−5.14820	−0.366794	−0.183397	−	0.983039i	$-0.558709\pi$
$197$	−5.14820	−0.366794	−0.183397	+	0.983039i	$0.558709\pi$
$198$	2.42352	0.172232
$199$	−3.42377	−0.242704	−0.121352	−	0.992610i	$-0.538723\pi$
$199$	−3.42377	−0.242704	−0.121352	+	0.992610i	$0.538723\pi$
$200$	−13.6631	−0.966130
$201$	−0.987185	−0.0696306
$202$	10.6990	0.752782
$203$	1.52962	0.107358
$204$	−2.95329	−0.206772
$205$	−5.05502	−0.353058
$206$	3.98403	0.277580
$207$	1.46675	0.101946
$208$	2.85022	0.197627
$209$	−1.09401	−0.0756739
$210$	3.58225	0.247199
$211$	−18.3075	−1.26034	−0.630172	−	0.776456i	$-0.717015\pi$
$211$	−18.3075	−1.26034	−0.630172	+	0.776456i	$0.717015\pi$
$212$	3.54779	0.243663
$213$	0.938839	0.0643282
$214$	4.12570	0.282027
$215$	−8.38293	−0.571711
$216$	−15.2457	−1.03734
$217$	36.6826	2.49018
$218$	−22.1570	−1.50066
$219$	−2.33424	−0.157733
$220$	0.422984	0.0285176
$221$	−5.90601	−0.397281
$222$	−13.3298	−0.894640
$223$	−13.8312	−0.926205	−0.463102	−	0.886305i	$-0.653264\pi$
$223$	−13.8312	−0.926205	−0.463102	+	0.886305i	$0.653264\pi$
$224$	−12.6590	−0.845813
$225$	9.00540	0.600360
$226$	3.20590	0.213253
$227$	−4.02566	−0.267193	−0.133596	−	0.991036i	$-0.542653\pi$
$227$	−4.02566	−0.267193	−0.133596	+	0.991036i	$0.542653\pi$
$228$	0.613792	0.0406494
$229$	−28.7740	−1.90144	−0.950719	−	0.310055i	$-0.899653\pi$
$229$	−28.7740	−1.90144	−0.950719	+	0.310055i	$0.899653\pi$
$230$	−0.644870	−0.0425215
$231$	4.02267	0.264672
$232$	1.15356	0.0757346
$233$	−11.0675	−0.725054	−0.362527	−	0.931973i	$-0.618086\pi$
$233$	−11.0675	−0.725054	−0.362527	+	0.931973i	$0.618086\pi$
$234$	−2.71916	−0.177757
$235$	7.61508	0.496753
$236$	−6.39427	−0.416232
$237$	−3.19962	−0.207838
$238$	−25.6651	−1.66362
$239$	23.8339	1.54169	0.770844	−	0.637024i	$-0.219835\pi$
$239$	23.8339	1.54169	0.770844	+	0.637024i	$0.219835\pi$
$240$	1.86642	0.120477
$241$	13.4590	0.866971	0.433485	−	0.901161i	$-0.357284\pi$
$241$	13.4590	0.866971	0.433485	+	0.901161i	$0.357284\pi$
$242$	−1.19652	−0.0769154
$243$	16.0470	1.02942
$244$	−5.59943	−0.358467
$245$	−7.14836	−0.456692
$246$	−8.02273	−0.511510
$247$	1.22746	0.0781016
$248$	27.6641	1.75667
$249$	−4.47981	−0.283897
$250$	−8.41189	−0.532014
$251$	−27.7320	−1.75043	−0.875216	−	0.483733i	$-0.839281\pi$
$251$	−27.7320	−1.75043	−0.875216	+	0.483733i	$0.839281\pi$
$252$	4.69077	0.295491
$253$	−0.724154	−0.0455272
$254$	10.3593	0.649998
$255$	−3.86744	−0.242189
$256$	−12.4342	−0.777140
$257$	−15.7445	−0.982114	−0.491057	−	0.871127i	$-0.663389\pi$
$257$	−15.7445	−0.982114	−0.491057	+	0.871127i	$0.663389\pi$
$258$	−13.3044	−0.828295
$259$	45.9856	2.85740
$260$	−0.474583	−0.0294324
$261$	−0.760311	−0.0470621
$262$	20.7847	1.28408
$263$	14.1490	0.872466	0.436233	−	0.899834i	$-0.356312\pi$
$263$	14.1490	0.872466	0.436233	+	0.899834i	$0.356312\pi$
$264$	3.03369	0.186711
$265$	4.64596	0.285399
$266$	5.33404	0.327051
$267$	−5.12024	−0.313354
$268$	0.568334	0.0347165
$269$	3.66802	0.223643	0.111821	−	0.993728i	$-0.464332\pi$
$269$	3.66802	0.223643	0.111821	+	0.993728i	$0.464332\pi$
$270$	−4.41790	−0.268865
$271$	32.4689	1.97235	0.986174	−	0.165712i	$-0.0529924\pi$
$271$	32.4689	1.97235	0.986174	+	0.165712i	$0.0529924\pi$
$272$	−13.3720	−0.810794
$273$	−4.51340	−0.273163
$274$	−25.6391	−1.54892
$275$	−4.44609	−0.268109
$276$	0.406287	0.0244556
$277$	−8.27566	−0.497236	−0.248618	−	0.968602i	$-0.579976\pi$
$277$	−8.27566	−0.497236	−0.248618	+	0.968602i	$0.579976\pi$
$278$	20.3807	1.22235
$279$	−18.2335	−1.09161
$280$	−9.31985	−0.556968
$281$	−17.0978	−1.01997	−0.509986	−	0.860183i	$-0.670349\pi$
$281$	−17.0978	−1.01997	−0.509986	+	0.860183i	$0.670349\pi$
$282$	12.0857	0.719695
$283$	−14.2677	−0.848130	−0.424065	−	0.905632i	$-0.639397\pi$
$283$	−14.2677	−0.848130	−0.424065	+	0.905632i	$0.639397\pi$
$284$	−0.540500	−0.0320728
$285$	0.803782	0.0476119
$286$	1.34249	0.0793828
$287$	27.6770	1.63372
$288$	6.29227	0.370775
$289$	10.7083	0.629901
$290$	0.334278	0.0196295
$291$	18.3520	1.07581
$292$	1.34385	0.0786427
$293$	−20.3642	−1.18969	−0.594843	−	0.803842i	$-0.702786\pi$
$293$	−20.3642	−1.18969	−0.594843	+	0.803842i	$0.702786\pi$
$294$	−11.3450	−0.661655
$295$	−8.37353	−0.487526
$296$	34.6799	2.01573
$297$	−4.96106	−0.287870
$298$	24.7293	1.43253
$299$	0.812493	0.0469877
$300$	2.49448	0.144019
$301$	45.8978	2.64550
$302$	−3.24697	−0.186842
$303$	−8.82719	−0.507109
$304$	2.77913	0.159394
$305$	−7.33265	−0.419866
$306$	12.7571	0.729273
$307$	8.76598	0.500301	0.250151	−	0.968207i	$-0.419520\pi$
$307$	8.76598	0.500301	0.250151	+	0.968207i	$0.419520\pi$
$308$	−2.31590	−0.131961
$309$	−3.28700	−0.186991
$310$	8.01651	0.455307
$311$	17.4388	0.988862	0.494431	−	0.869217i	$-0.335376\pi$
$311$	17.4388	0.988862	0.494431	+	0.869217i	$0.335376\pi$
$312$	−3.40376	−0.192700
$313$	19.5878	1.10717	0.553584	−	0.832793i	$-0.313260\pi$
$313$	19.5878	1.10717	0.553584	+	0.832793i	$0.313260\pi$
$314$	23.6408	1.33413
$315$	6.14273	0.346104
$316$	1.84206	0.103624
$317$	15.1231	0.849398	0.424699	−	0.905335i	$-0.360380\pi$
$317$	15.1231	0.849398	0.424699	+	0.905335i	$0.360380\pi$
$318$	7.37351	0.413486
$319$	0.375376	0.0210170
$320$	−6.54775	−0.366030
$321$	−3.40388	−0.189986
$322$	3.53076	0.196762
$323$	−5.75870	−0.320423
$324$	−0.670016	−0.0372231
$325$	4.98846	0.276710
$326$	−1.76776	−0.0979072
$327$	18.2806	1.01092
$328$	20.8725	1.15249
$329$	−41.6937	−2.29865
$330$	0.879103	0.0483930
$331$	32.4727	1.78486	0.892431	−	0.451183i	$-0.148998\pi$
$331$	32.4727	1.78486	0.892431	+	0.451183i	$0.148998\pi$
$332$	2.57908	0.141545
$333$	−22.8576	−1.25259
$334$	−0.871801	−0.0477028
$335$	0.744253	0.0406629
$336$	−10.2189	−0.557487
$337$	7.46901	0.406863	0.203431	−	0.979089i	$-0.434791\pi$
$337$	7.46901	0.406863	0.203431	+	0.979089i	$0.434791\pi$
$338$	14.0485	0.764140
$339$	−2.64501	−0.143657
$340$	2.22653	0.120751
$341$	9.00211	0.487492
$342$	−2.65134	−0.143368
$343$	10.6141	0.573107
$344$	34.6137	1.86625
$345$	0.532047	0.0286444
$346$	13.2536	0.712519
$347$	8.28225	0.444615	0.222307	−	0.974977i	$-0.428641\pi$
$347$	8.28225	0.444615	0.222307	+	0.974977i	$0.428641\pi$
$348$	−0.210605	−0.0112896
$349$	25.1876	1.34826	0.674131	−	0.738612i	$-0.264518\pi$
$349$	25.1876	1.34826	0.674131	+	0.738612i	$0.264518\pi$
$350$	21.6778	1.15873
$351$	5.56626	0.297105
$352$	−3.10658	−0.165581
$353$	−0.456526	−0.0242984	−0.0121492	−	0.999926i	$-0.503867\pi$
$353$	−0.456526	−0.0242984	−0.0121492	+	0.999926i	$0.503867\pi$
$354$	−13.2895	−0.706327
$355$	−0.707804	−0.0375663
$356$	2.94778	0.156232
$357$	21.1748	1.12069
$358$	−7.32430	−0.387101
$359$	−5.29880	−0.279660	−0.139830	−	0.990176i	$-0.544656\pi$
$359$	−5.29880	−0.279660	−0.139830	+	0.990176i	$0.544656\pi$
$360$	4.63253	0.244156
$361$	−17.8032	−0.937008
$362$	−19.2774	−1.01320
$363$	0.987185	0.0518138
$364$	2.59841	0.136194
$365$	1.75981	0.0921129
$366$	−11.6375	−0.608302
$367$	17.8911	0.933907	0.466954	−	0.884282i	$-0.345351\pi$
$367$	17.8911	0.933907	0.466954	+	0.884282i	$0.345351\pi$
$368$	1.83959	0.0958953
$369$	−13.7571	−0.716167
$370$	10.0496	0.522451
$371$	−25.4373	−1.32064
$372$	−5.05063	−0.261863
$373$	−18.9707	−0.982267	−0.491133	−	0.871084i	$-0.663417\pi$
$373$	−18.9707	−0.982267	−0.491133	+	0.871084i	$0.663417\pi$
$374$	−6.29834	−0.325679
$375$	6.94018	0.358389
$376$	−31.4432	−1.62156
$377$	−0.421168	−0.0216912
$378$	24.1887	1.24413
$379$	−12.6482	−0.649692	−0.324846	−	0.945767i	$-0.605313\pi$
$379$	−12.6482	−0.649692	−0.324846	+	0.945767i	$0.605313\pi$
$380$	−0.462747	−0.0237384
$381$	−8.54685	−0.437868
$382$	4.46295	0.228344
$383$	11.2321	0.573931	0.286966	−	0.957941i	$-0.407353\pi$
$383$	11.2321	0.573931	0.286966	+	0.957941i	$0.407353\pi$
$384$	−4.25827	−0.217304
$385$	−3.03275	−0.154563
$386$	8.67723	0.441659
$387$	−22.8140	−1.15970
$388$	−10.5654	−0.536379
$389$	−31.2055	−1.58218	−0.791090	−	0.611700i	$-0.790486\pi$
$389$	−31.2055	−1.58218	−0.791090	+	0.611700i	$0.790486\pi$
$390$	−0.986344	−0.0499455
$391$	−3.81185	−0.192774
$392$	29.5161	1.49079
$393$	−17.1483	−0.865019
$394$	6.15994	0.310333
$395$	2.41224	0.121373
$396$	1.15114	0.0578470
$397$	−20.6539	−1.03659	−0.518295	−	0.855202i	$-0.673433\pi$
$397$	−20.6539	−1.03659	−0.518295	+	0.855202i	$0.673433\pi$
$398$	4.09661	0.205345
$399$	−4.40082	−0.220317
$400$	11.2945	0.564726
$401$	−31.6619	−1.58112	−0.790560	−	0.612385i	$-0.790210\pi$
$401$	−31.6619	−1.58112	−0.790560	+	0.612385i	$0.790210\pi$
$402$	1.18119	0.0589123
$403$	−10.1003	−0.503130
$404$	5.08191	0.252835
$405$	−0.877410	−0.0435988
$406$	−1.83022	−0.0908323
$407$	11.2851	0.559382
$408$	15.9689	0.790580
$409$	2.37165	0.117271	0.0586353	−	0.998279i	$-0.481325\pi$
$409$	2.37165	0.117271	0.0586353	+	0.998279i	$0.481325\pi$
$410$	6.04845	0.298712
$411$	21.1534	1.04342
$412$	1.89236	0.0932301
$413$	45.8463	2.25595
$414$	−1.75500	−0.0862535
$415$	3.37740	0.165790
$416$	3.48555	0.170893
$417$	−16.8150	−0.823433
$418$	1.30900	0.0640254
$419$	15.3932	0.752008	0.376004	−	0.926618i	$-0.377298\pi$
$419$	15.3932	0.752008	0.376004	+	0.926618i	$0.377298\pi$
$420$	1.70153	0.0830259
$421$	−10.4301	−0.508331	−0.254166	−	0.967161i	$-0.581801\pi$
$421$	−10.4301	−0.508331	−0.254166	+	0.967161i	$0.581801\pi$
$422$	21.9054	1.06634
$423$	20.7243	1.00765
$424$	−19.1835	−0.931632
$425$	−23.4036	−1.13524
$426$	−1.12334	−0.0544261
$427$	40.1473	1.94287
$428$	1.95965	0.0947235
$429$	−1.10761	−0.0534760
$430$	10.0304	0.483707
$431$	8.80477	0.424111	0.212055	−	0.977258i	$-0.431984\pi$
$431$	8.80477	0.424111	0.212055	+	0.977258i	$0.431984\pi$
$432$	12.6027	0.606349
$433$	−25.9896	−1.24898	−0.624489	−	0.781033i	$-0.714693\pi$
$433$	−25.9896	−1.24898	−0.624489	+	0.781033i	$0.714693\pi$
$434$	−43.8916	−2.10686
$435$	−0.275794	−0.0132233
$436$	−10.5243	−0.504024
$437$	0.792228	0.0378974
$438$	2.79297	0.133453
$439$	10.6115	0.506460	0.253230	−	0.967406i	$-0.418507\pi$
$439$	10.6115	0.506460	0.253230	+	0.967406i	$0.418507\pi$
$440$	−2.28714	−0.109035
$441$	−19.4541	−0.926386
$442$	7.06667	0.336127
$443$	14.9726	0.711368	0.355684	−	0.934606i	$-0.384248\pi$
$443$	14.9726	0.711368	0.355684	+	0.934606i	$0.384248\pi$
$444$	−6.33151	−0.300480
$445$	3.86022	0.182992
$446$	16.5493	0.783634
$447$	−20.4028	−0.965017
$448$	35.8499	1.69375
$449$	−35.3977	−1.67052	−0.835260	−	0.549855i	$-0.814683\pi$
$449$	−35.3977	−1.67052	−0.835260	+	0.549855i	$0.814683\pi$
$450$	−10.7752	−0.507946
$451$	6.79208	0.319827
$452$	1.52276	0.0716248
$453$	2.67889	0.125865
$454$	4.81680	0.226063
$455$	3.40271	0.159522
$456$	−3.31887	−0.155420
$457$	40.8890	1.91271	0.956354	−	0.292209i	$-0.0943904\pi$
$457$	40.8890	1.91271	0.956354	+	0.292209i	$0.0943904\pi$
$458$	34.4287	1.60875
$459$	−26.1144	−1.21892
$460$	−0.306305	−0.0142816
$461$	21.2804	0.991128	0.495564	−	0.868571i	$-0.334961\pi$
$461$	21.2804	0.991128	0.495564	+	0.868571i	$0.334961\pi$
$462$	−4.81322	−0.223931
$463$	20.1486	0.936385	0.468193	−	0.883626i	$-0.344905\pi$
$463$	20.1486	0.936385	0.468193	+	0.883626i	$0.344905\pi$
$464$	−0.953578	−0.0442687
$465$	−6.61398	−0.306716
$466$	13.2425	0.613446
$467$	1.35142	0.0625364	0.0312682	−	0.999511i	$-0.490045\pi$
$467$	1.35142	0.0625364	0.0312682	+	0.999511i	$0.490045\pi$
$468$	−1.29157	−0.0597027
$469$	−4.07489	−0.188161
$470$	−9.11161	−0.420287
$471$	−19.5047	−0.898731
$472$	34.5749	1.59144
$473$	11.2636	0.517899
$474$	3.82842	0.175845
$475$	4.86404	0.223178
$476$	−12.1906	−0.558755
$477$	12.6439	0.578923
$478$	−28.5178	−1.30437
$479$	16.6752	0.761908	0.380954	−	0.924594i	$-0.375596\pi$
$479$	16.6752	0.761908	0.380954	+	0.924594i	$0.375596\pi$
$480$	2.28245	0.104179
$481$	−12.6618	−0.577327
$482$	−16.1040	−0.733517
$483$	−2.91303	−0.132548
$484$	−0.568334	−0.0258333
$485$	−13.8358	−0.628252
$486$	−19.2006	−0.870957
$487$	17.0062	0.770626	0.385313	−	0.922786i	$-0.374093\pi$
$487$	17.0062	0.770626	0.385313	+	0.922786i	$0.374093\pi$
$488$	30.2770	1.37058
$489$	1.45848	0.0659548
$490$	8.55318	0.386393
$491$	−30.9009	−1.39454	−0.697270	−	0.716809i	$-0.745602\pi$
$491$	−30.9009	−1.39454	−0.697270	+	0.716809i	$0.745602\pi$
$492$	−3.81070	−0.171799
$493$	1.97593	0.0889913
$494$	−1.46869	−0.0660793
$495$	1.50746	0.0677552
$496$	−22.8683	−1.02682
$497$	3.87533	0.173832
$498$	5.36020	0.240196
$499$	−21.7368	−0.973073	−0.486537	−	0.873660i	$-0.661740\pi$
$499$	−21.7368	−0.973073	−0.486537	+	0.873660i	$0.661740\pi$
$500$	−3.99554	−0.178686
$501$	0.719275	0.0321348
$502$	33.1820	1.48099
$503$	−29.8741	−1.33202	−0.666011	−	0.745942i	$-0.732000\pi$
$503$	−29.8741	−1.33202	−0.666011	+	0.745942i	$0.732000\pi$
$504$	−25.3638	−1.12979
$505$	6.65494	0.296141
$506$	0.866467	0.0385191
$507$	−11.5907	−0.514760
$508$	4.92052	0.218313
$509$	18.3002	0.811142	0.405571	−	0.914064i	$-0.367073\pi$
$509$	18.3002	0.811142	0.405571	+	0.914064i	$0.367073\pi$
$510$	4.62748	0.204908
$511$	−9.63524	−0.426238
$512$	23.5049	1.03878
$513$	5.42743	0.239627
$514$	18.8386	0.830937
$515$	2.47812	0.109199
$516$	−6.31942	−0.278197
$517$	−10.2318	−0.449996
$518$	−55.0228	−2.41756
$519$	−10.9348	−0.479986
$520$	2.56615	0.112533
$521$	19.0384	0.834086	0.417043	−	0.908887i	$-0.363066\pi$
$521$	19.0384	0.834086	0.417043	+	0.908887i	$0.363066\pi$
$522$	0.909729	0.0398178
$523$	5.90351	0.258142	0.129071	−	0.991635i	$-0.458800\pi$
$523$	5.90351	0.258142	0.129071	+	0.991635i	$0.458800\pi$
$524$	9.87249	0.431282
$525$	−17.8852	−0.780572
$526$	−16.9296	−0.738167
$527$	47.3859	2.06416
$528$	−2.50777	−0.109137
$529$	−22.4756	−0.977200
$530$	−5.55899	−0.241467
$531$	−22.7884	−0.988930
$532$	2.53361	0.109846
$533$	−7.62064	−0.330087
$534$	6.12648	0.265119
$535$	2.56624	0.110948
$536$	−3.07307	−0.132736
$537$	6.04287	0.260769
$538$	−4.38886	−0.189217
$539$	9.60475	0.413706
$540$	−2.09845	−0.0903029
$541$	−4.46800	−0.192094	−0.0960472	−	0.995377i	$-0.530620\pi$
$541$	−4.46800	−0.192094	−0.0960472	+	0.995377i	$0.530620\pi$
$542$	−38.8498	−1.66874
$543$	15.9048	0.682538
$544$	−16.3526	−0.701112
$545$	−13.7820	−0.590355
$546$	5.40038	0.231115
$547$	−0.520429	−0.0222519	−0.0111260	−	0.999938i	$-0.503542\pi$
$547$	−0.520429	−0.0222519	−0.0111260	+	0.999938i	$0.503542\pi$
$548$	−12.1783	−0.520230
$549$	−19.9556	−0.851686
$550$	5.31984	0.226839
$551$	−0.410663	−0.0174948
$552$	−2.19686	−0.0935044
$553$	−13.2074	−0.561634
$554$	9.90201	0.420696
$555$	−8.29133	−0.351947
$556$	9.68057	0.410548
$557$	28.6392	1.21348	0.606741	−	0.794900i	$-0.292477\pi$
$557$	28.6392	1.21348	0.606741	+	0.794900i	$0.292477\pi$
$558$	21.8168	0.923577
$559$	−12.6376	−0.534513
$560$	7.70419	0.325561
$561$	5.19641	0.219393
$562$	20.4580	0.862967
$563$	−11.4870	−0.484120	−0.242060	−	0.970261i	$-0.577823\pi$
$563$	−11.4870	−0.484120	−0.242060	+	0.970261i	$0.577823\pi$
$564$	5.74058	0.241722
$565$	1.99411	0.0838930
$566$	17.0717	0.717576
$567$	4.80395	0.201747
$568$	2.92257	0.122628
$569$	12.7634	0.535069	0.267535	−	0.963548i	$-0.413791\pi$
$569$	12.7634	0.535069	0.267535	+	0.963548i	$0.413791\pi$
$570$	−0.961743	−0.0402830
$571$	5.52770	0.231327	0.115664	−	0.993288i	$-0.463101\pi$
$571$	5.52770	0.231327	0.115664	+	0.993288i	$0.463101\pi$
$572$	0.637664	0.0266621
$573$	−3.68213	−0.153823
$574$	−33.1162	−1.38224
$575$	3.21965	0.134269
$576$	−17.8195	−0.742481
$577$	−10.8644	−0.452290	−0.226145	−	0.974094i	$-0.572612\pi$
$577$	−10.8644	−0.452290	−0.226145	+	0.974094i	$0.572612\pi$
$578$	−12.8127	−0.532940
$579$	−7.15910	−0.297522
$580$	0.158778	0.00659289
$581$	−18.4917	−0.767167
$582$	−21.9585	−0.910211
$583$	−6.24245	−0.258536
$584$	−7.26639	−0.300685
$585$	−1.69135	−0.0699288
$586$	24.3662	1.00656
$587$	−32.2354	−1.33050	−0.665249	−	0.746622i	$-0.731675\pi$
$587$	−32.2354	−1.33050	−0.665249	+	0.746622i	$0.731675\pi$
$588$	−5.38875	−0.222228
$589$	−9.84836	−0.405794
$590$	10.0191	0.412480
$591$	−5.08222	−0.209055
$592$	−28.6679	−1.17824
$593$	2.69079	0.110497	0.0552487	−	0.998473i	$-0.482405\pi$
$593$	2.69079	0.110497	0.0552487	+	0.998473i	$0.482405\pi$
$594$	5.93602	0.243558
$595$	−15.9640	−0.654460
$596$	11.7461	0.481139
$597$	−3.37989	−0.138330
$598$	−0.972167	−0.0397548
$599$	−23.7416	−0.970057	−0.485029	−	0.874498i	$-0.661191\pi$
$599$	−23.7416	−0.970057	−0.485029	+	0.874498i	$0.661191\pi$
$600$	−13.4880	−0.550647
$601$	−32.7751	−1.33693	−0.668463	−	0.743746i	$-0.733047\pi$
$601$	−32.7751	−1.33693	−0.668463	+	0.743746i	$0.733047\pi$
$602$	−54.9177	−2.23828
$603$	2.02547	0.0824834
$604$	−1.54227	−0.0627541
$605$	−0.744253	−0.0302582
$606$	10.5619	0.429049
$607$	−30.9890	−1.25780	−0.628902	−	0.777485i	$-0.716495\pi$
$607$	−30.9890	−1.25780	−0.628902	+	0.777485i	$0.716495\pi$
$608$	3.39861	0.137832
$609$	1.51001	0.0611888
$610$	8.77368	0.355236
$611$	11.4800	0.464432
$612$	6.05945	0.244939
$613$	−41.2233	−1.66499	−0.832496	−	0.554031i	$-0.813089\pi$
$613$	−41.2233	−1.66499	−0.832496	+	0.554031i	$0.813089\pi$
$614$	−10.4887	−0.423289
$615$	−4.99024	−0.201226
$616$	12.5224	0.504543
$617$	15.3401	0.617567	0.308784	−	0.951132i	$-0.400078\pi$
$617$	15.3401	0.617567	0.308784	+	0.951132i	$0.400078\pi$
$618$	3.93297	0.158207
$619$	−34.2142	−1.37518	−0.687591	−	0.726098i	$-0.741332\pi$
$619$	−34.2142	−1.37518	−0.687591	+	0.726098i	$0.741332\pi$
$620$	3.80775	0.152923
$621$	3.59257	0.144165
$622$	−20.8659	−0.836646
$623$	−21.1353	−0.846767
$624$	2.81370	0.112638
$625$	16.9981	0.679925
$626$	−23.4373	−0.936741
$627$	−1.07999	−0.0431305
$628$	11.2291	0.448090
$629$	59.4033	2.36856
$630$	−7.34992	−0.292828
$631$	−3.33447	−0.132743	−0.0663716	−	0.997795i	$-0.521142\pi$
$631$	−3.33447	−0.132743	−0.0663716	+	0.997795i	$0.521142\pi$
$632$	−9.96030	−0.396199
$633$	−18.0729	−0.718334
$634$	−18.0951	−0.718650
$635$	6.44359	0.255706
$636$	3.50233	0.138876
$637$	−10.7764	−0.426978
$638$	−0.449145	−0.0177818
$639$	−1.92627	−0.0762022
$640$	3.21037	0.126901
$641$	37.5285	1.48229	0.741143	−	0.671347i	$-0.234284\pi$
$641$	37.5285	1.48229	0.741143	+	0.671347i	$0.234284\pi$
$642$	4.07282	0.160742
$643$	−2.91739	−0.115051	−0.0575253	−	0.998344i	$-0.518321\pi$
$643$	−2.91739	−0.115051	−0.0575253	+	0.998344i	$0.518321\pi$
$644$	1.67707	0.0660857
$645$	−8.27550	−0.325848
$646$	6.89042	0.271100
$647$	25.3412	0.996266	0.498133	−	0.867101i	$-0.334019\pi$
$647$	25.3412	0.996266	0.498133	+	0.867101i	$0.334019\pi$
$648$	3.62288	0.142320
$649$	11.2509	0.441637
$650$	−5.96881	−0.234116
$651$	36.2125	1.41928
$652$	−0.839665	−0.0328838
$653$	2.51387	0.0983754	0.0491877	−	0.998790i	$-0.484337\pi$
$653$	2.51387	0.0983754	0.0491877	+	0.998790i	$0.484337\pi$
$654$	−21.8731	−0.855306
$655$	12.9284	0.505153
$656$	−17.2541	−0.673660
$657$	4.78929	0.186848
$658$	49.8874	1.94481
$659$	0.739150	0.0287932	0.0143966	−	0.999896i	$-0.495417\pi$
$659$	0.739150	0.0287932	0.0143966	+	0.999896i	$0.495417\pi$
$660$	0.417563	0.0162536
$661$	25.4426	0.989603	0.494802	−	0.869006i	$-0.335241\pi$
$661$	25.4426	0.989603	0.494802	+	0.869006i	$0.335241\pi$
$662$	−38.8544	−1.51012
$663$	−5.83032	−0.226431
$664$	−13.9455	−0.541190
$665$	3.31785	0.128661
$666$	27.3496	1.05978
$667$	−0.271830	−0.0105253
$668$	−0.414095	−0.0160218
$669$	−13.6539	−0.527892
$670$	−0.890515	−0.0344036
$671$	9.85237	0.380346
$672$	−12.4967	−0.482072
$673$	21.5175	0.829438	0.414719	−	0.909950i	$-0.363880\pi$
$673$	21.5175	0.829438	0.414719	+	0.909950i	$0.363880\pi$
$674$	−8.93684	−0.344234
$675$	22.0573	0.848987
$676$	6.67288	0.256649
$677$	−41.6194	−1.59956	−0.799781	−	0.600292i	$-0.795051\pi$
$677$	−41.6194	−1.59956	−0.799781	+	0.600292i	$0.795051\pi$
$678$	3.16482	0.121544
$679$	75.7531	2.90714
$680$	−12.0392	−0.461682
$681$	−3.97407	−0.152287
$682$	−10.7712	−0.412452
$683$	−21.1009	−0.807402	−0.403701	−	0.914891i	$-0.632276\pi$
$683$	−21.1009	−0.807402	−0.403701	+	0.914891i	$0.632276\pi$
$684$	−1.25935	−0.0481526
$685$	−15.9479	−0.609337
$686$	−12.7000	−0.484888
$687$	−28.4052	−1.08373
$688$	−28.6132	−1.09087
$689$	7.00396	0.266830
$690$	−0.636606	−0.0242352
$691$	−11.5428	−0.439108	−0.219554	−	0.975600i	$-0.570460\pi$
$691$	−11.5428	−0.439108	−0.219554	+	0.975600i	$0.570460\pi$
$692$	6.29531	0.239312
$693$	−8.25356	−0.313527
$694$	−9.90990	−0.376175
$695$	12.6771	0.480868
$696$	1.13877	0.0431651
$697$	35.7526	1.35423
$698$	−30.1376	−1.14072
$699$	−10.9256	−0.413246
$700$	10.2967	0.389178
$701$	28.6506	1.08212	0.541060	−	0.840984i	$-0.318023\pi$
$701$	28.6506	1.08212	0.541060	+	0.840984i	$0.318023\pi$
$702$	−6.66016	−0.251371
$703$	−12.3460	−0.465637
$704$	8.79775	0.331578
$705$	7.51749	0.283125
$706$	0.546244	0.0205582
$707$	−36.4368	−1.37035
$708$	−6.31233	−0.237232
$709$	1.57846	0.0592804	0.0296402	−	0.999561i	$-0.490564\pi$
$709$	1.57846	0.0592804	0.0296402	+	0.999561i	$0.490564\pi$
$710$	0.846904	0.0317837
$711$	6.56486	0.246201
$712$	−15.9391	−0.597344
$713$	−6.51891	−0.244135
$714$	−25.3361	−0.948182
$715$	0.835044	0.0312289
$716$	−3.47895	−0.130015
$717$	23.5285	0.878687
$718$	6.34014	0.236612
$719$	−25.9479	−0.967694	−0.483847	−	0.875152i	$-0.660761\pi$
$719$	−25.9479	−0.967694	−0.483847	+	0.875152i	$0.660761\pi$
$720$	−3.82944	−0.142715
$721$	−13.5681	−0.505301
$722$	21.3019	0.792774
$723$	13.2865	0.494131
$724$	−9.15655	−0.340300
$725$	−1.66895	−0.0619834
$726$	−1.18119	−0.0438380
$727$	8.36326	0.310176	0.155088	−	0.987901i	$-0.450434\pi$
$727$	8.36326	0.310176	0.155088	+	0.987901i	$0.450434\pi$
$728$	−14.0500	−0.520729
$729$	12.3046	0.455726
$730$	−2.10566	−0.0779339
$731$	59.2899	2.19292
$732$	−5.52767	−0.204309
$733$	−22.7609	−0.840694	−0.420347	−	0.907363i	$-0.638092\pi$
$733$	−22.7609	−0.840694	−0.420347	+	0.907363i	$0.638092\pi$
$734$	−21.4071	−0.790150
$735$	−7.05676	−0.260292
$736$	2.24964	0.0829228
$737$	−1.00000	−0.0368355
$738$	16.4607	0.605927
$739$	−20.1624	−0.741684	−0.370842	−	0.928696i	$-0.620931\pi$
$739$	−20.1624	−0.741684	−0.370842	+	0.928696i	$0.620931\pi$
$740$	4.77341	0.175474
$741$	1.21173	0.0445141
$742$	30.4363	1.11735
$743$	13.4527	0.493530	0.246765	−	0.969075i	$-0.420632\pi$
$743$	13.4527	0.493530	0.246765	+	0.969075i	$0.420632\pi$
$744$	27.3096	1.00122
$745$	15.3819	0.563551
$746$	22.6989	0.831066
$747$	9.19151	0.336300
$748$	−2.99163	−0.109385
$749$	−14.0505	−0.513395
$750$	−8.30408	−0.303222
$751$	6.38246	0.232899	0.116450	−	0.993197i	$-0.462849\pi$
$751$	6.38246	0.232899	0.116450	+	0.993197i	$0.462849\pi$
$752$	25.9923	0.947840
$753$	−27.3767	−0.997661
$754$	0.503937	0.0183523
$755$	−2.01966	−0.0735028
$756$	11.4893	0.417863
$757$	−5.35799	−0.194740	−0.0973698	−	0.995248i	$-0.531043\pi$
$757$	−5.35799	−0.194740	−0.0973698	+	0.995248i	$0.531043\pi$
$758$	15.1338	0.549685
$759$	−0.714874	−0.0259483
$760$	2.50214	0.0907623
$761$	−12.4122	−0.449943	−0.224971	−	0.974365i	$-0.572229\pi$
$761$	−12.4122	−0.449943	−0.224971	+	0.974365i	$0.572229\pi$
$762$	10.2265	0.370467
$763$	75.4583	2.73178
$764$	2.11985	0.0766934
$765$	7.93507	0.286893
$766$	−13.4394	−0.485586
$767$	−12.6234	−0.455805
$768$	−12.2749	−0.442932
$769$	−4.45773	−0.160750	−0.0803749	−	0.996765i	$-0.525612\pi$
$769$	−4.45773	−0.160750	−0.0803749	+	0.996765i	$0.525612\pi$
$770$	3.62875	0.130771
$771$	−15.5427	−0.559757
$772$	4.12158	0.148339
$773$	33.4450	1.20293	0.601467	−	0.798898i	$-0.294583\pi$
$773$	33.4450	1.20293	0.601467	+	0.798898i	$0.294583\pi$
$774$	27.2974	0.981185
$775$	−40.0242	−1.43771
$776$	57.1290	2.05081
$777$	45.3963	1.62858
$778$	37.3381	1.33863
$779$	−7.43057	−0.266228
$780$	−0.468501	−0.0167750
$781$	0.951027	0.0340304
$782$	4.56097	0.163100
$783$	−1.86226	−0.0665518
$784$	−24.3992	−0.871402
$785$	14.7049	0.524841
$786$	20.5184	0.731866
$787$	10.1233	0.360856	0.180428	−	0.983588i	$-0.442252\pi$
$787$	10.1233	0.360856	0.180428	+	0.983588i	$0.442252\pi$
$788$	2.92589	0.104231
$789$	13.9677	0.497263
$790$	−2.88630	−0.102690
$791$	−10.9181	−0.388202
$792$	−6.22440	−0.221174
$793$	−11.0543	−0.392548
$794$	24.7129	0.877027
$795$	4.58642	0.162664
$796$	1.94584	0.0689685
$797$	−3.94823	−0.139853	−0.0699267	−	0.997552i	$-0.522277\pi$
$797$	−3.94823	−0.139853	−0.0699267	+	0.997552i	$0.522277\pi$
$798$	5.26569	0.186403
$799$	−53.8591	−1.90540
$800$	13.8121	0.488332
$801$	10.5055	0.371194
$802$	37.8842	1.33774
$803$	−2.36454	−0.0834428
$804$	0.561050	0.0197867
$805$	2.19618	0.0774051
$806$	12.0852	0.425683
$807$	3.62101	0.127466
$808$	−27.4787	−0.966697
$809$	−33.0330	−1.16138	−0.580689	−	0.814125i	$-0.697217\pi$
$809$	−33.0330	−1.16138	−0.580689	+	0.814125i	$0.697217\pi$
$810$	1.04984	0.0368876
$811$	6.40582	0.224939	0.112469	−	0.993655i	$-0.464124\pi$
$811$	6.40582	0.224939	0.112469	+	0.993655i	$0.464124\pi$
$812$	−0.869332	−0.0305076
$813$	32.0528	1.12414
$814$	−13.5029	−0.473276
$815$	−1.09957	−0.0385163
$816$	−13.2006	−0.462113
$817$	−12.3224	−0.431106
$818$	−2.83774	−0.0992191
$819$	9.26041	0.323585
$820$	2.87294	0.100327
$821$	−27.9057	−0.973917	−0.486958	−	0.873425i	$-0.661894\pi$
$821$	−27.9057	−0.973917	−0.486958	+	0.873425i	$0.661894\pi$
$822$	−25.3106	−0.882808
$823$	40.0960	1.39766	0.698830	−	0.715288i	$-0.253704\pi$
$823$	40.0960	1.39766	0.698830	+	0.715288i	$0.253704\pi$
$824$	−10.2323	−0.356459
$825$	−4.38911	−0.152809
$826$	−54.8561	−1.90869
$827$	8.17363	0.284225	0.142113	−	0.989851i	$-0.454611\pi$
$827$	8.17363	0.284225	0.142113	+	0.989851i	$0.454611\pi$
$828$	−0.833603	−0.0289697
$829$	−40.7296	−1.41460	−0.707299	−	0.706914i	$-0.750087\pi$
$829$	−40.7296	−1.41460	−0.707299	+	0.706914i	$0.750087\pi$
$830$	−4.04113	−0.140270
$831$	−8.16960	−0.283400
$832$	−9.87098	−0.342215
$833$	50.5582	1.75174
$834$	20.1195	0.696681
$835$	−0.542272	−0.0187661
$836$	0.621760	0.0215040
$837$	−44.6600	−1.54368
$838$	−18.4183	−0.636251
$839$	−52.6913	−1.81911	−0.909553	−	0.415588i	$-0.863576\pi$
$839$	−52.6913	−1.81911	−0.909553	+	0.415588i	$0.863576\pi$
$840$	−9.20041	−0.317444
$841$	−28.8591	−0.995141
$842$	12.4798	0.430084
$843$	−16.8787	−0.581334
$844$	10.4048	0.358148
$845$	8.73838	0.300609
$846$	−24.7970	−0.852540
$847$	4.07489	0.140015
$848$	15.8579	0.544562
$849$	−14.0849	−0.483393
$850$	28.0030	0.960494
$851$	−8.17215	−0.280138
$852$	−0.533574	−0.0182799
$853$	−11.2478	−0.385117	−0.192559	−	0.981285i	$-0.561679\pi$
$853$	−11.2478	−0.385117	−0.192559	+	0.981285i	$0.561679\pi$
$854$	−48.0372	−1.64380
$855$	−1.64917	−0.0564004
$856$	−10.5962	−0.362169
$857$	−46.2429	−1.57963	−0.789814	−	0.613347i	$-0.789823\pi$
$857$	−46.2429	−1.57963	−0.789814	+	0.613347i	$0.789823\pi$
$858$	1.32528	0.0452444
$859$	−29.1473	−0.994494	−0.497247	−	0.867609i	$-0.665656\pi$
$859$	−29.1473	−0.994494	−0.497247	+	0.867609i	$0.665656\pi$
$860$	4.76430	0.162461
$861$	27.3223	0.931142
$862$	−10.5351	−0.358827
$863$	24.6460	0.838960	0.419480	−	0.907765i	$-0.362213\pi$
$863$	24.6460	0.838960	0.419480	+	0.907765i	$0.362213\pi$
$864$	15.4119	0.524324
$865$	8.24393	0.280302
$866$	31.0971	1.05672
$867$	10.5711	0.359013
$868$	−20.8480	−0.707626
$869$	−3.24116	−0.109949
$870$	0.329994	0.0111878
$871$	1.12199	0.0380172
$872$	56.9067	1.92710
$873$	−37.6538	−1.27439
$874$	−0.947919	−0.0320638
$875$	28.6476	0.968467
$876$	1.32662	0.0448225
$877$	−17.1256	−0.578292	−0.289146	−	0.957285i	$-0.593371\pi$
$877$	−17.1256	−0.578292	−0.289146	+	0.957285i	$0.593371\pi$
$878$	−12.6969	−0.428500
$879$	−20.1032	−0.678063
$880$	1.89065	0.0637337
$881$	27.3376	0.921027	0.460514	−	0.887653i	$-0.347665\pi$
$881$	27.3376	0.921027	0.460514	+	0.887653i	$0.347665\pi$
$882$	23.2773	0.783787
$883$	12.6231	0.424800	0.212400	−	0.977183i	$-0.431872\pi$
$883$	12.6231	0.424800	0.212400	+	0.977183i	$0.431872\pi$
$884$	3.35658	0.112894
$885$	−8.26622	−0.277866
$886$	−17.9150	−0.601866
$887$	30.8390	1.03547	0.517735	−	0.855541i	$-0.326775\pi$
$887$	30.8390	1.03547	0.517735	+	0.855541i	$0.326775\pi$
$888$	34.2355	1.14887
$889$	−35.2796	−1.18324
$890$	−4.61884	−0.154824
$891$	1.17891	0.0394951
$892$	7.86073	0.263197
$893$	11.1937	0.374583
$894$	24.4124	0.816472
$895$	−4.55581	−0.152284
$896$	−17.5773	−0.587215
$897$	0.802081	0.0267807
$898$	42.3541	1.41338
$899$	3.37917	0.112702
$900$	−5.11807	−0.170602
$901$	−32.8594	−1.09471
$902$	−8.12688	−0.270595
$903$	45.3096	1.50781
$904$	−8.23383	−0.273853
$905$	−11.9908	−0.398588
$906$	−3.20536	−0.106491
$907$	−36.9080	−1.22551	−0.612755	−	0.790273i	$-0.709939\pi$
$907$	−36.9080	−1.22551	−0.612755	+	0.790273i	$0.709939\pi$
$908$	2.28792	0.0759273
$909$	18.1113	0.600713
$910$	−4.07142	−0.134966
$911$	41.5486	1.37657	0.688283	−	0.725442i	$-0.258365\pi$
$911$	41.5486	1.37657	0.688283	+	0.725442i	$0.258365\pi$
$912$	2.74352	0.0908470
$913$	−4.53797	−0.150185
$914$	−48.9247	−1.61828
$915$	−7.23868	−0.239303
$916$	16.3532	0.540325
$917$	−70.7847	−2.33752
$918$	31.2465	1.03129
$919$	12.0892	0.398787	0.199393	−	0.979920i	$-0.436103\pi$
$919$	12.0892	0.398787	0.199393	+	0.979920i	$0.436103\pi$
$920$	1.65624	0.0546047
$921$	8.65364	0.285147
$922$	−25.4625	−0.838563
$923$	−1.06704	−0.0351221
$924$	−2.28622	−0.0752111
$925$	−50.1745	−1.64973
$926$	−24.1083	−0.792247
$927$	6.74414	0.221506
$928$	−1.16613	−0.0382802
$929$	53.1500	1.74380	0.871898	−	0.489688i	$-0.162889\pi$
$929$	53.1500	1.74380	0.871898	+	0.489688i	$0.162889\pi$
$930$	7.91378	0.259503
$931$	−10.5077	−0.344374
$932$	6.29001	0.206036
$933$	17.2153	0.563603
$934$	−1.61701	−0.0529101
$935$	−3.91765	−0.128121
$936$	6.98371	0.228270
$937$	−9.04574	−0.295511	−0.147756	−	0.989024i	$-0.547205\pi$
$937$	−9.04574	−0.295511	−0.147756	+	0.989024i	$0.547205\pi$
$938$	4.87570	0.159197
$939$	19.3368	0.631032
$940$	−4.32790	−0.141161
$941$	−39.1751	−1.27707	−0.638536	−	0.769592i	$-0.720460\pi$
$941$	−39.1751	−1.27707	−0.638536	+	0.769592i	$0.720460\pi$
$942$	23.3379	0.760389
$943$	−4.91851	−0.160169
$944$	−28.5810	−0.930234
$945$	15.0457	0.489436
$946$	−13.4771	−0.438178
$947$	−8.49648	−0.276099	−0.138049	−	0.990425i	$-0.544083\pi$
$947$	−8.49648	−0.276099	−0.138049	+	0.990425i	$0.544083\pi$
$948$	1.81845	0.0590606
$949$	2.65299	0.0861196
$950$	−5.81994	−0.188824
$951$	14.9293	0.484116
$952$	65.9164	2.13636
$953$	−10.0111	−0.324290	−0.162145	−	0.986767i	$-0.551841\pi$
$953$	−10.0111	−0.324290	−0.162145	+	0.986767i	$0.551841\pi$
$954$	−15.1287	−0.489809
$955$	2.77601	0.0898297
$956$	−13.5456	−0.438097
$957$	0.370565	0.0119787
$958$	−19.9522	−0.644627
$959$	87.3170	2.81961
$960$	−6.46384	−0.208619
$961$	50.0380	1.61413
$962$	15.1501	0.488458
$963$	6.98395	0.225055
$964$	−7.64920	−0.246364
$965$	5.39735	0.173747
$966$	3.48551	0.112144
$967$	−41.8887	−1.34705	−0.673525	−	0.739165i	$-0.735220\pi$
$967$	−41.8887	−1.34705	−0.673525	+	0.739165i	$0.735220\pi$
$968$	3.07307	0.0987722
$969$	−5.68490	−0.182625
$970$	16.5549	0.531544
$971$	−29.1024	−0.933941	−0.466971	−	0.884273i	$-0.654655\pi$
$971$	−29.1024	−0.933941	−0.466971	+	0.884273i	$0.654655\pi$
$972$	−9.12005	−0.292526
$973$	−69.4087	−2.22514
$974$	−20.3484	−0.652003
$975$	4.92454	0.157711
$976$	−25.0283	−0.801135
$977$	6.91499	0.221230	0.110615	−	0.993863i	$-0.464718\pi$
$977$	6.91499	0.221230	0.110615	+	0.993863i	$0.464718\pi$
$978$	−1.74511	−0.0558024
$979$	−5.18671	−0.165768
$980$	4.06266	0.129777
$981$	−37.5073	−1.19752
$982$	36.9737	1.17988
$983$	−3.48080	−0.111020	−0.0555102	−	0.998458i	$-0.517679\pi$
$983$	−3.48080	−0.111020	−0.0555102	+	0.998458i	$0.517679\pi$
$984$	20.6050	0.656865
$985$	3.83156	0.122084
$986$	−2.36424	−0.0752928
$987$	−41.1594	−1.31012
$988$	−0.697608	−0.0221939
$989$	−8.15655	−0.259363
$990$	−1.80371	−0.0573256
$991$	48.2549	1.53287	0.766434	−	0.642323i	$-0.222029\pi$
$991$	48.2549	1.53287	0.766434	+	0.642323i	$0.222029\pi$
$992$	−27.9657	−0.887913
$993$	32.0566	1.01728
$994$	−4.63692	−0.147074
$995$	2.54815	0.0807817
$996$	2.54603	0.0806740
$997$	34.7487	1.10050	0.550251	−	0.834999i	$-0.314532\pi$
$997$	34.7487	1.10050	0.550251	+	0.834999i	$0.314532\pi$
$998$	26.0086	0.823287
$999$	−55.9861	−1.77132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	737.2.a.f.1.6	✓	17
3.2	odd	2		6633.2.a.w.1.12		17
11.10	odd	2		8107.2.a.o.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
737.2.a.f.1.6	✓	17	1.1	even	1	trivial
6633.2.a.w.1.12		17	3.2	odd	2
8107.2.a.o.1.12		17	11.10	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:	\( N \)	\(=\)	\( 737 = 11 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	737.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19652 q^{2} +0.987185 q^{3} -0.568334 q^{4} -0.744253 q^{5} -1.18119 q^{6} +4.07489 q^{7} +3.07307 q^{8} -2.02547 q^{9} +O(q^{10})\)	\(q-1.19652 q^{2} +0.987185 q^{3} -0.568334 q^{4} -0.744253 q^{5} -1.18119 q^{6} +4.07489 q^{7} +3.07307 q^{8} -2.02547 q^{9} +0.890515 q^{10} +1.00000 q^{11} -0.561050 q^{12} -1.12199 q^{13} -4.87570 q^{14} -0.734715 q^{15} -2.54033 q^{16} +5.26387 q^{17} +2.42352 q^{18} -1.09401 q^{19} +0.422984 q^{20} +4.02267 q^{21} -1.19652 q^{22} -0.724154 q^{23} +3.03369 q^{24} -4.44609 q^{25} +1.34249 q^{26} -4.96106 q^{27} -2.31590 q^{28} +0.375376 q^{29} +0.879103 q^{30} +9.00211 q^{31} -3.10658 q^{32} +0.987185 q^{33} -6.29834 q^{34} -3.03275 q^{35} +1.15114 q^{36} +11.2851 q^{37} +1.30900 q^{38} -1.10761 q^{39} -2.28714 q^{40} +6.79208 q^{41} -4.81322 q^{42} +11.2636 q^{43} -0.568334 q^{44} +1.50746 q^{45} +0.866467 q^{46} -10.2318 q^{47} -2.50777 q^{48} +9.60475 q^{49} +5.31984 q^{50} +5.19641 q^{51} +0.637664 q^{52} -6.24245 q^{53} +5.93602 q^{54} -0.744253 q^{55} +12.5224 q^{56} -1.07999 q^{57} -0.449145 q^{58} +11.2509 q^{59} +0.417563 q^{60} +9.85237 q^{61} -10.7712 q^{62} -8.25356 q^{63} +8.79775 q^{64} +0.835044 q^{65} -1.18119 q^{66} -1.00000 q^{67} -2.99163 q^{68} -0.714874 q^{69} +3.62875 q^{70} +0.951027 q^{71} -6.22440 q^{72} -2.36454 q^{73} -13.5029 q^{74} -4.38911 q^{75} +0.621760 q^{76} +4.07489 q^{77} +1.32528 q^{78} -3.24116 q^{79} +1.89065 q^{80} +1.17891 q^{81} -8.12688 q^{82} -4.53797 q^{83} -2.28622 q^{84} -3.91765 q^{85} -13.4771 q^{86} +0.370565 q^{87} +3.07307 q^{88} -5.18671 q^{89} -1.80371 q^{90} -4.57199 q^{91} +0.411561 q^{92} +8.88674 q^{93} +12.2426 q^{94} +0.814216 q^{95} -3.06676 q^{96} +18.5902 q^{97} -11.4923 q^{98} -2.02547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9}+O(q^{10}) \) 17 * q + q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 - 6 * q^6 + 20 * q^7 + 25 * q^9	\( 17 q + q^{2} + 10 q^{3} + 19 q^{4} + 10 q^{5} - 6 q^{6} + 20 q^{7} + 25 q^{9} + 10 q^{10} + 17 q^{11} + 18 q^{12} + q^{13} - 11 q^{14} + 7 q^{15} + 19 q^{16} + 2 q^{17} - 24 q^{18} + 13 q^{19} + 3 q^{20} + 5 q^{21} + q^{22} + 16 q^{23} - 36 q^{24} + 33 q^{25} + 12 q^{26} + 19 q^{27} + 44 q^{28} - 5 q^{29} + 3 q^{30} + 16 q^{31} - 24 q^{32} + 10 q^{33} + 4 q^{34} - 2 q^{35} + 25 q^{36} + 29 q^{37} - 19 q^{38} + 2 q^{39} + 31 q^{40} - 6 q^{41} - 26 q^{42} + 19 q^{43} + 19 q^{44} + 20 q^{45} - 33 q^{46} + 40 q^{47} + 81 q^{48} + 23 q^{49} - 3 q^{50} - q^{51} - 28 q^{52} + 15 q^{53} - 27 q^{54} + 10 q^{55} - 38 q^{56} - 27 q^{57} - 12 q^{58} - 2 q^{59} - 59 q^{60} - 6 q^{61} + 3 q^{62} + 32 q^{63} - 4 q^{64} - 30 q^{65} - 6 q^{66} - 17 q^{67} - 13 q^{68} + 5 q^{69} + 71 q^{70} + 2 q^{71} - 47 q^{72} + 41 q^{73} - 13 q^{74} - 6 q^{75} + 21 q^{76} + 20 q^{77} + 31 q^{78} + 41 q^{79} - 23 q^{80} + 37 q^{81} - 8 q^{82} + 2 q^{83} - 16 q^{84} - 36 q^{85} - 54 q^{86} + 32 q^{87} + q^{89} - 44 q^{90} + 16 q^{91} + 36 q^{92} + 26 q^{93} + 12 q^{94} - 31 q^{95} - 72 q^{96} + 3 q^{97} - 64 q^{98} + 25 q^{99}+O(q^{100}) \) 17 * q + q^2 + 10 * q^3 + 19 * q^4 + 10 * q^5 - 6 * q^6 + 20 * q^7 + 25 * q^9 + 10 * q^10 + 17 * q^11 + 18 * q^12 + q^13 - 11 * q^14 + 7 * q^15 + 19 * q^16 + 2 * q^17 - 24 * q^18 + 13 * q^19 + 3 * q^20 + 5 * q^21 + q^22 + 16 * q^23 - 36 * q^24 + 33 * q^25 + 12 * q^26 + 19 * q^27 + 44 * q^28 - 5 * q^29 + 3 * q^30 + 16 * q^31 - 24 * q^32 + 10 * q^33 + 4 * q^34 - 2 * q^35 + 25 * q^36 + 29 * q^37 - 19 * q^38 + 2 * q^39 + 31 * q^40 - 6 * q^41 - 26 * q^42 + 19 * q^43 + 19 * q^44 + 20 * q^45 - 33 * q^46 + 40 * q^47 + 81 * q^48 + 23 * q^49 - 3 * q^50 - q^51 - 28 * q^52 + 15 * q^53 - 27 * q^54 + 10 * q^55 - 38 * q^56 - 27 * q^57 - 12 * q^58 - 2 * q^59 - 59 * q^60 - 6 * q^61 + 3 * q^62 + 32 * q^63 - 4 * q^64 - 30 * q^65 - 6 * q^66 - 17 * q^67 - 13 * q^68 + 5 * q^69 + 71 * q^70 + 2 * q^71 - 47 * q^72 + 41 * q^73 - 13 * q^74 - 6 * q^75 + 21 * q^76 + 20 * q^77 + 31 * q^78 + 41 * q^79 - 23 * q^80 + 37 * q^81 - 8 * q^82 + 2 * q^83 - 16 * q^84 - 36 * q^85 - 54 * q^86 + 32 * q^87 + q^89 - 44 * q^90 + 16 * q^91 + 36 * q^92 + 26 * q^93 + 12 * q^94 - 31 * q^95 - 72 * q^96 + 3 * q^97 - 64 * q^98 + 25 * q^99

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