LMFDB - Embedded newform 143.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, 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("143.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.396339$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12676 q^{2} +2.23925 q^{3} -0.730419 q^{4} -0.792677 q^{5} -2.52310 q^{6} +3.80694 q^{7} +3.07652 q^{8} +2.01426 q^{9} +O(q^{10})$	\(q-1.12676 q^{2} +2.23925 q^{3} -0.730419 q^{4} -0.792677 q^{5} -2.52310 q^{6} +3.80694 q^{7} +3.07652 q^{8} +2.01426 q^{9} +0.893154 q^{10} +1.00000 q^{11} -1.63559 q^{12} -1.00000 q^{13} -4.28949 q^{14} -1.77501 q^{15} -2.00565 q^{16} -3.83887 q^{17} -2.26958 q^{18} +7.92509 q^{19} +0.578986 q^{20} +8.52470 q^{21} -1.12676 q^{22} -2.44658 q^{23} +6.88911 q^{24} -4.37166 q^{25} +1.12676 q^{26} -2.20732 q^{27} -2.78066 q^{28} -2.56768 q^{29} +2.00000 q^{30} -2.32547 q^{31} -3.89315 q^{32} +2.23925 q^{33} +4.32547 q^{34} -3.01767 q^{35} -1.47125 q^{36} -6.09238 q^{37} -8.92965 q^{38} -2.23925 q^{39} -2.43869 q^{40} -7.74628 q^{41} -9.60527 q^{42} +10.2535 q^{43} -0.730419 q^{44} -1.59666 q^{45} +2.75670 q^{46} -5.36036 q^{47} -4.49116 q^{48} +7.49277 q^{49} +4.92580 q^{50} -8.59620 q^{51} +0.730419 q^{52} +4.49277 q^{53} +2.48712 q^{54} -0.792677 q^{55} +11.7121 q^{56} +17.7463 q^{57} +2.89315 q^{58} -6.89315 q^{59} +1.29650 q^{60} -6.82120 q^{61} +2.62024 q^{62} +7.66816 q^{63} +8.39794 q^{64} +0.792677 q^{65} -2.52310 q^{66} -4.97423 q^{67} +2.80398 q^{68} -5.47851 q^{69} +3.40018 q^{70} +10.0032 q^{71} +6.19691 q^{72} +12.4208 q^{73} +6.86463 q^{74} -9.78927 q^{75} -5.78863 q^{76} +3.80694 q^{77} +2.52310 q^{78} +3.48936 q^{79} +1.58983 q^{80} -10.9855 q^{81} +8.72818 q^{82} +6.28545 q^{83} -6.22660 q^{84} +3.04298 q^{85} -11.5532 q^{86} -5.74969 q^{87} +3.07652 q^{88} +10.7320 q^{89} +1.79905 q^{90} -3.80694 q^{91} +1.78703 q^{92} -5.20732 q^{93} +6.03982 q^{94} -6.28203 q^{95} -8.71776 q^{96} +15.9747 q^{97} -8.44253 q^{98} +2.01426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 3 q^{4} - q^{6} + 6 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 3 * q^4 - q^6 + 6 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 3 q^{2} + 3 q^{4} - q^{6} + 6 q^{7} + 9 q^{8} + 2 q^{9} - 8 q^{10} + 4 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{14} - 10 q^{15} + 5 q^{16} + 6 q^{17} - 15 q^{18} + 8 q^{19} - 24 q^{20} - 2 q^{21} + 3 q^{22} - 4 q^{23} + 2 q^{24} + 12 q^{25} - 3 q^{26} - 12 q^{27} - q^{28} - 10 q^{29} + 8 q^{30} + 2 q^{31} - 4 q^{32} + 6 q^{34} - 6 q^{35} - 28 q^{36} + 12 q^{37} - 5 q^{38} - 30 q^{40} + 8 q^{41} - 13 q^{42} + 26 q^{43} + 3 q^{44} + 26 q^{45} + 6 q^{46} - 18 q^{47} - 21 q^{48} + 6 q^{49} + 29 q^{50} - 22 q^{51} - 3 q^{52} - 6 q^{53} - q^{54} + 33 q^{56} + 32 q^{57} - 16 q^{59} + 26 q^{60} - 12 q^{61} + 12 q^{62} + 22 q^{63} + 5 q^{64} - q^{66} + 2 q^{67} - 18 q^{68} - 4 q^{69} - 28 q^{70} - 14 q^{71} - 6 q^{72} + 22 q^{73} + 28 q^{74} - 36 q^{75} - 6 q^{76} + 6 q^{77} + q^{78} - 10 q^{79} - 26 q^{80} + 4 q^{81} + 42 q^{82} - 2 q^{83} + 5 q^{84} + 48 q^{85} + 2 q^{86} + 16 q^{87} + 9 q^{88} + 10 q^{89} + 24 q^{90} - 6 q^{91} + 17 q^{92} - 24 q^{93} - 14 q^{94} + 2 q^{95} - 8 q^{96} + 22 q^{97} - 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 3 * q^4 - q^6 + 6 * q^7 + 9 * q^8 + 2 * q^9 - 8 * q^10 + 4 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^14 - 10 * q^15 + 5 * q^16 + 6 * q^17 - 15 * q^18 + 8 * q^19 - 24 * q^20 - 2 * q^21 + 3 * q^22 - 4 * q^23 + 2 * q^24 + 12 * q^25 - 3 * q^26 - 12 * q^27 - q^28 - 10 * q^29 + 8 * q^30 + 2 * q^31 - 4 * q^32 + 6 * q^34 - 6 * q^35 - 28 * q^36 + 12 * q^37 - 5 * q^38 - 30 * q^40 + 8 * q^41 - 13 * q^42 + 26 * q^43 + 3 * q^44 + 26 * q^45 + 6 * q^46 - 18 * q^47 - 21 * q^48 + 6 * q^49 + 29 * q^50 - 22 * q^51 - 3 * q^52 - 6 * q^53 - q^54 + 33 * q^56 + 32 * q^57 - 16 * q^59 + 26 * q^60 - 12 * q^61 + 12 * q^62 + 22 * q^63 + 5 * q^64 - q^66 + 2 * q^67 - 18 * q^68 - 4 * q^69 - 28 * q^70 - 14 * q^71 - 6 * q^72 + 22 * q^73 + 28 * q^74 - 36 * q^75 - 6 * q^76 + 6 * q^77 + q^78 - 10 * q^79 - 26 * q^80 + 4 * q^81 + 42 * q^82 - 2 * q^83 + 5 * q^84 + 48 * q^85 + 2 * q^86 + 16 * q^87 + 9 * q^88 + 10 * q^89 + 24 * q^90 - 6 * q^91 + 17 * q^92 - 24 * q^93 - 14 * q^94 + 2 * q^95 - 8 * q^96 + 22 * q^97 - 14 * q^98 + 2 * 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 $

$2$	−1.12676	−0.796738	−0.398369	−	0.917225i	$-0.630424\pi$
$2$	−1.12676	−0.796738	−0.398369	+	0.917225i	$0.630424\pi$
$3$	2.23925	1.29283	0.646417	−	0.762984i	$-0.276267\pi$
$3$	2.23925	1.29283	0.646417	+	0.762984i	$0.276267\pi$
$4$	−0.730419	−0.365209
$5$	−0.792677	−0.354496	−0.177248	−	0.984166i	$-0.556719\pi$
$5$	−0.792677	−0.354496	−0.177248	+	0.984166i	$0.556719\pi$
$6$	−2.52310	−1.03005
$7$	3.80694	1.43889	0.719443	−	0.694551i	$-0.244397\pi$
$7$	3.80694	1.43889	0.719443	+	0.694551i	$0.244397\pi$
$8$	3.07652	1.08771
$9$	2.01426	0.671420
$10$	0.893154	0.282440
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.63559	−0.472155
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.28949	−1.14642
$15$	−1.77501	−0.458304
$16$	−2.00565	−0.501413
$17$	−3.83887	−0.931062	−0.465531	−	0.885031i	$-0.654137\pi$
$17$	−3.83887	−0.931062	−0.465531	+	0.885031i	$0.654137\pi$
$18$	−2.26958	−0.534945
$19$	7.92509	1.81814	0.909070	−	0.416644i	$-0.136794\pi$
$19$	7.92509	1.81814	0.909070	+	0.416644i	$0.136794\pi$
$20$	0.578986	0.129465
$21$	8.52470	1.86024
$22$	−1.12676	−0.240225
$23$	−2.44658	−0.510147	−0.255073	−	0.966922i	$-0.582100\pi$
$23$	−2.44658	−0.510147	−0.255073	+	0.966922i	$0.582100\pi$
$24$	6.88911	1.40623
$25$	−4.37166	−0.874333
$26$	1.12676	0.220975
$27$	−2.20732	−0.424799
$28$	−2.78066	−0.525495
$29$	−2.56768	−0.476807	−0.238403	−	0.971166i	$-0.576624\pi$
$29$	−2.56768	−0.476807	−0.238403	+	0.971166i	$0.576624\pi$
$30$	2.00000	0.365148
$31$	−2.32547	−0.417667	−0.208834	−	0.977951i	$-0.566967\pi$
$31$	−2.32547	−0.417667	−0.208834	+	0.977951i	$0.566967\pi$
$32$	−3.89315	−0.688219
$33$	2.23925	0.389804
$34$	4.32547	0.741812
$35$	−3.01767	−0.510080
$36$	−1.47125	−0.245209
$37$	−6.09238	−1.00158	−0.500791	−	0.865568i	$-0.666957\pi$
$37$	−6.09238	−1.00158	−0.500791	+	0.865568i	$0.666957\pi$
$38$	−8.92965	−1.44858
$39$	−2.23925	−0.358568
$40$	−2.43869	−0.385590
$41$	−7.74628	−1.20977	−0.604883	−	0.796314i	$-0.706780\pi$
$41$	−7.74628	−1.20977	−0.604883	+	0.796314i	$0.706780\pi$
$42$	−9.60527	−1.48212
$43$	10.2535	1.56365	0.781823	−	0.623500i	$-0.214290\pi$
$43$	10.2535	1.56365	0.781823	+	0.623500i	$0.214290\pi$
$44$	−0.730419	−0.110115
$45$	−1.59666	−0.238016
$46$	2.75670	0.406453
$47$	−5.36036	−0.781889	−0.390944	−	0.920414i	$-0.627852\pi$
$47$	−5.36036	−0.781889	−0.390944	+	0.920414i	$0.627852\pi$
$48$	−4.49116	−0.648244
$49$	7.49277	1.07040
$50$	4.92580	0.696614
$51$	−8.59620	−1.20371
$52$	0.730419	0.101291
$53$	4.49277	0.617129	0.308565	−	0.951203i	$-0.400151\pi$
$53$	4.49277	0.617129	0.308565	+	0.951203i	$0.400151\pi$
$54$	2.48712	0.338454
$55$	−0.792677	−0.106885
$56$	11.7121	1.56510
$57$	17.7463	2.35055
$58$	2.89315	0.379890
$59$	−6.89315	−0.897412	−0.448706	−	0.893679i	$-0.648115\pi$
$59$	−6.89315	−0.897412	−0.448706	+	0.893679i	$0.648115\pi$
$60$	1.29650	0.167377
$61$	−6.82120	−0.873365	−0.436682	−	0.899616i	$-0.643847\pi$
$61$	−6.82120	−0.873365	−0.436682	+	0.899616i	$0.643847\pi$
$62$	2.62024	0.332771
$63$	7.66816	0.966097
$64$	8.39794	1.04974
$65$	0.792677	0.0983195
$66$	−2.52310	−0.310572
$67$	−4.97423	−0.607699	−0.303850	−	0.952720i	$-0.598272\pi$
$67$	−4.97423	−0.607699	−0.303850	+	0.952720i	$0.598272\pi$
$68$	2.80398	0.340033
$69$	−5.47851	−0.659535
$70$	3.40018	0.406400
$71$	10.0032	1.18716	0.593581	−	0.804774i	$-0.297714\pi$
$71$	10.0032	1.18716	0.593581	+	0.804774i	$0.297714\pi$
$72$	6.19691	0.730313
$73$	12.4208	1.45375	0.726873	−	0.686772i	$-0.240973\pi$
$73$	12.4208	1.45375	0.726873	+	0.686772i	$0.240973\pi$
$74$	6.86463	0.797998
$75$	−9.78927	−1.13037
$76$	−5.78863	−0.664001
$77$	3.80694	0.433841
$78$	2.52310	0.285684
$79$	3.48936	0.392583	0.196292	−	0.980546i	$-0.437110\pi$
$79$	3.48936	0.392583	0.196292	+	0.980546i	$0.437110\pi$
$80$	1.58983	0.177749
$81$	−10.9855	−1.22062
$82$	8.72818	0.963866
$83$	6.28545	0.689917	0.344959	−	0.938618i	$-0.387893\pi$
$83$	6.28545	0.689917	0.344959	+	0.938618i	$0.387893\pi$
$84$	−6.22660	−0.679378
$85$	3.04298	0.330058
$86$	−11.5532	−1.24582
$87$	−5.74969	−0.616432
$88$	3.07652	0.327958
$89$	10.7320	1.13759	0.568796	−	0.822479i	$-0.307409\pi$
$89$	10.7320	1.13759	0.568796	+	0.822479i	$0.307409\pi$
$90$	1.79905	0.189636
$91$	−3.80694	−0.399075
$92$	1.78703	0.186310
$93$	−5.20732	−0.539974
$94$	6.03982	0.622960
$95$	−6.28203	−0.644523
$96$	−8.71776	−0.889753
$97$	15.9747	1.62198	0.810992	−	0.585057i	$-0.198928\pi$
$97$	15.9747	1.62198	0.810992	+	0.585057i	$0.198928\pi$
$98$	−8.44253	−0.852824
$99$	2.01426	0.202441
$100$	3.19314	0.319314
$101$	−10.6315	−1.05788	−0.528939	−	0.848660i	$-0.677410\pi$
$101$	−10.6315	−1.05788	−0.528939	+	0.848660i	$0.677410\pi$
$102$	9.68583	0.959040
$103$	−0.418058	−0.0411924	−0.0205962	−	0.999788i	$-0.506556\pi$
$103$	−0.418058	−0.0411924	−0.0205962	+	0.999788i	$0.506556\pi$
$104$	−3.07652	−0.301677
$105$	−6.75733	−0.659448
$106$	−5.06226	−0.491690
$107$	−6.80398	−0.657766	−0.328883	−	0.944371i	$-0.606672\pi$
$107$	−6.80398	−0.657766	−0.328883	+	0.944371i	$0.606672\pi$
$108$	1.61227	0.155141
$109$	−12.9278	−1.23826	−0.619131	−	0.785288i	$-0.712515\pi$
$109$	−12.9278	−1.23826	−0.619131	+	0.785288i	$0.712515\pi$
$110$	0.893154	0.0851589
$111$	−13.6424	−1.29488
$112$	−7.63539	−0.721476
$113$	10.5852	0.995767	0.497884	−	0.867244i	$-0.334111\pi$
$113$	10.5852	0.995767	0.497884	+	0.867244i	$0.334111\pi$
$114$	−19.9957	−1.87277
$115$	1.93935	0.180845
$116$	1.87548	0.174134
$117$	−2.01426	−0.186218
$118$	7.76691	0.715002
$119$	−14.6143	−1.33969
$120$	−5.46084	−0.498504
$121$	1.00000	0.0909091
$122$	7.68583	0.695842
$123$	−17.3459	−1.56403
$124$	1.69857	0.152536
$125$	7.42870	0.664443
$126$	−8.64015	−0.769726
$127$	−16.8964	−1.49931	−0.749655	−	0.661829i	$-0.769781\pi$
$127$	−16.8964	−1.49931	−0.749655	+	0.661829i	$0.769781\pi$
$128$	−1.67613	−0.148151
$129$	22.9602	2.02154
$130$	−0.893154	−0.0783348
$131$	5.74969	0.502353	0.251177	−	0.967941i	$-0.419183\pi$
$131$	5.74969	0.502353	0.251177	+	0.967941i	$0.419183\pi$
$132$	−1.63559	−0.142360
$133$	30.1703	2.61610
$134$	5.60475	0.484177
$135$	1.74969	0.150590
$136$	−11.8103	−1.01273
$137$	−0.0719578	−0.00614777	−0.00307388	−	0.999995i	$-0.500978\pi$
$137$	−0.0719578	−0.00614777	−0.00307388	+	0.999995i	$0.500978\pi$
$138$	6.17295	0.525476
$139$	5.77821	0.490102	0.245051	−	0.969510i	$-0.421195\pi$
$139$	5.77821	0.490102	0.245051	+	0.969510i	$0.421195\pi$
$140$	2.20416	0.186286
$141$	−12.0032	−1.01085
$142$	−11.2712	−0.945857
$143$	−1.00000	−0.0836242
$144$	−4.03990	−0.336659
$145$	2.03534	0.169026
$146$	−13.9952	−1.15825
$147$	16.7782	1.38384
$148$	4.44999	0.365787
$149$	12.8816	1.05531	0.527653	−	0.849460i	$-0.323072\pi$
$149$	12.8816	1.05531	0.527653	+	0.849460i	$0.323072\pi$
$150$	11.0301	0.900606
$151$	−1.58535	−0.129014	−0.0645071	−	0.997917i	$-0.520548\pi$
$151$	−1.58535	−0.129014	−0.0645071	+	0.997917i	$0.520548\pi$
$152$	24.3817	1.97761
$153$	−7.73248	−0.625134
$154$	−4.28949	−0.345657
$155$	1.84335	0.148061
$156$	1.63559	0.130952
$157$	−13.3489	−1.06535	−0.532677	−	0.846318i	$-0.678814\pi$
$157$	−13.3489	−1.06535	−0.532677	+	0.846318i	$0.678814\pi$
$158$	−3.93166	−0.312786
$159$	10.0605	0.797846
$160$	3.08601	0.243971
$161$	−9.31397	−0.734043
$162$	12.3780	0.972510
$163$	−23.2310	−1.81959	−0.909794	−	0.415059i	$-0.863761\pi$
$163$	−23.2310	−1.81959	−0.909794	+	0.415059i	$0.863761\pi$
$164$	5.65803	0.441818
$165$	−1.77501	−0.138184
$166$	−7.08217	−0.549683
$167$	6.19582	0.479447	0.239723	−	0.970841i	$-0.422943\pi$
$167$	6.19582	0.479447	0.239723	+	0.970841i	$0.422943\pi$
$168$	26.2264	2.02341
$169$	1.00000	0.0769231
$170$	−3.42870	−0.262969
$171$	15.9632	1.22074
$172$	−7.48936	−0.571058
$173$	−20.1037	−1.52845	−0.764227	−	0.644947i	$-0.776880\pi$
$173$	−20.1037	−1.52845	−0.764227	+	0.644947i	$0.776880\pi$
$174$	6.47851	0.491134
$175$	−16.6426	−1.25807
$176$	−2.00565	−0.151182
$177$	−15.4355	−1.16021
$178$	−12.0924	−0.906362
$179$	−11.8787	−0.887855	−0.443928	−	0.896063i	$-0.646415\pi$
$179$	−11.8787	−0.887855	−0.443928	+	0.896063i	$0.646415\pi$
$180$	1.16623	0.0869255
$181$	−0.135569	−0.0100767	−0.00503836	−	0.999987i	$-0.501604\pi$
$181$	−0.135569	−0.0100767	−0.00503836	+	0.999987i	$0.501604\pi$
$182$	4.28949	0.317958
$183$	−15.2744	−1.12912
$184$	−7.52694	−0.554893
$185$	4.82929	0.355057
$186$	5.86739	0.430218
$187$	−3.83887	−0.280726
$188$	3.91531	0.285553
$189$	−8.40314	−0.611238
$190$	7.07833	0.513516
$191$	21.9740	1.58999	0.794993	−	0.606619i	$-0.207475\pi$
$191$	21.9740	1.58999	0.794993	+	0.606619i	$0.207475\pi$
$192$	18.8051	1.35714
$193$	5.59686	0.402871	0.201435	−	0.979502i	$-0.435439\pi$
$193$	5.59686	0.402871	0.201435	+	0.979502i	$0.435439\pi$
$194$	−17.9996	−1.29230
$195$	1.77501	0.127111
$196$	−5.47286	−0.390918
$197$	26.5073	1.88857	0.944283	−	0.329135i	$-0.106757\pi$
$197$	26.5073	1.88857	0.944283	+	0.329135i	$0.106757\pi$
$198$	−2.26958	−0.161292
$199$	−8.65390	−0.613459	−0.306729	−	0.951797i	$-0.599235\pi$
$199$	−8.65390	−0.613459	−0.306729	+	0.951797i	$0.599235\pi$
$200$	−13.4495	−0.951023
$201$	−11.1386	−0.785654
$202$	11.9792	0.842851
$203$	−9.77501	−0.686071
$204$	6.27883	0.439606
$205$	6.14030	0.428857
$206$	0.471049	0.0328196
$207$	−4.92804	−0.342523
$208$	2.00565	0.139067
$209$	7.92509	0.548190
$210$	7.61387	0.525407
$211$	1.70305	0.117243	0.0586213	−	0.998280i	$-0.481330\pi$
$211$	1.70305	0.117243	0.0586213	+	0.998280i	$0.481330\pi$
$212$	−3.28160	−0.225381
$213$	22.3997	1.53480
$214$	7.66643	0.524067
$215$	−8.12773	−0.554306
$216$	−6.79087	−0.462060
$217$	−8.85292	−0.600976
$218$	14.5665	0.986570
$219$	27.8134	1.87945
$220$	0.578986	0.0390352
$221$	3.83887	0.258230
$222$	15.3717	1.03168
$223$	5.03489	0.337161	0.168581	−	0.985688i	$-0.446082\pi$
$223$	5.03489	0.337161	0.168581	+	0.985688i	$0.446082\pi$
$224$	−14.8210	−0.990269
$225$	−8.80567	−0.587044
$226$	−11.9269	−0.793365
$227$	24.3751	1.61783	0.808915	−	0.587925i	$-0.200055\pi$
$227$	24.3751	1.61783	0.808915	+	0.587925i	$0.200055\pi$
$228$	−12.9622	−0.858444
$229$	−17.8787	−1.18146	−0.590729	−	0.806870i	$-0.701160\pi$
$229$	−17.8787	−1.18146	−0.590729	+	0.806870i	$0.701160\pi$
$230$	−2.18517	−0.144086
$231$	8.52470	0.560884
$232$	−7.89952	−0.518629
$233$	8.24221	0.539965	0.269983	−	0.962865i	$-0.412982\pi$
$233$	8.24221	0.539965	0.269983	+	0.962865i	$0.412982\pi$
$234$	2.26958	0.148367
$235$	4.24903	0.277176
$236$	5.03489	0.327743
$237$	7.81356	0.507545
$238$	16.4668	1.06738
$239$	−23.2099	−1.50132	−0.750661	−	0.660688i	$-0.770265\pi$
$239$	−23.2099	−1.50132	−0.750661	+	0.660688i	$0.770265\pi$
$240$	3.56004	0.229800
$241$	9.65390	0.621862	0.310931	−	0.950432i	$-0.399359\pi$
$241$	9.65390	0.621862	0.310931	+	0.950432i	$0.399359\pi$
$242$	−1.12676	−0.0724307
$243$	−17.9774	−1.15325
$244$	4.98233	0.318961
$245$	−5.93935	−0.379451
$246$	19.5446	1.24612
$247$	−7.92509	−0.504261
$248$	−7.15436	−0.454302
$249$	14.0747	0.891949
$250$	−8.37034	−0.529387
$251$	24.6028	1.55292	0.776458	−	0.630169i	$-0.217014\pi$
$251$	24.6028	1.55292	0.776458	+	0.630169i	$0.217014\pi$
$252$	−5.60097	−0.352828
$253$	−2.44658	−0.153815
$254$	19.0381	1.19456
$255$	6.81401	0.426710
$256$	−14.9073	−0.931706
$257$	14.3927	0.897795	0.448897	−	0.893583i	$-0.351817\pi$
$257$	14.3927	0.897795	0.448897	+	0.893583i	$0.351817\pi$
$258$	−25.8706	−1.61063
$259$	−23.1933	−1.44116
$260$	−0.578986	−0.0359072
$261$	−5.17198	−0.320138
$262$	−6.47851	−0.400244
$263$	25.8615	1.59469	0.797343	−	0.603526i	$-0.206238\pi$
$263$	25.8615	1.59469	0.797343	+	0.603526i	$0.206238\pi$
$264$	6.88911	0.423995
$265$	−3.56131	−0.218770
$266$	−33.9946	−2.08434
$267$	24.0317	1.47072
$268$	3.63327	0.221937
$269$	−25.2506	−1.53955	−0.769777	−	0.638313i	$-0.779633\pi$
$269$	−25.2506	−1.53955	−0.769777	+	0.638313i	$0.779633\pi$
$270$	−1.97148	−0.119980
$271$	2.31712	0.140755	0.0703777	−	0.997520i	$-0.477580\pi$
$271$	2.31712	0.140755	0.0703777	+	0.997520i	$0.477580\pi$
$272$	7.69943	0.466847
$273$	−8.52470	−0.515938
$274$	0.0810789	0.00489816
$275$	−4.37166	−0.263621
$276$	4.00160	0.240868
$277$	8.23412	0.494740	0.247370	−	0.968921i	$-0.420434\pi$
$277$	8.23412	0.494740	0.247370	+	0.968921i	$0.420434\pi$
$278$	−6.51064	−0.390482
$279$	−4.68410	−0.280430
$280$	−9.28392	−0.554820
$281$	9.07175	0.541175	0.270588	−	0.962695i	$-0.412782\pi$
$281$	9.07175	0.541175	0.270588	+	0.962695i	$0.412782\pi$
$282$	13.5247	0.805384
$283$	31.6488	1.88133	0.940663	−	0.339342i	$-0.110204\pi$
$283$	31.6488	1.88133	0.940663	+	0.339342i	$0.110204\pi$
$284$	−7.30653	−0.433563
$285$	−14.0671	−0.833261
$286$	1.12676	0.0666265
$287$	−29.4896	−1.74072
$288$	−7.84182	−0.462084
$289$	−2.26309	−0.133123
$290$	−2.29334	−0.134669
$291$	35.7714	2.09696
$292$	−9.07239	−0.530921
$293$	−1.24394	−0.0726716	−0.0363358	−	0.999340i	$-0.511569\pi$
$293$	−1.24394	−0.0726716	−0.0363358	+	0.999340i	$0.511569\pi$
$294$	−18.9050	−1.10256
$295$	5.46405	0.318129
$296$	−18.7433	−1.08943
$297$	−2.20732	−0.128082
$298$	−14.5145	−0.840802
$299$	2.44658	0.141489
$300$	7.15026	0.412820
$301$	39.0345	2.24991
$302$	1.78631	0.102791
$303$	−23.8067	−1.36766
$304$	−15.8950	−0.911639
$305$	5.40701	0.309604
$306$	8.71262	0.498068
$307$	6.54237	0.373393	0.186696	−	0.982418i	$-0.440222\pi$
$307$	6.54237	0.373393	0.186696	+	0.982418i	$0.440222\pi$
$308$	−2.78066	−0.158443
$309$	−0.936137	−0.0532550
$310$	−2.07701	−0.117966
$311$	−19.8816	−1.12738	−0.563692	−	0.825985i	$-0.690620\pi$
$311$	−19.8816	−1.12738	−0.563692	+	0.825985i	$0.690620\pi$
$312$	−6.88911	−0.390019
$313$	−12.2774	−0.693957	−0.346978	−	0.937873i	$-0.612792\pi$
$313$	−12.2774	−0.693957	−0.346978	+	0.937873i	$0.612792\pi$
$314$	15.0409	0.848808
$315$	−6.07837	−0.342478
$316$	−2.54869	−0.143375
$317$	18.8325	1.05774	0.528869	−	0.848703i	$-0.322616\pi$
$317$	18.8325	1.05774	0.528869	+	0.848703i	$0.322616\pi$
$318$	−11.3357	−0.635674
$319$	−2.56768	−0.143763
$320$	−6.65686	−0.372130
$321$	−15.2358	−0.850382
$322$	10.4946	0.584840
$323$	−30.4234	−1.69280
$324$	8.02404	0.445780
$325$	4.37166	0.242496
$326$	26.1756	1.44973
$327$	−28.9487	−1.60087
$328$	−23.8316	−1.31588
$329$	−20.4066	−1.12505
$330$	2.00000	0.110096
$331$	−11.0096	−0.605141	−0.302571	−	0.953127i	$-0.597845\pi$
$331$	−11.0096	−0.605141	−0.302571	+	0.953127i	$0.597845\pi$
$332$	−4.59101	−0.251964
$333$	−12.2716	−0.672482
$334$	−6.98118	−0.381993
$335$	3.94296	0.215427
$336$	−17.0976	−0.932749
$337$	19.5532	1.06513	0.532566	−	0.846389i	$-0.321228\pi$
$337$	19.5532	1.06513	0.532566	+	0.846389i	$0.321228\pi$
$338$	−1.12676	−0.0612875
$339$	23.7028	1.28736
$340$	−2.22265	−0.120540
$341$	−2.32547	−0.125931
$342$	−17.9866	−0.972605
$343$	1.87594	0.101291
$344$	31.5451	1.70080
$345$	4.34269	0.233802
$346$	22.6520	1.21778
$347$	4.57578	0.245641	0.122820	−	0.992429i	$-0.460806\pi$
$347$	4.57578	0.245641	0.122820	+	0.992429i	$0.460806\pi$
$348$	4.19968	0.225127
$349$	1.12386	0.0601588	0.0300794	−	0.999548i	$-0.490424\pi$
$349$	1.12386	0.0601588	0.0300794	+	0.999548i	$0.490424\pi$
$350$	18.7522	1.00235
$351$	2.20732	0.117818
$352$	−3.89315	−0.207506
$353$	−20.2133	−1.07584	−0.537922	−	0.842994i	$-0.680791\pi$
$353$	−20.2133	−1.07584	−0.537922	+	0.842994i	$0.680791\pi$
$354$	17.3921	0.924379
$355$	−7.92931	−0.420844
$356$	−7.83887	−0.415459
$357$	−32.7252	−1.73200
$358$	13.3844	0.707387
$359$	3.11474	0.164390	0.0821948	−	0.996616i	$-0.473807\pi$
$359$	3.11474	0.164390	0.0821948	+	0.996616i	$0.473807\pi$
$360$	−4.91215	−0.258893
$361$	43.8070	2.30563
$362$	0.152753	0.00802851
$363$	2.23925	0.117530
$364$	2.78066	0.145746
$365$	−9.84569	−0.515347
$366$	17.2105	0.899609
$367$	22.0324	1.15008	0.575041	−	0.818125i	$-0.304986\pi$
$367$	22.0324	1.15008	0.575041	+	0.818125i	$0.304986\pi$
$368$	4.90698	0.255794
$369$	−15.6030	−0.812261
$370$	−5.44144	−0.282887
$371$	17.1037	0.887979
$372$	3.80353	0.197204
$373$	2.26034	0.117036	0.0585179	−	0.998286i	$-0.481363\pi$
$373$	2.26034	0.117036	0.0585179	+	0.998286i	$0.481363\pi$
$374$	4.32547	0.223665
$375$	16.6348	0.859015
$376$	−16.4912	−0.850471
$377$	2.56768	0.132242
$378$	9.46830	0.486997
$379$	−18.4623	−0.948346	−0.474173	−	0.880432i	$-0.657253\pi$
$379$	−18.4623	−0.948346	−0.474173	+	0.880432i	$0.657253\pi$
$380$	4.58851	0.235386
$381$	−37.8353	−1.93836
$382$	−24.7594	−1.26680
$383$	21.5451	1.10090	0.550452	−	0.834867i	$-0.314455\pi$
$383$	21.5451	1.10090	0.550452	+	0.834867i	$0.314455\pi$
$384$	−3.75329	−0.191534
$385$	−3.01767	−0.153795
$386$	−6.30630	−0.320982
$387$	20.6532	1.04986
$388$	−11.6682	−0.592364
$389$	−31.2769	−1.58580	−0.792902	−	0.609349i	$-0.791431\pi$
$389$	−31.2769	−1.58580	−0.792902	+	0.609349i	$0.791431\pi$
$390$	−2.00000	−0.101274
$391$	9.39209	0.474978
$392$	23.0516	1.16428
$393$	12.8750	0.649459
$394$	−29.8673	−1.50469
$395$	−2.76593	−0.139169
$396$	−1.47125	−0.0739332
$397$	−7.68222	−0.385559	−0.192780	−	0.981242i	$-0.561750\pi$
$397$	−7.68222	−0.385559	−0.192780	+	0.981242i	$0.561750\pi$
$398$	9.75084	0.488766
$399$	67.5590	3.38218
$400$	8.76803	0.438402
$401$	−18.5264	−0.925166	−0.462583	−	0.886576i	$-0.653077\pi$
$401$	−18.5264	−0.925166	−0.462583	+	0.886576i	$0.653077\pi$
$402$	12.5505	0.625960
$403$	2.32547	0.115840
$404$	7.76548	0.386347
$405$	8.70798	0.432703
$406$	11.0141	0.546618
$407$	−6.09238	−0.301988
$408$	−26.4464	−1.30929
$409$	14.8131	0.732461	0.366230	−	0.930524i	$-0.380648\pi$
$409$	14.8131	0.732461	0.366230	+	0.930524i	$0.380648\pi$
$410$	−6.91863	−0.341687
$411$	−0.161132	−0.00794804
$412$	0.305357	0.0150439
$413$	−26.2418	−1.29127
$414$	5.55271	0.272901
$415$	−4.98233	−0.244573
$416$	3.89315	0.190878
$417$	12.9389	0.633620
$418$	−8.92965	−0.436763
$419$	−2.56789	−0.125449	−0.0627247	−	0.998031i	$-0.519979\pi$
$419$	−2.56789	−0.125449	−0.0627247	+	0.998031i	$0.519979\pi$
$420$	4.93568	0.240837
$421$	−3.92574	−0.191329	−0.0956645	−	0.995414i	$-0.530498\pi$
$421$	−3.92574	−0.191329	−0.0956645	+	0.995414i	$0.530498\pi$
$422$	−1.91892	−0.0934116
$423$	−10.7972	−0.524976
$424$	13.8221	0.671260
$425$	16.7822	0.814058
$426$	−25.2391	−1.22284
$427$	−25.9679	−1.25667
$428$	4.96975	0.240222
$429$	−2.23925	−0.108112
$430$	9.15797	0.441637
$431$	5.71455	0.275260	0.137630	−	0.990484i	$-0.456051\pi$
$431$	5.71455	0.275260	0.137630	+	0.990484i	$0.456051\pi$
$432$	4.42712	0.213000
$433$	−15.3127	−0.735881	−0.367941	−	0.929849i	$-0.619937\pi$
$433$	−15.3127	−0.735881	−0.367941	+	0.929849i	$0.619937\pi$
$434$	9.97510	0.478820
$435$	4.55765	0.218523
$436$	9.44273	0.452225
$437$	−19.3893	−0.927518
$438$	−31.3389	−1.49743
$439$	17.1226	0.817218	0.408609	−	0.912709i	$-0.366014\pi$
$439$	17.1226	0.817218	0.408609	+	0.912709i	$0.366014\pi$
$440$	−2.43869	−0.116260
$441$	15.0924	0.718685
$442$	−4.32547	−0.205742
$443$	17.3108	0.822461	0.411231	−	0.911531i	$-0.365099\pi$
$443$	17.3108	0.822461	0.411231	+	0.911531i	$0.365099\pi$
$444$	9.96466	0.472902
$445$	−8.50703	−0.403272
$446$	−5.67310	−0.268629
$447$	28.8453	1.36434
$448$	31.9704	1.51046
$449$	35.2310	1.66265	0.831326	−	0.555785i	$-0.187582\pi$
$449$	35.2310	1.66265	0.831326	+	0.555785i	$0.187582\pi$
$450$	9.92185	0.467720
$451$	−7.74628	−0.364758
$452$	−7.73159	−0.363663
$453$	−3.55001	−0.166794
$454$	−27.4648	−1.28899
$455$	3.01767	0.141471
$456$	54.5968	2.55673
$457$	18.0062	0.842293	0.421146	−	0.906993i	$-0.361628\pi$
$457$	18.0062	0.842293	0.421146	+	0.906993i	$0.361628\pi$
$458$	20.1449	0.941311
$459$	8.47362	0.395515
$460$	−1.41653	−0.0660462
$461$	−16.1569	−0.752502	−0.376251	−	0.926518i	$-0.622787\pi$
$461$	−16.1569	−0.752502	−0.376251	+	0.926518i	$0.622787\pi$
$462$	−9.60527	−0.446877
$463$	38.3170	1.78074	0.890370	−	0.455237i	$-0.150445\pi$
$463$	38.3170	1.78074	0.890370	+	0.455237i	$0.150445\pi$
$464$	5.14988	0.239077
$465$	4.12773	0.191419
$466$	−9.28697	−0.430211
$467$	19.7348	0.913217	0.456608	−	0.889668i	$-0.349064\pi$
$467$	19.7348	0.913217	0.456608	+	0.889668i	$0.349064\pi$
$468$	1.47125	0.0680087
$469$	−18.9366	−0.874411
$470$	−4.78763	−0.220837
$471$	−29.8915	−1.37733
$472$	−21.2069	−0.976127
$473$	10.2535	0.471457
$474$	−8.80398	−0.404380
$475$	−34.6458	−1.58966
$476$	10.6746	0.489268
$477$	9.04960	0.414353
$478$	26.1519	1.19616
$479$	20.8357	0.952008	0.476004	−	0.879443i	$-0.342085\pi$
$479$	20.8357	0.952008	0.476004	+	0.879443i	$0.342085\pi$
$480$	6.91037	0.315414
$481$	6.09238	0.277789
$482$	−10.8776	−0.495461
$483$	−20.8563	−0.948996
$484$	−0.730419	−0.0332008
$485$	−12.6628	−0.574987
$486$	20.2562	0.918840
$487$	22.6428	1.02605	0.513023	−	0.858375i	$-0.328526\pi$
$487$	22.6428	1.02605	0.513023	+	0.858375i	$0.328526\pi$
$488$	−20.9855	−0.949971
$489$	−52.0200	−2.35243
$490$	6.69220	0.302323
$491$	−41.8530	−1.88880	−0.944399	−	0.328801i	$-0.893355\pi$
$491$	−41.8530	−1.88880	−0.944399	+	0.328801i	$0.893355\pi$
$492$	12.6698	0.571197
$493$	9.85700	0.443937
$494$	8.92965	0.401764
$495$	−1.59666	−0.0717644
$496$	4.66409	0.209424
$497$	38.0816	1.70819
$498$	−15.8588	−0.710649
$499$	26.5854	1.19013	0.595063	−	0.803679i	$-0.297127\pi$
$499$	26.5854	1.19013	0.595063	+	0.803679i	$0.297127\pi$
$500$	−5.42606	−0.242661
$501$	13.8740	0.619845
$502$	−27.7214	−1.23727
$503$	−16.7090	−0.745018	−0.372509	−	0.928029i	$-0.621502\pi$
$503$	−16.7090	−0.745018	−0.372509	+	0.928029i	$0.621502\pi$
$504$	23.5912	1.05084
$505$	8.42738	0.375014
$506$	2.75670	0.122550
$507$	2.23925	0.0994488
$508$	12.3414	0.547562
$509$	−23.7429	−1.05238	−0.526192	−	0.850366i	$-0.676381\pi$
$509$	−23.7429	−1.05238	−0.526192	+	0.850366i	$0.676381\pi$
$510$	−7.67774	−0.339976
$511$	47.2852	2.09178
$512$	20.1492	0.890476
$513$	−17.4932	−0.772345
$514$	−16.2171	−0.715307
$515$	0.331385	0.0146026
$516$	−16.7706	−0.738283
$517$	−5.36036	−0.235748
$518$	26.1332	1.14823
$519$	−45.0173	−1.97604
$520$	2.43869	0.106943
$521$	−31.1190	−1.36335	−0.681673	−	0.731657i	$-0.738748\pi$
$521$	−31.1190	−1.36335	−0.681673	+	0.731657i	$0.738748\pi$
$522$	5.82756	0.255066
$523$	−25.4523	−1.11295	−0.556476	−	0.830863i	$-0.687847\pi$
$523$	−25.4523	−1.11295	−0.556476	+	0.830863i	$0.687847\pi$
$524$	−4.19968	−0.183464
$525$	−37.2671	−1.62647
$526$	−29.1396	−1.27055
$527$	8.92718	0.388874
$528$	−4.49116	−0.195453
$529$	−17.0143	−0.739750
$530$	4.01274	0.174302
$531$	−13.8846	−0.602540
$532$	−22.0369	−0.955423
$533$	7.74628	0.335529
$534$	−27.0779	−1.17178
$535$	5.39336	0.233175
$536$	−15.3033	−0.661003
$537$	−26.5994	−1.14785
$538$	28.4512	1.22662
$539$	7.49277	0.322736
$540$	−1.27801	−0.0549968
$541$	−2.61092	−0.112252	−0.0561261	−	0.998424i	$-0.517875\pi$
$541$	−2.61092	−0.112252	−0.0561261	+	0.998424i	$0.517875\pi$
$542$	−2.61084	−0.112145
$543$	−0.303572	−0.0130275
$544$	14.9453	0.640775
$545$	10.2476	0.438959
$546$	9.60527	0.411067
$547$	−28.4736	−1.21744	−0.608722	−	0.793384i	$-0.708318\pi$
$547$	−28.4736	−1.21744	−0.608722	+	0.793384i	$0.708318\pi$
$548$	0.0525593	0.00224522
$549$	−13.7397	−0.586395
$550$	4.92580	0.210037
$551$	−20.3491	−0.866901
$552$	−16.8547	−0.717385
$553$	13.2838	0.564883
$554$	−9.27785	−0.394178
$555$	10.8140	0.459029
$556$	−4.22051	−0.178990
$557$	−16.2946	−0.690423	−0.345211	−	0.938525i	$-0.612193\pi$
$557$	−16.2946	−0.690423	−0.345211	+	0.938525i	$0.612193\pi$
$558$	5.27785	0.223429
$559$	−10.2535	−0.433677
$560$	6.05240	0.255761
$561$	−8.59620	−0.362932
$562$	−10.2217	−0.431175
$563$	16.0068	0.674607	0.337304	−	0.941396i	$-0.390485\pi$
$563$	16.0068	0.674607	0.337304	+	0.941396i	$0.390485\pi$
$564$	8.76737	0.369173
$565$	−8.39061	−0.352995
$566$	−35.6605	−1.49892
$567$	−41.8212	−1.75633
$568$	30.7751	1.29129
$569$	−13.0977	−0.549085	−0.274543	−	0.961575i	$-0.588526\pi$
$569$	−13.0977	−0.549085	−0.274543	+	0.961575i	$0.588526\pi$
$570$	15.8502	0.663891
$571$	−3.74287	−0.156634	−0.0783171	−	0.996928i	$-0.524955\pi$
$571$	−3.74287	−0.156634	−0.0783171	+	0.996928i	$0.524955\pi$
$572$	0.730419	0.0305403
$573$	49.2054	2.05559
$574$	33.2276	1.38689
$575$	10.6956	0.446038
$576$	16.9156	0.704818
$577$	15.3454	0.638839	0.319420	−	0.947613i	$-0.396512\pi$
$577$	15.3454	0.638839	0.319420	+	0.947613i	$0.396512\pi$
$578$	2.54995	0.106064
$579$	12.5328	0.520845
$580$	−1.48665	−0.0617299
$581$	23.9283	0.992713
$582$	−40.3057	−1.67072
$583$	4.49277	0.186071
$584$	38.2129	1.58126
$585$	1.59666	0.0660137
$586$	1.40162	0.0579002
$587$	−16.5871	−0.684622	−0.342311	−	0.939587i	$-0.611210\pi$
$587$	−16.5871	−0.684622	−0.342311	+	0.939587i	$0.611210\pi$
$588$	−12.2551	−0.505393
$589$	−18.4296	−0.759377
$590$	−6.15665	−0.253465
$591$	59.3565	2.44160
$592$	12.2192	0.502206
$593$	−36.5181	−1.49962	−0.749810	−	0.661653i	$-0.769855\pi$
$593$	−36.5181	−1.49962	−0.749810	+	0.661653i	$0.769855\pi$
$594$	2.48712	0.102048
$595$	11.5844	0.474916
$596$	−9.40899	−0.385407
$597$	−19.3783	−0.793100
$598$	−2.75670	−0.112730
$599$	30.9310	1.26381	0.631904	−	0.775047i	$-0.282274\pi$
$599$	30.9310	1.26381	0.631904	+	0.775047i	$0.282274\pi$
$600$	−30.1169	−1.22952
$601$	−26.8588	−1.09559	−0.547797	−	0.836611i	$-0.684534\pi$
$601$	−26.8588	−1.09559	−0.547797	+	0.836611i	$0.684534\pi$
$602$	−43.9824	−1.79259
$603$	−10.0194	−0.408021
$604$	1.15797	0.0471172
$605$	−0.792677	−0.0322269
$606$	26.8244	1.08967
$607$	−40.3283	−1.63687	−0.818437	−	0.574596i	$-0.805159\pi$
$607$	−40.3283	−1.63687	−0.818437	+	0.574596i	$0.805159\pi$
$608$	−30.8536	−1.25128
$609$	−21.8887	−0.886976
$610$	−6.09238	−0.246673
$611$	5.36036	0.216857
$612$	5.64795	0.228305
$613$	−5.65538	−0.228419	−0.114209	−	0.993457i	$-0.536433\pi$
$613$	−5.65538	−0.228419	−0.114209	+	0.993457i	$0.536433\pi$
$614$	−7.37166	−0.297496
$615$	13.7497	0.554441
$616$	11.7121	0.471894
$617$	−35.9104	−1.44570	−0.722850	−	0.691005i	$-0.757168\pi$
$617$	−35.9104	−1.44570	−0.722850	+	0.691005i	$0.757168\pi$
$618$	1.05480	0.0424302
$619$	−19.7335	−0.793156	−0.396578	−	0.918001i	$-0.629802\pi$
$619$	−19.7335	−0.793156	−0.396578	+	0.918001i	$0.629802\pi$
$620$	−1.34642	−0.0540734
$621$	5.40039	0.216710
$622$	22.4018	0.898230
$623$	40.8561	1.63687
$624$	4.49116	0.179790
$625$	15.9698	0.638790
$626$	13.8336	0.552902
$627$	17.7463	0.708718
$628$	9.75025	0.389077
$629$	23.3879	0.932535
$630$	6.84885	0.272865
$631$	25.7778	1.02620	0.513099	−	0.858329i	$-0.328497\pi$
$631$	25.7778	1.02620	0.513099	+	0.858329i	$0.328497\pi$
$632$	10.7351	0.427018
$633$	3.81356	0.151575
$634$	−21.2197	−0.842740
$635$	13.3934	0.531499
$636$	−7.34834	−0.291381
$637$	−7.49277	−0.296874
$638$	2.89315	0.114541
$639$	20.1491	0.797085
$640$	1.32863	0.0525188
$641$	6.54808	0.258634	0.129317	−	0.991603i	$-0.458722\pi$
$641$	6.54808	0.258634	0.129317	+	0.991603i	$0.458722\pi$
$642$	17.1671	0.677531
$643$	−45.0843	−1.77795	−0.888976	−	0.457953i	$-0.848583\pi$
$643$	−45.0843	−1.77795	−0.888976	+	0.457953i	$0.848583\pi$
$644$	6.80309	0.268079
$645$	−18.2000	−0.716626
$646$	34.2797	1.34872
$647$	−33.4670	−1.31572	−0.657862	−	0.753139i	$-0.728539\pi$
$647$	−33.4670	−1.31572	−0.657862	+	0.753139i	$0.728539\pi$
$648$	−33.7972	−1.32768
$649$	−6.89315	−0.270580
$650$	−4.92580	−0.193206
$651$	−19.8239	−0.776962
$652$	16.9683	0.664531
$653$	8.57680	0.335636	0.167818	−	0.985818i	$-0.446328\pi$
$653$	8.57680	0.335636	0.167818	+	0.985818i	$0.446328\pi$
$654$	32.6182	1.27547
$655$	−4.55765	−0.178082
$656$	15.5363	0.606592
$657$	25.0187	0.976074
$658$	22.9932	0.896369
$659$	−11.8991	−0.463524	−0.231762	−	0.972773i	$-0.574449\pi$
$659$	−11.8991	−0.463524	−0.231762	+	0.972773i	$0.574449\pi$
$660$	1.29650	0.0504661
$661$	4.01258	0.156071	0.0780355	−	0.996951i	$-0.475135\pi$
$661$	4.01258	0.156071	0.0780355	+	0.996951i	$0.475135\pi$
$662$	12.4051	0.482139
$663$	8.59620	0.333849
$664$	19.3373	0.750432
$665$	−23.9153	−0.927396
$666$	13.8272	0.535791
$667$	6.28203	0.243241
$668$	−4.52554	−0.175098
$669$	11.2744	0.435893
$670$	−4.44276	−0.171639
$671$	−6.82120	−0.263329
$672$	−33.1880	−1.28025
$673$	39.6618	1.52885	0.764425	−	0.644713i	$-0.223023\pi$
$673$	39.6618	1.52885	0.764425	+	0.644713i	$0.223023\pi$
$674$	−22.0317	−0.848630
$675$	9.64967	0.371416
$676$	−0.730419	−0.0280930
$677$	32.7262	1.25777	0.628886	−	0.777498i	$-0.283511\pi$
$677$	32.7262	1.25777	0.628886	+	0.777498i	$0.283511\pi$
$678$	−26.7073	−1.02569
$679$	60.8146	2.33385
$680$	9.36179	0.359008
$681$	54.5820	2.09159
$682$	2.62024	0.100334
$683$	18.1128	0.693067	0.346534	−	0.938038i	$-0.387359\pi$
$683$	18.1128	0.693067	0.346534	+	0.938038i	$0.387359\pi$
$684$	−11.6598	−0.445824
$685$	0.0570393	0.00217936
$686$	−2.11373	−0.0807025
$687$	−40.0349	−1.52743
$688$	−20.5650	−0.784032
$689$	−4.49277	−0.171161
$690$	−4.89315	−0.186279
$691$	17.7075	0.673626	0.336813	−	0.941572i	$-0.390651\pi$
$691$	17.7075	0.673626	0.336813	+	0.941572i	$0.390651\pi$
$692$	14.6841	0.558206
$693$	7.66816	0.291289
$694$	−5.15579	−0.195711
$695$	−4.58026	−0.173739
$696$	−17.6890	−0.670501
$697$	29.7370	1.12637
$698$	−1.26632	−0.0479307
$699$	18.4564	0.698085
$700$	12.1561	0.459457
$701$	44.2337	1.67068	0.835342	−	0.549731i	$-0.185270\pi$
$701$	44.2337	1.67068	0.835342	+	0.549731i	$0.185270\pi$
$702$	−2.48712	−0.0938702
$703$	−48.2827	−1.82101
$704$	8.39794	0.316509
$705$	9.51467	0.358343
$706$	22.7755	0.857166
$707$	−40.4736	−1.52217
$708$	11.2744	0.423718
$709$	12.9892	0.487818	0.243909	−	0.969798i	$-0.421570\pi$
$709$	12.9892	0.487818	0.243909	+	0.969798i	$0.421570\pi$
$710$	8.93441	0.335302
$711$	7.02847	0.263588
$712$	33.0173	1.23737
$713$	5.68945	0.213071
$714$	36.8733	1.37995
$715$	0.792677	0.0296444
$716$	8.67642	0.324253
$717$	−51.9728	−1.94096
$718$	−3.50955	−0.130975
$719$	18.4717	0.688878	0.344439	−	0.938809i	$-0.388069\pi$
$719$	18.4717	0.688878	0.344439	+	0.938809i	$0.388069\pi$
$720$	3.20234	0.119344
$721$	−1.59152	−0.0592713
$722$	−49.3598	−1.83698
$723$	21.6175	0.803965
$724$	0.0990217	0.00368011
$725$	11.2250	0.416888
$726$	−2.52310	−0.0936409
$727$	−34.3321	−1.27331	−0.636653	−	0.771150i	$-0.719682\pi$
$727$	−34.3321	−1.27331	−0.636653	+	0.771150i	$0.719682\pi$
$728$	−11.7121	−0.434080
$729$	−7.29945	−0.270350
$730$	11.0937	0.410596
$731$	−39.3619	−1.45585
$732$	11.1567	0.412364
$733$	7.86718	0.290581	0.145291	−	0.989389i	$-0.453588\pi$
$733$	7.86718	0.290581	0.145291	+	0.989389i	$0.453588\pi$
$734$	−24.8251	−0.916313
$735$	−13.2997	−0.490567
$736$	9.52490	0.351093
$737$	−4.97423	−0.183228
$738$	17.5808	0.647159
$739$	−40.3710	−1.48507	−0.742536	−	0.669806i	$-0.766377\pi$
$739$	−40.3710	−1.48507	−0.742536	+	0.669806i	$0.766377\pi$
$740$	−3.52740	−0.129670
$741$	−17.7463	−0.651926
$742$	−19.2717	−0.707486
$743$	3.34906	0.122865	0.0614325	−	0.998111i	$-0.480433\pi$
$743$	3.34906	0.122865	0.0614325	+	0.998111i	$0.480433\pi$
$744$	−16.0204	−0.587337
$745$	−10.2110	−0.374102
$746$	−2.54685	−0.0932469
$747$	12.6605	0.463224
$748$	2.80398	0.102524
$749$	−25.9023	−0.946450
$750$	−18.7433	−0.684410
$751$	−23.5309	−0.858653	−0.429327	−	0.903149i	$-0.641249\pi$
$751$	−23.5309	−0.858653	−0.429327	+	0.903149i	$0.641249\pi$
$752$	10.7510	0.392049
$753$	55.0920	2.00766
$754$	−2.89315	−0.105362
$755$	1.25667	0.0457350
$756$	6.13781	0.223230
$757$	−0.729883	−0.0265280	−0.0132640	−	0.999912i	$-0.504222\pi$
$757$	−0.729883	−0.0265280	−0.0132640	+	0.999912i	$0.504222\pi$
$758$	20.8025	0.755583
$759$	−5.47851	−0.198857
$760$	−19.3268	−0.701056
$761$	−20.9455	−0.759274	−0.379637	−	0.925135i	$-0.623951\pi$
$761$	−20.9455	−0.759274	−0.379637	+	0.925135i	$0.623951\pi$
$762$	42.6311	1.54436
$763$	−49.2155	−1.78172
$764$	−16.0502	−0.580677
$765$	6.12936	0.221607
$766$	−24.2761	−0.877132
$767$	6.89315	0.248897
$768$	−33.3812	−1.20454
$769$	3.29629	0.118867	0.0594337	−	0.998232i	$-0.481071\pi$
$769$	3.29629	0.118867	0.0594337	+	0.998232i	$0.481071\pi$
$770$	3.40018	0.122534
$771$	32.2290	1.16070
$772$	−4.08805	−0.147132
$773$	−11.9096	−0.428357	−0.214178	−	0.976795i	$-0.568707\pi$
$773$	−11.9096	−0.428357	−0.214178	+	0.976795i	$0.568707\pi$
$774$	−23.2712	−0.836465
$775$	10.1662	0.365180
$776$	49.1464	1.76425
$777$	−51.9357	−1.86318
$778$	35.2415	1.26347
$779$	−61.3900	−2.19952
$780$	−1.29650	−0.0464220
$781$	10.0032	0.357943
$782$	−10.5826	−0.378433
$783$	5.66770	0.202547
$784$	−15.0279	−0.536710
$785$	10.5813	0.377664
$786$	−14.5070	−0.517449
$787$	−32.2978	−1.15129	−0.575646	−	0.817699i	$-0.695249\pi$
$787$	−32.2978	−1.15129	−0.575646	+	0.817699i	$0.695249\pi$
$788$	−19.3614	−0.689722
$789$	57.9104	2.06167
$790$	3.11653	0.110881
$791$	40.2970	1.43280
$792$	6.19691	0.220198
$793$	6.82120	0.242228
$794$	8.65599	0.307190
$795$	−7.97469	−0.282833
$796$	6.32097	0.224041
$797$	−4.86463	−0.172314	−0.0861571	−	0.996282i	$-0.527459\pi$
$797$	−4.86463	−0.172314	−0.0861571	+	0.996282i	$0.527459\pi$
$798$	−76.1226	−2.69471
$799$	20.5777	0.727987
$800$	17.0196	0.601732
$801$	21.6171	0.763802
$802$	20.8748	0.737114
$803$	12.4208	0.438321
$804$	8.13582	0.286928
$805$	7.38297	0.260215
$806$	−2.62024	−0.0922941
$807$	−56.5424	−1.99039
$808$	−32.7081	−1.15067
$809$	14.0775	0.494937	0.247469	−	0.968896i	$-0.420401\pi$
$809$	14.0775	0.494937	0.247469	+	0.968896i	$0.420401\pi$
$810$	−9.81178	−0.344751
$811$	−32.3366	−1.13549	−0.567745	−	0.823204i	$-0.692184\pi$
$811$	−32.3366	−1.13549	−0.567745	+	0.823204i	$0.692184\pi$
$812$	7.13985	0.250559
$813$	5.18863	0.181973
$814$	6.86463	0.240605
$815$	18.4146	0.645037
$816$	17.2410	0.603555
$817$	81.2600	2.84293
$818$	−16.6908	−0.583579
$819$	−7.66816	−0.267947
$820$	−4.48499	−0.156623
$821$	13.9494	0.486837	0.243418	−	0.969921i	$-0.421731\pi$
$821$	13.9494	0.486837	0.243418	+	0.969921i	$0.421731\pi$
$822$	0.181556	0.00633250
$823$	2.38913	0.0832799	0.0416399	−	0.999133i	$-0.486742\pi$
$823$	2.38913	0.0832799	0.0416399	+	0.999133i	$0.486742\pi$
$824$	−1.28616	−0.0448056
$825$	−9.78927	−0.340818
$826$	29.5681	1.02881
$827$	19.5036	0.678207	0.339104	−	0.940749i	$-0.389876\pi$
$827$	19.5036	0.678207	0.339104	+	0.940749i	$0.389876\pi$
$828$	3.59953	0.125092
$829$	14.2258	0.494083	0.247042	−	0.969005i	$-0.420542\pi$
$829$	14.2258	0.494083	0.247042	+	0.969005i	$0.420542\pi$
$830$	5.61387	0.194860
$831$	18.4383	0.639617
$832$	−8.39794	−0.291146
$833$	−28.7638	−0.996605
$834$	−14.5790	−0.504829
$835$	−4.91128	−0.169962
$836$	−5.78863	−0.200204
$837$	5.13307	0.177425
$838$	2.89338	0.0999503
$839$	−20.4373	−0.705572	−0.352786	−	0.935704i	$-0.614766\pi$
$839$	−20.4373	−0.705572	−0.352786	+	0.935704i	$0.614766\pi$
$840$	−20.7891	−0.717291
$841$	−22.4070	−0.772655
$842$	4.42336	0.152439
$843$	20.3140	0.699650
$844$	−1.24394	−0.0428181
$845$	−0.792677	−0.0272689
$846$	12.1658	0.418268
$847$	3.80694	0.130808
$848$	−9.01093	−0.309437
$849$	70.8697	2.43224
$850$	−18.9095	−0.648591
$851$	14.9055	0.510953
$852$	−16.3612	−0.560525
$853$	33.8278	1.15824	0.579121	−	0.815241i	$-0.303396\pi$
$853$	33.8278	1.15824	0.579121	+	0.815241i	$0.303396\pi$
$854$	29.2595	1.00124
$855$	−12.6536	−0.432746
$856$	−20.9326	−0.715461
$857$	−28.5469	−0.975142	−0.487571	−	0.873083i	$-0.662117\pi$
$857$	−28.5469	−0.975142	−0.487571	+	0.873083i	$0.662117\pi$
$858$	2.52310	0.0861371
$859$	−16.8037	−0.573336	−0.286668	−	0.958030i	$-0.592548\pi$
$859$	−16.8037	−0.573336	−0.286668	+	0.958030i	$0.592548\pi$
$860$	5.93664	0.202438
$861$	−66.0347	−2.25046
$862$	−6.43891	−0.219310
$863$	29.3051	0.997557	0.498779	−	0.866729i	$-0.333782\pi$
$863$	29.3051	0.997557	0.498779	+	0.866729i	$0.333782\pi$
$864$	8.59345	0.292355
$865$	15.9357	0.541831
$866$	17.2537	0.586304
$867$	−5.06764	−0.172106
$868$	6.46634	0.219482
$869$	3.48936	0.118368
$870$	−5.13537	−0.174105
$871$	4.97423	0.168545
$872$	−39.7727	−1.34687
$873$	32.1772	1.08903
$874$	21.8471	0.738988
$875$	28.2806	0.956059
$876$	−20.3154	−0.686393
$877$	32.5452	1.09897	0.549486	−	0.835503i	$-0.314824\pi$
$877$	32.5452	1.09897	0.549486	+	0.835503i	$0.314824\pi$
$878$	−19.2930	−0.651109
$879$	−2.78549	−0.0939523
$880$	1.58983	0.0535933
$881$	27.3004	0.919773	0.459886	−	0.887978i	$-0.347890\pi$
$881$	27.3004	0.919773	0.459886	+	0.887978i	$0.347890\pi$
$882$	−17.0054	−0.572603
$883$	42.0375	1.41467	0.707337	−	0.706876i	$-0.249896\pi$
$883$	42.0375	1.41467	0.707337	+	0.706876i	$0.249896\pi$
$884$	−2.80398	−0.0943081
$885$	12.2354	0.411288
$886$	−19.5051	−0.655286
$887$	6.61071	0.221966	0.110983	−	0.993822i	$-0.464600\pi$
$887$	6.61071	0.221966	0.110983	+	0.993822i	$0.464600\pi$
$888$	−41.9711	−1.40846
$889$	−64.3234	−2.15734
$890$	9.58535	0.321302
$891$	−10.9855	−0.368029
$892$	−3.67758	−0.123134
$893$	−42.4813	−1.42158
$894$	−32.5016	−1.08702
$895$	9.41597	0.314741
$896$	−6.38093	−0.213172
$897$	5.47851	0.182922
$898$	−39.6967	−1.32470
$899$	5.97107	0.199146
$900$	6.43182	0.214394
$901$	−17.2471	−0.574586
$902$	8.72818	0.290617
$903$	87.4081	2.90876
$904$	32.5654	1.08311
$905$	0.107462	0.00357216
$906$	4.00000	0.132891
$907$	−13.3521	−0.443348	−0.221674	−	0.975121i	$-0.571152\pi$
$907$	−13.3521	−0.443348	−0.221674	+	0.975121i	$0.571152\pi$
$908$	−17.8040	−0.590847
$909$	−21.4147	−0.710281
$910$	−3.40018	−0.112715
$911$	−54.2929	−1.79880	−0.899402	−	0.437123i	$-0.855998\pi$
$911$	−54.2929	−1.79880	−0.899402	+	0.437123i	$0.855998\pi$
$912$	−35.5929	−1.17860
$913$	6.28545	0.208018
$914$	−20.2886	−0.671086
$915$	12.1077	0.400267
$916$	13.0589	0.431479
$917$	21.8887	0.722829
$918$	−9.54771	−0.315121
$919$	8.80037	0.290297	0.145149	−	0.989410i	$-0.453634\pi$
$919$	8.80037	0.290297	0.145149	+	0.989410i	$0.453634\pi$
$920$	5.96643	0.196707
$921$	14.6500	0.482735
$922$	18.2049	0.599547
$923$	−10.0032	−0.329260
$924$	−6.22660	−0.204840
$925$	26.6338	0.875715
$926$	−43.1739	−1.41878
$927$	−0.842077	−0.0276574
$928$	9.99638	0.328147
$929$	−45.9163	−1.50647	−0.753233	−	0.657754i	$-0.771507\pi$
$929$	−45.9163	−1.50647	−0.753233	+	0.657754i	$0.771507\pi$
$930$	−4.65094	−0.152510
$931$	59.3808	1.94613
$932$	−6.02026	−0.197200
$933$	−44.5201	−1.45752
$934$	−22.2363	−0.727594
$935$	3.04298	0.0995162
$936$	−6.19691	−0.202552
$937$	31.9153	1.04263	0.521314	−	0.853365i	$-0.325442\pi$
$937$	31.9153	1.04263	0.521314	+	0.853365i	$0.325442\pi$
$938$	21.3369	0.696676
$939$	−27.4921	−0.897171
$940$	−3.10357	−0.101227
$941$	−24.5426	−0.800067	−0.400033	−	0.916501i	$-0.631001\pi$
$941$	−24.5426	−0.800067	−0.400033	+	0.916501i	$0.631001\pi$
$942$	33.6804	1.09737
$943$	18.9519	0.617158
$944$	13.8253	0.449974
$945$	6.66098	0.216682
$946$	−11.5532	−0.375628
$947$	−0.769548	−0.0250070	−0.0125035	−	0.999922i	$-0.503980\pi$
$947$	−0.769548	−0.0250070	−0.0125035	+	0.999922i	$0.503980\pi$
$948$	−5.70717	−0.185360
$949$	−12.4208	−0.403197
$950$	39.0374	1.26654
$951$	42.1708	1.36748
$952$	−44.9613	−1.45720
$953$	−3.12752	−0.101310	−0.0506551	−	0.998716i	$-0.516131\pi$
$953$	−3.12752	−0.101310	−0.0506551	+	0.998716i	$0.516131\pi$
$954$	−10.1967	−0.330130
$955$	−17.4183	−0.563643
$956$	16.9529	0.548297
$957$	−5.74969	−0.185861
$958$	−23.4768	−0.758500
$959$	−0.273939	−0.00884594
$960$	−14.9064	−0.481102
$961$	−25.5922	−0.825554
$962$	−6.86463	−0.221325
$963$	−13.7050	−0.441637
$964$	−7.05139	−0.227110
$965$	−4.43650	−0.142816
$966$	23.5000	0.756101
$967$	−6.97398	−0.224268	−0.112134	−	0.993693i	$-0.535769\pi$
$967$	−6.97398	−0.224268	−0.112134	+	0.993693i	$0.535769\pi$
$968$	3.07652	0.0988830
$969$	−68.1256	−2.18851
$970$	14.2679	0.458114
$971$	16.1410	0.517988	0.258994	−	0.965879i	$-0.416609\pi$
$971$	16.1410	0.517988	0.258994	+	0.965879i	$0.416609\pi$
$972$	13.1311	0.421179
$973$	21.9973	0.705201
$974$	−25.5130	−0.817489
$975$	9.78927	0.313507
$976$	13.6809	0.437916
$977$	14.5262	0.464734	0.232367	−	0.972628i	$-0.425353\pi$
$977$	14.5262	0.464734	0.232367	+	0.972628i	$0.425353\pi$
$978$	58.6139	1.87427
$979$	10.7320	0.342997
$980$	4.33821	0.138579
$981$	−26.0400	−0.831394
$982$	47.1581	1.50488
$983$	−34.9774	−1.11561	−0.557804	−	0.829973i	$-0.688356\pi$
$983$	−34.9774	−1.11561	−0.557804	+	0.829973i	$0.688356\pi$
$984$	−53.3650	−1.70121
$985$	−21.0117	−0.669489
$986$	−11.1064	−0.353701
$987$	−45.6955	−1.45450
$988$	5.78863	0.184161
$989$	−25.0860	−0.797689
$990$	1.79905	0.0571774
$991$	−7.42575	−0.235887	−0.117943	−	0.993020i	$-0.537630\pi$
$991$	−7.42575	−0.235887	−0.117943	+	0.993020i	$0.537630\pi$
$992$	9.05342	0.287446
$993$	−24.6532	−0.782347
$994$	−42.9087	−1.36098
$995$	6.85975	0.217469
$996$	−10.2804	−0.325748
$997$	−57.4270	−1.81873	−0.909366	−	0.415997i	$-0.863433\pi$
$997$	−57.4270	−1.81873	−0.909366	+	0.415997i	$0.863433\pi$
$998$	−29.9553	−0.948218
$999$	13.4479	0.425471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.a.b.1.1	✓	4
3.2	odd	2		1287.2.a.k.1.4		4
4.3	odd	2		2288.2.a.x.1.1		4
5.4	even	2		3575.2.a.k.1.4		4
7.6	odd	2		7007.2.a.n.1.1		4
8.3	odd	2		9152.2.a.cg.1.4		4
8.5	even	2		9152.2.a.ch.1.1		4
11.10	odd	2		1573.2.a.f.1.4		4
13.12	even	2		1859.2.a.i.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.a.b.1.1	✓	4	1.1	even	1	trivial
1287.2.a.k.1.4		4	3.2	odd	2
1573.2.a.f.1.4		4	11.10	odd	2
1859.2.a.i.1.4		4	13.12	even	2
2288.2.a.x.1.1		4	4.3	odd	2
3575.2.a.k.1.4		4	5.4	even	2
7007.2.a.n.1.1		4	7.6	odd	2
9152.2.a.cg.1.4		4	8.3	odd	2
9152.2.a.ch.1.1		4	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q-1.12676 q^{2} +2.23925 q^{3} -0.730419 q^{4} -0.792677 q^{5} -2.52310 q^{6} +3.80694 q^{7} +3.07652 q^{8} +2.01426 q^{9} +O(q^{10})\)	\(q-1.12676 q^{2} +2.23925 q^{3} -0.730419 q^{4} -0.792677 q^{5} -2.52310 q^{6} +3.80694 q^{7} +3.07652 q^{8} +2.01426 q^{9} +0.893154 q^{10} +1.00000 q^{11} -1.63559 q^{12} -1.00000 q^{13} -4.28949 q^{14} -1.77501 q^{15} -2.00565 q^{16} -3.83887 q^{17} -2.26958 q^{18} +7.92509 q^{19} +0.578986 q^{20} +8.52470 q^{21} -1.12676 q^{22} -2.44658 q^{23} +6.88911 q^{24} -4.37166 q^{25} +1.12676 q^{26} -2.20732 q^{27} -2.78066 q^{28} -2.56768 q^{29} +2.00000 q^{30} -2.32547 q^{31} -3.89315 q^{32} +2.23925 q^{33} +4.32547 q^{34} -3.01767 q^{35} -1.47125 q^{36} -6.09238 q^{37} -8.92965 q^{38} -2.23925 q^{39} -2.43869 q^{40} -7.74628 q^{41} -9.60527 q^{42} +10.2535 q^{43} -0.730419 q^{44} -1.59666 q^{45} +2.75670 q^{46} -5.36036 q^{47} -4.49116 q^{48} +7.49277 q^{49} +4.92580 q^{50} -8.59620 q^{51} +0.730419 q^{52} +4.49277 q^{53} +2.48712 q^{54} -0.792677 q^{55} +11.7121 q^{56} +17.7463 q^{57} +2.89315 q^{58} -6.89315 q^{59} +1.29650 q^{60} -6.82120 q^{61} +2.62024 q^{62} +7.66816 q^{63} +8.39794 q^{64} +0.792677 q^{65} -2.52310 q^{66} -4.97423 q^{67} +2.80398 q^{68} -5.47851 q^{69} +3.40018 q^{70} +10.0032 q^{71} +6.19691 q^{72} +12.4208 q^{73} +6.86463 q^{74} -9.78927 q^{75} -5.78863 q^{76} +3.80694 q^{77} +2.52310 q^{78} +3.48936 q^{79} +1.58983 q^{80} -10.9855 q^{81} +8.72818 q^{82} +6.28545 q^{83} -6.22660 q^{84} +3.04298 q^{85} -11.5532 q^{86} -5.74969 q^{87} +3.07652 q^{88} +10.7320 q^{89} +1.79905 q^{90} -3.80694 q^{91} +1.78703 q^{92} -5.20732 q^{93} +6.03982 q^{94} -6.28203 q^{95} -8.71776 q^{96} +15.9747 q^{97} -8.44253 q^{98} +2.01426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 3 q^{4} - q^{6} + 6 q^{7} + 9 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 3 * q^4 - q^6 + 6 * q^7 + 9 * q^8 + 2 * q^9	\( 4 q + 3 q^{2} + 3 q^{4} - q^{6} + 6 q^{7} + 9 q^{8} + 2 q^{9} - 8 q^{10} + 4 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{14} - 10 q^{15} + 5 q^{16} + 6 q^{17} - 15 q^{18} + 8 q^{19} - 24 q^{20} - 2 q^{21} + 3 q^{22} - 4 q^{23} + 2 q^{24} + 12 q^{25} - 3 q^{26} - 12 q^{27} - q^{28} - 10 q^{29} + 8 q^{30} + 2 q^{31} - 4 q^{32} + 6 q^{34} - 6 q^{35} - 28 q^{36} + 12 q^{37} - 5 q^{38} - 30 q^{40} + 8 q^{41} - 13 q^{42} + 26 q^{43} + 3 q^{44} + 26 q^{45} + 6 q^{46} - 18 q^{47} - 21 q^{48} + 6 q^{49} + 29 q^{50} - 22 q^{51} - 3 q^{52} - 6 q^{53} - q^{54} + 33 q^{56} + 32 q^{57} - 16 q^{59} + 26 q^{60} - 12 q^{61} + 12 q^{62} + 22 q^{63} + 5 q^{64} - q^{66} + 2 q^{67} - 18 q^{68} - 4 q^{69} - 28 q^{70} - 14 q^{71} - 6 q^{72} + 22 q^{73} + 28 q^{74} - 36 q^{75} - 6 q^{76} + 6 q^{77} + q^{78} - 10 q^{79} - 26 q^{80} + 4 q^{81} + 42 q^{82} - 2 q^{83} + 5 q^{84} + 48 q^{85} + 2 q^{86} + 16 q^{87} + 9 q^{88} + 10 q^{89} + 24 q^{90} - 6 q^{91} + 17 q^{92} - 24 q^{93} - 14 q^{94} + 2 q^{95} - 8 q^{96} + 22 q^{97} - 14 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 3 * q^4 - q^6 + 6 * q^7 + 9 * q^8 + 2 * q^9 - 8 * q^10 + 4 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^14 - 10 * q^15 + 5 * q^16 + 6 * q^17 - 15 * q^18 + 8 * q^19 - 24 * q^20 - 2 * q^21 + 3 * q^22 - 4 * q^23 + 2 * q^24 + 12 * q^25 - 3 * q^26 - 12 * q^27 - q^28 - 10 * q^29 + 8 * q^30 + 2 * q^31 - 4 * q^32 + 6 * q^34 - 6 * q^35 - 28 * q^36 + 12 * q^37 - 5 * q^38 - 30 * q^40 + 8 * q^41 - 13 * q^42 + 26 * q^43 + 3 * q^44 + 26 * q^45 + 6 * q^46 - 18 * q^47 - 21 * q^48 + 6 * q^49 + 29 * q^50 - 22 * q^51 - 3 * q^52 - 6 * q^53 - q^54 + 33 * q^56 + 32 * q^57 - 16 * q^59 + 26 * q^60 - 12 * q^61 + 12 * q^62 + 22 * q^63 + 5 * q^64 - q^66 + 2 * q^67 - 18 * q^68 - 4 * q^69 - 28 * q^70 - 14 * q^71 - 6 * q^72 + 22 * q^73 + 28 * q^74 - 36 * q^75 - 6 * q^76 + 6 * q^77 + q^78 - 10 * q^79 - 26 * q^80 + 4 * q^81 + 42 * q^82 - 2 * q^83 + 5 * q^84 + 48 * q^85 + 2 * q^86 + 16 * q^87 + 9 * q^88 + 10 * q^89 + 24 * q^90 - 6 * q^91 + 17 * q^92 - 24 * q^93 - 14 * q^94 + 2 * q^95 - 8 * q^96 + 22 * q^97 - 14 * q^98 + 2 * q^99

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