LMFDB - Embedded newform 4009.2.a.c.1.60

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.60
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89857 q^{2} -3.21324 q^{3} +1.60456 q^{4} -2.77491 q^{5} -6.10056 q^{6} -4.28441 q^{7} -0.750777 q^{8} +7.32493 q^{9} +O(q^{10})$	\(q+1.89857 q^{2} -3.21324 q^{3} +1.60456 q^{4} -2.77491 q^{5} -6.10056 q^{6} -4.28441 q^{7} -0.750777 q^{8} +7.32493 q^{9} -5.26836 q^{10} +0.954874 q^{11} -5.15583 q^{12} +3.64335 q^{13} -8.13424 q^{14} +8.91647 q^{15} -4.63451 q^{16} +7.80480 q^{17} +13.9069 q^{18} +1.00000 q^{19} -4.45250 q^{20} +13.7669 q^{21} +1.81289 q^{22} +4.41097 q^{23} +2.41243 q^{24} +2.70014 q^{25} +6.91714 q^{26} -13.8971 q^{27} -6.87458 q^{28} -0.794844 q^{29} +16.9285 q^{30} -9.81603 q^{31} -7.29738 q^{32} -3.06824 q^{33} +14.8179 q^{34} +11.8889 q^{35} +11.7533 q^{36} -8.18535 q^{37} +1.89857 q^{38} -11.7070 q^{39} +2.08334 q^{40} +7.83578 q^{41} +26.1373 q^{42} +9.10887 q^{43} +1.53215 q^{44} -20.3260 q^{45} +8.37451 q^{46} +6.72730 q^{47} +14.8918 q^{48} +11.3562 q^{49} +5.12640 q^{50} -25.0787 q^{51} +5.84595 q^{52} -8.51073 q^{53} -26.3845 q^{54} -2.64969 q^{55} +3.21664 q^{56} -3.21324 q^{57} -1.50907 q^{58} +10.8179 q^{59} +14.3070 q^{60} -0.969902 q^{61} -18.6364 q^{62} -31.3830 q^{63} -4.58553 q^{64} -10.1100 q^{65} -5.82527 q^{66} +7.36843 q^{67} +12.5232 q^{68} -14.1735 q^{69} +22.5718 q^{70} -14.0068 q^{71} -5.49939 q^{72} -2.15356 q^{73} -15.5404 q^{74} -8.67622 q^{75} +1.60456 q^{76} -4.09108 q^{77} -22.2264 q^{78} -3.62146 q^{79} +12.8604 q^{80} +22.6798 q^{81} +14.8768 q^{82} +0.838223 q^{83} +22.0897 q^{84} -21.6576 q^{85} +17.2938 q^{86} +2.55403 q^{87} -0.716898 q^{88} -5.20747 q^{89} -38.5904 q^{90} -15.6096 q^{91} +7.07764 q^{92} +31.5413 q^{93} +12.7722 q^{94} -2.77491 q^{95} +23.4482 q^{96} -12.8478 q^{97} +21.5605 q^{98} +6.99439 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	1.89857	1.34249	0.671245	−	0.741236i	$-0.265760\pi$
$2$	1.89857	1.34249	0.671245	+	0.741236i	$0.265760\pi$
$3$	−3.21324	−1.85517	−0.927583	−	0.373616i	$-0.878118\pi$
$3$	−3.21324	−1.85517	−0.927583	+	0.373616i	$0.878118\pi$
$4$	1.60456	0.802278
$5$	−2.77491	−1.24098	−0.620489	−	0.784215i	$-0.713066\pi$
$5$	−2.77491	−1.24098	−0.620489	+	0.784215i	$0.713066\pi$
$6$	−6.10056	−2.49054
$7$	−4.28441	−1.61936	−0.809678	−	0.586875i	$-0.800358\pi$
$7$	−4.28441	−1.61936	−0.809678	+	0.586875i	$0.800358\pi$
$8$	−0.750777	−0.265440
$9$	7.32493	2.44164
$10$	−5.26836	−1.66600
$11$	0.954874	0.287905	0.143953	−	0.989585i	$-0.454019\pi$
$11$	0.954874	0.287905	0.143953	+	0.989585i	$0.454019\pi$
$12$	−5.15583	−1.48836
$13$	3.64335	1.01048	0.505241	−	0.862978i	$-0.331403\pi$
$13$	3.64335	1.01048	0.505241	+	0.862978i	$0.331403\pi$
$14$	−8.13424	−2.17397
$15$	8.91647	2.30222
$16$	−4.63451	−1.15863
$17$	7.80480	1.89294	0.946471	−	0.322789i	$-0.104621\pi$
$17$	7.80480	1.89294	0.946471	+	0.322789i	$0.104621\pi$
$18$	13.9069	3.27788
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.45250	−0.995610
$21$	13.7669	3.00417
$22$	1.81289	0.386510
$23$	4.41097	0.919750	0.459875	−	0.887984i	$-0.347894\pi$
$23$	4.41097	0.919750	0.459875	+	0.887984i	$0.347894\pi$
$24$	2.41243	0.492435
$25$	2.70014	0.540029
$26$	6.91714	1.35656
$27$	−13.8971	−2.67449
$28$	−6.87458	−1.29917
$29$	−0.794844	−0.147599	−0.0737995	−	0.997273i	$-0.523512\pi$
$29$	−0.794844	−0.147599	−0.0737995	+	0.997273i	$0.523512\pi$
$30$	16.9285	3.09071
$31$	−9.81603	−1.76301	−0.881505	−	0.472174i	$-0.843469\pi$
$31$	−9.81603	−1.76301	−0.881505	+	0.472174i	$0.843469\pi$
$32$	−7.29738	−1.29001
$33$	−3.06824	−0.534113
$34$	14.8179	2.54125
$35$	11.8889	2.00959
$36$	11.7533	1.95888
$37$	−8.18535	−1.34566	−0.672832	−	0.739796i	$-0.734922\pi$
$37$	−8.18535	−1.34566	−0.672832	+	0.739796i	$0.734922\pi$
$38$	1.89857	0.307988
$39$	−11.7070	−1.87461
$40$	2.08334	0.329405
$41$	7.83578	1.22374	0.611872	−	0.790957i	$-0.290417\pi$
$41$	7.83578	1.22374	0.611872	+	0.790957i	$0.290417\pi$
$42$	26.1373	4.03307
$43$	9.10887	1.38909	0.694545	−	0.719449i	$-0.255606\pi$
$43$	9.10887	1.38909	0.694545	+	0.719449i	$0.255606\pi$
$44$	1.53215	0.230980
$45$	−20.3260	−3.03003
$46$	8.37451	1.23475
$47$	6.72730	0.981278	0.490639	−	0.871363i	$-0.336763\pi$
$47$	6.72730	0.981278	0.490639	+	0.871363i	$0.336763\pi$
$48$	14.8918	2.14945
$49$	11.3562	1.62231
$50$	5.12640	0.724983
$51$	−25.0787	−3.51172
$52$	5.84595	0.810688
$53$	−8.51073	−1.16904	−0.584519	−	0.811380i	$-0.698717\pi$
$53$	−8.51073	−1.16904	−0.584519	+	0.811380i	$0.698717\pi$
$54$	−26.3845	−3.59047
$55$	−2.64969	−0.357285
$56$	3.21664	0.429841
$57$	−3.21324	−0.425604
$58$	−1.50907	−0.198150
$59$	10.8179	1.40837	0.704183	−	0.710018i	$-0.251313\pi$
$59$	10.8179	1.40837	0.704183	+	0.710018i	$0.251313\pi$
$60$	14.3070	1.84702
$61$	−0.969902	−0.124183	−0.0620916	−	0.998070i	$-0.519777\pi$
$61$	−0.969902	−0.124183	−0.0620916	+	0.998070i	$0.519777\pi$
$62$	−18.6364	−2.36682
$63$	−31.3830	−3.95389
$64$	−4.58553	−0.573192
$65$	−10.1100	−1.25399
$66$	−5.82527	−0.717041
$67$	7.36843	0.900197	0.450098	−	0.892979i	$-0.351389\pi$
$67$	7.36843	0.900197	0.450098	+	0.892979i	$0.351389\pi$
$68$	12.5232	1.51867
$69$	−14.1735	−1.70629
$70$	22.5718	2.69785
$71$	−14.0068	−1.66230	−0.831149	−	0.556050i	$-0.812316\pi$
$71$	−14.0068	−1.66230	−0.831149	+	0.556050i	$0.812316\pi$
$72$	−5.49939	−0.648109
$73$	−2.15356	−0.252055	−0.126027	−	0.992027i	$-0.540223\pi$
$73$	−2.15356	−0.252055	−0.126027	+	0.992027i	$0.540223\pi$
$74$	−15.5404	−1.80654
$75$	−8.67622	−1.00184
$76$	1.60456	0.184055
$77$	−4.09108	−0.466221
$78$	−22.2264	−2.51665
$79$	−3.62146	−0.407446	−0.203723	−	0.979029i	$-0.565304\pi$
$79$	−3.62146	−0.407446	−0.203723	+	0.979029i	$0.565304\pi$
$80$	12.8604	1.43783
$81$	22.6798	2.51998
$82$	14.8768	1.64286
$83$	0.838223	0.0920070	0.0460035	−	0.998941i	$-0.485351\pi$
$83$	0.838223	0.0920070	0.0460035	+	0.998941i	$0.485351\pi$
$84$	22.0897	2.41018
$85$	−21.6576	−2.34910
$86$	17.2938	1.86484
$87$	2.55403	0.273821
$88$	−0.716898	−0.0764216
$89$	−5.20747	−0.551991	−0.275996	−	0.961159i	$-0.589008\pi$
$89$	−5.20747	−0.551991	−0.275996	+	0.961159i	$0.589008\pi$
$90$	−38.5904	−4.06778
$91$	−15.6096	−1.63633
$92$	7.07764	0.737895
$93$	31.5413	3.27068
$94$	12.7722	1.31736
$95$	−2.77491	−0.284700
$96$	23.4482	2.39318
$97$	−12.8478	−1.30450	−0.652250	−	0.758004i	$-0.726175\pi$
$97$	−12.8478	−1.30450	−0.652250	+	0.758004i	$0.726175\pi$
$98$	21.5605	2.17794
$99$	6.99439	0.702963
$100$	4.33253	0.433253
$101$	17.3535	1.72674	0.863371	−	0.504569i	$-0.168349\pi$
$101$	17.3535	1.72674	0.863371	+	0.504569i	$0.168349\pi$
$102$	−47.6136	−4.71445
$103$	−8.06320	−0.794490	−0.397245	−	0.917713i	$-0.630034\pi$
$103$	−8.06320	−0.794490	−0.397245	+	0.917713i	$0.630034\pi$
$104$	−2.73534	−0.268222
$105$	−38.2018	−3.72812
$106$	−16.1582	−1.56942
$107$	−17.6822	−1.70940	−0.854700	−	0.519123i	$-0.826259\pi$
$107$	−17.6822	−1.70940	−0.854700	+	0.519123i	$0.826259\pi$
$108$	−22.2986	−2.14568
$109$	2.75663	0.264037	0.132019	−	0.991247i	$-0.457854\pi$
$109$	2.75663	0.264037	0.132019	+	0.991247i	$0.457854\pi$
$110$	−5.03062	−0.479651
$111$	26.3015	2.49643
$112$	19.8562	1.87623
$113$	6.04358	0.568532	0.284266	−	0.958745i	$-0.408250\pi$
$113$	6.04358	0.568532	0.284266	+	0.958745i	$0.408250\pi$
$114$	−6.10056	−0.571369
$115$	−12.2400	−1.14139
$116$	−1.27537	−0.118415
$117$	26.6873	2.46724
$118$	20.5384	1.89072
$119$	−33.4390	−3.06535
$120$	−6.69428	−0.611101
$121$	−10.0882	−0.917110
$122$	−1.84142	−0.166715
$123$	−25.1783	−2.27025
$124$	−15.7504	−1.41442
$125$	6.38190	0.570815
$126$	−59.5828	−5.30805
$127$	−11.4627	−1.01715	−0.508573	−	0.861019i	$-0.669827\pi$
$127$	−11.4627	−1.01715	−0.508573	+	0.861019i	$0.669827\pi$
$128$	5.88881	0.520502
$129$	−29.2690	−2.57699
$130$	−19.1945	−1.68347
$131$	−0.213858	−0.0186848	−0.00934241	−	0.999956i	$-0.502974\pi$
$131$	−0.213858	−0.0186848	−0.00934241	+	0.999956i	$0.502974\pi$
$132$	−4.92317	−0.428507
$133$	−4.28441	−0.371506
$134$	13.9895	1.20850
$135$	38.5631	3.31898
$136$	−5.85966	−0.502462
$137$	−0.285104	−0.0243581	−0.0121791	−	0.999926i	$-0.503877\pi$
$137$	−0.285104	−0.0243581	−0.0121791	+	0.999926i	$0.503877\pi$
$138$	−26.9094	−2.29068
$139$	−8.05802	−0.683472	−0.341736	−	0.939796i	$-0.611015\pi$
$139$	−8.05802	−0.683472	−0.341736	+	0.939796i	$0.611015\pi$
$140$	19.0764	1.61225
$141$	−21.6165	−1.82043
$142$	−26.5928	−2.23162
$143$	3.47894	0.290923
$144$	−33.9475	−2.82896
$145$	2.20562	0.183167
$146$	−4.08867	−0.338381
$147$	−36.4902	−3.00966
$148$	−13.1339	−1.07960
$149$	8.02730	0.657622	0.328811	−	0.944396i	$-0.393352\pi$
$149$	8.02730	0.657622	0.328811	+	0.944396i	$0.393352\pi$
$150$	−16.4724	−1.34496
$151$	−15.0904	−1.22804	−0.614019	−	0.789291i	$-0.710448\pi$
$151$	−15.0904	−1.22804	−0.614019	+	0.789291i	$0.710448\pi$
$152$	−0.750777	−0.0608960
$153$	57.1696	4.62189
$154$	−7.76718	−0.625897
$155$	27.2386	2.18786
$156$	−18.7845	−1.50396
$157$	10.3458	0.825683	0.412841	−	0.910803i	$-0.364536\pi$
$157$	10.3458	0.825683	0.412841	+	0.910803i	$0.364536\pi$
$158$	−6.87558	−0.546992
$159$	27.3470	2.16876
$160$	20.2496	1.60087
$161$	−18.8984	−1.48940
$162$	43.0591	3.38304
$163$	−1.54285	−0.120846	−0.0604228	−	0.998173i	$-0.519245\pi$
$163$	−1.54285	−0.120846	−0.0604228	+	0.998173i	$0.519245\pi$
$164$	12.5730	0.981783
$165$	8.51411	0.662823
$166$	1.59142	0.123518
$167$	−6.13264	−0.474558	−0.237279	−	0.971442i	$-0.576256\pi$
$167$	−6.13264	−0.474558	−0.237279	+	0.971442i	$0.576256\pi$
$168$	−10.3358	−0.797427
$169$	0.273975	0.0210750
$170$	−41.1185	−3.15364
$171$	7.32493	0.560151
$172$	14.6157	1.11444
$173$	12.0709	0.917737	0.458868	−	0.888504i	$-0.348255\pi$
$173$	12.0709	0.917737	0.458868	+	0.888504i	$0.348255\pi$
$174$	4.84899	0.367601
$175$	−11.5685	−0.874499
$176$	−4.42538	−0.333575
$177$	−34.7604	−2.61275
$178$	−9.88674	−0.741042
$179$	−10.3563	−0.774069	−0.387035	−	0.922065i	$-0.626501\pi$
$179$	−10.3563	−0.774069	−0.387035	+	0.922065i	$0.626501\pi$
$180$	−32.6143	−2.43092
$181$	0.463058	0.0344189	0.0172094	−	0.999852i	$-0.494522\pi$
$181$	0.463058	0.0344189	0.0172094	+	0.999852i	$0.494522\pi$
$182$	−29.6359	−2.19676
$183$	3.11653	0.230381
$184$	−3.31165	−0.244138
$185$	22.7136	1.66994
$186$	59.8832	4.39085
$187$	7.45260	0.544988
$188$	10.7943	0.787258
$189$	59.5407	4.33095
$190$	−5.26836	−0.382207
$191$	−8.92851	−0.646044	−0.323022	−	0.946391i	$-0.604699\pi$
$191$	−8.92851	−0.646044	−0.323022	+	0.946391i	$0.604699\pi$
$192$	14.7344	1.06337
$193$	0.734281	0.0528547	0.0264273	−	0.999651i	$-0.491587\pi$
$193$	0.734281	0.0528547	0.0264273	+	0.999651i	$0.491587\pi$
$194$	−24.3925	−1.75128
$195$	32.4858	2.32636
$196$	18.2216	1.30155
$197$	19.8041	1.41099	0.705494	−	0.708716i	$-0.250725\pi$
$197$	19.8041	1.41099	0.705494	+	0.708716i	$0.250725\pi$
$198$	13.2793	0.943720
$199$	9.33125	0.661475	0.330737	−	0.943723i	$-0.392703\pi$
$199$	9.33125	0.661475	0.330737	+	0.943723i	$0.392703\pi$
$200$	−2.02721	−0.143345
$201$	−23.6765	−1.67001
$202$	32.9469	2.31813
$203$	3.40544	0.239015
$204$	−40.2402	−2.81738
$205$	−21.7436	−1.51864
$206$	−15.3085	−1.06659
$207$	32.3100	2.24570
$208$	−16.8851	−1.17077
$209$	0.954874	0.0660500
$210$	−72.5287	−5.00496
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−13.6559	−0.937894
$213$	45.0072	3.08384
$214$	−33.5708	−2.29485
$215$	−25.2763	−1.72383
$216$	10.4336	0.709916
$217$	42.0559	2.85494
$218$	5.23364	0.354467
$219$	6.91990	0.467603
$220$	−4.25158	−0.286642
$221$	28.4356	1.91278
$222$	49.9352	3.35143
$223$	−6.47435	−0.433555	−0.216777	−	0.976221i	$-0.569555\pi$
$223$	−6.47435	−0.433555	−0.216777	+	0.976221i	$0.569555\pi$
$224$	31.2650	2.08898
$225$	19.7784	1.31856
$226$	11.4741	0.763249
$227$	2.33109	0.154720	0.0773599	−	0.997003i	$-0.475351\pi$
$227$	2.33109	0.154720	0.0773599	+	0.997003i	$0.475351\pi$
$228$	−5.15583	−0.341453
$229$	−21.4519	−1.41758	−0.708789	−	0.705420i	$-0.750758\pi$
$229$	−21.4519	−1.41758	−0.708789	+	0.705420i	$0.750758\pi$
$230$	−23.2386	−1.53230
$231$	13.1456	0.864918
$232$	0.596751	0.0391786
$233$	11.6652	0.764215	0.382108	−	0.924118i	$-0.375198\pi$
$233$	11.6652	0.764215	0.382108	+	0.924118i	$0.375198\pi$
$234$	50.6675	3.31224
$235$	−18.6677	−1.21775
$236$	17.3579	1.12990
$237$	11.6366	0.755880
$238$	−63.4861	−4.11519
$239$	−22.0153	−1.42405	−0.712027	−	0.702152i	$-0.752223\pi$
$239$	−22.0153	−1.42405	−0.712027	+	0.702152i	$0.752223\pi$
$240$	−41.3235	−2.66742
$241$	21.0475	1.35579	0.677893	−	0.735160i	$-0.262893\pi$
$241$	21.0475	1.35579	0.677893	+	0.735160i	$0.262893\pi$
$242$	−19.1531	−1.23121
$243$	−31.1846	−2.00049
$244$	−1.55626	−0.0996294
$245$	−31.5124	−2.01326
$246$	−47.8026	−3.04778
$247$	3.64335	0.231821
$248$	7.36965	0.467973
$249$	−2.69342	−0.170688
$250$	12.1165	0.766313
$251$	14.2365	0.898602	0.449301	−	0.893380i	$-0.351673\pi$
$251$	14.2365	0.898602	0.449301	+	0.893380i	$0.351673\pi$
$252$	−50.3558	−3.17212
$253$	4.21192	0.264801
$254$	−21.7626	−1.36551
$255$	69.5913	4.35797
$256$	20.3514	1.27196
$257$	8.34577	0.520595	0.260298	−	0.965528i	$-0.416179\pi$
$257$	8.34577	0.520595	0.260298	+	0.965528i	$0.416179\pi$
$258$	−55.5692	−3.45959
$259$	35.0694	2.17911
$260$	−16.2220	−1.00605
$261$	−5.82218	−0.360384
$262$	−0.406023	−0.0250842
$263$	18.4904	1.14017	0.570083	−	0.821587i	$-0.306911\pi$
$263$	18.4904	1.14017	0.570083	+	0.821587i	$0.306911\pi$
$264$	2.30357	0.141775
$265$	23.6165	1.45075
$266$	−8.13424	−0.498742
$267$	16.7329	1.02404
$268$	11.8231	0.722208
$269$	−12.0064	−0.732043	−0.366021	−	0.930606i	$-0.619280\pi$
$269$	−12.0064	−0.732043	−0.366021	+	0.930606i	$0.619280\pi$
$270$	73.2146	4.45570
$271$	−20.5270	−1.24693	−0.623464	−	0.781852i	$-0.714275\pi$
$271$	−20.5270	−1.24693	−0.623464	+	0.781852i	$0.714275\pi$
$272$	−36.1714	−2.19322
$273$	50.1574	3.03567
$274$	−0.541290	−0.0327005
$275$	2.57830	0.155477
$276$	−22.7422	−1.36892
$277$	1.65998	0.0997386	0.0498693	−	0.998756i	$-0.484120\pi$
$277$	1.65998	0.0997386	0.0498693	+	0.998756i	$0.484120\pi$
$278$	−15.2987	−0.917554
$279$	−71.9017	−4.30464
$280$	−8.92589	−0.533424
$281$	−20.8096	−1.24140	−0.620699	−	0.784049i	$-0.713151\pi$
$281$	−20.8096	−1.24140	−0.620699	+	0.784049i	$0.713151\pi$
$282$	−41.0403	−2.44391
$283$	17.9533	1.06721	0.533607	−	0.845732i	$-0.320836\pi$
$283$	17.9533	1.06721	0.533607	+	0.845732i	$0.320836\pi$
$284$	−22.4746	−1.33363
$285$	8.91647	0.528166
$286$	6.60500	0.390562
$287$	−33.5717	−1.98168
$288$	−53.4528	−3.14973
$289$	43.9149	2.58323
$290$	4.18753	0.245900
$291$	41.2832	2.42006
$292$	−3.45550	−0.202218
$293$	−7.21331	−0.421406	−0.210703	−	0.977550i	$-0.567575\pi$
$293$	−7.21331	−0.421406	−0.210703	+	0.977550i	$0.567575\pi$
$294$	−69.2791	−4.04044
$295$	−30.0186	−1.74775
$296$	6.14537	0.357192
$297$	−13.2699	−0.770000
$298$	15.2404	0.882850
$299$	16.0707	0.929391
$300$	−13.9215	−0.803757
$301$	−39.0262	−2.24943
$302$	−28.6501	−1.64863
$303$	−55.7612	−3.20340
$304$	−4.63451	−0.265807
$305$	2.69139	0.154109
$306$	108.540	6.20484
$307$	−4.41962	−0.252241	−0.126120	−	0.992015i	$-0.540253\pi$
$307$	−4.41962	−0.252241	−0.126120	+	0.992015i	$0.540253\pi$
$308$	−6.56436	−0.374039
$309$	25.9090	1.47391
$310$	51.7144	2.93718
$311$	−4.03871	−0.229014	−0.114507	−	0.993422i	$-0.536529\pi$
$311$	−4.03871	−0.229014	−0.114507	+	0.993422i	$0.536529\pi$
$312$	8.78931	0.497597
$313$	−9.31552	−0.526544	−0.263272	−	0.964722i	$-0.584802\pi$
$313$	−9.31552	−0.526544	−0.263272	+	0.964722i	$0.584802\pi$
$314$	19.6421	1.10847
$315$	87.0852	4.90669
$316$	−5.81083	−0.326885
$317$	28.8918	1.62273	0.811363	−	0.584543i	$-0.198726\pi$
$317$	28.8918	1.62273	0.811363	+	0.584543i	$0.198726\pi$
$318$	51.9202	2.91154
$319$	−0.758977	−0.0424945
$320$	12.7245	0.711319
$321$	56.8171	3.17122
$322$	−35.8799	−1.99951
$323$	7.80480	0.434271
$324$	36.3910	2.02172
$325$	9.83756	0.545690
$326$	−2.92921	−0.162234
$327$	−8.85772	−0.489833
$328$	−5.88292	−0.324830
$329$	−28.8225	−1.58904
$330$	16.1646	0.889832
$331$	−24.5073	−1.34704	−0.673521	−	0.739168i	$-0.735219\pi$
$331$	−24.5073	−1.34704	−0.673521	+	0.739168i	$0.735219\pi$
$332$	1.34498	0.0738152
$333$	−59.9571	−3.28563
$334$	−11.6432	−0.637089
$335$	−20.4467	−1.11713
$336$	−63.8027	−3.48072
$337$	−24.6364	−1.34203	−0.671016	−	0.741442i	$-0.734142\pi$
$337$	−24.6364	−1.34203	−0.671016	+	0.741442i	$0.734142\pi$
$338$	0.520161	0.0282930
$339$	−19.4195	−1.05472
$340$	−34.7509	−1.88463
$341$	−9.37307	−0.507580
$342$	13.9069	0.751997
$343$	−18.6637	−1.00775
$344$	−6.83873	−0.368720
$345$	39.3303	2.11747
$346$	22.9175	1.23205
$347$	−28.4998	−1.52995	−0.764975	−	0.644061i	$-0.777248\pi$
$347$	−28.4998	−1.52995	−0.764975	+	0.644061i	$0.777248\pi$
$348$	4.09808	0.219680
$349$	−12.4819	−0.668143	−0.334071	−	0.942548i	$-0.608423\pi$
$349$	−12.4819	−0.668143	−0.334071	+	0.942548i	$0.608423\pi$
$350$	−21.9636	−1.17401
$351$	−50.6318	−2.70252
$352$	−6.96808	−0.371400
$353$	−18.8027	−1.00076	−0.500382	−	0.865804i	$-0.666807\pi$
$353$	−18.8027	−1.00076	−0.500382	+	0.865804i	$0.666807\pi$
$354$	−65.9950	−3.50760
$355$	38.8676	2.06288
$356$	−8.35568	−0.442850
$357$	107.448	5.68673
$358$	−19.6622	−1.03918
$359$	−32.8195	−1.73214	−0.866072	−	0.499919i	$-0.833363\pi$
$359$	−32.8195	−1.73214	−0.866072	+	0.499919i	$0.833363\pi$
$360$	15.2603	0.804290
$361$	1.00000	0.0526316
$362$	0.879147	0.0462070
$363$	32.4159	1.70139
$364$	−25.0465	−1.31279
$365$	5.97593	0.312794
$366$	5.91694	0.309283
$367$	10.8766	0.567756	0.283878	−	0.958860i	$-0.408379\pi$
$367$	10.8766	0.567756	0.283878	+	0.958860i	$0.408379\pi$
$368$	−20.4427	−1.06565
$369$	57.3966	2.98795
$370$	43.1234	2.24188
$371$	36.4635	1.89309
$372$	50.6098	2.62399
$373$	−19.1135	−0.989659	−0.494829	−	0.868990i	$-0.664769\pi$
$373$	−19.1135	−0.989659	−0.494829	+	0.868990i	$0.664769\pi$
$374$	14.1493	0.731641
$375$	−20.5066	−1.05896
$376$	−5.05071	−0.260470
$377$	−2.89589	−0.149146
$378$	113.042	5.81425
$379$	1.08868	0.0559220	0.0279610	−	0.999609i	$-0.491099\pi$
$379$	1.08868	0.0559220	0.0279610	+	0.999609i	$0.491099\pi$
$380$	−4.45250	−0.228409
$381$	36.8323	1.88698
$382$	−16.9514	−0.867308
$383$	1.27667	0.0652346	0.0326173	−	0.999468i	$-0.489616\pi$
$383$	1.27667	0.0652346	0.0326173	+	0.999468i	$0.489616\pi$
$384$	−18.9222	−0.965619
$385$	11.3524	0.578571
$386$	1.39408	0.0709569
$387$	66.7219	3.39166
$388$	−20.6151	−1.04657
$389$	−17.7989	−0.902440	−0.451220	−	0.892413i	$-0.649011\pi$
$389$	−17.7989	−0.902440	−0.451220	+	0.892413i	$0.649011\pi$
$390$	61.6764	3.12311
$391$	34.4267	1.74103
$392$	−8.52596	−0.430626
$393$	0.687176	0.0346635
$394$	37.5995	1.89424
$395$	10.0492	0.505632
$396$	11.2229	0.563971
$397$	8.97715	0.450550	0.225275	−	0.974295i	$-0.427672\pi$
$397$	8.97715	0.450550	0.225275	+	0.974295i	$0.427672\pi$
$398$	17.7160	0.888023
$399$	13.7669	0.689205
$400$	−12.5138	−0.625692
$401$	32.7726	1.63659	0.818294	−	0.574801i	$-0.194920\pi$
$401$	32.7726	1.63659	0.818294	+	0.574801i	$0.194920\pi$
$402$	−44.9515	−2.24198
$403$	−35.7632	−1.78149
$404$	27.8447	1.38533
$405$	−62.9345	−3.12724
$406$	6.46546	0.320875
$407$	−7.81598	−0.387424
$408$	18.8285	0.932151
$409$	−31.0804	−1.53683	−0.768414	−	0.639953i	$-0.778954\pi$
$409$	−31.0804	−1.53683	−0.768414	+	0.639953i	$0.778954\pi$
$410$	−41.2817	−2.03876
$411$	0.916110	0.0451884
$412$	−12.9379	−0.637402
$413$	−46.3482	−2.28065
$414$	61.3427	3.01483
$415$	−2.32600	−0.114179
$416$	−26.5869	−1.30353
$417$	25.8924	1.26795
$418$	1.81289	0.0886715
$419$	−30.5471	−1.49232	−0.746162	−	0.665764i	$-0.768106\pi$
$419$	−30.5471	−1.49232	−0.746162	+	0.665764i	$0.768106\pi$
$420$	−61.2970	−2.99099
$421$	−28.7107	−1.39928	−0.699638	−	0.714497i	$-0.746655\pi$
$421$	−28.7107	−1.39928	−0.699638	+	0.714497i	$0.746655\pi$
$422$	1.89857	0.0924208
$423$	49.2770	2.39593
$424$	6.38966	0.310309
$425$	21.0741	1.02224
$426$	85.4491	4.14002
$427$	4.15546	0.201097
$428$	−28.3720	−1.37141
$429$	−11.1787	−0.539712
$430$	−47.9888	−2.31423
$431$	−12.9892	−0.625669	−0.312834	−	0.949808i	$-0.601278\pi$
$431$	−12.9892	−0.625669	−0.312834	+	0.949808i	$0.601278\pi$
$432$	64.4060	3.09874
$433$	4.06544	0.195373	0.0976863	−	0.995217i	$-0.468856\pi$
$433$	4.06544	0.195373	0.0976863	+	0.995217i	$0.468856\pi$
$434$	79.8460	3.83273
$435$	−7.08721	−0.339806
$436$	4.42317	0.211831
$437$	4.41097	0.211005
$438$	13.1379	0.627753
$439$	3.01207	0.143758	0.0718791	−	0.997413i	$-0.477100\pi$
$439$	3.01207	0.143758	0.0718791	+	0.997413i	$0.477100\pi$
$440$	1.98933	0.0948375
$441$	83.1833	3.96111
$442$	53.9869	2.56789
$443$	−8.97725	−0.426522	−0.213261	−	0.976995i	$-0.568408\pi$
$443$	−8.97725	−0.426522	−0.213261	+	0.976995i	$0.568408\pi$
$444$	42.2023	2.00283
$445$	14.4503	0.685009
$446$	−12.2920	−0.582043
$447$	−25.7937	−1.22000
$448$	19.6463	0.928201
$449$	15.7411	0.742867	0.371433	−	0.928460i	$-0.378866\pi$
$449$	15.7411	0.742867	0.371433	+	0.928460i	$0.378866\pi$
$450$	37.5505	1.77015
$451$	7.48219	0.352323
$452$	9.69727	0.456121
$453$	48.4890	2.27821
$454$	4.42573	0.207710
$455$	43.3153	2.03065
$456$	2.41243	0.112972
$457$	10.9335	0.511448	0.255724	−	0.966750i	$-0.417686\pi$
$457$	10.9335	0.511448	0.255724	+	0.966750i	$0.417686\pi$
$458$	−40.7278	−1.90308
$459$	−108.464	−5.06265
$460$	−19.6398	−0.915712
$461$	−2.31388	−0.107768	−0.0538841	−	0.998547i	$-0.517160\pi$
$461$	−2.31388	−0.107768	−0.0538841	+	0.998547i	$0.517160\pi$
$462$	24.9578	1.16114
$463$	11.7865	0.547766	0.273883	−	0.961763i	$-0.411692\pi$
$463$	11.7865	0.547766	0.273883	+	0.961763i	$0.411692\pi$
$464$	3.68372	0.171012
$465$	−87.5243	−4.05884
$466$	22.1472	1.02595
$467$	17.8119	0.824239	0.412119	−	0.911130i	$-0.364789\pi$
$467$	17.8119	0.824239	0.412119	+	0.911130i	$0.364789\pi$
$468$	42.8212	1.97941
$469$	−31.5694	−1.45774
$470$	−35.4419	−1.63481
$471$	−33.2435	−1.53178
$472$	−8.12181	−0.373836
$473$	8.69783	0.399927
$474$	22.0929	1.01476
$475$	2.70014	0.123891
$476$	−53.6547	−2.45926
$477$	−62.3405	−2.85437
$478$	−41.7976	−1.91178
$479$	−26.2655	−1.20010	−0.600052	−	0.799961i	$-0.704853\pi$
$479$	−26.2655	−1.20010	−0.600052	+	0.799961i	$0.704853\pi$
$480$	−65.0668	−2.96988
$481$	−29.8221	−1.35977
$482$	39.9600	1.82013
$483$	60.7251	2.76309
$484$	−16.1871	−0.735778
$485$	35.6516	1.61886
$486$	−59.2060	−2.68564
$487$	−0.358162	−0.0162299	−0.00811493	−	0.999967i	$-0.502583\pi$
$487$	−0.358162	−0.0162299	−0.00811493	+	0.999967i	$0.502583\pi$
$488$	0.728180	0.0329632
$489$	4.95756	0.224189
$490$	−59.8285	−2.70277
$491$	13.9347	0.628866	0.314433	−	0.949280i	$-0.398186\pi$
$491$	13.9347	0.628866	0.314433	+	0.949280i	$0.398186\pi$
$492$	−40.3999	−1.82137
$493$	−6.20360	−0.279396
$494$	6.91714	0.311217
$495$	−19.4088	−0.872362
$496$	45.4925	2.04267
$497$	60.0108	2.69185
$498$	−5.11363	−0.229147
$499$	−8.94795	−0.400565	−0.200283	−	0.979738i	$-0.564186\pi$
$499$	−8.94795	−0.400565	−0.200283	+	0.979738i	$0.564186\pi$
$500$	10.2401	0.457952
$501$	19.7057	0.880385
$502$	27.0290	1.20636
$503$	−4.02183	−0.179325	−0.0896623	−	0.995972i	$-0.528579\pi$
$503$	−4.02183	−0.179325	−0.0896623	+	0.995972i	$0.528579\pi$
$504$	23.5616	1.04952
$505$	−48.1546	−2.14285
$506$	7.99661	0.355493
$507$	−0.880349	−0.0390977
$508$	−18.3925	−0.816035
$509$	−20.0683	−0.889512	−0.444756	−	0.895652i	$-0.646710\pi$
$509$	−20.0683	−0.889512	−0.444756	+	0.895652i	$0.646710\pi$
$510$	132.124	5.85053
$511$	9.22672	0.408166
$512$	26.8608	1.18709
$513$	−13.8971	−0.613570
$514$	15.8450	0.698893
$515$	22.3747	0.985946
$516$	−46.9638	−2.06747
$517$	6.42373	0.282515
$518$	66.5816	2.92543
$519$	−38.7869	−1.70255
$520$	7.59033	0.332858
$521$	−11.0257	−0.483045	−0.241523	−	0.970395i	$-0.577647\pi$
$521$	−11.0257	−0.483045	−0.241523	+	0.970395i	$0.577647\pi$
$522$	−11.0538	−0.483812
$523$	24.0014	1.04951	0.524753	−	0.851254i	$-0.324158\pi$
$523$	24.0014	1.04951	0.524753	+	0.851254i	$0.324158\pi$
$524$	−0.343146	−0.0149904
$525$	37.1725	1.62234
$526$	35.1053	1.53066
$527$	−76.6121	−3.33728
$528$	14.2198	0.618838
$529$	−3.54337	−0.154060
$530$	44.8376	1.94762
$531$	79.2401	3.43873
$532$	−6.87458	−0.298051
$533$	28.5485	1.23657
$534$	31.7685	1.37476
$535$	49.0665	2.12133
$536$	−5.53204	−0.238948
$537$	33.2774	1.43603
$538$	−22.7949	−0.982760
$539$	10.8437	0.467073
$540$	61.8767	2.66275
$541$	15.4268	0.663252	0.331626	−	0.943411i	$-0.392403\pi$
$541$	15.4268	0.663252	0.331626	+	0.943411i	$0.392403\pi$
$542$	−38.9719	−1.67399
$543$	−1.48792	−0.0638527
$544$	−56.9546	−2.44191
$545$	−7.64941	−0.327665
$546$	95.2272	4.07535
$547$	−27.6590	−1.18261	−0.591307	−	0.806447i	$-0.701388\pi$
$547$	−27.6590	−1.18261	−0.591307	+	0.806447i	$0.701388\pi$
$548$	−0.457466	−0.0195420
$549$	−7.10446	−0.303211
$550$	4.89507	0.208727
$551$	−0.794844	−0.0338615
$552$	10.6411	0.452917
$553$	15.5158	0.659800
$554$	3.15159	0.133898
$555$	−72.9844	−3.09802
$556$	−12.9295	−0.548335
$557$	−23.0792	−0.977896	−0.488948	−	0.872313i	$-0.662619\pi$
$557$	−23.0792	−0.977896	−0.488948	+	0.872313i	$0.662619\pi$
$558$	−136.510	−5.77894
$559$	33.1868	1.40365
$560$	−55.0991	−2.32836
$561$	−23.9470	−1.01104
$562$	−39.5085	−1.66656
$563$	1.68095	0.0708438	0.0354219	−	0.999372i	$-0.488722\pi$
$563$	1.68095	0.0708438	0.0354219	+	0.999372i	$0.488722\pi$
$564$	−34.6848	−1.46049
$565$	−16.7704	−0.705537
$566$	34.0856	1.43272
$567$	−97.1697	−4.08074
$568$	10.5160	0.441240
$569$	27.2237	1.14128	0.570639	−	0.821201i	$-0.306696\pi$
$569$	27.2237	1.14128	0.570639	+	0.821201i	$0.306696\pi$
$570$	16.9285	0.709057
$571$	−25.7696	−1.07843	−0.539213	−	0.842169i	$-0.681278\pi$
$571$	−25.7696	−1.07843	−0.539213	+	0.842169i	$0.681278\pi$
$572$	5.58215	0.233402
$573$	28.6895	1.19852
$574$	−63.7382	−2.66038
$575$	11.9102	0.496692
$576$	−33.5887	−1.39953
$577$	21.1245	0.879426	0.439713	−	0.898138i	$-0.355080\pi$
$577$	21.1245	0.879426	0.439713	+	0.898138i	$0.355080\pi$
$578$	83.3753	3.46796
$579$	−2.35942	−0.0980543
$580$	3.53905	0.146951
$581$	−3.59129	−0.148992
$582$	78.3789	3.24891
$583$	−8.12668	−0.336573
$584$	1.61684	0.0669053
$585$	−74.0548	−3.06179
$586$	−13.6949	−0.565733
$587$	−38.7791	−1.60058	−0.800292	−	0.599610i	$-0.795322\pi$
$587$	−38.7791	−1.60058	−0.800292	+	0.599610i	$0.795322\pi$
$588$	−58.5506	−2.41458
$589$	−9.81603	−0.404462
$590$	−56.9924	−2.34634
$591$	−63.6355	−2.61762
$592$	37.9351	1.55912
$593$	−40.0911	−1.64634	−0.823172	−	0.567793i	$-0.807797\pi$
$593$	−40.0911	−1.64634	−0.823172	+	0.567793i	$0.807797\pi$
$594$	−25.1939	−1.03372
$595$	92.7903	3.80403
$596$	12.8802	0.527596
$597$	−29.9836	−1.22715
$598$	30.5113	1.24770
$599$	−4.97056	−0.203092	−0.101546	−	0.994831i	$-0.532379\pi$
$599$	−4.97056	−0.203092	−0.101546	+	0.994831i	$0.532379\pi$
$600$	6.51390	0.265929
$601$	−37.1442	−1.51514	−0.757572	−	0.652751i	$-0.773615\pi$
$601$	−37.1442	−1.51514	−0.757572	+	0.652751i	$0.773615\pi$
$602$	−74.0938	−3.01984
$603$	53.9732	2.19796
$604$	−24.2134	−0.985227
$605$	27.9939	1.13811
$606$	−105.866	−4.30052
$607$	20.5789	0.835272	0.417636	−	0.908614i	$-0.362859\pi$
$607$	20.5789	0.835272	0.417636	+	0.908614i	$0.362859\pi$
$608$	−7.29738	−0.295948
$609$	−10.9425	−0.443413
$610$	5.10979	0.206889
$611$	24.5099	0.991565
$612$	91.7318	3.70804
$613$	−13.6981	−0.553261	−0.276631	−	0.960976i	$-0.589218\pi$
$613$	−13.6981	−0.553261	−0.276631	+	0.960976i	$0.589218\pi$
$614$	−8.39094	−0.338631
$615$	69.8675	2.81733
$616$	3.07149	0.123754
$617$	−22.8864	−0.921372	−0.460686	−	0.887563i	$-0.652397\pi$
$617$	−22.8864	−0.921372	−0.460686	+	0.887563i	$0.652397\pi$
$618$	49.1900	1.97871
$619$	−24.0572	−0.966940	−0.483470	−	0.875361i	$-0.660624\pi$
$619$	−24.0572	−0.966940	−0.483470	+	0.875361i	$0.660624\pi$
$620$	43.7059	1.75527
$621$	−61.2994	−2.45986
$622$	−7.66776	−0.307449
$623$	22.3110	0.893870
$624$	54.2560	2.17198
$625$	−31.2099	−1.24840
$626$	−17.6861	−0.706880
$627$	−3.06824	−0.122534
$628$	16.6004	0.662427
$629$	−63.8850	−2.54726
$630$	165.337	6.58718
$631$	−17.1811	−0.683968	−0.341984	−	0.939706i	$-0.611099\pi$
$631$	−17.1811	−0.683968	−0.341984	+	0.939706i	$0.611099\pi$
$632$	2.71891	0.108152
$633$	−3.21324	−0.127715
$634$	54.8530	2.17849
$635$	31.8079	1.26226
$636$	43.8798	1.73995
$637$	41.3745	1.63932
$638$	−1.44097	−0.0570485
$639$	−102.599	−4.05874
$640$	−16.3409	−0.645932
$641$	−29.9184	−1.18171	−0.590854	−	0.806779i	$-0.701209\pi$
$641$	−29.9184	−1.18171	−0.590854	+	0.806779i	$0.701209\pi$
$642$	107.871	4.25733
$643$	17.3218	0.683107	0.341553	−	0.939862i	$-0.389047\pi$
$643$	17.3218	0.683107	0.341553	+	0.939862i	$0.389047\pi$
$644$	−30.3235	−1.19491
$645$	81.2190	3.19800
$646$	14.8179	0.583004
$647$	14.1024	0.554422	0.277211	−	0.960809i	$-0.410590\pi$
$647$	14.1024	0.554422	0.277211	+	0.960809i	$0.410590\pi$
$648$	−17.0275	−0.668902
$649$	10.3297	0.405476
$650$	18.6773	0.732583
$651$	−135.136	−5.29639
$652$	−2.47560	−0.0969518
$653$	−6.35213	−0.248578	−0.124289	−	0.992246i	$-0.539665\pi$
$653$	−6.35213	−0.248578	−0.124289	+	0.992246i	$0.539665\pi$
$654$	−16.8170	−0.657596
$655$	0.593436	0.0231875
$656$	−36.3150	−1.41786
$657$	−15.7746	−0.615427
$658$	−54.7215	−2.13327
$659$	50.6288	1.97222	0.986110	−	0.166096i	$-0.0531162\pi$
$659$	50.6288	1.97222	0.986110	+	0.166096i	$0.0531162\pi$
$660$	13.6614	0.531768
$661$	26.0890	1.01475	0.507373	−	0.861727i	$-0.330617\pi$
$661$	26.0890	1.01475	0.507373	+	0.861727i	$0.330617\pi$
$662$	−46.5287	−1.80839
$663$	−91.3704	−3.54853
$664$	−0.629319	−0.0244223
$665$	11.8889	0.461031
$666$	−113.833	−4.41092
$667$	−3.50603	−0.135754
$668$	−9.84017	−0.380728
$669$	20.8037	0.804316
$670$	−38.8195	−1.49973
$671$	−0.926134	−0.0357530
$672$	−100.462	−3.87540
$673$	−25.5268	−0.983984	−0.491992	−	0.870600i	$-0.663731\pi$
$673$	−25.5268	−0.983984	−0.491992	+	0.870600i	$0.663731\pi$
$674$	−46.7739	−1.80166
$675$	−37.5240	−1.44430
$676$	0.439609	0.0169080
$677$	42.8328	1.64620	0.823099	−	0.567898i	$-0.192243\pi$
$677$	42.8328	1.64620	0.823099	+	0.567898i	$0.192243\pi$
$678$	−36.8692	−1.41595
$679$	55.0454	2.11245
$680$	16.2601	0.623545
$681$	−7.49036	−0.287031
$682$	−17.7954	−0.681421
$683$	27.2762	1.04370	0.521848	−	0.853039i	$-0.325243\pi$
$683$	27.2762	1.04370	0.521848	+	0.853039i	$0.325243\pi$
$684$	11.7533	0.449397
$685$	0.791140	0.0302279
$686$	−35.4343	−1.35289
$687$	68.9300	2.62984
$688$	−42.2152	−1.60944
$689$	−31.0075	−1.18129
$690$	74.6711	2.84268
$691$	11.9198	0.453452	0.226726	−	0.973959i	$-0.427198\pi$
$691$	11.9198	0.453452	0.226726	+	0.973959i	$0.427198\pi$
$692$	19.3685	0.736280
$693$	−29.9668	−1.13835
$694$	−54.1088	−2.05394
$695$	22.3603	0.848175
$696$	−1.91751	−0.0726829
$697$	61.1567	2.31648
$698$	−23.6978	−0.896975
$699$	−37.4832	−1.41775
$700$	−18.5624	−0.701591
$701$	−41.2532	−1.55811	−0.779056	−	0.626955i	$-0.784301\pi$
$701$	−41.2532	−1.55811	−0.779056	+	0.626955i	$0.784301\pi$
$702$	−96.1278	−3.62811
$703$	−8.18535	−0.308716
$704$	−4.37861	−0.165025
$705$	59.9838	2.25912
$706$	−35.6981	−1.34352
$707$	−74.3498	−2.79621
$708$	−55.7751	−2.09616
$709$	38.9582	1.46311	0.731553	−	0.681785i	$-0.238796\pi$
$709$	38.9582	1.46311	0.731553	+	0.681785i	$0.238796\pi$
$710$	73.7927	2.76939
$711$	−26.5269	−0.994837
$712$	3.90965	0.146520
$713$	−43.2982	−1.62153
$714$	203.996	7.63437
$715$	−9.65375	−0.361030
$716$	−16.6173	−0.621019
$717$	70.7406	2.64186
$718$	−62.3099	−2.32539
$719$	25.8309	0.963331	0.481666	−	0.876355i	$-0.340032\pi$
$719$	25.8309	0.963331	0.481666	+	0.876355i	$0.340032\pi$
$720$	94.2013	3.51068
$721$	34.5461	1.28656
$722$	1.89857	0.0706573
$723$	−67.6306	−2.51521
$724$	0.743003	0.0276135
$725$	−2.14619	−0.0797077
$726$	61.5437	2.28410
$727$	−27.8645	−1.03344	−0.516719	−	0.856155i	$-0.672847\pi$
$727$	−27.8645	−1.03344	−0.516719	+	0.856155i	$0.672847\pi$
$728$	11.7193	0.434347
$729$	32.1642	1.19127
$730$	11.3457	0.419923
$731$	71.0929	2.62947
$732$	5.00065	0.184829
$733$	−20.4501	−0.755342	−0.377671	−	0.925940i	$-0.623275\pi$
$733$	−20.4501	−0.755342	−0.377671	+	0.925940i	$0.623275\pi$
$734$	20.6500	0.762206
$735$	101.257	3.73493
$736$	−32.1885	−1.18648
$737$	7.03592	0.259172
$738$	108.971	4.01129
$739$	30.4128	1.11875	0.559376	−	0.828914i	$-0.311041\pi$
$739$	30.4128	1.11875	0.559376	+	0.828914i	$0.311041\pi$
$740$	36.4453	1.33976
$741$	−11.7070	−0.430066
$742$	69.2283	2.54145
$743$	−13.4929	−0.495008	−0.247504	−	0.968887i	$-0.579610\pi$
$743$	−13.4929	−0.495008	−0.247504	+	0.968887i	$0.579610\pi$
$744$	−23.6805	−0.868168
$745$	−22.2751	−0.816095
$746$	−36.2882	−1.32861
$747$	6.13993	0.224648
$748$	11.9581	0.437232
$749$	75.7577	2.76813
$750$	−38.9331	−1.42164
$751$	48.8244	1.78163	0.890813	−	0.454370i	$-0.150135\pi$
$751$	48.8244	1.78163	0.890813	+	0.454370i	$0.150135\pi$
$752$	−31.1778	−1.13694
$753$	−45.7454	−1.66706
$754$	−5.49805	−0.200227
$755$	41.8745	1.52397
$756$	95.5364	3.47462
$757$	11.8426	0.430425	0.215213	−	0.976567i	$-0.430956\pi$
$757$	11.8426	0.430425	0.215213	+	0.976567i	$0.430956\pi$
$758$	2.06694	0.0750747
$759$	−13.5339	−0.491250
$760$	2.08334	0.0755707
$761$	3.55660	0.128927	0.0644634	−	0.997920i	$-0.479466\pi$
$761$	3.55660	0.128927	0.0644634	+	0.997920i	$0.479466\pi$
$762$	69.9286	2.53325
$763$	−11.8105	−0.427570
$764$	−14.3263	−0.518307
$765$	−158.641	−5.73567
$766$	2.42384	0.0875768
$767$	39.4132	1.42313
$768$	−65.3939	−2.35970
$769$	−16.1485	−0.582329	−0.291164	−	0.956673i	$-0.594043\pi$
$769$	−16.1485	−0.582329	−0.291164	+	0.956673i	$0.594043\pi$
$770$	21.5533	0.776725
$771$	−26.8170	−0.965791
$772$	1.17819	0.0424042
$773$	−47.2994	−1.70124	−0.850620	−	0.525781i	$-0.823773\pi$
$773$	−47.2994	−1.70124	−0.850620	+	0.525781i	$0.823773\pi$
$774$	126.676	4.55327
$775$	−26.5047	−0.952076
$776$	9.64586	0.346266
$777$	−112.687	−4.04261
$778$	−33.7924	−1.21152
$779$	7.83578	0.280746
$780$	52.1253	1.86638
$781$	−13.3747	−0.478585
$782$	65.3614	2.33732
$783$	11.0460	0.394752
$784$	−52.6304	−1.87966
$785$	−28.7086	−1.02466
$786$	1.30465	0.0465353
$787$	−37.8312	−1.34854	−0.674269	−	0.738486i	$-0.735541\pi$
$787$	−37.8312	−1.34854	−0.674269	+	0.738486i	$0.735541\pi$
$788$	31.7769	1.13200
$789$	−59.4141	−2.11520
$790$	19.0791	0.678805
$791$	−25.8932	−0.920656
$792$	−5.25123	−0.186594
$793$	−3.53369	−0.125485
$794$	17.0437	0.604859
$795$	−75.8856	−2.69139
$796$	14.9725	0.530687
$797$	−18.6399	−0.660258	−0.330129	−	0.943936i	$-0.607092\pi$
$797$	−18.6399	−0.660258	−0.330129	+	0.943936i	$0.607092\pi$
$798$	26.1373	0.925250
$799$	52.5053	1.85750
$800$	−19.7040	−0.696640
$801$	−38.1444	−1.34777
$802$	62.2210	2.19710
$803$	−2.05638	−0.0725679
$804$	−37.9903	−1.33982
$805$	52.4414	1.84832
$806$	−67.8988	−2.39163
$807$	38.5795	1.35806
$808$	−13.0286	−0.458346
$809$	7.25119	0.254938	0.127469	−	0.991843i	$-0.459315\pi$
$809$	7.25119	0.254938	0.127469	+	0.991843i	$0.459315\pi$
$810$	−119.485	−4.19829
$811$	21.6465	0.760112	0.380056	−	0.924963i	$-0.375905\pi$
$811$	21.6465	0.760112	0.380056	+	0.924963i	$0.375905\pi$
$812$	5.46422	0.191757
$813$	65.9583	2.31326
$814$	−14.8392	−0.520112
$815$	4.28129	0.149967
$816$	116.228	4.06878
$817$	9.10887	0.318679
$818$	−59.0083	−2.06318
$819$	−114.339	−3.99534
$820$	−34.8889	−1.21837
$821$	−29.4821	−1.02893	−0.514467	−	0.857510i	$-0.672010\pi$
$821$	−29.4821	−1.02893	−0.514467	+	0.857510i	$0.672010\pi$
$822$	1.73930	0.0606649
$823$	−28.4590	−0.992017	−0.496008	−	0.868318i	$-0.665201\pi$
$823$	−28.4590	−0.992017	−0.496008	+	0.868318i	$0.665201\pi$
$824$	6.05366	0.210889
$825$	−8.28470	−0.288436
$826$	−87.9952	−3.06174
$827$	34.6981	1.20657	0.603285	−	0.797525i	$-0.293858\pi$
$827$	34.6981	1.20657	0.603285	+	0.797525i	$0.293858\pi$
$828$	51.8432	1.80168
$829$	17.6476	0.612925	0.306462	−	0.951883i	$-0.400855\pi$
$829$	17.6476	0.612925	0.306462	+	0.951883i	$0.400855\pi$
$830$	−4.41606	−0.153284
$831$	−5.33393	−0.185032
$832$	−16.7067	−0.579200
$833$	88.6328	3.07094
$834$	49.1584	1.70222
$835$	17.0176	0.588917
$836$	1.53215	0.0529905
$837$	136.414	4.71515
$838$	−57.9957	−2.00343
$839$	−33.7256	−1.16434	−0.582169	−	0.813068i	$-0.697796\pi$
$839$	−33.7256	−1.16434	−0.582169	+	0.813068i	$0.697796\pi$
$840$	28.6811	0.989590
$841$	−28.3682	−0.978215
$842$	−54.5093	−1.87851
$843$	66.8664	2.30300
$844$	1.60456	0.0552311
$845$	−0.760258	−0.0261537
$846$	93.5557	3.21651
$847$	43.2221	1.48513
$848$	39.4431	1.35448
$849$	−57.6884	−1.97986
$850$	40.0105	1.37235
$851$	−36.1053	−1.23767
$852$	72.2165	2.47410
$853$	5.59832	0.191683	0.0958414	−	0.995397i	$-0.469446\pi$
$853$	5.59832	0.191683	0.0958414	+	0.995397i	$0.469446\pi$
$854$	7.88942	0.269970
$855$	−20.3260	−0.695136
$856$	13.2754	0.453742
$857$	42.7121	1.45902	0.729509	−	0.683971i	$-0.239749\pi$
$857$	42.7121	1.45902	0.729509	+	0.683971i	$0.239749\pi$
$858$	−21.2235	−0.724557
$859$	10.8147	0.368993	0.184497	−	0.982833i	$-0.440935\pi$
$859$	10.8147	0.368993	0.184497	+	0.982833i	$0.440935\pi$
$860$	−40.5573	−1.38299
$861$	107.874	3.67634
$862$	−24.6609	−0.839953
$863$	−37.3321	−1.27080	−0.635399	−	0.772184i	$-0.719164\pi$
$863$	−37.3321	−1.27080	−0.635399	+	0.772184i	$0.719164\pi$
$864$	101.412	3.45011
$865$	−33.4958	−1.13889
$866$	7.71851	0.262286
$867$	−141.109	−4.79232
$868$	67.4811	2.29046
$869$	−3.45804	−0.117306
$870$	−13.4555	−0.456185
$871$	26.8457	0.909633
$872$	−2.06961	−0.0700859
$873$	−94.1095	−3.18512
$874$	8.37451	0.283272
$875$	−27.3427	−0.924352
$876$	11.1034	0.375148
$877$	−19.9874	−0.674928	−0.337464	−	0.941338i	$-0.609569\pi$
$877$	−19.9874	−0.674928	−0.337464	+	0.941338i	$0.609569\pi$
$878$	5.71862	0.192994
$879$	23.1781	0.781778
$880$	12.2800	0.413960
$881$	−32.3424	−1.08964	−0.544821	−	0.838552i	$-0.683402\pi$
$881$	−32.3424	−1.08964	−0.544821	+	0.838552i	$0.683402\pi$
$882$	157.929	5.31775
$883$	15.6159	0.525518	0.262759	−	0.964862i	$-0.415368\pi$
$883$	15.6159	0.525518	0.262759	+	0.964862i	$0.415368\pi$
$884$	45.6265	1.53458
$885$	96.4572	3.24237
$886$	−17.0439	−0.572601
$887$	−10.1898	−0.342142	−0.171071	−	0.985259i	$-0.554723\pi$
$887$	−10.1898	−0.342142	−0.171071	+	0.985259i	$0.554723\pi$
$888$	−19.7466	−0.662652
$889$	49.1108	1.64712
$890$	27.4348	0.919618
$891$	21.6564	0.725516
$892$	−10.3885	−0.347831
$893$	6.72730	0.225121
$894$	−48.9710	−1.63783
$895$	28.7379	0.960604
$896$	−25.2301	−0.842878
$897$	−51.6390	−1.72418
$898$	29.8855	0.997291
$899$	7.80222	0.260218
$900$	31.7355	1.05785
$901$	−66.4245	−2.21292
$902$	14.2054	0.472989
$903$	125.401	4.17307
$904$	−4.53738	−0.150911
$905$	−1.28495	−0.0427131
$906$	92.0597	3.05848
$907$	35.4074	1.17568	0.587842	−	0.808976i	$-0.299978\pi$
$907$	35.4074	1.17568	0.587842	+	0.808976i	$0.299978\pi$
$908$	3.74036	0.124128
$909$	127.114	4.21609
$910$	82.2370	2.72613
$911$	−21.4593	−0.710978	−0.355489	−	0.934680i	$-0.615686\pi$
$911$	−21.4593	−0.710978	−0.355489	+	0.934680i	$0.615686\pi$
$912$	14.8918	0.493117
$913$	0.800398	0.0264893
$914$	20.7580	0.686613
$915$	−8.64810	−0.285897
$916$	−34.4207	−1.13729
$917$	0.916254	0.0302574
$918$	−205.926	−6.79656
$919$	−31.7282	−1.04662	−0.523308	−	0.852144i	$-0.675302\pi$
$919$	−31.7282	−1.04662	−0.523308	+	0.852144i	$0.675302\pi$
$920$	9.18955	0.302970
$921$	14.2013	0.467949
$922$	−4.39306	−0.144678
$923$	−51.0315	−1.67972
$924$	21.0929	0.693905
$925$	−22.1016	−0.726697
$926$	22.3775	0.735370
$927$	−59.0624	−1.93986
$928$	5.80028	0.190404
$929$	−14.8728	−0.487962	−0.243981	−	0.969780i	$-0.578453\pi$
$929$	−14.8728	−0.487962	−0.243981	+	0.969780i	$0.578453\pi$
$930$	−166.171	−5.44895
$931$	11.3562	0.372184
$932$	18.7175	0.613113
$933$	12.9773	0.424859
$934$	33.8172	1.10653
$935$	−20.6803	−0.676319
$936$	−20.0362	−0.654903
$937$	15.7348	0.514034	0.257017	−	0.966407i	$-0.417260\pi$
$937$	15.7348	0.514034	0.257017	+	0.966407i	$0.417260\pi$
$938$	−59.9366	−1.95700
$939$	29.9330	0.976827
$940$	−29.9533	−0.976971
$941$	9.25314	0.301644	0.150822	−	0.988561i	$-0.451808\pi$
$941$	9.25314	0.301644	0.150822	+	0.988561i	$0.451808\pi$
$942$	−63.1150	−2.05640
$943$	34.5634	1.12554
$944$	−50.1355	−1.63177
$945$	−165.220	−5.37462
$946$	16.5134	0.536897
$947$	18.8210	0.611600	0.305800	−	0.952096i	$-0.401076\pi$
$947$	18.8210	0.611600	0.305800	+	0.952096i	$0.401076\pi$
$948$	18.6716	0.606426
$949$	−7.84615	−0.254697
$950$	5.12640	0.166322
$951$	−92.8364	−3.01043
$952$	25.1052	0.813665
$953$	5.36898	0.173918	0.0869591	−	0.996212i	$-0.472285\pi$
$953$	5.36898	0.173918	0.0869591	+	0.996212i	$0.472285\pi$
$954$	−118.358	−3.83197
$955$	24.7758	0.801727
$956$	−35.3248	−1.14249
$957$	2.43878	0.0788344
$958$	−49.8669	−1.61113
$959$	1.22150	0.0394444
$960$	−40.8868	−1.31962
$961$	65.3544	2.10821
$962$	−56.6192	−1.82548
$963$	−129.521	−4.17374
$964$	33.7718	1.08772
$965$	−2.03757	−0.0655916
$966$	115.291	3.70942
$967$	−28.3671	−0.912226	−0.456113	−	0.889922i	$-0.650759\pi$
$967$	−28.3671	−0.912226	−0.456113	+	0.889922i	$0.650759\pi$
$968$	7.57400	0.243438
$969$	−25.0787	−0.805644
$970$	67.6870	2.17330
$971$	46.4365	1.49022	0.745108	−	0.666943i	$-0.232398\pi$
$971$	46.4365	1.49022	0.745108	+	0.666943i	$0.232398\pi$
$972$	−50.0374	−1.60495
$973$	34.5239	1.10678
$974$	−0.679994	−0.0217884
$975$	−31.6105	−1.01235
$976$	4.49502	0.143882
$977$	8.03364	0.257019	0.128509	−	0.991708i	$-0.458981\pi$
$977$	8.03364	0.257019	0.128509	+	0.991708i	$0.458981\pi$
$978$	9.41227	0.300971
$979$	−4.97248	−0.158921
$980$	−50.5635	−1.61519
$981$	20.1921	0.644685
$982$	26.4560	0.844246
$983$	−20.8143	−0.663874	−0.331937	−	0.943302i	$-0.607702\pi$
$983$	−20.8143	−0.663874	−0.331937	+	0.943302i	$0.607702\pi$
$984$	18.9033	0.602614
$985$	−54.9548	−1.75101
$986$	−11.7780	−0.375086
$987$	92.6138	2.94793
$988$	5.84595	0.185985
$989$	40.1789	1.27762
$990$	−36.8489	−1.17114
$991$	54.1521	1.72020	0.860099	−	0.510127i	$-0.170402\pi$
$991$	54.1521	1.72020	0.860099	+	0.510127i	$0.170402\pi$
$992$	71.6313	2.27429
$993$	78.7479	2.49899
$994$	113.934	3.61378
$995$	−25.8934	−0.820876
$996$	−4.32174	−0.136939
$997$	29.3911	0.930826	0.465413	−	0.885094i	$-0.345906\pi$
$997$	29.3911	0.930826	0.465413	+	0.885094i	$0.345906\pi$
$998$	−16.9883	−0.537755
$999$	113.752	3.59896

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.60	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.60	✓	71	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q+1.89857 q^{2} -3.21324 q^{3} +1.60456 q^{4} -2.77491 q^{5} -6.10056 q^{6} -4.28441 q^{7} -0.750777 q^{8} +7.32493 q^{9} +O(q^{10})\)	\(q+1.89857 q^{2} -3.21324 q^{3} +1.60456 q^{4} -2.77491 q^{5} -6.10056 q^{6} -4.28441 q^{7} -0.750777 q^{8} +7.32493 q^{9} -5.26836 q^{10} +0.954874 q^{11} -5.15583 q^{12} +3.64335 q^{13} -8.13424 q^{14} +8.91647 q^{15} -4.63451 q^{16} +7.80480 q^{17} +13.9069 q^{18} +1.00000 q^{19} -4.45250 q^{20} +13.7669 q^{21} +1.81289 q^{22} +4.41097 q^{23} +2.41243 q^{24} +2.70014 q^{25} +6.91714 q^{26} -13.8971 q^{27} -6.87458 q^{28} -0.794844 q^{29} +16.9285 q^{30} -9.81603 q^{31} -7.29738 q^{32} -3.06824 q^{33} +14.8179 q^{34} +11.8889 q^{35} +11.7533 q^{36} -8.18535 q^{37} +1.89857 q^{38} -11.7070 q^{39} +2.08334 q^{40} +7.83578 q^{41} +26.1373 q^{42} +9.10887 q^{43} +1.53215 q^{44} -20.3260 q^{45} +8.37451 q^{46} +6.72730 q^{47} +14.8918 q^{48} +11.3562 q^{49} +5.12640 q^{50} -25.0787 q^{51} +5.84595 q^{52} -8.51073 q^{53} -26.3845 q^{54} -2.64969 q^{55} +3.21664 q^{56} -3.21324 q^{57} -1.50907 q^{58} +10.8179 q^{59} +14.3070 q^{60} -0.969902 q^{61} -18.6364 q^{62} -31.3830 q^{63} -4.58553 q^{64} -10.1100 q^{65} -5.82527 q^{66} +7.36843 q^{67} +12.5232 q^{68} -14.1735 q^{69} +22.5718 q^{70} -14.0068 q^{71} -5.49939 q^{72} -2.15356 q^{73} -15.5404 q^{74} -8.67622 q^{75} +1.60456 q^{76} -4.09108 q^{77} -22.2264 q^{78} -3.62146 q^{79} +12.8604 q^{80} +22.6798 q^{81} +14.8768 q^{82} +0.838223 q^{83} +22.0897 q^{84} -21.6576 q^{85} +17.2938 q^{86} +2.55403 q^{87} -0.716898 q^{88} -5.20747 q^{89} -38.5904 q^{90} -15.6096 q^{91} +7.07764 q^{92} +31.5413 q^{93} +12.7722 q^{94} -2.77491 q^{95} +23.4482 q^{96} -12.8478 q^{97} +21.5605 q^{98} +6.99439 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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