LMFDB - Embedded newform 3721.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3721,2,Mod(1,3721)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3721, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3721.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3721 = 61^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3721.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:	$29.7123345921$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 11 x^{14} + 86 x^{13} + 5 x^{12} - 562 x^{11} + 362 x^{10} + 1761 x^{9} - 1799 x^{8} + \cdots - 9 $ x^16 - 5x^15 - 11x^14 + 86x^13 + 5x^12 - 562x^11 + 362x^10 + 1761x^9 - 1799x^8 - 2672x^7 + 3614x^6 + 1572x^5 - 3212x^4 + 144x^3 + 1005x^2 - 279*x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 61)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.892823$ of defining polynomial
Character	$\chi$	$=$	3721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.892823 q^{2} +1.64555 q^{3} -1.20287 q^{4} +0.610081 q^{5} -1.46918 q^{6} -0.681125 q^{7} +2.85959 q^{8} -0.292175 q^{9} +O(q^{10})$	\(q-0.892823 q^{2} +1.64555 q^{3} -1.20287 q^{4} +0.610081 q^{5} -1.46918 q^{6} -0.681125 q^{7} +2.85959 q^{8} -0.292175 q^{9} -0.544695 q^{10} -0.856770 q^{11} -1.97937 q^{12} +0.513102 q^{13} +0.608124 q^{14} +1.00392 q^{15} -0.147377 q^{16} +1.01753 q^{17} +0.260860 q^{18} -4.22681 q^{19} -0.733846 q^{20} -1.12082 q^{21} +0.764944 q^{22} +8.41171 q^{23} +4.70560 q^{24} -4.62780 q^{25} -0.458110 q^{26} -5.41743 q^{27} +0.819302 q^{28} +6.74089 q^{29} -0.896321 q^{30} -10.8670 q^{31} -5.58761 q^{32} -1.40986 q^{33} -0.908475 q^{34} -0.415541 q^{35} +0.351447 q^{36} -2.30381 q^{37} +3.77379 q^{38} +0.844334 q^{39} +1.74458 q^{40} -3.58906 q^{41} +1.00070 q^{42} +3.26469 q^{43} +1.03058 q^{44} -0.178250 q^{45} -7.51017 q^{46} +3.73892 q^{47} -0.242516 q^{48} -6.53607 q^{49} +4.13181 q^{50} +1.67439 q^{51} -0.617194 q^{52} +5.86389 q^{53} +4.83681 q^{54} -0.522699 q^{55} -1.94774 q^{56} -6.95541 q^{57} -6.01842 q^{58} +8.86369 q^{59} -1.20758 q^{60} +9.70227 q^{62} +0.199008 q^{63} +5.28350 q^{64} +0.313034 q^{65} +1.25875 q^{66} -11.3160 q^{67} -1.22395 q^{68} +13.8419 q^{69} +0.371005 q^{70} -5.51317 q^{71} -0.835501 q^{72} -2.77352 q^{73} +2.05689 q^{74} -7.61526 q^{75} +5.08429 q^{76} +0.583567 q^{77} -0.753841 q^{78} -7.42540 q^{79} -0.0899122 q^{80} -8.03811 q^{81} +3.20440 q^{82} -10.7951 q^{83} +1.34820 q^{84} +0.620776 q^{85} -2.91479 q^{86} +11.0925 q^{87} -2.45001 q^{88} +8.44034 q^{89} +0.159146 q^{90} -0.349487 q^{91} -10.1182 q^{92} -17.8821 q^{93} -3.33819 q^{94} -2.57870 q^{95} -9.19467 q^{96} -10.6539 q^{97} +5.83555 q^{98} +0.250327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9} + 20 q^{10} - 9 q^{11} - 17 q^{12} - 11 q^{14} - 12 q^{15} + 9 q^{16} + 4 q^{17} - 35 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} - 11 q^{22} + 4 q^{23} + 15 q^{24} - 8 q^{25} + 19 q^{26} - 5 q^{27} + 22 q^{28} + 4 q^{29} - 24 q^{30} - 9 q^{31} - 34 q^{32} + 10 q^{33} - 6 q^{34} - 37 q^{35} + 20 q^{36} + 38 q^{37} + 18 q^{38} - 12 q^{39} + 60 q^{40} - 37 q^{41} + 17 q^{42} + 15 q^{43} - 34 q^{44} - 32 q^{45} - 41 q^{46} - 40 q^{47} - 43 q^{48} + 24 q^{49} - 28 q^{50} + 19 q^{51} - 56 q^{52} - 19 q^{53} + 6 q^{54} - 30 q^{55} - 58 q^{56} + 8 q^{57} - 21 q^{58} + q^{59} - 10 q^{60} - 37 q^{62} - 17 q^{63} + 28 q^{64} - 34 q^{65} - 59 q^{66} + 3 q^{67} - 2 q^{68} - 31 q^{69} + 17 q^{70} - 8 q^{71} + 9 q^{72} + 6 q^{73} + 10 q^{74} - q^{75} - 65 q^{76} - 39 q^{77} + 68 q^{78} - 56 q^{79} - 14 q^{80} - 56 q^{81} - 39 q^{82} + 6 q^{83} + 65 q^{84} + 53 q^{85} - 54 q^{86} + 83 q^{87} - 5 q^{88} + 66 q^{89} + 60 q^{90} + 5 q^{91} - 37 q^{92} - 67 q^{93} + 43 q^{94} - 39 q^{95} - 14 q^{96} + 13 q^{97} + 16 q^{98} + 47 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9 + 20 * q^10 - 9 * q^11 - 17 * q^12 - 11 * q^14 - 12 * q^15 + 9 * q^16 + 4 * q^17 - 35 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 - 11 * q^22 + 4 * q^23 + 15 * q^24 - 8 * q^25 + 19 * q^26 - 5 * q^27 + 22 * q^28 + 4 * q^29 - 24 * q^30 - 9 * q^31 - 34 * q^32 + 10 * q^33 - 6 * q^34 - 37 * q^35 + 20 * q^36 + 38 * q^37 + 18 * q^38 - 12 * q^39 + 60 * q^40 - 37 * q^41 + 17 * q^42 + 15 * q^43 - 34 * q^44 - 32 * q^45 - 41 * q^46 - 40 * q^47 - 43 * q^48 + 24 * q^49 - 28 * q^50 + 19 * q^51 - 56 * q^52 - 19 * q^53 + 6 * q^54 - 30 * q^55 - 58 * q^56 + 8 * q^57 - 21 * q^58 + q^59 - 10 * q^60 - 37 * q^62 - 17 * q^63 + 28 * q^64 - 34 * q^65 - 59 * q^66 + 3 * q^67 - 2 * q^68 - 31 * q^69 + 17 * q^70 - 8 * q^71 + 9 * q^72 + 6 * q^73 + 10 * q^74 - q^75 - 65 * q^76 - 39 * q^77 + 68 * q^78 - 56 * q^79 - 14 * q^80 - 56 * q^81 - 39 * q^82 + 6 * q^83 + 65 * q^84 + 53 * q^85 - 54 * q^86 + 83 * q^87 - 5 * q^88 + 66 * q^89 + 60 * q^90 + 5 * q^91 - 37 * q^92 - 67 * q^93 + 43 * q^94 - 39 * q^95 - 14 * q^96 + 13 * q^97 + 16 * q^98 + 47 * 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 $

$2$	−0.892823	−0.631321	−0.315661	−	0.948872i	$-0.602226\pi$
$2$	−0.892823	−0.631321	−0.315661	+	0.948872i	$0.602226\pi$
$3$	1.64555	0.950057	0.475029	−	0.879970i	$-0.342438\pi$
$3$	1.64555	0.950057	0.475029	+	0.879970i	$0.342438\pi$
$4$	−1.20287	−0.601433
$5$	0.610081	0.272837	0.136418	−	0.990651i	$-0.456441\pi$
$5$	0.610081	0.272837	0.136418	+	0.990651i	$0.456441\pi$
$6$	−1.46918	−0.599791
$7$	−0.681125	−0.257441	−0.128720	−	0.991681i	$-0.541087\pi$
$7$	−0.681125	−0.257441	−0.128720	+	0.991681i	$0.541087\pi$
$8$	2.85959	1.01102
$9$	−0.292175	−0.0973916
$10$	−0.544695	−0.172248
$11$	−0.856770	−0.258326	−0.129163	−	0.991623i	$-0.541229\pi$
$11$	−0.856770	−0.258326	−0.129163	+	0.991623i	$0.541229\pi$
$12$	−1.97937	−0.571396
$13$	0.513102	0.142309	0.0711545	−	0.997465i	$-0.477332\pi$
$13$	0.513102	0.142309	0.0711545	+	0.997465i	$0.477332\pi$
$14$	0.608124	0.162528
$15$	1.00392	0.259210
$16$	−0.147377	−0.0368444
$17$	1.01753	0.246787	0.123394	−	0.992358i	$-0.460622\pi$
$17$	1.01753	0.246787	0.123394	+	0.992358i	$0.460622\pi$
$18$	0.260860	0.0614854
$19$	−4.22681	−0.969696	−0.484848	−	0.874598i	$-0.661125\pi$
$19$	−4.22681	−0.969696	−0.484848	+	0.874598i	$0.661125\pi$
$20$	−0.733846	−0.164093
$21$	−1.12082	−0.244584
$22$	0.764944	0.163087
$23$	8.41171	1.75396	0.876981	−	0.480525i	$-0.159554\pi$
$23$	8.41171	1.75396	0.876981	+	0.480525i	$0.159554\pi$
$24$	4.70560	0.960526
$25$	−4.62780	−0.925560
$26$	−0.458110	−0.0898427
$27$	−5.41743	−1.04258
$28$	0.819302	0.154834
$29$	6.74089	1.25175	0.625876	−	0.779923i	$-0.284742\pi$
$29$	6.74089	1.25175	0.625876	+	0.779923i	$0.284742\pi$
$30$	−0.896321	−0.163645
$31$	−10.8670	−1.95176	−0.975881	−	0.218303i	$-0.929948\pi$
$31$	−10.8670	−1.95176	−0.975881	+	0.218303i	$0.929948\pi$
$32$	−5.58761	−0.987758
$33$	−1.40986	−0.245424
$34$	−0.908475	−0.155802
$35$	−0.415541	−0.0702393
$36$	0.351447	0.0585746
$37$	−2.30381	−0.378744	−0.189372	−	0.981905i	$-0.560645\pi$
$37$	−2.30381	−0.378744	−0.189372	+	0.981905i	$0.560645\pi$
$38$	3.77379	0.612190
$39$	0.844334	0.135202
$40$	1.74458	0.275843
$41$	−3.58906	−0.560517	−0.280259	−	0.959925i	$-0.590420\pi$
$41$	−3.58906	−0.560517	−0.280259	+	0.959925i	$0.590420\pi$
$42$	1.00070	0.154411
$43$	3.26469	0.497860	0.248930	−	0.968521i	$-0.419921\pi$
$43$	3.26469	0.497860	0.248930	+	0.968521i	$0.419921\pi$
$44$	1.03058	0.155366
$45$	−0.178250	−0.0265720
$46$	−7.51017	−1.10731
$47$	3.73892	0.545377	0.272688	−	0.962102i	$-0.412087\pi$
$47$	3.73892	0.545377	0.272688	+	0.962102i	$0.412087\pi$
$48$	−0.242516	−0.0350042
$49$	−6.53607	−0.933724
$50$	4.13181	0.584326
$51$	1.67439	0.234462
$52$	−0.617194	−0.0855894
$53$	5.86389	0.805467	0.402733	−	0.915317i	$-0.368060\pi$
$53$	5.86389	0.805467	0.402733	+	0.915317i	$0.368060\pi$
$54$	4.83681	0.658206
$55$	−0.522699	−0.0704808
$56$	−1.94774	−0.260278
$57$	−6.95541	−0.921267
$58$	−6.01842	−0.790258
$59$	8.86369	1.15395	0.576977	−	0.816760i	$-0.304232\pi$
$59$	8.86369	1.15395	0.576977	+	0.816760i	$0.304232\pi$
$60$	−1.20758	−0.155898
$61$	0	0
$61$	0	0
$62$	9.70227	1.23219
$63$	0.199008	0.0250726
$64$	5.28350	0.660437
$65$	0.313034	0.0388271
$66$	1.25875	0.154942
$67$	−11.3160	−1.38247	−0.691237	−	0.722628i	$-0.742934\pi$
$67$	−11.3160	−1.38247	−0.691237	+	0.722628i	$0.742934\pi$
$68$	−1.22395	−0.148426
$69$	13.8419	1.66636
$70$	0.371005	0.0443436
$71$	−5.51317	−0.654293	−0.327146	−	0.944974i	$-0.606087\pi$
$71$	−5.51317	−0.654293	−0.327146	+	0.944974i	$0.606087\pi$
$72$	−0.835501	−0.0984648
$73$	−2.77352	−0.324616	−0.162308	−	0.986740i	$-0.551894\pi$
$73$	−2.77352	−0.324616	−0.162308	+	0.986740i	$0.551894\pi$
$74$	2.05689	0.239109
$75$	−7.61526	−0.879335
$76$	5.08429	0.583208
$77$	0.583567	0.0665037
$78$	−0.753841	−0.0853557
$79$	−7.42540	−0.835423	−0.417711	−	0.908580i	$-0.637168\pi$
$79$	−7.42540	−0.835423	−0.417711	+	0.908580i	$0.637168\pi$
$80$	−0.0899122	−0.0100525
$81$	−8.03811	−0.893123
$82$	3.20440	0.353866
$83$	−10.7951	−1.18491	−0.592457	−	0.805602i	$-0.701842\pi$
$83$	−10.7951	−1.18491	−0.592457	+	0.805602i	$0.701842\pi$
$84$	1.34820	0.147101
$85$	0.620776	0.0673326
$86$	−2.91479	−0.314310
$87$	11.0925	1.18924
$88$	−2.45001	−0.261172
$89$	8.44034	0.894674	0.447337	−	0.894366i	$-0.352372\pi$
$89$	8.44034	0.894674	0.447337	+	0.894366i	$0.352372\pi$
$90$	0.159146	0.0167755
$91$	−0.349487	−0.0366362
$92$	−10.1182	−1.05489
$93$	−17.8821	−1.85429
$94$	−3.33819	−0.344308
$95$	−2.57870	−0.264569
$96$	−9.19467	−0.938427
$97$	−10.6539	−1.08174	−0.540871	−	0.841106i	$-0.681905\pi$
$97$	−10.6539	−1.08174	−0.540871	+	0.841106i	$0.681905\pi$
$98$	5.83555	0.589480
$99$	0.250327	0.0251588
$100$	5.56663	0.556663
$101$	−12.9422	−1.28780	−0.643901	−	0.765109i	$-0.722685\pi$
$101$	−12.9422	−1.28780	−0.643901	+	0.765109i	$0.722685\pi$
$102$	−1.49494	−0.148021
$103$	13.0169	1.28259	0.641294	−	0.767295i	$-0.278398\pi$
$103$	13.0169	1.28259	0.641294	+	0.767295i	$0.278398\pi$
$104$	1.46726	0.143877
$105$	−0.683793	−0.0667314
$106$	−5.23541	−0.508508
$107$	−8.68295	−0.839413	−0.419706	−	0.907660i	$-0.637867\pi$
$107$	−8.68295	−0.839413	−0.419706	+	0.907660i	$0.637867\pi$
$108$	6.51645	0.627045
$109$	13.5329	1.29621	0.648106	−	0.761550i	$-0.275561\pi$
$109$	13.5329	1.29621	0.648106	+	0.761550i	$0.275561\pi$
$110$	0.466678	0.0444960
$111$	−3.79103	−0.359828
$112$	0.100382	0.00948525
$113$	−1.87958	−0.176816	−0.0884080	−	0.996084i	$-0.528178\pi$
$113$	−1.87958	−0.176816	−0.0884080	+	0.996084i	$0.528178\pi$
$114$	6.20995	0.581615
$115$	5.13182	0.478545
$116$	−8.10839	−0.752846
$117$	−0.149916	−0.0138597
$118$	−7.91371	−0.728516
$119$	−0.693065	−0.0635332
$120$	2.87080	0.262067
$121$	−10.2659	−0.933268
$122$	0	0
$123$	−5.90597	−0.532523
$124$	13.0715	1.17385
$125$	−5.87374	−0.525363
$126$	−0.177679	−0.0158289
$127$	−11.3920	−1.01088	−0.505438	−	0.862863i	$-0.668669\pi$
$127$	−11.3920	−1.01088	−0.505438	+	0.862863i	$0.668669\pi$
$128$	6.45798	0.570810
$129$	5.37220	0.472995
$130$	−0.279484	−0.0245124
$131$	6.30508	0.550877	0.275439	−	0.961319i	$-0.411177\pi$
$131$	6.30508	0.550877	0.275439	+	0.961319i	$0.411177\pi$
$132$	1.69587	0.147606
$133$	2.87898	0.249640
$134$	10.1032	0.872785
$135$	−3.30507	−0.284455
$136$	2.90972	0.249507
$137$	10.3908	0.887744	0.443872	−	0.896090i	$-0.353604\pi$
$137$	10.3908	0.887744	0.443872	+	0.896090i	$0.353604\pi$
$138$	−12.3583	−1.05201
$139$	−9.24711	−0.784329	−0.392165	−	0.919895i	$-0.628274\pi$
$139$	−9.24711	−0.784329	−0.392165	+	0.919895i	$0.628274\pi$
$140$	0.499841	0.0422443
$141$	6.15256	0.518139
$142$	4.92228	0.413069
$143$	−0.439611	−0.0367621
$144$	0.0430600	0.00358833
$145$	4.11249	0.341524
$146$	2.47627	0.204937
$147$	−10.7554	−0.887091
$148$	2.77118	0.227789
$149$	−18.5006	−1.51563	−0.757815	−	0.652469i	$-0.773733\pi$
$149$	−18.5006	−1.51563	−0.757815	+	0.652469i	$0.773733\pi$
$150$	6.79908	0.555143
$151$	13.0474	1.06178	0.530889	−	0.847441i	$-0.321858\pi$
$151$	13.0474	1.06178	0.530889	+	0.847441i	$0.321858\pi$
$152$	−12.0870	−0.980381
$153$	−0.297297	−0.0240350
$154$	−0.521022	−0.0419852
$155$	−6.62972	−0.532512
$156$	−1.01562	−0.0813148
$157$	−10.4936	−0.837480	−0.418740	−	0.908106i	$-0.637528\pi$
$157$	−10.4936	−0.837480	−0.418740	+	0.908106i	$0.637528\pi$
$158$	6.62957	0.527420
$159$	9.64930	0.765239
$160$	−3.40889	−0.269497
$161$	−5.72942	−0.451542
$162$	7.17661	0.563848
$163$	−16.1970	−1.26865	−0.634325	−	0.773066i	$-0.718722\pi$
$163$	−16.1970	−1.26865	−0.634325	+	0.773066i	$0.718722\pi$
$164$	4.31716	0.337114
$165$	−0.860126	−0.0669607
$166$	9.63809	0.748061
$167$	−8.61767	−0.666856	−0.333428	−	0.942776i	$-0.608205\pi$
$167$	−8.61767	−0.666856	−0.333428	+	0.942776i	$0.608205\pi$
$168$	−3.20510	−0.247279
$169$	−12.7367	−0.979748
$170$	−0.554243	−0.0425085
$171$	1.23497	0.0944403
$172$	−3.92698	−0.299430
$173$	22.2536	1.69191	0.845955	−	0.533255i	$-0.179031\pi$
$173$	22.2536	1.69191	0.845955	+	0.533255i	$0.179031\pi$
$174$	−9.90360	−0.750790
$175$	3.15211	0.238277
$176$	0.126269	0.00951785
$177$	14.5856	1.09632
$178$	−7.53573	−0.564827
$179$	−9.91584	−0.741144	−0.370572	−	0.928804i	$-0.620838\pi$
$179$	−9.91584	−0.741144	−0.370572	+	0.928804i	$0.620838\pi$
$180$	0.214411	0.0159813
$181$	5.03589	0.374314	0.187157	−	0.982330i	$-0.440073\pi$
$181$	5.03589	0.374314	0.187157	+	0.982330i	$0.440073\pi$
$182$	0.312030	0.0231292
$183$	0	0
$184$	24.0541	1.77329
$185$	−1.40551	−0.103335
$186$	15.9655	1.17065
$187$	−0.871790	−0.0637516
$188$	−4.49742	−0.328008
$189$	3.68994	0.268404
$190$	2.30232	0.167028
$191$	2.63501	0.190663	0.0953313	−	0.995446i	$-0.469609\pi$
$191$	2.63501	0.190663	0.0953313	+	0.995446i	$0.469609\pi$
$192$	8.69424	0.627453
$193$	−9.93773	−0.715333	−0.357667	−	0.933849i	$-0.616428\pi$
$193$	−9.93773	−0.715333	−0.357667	+	0.933849i	$0.616428\pi$
$194$	9.51207	0.682927
$195$	0.515112	0.0368880
$196$	7.86202	0.561573
$197$	−10.6613	−0.759590	−0.379795	−	0.925071i	$-0.624005\pi$
$197$	−10.6613	−0.759590	−0.379795	+	0.925071i	$0.624005\pi$
$198$	−0.223497	−0.0158833
$199$	−10.6426	−0.754432	−0.377216	−	0.926125i	$-0.623118\pi$
$199$	−10.6426	−0.754432	−0.377216	+	0.926125i	$0.623118\pi$
$200$	−13.2336	−0.935759
$201$	−18.6211	−1.31343
$202$	11.5551	0.813016
$203$	−4.59139	−0.322252
$204$	−2.01407	−0.141013
$205$	−2.18962	−0.152930
$206$	−11.6217	−0.809725
$207$	−2.45769	−0.170821
$208$	−0.0756197	−0.00524328
$209$	3.62140	0.250498
$210$	0.610506	0.0421289
$211$	−1.07574	−0.0740567	−0.0370283	−	0.999314i	$-0.511789\pi$
$211$	−1.07574	−0.0740567	−0.0370283	+	0.999314i	$0.511789\pi$
$212$	−7.05347	−0.484435
$213$	−9.07218	−0.621615
$214$	7.75234	0.529939
$215$	1.99172	0.135834
$216$	−15.4916	−1.05407
$217$	7.40175	0.502464
$218$	−12.0824	−0.818326
$219$	−4.56396	−0.308404
$220$	0.628738	0.0423895
$221$	0.522097	0.0351201
$222$	3.38472	0.227167
$223$	−14.8547	−0.994745	−0.497372	−	0.867537i	$-0.665702\pi$
$223$	−14.8547	−0.994745	−0.497372	+	0.867537i	$0.665702\pi$
$224$	3.80586	0.254289
$225$	1.35213	0.0901418
$226$	1.67813	0.111628
$227$	−6.64505	−0.441047	−0.220524	−	0.975382i	$-0.570777\pi$
$227$	−6.64505	−0.441047	−0.220524	+	0.975382i	$0.570777\pi$
$228$	8.36643	0.554081
$229$	16.7740	1.10846	0.554228	−	0.832365i	$-0.313013\pi$
$229$	16.7740	1.10846	0.554228	+	0.832365i	$0.313013\pi$
$230$	−4.58181	−0.302116
$231$	0.960287	0.0631823
$232$	19.2762	1.26555
$233$	−20.8372	−1.36509	−0.682545	−	0.730844i	$-0.739127\pi$
$233$	−20.8372	−1.36509	−0.682545	+	0.730844i	$0.739127\pi$
$234$	0.133848	0.00874993
$235$	2.28104	0.148799
$236$	−10.6618	−0.694027
$237$	−12.2188	−0.793699
$238$	0.618785	0.0401099
$239$	26.1731	1.69300	0.846498	−	0.532392i	$-0.178707\pi$
$239$	26.1731	1.69300	0.846498	+	0.532392i	$0.178707\pi$
$240$	−0.147955	−0.00955044
$241$	20.0478	1.29139	0.645695	−	0.763595i	$-0.276568\pi$
$241$	20.0478	1.29139	0.645695	+	0.763595i	$0.276568\pi$
$242$	9.16567	0.589192
$243$	3.02520	0.194067
$244$	0	0
$245$	−3.98753	−0.254754
$246$	5.27299	0.336193
$247$	−2.16878	−0.137996
$248$	−31.0751	−1.97327
$249$	−17.7638	−1.12574
$250$	5.24421	0.331673
$251$	−15.0829	−0.952022	−0.476011	−	0.879439i	$-0.657918\pi$
$251$	−15.0829	−0.952022	−0.476011	+	0.879439i	$0.657918\pi$
$252$	−0.239380	−0.0150795
$253$	−7.20690	−0.453094
$254$	10.1710	0.638188
$255$	1.02152	0.0639698
$256$	−16.3328	−1.02080
$257$	13.4970	0.841922	0.420961	−	0.907079i	$-0.361693\pi$
$257$	13.4970	0.841922	0.420961	+	0.907079i	$0.361693\pi$
$258$	−4.79642	−0.298612
$259$	1.56918	0.0975042
$260$	−0.376538	−0.0233519
$261$	−1.96952	−0.121910
$262$	−5.62932	−0.347780
$263$	−5.24394	−0.323355	−0.161678	−	0.986844i	$-0.551690\pi$
$263$	−5.24394	−0.323355	−0.161678	+	0.986844i	$0.551690\pi$
$264$	−4.03161	−0.248129
$265$	3.57745	0.219761
$266$	−2.57042	−0.157603
$267$	13.8890	0.849991
$268$	13.6117	0.831466
$269$	−16.6792	−1.01695	−0.508475	−	0.861077i	$-0.669791\pi$
$269$	−16.6792	−1.01695	−0.508475	+	0.861077i	$0.669791\pi$
$270$	2.95084	0.179583
$271$	−2.57162	−0.156215	−0.0781075	−	0.996945i	$-0.524888\pi$
$271$	−2.57162	−0.156215	−0.0781075	+	0.996945i	$0.524888\pi$
$272$	−0.149961	−0.00909272
$273$	−0.575097	−0.0348064
$274$	−9.27713	−0.560452
$275$	3.96496	0.239096
$276$	−16.6499	−1.00221
$277$	−27.0696	−1.62645	−0.813227	−	0.581947i	$-0.802291\pi$
$277$	−27.0696	−1.62645	−0.813227	+	0.581947i	$0.802291\pi$
$278$	8.25603	0.495164
$279$	3.17505	0.190085
$280$	−1.18828	−0.0710133
$281$	17.2757	1.03058	0.515291	−	0.857015i	$-0.327684\pi$
$281$	17.2757	1.03058	0.515291	+	0.857015i	$0.327684\pi$
$282$	−5.49315	−0.327112
$283$	−26.6834	−1.58616	−0.793081	−	0.609116i	$-0.791524\pi$
$283$	−26.6834	−1.58616	−0.793081	+	0.609116i	$0.791524\pi$
$284$	6.63161	0.393514
$285$	−4.24336	−0.251355
$286$	0.392495	0.0232087
$287$	2.44460	0.144300
$288$	1.63256	0.0961994
$289$	−15.9646	−0.939096
$290$	−3.67173	−0.215611
$291$	−17.5315	−1.02772
$292$	3.33618	0.195235
$293$	26.8612	1.56925	0.784624	−	0.619972i	$-0.212856\pi$
$293$	26.8612	1.56925	0.784624	+	0.619972i	$0.212856\pi$
$294$	9.60268	0.560040
$295$	5.40757	0.314841
$296$	−6.58796	−0.382917
$297$	4.64149	0.269327
$298$	16.5178	0.956850
$299$	4.31607	0.249605
$300$	9.16015	0.528861
$301$	−2.22366	−0.128170
$302$	−11.6490	−0.670323
$303$	−21.2971	−1.22348
$304$	0.622936	0.0357278
$305$	0	0
$306$	0.265434	0.0151738
$307$	−2.78999	−0.159233	−0.0796167	−	0.996826i	$-0.525370\pi$
$307$	−2.78999	−0.159233	−0.0796167	+	0.996826i	$0.525370\pi$
$308$	−0.701954	−0.0399975
$309$	21.4198	1.21853
$310$	5.91917	0.336186
$311$	−3.67673	−0.208488	−0.104244	−	0.994552i	$-0.533242\pi$
$311$	−3.67673	−0.208488	−0.104244	+	0.994552i	$0.533242\pi$
$312$	2.41445	0.136691
$313$	−27.2134	−1.53819	−0.769095	−	0.639134i	$-0.779293\pi$
$313$	−27.2134	−1.53819	−0.769095	+	0.639134i	$0.779293\pi$
$314$	9.36892	0.528719
$315$	0.121411	0.00684072
$316$	8.93177	0.502451
$317$	28.9292	1.62483	0.812414	−	0.583081i	$-0.198153\pi$
$317$	28.9292	1.62483	0.812414	+	0.583081i	$0.198153\pi$
$318$	−8.61512	−0.483112
$319$	−5.77539	−0.323360
$320$	3.22336	0.180191
$321$	−14.2882	−0.797490
$322$	5.11536	0.285068
$323$	−4.30091	−0.239309
$324$	9.66878	0.537154
$325$	−2.37454	−0.131716
$326$	14.4611	0.800926
$327$	22.2689	1.23148
$328$	−10.2633	−0.566694
$329$	−2.54667	−0.140402
$330$	0.767941	0.0422737
$331$	11.6718	0.641540	0.320770	−	0.947157i	$-0.396058\pi$
$331$	11.6718	0.641540	0.320770	+	0.947157i	$0.396058\pi$
$332$	12.9850	0.712647
$333$	0.673115	0.0368865
$334$	7.69406	0.421000
$335$	−6.90370	−0.377189
$336$	0.165184	0.00901152
$337$	24.3299	1.32534	0.662668	−	0.748914i	$-0.269424\pi$
$337$	24.3299	1.32534	0.662668	+	0.748914i	$0.269424\pi$
$338$	11.3716	0.618536
$339$	−3.09294	−0.167985
$340$	−0.746711	−0.0404961
$341$	9.31048	0.504191
$342$	−1.10261	−0.0596222
$343$	9.21975	0.497820
$344$	9.33568	0.503346
$345$	8.44466	0.454645
$346$	−19.8685	−1.06814
$347$	4.06093	0.218002	0.109001	−	0.994042i	$-0.465235\pi$
$347$	4.06093	0.218002	0.109001	+	0.994042i	$0.465235\pi$
$348$	−13.3427	−0.715246
$349$	−0.880714	−0.0471435	−0.0235718	−	0.999722i	$-0.507504\pi$
$349$	−0.880714	−0.0471435	−0.0235718	+	0.999722i	$0.507504\pi$
$350$	−2.81428	−0.150429
$351$	−2.77970	−0.148369
$352$	4.78729	0.255164
$353$	−19.5543	−1.04077	−0.520385	−	0.853931i	$-0.674212\pi$
$353$	−19.5543	−1.04077	−0.520385	+	0.853931i	$0.674212\pi$
$354$	−13.0224	−0.692131
$355$	−3.36348	−0.178515
$356$	−10.1526	−0.538087
$357$	−1.14047	−0.0603602
$358$	8.85309	0.467900
$359$	0.724570	0.0382413	0.0191207	−	0.999817i	$-0.493913\pi$
$359$	0.724570	0.0382413	0.0191207	+	0.999817i	$0.493913\pi$
$360$	−0.509724	−0.0268648
$361$	−1.13410	−0.0596895
$362$	−4.49615	−0.236313
$363$	−16.8931	−0.886658
$364$	0.420386	0.0220342
$365$	−1.69208	−0.0885673
$366$	0	0
$367$	−0.914369	−0.0477297	−0.0238648	−	0.999715i	$-0.507597\pi$
$367$	−0.914369	−0.0477297	−0.0238648	+	0.999715i	$0.507597\pi$
$368$	−1.23970	−0.0646236
$369$	1.04863	0.0545897
$370$	1.25487	0.0652377
$371$	−3.99404	−0.207360
$372$	21.5098	1.11523
$373$	−15.6855	−0.812163	−0.406081	−	0.913837i	$-0.633105\pi$
$373$	−15.6855	−0.812163	−0.406081	+	0.913837i	$0.633105\pi$
$374$	0.778354	0.0402477
$375$	−9.66552	−0.499125
$376$	10.6918	0.551386
$377$	3.45877	0.178136
$378$	−3.29447	−0.169449
$379$	22.8752	1.17502	0.587509	−	0.809217i	$-0.300109\pi$
$379$	22.8752	1.17502	0.587509	+	0.809217i	$0.300109\pi$
$380$	3.10183	0.159120
$381$	−18.7461	−0.960390
$382$	−2.35260	−0.120369
$383$	5.51904	0.282010	0.141005	−	0.990009i	$-0.454967\pi$
$383$	5.51904	0.282010	0.141005	+	0.990009i	$0.454967\pi$
$384$	10.6269	0.542302
$385$	0.356023	0.0181446
$386$	8.87263	0.451605
$387$	−0.953859	−0.0484874
$388$	12.8152	0.650596
$389$	−12.4369	−0.630575	−0.315287	−	0.948996i	$-0.602101\pi$
$389$	−12.4369	−0.630575	−0.315287	+	0.948996i	$0.602101\pi$
$390$	−0.459904	−0.0232882
$391$	8.55917	0.432856
$392$	−18.6905	−0.944013
$393$	10.3753	0.523365
$394$	9.51870	0.479545
$395$	−4.53010	−0.227934
$396$	−0.301110	−0.0151313
$397$	9.46782	0.475176	0.237588	−	0.971366i	$-0.423643\pi$
$397$	9.46782	0.475176	0.237588	+	0.971366i	$0.423643\pi$
$398$	9.50193	0.476289
$399$	4.73750	0.237172
$400$	0.682033	0.0341017
$401$	21.8875	1.09301	0.546505	−	0.837456i	$-0.315958\pi$
$401$	21.8875	1.09301	0.546505	+	0.837456i	$0.315958\pi$
$402$	16.6253	0.829195
$403$	−5.57586	−0.277753
$404$	15.5678	0.774527
$405$	−4.90390	−0.243677
$406$	4.09930	0.203445
$407$	1.97383	0.0978394
$408$	4.78809	0.237046
$409$	−4.81215	−0.237945	−0.118973	−	0.992898i	$-0.537960\pi$
$409$	−4.81215	−0.237945	−0.118973	+	0.992898i	$0.537960\pi$
$410$	1.95494	0.0965477
$411$	17.0985	0.843408
$412$	−15.6575	−0.771392
$413$	−6.03728	−0.297075
$414$	2.19428	0.107843
$415$	−6.58587	−0.323288
$416$	−2.86701	−0.140567
$417$	−15.2165	−0.745158
$418$	−3.23327	−0.158144
$419$	−33.1001	−1.61704	−0.808522	−	0.588466i	$-0.799732\pi$
$419$	−33.1001	−1.61704	−0.808522	+	0.588466i	$0.799732\pi$
$420$	0.822512	0.0401345
$421$	−0.719531	−0.0350678	−0.0175339	−	0.999846i	$-0.505582\pi$
$421$	−0.719531	−0.0350678	−0.0175339	+	0.999846i	$0.505582\pi$
$422$	0.960441	0.0467535
$423$	−1.09242	−0.0531151
$424$	16.7683	0.814342
$425$	−4.70893	−0.228417
$426$	8.09985	0.392439
$427$	0	0
$428$	10.4444	0.504851
$429$	−0.723400	−0.0349261
$430$	−1.77826	−0.0857552
$431$	20.7061	0.997379	0.498689	−	0.866781i	$-0.333815\pi$
$431$	20.7061	0.997379	0.498689	+	0.866781i	$0.333815\pi$
$432$	0.798407	0.0384134
$433$	−31.2098	−1.49985	−0.749924	−	0.661524i	$-0.769910\pi$
$433$	−31.2098	−1.49985	−0.749924	+	0.661524i	$0.769910\pi$
$434$	−6.60845	−0.317216
$435$	6.76730	0.324467
$436$	−16.2782	−0.779585
$437$	−35.5547	−1.70081
$438$	4.07481	0.194702
$439$	−6.70188	−0.319863	−0.159932	−	0.987128i	$-0.551127\pi$
$439$	−6.70188	−0.319863	−0.159932	+	0.987128i	$0.551127\pi$
$440$	−1.49471	−0.0712574
$441$	1.90968	0.0909369
$442$	−0.466141	−0.0221720
$443$	4.36111	0.207203	0.103601	−	0.994619i	$-0.466963\pi$
$443$	4.36111	0.207203	0.103601	+	0.994619i	$0.466963\pi$
$444$	4.56010	0.216413
$445$	5.14929	0.244100
$446$	13.2626	0.628003
$447$	−30.4437	−1.43994
$448$	−3.59872	−0.170024
$449$	−35.2783	−1.66488	−0.832442	−	0.554112i	$-0.813058\pi$
$449$	−35.2783	−1.66488	−0.832442	+	0.554112i	$0.813058\pi$
$450$	−1.20721	−0.0569084
$451$	3.07500	0.144796
$452$	2.26088	0.106343
$453$	21.4700	1.00875
$454$	5.93285	0.278443
$455$	−0.213215	−0.00999569
$456$	−19.8896	−0.931418
$457$	38.1663	1.78534	0.892672	−	0.450708i	$-0.148828\pi$
$457$	38.1663	1.78534	0.892672	+	0.450708i	$0.148828\pi$
$458$	−14.9762	−0.699792
$459$	−5.51240	−0.257297
$460$	−6.17290	−0.287813
$461$	−16.9780	−0.790743	−0.395372	−	0.918521i	$-0.629384\pi$
$461$	−16.9780	−0.790743	−0.395372	+	0.918521i	$0.629384\pi$
$462$	−0.857367	−0.0398883
$463$	−10.5021	−0.488075	−0.244037	−	0.969766i	$-0.578472\pi$
$463$	−10.5021	−0.488075	−0.244037	+	0.969766i	$0.578472\pi$
$464$	−0.993455	−0.0461200
$465$	−10.9095	−0.505917
$466$	18.6039	0.861810
$467$	−30.8815	−1.42902	−0.714512	−	0.699623i	$-0.753351\pi$
$467$	−30.8815	−1.42902	−0.714512	+	0.699623i	$0.753351\pi$
$468$	0.180329	0.00833569
$469$	7.70763	0.355905
$470$	−2.03657	−0.0939398
$471$	−17.2677	−0.795653
$472$	25.3465	1.16667
$473$	−2.79709	−0.128610
$474$	10.9093	0.501079
$475$	19.5608	0.897512
$476$	0.833665	0.0382110
$477$	−1.71328	−0.0784457
$478$	−23.3679	−1.06882
$479$	38.5587	1.76179	0.880896	−	0.473309i	$-0.156941\pi$
$479$	38.5587	1.76179	0.880896	+	0.473309i	$0.156941\pi$
$480$	−5.60949	−0.256037
$481$	−1.18209	−0.0538987
$482$	−17.8991	−0.815282
$483$	−9.42803	−0.428990
$484$	12.3486	0.561298
$485$	−6.49976	−0.295139
$486$	−2.70097	−0.122518
$487$	26.4637	1.19918	0.599592	−	0.800306i	$-0.295330\pi$
$487$	26.4637	1.19918	0.599592	+	0.800306i	$0.295330\pi$
$488$	0	0
$489$	−26.6530	−1.20529
$490$	3.56016	0.160832
$491$	−40.0656	−1.80813	−0.904067	−	0.427391i	$-0.859433\pi$
$491$	−40.0656	−1.80813	−0.904067	+	0.427391i	$0.859433\pi$
$492$	7.10410	0.320277
$493$	6.85906	0.308917
$494$	1.93634	0.0871201
$495$	0.152720	0.00686424
$496$	1.60154	0.0719114
$497$	3.75516	0.168442
$498$	15.8599	0.710701
$499$	−24.8592	−1.11285	−0.556425	−	0.830898i	$-0.687827\pi$
$499$	−24.8592	−1.11285	−0.556425	+	0.830898i	$0.687827\pi$
$500$	7.06533	0.315971
$501$	−14.1808	−0.633551
$502$	13.4663	0.601032
$503$	−14.7315	−0.656846	−0.328423	−	0.944531i	$-0.606517\pi$
$503$	−14.7315	−0.656846	−0.328423	+	0.944531i	$0.606517\pi$
$504$	0.569081	0.0253489
$505$	−7.89582	−0.351359
$506$	6.43449	0.286048
$507$	−20.9589	−0.930817
$508$	13.7031	0.607975
$509$	0.811083	0.0359506	0.0179753	−	0.999838i	$-0.494278\pi$
$509$	0.811083	0.0359506	0.0179753	+	0.999838i	$0.494278\pi$
$510$	−0.912034	−0.0403855
$511$	1.88912	0.0835696
$512$	1.66637	0.0736437
$513$	22.8984	1.01099
$514$	−12.0505	−0.531523
$515$	7.94134	0.349937
$516$	−6.46204	−0.284475
$517$	−3.20339	−0.140885
$518$	−1.40100	−0.0615565
$519$	36.6193	1.60741
$520$	0.895150	0.0392549
$521$	31.3167	1.37201	0.686006	−	0.727596i	$-0.259362\pi$
$521$	31.3167	1.37201	0.686006	+	0.727596i	$0.259362\pi$
$522$	1.75843	0.0769645
$523$	19.2011	0.839607	0.419803	−	0.907615i	$-0.362099\pi$
$523$	19.2011	0.839607	0.419803	+	0.907615i	$0.362099\pi$
$524$	−7.58417	−0.331316
$525$	5.18695	0.226377
$526$	4.68191	0.204141
$527$	−11.0575	−0.481670
$528$	0.207781	0.00904250
$529$	47.7568	2.07638
$530$	−3.19403	−0.138740
$531$	−2.58975	−0.112385
$532$	−3.46303	−0.150142
$533$	−1.84156	−0.0797666
$534$	−12.4004	−0.536618
$535$	−5.29731	−0.229023
$536$	−32.3593	−1.39771
$537$	−16.3170	−0.704130
$538$	14.8916	0.642022
$539$	5.59991	0.241205
$540$	3.97556	0.171081
$541$	22.9398	0.986258	0.493129	−	0.869956i	$-0.335853\pi$
$541$	22.9398	0.986258	0.493129	+	0.869956i	$0.335853\pi$
$542$	2.29600	0.0986218
$543$	8.28679	0.355620
$544$	−5.68556	−0.243766
$545$	8.25614	0.353654
$546$	0.513460	0.0219740
$547$	−22.9081	−0.979480	−0.489740	−	0.871868i	$-0.662908\pi$
$547$	−22.9081	−0.979480	−0.489740	+	0.871868i	$0.662908\pi$
$548$	−12.4987	−0.533919
$549$	0	0
$550$	−3.54001	−0.150946
$551$	−28.4924	−1.21382
$552$	39.5821	1.68473
$553$	5.05762	0.215072
$554$	24.1683	1.02681
$555$	−2.31283	−0.0981743
$556$	11.1230	0.471722
$557$	8.60368	0.364550	0.182275	−	0.983248i	$-0.441654\pi$
$557$	8.60368	0.364550	0.182275	+	0.983248i	$0.441654\pi$
$558$	−2.83476	−0.120005
$559$	1.67512	0.0708500
$560$	0.0612414	0.00258792
$561$	−1.43457	−0.0605676
$562$	−15.4242	−0.650629
$563$	37.9901	1.60109	0.800546	−	0.599271i	$-0.204543\pi$
$563$	37.9901	1.60109	0.800546	+	0.599271i	$0.204543\pi$
$564$	−7.40071	−0.311626
$565$	−1.14670	−0.0482419
$566$	23.8235	1.00138
$567$	5.47496	0.229927
$568$	−15.7654	−0.661502
$569$	18.1187	0.759576	0.379788	−	0.925074i	$-0.375997\pi$
$569$	18.1187	0.759576	0.379788	+	0.925074i	$0.375997\pi$
$570$	3.78857	0.158686
$571$	33.5450	1.40381	0.701907	−	0.712268i	$-0.252332\pi$
$571$	33.5450	1.40381	0.701907	+	0.712268i	$0.252332\pi$
$572$	0.528793	0.0221100
$573$	4.33603	0.181140
$574$	−2.18259	−0.0910997
$575$	−38.9277	−1.62340
$576$	−1.54371	−0.0643211
$577$	−20.7429	−0.863537	−0.431769	−	0.901984i	$-0.642110\pi$
$577$	−20.7429	−0.863537	−0.431769	+	0.901984i	$0.642110\pi$
$578$	14.2536	0.592871
$579$	−16.3530	−0.679607
$580$	−4.94678	−0.205404
$581$	7.35279	0.305045
$582$	15.6526	0.648819
$583$	−5.02400	−0.208073
$584$	−7.93115	−0.328193
$585$	−0.0914607	−0.00378143
$586$	−23.9823	−0.990700
$587$	11.6212	0.479657	0.239829	−	0.970815i	$-0.422909\pi$
$587$	11.6212	0.479657	0.239829	+	0.970815i	$0.422909\pi$
$588$	12.9373	0.533526
$589$	45.9325	1.89262
$590$	−4.82800	−0.198766
$591$	−17.5438	−0.721653
$592$	0.339529	0.0139546
$593$	4.22725	0.173592	0.0867961	−	0.996226i	$-0.472337\pi$
$593$	4.22725	0.173592	0.0867961	+	0.996226i	$0.472337\pi$
$594$	−4.14403	−0.170032
$595$	−0.422826	−0.0173342
$596$	22.2538	0.911551
$597$	−17.5128	−0.716753
$598$	−3.85348	−0.157581
$599$	37.2796	1.52321	0.761603	−	0.648044i	$-0.224413\pi$
$599$	37.2796	1.52321	0.761603	+	0.648044i	$0.224413\pi$
$600$	−21.7766	−0.889024
$601$	−21.6834	−0.884485	−0.442242	−	0.896896i	$-0.645817\pi$
$601$	−21.6834	−0.884485	−0.442242	+	0.896896i	$0.645817\pi$
$602$	1.98533	0.0809162
$603$	3.30626	0.134641
$604$	−15.6942	−0.638589
$605$	−6.26306	−0.254630
$606$	19.0145	0.772412
$607$	−15.6022	−0.633273	−0.316636	−	0.948547i	$-0.602554\pi$
$607$	−15.6022	−0.633273	−0.316636	+	0.948547i	$0.602554\pi$
$608$	23.6177	0.957825
$609$	−7.55534	−0.306158
$610$	0	0
$611$	1.91845	0.0776120
$612$	0.357609	0.0144555
$613$	−10.7790	−0.435358	−0.217679	−	0.976020i	$-0.569849\pi$
$613$	−10.7790	−0.435358	−0.217679	+	0.976020i	$0.569849\pi$
$614$	2.49097	0.100527
$615$	−3.60312	−0.145292
$616$	1.66877	0.0672365
$617$	34.0885	1.37235	0.686177	−	0.727435i	$-0.259288\pi$
$617$	34.0885	1.37235	0.686177	+	0.727435i	$0.259288\pi$
$618$	−19.1241	−0.769285
$619$	−16.7470	−0.673118	−0.336559	−	0.941662i	$-0.609263\pi$
$619$	−16.7470	−0.673118	−0.336559	+	0.941662i	$0.609263\pi$
$620$	7.97467	0.320271
$621$	−45.5698	−1.82865
$622$	3.28267	0.131623
$623$	−5.74892	−0.230326
$624$	−0.124436	−0.00498142
$625$	19.5555	0.782222
$626$	24.2967	0.971093
$627$	5.95919	0.237987
$628$	12.6224	0.503688
$629$	−2.34420	−0.0934692
$630$	−0.108398	−0.00431869
$631$	12.6838	0.504935	0.252468	−	0.967605i	$-0.418758\pi$
$631$	12.6838	0.504935	0.252468	+	0.967605i	$0.418758\pi$
$632$	−21.2336	−0.844628
$633$	−1.77017	−0.0703581
$634$	−25.8287	−1.02579
$635$	−6.95004	−0.275804
$636$	−11.6068	−0.460241
$637$	−3.35367	−0.132877
$638$	5.15640	0.204144
$639$	1.61081	0.0637226
$640$	3.93989	0.155738
$641$	−19.0777	−0.753525	−0.376763	−	0.926310i	$-0.622963\pi$
$641$	−19.0777	−0.753525	−0.376763	+	0.926310i	$0.622963\pi$
$642$	12.7568	0.503473
$643$	25.1698	0.992600	0.496300	−	0.868151i	$-0.334692\pi$
$643$	25.1698	0.992600	0.496300	+	0.868151i	$0.334692\pi$
$644$	6.89173	0.271572
$645$	3.27748	0.129050
$646$	3.83995	0.151081
$647$	−16.1182	−0.633671	−0.316836	−	0.948480i	$-0.602620\pi$
$647$	−16.1182	−0.633671	−0.316836	+	0.948480i	$0.602620\pi$
$648$	−22.9857	−0.902965
$649$	−7.59414	−0.298096
$650$	2.12004	0.0831548
$651$	12.1799	0.477369
$652$	19.4829	0.763009
$653$	−19.2568	−0.753575	−0.376788	−	0.926300i	$-0.622971\pi$
$653$	−19.2568	−0.753575	−0.376788	+	0.926300i	$0.622971\pi$
$654$	−19.8822	−0.777457
$655$	3.84661	0.150299
$656$	0.528947	0.0206519
$657$	0.810354	0.0316149
$658$	2.27372	0.0886390
$659$	−34.4751	−1.34296	−0.671481	−	0.741022i	$-0.734341\pi$
$659$	−34.4751	−1.34296	−0.671481	+	0.741022i	$0.734341\pi$
$660$	1.03462	0.0402724
$661$	30.1959	1.17448	0.587242	−	0.809411i	$-0.300214\pi$
$661$	30.1959	1.17448	0.587242	+	0.809411i	$0.300214\pi$
$662$	−10.4209	−0.405018
$663$	0.859136	0.0333661
$664$	−30.8695	−1.19797
$665$	1.75641	0.0681108
$666$	−0.600973	−0.0232872
$667$	56.7024	2.19553
$668$	10.3659	0.401069
$669$	−24.4441	−0.945064
$670$	6.16378	0.238128
$671$	0	0
$672$	6.26272	0.241590
$673$	−7.99577	−0.308214	−0.154107	−	0.988054i	$-0.549250\pi$
$673$	−7.99577	−0.308214	−0.154107	+	0.988054i	$0.549250\pi$
$674$	−21.7223	−0.836712
$675$	25.0708	0.964975
$676$	15.3206	0.589253
$677$	5.29360	0.203450	0.101725	−	0.994813i	$-0.467564\pi$
$677$	5.29360	0.203450	0.101725	+	0.994813i	$0.467564\pi$
$678$	2.76145	0.106053
$679$	7.25665	0.278485
$680$	1.77517	0.0680746
$681$	−10.9347	−0.419020
$682$	−8.31261	−0.318306
$683$	−4.52236	−0.173043	−0.0865217	−	0.996250i	$-0.527575\pi$
$683$	−4.52236	−0.173043	−0.0865217	+	0.996250i	$0.527575\pi$
$684$	−1.48550	−0.0567995
$685$	6.33922	0.242209
$686$	−8.23161	−0.314284
$687$	27.6024	1.05310
$688$	−0.481141	−0.0183433
$689$	3.00877	0.114625
$690$	−7.53959	−0.287027
$691$	17.4098	0.662301	0.331150	−	0.943578i	$-0.392563\pi$
$691$	17.4098	0.662301	0.331150	+	0.943578i	$0.392563\pi$
$692$	−26.7681	−1.01757
$693$	−0.170504	−0.00647690
$694$	−3.62569	−0.137629
$695$	−5.64149	−0.213994
$696$	31.7199	1.20234
$697$	−3.65198	−0.138329
$698$	0.786322	0.0297627
$699$	−34.2886	−1.29691
$700$	−3.79157	−0.143308
$701$	34.4390	1.30074	0.650372	−	0.759616i	$-0.274613\pi$
$701$	34.4390	1.30074	0.650372	+	0.759616i	$0.274613\pi$
$702$	2.48178	0.0936686
$703$	9.73776	0.367266
$704$	−4.52674	−0.170608
$705$	3.75356	0.141367
$706$	17.4585	0.657061
$707$	8.81528	0.331533
$708$	−17.5446	−0.659365
$709$	12.9447	0.486150	0.243075	−	0.970007i	$-0.421844\pi$
$709$	12.9447	0.486150	0.243075	+	0.970007i	$0.421844\pi$
$710$	3.00299	0.112700
$711$	2.16951	0.0813632
$712$	24.1359	0.904532
$713$	−91.4096	−3.42332
$714$	1.01824	0.0381066
$715$	−0.268198	−0.0100300
$716$	11.9274	0.445749
$717$	43.0690	1.60844
$718$	−0.646913	−0.0241426
$719$	0.0293679	0.00109524	0.000547618	−	1.00000i	$-0.499826\pi$
$719$	0.0293679	0.00109524	0.000547618		1.00000i	$0.499826\pi$
$720$	0.0262701	0.000979028 0
$721$	−8.86610	−0.330191
$722$	1.01255	0.0376832
$723$	32.9896	1.22689
$724$	−6.05750	−0.225125
$725$	−31.1955	−1.15857
$726$	15.0825	0.559766
$727$	−33.7572	−1.25199	−0.625993	−	0.779829i	$-0.715306\pi$
$727$	−33.7572	−1.25199	−0.625993	+	0.779829i	$0.715306\pi$
$728$	−0.999390	−0.0370399
$729$	29.0924	1.07750
$730$	1.51072	0.0559144
$731$	3.32192	0.122866
$732$	0	0
$733$	−27.0169	−0.997891	−0.498945	−	0.866633i	$-0.666279\pi$
$733$	−27.0169	−0.997891	−0.498945	+	0.866633i	$0.666279\pi$
$734$	0.816370	0.0301328
$735$	−6.56167	−0.242031
$736$	−47.0013	−1.73249
$737$	9.69524	0.357129
$738$	−0.936244	−0.0344636
$739$	−15.2592	−0.561318	−0.280659	−	0.959808i	$-0.590553\pi$
$739$	−15.2592	−0.561318	−0.280659	+	0.959808i	$0.590553\pi$
$740$	1.69064	0.0621492
$741$	−3.56884	−0.131105
$742$	3.56597	0.130911
$743$	−8.97804	−0.329372	−0.164686	−	0.986346i	$-0.552661\pi$
$743$	−8.97804	−0.329372	−0.164686	+	0.986346i	$0.552661\pi$
$744$	−51.1355	−1.87472
$745$	−11.2869	−0.413520
$746$	14.0043	0.512735
$747$	3.15405	0.115401
$748$	1.04865	0.0383423
$749$	5.91418	0.216099
$750$	8.62960	0.315108
$751$	−34.7478	−1.26797	−0.633983	−	0.773347i	$-0.718581\pi$
$751$	−34.7478	−1.26797	−0.633983	+	0.773347i	$0.718581\pi$
$752$	−0.551032	−0.0200941
$753$	−24.8196	−0.904475
$754$	−3.08807	−0.112461
$755$	7.95994	0.289692
$756$	−4.43851	−0.161427
$757$	−10.3521	−0.376255	−0.188127	−	0.982145i	$-0.560242\pi$
$757$	−10.3521	−0.376255	−0.188127	+	0.982145i	$0.560242\pi$
$758$	−20.4235	−0.741814
$759$	−11.8593	−0.430465
$760$	−7.37402	−0.267484
$761$	−23.7787	−0.861977	−0.430988	−	0.902357i	$-0.641835\pi$
$761$	−23.7787	−0.861977	−0.430988	+	0.902357i	$0.641835\pi$
$762$	16.7369	0.606315
$763$	−9.21756	−0.333698
$764$	−3.16957	−0.114671
$765$	−0.181375	−0.00655763
$766$	−4.92752	−0.178039
$767$	4.54798	0.164218
$768$	−26.8764	−0.969820
$769$	−27.2477	−0.982577	−0.491288	−	0.870997i	$-0.663474\pi$
$769$	−27.2477	−0.982577	−0.491288	+	0.870997i	$0.663474\pi$
$770$	−0.317866	−0.0114551
$771$	22.2100	0.799874
$772$	11.9538	0.430225
$773$	33.9256	1.22022	0.610109	−	0.792317i	$-0.291126\pi$
$773$	33.9256	1.22022	0.610109	+	0.792317i	$0.291126\pi$
$774$	0.851628	0.0306111
$775$	50.2901	1.80647
$776$	−30.4659	−1.09366
$777$	2.58216	0.0926345
$778$	11.1039	0.398095
$779$	15.1703	0.543531
$780$	−0.619612	−0.0221857
$781$	4.72352	0.169021
$782$	−7.64182	−0.273271
$783$	−36.5183	−1.30506
$784$	0.963269	0.0344025
$785$	−6.40194	−0.228495
$786$	−9.26331	−0.330411
$787$	7.78853	0.277631	0.138815	−	0.990318i	$-0.455671\pi$
$787$	7.78853	0.277631	0.138815	+	0.990318i	$0.455671\pi$
$788$	12.8242	0.456843
$789$	−8.62915	−0.307206
$790$	4.04457	0.143899
$791$	1.28023	0.0455197
$792$	0.715833	0.0254360
$793$	0	0
$794$	−8.45309	−0.299989
$795$	5.88686	0.208785
$796$	12.8016	0.453740
$797$	−13.6238	−0.482580	−0.241290	−	0.970453i	$-0.577570\pi$
$797$	−13.6238	−0.482580	−0.241290	+	0.970453i	$0.577570\pi$
$798$	−4.22975	−0.149732
$799$	3.80446	0.134592
$800$	25.8583	0.914230
$801$	−2.46605	−0.0871337
$802$	−19.5417	−0.690041
$803$	2.37627	0.0838568
$804$	22.3987	0.789940
$805$	−3.49541	−0.123197
$806$	4.97825	0.175352
$807$	−27.4464	−0.966160
$808$	−37.0096	−1.30199
$809$	37.8488	1.33069	0.665347	−	0.746534i	$-0.268284\pi$
$809$	37.8488	1.33069	0.665347	+	0.746534i	$0.268284\pi$
$810$	4.37831	0.153838
$811$	24.6008	0.863852	0.431926	−	0.901909i	$-0.357834\pi$
$811$	24.6008	0.863852	0.431926	+	0.901909i	$0.357834\pi$
$812$	5.52283	0.193813
$813$	−4.23173	−0.148413
$814$	−1.76229	−0.0617681
$815$	−9.88151	−0.346134
$816$	−0.246768	−0.00863860
$817$	−13.7992	−0.482773
$818$	4.29640	0.150220
$819$	0.102111	0.00356806
$820$	2.63382	0.0919770
$821$	27.3594	0.954850	0.477425	−	0.878673i	$-0.341570\pi$
$821$	27.3594	0.954850	0.477425	+	0.878673i	$0.341570\pi$
$822$	−15.2660	−0.532461
$823$	25.2856	0.881400	0.440700	−	0.897654i	$-0.354730\pi$
$823$	25.2856	0.881400	0.440700	+	0.897654i	$0.354730\pi$
$824$	37.2229	1.29672
$825$	6.52453	0.227155
$826$	5.39022	0.187550
$827$	−5.86986	−0.204115	−0.102058	−	0.994779i	$-0.532543\pi$
$827$	−5.86986	−0.204115	−0.102058	+	0.994779i	$0.532543\pi$
$828$	2.95627	0.102738
$829$	0.527419	0.0183180	0.00915902	−	0.999958i	$-0.497085\pi$
$829$	0.527419	0.0183180	0.00915902	+	0.999958i	$0.497085\pi$
$830$	5.88002	0.204098
$831$	−44.5443	−1.54522
$832$	2.71098	0.0939862
$833$	−6.65065	−0.230431
$834$	13.5857	0.470434
$835$	−5.25748	−0.181943
$836$	−4.35606	−0.150658
$837$	58.8709	2.03488
$838$	29.5525	1.02087
$839$	15.7170	0.542612	0.271306	−	0.962493i	$-0.412545\pi$
$839$	15.7170	0.542612	0.271306	+	0.962493i	$0.412545\pi$
$840$	−1.95537	−0.0674667
$841$	16.4396	0.566883
$842$	0.642414	0.0221391
$843$	28.4280	0.979112
$844$	1.29397	0.0445402
$845$	−7.77044	−0.267311
$846$	0.975335	0.0335327
$847$	6.99239	0.240261
$848$	−0.864204	−0.0296769
$849$	−43.9088	−1.50694
$850$	4.20424	0.144204
$851$	−19.3790	−0.664302
$852$	10.9126	0.373860
$853$	0.923533	0.0316212	0.0158106	−	0.999875i	$-0.494967\pi$
$853$	0.923533	0.0316212	0.0158106	+	0.999875i	$0.494967\pi$
$854$	0	0
$855$	0.753430	0.0257668
$856$	−24.8297	−0.848662
$857$	−3.92514	−0.134080	−0.0670401	−	0.997750i	$-0.521356\pi$
$857$	−3.92514	−0.134080	−0.0670401	+	0.997750i	$0.521356\pi$
$858$	0.645868	0.0220496
$859$	49.4172	1.68609	0.843047	−	0.537840i	$-0.180760\pi$
$859$	49.4172	1.68609	0.843047	+	0.537840i	$0.180760\pi$
$860$	−2.39578	−0.0816954
$861$	4.02270	0.137093
$862$	−18.4869	−0.629666
$863$	46.6755	1.58885	0.794427	−	0.607360i	$-0.207772\pi$
$863$	46.6755	1.58885	0.794427	+	0.607360i	$0.207772\pi$
$864$	30.2705	1.02982
$865$	13.5765	0.461615
$866$	27.8648	0.946886
$867$	−26.2706	−0.892195
$868$	−8.90332	−0.302198
$869$	6.36186	0.215811
$870$	−6.04200	−0.204843
$871$	−5.80628	−0.196738
$872$	38.6985	1.31050
$873$	3.11281	0.105353
$874$	31.7440	1.07376
$875$	4.00075	0.135250
$876$	5.48984	0.185485
$877$	−2.66516	−0.0899961	−0.0449981	−	0.998987i	$-0.514328\pi$
$877$	−2.66516	−0.0899961	−0.0449981	+	0.998987i	$0.514328\pi$
$878$	5.98359	0.201936
$879$	44.2014	1.49088
$880$	0.0770341	0.00259682
$881$	41.2268	1.38897	0.694483	−	0.719509i	$-0.255633\pi$
$881$	41.2268	1.38897	0.694483	+	0.719509i	$0.255633\pi$
$882$	−1.70500	−0.0574104
$883$	19.5237	0.657026	0.328513	−	0.944500i	$-0.393453\pi$
$883$	19.5237	0.657026	0.328513	+	0.944500i	$0.393453\pi$
$884$	−0.628014	−0.0211224
$885$	8.89841	0.299117
$886$	−3.89370	−0.130811
$887$	41.6916	1.39987	0.699934	−	0.714207i	$-0.253213\pi$
$887$	41.6916	1.39987	0.699934	+	0.714207i	$0.253213\pi$
$888$	−10.8408	−0.363793
$889$	7.75937	0.260241
$890$	−4.59741	−0.154105
$891$	6.88681	0.230717
$892$	17.8682	0.598273
$893$	−15.8037	−0.528850
$894$	27.1808	0.909062
$895$	−6.04947	−0.202211
$896$	−4.39869	−0.146950
$897$	7.10229	0.237139
$898$	31.4973	1.05108
$899$	−73.2529	−2.44312
$900$	−1.62643	−0.0542143
$901$	5.96668	0.198779
$902$	−2.74543	−0.0914129
$903$	−3.65914	−0.121768
$904$	−5.37483	−0.178764
$905$	3.07230	0.102127
$906$	−19.1689	−0.636845
$907$	15.8483	0.526233	0.263116	−	0.964764i	$-0.415250\pi$
$907$	15.8483	0.526233	0.263116	+	0.964764i	$0.415250\pi$
$908$	7.99311	0.265261
$909$	3.78140	0.125421
$910$	0.190364	0.00631049
$911$	−15.4818	−0.512934	−0.256467	−	0.966553i	$-0.582558\pi$
$911$	−15.4818	−0.512934	−0.256467	+	0.966553i	$0.582558\pi$
$912$	1.02507	0.0339435
$913$	9.24890	0.306094
$914$	−34.0757	−1.12713
$915$	0	0
$916$	−20.1769	−0.666663
$917$	−4.29454	−0.141818
$918$	4.92160	0.162437
$919$	−8.01689	−0.264453	−0.132226	−	0.991220i	$-0.542213\pi$
$919$	−8.01689	−0.264453	−0.132226	+	0.991220i	$0.542213\pi$
$920$	14.6749	0.483818
$921$	−4.59107	−0.151281
$922$	15.1583	0.499213
$923$	−2.82882	−0.0931117
$924$	−1.15510	−0.0379999
$925$	10.6616	0.350550
$926$	9.37653	0.308132
$927$	−3.80320	−0.124913
$928$	−37.6654	−1.23643
$929$	34.5898	1.13486	0.567428	−	0.823423i	$-0.307939\pi$
$929$	34.5898	1.13486	0.567428	+	0.823423i	$0.307939\pi$
$930$	9.74027	0.319396
$931$	27.6267	0.905429
$932$	25.0644	0.821011
$933$	−6.05023	−0.198076
$934$	27.5717	0.902173
$935$	−0.531862	−0.0173938
$936$	−0.428698	−0.0140124
$937$	40.6365	1.32754	0.663768	−	0.747938i	$-0.268956\pi$
$937$	40.6365	1.32754	0.663768	+	0.747938i	$0.268956\pi$
$938$	−6.88155	−0.224691
$939$	−44.7809	−1.46137
$940$	−2.74379	−0.0894926
$941$	−8.05239	−0.262500	−0.131250	−	0.991349i	$-0.541899\pi$
$941$	−8.05239	−0.262500	−0.131250	+	0.991349i	$0.541899\pi$
$942$	15.4170	0.502313
$943$	−30.1901	−0.983126
$944$	−1.30631	−0.0425167
$945$	2.25117	0.0732304
$946$	2.49730	0.0811943
$947$	59.1489	1.92208	0.961040	−	0.276408i	$-0.0891440\pi$
$947$	59.1489	1.92208	0.961040	+	0.276408i	$0.0891440\pi$
$948$	14.6976	0.477357
$949$	−1.42310	−0.0461958
$950$	−17.4644	−0.566618
$951$	47.6044	1.54368
$952$	−1.98189	−0.0642333
$953$	−38.4936	−1.24693	−0.623464	−	0.781852i	$-0.714275\pi$
$953$	−38.4936	−1.24693	−0.623464	+	0.781852i	$0.714275\pi$
$954$	1.52966	0.0495244
$955$	1.60757	0.0520197
$956$	−31.4827	−1.01822
$957$	−9.50368	−0.307210
$958$	−34.4261	−1.11226
$959$	−7.07742	−0.228542
$960$	5.30419	0.171192
$961$	87.0906	2.80938
$962$	1.05540	0.0340274
$963$	2.53694	0.0817518
$964$	−24.1148	−0.776686
$965$	−6.06282	−0.195169
$966$	8.41757	0.270831
$967$	22.1116	0.711062	0.355531	−	0.934665i	$-0.384300\pi$
$967$	22.1116	0.711062	0.355531	+	0.934665i	$0.384300\pi$
$968$	−29.3564	−0.943551
$969$	−7.07734	−0.227357
$970$	5.80313	0.186327
$971$	14.3499	0.460510	0.230255	−	0.973130i	$-0.426044\pi$
$971$	14.3499	0.460510	0.230255	+	0.973130i	$0.426044\pi$
$972$	−3.63891	−0.116718
$973$	6.29843	0.201919
$974$	−23.6274	−0.757070
$975$	−3.90741	−0.125137
$976$	0	0
$977$	−44.1463	−1.41236	−0.706182	−	0.708030i	$-0.749584\pi$
$977$	−44.1463	−1.41236	−0.706182	+	0.708030i	$0.749584\pi$
$978$	23.7964	0.760926
$979$	−7.23143	−0.231117
$980$	4.79647	0.153218
$981$	−3.95396	−0.126240
$982$	35.7715	1.14151
$983$	−30.0005	−0.956866	−0.478433	−	0.878124i	$-0.658795\pi$
$983$	−30.0005	−0.956866	−0.478433	+	0.878124i	$0.658795\pi$
$984$	−16.8887	−0.538391
$985$	−6.50429	−0.207244
$986$	−6.12393	−0.195026
$987$	−4.19066	−0.133390
$988$	2.60876	0.0829957
$989$	27.4616	0.873228
$990$	−0.136352	−0.00433354
$991$	4.20221	0.133488	0.0667438	−	0.997770i	$-0.478739\pi$
$991$	4.20221	0.133488	0.0667438	+	0.997770i	$0.478739\pi$
$992$	60.7202	1.92787
$993$	19.2065	0.609500
$994$	−3.35269	−0.106341
$995$	−6.49283	−0.205837
$996$	21.3675	0.677055
$997$	30.6585	0.970963	0.485482	−	0.874247i	$-0.338644\pi$
$997$	30.6585	0.970963	0.485482	+	0.874247i	$0.338644\pi$
$998$	22.1948	0.702565
$999$	12.4807	0.394873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3721.2.a.j.1.7		16
61.15	even	15		61.2.i.a.42.3	yes	32
61.57	even	15		61.2.i.a.16.3	✓	32
61.60	even	2		3721.2.a.l.1.10		16
183.137	odd	30		549.2.bl.b.469.2		32
183.179	odd	30		549.2.bl.b.199.2		32
244.15	odd	30		976.2.bw.c.225.1		32
244.179	odd	30		976.2.bw.c.321.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.16.3	✓	32	61.57	even	15
61.2.i.a.42.3	yes	32	61.15	even	15
549.2.bl.b.199.2		32	183.179	odd	30
549.2.bl.b.469.2		32	183.137	odd	30
976.2.bw.c.225.1		32	244.15	odd	30
976.2.bw.c.321.1		32	244.179	odd	30
3721.2.a.j.1.7		16	1.1	even	1	trivial
3721.2.a.l.1.10		16	61.60	even	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:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.a (trivial)

\(f(q)\)	\(=\)	\(q-0.892823 q^{2} +1.64555 q^{3} -1.20287 q^{4} +0.610081 q^{5} -1.46918 q^{6} -0.681125 q^{7} +2.85959 q^{8} -0.292175 q^{9} +O(q^{10})\)	\(q-0.892823 q^{2} +1.64555 q^{3} -1.20287 q^{4} +0.610081 q^{5} -1.46918 q^{6} -0.681125 q^{7} +2.85959 q^{8} -0.292175 q^{9} -0.544695 q^{10} -0.856770 q^{11} -1.97937 q^{12} +0.513102 q^{13} +0.608124 q^{14} +1.00392 q^{15} -0.147377 q^{16} +1.01753 q^{17} +0.260860 q^{18} -4.22681 q^{19} -0.733846 q^{20} -1.12082 q^{21} +0.764944 q^{22} +8.41171 q^{23} +4.70560 q^{24} -4.62780 q^{25} -0.458110 q^{26} -5.41743 q^{27} +0.819302 q^{28} +6.74089 q^{29} -0.896321 q^{30} -10.8670 q^{31} -5.58761 q^{32} -1.40986 q^{33} -0.908475 q^{34} -0.415541 q^{35} +0.351447 q^{36} -2.30381 q^{37} +3.77379 q^{38} +0.844334 q^{39} +1.74458 q^{40} -3.58906 q^{41} +1.00070 q^{42} +3.26469 q^{43} +1.03058 q^{44} -0.178250 q^{45} -7.51017 q^{46} +3.73892 q^{47} -0.242516 q^{48} -6.53607 q^{49} +4.13181 q^{50} +1.67439 q^{51} -0.617194 q^{52} +5.86389 q^{53} +4.83681 q^{54} -0.522699 q^{55} -1.94774 q^{56} -6.95541 q^{57} -6.01842 q^{58} +8.86369 q^{59} -1.20758 q^{60} +9.70227 q^{62} +0.199008 q^{63} +5.28350 q^{64} +0.313034 q^{65} +1.25875 q^{66} -11.3160 q^{67} -1.22395 q^{68} +13.8419 q^{69} +0.371005 q^{70} -5.51317 q^{71} -0.835501 q^{72} -2.77352 q^{73} +2.05689 q^{74} -7.61526 q^{75} +5.08429 q^{76} +0.583567 q^{77} -0.753841 q^{78} -7.42540 q^{79} -0.0899122 q^{80} -8.03811 q^{81} +3.20440 q^{82} -10.7951 q^{83} +1.34820 q^{84} +0.620776 q^{85} -2.91479 q^{86} +11.0925 q^{87} -2.45001 q^{88} +8.44034 q^{89} +0.159146 q^{90} -0.349487 q^{91} -10.1182 q^{92} -17.8821 q^{93} -3.33819 q^{94} -2.57870 q^{95} -9.19467 q^{96} -10.6539 q^{97} +5.83555 q^{98} +0.250327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9} + 20 q^{10} - 9 q^{11} - 17 q^{12} - 11 q^{14} - 12 q^{15} + 9 q^{16} + 4 q^{17} - 35 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} - 11 q^{22} + 4 q^{23} + 15 q^{24} - 8 q^{25} + 19 q^{26} - 5 q^{27} + 22 q^{28} + 4 q^{29} - 24 q^{30} - 9 q^{31} - 34 q^{32} + 10 q^{33} - 6 q^{34} - 37 q^{35} + 20 q^{36} + 38 q^{37} + 18 q^{38} - 12 q^{39} + 60 q^{40} - 37 q^{41} + 17 q^{42} + 15 q^{43} - 34 q^{44} - 32 q^{45} - 41 q^{46} - 40 q^{47} - 43 q^{48} + 24 q^{49} - 28 q^{50} + 19 q^{51} - 56 q^{52} - 19 q^{53} + 6 q^{54} - 30 q^{55} - 58 q^{56} + 8 q^{57} - 21 q^{58} + q^{59} - 10 q^{60} - 37 q^{62} - 17 q^{63} + 28 q^{64} - 34 q^{65} - 59 q^{66} + 3 q^{67} - 2 q^{68} - 31 q^{69} + 17 q^{70} - 8 q^{71} + 9 q^{72} + 6 q^{73} + 10 q^{74} - q^{75} - 65 q^{76} - 39 q^{77} + 68 q^{78} - 56 q^{79} - 14 q^{80} - 56 q^{81} - 39 q^{82} + 6 q^{83} + 65 q^{84} + 53 q^{85} - 54 q^{86} + 83 q^{87} - 5 q^{88} + 66 q^{89} + 60 q^{90} + 5 q^{91} - 37 q^{92} - 67 q^{93} + 43 q^{94} - 39 q^{95} - 14 q^{96} + 13 q^{97} + 16 q^{98} + 47 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9 + 20 * q^10 - 9 * q^11 - 17 * q^12 - 11 * q^14 - 12 * q^15 + 9 * q^16 + 4 * q^17 - 35 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 - 11 * q^22 + 4 * q^23 + 15 * q^24 - 8 * q^25 + 19 * q^26 - 5 * q^27 + 22 * q^28 + 4 * q^29 - 24 * q^30 - 9 * q^31 - 34 * q^32 + 10 * q^33 - 6 * q^34 - 37 * q^35 + 20 * q^36 + 38 * q^37 + 18 * q^38 - 12 * q^39 + 60 * q^40 - 37 * q^41 + 17 * q^42 + 15 * q^43 - 34 * q^44 - 32 * q^45 - 41 * q^46 - 40 * q^47 - 43 * q^48 + 24 * q^49 - 28 * q^50 + 19 * q^51 - 56 * q^52 - 19 * q^53 + 6 * q^54 - 30 * q^55 - 58 * q^56 + 8 * q^57 - 21 * q^58 + q^59 - 10 * q^60 - 37 * q^62 - 17 * q^63 + 28 * q^64 - 34 * q^65 - 59 * q^66 + 3 * q^67 - 2 * q^68 - 31 * q^69 + 17 * q^70 - 8 * q^71 + 9 * q^72 + 6 * q^73 + 10 * q^74 - q^75 - 65 * q^76 - 39 * q^77 + 68 * q^78 - 56 * q^79 - 14 * q^80 - 56 * q^81 - 39 * q^82 + 6 * q^83 + 65 * q^84 + 53 * q^85 - 54 * q^86 + 83 * q^87 - 5 * q^88 + 66 * q^89 + 60 * q^90 + 5 * q^91 - 37 * q^92 - 67 * q^93 + 43 * q^94 - 39 * q^95 - 14 * q^96 + 13 * q^97 + 16 * q^98 + 47 * q^99

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