LMFDB - Embedded newform 6009.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$93$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07852 q^{2} -1.00000 q^{3} +2.32023 q^{4} -3.95771 q^{5} +2.07852 q^{6} -1.61443 q^{7} -0.665606 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.07852 q^{2} -1.00000 q^{3} +2.32023 q^{4} -3.95771 q^{5} +2.07852 q^{6} -1.61443 q^{7} -0.665606 q^{8} +1.00000 q^{9} +8.22618 q^{10} -5.23644 q^{11} -2.32023 q^{12} -0.606678 q^{13} +3.35562 q^{14} +3.95771 q^{15} -3.25699 q^{16} +7.06955 q^{17} -2.07852 q^{18} +4.24143 q^{19} -9.18281 q^{20} +1.61443 q^{21} +10.8840 q^{22} +0.409976 q^{23} +0.665606 q^{24} +10.6635 q^{25} +1.26099 q^{26} -1.00000 q^{27} -3.74586 q^{28} +8.50454 q^{29} -8.22618 q^{30} -1.37977 q^{31} +8.10092 q^{32} +5.23644 q^{33} -14.6942 q^{34} +6.38946 q^{35} +2.32023 q^{36} +5.87194 q^{37} -8.81588 q^{38} +0.606678 q^{39} +2.63428 q^{40} -9.02698 q^{41} -3.35562 q^{42} +6.80514 q^{43} -12.1498 q^{44} -3.95771 q^{45} -0.852142 q^{46} -8.94123 q^{47} +3.25699 q^{48} -4.39361 q^{49} -22.1643 q^{50} -7.06955 q^{51} -1.40763 q^{52} -10.8219 q^{53} +2.07852 q^{54} +20.7243 q^{55} +1.07458 q^{56} -4.24143 q^{57} -17.6768 q^{58} -9.61595 q^{59} +9.18281 q^{60} +6.86242 q^{61} +2.86787 q^{62} -1.61443 q^{63} -10.3239 q^{64} +2.40106 q^{65} -10.8840 q^{66} -5.20661 q^{67} +16.4030 q^{68} -0.409976 q^{69} -13.2806 q^{70} +5.12850 q^{71} -0.665606 q^{72} -5.90954 q^{73} -12.2049 q^{74} -10.6635 q^{75} +9.84109 q^{76} +8.45388 q^{77} -1.26099 q^{78} +0.707207 q^{79} +12.8902 q^{80} +1.00000 q^{81} +18.7627 q^{82} +3.48993 q^{83} +3.74586 q^{84} -27.9793 q^{85} -14.1446 q^{86} -8.50454 q^{87} +3.48541 q^{88} -13.6988 q^{89} +8.22618 q^{90} +0.979441 q^{91} +0.951240 q^{92} +1.37977 q^{93} +18.5845 q^{94} -16.7864 q^{95} -8.10092 q^{96} -3.78073 q^{97} +9.13219 q^{98} -5.23644 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) $ 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * 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 $

$2$	−2.07852	−1.46973	−0.734867	−	0.678212i	$-0.762755\pi$
$2$	−2.07852	−1.46973	−0.734867	+	0.678212i	$0.762755\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.32023	1.16012
$5$	−3.95771	−1.76994	−0.884972	−	0.465645i	$-0.845823\pi$
$5$	−3.95771	−1.76994	−0.884972	+	0.465645i	$0.845823\pi$
$6$	2.07852	0.848551
$7$	−1.61443	−0.610198	−0.305099	−	0.952321i	$-0.598690\pi$
$7$	−1.61443	−0.610198	−0.305099	+	0.952321i	$0.598690\pi$
$8$	−0.665606	−0.235327
$9$	1.00000	0.333333
$10$	8.22618	2.60134
$11$	−5.23644	−1.57885	−0.789424	−	0.613849i	$-0.789620\pi$
$11$	−5.23644	−1.57885	−0.789424	+	0.613849i	$0.789620\pi$
$12$	−2.32023	−0.669793
$13$	−0.606678	−0.168262	−0.0841312	−	0.996455i	$-0.526811\pi$
$13$	−0.606678	−0.168262	−0.0841312	+	0.996455i	$0.526811\pi$
$14$	3.35562	0.896828
$15$	3.95771	1.02188
$16$	−3.25699	−0.814247
$17$	7.06955	1.71462	0.857309	−	0.514801i	$-0.172134\pi$
$17$	7.06955	1.71462	0.857309	+	0.514801i	$0.172134\pi$
$18$	−2.07852	−0.489911
$19$	4.24143	0.973050	0.486525	−	0.873667i	$-0.338264\pi$
$19$	4.24143	0.973050	0.486525	+	0.873667i	$0.338264\pi$
$20$	−9.18281	−2.05334
$21$	1.61443	0.352298
$22$	10.8840	2.32048
$23$	0.409976	0.0854860	0.0427430	−	0.999086i	$-0.486390\pi$
$23$	0.409976	0.0854860	0.0427430	+	0.999086i	$0.486390\pi$
$24$	0.665606	0.135866
$25$	10.6635	2.13270
$26$	1.26099	0.247301
$27$	−1.00000	−0.192450
$28$	−3.74586	−0.707900
$29$	8.50454	1.57925	0.789627	−	0.613587i	$-0.210274\pi$
$29$	8.50454	1.57925	0.789627	+	0.613587i	$0.210274\pi$
$30$	−8.22618	−1.50189
$31$	−1.37977	−0.247814	−0.123907	−	0.992294i	$-0.539542\pi$
$31$	−1.37977	−0.247814	−0.123907	+	0.992294i	$0.539542\pi$
$32$	8.10092	1.43205
$33$	5.23644	0.911548
$34$	−14.6942	−2.52003
$35$	6.38946	1.08002
$36$	2.32023	0.386705
$37$	5.87194	0.965341	0.482670	−	0.875802i	$-0.339667\pi$
$37$	5.87194	0.965341	0.482670	+	0.875802i	$0.339667\pi$
$38$	−8.81588	−1.43012
$39$	0.606678	0.0971463
$40$	2.63428	0.416516
$41$	−9.02698	−1.40978	−0.704889	−	0.709318i	$-0.749003\pi$
$41$	−9.02698	−1.40978	−0.704889	+	0.709318i	$0.749003\pi$
$42$	−3.35562	−0.517784
$43$	6.80514	1.03777	0.518887	−	0.854843i	$-0.326346\pi$
$43$	6.80514	1.03777	0.518887	+	0.854843i	$0.326346\pi$
$44$	−12.1498	−1.83165
$45$	−3.95771	−0.589981
$46$	−0.852142	−0.125642
$47$	−8.94123	−1.30421	−0.652107	−	0.758127i	$-0.726115\pi$
$47$	−8.94123	−1.30421	−0.652107	+	0.758127i	$0.726115\pi$
$48$	3.25699	0.470106
$49$	−4.39361	−0.627658
$50$	−22.1643	−3.13450
$51$	−7.06955	−0.989936
$52$	−1.40763	−0.195204
$53$	−10.8219	−1.48650	−0.743252	−	0.669012i	$-0.766718\pi$
$53$	−10.8219	−1.48650	−0.743252	+	0.669012i	$0.766718\pi$
$54$	2.07852	0.282850
$55$	20.7243	2.79447
$56$	1.07458	0.143596
$57$	−4.24143	−0.561791
$58$	−17.6768	−2.32108
$59$	−9.61595	−1.25189	−0.625945	−	0.779867i	$-0.715287\pi$
$59$	−9.61595	−1.25189	−0.625945	+	0.779867i	$0.715287\pi$
$60$	9.18281	1.18550
$61$	6.86242	0.878643	0.439322	−	0.898330i	$-0.355219\pi$
$61$	6.86242	0.878643	0.439322	+	0.898330i	$0.355219\pi$
$62$	2.86787	0.364220
$63$	−1.61443	−0.203399
$64$	−10.3239	−1.29049
$65$	2.40106	0.297815
$66$	−10.8840	−1.33973
$67$	−5.20661	−0.636088	−0.318044	−	0.948076i	$-0.603026\pi$
$67$	−5.20661	−0.636088	−0.318044	+	0.948076i	$0.603026\pi$
$68$	16.4030	1.98916
$69$	−0.409976	−0.0493553
$70$	−13.2806	−1.58734
$71$	5.12850	0.608641	0.304321	−	0.952570i	$-0.401571\pi$
$71$	5.12850	0.608641	0.304321	+	0.952570i	$0.401571\pi$
$72$	−0.665606	−0.0784424
$73$	−5.90954	−0.691659	−0.345830	−	0.938297i	$-0.612402\pi$
$73$	−5.90954	−0.691659	−0.345830	+	0.938297i	$0.612402\pi$
$74$	−12.2049	−1.41879
$75$	−10.6635	−1.23132
$76$	9.84109	1.12885
$77$	8.45388	0.963409
$78$	−1.26099	−0.142779
$79$	0.707207	0.0795670	0.0397835	−	0.999208i	$-0.487333\pi$
$79$	0.707207	0.0795670	0.0397835	+	0.999208i	$0.487333\pi$
$80$	12.8902	1.44117
$81$	1.00000	0.111111
$82$	18.7627	2.07200
$83$	3.48993	0.383069	0.191535	−	0.981486i	$-0.438654\pi$
$83$	3.48993	0.383069	0.191535	+	0.981486i	$0.438654\pi$
$84$	3.74586	0.408706
$85$	−27.9793	−3.03478
$86$	−14.1446	−1.52525
$87$	−8.50454	−0.911783
$88$	3.48541	0.371546
$89$	−13.6988	−1.45207	−0.726035	−	0.687658i	$-0.758639\pi$
$89$	−13.6988	−1.45207	−0.726035	+	0.687658i	$0.758639\pi$
$90$	8.22618	0.867115
$91$	0.979441	0.102673
$92$	0.951240	0.0991736
$93$	1.37977	0.143075
$94$	18.5845	1.91685
$95$	−16.7864	−1.72224
$96$	−8.10092	−0.826797
$97$	−3.78073	−0.383875	−0.191937	−	0.981407i	$-0.561477\pi$
$97$	−3.78073	−0.383875	−0.191937	+	0.981407i	$0.561477\pi$
$98$	9.13219	0.922490
$99$	−5.23644	−0.526282
$100$	24.7418	2.47418
$101$	−8.97546	−0.893092	−0.446546	−	0.894761i	$-0.647346\pi$
$101$	−8.97546	−0.893092	−0.446546	+	0.894761i	$0.647346\pi$
$102$	14.6942	1.45494
$103$	7.09213	0.698809	0.349404	−	0.936972i	$-0.386384\pi$
$103$	7.09213	0.698809	0.349404	+	0.936972i	$0.386384\pi$
$104$	0.403809	0.0395967
$105$	−6.38946	−0.623548
$106$	22.4935	2.18476
$107$	−9.33865	−0.902801	−0.451401	−	0.892321i	$-0.649075\pi$
$107$	−9.33865	−0.902801	−0.451401	+	0.892321i	$0.649075\pi$
$108$	−2.32023	−0.223264
$109$	11.3433	1.08649	0.543244	−	0.839575i	$-0.317196\pi$
$109$	11.3433	1.08649	0.543244	+	0.839575i	$0.317196\pi$
$110$	−43.0759	−4.10713
$111$	−5.87194	−0.557340
$112$	5.25819	0.496852
$113$	11.6890	1.09961	0.549806	−	0.835293i	$-0.314702\pi$
$113$	11.6890	1.09961	0.549806	+	0.835293i	$0.314702\pi$
$114$	8.81588	0.825682
$115$	−1.62257	−0.151305
$116$	19.7325	1.83212
$117$	−0.606678	−0.0560874
$118$	19.9869	1.83995
$119$	−11.4133	−1.04626
$120$	−2.63428	−0.240476
$121$	16.4203	1.49276
$122$	−14.2637	−1.29137
$123$	9.02698	0.813935
$124$	−3.20138	−0.287493
$125$	−22.4145	−2.00482
$126$	3.35562	0.298943
$127$	16.3001	1.44640	0.723201	−	0.690637i	$-0.242670\pi$
$127$	16.3001	1.44640	0.723201	+	0.690637i	$0.242670\pi$
$128$	5.25659	0.464621
$129$	−6.80514	−0.599159
$130$	−4.99064	−0.437708
$131$	8.06237	0.704412	0.352206	−	0.935922i	$-0.385432\pi$
$131$	8.06237	0.704412	0.352206	+	0.935922i	$0.385432\pi$
$132$	12.1498	1.05750
$133$	−6.84750	−0.593753
$134$	10.8220	0.934880
$135$	3.95771	0.340626
$136$	−4.70554	−0.403497
$137$	−7.65811	−0.654277	−0.327138	−	0.944976i	$-0.606084\pi$
$137$	−7.65811	−0.654277	−0.327138	+	0.944976i	$0.606084\pi$
$138$	0.852142	0.0725392
$139$	2.47135	0.209617	0.104809	−	0.994492i	$-0.466577\pi$
$139$	2.47135	0.209617	0.104809	+	0.994492i	$0.466577\pi$
$140$	14.8250	1.25294
$141$	8.94123	0.752988
$142$	−10.6597	−0.894540
$143$	3.17684	0.265660
$144$	−3.25699	−0.271416
$145$	−33.6585	−2.79519
$146$	12.2831	1.01655
$147$	4.39361	0.362379
$148$	13.6243	1.11991
$149$	−9.63637	−0.789442	−0.394721	−	0.918801i	$-0.629159\pi$
$149$	−9.63637	−0.789442	−0.394721	+	0.918801i	$0.629159\pi$
$150$	22.1643	1.80970
$151$	15.2032	1.23722	0.618608	−	0.785700i	$-0.287697\pi$
$151$	15.2032	1.23722	0.618608	+	0.785700i	$0.287697\pi$
$152$	−2.82312	−0.228985
$153$	7.06955	0.571540
$154$	−17.5715	−1.41595
$155$	5.46073	0.438616
$156$	1.40763	0.112701
$157$	−18.3519	−1.46464	−0.732319	−	0.680962i	$-0.761562\pi$
$157$	−18.3519	−1.46464	−0.732319	+	0.680962i	$0.761562\pi$
$158$	−1.46994	−0.116942
$159$	10.8219	0.858233
$160$	−32.0611	−2.53465
$161$	−0.661879	−0.0521634
$162$	−2.07852	−0.163304
$163$	15.7762	1.23569	0.617844	−	0.786301i	$-0.288006\pi$
$163$	15.7762	1.23569	0.617844	+	0.786301i	$0.288006\pi$
$164$	−20.9447	−1.63550
$165$	−20.7243	−1.61339
$166$	−7.25387	−0.563009
$167$	−2.07234	−0.160362	−0.0801811	−	0.996780i	$-0.525550\pi$
$167$	−2.07234	−0.160362	−0.0801811	+	0.996780i	$0.525550\pi$
$168$	−1.07458	−0.0829053
$169$	−12.6319	−0.971688
$170$	58.1554	4.46032
$171$	4.24143	0.324350
$172$	15.7895	1.20394
$173$	−23.8657	−1.81447	−0.907236	−	0.420622i	$-0.861812\pi$
$173$	−23.8657	−1.81447	−0.907236	+	0.420622i	$0.861812\pi$
$174$	17.6768	1.34008
$175$	−17.2155	−1.30137
$176$	17.0550	1.28557
$177$	9.61595	0.722779
$178$	28.4732	2.13416
$179$	−4.66405	−0.348608	−0.174304	−	0.984692i	$-0.555767\pi$
$179$	−4.66405	−0.348608	−0.174304	+	0.984692i	$0.555767\pi$
$180$	−9.18281	−0.684446
$181$	−16.9991	−1.26353	−0.631767	−	0.775158i	$-0.717670\pi$
$181$	−16.9991	−1.26353	−0.631767	+	0.775158i	$0.717670\pi$
$182$	−2.03578	−0.150902
$183$	−6.86242	−0.507285
$184$	−0.272883	−0.0201172
$185$	−23.2395	−1.70860
$186$	−2.86787	−0.210283
$187$	−37.0193	−2.70712
$188$	−20.7457	−1.51304
$189$	1.61443	0.117433
$190$	34.8907	2.53124
$191$	23.1811	1.67732	0.838661	−	0.544653i	$-0.183339\pi$
$191$	23.1811	1.67732	0.838661	+	0.544653i	$0.183339\pi$
$192$	10.3239	0.745064
$193$	−18.9971	−1.36744	−0.683722	−	0.729743i	$-0.739640\pi$
$193$	−18.9971	−1.36744	−0.683722	+	0.729743i	$0.739640\pi$
$194$	7.85830	0.564193
$195$	−2.40106	−0.171943
$196$	−10.1942	−0.728156
$197$	−19.9580	−1.42195	−0.710976	−	0.703216i	$-0.751747\pi$
$197$	−19.9580	−1.42195	−0.710976	+	0.703216i	$0.751747\pi$
$198$	10.8840	0.773495
$199$	−6.24081	−0.442400	−0.221200	−	0.975229i	$-0.570997\pi$
$199$	−6.24081	−0.442400	−0.221200	+	0.975229i	$0.570997\pi$
$200$	−7.09769	−0.501883
$201$	5.20661	0.367246
$202$	18.6556	1.31261
$203$	−13.7300	−0.963658
$204$	−16.4030	−1.14844
$205$	35.7262	2.49523
$206$	−14.7411	−1.02706
$207$	0.409976	0.0284953
$208$	1.97595	0.137007
$209$	−22.2100	−1.53630
$210$	13.2806	0.916449
$211$	−0.972430	−0.0669448	−0.0334724	−	0.999440i	$-0.510657\pi$
$211$	−0.972430	−0.0669448	−0.0334724	+	0.999440i	$0.510657\pi$
$212$	−25.1093	−1.72452
$213$	−5.12850	−0.351399
$214$	19.4105	1.32688
$215$	−26.9328	−1.83680
$216$	0.665606	0.0452888
$217$	2.22754	0.151215
$218$	−23.5772	−1.59685
$219$	5.90954	0.399330
$220$	48.0853	3.24191
$221$	−4.28895	−0.288506
$222$	12.2049	0.819141
$223$	18.9051	1.26598	0.632990	−	0.774160i	$-0.281827\pi$
$223$	18.9051	1.26598	0.632990	+	0.774160i	$0.281827\pi$
$224$	−13.0784	−0.873836
$225$	10.6635	0.710900
$226$	−24.2958	−1.61614
$227$	3.58578	0.237997	0.118998	−	0.992894i	$-0.462032\pi$
$227$	3.58578	0.237997	0.118998	+	0.992894i	$0.462032\pi$
$228$	−9.84109	−0.651742
$229$	3.23856	0.214010	0.107005	−	0.994258i	$-0.465874\pi$
$229$	3.23856	0.214010	0.107005	+	0.994258i	$0.465874\pi$
$230$	3.37254	0.222378
$231$	−8.45388	−0.556225
$232$	−5.66067	−0.371642
$233$	12.6678	0.829896	0.414948	−	0.909845i	$-0.363800\pi$
$233$	12.6678	0.829896	0.414948	+	0.909845i	$0.363800\pi$
$234$	1.26099	0.0824336
$235$	35.3869	2.30838
$236$	−22.3112	−1.45234
$237$	−0.707207	−0.0459380
$238$	23.7228	1.53772
$239$	−3.22333	−0.208500	−0.104250	−	0.994551i	$-0.533244\pi$
$239$	−3.22333	−0.208500	−0.104250	+	0.994551i	$0.533244\pi$
$240$	−12.8902	−0.832061
$241$	−9.05014	−0.582971	−0.291485	−	0.956575i	$-0.594149\pi$
$241$	−9.05014	−0.582971	−0.291485	+	0.956575i	$0.594149\pi$
$242$	−34.1299	−2.19396
$243$	−1.00000	−0.0641500
$244$	15.9224	1.01933
$245$	17.3886	1.11092
$246$	−18.7627	−1.19627
$247$	−2.57318	−0.163728
$248$	0.918382	0.0583173
$249$	−3.48993	−0.221165
$250$	46.5890	2.94655
$251$	4.18347	0.264058	0.132029	−	0.991246i	$-0.457851\pi$
$251$	4.18347	0.264058	0.132029	+	0.991246i	$0.457851\pi$
$252$	−3.74586	−0.235967
$253$	−2.14682	−0.134969
$254$	−33.8801	−2.12583
$255$	27.9793	1.75213
$256$	9.72192	0.607620
$257$	14.5748	0.909150	0.454575	−	0.890708i	$-0.349791\pi$
$257$	14.5748	0.909150	0.454575	+	0.890708i	$0.349791\pi$
$258$	14.1446	0.880604
$259$	−9.47985	−0.589049
$260$	5.57101	0.345500
$261$	8.50454	0.526418
$262$	−16.7578	−1.03530
$263$	12.2769	0.757029	0.378514	−	0.925595i	$-0.376435\pi$
$263$	12.2769	0.757029	0.378514	+	0.925595i	$0.376435\pi$
$264$	−3.48541	−0.214512
$265$	42.8300	2.63103
$266$	14.2326	0.872659
$267$	13.6988	0.838353
$268$	−12.0805	−0.737936
$269$	30.8631	1.88176	0.940878	−	0.338746i	$-0.110003\pi$
$269$	30.8631	1.88176	0.940878	+	0.338746i	$0.110003\pi$
$270$	−8.22618	−0.500629
$271$	−11.1713	−0.678606	−0.339303	−	0.940677i	$-0.610191\pi$
$271$	−11.1713	−0.678606	−0.339303	+	0.940677i	$0.610191\pi$
$272$	−23.0255	−1.39612
$273$	−0.979441	−0.0592785
$274$	15.9175	0.961612
$275$	−55.8388	−3.36721
$276$	−0.951240	−0.0572579
$277$	−21.8570	−1.31326	−0.656629	−	0.754213i	$-0.728018\pi$
$277$	−21.8570	−1.31326	−0.656629	+	0.754213i	$0.728018\pi$
$278$	−5.13674	−0.308081
$279$	−1.37977	−0.0826046
$280$	−4.25286	−0.254157
$281$	13.4125	0.800123	0.400061	−	0.916488i	$-0.368989\pi$
$281$	13.4125	0.800123	0.400061	+	0.916488i	$0.368989\pi$
$282$	−18.5845	−1.10669
$283$	−3.66816	−0.218050	−0.109025	−	0.994039i	$-0.534773\pi$
$283$	−3.66816	−0.218050	−0.109025	+	0.994039i	$0.534773\pi$
$284$	11.8993	0.706094
$285$	16.7864	0.994338
$286$	−6.60311	−0.390450
$287$	14.5734	0.860243
$288$	8.10092	0.477351
$289$	32.9786	1.93992
$290$	69.9599	4.10818
$291$	3.78073	0.221630
$292$	−13.7115	−0.802405
$293$	−21.8840	−1.27848	−0.639239	−	0.769008i	$-0.720751\pi$
$293$	−21.8840	−1.27848	−0.639239	+	0.769008i	$0.720751\pi$
$294$	−9.13219	−0.532600
$295$	38.0572	2.21578
$296$	−3.90840	−0.227171
$297$	5.23644	0.303849
$298$	20.0294	1.16027
$299$	−0.248724	−0.0143841
$300$	−24.7418	−1.42847
$301$	−10.9864	−0.633248
$302$	−31.6000	−1.81838
$303$	8.97546	0.515627
$304$	−13.8143	−0.792303
$305$	−27.1595	−1.55515
$306$	−14.6942	−0.840011
$307$	−3.64350	−0.207946	−0.103973	−	0.994580i	$-0.533156\pi$
$307$	−3.64350	−0.207946	−0.103973	+	0.994580i	$0.533156\pi$
$308$	19.6150	1.11767
$309$	−7.09213	−0.403457
$310$	−11.3502	−0.644649
$311$	−3.53942	−0.200702	−0.100351	−	0.994952i	$-0.531997\pi$
$311$	−3.53942	−0.200702	−0.100351	+	0.994952i	$0.531997\pi$
$312$	−0.403809	−0.0228612
$313$	15.7316	0.889201	0.444600	−	0.895729i	$-0.353346\pi$
$313$	15.7316	0.889201	0.444600	+	0.895729i	$0.353346\pi$
$314$	38.1446	2.15263
$315$	6.38946	0.360005
$316$	1.64088	0.0923069
$317$	24.7915	1.39243	0.696214	−	0.717834i	$-0.254866\pi$
$317$	24.7915	1.39243	0.696214	+	0.717834i	$0.254866\pi$
$318$	−22.4935	−1.26137
$319$	−44.5336	−2.49340
$320$	40.8591	2.28409
$321$	9.33865	0.521233
$322$	1.37573	0.0766662
$323$	29.9850	1.66841
$324$	2.32023	0.128902
$325$	−6.46932	−0.358853
$326$	−32.7911	−1.81613
$327$	−11.3433	−0.627284
$328$	6.00841	0.331759
$329$	14.4350	0.795828
$330$	43.0759	2.37125
$331$	9.57328	0.526195	0.263097	−	0.964769i	$-0.415256\pi$
$331$	9.57328	0.526195	0.263097	+	0.964769i	$0.415256\pi$
$332$	8.09744	0.444405
$333$	5.87194	0.321780
$334$	4.30739	0.235690
$335$	20.6063	1.12584
$336$	−5.25819	−0.286858
$337$	−25.7797	−1.40431	−0.702155	−	0.712024i	$-0.747779\pi$
$337$	−25.7797	−1.40431	−0.702155	+	0.712024i	$0.747779\pi$
$338$	26.2557	1.42812
$339$	−11.6890	−0.634861
$340$	−64.9184	−3.52069
$341$	7.22508	0.391260
$342$	−8.81588	−0.476708
$343$	18.3942	0.993194
$344$	−4.52954	−0.244217
$345$	1.62257	0.0873562
$346$	49.6052	2.66679
$347$	−26.3216	−1.41302	−0.706509	−	0.707704i	$-0.749731\pi$
$347$	−26.3216	−1.41302	−0.706509	+	0.707704i	$0.749731\pi$
$348$	−19.7325	−1.05777
$349$	−31.3173	−1.67638	−0.838189	−	0.545380i	$-0.816385\pi$
$349$	−31.3173	−1.67638	−0.838189	+	0.545380i	$0.816385\pi$
$350$	35.7827	1.91267
$351$	0.606678	0.0323821
$352$	−42.4200	−2.26099
$353$	1.95648	0.104133	0.0520665	−	0.998644i	$-0.483419\pi$
$353$	1.95648	0.104133	0.0520665	+	0.998644i	$0.483419\pi$
$354$	−19.9869	−1.06229
$355$	−20.2972	−1.07726
$356$	−31.7844	−1.68457
$357$	11.4133	0.604057
$358$	9.69431	0.512360
$359$	11.6362	0.614134	0.307067	−	0.951688i	$-0.400652\pi$
$359$	11.6362	0.614134	0.307067	+	0.951688i	$0.400652\pi$
$360$	2.63428	0.138839
$361$	−1.01030	−0.0531736
$362$	35.3330	1.85706
$363$	−16.4203	−0.861844
$364$	2.27253	0.119113
$365$	23.3883	1.22420
$366$	14.2637	0.745574
$367$	−13.5363	−0.706592	−0.353296	−	0.935512i	$-0.614939\pi$
$367$	−13.5363	−0.706592	−0.353296	+	0.935512i	$0.614939\pi$
$368$	−1.33529	−0.0696067
$369$	−9.02698	−0.469926
$370$	48.3036	2.51118
$371$	17.4712	0.907061
$372$	3.20138	0.165984
$373$	−13.1551	−0.681148	−0.340574	−	0.940218i	$-0.610621\pi$
$373$	−13.1551	−0.681148	−0.340574	+	0.940218i	$0.610621\pi$
$374$	76.9453	3.97875
$375$	22.4145	1.15748
$376$	5.95134	0.306917
$377$	−5.15952	−0.265729
$378$	−3.35562	−0.172595
$379$	15.3898	0.790523	0.395262	−	0.918569i	$-0.370654\pi$
$379$	15.3898	0.790523	0.395262	+	0.918569i	$0.370654\pi$
$380$	−38.9482	−1.99800
$381$	−16.3001	−0.835081
$382$	−48.1822	−2.46522
$383$	5.30851	0.271252	0.135626	−	0.990760i	$-0.456695\pi$
$383$	5.30851	0.271252	0.135626	+	0.990760i	$0.456695\pi$
$384$	−5.25659	−0.268249
$385$	−33.4581	−1.70518
$386$	39.4859	2.00978
$387$	6.80514	0.345925
$388$	−8.77216	−0.445339
$389$	−12.3254	−0.624920	−0.312460	−	0.949931i	$-0.601153\pi$
$389$	−12.3254	−0.624920	−0.312460	+	0.949931i	$0.601153\pi$
$390$	4.99064	0.252711
$391$	2.89835	0.146576
$392$	2.92441	0.147705
$393$	−8.06237	−0.406693
$394$	41.4831	2.08989
$395$	−2.79892	−0.140829
$396$	−12.1498	−0.610548
$397$	6.47305	0.324873	0.162437	−	0.986719i	$-0.448065\pi$
$397$	6.47305	0.324873	0.162437	+	0.986719i	$0.448065\pi$
$398$	12.9716	0.650209
$399$	6.84750	0.342804
$400$	−34.7309	−1.73655
$401$	−1.36723	−0.0682760	−0.0341380	−	0.999417i	$-0.510869\pi$
$401$	−1.36723	−0.0682760	−0.0341380	+	0.999417i	$0.510869\pi$
$402$	−10.8220	−0.539753
$403$	0.837076	0.0416977
$404$	−20.8251	−1.03609
$405$	−3.95771	−0.196660
$406$	28.5380	1.41632
$407$	−30.7481	−1.52413
$408$	4.70554	0.232959
$409$	2.08941	0.103315	0.0516574	−	0.998665i	$-0.483550\pi$
$409$	2.08941	0.103315	0.0516574	+	0.998665i	$0.483550\pi$
$410$	−74.2575	−3.66732
$411$	7.65811	0.377747
$412$	16.4554	0.810699
$413$	15.5243	0.763901
$414$	−0.852142	−0.0418805
$415$	−13.8121	−0.678011
$416$	−4.91465	−0.240961
$417$	−2.47135	−0.121023
$418$	46.1638	2.25795
$419$	−1.66607	−0.0813929	−0.0406965	−	0.999172i	$-0.512958\pi$
$419$	−1.66607	−0.0813929	−0.0406965	+	0.999172i	$0.512958\pi$
$420$	−14.8250	−0.723387
$421$	−18.9300	−0.922592	−0.461296	−	0.887246i	$-0.652615\pi$
$421$	−18.9300	−0.922592	−0.461296	+	0.887246i	$0.652615\pi$
$422$	2.02121	0.0983910
$423$	−8.94123	−0.434738
$424$	7.20313	0.349815
$425$	75.3862	3.65677
$426$	10.6597	0.516463
$427$	−11.0789	−0.536146
$428$	−21.6678	−1.04735
$429$	−3.17684	−0.153379
$430$	55.9803	2.69961
$431$	25.4341	1.22512	0.612560	−	0.790424i	$-0.290140\pi$
$431$	25.4341	1.22512	0.612560	+	0.790424i	$0.290140\pi$
$432$	3.25699	0.156702
$433$	−2.51054	−0.120649	−0.0603245	−	0.998179i	$-0.519214\pi$
$433$	−2.51054	−0.120649	−0.0603245	+	0.998179i	$0.519214\pi$
$434$	−4.62998	−0.222246
$435$	33.6585	1.61380
$436$	26.3190	1.26045
$437$	1.73888	0.0831821
$438$	−12.2831	−0.586908
$439$	−23.1855	−1.10658	−0.553291	−	0.832988i	$-0.686628\pi$
$439$	−23.1855	−1.10658	−0.553291	+	0.832988i	$0.686628\pi$
$440$	−13.7943	−0.657615
$441$	−4.39361	−0.209219
$442$	8.91465	0.424027
$443$	−4.87542	−0.231638	−0.115819	−	0.993270i	$-0.536949\pi$
$443$	−4.87542	−0.231638	−0.115819	+	0.993270i	$0.536949\pi$
$444$	−13.6243	−0.646578
$445$	54.2159	2.57008
$446$	−39.2946	−1.86065
$447$	9.63637	0.455785
$448$	16.6673	0.787454
$449$	−4.55333	−0.214885	−0.107442	−	0.994211i	$-0.534266\pi$
$449$	−4.55333	−0.214885	−0.107442	+	0.994211i	$0.534266\pi$
$450$	−22.1643	−1.04483
$451$	47.2693	2.22582
$452$	27.1212	1.27568
$453$	−15.2032	−0.714307
$454$	−7.45311	−0.349792
$455$	−3.87635	−0.181726
$456$	2.82312	0.132205
$457$	22.7248	1.06302	0.531511	−	0.847051i	$-0.321624\pi$
$457$	22.7248	1.06302	0.531511	+	0.847051i	$0.321624\pi$
$458$	−6.73139	−0.314537
$459$	−7.06955	−0.329979
$460$	−3.76474	−0.175532
$461$	7.98314	0.371812	0.185906	−	0.982568i	$-0.440478\pi$
$461$	7.98314	0.371812	0.185906	+	0.982568i	$0.440478\pi$
$462$	17.5715	0.817502
$463$	−23.1189	−1.07442	−0.537212	−	0.843447i	$-0.680523\pi$
$463$	−23.1189	−1.07442	−0.537212	+	0.843447i	$0.680523\pi$
$464$	−27.6992	−1.28590
$465$	−5.46073	−0.253235
$466$	−26.3303	−1.21973
$467$	−3.84942	−0.178130	−0.0890650	−	0.996026i	$-0.528388\pi$
$467$	−3.84942	−0.178130	−0.0890650	+	0.996026i	$0.528388\pi$
$468$	−1.40763	−0.0650679
$469$	8.40571	0.388140
$470$	−73.5522	−3.39271
$471$	18.3519	0.845609
$472$	6.40044	0.294604
$473$	−35.6347	−1.63849
$474$	1.46994	0.0675166
$475$	45.2285	2.07522
$476$	−26.4815	−1.21378
$477$	−10.8219	−0.495501
$478$	6.69974	0.306439
$479$	39.0874	1.78595	0.892975	−	0.450107i	$-0.148614\pi$
$479$	39.0874	1.78595	0.892975	+	0.450107i	$0.148614\pi$
$480$	32.0611	1.46338
$481$	−3.56238	−0.162430
$482$	18.8109	0.856812
$483$	0.661879	0.0301165
$484$	38.0990	1.73177
$485$	14.9630	0.679436
$486$	2.07852	0.0942834
$487$	−39.3856	−1.78473	−0.892365	−	0.451314i	$-0.850956\pi$
$487$	−39.3856	−1.78473	−0.892365	+	0.451314i	$0.850956\pi$
$488$	−4.56767	−0.206769
$489$	−15.7762	−0.713425
$490$	−36.1426	−1.63276
$491$	40.3578	1.82132	0.910661	−	0.413155i	$-0.135573\pi$
$491$	40.3578	1.82132	0.910661	+	0.413155i	$0.135573\pi$
$492$	20.9447	0.944259
$493$	60.1233	2.70782
$494$	5.34840	0.240636
$495$	20.7243	0.931490
$496$	4.49389	0.201782
$497$	−8.27962	−0.371392
$498$	7.25387	0.325054
$499$	−21.7075	−0.971762	−0.485881	−	0.874025i	$-0.661501\pi$
$499$	−21.7075	−0.971762	−0.485881	+	0.874025i	$0.661501\pi$
$500$	−52.0069	−2.32582
$501$	2.07234	0.0925852
$502$	−8.69542	−0.388095
$503$	−14.8451	−0.661910	−0.330955	−	0.943647i	$-0.607371\pi$
$503$	−14.8451	−0.661910	−0.330955	+	0.943647i	$0.607371\pi$
$504$	1.07458	0.0478654
$505$	35.5223	1.58072
$506$	4.46220	0.198369
$507$	12.6319	0.561004
$508$	37.8201	1.67799
$509$	41.3434	1.83252	0.916258	−	0.400589i	$-0.131194\pi$
$509$	41.3434	1.83252	0.916258	+	0.400589i	$0.131194\pi$
$510$	−58.1554	−2.57516
$511$	9.54055	0.422049
$512$	−30.7203	−1.35766
$513$	−4.24143	−0.187264
$514$	−30.2939	−1.33621
$515$	−28.0686	−1.23685
$516$	−15.7895	−0.695094
$517$	46.8203	2.05915
$518$	19.7040	0.865745
$519$	23.8657	1.04759
$520$	−1.59816	−0.0700840
$521$	19.8851	0.871181	0.435590	−	0.900145i	$-0.356540\pi$
$521$	19.8851	0.871181	0.435590	+	0.900145i	$0.356540\pi$
$522$	−17.6768	−0.773694
$523$	13.4354	0.587488	0.293744	−	0.955884i	$-0.405099\pi$
$523$	13.4354	0.587488	0.293744	+	0.955884i	$0.405099\pi$
$524$	18.7066	0.817200
$525$	17.2155	0.751346
$526$	−25.5178	−1.11263
$527$	−9.75435	−0.424906
$528$	−17.0550	−0.742225
$529$	−22.8319	−0.992692
$530$	−89.0229	−3.86691
$531$	−9.61595	−0.417297
$532$	−15.8878	−0.688822
$533$	5.47647	0.237212
$534$	−28.4732	−1.23216
$535$	36.9597	1.59791
$536$	3.46555	0.149689
$537$	4.66405	0.201269
$538$	−64.1495	−2.76568
$539$	23.0069	0.990977
$540$	9.18281	0.395165
$541$	−3.00860	−0.129350	−0.0646749	−	0.997906i	$-0.520601\pi$
$541$	−3.00860	−0.129350	−0.0646749	+	0.997906i	$0.520601\pi$
$542$	23.2197	0.997370
$543$	16.9991	0.729502
$544$	57.2699	2.45543
$545$	−44.8934	−1.92302
$546$	2.03578	0.0871236
$547$	31.9229	1.36493	0.682463	−	0.730920i	$-0.260909\pi$
$547$	31.9229	1.36493	0.682463	+	0.730920i	$0.260909\pi$
$548$	−17.7686	−0.759037
$549$	6.86242	0.292881
$550$	116.062	4.94890
$551$	36.0714	1.53669
$552$	0.272883	0.0116147
$553$	−1.14174	−0.0485516
$554$	45.4301	1.93014
$555$	23.2395	0.986460
$556$	5.73411	0.243180
$557$	−46.7440	−1.98060	−0.990302	−	0.138929i	$-0.955634\pi$
$557$	−46.7440	−1.98060	−0.990302	+	0.138929i	$0.955634\pi$
$558$	2.86787	0.121407
$559$	−4.12853	−0.174618
$560$	−20.8104	−0.879400
$561$	37.0193	1.56296
$562$	−27.8781	−1.17597
$563$	−27.9172	−1.17657	−0.588285	−	0.808654i	$-0.700197\pi$
$563$	−27.9172	−1.17657	−0.588285	+	0.808654i	$0.700197\pi$
$564$	20.7457	0.873553
$565$	−46.2618	−1.94625
$566$	7.62434	0.320475
$567$	−1.61443	−0.0677998
$568$	−3.41356	−0.143230
$569$	−16.4385	−0.689137	−0.344569	−	0.938761i	$-0.611975\pi$
$569$	−16.4385	−0.689137	−0.344569	+	0.938761i	$0.611975\pi$
$570$	−34.8907	−1.46141
$571$	3.34884	0.140145	0.0700723	−	0.997542i	$-0.477677\pi$
$571$	3.34884	0.140145	0.0700723	+	0.997542i	$0.477677\pi$
$572$	7.37100	0.308197
$573$	−23.1811	−0.968403
$574$	−30.2912	−1.26433
$575$	4.37178	0.182316
$576$	−10.3239	−0.430163
$577$	−6.23906	−0.259736	−0.129868	−	0.991531i	$-0.541455\pi$
$577$	−6.23906	−0.259736	−0.129868	+	0.991531i	$0.541455\pi$
$578$	−68.5466	−2.85116
$579$	18.9971	0.789494
$580$	−78.0956	−3.24274
$581$	−5.63425	−0.233748
$582$	−7.85830	−0.325737
$583$	56.6683	2.34696
$584$	3.93342	0.162766
$585$	2.40106	0.0992716
$586$	45.4863	1.87902
$587$	29.4494	1.21551	0.607753	−	0.794126i	$-0.292071\pi$
$587$	29.4494	1.21551	0.607753	+	0.794126i	$0.292071\pi$
$588$	10.1942	0.420401
$589$	−5.85219	−0.241135
$590$	−79.1025	−3.25660
$591$	19.9580	0.820964
$592$	−19.1248	−0.786026
$593$	22.5134	0.924515	0.462257	−	0.886746i	$-0.347040\pi$
$593$	22.5134	0.924515	0.462257	+	0.886746i	$0.347040\pi$
$594$	−10.8840	−0.446577
$595$	45.1706	1.85182
$596$	−22.3586	−0.915844
$597$	6.24081	0.255420
$598$	0.516976	0.0211407
$599$	21.3801	0.873568	0.436784	−	0.899566i	$-0.356117\pi$
$599$	21.3801	0.873568	0.436784	+	0.899566i	$0.356117\pi$
$600$	7.09769	0.289762
$601$	34.4588	1.40561	0.702803	−	0.711385i	$-0.251932\pi$
$601$	34.4588	1.40561	0.702803	+	0.711385i	$0.251932\pi$
$602$	22.8355	0.930705
$603$	−5.20661	−0.212029
$604$	35.2749	1.43531
$605$	−64.9870	−2.64210
$606$	−18.6556	−0.757834
$607$	−11.3267	−0.459737	−0.229869	−	0.973222i	$-0.573830\pi$
$607$	−11.3267	−0.459737	−0.229869	+	0.973222i	$0.573830\pi$
$608$	34.3595	1.39346
$609$	13.7300	0.556368
$610$	56.4515	2.28565
$611$	5.42445	0.219450
$612$	16.4030	0.663052
$613$	−34.5349	−1.39485	−0.697425	−	0.716657i	$-0.745671\pi$
$613$	−34.5349	−1.39485	−0.697425	+	0.716657i	$0.745671\pi$
$614$	7.57308	0.305625
$615$	−35.7262	−1.44062
$616$	−5.62696	−0.226716
$617$	−16.1653	−0.650791	−0.325396	−	0.945578i	$-0.605497\pi$
$617$	−16.1653	−0.650791	−0.325396	+	0.945578i	$0.605497\pi$
$618$	14.7411	0.592975
$619$	−23.9988	−0.964595	−0.482298	−	0.876007i	$-0.660198\pi$
$619$	−23.9988	−0.964595	−0.482298	+	0.876007i	$0.660198\pi$
$620$	12.6702	0.508846
$621$	−0.409976	−0.0164518
$622$	7.35674	0.294979
$623$	22.1158	0.886050
$624$	−1.97595	−0.0791011
$625$	35.3928	1.41571
$626$	−32.6983	−1.30689
$627$	22.2100	0.886982
$628$	−42.5806	−1.69915
$629$	41.5120	1.65519
$630$	−13.2806	−0.529112
$631$	37.8321	1.50607	0.753036	−	0.657979i	$-0.228588\pi$
$631$	37.8321	1.50607	0.753036	+	0.657979i	$0.228588\pi$
$632$	−0.470721	−0.0187243
$633$	0.972430	0.0386506
$634$	−51.5295	−2.04650
$635$	−64.5113	−2.56005
$636$	25.1093	0.995650
$637$	2.66551	0.105611
$638$	92.5637	3.66463
$639$	5.12850	0.202880
$640$	−20.8041	−0.822354
$641$	−10.9317	−0.431775	−0.215887	−	0.976418i	$-0.569264\pi$
$641$	−10.9317	−0.431775	−0.215887	+	0.976418i	$0.569264\pi$
$642$	−19.4105	−0.766073
$643$	−0.707027	−0.0278824	−0.0139412	−	0.999903i	$-0.504438\pi$
$643$	−0.707027	−0.0278824	−0.0139412	+	0.999903i	$0.504438\pi$
$644$	−1.53571	−0.0605155
$645$	26.9328	1.06048
$646$	−62.3243	−2.45212
$647$	37.4180	1.47105	0.735526	−	0.677497i	$-0.236935\pi$
$647$	37.4180	1.47105	0.735526	+	0.677497i	$0.236935\pi$
$648$	−0.665606	−0.0261475
$649$	50.3534	1.97654
$650$	13.4466	0.527418
$651$	−2.22754	−0.0873043
$652$	36.6045	1.43354
$653$	−46.0513	−1.80213	−0.901064	−	0.433687i	$-0.857212\pi$
$653$	−46.0513	−1.80213	−0.901064	+	0.433687i	$0.857212\pi$
$654$	23.5772	0.921940
$655$	−31.9086	−1.24677
$656$	29.4008	1.14791
$657$	−5.90954	−0.230553
$658$	−30.0034	−1.16966
$659$	4.85676	0.189192	0.0945962	−	0.995516i	$-0.469844\pi$
$659$	4.85676	0.189192	0.0945962	+	0.995516i	$0.469844\pi$
$660$	−48.0853	−1.87172
$661$	−20.3392	−0.791101	−0.395551	−	0.918444i	$-0.629446\pi$
$661$	−20.3392	−0.791101	−0.395551	+	0.918444i	$0.629446\pi$
$662$	−19.8982	−0.773366
$663$	4.28895	0.166569
$664$	−2.32292	−0.0901466
$665$	27.1004	1.05091
$666$	−12.2049	−0.472931
$667$	3.48666	0.135004
$668$	−4.80830	−0.186039
$669$	−18.9051	−0.730914
$670$	−42.8305	−1.65469
$671$	−35.9347	−1.38724
$672$	13.0784	0.504510
$673$	18.1826	0.700888	0.350444	−	0.936584i	$-0.386031\pi$
$673$	18.1826	0.700888	0.350444	+	0.936584i	$0.386031\pi$
$674$	53.5836	2.06396
$675$	−10.6635	−0.410438
$676$	−29.3090	−1.12727
$677$	−37.9612	−1.45897	−0.729484	−	0.683998i	$-0.760240\pi$
$677$	−37.9612	−1.45897	−0.729484	+	0.683998i	$0.760240\pi$
$678$	24.2958	0.933076
$679$	6.10372	0.234239
$680$	18.6232	0.714166
$681$	−3.58578	−0.137407
$682$	−15.0174	−0.575048
$683$	−49.3639	−1.88886	−0.944428	−	0.328718i	$-0.893383\pi$
$683$	−49.3639	−1.88886	−0.944428	+	0.328718i	$0.893383\pi$
$684$	9.84109	0.376284
$685$	30.3086	1.15803
$686$	−38.2327	−1.45973
$687$	−3.23856	−0.123559
$688$	−22.1643	−0.845005
$689$	6.56542	0.250123
$690$	−3.37254	−0.128390
$691$	−16.0152	−0.609248	−0.304624	−	0.952473i	$-0.598531\pi$
$691$	−16.0152	−0.609248	−0.304624	+	0.952473i	$0.598531\pi$
$692$	−55.3738	−2.10500
$693$	8.45388	0.321136
$694$	54.7099	2.07676
$695$	−9.78090	−0.371011
$696$	5.66067	0.214567
$697$	−63.8167	−2.41723
$698$	65.0936	2.46383
$699$	−12.6678	−0.479141
$700$	−39.9439	−1.50974
$701$	−28.6105	−1.08060	−0.540301	−	0.841472i	$-0.681690\pi$
$701$	−28.6105	−1.08060	−0.540301	+	0.841472i	$0.681690\pi$
$702$	−1.26099	−0.0475930
$703$	24.9054	0.939325
$704$	54.0606	2.03749
$705$	−35.3869	−1.33275
$706$	−4.06658	−0.153048
$707$	14.4903	0.544963
$708$	22.3112	0.838508
$709$	14.5613	0.546861	0.273430	−	0.961892i	$-0.411842\pi$
$709$	14.5613	0.546861	0.273430	+	0.961892i	$0.411842\pi$
$710$	42.1880	1.58329
$711$	0.707207	0.0265223
$712$	9.11800	0.341712
$713$	−0.565672	−0.0211846
$714$	−23.7228	−0.887802
$715$	−12.5730	−0.470204
$716$	−10.8217	−0.404425
$717$	3.22333	0.120377
$718$	−24.1860	−0.902613
$719$	44.5355	1.66090	0.830448	−	0.557097i	$-0.188085\pi$
$719$	44.5355	1.66090	0.830448	+	0.557097i	$0.188085\pi$
$720$	12.8902	0.480391
$721$	−11.4498	−0.426412
$722$	2.09992	0.0781509
$723$	9.05014	0.336578
$724$	−39.4419	−1.46585
$725$	90.6882	3.36808
$726$	34.1299	1.26668
$727$	27.6421	1.02519	0.512594	−	0.858631i	$-0.328685\pi$
$727$	27.6421	1.02519	0.512594	+	0.858631i	$0.328685\pi$
$728$	−0.651922	−0.0241618
$729$	1.00000	0.0370370
$730$	−48.6129	−1.79924
$731$	48.1093	1.77939
$732$	−15.9224	−0.588509
$733$	39.7340	1.46761	0.733805	−	0.679360i	$-0.237743\pi$
$733$	39.7340	1.46761	0.733805	+	0.679360i	$0.237743\pi$
$734$	28.1355	1.03850
$735$	−17.3886	−0.641390
$736$	3.32118	0.122420
$737$	27.2641	1.00429
$738$	18.7627	0.690666
$739$	38.4017	1.41263	0.706314	−	0.707898i	$-0.250357\pi$
$739$	38.4017	1.41263	0.706314	+	0.707898i	$0.250357\pi$
$740$	−53.9209	−1.98217
$741$	2.57318	0.0945282
$742$	−36.3143	−1.33314
$743$	40.0415	1.46898	0.734490	−	0.678619i	$-0.237421\pi$
$743$	40.0415	1.46898	0.734490	+	0.678619i	$0.237421\pi$
$744$	−0.918382	−0.0336695
$745$	38.1380	1.39727
$746$	27.3432	1.00111
$747$	3.48993	0.127690
$748$	−85.8934	−3.14057
$749$	15.0766	0.550888
$750$	−46.5890	−1.70119
$751$	50.8410	1.85522	0.927608	−	0.373555i	$-0.121861\pi$
$751$	50.8410	1.85522	0.927608	+	0.373555i	$0.121861\pi$
$752$	29.1215	1.06195
$753$	−4.18347	−0.152454
$754$	10.7242	0.390551
$755$	−60.1698	−2.18980
$756$	3.74586	0.136235
$757$	40.6720	1.47825	0.739125	−	0.673569i	$-0.235239\pi$
$757$	40.6720	1.47825	0.739125	+	0.673569i	$0.235239\pi$
$758$	−31.9881	−1.16186
$759$	2.14682	0.0779245
$760$	11.1731	0.405291
$761$	36.2315	1.31339	0.656696	−	0.754156i	$-0.271954\pi$
$761$	36.2315	1.31339	0.656696	+	0.754156i	$0.271954\pi$
$762$	33.8801	1.22735
$763$	−18.3129	−0.662973
$764$	53.7854	1.94589
$765$	−27.9793	−1.01159
$766$	−11.0338	−0.398668
$767$	5.83379	0.210646
$768$	−9.72192	−0.350809
$769$	20.3360	0.733336	0.366668	−	0.930352i	$-0.380499\pi$
$769$	20.3360	0.733336	0.366668	+	0.930352i	$0.380499\pi$
$770$	69.5431	2.50616
$771$	−14.5748	−0.524898
$772$	−44.0777	−1.58639
$773$	−6.40509	−0.230375	−0.115188	−	0.993344i	$-0.536747\pi$
$773$	−6.40509	−0.230375	−0.115188	+	0.993344i	$0.536747\pi$
$774$	−14.1446	−0.508417
$775$	−14.7132	−0.528512
$776$	2.51647	0.0903361
$777$	9.47985	0.340088
$778$	25.6185	0.918466
$779$	−38.2873	−1.37178
$780$	−5.57101	−0.199474
$781$	−26.8551	−0.960952
$782$	−6.02427	−0.215427
$783$	−8.50454	−0.303928
$784$	14.3099	0.511069
$785$	72.6314	2.59233
$786$	16.7578	0.597730
$787$	10.1044	0.360183	0.180091	−	0.983650i	$-0.442361\pi$
$787$	10.1044	0.360183	0.180091	+	0.983650i	$0.442361\pi$
$788$	−46.3073	−1.64963
$789$	−12.2769	−0.437071
$790$	5.81761	0.206981
$791$	−18.8711	−0.670981
$792$	3.48541	0.123849
$793$	−4.16329	−0.147843
$794$	−13.4544	−0.477477
$795$	−42.8300	−1.51902
$796$	−14.4801	−0.513235
$797$	12.1873	0.431697	0.215848	−	0.976427i	$-0.430748\pi$
$797$	12.1873	0.431697	0.215848	+	0.976427i	$0.430748\pi$
$798$	−14.2326	−0.503830
$799$	−63.2105	−2.23623
$800$	86.3842	3.05414
$801$	−13.6988	−0.484023
$802$	2.84180	0.100348
$803$	30.9450	1.09202
$804$	12.0805	0.426048
$805$	2.61953	0.0923262
$806$	−1.73988	−0.0612845
$807$	−30.8631	−1.08643
$808$	5.97412	0.210169
$809$	56.0112	1.96925	0.984624	−	0.174687i	$-0.0558913\pi$
$809$	56.0112	1.96925	0.984624	+	0.174687i	$0.0558913\pi$
$810$	8.22618	0.289038
$811$	−40.8101	−1.43304	−0.716518	−	0.697569i	$-0.754265\pi$
$811$	−40.8101	−1.43304	−0.716518	+	0.697569i	$0.754265\pi$
$812$	−31.8568	−1.11795
$813$	11.1713	0.391794
$814$	63.9104	2.24006
$815$	−62.4378	−2.18710
$816$	23.0255	0.806052
$817$	28.8635	1.00981
$818$	−4.34288	−0.151845
$819$	0.979441	0.0342244
$820$	82.8931	2.89475
$821$	29.2328	1.02023	0.510116	−	0.860105i	$-0.329602\pi$
$821$	29.2328	1.02023	0.510116	+	0.860105i	$0.329602\pi$
$822$	−15.9175	−0.555187
$823$	−7.38401	−0.257390	−0.128695	−	0.991684i	$-0.541079\pi$
$823$	−7.38401	−0.257390	−0.128695	+	0.991684i	$0.541079\pi$
$824$	−4.72057	−0.164449
$825$	55.8388	1.94406
$826$	−32.2675	−1.12273
$827$	22.9500	0.798051	0.399025	−	0.916940i	$-0.369349\pi$
$827$	22.9500	0.798051	0.399025	+	0.916940i	$0.369349\pi$
$828$	0.951240	0.0330579
$829$	16.5628	0.575249	0.287624	−	0.957743i	$-0.407135\pi$
$829$	16.5628	0.575249	0.287624	+	0.957743i	$0.407135\pi$
$830$	28.7087	0.996495
$831$	21.8570	0.758210
$832$	6.26330	0.217141
$833$	−31.0609	−1.07619
$834$	5.13674	0.177871
$835$	8.20172	0.283832
$836$	−51.5323	−1.78228
$837$	1.37977	0.0476918
$838$	3.46296	0.119626
$839$	13.4556	0.464537	0.232269	−	0.972652i	$-0.425385\pi$
$839$	13.4556	0.464537	0.232269	+	0.972652i	$0.425385\pi$
$840$	4.25286	0.146738
$841$	43.3272	1.49404
$842$	39.3463	1.35596
$843$	−13.4125	−0.461951
$844$	−2.25626	−0.0776637
$845$	49.9936	1.71983
$846$	18.5845	0.638948
$847$	−26.5095	−0.910878
$848$	35.2468	1.21038
$849$	3.66816	0.125891
$850$	−156.692	−5.37447
$851$	2.40735	0.0825231
$852$	−11.8993	−0.407664
$853$	47.6229	1.63058	0.815289	−	0.579054i	$-0.196578\pi$
$853$	47.6229	1.63058	0.815289	+	0.579054i	$0.196578\pi$
$854$	23.0277	0.787992
$855$	−16.7864	−0.574081
$856$	6.21586	0.212454
$857$	−53.3685	−1.82303	−0.911517	−	0.411263i	$-0.865088\pi$
$857$	−53.3685	−1.82303	−0.911517	+	0.411263i	$0.865088\pi$
$858$	6.60311	0.225426
$859$	−24.8344	−0.847338	−0.423669	−	0.905817i	$-0.639258\pi$
$859$	−24.8344	−0.847338	−0.423669	+	0.905817i	$0.639258\pi$
$860$	−62.4903	−2.13090
$861$	−14.5734	−0.496662
$862$	−52.8653	−1.80060
$863$	33.9768	1.15658	0.578292	−	0.815830i	$-0.303719\pi$
$863$	33.9768	1.15658	0.578292	+	0.815830i	$0.303719\pi$
$864$	−8.10092	−0.275599
$865$	94.4534	3.21151
$866$	5.21821	0.177322
$867$	−32.9786	−1.12001
$868$	5.16841	0.175427
$869$	−3.70325	−0.125624
$870$	−69.9599	−2.37186
$871$	3.15874	0.107030
$872$	−7.55015	−0.255680
$873$	−3.78073	−0.127958
$874$	−3.61430	−0.122256
$875$	36.1867	1.22333
$876$	13.7115	0.463269
$877$	15.8657	0.535746	0.267873	−	0.963454i	$-0.413679\pi$
$877$	15.8657	0.535746	0.267873	+	0.963454i	$0.413679\pi$
$878$	48.1914	1.62638
$879$	21.8840	0.738130
$880$	−67.4990	−2.27539
$881$	−50.4130	−1.69846	−0.849228	−	0.528026i	$-0.822932\pi$
$881$	−50.4130	−1.69846	−0.849228	+	0.528026i	$0.822932\pi$
$882$	9.13219	0.307497
$883$	−35.5185	−1.19529	−0.597646	−	0.801760i	$-0.703897\pi$
$883$	−35.5185	−1.19529	−0.597646	+	0.801760i	$0.703897\pi$
$884$	−9.95135	−0.334700
$885$	−38.0572	−1.27928
$886$	10.1336	0.340446
$887$	11.7183	0.393462	0.196731	−	0.980457i	$-0.436967\pi$
$887$	11.7183	0.393462	0.196731	+	0.980457i	$0.436967\pi$
$888$	3.90840	0.131157
$889$	−26.3155	−0.882592
$890$	−112.689	−3.77733
$891$	−5.23644	−0.175427
$892$	43.8643	1.46868
$893$	−37.9236	−1.26906
$894$	−20.0294	−0.669882
$895$	18.4590	0.617016
$896$	−8.48641	−0.283511
$897$	0.248724	0.00830464
$898$	9.46416	0.315823
$899$	−11.7343	−0.391361
$900$	24.7418	0.824726
$901$	−76.5061	−2.54879
$902$	−98.2500	−3.27137
$903$	10.9864	0.365606
$904$	−7.78029	−0.258769
$905$	67.2777	2.23639
$906$	31.6000	1.04984
$907$	−25.1429	−0.834856	−0.417428	−	0.908710i	$-0.637068\pi$
$907$	−25.1429	−0.834856	−0.417428	+	0.908710i	$0.637068\pi$
$908$	8.31984	0.276104
$909$	−8.97546	−0.297697
$910$	8.05706	0.267089
$911$	20.6761	0.685029	0.342515	−	0.939513i	$-0.388721\pi$
$911$	20.6761	0.685029	0.342515	+	0.939513i	$0.388721\pi$
$912$	13.8143	0.457437
$913$	−18.2748	−0.604808
$914$	−47.2339	−1.56236
$915$	27.1595	0.897866
$916$	7.51420	0.248276
$917$	−13.0161	−0.429831
$918$	14.6942	0.484980
$919$	−15.4881	−0.510904	−0.255452	−	0.966822i	$-0.582224\pi$
$919$	−15.4881	−0.510904	−0.255452	+	0.966822i	$0.582224\pi$
$920$	1.07999	0.0356063
$921$	3.64350	0.120058
$922$	−16.5931	−0.546464
$923$	−3.11135	−0.102411
$924$	−19.6150	−0.645285
$925$	62.6154	2.05878
$926$	48.0529	1.57912
$927$	7.09213	0.232936
$928$	68.8946	2.26158
$929$	−53.0903	−1.74184	−0.870918	−	0.491429i	$-0.836475\pi$
$929$	−53.0903	−1.74184	−0.870918	+	0.491429i	$0.836475\pi$
$930$	11.3502	0.372188
$931$	−18.6352	−0.610743
$932$	29.3923	0.962775
$933$	3.53942	0.115875
$934$	8.00109	0.261804
$935$	146.512	4.79145
$936$	0.403809	0.0131989
$937$	−25.0150	−0.817203	−0.408602	−	0.912713i	$-0.633983\pi$
$937$	−25.0150	−0.817203	−0.408602	+	0.912713i	$0.633983\pi$
$938$	−17.4714	−0.570462
$939$	−15.7316	−0.513380
$940$	82.1057	2.67799
$941$	−48.2301	−1.57226	−0.786129	−	0.618063i	$-0.787918\pi$
$941$	−48.2301	−1.57226	−0.786129	+	0.618063i	$0.787918\pi$
$942$	−38.1446	−1.24282
$943$	−3.70085	−0.120516
$944$	31.3191	1.01935
$945$	−6.38946	−0.207849
$946$	74.0674	2.40814
$947$	12.8559	0.417762	0.208881	−	0.977941i	$-0.433018\pi$
$947$	12.8559	0.417762	0.208881	+	0.977941i	$0.433018\pi$
$948$	−1.64088	−0.0532934
$949$	3.58519	0.116380
$950$	−94.0081	−3.05003
$951$	−24.7915	−0.803919
$952$	7.59677	0.246213
$953$	−8.27672	−0.268109	−0.134055	−	0.990974i	$-0.542800\pi$
$953$	−8.27672	−0.268109	−0.134055	+	0.990974i	$0.542800\pi$
$954$	22.4935	0.728254
$955$	−91.7440	−2.96877
$956$	−7.47887	−0.241884
$957$	44.5336	1.43957
$958$	−81.2438	−2.62487
$959$	12.3635	0.399238
$960$	−40.8591	−1.31872
$961$	−29.0962	−0.938588
$962$	7.40446	0.238729
$963$	−9.33865	−0.300934
$964$	−20.9984	−0.676314
$965$	75.1852	2.42030
$966$	−1.37573	−0.0442633
$967$	−15.8630	−0.510119	−0.255059	−	0.966925i	$-0.582095\pi$
$967$	−15.8630	−0.510119	−0.255059	+	0.966925i	$0.582095\pi$
$968$	−10.9295	−0.351287
$969$	−29.9850	−0.963257
$970$	−31.1009	−0.998590
$971$	−23.5107	−0.754494	−0.377247	−	0.926113i	$-0.623129\pi$
$971$	−23.5107	−0.754494	−0.377247	+	0.926113i	$0.623129\pi$
$972$	−2.32023	−0.0744215
$973$	−3.98983	−0.127908
$974$	81.8636	2.62308
$975$	6.46932	0.207184
$976$	−22.3508	−0.715433
$977$	39.1000	1.25092	0.625460	−	0.780256i	$-0.284911\pi$
$977$	39.1000	1.25092	0.625460	+	0.780256i	$0.284911\pi$
$978$	32.7911	1.04854
$979$	71.7330	2.29260
$980$	40.3457	1.28880
$981$	11.3433	0.362163
$982$	−83.8843	−2.67686
$983$	−59.4939	−1.89756	−0.948781	−	0.315935i	$-0.897682\pi$
$983$	−59.4939	−1.89756	−0.948781	+	0.315935i	$0.897682\pi$
$984$	−6.00841	−0.191541
$985$	78.9882	2.51677
$986$	−124.967	−3.97977
$987$	−14.4350	−0.459472
$988$	−5.97038	−0.189943
$989$	2.78995	0.0887151
$990$	−43.0759	−1.36904
$991$	−6.67124	−0.211919	−0.105960	−	0.994370i	$-0.533791\pi$
$991$	−6.67124	−0.211919	−0.105960	+	0.994370i	$0.533791\pi$
$992$	−11.1774	−0.354883
$993$	−9.57328	−0.303799
$994$	17.2093	0.545847
$995$	24.6994	0.783022
$996$	−8.09744	−0.256577
$997$	−6.34453	−0.200933	−0.100467	−	0.994940i	$-0.532034\pi$
$997$	−6.34453	−0.200933	−0.100467	+	0.994940i	$0.532034\pi$
$998$	45.1194	1.42823
$999$	−5.87194	−0.185780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.16	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.16	✓	93	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.07852 q^{2} -1.00000 q^{3} +2.32023 q^{4} -3.95771 q^{5} +2.07852 q^{6} -1.61443 q^{7} -0.665606 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.07852 q^{2} -1.00000 q^{3} +2.32023 q^{4} -3.95771 q^{5} +2.07852 q^{6} -1.61443 q^{7} -0.665606 q^{8} +1.00000 q^{9} +8.22618 q^{10} -5.23644 q^{11} -2.32023 q^{12} -0.606678 q^{13} +3.35562 q^{14} +3.95771 q^{15} -3.25699 q^{16} +7.06955 q^{17} -2.07852 q^{18} +4.24143 q^{19} -9.18281 q^{20} +1.61443 q^{21} +10.8840 q^{22} +0.409976 q^{23} +0.665606 q^{24} +10.6635 q^{25} +1.26099 q^{26} -1.00000 q^{27} -3.74586 q^{28} +8.50454 q^{29} -8.22618 q^{30} -1.37977 q^{31} +8.10092 q^{32} +5.23644 q^{33} -14.6942 q^{34} +6.38946 q^{35} +2.32023 q^{36} +5.87194 q^{37} -8.81588 q^{38} +0.606678 q^{39} +2.63428 q^{40} -9.02698 q^{41} -3.35562 q^{42} +6.80514 q^{43} -12.1498 q^{44} -3.95771 q^{45} -0.852142 q^{46} -8.94123 q^{47} +3.25699 q^{48} -4.39361 q^{49} -22.1643 q^{50} -7.06955 q^{51} -1.40763 q^{52} -10.8219 q^{53} +2.07852 q^{54} +20.7243 q^{55} +1.07458 q^{56} -4.24143 q^{57} -17.6768 q^{58} -9.61595 q^{59} +9.18281 q^{60} +6.86242 q^{61} +2.86787 q^{62} -1.61443 q^{63} -10.3239 q^{64} +2.40106 q^{65} -10.8840 q^{66} -5.20661 q^{67} +16.4030 q^{68} -0.409976 q^{69} -13.2806 q^{70} +5.12850 q^{71} -0.665606 q^{72} -5.90954 q^{73} -12.2049 q^{74} -10.6635 q^{75} +9.84109 q^{76} +8.45388 q^{77} -1.26099 q^{78} +0.707207 q^{79} +12.8902 q^{80} +1.00000 q^{81} +18.7627 q^{82} +3.48993 q^{83} +3.74586 q^{84} -27.9793 q^{85} -14.1446 q^{86} -8.50454 q^{87} +3.48541 q^{88} -13.6988 q^{89} +8.22618 q^{90} +0.979441 q^{91} +0.951240 q^{92} +1.37977 q^{93} +18.5845 q^{94} -16.7864 q^{95} -8.10092 q^{96} -3.78073 q^{97} +9.13219 q^{98} -5.23644 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

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