LMFDB - Embedded newform 6002.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.43088 q^{3} +1.00000 q^{4} +1.76140 q^{5} +1.43088 q^{6} -2.51027 q^{7} -1.00000 q^{8} -0.952590 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.43088 q^{3} +1.00000 q^{4} +1.76140 q^{5} +1.43088 q^{6} -2.51027 q^{7} -1.00000 q^{8} -0.952590 q^{9} -1.76140 q^{10} +0.426115 q^{11} -1.43088 q^{12} +2.36812 q^{13} +2.51027 q^{14} -2.52034 q^{15} +1.00000 q^{16} +1.17786 q^{17} +0.952590 q^{18} +4.16191 q^{19} +1.76140 q^{20} +3.59188 q^{21} -0.426115 q^{22} +0.564874 q^{23} +1.43088 q^{24} -1.89748 q^{25} -2.36812 q^{26} +5.65567 q^{27} -2.51027 q^{28} +5.56470 q^{29} +2.52034 q^{30} +4.96269 q^{31} -1.00000 q^{32} -0.609718 q^{33} -1.17786 q^{34} -4.42158 q^{35} -0.952590 q^{36} -7.80266 q^{37} -4.16191 q^{38} -3.38849 q^{39} -1.76140 q^{40} +2.79972 q^{41} -3.59188 q^{42} +4.58262 q^{43} +0.426115 q^{44} -1.67789 q^{45} -0.564874 q^{46} +2.12678 q^{47} -1.43088 q^{48} -0.698559 q^{49} +1.89748 q^{50} -1.68538 q^{51} +2.36812 q^{52} -2.64144 q^{53} -5.65567 q^{54} +0.750558 q^{55} +2.51027 q^{56} -5.95518 q^{57} -5.56470 q^{58} -10.8114 q^{59} -2.52034 q^{60} -10.5327 q^{61} -4.96269 q^{62} +2.39126 q^{63} +1.00000 q^{64} +4.17121 q^{65} +0.609718 q^{66} +1.61399 q^{67} +1.17786 q^{68} -0.808265 q^{69} +4.42158 q^{70} -7.61236 q^{71} +0.952590 q^{72} +7.66690 q^{73} +7.80266 q^{74} +2.71506 q^{75} +4.16191 q^{76} -1.06966 q^{77} +3.38849 q^{78} -6.21483 q^{79} +1.76140 q^{80} -5.23480 q^{81} -2.79972 q^{82} +3.39551 q^{83} +3.59188 q^{84} +2.07469 q^{85} -4.58262 q^{86} -7.96240 q^{87} -0.426115 q^{88} -7.55320 q^{89} +1.67789 q^{90} -5.94462 q^{91} +0.564874 q^{92} -7.10100 q^{93} -2.12678 q^{94} +7.33078 q^{95} +1.43088 q^{96} -0.830275 q^{97} +0.698559 q^{98} -0.405913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.43088	−0.826117	−0.413059	−	0.910704i	$-0.635540\pi$
$3$	−1.43088	−0.826117	−0.413059	+	0.910704i	$0.635540\pi$
$4$	1.00000	0.500000
$5$	1.76140	0.787721	0.393860	−	0.919170i	$-0.371139\pi$
$5$	1.76140	0.787721	0.393860	+	0.919170i	$0.371139\pi$
$6$	1.43088	0.584153
$7$	−2.51027	−0.948792	−0.474396	−	0.880312i	$-0.657333\pi$
$7$	−2.51027	−0.948792	−0.474396	+	0.880312i	$0.657333\pi$
$8$	−1.00000	−0.353553
$9$	−0.952590	−0.317530
$10$	−1.76140	−0.557003
$11$	0.426115	0.128478	0.0642392	−	0.997935i	$-0.479538\pi$
$11$	0.426115	0.128478	0.0642392	+	0.997935i	$0.479538\pi$
$12$	−1.43088	−0.413059
$13$	2.36812	0.656799	0.328400	−	0.944539i	$-0.393491\pi$
$13$	2.36812	0.656799	0.328400	+	0.944539i	$0.393491\pi$
$14$	2.51027	0.670897
$15$	−2.52034	−0.650750
$16$	1.00000	0.250000
$17$	1.17786	0.285674	0.142837	−	0.989746i	$-0.454378\pi$
$17$	1.17786	0.285674	0.142837	+	0.989746i	$0.454378\pi$
$18$	0.952590	0.224528
$19$	4.16191	0.954808	0.477404	−	0.878684i	$-0.341578\pi$
$19$	4.16191	0.954808	0.477404	+	0.878684i	$0.341578\pi$
$20$	1.76140	0.393860
$21$	3.59188	0.783813
$22$	−0.426115	−0.0908480
$23$	0.564874	0.117784	0.0588921	−	0.998264i	$-0.481243\pi$
$23$	0.564874	0.117784	0.0588921	+	0.998264i	$0.481243\pi$
$24$	1.43088	0.292077
$25$	−1.89748	−0.379496
$26$	−2.36812	−0.464427
$27$	5.65567	1.08843
$28$	−2.51027	−0.474396
$29$	5.56470	1.03334	0.516669	−	0.856185i	$-0.327172\pi$
$29$	5.56470	1.03334	0.516669	+	0.856185i	$0.327172\pi$
$30$	2.52034	0.460150
$31$	4.96269	0.891326	0.445663	−	0.895201i	$-0.352968\pi$
$31$	4.96269	0.891326	0.445663	+	0.895201i	$0.352968\pi$
$32$	−1.00000	−0.176777
$33$	−0.609718	−0.106138
$34$	−1.17786	−0.202002
$35$	−4.42158	−0.747383
$36$	−0.952590	−0.158765
$37$	−7.80266	−1.28275	−0.641375	−	0.767228i	$-0.721636\pi$
$37$	−7.80266	−1.28275	−0.641375	+	0.767228i	$0.721636\pi$
$38$	−4.16191	−0.675151
$39$	−3.38849	−0.542593
$40$	−1.76140	−0.278501
$41$	2.79972	0.437242	0.218621	−	0.975810i	$-0.429844\pi$
$41$	2.79972	0.437242	0.218621	+	0.975810i	$0.429844\pi$
$42$	−3.59188	−0.554240
$43$	4.58262	0.698843	0.349422	−	0.936966i	$-0.386378\pi$
$43$	4.58262	0.698843	0.349422	+	0.936966i	$0.386378\pi$
$44$	0.426115	0.0642392
$45$	−1.67789	−0.250125
$46$	−0.564874	−0.0832861
$47$	2.12678	0.310223	0.155112	−	0.987897i	$-0.450426\pi$
$47$	2.12678	0.310223	0.155112	+	0.987897i	$0.450426\pi$
$48$	−1.43088	−0.206529
$49$	−0.698559	−0.0997941
$50$	1.89748	0.268344
$51$	−1.68538	−0.236000
$52$	2.36812	0.328400
$53$	−2.64144	−0.362829	−0.181415	−	0.983407i	$-0.558068\pi$
$53$	−2.64144	−0.362829	−0.181415	+	0.983407i	$0.558068\pi$
$54$	−5.65567	−0.769639
$55$	0.750558	0.101205
$56$	2.51027	0.335449
$57$	−5.95518	−0.788783
$58$	−5.56470	−0.730681
$59$	−10.8114	−1.40752	−0.703762	−	0.710435i	$-0.748498\pi$
$59$	−10.8114	−1.40752	−0.703762	+	0.710435i	$0.748498\pi$
$60$	−2.52034	−0.325375
$61$	−10.5327	−1.34857	−0.674287	−	0.738469i	$-0.735549\pi$
$61$	−10.5327	−1.34857	−0.674287	+	0.738469i	$0.735549\pi$
$62$	−4.96269	−0.630263
$63$	2.39126	0.301270
$64$	1.00000	0.125000
$65$	4.17121	0.517374
$66$	0.609718	0.0750511
$67$	1.61399	0.197180	0.0985902	−	0.995128i	$-0.468567\pi$
$67$	1.61399	0.197180	0.0985902	+	0.995128i	$0.468567\pi$
$68$	1.17786	0.142837
$69$	−0.808265	−0.0973036
$70$	4.42158	0.528480
$71$	−7.61236	−0.903420	−0.451710	−	0.892165i	$-0.649186\pi$
$71$	−7.61236	−0.903420	−0.451710	+	0.892165i	$0.649186\pi$
$72$	0.952590	0.112264
$73$	7.66690	0.897343	0.448671	−	0.893697i	$-0.351897\pi$
$73$	7.66690	0.897343	0.448671	+	0.893697i	$0.351897\pi$
$74$	7.80266	0.907041
$75$	2.71506	0.313508
$76$	4.16191	0.477404
$77$	−1.06966	−0.121899
$78$	3.38849	0.383671
$79$	−6.21483	−0.699223	−0.349612	−	0.936895i	$-0.613686\pi$
$79$	−6.21483	−0.699223	−0.349612	+	0.936895i	$0.613686\pi$
$80$	1.76140	0.196930
$81$	−5.23480	−0.581645
$82$	−2.79972	−0.309177
$83$	3.39551	0.372705	0.186353	−	0.982483i	$-0.440333\pi$
$83$	3.39551	0.372705	0.186353	+	0.982483i	$0.440333\pi$
$84$	3.59188	0.391907
$85$	2.07469	0.225031
$86$	−4.58262	−0.494157
$87$	−7.96240	−0.853659
$88$	−0.426115	−0.0454240
$89$	−7.55320	−0.800637	−0.400319	−	0.916376i	$-0.631101\pi$
$89$	−7.55320	−0.800637	−0.400319	+	0.916376i	$0.631101\pi$
$90$	1.67789	0.176865
$91$	−5.94462	−0.623166
$92$	0.564874	0.0588921
$93$	−7.10100	−0.736340
$94$	−2.12678	−0.219361
$95$	7.33078	0.752122
$96$	1.43088	0.146038
$97$	−0.830275	−0.0843017	−0.0421508	−	0.999111i	$-0.513421\pi$
$97$	−0.830275	−0.0843017	−0.0421508	+	0.999111i	$0.513421\pi$
$98$	0.698559	0.0705651
$99$	−0.405913	−0.0407958
$100$	−1.89748	−0.189748
$101$	9.46598	0.941901	0.470950	−	0.882160i	$-0.343911\pi$
$101$	9.46598	0.941901	0.470950	+	0.882160i	$0.343911\pi$
$102$	1.68538	0.166877
$103$	11.4877	1.13191	0.565957	−	0.824435i	$-0.308507\pi$
$103$	11.4877	1.13191	0.565957	+	0.824435i	$0.308507\pi$
$104$	−2.36812	−0.232214
$105$	6.32674	0.617426
$106$	2.64144	0.256559
$107$	12.8788	1.24504	0.622518	−	0.782606i	$-0.286110\pi$
$107$	12.8788	1.24504	0.622518	+	0.782606i	$0.286110\pi$
$108$	5.65567	0.544217
$109$	−5.89737	−0.564866	−0.282433	−	0.959287i	$-0.591141\pi$
$109$	−5.89737	−0.564866	−0.282433	+	0.959287i	$0.591141\pi$
$110$	−0.750558	−0.0715629
$111$	11.1646	1.05970
$112$	−2.51027	−0.237198
$113$	−3.52585	−0.331684	−0.165842	−	0.986152i	$-0.553034\pi$
$113$	−3.52585	−0.331684	−0.165842	+	0.986152i	$0.553034\pi$
$114$	5.95518	0.557754
$115$	0.994967	0.0927811
$116$	5.56470	0.516669
$117$	−2.25585	−0.208553
$118$	10.8114	0.995270
$119$	−2.95675	−0.271045
$120$	2.52034	0.230075
$121$	−10.8184	−0.983493
$122$	10.5327	0.953586
$123$	−4.00605	−0.361213
$124$	4.96269	0.445663
$125$	−12.1492	−1.08666
$126$	−2.39126	−0.213030
$127$	15.5817	1.38265	0.691327	−	0.722542i	$-0.257027\pi$
$127$	15.5817	1.38265	0.691327	+	0.722542i	$0.257027\pi$
$128$	−1.00000	−0.0883883
$129$	−6.55717	−0.577327
$130$	−4.17121	−0.365839
$131$	5.16970	0.451678	0.225839	−	0.974165i	$-0.427488\pi$
$131$	5.16970	0.451678	0.225839	+	0.974165i	$0.427488\pi$
$132$	−0.609718	−0.0530691
$133$	−10.4475	−0.905914
$134$	−1.61399	−0.139428
$135$	9.96189	0.857383
$136$	−1.17786	−0.101001
$137$	12.1938	1.04179	0.520893	−	0.853622i	$-0.325599\pi$
$137$	12.1938	1.04179	0.520893	+	0.853622i	$0.325599\pi$
$138$	0.808265	0.0688041
$139$	0.705047	0.0598013	0.0299007	−	0.999553i	$-0.490481\pi$
$139$	0.705047	0.0598013	0.0299007	+	0.999553i	$0.490481\pi$
$140$	−4.42158	−0.373692
$141$	−3.04316	−0.256281
$142$	7.61236	0.638815
$143$	1.00909	0.0843845
$144$	−0.952590	−0.0793825
$145$	9.80165	0.813982
$146$	−7.66690	−0.634517
$147$	0.999552	0.0824416
$148$	−7.80266	−0.641375
$149$	5.63205	0.461395	0.230698	−	0.973025i	$-0.425899\pi$
$149$	5.63205	0.461395	0.230698	+	0.973025i	$0.425899\pi$
$150$	−2.71506	−0.221684
$151$	0.488897	0.0397859	0.0198929	−	0.999802i	$-0.493667\pi$
$151$	0.488897	0.0397859	0.0198929	+	0.999802i	$0.493667\pi$
$152$	−4.16191	−0.337575
$153$	−1.12202	−0.0907101
$154$	1.06966	0.0861958
$155$	8.74127	0.702116
$156$	−3.38849	−0.271297
$157$	22.3445	1.78329	0.891643	−	0.452739i	$-0.149553\pi$
$157$	22.3445	1.78329	0.891643	+	0.452739i	$0.149553\pi$
$158$	6.21483	0.494426
$159$	3.77957	0.299740
$160$	−1.76140	−0.139251
$161$	−1.41798	−0.111753
$162$	5.23480	0.411285
$163$	−8.34256	−0.653440	−0.326720	−	0.945121i	$-0.605943\pi$
$163$	−8.34256	−0.653440	−0.326720	+	0.945121i	$0.605943\pi$
$164$	2.79972	0.218621
$165$	−1.07396	−0.0836074
$166$	−3.39551	−0.263543
$167$	6.70379	0.518755	0.259377	−	0.965776i	$-0.416483\pi$
$167$	6.70379	0.518755	0.259377	+	0.965776i	$0.416483\pi$
$168$	−3.59188	−0.277120
$169$	−7.39199	−0.568615
$170$	−2.07469	−0.159121
$171$	−3.96459	−0.303180
$172$	4.58262	0.349422
$173$	−15.7600	−1.19821	−0.599107	−	0.800669i	$-0.704478\pi$
$173$	−15.7600	−1.19821	−0.599107	+	0.800669i	$0.704478\pi$
$174$	7.96240	0.603628
$175$	4.76318	0.360062
$176$	0.426115	0.0321196
$177$	15.4698	1.16278
$178$	7.55320	0.566136
$179$	14.4410	1.07937	0.539686	−	0.841866i	$-0.318543\pi$
$179$	14.4410	1.07937	0.539686	+	0.841866i	$0.318543\pi$
$180$	−1.67789	−0.125063
$181$	19.5217	1.45103	0.725517	−	0.688204i	$-0.241601\pi$
$181$	19.5217	1.45103	0.725517	+	0.688204i	$0.241601\pi$
$182$	5.94462	0.440645
$183$	15.0710	1.11408
$184$	−0.564874	−0.0416430
$185$	−13.7436	−1.01045
$186$	7.10100	0.520671
$187$	0.501905	0.0367029
$188$	2.12678	0.155112
$189$	−14.1972	−1.03270
$190$	−7.33078	−0.531831
$191$	−7.70373	−0.557422	−0.278711	−	0.960375i	$-0.589907\pi$
$191$	−7.70373	−0.557422	−0.278711	+	0.960375i	$0.589907\pi$
$192$	−1.43088	−0.103265
$193$	−12.8259	−0.923227	−0.461613	−	0.887081i	$-0.652729\pi$
$193$	−12.8259	−0.923227	−0.461613	+	0.887081i	$0.652729\pi$
$194$	0.830275	0.0596103
$195$	−5.96848	−0.427412
$196$	−0.698559	−0.0498970
$197$	9.87114	0.703290	0.351645	−	0.936133i	$-0.385622\pi$
$197$	9.87114	0.703290	0.351645	+	0.936133i	$0.385622\pi$
$198$	0.405913	0.0288470
$199$	−6.75899	−0.479132	−0.239566	−	0.970880i	$-0.577005\pi$
$199$	−6.75899	−0.479132	−0.239566	+	0.970880i	$0.577005\pi$
$200$	1.89748	0.134172
$201$	−2.30942	−0.162894
$202$	−9.46598	−0.666024
$203$	−13.9689	−0.980423
$204$	−1.68538	−0.118000
$205$	4.93141	0.344425
$206$	−11.4877	−0.800384
$207$	−0.538093	−0.0374000
$208$	2.36812	0.164200
$209$	1.77345	0.122672
$210$	−6.32674	−0.436586
$211$	10.7534	0.740298	0.370149	−	0.928972i	$-0.379307\pi$
$211$	10.7534	0.740298	0.370149	+	0.928972i	$0.379307\pi$
$212$	−2.64144	−0.181415
$213$	10.8923	0.746331
$214$	−12.8788	−0.880373
$215$	8.07182	0.550493
$216$	−5.65567	−0.384820
$217$	−12.4577	−0.845683
$218$	5.89737	0.399420
$219$	−10.9704	−0.741310
$220$	0.750558	0.0506026
$221$	2.78933	0.187630
$222$	−11.1646	−0.749322
$223$	−1.45424	−0.0973832	−0.0486916	−	0.998814i	$-0.515505\pi$
$223$	−1.45424	−0.0973832	−0.0486916	+	0.998814i	$0.515505\pi$
$224$	2.51027	0.167724
$225$	1.80752	0.120501
$226$	3.52585	0.234536
$227$	−6.34583	−0.421188	−0.210594	−	0.977574i	$-0.567540\pi$
$227$	−6.34583	−0.421188	−0.210594	+	0.977574i	$0.567540\pi$
$228$	−5.95518	−0.394392
$229$	20.2609	1.33888	0.669438	−	0.742868i	$-0.266535\pi$
$229$	20.2609	1.33888	0.669438	+	0.742868i	$0.266535\pi$
$230$	−0.994967	−0.0656062
$231$	1.53056	0.100703
$232$	−5.56470	−0.365340
$233$	11.9803	0.784855	0.392427	−	0.919783i	$-0.371635\pi$
$233$	11.9803	0.784855	0.392427	+	0.919783i	$0.371635\pi$
$234$	2.25585	0.147470
$235$	3.74611	0.244369
$236$	−10.8114	−0.703762
$237$	8.89267	0.577641
$238$	2.95675	0.191658
$239$	−17.2958	−1.11877	−0.559385	−	0.828908i	$-0.688963\pi$
$239$	−17.2958	−1.11877	−0.559385	+	0.828908i	$0.688963\pi$
$240$	−2.52034	−0.162687
$241$	−1.24242	−0.0800312	−0.0400156	−	0.999199i	$-0.512741\pi$
$241$	−1.24242	−0.0800312	−0.0400156	+	0.999199i	$0.512741\pi$
$242$	10.8184	0.695435
$243$	−9.47666	−0.607928
$244$	−10.5327	−0.674287
$245$	−1.23044	−0.0786099
$246$	4.00605	0.255417
$247$	9.85591	0.627117
$248$	−4.96269	−0.315131
$249$	−4.85855	−0.307898
$250$	12.1492	0.768383
$251$	8.89754	0.561608	0.280804	−	0.959765i	$-0.409399\pi$
$251$	8.89754	0.561608	0.280804	+	0.959765i	$0.409399\pi$
$252$	2.39126	0.150635
$253$	0.240701	0.0151327
$254$	−15.5817	−0.977683
$255$	−2.96862	−0.185902
$256$	1.00000	0.0625000
$257$	8.39597	0.523726	0.261863	−	0.965105i	$-0.415663\pi$
$257$	8.39597	0.523726	0.261863	+	0.965105i	$0.415663\pi$
$258$	6.55717	0.408232
$259$	19.5868	1.21706
$260$	4.17121	0.258687
$261$	−5.30088	−0.328116
$262$	−5.16970	−0.319385
$263$	22.8986	1.41199	0.705994	−	0.708218i	$-0.250501\pi$
$263$	22.8986	1.41199	0.705994	+	0.708218i	$0.250501\pi$
$264$	0.609718	0.0375256
$265$	−4.65262	−0.285808
$266$	10.4475	0.640578
$267$	10.8077	0.661420
$268$	1.61399	0.0985902
$269$	12.7598	0.777979	0.388990	−	0.921242i	$-0.372824\pi$
$269$	12.7598	0.777979	0.388990	+	0.921242i	$0.372824\pi$
$270$	−9.96189	−0.606261
$271$	−13.8926	−0.843915	−0.421957	−	0.906616i	$-0.638657\pi$
$271$	−13.8926	−0.843915	−0.421957	+	0.906616i	$0.638657\pi$
$272$	1.17786	0.0714185
$273$	8.50602	0.514808
$274$	−12.1938	−0.736654
$275$	−0.808544	−0.0487570
$276$	−0.808265	−0.0486518
$277$	−26.2001	−1.57421	−0.787106	−	0.616818i	$-0.788421\pi$
$277$	−26.2001	−1.57421	−0.787106	+	0.616818i	$0.788421\pi$
$278$	−0.705047	−0.0422859
$279$	−4.72741	−0.283023
$280$	4.42158	0.264240
$281$	−19.0989	−1.13934	−0.569671	−	0.821873i	$-0.692929\pi$
$281$	−19.0989	−1.13934	−0.569671	+	0.821873i	$0.692929\pi$
$282$	3.04316	0.181218
$283$	24.0563	1.43000	0.714998	−	0.699127i	$-0.246428\pi$
$283$	24.0563	1.43000	0.714998	+	0.699127i	$0.246428\pi$
$284$	−7.61236	−0.451710
$285$	−10.4894	−0.621341
$286$	−1.00909	−0.0596689
$287$	−7.02804	−0.414852
$288$	0.952590	0.0561319
$289$	−15.6126	−0.918390
$290$	−9.80165	−0.575572
$291$	1.18802	0.0696431
$292$	7.66690	0.448671
$293$	20.1575	1.17761	0.588805	−	0.808275i	$-0.299598\pi$
$293$	20.1575	1.17761	0.588805	+	0.808275i	$0.299598\pi$
$294$	−0.999552	−0.0582950
$295$	−19.0432	−1.10874
$296$	7.80266	0.453520
$297$	2.40997	0.139840
$298$	−5.63205	−0.326256
$299$	1.33769	0.0773606
$300$	2.71506	0.156754
$301$	−11.5036	−0.663057
$302$	−0.488897	−0.0281329
$303$	−13.5447	−0.778121
$304$	4.16191	0.238702
$305$	−18.5523	−1.06230
$306$	1.12202	0.0641417
$307$	34.0889	1.94556	0.972778	−	0.231737i	$-0.0744409\pi$
$307$	34.0889	1.94556	0.972778	+	0.231737i	$0.0744409\pi$
$308$	−1.06966	−0.0609497
$309$	−16.4375	−0.935094
$310$	−8.74127	−0.496471
$311$	26.9597	1.52875	0.764373	−	0.644774i	$-0.223049\pi$
$311$	26.9597	1.52875	0.764373	+	0.644774i	$0.223049\pi$
$312$	3.38849	0.191836
$313$	−28.4742	−1.60946	−0.804729	−	0.593642i	$-0.797690\pi$
$313$	−28.4742	−1.60946	−0.804729	+	0.593642i	$0.797690\pi$
$314$	−22.3445	−1.26097
$315$	4.21195	0.237317
$316$	−6.21483	−0.349612
$317$	−9.74107	−0.547113	−0.273556	−	0.961856i	$-0.588200\pi$
$317$	−9.74107	−0.547113	−0.273556	+	0.961856i	$0.588200\pi$
$318$	−3.77957	−0.211948
$319$	2.37120	0.132762
$320$	1.76140	0.0984651
$321$	−18.4279	−1.02855
$322$	1.41798	0.0790211
$323$	4.90216	0.272764
$324$	−5.23480	−0.290822
$325$	−4.49346	−0.249252
$326$	8.34256	0.462052
$327$	8.43841	0.466645
$328$	−2.79972	−0.154589
$329$	−5.33879	−0.294337
$330$	1.07396	0.0591193
$331$	14.9670	0.822663	0.411331	−	0.911486i	$-0.365064\pi$
$331$	14.9670	0.822663	0.411331	+	0.911486i	$0.365064\pi$
$332$	3.39551	0.186353
$333$	7.43274	0.407312
$334$	−6.70379	−0.366815
$335$	2.84288	0.155323
$336$	3.59188	0.195953
$337$	2.60810	0.142072	0.0710362	−	0.997474i	$-0.477369\pi$
$337$	2.60810	0.142072	0.0710362	+	0.997474i	$0.477369\pi$
$338$	7.39199	0.402071
$339$	5.04506	0.274010
$340$	2.07469	0.112516
$341$	2.11468	0.114516
$342$	3.96459	0.214381
$343$	19.3254	1.04348
$344$	−4.58262	−0.247078
$345$	−1.42368	−0.0766481
$346$	15.7600	0.847265
$347$	22.3793	1.20139	0.600693	−	0.799480i	$-0.294891\pi$
$347$	22.3793	1.20139	0.600693	+	0.799480i	$0.294891\pi$
$348$	−7.96240	−0.426829
$349$	−21.6245	−1.15753	−0.578765	−	0.815494i	$-0.696465\pi$
$349$	−21.6245	−1.15753	−0.578765	+	0.815494i	$0.696465\pi$
$350$	−4.76318	−0.254603
$351$	13.3933	0.714883
$352$	−0.426115	−0.0227120
$353$	−19.7148	−1.04931	−0.524657	−	0.851314i	$-0.675806\pi$
$353$	−19.7148	−1.04931	−0.524657	+	0.851314i	$0.675806\pi$
$354$	−15.4698	−0.822210
$355$	−13.4084	−0.711643
$356$	−7.55320	−0.400319
$357$	4.23075	0.223915
$358$	−14.4410	−0.763232
$359$	−16.1402	−0.851845	−0.425923	−	0.904760i	$-0.640050\pi$
$359$	−16.1402	−0.851845	−0.425923	+	0.904760i	$0.640050\pi$
$360$	1.67789	0.0884326
$361$	−1.67851	−0.0883424
$362$	−19.5217	−1.02604
$363$	15.4798	0.812481
$364$	−5.94462	−0.311583
$365$	13.5045	0.706856
$366$	−15.0710	−0.787774
$367$	9.31697	0.486342	0.243171	−	0.969983i	$-0.421812\pi$
$367$	9.31697	0.486342	0.243171	+	0.969983i	$0.421812\pi$
$368$	0.564874	0.0294461
$369$	−2.66698	−0.138838
$370$	13.7436	0.714495
$371$	6.63071	0.344249
$372$	−7.10100	−0.368170
$373$	34.6757	1.79544	0.897721	−	0.440565i	$-0.145222\pi$
$373$	34.6757	1.79544	0.897721	+	0.440565i	$0.145222\pi$
$374$	−0.501905	−0.0259529
$375$	17.3840	0.897707
$376$	−2.12678	−0.109680
$377$	13.1779	0.678696
$378$	14.1972	0.730228
$379$	30.9474	1.58966	0.794831	−	0.606831i	$-0.207560\pi$
$379$	30.9474	1.58966	0.794831	+	0.606831i	$0.207560\pi$
$380$	7.33078	0.376061
$381$	−22.2955	−1.14223
$382$	7.70373	0.394157
$383$	1.36435	0.0697149	0.0348574	−	0.999392i	$-0.488902\pi$
$383$	1.36435	0.0697149	0.0348574	+	0.999392i	$0.488902\pi$
$384$	1.43088	0.0730192
$385$	−1.88410	−0.0960226
$386$	12.8259	0.652820
$387$	−4.36536	−0.221904
$388$	−0.830275	−0.0421508
$389$	11.7924	0.597900	0.298950	−	0.954269i	$-0.403364\pi$
$389$	11.7924	0.597900	0.298950	+	0.954269i	$0.403364\pi$
$390$	5.96848	0.302226
$391$	0.665344	0.0336479
$392$	0.698559	0.0352825
$393$	−7.39720	−0.373139
$394$	−9.87114	−0.497301
$395$	−10.9468	−0.550793
$396$	−0.405913	−0.0203979
$397$	6.16089	0.309206	0.154603	−	0.987977i	$-0.450590\pi$
$397$	6.16089	0.309206	0.154603	+	0.987977i	$0.450590\pi$
$398$	6.75899	0.338798
$399$	14.9491	0.748391
$400$	−1.89748	−0.0948739
$401$	−11.9466	−0.596582	−0.298291	−	0.954475i	$-0.596417\pi$
$401$	−11.9466	−0.596582	−0.298291	+	0.954475i	$0.596417\pi$
$402$	2.30942	0.115184
$403$	11.7523	0.585422
$404$	9.46598	0.470950
$405$	−9.22057	−0.458174
$406$	13.9689	0.693264
$407$	−3.32483	−0.164806
$408$	1.68538	0.0834387
$409$	33.6358	1.66318	0.831591	−	0.555389i	$-0.187431\pi$
$409$	33.6358	1.66318	0.831591	+	0.555389i	$0.187431\pi$
$410$	−4.93141	−0.243545
$411$	−17.4478	−0.860638
$412$	11.4877	0.565957
$413$	27.1395	1.33545
$414$	0.538093	0.0264458
$415$	5.98084	0.293588
$416$	−2.36812	−0.116107
$417$	−1.00884	−0.0494029
$418$	−1.77345	−0.0867424
$419$	23.4147	1.14388	0.571942	−	0.820294i	$-0.306190\pi$
$419$	23.4147	1.14388	0.571942	+	0.820294i	$0.306190\pi$
$420$	6.32674	0.308713
$421$	−12.8635	−0.626928	−0.313464	−	0.949600i	$-0.601489\pi$
$421$	−12.8635	−0.626928	−0.313464	+	0.949600i	$0.601489\pi$
$422$	−10.7534	−0.523469
$423$	−2.02595	−0.0985052
$424$	2.64144	0.128279
$425$	−2.23497	−0.108412
$426$	−10.8923	−0.527736
$427$	26.4399	1.27952
$428$	12.8788	0.622518
$429$	−1.44389	−0.0697115
$430$	−8.07182	−0.389258
$431$	−14.9811	−0.721614	−0.360807	−	0.932640i	$-0.617499\pi$
$431$	−14.9811	−0.721614	−0.360807	+	0.932640i	$0.617499\pi$
$432$	5.65567	0.272109
$433$	40.0900	1.92660	0.963300	−	0.268426i	$-0.0865036\pi$
$433$	40.0900	1.92660	0.963300	+	0.268426i	$0.0865036\pi$
$434$	12.4577	0.597988
$435$	−14.0250	−0.672445
$436$	−5.89737	−0.282433
$437$	2.35095	0.112461
$438$	10.9704	0.524186
$439$	30.2196	1.44230	0.721151	−	0.692778i	$-0.243613\pi$
$439$	30.2196	1.44230	0.721151	+	0.692778i	$0.243613\pi$
$440$	−0.750558	−0.0357814
$441$	0.665440	0.0316876
$442$	−2.78933	−0.132675
$443$	−32.0110	−1.52089	−0.760444	−	0.649403i	$-0.775019\pi$
$443$	−32.0110	−1.52089	−0.760444	+	0.649403i	$0.775019\pi$
$444$	11.1646	0.529851
$445$	−13.3042	−0.630679
$446$	1.45424	0.0688603
$447$	−8.05877	−0.381167
$448$	−2.51027	−0.118599
$449$	−22.5351	−1.06349	−0.531747	−	0.846903i	$-0.678464\pi$
$449$	−22.5351	−1.06349	−0.531747	+	0.846903i	$0.678464\pi$
$450$	−1.80752	−0.0852073
$451$	1.19300	0.0561762
$452$	−3.52585	−0.165842
$453$	−0.699552	−0.0328678
$454$	6.34583	0.297825
$455$	−10.4708	−0.490881
$456$	5.95518	0.278877
$457$	−15.9868	−0.747832	−0.373916	−	0.927463i	$-0.621985\pi$
$457$	−15.9868	−0.747832	−0.373916	+	0.927463i	$0.621985\pi$
$458$	−20.2609	−0.946729
$459$	6.66161	0.310937
$460$	0.994967	0.0463906
$461$	38.1422	1.77646	0.888229	−	0.459401i	$-0.151936\pi$
$461$	38.1422	1.77646	0.888229	+	0.459401i	$0.151936\pi$
$462$	−1.53056	−0.0712079
$463$	4.50852	0.209528	0.104764	−	0.994497i	$-0.466591\pi$
$463$	4.50852	0.209528	0.104764	+	0.994497i	$0.466591\pi$
$464$	5.56470	0.258335
$465$	−12.5077	−0.580030
$466$	−11.9803	−0.554976
$467$	9.68145	0.448004	0.224002	−	0.974589i	$-0.428088\pi$
$467$	9.68145	0.448004	0.224002	+	0.974589i	$0.428088\pi$
$468$	−2.25585	−0.104277
$469$	−4.05155	−0.187083
$470$	−3.74611	−0.172795
$471$	−31.9723	−1.47320
$472$	10.8114	0.497635
$473$	1.95272	0.0897863
$474$	−8.89267	−0.408454
$475$	−7.89713	−0.362345
$476$	−2.95675	−0.135523
$477$	2.51621	0.115209
$478$	17.2958	0.791090
$479$	21.5955	0.986724	0.493362	−	0.869824i	$-0.335768\pi$
$479$	21.5955	0.986724	0.493362	+	0.869824i	$0.335768\pi$
$480$	2.52034	0.115037
$481$	−18.4777	−0.842509
$482$	1.24242	0.0565906
$483$	2.02896	0.0923209
$484$	−10.8184	−0.491747
$485$	−1.46244	−0.0664062
$486$	9.47666	0.429870
$487$	−32.9715	−1.49408	−0.747041	−	0.664778i	$-0.768526\pi$
$487$	−32.9715	−1.49408	−0.747041	+	0.664778i	$0.768526\pi$
$488$	10.5327	0.476793
$489$	11.9372	0.539818
$490$	1.23044	0.0555856
$491$	−8.47458	−0.382452	−0.191226	−	0.981546i	$-0.561246\pi$
$491$	−8.47458	−0.382452	−0.191226	+	0.981546i	$0.561246\pi$
$492$	−4.00605	−0.180607
$493$	6.55446	0.295198
$494$	−9.85591	−0.443439
$495$	−0.714974	−0.0321357
$496$	4.96269	0.222831
$497$	19.1090	0.857158
$498$	4.85855	0.217717
$499$	−2.95237	−0.132166	−0.0660832	−	0.997814i	$-0.521050\pi$
$499$	−2.95237	−0.132166	−0.0660832	+	0.997814i	$0.521050\pi$
$500$	−12.1492	−0.543329
$501$	−9.59230	−0.428553
$502$	−8.89754	−0.397117
$503$	−16.8983	−0.753459	−0.376730	−	0.926323i	$-0.622951\pi$
$503$	−16.8983	−0.753459	−0.376730	+	0.926323i	$0.622951\pi$
$504$	−2.39126	−0.106515
$505$	16.6734	0.741955
$506$	−0.240701	−0.0107005
$507$	10.5770	0.469743
$508$	15.5817	0.691327
$509$	−27.5333	−1.22039	−0.610196	−	0.792251i	$-0.708909\pi$
$509$	−27.5333	−1.22039	−0.610196	+	0.792251i	$0.708909\pi$
$510$	2.96862	0.131453
$511$	−19.2460	−0.851391
$512$	−1.00000	−0.0441942
$513$	23.5384	1.03925
$514$	−8.39597	−0.370330
$515$	20.2344	0.891633
$516$	−6.55717	−0.288663
$517$	0.906254	0.0398570
$518$	−19.5868	−0.860593
$519$	22.5507	0.989865
$520$	−4.17121	−0.182919
$521$	−36.3939	−1.59445	−0.797223	−	0.603685i	$-0.793698\pi$
$521$	−36.3939	−1.59445	−0.797223	+	0.603685i	$0.793698\pi$
$522$	5.30088	0.232013
$523$	30.3188	1.32575	0.662874	−	0.748731i	$-0.269336\pi$
$523$	30.3188	1.32575	0.662874	+	0.748731i	$0.269336\pi$
$524$	5.16970	0.225839
$525$	−6.81552	−0.297454
$526$	−22.8986	−0.998426
$527$	5.84538	0.254629
$528$	−0.609718	−0.0265346
$529$	−22.6809	−0.986127
$530$	4.65262	0.202097
$531$	10.2988	0.446931
$532$	−10.4475	−0.452957
$533$	6.63007	0.287180
$534$	−10.8077	−0.467695
$535$	22.6846	0.980741
$536$	−1.61399	−0.0697138
$537$	−20.6633	−0.891689
$538$	−12.7598	−0.550114
$539$	−0.297666	−0.0128214
$540$	9.96189	0.428691
$541$	−0.720278	−0.0309672	−0.0154836	−	0.999880i	$-0.504929\pi$
$541$	−0.720278	−0.0309672	−0.0154836	+	0.999880i	$0.504929\pi$
$542$	13.8926	0.596738
$543$	−27.9331	−1.19872
$544$	−1.17786	−0.0505005
$545$	−10.3876	−0.444957
$546$	−8.50602	−0.364024
$547$	−14.2282	−0.608355	−0.304177	−	0.952615i	$-0.598382\pi$
$547$	−14.2282	−0.608355	−0.304177	+	0.952615i	$0.598382\pi$
$548$	12.1938	0.520893
$549$	10.0333	0.428213
$550$	0.808544	0.0344764
$551$	23.1598	0.986639
$552$	0.808265	0.0344020
$553$	15.6009	0.663418
$554$	26.2001	1.11314
$555$	19.6654	0.834749
$556$	0.705047	0.0299007
$557$	35.7714	1.51568	0.757842	−	0.652438i	$-0.226254\pi$
$557$	35.7714	1.51568	0.757842	+	0.652438i	$0.226254\pi$
$558$	4.72741	0.200127
$559$	10.8522	0.459000
$560$	−4.42158	−0.186846
$561$	−0.718165	−0.0303209
$562$	19.0989	0.805637
$563$	−5.96451	−0.251374	−0.125687	−	0.992070i	$-0.540114\pi$
$563$	−5.96451	−0.251374	−0.125687	+	0.992070i	$0.540114\pi$
$564$	−3.04316	−0.128140
$565$	−6.21043	−0.261275
$566$	−24.0563	−1.01116
$567$	13.1408	0.551860
$568$	7.61236	0.319407
$569$	16.6588	0.698372	0.349186	−	0.937053i	$-0.386458\pi$
$569$	16.6588	0.698372	0.349186	+	0.937053i	$0.386458\pi$
$570$	10.4894	0.439354
$571$	46.4120	1.94228	0.971141	−	0.238508i	$-0.0766583\pi$
$571$	46.4120	1.94228	0.971141	+	0.238508i	$0.0766583\pi$
$572$	1.00909	0.0421923
$573$	11.0231	0.460496
$574$	7.02804	0.293345
$575$	−1.07184	−0.0446986
$576$	−0.952590	−0.0396913
$577$	31.8256	1.32492	0.662460	−	0.749098i	$-0.269513\pi$
$577$	31.8256	1.32492	0.662460	+	0.749098i	$0.269513\pi$
$578$	15.6126	0.649400
$579$	18.3523	0.762694
$580$	9.80165	0.406991
$581$	−8.52363	−0.353620
$582$	−1.18802	−0.0492451
$583$	−1.12556	−0.0466157
$584$	−7.66690	−0.317259
$585$	−3.97345	−0.164282
$586$	−20.1575	−0.832697
$587$	32.4731	1.34031	0.670154	−	0.742222i	$-0.266228\pi$
$587$	32.4731	1.34031	0.670154	+	0.742222i	$0.266228\pi$
$588$	0.999552	0.0412208
$589$	20.6543	0.851045
$590$	19.0432	0.783995
$591$	−14.1244	−0.581000
$592$	−7.80266	−0.320687
$593$	32.5180	1.33535	0.667677	−	0.744451i	$-0.267289\pi$
$593$	32.5180	1.33535	0.667677	+	0.744451i	$0.267289\pi$
$594$	−2.40997	−0.0988821
$595$	−5.20802	−0.213508
$596$	5.63205	0.230698
$597$	9.67129	0.395820
$598$	−1.33769	−0.0547022
$599$	−20.8382	−0.851425	−0.425712	−	0.904859i	$-0.639976\pi$
$599$	−20.8382	−0.851425	−0.425712	+	0.904859i	$0.639976\pi$
$600$	−2.71506	−0.110842
$601$	28.5665	1.16525	0.582626	−	0.812740i	$-0.302025\pi$
$601$	28.5665	1.16525	0.582626	+	0.812740i	$0.302025\pi$
$602$	11.5036	0.468852
$603$	−1.53747	−0.0626107
$604$	0.488897	0.0198929
$605$	−19.0555	−0.774718
$606$	13.5447	0.550214
$607$	34.8420	1.41419	0.707097	−	0.707117i	$-0.250005\pi$
$607$	34.8420	1.41419	0.707097	+	0.707117i	$0.250005\pi$
$608$	−4.16191	−0.168788
$609$	19.9878	0.809945
$610$	18.5523	0.751159
$611$	5.03648	0.203754
$612$	−1.12202	−0.0453550
$613$	25.1927	1.01752	0.508761	−	0.860908i	$-0.330104\pi$
$613$	25.1927	1.01752	0.508761	+	0.860908i	$0.330104\pi$
$614$	−34.0889	−1.37572
$615$	−7.05625	−0.284535
$616$	1.06966	0.0430979
$617$	17.2947	0.696257	0.348129	−	0.937447i	$-0.386817\pi$
$617$	17.2947	0.696257	0.348129	+	0.937447i	$0.386817\pi$
$618$	16.4375	0.661211
$619$	42.9877	1.72782	0.863910	−	0.503646i	$-0.168008\pi$
$619$	42.9877	1.72782	0.863910	+	0.503646i	$0.168008\pi$
$620$	8.74127	0.351058
$621$	3.19474	0.128200
$622$	−26.9597	−1.08099
$623$	18.9605	0.759638
$624$	−3.38849	−0.135648
$625$	−11.9122	−0.476487
$626$	28.4742	1.13806
$627$	−2.53759	−0.101342
$628$	22.3445	0.891643
$629$	−9.19047	−0.366448
$630$	−4.21195	−0.167808
$631$	30.1710	1.20109	0.600544	−	0.799592i	$-0.294951\pi$
$631$	30.1710	1.20109	0.600544	+	0.799592i	$0.294951\pi$
$632$	6.21483	0.247213
$633$	−15.3869	−0.611573
$634$	9.74107	0.386867
$635$	27.4456	1.08914
$636$	3.77957	0.149870
$637$	−1.65427	−0.0655447
$638$	−2.37120	−0.0938767
$639$	7.25145	0.286863
$640$	−1.76140	−0.0696254
$641$	47.9556	1.89413	0.947067	−	0.321036i	$-0.104031\pi$
$641$	47.9556	1.89413	0.947067	+	0.321036i	$0.104031\pi$
$642$	18.4279	0.727292
$643$	−2.06124	−0.0812876	−0.0406438	−	0.999174i	$-0.512941\pi$
$643$	−2.06124	−0.0812876	−0.0406438	+	0.999174i	$0.512941\pi$
$644$	−1.41798	−0.0558764
$645$	−11.5498	−0.454772
$646$	−4.90216	−0.192873
$647$	−5.63284	−0.221450	−0.110725	−	0.993851i	$-0.535317\pi$
$647$	−5.63284	−0.221450	−0.110725	+	0.993851i	$0.535317\pi$
$648$	5.23480	0.205642
$649$	−4.60690	−0.180837
$650$	4.49346	0.176248
$651$	17.8254	0.698633
$652$	−8.34256	−0.326720
$653$	9.14797	0.357988	0.178994	−	0.983850i	$-0.442716\pi$
$653$	9.14797	0.357988	0.178994	+	0.983850i	$0.442716\pi$
$654$	−8.43841	−0.329968
$655$	9.10589	0.355797
$656$	2.79972	0.109311
$657$	−7.30341	−0.284933
$658$	5.33879	0.208128
$659$	−45.7066	−1.78048	−0.890238	−	0.455495i	$-0.849462\pi$
$659$	−45.7066	−1.78048	−0.890238	+	0.455495i	$0.849462\pi$
$660$	−1.07396	−0.0418037
$661$	13.9077	0.540947	0.270474	−	0.962727i	$-0.412820\pi$
$661$	13.9077	0.540947	0.270474	+	0.962727i	$0.412820\pi$
$662$	−14.9670	−0.581710
$663$	−3.99118	−0.155005
$664$	−3.39551	−0.131771
$665$	−18.4022	−0.713607
$666$	−7.43274	−0.288013
$667$	3.14335	0.121711
$668$	6.70379	0.259377
$669$	2.08084	0.0804500
$670$	−2.84288	−0.109830
$671$	−4.48814	−0.173263
$672$	−3.59188	−0.138560
$673$	−37.4249	−1.44263	−0.721313	−	0.692610i	$-0.756461\pi$
$673$	−37.4249	−1.44263	−0.721313	+	0.692610i	$0.756461\pi$
$674$	−2.60810	−0.100460
$675$	−10.7315	−0.413056
$676$	−7.39199	−0.284307
$677$	−14.8597	−0.571106	−0.285553	−	0.958363i	$-0.592177\pi$
$677$	−14.8597	−0.571106	−0.285553	+	0.958363i	$0.592177\pi$
$678$	−5.04506	−0.193754
$679$	2.08421	0.0799847
$680$	−2.07469	−0.0795606
$681$	9.08011	0.347950
$682$	−2.11468	−0.0809752
$683$	7.73460	0.295956	0.147978	−	0.988991i	$-0.452723\pi$
$683$	7.73460	0.295956	0.147978	+	0.988991i	$0.452723\pi$
$684$	−3.96459	−0.151590
$685$	21.4781	0.820637
$686$	−19.3254	−0.737849
$687$	−28.9908	−1.10607
$688$	4.58262	0.174711
$689$	−6.25525	−0.238306
$690$	1.42368	0.0541984
$691$	2.77263	0.105476	0.0527379	−	0.998608i	$-0.483205\pi$
$691$	2.77263	0.105476	0.0527379	+	0.998608i	$0.483205\pi$
$692$	−15.7600	−0.599107
$693$	1.01895	0.0387067
$694$	−22.3793	−0.849508
$695$	1.24187	0.0471068
$696$	7.96240	0.301814
$697$	3.29768	0.124909
$698$	21.6245	0.818498
$699$	−17.1423	−0.648382
$700$	4.76318	0.180031
$701$	14.3787	0.543075	0.271537	−	0.962428i	$-0.412468\pi$
$701$	14.3787	0.543075	0.271537	+	0.962428i	$0.412468\pi$
$702$	−13.3933	−0.505498
$703$	−32.4740	−1.22478
$704$	0.426115	0.0160598
$705$	−5.36022	−0.201878
$706$	19.7148	0.741977
$707$	−23.7622	−0.893668
$708$	15.4698	0.581390
$709$	13.3959	0.503092	0.251546	−	0.967845i	$-0.419061\pi$
$709$	13.3959	0.503092	0.251546	+	0.967845i	$0.419061\pi$
$710$	13.4084	0.503208
$711$	5.92019	0.222024
$712$	7.55320	0.283068
$713$	2.80329	0.104984
$714$	−4.23075	−0.158332
$715$	1.77741	0.0664715
$716$	14.4410	0.539686
$717$	24.7481	0.924236
$718$	16.1402	0.602346
$719$	−12.6088	−0.470230	−0.235115	−	0.971968i	$-0.575547\pi$
$719$	−12.6088	−0.470230	−0.235115	+	0.971968i	$0.575547\pi$
$720$	−1.67789	−0.0625313
$721$	−28.8371	−1.07395
$722$	1.67851	0.0624675
$723$	1.77775	0.0661151
$724$	19.5217	0.725517
$725$	−10.5589	−0.392148
$726$	−15.4798	−0.574511
$727$	33.7211	1.25065	0.625323	−	0.780366i	$-0.284967\pi$
$727$	33.7211	1.25065	0.625323	+	0.780366i	$0.284967\pi$
$728$	5.94462	0.220322
$729$	29.2643	1.08386
$730$	−13.5045	−0.499822
$731$	5.39770	0.199641
$732$	15.0710	0.557040
$733$	−26.6972	−0.986084	−0.493042	−	0.870006i	$-0.664115\pi$
$733$	−26.6972	−0.986084	−0.493042	+	0.870006i	$0.664115\pi$
$734$	−9.31697	−0.343896
$735$	1.76061	0.0649410
$736$	−0.564874	−0.0208215
$737$	0.687746	0.0253334
$738$	2.66698	0.0981730
$739$	−12.3855	−0.455610	−0.227805	−	0.973707i	$-0.573155\pi$
$739$	−12.3855	−0.455610	−0.227805	+	0.973707i	$0.573155\pi$
$740$	−13.7436	−0.505224
$741$	−14.1026	−0.518072
$742$	−6.63071	−0.243421
$743$	−4.03390	−0.147990	−0.0739948	−	0.997259i	$-0.523575\pi$
$743$	−4.03390	−0.147990	−0.0739948	+	0.997259i	$0.523575\pi$
$744$	7.10100	0.260335
$745$	9.92027	0.363451
$746$	−34.6757	−1.26957
$747$	−3.23453	−0.118345
$748$	0.501905	0.0183515
$749$	−32.3291	−1.18128
$750$	−17.3840	−0.634775
$751$	18.2252	0.665047	0.332523	−	0.943095i	$-0.392100\pi$
$751$	18.2252	0.665047	0.332523	+	0.943095i	$0.392100\pi$
$752$	2.12678	0.0775558
$753$	−12.7313	−0.463954
$754$	−13.1779	−0.479910
$755$	0.861142	0.0313402
$756$	−14.1972	−0.516349
$757$	−37.7544	−1.37221	−0.686103	−	0.727504i	$-0.740680\pi$
$757$	−37.7544	−1.37221	−0.686103	+	0.727504i	$0.740680\pi$
$758$	−30.9474	−1.12406
$759$	−0.344414	−0.0125014
$760$	−7.33078	−0.265915
$761$	36.0971	1.30852	0.654259	−	0.756271i	$-0.272981\pi$
$761$	36.0971	1.30852	0.654259	+	0.756271i	$0.272981\pi$
$762$	22.2955	0.807681
$763$	14.8040	0.535940
$764$	−7.70373	−0.278711
$765$	−1.97633	−0.0714542
$766$	−1.36435	−0.0492959
$767$	−25.6027	−0.924461
$768$	−1.43088	−0.0516323
$769$	13.2284	0.477029	0.238515	−	0.971139i	$-0.423340\pi$
$769$	13.2284	0.477029	0.238515	+	0.971139i	$0.423340\pi$
$770$	1.88410	0.0678983
$771$	−12.0136	−0.432659
$772$	−12.8259	−0.461613
$773$	41.3528	1.48736	0.743679	−	0.668537i	$-0.233079\pi$
$773$	41.3528	1.48736	0.743679	+	0.668537i	$0.233079\pi$
$774$	4.36536	0.156910
$775$	−9.41660	−0.338254
$776$	0.830275	0.0298051
$777$	−28.0263	−1.00544
$778$	−11.7924	−0.422779
$779$	11.6522	0.417482
$780$	−5.96848	−0.213706
$781$	−3.24374	−0.116070
$782$	−0.665344	−0.0237927
$783$	31.4721	1.12472
$784$	−0.698559	−0.0249485
$785$	39.3576	1.40473
$786$	7.39720	0.263849
$787$	−8.80428	−0.313839	−0.156919	−	0.987611i	$-0.550156\pi$
$787$	−8.80428	−0.313839	−0.156919	+	0.987611i	$0.550156\pi$
$788$	9.87114	0.351645
$789$	−32.7651	−1.16647
$790$	10.9468	0.389469
$791$	8.85083	0.314699
$792$	0.405913	0.0144235
$793$	−24.9427	−0.885742
$794$	−6.16089	−0.218642
$795$	6.65733	0.236111
$796$	−6.75899	−0.239566
$797$	−39.6977	−1.40617	−0.703083	−	0.711108i	$-0.748194\pi$
$797$	−39.6977	−1.40617	−0.703083	+	0.711108i	$0.748194\pi$
$798$	−14.9491	−0.529192
$799$	2.50506	0.0886226
$800$	1.89748	0.0670860
$801$	7.19510	0.254226
$802$	11.9466	0.421847
$803$	3.26698	0.115289
$804$	−2.30942	−0.0814471
$805$	−2.49763	−0.0880300
$806$	−11.7523	−0.413956
$807$	−18.2577	−0.642702
$808$	−9.46598	−0.333012
$809$	17.8953	0.629166	0.314583	−	0.949230i	$-0.398135\pi$
$809$	17.8953	0.629166	0.314583	+	0.949230i	$0.398135\pi$
$810$	9.22057	0.323978
$811$	−4.73690	−0.166335	−0.0831675	−	0.996536i	$-0.526504\pi$
$811$	−4.73690	−0.166335	−0.0831675	+	0.996536i	$0.526504\pi$
$812$	−13.9689	−0.490212
$813$	19.8786	0.697173
$814$	3.32483	0.116535
$815$	−14.6946	−0.514728
$816$	−1.68538	−0.0590000
$817$	19.0725	0.667261
$818$	−33.6358	−1.17605
$819$	5.66279	0.197874
$820$	4.93141	0.172212
$821$	28.0651	0.979478	0.489739	−	0.871869i	$-0.337092\pi$
$821$	28.0651	0.979478	0.489739	+	0.871869i	$0.337092\pi$
$822$	17.4478	0.608563
$823$	−13.7752	−0.480172	−0.240086	−	0.970752i	$-0.577176\pi$
$823$	−13.7752	−0.480172	−0.240086	+	0.970752i	$0.577176\pi$
$824$	−11.4877	−0.400192
$825$	1.15693	0.0402790
$826$	−27.1395	−0.944304
$827$	−21.1312	−0.734802	−0.367401	−	0.930063i	$-0.619752\pi$
$827$	−21.1312	−0.734802	−0.367401	+	0.930063i	$0.619752\pi$
$828$	−0.538093	−0.0187000
$829$	−29.2125	−1.01459	−0.507296	−	0.861772i	$-0.669355\pi$
$829$	−29.2125	−1.01459	−0.507296	+	0.861772i	$0.669355\pi$
$830$	−5.98084	−0.207598
$831$	37.4891	1.30048
$832$	2.36812	0.0820999
$833$	−0.822807	−0.0285086
$834$	1.00884	0.0349331
$835$	11.8080	0.408634
$836$	1.77345	0.0613361
$837$	28.0674	0.970150
$838$	−23.4147	−0.808849
$839$	0.222246	0.00767278	0.00383639	−	0.999993i	$-0.498779\pi$
$839$	0.222246	0.00767278	0.00383639	+	0.999993i	$0.498779\pi$
$840$	−6.32674	−0.218293
$841$	1.96587	0.0677885
$842$	12.8635	0.443305
$843$	27.3281	0.941230
$844$	10.7534	0.370149
$845$	−13.0202	−0.447910
$846$	2.02595	0.0696537
$847$	27.1571	0.933130
$848$	−2.64144	−0.0907073
$849$	−34.4215	−1.18134
$850$	2.23497	0.0766589
$851$	−4.40752	−0.151088
$852$	10.8923	0.373166
$853$	−29.7487	−1.01858	−0.509288	−	0.860596i	$-0.670091\pi$
$853$	−29.7487	−1.01858	−0.509288	+	0.860596i	$0.670091\pi$
$854$	−26.4399	−0.904754
$855$	−6.98323	−0.238821
$856$	−12.8788	−0.440187
$857$	16.2028	0.553476	0.276738	−	0.960945i	$-0.410747\pi$
$857$	16.2028	0.553476	0.276738	+	0.960945i	$0.410747\pi$
$858$	1.44389	0.0492935
$859$	−14.8527	−0.506769	−0.253384	−	0.967366i	$-0.581544\pi$
$859$	−14.8527	−0.506769	−0.253384	+	0.967366i	$0.581544\pi$
$860$	8.07182	0.275247
$861$	10.0563	0.342716
$862$	14.9811	0.510258
$863$	−33.2835	−1.13298	−0.566491	−	0.824068i	$-0.691699\pi$
$863$	−33.2835	−1.13298	−0.566491	+	0.824068i	$0.691699\pi$
$864$	−5.65567	−0.192410
$865$	−27.7597	−0.943858
$866$	−40.0900	−1.36231
$867$	22.3398	0.758698
$868$	−12.4577	−0.422841
$869$	−2.64823	−0.0898352
$870$	14.0250	0.475490
$871$	3.82213	0.129508
$872$	5.89737	0.199710
$873$	0.790912	0.0267683
$874$	−2.35095	−0.0795222
$875$	30.4977	1.03101
$876$	−10.9704	−0.370655
$877$	23.6628	0.799035	0.399517	−	0.916726i	$-0.369178\pi$
$877$	23.6628	0.799035	0.399517	+	0.916726i	$0.369178\pi$
$878$	−30.2196	−1.01986
$879$	−28.8428	−0.972845
$880$	0.750558	0.0253013
$881$	−32.3440	−1.08970	−0.544848	−	0.838535i	$-0.683413\pi$
$881$	−32.3440	−1.08970	−0.544848	+	0.838535i	$0.683413\pi$
$882$	−0.665440	−0.0224065
$883$	−12.2889	−0.413553	−0.206777	−	0.978388i	$-0.566297\pi$
$883$	−12.2889	−0.413553	−0.206777	+	0.978388i	$0.566297\pi$
$884$	2.78933	0.0938152
$885$	27.2485	0.915947
$886$	32.0110	1.07543
$887$	17.6252	0.591798	0.295899	−	0.955219i	$-0.404381\pi$
$887$	17.6252	0.591798	0.295899	+	0.955219i	$0.404381\pi$
$888$	−11.1646	−0.374661
$889$	−39.1143	−1.31185
$890$	13.3042	0.445957
$891$	−2.23063	−0.0747288
$892$	−1.45424	−0.0486916
$893$	8.85148	0.296203
$894$	8.05877	0.269526
$895$	25.4364	0.850244
$896$	2.51027	0.0838621
$897$	−1.91407	−0.0639089
$898$	22.5351	0.752004
$899$	27.6159	0.921041
$900$	1.80752	0.0602506
$901$	−3.11125	−0.103651
$902$	−1.19300	−0.0397226
$903$	16.4602	0.547763
$904$	3.52585	0.117268
$905$	34.3854	1.14301
$906$	0.699552	0.0232411
$907$	26.0347	0.864468	0.432234	−	0.901762i	$-0.357726\pi$
$907$	26.0347	0.864468	0.432234	+	0.901762i	$0.357726\pi$
$908$	−6.34583	−0.210594
$909$	−9.01720	−0.299082
$910$	10.4708	0.347105
$911$	2.67283	0.0885549	0.0442775	−	0.999019i	$-0.485901\pi$
$911$	2.67283	0.0885549	0.0442775	+	0.999019i	$0.485901\pi$
$912$	−5.95518	−0.197196
$913$	1.44688	0.0478846
$914$	15.9868	0.528797
$915$	26.5460	0.877584
$916$	20.2609	0.669438
$917$	−12.9773	−0.428549
$918$	−6.66161	−0.219866
$919$	46.0978	1.52063	0.760313	−	0.649557i	$-0.225046\pi$
$919$	46.0978	1.52063	0.760313	+	0.649557i	$0.225046\pi$
$920$	−0.994967	−0.0328031
$921$	−48.7770	−1.60726
$922$	−38.1422	−1.25615
$923$	−18.0270	−0.593366
$924$	1.53056	0.0503516
$925$	14.8054	0.486798
$926$	−4.50852	−0.148159
$927$	−10.9430	−0.359417
$928$	−5.56470	−0.182670
$929$	−45.1771	−1.48221	−0.741106	−	0.671388i	$-0.765699\pi$
$929$	−45.1771	−1.48221	−0.741106	+	0.671388i	$0.765699\pi$
$930$	12.5077	0.410143
$931$	−2.90734	−0.0952841
$932$	11.9803	0.392427
$933$	−38.5761	−1.26292
$934$	−9.68145	−0.316787
$935$	0.884055	0.0289117
$936$	2.25585	0.0737348
$937$	8.97779	0.293291	0.146646	−	0.989189i	$-0.453152\pi$
$937$	8.97779	0.293291	0.146646	+	0.989189i	$0.453152\pi$
$938$	4.05155	0.132288
$939$	40.7431	1.32960
$940$	3.74611	0.122185
$941$	39.9776	1.30323	0.651617	−	0.758548i	$-0.274091\pi$
$941$	39.9776	1.30323	0.651617	+	0.758548i	$0.274091\pi$
$942$	31.9723	1.04171
$943$	1.58149	0.0515003
$944$	−10.8114	−0.351881
$945$	−25.0070	−0.813478
$946$	−1.95272	−0.0634885
$947$	−31.6606	−1.02883	−0.514415	−	0.857541i	$-0.671991\pi$
$947$	−31.6606	−1.02883	−0.514415	+	0.857541i	$0.671991\pi$
$948$	8.89267	0.288820
$949$	18.1562	0.589374
$950$	7.89713	0.256217
$951$	13.9383	0.451979
$952$	2.95675	0.0958289
$953$	−53.3129	−1.72698	−0.863488	−	0.504370i	$-0.831725\pi$
$953$	−53.3129	−1.72698	−0.863488	+	0.504370i	$0.831725\pi$
$954$	−2.51621	−0.0814652
$955$	−13.5693	−0.439093
$956$	−17.2958	−0.559385
$957$	−3.39290	−0.109677
$958$	−21.5955	−0.697719
$959$	−30.6097	−0.988438
$960$	−2.52034	−0.0813437
$961$	−6.37169	−0.205538
$962$	18.4777	0.595744
$963$	−12.2682	−0.395336
$964$	−1.24242	−0.0400156
$965$	−22.5915	−0.727245
$966$	−2.02896	−0.0652807
$967$	−14.4647	−0.465154	−0.232577	−	0.972578i	$-0.574716\pi$
$967$	−14.4647	−0.465154	−0.232577	+	0.972578i	$0.574716\pi$
$968$	10.8184	0.347717
$969$	−7.01439	−0.225335
$970$	1.46244	0.0469563
$971$	18.5075	0.593933	0.296967	−	0.954888i	$-0.404025\pi$
$971$	18.5075	0.593933	0.296967	+	0.954888i	$0.404025\pi$
$972$	−9.47666	−0.303964
$973$	−1.76986	−0.0567390
$974$	32.9715	1.05648
$975$	6.42959	0.205912
$976$	−10.5327	−0.337143
$977$	29.6838	0.949670	0.474835	−	0.880075i	$-0.342508\pi$
$977$	29.6838	0.949670	0.474835	+	0.880075i	$0.342508\pi$
$978$	−11.9372	−0.381709
$979$	−3.21853	−0.102865
$980$	−1.23044	−0.0393049
$981$	5.61778	0.179362
$982$	8.47458	0.270435
$983$	−16.8347	−0.536944	−0.268472	−	0.963287i	$-0.586519\pi$
$983$	−16.8347	−0.536944	−0.268472	+	0.963287i	$0.586519\pi$
$984$	4.00605	0.127708
$985$	17.3870	0.553996
$986$	−6.55446	−0.208736
$987$	7.63916	0.243157
$988$	9.85591	0.313558
$989$	2.58860	0.0823128
$990$	0.714974	0.0227234
$991$	−27.3533	−0.868905	−0.434452	−	0.900695i	$-0.643058\pi$
$991$	−27.3533	−0.868905	−0.434452	+	0.900695i	$0.643058\pi$
$992$	−4.96269	−0.157566
$993$	−21.4160	−0.679616
$994$	−19.1090	−0.606102
$995$	−11.9053	−0.377423
$996$	−4.85855	−0.153949
$997$	22.0371	0.697923	0.348961	−	0.937137i	$-0.386534\pi$
$997$	22.0371	0.697923	0.348961	+	0.937137i	$0.386534\pi$
$998$	2.95237	0.0934557
$999$	−44.1293	−1.39619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.17	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.17	✓	69	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.43088 q^{3} +1.00000 q^{4} +1.76140 q^{5} +1.43088 q^{6} -2.51027 q^{7} -1.00000 q^{8} -0.952590 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.43088 q^{3} +1.00000 q^{4} +1.76140 q^{5} +1.43088 q^{6} -2.51027 q^{7} -1.00000 q^{8} -0.952590 q^{9} -1.76140 q^{10} +0.426115 q^{11} -1.43088 q^{12} +2.36812 q^{13} +2.51027 q^{14} -2.52034 q^{15} +1.00000 q^{16} +1.17786 q^{17} +0.952590 q^{18} +4.16191 q^{19} +1.76140 q^{20} +3.59188 q^{21} -0.426115 q^{22} +0.564874 q^{23} +1.43088 q^{24} -1.89748 q^{25} -2.36812 q^{26} +5.65567 q^{27} -2.51027 q^{28} +5.56470 q^{29} +2.52034 q^{30} +4.96269 q^{31} -1.00000 q^{32} -0.609718 q^{33} -1.17786 q^{34} -4.42158 q^{35} -0.952590 q^{36} -7.80266 q^{37} -4.16191 q^{38} -3.38849 q^{39} -1.76140 q^{40} +2.79972 q^{41} -3.59188 q^{42} +4.58262 q^{43} +0.426115 q^{44} -1.67789 q^{45} -0.564874 q^{46} +2.12678 q^{47} -1.43088 q^{48} -0.698559 q^{49} +1.89748 q^{50} -1.68538 q^{51} +2.36812 q^{52} -2.64144 q^{53} -5.65567 q^{54} +0.750558 q^{55} +2.51027 q^{56} -5.95518 q^{57} -5.56470 q^{58} -10.8114 q^{59} -2.52034 q^{60} -10.5327 q^{61} -4.96269 q^{62} +2.39126 q^{63} +1.00000 q^{64} +4.17121 q^{65} +0.609718 q^{66} +1.61399 q^{67} +1.17786 q^{68} -0.808265 q^{69} +4.42158 q^{70} -7.61236 q^{71} +0.952590 q^{72} +7.66690 q^{73} +7.80266 q^{74} +2.71506 q^{75} +4.16191 q^{76} -1.06966 q^{77} +3.38849 q^{78} -6.21483 q^{79} +1.76140 q^{80} -5.23480 q^{81} -2.79972 q^{82} +3.39551 q^{83} +3.59188 q^{84} +2.07469 q^{85} -4.58262 q^{86} -7.96240 q^{87} -0.426115 q^{88} -7.55320 q^{89} +1.67789 q^{90} -5.94462 q^{91} +0.564874 q^{92} -7.10100 q^{93} -2.12678 q^{94} +7.33078 q^{95} +1.43088 q^{96} -0.830275 q^{97} +0.698559 q^{98} -0.405913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

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