LMFDB - Embedded newform 6001.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76448 q^{2} -0.301476 q^{3} +5.64235 q^{4} -1.88471 q^{5} +0.833425 q^{6} +2.57260 q^{7} -10.0692 q^{8} -2.90911 q^{9} +O(q^{10})$	\(q-2.76448 q^{2} -0.301476 q^{3} +5.64235 q^{4} -1.88471 q^{5} +0.833425 q^{6} +2.57260 q^{7} -10.0692 q^{8} -2.90911 q^{9} +5.21024 q^{10} +0.511734 q^{11} -1.70103 q^{12} +3.43977 q^{13} -7.11191 q^{14} +0.568195 q^{15} +16.5514 q^{16} -1.00000 q^{17} +8.04218 q^{18} +6.64750 q^{19} -10.6342 q^{20} -0.775578 q^{21} -1.41468 q^{22} -3.04629 q^{23} +3.03562 q^{24} -1.44787 q^{25} -9.50919 q^{26} +1.78146 q^{27} +14.5155 q^{28} +2.01348 q^{29} -1.57076 q^{30} -7.49344 q^{31} -25.6176 q^{32} -0.154276 q^{33} +2.76448 q^{34} -4.84861 q^{35} -16.4142 q^{36} +7.15663 q^{37} -18.3769 q^{38} -1.03701 q^{39} +18.9775 q^{40} +6.85979 q^{41} +2.14407 q^{42} -10.5535 q^{43} +2.88738 q^{44} +5.48283 q^{45} +8.42141 q^{46} +0.219973 q^{47} -4.98985 q^{48} -0.381721 q^{49} +4.00261 q^{50} +0.301476 q^{51} +19.4084 q^{52} -8.99235 q^{53} -4.92480 q^{54} -0.964469 q^{55} -25.9040 q^{56} -2.00406 q^{57} -5.56622 q^{58} -11.0607 q^{59} +3.20595 q^{60} -8.81765 q^{61} +20.7155 q^{62} -7.48399 q^{63} +37.7166 q^{64} -6.48297 q^{65} +0.426492 q^{66} +10.6431 q^{67} -5.64235 q^{68} +0.918384 q^{69} +13.4039 q^{70} -10.3609 q^{71} +29.2924 q^{72} +10.1586 q^{73} -19.7844 q^{74} +0.436499 q^{75} +37.5075 q^{76} +1.31649 q^{77} +2.86679 q^{78} +0.135655 q^{79} -31.1946 q^{80} +8.19027 q^{81} -18.9637 q^{82} +14.4050 q^{83} -4.37608 q^{84} +1.88471 q^{85} +29.1749 q^{86} -0.607016 q^{87} -5.15275 q^{88} +9.50117 q^{89} -15.1572 q^{90} +8.84917 q^{91} -17.1882 q^{92} +2.25909 q^{93} -0.608110 q^{94} -12.5286 q^{95} +7.72310 q^{96} +10.9176 q^{97} +1.05526 q^{98} -1.48869 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.76448	−1.95478	−0.977391	−	0.211439i	$-0.932185\pi$
$2$	−2.76448	−1.95478	−0.977391	+	0.211439i	$0.932185\pi$
$3$	−0.301476	−0.174057	−0.0870287	−	0.996206i	$-0.527737\pi$
$3$	−0.301476	−0.174057	−0.0870287	+	0.996206i	$0.527737\pi$
$4$	5.64235	2.82117
$5$	−1.88471	−0.842867	−0.421434	−	0.906859i	$-0.638473\pi$
$5$	−1.88471	−0.842867	−0.421434	+	0.906859i	$0.638473\pi$
$6$	0.833425	0.340244
$7$	2.57260	0.972352	0.486176	−	0.873861i	$-0.338391\pi$
$7$	2.57260	0.972352	0.486176	+	0.873861i	$0.338391\pi$
$8$	−10.0692	−3.56000
$9$	−2.90911	−0.969704
$10$	5.21024	1.64762
$11$	0.511734	0.154293	0.0771467	−	0.997020i	$-0.475419\pi$
$11$	0.511734	0.154293	0.0771467	+	0.997020i	$0.475419\pi$
$12$	−1.70103	−0.491046
$13$	3.43977	0.954022	0.477011	−	0.878897i	$-0.341720\pi$
$13$	3.43977	0.954022	0.477011	+	0.878897i	$0.341720\pi$
$14$	−7.11191	−1.90074
$15$	0.568195	0.146707
$16$	16.5514	4.13785
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	8.04218	1.89556
$19$	6.64750	1.52504	0.762520	−	0.646964i	$-0.223962\pi$
$19$	6.64750	1.52504	0.762520	+	0.646964i	$0.223962\pi$
$20$	−10.6342	−2.37788
$21$	−0.775578	−0.169245
$22$	−1.41468	−0.301610
$23$	−3.04629	−0.635195	−0.317598	−	0.948226i	$-0.602876\pi$
$23$	−3.04629	−0.635195	−0.317598	+	0.948226i	$0.602876\pi$
$24$	3.03562	0.619644
$25$	−1.44787	−0.289574
$26$	−9.50919	−1.86490
$27$	1.78146	0.342842
$28$	14.5155	2.74317
$29$	2.01348	0.373894	0.186947	−	0.982370i	$-0.440141\pi$
$29$	2.01348	0.373894	0.186947	+	0.982370i	$0.440141\pi$
$30$	−1.57076	−0.286781
$31$	−7.49344	−1.34586	−0.672931	−	0.739705i	$-0.734965\pi$
$31$	−7.49344	−1.34586	−0.672931	+	0.739705i	$0.734965\pi$
$32$	−25.6176	−4.52860
$33$	−0.154276	−0.0268559
$34$	2.76448	0.474104
$35$	−4.84861	−0.819564
$36$	−16.4142	−2.73570
$37$	7.15663	1.17654	0.588271	−	0.808664i	$-0.299809\pi$
$37$	7.15663	1.17654	0.588271	+	0.808664i	$0.299809\pi$
$38$	−18.3769	−2.98112
$39$	−1.03701	−0.166055
$40$	18.9775	3.00061
$41$	6.85979	1.07132	0.535659	−	0.844434i	$-0.320063\pi$
$41$	6.85979	1.07132	0.535659	+	0.844434i	$0.320063\pi$
$42$	2.14407	0.330837
$43$	−10.5535	−1.60939	−0.804696	−	0.593687i	$-0.797672\pi$
$43$	−10.5535	−1.60939	−0.804696	+	0.593687i	$0.797672\pi$
$44$	2.88738	0.435289
$45$	5.48283	0.817332
$46$	8.42141	1.24167
$47$	0.219973	0.0320863	0.0160432	−	0.999871i	$-0.494893\pi$
$47$	0.219973	0.0320863	0.0160432	+	0.999871i	$0.494893\pi$
$48$	−4.98985	−0.720224
$49$	−0.381721	−0.0545315
$50$	4.00261	0.566055
$51$	0.301476	0.0422151
$52$	19.4084	2.69146
$53$	−8.99235	−1.23519	−0.617597	−	0.786495i	$-0.711894\pi$
$53$	−8.99235	−1.23519	−0.617597	+	0.786495i	$0.711894\pi$
$54$	−4.92480	−0.670181
$55$	−0.964469	−0.130049
$56$	−25.9040	−3.46157
$57$	−2.00406	−0.265445
$58$	−5.56622	−0.730881
$59$	−11.0607	−1.43998	−0.719991	−	0.693984i	$-0.755854\pi$
$59$	−11.0607	−1.43998	−0.719991	+	0.693984i	$0.755854\pi$
$60$	3.20595	0.413887
$61$	−8.81765	−1.12898	−0.564492	−	0.825438i	$-0.690928\pi$
$61$	−8.81765	−1.12898	−0.564492	+	0.825438i	$0.690928\pi$
$62$	20.7155	2.63087
$63$	−7.48399	−0.942894
$64$	37.7166	4.71457
$65$	−6.48297	−0.804114
$66$	0.426492	0.0524975
$67$	10.6431	1.30026	0.650129	−	0.759824i	$-0.274715\pi$
$67$	10.6431	1.30026	0.650129	+	0.759824i	$0.274715\pi$
$68$	−5.64235	−0.684235
$69$	0.918384	0.110560
$70$	13.4039	1.60207
$71$	−10.3609	−1.22961	−0.614807	−	0.788678i	$-0.710766\pi$
$71$	−10.3609	−1.22961	−0.614807	+	0.788678i	$0.710766\pi$
$72$	29.2924	3.45215
$73$	10.1586	1.18898	0.594488	−	0.804104i	$-0.297355\pi$
$73$	10.1586	1.18898	0.594488	+	0.804104i	$0.297355\pi$
$74$	−19.7844	−2.29988
$75$	0.436499	0.0504026
$76$	37.5075	4.30241
$77$	1.31649	0.150028
$78$	2.86679	0.324600
$79$	0.135655	0.0152624	0.00763119	−	0.999971i	$-0.497571\pi$
$79$	0.135655	0.0152624	0.00763119	+	0.999971i	$0.497571\pi$
$80$	−31.1946	−3.48766
$81$	8.19027	0.910030
$82$	−18.9637	−2.09419
$83$	14.4050	1.58115	0.790576	−	0.612364i	$-0.209781\pi$
$83$	14.4050	1.58115	0.790576	+	0.612364i	$0.209781\pi$
$84$	−4.37608	−0.477470
$85$	1.88471	0.204425
$86$	29.1749	3.14601
$87$	−0.607016	−0.0650789
$88$	−5.15275	−0.549285
$89$	9.50117	1.00712	0.503561	−	0.863960i	$-0.332023\pi$
$89$	9.50117	1.00712	0.503561	+	0.863960i	$0.332023\pi$
$90$	−15.1572	−1.59771
$91$	8.84917	0.927645
$92$	−17.1882	−1.79200
$93$	2.25909	0.234257
$94$	−0.608110	−0.0627218
$95$	−12.5286	−1.28541
$96$	7.72310	0.788236
$97$	10.9176	1.10852	0.554258	−	0.832345i	$-0.313002\pi$
$97$	10.9176	1.10852	0.554258	+	0.832345i	$0.313002\pi$
$98$	1.05526	0.106597
$99$	−1.48869	−0.149619
$100$	−8.16940	−0.816940
$101$	−7.69579	−0.765759	−0.382880	−	0.923798i	$-0.625068\pi$
$101$	−7.69579	−0.765759	−0.382880	+	0.923798i	$0.625068\pi$
$102$	−0.833425	−0.0825214
$103$	−9.78956	−0.964594	−0.482297	−	0.876008i	$-0.660197\pi$
$103$	−9.78956	−0.964594	−0.482297	+	0.876008i	$0.660197\pi$
$104$	−34.6358	−3.39632
$105$	1.46174	0.142651
$106$	24.8592	2.41454
$107$	9.79284	0.946710	0.473355	−	0.880872i	$-0.343043\pi$
$107$	9.79284	0.946710	0.473355	+	0.880872i	$0.343043\pi$
$108$	10.0516	0.967216
$109$	−15.7452	−1.50811	−0.754057	−	0.656809i	$-0.771906\pi$
$109$	−15.7452	−1.50811	−0.754057	+	0.656809i	$0.771906\pi$
$110$	2.66625	0.254217
$111$	−2.15755	−0.204786
$112$	42.5802	4.02345
$113$	2.40793	0.226519	0.113260	−	0.993565i	$-0.463871\pi$
$113$	2.40793	0.226519	0.113260	+	0.993565i	$0.463871\pi$
$114$	5.54019	0.518886
$115$	5.74137	0.535386
$116$	11.3608	1.05482
$117$	−10.0067	−0.925119
$118$	30.5771	2.81485
$119$	−2.57260	−0.235830
$120$	−5.72127	−0.522278
$121$	−10.7381	−0.976194
$122$	24.3762	2.20692
$123$	−2.06806	−0.186471
$124$	−42.2806	−3.79691
$125$	12.1524	1.08694
$126$	20.6893	1.84315
$127$	−20.1562	−1.78858	−0.894288	−	0.447492i	$-0.852317\pi$
$127$	−20.1562	−1.78858	−0.894288	+	0.447492i	$0.852317\pi$
$128$	−53.0315	−4.68737
$129$	3.18163	0.280127
$130$	17.9220	1.57187
$131$	3.31533	0.289661	0.144831	−	0.989456i	$-0.453736\pi$
$131$	3.31533	0.289661	0.144831	+	0.989456i	$0.453736\pi$
$132$	−0.870476	−0.0757652
$133$	17.1014	1.48288
$134$	−29.4226	−2.54172
$135$	−3.35753	−0.288970
$136$	10.0692	0.863427
$137$	12.9881	1.10964	0.554822	−	0.831969i	$-0.312786\pi$
$137$	12.9881	1.10964	0.554822	+	0.831969i	$0.312786\pi$
$138$	−2.53885	−0.216122
$139$	−20.7488	−1.75989	−0.879946	−	0.475073i	$-0.842422\pi$
$139$	−20.7488	−1.75989	−0.879946	+	0.475073i	$0.842422\pi$
$140$	−27.3575	−2.31213
$141$	−0.0663165	−0.00558486
$142$	28.6425	2.40363
$143$	1.76025	0.147199
$144$	−48.1499	−4.01249
$145$	−3.79482	−0.315143
$146$	−28.0833	−2.32419
$147$	0.115080	0.00949162
$148$	40.3802	3.31923
$149$	2.30551	0.188874	0.0944372	−	0.995531i	$-0.469895\pi$
$149$	2.30551	0.188874	0.0944372	+	0.995531i	$0.469895\pi$
$150$	−1.20669	−0.0985261
$151$	19.6117	1.59598	0.797989	−	0.602672i	$-0.205897\pi$
$151$	19.6117	1.59598	0.797989	+	0.602672i	$0.205897\pi$
$152$	−66.9350	−5.42914
$153$	2.90911	0.235188
$154$	−3.63940	−0.293271
$155$	14.1230	1.13438
$156$	−5.85117	−0.468469
$157$	−15.3103	−1.22189	−0.610947	−	0.791671i	$-0.709211\pi$
$157$	−15.3103	−1.22189	−0.610947	+	0.791671i	$0.709211\pi$
$158$	−0.375016	−0.0298347
$159$	2.71098	0.214995
$160$	48.2818	3.81701
$161$	−7.83689	−0.617634
$162$	−22.6418	−1.77891
$163$	−8.41412	−0.659045	−0.329522	−	0.944148i	$-0.606888\pi$
$163$	−8.41412	−0.659045	−0.329522	+	0.944148i	$0.606888\pi$
$164$	38.7053	3.02238
$165$	0.290764	0.0226360
$166$	−39.8223	−3.09081
$167$	−12.8541	−0.994680	−0.497340	−	0.867556i	$-0.665690\pi$
$167$	−12.8541	−0.994680	−0.497340	+	0.867556i	$0.665690\pi$
$168$	7.80945	0.602512
$169$	−1.16795	−0.0898427
$170$	−5.21024	−0.399607
$171$	−19.3383	−1.47884
$172$	−59.5465	−4.54037
$173$	−5.07635	−0.385948	−0.192974	−	0.981204i	$-0.561813\pi$
$173$	−5.07635	−0.385948	−0.192974	+	0.981204i	$0.561813\pi$
$174$	1.67808	0.127215
$175$	−3.72480	−0.281568
$176$	8.46991	0.638443
$177$	3.33454	0.250639
$178$	−26.2658	−1.96870
$179$	24.7519	1.85005	0.925023	−	0.379910i	$-0.124045\pi$
$179$	24.7519	1.85005	0.925023	+	0.379910i	$0.124045\pi$
$180$	30.9360	2.30584
$181$	3.89776	0.289718	0.144859	−	0.989452i	$-0.453727\pi$
$181$	3.89776	0.289718	0.144859	+	0.989452i	$0.453727\pi$
$182$	−24.4633	−1.81334
$183$	2.65831	0.196508
$184$	30.6737	2.26130
$185$	−13.4882	−0.991669
$186$	−6.24522	−0.457922
$187$	−0.511734	−0.0374217
$188$	1.24116	0.0905211
$189$	4.58298	0.333363
$190$	34.6351	2.51269
$191$	23.4730	1.69845	0.849225	−	0.528032i	$-0.177070\pi$
$191$	23.4730	1.69845	0.849225	+	0.528032i	$0.177070\pi$
$192$	−11.3707	−0.820606
$193$	3.94104	0.283682	0.141841	−	0.989889i	$-0.454698\pi$
$193$	3.94104	0.283682	0.141841	+	0.989889i	$0.454698\pi$
$194$	−30.1815	−2.16691
$195$	1.95446	0.139962
$196$	−2.15380	−0.153843
$197$	−20.9314	−1.49130	−0.745651	−	0.666337i	$-0.767861\pi$
$197$	−20.9314	−1.49130	−0.745651	+	0.666337i	$0.767861\pi$
$198$	4.11545	0.292473
$199$	19.9723	1.41580	0.707899	−	0.706314i	$-0.249643\pi$
$199$	19.9723	1.41580	0.707899	+	0.706314i	$0.249643\pi$
$200$	14.5789	1.03089
$201$	−3.20863	−0.226320
$202$	21.2748	1.49689
$203$	5.17988	0.363556
$204$	1.70103	0.119096
$205$	−12.9287	−0.902979
$206$	27.0630	1.88557
$207$	8.86200	0.615952
$208$	56.9331	3.94760
$209$	3.40175	0.235304
$210$	−4.04095	−0.278852
$211$	−19.7670	−1.36082	−0.680409	−	0.732832i	$-0.738198\pi$
$211$	−19.7670	−1.36082	−0.680409	+	0.732832i	$0.738198\pi$
$212$	−50.7380	−3.48470
$213$	3.12357	0.214023
$214$	−27.0721	−1.85061
$215$	19.8903	1.35650
$216$	−17.9378	−1.22052
$217$	−19.2776	−1.30865
$218$	43.5272	2.94803
$219$	−3.06258	−0.206950
$220$	−5.44187	−0.366891
$221$	−3.43977	−0.231384
$222$	5.96451	0.400312
$223$	7.88232	0.527839	0.263920	−	0.964545i	$-0.414985\pi$
$223$	7.88232	0.527839	0.263920	+	0.964545i	$0.414985\pi$
$224$	−65.9039	−4.40339
$225$	4.21202	0.280802
$226$	−6.65668	−0.442796
$227$	−9.16321	−0.608184	−0.304092	−	0.952643i	$-0.598353\pi$
$227$	−9.16321	−0.608184	−0.304092	+	0.952643i	$0.598353\pi$
$228$	−11.3076	−0.748865
$229$	−3.50203	−0.231420	−0.115710	−	0.993283i	$-0.536914\pi$
$229$	−3.50203	−0.231420	−0.115710	+	0.993283i	$0.536914\pi$
$230$	−15.8719	−1.04656
$231$	−0.396889	−0.0261134
$232$	−20.2741	−1.33106
$233$	−20.8910	−1.36861	−0.684307	−	0.729194i	$-0.739895\pi$
$233$	−20.8910	−1.36861	−0.684307	+	0.729194i	$0.739895\pi$
$234$	27.6633	1.80841
$235$	−0.414584	−0.0270445
$236$	−62.4084	−4.06244
$237$	−0.0408968	−0.00265653
$238$	7.11191	0.460996
$239$	−25.2505	−1.63332	−0.816660	−	0.577119i	$-0.804177\pi$
$239$	−25.2505	−1.63332	−0.816660	+	0.577119i	$0.804177\pi$
$240$	9.40442	0.607053
$241$	2.28287	0.147053	0.0735263	−	0.997293i	$-0.476575\pi$
$241$	2.28287	0.147053	0.0735263	+	0.997293i	$0.476575\pi$
$242$	29.6853	1.90825
$243$	−7.81354	−0.501239
$244$	−49.7523	−3.18506
$245$	0.719433	0.0459629
$246$	5.71712	0.364510
$247$	22.8659	1.45492
$248$	75.4530	4.79127
$249$	−4.34276	−0.275211
$250$	−33.5950	−2.12473
$251$	−3.51954	−0.222151	−0.111076	−	0.993812i	$-0.535430\pi$
$251$	−3.51954	−0.222151	−0.111076	+	0.993812i	$0.535430\pi$
$252$	−42.2273	−2.66007
$253$	−1.55889	−0.0980065
$254$	55.7215	3.49628
$255$	−0.568195	−0.0355817
$256$	71.1714	4.44821
$257$	20.9175	1.30480	0.652399	−	0.757875i	$-0.273763\pi$
$257$	20.9175	1.30480	0.652399	+	0.757875i	$0.273763\pi$
$258$	−8.79554	−0.547586
$259$	18.4112	1.14401
$260$	−36.5792	−2.26855
$261$	−5.85744	−0.362566
$262$	−9.16516	−0.566225
$263$	3.07993	0.189917	0.0949584	−	0.995481i	$-0.469728\pi$
$263$	3.07993	0.189917	0.0949584	+	0.995481i	$0.469728\pi$
$264$	1.55343	0.0956071
$265$	16.9480	1.04110
$266$	−47.2764	−2.89870
$267$	−2.86438	−0.175297
$268$	60.0519	3.66826
$269$	−8.76079	−0.534155	−0.267077	−	0.963675i	$-0.586058\pi$
$269$	−8.76079	−0.534155	−0.267077	+	0.963675i	$0.586058\pi$
$270$	9.28182	0.564873
$271$	−0.411054	−0.0249697	−0.0124849	−	0.999922i	$-0.503974\pi$
$271$	−0.411054	−0.0249697	−0.0124849	+	0.999922i	$0.503974\pi$
$272$	−16.5514	−1.00358
$273$	−2.66781	−0.161463
$274$	−35.9052	−2.16911
$275$	−0.740925	−0.0446795
$276$	5.18184	0.311910
$277$	22.7627	1.36768	0.683840	−	0.729632i	$-0.260309\pi$
$277$	22.7627	1.36768	0.683840	+	0.729632i	$0.260309\pi$
$278$	57.3597	3.44021
$279$	21.7993	1.30509
$280$	48.8216	2.91765
$281$	19.1114	1.14009	0.570046	−	0.821613i	$-0.306926\pi$
$281$	19.1114	1.14009	0.570046	+	0.821613i	$0.306926\pi$
$282$	0.183331	0.0109172
$283$	7.44988	0.442849	0.221425	−	0.975177i	$-0.428929\pi$
$283$	7.44988	0.442849	0.221425	+	0.975177i	$0.428929\pi$
$284$	−58.4599	−3.46895
$285$	3.77707	0.223735
$286$	−4.86617	−0.287743
$287$	17.6475	1.04170
$288$	74.5245	4.39140
$289$	1.00000	0.0588235
$290$	10.4907	0.616036
$291$	−3.29140	−0.192945
$292$	57.3185	3.35431
$293$	−10.2878	−0.601021	−0.300511	−	0.953778i	$-0.597157\pi$
$293$	−10.2878	−0.601021	−0.300511	+	0.953778i	$0.597157\pi$
$294$	−0.318136	−0.0185540
$295$	20.8462	1.21371
$296$	−72.0615	−4.18849
$297$	0.911631	0.0528982
$298$	−6.37353	−0.369208
$299$	−10.4785	−0.605990
$300$	2.46288	0.142194
$301$	−27.1499	−1.56490
$302$	−54.2162	−3.11979
$303$	2.32010	0.133286
$304$	110.025	6.31039
$305$	16.6187	0.951584
$306$	−8.04218	−0.459741
$307$	9.09764	0.519230	0.259615	−	0.965712i	$-0.416404\pi$
$307$	9.09764	0.519230	0.259615	+	0.965712i	$0.416404\pi$
$308$	7.42808	0.423254
$309$	2.95132	0.167895
$310$	−39.0426	−2.21747
$311$	−24.1642	−1.37023	−0.685113	−	0.728436i	$-0.740247\pi$
$311$	−24.1642	−1.37023	−0.685113	+	0.728436i	$0.740247\pi$
$312$	10.4419	0.591154
$313$	6.28093	0.355019	0.177510	−	0.984119i	$-0.443196\pi$
$313$	6.28093	0.355019	0.177510	+	0.984119i	$0.443196\pi$
$314$	42.3250	2.38854
$315$	14.1051	0.794734
$316$	0.765413	0.0430579
$317$	15.4222	0.866196	0.433098	−	0.901347i	$-0.357420\pi$
$317$	15.4222	0.866196	0.433098	+	0.901347i	$0.357420\pi$
$318$	−7.49445	−0.420268
$319$	1.03036	0.0576893
$320$	−71.0848	−3.97376
$321$	−2.95231	−0.164782
$322$	21.6649	1.20734
$323$	−6.64750	−0.369877
$324$	46.2124	2.56735
$325$	−4.98035	−0.276260
$326$	23.2607	1.28829
$327$	4.74679	0.262498
$328$	−69.0726	−3.81389
$329$	0.565902	0.0311992
$330$	−0.803812	−0.0442484
$331$	15.0260	0.825906	0.412953	−	0.910752i	$-0.364497\pi$
$331$	15.0260	0.825906	0.412953	+	0.910752i	$0.364497\pi$
$332$	81.2779	4.46070
$333$	−20.8194	−1.14090
$334$	35.5349	1.94438
$335$	−20.0591	−1.09595
$336$	−12.8369	−0.700311
$337$	30.5505	1.66419	0.832097	−	0.554630i	$-0.187140\pi$
$337$	30.5505	1.66419	0.832097	+	0.554630i	$0.187140\pi$
$338$	3.22879	0.175623
$339$	−0.725935	−0.0394274
$340$	10.6342	0.576720
$341$	−3.83465	−0.207658
$342$	53.4604	2.89081
$343$	−18.9902	−1.02538
$344$	106.265	5.72943
$345$	−1.73089	−0.0931878
$346$	14.0335	0.754444
$347$	28.0810	1.50747	0.753734	−	0.657179i	$-0.228251\pi$
$347$	28.0810	1.50747	0.753734	+	0.657179i	$0.228251\pi$
$348$	−3.42500	−0.183599
$349$	−27.7103	−1.48330	−0.741649	−	0.670788i	$-0.765956\pi$
$349$	−27.7103	−1.48330	−0.741649	+	0.670788i	$0.765956\pi$
$350$	10.2971	0.550405
$351$	6.12781	0.327078
$352$	−13.1094	−0.698733
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−9.21827	−0.489946
$355$	19.5273	1.03640
$356$	53.6089	2.84127
$357$	0.775578	0.0410480
$358$	−68.4262	−3.61644
$359$	−6.42984	−0.339354	−0.169677	−	0.985500i	$-0.554272\pi$
$359$	−6.42984	−0.339354	−0.169677	+	0.985500i	$0.554272\pi$
$360$	−55.2077	−2.90970
$361$	25.1892	1.32575
$362$	−10.7753	−0.566336
$363$	3.23729	0.169914
$364$	49.9301	2.61705
$365$	−19.1460	−1.00215
$366$	−7.34885	−0.384131
$367$	19.0509	0.994447	0.497224	−	0.867622i	$-0.334353\pi$
$367$	19.0509	0.994447	0.497224	+	0.867622i	$0.334353\pi$
$368$	−50.4204	−2.62834
$369$	−19.9559	−1.03886
$370$	37.2878	1.93850
$371$	−23.1337	−1.20104
$372$	12.7466	0.660880
$373$	−23.2312	−1.20287	−0.601433	−	0.798923i	$-0.705403\pi$
$373$	−23.2312	−1.20287	−0.601433	+	0.798923i	$0.705403\pi$
$374$	1.41468	0.0731512
$375$	−3.66365	−0.189190
$376$	−2.21495	−0.114227
$377$	6.92591	0.356703
$378$	−12.6696	−0.651651
$379$	−27.5957	−1.41750	−0.708748	−	0.705462i	$-0.750740\pi$
$379$	−27.5957	−1.41750	−0.708748	+	0.705462i	$0.750740\pi$
$380$	−70.6907	−3.62636
$381$	6.07662	0.311315
$382$	−64.8907	−3.32010
$383$	28.2414	1.44307	0.721534	−	0.692379i	$-0.243437\pi$
$383$	28.2414	1.44307	0.721534	+	0.692379i	$0.243437\pi$
$384$	15.9877	0.815871
$385$	−2.48119	−0.126453
$386$	−10.8949	−0.554537
$387$	30.7013	1.56063
$388$	61.6010	3.12732
$389$	7.58797	0.384725	0.192363	−	0.981324i	$-0.438385\pi$
$389$	7.58797	0.384725	0.192363	+	0.981324i	$0.438385\pi$
$390$	−5.40307	−0.273595
$391$	3.04629	0.154058
$392$	3.84362	0.194132
$393$	−0.999492	−0.0504177
$394$	57.8645	2.91517
$395$	−0.255670	−0.0128642
$396$	−8.39971	−0.422101
$397$	−13.7218	−0.688679	−0.344340	−	0.938845i	$-0.611897\pi$
$397$	−13.7218	−0.688679	−0.344340	+	0.938845i	$0.611897\pi$
$398$	−55.2130	−2.76758
$399$	−5.15565	−0.258106
$400$	−23.9643	−1.19822
$401$	−22.1761	−1.10742	−0.553712	−	0.832709i	$-0.686789\pi$
$401$	−22.1761	−1.10742	−0.553712	+	0.832709i	$0.686789\pi$
$402$	8.87020	0.442406
$403$	−25.7757	−1.28398
$404$	−43.4223	−2.16034
$405$	−15.4363	−0.767035
$406$	−14.3197	−0.710673
$407$	3.66229	0.181533
$408$	−3.03562	−0.150286
$409$	−6.44999	−0.318931	−0.159466	−	0.987203i	$-0.550977\pi$
$409$	−6.44999	−0.318931	−0.159466	+	0.987203i	$0.550977\pi$
$410$	35.7411	1.76513
$411$	−3.91559	−0.193142
$412$	−55.2361	−2.72129
$413$	−28.4548	−1.40017
$414$	−24.4988	−1.20405
$415$	−27.1492	−1.33270
$416$	−88.1188	−4.32038
$417$	6.25528	0.306322
$418$	−9.40406	−0.459968
$419$	9.44679	0.461506	0.230753	−	0.973012i	$-0.425881\pi$
$419$	9.44679	0.461506	0.230753	+	0.973012i	$0.425881\pi$
$420$	8.24764	0.402444
$421$	−25.8966	−1.26212	−0.631062	−	0.775732i	$-0.717381\pi$
$421$	−25.8966	−1.26212	−0.631062	+	0.775732i	$0.717381\pi$
$422$	54.6456	2.66011
$423$	−0.639925	−0.0311142
$424$	90.5458	4.39729
$425$	1.44787	0.0702321
$426$	−8.63504	−0.418369
$427$	−22.6843	−1.09777
$428$	55.2546	2.67083
$429$	−0.530673	−0.0256211
$430$	−54.9862	−2.65167
$431$	−3.96217	−0.190851	−0.0954254	−	0.995437i	$-0.530421\pi$
$431$	−3.96217	−0.190851	−0.0954254	+	0.995437i	$0.530421\pi$
$432$	29.4856	1.41863
$433$	−14.9062	−0.716346	−0.358173	−	0.933655i	$-0.616600\pi$
$433$	−14.9062	−0.716346	−0.358173	+	0.933655i	$0.616600\pi$
$434$	53.2927	2.55813
$435$	1.14405	0.0548529
$436$	−88.8398	−4.25465
$437$	−20.2502	−0.968699
$438$	8.46644	0.404542
$439$	−10.4730	−0.499849	−0.249924	−	0.968265i	$-0.580406\pi$
$439$	−10.4730	−0.499849	−0.249924	+	0.968265i	$0.580406\pi$
$440$	9.71143	0.462974
$441$	1.11047	0.0528795
$442$	9.50919	0.452306
$443$	−38.7890	−1.84292	−0.921460	−	0.388473i	$-0.873003\pi$
$443$	−38.7890	−1.84292	−0.921460	+	0.388473i	$0.873003\pi$
$444$	−12.1737	−0.577737
$445$	−17.9069	−0.848871
$446$	−21.7905	−1.03181
$447$	−0.695055	−0.0328750
$448$	97.0298	4.58423
$449$	−30.1845	−1.42449	−0.712247	−	0.701929i	$-0.752322\pi$
$449$	−30.1845	−1.42449	−0.712247	+	0.701929i	$0.752322\pi$
$450$	−11.6441	−0.548906
$451$	3.51038	0.165297
$452$	13.5864	0.639051
$453$	−5.91246	−0.277792
$454$	25.3315	1.18887
$455$	−16.6781	−0.781882
$456$	20.1793	0.944983
$457$	−34.4170	−1.60996	−0.804980	−	0.593302i	$-0.797824\pi$
$457$	−34.4170	−1.60996	−0.804980	+	0.593302i	$0.797824\pi$
$458$	9.68128	0.452377
$459$	−1.78146	−0.0831513
$460$	32.3948	1.51042
$461$	15.2949	0.712355	0.356177	−	0.934418i	$-0.384080\pi$
$461$	15.2949	0.712355	0.356177	+	0.934418i	$0.384080\pi$
$462$	1.09719	0.0510460
$463$	6.90426	0.320868	0.160434	−	0.987047i	$-0.448711\pi$
$463$	6.90426	0.320868	0.160434	+	0.987047i	$0.448711\pi$
$464$	33.3259	1.54712
$465$	−4.25774	−0.197448
$466$	57.7527	2.67534
$467$	8.76261	0.405485	0.202743	−	0.979232i	$-0.435015\pi$
$467$	8.76261	0.405485	0.202743	+	0.979232i	$0.435015\pi$
$468$	−56.4612	−2.60992
$469$	27.3804	1.26431
$470$	1.14611	0.0528661
$471$	4.61569	0.212680
$472$	111.372	5.12633
$473$	−5.40057	−0.248319
$474$	0.113058	0.00519294
$475$	−9.62473	−0.441613
$476$	−14.5155	−0.665318
$477$	26.1597	1.19777
$478$	69.8046	3.19279
$479$	−18.8090	−0.859406	−0.429703	−	0.902970i	$-0.641382\pi$
$479$	−18.8090	−0.859406	−0.429703	+	0.902970i	$0.641382\pi$
$480$	−14.5558	−0.664378
$481$	24.6172	1.12245
$482$	−6.31095	−0.287456
$483$	2.36264	0.107504
$484$	−60.5883	−2.75401
$485$	−20.5765	−0.934332
$486$	21.6004	0.979813
$487$	−3.90658	−0.177024	−0.0885121	−	0.996075i	$-0.528211\pi$
$487$	−3.90658	−0.177024	−0.0885121	+	0.996075i	$0.528211\pi$
$488$	88.7867	4.01918
$489$	2.53666	0.114712
$490$	−1.98886	−0.0898474
$491$	−23.6229	−1.06609	−0.533043	−	0.846088i	$-0.678951\pi$
$491$	−23.6229	−1.06609	−0.533043	+	0.846088i	$0.678951\pi$
$492$	−11.6687	−0.526067
$493$	−2.01348	−0.0906825
$494$	−63.2123	−2.84406
$495$	2.80575	0.126109
$496$	−124.027	−5.56898
$497$	−26.6545	−1.19562
$498$	12.0055	0.537978
$499$	25.3792	1.13613	0.568066	−	0.822983i	$-0.307692\pi$
$499$	25.3792	1.13613	0.568066	+	0.822983i	$0.307692\pi$
$500$	68.5679	3.06645
$501$	3.87520	0.173131
$502$	9.72969	0.434257
$503$	−23.7802	−1.06031	−0.530153	−	0.847902i	$-0.677866\pi$
$503$	−23.7802	−1.06031	−0.530153	+	0.847902i	$0.677866\pi$
$504$	75.3578	3.35670
$505$	14.5043	0.645434
$506$	4.30952	0.191581
$507$	0.352111	0.0156378
$508$	−113.728	−5.04589
$509$	−22.3803	−0.991989	−0.495995	−	0.868326i	$-0.665196\pi$
$509$	−22.3803	−0.991989	−0.495995	+	0.868326i	$0.665196\pi$
$510$	1.57076	0.0695546
$511$	26.1341	1.15610
$512$	−90.6888	−4.00792
$513$	11.8422	0.522847
$514$	−57.8260	−2.55060
$515$	18.4505	0.813025
$516$	17.9518	0.790286
$517$	0.112567	0.00495071
$518$	−50.8973	−2.23630
$519$	1.53040	0.0671770
$520$	65.2784	2.86265
$521$	14.1856	0.621484	0.310742	−	0.950494i	$-0.399422\pi$
$521$	14.1856	0.621484	0.310742	+	0.950494i	$0.399422\pi$
$522$	16.1928	0.708738
$523$	21.9519	0.959890	0.479945	−	0.877299i	$-0.340657\pi$
$523$	21.9519	0.959890	0.479945	+	0.877299i	$0.340657\pi$
$524$	18.7062	0.817186
$525$	1.12294	0.0490090
$526$	−8.51441	−0.371246
$527$	7.49344	0.326419
$528$	−2.55348	−0.111126
$529$	−13.7201	−0.596527
$530$	−46.8523	−2.03513
$531$	32.1768	1.39636
$532$	96.4919	4.18345
$533$	23.5961	1.02206
$534$	7.91851	0.342668
$535$	−18.4567	−0.797951
$536$	−107.167	−4.62892
$537$	−7.46212	−0.322014
$538$	24.2190	1.04416
$539$	−0.195339	−0.00841386
$540$	−18.9443	−0.815235
$541$	23.6979	1.01885	0.509427	−	0.860514i	$-0.329858\pi$
$541$	23.6979	1.01885	0.509427	+	0.860514i	$0.329858\pi$
$542$	1.13635	0.0488104
$543$	−1.17508	−0.0504276
$544$	25.6176	1.09835
$545$	29.6751	1.27114
$546$	7.37512	0.315626
$547$	−6.64898	−0.284290	−0.142145	−	0.989846i	$-0.545400\pi$
$547$	−6.64898	−0.284290	−0.142145	+	0.989846i	$0.545400\pi$
$548$	73.2831	3.13050
$549$	25.6515	1.09478
$550$	2.04827	0.0873386
$551$	13.3846	0.570203
$552$	−9.24739	−0.393595
$553$	0.348987	0.0148404
$554$	−62.9271	−2.67352
$555$	4.06636	0.172607
$556$	−117.072	−4.96497
$557$	10.8385	0.459240	0.229620	−	0.973280i	$-0.426252\pi$
$557$	10.8385	0.459240	0.229620	+	0.973280i	$0.426252\pi$
$558$	−60.2636	−2.55116
$559$	−36.3016	−1.53539
$560$	−80.2512	−3.39123
$561$	0.154276	0.00651352
$562$	−52.8331	−2.22863
$563$	32.6541	1.37621	0.688104	−	0.725612i	$-0.258443\pi$
$563$	32.6541	1.37621	0.688104	+	0.725612i	$0.258443\pi$
$564$	−0.374181	−0.0157559
$565$	−4.53825	−0.190926
$566$	−20.5950	−0.865674
$567$	21.0703	0.884869
$568$	104.326	4.37742
$569$	−13.5338	−0.567368	−0.283684	−	0.958918i	$-0.591557\pi$
$569$	−13.5338	−0.567368	−0.283684	+	0.958918i	$0.591557\pi$
$570$	−10.4416	−0.437352
$571$	−14.0091	−0.586264	−0.293132	−	0.956072i	$-0.594698\pi$
$571$	−14.0091	−0.586264	−0.293132	+	0.956072i	$0.594698\pi$
$572$	9.93193	0.415275
$573$	−7.07656	−0.295628
$574$	−48.7861	−2.03629
$575$	4.41064	0.183936
$576$	−109.722	−4.57174
$577$	−2.60919	−0.108622	−0.0543111	−	0.998524i	$-0.517296\pi$
$577$	−2.60919	−0.108622	−0.0543111	+	0.998524i	$0.517296\pi$
$578$	−2.76448	−0.114987
$579$	−1.18813	−0.0493770
$580$	−21.4117	−0.889073
$581$	37.0583	1.53744
$582$	9.09901	0.377166
$583$	−4.60169	−0.190582
$584$	−102.289	−4.23275
$585$	18.8597	0.779752
$586$	28.4405	1.17487
$587$	16.1748	0.667604	0.333802	−	0.942643i	$-0.391668\pi$
$587$	16.1748	0.667604	0.333802	+	0.942643i	$0.391668\pi$
$588$	0.649320	0.0267775
$589$	−49.8126	−2.05249
$590$	−57.6289	−2.37255
$591$	6.31032	0.259572
$592$	118.452	4.86836
$593$	8.23758	0.338277	0.169138	−	0.985592i	$-0.445902\pi$
$593$	8.23758	0.338277	0.169138	+	0.985592i	$0.445902\pi$
$594$	−2.52019	−0.103404
$595$	4.84861	0.198773
$596$	13.0085	0.532848
$597$	−6.02117	−0.246430
$598$	28.9677	1.18458
$599$	−26.4197	−1.07948	−0.539739	−	0.841832i	$-0.681477\pi$
$599$	−26.4197	−1.07948	−0.539739	+	0.841832i	$0.681477\pi$
$600$	−4.39520	−0.179433
$601$	12.4447	0.507631	0.253816	−	0.967253i	$-0.418314\pi$
$601$	12.4447	0.507631	0.253816	+	0.967253i	$0.418314\pi$
$602$	75.0554	3.05903
$603$	−30.9619	−1.26087
$604$	110.656	4.50253
$605$	20.2382	0.822802
$606$	−6.41386	−0.260545
$607$	11.8847	0.482386	0.241193	−	0.970477i	$-0.422461\pi$
$607$	11.8847	0.482386	0.241193	+	0.970477i	$0.422461\pi$
$608$	−170.293	−6.90630
$609$	−1.56161	−0.0632796
$610$	−45.9421	−1.86014
$611$	0.756656	0.0306110
$612$	16.4142	0.663506
$613$	−45.7580	−1.84815	−0.924075	−	0.382212i	$-0.875162\pi$
$613$	−45.7580	−1.84815	−0.924075	+	0.382212i	$0.875162\pi$
$614$	−25.1502	−1.01498
$615$	3.89770	0.157170
$616$	−13.2560	−0.534098
$617$	−34.0323	−1.37009	−0.685044	−	0.728502i	$-0.740217\pi$
$617$	−34.0323	−1.37009	−0.685044	+	0.728502i	$0.740217\pi$
$618$	−8.15886	−0.328198
$619$	−13.2957	−0.534399	−0.267199	−	0.963641i	$-0.586098\pi$
$619$	−13.2957	−0.534399	−0.267199	+	0.963641i	$0.586098\pi$
$620$	79.6867	3.20029
$621$	−5.42683	−0.217771
$622$	66.8015	2.67850
$623$	24.4427	0.979277
$624$	−17.1640	−0.687109
$625$	−15.6643	−0.626572
$626$	−17.3635	−0.693986
$627$	−1.02555	−0.0409564
$628$	−86.3860	−3.44718
$629$	−7.15663	−0.285353
$630$	−38.9934	−1.55353
$631$	−32.8221	−1.30663	−0.653313	−	0.757088i	$-0.726621\pi$
$631$	−32.8221	−1.30663	−0.653313	+	0.757088i	$0.726621\pi$
$632$	−1.36594	−0.0543341
$633$	5.95929	0.236861
$634$	−42.6343	−1.69322
$635$	37.9886	1.50753
$636$	15.2963	0.606537
$637$	−1.31303	−0.0520243
$638$	−2.84842	−0.112770
$639$	30.1410	1.19236
$640$	99.9490	3.95083
$641$	−29.8205	−1.17784	−0.588919	−	0.808192i	$-0.700446\pi$
$641$	−29.8205	−1.17784	−0.588919	+	0.808192i	$0.700446\pi$
$642$	8.16160	0.322113
$643$	3.97868	0.156904	0.0784518	−	0.996918i	$-0.475002\pi$
$643$	3.97868	0.156904	0.0784518	+	0.996918i	$0.475002\pi$
$644$	−44.2185	−1.74245
$645$	−5.99644	−0.236110
$646$	18.3769	0.723028
$647$	5.98206	0.235179	0.117589	−	0.993062i	$-0.462483\pi$
$647$	5.98206	0.235179	0.117589	+	0.993062i	$0.462483\pi$
$648$	−82.4695	−3.23971
$649$	−5.66014	−0.222180
$650$	13.7681	0.540029
$651$	5.81175	0.227780
$652$	−47.4754	−1.85928
$653$	8.38674	0.328198	0.164099	−	0.986444i	$-0.447528\pi$
$653$	8.38674	0.328198	0.164099	+	0.986444i	$0.447528\pi$
$654$	−13.1224	−0.513127
$655$	−6.24843	−0.244146
$656$	113.539	4.43296
$657$	−29.5526	−1.15295
$658$	−1.56442	−0.0609876
$659$	−44.9451	−1.75081	−0.875406	−	0.483389i	$-0.839406\pi$
$659$	−44.9451	−1.75081	−0.875406	+	0.483389i	$0.839406\pi$
$660$	1.64059	0.0638600
$661$	−46.0571	−1.79141	−0.895707	−	0.444644i	$-0.853330\pi$
$661$	−46.0571	−1.79141	−0.895707	+	0.444644i	$0.853330\pi$
$662$	−41.5392	−1.61447
$663$	1.03701	0.0402741
$664$	−145.047	−5.62890
$665$	−32.2311	−1.24987
$666$	57.5549	2.23021
$667$	−6.13364	−0.237496
$668$	−72.5273	−2.80617
$669$	−2.37633	−0.0918743
$670$	55.4530	2.14234
$671$	−4.51229	−0.174195
$672$	19.8685	0.766443
$673$	−16.6834	−0.643099	−0.321549	−	0.946893i	$-0.604204\pi$
$673$	−16.6834	−0.643099	−0.321549	+	0.946893i	$0.604204\pi$
$674$	−84.4563	−3.25314
$675$	−2.57932	−0.0992781
$676$	−6.59001	−0.253462
$677$	13.3238	0.512075	0.256037	−	0.966667i	$-0.417583\pi$
$677$	13.3238	0.512075	0.256037	+	0.966667i	$0.417583\pi$
$678$	2.00683	0.0770719
$679$	28.0867	1.07787
$680$	−18.9775	−0.727754
$681$	2.76249	0.105859
$682$	10.6008	0.405926
$683$	−12.9831	−0.496785	−0.248392	−	0.968660i	$-0.579902\pi$
$683$	−12.9831	−0.496785	−0.248392	+	0.968660i	$0.579902\pi$
$684$	−109.114	−4.17206
$685$	−24.4787	−0.935283
$686$	52.4981	2.00439
$687$	1.05578	0.0402804
$688$	−174.675	−6.65942
$689$	−30.9316	−1.17840
$690$	4.78500	0.182162
$691$	−10.7287	−0.408140	−0.204070	−	0.978956i	$-0.565417\pi$
$691$	−10.7287	−0.408140	−0.204070	+	0.978956i	$0.565417\pi$
$692$	−28.6425	−1.08883
$693$	−3.82981	−0.145482
$694$	−77.6294	−2.94677
$695$	39.1055	1.48336
$696$	6.11217	0.231681
$697$	−6.85979	−0.259833
$698$	76.6045	2.89952
$699$	6.29814	0.238217
$700$	−21.0166	−0.794353
$701$	−27.9100	−1.05415	−0.527074	−	0.849819i	$-0.676711\pi$
$701$	−27.9100	−1.05415	−0.527074	+	0.849819i	$0.676711\pi$
$702$	−16.9402	−0.639367
$703$	47.5737	1.79427
$704$	19.3008	0.727428
$705$	0.124987	0.00470730
$706$	2.76448	0.104043
$707$	−19.7982	−0.744588
$708$	18.8146	0.707098
$709$	−31.2170	−1.17238	−0.586190	−	0.810173i	$-0.699373\pi$
$709$	−31.2170	−1.17238	−0.586190	+	0.810173i	$0.699373\pi$
$710$	−53.9828	−2.02594
$711$	−0.394636	−0.0148000
$712$	−95.6692	−3.58536
$713$	22.8272	0.854885
$714$	−2.14407	−0.0802398
$715$	−3.31755	−0.124070
$716$	139.659	5.21930
$717$	7.61243	0.284291
$718$	17.7752	0.663363
$719$	48.7906	1.81958	0.909792	−	0.415064i	$-0.136241\pi$
$719$	48.7906	1.81958	0.909792	+	0.415064i	$0.136241\pi$
$720$	90.7485	3.38200
$721$	−25.1846	−0.937925
$722$	−69.6351	−2.59155
$723$	−0.688231	−0.0255956
$724$	21.9925	0.817345
$725$	−2.91526	−0.108270
$726$	−8.94942	−0.332144
$727$	−27.7418	−1.02889	−0.514444	−	0.857524i	$-0.672002\pi$
$727$	−27.7418	−1.02889	−0.514444	+	0.857524i	$0.672002\pi$
$728$	−89.1041	−3.30242
$729$	−22.2152	−0.822786
$730$	52.9288	1.95898
$731$	10.5535	0.390335
$732$	14.9991	0.554384
$733$	35.8385	1.32372	0.661862	−	0.749626i	$-0.269767\pi$
$733$	35.8385	1.32372	0.661862	+	0.749626i	$0.269767\pi$
$734$	−52.6657	−1.94393
$735$	−0.216892	−0.00800017
$736$	78.0387	2.87655
$737$	5.44642	0.200621
$738$	55.1676	2.03075
$739$	12.3202	0.453206	0.226603	−	0.973987i	$-0.427238\pi$
$739$	12.3202	0.453206	0.226603	+	0.973987i	$0.427238\pi$
$740$	−76.1049	−2.79767
$741$	−6.89352	−0.253240
$742$	63.9527	2.34778
$743$	26.5205	0.972944	0.486472	−	0.873696i	$-0.338284\pi$
$743$	26.5205	0.972944	0.486472	+	0.873696i	$0.338284\pi$
$744$	−22.7473	−0.833956
$745$	−4.34521	−0.159196
$746$	64.2222	2.35134
$747$	−41.9057	−1.53325
$748$	−2.88738	−0.105573
$749$	25.1931	0.920535
$750$	10.1281	0.369825
$751$	−32.9244	−1.20143	−0.600714	−	0.799464i	$-0.705117\pi$
$751$	−32.9244	−1.20143	−0.600714	+	0.799464i	$0.705117\pi$
$752$	3.64086	0.132768
$753$	1.06106	0.0386670
$754$	−19.1465	−0.697276
$755$	−36.9624	−1.34520
$756$	25.8588	0.940474
$757$	12.9922	0.472211	0.236106	−	0.971727i	$-0.424129\pi$
$757$	12.9922	0.472211	0.236106	+	0.971727i	$0.424129\pi$
$758$	76.2878	2.77090
$759$	0.469968	0.0170588
$760$	126.153	4.57605
$761$	−22.2069	−0.805000	−0.402500	−	0.915420i	$-0.631859\pi$
$761$	−22.2069	−0.805000	−0.402500	+	0.915420i	$0.631859\pi$
$762$	−16.7987	−0.608553
$763$	−40.5061	−1.46642
$764$	132.443	4.79162
$765$	−5.48283	−0.198232
$766$	−78.0728	−2.82088
$767$	−38.0463	−1.37377
$768$	−21.4565	−0.774244
$769$	−22.8498	−0.823984	−0.411992	−	0.911187i	$-0.635167\pi$
$769$	−22.8498	−0.823984	−0.411992	+	0.911187i	$0.635167\pi$
$770$	6.85921	0.247189
$771$	−6.30613	−0.227110
$772$	22.2367	0.800318
$773$	−39.5057	−1.42092	−0.710461	−	0.703737i	$-0.751514\pi$
$773$	−39.5057	−1.42092	−0.710461	+	0.703737i	$0.751514\pi$
$774$	−84.8731	−3.05070
$775$	10.8495	0.389727
$776$	−109.932	−3.94631
$777$	−5.55053	−0.199124
$778$	−20.9768	−0.752055
$779$	45.6004	1.63380
$780$	11.0278	0.394857
$781$	−5.30202	−0.189721
$782$	−8.42141	−0.301149
$783$	3.58693	0.128186
$784$	−6.31801	−0.225643
$785$	28.8555	1.02990
$786$	2.76308	0.0985557
$787$	43.9013	1.56491	0.782457	−	0.622705i	$-0.213966\pi$
$787$	43.9013	1.56491	0.782457	+	0.622705i	$0.213966\pi$
$788$	−118.102	−4.20722
$789$	−0.928526	−0.0330564
$790$	0.706796	0.0251467
$791$	6.19465	0.220257
$792$	14.9899	0.532644
$793$	−30.3307	−1.07708
$794$	37.9337	1.34622
$795$	−5.10941	−0.181212
$796$	112.691	3.99421
$797$	13.0925	0.463762	0.231881	−	0.972744i	$-0.425512\pi$
$797$	13.0925	0.463762	0.231881	+	0.972744i	$0.425512\pi$
$798$	14.2527	0.504540
$799$	−0.219973	−0.00778207
$800$	37.0910	1.31137
$801$	−27.6400	−0.976610
$802$	61.3055	2.16477
$803$	5.19851	0.183451
$804$	−18.1042	−0.638487
$805$	14.7703	0.520583
$806$	71.2565	2.50990
$807$	2.64117	0.0929735
$808$	77.4904	2.72610
$809$	36.9294	1.29837	0.649185	−	0.760630i	$-0.275110\pi$
$809$	36.9294	1.29837	0.649185	+	0.760630i	$0.275110\pi$
$810$	42.6733	1.49939
$811$	−32.8662	−1.15409	−0.577044	−	0.816713i	$-0.695794\pi$
$811$	−32.8662	−1.15409	−0.577044	+	0.816713i	$0.695794\pi$
$812$	29.2267	1.02566
$813$	0.123923	0.00434616
$814$	−10.1243	−0.354857
$815$	15.8582	0.555487
$816$	4.98985	0.174680
$817$	−70.1543	−2.45439
$818$	17.8309	0.623441
$819$	−25.7432	−0.899541
$820$	−72.9482	−2.54746
$821$	−3.77231	−0.131654	−0.0658272	−	0.997831i	$-0.520969\pi$
$821$	−3.77231	−0.131654	−0.0658272	+	0.997831i	$0.520969\pi$
$822$	10.8246	0.377550
$823$	−45.8040	−1.59663	−0.798313	−	0.602243i	$-0.794274\pi$
$823$	−45.8040	−1.59663	−0.798313	+	0.602243i	$0.794274\pi$
$824$	98.5731	3.43396
$825$	0.223371	0.00777679
$826$	78.6627	2.73703
$827$	−46.6056	−1.62064	−0.810318	−	0.585990i	$-0.800706\pi$
$827$	−46.6056	−1.62064	−0.810318	+	0.585990i	$0.800706\pi$
$828$	50.0025	1.73771
$829$	28.5752	0.992457	0.496228	−	0.868192i	$-0.334718\pi$
$829$	28.5752	0.992457	0.496228	+	0.868192i	$0.334718\pi$
$830$	75.0534	2.60514
$831$	−6.86242	−0.238055
$832$	129.737	4.49781
$833$	0.381721	0.0132258
$834$	−17.2926	−0.598794
$835$	24.2262	0.838383
$836$	19.1938	0.663833
$837$	−13.3492	−0.461417
$838$	−26.1155	−0.902143
$839$	−1.27755	−0.0441059	−0.0220530	−	0.999757i	$-0.507020\pi$
$839$	−1.27755	−0.0441059	−0.0220530	+	0.999757i	$0.507020\pi$
$840$	−14.7185	−0.507838
$841$	−24.9459	−0.860204
$842$	71.5907	2.46718
$843$	−5.76164	−0.198441
$844$	−111.533	−3.83911
$845$	2.20125	0.0757255
$846$	1.76906	0.0608215
$847$	−27.6249	−0.949204
$848$	−148.836	−5.11105
$849$	−2.24596	−0.0770812
$850$	−4.00261	−0.137289
$851$	−21.8012	−0.747334
$852$	17.6243	0.603797
$853$	24.8724	0.851615	0.425808	−	0.904814i	$-0.359990\pi$
$853$	24.8724	0.851615	0.425808	+	0.904814i	$0.359990\pi$
$854$	62.7103	2.14590
$855$	36.4471	1.24646
$856$	−98.6061	−3.37029
$857$	−48.1801	−1.64580	−0.822900	−	0.568187i	$-0.807645\pi$
$857$	−48.1801	−1.64580	−0.822900	+	0.568187i	$0.807645\pi$
$858$	1.46703	0.0500837
$859$	47.6271	1.62501	0.812507	−	0.582951i	$-0.198102\pi$
$859$	47.6271	1.62501	0.812507	+	0.582951i	$0.198102\pi$
$860$	112.228	3.82693
$861$	−5.32030	−0.181315
$862$	10.9533	0.373072
$863$	−55.3072	−1.88268	−0.941340	−	0.337461i	$-0.890432\pi$
$863$	−55.3072	−1.88268	−0.941340	+	0.337461i	$0.890432\pi$
$864$	−45.6367	−1.55259
$865$	9.56744	0.325303
$866$	41.2079	1.40030
$867$	−0.301476	−0.0102387
$868$	−108.771	−3.69193
$869$	0.0694193	0.00235489
$870$	−3.16270	−0.107226
$871$	36.6098	1.24047
$872$	158.541	5.36889
$873$	−31.7606	−1.07493
$874$	55.9813	1.89360
$875$	31.2632	1.05689
$876$	−17.2802	−0.583842
$877$	7.75219	0.261773	0.130886	−	0.991397i	$-0.458218\pi$
$877$	7.75219	0.261773	0.130886	+	0.991397i	$0.458218\pi$
$878$	28.9524	0.977096
$879$	3.10154	0.104612
$880$	−15.9633	−0.538123
$881$	0.804823	0.0271152	0.0135576	−	0.999908i	$-0.495684\pi$
$881$	0.804823	0.0271152	0.0135576	+	0.999908i	$0.495684\pi$
$882$	−3.06987	−0.103368
$883$	−19.9955	−0.672903	−0.336452	−	0.941701i	$-0.609227\pi$
$883$	−19.9955	−0.672903	−0.336452	+	0.941701i	$0.609227\pi$
$884$	−19.4084	−0.652775
$885$	−6.28464	−0.211256
$886$	107.231	3.60251
$887$	−30.9782	−1.04014	−0.520072	−	0.854122i	$-0.674095\pi$
$887$	−30.9782	−1.04014	−0.520072	+	0.854122i	$0.674095\pi$
$888$	21.7248	0.729038
$889$	−51.8540	−1.73913
$890$	49.5034	1.65936
$891$	4.19124	0.140412
$892$	44.4748	1.48913
$893$	1.46227	0.0489329
$894$	1.92147	0.0642634
$895$	−46.6502	−1.55934
$896$	−136.429	−4.55777
$897$	3.15903	0.105477
$898$	83.4444	2.78457
$899$	−15.0879	−0.503209
$900$	23.7657	0.792190
$901$	8.99235	0.299579
$902$	−9.70438	−0.323121
$903$	8.18506	0.272382
$904$	−24.2460	−0.806409
$905$	−7.34614	−0.244194
$906$	16.3449	0.543023
$907$	−53.5485	−1.77805	−0.889024	−	0.457861i	$-0.848616\pi$
$907$	−53.5485	−1.77805	−0.889024	+	0.457861i	$0.848616\pi$
$908$	−51.7020	−1.71579
$909$	22.3879	0.742560
$910$	46.1063	1.52841
$911$	19.4298	0.643739	0.321869	−	0.946784i	$-0.395689\pi$
$911$	19.4298	0.643739	0.321869	+	0.946784i	$0.395689\pi$
$912$	−33.1700	−1.09837
$913$	7.37151	0.243961
$914$	95.1452	3.14712
$915$	−5.01014	−0.165630
$916$	−19.7597	−0.652878
$917$	8.52902	0.281653
$918$	4.92480	0.162543
$919$	−28.1467	−0.928474	−0.464237	−	0.885711i	$-0.653671\pi$
$919$	−28.1467	−0.928474	−0.464237	+	0.885711i	$0.653671\pi$
$920$	−57.8110	−1.90597
$921$	−2.74272	−0.0903757
$922$	−42.2825	−1.39250
$923$	−35.6392	−1.17308
$924$	−2.23939	−0.0736705
$925$	−10.3619	−0.340697
$926$	−19.0867	−0.627228
$927$	28.4789	0.935371
$928$	−51.5805	−1.69321
$929$	−48.5733	−1.59364	−0.796820	−	0.604217i	$-0.793486\pi$
$929$	−48.5733	−1.59364	−0.796820	+	0.604217i	$0.793486\pi$
$930$	11.7704	0.385967
$931$	−2.53749	−0.0831628
$932$	−117.874	−3.86110
$933$	7.28494	0.238498
$934$	−24.2240	−0.792635
$935$	0.964469	0.0315415
$936$	100.759	3.29342
$937$	18.8888	0.617069	0.308535	−	0.951213i	$-0.400161\pi$
$937$	18.8888	0.617069	0.308535	+	0.951213i	$0.400161\pi$
$938$	−75.6925	−2.47145
$939$	−1.89355	−0.0617937
$940$	−2.33923	−0.0762973
$941$	48.3633	1.57660	0.788299	−	0.615292i	$-0.210962\pi$
$941$	48.3633	1.57660	0.788299	+	0.615292i	$0.210962\pi$
$942$	−12.7600	−0.415743
$943$	−20.8969	−0.680497
$944$	−183.070	−5.95843
$945$	−8.63758	−0.280981
$946$	14.9298	0.485409
$947$	44.0326	1.43087	0.715434	−	0.698680i	$-0.246229\pi$
$947$	44.0326	1.43087	0.715434	+	0.698680i	$0.246229\pi$
$948$	−0.230754	−0.00749454
$949$	34.9433	1.13431
$950$	26.6074	0.863257
$951$	−4.64942	−0.150768
$952$	25.9040	0.839555
$953$	−22.1165	−0.716423	−0.358212	−	0.933640i	$-0.616613\pi$
$953$	−22.1165	−0.716423	−0.358212	+	0.933640i	$0.616613\pi$
$954$	−72.3181	−2.34138
$955$	−44.2398	−1.43157
$956$	−142.472	−4.60788
$957$	−0.310630	−0.0100413
$958$	51.9971	1.67995
$959$	33.4131	1.07896
$960$	21.4304	0.691662
$961$	25.1517	0.811345
$962$	−68.0537	−2.19414
$963$	−28.4885	−0.918028
$964$	12.8807	0.414861
$965$	−7.42772	−0.239107
$966$	−6.53146	−0.210146
$967$	15.8149	0.508574	0.254287	−	0.967129i	$-0.418159\pi$
$967$	15.8149	0.508574	0.254287	+	0.967129i	$0.418159\pi$
$968$	108.124	3.47525
$969$	2.00406	0.0643798
$970$	56.8834	1.82641
$971$	−38.4301	−1.23328	−0.616641	−	0.787245i	$-0.711507\pi$
$971$	−38.4301	−1.23328	−0.616641	+	0.787245i	$0.711507\pi$
$972$	−44.0867	−1.41408
$973$	−53.3785	−1.71124
$974$	10.7997	0.346044
$975$	1.50146	0.0480851
$976$	−145.945	−4.67157
$977$	−35.8746	−1.14773	−0.573865	−	0.818950i	$-0.694557\pi$
$977$	−35.8746	−1.14773	−0.573865	+	0.818950i	$0.694557\pi$
$978$	−7.01254	−0.224236
$979$	4.86207	0.155392
$980$	4.05929	0.129669
$981$	45.8045	1.46242
$982$	65.3050	2.08396
$983$	−7.66639	−0.244520	−0.122260	−	0.992498i	$-0.539014\pi$
$983$	−7.66639	−0.244520	−0.122260	+	0.992498i	$0.539014\pi$
$984$	20.8237	0.663836
$985$	39.4496	1.25697
$986$	5.56622	0.177265
$987$	−0.170606	−0.00543045
$988$	129.017	4.10459
$989$	32.1490	1.02228
$990$	−7.75643	−0.246516
$991$	−51.2314	−1.62742	−0.813709	−	0.581273i	$-0.802555\pi$
$991$	−51.2314	−1.62742	−0.813709	+	0.581273i	$0.802555\pi$
$992$	191.964	6.09487
$993$	−4.52999	−0.143755
$994$	73.6858	2.33717
$995$	−37.6419	−1.19333
$996$	−24.5034	−0.776419
$997$	29.9438	0.948331	0.474165	−	0.880436i	$-0.342750\pi$
$997$	29.9438	0.948331	0.474165	+	0.880436i	$0.342750\pi$
$998$	−70.1604	−2.22089
$999$	12.7492	0.403368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.2	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.2	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76448 q^{2} -0.301476 q^{3} +5.64235 q^{4} -1.88471 q^{5} +0.833425 q^{6} +2.57260 q^{7} -10.0692 q^{8} -2.90911 q^{9} +O(q^{10})\)	\(q-2.76448 q^{2} -0.301476 q^{3} +5.64235 q^{4} -1.88471 q^{5} +0.833425 q^{6} +2.57260 q^{7} -10.0692 q^{8} -2.90911 q^{9} +5.21024 q^{10} +0.511734 q^{11} -1.70103 q^{12} +3.43977 q^{13} -7.11191 q^{14} +0.568195 q^{15} +16.5514 q^{16} -1.00000 q^{17} +8.04218 q^{18} +6.64750 q^{19} -10.6342 q^{20} -0.775578 q^{21} -1.41468 q^{22} -3.04629 q^{23} +3.03562 q^{24} -1.44787 q^{25} -9.50919 q^{26} +1.78146 q^{27} +14.5155 q^{28} +2.01348 q^{29} -1.57076 q^{30} -7.49344 q^{31} -25.6176 q^{32} -0.154276 q^{33} +2.76448 q^{34} -4.84861 q^{35} -16.4142 q^{36} +7.15663 q^{37} -18.3769 q^{38} -1.03701 q^{39} +18.9775 q^{40} +6.85979 q^{41} +2.14407 q^{42} -10.5535 q^{43} +2.88738 q^{44} +5.48283 q^{45} +8.42141 q^{46} +0.219973 q^{47} -4.98985 q^{48} -0.381721 q^{49} +4.00261 q^{50} +0.301476 q^{51} +19.4084 q^{52} -8.99235 q^{53} -4.92480 q^{54} -0.964469 q^{55} -25.9040 q^{56} -2.00406 q^{57} -5.56622 q^{58} -11.0607 q^{59} +3.20595 q^{60} -8.81765 q^{61} +20.7155 q^{62} -7.48399 q^{63} +37.7166 q^{64} -6.48297 q^{65} +0.426492 q^{66} +10.6431 q^{67} -5.64235 q^{68} +0.918384 q^{69} +13.4039 q^{70} -10.3609 q^{71} +29.2924 q^{72} +10.1586 q^{73} -19.7844 q^{74} +0.436499 q^{75} +37.5075 q^{76} +1.31649 q^{77} +2.86679 q^{78} +0.135655 q^{79} -31.1946 q^{80} +8.19027 q^{81} -18.9637 q^{82} +14.4050 q^{83} -4.37608 q^{84} +1.88471 q^{85} +29.1749 q^{86} -0.607016 q^{87} -5.15275 q^{88} +9.50117 q^{89} -15.1572 q^{90} +8.84917 q^{91} -17.1882 q^{92} +2.25909 q^{93} -0.608110 q^{94} -12.5286 q^{95} +7.72310 q^{96} +10.9176 q^{97} +1.05526 q^{98} -1.48869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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