LMFDB - Embedded newform 1931.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1931,2,Mod(1,1931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1931, 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("1931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1931 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1931.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:	$15.4191126303$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82191 q^{2} -2.51033 q^{3} +5.96320 q^{4} -0.272521 q^{5} +7.08394 q^{6} +0.922658 q^{7} -11.1838 q^{8} +3.30177 q^{9} +O(q^{10})$	\(q-2.82191 q^{2} -2.51033 q^{3} +5.96320 q^{4} -0.272521 q^{5} +7.08394 q^{6} +0.922658 q^{7} -11.1838 q^{8} +3.30177 q^{9} +0.769032 q^{10} -3.56966 q^{11} -14.9696 q^{12} -7.00057 q^{13} -2.60366 q^{14} +0.684119 q^{15} +19.6334 q^{16} -7.07044 q^{17} -9.31730 q^{18} -0.937366 q^{19} -1.62510 q^{20} -2.31618 q^{21} +10.0733 q^{22} -6.88862 q^{23} +28.0751 q^{24} -4.92573 q^{25} +19.7550 q^{26} -0.757535 q^{27} +5.50199 q^{28} -1.96878 q^{29} -1.93052 q^{30} -3.22338 q^{31} -33.0361 q^{32} +8.96103 q^{33} +19.9522 q^{34} -0.251444 q^{35} +19.6891 q^{36} +6.73352 q^{37} +2.64517 q^{38} +17.5738 q^{39} +3.04783 q^{40} +2.23099 q^{41} +6.53605 q^{42} -1.37797 q^{43} -21.2866 q^{44} -0.899802 q^{45} +19.4391 q^{46} -3.41891 q^{47} -49.2863 q^{48} -6.14870 q^{49} +13.9000 q^{50} +17.7492 q^{51} -41.7458 q^{52} +6.55115 q^{53} +2.13770 q^{54} +0.972808 q^{55} -10.3188 q^{56} +2.35310 q^{57} +5.55572 q^{58} -8.51101 q^{59} +4.07954 q^{60} -3.94263 q^{61} +9.09611 q^{62} +3.04640 q^{63} +53.9582 q^{64} +1.90780 q^{65} -25.2873 q^{66} -8.61607 q^{67} -42.1625 q^{68} +17.2927 q^{69} +0.709553 q^{70} -5.18624 q^{71} -36.9264 q^{72} +1.66664 q^{73} -19.0014 q^{74} +12.3652 q^{75} -5.58970 q^{76} -3.29357 q^{77} -49.5916 q^{78} -1.34727 q^{79} -5.35051 q^{80} -8.00364 q^{81} -6.29565 q^{82} +4.28379 q^{83} -13.8118 q^{84} +1.92685 q^{85} +3.88852 q^{86} +4.94228 q^{87} +39.9224 q^{88} -4.90259 q^{89} +2.53916 q^{90} -6.45913 q^{91} -41.0783 q^{92} +8.09176 q^{93} +9.64788 q^{94} +0.255452 q^{95} +82.9315 q^{96} -4.37366 q^{97} +17.3511 q^{98} -11.7862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9}+O(q^{10}) $ 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9} + 14 q^{10} + 29 q^{11} + 15 q^{12} + 41 q^{13} + 4 q^{14} + 22 q^{15} + 187 q^{16} + 9 q^{17} + 11 q^{18} + 34 q^{19} + 42 q^{20} + 72 q^{21} + 17 q^{22} + 19 q^{23} + 33 q^{24} + 172 q^{25} + 28 q^{26} + 36 q^{27} + 47 q^{28} + 68 q^{29} + q^{30} + 76 q^{31} + 9 q^{32} + 8 q^{33} + 50 q^{34} + 7 q^{35} + 198 q^{36} + 141 q^{37} - 13 q^{38} + 42 q^{39} + 32 q^{40} + 35 q^{41} - 46 q^{42} + 45 q^{43} + 67 q^{44} + 106 q^{45} + 86 q^{46} - 5 q^{47} + 7 q^{48} + 203 q^{49} + 4 q^{50} + 5 q^{51} + 30 q^{52} + 47 q^{53} + 20 q^{54} + 11 q^{55} - 4 q^{56} + 19 q^{57} + 92 q^{58} + 30 q^{59} + 35 q^{60} + 153 q^{61} - 20 q^{62} + 19 q^{63} + 276 q^{64} - 7 q^{65} - 18 q^{66} + 39 q^{67} - 7 q^{68} + 55 q^{69} - 8 q^{70} + 47 q^{71} - 4 q^{72} + 86 q^{73} + 9 q^{74} + 11 q^{75} + 50 q^{76} + 15 q^{77} - 15 q^{78} + 89 q^{79} + 26 q^{80} + 201 q^{81} - 9 q^{82} - 15 q^{83} + 60 q^{84} + 239 q^{85} + 13 q^{86} - 22 q^{87} + 5 q^{88} + 14 q^{89} - 85 q^{90} + 58 q^{91} - 4 q^{92} + 86 q^{93} + 21 q^{94} - 10 q^{95} + 6 q^{96} + 46 q^{97} - 68 q^{98} + 100 q^{99}+O(q^{100}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9 + 14 * q^10 + 29 * q^11 + 15 * q^12 + 41 * q^13 + 4 * q^14 + 22 * q^15 + 187 * q^16 + 9 * q^17 + 11 * q^18 + 34 * q^19 + 42 * q^20 + 72 * q^21 + 17 * q^22 + 19 * q^23 + 33 * q^24 + 172 * q^25 + 28 * q^26 + 36 * q^27 + 47 * q^28 + 68 * q^29 + q^30 + 76 * q^31 + 9 * q^32 + 8 * q^33 + 50 * q^34 + 7 * q^35 + 198 * q^36 + 141 * q^37 - 13 * q^38 + 42 * q^39 + 32 * q^40 + 35 * q^41 - 46 * q^42 + 45 * q^43 + 67 * q^44 + 106 * q^45 + 86 * q^46 - 5 * q^47 + 7 * q^48 + 203 * q^49 + 4 * q^50 + 5 * q^51 + 30 * q^52 + 47 * q^53 + 20 * q^54 + 11 * q^55 - 4 * q^56 + 19 * q^57 + 92 * q^58 + 30 * q^59 + 35 * q^60 + 153 * q^61 - 20 * q^62 + 19 * q^63 + 276 * q^64 - 7 * q^65 - 18 * q^66 + 39 * q^67 - 7 * q^68 + 55 * q^69 - 8 * q^70 + 47 * q^71 - 4 * q^72 + 86 * q^73 + 9 * q^74 + 11 * q^75 + 50 * q^76 + 15 * q^77 - 15 * q^78 + 89 * q^79 + 26 * q^80 + 201 * q^81 - 9 * q^82 - 15 * q^83 + 60 * q^84 + 239 * q^85 + 13 * q^86 - 22 * q^87 + 5 * q^88 + 14 * q^89 - 85 * q^90 + 58 * q^91 - 4 * q^92 + 86 * q^93 + 21 * q^94 - 10 * q^95 + 6 * q^96 + 46 * q^97 - 68 * q^98 + 100 * 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 $

$2$	−2.82191	−1.99539	−0.997697	−	0.0678215i	$-0.978395\pi$
$2$	−2.82191	−1.99539	−0.997697	+	0.0678215i	$0.978395\pi$
$3$	−2.51033	−1.44934	−0.724670	−	0.689096i	$-0.758008\pi$
$3$	−2.51033	−1.44934	−0.724670	+	0.689096i	$0.758008\pi$
$4$	5.96320	2.98160
$5$	−0.272521	−0.121875	−0.0609376	−	0.998142i	$-0.519409\pi$
$5$	−0.272521	−0.121875	−0.0609376	+	0.998142i	$0.519409\pi$
$6$	7.08394	2.89201
$7$	0.922658	0.348732	0.174366	−	0.984681i	$-0.444212\pi$
$7$	0.922658	0.348732	0.174366	+	0.984681i	$0.444212\pi$
$8$	−11.1838	−3.95408
$9$	3.30177	1.10059
$10$	0.769032	0.243189
$11$	−3.56966	−1.07629	−0.538147	−	0.842851i	$-0.680875\pi$
$11$	−3.56966	−1.07629	−0.538147	+	0.842851i	$0.680875\pi$
$12$	−14.9696	−4.32136
$13$	−7.00057	−1.94161	−0.970805	−	0.239872i	$-0.922895\pi$
$13$	−7.00057	−1.94161	−0.970805	+	0.239872i	$0.922895\pi$
$14$	−2.60366	−0.695858
$15$	0.684119	0.176639
$16$	19.6334	4.90834
$17$	−7.07044	−1.71483	−0.857417	−	0.514622i	$-0.827932\pi$
$17$	−7.07044	−1.71483	−0.857417	+	0.514622i	$0.827932\pi$
$18$	−9.31730	−2.19611
$19$	−0.937366	−0.215046	−0.107523	−	0.994203i	$-0.534292\pi$
$19$	−0.937366	−0.215046	−0.107523	+	0.994203i	$0.534292\pi$
$20$	−1.62510	−0.363383
$21$	−2.31618	−0.505431
$22$	10.0733	2.14763
$23$	−6.88862	−1.43638	−0.718189	−	0.695848i	$-0.755029\pi$
$23$	−6.88862	−1.43638	−0.718189	+	0.695848i	$0.755029\pi$
$24$	28.0751	5.73080
$25$	−4.92573	−0.985146
$26$	19.7550	3.87428
$27$	−0.757535	−0.145788
$28$	5.50199	1.03978
$29$	−1.96878	−0.365593	−0.182796	−	0.983151i	$-0.558515\pi$
$29$	−1.96878	−0.365593	−0.182796	+	0.983151i	$0.558515\pi$
$30$	−1.93052	−0.352464
$31$	−3.22338	−0.578937	−0.289468	−	0.957188i	$-0.593479\pi$
$31$	−3.22338	−0.578937	−0.289468	+	0.957188i	$0.593479\pi$
$32$	−33.0361	−5.84001
$33$	8.96103	1.55992
$34$	19.9522	3.42177
$35$	−0.251444	−0.0425018
$36$	19.6891	3.28152
$37$	6.73352	1.10698	0.553492	−	0.832855i	$-0.313295\pi$
$37$	6.73352	1.10698	0.553492	+	0.832855i	$0.313295\pi$
$38$	2.64517	0.429103
$39$	17.5738	2.81405
$40$	3.04783	0.481904
$41$	2.23099	0.348421	0.174211	−	0.984708i	$-0.444263\pi$
$41$	2.23099	0.348421	0.174211	+	0.984708i	$0.444263\pi$
$42$	6.53605	1.00854
$43$	−1.37797	−0.210139	−0.105069	−	0.994465i	$-0.533506\pi$
$43$	−1.37797	−0.210139	−0.105069	+	0.994465i	$0.533506\pi$
$44$	−21.2866	−3.20908
$45$	−0.899802	−0.134134
$46$	19.4391	2.86614
$47$	−3.41891	−0.498700	−0.249350	−	0.968413i	$-0.580217\pi$
$47$	−3.41891	−0.498700	−0.249350	+	0.968413i	$0.580217\pi$
$48$	−49.2863	−7.11386
$49$	−6.14870	−0.878386
$50$	13.9000	1.96576
$51$	17.7492	2.48538
$52$	−41.7458	−5.78910
$53$	6.55115	0.899870	0.449935	−	0.893061i	$-0.351447\pi$
$53$	6.55115	0.899870	0.449935	+	0.893061i	$0.351447\pi$
$54$	2.13770	0.290904
$55$	0.972808	0.131173
$56$	−10.3188	−1.37891
$57$	2.35310	0.311676
$58$	5.55572	0.729502
$59$	−8.51101	−1.10804	−0.554020	−	0.832504i	$-0.686907\pi$
$59$	−8.51101	−1.10804	−0.554020	+	0.832504i	$0.686907\pi$
$60$	4.07954	0.526666
$61$	−3.94263	−0.504802	−0.252401	−	0.967623i	$-0.581220\pi$
$61$	−3.94263	−0.504802	−0.252401	+	0.967623i	$0.581220\pi$
$62$	9.09611	1.15521
$63$	3.04640	0.383810
$64$	53.9582	6.74478
$65$	1.90780	0.236634
$66$	−25.2873	−3.11265
$67$	−8.61607	−1.05262	−0.526310	−	0.850293i	$-0.676425\pi$
$67$	−8.61607	−1.05262	−0.526310	+	0.850293i	$0.676425\pi$
$68$	−42.1625	−5.11295
$69$	17.2927	2.08180
$70$	0.709553	0.0848078
$71$	−5.18624	−0.615493	−0.307747	−	0.951468i	$-0.599575\pi$
$71$	−5.18624	−0.615493	−0.307747	+	0.951468i	$0.599575\pi$
$72$	−36.9264	−4.35181
$73$	1.66664	0.195065	0.0975326	−	0.995232i	$-0.468905\pi$
$73$	1.66664	0.195065	0.0975326	+	0.995232i	$0.468905\pi$
$74$	−19.0014	−2.20887
$75$	12.3652	1.42781
$76$	−5.58970	−0.641183
$77$	−3.29357	−0.375338
$78$	−49.5916	−5.61515
$79$	−1.34727	−0.151580	−0.0757901	−	0.997124i	$-0.524148\pi$
$79$	−1.34727	−0.151580	−0.0757901	+	0.997124i	$0.524148\pi$
$80$	−5.35051	−0.598205
$81$	−8.00364	−0.889293
$82$	−6.29565	−0.695238
$83$	4.28379	0.470207	0.235103	−	0.971970i	$-0.424457\pi$
$83$	4.28379	0.470207	0.235103	+	0.971970i	$0.424457\pi$
$84$	−13.8118	−1.50699
$85$	1.92685	0.208996
$86$	3.88852	0.419310
$87$	4.94228	0.529868
$88$	39.9224	4.25575
$89$	−4.90259	−0.519673	−0.259837	−	0.965653i	$-0.583669\pi$
$89$	−4.90259	−0.519673	−0.259837	+	0.965653i	$0.583669\pi$
$90$	2.53916	0.267651
$91$	−6.45913	−0.677101
$92$	−41.0783	−4.28270
$93$	8.09176	0.839077
$94$	9.64788	0.995103
$95$	0.255452	0.0262088
$96$	82.9315	8.46416
$97$	−4.37366	−0.444077	−0.222039	−	0.975038i	$-0.571271\pi$
$97$	−4.37366	−0.444077	−0.222039	+	0.975038i	$0.571271\pi$
$98$	17.3511	1.75273
$99$	−11.7862	−1.18456
$100$	−29.3731	−2.93731
$101$	1.18481	0.117893	0.0589467	−	0.998261i	$-0.481226\pi$
$101$	1.18481	0.117893	0.0589467	+	0.998261i	$0.481226\pi$
$102$	−50.0866	−4.95931
$103$	−10.4303	−1.02773	−0.513865	−	0.857871i	$-0.671787\pi$
$103$	−10.4303	−1.02773	−0.513865	+	0.857871i	$0.671787\pi$
$104$	78.2931	7.67727
$105$	0.631207	0.0615995
$106$	−18.4868	−1.79560
$107$	−5.82779	−0.563393	−0.281697	−	0.959504i	$-0.590897\pi$
$107$	−5.82779	−0.563393	−0.281697	+	0.959504i	$0.590897\pi$
$108$	−4.51733	−0.434681
$109$	−12.4870	−1.19604	−0.598021	−	0.801480i	$-0.704046\pi$
$109$	−12.4870	−1.19604	−0.598021	+	0.801480i	$0.704046\pi$
$110$	−2.74518	−0.261743
$111$	−16.9034	−1.60440
$112$	18.1149	1.71170
$113$	−1.04087	−0.0979170	−0.0489585	−	0.998801i	$-0.515590\pi$
$113$	−1.04087	−0.0979170	−0.0489585	+	0.998801i	$0.515590\pi$
$114$	−6.64024	−0.621916
$115$	1.87730	0.175059
$116$	−11.7402	−1.09005
$117$	−23.1143	−2.13691
$118$	24.0173	2.21098
$119$	−6.52360	−0.598017
$120$	−7.65106	−0.698443
$121$	1.74247	0.158407
$122$	11.1258	1.00728
$123$	−5.60051	−0.504981
$124$	−19.2217	−1.72616
$125$	2.70497	0.241940
$126$	−8.59668	−0.765853
$127$	10.3033	0.914273	0.457136	−	0.889397i	$-0.348875\pi$
$127$	10.3033	0.914273	0.457136	+	0.889397i	$0.348875\pi$
$128$	−86.1933	−7.61849
$129$	3.45916	0.304562
$130$	−5.38366	−0.472178
$131$	17.4926	1.52833	0.764167	−	0.645019i	$-0.223151\pi$
$131$	17.4926	1.52833	0.764167	+	0.645019i	$0.223151\pi$
$132$	53.4364	4.65105
$133$	−0.864868	−0.0749935
$134$	24.3138	2.10039
$135$	0.206444	0.0177679
$136$	79.0745	6.78058
$137$	16.8452	1.43919	0.719593	−	0.694396i	$-0.244328\pi$
$137$	16.8452	1.43919	0.719593	+	0.694396i	$0.244328\pi$
$138$	−48.7986	−4.15401
$139$	3.11943	0.264587	0.132293	−	0.991211i	$-0.457766\pi$
$139$	3.11943	0.264587	0.132293	+	0.991211i	$0.457766\pi$
$140$	−1.49941	−0.126723
$141$	8.58261	0.722786
$142$	14.6351	1.22815
$143$	24.9897	2.08974
$144$	64.8248	5.40207
$145$	0.536533	0.0445567
$146$	−4.70311	−0.389232
$147$	15.4353	1.27308
$148$	40.1533	3.30058
$149$	1.55687	0.127543	0.0637717	−	0.997965i	$-0.479687\pi$
$149$	1.55687	0.127543	0.0637717	+	0.997965i	$0.479687\pi$
$150$	−34.8936	−2.84905
$151$	−13.6869	−1.11382	−0.556911	−	0.830572i	$-0.688013\pi$
$151$	−13.6869	−1.11382	−0.556911	+	0.830572i	$0.688013\pi$
$152$	10.4833	0.850310
$153$	−23.3450	−1.88733
$154$	9.29419	0.748947
$155$	0.878440	0.0705580
$156$	104.796	8.39038
$157$	15.5067	1.23757	0.618783	−	0.785562i	$-0.287626\pi$
$157$	15.5067	1.23757	0.618783	+	0.785562i	$0.287626\pi$
$158$	3.80189	0.302462
$159$	−16.4456	−1.30422
$160$	9.00303	0.711752
$161$	−6.35584	−0.500911
$162$	22.5856	1.77449
$163$	19.3957	1.51919	0.759593	−	0.650399i	$-0.225398\pi$
$163$	19.3957	1.51919	0.759593	+	0.650399i	$0.225398\pi$
$164$	13.3038	1.03885
$165$	−2.44207	−0.190115
$166$	−12.0885	−0.938248
$167$	−23.4085	−1.81140	−0.905701	−	0.423916i	$-0.860655\pi$
$167$	−23.4085	−1.81140	−0.905701	+	0.423916i	$0.860655\pi$
$168$	25.9037	1.99851
$169$	36.0080	2.76985
$170$	−5.43739	−0.417029
$171$	−3.09496	−0.236678
$172$	−8.21712	−0.626549
$173$	−3.45139	−0.262405	−0.131202	−	0.991356i	$-0.541884\pi$
$173$	−3.45139	−0.262405	−0.131202	+	0.991356i	$0.541884\pi$
$174$	−13.9467	−1.05730
$175$	−4.54476	−0.343552
$176$	−70.0845	−5.28282
$177$	21.3655	1.60593
$178$	13.8347	1.03695
$179$	−23.0085	−1.71974	−0.859868	−	0.510516i	$-0.829454\pi$
$179$	−23.0085	−1.71974	−0.859868	+	0.510516i	$0.829454\pi$
$180$	−5.36570	−0.399936
$181$	−23.1822	−1.72312	−0.861560	−	0.507656i	$-0.830512\pi$
$181$	−23.1822	−1.72312	−0.861560	+	0.507656i	$0.830512\pi$
$182$	18.2271	1.35108
$183$	9.89731	0.731630
$184$	77.0411	5.67955
$185$	−1.83503	−0.134914
$186$	−22.8343	−1.67429
$187$	25.2391	1.84566
$188$	−20.3877	−1.48692
$189$	−0.698945	−0.0508408
$190$	−0.720864	−0.0522969
$191$	−16.9981	−1.22994	−0.614969	−	0.788552i	$-0.710831\pi$
$191$	−16.9981	−1.22994	−0.614969	+	0.788552i	$0.710831\pi$
$192$	−135.453	−9.77548
$193$	−4.14210	−0.298155	−0.149078	−	0.988826i	$-0.547630\pi$
$193$	−4.14210	−0.298155	−0.149078	+	0.988826i	$0.547630\pi$
$194$	12.3421	0.886110
$195$	−4.78922	−0.342963
$196$	−36.6660	−2.61900
$197$	−8.88708	−0.633178	−0.316589	−	0.948563i	$-0.602538\pi$
$197$	−8.88708	−0.633178	−0.316589	+	0.948563i	$0.602538\pi$
$198$	33.2596	2.36366
$199$	8.71532	0.617813	0.308906	−	0.951092i	$-0.400037\pi$
$199$	8.71532	0.617813	0.308906	+	0.951092i	$0.400037\pi$
$200$	55.0885	3.89534
$201$	21.6292	1.52561
$202$	−3.34345	−0.235244
$203$	−1.81651	−0.127494
$204$	105.842	7.41041
$205$	−0.607991	−0.0424639
$206$	29.4335	2.05073
$207$	−22.7446	−1.58086
$208$	−137.445	−9.53008
$209$	3.34608	0.231453
$210$	−1.78121	−0.122915
$211$	−12.1929	−0.839393	−0.419696	−	0.907665i	$-0.637863\pi$
$211$	−12.1929	−0.839393	−0.419696	+	0.907665i	$0.637863\pi$
$212$	39.0658	2.68305
$213$	13.0192	0.892060
$214$	16.4455	1.12419
$215$	0.375526	0.0256107
$216$	8.47213	0.576456
$217$	−2.97408	−0.201894
$218$	35.2374	2.38658
$219$	−4.18382	−0.282716
$220$	5.80105	0.391107
$221$	49.4971	3.32954
$222$	47.6998	3.20140
$223$	8.63257	0.578079	0.289040	−	0.957317i	$-0.406664\pi$
$223$	8.63257	0.578079	0.289040	+	0.957317i	$0.406664\pi$
$224$	−30.4810	−2.03660
$225$	−16.2636	−1.08424
$226$	2.93725	0.195383
$227$	−5.03483	−0.334173	−0.167087	−	0.985942i	$-0.553436\pi$
$227$	−5.03483	−0.334173	−0.167087	+	0.985942i	$0.553436\pi$
$228$	14.0320	0.929292
$229$	19.5521	1.29204	0.646019	−	0.763321i	$-0.276433\pi$
$229$	19.5521	1.29204	0.646019	+	0.763321i	$0.276433\pi$
$230$	−5.29757	−0.349311
$231$	8.26797	0.543992
$232$	22.0184	1.44558
$233$	15.2396	0.998382	0.499191	−	0.866492i	$-0.333631\pi$
$233$	15.2396	0.998382	0.499191	+	0.866492i	$0.333631\pi$
$234$	65.2265	4.26399
$235$	0.931726	0.0607791
$236$	−50.7529	−3.30373
$237$	3.38211	0.219691
$238$	18.4090	1.19328
$239$	12.2498	0.792372	0.396186	−	0.918170i	$-0.370334\pi$
$239$	12.2498	0.792372	0.396186	+	0.918170i	$0.370334\pi$
$240$	13.4316	0.867003
$241$	−17.0143	−1.09599	−0.547994	−	0.836482i	$-0.684608\pi$
$241$	−17.0143	−1.09599	−0.547994	+	0.836482i	$0.684608\pi$
$242$	−4.91711	−0.316084
$243$	22.3644	1.43468
$244$	−23.5107	−1.50512
$245$	1.67565	0.107053
$246$	15.8042	1.00764
$247$	6.56209	0.417536
$248$	36.0497	2.28916
$249$	−10.7537	−0.681490
$250$	−7.63320	−0.482766
$251$	−17.1046	−1.07963	−0.539815	−	0.841784i	$-0.681506\pi$
$251$	−17.1046	−1.07963	−0.539815	+	0.841784i	$0.681506\pi$
$252$	18.1663	1.14437
$253$	24.5900	1.54596
$254$	−29.0751	−1.82434
$255$	−4.83702	−0.302906
$256$	135.314	8.45711
$257$	−18.2311	−1.13723	−0.568613	−	0.822605i	$-0.692520\pi$
$257$	−18.2311	−1.13723	−0.568613	+	0.822605i	$0.692520\pi$
$258$	−9.76147	−0.607722
$259$	6.21273	0.386040
$260$	11.3766	0.705548
$261$	−6.50044	−0.402367
$262$	−49.3625	−3.04963
$263$	19.8729	1.22541	0.612707	−	0.790310i	$-0.290080\pi$
$263$	19.8729	1.22541	0.612707	+	0.790310i	$0.290080\pi$
$264$	−100.219	−6.16803
$265$	−1.78533	−0.109672
$266$	2.44058	0.149642
$267$	12.3071	0.753183
$268$	−51.3793	−3.13849
$269$	30.7540	1.87510	0.937551	−	0.347847i	$-0.113087\pi$
$269$	30.7540	1.87510	0.937551	+	0.347847i	$0.113087\pi$
$270$	−0.582568	−0.0354540
$271$	−19.4436	−1.18112	−0.590559	−	0.806995i	$-0.701093\pi$
$271$	−19.4436	−1.18112	−0.590559	+	0.806995i	$0.701093\pi$
$272$	−138.817	−8.41699
$273$	16.2146	0.981350
$274$	−47.5358	−2.87174
$275$	17.5832	1.06031
$276$	103.120	6.20710
$277$	2.97363	0.178668	0.0893341	−	0.996002i	$-0.471526\pi$
$277$	2.97363	0.178668	0.0893341	+	0.996002i	$0.471526\pi$
$278$	−8.80277	−0.527955
$279$	−10.6429	−0.637171
$280$	2.81210	0.168055
$281$	29.9658	1.78761	0.893805	−	0.448455i	$-0.148026\pi$
$281$	29.9658	1.78761	0.893805	+	0.448455i	$0.148026\pi$
$282$	−24.2194	−1.44224
$283$	−17.5993	−1.04617	−0.523086	−	0.852280i	$-0.675219\pi$
$283$	−17.5993	−1.04617	−0.523086	+	0.852280i	$0.675219\pi$
$284$	−30.9266	−1.83516
$285$	−0.641269	−0.0379855
$286$	−70.5187	−4.16986
$287$	2.05844	0.121506
$288$	−109.077	−6.42745
$289$	32.9911	1.94066
$290$	−1.51405	−0.0889082
$291$	10.9793	0.643620
$292$	9.93850	0.581607
$293$	−18.7377	−1.09467	−0.547335	−	0.836914i	$-0.684358\pi$
$293$	−18.7377	−1.09467	−0.547335	+	0.836914i	$0.684358\pi$
$294$	−43.5571	−2.54030
$295$	2.31943	0.135042
$296$	−75.3064	−4.37710
$297$	2.70414	0.156910
$298$	−4.39334	−0.254500
$299$	48.2243	2.78888
$300$	73.7363	4.25717
$301$	−1.27140	−0.0732820
$302$	38.6232	2.22251
$303$	−2.97428	−0.170868
$304$	−18.4036	−1.05552
$305$	1.07445	0.0615229
$306$	65.8775	3.76596
$307$	−17.3243	−0.988750	−0.494375	−	0.869249i	$-0.664603\pi$
$307$	−17.3243	−0.988750	−0.494375	+	0.869249i	$0.664603\pi$
$308$	−19.6402	−1.11911
$309$	26.1836	1.48953
$310$	−2.47888	−0.140791
$311$	−1.29025	−0.0731632	−0.0365816	−	0.999331i	$-0.511647\pi$
$311$	−1.29025	−0.0731632	−0.0365816	+	0.999331i	$0.511647\pi$
$312$	−196.542	−11.1270
$313$	2.17495	0.122936	0.0614678	−	0.998109i	$-0.480422\pi$
$313$	2.17495	0.122936	0.0614678	+	0.998109i	$0.480422\pi$
$314$	−43.7585	−2.46943
$315$	−0.830209	−0.0467770
$316$	−8.03407	−0.451952
$317$	−11.6790	−0.655961	−0.327980	−	0.944685i	$-0.606368\pi$
$317$	−11.6790	−0.655961	−0.327980	+	0.944685i	$0.606368\pi$
$318$	46.4080	2.60243
$319$	7.02786	0.393485
$320$	−14.7048	−0.822021
$321$	14.6297	0.816549
$322$	17.9356	0.999514
$323$	6.62759	0.368769
$324$	−47.7273	−2.65152
$325$	34.4829	1.91277
$326$	−54.7329	−3.03138
$327$	31.3466	1.73347
$328$	−24.9509	−1.37768
$329$	−3.15449	−0.173912
$330$	6.89132	0.379355
$331$	−3.10580	−0.170710	−0.0853552	−	0.996351i	$-0.527203\pi$
$331$	−3.10580	−0.170710	−0.0853552	+	0.996351i	$0.527203\pi$
$332$	25.5451	1.40197
$333$	22.2325	1.21833
$334$	66.0567	3.61446
$335$	2.34806	0.128288
$336$	−45.4744	−2.48083
$337$	−20.0199	−1.09055	−0.545277	−	0.838256i	$-0.683576\pi$
$337$	−20.0199	−1.09055	−0.545277	+	0.838256i	$0.683576\pi$
$338$	−101.612	−5.52694
$339$	2.61293	0.141915
$340$	11.4902	0.623142
$341$	11.5064	0.623106
$342$	8.73372	0.472265
$343$	−12.1318	−0.655053
$344$	15.4110	0.830904
$345$	−4.71264	−0.253720
$346$	9.73953	0.523601
$347$	−17.4537	−0.936964	−0.468482	−	0.883473i	$-0.655199\pi$
$347$	−17.4537	−0.936964	−0.468482	+	0.883473i	$0.655199\pi$
$348$	29.4718	1.57986
$349$	−15.1612	−0.811560	−0.405780	−	0.913971i	$-0.633000\pi$
$349$	−15.1612	−0.811560	−0.405780	+	0.913971i	$0.633000\pi$
$350$	12.8249	0.685522
$351$	5.30318	0.283063
$352$	117.928	6.28556
$353$	−5.82869	−0.310230	−0.155115	−	0.987896i	$-0.549575\pi$
$353$	−5.82869	−0.310230	−0.155115	+	0.987896i	$0.549575\pi$
$354$	−60.2915	−3.20446
$355$	1.41336	0.0750134
$356$	−29.2351	−1.54946
$357$	16.3764	0.866731
$358$	64.9280	3.43155
$359$	−31.8814	−1.68264	−0.841319	−	0.540539i	$-0.818220\pi$
$359$	−31.8814	−1.68264	−0.841319	+	0.540539i	$0.818220\pi$
$360$	10.0632	0.530378
$361$	−18.1213	−0.953755
$362$	65.4182	3.43830
$363$	−4.37419	−0.229585
$364$	−38.5171	−2.01884
$365$	−0.454194	−0.0237736
$366$	−27.9294	−1.45989
$367$	−10.0172	−0.522892	−0.261446	−	0.965218i	$-0.584199\pi$
$367$	−10.0172	−0.522892	−0.261446	+	0.965218i	$0.584199\pi$
$368$	−135.247	−7.05023
$369$	7.36619	0.383469
$370$	5.17829	0.269206
$371$	6.04447	0.313813
$372$	48.2528	2.50179
$373$	37.2554	1.92901	0.964505	−	0.264063i	$-0.0850628\pi$
$373$	37.2554	1.92901	0.964505	+	0.264063i	$0.0850628\pi$
$374$	−71.2225	−3.68283
$375$	−6.79038	−0.350654
$376$	38.2365	1.97190
$377$	13.7826	0.709838
$378$	1.97236	0.101447
$379$	23.8472	1.22495	0.612473	−	0.790492i	$-0.290175\pi$
$379$	23.8472	1.22495	0.612473	+	0.790492i	$0.290175\pi$
$380$	1.52331	0.0781442
$381$	−25.8648	−1.32509
$382$	47.9671	2.45421
$383$	16.2822	0.831982	0.415991	−	0.909369i	$-0.363435\pi$
$383$	16.2822	0.831982	0.415991	+	0.909369i	$0.363435\pi$
$384$	216.374	11.0418
$385$	0.897569	0.0457443
$386$	11.6887	0.594937
$387$	−4.54974	−0.231276
$388$	−26.0810	−1.32406
$389$	37.6474	1.90880	0.954401	−	0.298529i	$-0.0964958\pi$
$389$	37.6474	1.90880	0.954401	+	0.298529i	$0.0964958\pi$
$390$	13.5148	0.684347
$391$	48.7056	2.46315
$392$	68.7660	3.47321
$393$	−43.9122	−2.21508
$394$	25.0786	1.26344
$395$	0.367161	0.0184739
$396$	−70.2834	−3.53187
$397$	−20.4951	−1.02862	−0.514310	−	0.857604i	$-0.671952\pi$
$397$	−20.4951	−1.02862	−0.514310	+	0.857604i	$0.671952\pi$
$398$	−24.5939	−1.23278
$399$	2.17110	0.108691
$400$	−96.7087	−4.83544
$401$	23.6331	1.18018	0.590091	−	0.807337i	$-0.299092\pi$
$401$	23.6331	1.18018	0.590091	+	0.807337i	$0.299092\pi$
$402$	−61.0357	−3.04418
$403$	22.5655	1.12407
$404$	7.06529	0.351511
$405$	2.18116	0.108383
$406$	5.12603	0.254400
$407$	−24.0364	−1.19144
$408$	−198.503	−9.82738
$409$	−24.0910	−1.19122	−0.595612	−	0.803272i	$-0.703090\pi$
$409$	−24.0910	−1.19122	−0.595612	+	0.803272i	$0.703090\pi$
$410$	1.71570	0.0847323
$411$	−42.2871	−2.08587
$412$	−62.1981	−3.06428
$413$	−7.85275	−0.386409
$414$	64.1834	3.15444
$415$	−1.16742	−0.0573065
$416$	231.271	11.3390
$417$	−7.83081	−0.383476
$418$	−9.44234	−0.461840
$419$	−11.3076	−0.552414	−0.276207	−	0.961098i	$-0.589077\pi$
$419$	−11.3076	−0.552414	−0.276207	+	0.961098i	$0.589077\pi$
$420$	3.76402	0.183665
$421$	36.9063	1.79870	0.899352	−	0.437225i	$-0.144039\pi$
$421$	36.9063	1.79870	0.899352	+	0.437225i	$0.144039\pi$
$422$	34.4073	1.67492
$423$	−11.2885	−0.548863
$424$	−73.2669	−3.55815
$425$	34.8271	1.68936
$426$	−36.7390	−1.78001
$427$	−3.63770	−0.176041
$428$	−34.7523	−1.67981
$429$	−62.7323	−3.02875
$430$	−1.05970	−0.0511034
$431$	−13.2498	−0.638220	−0.319110	−	0.947718i	$-0.603384\pi$
$431$	−13.2498	−0.638220	−0.319110	+	0.947718i	$0.603384\pi$
$432$	−14.8730	−0.715576
$433$	26.6104	1.27881	0.639407	−	0.768868i	$-0.279180\pi$
$433$	26.6104	1.27881	0.639407	+	0.768868i	$0.279180\pi$
$434$	8.39260	0.402858
$435$	−1.34688	−0.0645778
$436$	−74.4628	−3.56612
$437$	6.45716	0.308888
$438$	11.8064	0.564130
$439$	−24.2324	−1.15655	−0.578274	−	0.815842i	$-0.696274\pi$
$439$	−24.2324	−1.15655	−0.578274	+	0.815842i	$0.696274\pi$
$440$	−10.8797	−0.518670
$441$	−20.3016	−0.966742
$442$	−139.677	−6.64374
$443$	−5.94914	−0.282652	−0.141326	−	0.989963i	$-0.545137\pi$
$443$	−5.94914	−0.282652	−0.141326	+	0.989963i	$0.545137\pi$
$444$	−100.798	−4.78367
$445$	1.33606	0.0633353
$446$	−24.3604	−1.15350
$447$	−3.90825	−0.184854
$448$	49.7850	2.35212
$449$	−2.76326	−0.130406	−0.0652031	−	0.997872i	$-0.520770\pi$
$449$	−2.76326	−0.130406	−0.0652031	+	0.997872i	$0.520770\pi$
$450$	45.8945	2.16349
$451$	−7.96386	−0.375003
$452$	−6.20693	−0.291949
$453$	34.3586	1.61431
$454$	14.2079	0.666808
$455$	1.76025	0.0825218
$456$	−26.3166	−1.23239
$457$	15.0896	0.705862	0.352931	−	0.935649i	$-0.385185\pi$
$457$	15.0896	0.705862	0.352931	+	0.935649i	$0.385185\pi$
$458$	−55.1743	−2.57813
$459$	5.35611	0.250002
$460$	11.1947	0.521955
$461$	27.6900	1.28965	0.644826	−	0.764329i	$-0.276930\pi$
$461$	27.6900	1.28965	0.644826	+	0.764329i	$0.276930\pi$
$462$	−23.3315	−1.08548
$463$	−19.7988	−0.920129	−0.460065	−	0.887885i	$-0.652174\pi$
$463$	−19.7988	−0.920129	−0.460065	+	0.887885i	$0.652174\pi$
$464$	−38.6537	−1.79445
$465$	−2.20518	−0.102263
$466$	−43.0050	−1.99217
$467$	19.6070	0.907302	0.453651	−	0.891179i	$-0.350121\pi$
$467$	19.6070	0.907302	0.453651	+	0.891179i	$0.350121\pi$
$468$	−137.835	−6.37142
$469$	−7.94968	−0.367082
$470$	−2.62925	−0.121278
$471$	−38.9268	−1.79365
$472$	95.1856	4.38127
$473$	4.91889	0.226171
$474$	−9.54401	−0.438371
$475$	4.61721	0.211852
$476$	−38.9015	−1.78305
$477$	21.6304	0.990387
$478$	−34.5678	−1.58110
$479$	1.14635	0.0523780	0.0261890	−	0.999657i	$-0.491663\pi$
$479$	1.14635	0.0523780	0.0261890	+	0.999657i	$0.491663\pi$
$480$	−22.6006	−1.03157
$481$	−47.1385	−2.14933
$482$	48.0129	2.18693
$483$	15.9553	0.725990
$484$	10.3907	0.472306
$485$	1.19191	0.0541220
$486$	−63.1104	−2.86275
$487$	−28.9351	−1.31118	−0.655588	−	0.755119i	$-0.727579\pi$
$487$	−28.9351	−1.31118	−0.655588	+	0.755119i	$0.727579\pi$
$488$	44.0937	1.99603
$489$	−48.6896	−2.20182
$490$	−4.72855	−0.213614
$491$	−40.8238	−1.84235	−0.921176	−	0.389146i	$-0.872770\pi$
$491$	−40.8238	−1.84235	−0.921176	+	0.389146i	$0.872770\pi$
$492$	−33.3970	−1.50565
$493$	13.9201	0.626931
$494$	−18.5177	−0.833149
$495$	3.21199	0.144368
$496$	−63.2859	−2.84162
$497$	−4.78512	−0.214642
$498$	30.3461	1.35984
$499$	17.2601	0.772666	0.386333	−	0.922359i	$-0.373742\pi$
$499$	17.2601	0.772666	0.386333	+	0.922359i	$0.373742\pi$
$500$	16.1303	0.721369
$501$	58.7631	2.62534
$502$	48.2676	2.15429
$503$	−42.5744	−1.89830	−0.949150	−	0.314825i	$-0.898054\pi$
$503$	−42.5744	−1.89830	−0.949150	+	0.314825i	$0.898054\pi$
$504$	−34.0704	−1.51762
$505$	−0.322887	−0.0143683
$506$	−69.3910	−3.08481
$507$	−90.3920	−4.01445
$508$	61.4408	2.72600
$509$	23.2960	1.03258	0.516290	−	0.856414i	$-0.327313\pi$
$509$	23.2960	1.03258	0.516290	+	0.856414i	$0.327313\pi$
$510$	13.6497	0.604417
$511$	1.53774	0.0680255
$512$	−209.457	−9.25679
$513$	0.710087	0.0313511
$514$	51.4467	2.26921
$515$	2.84248	0.125255
$516$	20.6277	0.908084
$517$	12.2044	0.536747
$518$	−17.5318	−0.770303
$519$	8.66414	0.380314
$520$	−21.3365	−0.935669
$521$	12.6492	0.554170	0.277085	−	0.960845i	$-0.410632\pi$
$521$	12.6492	0.554170	0.277085	+	0.960845i	$0.410632\pi$
$522$	18.3437	0.802882
$523$	−2.76502	−0.120906	−0.0604530	−	0.998171i	$-0.519255\pi$
$523$	−2.76502	−0.120906	−0.0604530	+	0.998171i	$0.519255\pi$
$524$	104.312	4.55688
$525$	11.4089	0.497924
$526$	−56.0796	−2.44519
$527$	22.7907	0.992780
$528$	175.935	7.65660
$529$	24.4531	1.06318
$530$	5.03804	0.218839
$531$	−28.1014	−1.21950
$532$	−5.15738	−0.223601
$533$	−15.6182	−0.676498
$534$	−34.7296	−1.50290
$535$	1.58820	0.0686637
$536$	96.3605	4.16214
$537$	57.7590	2.49248
$538$	−86.7851	−3.74157
$539$	21.9488	0.945401
$540$	1.23107	0.0529768
$541$	11.8482	0.509393	0.254696	−	0.967021i	$-0.418024\pi$
$541$	11.8482	0.509393	0.254696	+	0.967021i	$0.418024\pi$
$542$	54.8683	2.35679
$543$	58.1950	2.49739
$544$	233.580	10.0146
$545$	3.40299	0.145768
$546$	−45.7561	−1.95818
$547$	5.87215	0.251075	0.125538	−	0.992089i	$-0.459934\pi$
$547$	5.87215	0.251075	0.125538	+	0.992089i	$0.459934\pi$
$548$	100.452	4.29108
$549$	−13.0176	−0.555580
$550$	−49.6183	−2.11573
$551$	1.84546	0.0786194
$552$	−193.399	−8.23160
$553$	−1.24307	−0.0528608
$554$	−8.39133	−0.356514
$555$	4.60653	0.195536
$556$	18.6018	0.788892
$557$	13.8496	0.586825	0.293413	−	0.955986i	$-0.405209\pi$
$557$	13.8496	0.586825	0.293413	+	0.955986i	$0.405209\pi$
$558$	30.0332	1.27141
$559$	9.64658	0.408007
$560$	−4.93669	−0.208613
$561$	−63.3585	−2.67500
$562$	−84.5610	−3.56699
$563$	34.3185	1.44635	0.723176	−	0.690664i	$-0.242682\pi$
$563$	34.3185	1.44635	0.723176	+	0.690664i	$0.242682\pi$
$564$	51.1798	2.15506
$565$	0.283660	0.0119337
$566$	49.6638	2.08753
$567$	−7.38462	−0.310125
$568$	58.0020	2.43371
$569$	12.8398	0.538271	0.269136	−	0.963102i	$-0.413262\pi$
$569$	12.8398	0.538271	0.269136	+	0.963102i	$0.413262\pi$
$570$	1.80961	0.0757961
$571$	−13.3975	−0.560666	−0.280333	−	0.959903i	$-0.590445\pi$
$571$	−13.3975	−0.560666	−0.280333	+	0.959903i	$0.590445\pi$
$572$	149.018	6.23077
$573$	42.6708	1.78260
$574$	−5.80873	−0.242452
$575$	33.9315	1.41504
$576$	178.157	7.42323
$577$	−12.9016	−0.537102	−0.268551	−	0.963265i	$-0.586545\pi$
$577$	−12.9016	−0.537102	−0.268551	+	0.963265i	$0.586545\pi$
$578$	−93.0982	−3.87237
$579$	10.3981	0.432128
$580$	3.19946	0.132850
$581$	3.95247	0.163976
$582$	−30.9827	−1.28428
$583$	−23.3854	−0.968524
$584$	−18.6394	−0.771303
$585$	6.29912	0.260437
$586$	52.8763	2.18430
$587$	19.4887	0.804385	0.402192	−	0.915555i	$-0.368248\pi$
$587$	19.4887	0.804385	0.402192	+	0.915555i	$0.368248\pi$
$588$	92.0437	3.79582
$589$	3.02149	0.124498
$590$	−6.54524	−0.269463
$591$	22.3095	0.917691
$592$	132.202	5.43345
$593$	−40.8695	−1.67831	−0.839155	−	0.543892i	$-0.816950\pi$
$593$	−40.8695	−1.67831	−0.839155	+	0.543892i	$0.816950\pi$
$594$	−7.63086	−0.313098
$595$	1.77782	0.0728835
$596$	9.28391	0.380284
$597$	−21.8784	−0.895422
$598$	−136.085	−5.56492
$599$	−16.2393	−0.663521	−0.331761	−	0.943364i	$-0.607643\pi$
$599$	−16.2393	−0.663521	−0.331761	+	0.943364i	$0.607643\pi$
$600$	−138.290	−5.64568
$601$	−40.4369	−1.64945	−0.824727	−	0.565531i	$-0.808671\pi$
$601$	−40.4369	−1.64945	−0.824727	+	0.565531i	$0.808671\pi$
$602$	3.58777	0.146227
$603$	−28.4482	−1.15850
$604$	−81.6176	−3.32097
$605$	−0.474861	−0.0193058
$606$	8.39316	0.340949
$607$	−13.6853	−0.555468	−0.277734	−	0.960658i	$-0.589583\pi$
$607$	−13.6853	−0.555468	−0.277734	+	0.960658i	$0.589583\pi$
$608$	30.9669	1.25587
$609$	4.56004	0.184782
$610$	−3.03201	−0.122762
$611$	23.9343	0.968280
$612$	−139.211	−5.62726
$613$	3.35269	0.135414	0.0677069	−	0.997705i	$-0.478432\pi$
$613$	3.35269	0.135414	0.0677069	+	0.997705i	$0.478432\pi$
$614$	48.8877	1.97295
$615$	1.52626	0.0615447
$616$	36.8347	1.48411
$617$	26.1699	1.05356	0.526780	−	0.850002i	$-0.323399\pi$
$617$	26.1699	1.05356	0.526780	+	0.850002i	$0.323399\pi$
$618$	−73.8878	−2.97220
$619$	8.06039	0.323974	0.161987	−	0.986793i	$-0.448210\pi$
$619$	8.06039	0.323974	0.161987	+	0.986793i	$0.448210\pi$
$620$	5.23832	0.210376
$621$	5.21837	0.209406
$622$	3.64097	0.145989
$623$	−4.52341	−0.181227
$624$	345.032	13.8123
$625$	23.8915	0.955660
$626$	−6.13754	−0.245305
$627$	−8.39976	−0.335454
$628$	92.4693	3.68993
$629$	−47.6089	−1.89829
$630$	2.34278	0.0933385
$631$	23.1478	0.921498	0.460749	−	0.887530i	$-0.347581\pi$
$631$	23.1478	0.921498	0.460749	+	0.887530i	$0.347581\pi$
$632$	15.0677	0.599360
$633$	30.6082	1.21657
$634$	32.9573	1.30890
$635$	−2.80788	−0.111427
$636$	−98.0682	−3.88866
$637$	43.0444	1.70548
$638$	−19.8320	−0.785158
$639$	−17.1238	−0.677405
$640$	23.4895	0.928505
$641$	33.1051	1.30757	0.653787	−	0.756678i	$-0.273179\pi$
$641$	33.1051	1.30757	0.653787	+	0.756678i	$0.273179\pi$
$642$	−41.2837	−1.62934
$643$	−10.0087	−0.394703	−0.197352	−	0.980333i	$-0.563234\pi$
$643$	−10.0087	−0.394703	−0.197352	+	0.980333i	$0.563234\pi$
$644$	−37.9012	−1.49352
$645$	−0.942696	−0.0371186
$646$	−18.7025	−0.735840
$647$	−31.5833	−1.24167	−0.620834	−	0.783942i	$-0.713206\pi$
$647$	−31.5833	−1.24167	−0.620834	+	0.783942i	$0.713206\pi$
$648$	89.5112	3.51633
$649$	30.3814	1.19257
$650$	−97.3079	−3.81673
$651$	7.46593	0.292613
$652$	115.660	4.52961
$653$	34.5686	1.35277	0.676387	−	0.736546i	$-0.263545\pi$
$653$	34.5686	1.35277	0.676387	+	0.736546i	$0.263545\pi$
$654$	−88.4575	−3.45896
$655$	−4.76710	−0.186266
$656$	43.8018	1.71017
$657$	5.50285	0.214687
$658$	8.90169	0.347024
$659$	−18.2223	−0.709840	−0.354920	−	0.934897i	$-0.615492\pi$
$659$	−18.2223	−0.709840	−0.354920	+	0.934897i	$0.615492\pi$
$660$	−14.5626	−0.566847
$661$	−25.6487	−0.997617	−0.498808	−	0.866712i	$-0.666229\pi$
$661$	−25.6487	−0.997617	−0.498808	+	0.866712i	$0.666229\pi$
$662$	8.76432	0.340635
$663$	−124.254	−4.82563
$664$	−47.9091	−1.85923
$665$	0.235695	0.00913985
$666$	−62.7382	−2.43106
$667$	13.5622	0.525129
$668$	−139.589	−5.40088
$669$	−21.6706	−0.837834
$670$	−6.62603	−0.255986
$671$	14.0739	0.543315
$672$	76.5174	2.95172
$673$	−9.32134	−0.359311	−0.179656	−	0.983730i	$-0.557498\pi$
$673$	−9.32134	−0.359311	−0.179656	+	0.983730i	$0.557498\pi$
$674$	56.4945	2.17609
$675$	3.73141	0.143622
$676$	214.723	8.25858
$677$	−6.45117	−0.247939	−0.123969	−	0.992286i	$-0.539562\pi$
$677$	−6.45117	−0.247939	−0.123969	+	0.992286i	$0.539562\pi$
$678$	−7.37348	−0.283177
$679$	−4.03539	−0.154864
$680$	−21.5495	−0.826385
$681$	12.6391	0.484331
$682$	−32.4700	−1.24334
$683$	10.9804	0.420155	0.210078	−	0.977685i	$-0.432628\pi$
$683$	10.9804	0.420155	0.210078	+	0.977685i	$0.432628\pi$
$684$	−18.4559	−0.705678
$685$	−4.59068	−0.175401
$686$	34.2348	1.30709
$687$	−49.0822	−1.87260
$688$	−27.0542	−1.03143
$689$	−45.8618	−1.74720
$690$	13.2987	0.506271
$691$	36.5614	1.39086	0.695430	−	0.718594i	$-0.255214\pi$
$691$	36.5614	1.39086	0.695430	+	0.718594i	$0.255214\pi$
$692$	−20.5813	−0.782386
$693$	−10.8746	−0.413092
$694$	49.2529	1.86961
$695$	−0.850111	−0.0322466
$696$	−55.2736	−2.09514
$697$	−15.7741	−0.597485
$698$	42.7836	1.61938
$699$	−38.2566	−1.44700
$700$	−27.1013	−1.02433
$701$	−8.93507	−0.337473	−0.168736	−	0.985661i	$-0.553969\pi$
$701$	−8.93507	−0.337473	−0.168736	+	0.985661i	$0.553969\pi$
$702$	−14.9651	−0.564822
$703$	−6.31177	−0.238053
$704$	−192.612	−7.25936
$705$	−2.33894	−0.0880897
$706$	16.4481	0.619031
$707$	1.09318	0.0411132
$708$	127.407	4.78823
$709$	−5.23084	−0.196448	−0.0982242	−	0.995164i	$-0.531316\pi$
$709$	−5.23084	−0.196448	−0.0982242	+	0.995164i	$0.531316\pi$
$710$	−3.98838	−0.149681
$711$	−4.44838	−0.166827
$712$	54.8296	2.05483
$713$	22.2047	0.831572
$714$	−46.2128	−1.72947
$715$	−6.81021	−0.254688
$716$	−137.204	−5.12757
$717$	−30.7510	−1.14842
$718$	89.9667	3.35753
$719$	21.0607	0.785430	0.392715	−	0.919660i	$-0.371536\pi$
$719$	21.0607	0.785430	0.392715	+	0.919660i	$0.371536\pi$
$720$	−17.6661	−0.658378
$721$	−9.62362	−0.358402
$722$	51.1369	1.90312
$723$	42.7116	1.58846
$724$	−138.240	−5.13765
$725$	9.69767	0.360162
$726$	12.3436	0.458113
$727$	−2.78668	−0.103352	−0.0516762	−	0.998664i	$-0.516456\pi$
$727$	−2.78668	−0.103352	−0.0516762	+	0.998664i	$0.516456\pi$
$728$	72.2377	2.67731
$729$	−32.1311	−1.19004
$730$	1.28170	0.0474377
$731$	9.74286	0.360353
$732$	59.0197	2.18143
$733$	−7.42809	−0.274363	−0.137181	−	0.990546i	$-0.543804\pi$
$733$	−7.42809	−0.274363	−0.137181	+	0.990546i	$0.543804\pi$
$734$	28.2676	1.04338
$735$	−4.20644	−0.155157
$736$	227.573	8.38845
$737$	30.7564	1.13293
$738$	−20.7868	−0.765171
$739$	30.8642	1.13536	0.567679	−	0.823250i	$-0.307842\pi$
$739$	30.8642	1.13536	0.567679	+	0.823250i	$0.307842\pi$
$740$	−10.9426	−0.402259
$741$	−16.4730	−0.605152
$742$	−17.0570	−0.626181
$743$	−9.38029	−0.344130	−0.172065	−	0.985086i	$-0.555044\pi$
$743$	−9.38029	−0.344130	−0.172065	+	0.985086i	$0.555044\pi$
$744$	−90.4968	−3.31777
$745$	−0.424279	−0.0155444
$746$	−105.132	−3.84914
$747$	14.1441	0.517504
$748$	150.506	5.50303
$749$	−5.37705	−0.196473
$750$	19.1619	0.699693
$751$	−22.0725	−0.805438	−0.402719	−	0.915324i	$-0.631935\pi$
$751$	−22.0725	−0.805438	−0.402719	+	0.915324i	$0.631935\pi$
$752$	−67.1248	−2.44779
$753$	42.9381	1.56475
$754$	−38.8932	−1.41641
$755$	3.72996	0.135747
$756$	−4.16795	−0.151587
$757$	16.6811	0.606287	0.303143	−	0.952945i	$-0.401964\pi$
$757$	16.6811	0.606287	0.303143	+	0.952945i	$0.401964\pi$
$758$	−67.2946	−2.44425
$759$	−61.7292	−2.24063
$760$	−2.85693	−0.103632
$761$	45.1836	1.63790	0.818952	−	0.573862i	$-0.194555\pi$
$761$	45.1836	1.63790	0.818952	+	0.573862i	$0.194555\pi$
$762$	72.9882	2.64408
$763$	−11.5213	−0.417098
$764$	−101.363	−3.66718
$765$	6.36199	0.230018
$766$	−45.9470	−1.66013
$767$	59.5819	2.15138
$768$	−339.683	−12.2572
$769$	−32.4857	−1.17146	−0.585732	−	0.810505i	$-0.699193\pi$
$769$	−32.4857	−1.17146	−0.585732	+	0.810505i	$0.699193\pi$
$770$	−2.53286	−0.0912780
$771$	45.7662	1.64823
$772$	−24.7002	−0.888979
$773$	9.77799	0.351690	0.175845	−	0.984418i	$-0.443734\pi$
$773$	9.77799	0.351690	0.175845	+	0.984418i	$0.443734\pi$
$774$	12.8390	0.461487
$775$	15.8775	0.570338
$776$	48.9142	1.75592
$777$	−15.5960	−0.559504
$778$	−106.238	−3.80881
$779$	−2.09125	−0.0749268
$780$	−28.5591	−1.02258
$781$	18.5131	0.662451
$782$	−137.443	−4.91496
$783$	1.49142	0.0532989
$784$	−120.720	−4.31142
$785$	−4.22589	−0.150829
$786$	123.916	4.41995
$787$	15.2333	0.543009	0.271504	−	0.962437i	$-0.412479\pi$
$787$	15.2333	0.543009	0.271504	+	0.962437i	$0.412479\pi$
$788$	−52.9954	−1.88788
$789$	−49.8875	−1.77604
$790$	−1.03610	−0.0368627
$791$	−0.960368	−0.0341468
$792$	131.815	4.68383
$793$	27.6007	0.980128
$794$	57.8354	2.05250
$795$	4.48176	0.158952
$796$	51.9712	1.84207
$797$	−8.70519	−0.308354	−0.154177	−	0.988043i	$-0.549273\pi$
$797$	−8.70519	−0.308354	−0.154177	+	0.988043i	$0.549273\pi$
$798$	−6.12667	−0.216882
$799$	24.1732	0.855187
$800$	162.727	5.75326
$801$	−16.1872	−0.571946
$802$	−66.6906	−2.35493
$803$	−5.94933	−0.209947
$804$	128.979	4.54875
$805$	1.73210	0.0610486
$806$	−63.6780	−2.24296
$807$	−77.2027	−2.71766
$808$	−13.2507	−0.466160
$809$	−29.4875	−1.03673	−0.518363	−	0.855161i	$-0.673458\pi$
$809$	−29.4875	−1.03673	−0.518363	+	0.855161i	$0.673458\pi$
$810$	−6.15505	−0.216266
$811$	23.7370	0.833519	0.416760	−	0.909017i	$-0.363166\pi$
$811$	23.7370	0.833519	0.416760	+	0.909017i	$0.363166\pi$
$812$	−10.8322	−0.380136
$813$	48.8100	1.71184
$814$	67.8286	2.37739
$815$	−5.28573	−0.185151
$816$	348.476	12.1991
$817$	1.29166	0.0451896
$818$	67.9828	2.37696
$819$	−21.3265	−0.745210
$820$	−3.62557	−0.126610
$821$	−0.561119	−0.0195832	−0.00979159	−	0.999952i	$-0.503117\pi$
$821$	−0.561119	−0.0195832	−0.00979159	+	0.999952i	$0.503117\pi$
$822$	119.331	4.16214
$823$	−39.0654	−1.36173	−0.680867	−	0.732407i	$-0.738397\pi$
$823$	−39.0654	−1.36173	−0.680867	+	0.732407i	$0.738397\pi$
$824$	116.651	4.06372
$825$	−44.1396	−1.53675
$826$	22.1598	0.771038
$827$	−20.0574	−0.697463	−0.348731	−	0.937223i	$-0.613387\pi$
$827$	−20.0574	−0.697463	−0.348731	+	0.937223i	$0.613387\pi$
$828$	−135.631	−4.71350
$829$	−27.3742	−0.950744	−0.475372	−	0.879785i	$-0.657687\pi$
$829$	−27.3742	−0.950744	−0.475372	+	0.879785i	$0.657687\pi$
$830$	3.29437	0.114349
$831$	−7.46480	−0.258951
$832$	−377.738	−13.0957
$833$	43.4740	1.50629
$834$	22.0979	0.765187
$835$	6.37931	0.220765
$836$	19.9533	0.690100
$837$	2.44183	0.0844019
$838$	31.9092	1.10228
$839$	−27.5350	−0.950614	−0.475307	−	0.879820i	$-0.657663\pi$
$839$	−27.5350	−0.950614	−0.475307	+	0.879820i	$0.657663\pi$
$840$	−7.05931	−0.243569
$841$	−25.1239	−0.866342
$842$	−104.147	−3.58913
$843$	−75.2241	−2.59086
$844$	−72.7086	−2.50273
$845$	−9.81294	−0.337576
$846$	31.8551	1.09520
$847$	1.60771	0.0552415
$848$	128.621	4.41687
$849$	44.1802	1.51626
$850$	−98.2791	−3.37095
$851$	−46.3847	−1.59005
$852$	77.6360	2.65977
$853$	−9.26055	−0.317075	−0.158538	−	0.987353i	$-0.550678\pi$
$853$	−9.26055	−0.317075	−0.158538	+	0.987353i	$0.550678\pi$
$854$	10.2653	0.351270
$855$	0.843443	0.0288451
$856$	65.1769	2.22770
$857$	1.73563	0.0592881	0.0296441	−	0.999561i	$-0.490563\pi$
$857$	1.73563	0.0592881	0.0296441	+	0.999561i	$0.490563\pi$
$858$	177.025	6.04354
$859$	−32.2332	−1.09978	−0.549891	−	0.835236i	$-0.685331\pi$
$859$	−32.2332	−1.09978	−0.549891	+	0.835236i	$0.685331\pi$
$860$	2.23934	0.0763608
$861$	−5.16736	−0.176103
$862$	37.3898	1.27350
$863$	−0.533358	−0.0181557	−0.00907785	−	0.999959i	$-0.502890\pi$
$863$	−0.533358	−0.0181557	−0.00907785	+	0.999959i	$0.502890\pi$
$864$	25.0260	0.851401
$865$	0.940578	0.0319806
$866$	−75.0923	−2.55174
$867$	−82.8187	−2.81267
$868$	−17.7350	−0.601966
$869$	4.80931	0.163145
$870$	3.80077	0.128858
$871$	60.3174	2.04378
$872$	139.653	4.72924
$873$	−14.4408	−0.488747
$874$	−18.2216	−0.616353
$875$	2.49576	0.0843722
$876$	−24.9489	−0.842946
$877$	−16.3465	−0.551981	−0.275990	−	0.961160i	$-0.589006\pi$
$877$	−16.3465	−0.551981	−0.275990	+	0.961160i	$0.589006\pi$
$878$	68.3817	2.30777
$879$	47.0379	1.58655
$880$	19.0995	0.643844
$881$	−49.9842	−1.68401	−0.842005	−	0.539469i	$-0.818625\pi$
$881$	−49.9842	−1.68401	−0.842005	+	0.539469i	$0.818625\pi$
$882$	57.2893	1.92903
$883$	6.87718	0.231436	0.115718	−	0.993282i	$-0.463083\pi$
$883$	6.87718	0.231436	0.115718	+	0.993282i	$0.463083\pi$
$884$	295.161	9.92735
$885$	−5.82254	−0.195723
$886$	16.7880	0.564003
$887$	29.5622	0.992600	0.496300	−	0.868151i	$-0.334692\pi$
$887$	29.5622	0.992600	0.496300	+	0.868151i	$0.334692\pi$
$888$	189.044	6.34391
$889$	9.50645	0.318836
$890$	−3.77024	−0.126379
$891$	28.5703	0.957140
$892$	51.4777	1.72360
$893$	3.20477	0.107244
$894$	11.0288	0.368857
$895$	6.27030	0.209593
$896$	−79.5269	−2.65681
$897$	−121.059	−4.04204
$898$	7.79768	0.260212
$899$	6.34612	0.211655
$900$	−96.9832	−3.23277
$901$	−46.3195	−1.54313
$902$	22.4733	0.748280
$903$	3.19162	0.106211
$904$	11.6409	0.387171
$905$	6.31764	0.210005
$906$	−96.9570	−3.22118
$907$	−27.1515	−0.901550	−0.450775	−	0.892638i	$-0.648852\pi$
$907$	−27.1515	−0.901550	−0.450775	+	0.892638i	$0.648852\pi$
$908$	−30.0237	−0.996372
$909$	3.91198	0.129752
$910$	−4.96728	−0.164664
$911$	−48.8939	−1.61993	−0.809964	−	0.586480i	$-0.800513\pi$
$911$	−48.8939	−1.61993	−0.809964	+	0.586480i	$0.800513\pi$
$912$	46.1993	1.52981
$913$	−15.2917	−0.506080
$914$	−42.5816	−1.40847
$915$	−2.69723	−0.0891676
$916$	116.593	3.85234
$917$	16.1397	0.532978
$918$	−15.1145	−0.498852
$919$	−34.4212	−1.13545	−0.567725	−	0.823218i	$-0.692176\pi$
$919$	−34.4212	−1.13545	−0.567725	+	0.823218i	$0.692176\pi$
$920$	−20.9953	−0.692196
$921$	43.4897	1.43304
$922$	−78.1389	−2.57337
$923$	36.3066	1.19505
$924$	49.3035	1.62197
$925$	−33.1675	−1.09054
$926$	55.8706	1.83602
$927$	−34.4385	−1.13111
$928$	65.0406	2.13506
$929$	22.4675	0.737136	0.368568	−	0.929601i	$-0.379848\pi$
$929$	22.4675	0.737136	0.368568	+	0.929601i	$0.379848\pi$
$930$	6.22282	0.204054
$931$	5.76358	0.188894
$932$	90.8770	2.97678
$933$	3.23895	0.106038
$934$	−55.3292	−1.81043
$935$	−6.87818	−0.224941
$936$	258.506	8.44952
$937$	−24.6860	−0.806456	−0.403228	−	0.915100i	$-0.632112\pi$
$937$	−24.6860	−0.806456	−0.403228	+	0.915100i	$0.632112\pi$
$938$	22.4333	0.732474
$939$	−5.45986	−0.178176
$940$	5.55607	0.181219
$941$	20.9835	0.684042	0.342021	−	0.939692i	$-0.388889\pi$
$941$	20.9835	0.684042	0.342021	+	0.939692i	$0.388889\pi$
$942$	109.848	3.57905
$943$	−15.3684	−0.500465
$944$	−167.100	−5.43864
$945$	0.190477	0.00619623
$946$	−13.8807	−0.451300
$947$	26.4863	0.860688	0.430344	−	0.902665i	$-0.358392\pi$
$947$	26.4863	0.860688	0.430344	+	0.902665i	$0.358392\pi$
$948$	20.1682	0.655032
$949$	−11.6674	−0.378740
$950$	−13.0294	−0.422729
$951$	29.3183	0.950711
$952$	72.9587	2.36461
$953$	7.29640	0.236354	0.118177	−	0.992993i	$-0.462295\pi$
$953$	7.29640	0.236354	0.118177	+	0.992993i	$0.462295\pi$
$954$	−61.0391	−1.97621
$955$	4.63233	0.149899
$956$	73.0479	2.36254
$957$	−17.6423	−0.570294
$958$	−3.23490	−0.104515
$959$	15.5424	0.501890
$960$	36.9138	1.19139
$961$	−20.6098	−0.664832
$962$	133.021	4.28876
$963$	−19.2420	−0.620065
$964$	−101.460	−3.26780
$965$	1.12881	0.0363377
$966$	−45.0244	−1.44864
$967$	46.7256	1.50259	0.751296	−	0.659965i	$-0.229429\pi$
$967$	46.7256	1.50259	0.751296	+	0.659965i	$0.229429\pi$
$968$	−19.4875	−0.626352
$969$	−16.6374	−0.534472
$970$	−3.36348	−0.107995
$971$	−8.72295	−0.279933	−0.139966	−	0.990156i	$-0.544699\pi$
$971$	−8.72295	−0.279933	−0.139966	+	0.990156i	$0.544699\pi$
$972$	133.363	4.27763
$973$	2.87817	0.0922698
$974$	81.6525	2.61631
$975$	−86.5636	−2.77225
$976$	−77.4071	−2.47774
$977$	−23.0642	−0.737889	−0.368944	−	0.929451i	$-0.620281\pi$
$977$	−23.0642	−0.737889	−0.368944	+	0.929451i	$0.620281\pi$
$978$	137.398	4.39350
$979$	17.5006	0.559321
$980$	9.99225	0.319191
$981$	−41.2293	−1.31635
$982$	115.201	3.67622
$983$	29.5979	0.944026	0.472013	−	0.881592i	$-0.343528\pi$
$983$	29.5979	0.944026	0.472013	+	0.881592i	$0.343528\pi$
$984$	62.6351	1.99673
$985$	2.42192	0.0771687
$986$	−39.2814	−1.25097
$987$	7.91881	0.252058
$988$	39.1311	1.24493
$989$	9.49232	0.301838
$990$	−9.06395	−0.288071
$991$	30.6277	0.972921	0.486460	−	0.873703i	$-0.338288\pi$
$991$	30.6277	0.972921	0.486460	+	0.873703i	$0.338288\pi$
$992$	106.488	3.38099
$993$	7.79660	0.247418
$994$	13.5032	0.428296
$995$	−2.37511	−0.0752961
$996$	−64.1266	−2.03193
$997$	−38.7375	−1.22683	−0.613415	−	0.789761i	$-0.710205\pi$
$997$	−38.7375	−1.22683	−0.613415	+	0.789761i	$0.710205\pi$
$998$	−48.7064	−1.54177
$999$	−5.10087	−0.161385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1931.2.a.b.1.1	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1931.2.a.b.1.1	✓	101	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1931 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1931.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82191 q^{2} -2.51033 q^{3} +5.96320 q^{4} -0.272521 q^{5} +7.08394 q^{6} +0.922658 q^{7} -11.1838 q^{8} +3.30177 q^{9} +O(q^{10})\)	\(q-2.82191 q^{2} -2.51033 q^{3} +5.96320 q^{4} -0.272521 q^{5} +7.08394 q^{6} +0.922658 q^{7} -11.1838 q^{8} +3.30177 q^{9} +0.769032 q^{10} -3.56966 q^{11} -14.9696 q^{12} -7.00057 q^{13} -2.60366 q^{14} +0.684119 q^{15} +19.6334 q^{16} -7.07044 q^{17} -9.31730 q^{18} -0.937366 q^{19} -1.62510 q^{20} -2.31618 q^{21} +10.0733 q^{22} -6.88862 q^{23} +28.0751 q^{24} -4.92573 q^{25} +19.7550 q^{26} -0.757535 q^{27} +5.50199 q^{28} -1.96878 q^{29} -1.93052 q^{30} -3.22338 q^{31} -33.0361 q^{32} +8.96103 q^{33} +19.9522 q^{34} -0.251444 q^{35} +19.6891 q^{36} +6.73352 q^{37} +2.64517 q^{38} +17.5738 q^{39} +3.04783 q^{40} +2.23099 q^{41} +6.53605 q^{42} -1.37797 q^{43} -21.2866 q^{44} -0.899802 q^{45} +19.4391 q^{46} -3.41891 q^{47} -49.2863 q^{48} -6.14870 q^{49} +13.9000 q^{50} +17.7492 q^{51} -41.7458 q^{52} +6.55115 q^{53} +2.13770 q^{54} +0.972808 q^{55} -10.3188 q^{56} +2.35310 q^{57} +5.55572 q^{58} -8.51101 q^{59} +4.07954 q^{60} -3.94263 q^{61} +9.09611 q^{62} +3.04640 q^{63} +53.9582 q^{64} +1.90780 q^{65} -25.2873 q^{66} -8.61607 q^{67} -42.1625 q^{68} +17.2927 q^{69} +0.709553 q^{70} -5.18624 q^{71} -36.9264 q^{72} +1.66664 q^{73} -19.0014 q^{74} +12.3652 q^{75} -5.58970 q^{76} -3.29357 q^{77} -49.5916 q^{78} -1.34727 q^{79} -5.35051 q^{80} -8.00364 q^{81} -6.29565 q^{82} +4.28379 q^{83} -13.8118 q^{84} +1.92685 q^{85} +3.88852 q^{86} +4.94228 q^{87} +39.9224 q^{88} -4.90259 q^{89} +2.53916 q^{90} -6.45913 q^{91} -41.0783 q^{92} +8.09176 q^{93} +9.64788 q^{94} +0.255452 q^{95} +82.9315 q^{96} -4.37366 q^{97} +17.3511 q^{98} -11.7862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9}+O(q^{10}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9} + 14 q^{10} + 29 q^{11} + 15 q^{12} + 41 q^{13} + 4 q^{14} + 22 q^{15} + 187 q^{16} + 9 q^{17} + 11 q^{18} + 34 q^{19} + 42 q^{20} + 72 q^{21} + 17 q^{22} + 19 q^{23} + 33 q^{24} + 172 q^{25} + 28 q^{26} + 36 q^{27} + 47 q^{28} + 68 q^{29} + q^{30} + 76 q^{31} + 9 q^{32} + 8 q^{33} + 50 q^{34} + 7 q^{35} + 198 q^{36} + 141 q^{37} - 13 q^{38} + 42 q^{39} + 32 q^{40} + 35 q^{41} - 46 q^{42} + 45 q^{43} + 67 q^{44} + 106 q^{45} + 86 q^{46} - 5 q^{47} + 7 q^{48} + 203 q^{49} + 4 q^{50} + 5 q^{51} + 30 q^{52} + 47 q^{53} + 20 q^{54} + 11 q^{55} - 4 q^{56} + 19 q^{57} + 92 q^{58} + 30 q^{59} + 35 q^{60} + 153 q^{61} - 20 q^{62} + 19 q^{63} + 276 q^{64} - 7 q^{65} - 18 q^{66} + 39 q^{67} - 7 q^{68} + 55 q^{69} - 8 q^{70} + 47 q^{71} - 4 q^{72} + 86 q^{73} + 9 q^{74} + 11 q^{75} + 50 q^{76} + 15 q^{77} - 15 q^{78} + 89 q^{79} + 26 q^{80} + 201 q^{81} - 9 q^{82} - 15 q^{83} + 60 q^{84} + 239 q^{85} + 13 q^{86} - 22 q^{87} + 5 q^{88} + 14 q^{89} - 85 q^{90} + 58 q^{91} - 4 q^{92} + 86 q^{93} + 21 q^{94} - 10 q^{95} + 6 q^{96} + 46 q^{97} - 68 q^{98} + 100 q^{99}+O(q^{100}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9 + 14 * q^10 + 29 * q^11 + 15 * q^12 + 41 * q^13 + 4 * q^14 + 22 * q^15 + 187 * q^16 + 9 * q^17 + 11 * q^18 + 34 * q^19 + 42 * q^20 + 72 * q^21 + 17 * q^22 + 19 * q^23 + 33 * q^24 + 172 * q^25 + 28 * q^26 + 36 * q^27 + 47 * q^28 + 68 * q^29 + q^30 + 76 * q^31 + 9 * q^32 + 8 * q^33 + 50 * q^34 + 7 * q^35 + 198 * q^36 + 141 * q^37 - 13 * q^38 + 42 * q^39 + 32 * q^40 + 35 * q^41 - 46 * q^42 + 45 * q^43 + 67 * q^44 + 106 * q^45 + 86 * q^46 - 5 * q^47 + 7 * q^48 + 203 * q^49 + 4 * q^50 + 5 * q^51 + 30 * q^52 + 47 * q^53 + 20 * q^54 + 11 * q^55 - 4 * q^56 + 19 * q^57 + 92 * q^58 + 30 * q^59 + 35 * q^60 + 153 * q^61 - 20 * q^62 + 19 * q^63 + 276 * q^64 - 7 * q^65 - 18 * q^66 + 39 * q^67 - 7 * q^68 + 55 * q^69 - 8 * q^70 + 47 * q^71 - 4 * q^72 + 86 * q^73 + 9 * q^74 + 11 * q^75 + 50 * q^76 + 15 * q^77 - 15 * q^78 + 89 * q^79 + 26 * q^80 + 201 * q^81 - 9 * q^82 - 15 * q^83 + 60 * q^84 + 239 * q^85 + 13 * q^86 - 22 * q^87 + 5 * q^88 + 14 * q^89 - 85 * q^90 + 58 * q^91 - 4 * q^92 + 86 * q^93 + 21 * q^94 - 10 * q^95 + 6 * q^96 + 46 * q^97 - 68 * q^98 + 100 * q^99

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