LMFDB - Embedded newform 6009.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.31255 q^{2} +1.00000 q^{3} +3.34790 q^{4} -0.928530 q^{5} -2.31255 q^{6} -3.24971 q^{7} -3.11708 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.31255 q^{2} +1.00000 q^{3} +3.34790 q^{4} -0.928530 q^{5} -2.31255 q^{6} -3.24971 q^{7} -3.11708 q^{8} +1.00000 q^{9} +2.14727 q^{10} +0.329184 q^{11} +3.34790 q^{12} +0.592318 q^{13} +7.51512 q^{14} -0.928530 q^{15} +0.512619 q^{16} +5.04091 q^{17} -2.31255 q^{18} +6.69512 q^{19} -3.10862 q^{20} -3.24971 q^{21} -0.761254 q^{22} +1.05858 q^{23} -3.11708 q^{24} -4.13783 q^{25} -1.36977 q^{26} +1.00000 q^{27} -10.8797 q^{28} +0.590233 q^{29} +2.14727 q^{30} +6.88920 q^{31} +5.04870 q^{32} +0.329184 q^{33} -11.6574 q^{34} +3.01745 q^{35} +3.34790 q^{36} +4.96412 q^{37} -15.4828 q^{38} +0.592318 q^{39} +2.89430 q^{40} +2.02487 q^{41} +7.51512 q^{42} -3.24530 q^{43} +1.10207 q^{44} -0.928530 q^{45} -2.44802 q^{46} -9.11946 q^{47} +0.512619 q^{48} +3.56061 q^{49} +9.56895 q^{50} +5.04091 q^{51} +1.98302 q^{52} -2.44449 q^{53} -2.31255 q^{54} -0.305657 q^{55} +10.1296 q^{56} +6.69512 q^{57} -1.36495 q^{58} +13.0338 q^{59} -3.10862 q^{60} +2.76606 q^{61} -15.9316 q^{62} -3.24971 q^{63} -12.7006 q^{64} -0.549985 q^{65} -0.761254 q^{66} -4.36837 q^{67} +16.8764 q^{68} +1.05858 q^{69} -6.97802 q^{70} +10.7817 q^{71} -3.11708 q^{72} -8.52084 q^{73} -11.4798 q^{74} -4.13783 q^{75} +22.4146 q^{76} -1.06975 q^{77} -1.36977 q^{78} -8.69778 q^{79} -0.475983 q^{80} +1.00000 q^{81} -4.68261 q^{82} -16.5142 q^{83} -10.8797 q^{84} -4.68063 q^{85} +7.50493 q^{86} +0.590233 q^{87} -1.02609 q^{88} -9.56770 q^{89} +2.14727 q^{90} -1.92486 q^{91} +3.54402 q^{92} +6.88920 q^{93} +21.0892 q^{94} -6.21662 q^{95} +5.04870 q^{96} -7.26277 q^{97} -8.23409 q^{98} +0.329184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) $ 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.31255	−1.63522	−0.817611	−	0.575772i	$-0.804702\pi$
$2$	−2.31255	−1.63522	−0.817611	+	0.575772i	$0.804702\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.34790	1.67395
$5$	−0.928530	−0.415251	−0.207626	−	0.978208i	$-0.566574\pi$
$5$	−0.928530	−0.415251	−0.207626	+	0.978208i	$0.566574\pi$
$6$	−2.31255	−0.944095
$7$	−3.24971	−1.22827	−0.614137	−	0.789199i	$-0.710496\pi$
$7$	−3.24971	−1.22827	−0.614137	+	0.789199i	$0.710496\pi$
$8$	−3.11708	−1.10205
$9$	1.00000	0.333333
$10$	2.14727	0.679028
$11$	0.329184	0.0992526	0.0496263	−	0.998768i	$-0.484197\pi$
$11$	0.329184	0.0992526	0.0496263	+	0.998768i	$0.484197\pi$
$12$	3.34790	0.966455
$13$	0.592318	0.164280	0.0821398	−	0.996621i	$-0.473825\pi$
$13$	0.592318	0.164280	0.0821398	+	0.996621i	$0.473825\pi$
$14$	7.51512	2.00850
$15$	−0.928530	−0.239745
$16$	0.512619	0.128155
$17$	5.04091	1.22260	0.611300	−	0.791399i	$-0.290647\pi$
$17$	5.04091	1.22260	0.611300	+	0.791399i	$0.290647\pi$
$18$	−2.31255	−0.545074
$19$	6.69512	1.53597	0.767983	−	0.640470i	$-0.221260\pi$
$19$	6.69512	1.53597	0.767983	+	0.640470i	$0.221260\pi$
$20$	−3.10862	−0.695109
$21$	−3.24971	−0.709145
$22$	−0.761254	−0.162300
$23$	1.05858	0.220729	0.110365	−	0.993891i	$-0.464798\pi$
$23$	1.05858	0.220729	0.110365	+	0.993891i	$0.464798\pi$
$24$	−3.11708	−0.636272
$25$	−4.13783	−0.827566
$26$	−1.36977	−0.268633
$27$	1.00000	0.192450
$28$	−10.8797	−2.05607
$29$	0.590233	0.109604	0.0548018	−	0.998497i	$-0.482547\pi$
$29$	0.590233	0.109604	0.0548018	+	0.998497i	$0.482547\pi$
$30$	2.14727	0.392037
$31$	6.88920	1.23734	0.618669	−	0.785652i	$-0.287672\pi$
$31$	6.88920	1.23734	0.618669	+	0.785652i	$0.287672\pi$
$32$	5.04870	0.892493
$33$	0.329184	0.0573035
$34$	−11.6574	−1.99922
$35$	3.01745	0.510043
$36$	3.34790	0.557983
$37$	4.96412	0.816096	0.408048	−	0.912961i	$-0.366210\pi$
$37$	4.96412	0.816096	0.408048	+	0.912961i	$0.366210\pi$
$38$	−15.4828	−2.51164
$39$	0.592318	0.0948468
$40$	2.89430	0.457630
$41$	2.02487	0.316231	0.158116	−	0.987421i	$-0.449458\pi$
$41$	2.02487	0.316231	0.158116	+	0.987421i	$0.449458\pi$
$42$	7.51512	1.15961
$43$	−3.24530	−0.494904	−0.247452	−	0.968900i	$-0.579593\pi$
$43$	−3.24530	−0.494904	−0.247452	+	0.968900i	$0.579593\pi$
$44$	1.10207	0.166144
$45$	−0.928530	−0.138417
$46$	−2.44802	−0.360941
$47$	−9.11946	−1.33021	−0.665105	−	0.746750i	$-0.731613\pi$
$47$	−9.11946	−1.33021	−0.665105	+	0.746750i	$0.731613\pi$
$48$	0.512619	0.0739902
$49$	3.56061	0.508658
$50$	9.56895	1.35325
$51$	5.04091	0.705868
$52$	1.98302	0.274995
$53$	−2.44449	−0.335777	−0.167888	−	0.985806i	$-0.553695\pi$
$53$	−2.44449	−0.335777	−0.167888	+	0.985806i	$0.553695\pi$
$54$	−2.31255	−0.314698
$55$	−0.305657	−0.0412148
$56$	10.1296	1.35363
$57$	6.69512	0.886791
$58$	−1.36495	−0.179226
$59$	13.0338	1.69686	0.848428	−	0.529311i	$-0.177549\pi$
$59$	13.0338	1.69686	0.848428	+	0.529311i	$0.177549\pi$
$60$	−3.10862	−0.401322
$61$	2.76606	0.354157	0.177079	−	0.984197i	$-0.443335\pi$
$61$	2.76606	0.354157	0.177079	+	0.984197i	$0.443335\pi$
$62$	−15.9316	−2.02332
$63$	−3.24971	−0.409425
$64$	−12.7006	−1.58758
$65$	−0.549985	−0.0682173
$66$	−0.761254	−0.0937039
$67$	−4.36837	−0.533681	−0.266841	−	0.963741i	$-0.585980\pi$
$67$	−4.36837	−0.533681	−0.266841	+	0.963741i	$0.585980\pi$
$68$	16.8764	2.04657
$69$	1.05858	0.127438
$70$	−6.97802	−0.834032
$71$	10.7817	1.27956	0.639779	−	0.768559i	$-0.279026\pi$
$71$	10.7817	1.27956	0.639779	+	0.768559i	$0.279026\pi$
$72$	−3.11708	−0.367352
$73$	−8.52084	−0.997289	−0.498645	−	0.866807i	$-0.666169\pi$
$73$	−8.52084	−0.997289	−0.498645	+	0.866807i	$0.666169\pi$
$74$	−11.4798	−1.33450
$75$	−4.13783	−0.477796
$76$	22.4146	2.57113
$77$	−1.06975	−0.121909
$78$	−1.36977	−0.155096
$79$	−8.69778	−0.978576	−0.489288	−	0.872122i	$-0.662743\pi$
$79$	−8.69778	−0.978576	−0.489288	+	0.872122i	$0.662743\pi$
$80$	−0.475983	−0.0532165
$81$	1.00000	0.111111
$82$	−4.68261	−0.517108
$83$	−16.5142	−1.81267	−0.906337	−	0.422556i	$-0.861133\pi$
$83$	−16.5142	−1.81267	−0.906337	+	0.422556i	$0.861133\pi$
$84$	−10.8797	−1.18707
$85$	−4.68063	−0.507686
$86$	7.50493	0.809277
$87$	0.590233	0.0632797
$88$	−1.02609	−0.109382
$89$	−9.56770	−1.01417	−0.507087	−	0.861895i	$-0.669278\pi$
$89$	−9.56770	−1.01417	−0.507087	+	0.861895i	$0.669278\pi$
$90$	2.14727	0.226343
$91$	−1.92486	−0.201780
$92$	3.54402	0.369490
$93$	6.88920	0.714377
$94$	21.0892	2.17519
$95$	−6.21662	−0.637812
$96$	5.04870	0.515281
$97$	−7.26277	−0.737422	−0.368711	−	0.929544i	$-0.620201\pi$
$97$	−7.26277	−0.737422	−0.368711	+	0.929544i	$0.620201\pi$
$98$	−8.23409	−0.831769
$99$	0.329184	0.0330842
$100$	−13.8530	−1.38530
$101$	−0.430627	−0.0428490	−0.0214245	−	0.999770i	$-0.506820\pi$
$101$	−0.430627	−0.0428490	−0.0214245	+	0.999770i	$0.506820\pi$
$102$	−11.6574	−1.15425
$103$	−3.66768	−0.361387	−0.180694	−	0.983539i	$-0.557834\pi$
$103$	−3.66768	−0.361387	−0.180694	+	0.983539i	$0.557834\pi$
$104$	−1.84630	−0.181045
$105$	3.01745	0.294473
$106$	5.65302	0.549070
$107$	16.7726	1.62147	0.810736	−	0.585412i	$-0.199067\pi$
$107$	16.7726	1.62147	0.810736	+	0.585412i	$0.199067\pi$
$108$	3.34790	0.322152
$109$	1.71654	0.164414	0.0822072	−	0.996615i	$-0.473803\pi$
$109$	1.71654	0.164414	0.0822072	+	0.996615i	$0.473803\pi$
$110$	0.706848	0.0673953
$111$	4.96412	0.471173
$112$	−1.66586	−0.157409
$113$	7.43766	0.699676	0.349838	−	0.936810i	$-0.386237\pi$
$113$	7.43766	0.699676	0.349838	+	0.936810i	$0.386237\pi$
$114$	−15.4828	−1.45010
$115$	−0.982925	−0.0916582
$116$	1.97604	0.183471
$117$	0.592318	0.0547598
$118$	−30.1413	−2.77473
$119$	−16.3815	−1.50169
$120$	2.89430	0.264213
$121$	−10.8916	−0.990149
$122$	−6.39665	−0.579126
$123$	2.02487	0.182576
$124$	23.0643	2.07124
$125$	8.48475	0.758899
$126$	7.51512	0.669500
$127$	−15.6791	−1.39129	−0.695647	−	0.718384i	$-0.744882\pi$
$127$	−15.6791	−1.39129	−0.695647	+	0.718384i	$0.744882\pi$
$128$	19.2735	1.70355
$129$	−3.24530	−0.285733
$130$	1.27187	0.111550
$131$	16.4766	1.43957	0.719783	−	0.694199i	$-0.244241\pi$
$131$	16.4766	1.43957	0.719783	+	0.694199i	$0.244241\pi$
$132$	1.10207	0.0959232
$133$	−21.7572	−1.88659
$134$	10.1021	0.872687
$135$	−0.928530	−0.0799152
$136$	−15.7129	−1.34737
$137$	2.22437	0.190040	0.0950202	−	0.995475i	$-0.469708\pi$
$137$	2.22437	0.190040	0.0950202	+	0.995475i	$0.469708\pi$
$138$	−2.44802	−0.208390
$139$	−15.9264	−1.35086	−0.675431	−	0.737424i	$-0.736042\pi$
$139$	−15.9264	−1.35086	−0.675431	+	0.737424i	$0.736042\pi$
$140$	10.1021	0.853785
$141$	−9.11946	−0.767997
$142$	−24.9333	−2.09236
$143$	0.194982	0.0163052
$144$	0.512619	0.0427183
$145$	−0.548050	−0.0455130
$146$	19.7049	1.63079
$147$	3.56061	0.293674
$148$	16.6193	1.36610
$149$	8.64608	0.708315	0.354157	−	0.935186i	$-0.384768\pi$
$149$	8.64608	0.708315	0.354157	+	0.935186i	$0.384768\pi$
$150$	9.56895	0.781302
$151$	−8.72186	−0.709775	−0.354888	−	0.934909i	$-0.615481\pi$
$151$	−8.72186	−0.709775	−0.354888	+	0.934909i	$0.615481\pi$
$152$	−20.8692	−1.69272
$153$	5.04091	0.407533
$154$	2.47386	0.199349
$155$	−6.39683	−0.513806
$156$	1.98302	0.158769
$157$	20.4614	1.63300	0.816500	−	0.577345i	$-0.195911\pi$
$157$	20.4614	1.63300	0.816500	+	0.577345i	$0.195911\pi$
$158$	20.1141	1.60019
$159$	−2.44449	−0.193861
$160$	−4.68787	−0.370609
$161$	−3.44008	−0.271116
$162$	−2.31255	−0.181691
$163$	−12.1831	−0.954255	−0.477127	−	0.878834i	$-0.658322\pi$
$163$	−12.1831	−0.954255	−0.477127	+	0.878834i	$0.658322\pi$
$164$	6.77905	0.529355
$165$	−0.305657	−0.0237954
$166$	38.1900	2.96412
$167$	11.1113	0.859817	0.429909	−	0.902872i	$-0.358546\pi$
$167$	11.1113	0.859817	0.429909	+	0.902872i	$0.358546\pi$
$168$	10.1296	0.781516
$169$	−12.6492	−0.973012
$170$	10.8242	0.830179
$171$	6.69512	0.511989
$172$	−10.8649	−0.828443
$173$	12.4397	0.945773	0.472887	−	0.881123i	$-0.343212\pi$
$173$	12.4397	0.945773	0.472887	+	0.881123i	$0.343212\pi$
$174$	−1.36495	−0.103476
$175$	13.4467	1.01648
$176$	0.168746	0.0127197
$177$	13.0338	0.979680
$178$	22.1258	1.65840
$179$	14.8747	1.11179	0.555895	−	0.831253i	$-0.312376\pi$
$179$	14.8747	1.11179	0.555895	+	0.831253i	$0.312376\pi$
$180$	−3.10862	−0.231703
$181$	24.3264	1.80816	0.904082	−	0.427358i	$-0.140556\pi$
$181$	24.3264	1.80816	0.904082	+	0.427358i	$0.140556\pi$
$182$	4.45134	0.329955
$183$	2.76606	0.204473
$184$	−3.29968	−0.243256
$185$	−4.60933	−0.338885
$186$	−15.9316	−1.16816
$187$	1.65938	0.121346
$188$	−30.5310	−2.22670
$189$	−3.24971	−0.236382
$190$	14.3763	1.04296
$191$	−6.57252	−0.475571	−0.237786	−	0.971318i	$-0.576422\pi$
$191$	−6.57252	−0.475571	−0.237786	+	0.971318i	$0.576422\pi$
$192$	−12.7006	−0.916589
$193$	−11.0797	−0.797537	−0.398768	−	0.917052i	$-0.630562\pi$
$193$	−11.0797	−0.797537	−0.398768	+	0.917052i	$0.630562\pi$
$194$	16.7955	1.20585
$195$	−0.549985	−0.0393853
$196$	11.9205	0.851468
$197$	12.7008	0.904896	0.452448	−	0.891791i	$-0.350551\pi$
$197$	12.7008	0.904896	0.452448	+	0.891791i	$0.350551\pi$
$198$	−0.761254	−0.0541000
$199$	25.6610	1.81906	0.909529	−	0.415641i	$-0.136443\pi$
$199$	25.6610	1.81906	0.909529	+	0.415641i	$0.136443\pi$
$200$	12.8980	0.912023
$201$	−4.36837	−0.308121
$202$	0.995848	0.0700676
$203$	−1.91809	−0.134623
$204$	16.8764	1.18159
$205$	−1.88015	−0.131315
$206$	8.48170	0.590948
$207$	1.05858	0.0735765
$208$	0.303634	0.0210532
$209$	2.20393	0.152449
$210$	−6.97802	−0.481529
$211$	11.3992	0.784754	0.392377	−	0.919805i	$-0.371653\pi$
$211$	11.3992	0.784754	0.392377	+	0.919805i	$0.371653\pi$
$212$	−8.18391	−0.562073
$213$	10.7817	0.738753
$214$	−38.7876	−2.65147
$215$	3.01336	0.205509
$216$	−3.11708	−0.212091
$217$	−22.3879	−1.51979
$218$	−3.96958	−0.268854
$219$	−8.52084	−0.575785
$220$	−1.02331	−0.0689914
$221$	2.98582	0.200848
$222$	−11.4798	−0.770472
$223$	12.5424	0.839903	0.419952	−	0.907547i	$-0.362047\pi$
$223$	12.5424	0.839903	0.419952	+	0.907547i	$0.362047\pi$
$224$	−16.4068	−1.09623
$225$	−4.13783	−0.275855
$226$	−17.2000	−1.14413
$227$	19.9226	1.32231	0.661155	−	0.750249i	$-0.270067\pi$
$227$	19.9226	1.32231	0.661155	+	0.750249i	$0.270067\pi$
$228$	22.4146	1.48444
$229$	13.5469	0.895203	0.447601	−	0.894233i	$-0.352278\pi$
$229$	13.5469	0.895203	0.447601	+	0.894233i	$0.352278\pi$
$230$	2.27306	0.149881
$231$	−1.06975	−0.0703845
$232$	−1.83981	−0.120789
$233$	17.5557	1.15011	0.575057	−	0.818114i	$-0.304980\pi$
$233$	17.5557	1.15011	0.575057	+	0.818114i	$0.304980\pi$
$234$	−1.36977	−0.0895444
$235$	8.46770	0.552372
$236$	43.6358	2.84045
$237$	−8.69778	−0.564981
$238$	37.8830	2.45559
$239$	−13.8290	−0.894526	−0.447263	−	0.894402i	$-0.647601\pi$
$239$	−13.8290	−0.894526	−0.447263	+	0.894402i	$0.647601\pi$
$240$	−0.475983	−0.0307245
$241$	−8.63516	−0.556239	−0.278120	−	0.960546i	$-0.589711\pi$
$241$	−8.63516	−0.556239	−0.278120	+	0.960546i	$0.589711\pi$
$242$	25.1875	1.61911
$243$	1.00000	0.0641500
$244$	9.26048	0.592841
$245$	−3.30613	−0.211221
$246$	−4.68261	−0.298552
$247$	3.96564	0.252328
$248$	−21.4742	−1.36361
$249$	−16.5142	−1.04655
$250$	−19.6214	−1.24097
$251$	−8.82566	−0.557071	−0.278535	−	0.960426i	$-0.589849\pi$
$251$	−8.82566	−0.557071	−0.278535	+	0.960426i	$0.589849\pi$
$252$	−10.8797	−0.685356
$253$	0.348468	0.0219080
$254$	36.2587	2.27507
$255$	−4.68063	−0.293113
$256$	−19.1696	−1.19810
$257$	−7.04530	−0.439474	−0.219737	−	0.975559i	$-0.570520\pi$
$257$	−7.04530	−0.439474	−0.219737	+	0.975559i	$0.570520\pi$
$258$	7.50493	0.467236
$259$	−16.1319	−1.00239
$260$	−1.84129	−0.114192
$261$	0.590233	0.0365345
$262$	−38.1030	−2.35401
$263$	19.9935	1.23285	0.616426	−	0.787413i	$-0.288580\pi$
$263$	19.9935	1.23285	0.616426	+	0.787413i	$0.288580\pi$
$264$	−1.02609	−0.0631516
$265$	2.26979	0.139432
$266$	50.3146	3.08499
$267$	−9.56770	−0.585534
$268$	−14.6248	−0.893355
$269$	20.4812	1.24876	0.624380	−	0.781121i	$-0.285352\pi$
$269$	20.4812	1.24876	0.624380	+	0.781121i	$0.285352\pi$
$270$	2.14727	0.130679
$271$	14.1482	0.859440	0.429720	−	0.902962i	$-0.358612\pi$
$271$	14.1482	0.859440	0.429720	+	0.902962i	$0.358612\pi$
$272$	2.58407	0.156682
$273$	−1.92486	−0.116498
$274$	−5.14396	−0.310758
$275$	−1.36211	−0.0821381
$276$	3.54402	0.213325
$277$	29.7316	1.78640	0.893200	−	0.449660i	$-0.148455\pi$
$277$	29.7316	1.78640	0.893200	+	0.449660i	$0.148455\pi$
$278$	36.8307	2.20896
$279$	6.88920	0.412446
$280$	−9.40565	−0.562095
$281$	−19.0490	−1.13637	−0.568184	−	0.822901i	$-0.692354\pi$
$281$	−19.0490	−1.13637	−0.568184	+	0.822901i	$0.692354\pi$
$282$	21.0892	1.25585
$283$	−16.9776	−1.00922	−0.504608	−	0.863348i	$-0.668363\pi$
$283$	−16.9776	−1.00922	−0.504608	+	0.863348i	$0.668363\pi$
$284$	36.0962	2.14191
$285$	−6.21662	−0.368241
$286$	−0.450905	−0.0266626
$287$	−6.58023	−0.388419
$288$	5.04870	0.297498
$289$	8.41074	0.494749
$290$	1.26739	0.0744239
$291$	−7.26277	−0.425751
$292$	−28.5269	−1.66941
$293$	−11.3650	−0.663950	−0.331975	−	0.943288i	$-0.607715\pi$
$293$	−11.3650	−0.663950	−0.331975	+	0.943288i	$0.607715\pi$
$294$	−8.23409	−0.480222
$295$	−12.1023	−0.704622
$296$	−15.4736	−0.899382
$297$	0.329184	0.0191012
$298$	−19.9945	−1.15825
$299$	0.627017	0.0362613
$300$	−13.8530	−0.799805
$301$	10.5463	0.607878
$302$	20.1698	1.16064
$303$	−0.430627	−0.0247389
$304$	3.43205	0.196842
$305$	−2.56837	−0.147064
$306$	−11.6574	−0.666407
$307$	−22.0290	−1.25726	−0.628630	−	0.777705i	$-0.716384\pi$
$307$	−22.0290	−1.25726	−0.628630	+	0.777705i	$0.716384\pi$
$308$	−3.58142	−0.204070
$309$	−3.66768	−0.208647
$310$	14.7930	0.840186
$311$	−11.5856	−0.656960	−0.328480	−	0.944511i	$-0.606536\pi$
$311$	−11.5856	−0.656960	−0.328480	+	0.944511i	$0.606536\pi$
$312$	−1.84630	−0.104526
$313$	21.5529	1.21824	0.609122	−	0.793076i	$-0.291522\pi$
$313$	21.5529	1.21824	0.609122	+	0.793076i	$0.291522\pi$
$314$	−47.3181	−2.67032
$315$	3.01745	0.170014
$316$	−29.1193	−1.63809
$317$	10.1380	0.569405	0.284702	−	0.958616i	$-0.408105\pi$
$317$	10.1380	0.569405	0.284702	+	0.958616i	$0.408105\pi$
$318$	5.65302	0.317005
$319$	0.194295	0.0108784
$320$	11.7929	0.659244
$321$	16.7726	0.936157
$322$	7.95537	0.443335
$323$	33.7495	1.87787
$324$	3.34790	0.185994
$325$	−2.45091	−0.135952
$326$	28.1741	1.56042
$327$	1.71654	0.0949247
$328$	−6.31168	−0.348504
$329$	29.6356	1.63386
$330$	0.706848	0.0389107
$331$	−17.5544	−0.964878	−0.482439	−	0.875930i	$-0.660249\pi$
$331$	−17.5544	−0.964878	−0.482439	+	0.875930i	$0.660249\pi$
$332$	−55.2880	−3.03432
$333$	4.96412	0.272032
$334$	−25.6954	−1.40599
$335$	4.05616	0.221612
$336$	−1.66586	−0.0908803
$337$	−19.6132	−1.06840	−0.534200	−	0.845358i	$-0.679387\pi$
$337$	−19.6132	−1.06840	−0.534200	+	0.845358i	$0.679387\pi$
$338$	29.2518	1.59109
$339$	7.43766	0.403958
$340$	−15.6703	−0.849840
$341$	2.26781	0.122809
$342$	−15.4828	−0.837215
$343$	11.1770	0.603503
$344$	10.1159	0.545411
$345$	−0.982925	−0.0529189
$346$	−28.7675	−1.54655
$347$	−8.10287	−0.434985	−0.217492	−	0.976062i	$-0.569788\pi$
$347$	−8.10287	−0.434985	−0.217492	+	0.976062i	$0.569788\pi$
$348$	1.97604	0.105927
$349$	31.3368	1.67742	0.838711	−	0.544577i	$-0.183310\pi$
$349$	31.3368	1.67742	0.838711	+	0.544577i	$0.183310\pi$
$350$	−31.0963	−1.66217
$351$	0.592318	0.0316156
$352$	1.66195	0.0885823
$353$	35.9622	1.91407	0.957037	−	0.289967i	$-0.0936444\pi$
$353$	35.9622	1.91407	0.957037	+	0.289967i	$0.0936444\pi$
$354$	−30.1413	−1.60199
$355$	−10.0112	−0.531338
$356$	−32.0317	−1.69767
$357$	−16.3815	−0.867000
$358$	−34.3986	−1.81802
$359$	−22.3657	−1.18041	−0.590207	−	0.807252i	$-0.700954\pi$
$359$	−22.3657	−1.18041	−0.590207	+	0.807252i	$0.700954\pi$
$360$	2.89430	0.152543
$361$	25.8247	1.35919
$362$	−56.2560	−2.95675
$363$	−10.8916	−0.571663
$364$	−6.44424	−0.337770
$365$	7.91186	0.414126
$366$	−6.39665	−0.334358
$367$	25.8926	1.35158	0.675792	−	0.737093i	$-0.263802\pi$
$367$	25.8926	1.35158	0.675792	+	0.737093i	$0.263802\pi$
$368$	0.542649	0.0282876
$369$	2.02487	0.105410
$370$	10.6593	0.554152
$371$	7.94389	0.412426
$372$	23.0643	1.19583
$373$	−4.84291	−0.250756	−0.125378	−	0.992109i	$-0.540014\pi$
$373$	−4.84291	−0.250756	−0.125378	+	0.992109i	$0.540014\pi$
$374$	−3.83741	−0.198428
$375$	8.48475	0.438151
$376$	28.4261	1.46596
$377$	0.349606	0.0180056
$378$	7.51512	0.386536
$379$	33.5281	1.72223	0.861113	−	0.508414i	$-0.169768\pi$
$379$	33.5281	1.72223	0.861113	+	0.508414i	$0.169768\pi$
$380$	−20.8126	−1.06766
$381$	−15.6791	−0.803264
$382$	15.1993	0.777664
$383$	2.38160	0.121694	0.0608470	−	0.998147i	$-0.480620\pi$
$383$	2.38160	0.121694	0.0608470	+	0.998147i	$0.480620\pi$
$384$	19.2735	0.983545
$385$	0.993296	0.0506231
$386$	25.6225	1.30415
$387$	−3.24530	−0.164968
$388$	−24.3150	−1.23441
$389$	−3.60770	−0.182918	−0.0914588	−	0.995809i	$-0.529153\pi$
$389$	−3.60770	−0.182918	−0.0914588	+	0.995809i	$0.529153\pi$
$390$	1.27187	0.0644036
$391$	5.33621	0.269864
$392$	−11.0987	−0.560569
$393$	16.4766	0.831134
$394$	−29.3713	−1.47971
$395$	8.07615	0.406355
$396$	1.10207	0.0553813
$397$	−32.2859	−1.62038	−0.810192	−	0.586165i	$-0.800637\pi$
$397$	−32.2859	−1.62038	−0.810192	+	0.586165i	$0.800637\pi$
$398$	−59.3423	−2.97456
$399$	−21.7572	−1.08922
$400$	−2.12113	−0.106057
$401$	−37.4388	−1.86960	−0.934802	−	0.355169i	$-0.884423\pi$
$401$	−37.4388	−1.86960	−0.934802	+	0.355169i	$0.884423\pi$
$402$	10.1021	0.503846
$403$	4.08060	0.203269
$404$	−1.44170	−0.0717270
$405$	−0.928530	−0.0461390
$406$	4.43568	0.220139
$407$	1.63411	0.0809996
$408$	−15.7129	−0.777905
$409$	−24.9644	−1.23441	−0.617204	−	0.786803i	$-0.711735\pi$
$409$	−24.9644	−1.23441	−0.617204	+	0.786803i	$0.711735\pi$
$410$	4.34795	0.214730
$411$	2.22437	0.109720
$412$	−12.2790	−0.604943
$413$	−42.3560	−2.08420
$414$	−2.44802	−0.120314
$415$	15.3340	0.752715
$416$	2.99044	0.146618
$417$	−15.9264	−0.779920
$418$	−5.09669	−0.249287
$419$	−3.42259	−0.167205	−0.0836023	−	0.996499i	$-0.526643\pi$
$419$	−3.42259	−0.167205	−0.0836023	+	0.996499i	$0.526643\pi$
$420$	10.1021	0.492933
$421$	−28.8837	−1.40770	−0.703852	−	0.710347i	$-0.748538\pi$
$421$	−28.8837	−1.40770	−0.703852	+	0.710347i	$0.748538\pi$
$422$	−26.3613	−1.28325
$423$	−9.11946	−0.443403
$424$	7.61968	0.370045
$425$	−20.8584	−1.01178
$426$	−24.9333	−1.20802
$427$	−8.98888	−0.435003
$428$	56.1531	2.71426
$429$	0.194982	0.00941380
$430$	−6.96855	−0.336053
$431$	−11.3464	−0.546535	−0.273268	−	0.961938i	$-0.588104\pi$
$431$	−11.3464	−0.546535	−0.273268	+	0.961938i	$0.588104\pi$
$432$	0.512619	0.0246634
$433$	−28.3926	−1.36446	−0.682231	−	0.731136i	$-0.738990\pi$
$433$	−28.3926	−1.36446	−0.682231	+	0.731136i	$0.738990\pi$
$434$	51.7732	2.48519
$435$	−0.548050	−0.0262770
$436$	5.74679	0.275221
$437$	7.08733	0.339033
$438$	19.7049	0.941536
$439$	25.6181	1.22268	0.611342	−	0.791367i	$-0.290630\pi$
$439$	25.6181	1.22268	0.611342	+	0.791367i	$0.290630\pi$
$440$	0.952758	0.0454209
$441$	3.56061	0.169553
$442$	−6.90486	−0.328431
$443$	1.65430	0.0785982	0.0392991	−	0.999227i	$-0.487487\pi$
$443$	1.65430	0.0785982	0.0392991	+	0.999227i	$0.487487\pi$
$444$	16.6193	0.788719
$445$	8.88390	0.421137
$446$	−29.0050	−1.37343
$447$	8.64608	0.408946
$448$	41.2733	1.94998
$449$	−6.57901	−0.310483	−0.155241	−	0.987877i	$-0.549616\pi$
$449$	−6.57901	−0.310483	−0.155241	+	0.987877i	$0.549616\pi$
$450$	9.56895	0.451085
$451$	0.666553	0.0313868
$452$	24.9005	1.17122
$453$	−8.72186	−0.409789
$454$	−46.0721	−2.16227
$455$	1.78729	0.0837895
$456$	−20.8692	−0.977292
$457$	23.3278	1.09123	0.545614	−	0.838036i	$-0.316296\pi$
$457$	23.3278	1.09123	0.545614	+	0.838036i	$0.316296\pi$
$458$	−31.3279	−1.46385
$459$	5.04091	0.235289
$460$	−3.29073	−0.153431
$461$	22.8739	1.06535	0.532673	−	0.846321i	$-0.321188\pi$
$461$	22.8739	1.06535	0.532673	+	0.846321i	$0.321188\pi$
$462$	2.47386	0.115094
$463$	42.6388	1.98160	0.990798	−	0.135351i	$-0.0432163\pi$
$463$	42.6388	1.98160	0.990798	+	0.135351i	$0.0432163\pi$
$464$	0.302565	0.0140462
$465$	−6.39683	−0.296646
$466$	−40.5985	−1.88069
$467$	−33.3107	−1.54144	−0.770718	−	0.637176i	$-0.780102\pi$
$467$	−33.3107	−1.54144	−0.770718	+	0.637176i	$0.780102\pi$
$468$	1.98302	0.0916651
$469$	14.1959	0.655507
$470$	−19.5820	−0.903250
$471$	20.4614	0.942813
$472$	−40.6274	−1.87003
$473$	−1.06830	−0.0491205
$474$	20.1141	0.923870
$475$	−27.7033	−1.27111
$476$	−54.8435	−2.51375
$477$	−2.44449	−0.111926
$478$	31.9804	1.46275
$479$	28.7595	1.31406	0.657029	−	0.753866i	$-0.271813\pi$
$479$	28.7595	1.31406	0.657029	+	0.753866i	$0.271813\pi$
$480$	−4.68787	−0.213971
$481$	2.94034	0.134068
$482$	19.9692	0.909574
$483$	−3.44008	−0.156529
$484$	−36.4641	−1.65746
$485$	6.74370	0.306216
$486$	−2.31255	−0.104899
$487$	−38.8545	−1.76066	−0.880332	−	0.474359i	$-0.842680\pi$
$487$	−38.8545	−1.76066	−0.880332	+	0.474359i	$0.842680\pi$
$488$	−8.62203	−0.390301
$489$	−12.1831	−0.550939
$490$	7.64560	0.345393
$491$	24.6901	1.11425	0.557125	−	0.830429i	$-0.311904\pi$
$491$	24.6901	1.11425	0.557125	+	0.830429i	$0.311904\pi$
$492$	6.77905	0.305623
$493$	2.97531	0.134001
$494$	−9.17075	−0.412612
$495$	−0.305657	−0.0137383
$496$	3.53154	0.158571
$497$	−35.0375	−1.57165
$498$	38.1900	1.71134
$499$	18.5909	0.832243	0.416121	−	0.909309i	$-0.363389\pi$
$499$	18.5909	0.832243	0.416121	+	0.909309i	$0.363389\pi$
$500$	28.4061	1.27036
$501$	11.1113	0.496416
$502$	20.4098	0.910934
$503$	38.6183	1.72191	0.860953	−	0.508684i	$-0.169868\pi$
$503$	38.6183	1.72191	0.860953	+	0.508684i	$0.169868\pi$
$504$	10.1296	0.451209
$505$	0.399850	0.0177931
$506$	−0.805850	−0.0358244
$507$	−12.6492	−0.561769
$508$	−52.4920	−2.32896
$509$	−34.6349	−1.53517	−0.767583	−	0.640949i	$-0.778541\pi$
$509$	−34.6349	−1.53517	−0.767583	+	0.640949i	$0.778541\pi$
$510$	10.8242	0.479304
$511$	27.6903	1.22494
$512$	5.78382	0.255611
$513$	6.69512	0.295597
$514$	16.2926	0.718637
$515$	3.40555	0.150066
$516$	−10.8649	−0.478302
$517$	−3.00198	−0.132027
$518$	37.3059	1.63913
$519$	12.4397	0.546042
$520$	1.71435	0.0751792
$521$	36.1963	1.58579	0.792895	−	0.609358i	$-0.208573\pi$
$521$	36.1963	1.58579	0.792895	+	0.609358i	$0.208573\pi$
$522$	−1.36495	−0.0597420
$523$	31.6423	1.38362	0.691810	−	0.722080i	$-0.256814\pi$
$523$	31.6423	1.38362	0.691810	+	0.722080i	$0.256814\pi$
$524$	55.1619	2.40976
$525$	13.4467	0.586864
$526$	−46.2360	−2.01599
$527$	34.7278	1.51277
$528$	0.168746	0.00734373
$529$	−21.8794	−0.951279
$530$	−5.24900	−0.228002
$531$	13.0338	0.565619
$532$	−72.8409	−3.15805
$533$	1.19937	0.0519503
$534$	22.1258	0.957477
$535$	−15.5739	−0.673318
$536$	13.6166	0.588146
$537$	14.8747	0.641892
$538$	−47.3638	−2.04200
$539$	1.17209	0.0504857
$540$	−3.10862	−0.133774
$541$	39.7790	1.71023	0.855116	−	0.518437i	$-0.173486\pi$
$541$	39.7790	1.71023	0.855116	+	0.518437i	$0.173486\pi$
$542$	−32.7184	−1.40538
$543$	24.3264	1.04394
$544$	25.4500	1.09116
$545$	−1.59386	−0.0682733
$546$	4.45134	0.190500
$547$	7.98586	0.341451	0.170725	−	0.985319i	$-0.445389\pi$
$547$	7.98586	0.341451	0.170725	+	0.985319i	$0.445389\pi$
$548$	7.44695	0.318118
$549$	2.76606	0.118052
$550$	3.14994	0.134314
$551$	3.95169	0.168347
$552$	−3.29968	−0.140444
$553$	28.2652	1.20196
$554$	−68.7559	−2.92116
$555$	−4.60933	−0.195655
$556$	−53.3200	−2.26127
$557$	−11.3152	−0.479440	−0.239720	−	0.970842i	$-0.577056\pi$
$557$	−11.3152	−0.479440	−0.239720	+	0.970842i	$0.577056\pi$
$558$	−15.9316	−0.674440
$559$	−1.92225	−0.0813025
$560$	1.54680	0.0653644
$561$	1.65938	0.0700593
$562$	44.0518	1.85821
$563$	1.36551	0.0575495	0.0287747	−	0.999586i	$-0.490839\pi$
$563$	1.36551	0.0575495	0.0287747	+	0.999586i	$0.490839\pi$
$564$	−30.5310	−1.28559
$565$	−6.90609	−0.290541
$566$	39.2617	1.65029
$567$	−3.24971	−0.136475
$568$	−33.6076	−1.41014
$569$	39.6985	1.66425	0.832123	−	0.554591i	$-0.187125\pi$
$569$	39.6985	1.66425	0.832123	+	0.554591i	$0.187125\pi$
$570$	14.3763	0.602155
$571$	−36.3322	−1.52045	−0.760227	−	0.649658i	$-0.774912\pi$
$571$	−36.3322	−1.52045	−0.760227	+	0.649658i	$0.774912\pi$
$572$	0.652778	0.0272940
$573$	−6.57252	−0.274571
$574$	15.2171	0.635150
$575$	−4.38023	−0.182668
$576$	−12.7006	−0.529193
$577$	−26.6785	−1.11064	−0.555320	−	0.831636i	$-0.687404\pi$
$577$	−26.6785	−1.11064	−0.555320	+	0.831636i	$0.687404\pi$
$578$	−19.4503	−0.809024
$579$	−11.0797	−0.460458
$580$	−1.83481	−0.0761865
$581$	53.6665	2.22646
$582$	16.7955	0.696197
$583$	−0.804687	−0.0333267
$584$	26.5602	1.09907
$585$	−0.549985	−0.0227391
$586$	26.2821	1.08571
$587$	−8.35755	−0.344953	−0.172476	−	0.985014i	$-0.555177\pi$
$587$	−8.35755	−0.344953	−0.172476	+	0.985014i	$0.555177\pi$
$588$	11.9205	0.491595
$589$	46.1240	1.90051
$590$	27.9871	1.15221
$591$	12.7008	0.522442
$592$	2.54470	0.104587
$593$	−5.85647	−0.240496	−0.120248	−	0.992744i	$-0.538369\pi$
$593$	−5.85647	−0.240496	−0.120248	+	0.992744i	$0.538369\pi$
$594$	−0.761254	−0.0312346
$595$	15.2107	0.623578
$596$	28.9462	1.18568
$597$	25.6610	1.05023
$598$	−1.45001	−0.0592953
$599$	−4.33484	−0.177117	−0.0885585	−	0.996071i	$-0.528226\pi$
$599$	−4.33484	−0.177117	−0.0885585	+	0.996071i	$0.528226\pi$
$600$	12.8980	0.526557
$601$	45.6906	1.86376	0.931879	−	0.362769i	$-0.118168\pi$
$601$	45.6906	1.86376	0.931879	+	0.362769i	$0.118168\pi$
$602$	−24.3888	−0.994014
$603$	−4.36837	−0.177894
$604$	−29.1999	−1.18813
$605$	10.1132	0.411161
$606$	0.995848	0.0404535
$607$	28.7358	1.16635	0.583176	−	0.812346i	$-0.301810\pi$
$607$	28.7358	1.16635	0.583176	+	0.812346i	$0.301810\pi$
$608$	33.8017	1.37084
$609$	−1.91809	−0.0777248
$610$	5.93949	0.240483
$611$	−5.40162	−0.218526
$612$	16.8764	0.682189
$613$	1.26956	0.0512771	0.0256386	−	0.999671i	$-0.491838\pi$
$613$	1.26956	0.0512771	0.0256386	+	0.999671i	$0.491838\pi$
$614$	50.9431	2.05590
$615$	−1.88015	−0.0758150
$616$	3.33450	0.134351
$617$	−43.3083	−1.74353	−0.871764	−	0.489926i	$-0.837024\pi$
$617$	−43.3083	−1.74353	−0.871764	+	0.489926i	$0.837024\pi$
$618$	8.48170	0.341184
$619$	−7.44639	−0.299296	−0.149648	−	0.988739i	$-0.547814\pi$
$619$	−7.44639	−0.299296	−0.149648	+	0.988739i	$0.547814\pi$
$620$	−21.4159	−0.860085
$621$	1.05858	0.0424794
$622$	26.7924	1.07428
$623$	31.0922	1.24568
$624$	0.303634	0.0121551
$625$	12.8108	0.512432
$626$	−49.8423	−1.99210
$627$	2.20393	0.0880163
$628$	68.5028	2.73356
$629$	25.0236	0.997758
$630$	−6.97802	−0.278011
$631$	12.5424	0.499305	0.249652	−	0.968336i	$-0.419684\pi$
$631$	12.5424	0.499305	0.249652	+	0.968336i	$0.419684\pi$
$632$	27.1117	1.07844
$633$	11.3992	0.453078
$634$	−23.4446	−0.931103
$635$	14.5585	0.577737
$636$	−8.18391	−0.324513
$637$	2.10901	0.0835621
$638$	−0.449318	−0.0177887
$639$	10.7817	0.426519
$640$	−17.8960	−0.707401
$641$	−0.595559	−0.0235232	−0.0117616	−	0.999931i	$-0.503744\pi$
$641$	−0.595559	−0.0235232	−0.0117616	+	0.999931i	$0.503744\pi$
$642$	−38.7876	−1.53082
$643$	31.9998	1.26195	0.630975	−	0.775803i	$-0.282655\pi$
$643$	31.9998	1.26195	0.630975	+	0.775803i	$0.282655\pi$
$644$	−11.5170	−0.453835
$645$	3.01336	0.118651
$646$	−78.0474	−3.07074
$647$	−23.6441	−0.929544	−0.464772	−	0.885430i	$-0.653864\pi$
$647$	−23.6441	−0.929544	−0.464772	+	0.885430i	$0.653864\pi$
$648$	−3.11708	−0.122451
$649$	4.29051	0.168417
$650$	5.66786	0.222312
$651$	−22.3879	−0.877451
$652$	−40.7878	−1.59737
$653$	−1.15161	−0.0450660	−0.0225330	−	0.999746i	$-0.507173\pi$
$653$	−1.15161	−0.0450660	−0.0225330	+	0.999746i	$0.507173\pi$
$654$	−3.96958	−0.155223
$655$	−15.2990	−0.597782
$656$	1.03799	0.0405266
$657$	−8.52084	−0.332430
$658$	−68.5339	−2.67173
$659$	1.09090	0.0424953	0.0212477	−	0.999774i	$-0.493236\pi$
$659$	1.09090	0.0424953	0.0212477	+	0.999774i	$0.493236\pi$
$660$	−1.02331	−0.0398322
$661$	27.7406	1.07898	0.539491	−	0.841991i	$-0.318617\pi$
$661$	27.7406	1.07898	0.539491	+	0.841991i	$0.318617\pi$
$662$	40.5955	1.57779
$663$	2.98582	0.115960
$664$	51.4762	1.99767
$665$	20.2022	0.783408
$666$	−11.4798	−0.444832
$667$	0.624810	0.0241927
$668$	37.1994	1.43929
$669$	12.5424	0.484918
$670$	−9.38009	−0.362384
$671$	0.910541	0.0351511
$672$	−16.4068	−0.632907
$673$	−28.8760	−1.11309	−0.556544	−	0.830818i	$-0.687873\pi$
$673$	−28.8760	−1.11309	−0.556544	+	0.830818i	$0.687873\pi$
$674$	45.3566	1.74707
$675$	−4.13783	−0.159265
$676$	−42.3481	−1.62877
$677$	−6.20083	−0.238317	−0.119159	−	0.992875i	$-0.538020\pi$
$677$	−6.20083	−0.238317	−0.119159	+	0.992875i	$0.538020\pi$
$678$	−17.2000	−0.660561
$679$	23.6019	0.905757
$680$	14.5899	0.559498
$681$	19.9226	0.763436
$682$	−5.24444	−0.200820
$683$	−17.1804	−0.657389	−0.328694	−	0.944436i	$-0.606609\pi$
$683$	−17.1804	−0.657389	−0.328694	+	0.944436i	$0.606609\pi$
$684$	22.4146	0.857043
$685$	−2.06539	−0.0789146
$686$	−25.8475	−0.986860
$687$	13.5469	0.516846
$688$	−1.66360	−0.0634243
$689$	−1.44792	−0.0551613
$690$	2.27306	0.0865341
$691$	7.60567	0.289333	0.144667	−	0.989480i	$-0.453789\pi$
$691$	7.60567	0.289333	0.144667	+	0.989480i	$0.453789\pi$
$692$	41.6468	1.58318
$693$	−1.06975	−0.0406365
$694$	18.7383	0.711296
$695$	14.7882	0.560947
$696$	−1.83981	−0.0697377
$697$	10.2072	0.386624
$698$	−72.4680	−2.74296
$699$	17.5557	0.664018
$700$	45.0183	1.70153
$701$	−14.7751	−0.558048	−0.279024	−	0.960284i	$-0.590011\pi$
$701$	−14.7751	−0.558048	−0.279024	+	0.960284i	$0.590011\pi$
$702$	−1.36977	−0.0516985
$703$	33.2354	1.25350
$704$	−4.18084	−0.157571
$705$	8.46770	0.318912
$706$	−83.1644	−3.12993
$707$	1.39941	0.0526303
$708$	43.6358	1.63993
$709$	41.7805	1.56910	0.784549	−	0.620067i	$-0.212895\pi$
$709$	41.7805	1.56910	0.784549	+	0.620067i	$0.212895\pi$
$710$	23.1514	0.868855
$711$	−8.69778	−0.326192
$712$	29.8233	1.11768
$713$	7.29278	0.273117
$714$	37.8830	1.41774
$715$	−0.181046	−0.00677074
$716$	49.7990	1.86108
$717$	−13.8290	−0.516455
$718$	51.7218	1.93024
$719$	25.0183	0.933025	0.466512	−	0.884515i	$-0.345510\pi$
$719$	25.0183	0.933025	0.466512	+	0.884515i	$0.345510\pi$
$720$	−0.475983	−0.0177388
$721$	11.9189	0.443882
$722$	−59.7209	−2.22258
$723$	−8.63516	−0.321145
$724$	81.4422	3.02677
$725$	−2.44229	−0.0907043
$726$	25.1875	0.934795
$727$	−42.3832	−1.57191	−0.785954	−	0.618286i	$-0.787828\pi$
$727$	−42.3832	−1.57191	−0.785954	+	0.618286i	$0.787828\pi$
$728$	5.99995	0.222373
$729$	1.00000	0.0370370
$730$	−18.2966	−0.677187
$731$	−16.3593	−0.605069
$732$	9.26048	0.342277
$733$	−24.3296	−0.898633	−0.449316	−	0.893373i	$-0.648332\pi$
$733$	−24.3296	−0.898633	−0.449316	+	0.893373i	$0.648332\pi$
$734$	−59.8780	−2.21014
$735$	−3.30613	−0.121948
$736$	5.34446	0.197000
$737$	−1.43800	−0.0529693
$738$	−4.68261	−0.172369
$739$	48.9719	1.80146	0.900730	−	0.434379i	$-0.143032\pi$
$739$	48.9719	1.80146	0.900730	+	0.434379i	$0.143032\pi$
$740$	−15.4316	−0.567276
$741$	3.96564	0.145682
$742$	−18.3707	−0.674408
$743$	30.3889	1.11486	0.557431	−	0.830223i	$-0.311787\pi$
$743$	30.3889	1.11486	0.557431	+	0.830223i	$0.311787\pi$
$744$	−21.4742	−0.787282
$745$	−8.02815	−0.294129
$746$	11.1995	0.410042
$747$	−16.5142	−0.604225
$748$	5.55545	0.203127
$749$	−54.5062	−1.99161
$750$	−19.6214	−0.716473
$751$	−32.8909	−1.20021	−0.600103	−	0.799923i	$-0.704874\pi$
$751$	−32.8909	−1.20021	−0.600103	+	0.799923i	$0.704874\pi$
$752$	−4.67481	−0.170473
$753$	−8.82566	−0.321625
$754$	−0.808482	−0.0294432
$755$	8.09851	0.294735
$756$	−10.8797	−0.395690
$757$	5.44790	0.198007	0.0990037	−	0.995087i	$-0.468434\pi$
$757$	5.44790	0.198007	0.0990037	+	0.995087i	$0.468434\pi$
$758$	−77.5356	−2.81622
$759$	0.348468	0.0126486
$760$	19.3777	0.702904
$761$	33.4176	1.21139	0.605693	−	0.795698i	$-0.292896\pi$
$761$	33.4176	1.21139	0.605693	+	0.795698i	$0.292896\pi$
$762$	36.2587	1.31351
$763$	−5.57824	−0.201946
$764$	−22.0041	−0.796082
$765$	−4.68063	−0.169229
$766$	−5.50757	−0.198996
$767$	7.72016	0.278759
$768$	−19.1696	−0.691724
$769$	−18.0781	−0.651912	−0.325956	−	0.945385i	$-0.605686\pi$
$769$	−18.0781	−0.651912	−0.325956	+	0.945385i	$0.605686\pi$
$770$	−2.29705	−0.0827799
$771$	−7.04530	−0.253730
$772$	−37.0938	−1.33504
$773$	3.49042	0.125542	0.0627708	−	0.998028i	$-0.480006\pi$
$773$	3.49042	0.125542	0.0627708	+	0.998028i	$0.480006\pi$
$774$	7.50493	0.269759
$775$	−28.5064	−1.02398
$776$	22.6386	0.812680
$777$	−16.1319	−0.578730
$778$	8.34299	0.299111
$779$	13.5567	0.485720
$780$	−1.84129	−0.0659289
$781$	3.54917	0.126999
$782$	−12.3403	−0.441287
$783$	0.590233	0.0210932
$784$	1.82524	0.0651870
$785$	−18.9991	−0.678105
$786$	−38.1030	−1.35909
$787$	20.0843	0.715927	0.357964	−	0.933735i	$-0.383471\pi$
$787$	20.0843	0.715927	0.357964	+	0.933735i	$0.383471\pi$
$788$	42.5210	1.51475
$789$	19.9935	0.711788
$790$	−18.6765	−0.664481
$791$	−24.1702	−0.859394
$792$	−1.02609	−0.0364606
$793$	1.63839	0.0581808
$794$	74.6628	2.64968
$795$	2.26979	0.0805010
$796$	85.9103	3.04501
$797$	−15.1326	−0.536025	−0.268012	−	0.963415i	$-0.586367\pi$
$797$	−15.1326	−0.536025	−0.268012	+	0.963415i	$0.586367\pi$
$798$	50.3146	1.78112
$799$	−45.9703	−1.62631
$800$	−20.8907	−0.738597
$801$	−9.56770	−0.338058
$802$	86.5792	3.05722
$803$	−2.80492	−0.0989836
$804$	−14.6248	−0.515779
$805$	3.19422	0.112581
$806$	−9.43660	−0.332390
$807$	20.4812	0.720971
$808$	1.34230	0.0472219
$809$	26.0121	0.914537	0.457268	−	0.889329i	$-0.348828\pi$
$809$	26.0121	0.914537	0.457268	+	0.889329i	$0.348828\pi$
$810$	2.14727	0.0754475
$811$	24.4631	0.859015	0.429508	−	0.903063i	$-0.358687\pi$
$811$	24.4631	0.859015	0.429508	+	0.903063i	$0.358687\pi$
$812$	−6.42156	−0.225352
$813$	14.1482	0.496198
$814$	−3.77896	−0.132452
$815$	11.3124	0.396256
$816$	2.58407	0.0904604
$817$	−21.7277	−0.760156
$818$	57.7314	2.01853
$819$	−1.92486	−0.0672601
$820$	−6.29455	−0.219815
$821$	30.7733	1.07400	0.536999	−	0.843583i	$-0.319558\pi$
$821$	30.7733	1.07400	0.536999	+	0.843583i	$0.319558\pi$
$822$	−5.14396	−0.179416
$823$	37.5909	1.31034	0.655169	−	0.755483i	$-0.272597\pi$
$823$	37.5909	1.31034	0.655169	+	0.755483i	$0.272597\pi$
$824$	11.4325	0.398268
$825$	−1.36211	−0.0474225
$826$	97.9506	3.40814
$827$	18.4607	0.641943	0.320971	−	0.947089i	$-0.395991\pi$
$827$	18.4607	0.641943	0.320971	+	0.947089i	$0.395991\pi$
$828$	3.54402	0.123163
$829$	−19.9588	−0.693199	−0.346599	−	0.938013i	$-0.612664\pi$
$829$	−19.9588	−0.693199	−0.346599	+	0.938013i	$0.612664\pi$
$830$	−35.4606	−1.23086
$831$	29.7316	1.03138
$832$	−7.52281	−0.260807
$833$	17.9487	0.621885
$834$	36.8307	1.27534
$835$	−10.3172	−0.357040
$836$	7.37851	0.255191
$837$	6.88920	0.238126
$838$	7.91492	0.273417
$839$	17.4732	0.603241	0.301621	−	0.953428i	$-0.402472\pi$
$839$	17.4732	0.603241	0.301621	+	0.953428i	$0.402472\pi$
$840$	−9.40565	−0.324526
$841$	−28.6516	−0.987987
$842$	66.7950	2.30191
$843$	−19.0490	−0.656083
$844$	38.1634	1.31364
$845$	11.7451	0.404045
$846$	21.0892	0.725063
$847$	35.3947	1.21617
$848$	−1.25309	−0.0430314
$849$	−16.9776	−0.582671
$850$	48.2362	1.65449
$851$	5.25492	0.180136
$852$	36.0962	1.23663
$853$	−30.0509	−1.02892	−0.514462	−	0.857513i	$-0.672008\pi$
$853$	−30.0509	−1.02892	−0.514462	+	0.857513i	$0.672008\pi$
$854$	20.7873	0.711325
$855$	−6.21662	−0.212604
$856$	−52.2817	−1.78695
$857$	−23.2400	−0.793862	−0.396931	−	0.917849i	$-0.629925\pi$
$857$	−23.2400	−0.793862	−0.396931	+	0.917849i	$0.629925\pi$
$858$	−0.450905	−0.0153936
$859$	34.7404	1.18533	0.592664	−	0.805449i	$-0.298076\pi$
$859$	34.7404	1.18533	0.592664	+	0.805449i	$0.298076\pi$
$860$	10.0884	0.344012
$861$	−6.58023	−0.224254
$862$	26.2391	0.893706
$863$	31.6433	1.07715	0.538574	−	0.842578i	$-0.318963\pi$
$863$	31.6433	1.07715	0.538574	+	0.842578i	$0.318963\pi$
$864$	5.04870	0.171760
$865$	−11.5506	−0.392734
$866$	65.6594	2.23120
$867$	8.41074	0.285644
$868$	−74.9524	−2.54405
$869$	−2.86317	−0.0971263
$870$	1.26739	0.0429687
$871$	−2.58746	−0.0876729
$872$	−5.35058	−0.181194
$873$	−7.26277	−0.245807
$874$	−16.3898	−0.554394
$875$	−27.5730	−0.932137
$876$	−28.5269	−0.963835
$877$	18.1891	0.614203	0.307101	−	0.951677i	$-0.400641\pi$
$877$	18.1891	0.614203	0.307101	+	0.951677i	$0.400641\pi$
$878$	−59.2431	−1.99936
$879$	−11.3650	−0.383332
$880$	−0.156686	−0.00528187
$881$	7.36015	0.247970	0.123985	−	0.992284i	$-0.460433\pi$
$881$	7.36015	0.247970	0.123985	+	0.992284i	$0.460433\pi$
$882$	−8.23409	−0.277256
$883$	26.0257	0.875835	0.437918	−	0.899015i	$-0.355716\pi$
$883$	26.0257	0.875835	0.437918	+	0.899015i	$0.355716\pi$
$884$	9.99622	0.336209
$885$	−12.1023	−0.406814
$886$	−3.82566	−0.128525
$887$	−18.0346	−0.605541	−0.302771	−	0.953063i	$-0.597912\pi$
$887$	−18.0346	−0.605541	−0.302771	+	0.953063i	$0.597912\pi$
$888$	−15.4736	−0.519258
$889$	50.9525	1.70889
$890$	−20.5445	−0.688652
$891$	0.329184	0.0110281
$892$	41.9908	1.40595
$893$	−61.0559	−2.04316
$894$	−19.9945	−0.668717
$895$	−13.8116	−0.461672
$896$	−62.6331	−2.09243
$897$	0.627017	0.0209355
$898$	15.2143	0.507708
$899$	4.06624	0.135617
$900$	−13.8530	−0.461768
$901$	−12.3225	−0.410521
$902$	−1.54144	−0.0513243
$903$	10.5463	0.350958
$904$	−23.1838	−0.771081
$905$	−22.5878	−0.750843
$906$	20.1698	0.670095
$907$	4.44167	0.147483	0.0737417	−	0.997277i	$-0.476506\pi$
$907$	4.44167	0.147483	0.0737417	+	0.997277i	$0.476506\pi$
$908$	66.6988	2.21348
$909$	−0.430627	−0.0142830
$910$	−4.13321	−0.137014
$911$	43.4322	1.43897	0.719487	−	0.694506i	$-0.244377\pi$
$911$	43.4322	1.43897	0.719487	+	0.694506i	$0.244377\pi$
$912$	3.43205	0.113647
$913$	−5.43622	−0.179913
$914$	−53.9468	−1.78440
$915$	−2.56837	−0.0849076
$916$	45.3535	1.49852
$917$	−53.5441	−1.76818
$918$	−11.6574	−0.384750
$919$	9.89761	0.326492	0.163246	−	0.986585i	$-0.447804\pi$
$919$	9.89761	0.326492	0.163246	+	0.986585i	$0.447804\pi$
$920$	3.06386	0.101012
$921$	−22.0290	−0.725879
$922$	−52.8972	−1.74208
$923$	6.38622	0.210205
$924$	−3.58142	−0.117820
$925$	−20.5407	−0.675373
$926$	−98.6046	−3.24035
$927$	−3.66768	−0.120462
$928$	2.97991	0.0978205
$929$	−2.08968	−0.0685600	−0.0342800	−	0.999412i	$-0.510914\pi$
$929$	−2.08968	−0.0685600	−0.0342800	+	0.999412i	$0.510914\pi$
$930$	14.7930	0.485082
$931$	23.8387	0.781282
$932$	58.7747	1.92523
$933$	−11.5856	−0.379296
$934$	77.0328	2.52059
$935$	−1.54079	−0.0503892
$936$	−1.84630	−0.0603483
$937$	59.4274	1.94141	0.970704	−	0.240279i	$-0.0772388\pi$
$937$	59.4274	1.94141	0.970704	+	0.240279i	$0.0772388\pi$
$938$	−32.8288	−1.07190
$939$	21.5529	0.703354
$940$	28.3490	0.924641
$941$	4.11122	0.134022	0.0670109	−	0.997752i	$-0.478654\pi$
$941$	4.11122	0.134022	0.0670109	+	0.997752i	$0.478654\pi$
$942$	−47.3181	−1.54171
$943$	2.14349	0.0698015
$944$	6.68138	0.217460
$945$	3.01745	0.0981577
$946$	2.47050	0.0803229
$947$	45.5446	1.48000	0.740000	−	0.672606i	$-0.234825\pi$
$947$	45.5446	1.48000	0.740000	+	0.672606i	$0.234825\pi$
$948$	−29.1193	−0.945750
$949$	−5.04705	−0.163834
$950$	64.0653	2.07855
$951$	10.1380	0.328746
$952$	51.0624	1.65494
$953$	−56.4212	−1.82766	−0.913830	−	0.406096i	$-0.866890\pi$
$953$	−56.4212	−1.82766	−0.913830	+	0.406096i	$0.866890\pi$
$954$	5.65302	0.183023
$955$	6.10279	0.197482
$956$	−46.2982	−1.49739
$957$	0.194295	0.00628067
$958$	−66.5080	−2.14877
$959$	−7.22854	−0.233422
$960$	11.7929	0.380615
$961$	16.4611	0.531003
$962$	−6.79968	−0.219230
$963$	16.7726	0.540491
$964$	−28.9096	−0.931116
$965$	10.2879	0.331178
$966$	7.95537	0.255960
$967$	−0.117202	−0.00376897	−0.00188449	−	0.999998i	$-0.500600\pi$
$967$	−0.117202	−0.00376897	−0.00188449	+	0.999998i	$0.500600\pi$
$968$	33.9501	1.09120
$969$	33.7495	1.08419
$970$	−15.5952	−0.500730
$971$	24.1737	0.775771	0.387886	−	0.921708i	$-0.373206\pi$
$971$	24.1737	0.775771	0.387886	+	0.921708i	$0.373206\pi$
$972$	3.34790	0.107384
$973$	51.7562	1.65923
$974$	89.8529	2.87907
$975$	−2.45091	−0.0784920
$976$	1.41793	0.0453870
$977$	−2.69919	−0.0863546	−0.0431773	−	0.999067i	$-0.513748\pi$
$977$	−2.69919	−0.0863546	−0.0431773	+	0.999067i	$0.513748\pi$
$978$	28.1741	0.900908
$979$	−3.14953	−0.100659
$980$	−11.0686	−0.353573
$981$	1.71654	0.0548048
$982$	−57.0972	−1.82205
$983$	−38.0701	−1.21425	−0.607123	−	0.794608i	$-0.707677\pi$
$983$	−38.0701	−1.21425	−0.607123	+	0.794608i	$0.707677\pi$
$984$	−6.31168	−0.201209
$985$	−11.7931	−0.375759
$986$	−6.88056	−0.219122
$987$	29.6356	0.943311
$988$	13.2766	0.422384
$989$	−3.43541	−0.109240
$990$	0.706848	0.0224651
$991$	−4.51631	−0.143465	−0.0717327	−	0.997424i	$-0.522853\pi$
$991$	−4.51631	−0.143465	−0.0717327	+	0.997424i	$0.522853\pi$
$992$	34.7815	1.10432
$993$	−17.5544	−0.557073
$994$	81.0261	2.56999
$995$	−23.8270	−0.755366
$996$	−55.2880	−1.75187
$997$	7.41126	0.234717	0.117358	−	0.993090i	$-0.462557\pi$
$997$	7.41126	0.234717	0.117358	+	0.993090i	$0.462557\pi$
$998$	−42.9924	−1.36090
$999$	4.96412	0.157058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.c.1.9	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.c.1.9	✓	92	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.31255 q^{2} +1.00000 q^{3} +3.34790 q^{4} -0.928530 q^{5} -2.31255 q^{6} -3.24971 q^{7} -3.11708 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.31255 q^{2} +1.00000 q^{3} +3.34790 q^{4} -0.928530 q^{5} -2.31255 q^{6} -3.24971 q^{7} -3.11708 q^{8} +1.00000 q^{9} +2.14727 q^{10} +0.329184 q^{11} +3.34790 q^{12} +0.592318 q^{13} +7.51512 q^{14} -0.928530 q^{15} +0.512619 q^{16} +5.04091 q^{17} -2.31255 q^{18} +6.69512 q^{19} -3.10862 q^{20} -3.24971 q^{21} -0.761254 q^{22} +1.05858 q^{23} -3.11708 q^{24} -4.13783 q^{25} -1.36977 q^{26} +1.00000 q^{27} -10.8797 q^{28} +0.590233 q^{29} +2.14727 q^{30} +6.88920 q^{31} +5.04870 q^{32} +0.329184 q^{33} -11.6574 q^{34} +3.01745 q^{35} +3.34790 q^{36} +4.96412 q^{37} -15.4828 q^{38} +0.592318 q^{39} +2.89430 q^{40} +2.02487 q^{41} +7.51512 q^{42} -3.24530 q^{43} +1.10207 q^{44} -0.928530 q^{45} -2.44802 q^{46} -9.11946 q^{47} +0.512619 q^{48} +3.56061 q^{49} +9.56895 q^{50} +5.04091 q^{51} +1.98302 q^{52} -2.44449 q^{53} -2.31255 q^{54} -0.305657 q^{55} +10.1296 q^{56} +6.69512 q^{57} -1.36495 q^{58} +13.0338 q^{59} -3.10862 q^{60} +2.76606 q^{61} -15.9316 q^{62} -3.24971 q^{63} -12.7006 q^{64} -0.549985 q^{65} -0.761254 q^{66} -4.36837 q^{67} +16.8764 q^{68} +1.05858 q^{69} -6.97802 q^{70} +10.7817 q^{71} -3.11708 q^{72} -8.52084 q^{73} -11.4798 q^{74} -4.13783 q^{75} +22.4146 q^{76} -1.06975 q^{77} -1.36977 q^{78} -8.69778 q^{79} -0.475983 q^{80} +1.00000 q^{81} -4.68261 q^{82} -16.5142 q^{83} -10.8797 q^{84} -4.68063 q^{85} +7.50493 q^{86} +0.590233 q^{87} -1.02609 q^{88} -9.56770 q^{89} +2.14727 q^{90} -1.92486 q^{91} +3.54402 q^{92} +6.88920 q^{93} +21.0892 q^{94} -6.21662 q^{95} +5.04870 q^{96} -7.26277 q^{97} -8.23409 q^{98} +0.329184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9}+O(q^{10}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9	\( 92 q + 17 q^{2} + 92 q^{3} + 107 q^{4} + 34 q^{5} + 17 q^{6} + 22 q^{7} + 51 q^{8} + 92 q^{9} + 13 q^{10} + 40 q^{11} + 107 q^{12} + 6 q^{13} + 37 q^{14} + 34 q^{15} + 133 q^{16} + 77 q^{17} + 17 q^{18} + 34 q^{19} + 55 q^{20} + 22 q^{21} + 8 q^{22} + 83 q^{23} + 51 q^{24} + 110 q^{25} + 22 q^{26} + 92 q^{27} + 32 q^{28} + 97 q^{29} + 13 q^{30} + 44 q^{31} + 104 q^{32} + 40 q^{33} + 20 q^{34} + 80 q^{35} + 107 q^{36} + 12 q^{37} + 54 q^{38} + 6 q^{39} + 23 q^{40} + 67 q^{41} + 37 q^{42} + 30 q^{43} + 87 q^{44} + 34 q^{45} + 33 q^{46} + 69 q^{47} + 133 q^{48} + 112 q^{49} + 58 q^{50} + 77 q^{51} - 3 q^{52} + 113 q^{53} + 17 q^{54} + 42 q^{55} + 92 q^{56} + 34 q^{57} - 30 q^{58} + 72 q^{59} + 55 q^{60} + 19 q^{61} + 60 q^{62} + 22 q^{63} + 147 q^{64} + 74 q^{65} + 8 q^{66} + 26 q^{67} + 171 q^{68} + 83 q^{69} - 35 q^{70} + 134 q^{71} + 51 q^{72} - 17 q^{73} + 95 q^{74} + 110 q^{75} + 27 q^{76} + 108 q^{77} + 22 q^{78} + 159 q^{79} + 79 q^{80} + 92 q^{81} - 64 q^{82} + 73 q^{83} + 32 q^{84} - 4 q^{85} + 22 q^{86} + 97 q^{87} - 16 q^{88} + 50 q^{89} + 13 q^{90} + 17 q^{91} + 154 q^{92} + 44 q^{93} + 8 q^{94} + 155 q^{95} + 104 q^{96} - 20 q^{97} + 63 q^{98} + 40 q^{99}+O(q^{100}) \) 92 * q + 17 * q^2 + 92 * q^3 + 107 * q^4 + 34 * q^5 + 17 * q^6 + 22 * q^7 + 51 * q^8 + 92 * q^9 + 13 * q^10 + 40 * q^11 + 107 * q^12 + 6 * q^13 + 37 * q^14 + 34 * q^15 + 133 * q^16 + 77 * q^17 + 17 * q^18 + 34 * q^19 + 55 * q^20 + 22 * q^21 + 8 * q^22 + 83 * q^23 + 51 * q^24 + 110 * q^25 + 22 * q^26 + 92 * q^27 + 32 * q^28 + 97 * q^29 + 13 * q^30 + 44 * q^31 + 104 * q^32 + 40 * q^33 + 20 * q^34 + 80 * q^35 + 107 * q^36 + 12 * q^37 + 54 * q^38 + 6 * q^39 + 23 * q^40 + 67 * q^41 + 37 * q^42 + 30 * q^43 + 87 * q^44 + 34 * q^45 + 33 * q^46 + 69 * q^47 + 133 * q^48 + 112 * q^49 + 58 * q^50 + 77 * q^51 - 3 * q^52 + 113 * q^53 + 17 * q^54 + 42 * q^55 + 92 * q^56 + 34 * q^57 - 30 * q^58 + 72 * q^59 + 55 * q^60 + 19 * q^61 + 60 * q^62 + 22 * q^63 + 147 * q^64 + 74 * q^65 + 8 * q^66 + 26 * q^67 + 171 * q^68 + 83 * q^69 - 35 * q^70 + 134 * q^71 + 51 * q^72 - 17 * q^73 + 95 * q^74 + 110 * q^75 + 27 * q^76 + 108 * q^77 + 22 * q^78 + 159 * q^79 + 79 * q^80 + 92 * q^81 - 64 * q^82 + 73 * q^83 + 32 * q^84 - 4 * q^85 + 22 * q^86 + 97 * q^87 - 16 * q^88 + 50 * q^89 + 13 * q^90 + 17 * q^91 + 154 * q^92 + 44 * q^93 + 8 * q^94 + 155 * q^95 + 104 * q^96 - 20 * q^97 + 63 * q^98 + 40 * q^99

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