LMFDB - Embedded newform 6009.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.66735 q^{2} +1.00000 q^{3} +0.780065 q^{4} -0.964493 q^{5} -1.66735 q^{6} +4.83846 q^{7} +2.03406 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.66735 q^{2} +1.00000 q^{3} +0.780065 q^{4} -0.964493 q^{5} -1.66735 q^{6} +4.83846 q^{7} +2.03406 q^{8} +1.00000 q^{9} +1.60815 q^{10} +2.75025 q^{11} +0.780065 q^{12} -2.72312 q^{13} -8.06743 q^{14} -0.964493 q^{15} -4.95163 q^{16} +0.356108 q^{17} -1.66735 q^{18} -5.39349 q^{19} -0.752367 q^{20} +4.83846 q^{21} -4.58563 q^{22} +1.11811 q^{23} +2.03406 q^{24} -4.06975 q^{25} +4.54039 q^{26} +1.00000 q^{27} +3.77432 q^{28} -6.14045 q^{29} +1.60815 q^{30} +3.34126 q^{31} +4.18799 q^{32} +2.75025 q^{33} -0.593758 q^{34} -4.66666 q^{35} +0.780065 q^{36} +2.59348 q^{37} +8.99285 q^{38} -2.72312 q^{39} -1.96184 q^{40} -4.32265 q^{41} -8.06743 q^{42} +4.19691 q^{43} +2.14537 q^{44} -0.964493 q^{45} -1.86429 q^{46} +11.0956 q^{47} -4.95163 q^{48} +16.4107 q^{49} +6.78572 q^{50} +0.356108 q^{51} -2.12421 q^{52} +2.87941 q^{53} -1.66735 q^{54} -2.65259 q^{55} +9.84173 q^{56} -5.39349 q^{57} +10.2383 q^{58} +0.303556 q^{59} -0.752367 q^{60} -10.4558 q^{61} -5.57106 q^{62} +4.83846 q^{63} +2.92040 q^{64} +2.62642 q^{65} -4.58563 q^{66} -7.83651 q^{67} +0.277787 q^{68} +1.11811 q^{69} +7.78097 q^{70} +0.213531 q^{71} +2.03406 q^{72} +11.7418 q^{73} -4.32425 q^{74} -4.06975 q^{75} -4.20727 q^{76} +13.3070 q^{77} +4.54039 q^{78} +13.3274 q^{79} +4.77581 q^{80} +1.00000 q^{81} +7.20738 q^{82} +3.64575 q^{83} +3.77432 q^{84} -0.343464 q^{85} -6.99773 q^{86} -6.14045 q^{87} +5.59417 q^{88} +14.2197 q^{89} +1.60815 q^{90} -13.1757 q^{91} +0.872202 q^{92} +3.34126 q^{93} -18.5003 q^{94} +5.20198 q^{95} +4.18799 q^{96} -0.683232 q^{97} -27.3625 q^{98} +2.75025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * 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 $

$2$	−1.66735	−1.17900	−0.589498	−	0.807770i	$-0.700674\pi$
$2$	−1.66735	−1.17900	−0.589498	+	0.807770i	$0.700674\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.780065	0.390033
$5$	−0.964493	−0.431334	−0.215667	−	0.976467i	$-0.569193\pi$
$5$	−0.964493	−0.431334	−0.215667	+	0.976467i	$0.569193\pi$
$6$	−1.66735	−0.680694
$7$	4.83846	1.82877	0.914384	−	0.404849i	$-0.132676\pi$
$7$	4.83846	1.82877	0.914384	+	0.404849i	$0.132676\pi$
$8$	2.03406	0.719149
$9$	1.00000	0.333333
$10$	1.60815	0.508542
$11$	2.75025	0.829231	0.414615	−	0.909997i	$-0.363916\pi$
$11$	2.75025	0.829231	0.414615	+	0.909997i	$0.363916\pi$
$12$	0.780065	0.225185
$13$	−2.72312	−0.755256	−0.377628	−	0.925957i	$-0.623260\pi$
$13$	−2.72312	−0.755256	−0.377628	+	0.925957i	$0.623260\pi$
$14$	−8.06743	−2.15611
$15$	−0.964493	−0.249031
$16$	−4.95163	−1.23791
$17$	0.356108	0.0863689	0.0431844	−	0.999067i	$-0.486250\pi$
$17$	0.356108	0.0863689	0.0431844	+	0.999067i	$0.486250\pi$
$18$	−1.66735	−0.392999
$19$	−5.39349	−1.23735	−0.618676	−	0.785646i	$-0.712331\pi$
$19$	−5.39349	−1.23735	−0.618676	+	0.785646i	$0.712331\pi$
$20$	−0.752367	−0.168234
$21$	4.83846	1.05584
$22$	−4.58563	−0.977660
$23$	1.11811	0.233143	0.116571	−	0.993182i	$-0.462810\pi$
$23$	1.11811	0.233143	0.116571	+	0.993182i	$0.462810\pi$
$24$	2.03406	0.415201
$25$	−4.06975	−0.813951
$26$	4.54039	0.890444
$27$	1.00000	0.192450
$28$	3.77432	0.713279
$29$	−6.14045	−1.14025	−0.570126	−	0.821557i	$-0.693106\pi$
$29$	−6.14045	−1.14025	−0.570126	+	0.821557i	$0.693106\pi$
$30$	1.60815	0.293607
$31$	3.34126	0.600108	0.300054	−	0.953922i	$-0.402995\pi$
$31$	3.34126	0.600108	0.300054	+	0.953922i	$0.402995\pi$
$32$	4.18799	0.740339
$33$	2.75025	0.478757
$34$	−0.593758	−0.101829
$35$	−4.66666	−0.788810
$36$	0.780065	0.130011
$37$	2.59348	0.426366	0.213183	−	0.977012i	$-0.431617\pi$
$37$	2.59348	0.426366	0.213183	+	0.977012i	$0.431617\pi$
$38$	8.99285	1.45883
$39$	−2.72312	−0.436047
$40$	−1.96184	−0.310194
$41$	−4.32265	−0.675084	−0.337542	−	0.941310i	$-0.609596\pi$
$41$	−4.32265	−0.675084	−0.337542	+	0.941310i	$0.609596\pi$
$42$	−8.06743	−1.24483
$43$	4.19691	0.640023	0.320011	−	0.947414i	$-0.396313\pi$
$43$	4.19691	0.640023	0.320011	+	0.947414i	$0.396313\pi$
$44$	2.14537	0.323427
$45$	−0.964493	−0.143778
$46$	−1.86429	−0.274875
$47$	11.0956	1.61846	0.809229	−	0.587493i	$-0.199885\pi$
$47$	11.0956	1.61846	0.809229	+	0.587493i	$0.199885\pi$
$48$	−4.95163	−0.714706
$49$	16.4107	2.34439
$50$	6.78572	0.959645
$51$	0.356108	0.0498651
$52$	−2.12421	−0.294575
$53$	2.87941	0.395517	0.197758	−	0.980251i	$-0.436634\pi$
$53$	2.87941	0.395517	0.197758	+	0.980251i	$0.436634\pi$
$54$	−1.66735	−0.226898
$55$	−2.65259	−0.357676
$56$	9.84173	1.31516
$57$	−5.39349	−0.714385
$58$	10.2383	1.34435
$59$	0.303556	0.0395196	0.0197598	−	0.999805i	$-0.493710\pi$
$59$	0.303556	0.0395196	0.0197598	+	0.999805i	$0.493710\pi$
$60$	−0.752367	−0.0971302
$61$	−10.4558	−1.33873	−0.669365	−	0.742934i	$-0.733434\pi$
$61$	−10.4558	−1.33873	−0.669365	+	0.742934i	$0.733434\pi$
$62$	−5.57106	−0.707525
$63$	4.83846	0.609589
$64$	2.92040	0.365050
$65$	2.62642	0.325768
$66$	−4.58563	−0.564452
$67$	−7.83651	−0.957382	−0.478691	−	0.877983i	$-0.658889\pi$
$67$	−7.83651	−0.957382	−0.478691	+	0.877983i	$0.658889\pi$
$68$	0.277787	0.0336867
$69$	1.11811	0.134605
$70$	7.78097	0.930004
$71$	0.213531	0.0253414	0.0126707	−	0.999920i	$-0.495967\pi$
$71$	0.213531	0.0253414	0.0126707	+	0.999920i	$0.495967\pi$
$72$	2.03406	0.239716
$73$	11.7418	1.37427	0.687137	−	0.726528i	$-0.258867\pi$
$73$	11.7418	1.37427	0.687137	+	0.726528i	$0.258867\pi$
$74$	−4.32425	−0.502684
$75$	−4.06975	−0.469935
$76$	−4.20727	−0.482608
$77$	13.3070	1.51647
$78$	4.54039	0.514098
$79$	13.3274	1.49945	0.749725	−	0.661749i	$-0.230186\pi$
$79$	13.3274	1.49945	0.749725	+	0.661749i	$0.230186\pi$
$80$	4.77581	0.533952
$81$	1.00000	0.111111
$82$	7.20738	0.795922
$83$	3.64575	0.400173	0.200087	−	0.979778i	$-0.435878\pi$
$83$	3.64575	0.400173	0.200087	+	0.979778i	$0.435878\pi$
$84$	3.77432	0.411812
$85$	−0.343464	−0.0372539
$86$	−6.99773	−0.754585
$87$	−6.14045	−0.658325
$88$	5.59417	0.596341
$89$	14.2197	1.50729	0.753643	−	0.657283i	$-0.228295\pi$
$89$	14.2197	1.50729	0.753643	+	0.657283i	$0.228295\pi$
$90$	1.60815	0.169514
$91$	−13.1757	−1.38119
$92$	0.872202	0.0909334
$93$	3.34126	0.346472
$94$	−18.5003	−1.90816
$95$	5.20198	0.533712
$96$	4.18799	0.427435
$97$	−0.683232	−0.0693717	−0.0346858	−	0.999398i	$-0.511043\pi$
$97$	−0.683232	−0.0693717	−0.0346858	+	0.999398i	$0.511043\pi$
$98$	−27.3625	−2.76403
$99$	2.75025	0.276410
$100$	−3.17467	−0.317467
$101$	2.40148	0.238956	0.119478	−	0.992837i	$-0.461878\pi$
$101$	2.40148	0.238956	0.119478	+	0.992837i	$0.461878\pi$
$102$	−0.593758	−0.0587908
$103$	7.83665	0.772168	0.386084	−	0.922464i	$-0.373827\pi$
$103$	7.83665	0.772168	0.386084	+	0.922464i	$0.373827\pi$
$104$	−5.53898	−0.543142
$105$	−4.66666	−0.455420
$106$	−4.80099	−0.466313
$107$	10.5939	1.02415	0.512074	−	0.858941i	$-0.328877\pi$
$107$	10.5939	1.02415	0.512074	+	0.858941i	$0.328877\pi$
$108$	0.780065	0.0750618
$109$	2.18309	0.209102	0.104551	−	0.994520i	$-0.466659\pi$
$109$	2.18309	0.209102	0.104551	+	0.994520i	$0.466659\pi$
$110$	4.42281	0.421698
$111$	2.59348	0.246162
$112$	−23.9583	−2.26384
$113$	12.7515	1.19956	0.599780	−	0.800165i	$-0.295255\pi$
$113$	12.7515	1.19956	0.599780	+	0.800165i	$0.295255\pi$
$114$	8.99285	0.842258
$115$	−1.07841	−0.100563
$116$	−4.78995	−0.444736
$117$	−2.72312	−0.251752
$118$	−0.506135	−0.0465935
$119$	1.72302	0.157949
$120$	−1.96184	−0.179090
$121$	−3.43614	−0.312376
$122$	17.4335	1.57836
$123$	−4.32265	−0.389760
$124$	2.60640	0.234062
$125$	8.74771	0.782419
$126$	−8.06743	−0.718703
$127$	9.09729	0.807254	0.403627	−	0.914924i	$-0.367749\pi$
$127$	9.09729	0.807254	0.403627	+	0.914924i	$0.367749\pi$
$128$	−13.2453	−1.17073
$129$	4.19691	0.369517
$130$	−4.37918	−0.384079
$131$	9.20696	0.804415	0.402208	−	0.915548i	$-0.368243\pi$
$131$	9.20696	0.804415	0.402208	+	0.915548i	$0.368243\pi$
$132$	2.14537	0.186731
$133$	−26.0962	−2.26283
$134$	13.0662	1.12875
$135$	−0.964493	−0.0830103
$136$	0.724346	0.0621121
$137$	21.0354	1.79718	0.898589	−	0.438792i	$-0.144594\pi$
$137$	21.0354	1.79718	0.898589	+	0.438792i	$0.144594\pi$
$138$	−1.86429	−0.158699
$139$	−16.7714	−1.42253	−0.711266	−	0.702923i	$-0.751878\pi$
$139$	−16.7714	−1.42253	−0.711266	+	0.702923i	$0.751878\pi$
$140$	−3.64030	−0.307662
$141$	11.0956	0.934417
$142$	−0.356031	−0.0298774
$143$	−7.48924	−0.626282
$144$	−4.95163	−0.412636
$145$	5.92242	0.491830
$146$	−19.5777	−1.62026
$147$	16.4107	1.35353
$148$	2.02309	0.166297
$149$	−10.2006	−0.835668	−0.417834	−	0.908523i	$-0.637211\pi$
$149$	−10.2006	−0.835668	−0.417834	+	0.908523i	$0.637211\pi$
$150$	6.78572	0.554051
$151$	3.07560	0.250289	0.125144	−	0.992139i	$-0.460061\pi$
$151$	3.07560	0.250289	0.125144	+	0.992139i	$0.460061\pi$
$152$	−10.9707	−0.889840
$153$	0.356108	0.0287896
$154$	−22.1874	−1.78791
$155$	−3.22262	−0.258847
$156$	−2.12421	−0.170073
$157$	−19.3372	−1.54328	−0.771638	−	0.636062i	$-0.780562\pi$
$157$	−19.3372	−1.54328	−0.771638	+	0.636062i	$0.780562\pi$
$158$	−22.2215	−1.76785
$159$	2.87941	0.228352
$160$	−4.03929	−0.319334
$161$	5.40995	0.426364
$162$	−1.66735	−0.131000
$163$	−5.68043	−0.444926	−0.222463	−	0.974941i	$-0.571410\pi$
$163$	−5.68043	−0.444926	−0.222463	+	0.974941i	$0.571410\pi$
$164$	−3.37195	−0.263305
$165$	−2.65259	−0.206504
$166$	−6.07875	−0.471803
$167$	18.7871	1.45379	0.726894	−	0.686749i	$-0.240963\pi$
$167$	18.7871	1.45379	0.726894	+	0.686749i	$0.240963\pi$
$168$	9.84173	0.759306
$169$	−5.58464	−0.429588
$170$	0.572675	0.0439222
$171$	−5.39349	−0.412451
$172$	3.27386	0.249630
$173$	11.3557	0.863360	0.431680	−	0.902027i	$-0.357921\pi$
$173$	11.3557	0.863360	0.431680	+	0.902027i	$0.357921\pi$
$174$	10.2383	0.776163
$175$	−19.6914	−1.48853
$176$	−13.6182	−1.02651
$177$	0.303556	0.0228167
$178$	−23.7093	−1.77709
$179$	−5.14203	−0.384333	−0.192167	−	0.981362i	$-0.561551\pi$
$179$	−5.14203	−0.384333	−0.192167	+	0.981362i	$0.561551\pi$
$180$	−0.752367	−0.0560782
$181$	−23.8120	−1.76993	−0.884964	−	0.465659i	$-0.845817\pi$
$181$	−23.8120	−1.76993	−0.884964	+	0.465659i	$0.845817\pi$
$182$	21.9685	1.62842
$183$	−10.4558	−0.772916
$184$	2.27431	0.167665
$185$	−2.50139	−0.183906
$186$	−5.57106	−0.408490
$187$	0.979385	0.0716197
$188$	8.65529	0.631252
$189$	4.83846	0.351946
$190$	−8.67354	−0.629245
$191$	−1.27165	−0.0920131	−0.0460066	−	0.998941i	$-0.514650\pi$
$191$	−1.27165	−0.0920131	−0.0460066	+	0.998941i	$0.514650\pi$
$192$	2.92040	0.210762
$193$	14.1600	1.01926	0.509631	−	0.860393i	$-0.329782\pi$
$193$	14.1600	1.01926	0.509631	+	0.860393i	$0.329782\pi$
$194$	1.13919	0.0817889
$195$	2.62642	0.188082
$196$	12.8014	0.914389
$197$	−4.33668	−0.308976	−0.154488	−	0.987995i	$-0.549373\pi$
$197$	−4.33668	−0.308976	−0.154488	+	0.987995i	$0.549373\pi$
$198$	−4.58563	−0.325887
$199$	6.39140	0.453074	0.226537	−	0.974003i	$-0.427260\pi$
$199$	6.39140	0.453074	0.226537	+	0.974003i	$0.427260\pi$
$200$	−8.27813	−0.585352
$201$	−7.83651	−0.552745
$202$	−4.00412	−0.281729
$203$	−29.7103	−2.08526
$204$	0.277787	0.0194490
$205$	4.16916	0.291187
$206$	−13.0665	−0.910384
$207$	1.11811	0.0777143
$208$	13.4839	0.934937
$209$	−14.8334	−1.02605
$210$	7.78097	0.536938
$211$	−8.75907	−0.602999	−0.301499	−	0.953466i	$-0.597487\pi$
$211$	−8.75907	−0.602999	−0.301499	+	0.953466i	$0.597487\pi$
$212$	2.24613	0.154265
$213$	0.213531	0.0146309
$214$	−17.6637	−1.20747
$215$	−4.04789	−0.276064
$216$	2.03406	0.138400
$217$	16.1666	1.09746
$218$	−3.63998	−0.246530
$219$	11.7418	0.793437
$220$	−2.06920	−0.139505
$221$	−0.969723	−0.0652306
$222$	−4.32425	−0.290225
$223$	−26.5259	−1.77631	−0.888154	−	0.459546i	$-0.848012\pi$
$223$	−26.5259	−1.77631	−0.888154	+	0.459546i	$0.848012\pi$
$224$	20.2634	1.35391
$225$	−4.06975	−0.271317
$226$	−21.2612	−1.41428
$227$	26.4072	1.75271	0.876355	−	0.481667i	$-0.159968\pi$
$227$	26.4072	1.75271	0.876355	+	0.481667i	$0.159968\pi$
$228$	−4.20727	−0.278634
$229$	9.39902	0.621105	0.310553	−	0.950556i	$-0.399486\pi$
$229$	9.39902	0.621105	0.310553	+	0.950556i	$0.399486\pi$
$230$	1.79809	0.118563
$231$	13.3070	0.875535
$232$	−12.4901	−0.820012
$233$	17.2830	1.13225	0.566123	−	0.824321i	$-0.308443\pi$
$233$	17.2830	1.13225	0.566123	+	0.824321i	$0.308443\pi$
$234$	4.54039	0.296815
$235$	−10.7016	−0.698097
$236$	0.236793	0.0154139
$237$	13.3274	0.865708
$238$	−2.87287	−0.186221
$239$	25.8908	1.67474	0.837370	−	0.546637i	$-0.184092\pi$
$239$	25.8908	1.67474	0.837370	+	0.546637i	$0.184092\pi$
$240$	4.77581	0.308277
$241$	14.0564	0.905451	0.452726	−	0.891650i	$-0.350452\pi$
$241$	14.0564	0.905451	0.452726	+	0.891650i	$0.350452\pi$
$242$	5.72925	0.368290
$243$	1.00000	0.0641500
$244$	−8.15621	−0.522148
$245$	−15.8280	−1.01122
$246$	7.20738	0.459526
$247$	14.6871	0.934517
$248$	6.79633	0.431567
$249$	3.64575	0.231040
$250$	−14.5855	−0.922469
$251$	−23.1528	−1.46139	−0.730697	−	0.682702i	$-0.760805\pi$
$251$	−23.1528	−1.46139	−0.730697	+	0.682702i	$0.760805\pi$
$252$	3.77432	0.237760
$253$	3.07509	0.193329
$254$	−15.1684	−0.951750
$255$	−0.343464	−0.0215085
$256$	16.2438	1.01524
$257$	2.66446	0.166205	0.0831023	−	0.996541i	$-0.473517\pi$
$257$	2.66446	0.166205	0.0831023	+	0.996541i	$0.473517\pi$
$258$	−6.99773	−0.435660
$259$	12.5485	0.779724
$260$	2.04878	0.127060
$261$	−6.14045	−0.380084
$262$	−15.3512	−0.948403
$263$	4.66565	0.287697	0.143848	−	0.989600i	$-0.454052\pi$
$263$	4.66565	0.287697	0.143848	+	0.989600i	$0.454052\pi$
$264$	5.59417	0.344298
$265$	−2.77717	−0.170600
$266$	43.5116	2.66787
$267$	14.2197	0.870233
$268$	−6.11299	−0.373410
$269$	4.26915	0.260295	0.130147	−	0.991495i	$-0.458455\pi$
$269$	4.26915	0.260295	0.130147	+	0.991495i	$0.458455\pi$
$270$	1.60815	0.0978689
$271$	−5.39310	−0.327607	−0.163804	−	0.986493i	$-0.552376\pi$
$271$	−5.39310	−0.327607	−0.163804	+	0.986493i	$0.552376\pi$
$272$	−1.76331	−0.106917
$273$	−13.1757	−0.797429
$274$	−35.0735	−2.11887
$275$	−11.1928	−0.674953
$276$	0.872202	0.0525004
$277$	21.4704	1.29003	0.645015	−	0.764170i	$-0.276851\pi$
$277$	21.4704	1.29003	0.645015	+	0.764170i	$0.276851\pi$
$278$	27.9638	1.67716
$279$	3.34126	0.200036
$280$	−9.49228	−0.567272
$281$	2.81541	0.167953	0.0839765	−	0.996468i	$-0.473238\pi$
$281$	2.81541	0.167953	0.0839765	+	0.996468i	$0.473238\pi$
$282$	−18.5003	−1.10167
$283$	−17.2174	−1.02347	−0.511735	−	0.859143i	$-0.670997\pi$
$283$	−17.2174	−1.02347	−0.511735	+	0.859143i	$0.670997\pi$
$284$	0.166568	0.00988398
$285$	5.20198	0.308139
$286$	12.4872	0.738384
$287$	−20.9150	−1.23457
$288$	4.18799	0.246780
$289$	−16.8732	−0.992540
$290$	−9.87476	−0.579866
$291$	−0.683232	−0.0400517
$292$	9.15937	0.536012
$293$	−4.66351	−0.272445	−0.136223	−	0.990678i	$-0.543496\pi$
$293$	−4.66351	−0.272445	−0.136223	+	0.990678i	$0.543496\pi$
$294$	−27.3625	−1.59581
$295$	−0.292777	−0.0170462
$296$	5.27530	0.306621
$297$	2.75025	0.159586
$298$	17.0081	0.985250
$299$	−3.04475	−0.176083
$300$	−3.17467	−0.183290
$301$	20.3066	1.17045
$302$	−5.12811	−0.295089
$303$	2.40148	0.137962
$304$	26.7066	1.53173
$305$	10.0846	0.577440
$306$	−0.593758	−0.0339429
$307$	−24.4001	−1.39259	−0.696294	−	0.717756i	$-0.745169\pi$
$307$	−24.4001	−1.39259	−0.696294	+	0.717756i	$0.745169\pi$
$308$	10.3803	0.591473
$309$	7.83665	0.445812
$310$	5.37325	0.305180
$311$	−13.7692	−0.780780	−0.390390	−	0.920650i	$-0.627660\pi$
$311$	−13.7692	−0.780780	−0.390390	+	0.920650i	$0.627660\pi$
$312$	−5.53898	−0.313583
$313$	10.4214	0.589051	0.294525	−	0.955644i	$-0.404838\pi$
$313$	10.4214	0.589051	0.294525	+	0.955644i	$0.404838\pi$
$314$	32.2419	1.81952
$315$	−4.66666	−0.262937
$316$	10.3962	0.584835
$317$	23.6678	1.32932	0.664658	−	0.747148i	$-0.268577\pi$
$317$	23.6678	1.32932	0.664658	+	0.747148i	$0.268577\pi$
$318$	−4.80099	−0.269226
$319$	−16.8878	−0.945533
$320$	−2.81671	−0.157459
$321$	10.5939	0.591292
$322$	−9.02030	−0.502682
$323$	−1.92066	−0.106869
$324$	0.780065	0.0433370
$325$	11.0824	0.614741
$326$	9.47128	0.524566
$327$	2.18309	0.120725
$328$	−8.79253	−0.485486
$329$	53.6856	2.95978
$330$	4.42281	0.243468
$331$	11.3945	0.626301	0.313150	−	0.949704i	$-0.398616\pi$
$331$	11.3945	0.626301	0.313150	+	0.949704i	$0.398616\pi$
$332$	2.84392	0.156081
$333$	2.59348	0.142122
$334$	−31.3247	−1.71401
$335$	7.55825	0.412952
$336$	−23.9583	−1.30703
$337$	11.2514	0.612905	0.306453	−	0.951886i	$-0.400858\pi$
$337$	11.2514	0.612905	0.306453	+	0.951886i	$0.400858\pi$
$338$	9.31157	0.506483
$339$	12.7515	0.692566
$340$	−0.267924	−0.0145302
$341$	9.18929	0.497628
$342$	8.99285	0.486278
$343$	45.5335	2.45858
$344$	8.53677	0.460272
$345$	−1.07841	−0.0580598
$346$	−18.9340	−1.01790
$347$	22.5935	1.21288	0.606441	−	0.795128i	$-0.292596\pi$
$347$	22.5935	1.21288	0.606441	+	0.795128i	$0.292596\pi$
$348$	−4.78995	−0.256768
$349$	23.1064	1.23686	0.618429	−	0.785841i	$-0.287769\pi$
$349$	23.1064	1.23686	0.618429	+	0.785841i	$0.287769\pi$
$350$	32.8324	1.75497
$351$	−2.72312	−0.145349
$352$	11.5180	0.613912
$353$	−3.98269	−0.211977	−0.105989	−	0.994367i	$-0.533801\pi$
$353$	−3.98269	−0.211977	−0.105989	+	0.994367i	$0.533801\pi$
$354$	−0.506135	−0.0269008
$355$	−0.205949	−0.0109306
$356$	11.0923	0.587891
$357$	1.72302	0.0911916
$358$	8.57358	0.453128
$359$	−9.45160	−0.498836	−0.249418	−	0.968396i	$-0.580239\pi$
$359$	−9.45160	−0.498836	−0.249418	+	0.968396i	$0.580239\pi$
$360$	−1.96184	−0.103398
$361$	10.0897	0.531039
$362$	39.7029	2.08674
$363$	−3.43614	−0.180350
$364$	−10.2779	−0.538708
$365$	−11.3249	−0.592771
$366$	17.4335	0.911265
$367$	37.4394	1.95432	0.977162	−	0.212498i	$-0.0681598\pi$
$367$	37.4394	1.95432	0.977162	+	0.212498i	$0.0681598\pi$
$368$	−5.53649	−0.288609
$369$	−4.32265	−0.225028
$370$	4.17071	0.216825
$371$	13.9319	0.723308
$372$	2.60640	0.135136
$373$	−13.9834	−0.724031	−0.362016	−	0.932172i	$-0.617911\pi$
$373$	−13.9834	−0.724031	−0.362016	+	0.932172i	$0.617911\pi$
$374$	−1.63298	−0.0844394
$375$	8.74771	0.451730
$376$	22.5691	1.16391
$377$	16.7212	0.861183
$378$	−8.06743	−0.414944
$379$	26.2741	1.34961	0.674805	−	0.737997i	$-0.264228\pi$
$379$	26.2741	1.34961	0.674805	+	0.737997i	$0.264228\pi$
$380$	4.05789	0.208165
$381$	9.09729	0.466068
$382$	2.12028	0.108483
$383$	11.3407	0.579484	0.289742	−	0.957105i	$-0.406430\pi$
$383$	11.3407	0.579484	0.289742	+	0.957105i	$0.406430\pi$
$384$	−13.2453	−0.675922
$385$	−12.8345	−0.654106
$386$	−23.6098	−1.20171
$387$	4.19691	0.213341
$388$	−0.532965	−0.0270572
$389$	−7.01435	−0.355641	−0.177821	−	0.984063i	$-0.556905\pi$
$389$	−7.01435	−0.355641	−0.177821	+	0.984063i	$0.556905\pi$
$390$	−4.37918	−0.221748
$391$	0.398169	0.0201363
$392$	33.3804	1.68597
$393$	9.20696	0.464429
$394$	7.23078	0.364281
$395$	−12.8542	−0.646764
$396$	2.14537	0.107809
$397$	−33.8969	−1.70124	−0.850619	−	0.525782i	$-0.823773\pi$
$397$	−33.8969	−1.70124	−0.850619	+	0.525782i	$0.823773\pi$
$398$	−10.6567	−0.534173
$399$	−26.0962	−1.30644
$400$	20.1519	1.00760
$401$	−10.9446	−0.546547	−0.273273	−	0.961936i	$-0.588106\pi$
$401$	−10.9446	−0.546547	−0.273273	+	0.961936i	$0.588106\pi$
$402$	13.0662	0.651684
$403$	−9.09863	−0.453235
$404$	1.87331	0.0932008
$405$	−0.964493	−0.0479260
$406$	49.5376	2.45851
$407$	7.13272	0.353556
$408$	0.724346	0.0358604
$409$	−15.7658	−0.779567	−0.389784	−	0.920906i	$-0.627450\pi$
$409$	−15.7658	−0.779567	−0.389784	+	0.920906i	$0.627450\pi$
$410$	−6.95147	−0.343308
$411$	21.0354	1.03760
$412$	6.11310	0.301171
$413$	1.46874	0.0722721
$414$	−1.86429	−0.0916249
$415$	−3.51630	−0.172608
$416$	−11.4044	−0.559146
$417$	−16.7714	−0.821299
$418$	24.7326	1.20971
$419$	2.48537	0.121418	0.0607092	−	0.998155i	$-0.480664\pi$
$419$	2.48537	0.121418	0.0607092	+	0.998155i	$0.480664\pi$
$420$	−3.64030	−0.177629
$421$	18.5133	0.902283	0.451141	−	0.892452i	$-0.351017\pi$
$421$	18.5133	0.902283	0.451141	+	0.892452i	$0.351017\pi$
$422$	14.6045	0.710934
$423$	11.0956	0.539486
$424$	5.85689	0.284436
$425$	−1.44927	−0.0703000
$426$	−0.356031	−0.0172498
$427$	−50.5901	−2.44822
$428$	8.26391	0.399451
$429$	−7.48924	−0.361584
$430$	6.74926	0.325478
$431$	−30.0779	−1.44880	−0.724400	−	0.689380i	$-0.757883\pi$
$431$	−30.0779	−1.44880	−0.724400	+	0.689380i	$0.757883\pi$
$432$	−4.95163	−0.238235
$433$	24.1201	1.15914	0.579569	−	0.814923i	$-0.303221\pi$
$433$	24.1201	1.15914	0.579569	+	0.814923i	$0.303221\pi$
$434$	−26.9554	−1.29390
$435$	5.92242	0.283958
$436$	1.70295	0.0815566
$437$	−6.03054	−0.288480
$438$	−19.5777	−0.935460
$439$	−20.8891	−0.996981	−0.498491	−	0.866895i	$-0.666112\pi$
$439$	−20.8891	−0.996981	−0.498491	+	0.866895i	$0.666112\pi$
$440$	−5.39554	−0.257222
$441$	16.4107	0.781463
$442$	1.61687	0.0769067
$443$	−33.7670	−1.60432	−0.802159	−	0.597110i	$-0.796316\pi$
$443$	−33.7670	−1.60432	−0.802159	+	0.597110i	$0.796316\pi$
$444$	2.02309	0.0960114
$445$	−13.7148	−0.650145
$446$	44.2281	2.09426
$447$	−10.2006	−0.482473
$448$	14.1303	0.667592
$449$	15.9319	0.751874	0.375937	−	0.926645i	$-0.377321\pi$
$449$	15.9319	0.751874	0.375937	+	0.926645i	$0.377321\pi$
$450$	6.78572	0.319882
$451$	−11.8884	−0.559801
$452$	9.94700	0.467867
$453$	3.07560	0.144504
$454$	−44.0302	−2.06644
$455$	12.7079	0.595754
$456$	−10.9707	−0.513750
$457$	22.0372	1.03086	0.515428	−	0.856933i	$-0.327633\pi$
$457$	22.0372	1.03086	0.515428	+	0.856933i	$0.327633\pi$
$458$	−15.6715	−0.732281
$459$	0.356108	0.0166217
$460$	−0.841233	−0.0392227
$461$	22.1345	1.03091	0.515453	−	0.856918i	$-0.327624\pi$
$461$	22.1345	1.03091	0.515453	+	0.856918i	$0.327624\pi$
$462$	−22.1874	−1.03225
$463$	29.5524	1.37342	0.686709	−	0.726932i	$-0.259055\pi$
$463$	29.5524	1.37342	0.686709	+	0.726932i	$0.259055\pi$
$464$	30.4052	1.41153
$465$	−3.22262	−0.149445
$466$	−28.8168	−1.33491
$467$	16.4380	0.760662	0.380331	−	0.924850i	$-0.375810\pi$
$467$	16.4380	0.760662	0.380331	+	0.924850i	$0.375810\pi$
$468$	−2.12421	−0.0981915
$469$	−37.9167	−1.75083
$470$	17.8434	0.823053
$471$	−19.3372	−0.891011
$472$	0.617451	0.0284205
$473$	11.5425	0.530727
$474$	−22.2215	−1.02067
$475$	21.9502	1.00714
$476$	1.34406	0.0616051
$477$	2.87941	0.131839
$478$	−43.1692	−1.97451
$479$	−35.9100	−1.64077	−0.820384	−	0.571812i	$-0.806241\pi$
$479$	−35.9100	−1.64077	−0.820384	+	0.571812i	$0.806241\pi$
$480$	−4.03929	−0.184367
$481$	−7.06235	−0.322015
$482$	−23.4370	−1.06752
$483$	5.40995	0.246161
$484$	−2.68041	−0.121837
$485$	0.658972	0.0299224
$486$	−1.66735	−0.0756327
$487$	11.5261	0.522297	0.261149	−	0.965299i	$-0.415899\pi$
$487$	11.5261	0.522297	0.261149	+	0.965299i	$0.415899\pi$
$488$	−21.2678	−0.962746
$489$	−5.68043	−0.256878
$490$	26.3909	1.19222
$491$	−8.16131	−0.368315	−0.184157	−	0.982897i	$-0.558956\pi$
$491$	−8.16131	−0.368315	−0.184157	+	0.982897i	$0.558956\pi$
$492$	−3.37195	−0.152019
$493$	−2.18666	−0.0984824
$494$	−24.4886	−1.10179
$495$	−2.65259	−0.119225
$496$	−16.5447	−0.742878
$497$	1.03316	0.0463436
$498$	−6.07875	−0.272395
$499$	−4.53352	−0.202948	−0.101474	−	0.994838i	$-0.532356\pi$
$499$	−4.53352	−0.202948	−0.101474	+	0.994838i	$0.532356\pi$
$500$	6.82379	0.305169
$501$	18.7871	0.839345
$502$	38.6039	1.72298
$503$	−15.1516	−0.675578	−0.337789	−	0.941222i	$-0.609679\pi$
$503$	−15.1516	−0.675578	−0.337789	+	0.941222i	$0.609679\pi$
$504$	9.84173	0.438386
$505$	−2.31621	−0.103070
$506$	−5.12726	−0.227935
$507$	−5.58464	−0.248023
$508$	7.09648	0.314855
$509$	−32.4245	−1.43719	−0.718596	−	0.695428i	$-0.755215\pi$
$509$	−32.4245	−1.43719	−0.718596	+	0.695428i	$0.755215\pi$
$510$	0.572675	0.0253585
$511$	56.8123	2.51323
$512$	−0.593533	−0.0262307
$513$	−5.39349	−0.238128
$514$	−4.44260	−0.195955
$515$	−7.55840	−0.333063
$516$	3.27386	0.144124
$517$	30.5156	1.34208
$518$	−20.9227	−0.919292
$519$	11.3557	0.498461
$520$	5.34231	0.234276
$521$	−21.5352	−0.943472	−0.471736	−	0.881740i	$-0.656373\pi$
$521$	−21.5352	−0.943472	−0.471736	+	0.881740i	$0.656373\pi$
$522$	10.2383	0.448118
$523$	8.72703	0.381606	0.190803	−	0.981628i	$-0.438891\pi$
$523$	8.72703	0.381606	0.190803	+	0.981628i	$0.438891\pi$
$524$	7.18203	0.313748
$525$	−19.6914	−0.859401
$526$	−7.77929	−0.339193
$527$	1.18985	0.0518306
$528$	−13.6182	−0.592656
$529$	−21.7498	−0.945644
$530$	4.63052	0.201137
$531$	0.303556	0.0131732
$532$	−20.3567	−0.882577
$533$	11.7711	0.509862
$534$	−23.7093	−1.02600
$535$	−10.2177	−0.441750
$536$	−15.9399	−0.688500
$537$	−5.14203	−0.221895
$538$	−7.11819	−0.306887
$539$	45.1336	1.94404
$540$	−0.752367	−0.0323767
$541$	26.7264	1.14906	0.574530	−	0.818484i	$-0.305185\pi$
$541$	26.7264	1.14906	0.574530	+	0.818484i	$0.305185\pi$
$542$	8.99220	0.386248
$543$	−23.8120	−1.02187
$544$	1.49138	0.0639422
$545$	−2.10557	−0.0901928
$546$	21.9685	0.940166
$547$	−1.33431	−0.0570511	−0.0285256	−	0.999593i	$-0.509081\pi$
$547$	−1.33431	−0.0570511	−0.0285256	+	0.999593i	$0.509081\pi$
$548$	16.4090	0.700958
$549$	−10.4558	−0.446243
$550$	18.6624	0.795767
$551$	33.1185	1.41089
$552$	2.27431	0.0968012
$553$	64.4842	2.74215
$554$	−35.7987	−1.52094
$555$	−2.50139	−0.106178
$556$	−13.0828	−0.554834
$557$	−16.1757	−0.685385	−0.342693	−	0.939448i	$-0.611339\pi$
$557$	−16.1757	−0.685385	−0.342693	+	0.939448i	$0.611339\pi$
$558$	−5.57106	−0.235842
$559$	−11.4287	−0.483381
$560$	23.1076	0.976474
$561$	0.979385	0.0413497
$562$	−4.69428	−0.198016
$563$	−26.0088	−1.09614	−0.548069	−	0.836433i	$-0.684637\pi$
$563$	−26.0088	−1.09614	−0.548069	+	0.836433i	$0.684637\pi$
$564$	8.65529	0.364453
$565$	−12.2987	−0.517411
$566$	28.7075	1.20667
$567$	4.83846	0.203196
$568$	0.434334	0.0182243
$569$	−27.9424	−1.17141	−0.585704	−	0.810525i	$-0.699182\pi$
$569$	−27.9424	−1.17141	−0.585704	+	0.810525i	$0.699182\pi$
$570$	−8.67354	−0.363295
$571$	−5.65810	−0.236784	−0.118392	−	0.992967i	$-0.537774\pi$
$571$	−5.65810	−0.236784	−0.118392	+	0.992967i	$0.537774\pi$
$572$	−5.84210	−0.244270
$573$	−1.27165	−0.0531238
$574$	34.8726	1.45556
$575$	−4.55045	−0.189767
$576$	2.92040	0.121683
$577$	−10.1727	−0.423495	−0.211748	−	0.977324i	$-0.567915\pi$
$577$	−10.1727	−0.423495	−0.211748	+	0.977324i	$0.567915\pi$
$578$	28.1336	1.17020
$579$	14.1600	0.588471
$580$	4.61987	0.191830
$581$	17.6398	0.731824
$582$	1.13919	0.0472209
$583$	7.91908	0.327975
$584$	23.8835	0.988308
$585$	2.62642	0.108589
$586$	7.77571	0.321212
$587$	16.3736	0.675812	0.337906	−	0.941180i	$-0.390281\pi$
$587$	16.3736	0.675812	0.337906	+	0.941180i	$0.390281\pi$
$588$	12.8014	0.527923
$589$	−18.0210	−0.742544
$590$	0.488163	0.0200974
$591$	−4.33668	−0.178387
$592$	−12.8420	−0.527801
$593$	19.9376	0.818738	0.409369	−	0.912369i	$-0.365749\pi$
$593$	19.9376	0.818738	0.409369	+	0.912369i	$0.365749\pi$
$594$	−4.58563	−0.188151
$595$	−1.66184	−0.0681286
$596$	−7.95716	−0.325938
$597$	6.39140	0.261583
$598$	5.07668	0.207601
$599$	−43.3722	−1.77214	−0.886070	−	0.463551i	$-0.846575\pi$
$599$	−43.3722	−1.77214	−0.886070	+	0.463551i	$0.846575\pi$
$600$	−8.27813	−0.337953
$601$	19.6179	0.800230	0.400115	−	0.916465i	$-0.368970\pi$
$601$	19.6179	0.800230	0.400115	+	0.916465i	$0.368970\pi$
$602$	−33.8583	−1.37996
$603$	−7.83651	−0.319127
$604$	2.39917	0.0976207
$605$	3.31413	0.134738
$606$	−4.00412	−0.162656
$607$	−17.6170	−0.715051	−0.357526	−	0.933903i	$-0.616379\pi$
$607$	−17.6170	−0.715051	−0.357526	+	0.933903i	$0.616379\pi$
$608$	−22.5879	−0.916059
$609$	−29.7103	−1.20392
$610$	−16.8145	−0.680799
$611$	−30.2146	−1.22235
$612$	0.277787	0.0112289
$613$	−43.2639	−1.74741	−0.873707	−	0.486453i	$-0.838290\pi$
$613$	−43.2639	−1.74741	−0.873707	+	0.486453i	$0.838290\pi$
$614$	40.6836	1.64186
$615$	4.16916	0.168117
$616$	27.0672	1.09057
$617$	−0.572638	−0.0230535	−0.0115268	−	0.999934i	$-0.503669\pi$
$617$	−0.572638	−0.0230535	−0.0115268	+	0.999934i	$0.503669\pi$
$618$	−13.0665	−0.525610
$619$	6.42941	0.258420	0.129210	−	0.991617i	$-0.458756\pi$
$619$	6.42941	0.258420	0.129210	+	0.991617i	$0.458756\pi$
$620$	−2.51385	−0.100959
$621$	1.11811	0.0448684
$622$	22.9581	0.920537
$623$	68.8016	2.75648
$624$	13.4839	0.539786
$625$	11.9117	0.476467
$626$	−17.3761	−0.694489
$627$	−14.8334	−0.592390
$628$	−15.0843	−0.601928
$629$	0.923560	0.0368247
$630$	7.78097	0.310001
$631$	−21.7519	−0.865928	−0.432964	−	0.901411i	$-0.642532\pi$
$631$	−21.7519	−0.865928	−0.432964	+	0.901411i	$0.642532\pi$
$632$	27.1088	1.07833
$633$	−8.75907	−0.348142
$634$	−39.4625	−1.56726
$635$	−8.77427	−0.348196
$636$	2.24613	0.0890647
$637$	−44.6883	−1.77062
$638$	28.1579	1.11478
$639$	0.213531	0.00844714
$640$	12.7750	0.504977
$641$	13.2244	0.522331	0.261165	−	0.965294i	$-0.415893\pi$
$641$	13.2244	0.522331	0.261165	+	0.965294i	$0.415893\pi$
$642$	−17.6637	−0.697131
$643$	38.2453	1.50825	0.754124	−	0.656732i	$-0.228062\pi$
$643$	38.2453	1.50825	0.754124	+	0.656732i	$0.228062\pi$
$644$	4.22012	0.166296
$645$	−4.04789	−0.159385
$646$	3.20243	0.125998
$647$	−33.4188	−1.31383	−0.656915	−	0.753964i	$-0.728139\pi$
$647$	−33.4188	−1.31383	−0.656915	+	0.753964i	$0.728139\pi$
$648$	2.03406	0.0799055
$649$	0.834854	0.0327709
$650$	−18.4783	−0.724778
$651$	16.1666	0.633617
$652$	−4.43111	−0.173535
$653$	29.5998	1.15833	0.579164	−	0.815211i	$-0.303379\pi$
$653$	29.5998	1.15833	0.579164	+	0.815211i	$0.303379\pi$
$654$	−3.63998	−0.142334
$655$	−8.88004	−0.346972
$656$	21.4042	0.835692
$657$	11.7418	0.458091
$658$	−89.5129	−3.48957
$659$	11.6734	0.454729	0.227365	−	0.973810i	$-0.426989\pi$
$659$	11.6734	0.454729	0.227365	+	0.973810i	$0.426989\pi$
$660$	−2.06920	−0.0805434
$661$	−28.4250	−1.10560	−0.552801	−	0.833313i	$-0.686441\pi$
$661$	−28.4250	−1.10560	−0.552801	+	0.833313i	$0.686441\pi$
$662$	−18.9987	−0.738406
$663$	−0.969723	−0.0376609
$664$	7.41568	0.287784
$665$	25.1696	0.976035
$666$	−4.32425	−0.167561
$667$	−6.86572	−0.265842
$668$	14.6552	0.567025
$669$	−26.5259	−1.02555
$670$	−12.6023	−0.486868
$671$	−28.7561	−1.11012
$672$	20.2634	0.781679
$673$	−18.7715	−0.723589	−0.361794	−	0.932258i	$-0.617836\pi$
$673$	−18.7715	−0.723589	−0.361794	+	0.932258i	$0.617836\pi$
$674$	−18.7601	−0.722613
$675$	−4.06975	−0.156645
$676$	−4.35639	−0.167553
$677$	40.4203	1.55348	0.776740	−	0.629821i	$-0.216872\pi$
$677$	40.4203	1.55348	0.776740	+	0.629821i	$0.216872\pi$
$678$	−21.2612	−0.816533
$679$	−3.30579	−0.126865
$680$	−0.698626	−0.0267911
$681$	26.4072	1.01193
$682$	−15.3218	−0.586702
$683$	−1.84211	−0.0704866	−0.0352433	−	0.999379i	$-0.511221\pi$
$683$	−1.84211	−0.0704866	−0.0352433	+	0.999379i	$0.511221\pi$
$684$	−4.20727	−0.160869
$685$	−20.2885	−0.775184
$686$	−75.9204	−2.89865
$687$	9.39902	0.358595
$688$	−20.7815	−0.792289
$689$	−7.84096	−0.298717
$690$	1.79809	0.0684523
$691$	−12.4512	−0.473667	−0.236834	−	0.971550i	$-0.576110\pi$
$691$	−12.4512	−0.473667	−0.236834	+	0.971550i	$0.576110\pi$
$692$	8.85821	0.336739
$693$	13.3070	0.505490
$694$	−37.6713	−1.42998
$695$	16.1759	0.613586
$696$	−12.4901	−0.473434
$697$	−1.53933	−0.0583063
$698$	−38.5265	−1.45825
$699$	17.2830	0.653702
$700$	−15.3605	−0.580574
$701$	−3.08617	−0.116563	−0.0582816	−	0.998300i	$-0.518562\pi$
$701$	−3.08617	−0.116563	−0.0582816	+	0.998300i	$0.518562\pi$
$702$	4.54039	0.171366
$703$	−13.9879	−0.527564
$704$	8.03183	0.302711
$705$	−10.7016	−0.403046
$706$	6.64056	0.249921
$707$	11.6195	0.436996
$708$	0.236793	0.00889924
$709$	42.9942	1.61468	0.807340	−	0.590086i	$-0.200906\pi$
$709$	42.9942	1.61468	0.807340	+	0.590086i	$0.200906\pi$
$710$	0.343389	0.0128872
$711$	13.3274	0.499817
$712$	28.9238	1.08396
$713$	3.73591	0.139911
$714$	−2.87287	−0.107515
$715$	7.22332	0.270137
$716$	−4.01112	−0.149903
$717$	25.8908	0.966911
$718$	15.7591	0.588126
$719$	6.44245	0.240263	0.120131	−	0.992758i	$-0.461668\pi$
$719$	6.44245	0.240263	0.120131	+	0.992758i	$0.461668\pi$
$720$	4.77581	0.177984
$721$	37.9174	1.41212
$722$	−16.8232	−0.626093
$723$	14.0564	0.522763
$724$	−18.5749	−0.690330
$725$	24.9901	0.928110
$726$	5.72925	0.212632
$727$	31.4740	1.16731	0.583653	−	0.812003i	$-0.301623\pi$
$727$	31.4740	1.16731	0.583653	+	0.812003i	$0.301623\pi$
$728$	−26.8002	−0.993280
$729$	1.00000	0.0370370
$730$	18.8826	0.698875
$731$	1.49455	0.0552780
$732$	−8.15621	−0.301462
$733$	−34.6751	−1.28075	−0.640376	−	0.768061i	$-0.721222\pi$
$733$	−34.6751	−1.28075	−0.640376	+	0.768061i	$0.721222\pi$
$734$	−62.4248	−2.30414
$735$	−15.8280	−0.583826
$736$	4.68265	0.172605
$737$	−21.5523	−0.793891
$738$	7.20738	0.265307
$739$	47.4389	1.74507	0.872535	−	0.488552i	$-0.162475\pi$
$739$	47.4389	1.74507	0.872535	+	0.488552i	$0.162475\pi$
$740$	−1.95125	−0.0717294
$741$	14.6871	0.539544
$742$	−23.2294	−0.852778
$743$	−31.3927	−1.15169	−0.575844	−	0.817560i	$-0.695326\pi$
$743$	−31.3927	−1.15169	−0.575844	+	0.817560i	$0.695326\pi$
$744$	6.79633	0.249165
$745$	9.83843	0.360452
$746$	23.3152	0.853630
$747$	3.64575	0.133391
$748$	0.763984	0.0279340
$749$	51.2580	1.87293
$750$	−14.5855	−0.532588
$751$	−27.6917	−1.01049	−0.505243	−	0.862977i	$-0.668597\pi$
$751$	−27.6917	−1.01049	−0.505243	+	0.862977i	$0.668597\pi$
$752$	−54.9413	−2.00350
$753$	−23.1528	−0.843736
$754$	−27.8801	−1.01533
$755$	−2.96639	−0.107958
$756$	3.77432	0.137271
$757$	38.3017	1.39210	0.696049	−	0.717994i	$-0.254940\pi$
$757$	38.3017	1.39210	0.696049	+	0.717994i	$0.254940\pi$
$758$	−43.8082	−1.59118
$759$	3.07509	0.111619
$760$	10.5812	0.383819
$761$	−4.05825	−0.147112	−0.0735558	−	0.997291i	$-0.523435\pi$
$761$	−4.05825	−0.147112	−0.0735558	+	0.997291i	$0.523435\pi$
$762$	−15.1684	−0.549493
$763$	10.5628	0.382399
$764$	−0.991968	−0.0358881
$765$	−0.343464	−0.0124180
$766$	−18.9090	−0.683210
$767$	−0.826617	−0.0298474
$768$	16.2438	0.586148
$769$	15.6502	0.564361	0.282180	−	0.959361i	$-0.408942\pi$
$769$	15.6502	0.564361	0.282180	+	0.959361i	$0.408942\pi$
$770$	21.3996	0.771188
$771$	2.66446	0.0959583
$772$	11.0458	0.397546
$773$	28.8374	1.03721	0.518604	−	0.855015i	$-0.326452\pi$
$773$	28.8374	1.03721	0.518604	+	0.855015i	$0.326452\pi$
$774$	−6.99773	−0.251528
$775$	−13.5981	−0.488458
$776$	−1.38974	−0.0498886
$777$	12.5485	0.450174
$778$	11.6954	0.419300
$779$	23.3142	0.835317
$780$	2.04878	0.0733582
$781$	0.587262	0.0210139
$782$	−0.663889	−0.0237406
$783$	−6.14045	−0.219442
$784$	−81.2598	−2.90214
$785$	18.6506	0.665668
$786$	−15.3512	−0.547561
$787$	10.8294	0.386026	0.193013	−	0.981196i	$-0.438174\pi$
$787$	10.8294	0.386026	0.193013	+	0.981196i	$0.438174\pi$
$788$	−3.38289	−0.120511
$789$	4.66565	0.166102
$790$	21.4325	0.762533
$791$	61.6976	2.19371
$792$	5.59417	0.198780
$793$	28.4724	1.01108
$794$	56.5182	2.00575
$795$	−2.77717	−0.0984960
$796$	4.98571	0.176714
$797$	25.9548	0.919367	0.459684	−	0.888083i	$-0.347963\pi$
$797$	25.9548	0.919367	0.459684	+	0.888083i	$0.347963\pi$
$798$	43.5116	1.54029
$799$	3.95123	0.139784
$800$	−17.0441	−0.602599
$801$	14.2197	0.502429
$802$	18.2485	0.644377
$803$	32.2929	1.13959
$804$	−6.11299	−0.215588
$805$	−5.21786	−0.183905
$806$	15.1706	0.534363
$807$	4.26915	0.150281
$808$	4.88476	0.171845
$809$	−3.19949	−0.112488	−0.0562441	−	0.998417i	$-0.517913\pi$
$809$	−3.19949	−0.112488	−0.0562441	+	0.998417i	$0.517913\pi$
$810$	1.60815	0.0565046
$811$	−12.8221	−0.450243	−0.225122	−	0.974331i	$-0.572278\pi$
$811$	−12.8221	−0.450243	−0.225122	+	0.974331i	$0.572278\pi$
$812$	−23.1760	−0.813319
$813$	−5.39310	−0.189144
$814$	−11.8928	−0.416841
$815$	5.47873	0.191912
$816$	−1.76331	−0.0617284
$817$	−22.6360	−0.791933
$818$	26.2871	0.919107
$819$	−13.1757	−0.460396
$820$	3.25222	0.113572
$821$	−11.7601	−0.410430	−0.205215	−	0.978717i	$-0.565789\pi$
$821$	−11.7601	−0.410430	−0.205215	+	0.978717i	$0.565789\pi$
$822$	−35.0735	−1.22333
$823$	−42.5944	−1.48475	−0.742374	−	0.669986i	$-0.766300\pi$
$823$	−42.5944	−1.48475	−0.742374	+	0.669986i	$0.766300\pi$
$824$	15.9402	0.555304
$825$	−11.1928	−0.389684
$826$	−2.44891	−0.0852086
$827$	−2.70036	−0.0939008	−0.0469504	−	0.998897i	$-0.514950\pi$
$827$	−2.70036	−0.0939008	−0.0469504	+	0.998897i	$0.514950\pi$
$828$	0.872202	0.0303111
$829$	7.27108	0.252535	0.126268	−	0.991996i	$-0.459700\pi$
$829$	7.27108	0.252535	0.126268	+	0.991996i	$0.459700\pi$
$830$	5.86291	0.203505
$831$	21.4704	0.744799
$832$	−7.95259	−0.275706
$833$	5.84399	0.202482
$834$	27.9638	0.968308
$835$	−18.1200	−0.627069
$836$	−11.5710	−0.400193
$837$	3.34126	0.115491
$838$	−4.14399	−0.143152
$839$	−23.1985	−0.800901	−0.400451	−	0.916318i	$-0.631146\pi$
$839$	−23.1985	−0.800901	−0.400451	+	0.916318i	$0.631146\pi$
$840$	−9.49228	−0.327515
$841$	8.70513	0.300177
$842$	−30.8682	−1.06379
$843$	2.81541	0.0969677
$844$	−6.83264	−0.235189
$845$	5.38635	0.185296
$846$	−18.5003	−0.636052
$847$	−16.6256	−0.571263
$848$	−14.2578	−0.489613
$849$	−17.2174	−0.590901
$850$	2.41645	0.0828835
$851$	2.89981	0.0994042
$852$	0.166568	0.00570652
$853$	0.401910	0.0137611	0.00688057	−	0.999976i	$-0.497810\pi$
$853$	0.401910	0.0137611	0.00688057	+	0.999976i	$0.497810\pi$
$854$	84.3515	2.88645
$855$	5.20198	0.177904
$856$	21.5486	0.736515
$857$	16.8883	0.576894	0.288447	−	0.957496i	$-0.406861\pi$
$857$	16.8883	0.576894	0.288447	+	0.957496i	$0.406861\pi$
$858$	12.4872	0.426306
$859$	35.4777	1.21048	0.605241	−	0.796042i	$-0.293077\pi$
$859$	35.4777	1.21048	0.605241	+	0.796042i	$0.293077\pi$
$860$	−3.15762	−0.107674
$861$	−20.9150	−0.712781
$862$	50.1504	1.70813
$863$	52.0178	1.77071	0.885353	−	0.464920i	$-0.153917\pi$
$863$	52.0178	1.77071	0.885353	+	0.464920i	$0.153917\pi$
$864$	4.18799	0.142478
$865$	−10.9525	−0.372397
$866$	−40.2167	−1.36662
$867$	−16.8732	−0.573043
$868$	12.6110	0.428044
$869$	36.6537	1.24339
$870$	−9.87476	−0.334786
$871$	21.3397	0.723069
$872$	4.44054	0.150375
$873$	−0.683232	−0.0231239
$874$	10.0550	0.340117
$875$	42.3255	1.43086
$876$	9.15937	0.309466
$877$	23.2897	0.786438	0.393219	−	0.919445i	$-0.371361\pi$
$877$	23.2897	0.786438	0.393219	+	0.919445i	$0.371361\pi$
$878$	34.8295	1.17544
$879$	−4.66351	−0.157296
$880$	13.1347	0.442769
$881$	7.85818	0.264749	0.132374	−	0.991200i	$-0.457740\pi$
$881$	7.85818	0.264749	0.132374	+	0.991200i	$0.457740\pi$
$882$	−27.3625	−0.921342
$883$	−27.7667	−0.934425	−0.467213	−	0.884145i	$-0.654742\pi$
$883$	−27.7667	−0.934425	−0.467213	+	0.884145i	$0.654742\pi$
$884$	−0.756447	−0.0254421
$885$	−0.292777	−0.00984160
$886$	56.3015	1.89149
$887$	−6.18776	−0.207764	−0.103882	−	0.994590i	$-0.533127\pi$
$887$	−6.18776	−0.207764	−0.103882	+	0.994590i	$0.533127\pi$
$888$	5.27530	0.177028
$889$	44.0169	1.47628
$890$	22.8674	0.766518
$891$	2.75025	0.0921368
$892$	−20.6920	−0.692818
$893$	−59.8440	−2.00260
$894$	17.0081	0.568834
$895$	4.95945	0.165776
$896$	−64.0870	−2.14100
$897$	−3.04475	−0.101661
$898$	−26.5641	−0.886457
$899$	−20.5168	−0.684275
$900$	−3.17467	−0.105822
$901$	1.02538	0.0341604
$902$	19.8221	0.660003
$903$	20.3066	0.675761
$904$	25.9373	0.862662
$905$	22.9665	0.763431
$906$	−5.12811	−0.170370
$907$	−31.9412	−1.06059	−0.530296	−	0.847813i	$-0.677919\pi$
$907$	−31.9412	−1.06059	−0.530296	+	0.847813i	$0.677919\pi$
$908$	20.5994	0.683614
$909$	2.40148	0.0796521
$910$	−21.1885	−0.702391
$911$	−33.9608	−1.12517	−0.562586	−	0.826739i	$-0.690194\pi$
$911$	−33.9608	−1.12517	−0.562586	+	0.826739i	$0.690194\pi$
$912$	26.7066	0.884343
$913$	10.0267	0.331836
$914$	−36.7438	−1.21538
$915$	10.0846	0.333385
$916$	7.33185	0.242251
$917$	44.5475	1.47109
$918$	−0.593758	−0.0195969
$919$	−5.96995	−0.196931	−0.0984653	−	0.995140i	$-0.531393\pi$
$919$	−5.96995	−0.196931	−0.0984653	+	0.995140i	$0.531393\pi$
$920$	−2.19356	−0.0723195
$921$	−24.4001	−0.804011
$922$	−36.9060	−1.21543
$923$	−0.581468	−0.0191393
$924$	10.3803	0.341487
$925$	−10.5548	−0.347041
$926$	−49.2743	−1.61926
$927$	7.83665	0.257389
$928$	−25.7161	−0.844174
$929$	19.2091	0.630231	0.315116	−	0.949053i	$-0.397957\pi$
$929$	19.2091	0.630231	0.315116	+	0.949053i	$0.397957\pi$
$930$	5.37325	0.176196
$931$	−88.5111	−2.90083
$932$	13.4818	0.441613
$933$	−13.7692	−0.450784
$934$	−27.4080	−0.896818
$935$	−0.944610	−0.0308920
$936$	−5.53898	−0.181047
$937$	−7.44565	−0.243239	−0.121619	−	0.992577i	$-0.538809\pi$
$937$	−7.44565	−0.243239	−0.121619	+	0.992577i	$0.538809\pi$
$938$	63.2204	2.06422
$939$	10.4214	0.340089
$940$	−8.34796	−0.272280
$941$	58.3805	1.90315	0.951575	−	0.307418i	$-0.0994649\pi$
$941$	58.3805	1.90315	0.951575	+	0.307418i	$0.0994649\pi$
$942$	32.2419	1.05050
$943$	−4.83322	−0.157391
$944$	−1.50310	−0.0489216
$945$	−4.66666	−0.151807
$946$	−19.2455	−0.625725
$947$	−6.36350	−0.206786	−0.103393	−	0.994641i	$-0.532970\pi$
$947$	−6.36350	−0.206786	−0.103393	+	0.994641i	$0.532970\pi$
$948$	10.3962	0.337654
$949$	−31.9743	−1.03793
$950$	−36.5987	−1.18742
$951$	23.6678	0.767480
$952$	3.50472	0.113589
$953$	27.5184	0.891408	0.445704	−	0.895180i	$-0.352953\pi$
$953$	27.5184	0.891408	0.445704	+	0.895180i	$0.352953\pi$
$954$	−4.80099	−0.155438
$955$	1.22649	0.0396884
$956$	20.1966	0.653203
$957$	−16.8878	−0.545904
$958$	59.8746	1.93446
$959$	101.779	3.28662
$960$	−2.81671	−0.0909088
$961$	−19.8360	−0.639871
$962$	11.7754	0.379655
$963$	10.5939	0.341383
$964$	10.9649	0.353156
$965$	−13.6573	−0.439643
$966$	−9.02030	−0.290223
$967$	−10.1257	−0.325620	−0.162810	−	0.986657i	$-0.552056\pi$
$967$	−10.1257	−0.325620	−0.162810	+	0.986657i	$0.552056\pi$
$968$	−6.98931	−0.224645
$969$	−1.92066	−0.0617006
$970$	−1.09874	−0.0352784
$971$	−9.04454	−0.290253	−0.145127	−	0.989413i	$-0.546359\pi$
$971$	−9.04454	−0.290253	−0.145127	+	0.989413i	$0.546359\pi$
$972$	0.780065	0.0250206
$973$	−81.1478	−2.60148
$974$	−19.2181	−0.615787
$975$	11.0824	0.354921
$976$	51.7733	1.65722
$977$	−30.5525	−0.977461	−0.488731	−	0.872435i	$-0.662540\pi$
$977$	−30.5525	−0.977461	−0.488731	+	0.872435i	$0.662540\pi$
$978$	9.47128	0.302858
$979$	39.1077	1.24989
$980$	−12.3469	−0.394407
$981$	2.18309	0.0697006
$982$	13.6078	0.434242
$983$	16.4155	0.523574	0.261787	−	0.965126i	$-0.415688\pi$
$983$	16.4155	0.523574	0.261787	+	0.965126i	$0.415688\pi$
$984$	−8.79253	−0.280296
$985$	4.18270	0.133272
$986$	3.64594	0.116110
$987$	53.6856	1.70883
$988$	11.4569	0.364492
$989$	4.69262	0.149217
$990$	4.42281	0.140566
$991$	−28.7606	−0.913612	−0.456806	−	0.889566i	$-0.651007\pi$
$991$	−28.7606	−0.913612	−0.456806	+	0.889566i	$0.651007\pi$
$992$	13.9932	0.444283
$993$	11.3945	0.361595
$994$	−1.72264	−0.0546389
$995$	−6.16446	−0.195427
$996$	2.84392	0.0901132
$997$	34.0765	1.07921	0.539606	−	0.841917i	$-0.318573\pi$
$997$	34.0765	1.07921	0.539606	+	0.841917i	$0.318573\pi$
$998$	7.55898	0.239275
$999$	2.59348	0.0820541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.c.1.20	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.c.1.20	✓	92	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.66735 q^{2} +1.00000 q^{3} +0.780065 q^{4} -0.964493 q^{5} -1.66735 q^{6} +4.83846 q^{7} +2.03406 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.66735 q^{2} +1.00000 q^{3} +0.780065 q^{4} -0.964493 q^{5} -1.66735 q^{6} +4.83846 q^{7} +2.03406 q^{8} +1.00000 q^{9} +1.60815 q^{10} +2.75025 q^{11} +0.780065 q^{12} -2.72312 q^{13} -8.06743 q^{14} -0.964493 q^{15} -4.95163 q^{16} +0.356108 q^{17} -1.66735 q^{18} -5.39349 q^{19} -0.752367 q^{20} +4.83846 q^{21} -4.58563 q^{22} +1.11811 q^{23} +2.03406 q^{24} -4.06975 q^{25} +4.54039 q^{26} +1.00000 q^{27} +3.77432 q^{28} -6.14045 q^{29} +1.60815 q^{30} +3.34126 q^{31} +4.18799 q^{32} +2.75025 q^{33} -0.593758 q^{34} -4.66666 q^{35} +0.780065 q^{36} +2.59348 q^{37} +8.99285 q^{38} -2.72312 q^{39} -1.96184 q^{40} -4.32265 q^{41} -8.06743 q^{42} +4.19691 q^{43} +2.14537 q^{44} -0.964493 q^{45} -1.86429 q^{46} +11.0956 q^{47} -4.95163 q^{48} +16.4107 q^{49} +6.78572 q^{50} +0.356108 q^{51} -2.12421 q^{52} +2.87941 q^{53} -1.66735 q^{54} -2.65259 q^{55} +9.84173 q^{56} -5.39349 q^{57} +10.2383 q^{58} +0.303556 q^{59} -0.752367 q^{60} -10.4558 q^{61} -5.57106 q^{62} +4.83846 q^{63} +2.92040 q^{64} +2.62642 q^{65} -4.58563 q^{66} -7.83651 q^{67} +0.277787 q^{68} +1.11811 q^{69} +7.78097 q^{70} +0.213531 q^{71} +2.03406 q^{72} +11.7418 q^{73} -4.32425 q^{74} -4.06975 q^{75} -4.20727 q^{76} +13.3070 q^{77} +4.54039 q^{78} +13.3274 q^{79} +4.77581 q^{80} +1.00000 q^{81} +7.20738 q^{82} +3.64575 q^{83} +3.77432 q^{84} -0.343464 q^{85} -6.99773 q^{86} -6.14045 q^{87} +5.59417 q^{88} +14.2197 q^{89} +1.60815 q^{90} -13.1757 q^{91} +0.872202 q^{92} +3.34126 q^{93} -18.5003 q^{94} +5.20198 q^{95} +4.18799 q^{96} -0.683232 q^{97} -27.3625 q^{98} +2.75025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

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