LMFDB - Embedded newform 731.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.68194 q^{2} +2.28817 q^{3} +5.19279 q^{4} -3.20246 q^{5} +6.13674 q^{6} +1.43094 q^{7} +8.56287 q^{8} +2.23574 q^{9} +O(q^{10})$	\(q+2.68194 q^{2} +2.28817 q^{3} +5.19279 q^{4} -3.20246 q^{5} +6.13674 q^{6} +1.43094 q^{7} +8.56287 q^{8} +2.23574 q^{9} -8.58881 q^{10} -3.42614 q^{11} +11.8820 q^{12} -3.89902 q^{13} +3.83769 q^{14} -7.32780 q^{15} +12.5795 q^{16} -1.00000 q^{17} +5.99613 q^{18} +4.96450 q^{19} -16.6297 q^{20} +3.27424 q^{21} -9.18868 q^{22} -0.321543 q^{23} +19.5933 q^{24} +5.25578 q^{25} -10.4569 q^{26} -1.74875 q^{27} +7.43056 q^{28} -8.11153 q^{29} -19.6527 q^{30} +1.53837 q^{31} +16.6117 q^{32} -7.83960 q^{33} -2.68194 q^{34} -4.58253 q^{35} +11.6098 q^{36} +11.1955 q^{37} +13.3145 q^{38} -8.92163 q^{39} -27.4223 q^{40} -9.77217 q^{41} +8.78130 q^{42} +1.00000 q^{43} -17.7912 q^{44} -7.15989 q^{45} -0.862359 q^{46} +8.36045 q^{47} +28.7841 q^{48} -4.95242 q^{49} +14.0957 q^{50} -2.28817 q^{51} -20.2468 q^{52} +5.46345 q^{53} -4.69004 q^{54} +10.9721 q^{55} +12.2529 q^{56} +11.3596 q^{57} -21.7546 q^{58} -9.64747 q^{59} -38.0517 q^{60} +7.02951 q^{61} +4.12580 q^{62} +3.19921 q^{63} +19.3926 q^{64} +12.4865 q^{65} -21.0253 q^{66} +2.47649 q^{67} -5.19279 q^{68} -0.735747 q^{69} -12.2901 q^{70} +10.1912 q^{71} +19.1444 q^{72} -7.32300 q^{73} +30.0255 q^{74} +12.0261 q^{75} +25.7796 q^{76} -4.90259 q^{77} -23.9273 q^{78} +5.73108 q^{79} -40.2854 q^{80} -10.7087 q^{81} -26.2084 q^{82} +17.4925 q^{83} +17.0024 q^{84} +3.20246 q^{85} +2.68194 q^{86} -18.5606 q^{87} -29.3376 q^{88} -7.18843 q^{89} -19.2024 q^{90} -5.57925 q^{91} -1.66971 q^{92} +3.52005 q^{93} +22.4222 q^{94} -15.8986 q^{95} +38.0105 q^{96} -13.1749 q^{97} -13.2821 q^{98} -7.65996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.68194	1.89642	0.948208	−	0.317649i	$-0.102893\pi$
$2$	2.68194	1.89642	0.948208	+	0.317649i	$0.102893\pi$
$3$	2.28817	1.32108	0.660539	−	0.750792i	$-0.270328\pi$
$3$	2.28817	1.32108	0.660539	+	0.750792i	$0.270328\pi$
$4$	5.19279	2.59640
$5$	−3.20246	−1.43219	−0.716093	−	0.698005i	$-0.754071\pi$
$5$	−3.20246	−1.43219	−0.716093	+	0.698005i	$0.754071\pi$
$6$	6.13674	2.50531
$7$	1.43094	0.540844	0.270422	−	0.962742i	$-0.412837\pi$
$7$	1.43094	0.540844	0.270422	+	0.962742i	$0.412837\pi$
$8$	8.56287	3.02743
$9$	2.23574	0.745248
$10$	−8.58881	−2.71602
$11$	−3.42614	−1.03302	−0.516509	−	0.856281i	$-0.672769\pi$
$11$	−3.42614	−1.03302	−0.516509	+	0.856281i	$0.672769\pi$
$12$	11.8820	3.43004
$13$	−3.89902	−1.08139	−0.540696	−	0.841218i	$-0.681839\pi$
$13$	−3.89902	−1.08139	−0.540696	+	0.841218i	$0.681839\pi$
$14$	3.83769	1.02566
$15$	−7.32780	−1.89203
$16$	12.5795	3.14488
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.99613	1.41330
$19$	4.96450	1.13893	0.569467	−	0.822014i	$-0.307149\pi$
$19$	4.96450	1.13893	0.569467	+	0.822014i	$0.307149\pi$
$20$	−16.6297	−3.71852
$21$	3.27424	0.714497
$22$	−9.18868	−1.95903
$23$	−0.321543	−0.0670464	−0.0335232	−	0.999438i	$-0.510673\pi$
$23$	−0.321543	−0.0670464	−0.0335232	+	0.999438i	$0.510673\pi$
$24$	19.5933	3.99947
$25$	5.25578	1.05116
$26$	−10.4569	−2.05077
$27$	−1.74875	−0.336547
$28$	7.43056	1.40424
$29$	−8.11153	−1.50627	−0.753137	−	0.657864i	$-0.771460\pi$
$29$	−8.11153	−1.50627	−0.753137	+	0.657864i	$0.771460\pi$
$30$	−19.6527	−3.58808
$31$	1.53837	0.276299	0.138149	−	0.990411i	$-0.455885\pi$
$31$	1.53837	0.276299	0.138149	+	0.990411i	$0.455885\pi$
$32$	16.6117	2.93656
$33$	−7.83960	−1.36470
$34$	−2.68194	−0.459949
$35$	−4.58253	−0.774589
$36$	11.6098	1.93496
$37$	11.1955	1.84052	0.920261	−	0.391305i	$-0.127976\pi$
$37$	11.1955	1.84052	0.920261	+	0.391305i	$0.127976\pi$
$38$	13.3145	2.15989
$39$	−8.92163	−1.42860
$40$	−27.4223	−4.33584
$41$	−9.77217	−1.52616	−0.763078	−	0.646306i	$-0.776313\pi$
$41$	−9.77217	−1.52616	−0.763078	+	0.646306i	$0.776313\pi$
$42$	8.78130	1.35498
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−17.7912	−2.68213
$45$	−7.15989	−1.06733
$46$	−0.862359	−0.127148
$47$	8.36045	1.21950	0.609748	−	0.792595i	$-0.291271\pi$
$47$	8.36045	1.21950	0.609748	+	0.792595i	$0.291271\pi$
$48$	28.7841	4.15463
$49$	−4.95242	−0.707488
$50$	14.0957	1.99343
$51$	−2.28817	−0.320409
$52$	−20.2468	−2.80772
$53$	5.46345	0.750463	0.375231	−	0.926931i	$-0.377563\pi$
$53$	5.46345	0.750463	0.375231	+	0.926931i	$0.377563\pi$
$54$	−4.69004	−0.638234
$55$	10.9721	1.47947
$56$	12.2529	1.63737
$57$	11.3596	1.50462
$58$	−21.7546	−2.85652
$59$	−9.64747	−1.25599	−0.627997	−	0.778216i	$-0.716125\pi$
$59$	−9.64747	−1.25599	−0.627997	+	0.778216i	$0.716125\pi$
$60$	−38.0517	−4.91246
$61$	7.02951	0.900037	0.450018	−	0.893019i	$-0.351417\pi$
$61$	7.02951	0.900037	0.450018	+	0.893019i	$0.351417\pi$
$62$	4.12580	0.523977
$63$	3.19921	0.403063
$64$	19.3926	2.42407
$65$	12.4865	1.54875
$66$	−21.0253	−2.58804
$67$	2.47649	0.302552	0.151276	−	0.988492i	$-0.451662\pi$
$67$	2.47649	0.302552	0.151276	+	0.988492i	$0.451662\pi$
$68$	−5.19279	−0.629719
$69$	−0.735747	−0.0885735
$70$	−12.2901	−1.46894
$71$	10.1912	1.20947	0.604736	−	0.796426i	$-0.293279\pi$
$71$	10.1912	1.20947	0.604736	+	0.796426i	$0.293279\pi$
$72$	19.1444	2.25619
$73$	−7.32300	−0.857093	−0.428546	−	0.903520i	$-0.640974\pi$
$73$	−7.32300	−0.857093	−0.428546	+	0.903520i	$0.640974\pi$
$74$	30.0255	3.49040
$75$	12.0261	1.38866
$76$	25.7796	2.95713
$77$	−4.90259	−0.558702
$78$	−23.9273	−2.70923
$79$	5.73108	0.644797	0.322399	−	0.946604i	$-0.395511\pi$
$79$	5.73108	0.644797	0.322399	+	0.946604i	$0.395511\pi$
$80$	−40.2854	−4.50405
$81$	−10.7087	−1.18985
$82$	−26.2084	−2.89423
$83$	17.4925	1.92005	0.960025	−	0.279914i	$-0.0903059\pi$
$83$	17.4925	1.92005	0.960025	+	0.279914i	$0.0903059\pi$
$84$	17.0024	1.85512
$85$	3.20246	0.347356
$86$	2.68194	0.289201
$87$	−18.5606	−1.98990
$88$	−29.3376	−3.12739
$89$	−7.18843	−0.761972	−0.380986	−	0.924581i	$-0.624415\pi$
$89$	−7.18843	−0.761972	−0.380986	+	0.924581i	$0.624415\pi$
$90$	−19.2024	−2.02411
$91$	−5.57925	−0.584864
$92$	−1.66971	−0.174079
$93$	3.52005	0.365012
$94$	22.4222	2.31267
$95$	−15.8986	−1.63117
$96$	38.0105	3.87943
$97$	−13.1749	−1.33771	−0.668856	−	0.743392i	$-0.733216\pi$
$97$	−13.1749	−1.33771	−0.668856	+	0.743392i	$0.733216\pi$
$98$	−13.2821	−1.34169
$99$	−7.65996	−0.769855
$100$	27.2922	2.72922
$101$	2.75900	0.274531	0.137265	−	0.990534i	$-0.456169\pi$
$101$	2.75900	0.274531	0.137265	+	0.990534i	$0.456169\pi$
$102$	−6.13674	−0.607628
$103$	0.788917	0.0777343	0.0388672	−	0.999244i	$-0.487625\pi$
$103$	0.788917	0.0777343	0.0388672	+	0.999244i	$0.487625\pi$
$104$	−33.3868	−3.27384
$105$	−10.4856	−1.02329
$106$	14.6526	1.42319
$107$	3.10783	0.300445	0.150223	−	0.988652i	$-0.452001\pi$
$107$	3.10783	0.300445	0.150223	+	0.988652i	$0.452001\pi$
$108$	−9.08090	−0.873810
$109$	−0.926802	−0.0887715	−0.0443858	−	0.999014i	$-0.514133\pi$
$109$	−0.926802	−0.0887715	−0.0443858	+	0.999014i	$0.514133\pi$
$110$	29.4264	2.80570
$111$	25.6172	2.43147
$112$	18.0005	1.70089
$113$	−11.6883	−1.09954	−0.549770	−	0.835316i	$-0.685285\pi$
$113$	−11.6883	−1.09954	−0.549770	+	0.835316i	$0.685285\pi$
$114$	30.4659	2.85339
$115$	1.02973	0.0960229
$116$	−42.1215	−3.91088
$117$	−8.71720	−0.805905
$118$	−25.8739	−2.38189
$119$	−1.43094	−0.131174
$120$	−62.7470	−5.72799
$121$	0.738408	0.0671280
$122$	18.8527	1.70684
$123$	−22.3604	−2.01617
$124$	7.98841	0.717381
$125$	−0.819129	−0.0732651
$126$	8.58008	0.764375
$127$	14.6129	1.29669	0.648344	−	0.761347i	$-0.275462\pi$
$127$	14.6129	1.29669	0.648344	+	0.761347i	$0.275462\pi$
$128$	18.7863	1.66049
$129$	2.28817	0.201463
$130$	33.4879	2.93708
$131$	−2.72882	−0.238418	−0.119209	−	0.992869i	$-0.538036\pi$
$131$	−2.72882	−0.238418	−0.119209	+	0.992869i	$0.538036\pi$
$132$	−40.7094	−3.54330
$133$	7.10389	0.615986
$134$	6.64180	0.573764
$135$	5.60032	0.481998
$136$	−8.56287	−0.734260
$137$	3.64822	0.311689	0.155844	−	0.987782i	$-0.450190\pi$
$137$	3.64822	0.311689	0.155844	+	0.987782i	$0.450190\pi$
$138$	−1.97323	−0.167972
$139$	0.604719	0.0512916	0.0256458	−	0.999671i	$-0.491836\pi$
$139$	0.604719	0.0512916	0.0256458	+	0.999671i	$0.491836\pi$
$140$	−23.7961	−2.01114
$141$	19.1302	1.61105
$142$	27.3321	2.29366
$143$	13.3586	1.11710
$144$	28.1245	2.34371
$145$	25.9769	2.15726
$146$	−19.6398	−1.62540
$147$	−11.3320	−0.934647
$148$	58.1357	4.77872
$149$	20.0399	1.64174	0.820868	−	0.571118i	$-0.193490\pi$
$149$	20.0399	1.64174	0.820868	+	0.571118i	$0.193490\pi$
$150$	32.2534	2.63348
$151$	−1.25123	−0.101824	−0.0509119	−	0.998703i	$-0.516213\pi$
$151$	−1.25123	−0.101824	−0.0509119	+	0.998703i	$0.516213\pi$
$152$	42.5104	3.44805
$153$	−2.23574	−0.180749
$154$	−13.1484	−1.05953
$155$	−4.92656	−0.395711
$156$	−46.3282	−3.70922
$157$	−2.71480	−0.216665	−0.108332	−	0.994115i	$-0.534551\pi$
$157$	−2.71480	−0.216665	−0.108332	+	0.994115i	$0.534551\pi$
$158$	15.3704	1.22280
$159$	12.5013	0.991420
$160$	−53.1984	−4.20570
$161$	−0.460108	−0.0362616
$162$	−28.7200	−2.25646
$163$	25.1364	1.96883	0.984416	−	0.175857i	$-0.0562698\pi$
$163$	25.1364	1.96883	0.984416	+	0.175857i	$0.0562698\pi$
$164$	−50.7449	−3.96251
$165$	25.1060	1.95450
$166$	46.9138	3.64122
$167$	8.15913	0.631373	0.315686	−	0.948864i	$-0.397765\pi$
$167$	8.15913	0.631373	0.315686	+	0.948864i	$0.397765\pi$
$168$	28.0369	2.16309
$169$	2.20233	0.169410
$170$	8.58881	0.658732
$171$	11.0994	0.848789
$172$	5.19279	0.395947
$173$	−15.0511	−1.14431	−0.572156	−	0.820145i	$-0.693893\pi$
$173$	−15.0511	−1.14431	−0.572156	+	0.820145i	$0.693893\pi$
$174$	−49.7784	−3.77369
$175$	7.52070	0.568511
$176$	−43.0991	−3.24872
$177$	−22.0751	−1.65927
$178$	−19.2789	−1.44502
$179$	10.2681	0.767477	0.383739	−	0.923442i	$-0.374636\pi$
$179$	10.2681	0.767477	0.383739	+	0.923442i	$0.374636\pi$
$180$	−37.1798	−2.77122
$181$	−16.6071	−1.23440	−0.617200	−	0.786807i	$-0.711733\pi$
$181$	−16.6071	−1.23440	−0.617200	+	0.786807i	$0.711733\pi$
$182$	−14.9632	−1.10915
$183$	16.0847	1.18902
$184$	−2.75333	−0.202978
$185$	−35.8531	−2.63597
$186$	9.44055	0.692215
$187$	3.42614	0.250544
$188$	43.4141	3.16630
$189$	−2.50236	−0.182020
$190$	−42.6392	−3.09337
$191$	−3.51547	−0.254371	−0.127185	−	0.991879i	$-0.540594\pi$
$191$	−3.51547	−0.254371	−0.127185	+	0.991879i	$0.540594\pi$
$192$	44.3736	3.20239
$193$	−3.62041	−0.260603	−0.130302	−	0.991474i	$-0.541595\pi$
$193$	−3.62041	−0.260603	−0.130302	+	0.991474i	$0.541595\pi$
$194$	−35.3344	−2.53686
$195$	28.5712	2.04603
$196$	−25.7169	−1.83692
$197$	−24.9199	−1.77547	−0.887735	−	0.460355i	$-0.847722\pi$
$197$	−24.9199	−1.77547	−0.887735	+	0.460355i	$0.847722\pi$
$198$	−20.5435	−1.45997
$199$	−4.17714	−0.296110	−0.148055	−	0.988979i	$-0.547301\pi$
$199$	−4.17714	−0.296110	−0.148055	+	0.988979i	$0.547301\pi$
$200$	45.0046	3.18230
$201$	5.66665	0.399695
$202$	7.39946	0.520624
$203$	−11.6071	−0.814658
$204$	−11.8820	−0.831907
$205$	31.2950	2.18574
$206$	2.11583	0.147417
$207$	−0.718888	−0.0499662
$208$	−49.0477	−3.40085
$209$	−17.0091	−1.17654
$210$	−28.1218	−1.94059
$211$	28.3717	1.95319	0.976593	−	0.215096i	$-0.0690066\pi$
$211$	28.3717	1.95319	0.976593	+	0.215096i	$0.0690066\pi$
$212$	28.3706	1.94850
$213$	23.3192	1.59781
$214$	8.33500	0.569769
$215$	−3.20246	−0.218406
$216$	−14.9743	−1.01887
$217$	2.20131	0.149434
$218$	−2.48563	−0.168348
$219$	−16.7563	−1.13229
$220$	56.9757	3.84130
$221$	3.89902	0.262276
$222$	68.7037	4.61109
$223$	0.683815	0.0457916	0.0228958	−	0.999738i	$-0.492711\pi$
$223$	0.683815	0.0457916	0.0228958	+	0.999738i	$0.492711\pi$
$224$	23.7703	1.58822
$225$	11.7506	0.783372
$226$	−31.3472	−2.08518
$227$	−0.407106	−0.0270206	−0.0135103	−	0.999909i	$-0.504301\pi$
$227$	−0.407106	−0.0270206	−0.0135103	+	0.999909i	$0.504301\pi$
$228$	58.9883	3.90659
$229$	−16.7061	−1.10397	−0.551986	−	0.833853i	$-0.686130\pi$
$229$	−16.7061	−1.10397	−0.551986	+	0.833853i	$0.686130\pi$
$230$	2.76167	0.182099
$231$	−11.2180	−0.738089
$232$	−69.4580	−4.56014
$233$	9.85163	0.645402	0.322701	−	0.946501i	$-0.395409\pi$
$233$	9.85163	0.645402	0.322701	+	0.946501i	$0.395409\pi$
$234$	−23.3790	−1.52833
$235$	−26.7740	−1.74655
$236$	−50.0973	−3.26106
$237$	13.1137	0.851828
$238$	−3.83769	−0.248760
$239$	−27.1902	−1.75879	−0.879394	−	0.476094i	$-0.842052\pi$
$239$	−27.1902	−1.75879	−0.879394	+	0.476094i	$0.842052\pi$
$240$	−92.1801	−5.95020
$241$	−16.6306	−1.07127	−0.535637	−	0.844449i	$-0.679928\pi$
$241$	−16.6306	−1.07127	−0.535637	+	0.844449i	$0.679928\pi$
$242$	1.98036	0.127303
$243$	−19.2571	−1.23534
$244$	36.5028	2.33685
$245$	15.8599	1.01325
$246$	−59.9693	−3.82350
$247$	−19.3567	−1.23164
$248$	13.1728	0.836475
$249$	40.0259	2.53654
$250$	−2.19685	−0.138941
$251$	15.8669	1.00151	0.500755	−	0.865589i	$-0.333056\pi$
$251$	15.8669	1.00151	0.500755	+	0.865589i	$0.333056\pi$
$252$	16.6128	1.04651
$253$	1.10165	0.0692602
$254$	39.1910	2.45906
$255$	7.32780	0.458885
$256$	11.5984	0.724902
$257$	−17.9498	−1.11968	−0.559838	−	0.828602i	$-0.689137\pi$
$257$	−17.9498	−1.11968	−0.559838	+	0.828602i	$0.689137\pi$
$258$	6.13674	0.382057
$259$	16.0200	0.995435
$260$	64.8396	4.02118
$261$	−18.1353	−1.12255
$262$	−7.31853	−0.452141
$263$	18.9009	1.16548	0.582741	−	0.812658i	$-0.301980\pi$
$263$	18.9009	1.16548	0.582741	+	0.812658i	$0.301980\pi$
$264$	−67.1295	−4.13153
$265$	−17.4965	−1.07480
$266$	19.0522	1.16817
$267$	−16.4484	−1.00662
$268$	12.8599	0.785544
$269$	24.5657	1.49779	0.748897	−	0.662686i	$-0.230584\pi$
$269$	24.5657	1.49779	0.748897	+	0.662686i	$0.230584\pi$
$270$	15.0197	0.914070
$271$	−0.00951163	−0.000577790 0	−0.000288895	−	1.00000i	$-0.500092\pi$
$271$	−0.00951163	−0.000577790 0	−0.000288895		1.00000i	$0.500092\pi$
$272$	−12.5795	−0.762744
$273$	−12.7663	−0.772652
$274$	9.78431	0.591092
$275$	−18.0070	−1.08586
$276$	−3.82058	−0.229972
$277$	20.2470	1.21653	0.608263	−	0.793736i	$-0.291867\pi$
$277$	20.2470	1.21653	0.608263	+	0.793736i	$0.291867\pi$
$278$	1.62182	0.0972703
$279$	3.43939	0.205911
$280$	−39.2396	−2.34501
$281$	−21.5873	−1.28779	−0.643896	−	0.765113i	$-0.722683\pi$
$281$	−21.5873	−1.28779	−0.643896	+	0.765113i	$0.722683\pi$
$282$	51.3059	3.05522
$283$	−22.8225	−1.35666	−0.678328	−	0.734759i	$-0.737295\pi$
$283$	−22.8225	−1.35666	−0.678328	+	0.734759i	$0.737295\pi$
$284$	52.9207	3.14027
$285$	−36.3789	−2.15490
$286$	35.8268	2.11848
$287$	−13.9834	−0.825412
$288$	37.1395	2.18847
$289$	1.00000	0.0588235
$290$	69.6684	4.09107
$291$	−30.1466	−1.76722
$292$	−38.0268	−2.22535
$293$	21.5330	1.25797	0.628987	−	0.777416i	$-0.283470\pi$
$293$	21.5330	1.25797	0.628987	+	0.777416i	$0.283470\pi$
$294$	−30.3917	−1.77248
$295$	30.8957	1.79882
$296$	95.8653	5.57206
$297$	5.99146	0.347660
$298$	53.7459	3.11342
$299$	1.25370	0.0725035
$300$	62.4493	3.60551
$301$	1.43094	0.0824779
$302$	−3.35572	−0.193100
$303$	6.31307	0.362676
$304$	62.4510	3.58181
$305$	−22.5118	−1.28902
$306$	−5.99613	−0.342776
$307$	10.6728	0.609128	0.304564	−	0.952492i	$-0.401489\pi$
$307$	10.6728	0.609128	0.304564	+	0.952492i	$0.401489\pi$
$308$	−25.4581	−1.45061
$309$	1.80518	0.102693
$310$	−13.2127	−0.750433
$311$	6.17025	0.349883	0.174941	−	0.984579i	$-0.444026\pi$
$311$	6.17025	0.349883	0.174941	+	0.984579i	$0.444026\pi$
$312$	−76.3948	−4.32500
$313$	−26.0596	−1.47298	−0.736489	−	0.676450i	$-0.763518\pi$
$313$	−26.0596	−1.47298	−0.736489	+	0.676450i	$0.763518\pi$
$314$	−7.28093	−0.410887
$315$	−10.2454	−0.577261
$316$	29.7603	1.67415
$317$	−14.0057	−0.786636	−0.393318	−	0.919403i	$-0.628673\pi$
$317$	−14.0057	−0.786636	−0.393318	+	0.919403i	$0.628673\pi$
$318$	33.5278	1.88014
$319$	27.7912	1.55601
$320$	−62.1040	−3.47172
$321$	7.11125	0.396912
$322$	−1.23398	−0.0687671
$323$	−4.96450	−0.276232
$324$	−55.6080	−3.08933
$325$	−20.4924	−1.13671
$326$	67.4141	3.73372
$327$	−2.12068	−0.117274
$328$	−83.6778	−4.62034
$329$	11.9633	0.659557
$330$	67.3328	3.70655
$331$	−22.9483	−1.26135	−0.630676	−	0.776046i	$-0.717222\pi$
$331$	−22.9483	−1.26135	−0.630676	+	0.776046i	$0.717222\pi$
$332$	90.8349	4.98521
$333$	25.0302	1.37165
$334$	21.8823	1.19735
$335$	−7.93088	−0.433310
$336$	41.1883	2.24700
$337$	17.7568	0.967275	0.483637	−	0.875269i	$-0.339315\pi$
$337$	17.7568	0.967275	0.483637	+	0.875269i	$0.339315\pi$
$338$	5.90650	0.321271
$339$	−26.7448	−1.45258
$340$	16.6297	0.901874
$341$	−5.27065	−0.285422
$342$	29.7678	1.60966
$343$	−17.1032	−0.923484
$344$	8.56287	0.461679
$345$	2.35620	0.126854
$346$	−40.3660	−2.17009
$347$	31.1940	1.67458	0.837291	−	0.546758i	$-0.184138\pi$
$347$	31.1940	1.67458	0.837291	+	0.546758i	$0.184138\pi$
$348$	−96.3813	−5.16658
$349$	4.82321	0.258181	0.129090	−	0.991633i	$-0.458794\pi$
$349$	4.82321	0.258181	0.129090	+	0.991633i	$0.458794\pi$
$350$	20.1700	1.07813
$351$	6.81841	0.363940
$352$	−56.9140	−3.03353
$353$	−28.0660	−1.49380	−0.746902	−	0.664934i	$-0.768460\pi$
$353$	−28.0660	−1.49380	−0.746902	+	0.664934i	$0.768460\pi$
$354$	−59.2040	−3.14666
$355$	−32.6369	−1.73219
$356$	−37.3280	−1.97838
$357$	−3.27424	−0.173291
$358$	27.5385	1.45546
$359$	−10.3222	−0.544787	−0.272394	−	0.962186i	$-0.587815\pi$
$359$	−10.3222	−0.544787	−0.272394	+	0.962186i	$0.587815\pi$
$360$	−61.3092	−3.23128
$361$	5.64628	0.297172
$362$	−44.5393	−2.34094
$363$	1.68961	0.0886814
$364$	−28.9719	−1.51854
$365$	23.4517	1.22752
$366$	43.1383	2.25487
$367$	8.77402	0.458000	0.229000	−	0.973426i	$-0.426454\pi$
$367$	8.77402	0.458000	0.229000	+	0.973426i	$0.426454\pi$
$368$	−4.04485	−0.210853
$369$	−21.8481	−1.13737
$370$	−96.1557	−4.99890
$371$	7.81786	0.405883
$372$	18.2789	0.947716
$373$	−7.77398	−0.402521	−0.201261	−	0.979538i	$-0.564504\pi$
$373$	−7.77398	−0.402521	−0.201261	+	0.979538i	$0.564504\pi$
$374$	9.18868	0.475136
$375$	−1.87431	−0.0967889
$376$	71.5894	3.69194
$377$	31.6270	1.62887
$378$	−6.71116	−0.345185
$379$	−29.2186	−1.50086	−0.750430	−	0.660950i	$-0.770154\pi$
$379$	−29.2186	−1.50086	−0.750430	+	0.660950i	$0.770154\pi$
$380$	−82.5583	−4.23515
$381$	33.4369	1.71303
$382$	−9.42829	−0.482393
$383$	−13.5274	−0.691217	−0.345608	−	0.938379i	$-0.612327\pi$
$383$	−13.5274	−0.691217	−0.345608	+	0.938379i	$0.612327\pi$
$384$	42.9862	2.19363
$385$	15.7004	0.800165
$386$	−9.70973	−0.494212
$387$	2.23574	0.113649
$388$	−68.4147	−3.47323
$389$	29.2091	1.48096	0.740481	−	0.672077i	$-0.234598\pi$
$389$	29.2091	1.48096	0.740481	+	0.672077i	$0.234598\pi$
$390$	76.6262	3.88012
$391$	0.321543	0.0162611
$392$	−42.4069	−2.14187
$393$	−6.24402	−0.314969
$394$	−66.8336	−3.36703
$395$	−18.3536	−0.923470
$396$	−39.7766	−1.99885
$397$	17.3996	0.873259	0.436629	−	0.899642i	$-0.356172\pi$
$397$	17.3996	0.873259	0.436629	+	0.899642i	$0.356172\pi$
$398$	−11.2028	−0.561548
$399$	16.2550	0.813765
$400$	66.1151	3.30576
$401$	−3.54140	−0.176849	−0.0884246	−	0.996083i	$-0.528183\pi$
$401$	−3.54140	−0.176849	−0.0884246	+	0.996083i	$0.528183\pi$
$402$	15.1976	0.757987
$403$	−5.99811	−0.298787
$404$	14.3269	0.712790
$405$	34.2942	1.70409
$406$	−31.1295	−1.54493
$407$	−38.3572	−1.90129
$408$	−19.5933	−0.970015
$409$	14.5001	0.716986	0.358493	−	0.933532i	$-0.383291\pi$
$409$	14.5001	0.716986	0.358493	+	0.933532i	$0.383291\pi$
$410$	83.9314	4.14507
$411$	8.34777	0.411765
$412$	4.09668	0.201829
$413$	−13.8049	−0.679296
$414$	−1.92801	−0.0947567
$415$	−56.0191	−2.74987
$416$	−64.7693	−3.17558
$417$	1.38370	0.0677603
$418$	−45.6172	−2.23121
$419$	25.3216	1.23704	0.618520	−	0.785769i	$-0.287733\pi$
$419$	25.3216	1.23704	0.618520	+	0.785769i	$0.287733\pi$
$420$	−54.4497	−2.65687
$421$	−0.287802	−0.0140266	−0.00701330	−	0.999975i	$-0.502232\pi$
$421$	−0.287802	−0.0140266	−0.00701330	+	0.999975i	$0.502232\pi$
$422$	76.0910	3.70405
$423$	18.6918	0.908827
$424$	46.7828	2.27197
$425$	−5.25578	−0.254943
$426$	62.5407	3.03011
$427$	10.0588	0.486779
$428$	16.1383	0.780074
$429$	30.5667	1.47578
$430$	−8.58881	−0.414189
$431$	−17.1962	−0.828313	−0.414157	−	0.910206i	$-0.635923\pi$
$431$	−17.1962	−0.828313	−0.414157	+	0.910206i	$0.635923\pi$
$432$	−21.9984	−1.05840
$433$	11.9433	0.573956	0.286978	−	0.957937i	$-0.407349\pi$
$433$	11.9433	0.573956	0.286978	+	0.957937i	$0.407349\pi$
$434$	5.90377	0.283390
$435$	59.4397	2.84991
$436$	−4.81269	−0.230486
$437$	−1.59630	−0.0763615
$438$	−44.9394	−2.14729
$439$	−6.18648	−0.295265	−0.147632	−	0.989042i	$-0.547165\pi$
$439$	−6.18648	−0.295265	−0.147632	+	0.989042i	$0.547165\pi$
$440$	93.9525	4.47901
$441$	−11.0723	−0.527254
$442$	10.4569	0.497385
$443$	14.8176	0.704005	0.352002	−	0.935999i	$-0.385501\pi$
$443$	14.8176	0.704005	0.352002	+	0.935999i	$0.385501\pi$
$444$	133.025	6.31307
$445$	23.0207	1.09129
$446$	1.83395	0.0868400
$447$	45.8549	2.16886
$448$	27.7496	1.31104
$449$	−0.865461	−0.0408436	−0.0204218	−	0.999791i	$-0.506501\pi$
$449$	−0.865461	−0.0408436	−0.0204218	+	0.999791i	$0.506501\pi$
$450$	31.5143	1.48560
$451$	33.4808	1.57655
$452$	−60.6947	−2.85484
$453$	−2.86304	−0.134517
$454$	−1.09183	−0.0512423
$455$	17.8674	0.837634
$456$	97.2712	4.55514
$457$	40.4299	1.89123	0.945615	−	0.325289i	$-0.105462\pi$
$457$	40.4299	1.89123	0.945615	+	0.325289i	$0.105462\pi$
$458$	−44.8048	−2.09359
$459$	1.74875	0.0816247
$460$	5.34718	0.249313
$461$	−40.6121	−1.89149	−0.945747	−	0.324904i	$-0.894668\pi$
$461$	−40.6121	−1.89149	−0.945747	+	0.324904i	$0.894668\pi$
$462$	−30.0859	−1.39972
$463$	−25.1925	−1.17080	−0.585398	−	0.810746i	$-0.699062\pi$
$463$	−25.1925	−1.17080	−0.585398	+	0.810746i	$0.699062\pi$
$464$	−102.039	−4.73704
$465$	−11.2728	−0.522765
$466$	26.4215	1.22395
$467$	24.6866	1.14236	0.571179	−	0.820825i	$-0.306486\pi$
$467$	24.6866	1.14236	0.571179	+	0.820825i	$0.306486\pi$
$468$	−45.2666	−2.09245
$469$	3.54371	0.163633
$470$	−71.8063	−3.31218
$471$	−6.21194	−0.286231
$472$	−82.6100	−3.80243
$473$	−3.42614	−0.157534
$474$	35.1702	1.61542
$475$	26.0923	1.19720
$476$	−7.43056	−0.340579
$477$	12.2149	0.559281
$478$	−72.9225	−3.33540
$479$	−30.4101	−1.38947	−0.694735	−	0.719265i	$-0.744479\pi$
$479$	−30.4101	−1.38947	−0.694735	+	0.719265i	$0.744479\pi$
$480$	−121.727	−5.55606
$481$	−43.6513	−1.99033
$482$	−44.6023	−2.03158
$483$	−1.05281	−0.0479044
$484$	3.83440	0.174291
$485$	42.1923	1.91585
$486$	−51.6463	−2.34272
$487$	9.39764	0.425848	0.212924	−	0.977069i	$-0.431701\pi$
$487$	9.39764	0.425848	0.212924	+	0.977069i	$0.431701\pi$
$488$	60.1928	2.72480
$489$	57.5164	2.60098
$490$	42.5354	1.92155
$491$	−20.4180	−0.921450	−0.460725	−	0.887543i	$-0.652411\pi$
$491$	−20.4180	−0.921450	−0.460725	+	0.887543i	$0.652411\pi$
$492$	−116.113	−5.23478
$493$	8.11153	0.365325
$494$	−51.9134	−2.33569
$495$	24.5308	1.10258
$496$	19.3519	0.868925
$497$	14.5830	0.654135
$498$	107.347	4.81033
$499$	28.5686	1.27891	0.639453	−	0.768830i	$-0.279161\pi$
$499$	28.5686	1.27891	0.639453	+	0.768830i	$0.279161\pi$
$500$	−4.25357	−0.190225
$501$	18.6695	0.834093
$502$	42.5541	1.89928
$503$	8.55041	0.381244	0.190622	−	0.981664i	$-0.438950\pi$
$503$	8.55041	0.381244	0.190622	+	0.981664i	$0.438950\pi$
$504$	27.3944	1.22024
$505$	−8.83559	−0.393179
$506$	2.95456	0.131346
$507$	5.03930	0.223803
$508$	75.8819	3.36672
$509$	10.7446	0.476246	0.238123	−	0.971235i	$-0.423468\pi$
$509$	10.7446	0.476246	0.238123	+	0.971235i	$0.423468\pi$
$510$	19.6527	0.870236
$511$	−10.4788	−0.463553
$512$	−6.46624	−0.285770
$513$	−8.68168	−0.383306
$514$	−48.1402	−2.12337
$515$	−2.52648	−0.111330
$516$	11.8820	0.523077
$517$	−28.6440	−1.25976
$518$	42.9647	1.88776
$519$	−34.4395	−1.51173
$520$	106.920	4.68875
$521$	−16.2345	−0.711246	−0.355623	−	0.934630i	$-0.615731\pi$
$521$	−16.2345	−0.711246	−0.355623	+	0.934630i	$0.615731\pi$
$522$	−48.6378	−2.12882
$523$	0.884111	0.0386595	0.0193297	−	0.999813i	$-0.493847\pi$
$523$	0.884111	0.0386595	0.0193297	+	0.999813i	$0.493847\pi$
$524$	−14.1702	−0.619029
$525$	17.2087	0.751048
$526$	50.6912	2.21024
$527$	−1.53837	−0.0670123
$528$	−98.6183	−4.29181
$529$	−22.8966	−0.995505
$530$	−46.9245	−2.03827
$531$	−21.5693	−0.936027
$532$	36.8890	1.59934
$533$	38.1019	1.65037
$534$	−44.1135	−1.90898
$535$	−9.95271	−0.430293
$536$	21.2059	0.915955
$537$	23.4953	1.01390
$538$	65.8836	2.84044
$539$	16.9677	0.730849
$540$	29.0813	1.25146
$541$	−41.9375	−1.80303	−0.901516	−	0.432746i	$-0.857545\pi$
$541$	−41.9375	−1.80303	−0.901516	+	0.432746i	$0.857545\pi$
$542$	−0.0255096	−0.00109573
$543$	−38.0000	−1.63074
$544$	−16.6117	−0.712221
$545$	2.96805	0.127137
$546$	−34.2384	−1.46527
$547$	−16.7683	−0.716959	−0.358479	−	0.933538i	$-0.616705\pi$
$547$	−16.7683	−0.716959	−0.358479	+	0.933538i	$0.616705\pi$
$548$	18.9445	0.809268
$549$	15.7162	0.670750
$550$	−48.2937	−2.05925
$551$	−40.2697	−1.71555
$552$	−6.30011	−0.268150
$553$	8.20083	0.348735
$554$	54.3013	2.30704
$555$	−82.0381	−3.48232
$556$	3.14018	0.133173
$557$	1.06210	0.0450025	0.0225013	−	0.999747i	$-0.492837\pi$
$557$	1.06210	0.0450025	0.0225013	+	0.999747i	$0.492837\pi$
$558$	9.22423	0.390493
$559$	−3.89902	−0.164911
$560$	−57.6459	−2.43599
$561$	7.83960	0.330988
$562$	−57.8959	−2.44219
$563$	−0.475928	−0.0200580	−0.0100290	−	0.999950i	$-0.503192\pi$
$563$	−0.475928	−0.0200580	−0.0100290	+	0.999950i	$0.503192\pi$
$564$	99.3390	4.18293
$565$	37.4313	1.57474
$566$	−61.2085	−2.57279
$567$	−15.3235	−0.643525
$568$	87.2658	3.66159
$569$	44.4744	1.86447	0.932233	−	0.361860i	$-0.117858\pi$
$569$	44.4744	1.86447	0.932233	+	0.361860i	$0.117858\pi$
$570$	−97.5659	−4.08658
$571$	32.4252	1.35695	0.678477	−	0.734622i	$-0.262640\pi$
$571$	32.4252	1.35695	0.678477	+	0.734622i	$0.262640\pi$
$572$	69.3682	2.90043
$573$	−8.04402	−0.336044
$574$	−37.5025	−1.56533
$575$	−1.68996	−0.0704762
$576$	43.3568	1.80653
$577$	5.37745	0.223866	0.111933	−	0.993716i	$-0.464296\pi$
$577$	5.37745	0.223866	0.111933	+	0.993716i	$0.464296\pi$
$578$	2.68194	0.111554
$579$	−8.28414	−0.344277
$580$	134.893	5.60111
$581$	25.0307	1.03845
$582$	−80.8512	−3.35139
$583$	−18.7185	−0.775242
$584$	−62.7059	−2.59479
$585$	27.9165	1.15421
$586$	57.7503	2.38564
$587$	−34.4824	−1.42324	−0.711621	−	0.702563i	$-0.752039\pi$
$587$	−34.4824	−1.42324	−0.711621	+	0.702563i	$0.752039\pi$
$588$	−58.8447	−2.42671
$589$	7.63722	0.314686
$590$	82.8603	3.41130
$591$	−57.0211	−2.34553
$592$	140.833	5.78821
$593$	29.3131	1.20374	0.601871	−	0.798593i	$-0.294422\pi$
$593$	29.3131	1.20374	0.601871	+	0.798593i	$0.294422\pi$
$594$	16.0687	0.659308
$595$	4.58253	0.187865
$596$	104.063	4.26260
$597$	−9.55804	−0.391184
$598$	3.36235	0.137497
$599$	−28.6923	−1.17234	−0.586168	−	0.810190i	$-0.699364\pi$
$599$	−28.6923	−1.17234	−0.586168	+	0.810190i	$0.699364\pi$
$600$	102.978	4.20407
$601$	2.03111	0.0828508	0.0414254	−	0.999142i	$-0.486810\pi$
$601$	2.03111	0.0828508	0.0414254	+	0.999142i	$0.486810\pi$
$602$	3.83769	0.156412
$603$	5.53680	0.225476
$604$	−6.49738	−0.264375
$605$	−2.36473	−0.0961398
$606$	16.9313	0.687786
$607$	−3.82263	−0.155156	−0.0775779	−	0.996986i	$-0.524719\pi$
$607$	−3.82263	−0.155156	−0.0775779	+	0.996986i	$0.524719\pi$
$608$	82.4689	3.34455
$609$	−26.5591	−1.07623
$610$	−60.3751	−2.44452
$611$	−32.5975	−1.31875
$612$	−11.6098	−0.469296
$613$	−11.9778	−0.483778	−0.241889	−	0.970304i	$-0.577767\pi$
$613$	−11.9778	−0.483778	−0.241889	+	0.970304i	$0.577767\pi$
$614$	28.6238	1.15516
$615$	71.6085	2.88753
$616$	−41.9802	−1.69143
$617$	−40.9834	−1.64993	−0.824965	−	0.565184i	$-0.808805\pi$
$617$	−40.9834	−1.64993	−0.824965	+	0.565184i	$0.808805\pi$
$618$	4.84138	0.194749
$619$	34.0870	1.37007	0.685035	−	0.728510i	$-0.259787\pi$
$619$	34.0870	1.37007	0.685035	+	0.728510i	$0.259787\pi$
$620$	−25.5826	−1.02742
$621$	0.562299	0.0225643
$622$	16.5482	0.663523
$623$	−10.2862	−0.412108
$624$	−112.230	−4.49278
$625$	−23.6557	−0.946227
$626$	−69.8903	−2.79338
$627$	−38.9197	−1.55430
$628$	−14.0974	−0.562547
$629$	−11.1955	−0.446392
$630$	−27.4774	−1.09473
$631$	−16.5237	−0.657798	−0.328899	−	0.944365i	$-0.606678\pi$
$631$	−16.5237	−0.657798	−0.328899	+	0.944365i	$0.606678\pi$
$632$	49.0745	1.95208
$633$	64.9193	2.58031
$634$	−37.5623	−1.49179
$635$	−46.7974	−1.85710
$636$	64.9168	2.57412
$637$	19.3096	0.765072
$638$	74.5343	2.95084
$639$	22.7849	0.901356
$640$	−60.1623	−2.37812
$641$	−1.38113	−0.0545512	−0.0272756	−	0.999628i	$-0.508683\pi$
$641$	−1.38113	−0.0545512	−0.0272756	+	0.999628i	$0.508683\pi$
$642$	19.0719	0.752710
$643$	−4.55894	−0.179787	−0.0898935	−	0.995951i	$-0.528653\pi$
$643$	−4.55894	−0.179787	−0.0898935	+	0.995951i	$0.528653\pi$
$644$	−2.38925	−0.0941495
$645$	−7.32780	−0.288532
$646$	−13.3145	−0.523851
$647$	0.339320	0.0133400	0.00667002	−	0.999978i	$-0.497877\pi$
$647$	0.339320	0.0133400	0.00667002	+	0.999978i	$0.497877\pi$
$648$	−91.6970	−3.60220
$649$	33.0535	1.29747
$650$	−54.9593	−2.15568
$651$	5.03697	0.197415
$652$	130.528	5.11187
$653$	2.60440	0.101918	0.0509591	−	0.998701i	$-0.483772\pi$
$653$	2.60440	0.101918	0.0509591	+	0.998701i	$0.483772\pi$
$654$	−5.68754	−0.222401
$655$	8.73896	0.341459
$656$	−122.929	−4.79957
$657$	−16.3724	−0.638746
$658$	32.0848	1.25079
$659$	−31.4147	−1.22374	−0.611872	−	0.790957i	$-0.709583\pi$
$659$	−31.4147	−1.22374	−0.611872	+	0.790957i	$0.709583\pi$
$660$	130.370	5.07466
$661$	30.9716	1.20466	0.602329	−	0.798248i	$-0.294240\pi$
$661$	30.9716	1.20466	0.602329	+	0.798248i	$0.294240\pi$
$662$	−61.5459	−2.39205
$663$	8.92163	0.346487
$664$	149.786	5.81282
$665$	−22.7500	−0.882206
$666$	67.1294	2.60121
$667$	2.60821	0.100990
$668$	42.3687	1.63929
$669$	1.56469	0.0604943
$670$	−21.2701	−0.821737
$671$	−24.0841	−0.929755
$672$	54.3907	2.09817
$673$	39.2630	1.51348	0.756739	−	0.653717i	$-0.226791\pi$
$673$	39.2630	1.51348	0.756739	+	0.653717i	$0.226791\pi$
$674$	47.6226	1.83436
$675$	−9.19106	−0.353764
$676$	11.4362	0.439854
$677$	−13.7028	−0.526640	−0.263320	−	0.964709i	$-0.584818\pi$
$677$	−13.7028	−0.526640	−0.263320	+	0.964709i	$0.584818\pi$
$678$	−71.7279	−2.75469
$679$	−18.8525	−0.723493
$680$	27.4223	1.05160
$681$	−0.931530	−0.0356963
$682$	−14.1356	−0.541278
$683$	14.5922	0.558355	0.279177	−	0.960240i	$-0.409938\pi$
$683$	14.5922	0.558355	0.279177	+	0.960240i	$0.409938\pi$
$684$	57.6366	2.20379
$685$	−11.6833	−0.446396
$686$	−45.8696	−1.75131
$687$	−38.2266	−1.45843
$688$	12.5795	0.479589
$689$	−21.3021	−0.811545
$690$	6.31919	0.240568
$691$	−16.1724	−0.615226	−0.307613	−	0.951512i	$-0.599530\pi$
$691$	−16.1724	−0.615226	−0.307613	+	0.951512i	$0.599530\pi$
$692$	−78.1571	−2.97109
$693$	−10.9609	−0.416371
$694$	83.6604	3.17570
$695$	−1.93659	−0.0734591
$696$	−158.932	−6.02430
$697$	9.77217	0.370147
$698$	12.9356	0.489618
$699$	22.5423	0.852627
$700$	39.0534	1.47608
$701$	−30.2783	−1.14359	−0.571797	−	0.820395i	$-0.693754\pi$
$701$	−30.2783	−1.14359	−0.571797	+	0.820395i	$0.693754\pi$
$702$	18.2866	0.690182
$703$	55.5799	2.09623
$704$	−66.4416	−2.50411
$705$	−61.2637	−2.30732
$706$	−75.2714	−2.83288
$707$	3.94796	0.148478
$708$	−114.631	−4.30811
$709$	13.3275	0.500525	0.250262	−	0.968178i	$-0.419483\pi$
$709$	13.3275	0.500525	0.250262	+	0.968178i	$0.419483\pi$
$710$	−87.5302	−3.28495
$711$	12.8132	0.480534
$712$	−61.5536	−2.30682
$713$	−0.494651	−0.0185248
$714$	−8.78130	−0.328632
$715$	−42.7803	−1.59989
$716$	53.3204	1.99268
$717$	−62.2160	−2.32350
$718$	−27.6836	−1.03314
$719$	29.8884	1.11465	0.557325	−	0.830295i	$-0.311828\pi$
$719$	29.8884	1.11465	0.557325	+	0.830295i	$0.311828\pi$
$720$	−90.0679	−3.35663
$721$	1.12889	0.0420421
$722$	15.1430	0.563563
$723$	−38.0538	−1.41524
$724$	−86.2374	−3.20499
$725$	−42.6324	−1.58333
$726$	4.53142	0.168177
$727$	−16.6325	−0.616865	−0.308433	−	0.951246i	$-0.599804\pi$
$727$	−16.6325	−0.616865	−0.308433	+	0.951246i	$0.599804\pi$
$728$	−47.7744	−1.77064
$729$	−11.9375	−0.442130
$730$	62.8959	2.32788
$731$	−1.00000	−0.0369863
$732$	83.5247	3.08716
$733$	−14.6412	−0.540786	−0.270393	−	0.962750i	$-0.587154\pi$
$733$	−14.6412	−0.540786	−0.270393	+	0.962750i	$0.587154\pi$
$734$	23.5314	0.868559
$735$	36.2903	1.33859
$736$	−5.34138	−0.196886
$737$	−8.48480	−0.312542
$738$	−58.5952	−2.15692
$739$	−28.9347	−1.06438	−0.532190	−	0.846625i	$-0.678631\pi$
$739$	−28.9347	−1.06438	−0.532190	+	0.846625i	$0.678631\pi$
$740$	−186.178	−6.84402
$741$	−44.2914	−1.62709
$742$	20.9670	0.769723
$743$	−12.0098	−0.440596	−0.220298	−	0.975433i	$-0.570703\pi$
$743$	−12.0098	−0.440596	−0.220298	+	0.975433i	$0.570703\pi$
$744$	30.1417	1.10505
$745$	−64.1772	−2.35127
$746$	−20.8493	−0.763348
$747$	39.1087	1.43091
$748$	17.7912	0.650511
$749$	4.44711	0.162494
$750$	−5.02678	−0.183552
$751$	−37.5602	−1.37059	−0.685295	−	0.728266i	$-0.740327\pi$
$751$	−37.5602	−1.37059	−0.685295	+	0.728266i	$0.740327\pi$
$752$	105.170	3.83517
$753$	36.3062	1.32307
$754$	84.8216	3.08902
$755$	4.00702	0.145830
$756$	−12.9942	−0.472595
$757$	−4.29155	−0.155979	−0.0779895	−	0.996954i	$-0.524850\pi$
$757$	−4.29155	−0.155979	−0.0779895	+	0.996954i	$0.524850\pi$
$758$	−78.3625	−2.84626
$759$	2.52077	0.0914981
$760$	−136.138	−4.93824
$761$	−39.3992	−1.42822	−0.714110	−	0.700034i	$-0.753168\pi$
$761$	−39.3992	−1.42822	−0.714110	+	0.700034i	$0.753168\pi$
$762$	89.6758	3.24861
$763$	−1.32620	−0.0480115
$764$	−18.2551	−0.660447
$765$	7.15989	0.258866
$766$	−36.2796	−1.31083
$767$	37.6156	1.35822
$768$	26.5392	0.957652
$769$	20.9645	0.755998	0.377999	−	0.925806i	$-0.376612\pi$
$769$	20.9645	0.755998	0.377999	+	0.925806i	$0.376612\pi$
$770$	42.1074	1.51745
$771$	−41.0722	−1.47918
$772$	−18.8001	−0.676629
$773$	−17.2985	−0.622183	−0.311092	−	0.950380i	$-0.600695\pi$
$773$	−17.2985	−0.622183	−0.311092	+	0.950380i	$0.600695\pi$
$774$	5.99613	0.215526
$775$	8.08531	0.290433
$776$	−112.815	−4.04983
$777$	36.6566	1.31505
$778$	78.3371	2.80852
$779$	−48.5140	−1.73819
$780$	148.364	5.31229
$781$	−34.9164	−1.24941
$782$	0.862359	0.0308379
$783$	14.1851	0.506932
$784$	−62.2989	−2.22496
$785$	8.69406	0.310304
$786$	−16.7461	−0.597313
$787$	−29.6773	−1.05788	−0.528940	−	0.848659i	$-0.677411\pi$
$787$	−29.6773	−1.05788	−0.528940	+	0.848659i	$0.677411\pi$
$788$	−129.404	−4.60982
$789$	43.2487	1.53969
$790$	−49.2232	−1.75128
$791$	−16.7252	−0.594679
$792$	−65.5913	−2.33068
$793$	−27.4082	−0.973293
$794$	46.6645	1.65606
$795$	−40.0351	−1.41990
$796$	−21.6910	−0.768819
$797$	22.8799	0.810448	0.405224	−	0.914217i	$-0.367193\pi$
$797$	22.8799	0.810448	0.405224	+	0.914217i	$0.367193\pi$
$798$	43.5948	1.54324
$799$	−8.36045	−0.295771
$800$	87.3075	3.08679
$801$	−16.0715	−0.567858
$802$	−9.49783	−0.335380
$803$	25.0896	0.885393
$804$	29.4257	1.03777
$805$	1.47348	0.0519334
$806$	−16.0866	−0.566625
$807$	56.2105	1.97870
$808$	23.6249	0.831123
$809$	23.5241	0.827063	0.413531	−	0.910490i	$-0.364295\pi$
$809$	23.5241	0.827063	0.413531	+	0.910490i	$0.364295\pi$
$810$	91.9749	3.23167
$811$	−7.25164	−0.254640	−0.127320	−	0.991862i	$-0.540637\pi$
$811$	−7.25164	−0.254640	−0.127320	+	0.991862i	$0.540637\pi$
$812$	−60.2732	−2.11518
$813$	−0.0217643	−0.000763306 0
$814$	−102.872	−3.60565
$815$	−80.4983	−2.81973
$816$	−28.7841	−1.00765
$817$	4.96450	0.173686
$818$	38.8885	1.35970
$819$	−12.4738	−0.435869
$820$	162.509	5.67505
$821$	−26.2996	−0.917863	−0.458931	−	0.888472i	$-0.651768\pi$
$821$	−26.2996	−0.917863	−0.458931	+	0.888472i	$0.651768\pi$
$822$	22.3882	0.780879
$823$	33.3911	1.16394	0.581970	−	0.813211i	$-0.302282\pi$
$823$	33.3911	1.16394	0.581970	+	0.813211i	$0.302282\pi$
$824$	6.75540	0.235335
$825$	−41.2032	−1.43451
$826$	−37.0240	−1.28823
$827$	29.5975	1.02920	0.514602	−	0.857429i	$-0.327940\pi$
$827$	29.5975	1.02920	0.514602	+	0.857429i	$0.327940\pi$
$828$	−3.73304	−0.129732
$829$	16.1523	0.560994	0.280497	−	0.959855i	$-0.409501\pi$
$829$	16.1523	0.560994	0.280497	+	0.959855i	$0.409501\pi$
$830$	−150.240	−5.21490
$831$	46.3287	1.60713
$832$	−75.6119	−2.62137
$833$	4.95242	0.171591
$834$	3.71101	0.128502
$835$	−26.1293	−0.904243
$836$	−88.3245	−3.05477
$837$	−2.69022	−0.0929876
$838$	67.9109	2.34594
$839$	39.6097	1.36748	0.683739	−	0.729726i	$-0.260352\pi$
$839$	39.6097	1.36748	0.683739	+	0.729726i	$0.260352\pi$
$840$	−89.7871	−3.09795
$841$	36.7969	1.26886
$842$	−0.771866	−0.0266003
$843$	−49.3956	−1.70127
$844$	147.328	5.07124
$845$	−7.05287	−0.242626
$846$	50.1303	1.72352
$847$	1.05662	0.0363058
$848$	68.7275	2.36011
$849$	−52.2219	−1.79225
$850$	−14.0957	−0.483478
$851$	−3.59982	−0.123400
$852$	121.092	4.14854
$853$	−16.3463	−0.559687	−0.279843	−	0.960046i	$-0.590283\pi$
$853$	−16.3463	−0.559687	−0.279843	+	0.960046i	$0.590283\pi$
$854$	26.9771	0.923136
$855$	−35.5453	−1.21562
$856$	26.6119	0.909577
$857$	−26.9281	−0.919846	−0.459923	−	0.887959i	$-0.652123\pi$
$857$	−26.9281	−0.919846	−0.459923	+	0.887959i	$0.652123\pi$
$858$	81.9780	2.79868
$859$	−27.0585	−0.923225	−0.461613	−	0.887082i	$-0.652729\pi$
$859$	−27.0585	−0.923225	−0.461613	+	0.887082i	$0.652729\pi$
$860$	−16.6297	−0.567069
$861$	−31.9964	−1.09043
$862$	−46.1192	−1.57083
$863$	−23.4483	−0.798190	−0.399095	−	0.916910i	$-0.630676\pi$
$863$	−23.4483	−0.798190	−0.399095	+	0.916910i	$0.630676\pi$
$864$	−29.0498	−0.988293
$865$	48.2005	1.63887
$866$	32.0311	1.08846
$867$	2.28817	0.0777105
$868$	11.4309	0.387991
$869$	−19.6355	−0.666088
$870$	159.413	5.40462
$871$	−9.65589	−0.327177
$872$	−7.93608	−0.268750
$873$	−29.4558	−0.996927
$874$	−4.28118	−0.144813
$875$	−1.17212	−0.0396250
$876$	−87.0120	−2.93986
$877$	−12.3085	−0.415627	−0.207814	−	0.978168i	$-0.566635\pi$
$877$	−12.3085	−0.415627	−0.207814	+	0.978168i	$0.566635\pi$
$878$	−16.5918	−0.559945
$879$	49.2714	1.66188
$880$	138.023	4.65277
$881$	51.9139	1.74902	0.874512	−	0.485003i	$-0.161182\pi$
$881$	51.9139	1.74902	0.874512	+	0.485003i	$0.161182\pi$
$882$	−29.6953	−0.999893
$883$	−32.6418	−1.09848	−0.549242	−	0.835663i	$-0.685084\pi$
$883$	−32.6418	−1.09848	−0.549242	+	0.835663i	$0.685084\pi$
$884$	20.2468	0.680973
$885$	70.6947	2.37638
$886$	39.7398	1.33509
$887$	5.95238	0.199861	0.0999307	−	0.994994i	$-0.468138\pi$
$887$	5.95238	0.199861	0.0999307	+	0.994994i	$0.468138\pi$
$888$	219.357	7.36112
$889$	20.9102	0.701306
$890$	61.7401	2.06953
$891$	36.6894	1.22914
$892$	3.55091	0.118893
$893$	41.5055	1.38893
$894$	122.980	4.11307
$895$	−32.8834	−1.09917
$896$	26.8820	0.898063
$897$	2.86869	0.0957827
$898$	−2.32111	−0.0774565
$899$	−12.4785	−0.416181
$900$	61.0183	2.03394
$901$	−5.46345	−0.182014
$902$	89.7934	2.98979
$903$	3.27424	0.108960
$904$	−100.085	−3.32878
$905$	53.1838	1.76789
$906$	−7.67848	−0.255100
$907$	54.6367	1.81418	0.907091	−	0.420935i	$-0.138298\pi$
$907$	54.6367	1.81418	0.907091	+	0.420935i	$0.138298\pi$
$908$	−2.11402	−0.0701561
$909$	6.16841	0.204593
$910$	47.9191	1.58850
$911$	−32.7463	−1.08493	−0.542467	−	0.840077i	$-0.682510\pi$
$911$	−32.7463	−1.08493	−0.542467	+	0.840077i	$0.682510\pi$
$912$	142.899	4.73185
$913$	−59.9316	−1.98345
$914$	108.430	3.58656
$915$	−51.5108	−1.70290
$916$	−86.7515	−2.86635
$917$	−3.90478	−0.128947
$918$	4.69004	0.154795
$919$	25.6132	0.844902	0.422451	−	0.906386i	$-0.361170\pi$
$919$	25.6132	0.844902	0.422451	+	0.906386i	$0.361170\pi$
$920$	8.81745	0.290703
$921$	24.4212	0.804706
$922$	−108.919	−3.58706
$923$	−39.7356	−1.30791
$924$	−58.2526	−1.91637
$925$	58.8409	1.93468
$926$	−67.5648	−2.22032
$927$	1.76382	0.0579314
$928$	−134.746	−4.42327
$929$	38.5359	1.26432	0.632161	−	0.774837i	$-0.282168\pi$
$929$	38.5359	1.26432	0.632161	+	0.774837i	$0.282168\pi$
$930$	−30.2330	−0.991381
$931$	−24.5863	−0.805783
$932$	51.1575	1.67572
$933$	14.1186	0.462222
$934$	66.2079	2.16639
$935$	−10.9721	−0.358825
$936$	−74.6443	−2.43982
$937$	−3.93281	−0.128479	−0.0642397	−	0.997934i	$-0.520462\pi$
$937$	−3.93281	−0.128479	−0.0642397	+	0.997934i	$0.520462\pi$
$938$	9.50400	0.310317
$939$	−59.6290	−1.94592
$940$	−139.032	−4.53472
$941$	18.7095	0.609914	0.304957	−	0.952366i	$-0.401358\pi$
$941$	18.7095	0.609914	0.304957	+	0.952366i	$0.401358\pi$
$942$	−16.6600	−0.542813
$943$	3.14218	0.102323
$944$	−121.360	−3.94994
$945$	8.01371	0.260686
$946$	−9.18868	−0.298750
$947$	−17.9663	−0.583825	−0.291913	−	0.956445i	$-0.594292\pi$
$947$	−17.9663	−0.583825	−0.291913	+	0.956445i	$0.594292\pi$
$948$	68.0968	2.21168
$949$	28.5525	0.926853
$950$	69.9780	2.27039
$951$	−32.0474	−1.03921
$952$	−12.2529	−0.397120
$953$	−10.4009	−0.336917	−0.168459	−	0.985709i	$-0.553879\pi$
$953$	−10.4009	−0.336917	−0.168459	+	0.985709i	$0.553879\pi$
$954$	32.7595	1.06063
$955$	11.2582	0.364306
$956$	−141.193	−4.56651
$957$	63.5911	2.05561
$958$	−81.5579	−2.63502
$959$	5.22038	0.168575
$960$	−142.105	−4.58641
$961$	−28.6334	−0.923659
$962$	−117.070	−3.77449
$963$	6.94831	0.223906
$964$	−86.3594	−2.78145
$965$	11.5942	0.373232
$966$	−2.82357	−0.0908468
$967$	21.8391	0.702299	0.351149	−	0.936319i	$-0.385791\pi$
$967$	21.8391	0.702299	0.351149	+	0.936319i	$0.385791\pi$
$968$	6.32289	0.203225
$969$	−11.3596	−0.364924
$970$	113.157	3.63325
$971$	11.1017	0.356272	0.178136	−	0.984006i	$-0.442993\pi$
$971$	11.1017	0.356272	0.178136	+	0.984006i	$0.442993\pi$
$972$	−99.9980	−3.20744
$973$	0.865316	0.0277408
$974$	25.2039	0.807585
$975$	−46.8901	−1.50169
$976$	88.4278	2.83050
$977$	−15.0049	−0.480048	−0.240024	−	0.970767i	$-0.577155\pi$
$977$	−15.0049	−0.480048	−0.240024	+	0.970767i	$0.577155\pi$
$978$	154.255	4.93254
$979$	24.6285	0.787131
$980$	82.3574	2.63081
$981$	−2.07209	−0.0661568
$982$	−54.7597	−1.74745
$983$	29.0946	0.927975	0.463987	−	0.885842i	$-0.346418\pi$
$983$	29.0946	0.927975	0.463987	+	0.885842i	$0.346418\pi$
$984$	−191.470	−6.10383
$985$	79.8051	2.54280
$986$	21.7546	0.692808
$987$	27.3741	0.871327
$988$	−100.515	−3.19781
$989$	−0.321543	−0.0102245
$990$	65.7900	2.09094
$991$	−0.541105	−0.0171888	−0.00859438	−	0.999963i	$-0.502736\pi$
$991$	−0.541105	−0.0171888	−0.00859438	+	0.999963i	$0.502736\pi$
$992$	25.5549	0.811368
$993$	−52.5097	−1.66635
$994$	39.1106	1.24051
$995$	13.3772	0.424084
$996$	207.846	6.58585
$997$	−8.82268	−0.279417	−0.139709	−	0.990193i	$-0.544617\pi$
$997$	−8.82268	−0.279417	−0.139709	+	0.990193i	$0.544617\pi$
$998$	76.6192	2.42534
$999$	−19.5781	−0.619423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.19	✓	21
3.2	odd	2		6579.2.a.u.1.3		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.19	✓	21	1.1	even	1	trivial
6579.2.a.u.1.3		21	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.68194 q^{2} +2.28817 q^{3} +5.19279 q^{4} -3.20246 q^{5} +6.13674 q^{6} +1.43094 q^{7} +8.56287 q^{8} +2.23574 q^{9} +O(q^{10})\)	\(q+2.68194 q^{2} +2.28817 q^{3} +5.19279 q^{4} -3.20246 q^{5} +6.13674 q^{6} +1.43094 q^{7} +8.56287 q^{8} +2.23574 q^{9} -8.58881 q^{10} -3.42614 q^{11} +11.8820 q^{12} -3.89902 q^{13} +3.83769 q^{14} -7.32780 q^{15} +12.5795 q^{16} -1.00000 q^{17} +5.99613 q^{18} +4.96450 q^{19} -16.6297 q^{20} +3.27424 q^{21} -9.18868 q^{22} -0.321543 q^{23} +19.5933 q^{24} +5.25578 q^{25} -10.4569 q^{26} -1.74875 q^{27} +7.43056 q^{28} -8.11153 q^{29} -19.6527 q^{30} +1.53837 q^{31} +16.6117 q^{32} -7.83960 q^{33} -2.68194 q^{34} -4.58253 q^{35} +11.6098 q^{36} +11.1955 q^{37} +13.3145 q^{38} -8.92163 q^{39} -27.4223 q^{40} -9.77217 q^{41} +8.78130 q^{42} +1.00000 q^{43} -17.7912 q^{44} -7.15989 q^{45} -0.862359 q^{46} +8.36045 q^{47} +28.7841 q^{48} -4.95242 q^{49} +14.0957 q^{50} -2.28817 q^{51} -20.2468 q^{52} +5.46345 q^{53} -4.69004 q^{54} +10.9721 q^{55} +12.2529 q^{56} +11.3596 q^{57} -21.7546 q^{58} -9.64747 q^{59} -38.0517 q^{60} +7.02951 q^{61} +4.12580 q^{62} +3.19921 q^{63} +19.3926 q^{64} +12.4865 q^{65} -21.0253 q^{66} +2.47649 q^{67} -5.19279 q^{68} -0.735747 q^{69} -12.2901 q^{70} +10.1912 q^{71} +19.1444 q^{72} -7.32300 q^{73} +30.0255 q^{74} +12.0261 q^{75} +25.7796 q^{76} -4.90259 q^{77} -23.9273 q^{78} +5.73108 q^{79} -40.2854 q^{80} -10.7087 q^{81} -26.2084 q^{82} +17.4925 q^{83} +17.0024 q^{84} +3.20246 q^{85} +2.68194 q^{86} -18.5606 q^{87} -29.3376 q^{88} -7.18843 q^{89} -19.2024 q^{90} -5.57925 q^{91} -1.66971 q^{92} +3.52005 q^{93} +22.4222 q^{94} -15.8986 q^{95} +38.0105 q^{96} -13.1749 q^{97} -13.2821 q^{98} -7.65996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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