LMFDB - Embedded newform 731.2.a.f.1.4

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			1.4
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)

$f(q)$	$=$	$q-1.94262 q^{2} +3.44146 q^{3} +1.77376 q^{4} +0.802251 q^{5} -6.68543 q^{6} -1.20527 q^{7} +0.439504 q^{8} +8.84362 q^{9} +O(q^{10})$	\(q-1.94262 q^{2} +3.44146 q^{3} +1.77376 q^{4} +0.802251 q^{5} -6.68543 q^{6} -1.20527 q^{7} +0.439504 q^{8} +8.84362 q^{9} -1.55846 q^{10} -3.00130 q^{11} +6.10431 q^{12} +2.47799 q^{13} +2.34137 q^{14} +2.76091 q^{15} -4.40130 q^{16} -1.00000 q^{17} -17.1798 q^{18} +6.97452 q^{19} +1.42300 q^{20} -4.14787 q^{21} +5.83037 q^{22} -3.49722 q^{23} +1.51253 q^{24} -4.35639 q^{25} -4.81378 q^{26} +20.1106 q^{27} -2.13785 q^{28} +10.3464 q^{29} -5.36339 q^{30} +3.97322 q^{31} +7.67103 q^{32} -10.3288 q^{33} +1.94262 q^{34} -0.966926 q^{35} +15.6864 q^{36} -1.02340 q^{37} -13.5488 q^{38} +8.52788 q^{39} +0.352592 q^{40} -5.47445 q^{41} +8.05772 q^{42} +1.00000 q^{43} -5.32357 q^{44} +7.09480 q^{45} +6.79375 q^{46} -5.14785 q^{47} -15.1469 q^{48} -5.54733 q^{49} +8.46280 q^{50} -3.44146 q^{51} +4.39534 q^{52} +4.20040 q^{53} -39.0671 q^{54} -2.40779 q^{55} -0.529719 q^{56} +24.0025 q^{57} -20.0990 q^{58} -12.2106 q^{59} +4.89718 q^{60} +4.73618 q^{61} -7.71844 q^{62} -10.6589 q^{63} -6.09926 q^{64} +1.98797 q^{65} +20.0650 q^{66} -7.94076 q^{67} -1.77376 q^{68} -12.0355 q^{69} +1.87837 q^{70} -3.68941 q^{71} +3.88681 q^{72} +8.84391 q^{73} +1.98807 q^{74} -14.9923 q^{75} +12.3711 q^{76} +3.61736 q^{77} -16.5664 q^{78} +7.36603 q^{79} -3.53095 q^{80} +42.6788 q^{81} +10.6348 q^{82} -7.11998 q^{83} -7.35732 q^{84} -0.802251 q^{85} -1.94262 q^{86} +35.6066 q^{87} -1.31908 q^{88} +2.45098 q^{89} -13.7825 q^{90} -2.98663 q^{91} -6.20321 q^{92} +13.6737 q^{93} +10.0003 q^{94} +5.59531 q^{95} +26.3995 q^{96} -3.37567 q^{97} +10.7763 q^{98} -26.5423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.94262	−1.37364	−0.686818	−	0.726829i	$-0.740993\pi$
$2$	−1.94262	−1.37364	−0.686818	+	0.726829i	$0.740993\pi$
$3$	3.44146	1.98693	0.993463	−	0.114155i	$-0.0364159\pi$
$3$	3.44146	1.98693	0.993463	+	0.114155i	$0.0364159\pi$
$4$	1.77376	0.886878
$5$	0.802251	0.358777	0.179389	−	0.983778i	$-0.442588\pi$
$5$	0.802251	0.358777	0.179389	+	0.983778i	$0.442588\pi$
$6$	−6.68543	−2.72931
$7$	−1.20527	−0.455548	−0.227774	−	0.973714i	$-0.573145\pi$
$7$	−1.20527	−0.455548	−0.227774	+	0.973714i	$0.573145\pi$
$8$	0.439504	0.155388
$9$	8.84362	2.94787
$10$	−1.55846	−0.492830
$11$	−3.00130	−0.904925	−0.452463	−	0.891783i	$-0.649454\pi$
$11$	−3.00130	−0.904925	−0.452463	+	0.891783i	$0.649454\pi$
$12$	6.10431	1.76216
$13$	2.47799	0.687270	0.343635	−	0.939103i	$-0.388342\pi$
$13$	2.47799	0.687270	0.343635	+	0.939103i	$0.388342\pi$
$14$	2.34137	0.625757
$15$	2.76091	0.712864
$16$	−4.40130	−1.10033
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−17.1798	−4.04931
$19$	6.97452	1.60006	0.800032	−	0.599958i	$-0.204816\pi$
$19$	6.97452	1.60006	0.800032	+	0.599958i	$0.204816\pi$
$20$	1.42300	0.318192
$21$	−4.14787	−0.905140
$22$	5.83037	1.24304
$23$	−3.49722	−0.729220	−0.364610	−	0.931160i	$-0.618798\pi$
$23$	−3.49722	−0.729220	−0.364610	+	0.931160i	$0.618798\pi$
$24$	1.51253	0.308745
$25$	−4.35639	−0.871279
$26$	−4.81378	−0.944059
$27$	20.1106	3.87028
$28$	−2.13785	−0.404016
$29$	10.3464	1.92127	0.960636	−	0.277809i	$-0.0896081\pi$
$29$	10.3464	1.92127	0.960636	+	0.277809i	$0.0896081\pi$
$30$	−5.36339	−0.979217
$31$	3.97322	0.713611	0.356806	−	0.934179i	$-0.383866\pi$
$31$	3.97322	0.713611	0.356806	+	0.934179i	$0.383866\pi$
$32$	7.67103	1.35606
$33$	−10.3288	−1.79802
$34$	1.94262	0.333156
$35$	−0.966926	−0.163440
$36$	15.6864	2.61441
$37$	−1.02340	−0.168246	−0.0841228	−	0.996455i	$-0.526809\pi$
$37$	−1.02340	−0.168246	−0.0841228	+	0.996455i	$0.526809\pi$
$38$	−13.5488	−2.19791
$39$	8.52788	1.36555
$40$	0.352592	0.0557497
$41$	−5.47445	−0.854965	−0.427483	−	0.904024i	$-0.640600\pi$
$41$	−5.47445	−0.854965	−0.427483	+	0.904024i	$0.640600\pi$
$42$	8.05772	1.24333
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−5.32357	−0.802559
$45$	7.09480	1.05763
$46$	6.79375	1.00168
$47$	−5.14785	−0.750890	−0.375445	−	0.926845i	$-0.622510\pi$
$47$	−5.14785	−0.750890	−0.375445	+	0.926845i	$0.622510\pi$
$48$	−15.1469	−2.18626
$49$	−5.54733	−0.792476
$50$	8.46280	1.19682
$51$	−3.44146	−0.481900
$52$	4.39534	0.609525
$53$	4.20040	0.576969	0.288485	−	0.957485i	$-0.406849\pi$
$53$	4.20040	0.576969	0.288485	+	0.957485i	$0.406849\pi$
$54$	−39.0671	−5.31636
$55$	−2.40779	−0.324667
$56$	−0.529719	−0.0707867
$57$	24.0025	3.17921
$58$	−20.0990	−2.63913
$59$	−12.2106	−1.58968	−0.794839	−	0.606820i	$-0.792445\pi$
$59$	−12.2106	−1.58968	−0.794839	+	0.606820i	$0.792445\pi$
$60$	4.89718	0.632224
$61$	4.73618	0.606406	0.303203	−	0.952926i	$-0.401944\pi$
$61$	4.73618	0.606406	0.303203	+	0.952926i	$0.401944\pi$
$62$	−7.71844	−0.980242
$63$	−10.6589	−1.34290
$64$	−6.09926	−0.762408
$65$	1.98797	0.246577
$66$	20.0650	2.46983
$67$	−7.94076	−0.970118	−0.485059	−	0.874481i	$-0.661202\pi$
$67$	−7.94076	−0.970118	−0.485059	+	0.874481i	$0.661202\pi$
$68$	−1.77376	−0.215100
$69$	−12.0355	−1.44891
$70$	1.87837	0.224508
$71$	−3.68941	−0.437853	−0.218926	−	0.975741i	$-0.570255\pi$
$71$	−3.68941	−0.437853	−0.218926	+	0.975741i	$0.570255\pi$
$72$	3.88681	0.458065
$73$	8.84391	1.03510	0.517551	−	0.855653i	$-0.326844\pi$
$73$	8.84391	1.03510	0.517551	+	0.855653i	$0.326844\pi$
$74$	1.98807	0.231108
$75$	−14.9923	−1.73117
$76$	12.3711	1.41906
$77$	3.61736	0.412237
$78$	−16.5664	−1.87578
$79$	7.36603	0.828743	0.414371	−	0.910108i	$-0.364002\pi$
$79$	7.36603	0.828743	0.414371	+	0.910108i	$0.364002\pi$
$80$	−3.53095	−0.394772
$81$	42.6788	4.74209
$82$	10.6348	1.17441
$83$	−7.11998	−0.781520	−0.390760	−	0.920493i	$-0.627788\pi$
$83$	−7.11998	−0.781520	−0.390760	+	0.920493i	$0.627788\pi$
$84$	−7.35732	−0.802749
$85$	−0.802251	−0.0870163
$86$	−1.94262	−0.209478
$87$	35.6066	3.81743
$88$	−1.31908	−0.140615
$89$	2.45098	0.259803	0.129902	−	0.991527i	$-0.458534\pi$
$89$	2.45098	0.259803	0.129902	+	0.991527i	$0.458534\pi$
$90$	−13.7825	−1.45280
$91$	−2.98663	−0.313084
$92$	−6.20321	−0.646729
$93$	13.6737	1.41789
$94$	10.0003	1.03145
$95$	5.59531	0.574067
$96$	26.3995	2.69439
$97$	−3.37567	−0.342747	−0.171374	−	0.985206i	$-0.554821\pi$
$97$	−3.37567	−0.342747	−0.171374	+	0.985206i	$0.554821\pi$
$98$	10.7763	1.08857
$99$	−26.5423	−2.66761
$100$	−7.72718	−0.772718
$101$	−8.38503	−0.834341	−0.417171	−	0.908828i	$-0.636978\pi$
$101$	−8.38503	−0.834341	−0.417171	+	0.908828i	$0.636978\pi$
$102$	6.68543	0.661956
$103$	19.5879	1.93005	0.965025	−	0.262158i	$-0.0844340\pi$
$103$	19.5879	1.93005	0.965025	+	0.262158i	$0.0844340\pi$
$104$	1.08908	0.106794
$105$	−3.32763	−0.324744
$106$	−8.15977	−0.792546
$107$	−16.4354	−1.58887	−0.794437	−	0.607346i	$-0.792234\pi$
$107$	−16.4354	−1.58887	−0.794437	+	0.607346i	$0.792234\pi$
$108$	35.6713	3.43247
$109$	6.81699	0.652949	0.326474	−	0.945206i	$-0.394139\pi$
$109$	6.81699	0.652949	0.326474	+	0.945206i	$0.394139\pi$
$110$	4.67742	0.445974
$111$	−3.52198	−0.334292
$112$	5.30474	0.501251
$113$	5.42837	0.510658	0.255329	−	0.966854i	$-0.417816\pi$
$113$	5.42837	0.510658	0.255329	+	0.966854i	$0.417816\pi$
$114$	−46.6276	−4.36708
$115$	−2.80564	−0.261628
$116$	18.3519	1.70394
$117$	21.9144	2.02599
$118$	23.7204	2.18364
$119$	1.20527	0.110487
$120$	1.21343	0.110771
$121$	−1.99221	−0.181110
$122$	−9.20058	−0.832981
$123$	−18.8401	−1.69875
$124$	7.04752	0.632886
$125$	−7.50617	−0.671373
$126$	20.7062	1.84465
$127$	14.1380	1.25455	0.627273	−	0.778800i	$-0.284171\pi$
$127$	14.1380	1.25455	0.627273	+	0.778800i	$0.284171\pi$
$128$	−3.49353	−0.308788
$129$	3.44146	0.303003
$130$	−3.86185	−0.338707
$131$	−7.07025	−0.617731	−0.308865	−	0.951106i	$-0.599949\pi$
$131$	−7.07025	−0.617731	−0.308865	+	0.951106i	$0.599949\pi$
$132$	−18.3208	−1.59462
$133$	−8.40615	−0.728906
$134$	15.4258	1.33259
$135$	16.1337	1.38857
$136$	−0.439504	−0.0376871
$137$	−17.5641	−1.50060	−0.750301	−	0.661097i	$-0.770091\pi$
$137$	−17.5641	−1.50060	−0.750301	+	0.661097i	$0.770091\pi$
$138$	23.3804	1.99027
$139$	−0.421635	−0.0357626	−0.0178813	−	0.999840i	$-0.505692\pi$
$139$	−0.421635	−0.0357626	−0.0178813	+	0.999840i	$0.505692\pi$
$140$	−1.71509	−0.144952
$141$	−17.7161	−1.49196
$142$	7.16711	0.601451
$143$	−7.43717	−0.621928
$144$	−38.9235	−3.24362
$145$	8.30038	0.689309
$146$	−17.1803	−1.42185
$147$	−19.0909	−1.57459
$148$	−1.81526	−0.149213
$149$	19.3659	1.58652	0.793260	−	0.608883i	$-0.208382\pi$
$149$	19.3659	1.58652	0.793260	+	0.608883i	$0.208382\pi$
$150$	29.1244	2.37799
$151$	−12.9895	−1.05707	−0.528536	−	0.848911i	$-0.677259\pi$
$151$	−12.9895	−1.05707	−0.528536	+	0.848911i	$0.677259\pi$
$152$	3.06533	0.248631
$153$	−8.84362	−0.714965
$154$	−7.02715	−0.566264
$155$	3.18752	0.256028
$156$	15.1264	1.21108
$157$	1.97924	0.157961	0.0789804	−	0.996876i	$-0.474834\pi$
$157$	1.97924	0.157961	0.0789804	+	0.996876i	$0.474834\pi$
$158$	−14.3094	−1.13839
$159$	14.4555	1.14640
$160$	6.15409	0.486523
$161$	4.21508	0.332195
$162$	−82.9086	−6.51391
$163$	3.21280	0.251646	0.125823	−	0.992053i	$-0.459843\pi$
$163$	3.21280	0.251646	0.125823	+	0.992053i	$0.459843\pi$
$164$	−9.71034	−0.758250
$165$	−8.28631	−0.645089
$166$	13.8314	1.07352
$167$	0.115037	0.00890185	0.00445093	−	0.999990i	$-0.498583\pi$
$167$	0.115037	0.00890185	0.00445093	+	0.999990i	$0.498583\pi$
$168$	−1.82301	−0.140648
$169$	−6.85958	−0.527660
$170$	1.55846	0.119529
$171$	61.6800	4.71679
$172$	1.77376	0.135248
$173$	−18.2384	−1.38664	−0.693321	−	0.720629i	$-0.743853\pi$
$173$	−18.2384	−1.38664	−0.693321	+	0.720629i	$0.743853\pi$
$174$	−69.1699	−5.24376
$175$	5.25062	0.396909
$176$	13.2096	0.995712
$177$	−42.0221	−3.15857
$178$	−4.76131	−0.356875
$179$	−8.40652	−0.628333	−0.314166	−	0.949368i	$-0.601725\pi$
$179$	−8.40652	−0.628333	−0.314166	+	0.949368i	$0.601725\pi$
$180$	12.5845	0.937990
$181$	−3.36388	−0.250035	−0.125017	−	0.992155i	$-0.539899\pi$
$181$	−3.36388	−0.250035	−0.125017	+	0.992155i	$0.539899\pi$
$182$	5.80188	0.430064
$183$	16.2994	1.20488
$184$	−1.53704	−0.113312
$185$	−0.821022	−0.0603627
$186$	−26.5627	−1.94767
$187$	3.00130	0.219477
$188$	−9.13102	−0.665948
$189$	−24.2386	−1.76310
$190$	−10.8695	−0.788559
$191$	−16.2090	−1.17284	−0.586421	−	0.810006i	$-0.699464\pi$
$191$	−16.2090	−1.17284	−0.586421	+	0.810006i	$0.699464\pi$
$192$	−20.9903	−1.51485
$193$	−16.1983	−1.16598	−0.582990	−	0.812479i	$-0.698117\pi$
$193$	−16.1983	−1.16598	−0.582990	+	0.812479i	$0.698117\pi$
$194$	6.55763	0.470810
$195$	6.84150	0.489930
$196$	−9.83962	−0.702830
$197$	−9.83408	−0.700649	−0.350325	−	0.936628i	$-0.613929\pi$
$197$	−9.83408	−0.700649	−0.350325	+	0.936628i	$0.613929\pi$
$198$	51.5616	3.66432
$199$	0.176515	0.0125128	0.00625642	−	0.999980i	$-0.498009\pi$
$199$	0.176515	0.0125128	0.00625642	+	0.999980i	$0.498009\pi$
$200$	−1.91465	−0.135386
$201$	−27.3278	−1.92755
$202$	16.2889	1.14608
$203$	−12.4701	−0.875232
$204$	−6.10431	−0.427387
$205$	−4.39188	−0.306742
$206$	−38.0517	−2.65119
$207$	−30.9281	−2.14965
$208$	−10.9064	−0.756220
$209$	−20.9326	−1.44794
$210$	6.46431	0.446080
$211$	0.0693590	0.00477487	0.00238743	−	0.999997i	$-0.499240\pi$
$211$	0.0693590	0.00477487	0.00238743	+	0.999997i	$0.499240\pi$
$212$	7.45049	0.511702
$213$	−12.6970	−0.869981
$214$	31.9278	2.18254
$215$	0.802251	0.0547130
$216$	8.83868	0.601396
$217$	−4.78879	−0.325084
$218$	−13.2428	−0.896915
$219$	30.4359	2.05667
$220$	−4.27084	−0.287940
$221$	−2.47799	−0.166687
$222$	6.84185	0.459195
$223$	−24.0227	−1.60868	−0.804338	−	0.594172i	$-0.797480\pi$
$223$	−24.0227	−1.60868	−0.804338	+	0.594172i	$0.797480\pi$
$224$	−9.24563	−0.617750
$225$	−38.5263	−2.56842
$226$	−10.5452	−0.701459
$227$	−16.9843	−1.12729	−0.563643	−	0.826019i	$-0.690601\pi$
$227$	−16.9843	−1.12729	−0.563643	+	0.826019i	$0.690601\pi$
$228$	42.5746	2.81957
$229$	−3.22382	−0.213036	−0.106518	−	0.994311i	$-0.533970\pi$
$229$	−3.22382	−0.213036	−0.106518	+	0.994311i	$0.533970\pi$
$230$	5.45029	0.359381
$231$	12.4490	0.819084
$232$	4.54727	0.298543
$233$	24.5864	1.61071	0.805353	−	0.592795i	$-0.201976\pi$
$233$	24.5864	1.61071	0.805353	+	0.592795i	$0.201976\pi$
$234$	−42.5712	−2.78297
$235$	−4.12986	−0.269403
$236$	−21.6586	−1.40985
$237$	25.3499	1.64665
$238$	−2.34137	−0.151768
$239$	−25.3352	−1.63880	−0.819399	−	0.573223i	$-0.805693\pi$
$239$	−25.3352	−1.63880	−0.819399	+	0.573223i	$0.805693\pi$
$240$	−12.1516	−0.784382
$241$	19.6585	1.26632	0.633158	−	0.774023i	$-0.281759\pi$
$241$	19.6585	1.26632	0.633158	+	0.774023i	$0.281759\pi$
$242$	3.87011	0.248780
$243$	86.5456	5.55190
$244$	8.40083	0.537808
$245$	−4.45035	−0.284323
$246$	36.5990	2.33347
$247$	17.2828	1.09968
$248$	1.74624	0.110887
$249$	−24.5031	−1.55282
$250$	14.5816	0.922222
$251$	13.9100	0.877994	0.438997	−	0.898489i	$-0.355334\pi$
$251$	13.9100	0.877994	0.438997	+	0.898489i	$0.355334\pi$
$252$	−18.9063	−1.19099
$253$	10.4962	0.659889
$254$	−27.4647	−1.72329
$255$	−2.76091	−0.172895
$256$	18.9851	1.18657
$257$	21.7055	1.35395	0.676975	−	0.736006i	$-0.263291\pi$
$257$	21.7055	1.35395	0.676975	+	0.736006i	$0.263291\pi$
$258$	−6.68543	−0.416217
$259$	1.23347	0.0766439
$260$	3.52617	0.218684
$261$	91.4994	5.66367
$262$	13.7348	0.848538
$263$	8.77487	0.541082	0.270541	−	0.962708i	$-0.412797\pi$
$263$	8.77487	0.541082	0.270541	+	0.962708i	$0.412797\pi$
$264$	−4.53956	−0.279391
$265$	3.36977	0.207004
$266$	16.3299	1.00125
$267$	8.43494	0.516210
$268$	−14.0850	−0.860377
$269$	−21.3796	−1.30354	−0.651770	−	0.758417i	$-0.725973\pi$
$269$	−21.3796	−1.30354	−0.651770	+	0.758417i	$0.725973\pi$
$270$	−31.3416	−1.90739
$271$	11.1523	0.677452	0.338726	−	0.940885i	$-0.390004\pi$
$271$	11.1523	0.677452	0.338726	+	0.940885i	$0.390004\pi$
$272$	4.40130	0.266868
$273$	−10.2784	−0.622075
$274$	34.1203	2.06128
$275$	13.0748	0.788442
$276$	−21.3481	−1.28500
$277$	−12.9595	−0.778663	−0.389331	−	0.921098i	$-0.627294\pi$
$277$	−12.9595	−0.778663	−0.389331	+	0.921098i	$0.627294\pi$
$278$	0.819075	0.0491248
$279$	35.1376	2.10364
$280$	−0.424968	−0.0253967
$281$	5.12056	0.305467	0.152733	−	0.988267i	$-0.451192\pi$
$281$	5.12056	0.305467	0.152733	+	0.988267i	$0.451192\pi$
$282$	34.4156	2.04942
$283$	−10.6290	−0.631831	−0.315915	−	0.948787i	$-0.602312\pi$
$283$	−10.6290	−0.631831	−0.315915	+	0.948787i	$0.602312\pi$
$284$	−6.54412	−0.388322
$285$	19.2560	1.14063
$286$	14.4476	0.854303
$287$	6.59817	0.389478
$288$	67.8397	3.99749
$289$	1.00000	0.0588235
$290$	−16.1245	−0.946861
$291$	−11.6172	−0.681013
$292$	15.6869	0.918009
$293$	2.33981	0.136693	0.0683467	−	0.997662i	$-0.478228\pi$
$293$	2.33981	0.136693	0.0683467	+	0.997662i	$0.478228\pi$
$294$	37.0863	2.16292
$295$	−9.79593	−0.570341
$296$	−0.449787	−0.0261434
$297$	−60.3578	−3.50232
$298$	−37.6206	−2.17930
$299$	−8.66605	−0.501171
$300$	−26.5928	−1.53533
$301$	−1.20527	−0.0694704
$302$	25.2336	1.45203
$303$	−28.8567	−1.65777
$304$	−30.6969	−1.76059
$305$	3.79960	0.217565
$306$	17.1798	0.982102
$307$	−17.9020	−1.02172	−0.510859	−	0.859664i	$-0.670673\pi$
$307$	−17.9020	−1.02172	−0.510859	+	0.859664i	$0.670673\pi$
$308$	6.41632	0.365604
$309$	67.4108	3.83487
$310$	−6.19212	−0.351689
$311$	−4.21724	−0.239138	−0.119569	−	0.992826i	$-0.538151\pi$
$311$	−4.21724	−0.239138	−0.119569	+	0.992826i	$0.538151\pi$
$312$	3.74804	0.212191
$313$	−16.7414	−0.946281	−0.473140	−	0.880987i	$-0.656880\pi$
$313$	−16.7414	−0.946281	−0.473140	+	0.880987i	$0.656880\pi$
$314$	−3.84491	−0.216981
$315$	−8.55113	−0.481802
$316$	13.0655	0.734994
$317$	−4.03762	−0.226775	−0.113388	−	0.993551i	$-0.536170\pi$
$317$	−4.03762	−0.226775	−0.113388	+	0.993551i	$0.536170\pi$
$318$	−28.0815	−1.57473
$319$	−31.0525	−1.73861
$320$	−4.89314	−0.273535
$321$	−56.5619	−3.15698
$322$	−8.18827	−0.456315
$323$	−6.97452	−0.388072
$324$	75.7018	4.20566
$325$	−10.7951	−0.598804
$326$	−6.24123	−0.345670
$327$	23.4604	1.29736
$328$	−2.40604	−0.132851
$329$	6.20453	0.342067
$330$	16.0971	0.886118
$331$	−23.4609	−1.28953	−0.644763	−	0.764382i	$-0.723044\pi$
$331$	−23.4609	−1.28953	−0.644763	+	0.764382i	$0.723044\pi$
$332$	−12.6291	−0.693113
$333$	−9.05055	−0.495967
$334$	−0.223473	−0.0122279
$335$	−6.37048	−0.348056
$336$	18.2560	0.995948
$337$	−27.5530	−1.50091	−0.750454	−	0.660923i	$-0.770165\pi$
$337$	−27.5530	−1.50091	−0.750454	+	0.660923i	$0.770165\pi$
$338$	13.3255	0.724814
$339$	18.6815	1.01464
$340$	−1.42300	−0.0771729
$341$	−11.9248	−0.645765
$342$	−119.821	−6.47915
$343$	15.1229	0.816559
$344$	0.439504	0.0236965
$345$	−9.65550	−0.519835
$346$	35.4302	1.90474
$347$	2.01215	0.108018	0.0540089	−	0.998540i	$-0.482800\pi$
$347$	2.01215	0.108018	0.0540089	+	0.998540i	$0.482800\pi$
$348$	63.1574	3.38559
$349$	−2.47849	−0.132671	−0.0663353	−	0.997797i	$-0.521131\pi$
$349$	−2.47849	−0.132671	−0.0663353	+	0.997797i	$0.521131\pi$
$350$	−10.1999	−0.545209
$351$	49.8337	2.65993
$352$	−23.0230	−1.22713
$353$	5.38067	0.286384	0.143192	−	0.989695i	$-0.454263\pi$
$353$	5.38067	0.286384	0.143192	+	0.989695i	$0.454263\pi$
$354$	81.6328	4.33873
$355$	−2.95983	−0.157092
$356$	4.34744	0.230414
$357$	4.14787	0.219529
$358$	16.3306	0.863101
$359$	34.9163	1.84281	0.921405	−	0.388604i	$-0.127043\pi$
$359$	34.9163	1.84281	0.921405	+	0.388604i	$0.127043\pi$
$360$	3.11819	0.164343
$361$	29.6439	1.56020
$362$	6.53472	0.343457
$363$	−6.85612	−0.359853
$364$	−5.29756	−0.277668
$365$	7.09503	0.371371
$366$	−31.6634	−1.65507
$367$	−6.72354	−0.350966	−0.175483	−	0.984482i	$-0.556149\pi$
$367$	−6.72354	−0.350966	−0.175483	+	0.984482i	$0.556149\pi$
$368$	15.3923	0.802379
$369$	−48.4140	−2.52033
$370$	1.59493	0.0829165
$371$	−5.06260	−0.262837
$372$	24.2537	1.25750
$373$	−6.55821	−0.339571	−0.169786	−	0.985481i	$-0.554308\pi$
$373$	−6.55821	−0.339571	−0.169786	+	0.985481i	$0.554308\pi$
$374$	−5.83037	−0.301481
$375$	−25.8322	−1.33397
$376$	−2.26250	−0.116679
$377$	25.6382	1.32043
$378$	47.0863	2.42186
$379$	−6.90454	−0.354663	−0.177331	−	0.984151i	$-0.556746\pi$
$379$	−6.90454	−0.354663	−0.177331	+	0.984151i	$0.556746\pi$
$380$	9.92472	0.509127
$381$	48.6554	2.49269
$382$	31.4879	1.61106
$383$	−3.07587	−0.157170	−0.0785849	−	0.996907i	$-0.525040\pi$
$383$	−3.07587	−0.157170	−0.0785849	+	0.996907i	$0.525040\pi$
$384$	−12.0228	−0.613538
$385$	2.90203	0.147901
$386$	31.4671	1.60163
$387$	8.84362	0.449547
$388$	−5.98762	−0.303975
$389$	21.7015	1.10031	0.550154	−	0.835063i	$-0.314569\pi$
$389$	21.7015	1.10031	0.550154	+	0.835063i	$0.314569\pi$
$390$	−13.2904	−0.672986
$391$	3.49722	0.176862
$392$	−2.43807	−0.123141
$393$	−24.3320	−1.22739
$394$	19.1038	0.962438
$395$	5.90940	0.297334
$396$	−47.0797	−2.36584
$397$	−23.4833	−1.17859	−0.589296	−	0.807917i	$-0.700595\pi$
$397$	−23.4833	−1.17859	−0.589296	+	0.807917i	$0.700595\pi$
$398$	−0.342902	−0.0171881
$399$	−28.9294	−1.44828
$400$	19.1738	0.958690
$401$	−10.0686	−0.502800	−0.251400	−	0.967883i	$-0.580891\pi$
$401$	−10.0686	−0.502800	−0.251400	+	0.967883i	$0.580891\pi$
$402$	53.0874	2.64776
$403$	9.84558	0.490443
$404$	−14.8730	−0.739959
$405$	34.2391	1.70136
$406$	24.2247	1.20225
$407$	3.07152	0.152250
$408$	−1.51253	−0.0748816
$409$	−2.05776	−0.101749	−0.0508747	−	0.998705i	$-0.516201\pi$
$409$	−2.05776	−0.101749	−0.0508747	+	0.998705i	$0.516201\pi$
$410$	8.53174	0.421353
$411$	−60.4461	−2.98158
$412$	34.7441	1.71172
$413$	14.7170	0.724175
$414$	60.0813	2.95284
$415$	−5.71201	−0.280392
$416$	19.0087	0.931978
$417$	−1.45104	−0.0710577
$418$	40.6640	1.98894
$419$	−5.46128	−0.266801	−0.133400	−	0.991062i	$-0.542590\pi$
$419$	−5.46128	−0.266801	−0.133400	+	0.991062i	$0.542590\pi$
$420$	−5.90241	−0.288008
$421$	6.11888	0.298216	0.149108	−	0.988821i	$-0.452360\pi$
$421$	6.11888	0.298216	0.149108	+	0.988821i	$0.452360\pi$
$422$	−0.134738	−0.00655893
$423$	−45.5256	−2.21353
$424$	1.84609	0.0896542
$425$	4.35639	0.211316
$426$	24.6653	1.19504
$427$	−5.70836	−0.276247
$428$	−29.1525	−1.40914
$429$	−25.5947	−1.23572
$430$	−1.55846	−0.0751559
$431$	−38.8954	−1.87353	−0.936763	−	0.349965i	$-0.886194\pi$
$431$	−38.8954	−1.87353	−0.936763	+	0.349965i	$0.886194\pi$
$432$	−88.5127	−4.25857
$433$	12.3783	0.594863	0.297432	−	0.954743i	$-0.403870\pi$
$433$	12.3783	0.594863	0.297432	+	0.954743i	$0.403870\pi$
$434$	9.30277	0.446547
$435$	28.5654	1.36961
$436$	12.0917	0.579086
$437$	−24.3914	−1.16680
$438$	−59.1253	−2.82512
$439$	25.8872	1.23553	0.617764	−	0.786363i	$-0.288039\pi$
$439$	25.8872	1.23553	0.617764	+	0.786363i	$0.288039\pi$
$440$	−1.05823	−0.0504493
$441$	−49.0585	−2.33612
$442$	4.81378	0.228968
$443$	−7.45703	−0.354294	−0.177147	−	0.984184i	$-0.556687\pi$
$443$	−7.45703	−0.354294	−0.177147	+	0.984184i	$0.556687\pi$
$444$	−6.24714	−0.296476
$445$	1.96630	0.0932115
$446$	46.6668	2.20974
$447$	66.6470	3.15230
$448$	7.35124	0.347313
$449$	23.3319	1.10110	0.550550	−	0.834802i	$-0.314418\pi$
$449$	23.3319	1.10110	0.550550	+	0.834802i	$0.314418\pi$
$450$	74.8418	3.52808
$451$	16.4305	0.773680
$452$	9.62861	0.452892
$453$	−44.7028	−2.10032
$454$	32.9939	1.54848
$455$	−2.39603	−0.112328
$456$	10.5492	0.494011
$457$	16.0067	0.748762	0.374381	−	0.927275i	$-0.377855\pi$
$457$	16.0067	0.748762	0.374381	+	0.927275i	$0.377855\pi$
$458$	6.26265	0.292634
$459$	−20.1106	−0.938682
$460$	−4.97653	−0.232032
$461$	38.1736	1.77792	0.888960	−	0.457985i	$-0.151428\pi$
$461$	38.1736	1.77792	0.888960	+	0.457985i	$0.151428\pi$
$462$	−24.1836	−1.12512
$463$	7.75088	0.360214	0.180107	−	0.983647i	$-0.442356\pi$
$463$	7.75088	0.360214	0.180107	+	0.983647i	$0.442356\pi$
$464$	−45.5375	−2.11402
$465$	10.9697	0.508708
$466$	−47.7619	−2.21253
$467$	11.3078	0.523263	0.261632	−	0.965168i	$-0.415739\pi$
$467$	11.3078	0.523263	0.261632	+	0.965168i	$0.415739\pi$
$468$	38.8708	1.79680
$469$	9.57073	0.441935
$470$	8.02274	0.370061
$471$	6.81148	0.313856
$472$	−5.36659	−0.247017
$473$	−3.00130	−0.138000
$474$	−49.2450	−2.26190
$475$	−30.3837	−1.39410
$476$	2.13785	0.0979882
$477$	37.1468	1.70083
$478$	49.2166	2.25111
$479$	33.0524	1.51020	0.755102	−	0.655608i	$-0.227587\pi$
$479$	33.0524	1.51020	0.755102	+	0.655608i	$0.227587\pi$
$480$	21.1790	0.966686
$481$	−2.53597	−0.115630
$482$	−38.1889	−1.73946
$483$	14.5060	0.660046
$484$	−3.53370	−0.160623
$485$	−2.70813	−0.122970
$486$	−168.125	−7.62630
$487$	15.0037	0.679882	0.339941	−	0.940447i	$-0.389593\pi$
$487$	15.0037	0.679882	0.339941	+	0.940447i	$0.389593\pi$
$488$	2.08157	0.0942282
$489$	11.0567	0.500002
$490$	8.64532	0.390556
$491$	28.6400	1.29251	0.646253	−	0.763123i	$-0.276335\pi$
$491$	28.6400	1.29251	0.646253	+	0.763123i	$0.276335\pi$
$492$	−33.4177	−1.50659
$493$	−10.3464	−0.465977
$494$	−33.5738	−1.51055
$495$	−21.2936	−0.957077
$496$	−17.4873	−0.785204
$497$	4.44673	0.199463
$498$	47.6001	2.13301
$499$	−6.04925	−0.270802	−0.135401	−	0.990791i	$-0.543232\pi$
$499$	−6.04925	−0.270802	−0.135401	+	0.990791i	$0.543232\pi$
$500$	−13.3141	−0.595426
$501$	0.395896	0.0176873
$502$	−27.0219	−1.20604
$503$	13.1798	0.587657	0.293829	−	0.955858i	$-0.405071\pi$
$503$	13.1798	0.587657	0.293829	+	0.955858i	$0.405071\pi$
$504$	−4.68464	−0.208670
$505$	−6.72689	−0.299343
$506$	−20.3901	−0.906448
$507$	−23.6070	−1.04842
$508$	25.0774	1.11263
$509$	−0.842630	−0.0373489	−0.0186745	−	0.999826i	$-0.505945\pi$
$509$	−0.842630	−0.0373489	−0.0186745	+	0.999826i	$0.505945\pi$
$510$	5.36339	0.237495
$511$	−10.6593	−0.471538
$512$	−29.8937	−1.32113
$513$	140.262	6.19270
$514$	−42.1654	−1.85984
$515$	15.7144	0.692458
$516$	6.10431	0.268727
$517$	15.4502	0.679500
$518$	−2.39615	−0.105281
$519$	−62.7667	−2.75515
$520$	0.873719	0.0383151
$521$	13.5495	0.593615	0.296808	−	0.954937i	$-0.404078\pi$
$521$	13.5495	0.593615	0.296808	+	0.954937i	$0.404078\pi$
$522$	−177.748	−7.77983
$523$	4.09225	0.178942	0.0894708	−	0.995989i	$-0.471482\pi$
$523$	4.09225	0.178942	0.0894708	+	0.995989i	$0.471482\pi$
$524$	−12.5409	−0.547852
$525$	18.0698	0.788629
$526$	−17.0462	−0.743250
$527$	−3.97322	−0.173076
$528$	45.4603	1.97841
$529$	−10.7695	−0.468239
$530$	−6.54618	−0.284348
$531$	−107.986	−4.68617
$532$	−14.9105	−0.646451
$533$	−13.5656	−0.587592
$534$	−16.3858	−0.709085
$535$	−13.1853	−0.570052
$536$	−3.48999	−0.150745
$537$	−28.9307	−1.24845
$538$	41.5324	1.79059
$539$	16.6492	0.717132
$540$	28.6173	1.23149
$541$	26.3756	1.13397	0.566987	−	0.823727i	$-0.308109\pi$
$541$	26.3756	1.13397	0.566987	+	0.823727i	$0.308109\pi$
$542$	−21.6646	−0.930574
$543$	−11.5766	−0.496801
$544$	−7.67103	−0.328893
$545$	5.46893	0.234263
$546$	19.9669	0.854506
$547$	−13.9707	−0.597342	−0.298671	−	0.954356i	$-0.596543\pi$
$547$	−13.9707	−0.597342	−0.298671	+	0.954356i	$0.596543\pi$
$548$	−31.1544	−1.33085
$549$	41.8850	1.78761
$550$	−25.3994	−1.08303
$551$	72.1609	3.07416
$552$	−5.28966	−0.225143
$553$	−8.87802	−0.377532
$554$	25.1754	1.06960
$555$	−2.82551	−0.119936
$556$	−0.747878	−0.0317171
$557$	−32.4144	−1.37344	−0.686721	−	0.726921i	$-0.740950\pi$
$557$	−32.4144	−1.37344	−0.686721	+	0.726921i	$0.740950\pi$
$558$	−68.2590	−2.88963
$559$	2.47799	0.104808
$560$	4.25573	0.179837
$561$	10.3288	0.436084
$562$	−9.94728	−0.419601
$563$	20.2268	0.852458	0.426229	−	0.904615i	$-0.359842\pi$
$563$	20.2268	0.852458	0.426229	+	0.904615i	$0.359842\pi$
$564$	−31.4240	−1.32319
$565$	4.35492	0.183213
$566$	20.6481	0.867906
$567$	−51.4394	−2.16025
$568$	−1.62151	−0.0680371
$569$	40.9212	1.71551	0.857753	−	0.514062i	$-0.171860\pi$
$569$	40.9212	1.71551	0.857753	+	0.514062i	$0.171860\pi$
$570$	−37.4070	−1.56681
$571$	8.70341	0.364226	0.182113	−	0.983278i	$-0.441706\pi$
$571$	8.70341	0.364226	0.182113	+	0.983278i	$0.441706\pi$
$572$	−13.1917	−0.551574
$573$	−55.7826	−2.33035
$574$	−12.8177	−0.535001
$575$	15.2352	0.635354
$576$	−53.9396	−2.24748
$577$	46.4282	1.93283	0.966416	−	0.256982i	$-0.0827282\pi$
$577$	46.4282	1.93283	0.966416	+	0.256982i	$0.0827282\pi$
$578$	−1.94262	−0.0808022
$579$	−55.7458	−2.31672
$580$	14.7229	0.611334
$581$	8.58148	0.356020
$582$	22.5678	0.935465
$583$	−12.6067	−0.522114
$584$	3.88693	0.160842
$585$	17.5808	0.726878
$586$	−4.54536	−0.187767
$587$	3.90916	0.161349	0.0806743	−	0.996741i	$-0.474293\pi$
$587$	3.90916	0.161349	0.0806743	+	0.996741i	$0.474293\pi$
$588$	−33.8626	−1.39647
$589$	27.7113	1.14182
$590$	19.0297	0.783441
$591$	−33.8436	−1.39214
$592$	4.50428	0.185125
$593$	−4.07064	−0.167161	−0.0835806	−	0.996501i	$-0.526636\pi$
$593$	−4.07064	−0.167161	−0.0835806	+	0.996501i	$0.526636\pi$
$594$	117.252	4.81091
$595$	0.966926	0.0396401
$596$	34.3505	1.40705
$597$	0.607470	0.0248621
$598$	16.8348	0.688426
$599$	7.67258	0.313493	0.156747	−	0.987639i	$-0.449899\pi$
$599$	7.67258	0.313493	0.156747	+	0.987639i	$0.449899\pi$
$600$	−6.58919	−0.269003
$601$	−0.320417	−0.0130701	−0.00653503	−	0.999979i	$-0.502080\pi$
$601$	−0.320417	−0.0130701	−0.00653503	+	0.999979i	$0.502080\pi$
$602$	2.34137	0.0954271
$603$	−70.2251	−2.85979
$604$	−23.0402	−0.937494
$605$	−1.59826	−0.0649783
$606$	56.0575	2.27718
$607$	−10.9568	−0.444724	−0.222362	−	0.974964i	$-0.571377\pi$
$607$	−10.9568	−0.444724	−0.222362	+	0.974964i	$0.571377\pi$
$608$	53.5017	2.16978
$609$	−42.9154	−1.73902
$610$	−7.38117	−0.298855
$611$	−12.7563	−0.516064
$612$	−15.6864	−0.634087
$613$	−11.2035	−0.452506	−0.226253	−	0.974069i	$-0.572648\pi$
$613$	−11.2035	−0.452506	−0.226253	+	0.974069i	$0.572648\pi$
$614$	34.7766	1.40347
$615$	−15.1145	−0.609474
$616$	1.58985	0.0640567
$617$	−14.3589	−0.578068	−0.289034	−	0.957319i	$-0.593334\pi$
$617$	−14.3589	−0.578068	−0.289034	+	0.957319i	$0.593334\pi$
$618$	−130.953	−5.26771
$619$	−5.41673	−0.217717	−0.108858	−	0.994057i	$-0.534719\pi$
$619$	−5.41673	−0.217717	−0.108858	+	0.994057i	$0.534719\pi$
$620$	5.65388	0.227065
$621$	−70.3310	−2.82229
$622$	8.19248	0.328488
$623$	−2.95408	−0.118353
$624$	−37.5338	−1.50255
$625$	15.7601	0.630405
$626$	32.5221	1.29985
$627$	−72.0386	−2.87695
$628$	3.51069	0.140092
$629$	1.02340	0.0408056
$630$	16.6116	0.661820
$631$	−10.0597	−0.400470	−0.200235	−	0.979748i	$-0.564171\pi$
$631$	−10.0597	−0.400470	−0.200235	+	0.979748i	$0.564171\pi$
$632$	3.23740	0.128777
$633$	0.238696	0.00948731
$634$	7.84354	0.311507
$635$	11.3422	0.450103
$636$	25.6405	1.01671
$637$	−13.7462	−0.544645
$638$	60.3232	2.38822
$639$	−32.6278	−1.29074
$640$	−2.80269	−0.110786
$641$	26.5720	1.04953	0.524766	−	0.851247i	$-0.324153\pi$
$641$	26.5720	1.04953	0.524766	+	0.851247i	$0.324153\pi$
$642$	109.878	4.33654
$643$	26.9566	1.06307	0.531533	−	0.847038i	$-0.321616\pi$
$643$	26.9566	1.06307	0.531533	+	0.847038i	$0.321616\pi$
$644$	7.47652	0.294616
$645$	2.76091	0.108711
$646$	13.5488	0.533071
$647$	−1.58124	−0.0621650	−0.0310825	−	0.999517i	$-0.509895\pi$
$647$	−1.58124	−0.0621650	−0.0310825	+	0.999517i	$0.509895\pi$
$648$	18.7575	0.736865
$649$	36.6475	1.43854
$650$	20.9707	0.822539
$651$	−16.4804	−0.645918
$652$	5.69872	0.223179
$653$	−9.95811	−0.389691	−0.194846	−	0.980834i	$-0.562421\pi$
$653$	−9.95811	−0.389691	−0.194846	+	0.980834i	$0.562421\pi$
$654$	−45.5745	−1.78210
$655$	−5.67212	−0.221628
$656$	24.0947	0.940740
$657$	78.2122	3.05135
$658$	−12.0530	−0.469875
$659$	29.2068	1.13774	0.568868	−	0.822429i	$-0.307381\pi$
$659$	29.2068	1.13774	0.568868	+	0.822429i	$0.307381\pi$
$660$	−14.6979	−0.572115
$661$	40.9977	1.59462	0.797312	−	0.603567i	$-0.206254\pi$
$661$	40.9977	1.59462	0.797312	+	0.603567i	$0.206254\pi$
$662$	45.5755	1.77134
$663$	−8.52788	−0.331196
$664$	−3.12926	−0.121439
$665$	−6.74384	−0.261515
$666$	17.5817	0.681279
$667$	−36.1835	−1.40103
$668$	0.204048	0.00789486
$669$	−82.6729	−3.19632
$670$	12.3754	0.478103
$671$	−14.2147	−0.548752
$672$	−31.8185	−1.22742
$673$	−38.1175	−1.46932	−0.734661	−	0.678434i	$-0.762659\pi$
$673$	−38.1175	−1.46932	−0.734661	+	0.678434i	$0.762659\pi$
$674$	53.5249	2.06170
$675$	−87.6096	−3.37210
$676$	−12.1672	−0.467971
$677$	39.9612	1.53583	0.767917	−	0.640550i	$-0.221293\pi$
$677$	39.9612	1.53583	0.767917	+	0.640550i	$0.221293\pi$
$678$	−36.2910	−1.39375
$679$	4.06858	0.156138
$680$	−0.352592	−0.0135213
$681$	−58.4507	−2.23983
$682$	23.1653	0.887046
$683$	−39.5902	−1.51488	−0.757439	−	0.652906i	$-0.773550\pi$
$683$	−39.5902	−1.51488	−0.757439	+	0.652906i	$0.773550\pi$
$684$	109.405	4.18322
$685$	−14.0908	−0.538382
$686$	−29.3779	−1.12166
$687$	−11.0946	−0.423287
$688$	−4.40130	−0.167798
$689$	10.4085	0.396534
$690$	18.7569	0.714064
$691$	23.4777	0.893134	0.446567	−	0.894750i	$-0.352647\pi$
$691$	23.4777	0.893134	0.446567	+	0.894750i	$0.352647\pi$
$692$	−32.3505	−1.22978
$693$	31.9906	1.21522
$694$	−3.90883	−0.148377
$695$	−0.338257	−0.0128308
$696$	15.6492	0.593183
$697$	5.47445	0.207360
$698$	4.81476	0.182241
$699$	84.6129	3.20035
$700$	9.31331	0.352010
$701$	46.0984	1.74111	0.870557	−	0.492068i	$-0.163759\pi$
$701$	46.0984	1.74111	0.870557	+	0.492068i	$0.163759\pi$
$702$	−96.8078	−3.65378
$703$	−7.13771	−0.269204
$704$	18.3057	0.689922
$705$	−14.2127	−0.535283
$706$	−10.4526	−0.393388
$707$	10.1062	0.380082
$708$	−74.5370	−2.80127
$709$	44.1793	1.65919	0.829595	−	0.558366i	$-0.188572\pi$
$709$	44.1793	1.65919	0.829595	+	0.558366i	$0.188572\pi$
$710$	5.74982	0.215787
$711$	65.1424	2.44303
$712$	1.07721	0.0403703
$713$	−13.8952	−0.520379
$714$	−8.05772	−0.301553
$715$	−5.96648	−0.223134
$716$	−14.9111	−0.557255
$717$	−87.1900	−3.25617
$718$	−67.8289	−2.53135
$719$	−49.0125	−1.82786	−0.913929	−	0.405875i	$-0.866967\pi$
$719$	−49.0125	−1.82786	−0.913929	+	0.405875i	$0.866967\pi$
$720$	−31.2264	−1.16374
$721$	−23.6086	−0.879230
$722$	−57.5866	−2.14315
$723$	67.6539	2.51607
$724$	−5.96670	−0.221751
$725$	−45.0729	−1.67396
$726$	13.3188	0.494307
$727$	−2.42185	−0.0898214	−0.0449107	−	0.998991i	$-0.514300\pi$
$727$	−2.42185	−0.0898214	−0.0449107	+	0.998991i	$0.514300\pi$
$728$	−1.31264	−0.0486496
$729$	169.806	6.28913
$730$	−13.7829	−0.510129
$731$	−1.00000	−0.0369863
$732$	28.9111	1.06859
$733$	18.6928	0.690434	0.345217	−	0.938523i	$-0.387805\pi$
$733$	18.6928	0.690434	0.345217	+	0.938523i	$0.387805\pi$
$734$	13.0613	0.482100
$735$	−15.3157	−0.564928
$736$	−26.8272	−0.988865
$737$	23.8326	0.877884
$738$	94.0498	3.46202
$739$	−13.9608	−0.513555	−0.256777	−	0.966471i	$-0.582661\pi$
$739$	−13.9608	−0.513555	−0.256777	+	0.966471i	$0.582661\pi$
$740$	−1.45629	−0.0535344
$741$	59.4778	2.18497
$742$	9.83469	0.361043
$743$	−54.2799	−1.99134	−0.995668	−	0.0929841i	$-0.970359\pi$
$743$	−54.2799	−1.99134	−0.995668	+	0.0929841i	$0.970359\pi$
$744$	6.00963	0.220324
$745$	15.5363	0.569207
$746$	12.7401	0.466448
$747$	−62.9664	−2.30382
$748$	5.32357	0.194649
$749$	19.8091	0.723808
$750$	50.1820	1.83239
$751$	29.2647	1.06788	0.533942	−	0.845521i	$-0.320710\pi$
$751$	29.2647	1.06788	0.533942	+	0.845521i	$0.320710\pi$
$752$	22.6572	0.826224
$753$	47.8708	1.74451
$754$	−49.8051	−1.81380
$755$	−10.4208	−0.379253
$756$	−42.9934	−1.56365
$757$	−25.1284	−0.913308	−0.456654	−	0.889644i	$-0.650952\pi$
$757$	−25.1284	−0.913308	−0.456654	+	0.889644i	$0.650952\pi$
$758$	13.4129	0.487178
$759$	36.1222	1.31115
$760$	2.45916	0.0892031
$761$	1.91562	0.0694412	0.0347206	−	0.999397i	$-0.488946\pi$
$761$	1.91562	0.0694412	0.0347206	+	0.999397i	$0.488946\pi$
$762$	−94.5187	−3.42405
$763$	−8.21629	−0.297450
$764$	−28.7508	−1.04017
$765$	−7.09480	−0.256513
$766$	5.97524	0.215894
$767$	−30.2576	−1.09254
$768$	65.3365	2.35763
$769$	1.95152	0.0703736	0.0351868	−	0.999381i	$-0.488797\pi$
$769$	1.95152	0.0703736	0.0351868	+	0.999381i	$0.488797\pi$
$770$	−5.63753	−0.203163
$771$	74.6984	2.69020
$772$	−28.7319	−1.03408
$773$	−3.95293	−0.142177	−0.0710886	−	0.997470i	$-0.522647\pi$
$773$	−3.95293	−0.142177	−0.0710886	+	0.997470i	$0.522647\pi$
$774$	−17.1798	−0.617514
$775$	−17.3089	−0.621754
$776$	−1.48362	−0.0532588
$777$	4.24492	0.152286
$778$	−42.1576	−1.51142
$779$	−38.1816	−1.36800
$780$	12.1352	0.434508
$781$	11.0730	0.396224
$782$	−6.79375	−0.242944
$783$	208.072	7.43587
$784$	24.4155	0.871981
$785$	1.58785	0.0566727
$786$	47.2677	1.68598
$787$	−39.7388	−1.41654	−0.708268	−	0.705944i	$-0.750523\pi$
$787$	−39.7388	−1.41654	−0.708268	+	0.705944i	$0.750523\pi$
$788$	−17.4433	−0.621391
$789$	30.1983	1.07509
$790$	−11.4797	−0.408429
$791$	−6.54264	−0.232629
$792$	−11.6655	−0.414514
$793$	11.7362	0.416764
$794$	45.6190	1.61896
$795$	11.5969	0.411301
$796$	0.313095	0.0110974
$797$	30.4408	1.07827	0.539133	−	0.842220i	$-0.318752\pi$
$797$	30.4408	1.07827	0.539133	+	0.842220i	$0.318752\pi$
$798$	56.1987	1.98941
$799$	5.14785	0.182118
$800$	−33.4180	−1.18151
$801$	21.6755	0.765867
$802$	19.5594	0.690665
$803$	−26.5432	−0.936689
$804$	−48.4728	−1.70950
$805$	3.38155	0.119184
$806$	−19.1262	−0.673691
$807$	−73.5771	−2.59004
$808$	−3.68525	−0.129647
$809$	−5.82633	−0.204843	−0.102421	−	0.994741i	$-0.532659\pi$
$809$	−5.82633	−0.204843	−0.102421	+	0.994741i	$0.532659\pi$
$810$	−66.5135	−2.33704
$811$	−30.4170	−1.06808	−0.534042	−	0.845458i	$-0.679328\pi$
$811$	−30.4170	−1.06808	−0.534042	+	0.845458i	$0.679328\pi$
$812$	−22.1190	−0.776224
$813$	38.3801	1.34605
$814$	−5.96679	−0.209136
$815$	2.57747	0.0902848
$816$	15.1469	0.530247
$817$	6.97452	0.244007
$818$	3.99743	0.139767
$819$	−26.4127	−0.922933
$820$	−7.79013	−0.272043
$821$	−29.2534	−1.02095	−0.510475	−	0.859893i	$-0.670530\pi$
$821$	−29.2534	−1.02095	−0.510475	+	0.859893i	$0.670530\pi$
$822$	117.423	4.09561
$823$	10.1462	0.353673	0.176837	−	0.984240i	$-0.443414\pi$
$823$	10.1462	0.353673	0.176837	+	0.984240i	$0.443414\pi$
$824$	8.60894	0.299907
$825$	44.9965	1.56658
$826$	−28.5894	−0.994753
$827$	19.7934	0.688284	0.344142	−	0.938918i	$-0.388170\pi$
$827$	19.7934	0.688284	0.344142	+	0.938918i	$0.388170\pi$
$828$	−54.8588	−1.90648
$829$	22.5717	0.783946	0.391973	−	0.919977i	$-0.371793\pi$
$829$	22.5717	0.783946	0.391973	+	0.919977i	$0.371793\pi$
$830$	11.0962	0.385156
$831$	−44.5997	−1.54715
$832$	−15.1139	−0.523980
$833$	5.54733	0.192204
$834$	2.81881	0.0976074
$835$	0.0922887	0.00319378
$836$	−37.1293	−1.28414
$837$	79.9037	2.76188
$838$	10.6092	0.366487
$839$	22.6829	0.783101	0.391550	−	0.920157i	$-0.371939\pi$
$839$	22.6829	0.783101	0.391550	+	0.920157i	$0.371939\pi$
$840$	−1.46251	−0.0504613
$841$	78.0474	2.69129
$842$	−11.8866	−0.409640
$843$	17.6222	0.606940
$844$	0.123026	0.00423473
$845$	−5.50311	−0.189313
$846$	88.4388	3.04059
$847$	2.40115	0.0825045
$848$	−18.4872	−0.634854
$849$	−36.5794	−1.25540
$850$	−8.46280	−0.290272
$851$	3.57904	0.122688
$852$	−22.5213	−0.771567
$853$	−13.4230	−0.459596	−0.229798	−	0.973238i	$-0.573806\pi$
$853$	−13.4230	−0.459596	−0.229798	+	0.973238i	$0.573806\pi$
$854$	11.0892	0.379463
$855$	49.4828	1.69228
$856$	−7.22344	−0.246892
$857$	−50.4826	−1.72445	−0.862226	−	0.506524i	$-0.830930\pi$
$857$	−50.4826	−1.72445	−0.862226	+	0.506524i	$0.830930\pi$
$858$	49.7207	1.69744
$859$	31.5186	1.07540	0.537700	−	0.843136i	$-0.319293\pi$
$859$	31.5186	1.07540	0.537700	+	0.843136i	$0.319293\pi$
$860$	1.42300	0.0485238
$861$	22.7073	0.773863
$862$	75.5588	2.57354
$863$	3.16300	0.107670	0.0538348	−	0.998550i	$-0.482856\pi$
$863$	3.16300	0.107670	0.0538348	+	0.998550i	$0.482856\pi$
$864$	154.269	5.24833
$865$	−14.6318	−0.497496
$866$	−24.0463	−0.817126
$867$	3.44146	0.116878
$868$	−8.49414	−0.288310
$869$	−22.1076	−0.749950
$870$	−55.4916	−1.88134
$871$	−19.6771	−0.666733
$872$	2.99609	0.101460
$873$	−29.8531	−1.01038
$874$	47.3831	1.60276
$875$	9.04694	0.305842
$876$	53.9859	1.82402
$877$	37.7653	1.27524	0.637622	−	0.770349i	$-0.279918\pi$
$877$	37.7653	1.27524	0.637622	+	0.770349i	$0.279918\pi$
$878$	−50.2889	−1.69717
$879$	8.05237	0.271600
$880$	10.5974	0.357239
$881$	−25.2658	−0.851225	−0.425613	−	0.904905i	$-0.639941\pi$
$881$	−25.2658	−0.851225	−0.425613	+	0.904905i	$0.639941\pi$
$882$	95.3019	3.20898
$883$	29.8552	1.00471	0.502353	−	0.864663i	$-0.332468\pi$
$883$	29.8552	1.00471	0.502353	+	0.864663i	$0.332468\pi$
$884$	−4.39534	−0.147831
$885$	−33.7123	−1.13323
$886$	14.4861	0.486671
$887$	26.0541	0.874810	0.437405	−	0.899265i	$-0.355898\pi$
$887$	26.0541	0.874810	0.437405	+	0.899265i	$0.355898\pi$
$888$	−1.54792	−0.0519449
$889$	−17.0401	−0.571506
$890$	−3.81976	−0.128039
$891$	−128.092	−4.29124
$892$	−42.6103	−1.42670
$893$	−35.9037	−1.20147
$894$	−129.470	−4.33011
$895$	−6.74414	−0.225432
$896$	4.21064	0.140668
$897$	−29.8238	−0.995789
$898$	−45.3249	−1.51251
$899$	41.1084	1.37104
$900$	−68.3363	−2.27788
$901$	−4.20040	−0.139936
$902$	−31.9181	−1.06276
$903$	−4.14787	−0.138033
$904$	2.38579	0.0793502
$905$	−2.69867	−0.0897069
$906$	86.8405	2.88508
$907$	−40.8512	−1.35644	−0.678220	−	0.734859i	$-0.737248\pi$
$907$	−40.8512	−1.35644	−0.678220	+	0.734859i	$0.737248\pi$
$908$	−30.1260	−0.999766
$909$	−74.1540	−2.45953
$910$	4.65456	0.154297
$911$	−13.7740	−0.456353	−0.228177	−	0.973620i	$-0.573276\pi$
$911$	−13.7740	−0.456353	−0.228177	+	0.973620i	$0.573276\pi$
$912$	−105.642	−3.49816
$913$	21.3692	0.707217
$914$	−31.0949	−1.02853
$915$	13.0762	0.432285
$916$	−5.71827	−0.188937
$917$	8.52154	0.281406
$918$	39.0671	1.28941
$919$	−23.7676	−0.784019	−0.392010	−	0.919961i	$-0.628220\pi$
$919$	−23.7676	−0.784019	−0.392010	+	0.919961i	$0.628220\pi$
$920$	−1.23309	−0.0406538
$921$	−61.6088	−2.03008
$922$	−74.1566	−2.44222
$923$	−9.14231	−0.300923
$924$	22.0815	0.726428
$925$	4.45832	0.146589
$926$	−15.0570	−0.494803
$927$	173.228	5.68955
$928$	79.3673	2.60536
$929$	−40.2941	−1.32200	−0.661002	−	0.750384i	$-0.729869\pi$
$929$	−40.2941	−1.32200	−0.661002	+	0.750384i	$0.729869\pi$
$930$	−21.3099	−0.698780
$931$	−38.6900	−1.26801
$932$	43.6102	1.42850
$933$	−14.5134	−0.475149
$934$	−21.9667	−0.718774
$935$	2.40779	0.0787432
$936$	9.63145	0.314814
$937$	3.58622	0.117157	0.0585784	−	0.998283i	$-0.481343\pi$
$937$	3.58622	0.117157	0.0585784	+	0.998283i	$0.481343\pi$
$938$	−18.5923	−0.607059
$939$	−57.6149	−1.88019
$940$	−7.32537	−0.238927
$941$	26.2020	0.854161	0.427081	−	0.904214i	$-0.359542\pi$
$941$	26.2020	0.854161	0.427081	+	0.904214i	$0.359542\pi$
$942$	−13.2321	−0.431125
$943$	19.1453	0.623458
$944$	53.7423	1.74916
$945$	−19.4454	−0.632560
$946$	5.83037	0.189562
$947$	13.9735	0.454079	0.227039	−	0.973886i	$-0.427095\pi$
$947$	13.9735	0.454079	0.227039	+	0.973886i	$0.427095\pi$
$948$	44.9645	1.46038
$949$	21.9151	0.711394
$950$	59.0239	1.91499
$951$	−13.8953	−0.450585
$952$	0.529719	0.0171683
$953$	−3.88307	−0.125785	−0.0628925	−	0.998020i	$-0.520033\pi$
$953$	−3.88307	−0.125785	−0.0628925	+	0.998020i	$0.520033\pi$
$954$	−72.1619	−2.33633
$955$	−13.0037	−0.420790
$956$	−44.9385	−1.45342
$957$	−106.866	−3.45449
$958$	−64.2081	−2.07447
$959$	21.1694	0.683596
$960$	−16.8395	−0.543493
$961$	−15.2135	−0.490759
$962$	4.92641	0.158834
$963$	−145.349	−4.68380
$964$	34.8694	1.12307
$965$	−12.9951	−0.418327
$966$	−28.1796	−0.906664
$967$	−34.7927	−1.11886	−0.559429	−	0.828878i	$-0.688980\pi$
$967$	−34.7927	−1.11886	−0.559429	+	0.828878i	$0.688980\pi$
$968$	−0.875586	−0.0281424
$969$	−24.0025	−0.771071
$970$	5.26086	0.168916
$971$	37.6992	1.20982	0.604912	−	0.796292i	$-0.293208\pi$
$971$	37.6992	1.20982	0.604912	+	0.796292i	$0.293208\pi$
$972$	153.511	4.92386
$973$	0.508182	0.0162916
$974$	−29.1464	−0.933911
$975$	−37.1508	−1.18978
$976$	−20.8454	−0.667244
$977$	−17.4325	−0.557716	−0.278858	−	0.960332i	$-0.589956\pi$
$977$	−17.4325	−0.557716	−0.278858	+	0.960332i	$0.589956\pi$
$978$	−21.4789	−0.686821
$979$	−7.35612	−0.235102
$980$	−7.89384	−0.252159
$981$	60.2869	1.92481
$982$	−55.6366	−1.77543
$983$	14.8451	0.473484	0.236742	−	0.971573i	$-0.423920\pi$
$983$	14.8451	0.473484	0.236742	+	0.971573i	$0.423920\pi$
$984$	−8.28029	−0.263966
$985$	−7.88940	−0.251377
$986$	20.0990	0.640083
$987$	21.3526	0.679661
$988$	30.6554	0.975278
$989$	−3.49722	−0.111205
$990$	41.3653	1.31468
$991$	36.5145	1.15992	0.579961	−	0.814644i	$-0.303068\pi$
$991$	36.5145	1.15992	0.579961	+	0.814644i	$0.303068\pi$
$992$	30.4787	0.967699
$993$	−80.7396	−2.56219
$994$	−8.63828	−0.273990
$995$	0.141610	0.00448932
$996$	−43.4626	−1.37716
$997$	−9.03858	−0.286255	−0.143127	−	0.989704i	$-0.545716\pi$
$997$	−9.03858	−0.286255	−0.143127	+	0.989704i	$0.545716\pi$
$998$	11.7514	0.371983
$999$	−20.5811	−0.651158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.4	✓	21
3.2	odd	2		6579.2.a.u.1.18		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.4	✓	21	1.1	even	1	trivial
6579.2.a.u.1.18		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)

\(f(q)\)	\(=\)	\(q-1.94262 q^{2} +3.44146 q^{3} +1.77376 q^{4} +0.802251 q^{5} -6.68543 q^{6} -1.20527 q^{7} +0.439504 q^{8} +8.84362 q^{9} +O(q^{10})\)	\(q-1.94262 q^{2} +3.44146 q^{3} +1.77376 q^{4} +0.802251 q^{5} -6.68543 q^{6} -1.20527 q^{7} +0.439504 q^{8} +8.84362 q^{9} -1.55846 q^{10} -3.00130 q^{11} +6.10431 q^{12} +2.47799 q^{13} +2.34137 q^{14} +2.76091 q^{15} -4.40130 q^{16} -1.00000 q^{17} -17.1798 q^{18} +6.97452 q^{19} +1.42300 q^{20} -4.14787 q^{21} +5.83037 q^{22} -3.49722 q^{23} +1.51253 q^{24} -4.35639 q^{25} -4.81378 q^{26} +20.1106 q^{27} -2.13785 q^{28} +10.3464 q^{29} -5.36339 q^{30} +3.97322 q^{31} +7.67103 q^{32} -10.3288 q^{33} +1.94262 q^{34} -0.966926 q^{35} +15.6864 q^{36} -1.02340 q^{37} -13.5488 q^{38} +8.52788 q^{39} +0.352592 q^{40} -5.47445 q^{41} +8.05772 q^{42} +1.00000 q^{43} -5.32357 q^{44} +7.09480 q^{45} +6.79375 q^{46} -5.14785 q^{47} -15.1469 q^{48} -5.54733 q^{49} +8.46280 q^{50} -3.44146 q^{51} +4.39534 q^{52} +4.20040 q^{53} -39.0671 q^{54} -2.40779 q^{55} -0.529719 q^{56} +24.0025 q^{57} -20.0990 q^{58} -12.2106 q^{59} +4.89718 q^{60} +4.73618 q^{61} -7.71844 q^{62} -10.6589 q^{63} -6.09926 q^{64} +1.98797 q^{65} +20.0650 q^{66} -7.94076 q^{67} -1.77376 q^{68} -12.0355 q^{69} +1.87837 q^{70} -3.68941 q^{71} +3.88681 q^{72} +8.84391 q^{73} +1.98807 q^{74} -14.9923 q^{75} +12.3711 q^{76} +3.61736 q^{77} -16.5664 q^{78} +7.36603 q^{79} -3.53095 q^{80} +42.6788 q^{81} +10.6348 q^{82} -7.11998 q^{83} -7.35732 q^{84} -0.802251 q^{85} -1.94262 q^{86} +35.6066 q^{87} -1.31908 q^{88} +2.45098 q^{89} -13.7825 q^{90} -2.98663 q^{91} -6.20321 q^{92} +13.6737 q^{93} +10.0003 q^{94} +5.59531 q^{95} +26.3995 q^{96} -3.37567 q^{97} +10.7763 q^{98} -26.5423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 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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