LMFDB - Embedded newform 8015.2.a.k.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08886 q^{2} -0.324198 q^{3} +2.36335 q^{4} -1.00000 q^{5} +0.677204 q^{6} -1.00000 q^{7} -0.758978 q^{8} -2.89490 q^{9} +O(q^{10})$	\(q-2.08886 q^{2} -0.324198 q^{3} +2.36335 q^{4} -1.00000 q^{5} +0.677204 q^{6} -1.00000 q^{7} -0.758978 q^{8} -2.89490 q^{9} +2.08886 q^{10} -3.93545 q^{11} -0.766191 q^{12} -1.67041 q^{13} +2.08886 q^{14} +0.324198 q^{15} -3.14129 q^{16} -1.01192 q^{17} +6.04704 q^{18} +1.87234 q^{19} -2.36335 q^{20} +0.324198 q^{21} +8.22062 q^{22} +0.464469 q^{23} +0.246059 q^{24} +1.00000 q^{25} +3.48925 q^{26} +1.91111 q^{27} -2.36335 q^{28} -7.71012 q^{29} -0.677204 q^{30} +3.42228 q^{31} +8.07968 q^{32} +1.27586 q^{33} +2.11376 q^{34} +1.00000 q^{35} -6.84164 q^{36} +2.24479 q^{37} -3.91106 q^{38} +0.541542 q^{39} +0.758978 q^{40} +9.56656 q^{41} -0.677204 q^{42} -10.3611 q^{43} -9.30084 q^{44} +2.89490 q^{45} -0.970213 q^{46} +4.47916 q^{47} +1.01840 q^{48} +1.00000 q^{49} -2.08886 q^{50} +0.328062 q^{51} -3.94775 q^{52} +7.31789 q^{53} -3.99205 q^{54} +3.93545 q^{55} +0.758978 q^{56} -0.607008 q^{57} +16.1054 q^{58} +8.41562 q^{59} +0.766191 q^{60} -9.55983 q^{61} -7.14867 q^{62} +2.89490 q^{63} -10.5948 q^{64} +1.67041 q^{65} -2.66510 q^{66} -3.30864 q^{67} -2.39152 q^{68} -0.150580 q^{69} -2.08886 q^{70} +2.49216 q^{71} +2.19716 q^{72} +12.1785 q^{73} -4.68906 q^{74} -0.324198 q^{75} +4.42498 q^{76} +3.93545 q^{77} -1.13121 q^{78} +8.14883 q^{79} +3.14129 q^{80} +8.06511 q^{81} -19.9832 q^{82} +16.0837 q^{83} +0.766191 q^{84} +1.01192 q^{85} +21.6429 q^{86} +2.49960 q^{87} +2.98692 q^{88} +7.25905 q^{89} -6.04704 q^{90} +1.67041 q^{91} +1.09770 q^{92} -1.10949 q^{93} -9.35635 q^{94} -1.87234 q^{95} -2.61941 q^{96} +0.907099 q^{97} -2.08886 q^{98} +11.3927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−2.08886	−1.47705	−0.738524	−	0.674227i	$-0.764477\pi$
$2$	−2.08886	−1.47705	−0.738524	+	0.674227i	$0.764477\pi$
$3$	−0.324198	−0.187176	−0.0935878	−	0.995611i	$-0.529834\pi$
$3$	−0.324198	−0.187176	−0.0935878	+	0.995611i	$0.529834\pi$
$4$	2.36335	1.18167
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.677204	0.276467
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.758978	−0.268339
$9$	−2.89490	−0.964965
$10$	2.08886	0.660556
$11$	−3.93545	−1.18658	−0.593292	−	0.804987i	$-0.702172\pi$
$11$	−3.93545	−1.18658	−0.593292	+	0.804987i	$0.702172\pi$
$12$	−0.766191	−0.221180
$13$	−1.67041	−0.463288	−0.231644	−	0.972801i	$-0.574410\pi$
$13$	−1.67041	−0.463288	−0.231644	+	0.972801i	$0.574410\pi$
$14$	2.08886	0.558272
$15$	0.324198	0.0837074
$16$	−3.14129	−0.785323
$17$	−1.01192	−0.245427	−0.122713	−	0.992442i	$-0.539160\pi$
$17$	−1.01192	−0.245427	−0.122713	+	0.992442i	$0.539160\pi$
$18$	6.04704	1.42530
$19$	1.87234	0.429544	0.214772	−	0.976664i	$-0.431099\pi$
$19$	1.87234	0.429544	0.214772	+	0.976664i	$0.431099\pi$
$20$	−2.36335	−0.528460
$21$	0.324198	0.0707457
$22$	8.22062	1.75264
$23$	0.464469	0.0968486	0.0484243	−	0.998827i	$-0.484580\pi$
$23$	0.464469	0.0968486	0.0484243	+	0.998827i	$0.484580\pi$
$24$	0.246059	0.0502265
$25$	1.00000	0.200000
$26$	3.48925	0.684298
$27$	1.91111	0.367793
$28$	−2.36335	−0.446630
$29$	−7.71012	−1.43173	−0.715867	−	0.698237i	$-0.753968\pi$
$29$	−7.71012	−1.43173	−0.715867	+	0.698237i	$0.753968\pi$
$30$	−0.677204	−0.123640
$31$	3.42228	0.614660	0.307330	−	0.951603i	$-0.400565\pi$
$31$	3.42228	0.614660	0.307330	+	0.951603i	$0.400565\pi$
$32$	8.07968	1.42830
$33$	1.27586	0.222099
$34$	2.11376	0.362507
$35$	1.00000	0.169031
$36$	−6.84164	−1.14027
$37$	2.24479	0.369041	0.184521	−	0.982829i	$-0.440927\pi$
$37$	2.24479	0.369041	0.184521	+	0.982829i	$0.440927\pi$
$38$	−3.91106	−0.634458
$39$	0.541542	0.0867161
$40$	0.758978	0.120005
$41$	9.56656	1.49405	0.747023	−	0.664798i	$-0.231482\pi$
$41$	9.56656	1.49405	0.747023	+	0.664798i	$0.231482\pi$
$42$	−0.677204	−0.104495
$43$	−10.3611	−1.58006	−0.790028	−	0.613071i	$-0.789934\pi$
$43$	−10.3611	−1.58006	−0.790028	+	0.613071i	$0.789934\pi$
$44$	−9.30084	−1.40215
$45$	2.89490	0.431546
$46$	−0.970213	−0.143050
$47$	4.47916	0.653353	0.326676	−	0.945136i	$-0.394071\pi$
$47$	4.47916	0.653353	0.326676	+	0.945136i	$0.394071\pi$
$48$	1.01840	0.146993
$49$	1.00000	0.142857
$50$	−2.08886	−0.295410
$51$	0.328062	0.0459379
$52$	−3.94775	−0.547454
$53$	7.31789	1.00519	0.502595	−	0.864522i	$-0.332379\pi$
$53$	7.31789	1.00519	0.502595	+	0.864522i	$0.332379\pi$
$54$	−3.99205	−0.543249
$55$	3.93545	0.530657
$56$	0.758978	0.101423
$57$	−0.607008	−0.0804001
$58$	16.1054	2.11474
$59$	8.41562	1.09562	0.547810	−	0.836603i	$-0.315462\pi$
$59$	8.41562	1.09562	0.547810	+	0.836603i	$0.315462\pi$
$60$	0.766191	0.0989148
$61$	−9.55983	−1.22401	−0.612005	−	0.790854i	$-0.709637\pi$
$61$	−9.55983	−1.22401	−0.612005	+	0.790854i	$0.709637\pi$
$62$	−7.14867	−0.907882
$63$	2.89490	0.364723
$64$	−10.5948	−1.32434
$65$	1.67041	0.207189
$66$	−2.66510	−0.328052
$67$	−3.30864	−0.404215	−0.202108	−	0.979363i	$-0.564779\pi$
$67$	−3.30864	−0.404215	−0.202108	+	0.979363i	$0.564779\pi$
$68$	−2.39152	−0.290014
$69$	−0.150580	−0.0181277
$70$	−2.08886	−0.249667
$71$	2.49216	0.295765	0.147883	−	0.989005i	$-0.452754\pi$
$71$	2.49216	0.295765	0.147883	+	0.989005i	$0.452754\pi$
$72$	2.19716	0.258938
$73$	12.1785	1.42538	0.712692	−	0.701477i	$-0.247476\pi$
$73$	12.1785	1.42538	0.712692	+	0.701477i	$0.247476\pi$
$74$	−4.68906	−0.545092
$75$	−0.324198	−0.0374351
$76$	4.42498	0.507580
$77$	3.93545	0.448487
$78$	−1.13121	−0.128084
$79$	8.14883	0.916815	0.458407	−	0.888742i	$-0.348420\pi$
$79$	8.14883	0.916815	0.458407	+	0.888742i	$0.348420\pi$
$80$	3.14129	0.351207
$81$	8.06511	0.896123
$82$	−19.9832	−2.20678
$83$	16.0837	1.76541	0.882707	−	0.469924i	$-0.155719\pi$
$83$	16.0837	1.76541	0.882707	+	0.469924i	$0.155719\pi$
$84$	0.766191	0.0835983
$85$	1.01192	0.109758
$86$	21.6429	2.33382
$87$	2.49960	0.267986
$88$	2.98692	0.318407
$89$	7.25905	0.769457	0.384729	−	0.923030i	$-0.374295\pi$
$89$	7.25905	0.769457	0.384729	+	0.923030i	$0.374295\pi$
$90$	−6.04704	−0.637414
$91$	1.67041	0.175106
$92$	1.09770	0.114443
$93$	−1.10949	−0.115049
$94$	−9.35635	−0.965034
$95$	−1.87234	−0.192098
$96$	−2.61941	−0.267343
$97$	0.907099	0.0921020	0.0460510	−	0.998939i	$-0.485336\pi$
$97$	0.907099	0.0921020	0.0460510	+	0.998939i	$0.485336\pi$
$98$	−2.08886	−0.211007
$99$	11.3927	1.14501
$100$	2.36335	0.236335
$101$	−0.811988	−0.0807958	−0.0403979	−	0.999184i	$-0.512863\pi$
$101$	−0.811988	−0.0807958	−0.0403979	+	0.999184i	$0.512863\pi$
$102$	−0.685276	−0.0678525
$103$	−1.78952	−0.176327	−0.0881635	−	0.996106i	$-0.528100\pi$
$103$	−1.78952	−0.176327	−0.0881635	+	0.996106i	$0.528100\pi$
$104$	1.26780	0.124318
$105$	−0.324198	−0.0316384
$106$	−15.2861	−1.48471
$107$	−16.5877	−1.60360	−0.801798	−	0.597596i	$-0.796123\pi$
$107$	−16.5877	−1.60360	−0.801798	+	0.597596i	$0.796123\pi$
$108$	4.51661	0.434611
$109$	2.74028	0.262471	0.131236	−	0.991351i	$-0.458106\pi$
$109$	2.74028	0.262471	0.131236	+	0.991351i	$0.458106\pi$
$110$	−8.22062	−0.783805
$111$	−0.727755	−0.0690755
$112$	3.14129	0.296824
$113$	−16.8957	−1.58941	−0.794706	−	0.606995i	$-0.792375\pi$
$113$	−16.8957	−1.58941	−0.794706	+	0.606995i	$0.792375\pi$
$114$	1.26796	0.118755
$115$	−0.464469	−0.0433120
$116$	−18.2217	−1.69184
$117$	4.83565	0.447056
$118$	−17.5791	−1.61828
$119$	1.01192	0.0927626
$120$	−0.246059	−0.0224620
$121$	4.48780	0.407982
$122$	19.9692	1.80792
$123$	−3.10146	−0.279649
$124$	8.08803	0.726326
$125$	−1.00000	−0.0894427
$126$	−6.04704	−0.538713
$127$	9.83617	0.872819	0.436409	−	0.899748i	$-0.356250\pi$
$127$	9.83617	0.872819	0.436409	+	0.899748i	$0.356250\pi$
$128$	5.97162	0.527822
$129$	3.35905	0.295748
$130$	−3.48925	−0.306027
$131$	11.4936	1.00420	0.502101	−	0.864809i	$-0.332561\pi$
$131$	11.4936	1.00420	0.502101	+	0.864809i	$0.332561\pi$
$132$	3.01531	0.262449
$133$	−1.87234	−0.162352
$134$	6.91130	0.597046
$135$	−1.91111	−0.164482
$136$	0.768025	0.0658576
$137$	−4.78289	−0.408630	−0.204315	−	0.978905i	$-0.565497\pi$
$137$	−4.78289	−0.408630	−0.204315	+	0.978905i	$0.565497\pi$
$138$	0.314541	0.0267755
$139$	−4.99193	−0.423410	−0.211705	−	0.977334i	$-0.567902\pi$
$139$	−4.99193	−0.423410	−0.211705	+	0.977334i	$0.567902\pi$
$140$	2.36335	0.199739
$141$	−1.45213	−0.122292
$142$	−5.20578	−0.436860
$143$	6.57381	0.549730
$144$	9.09371	0.757809
$145$	7.71012	0.640291
$146$	−25.4392	−2.10536
$147$	−0.324198	−0.0267394
$148$	5.30521	0.436086
$149$	23.8293	1.95217	0.976086	−	0.217386i	$-0.0697530\pi$
$149$	23.8293	1.95217	0.976086	+	0.217386i	$0.0697530\pi$
$150$	0.677204	0.0552935
$151$	−16.6063	−1.35140	−0.675701	−	0.737176i	$-0.736159\pi$
$151$	−16.6063	−1.35140	−0.675701	+	0.737176i	$0.736159\pi$
$152$	−1.42106	−0.115263
$153$	2.92940	0.236828
$154$	−8.22062	−0.662437
$155$	−3.42228	−0.274884
$156$	1.27985	0.102470
$157$	19.2678	1.53773	0.768867	−	0.639409i	$-0.220821\pi$
$157$	19.2678	1.53773	0.768867	+	0.639409i	$0.220821\pi$
$158$	−17.0218	−1.35418
$159$	−2.37244	−0.188147
$160$	−8.07968	−0.638755
$161$	−0.464469	−0.0366053
$162$	−16.8469	−1.32362
$163$	−20.2679	−1.58751	−0.793754	−	0.608239i	$-0.791876\pi$
$163$	−20.2679	−1.58751	−0.793754	+	0.608239i	$0.791876\pi$
$164$	22.6091	1.76547
$165$	−1.27586	−0.0993259
$166$	−33.5966	−2.60760
$167$	−10.0135	−0.774869	−0.387435	−	0.921897i	$-0.626639\pi$
$167$	−10.0135	−0.774869	−0.387435	+	0.921897i	$0.626639\pi$
$168$	−0.246059	−0.0189838
$169$	−10.2097	−0.785365
$170$	−2.11376	−0.162118
$171$	−5.42023	−0.414495
$172$	−24.4869	−1.86711
$173$	−7.43891	−0.565570	−0.282785	−	0.959183i	$-0.591258\pi$
$173$	−7.43891	−0.565570	−0.282785	+	0.959183i	$0.591258\pi$
$174$	−5.22133	−0.395828
$175$	−1.00000	−0.0755929
$176$	12.3624	0.931851
$177$	−2.72832	−0.205073
$178$	−15.1631	−1.13653
$179$	−0.480019	−0.0358783	−0.0179391	−	0.999839i	$-0.505711\pi$
$179$	−0.480019	−0.0358783	−0.0179391	+	0.999839i	$0.505711\pi$
$180$	6.84164	0.509946
$181$	−12.5602	−0.933596	−0.466798	−	0.884364i	$-0.654592\pi$
$181$	−12.5602	−0.933596	−0.466798	+	0.884364i	$0.654592\pi$
$182$	−3.48925	−0.258640
$183$	3.09927	0.229105
$184$	−0.352522	−0.0259883
$185$	−2.24479	−0.165040
$186$	2.31758	0.169933
$187$	3.98236	0.291219
$188$	10.5858	0.772049
$189$	−1.91111	−0.139013
$190$	3.91106	0.283738
$191$	2.37160	0.171603	0.0858015	−	0.996312i	$-0.472655\pi$
$191$	2.37160	0.171603	0.0858015	+	0.996312i	$0.472655\pi$
$192$	3.43479	0.247885
$193$	−11.5628	−0.832306	−0.416153	−	0.909295i	$-0.636622\pi$
$193$	−11.5628	−0.832306	−0.416153	+	0.909295i	$0.636622\pi$
$194$	−1.89481	−0.136039
$195$	−0.541542	−0.0387806
$196$	2.36335	0.168810
$197$	−0.472448	−0.0336605	−0.0168303	−	0.999858i	$-0.505357\pi$
$197$	−0.472448	−0.0336605	−0.0168303	+	0.999858i	$0.505357\pi$
$198$	−23.7978	−1.69124
$199$	7.04925	0.499708	0.249854	−	0.968284i	$-0.419617\pi$
$199$	7.04925	0.499708	0.249854	+	0.968284i	$0.419617\pi$
$200$	−0.758978	−0.0536678
$201$	1.07265	0.0756592
$202$	1.69613	0.119339
$203$	7.71012	0.541145
$204$	0.775324	0.0542835
$205$	−9.56656	−0.668158
$206$	3.73807	0.260444
$207$	−1.34459	−0.0934555
$208$	5.24723	0.363830
$209$	−7.36851	−0.509690
$210$	0.677204	0.0467315
$211$	17.5505	1.20822	0.604112	−	0.796899i	$-0.293528\pi$
$211$	17.5505	1.20822	0.604112	+	0.796899i	$0.293528\pi$
$212$	17.2947	1.18780
$213$	−0.807953	−0.0553600
$214$	34.6495	2.36859
$215$	10.3611	0.706622
$216$	−1.45049	−0.0986934
$217$	−3.42228	−0.232320
$218$	−5.72407	−0.387683
$219$	−3.94824	−0.266797
$220$	9.30084	0.627062
$221$	1.69032	0.113703
$222$	1.52018	0.102028
$223$	−23.5288	−1.57561	−0.787803	−	0.615927i	$-0.788782\pi$
$223$	−23.5288	−1.57561	−0.787803	+	0.615927i	$0.788782\pi$
$224$	−8.07968	−0.539846
$225$	−2.89490	−0.192993
$226$	35.2927	2.34764
$227$	21.3823	1.41919	0.709596	−	0.704609i	$-0.248878\pi$
$227$	21.3823	1.41919	0.709596	+	0.704609i	$0.248878\pi$
$228$	−1.43457	−0.0950066
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	0.970213	0.0639739
$231$	−1.27586	−0.0839457
$232$	5.85181	0.384190
$233$	12.5045	0.819194	0.409597	−	0.912267i	$-0.365669\pi$
$233$	12.5045	0.819194	0.409597	+	0.912267i	$0.365669\pi$
$234$	−10.1010	−0.660324
$235$	−4.47916	−0.292188
$236$	19.8890	1.29466
$237$	−2.64183	−0.171605
$238$	−2.11376	−0.137015
$239$	−9.36421	−0.605721	−0.302860	−	0.953035i	$-0.597942\pi$
$239$	−9.36421	−0.605721	−0.302860	+	0.953035i	$0.597942\pi$
$240$	−1.01840	−0.0657373
$241$	14.2925	0.920662	0.460331	−	0.887747i	$-0.347731\pi$
$241$	14.2925	0.920662	0.460331	+	0.887747i	$0.347731\pi$
$242$	−9.37439	−0.602609
$243$	−8.34802	−0.535526
$244$	−22.5932	−1.44638
$245$	−1.00000	−0.0638877
$246$	6.47852	0.413055
$247$	−3.12757	−0.199002
$248$	−2.59743	−0.164937
$249$	−5.21429	−0.330442
$250$	2.08886	0.132111
$251$	18.2415	1.15139	0.575697	−	0.817663i	$-0.304731\pi$
$251$	18.2415	1.15139	0.575697	+	0.817663i	$0.304731\pi$
$252$	6.84164	0.430983
$253$	−1.82790	−0.114919
$254$	−20.5464	−1.28920
$255$	−0.328062	−0.0205440
$256$	8.71561	0.544726
$257$	−0.522087	−0.0325669	−0.0162835	−	0.999867i	$-0.505183\pi$
$257$	−0.522087	−0.0325669	−0.0162835	+	0.999867i	$0.505183\pi$
$258$	−7.01659	−0.436834
$259$	−2.24479	−0.139484
$260$	3.94775	0.244829
$261$	22.3200	1.38157
$262$	−24.0086	−1.48325
$263$	−29.2989	−1.80665	−0.903325	−	0.428957i	$-0.858881\pi$
$263$	−29.2989	−1.80665	−0.903325	+	0.428957i	$0.858881\pi$
$264$	−0.968353	−0.0595980
$265$	−7.31789	−0.449534
$266$	3.91106	0.239802
$267$	−2.35336	−0.144024
$268$	−7.81947	−0.477650
$269$	20.5861	1.25516	0.627578	−	0.778554i	$-0.284046\pi$
$269$	20.5861	1.25516	0.627578	+	0.778554i	$0.284046\pi$
$270$	3.99205	0.242948
$271$	0.782106	0.0475095	0.0237548	−	0.999718i	$-0.492438\pi$
$271$	0.782106	0.0475095	0.0237548	+	0.999718i	$0.492438\pi$
$272$	3.17873	0.192739
$273$	−0.541542	−0.0327756
$274$	9.99080	0.603567
$275$	−3.93545	−0.237317
$276$	−0.355872	−0.0214210
$277$	−1.45462	−0.0873995	−0.0436998	−	0.999045i	$-0.513914\pi$
$277$	−1.45462	−0.0873995	−0.0436998	+	0.999045i	$0.513914\pi$
$278$	10.4275	0.625397
$279$	−9.90715	−0.593125
$280$	−0.758978	−0.0453576
$281$	−6.59861	−0.393640	−0.196820	−	0.980440i	$-0.563062\pi$
$281$	−6.59861	−0.393640	−0.196820	+	0.980440i	$0.563062\pi$
$282$	3.03330	0.180631
$283$	−9.38426	−0.557837	−0.278918	−	0.960315i	$-0.589976\pi$
$283$	−9.38426	−0.557837	−0.278918	+	0.960315i	$0.589976\pi$
$284$	5.88984	0.349498
$285$	0.607008	0.0359560
$286$	−13.7318	−0.811977
$287$	−9.56656	−0.564696
$288$	−23.3898	−1.37826
$289$	−15.9760	−0.939766
$290$	−16.1054	−0.945741
$291$	−0.294079	−0.0172392
$292$	28.7820	1.68434
$293$	16.1488	0.943425	0.471712	−	0.881753i	$-0.343636\pi$
$293$	16.1488	0.943425	0.471712	+	0.881753i	$0.343636\pi$
$294$	0.677204	0.0394953
$295$	−8.41562	−0.489976
$296$	−1.70375	−0.0990282
$297$	−7.52109	−0.436418
$298$	−49.7761	−2.88345
$299$	−0.775853	−0.0448687
$300$	−0.766191	−0.0442360
$301$	10.3611	0.597205
$302$	34.6883	1.99609
$303$	0.263245	0.0151230
$304$	−5.88156	−0.337331
$305$	9.55983	0.547394
$306$	−6.11912	−0.349807
$307$	−8.11623	−0.463218	−0.231609	−	0.972809i	$-0.574399\pi$
$307$	−8.11623	−0.463218	−0.231609	+	0.972809i	$0.574399\pi$
$308$	9.30084	0.529964
$309$	0.580159	0.0330041
$310$	7.14867	0.406017
$311$	−26.4639	−1.50063	−0.750315	−	0.661080i	$-0.770098\pi$
$311$	−26.4639	−1.50063	−0.750315	+	0.661080i	$0.770098\pi$
$312$	−0.411018	−0.0232693
$313$	−28.4390	−1.60747	−0.803734	−	0.594989i	$-0.797157\pi$
$313$	−28.4390	−1.60747	−0.803734	+	0.594989i	$0.797157\pi$
$314$	−40.2477	−2.27131
$315$	−2.89490	−0.163109
$316$	19.2585	1.08337
$317$	8.95945	0.503213	0.251606	−	0.967830i	$-0.419041\pi$
$317$	8.95945	0.503213	0.251606	+	0.967830i	$0.419041\pi$
$318$	4.95570	0.277902
$319$	30.3428	1.69887
$320$	10.5948	0.592265
$321$	5.37770	0.300154
$322$	0.970213	0.0540678
$323$	−1.89466	−0.105422
$324$	19.0606	1.05892
$325$	−1.67041	−0.0926575
$326$	42.3369	2.34483
$327$	−0.888392	−0.0491282
$328$	−7.26081	−0.400911
$329$	−4.47916	−0.246944
$330$	2.66510	0.146709
$331$	29.4540	1.61894	0.809470	−	0.587161i	$-0.199755\pi$
$331$	29.4540	1.61894	0.809470	+	0.587161i	$0.199755\pi$
$332$	38.0113	2.08614
$333$	−6.49843	−0.356112
$334$	20.9169	1.14452
$335$	3.30864	0.180771
$336$	−1.01840	−0.0555582
$337$	−15.2272	−0.829478	−0.414739	−	0.909941i	$-0.636127\pi$
$337$	−15.2272	−0.829478	−0.414739	+	0.909941i	$0.636127\pi$
$338$	21.3267	1.16002
$339$	5.47754	0.297499
$340$	2.39152	0.129698
$341$	−13.4682	−0.729345
$342$	11.3221	0.612230
$343$	−1.00000	−0.0539949
$344$	7.86386	0.423991
$345$	0.150580	0.00810695
$346$	15.5389	0.835374
$347$	9.21147	0.494498	0.247249	−	0.968952i	$-0.420473\pi$
$347$	9.21147	0.494498	0.247249	+	0.968952i	$0.420473\pi$
$348$	5.90742	0.316671
$349$	4.33302	0.231941	0.115971	−	0.993253i	$-0.463002\pi$
$349$	4.33302	0.231941	0.115971	+	0.993253i	$0.463002\pi$
$350$	2.08886	0.111654
$351$	−3.19233	−0.170394
$352$	−31.7972	−1.69480
$353$	3.17109	0.168780	0.0843900	−	0.996433i	$-0.473106\pi$
$353$	3.17109	0.168780	0.0843900	+	0.996433i	$0.473106\pi$
$354$	5.69909	0.302903
$355$	−2.49216	−0.132270
$356$	17.1556	0.909247
$357$	−0.328062	−0.0173629
$358$	1.00269	0.0529940
$359$	31.8744	1.68227	0.841134	−	0.540826i	$-0.181888\pi$
$359$	31.8744	1.68227	0.841134	+	0.540826i	$0.181888\pi$
$360$	−2.19716	−0.115801
$361$	−15.4943	−0.815492
$362$	26.2366	1.37897
$363$	−1.45493	−0.0763642
$364$	3.94775	0.206918
$365$	−12.1785	−0.637451
$366$	−6.47395	−0.338399
$367$	2.14177	0.111799	0.0558997	−	0.998436i	$-0.482197\pi$
$367$	2.14177	0.111799	0.0558997	+	0.998436i	$0.482197\pi$
$368$	−1.45903	−0.0760574
$369$	−27.6942	−1.44170
$370$	4.68906	0.243772
$371$	−7.31789	−0.379926
$372$	−2.62212	−0.135951
$373$	1.78578	0.0924642	0.0462321	−	0.998931i	$-0.485279\pi$
$373$	1.78578	0.0924642	0.0462321	+	0.998931i	$0.485279\pi$
$374$	−8.31861	−0.430145
$375$	0.324198	0.0167415
$376$	−3.39958	−0.175320
$377$	12.8790	0.663305
$378$	3.99205	0.205329
$379$	34.7730	1.78617	0.893085	−	0.449887i	$-0.148536\pi$
$379$	34.7730	1.78617	0.893085	+	0.449887i	$0.148536\pi$
$380$	−4.42498	−0.226997
$381$	−3.18886	−0.163370
$382$	−4.95395	−0.253466
$383$	−6.73272	−0.344026	−0.172013	−	0.985095i	$-0.555027\pi$
$383$	−6.73272	−0.344026	−0.172013	+	0.985095i	$0.555027\pi$
$384$	−1.93598	−0.0987953
$385$	−3.93545	−0.200569
$386$	24.1530	1.22936
$387$	29.9944	1.52470
$388$	2.14379	0.108834
$389$	17.7338	0.899141	0.449570	−	0.893245i	$-0.351577\pi$
$389$	17.7338	0.899141	0.449570	+	0.893245i	$0.351577\pi$
$390$	1.13121	0.0572809
$391$	−0.470006	−0.0237692
$392$	−0.758978	−0.0383342
$393$	−3.72620	−0.187962
$394$	0.986879	0.0497182
$395$	−8.14883	−0.410012
$396$	26.9250	1.35303
$397$	33.1431	1.66341	0.831703	−	0.555221i	$-0.187366\pi$
$397$	33.1431	1.66341	0.831703	+	0.555221i	$0.187366\pi$
$398$	−14.7249	−0.738093
$399$	0.607008	0.0303884
$400$	−3.14129	−0.157065
$401$	−0.863227	−0.0431075	−0.0215537	−	0.999768i	$-0.506861\pi$
$401$	−0.863227	−0.0431075	−0.0215537	+	0.999768i	$0.506861\pi$
$402$	−2.24063	−0.111752
$403$	−5.71660	−0.284764
$404$	−1.91901	−0.0954742
$405$	−8.06511	−0.400759
$406$	−16.1054	−0.799297
$407$	−8.83427	−0.437898
$408$	−0.248992	−0.0123269
$409$	34.5688	1.70932	0.854659	−	0.519189i	$-0.173766\pi$
$409$	34.5688	1.70932	0.854659	+	0.519189i	$0.173766\pi$
$410$	19.9832	0.986902
$411$	1.55060	0.0764856
$412$	−4.22926	−0.208361
$413$	−8.41562	−0.414105
$414$	2.80866	0.138038
$415$	−16.0837	−0.789517
$416$	−13.4964	−0.661713
$417$	1.61837	0.0792520
$418$	15.3918	0.752837
$419$	−10.6611	−0.520826	−0.260413	−	0.965497i	$-0.583859\pi$
$419$	−10.6611	−0.520826	−0.260413	+	0.965497i	$0.583859\pi$
$420$	−0.766191	−0.0373863
$421$	−34.6814	−1.69027	−0.845133	−	0.534556i	$-0.820479\pi$
$421$	−34.6814	−1.69027	−0.845133	+	0.534556i	$0.820479\pi$
$422$	−36.6605	−1.78461
$423$	−12.9667	−0.630463
$424$	−5.55411	−0.269732
$425$	−1.01192	−0.0490853
$426$	1.68770	0.0817694
$427$	9.55983	0.462632
$428$	−39.2025	−1.89492
$429$	−2.13121	−0.102896
$430$	−21.6429	−1.04372
$431$	14.9975	0.722404	0.361202	−	0.932488i	$-0.382366\pi$
$431$	14.9975	0.722404	0.361202	+	0.932488i	$0.382366\pi$
$432$	−6.00335	−0.288836
$433$	−17.7964	−0.855240	−0.427620	−	0.903959i	$-0.640648\pi$
$433$	−17.7964	−0.855240	−0.427620	+	0.903959i	$0.640648\pi$
$434$	7.14867	0.343147
$435$	−2.49960	−0.119847
$436$	6.47623	0.310155
$437$	0.869644	0.0416007
$438$	8.24732	0.394072
$439$	−19.9023	−0.949887	−0.474943	−	0.880016i	$-0.657531\pi$
$439$	−19.9023	−0.949887	−0.474943	+	0.880016i	$0.657531\pi$
$440$	−2.98692	−0.142396
$441$	−2.89490	−0.137852
$442$	−3.53084	−0.167945
$443$	3.60677	0.171363	0.0856814	−	0.996323i	$-0.472693\pi$
$443$	3.60677	0.171363	0.0856814	+	0.996323i	$0.472693\pi$
$444$	−1.71994	−0.0816246
$445$	−7.25905	−0.344112
$446$	49.1485	2.32725
$447$	−7.72540	−0.365399
$448$	10.5948	0.500555
$449$	−32.3831	−1.52825	−0.764126	−	0.645068i	$-0.776829\pi$
$449$	−32.3831	−1.52825	−0.764126	+	0.645068i	$0.776829\pi$
$450$	6.04704	0.285060
$451$	−37.6488	−1.77281
$452$	−39.9303	−1.87816
$453$	5.38372	0.252949
$454$	−44.6646	−2.09621
$455$	−1.67041	−0.0783099
$456$	0.460705	0.0215745
$457$	−3.36274	−0.157302	−0.0786512	−	0.996902i	$-0.525061\pi$
$457$	−3.36274	−0.157302	−0.0786512	+	0.996902i	$0.525061\pi$
$458$	2.08886	0.0976061
$459$	−1.93389	−0.0902663
$460$	−1.09770	−0.0511806
$461$	37.6573	1.75387	0.876937	−	0.480605i	$-0.159583\pi$
$461$	37.6573	1.75387	0.876937	+	0.480605i	$0.159583\pi$
$462$	2.66510	0.123992
$463$	−35.2514	−1.63827	−0.819136	−	0.573599i	$-0.805547\pi$
$463$	−35.2514	−1.63827	−0.819136	+	0.573599i	$0.805547\pi$
$464$	24.2197	1.12437
$465$	1.10949	0.0514516
$466$	−26.1201	−1.20999
$467$	−6.93304	−0.320823	−0.160411	−	0.987050i	$-0.551282\pi$
$467$	−6.93304	−0.320823	−0.160411	+	0.987050i	$0.551282\pi$
$468$	11.4283	0.528274
$469$	3.30864	0.152779
$470$	9.35635	0.431576
$471$	−6.24656	−0.287826
$472$	−6.38726	−0.293998
$473$	40.7757	1.87487
$474$	5.51842	0.253469
$475$	1.87234	0.0859088
$476$	2.39152	0.109615
$477$	−21.1845	−0.969973
$478$	19.5605	0.894679
$479$	−4.84548	−0.221396	−0.110698	−	0.993854i	$-0.535309\pi$
$479$	−4.84548	−0.221396	−0.110698	+	0.993854i	$0.535309\pi$
$480$	2.61941	0.119559
$481$	−3.74971	−0.170972
$482$	−29.8551	−1.35986
$483$	0.150580	0.00685162
$484$	10.6062	0.482101
$485$	−0.907099	−0.0411893
$486$	17.4379	0.790998
$487$	35.6312	1.61460	0.807301	−	0.590140i	$-0.200927\pi$
$487$	35.6312	1.61460	0.807301	+	0.590140i	$0.200927\pi$
$488$	7.25570	0.328450
$489$	6.57081	0.297143
$490$	2.08886	0.0943652
$491$	5.88648	0.265653	0.132826	−	0.991139i	$-0.457595\pi$
$491$	5.88648	0.265653	0.132826	+	0.991139i	$0.457595\pi$
$492$	−7.32981	−0.330453
$493$	7.80203	0.351386
$494$	6.53306	0.293936
$495$	−11.3927	−0.512065
$496$	−10.7504	−0.482706
$497$	−2.49216	−0.111789
$498$	10.8919	0.488079
$499$	1.11873	0.0500814	0.0250407	−	0.999686i	$-0.492028\pi$
$499$	1.11873	0.0500814	0.0250407	+	0.999686i	$0.492028\pi$
$500$	−2.36335	−0.105692
$501$	3.24636	0.145037
$502$	−38.1040	−1.70066
$503$	−9.45469	−0.421564	−0.210782	−	0.977533i	$-0.567601\pi$
$503$	−9.45469	−0.421564	−0.210782	+	0.977533i	$0.567601\pi$
$504$	−2.19716	−0.0978693
$505$	0.811988	0.0361330
$506$	3.81823	0.169741
$507$	3.30997	0.147001
$508$	23.2463	1.03139
$509$	18.3431	0.813043	0.406522	−	0.913641i	$-0.366742\pi$
$509$	18.3431	0.813043	0.406522	+	0.913641i	$0.366742\pi$
$510$	0.685276	0.0303445
$511$	−12.1785	−0.538745
$512$	−30.1490	−1.33241
$513$	3.57825	0.157984
$514$	1.09057	0.0481029
$515$	1.78952	0.0788558
$516$	7.93859	0.349477
$517$	−17.6275	−0.775258
$518$	4.68906	0.206025
$519$	2.41168	0.105861
$520$	−1.26780	−0.0555968
$521$	5.08221	0.222656	0.111328	−	0.993784i	$-0.464490\pi$
$521$	5.08221	0.222656	0.111328	+	0.993784i	$0.464490\pi$
$522$	−46.6234	−2.04065
$523$	24.2038	1.05836	0.529180	−	0.848510i	$-0.322500\pi$
$523$	24.2038	1.05836	0.529180	+	0.848510i	$0.322500\pi$
$524$	27.1634	1.18664
$525$	0.324198	0.0141491
$526$	61.2014	2.66851
$527$	−3.46307	−0.150854
$528$	−4.00786	−0.174420
$529$	−22.7843	−0.990620
$530$	15.2861	0.663984
$531$	−24.3623	−1.05724
$532$	−4.42498	−0.191847
$533$	−15.9801	−0.692173
$534$	4.91585	0.212730
$535$	16.5877	0.717150
$536$	2.51119	0.108467
$537$	0.155621	0.00671554
$538$	−43.0015	−1.85393
$539$	−3.93545	−0.169512
$540$	−4.51661	−0.194364
$541$	4.05863	0.174494	0.0872471	−	0.996187i	$-0.472193\pi$
$541$	4.05863	0.174494	0.0872471	+	0.996187i	$0.472193\pi$
$542$	−1.63371	−0.0701739
$543$	4.07200	0.174746
$544$	−8.17599	−0.350543
$545$	−2.74028	−0.117381
$546$	1.13121	0.0484112
$547$	−7.35994	−0.314688	−0.157344	−	0.987544i	$-0.550293\pi$
$547$	−7.35994	−0.314688	−0.157344	+	0.987544i	$0.550293\pi$
$548$	−11.3036	−0.482867
$549$	27.6747	1.18113
$550$	8.22062	0.350528
$551$	−14.4360	−0.614993
$552$	0.114287	0.00486437
$553$	−8.14883	−0.346523
$554$	3.03850	0.129093
$555$	0.727755	0.0308915
$556$	−11.7977	−0.500332
$557$	−37.4593	−1.58720	−0.793601	−	0.608438i	$-0.791796\pi$
$557$	−37.4593	−1.58720	−0.793601	+	0.608438i	$0.791796\pi$
$558$	20.6947	0.876075
$559$	17.3073	0.732020
$560$	−3.14129	−0.132744
$561$	−1.29107	−0.0545091
$562$	13.7836	0.581426
$563$	−12.8578	−0.541892	−0.270946	−	0.962595i	$-0.587337\pi$
$563$	−12.8578	−0.541892	−0.270946	+	0.962595i	$0.587337\pi$
$564$	−3.43189	−0.144509
$565$	16.8957	0.710807
$566$	19.6024	0.823952
$567$	−8.06511	−0.338703
$568$	−1.89150	−0.0793654
$569$	−42.6116	−1.78637	−0.893185	−	0.449689i	$-0.851535\pi$
$569$	−42.6116	−1.78637	−0.893185	+	0.449689i	$0.851535\pi$
$570$	−1.26796	−0.0531088
$571$	7.77989	0.325578	0.162789	−	0.986661i	$-0.447951\pi$
$571$	7.77989	0.325578	0.162789	+	0.986661i	$0.447951\pi$
$572$	15.5362	0.649600
$573$	−0.768868	−0.0321199
$574$	19.9832	0.834084
$575$	0.464469	0.0193697
$576$	30.6707	1.27795
$577$	11.1999	0.466259	0.233129	−	0.972446i	$-0.425103\pi$
$577$	11.1999	0.466259	0.233129	+	0.972446i	$0.425103\pi$
$578$	33.3717	1.38808
$579$	3.74862	0.155787
$580$	18.2217	0.756614
$581$	−16.0837	−0.667264
$582$	0.614291	0.0254632
$583$	−28.7992	−1.19274
$584$	−9.24320	−0.382486
$585$	−4.83565	−0.199930
$586$	−33.7327	−1.39348
$587$	−10.6065	−0.437776	−0.218888	−	0.975750i	$-0.570243\pi$
$587$	−10.6065	−0.437776	−0.218888	+	0.975750i	$0.570243\pi$
$588$	−0.766191	−0.0315972
$589$	6.40767	0.264023
$590$	17.5791	0.723718
$591$	0.153167	0.00630043
$592$	−7.05154	−0.289816
$593$	−30.1687	−1.23888	−0.619440	−	0.785044i	$-0.712640\pi$
$593$	−30.1687	−1.23888	−0.619440	+	0.785044i	$0.712640\pi$
$594$	15.7105	0.644610
$595$	−1.01192	−0.0414847
$596$	56.3168	2.30683
$597$	−2.28535	−0.0935331
$598$	1.62065	0.0662733
$599$	15.5209	0.634167	0.317083	−	0.948398i	$-0.397296\pi$
$599$	15.5209	0.634167	0.317083	+	0.948398i	$0.397296\pi$
$600$	0.246059	0.0100453
$601$	13.4984	0.550611	0.275305	−	0.961357i	$-0.411221\pi$
$601$	13.4984	0.550611	0.275305	+	0.961357i	$0.411221\pi$
$602$	−21.6429	−0.882101
$603$	9.57818	0.390054
$604$	−39.2464	−1.59692
$605$	−4.48780	−0.182455
$606$	−0.549882	−0.0223374
$607$	−27.7028	−1.12442	−0.562210	−	0.826994i	$-0.690049\pi$
$607$	−27.7028	−1.12442	−0.562210	+	0.826994i	$0.690049\pi$
$608$	15.1279	0.613517
$609$	−2.49960	−0.101289
$610$	−19.9692	−0.808528
$611$	−7.48202	−0.302690
$612$	6.92319	0.279853
$613$	−17.7951	−0.718736	−0.359368	−	0.933196i	$-0.617008\pi$
$613$	−17.7951	−0.718736	−0.359368	+	0.933196i	$0.617008\pi$
$614$	16.9537	0.684195
$615$	3.10146	0.125063
$616$	−2.98692	−0.120347
$617$	−1.00075	−0.0402888	−0.0201444	−	0.999797i	$-0.506413\pi$
$617$	−1.00075	−0.0402888	−0.0201444	+	0.999797i	$0.506413\pi$
$618$	−1.21187	−0.0487487
$619$	11.5022	0.462313	0.231157	−	0.972917i	$-0.425749\pi$
$619$	11.5022	0.462313	0.231157	+	0.972917i	$0.425749\pi$
$620$	−8.08803	−0.324823
$621$	0.887653	0.0356203
$622$	55.2794	2.21650
$623$	−7.25905	−0.290828
$624$	−1.70114	−0.0681001
$625$	1.00000	0.0400000
$626$	59.4052	2.37431
$627$	2.38885	0.0954015
$628$	45.5363	1.81710
$629$	−2.27155	−0.0905725
$630$	6.04704	0.240920
$631$	−45.4846	−1.81071	−0.905357	−	0.424651i	$-0.860397\pi$
$631$	−45.4846	−1.81071	−0.905357	+	0.424651i	$0.860397\pi$
$632$	−6.18478	−0.246017
$633$	−5.68982	−0.226150
$634$	−18.7151	−0.743270
$635$	−9.83617	−0.390336
$636$	−5.60690	−0.222328
$637$	−1.67041	−0.0661839
$638$	−63.3820	−2.50932
$639$	−7.21455	−0.285403
$640$	−5.97162	−0.236049
$641$	20.5483	0.811609	0.405804	−	0.913960i	$-0.366991\pi$
$641$	20.5483	0.811609	0.405804	+	0.913960i	$0.366991\pi$
$642$	−11.2333	−0.443342
$643$	3.89285	0.153519	0.0767594	−	0.997050i	$-0.475543\pi$
$643$	3.89285	0.153519	0.0767594	+	0.997050i	$0.475543\pi$
$644$	−1.09770	−0.0432555
$645$	−3.35905	−0.132262
$646$	3.95768	0.155713
$647$	−34.8544	−1.37027	−0.685133	−	0.728418i	$-0.740256\pi$
$647$	−34.8544	−1.37027	−0.685133	+	0.728418i	$0.740256\pi$
$648$	−6.12124	−0.240465
$649$	−33.1193	−1.30004
$650$	3.48925	0.136860
$651$	1.10949	0.0434845
$652$	−47.9001	−1.87591
$653$	−16.5243	−0.646646	−0.323323	−	0.946289i	$-0.604800\pi$
$653$	−16.5243	−0.646646	−0.323323	+	0.946289i	$0.604800\pi$
$654$	1.85573	0.0725647
$655$	−11.4936	−0.449093
$656$	−30.0514	−1.17331
$657$	−35.2555	−1.37545
$658$	9.35635	0.364748
$659$	−36.2422	−1.41180	−0.705898	−	0.708313i	$-0.749456\pi$
$659$	−36.2422	−1.41180	−0.705898	+	0.708313i	$0.749456\pi$
$660$	−3.01531	−0.117371
$661$	43.8473	1.70546	0.852731	−	0.522351i	$-0.174945\pi$
$661$	43.8473	1.70546	0.852731	+	0.522351i	$0.174945\pi$
$662$	−61.5254	−2.39125
$663$	−0.547997	−0.0212824
$664$	−12.2072	−0.473730
$665$	1.87234	0.0726062
$666$	13.5743	0.525995
$667$	−3.58112	−0.138661
$668$	−23.6654	−0.915642
$669$	7.62799	0.294915
$670$	−6.91130	−0.267007
$671$	37.6223	1.45239
$672$	2.61941	0.101046
$673$	−0.500754	−0.0193026	−0.00965132	−	0.999953i	$-0.503072\pi$
$673$	−0.500754	−0.0193026	−0.00965132	+	0.999953i	$0.503072\pi$
$674$	31.8075	1.22518
$675$	1.91111	0.0735587
$676$	−24.1291	−0.928044
$677$	−0.381927	−0.0146786	−0.00733931	−	0.999973i	$-0.502336\pi$
$677$	−0.381927	−0.0146786	−0.00733931	+	0.999973i	$0.502336\pi$
$678$	−11.4418	−0.439420
$679$	−0.907099	−0.0348113
$680$	−0.768025	−0.0294524
$681$	−6.93208	−0.265638
$682$	28.1333	1.07728
$683$	−14.4088	−0.551336	−0.275668	−	0.961253i	$-0.588899\pi$
$683$	−14.4088	−0.551336	−0.275668	+	0.961253i	$0.588899\pi$
$684$	−12.8099	−0.489798
$685$	4.78289	0.182745
$686$	2.08886	0.0797531
$687$	0.324198	0.0123689
$688$	32.5473	1.24085
$689$	−12.2239	−0.465692
$690$	−0.314541	−0.0119744
$691$	−13.6635	−0.519782	−0.259891	−	0.965638i	$-0.583687\pi$
$691$	−13.6635	−0.519782	−0.259891	+	0.965638i	$0.583687\pi$
$692$	−17.5807	−0.668318
$693$	−11.3927	−0.432774
$694$	−19.2415	−0.730397
$695$	4.99193	0.189355
$696$	−1.89714	−0.0719110
$697$	−9.68060	−0.366679
$698$	−9.05108	−0.342588
$699$	−4.05391	−0.153333
$700$	−2.36335	−0.0893260
$701$	−5.67236	−0.214242	−0.107121	−	0.994246i	$-0.534163\pi$
$701$	−5.67236	−0.214242	−0.107121	+	0.994246i	$0.534163\pi$
$702$	6.66834	0.251680
$703$	4.20301	0.158519
$704$	41.6952	1.57145
$705$	1.45213	0.0546905
$706$	−6.62397	−0.249296
$707$	0.811988	0.0305380
$708$	−6.44797	−0.242329
$709$	−0.657287	−0.0246849	−0.0123425	−	0.999924i	$-0.503929\pi$
$709$	−0.657287	−0.0246849	−0.0123425	+	0.999924i	$0.503929\pi$
$710$	5.20578	0.195370
$711$	−23.5900	−0.884695
$712$	−5.50945	−0.206476
$713$	1.58954	0.0595289
$714$	0.685276	0.0256458
$715$	−6.57381	−0.245847
$716$	−1.13445	−0.0423964
$717$	3.03585	0.113376
$718$	−66.5813	−2.48479
$719$	32.0949	1.19694	0.598469	−	0.801146i	$-0.295776\pi$
$719$	32.0949	1.19694	0.598469	+	0.801146i	$0.295776\pi$
$720$	−9.09371	−0.338903
$721$	1.78952	0.0666453
$722$	32.3656	1.20452
$723$	−4.63360	−0.172325
$724$	−29.6842	−1.10320
$725$	−7.71012	−0.286347
$726$	3.03915	0.112794
$727$	−0.458061	−0.0169886	−0.00849428	−	0.999964i	$-0.502704\pi$
$727$	−0.458061	−0.0169886	−0.00849428	+	0.999964i	$0.502704\pi$
$728$	−1.26780	−0.0469879
$729$	−21.4889	−0.795886
$730$	25.4392	0.941546
$731$	10.4846	0.387788
$732$	7.32465	0.270727
$733$	−8.65313	−0.319611	−0.159805	−	0.987149i	$-0.551087\pi$
$733$	−8.65313	−0.319611	−0.159805	+	0.987149i	$0.551087\pi$
$734$	−4.47386	−0.165133
$735$	0.324198	0.0119582
$736$	3.75276	0.138329
$737$	13.0210	0.479635
$738$	57.8494	2.12947
$739$	47.4585	1.74579	0.872894	−	0.487911i	$-0.162241\pi$
$739$	47.4585	1.74579	0.872894	+	0.487911i	$0.162241\pi$
$740$	−5.30521	−0.195024
$741$	1.01395	0.0372484
$742$	15.2861	0.561169
$743$	2.95128	0.108272	0.0541359	−	0.998534i	$-0.482760\pi$
$743$	2.95128	0.108272	0.0541359	+	0.998534i	$0.482760\pi$
$744$	0.842082	0.0308722
$745$	−23.8293	−0.873038
$746$	−3.73025	−0.136574
$747$	−46.5606	−1.70356
$748$	9.41170	0.344126
$749$	16.5877	0.606102
$750$	−0.677204	−0.0247280
$751$	30.3263	1.10662	0.553312	−	0.832974i	$-0.313364\pi$
$751$	30.3263	1.10662	0.553312	+	0.832974i	$0.313364\pi$
$752$	−14.0703	−0.513093
$753$	−5.91385	−0.215513
$754$	−26.9025	−0.979733
$755$	16.6063	0.604366
$756$	−4.51661	−0.164268
$757$	−26.4586	−0.961656	−0.480828	−	0.876815i	$-0.659664\pi$
$757$	−26.4586	−0.961656	−0.480828	+	0.876815i	$0.659664\pi$
$758$	−72.6361	−2.63826
$759$	0.592600	0.0215100
$760$	1.42106	0.0515474
$761$	−3.77177	−0.136726	−0.0683632	−	0.997660i	$-0.521778\pi$
$761$	−3.77177	−0.136726	−0.0683632	+	0.997660i	$0.521778\pi$
$762$	6.66109	0.241306
$763$	−2.74028	−0.0992048
$764$	5.60491	0.202779
$765$	−2.92940	−0.105913
$766$	14.0637	0.508143
$767$	−14.0575	−0.507587
$768$	−2.82558	−0.101959
$769$	−48.1869	−1.73766	−0.868831	−	0.495109i	$-0.835128\pi$
$769$	−48.1869	−1.73766	−0.868831	+	0.495109i	$0.835128\pi$
$770$	8.22062	0.296251
$771$	0.169259	0.00609573
$772$	−27.3268	−0.983513
$773$	40.3648	1.45182	0.725911	−	0.687789i	$-0.241419\pi$
$773$	40.3648	1.45182	0.725911	+	0.687789i	$0.241419\pi$
$774$	−62.6541	−2.25205
$775$	3.42228	0.122932
$776$	−0.688468	−0.0247146
$777$	0.727755	0.0261081
$778$	−37.0435	−1.32807
$779$	17.9119	0.641759
$780$	−1.27985	−0.0458260
$781$	−9.80779	−0.350950
$782$	0.981778	0.0351083
$783$	−14.7349	−0.526582
$784$	−3.14129	−0.112189
$785$	−19.2678	−0.687696
$786$	7.78352	0.277629
$787$	44.7645	1.59568	0.797841	−	0.602868i	$-0.205976\pi$
$787$	44.7645	1.59568	0.797841	+	0.602868i	$0.205976\pi$
$788$	−1.11656	−0.0397757
$789$	9.49864	0.338161
$790$	17.0218	0.605608
$791$	16.8957	0.600741
$792$	−8.64683	−0.307252
$793$	15.9688	0.567069
$794$	−69.2314	−2.45693
$795$	2.37244	0.0841418
$796$	16.6598	0.590491
$797$	−0.0538633	−0.00190794	−0.000953968	−	1.00000i	$-0.500304\pi$
$797$	−0.0538633	−0.00190794	−0.000953968		1.00000i	$0.500304\pi$
$798$	−1.26796	−0.0448851
$799$	−4.53255	−0.160350
$800$	8.07968	0.285660
$801$	−21.0142	−0.742500
$802$	1.80316	0.0636719
$803$	−47.9279	−1.69134
$804$	2.53505	0.0894044
$805$	0.464469	0.0163704
$806$	11.9412	0.420611
$807$	−6.67396	−0.234935
$808$	0.616281	0.0216807
$809$	22.6641	0.796826	0.398413	−	0.917206i	$-0.369561\pi$
$809$	22.6641	0.796826	0.398413	+	0.917206i	$0.369561\pi$
$810$	16.8469	0.591940
$811$	−17.3284	−0.608481	−0.304241	−	0.952595i	$-0.598403\pi$
$811$	−17.3284	−0.608481	−0.304241	+	0.952595i	$0.598403\pi$
$812$	18.2217	0.639456
$813$	−0.253557	−0.00889262
$814$	18.4536	0.646797
$815$	20.2679	0.709955
$816$	−1.03054	−0.0360760
$817$	−19.3995	−0.678704
$818$	−72.2095	−2.52475
$819$	−4.83565	−0.168971
$820$	−22.6091	−0.789544
$821$	−1.43532	−0.0500930	−0.0250465	−	0.999686i	$-0.507973\pi$
$821$	−1.43532	−0.0500930	−0.0250465	+	0.999686i	$0.507973\pi$
$822$	−3.23899	−0.112973
$823$	−4.86827	−0.169697	−0.0848486	−	0.996394i	$-0.527041\pi$
$823$	−4.86827	−0.169697	−0.0848486	+	0.996394i	$0.527041\pi$
$824$	1.35821	0.0473154
$825$	1.27586	0.0444199
$826$	17.5791	0.611654
$827$	−14.2708	−0.496243	−0.248122	−	0.968729i	$-0.579813\pi$
$827$	−14.2708	−0.496243	−0.248122	+	0.968729i	$0.579813\pi$
$828$	−3.17773	−0.110434
$829$	−34.4153	−1.19529	−0.597646	−	0.801760i	$-0.703897\pi$
$829$	−34.4153	−1.19529	−0.597646	+	0.801760i	$0.703897\pi$
$830$	33.5966	1.16616
$831$	0.471584	0.0163591
$832$	17.6975	0.613552
$833$	−1.01192	−0.0350609
$834$	−3.38055	−0.117059
$835$	10.0135	0.346532
$836$	−17.4143	−0.602287
$837$	6.54036	0.226068
$838$	22.2695	0.769286
$839$	17.0362	0.588156	0.294078	−	0.955781i	$-0.404987\pi$
$839$	17.0362	0.588156	0.294078	+	0.955781i	$0.404987\pi$
$840$	0.246059	0.00848983
$841$	30.4460	1.04986
$842$	72.4446	2.49661
$843$	2.13925	0.0736798
$844$	41.4778	1.42773
$845$	10.2097	0.351226
$846$	27.0857	0.931224
$847$	−4.48780	−0.154203
$848$	−22.9876	−0.789398
$849$	3.04236	0.104413
$850$	2.11376	0.0725014
$851$	1.04264	0.0357411
$852$	−1.90947	−0.0654174
$853$	−36.9589	−1.26545	−0.632724	−	0.774378i	$-0.718063\pi$
$853$	−36.9589	−1.26545	−0.632724	+	0.774378i	$0.718063\pi$
$854$	−19.9692	−0.683331
$855$	5.42023	0.185368
$856$	12.5897	0.430307
$857$	46.0741	1.57386	0.786931	−	0.617041i	$-0.211669\pi$
$857$	46.0741	1.57386	0.786931	+	0.617041i	$0.211669\pi$
$858$	4.45181	0.151982
$859$	−41.4572	−1.41450	−0.707251	−	0.706962i	$-0.750065\pi$
$859$	−41.4572	−1.41450	−0.707251	+	0.706962i	$0.750065\pi$
$860$	24.4869	0.834996
$861$	3.10146	0.105697
$862$	−31.3277	−1.06703
$863$	−8.20510	−0.279305	−0.139652	−	0.990201i	$-0.544599\pi$
$863$	−8.20510	−0.279305	−0.139652	+	0.990201i	$0.544599\pi$
$864$	15.4412	0.525319
$865$	7.43891	0.252931
$866$	37.1742	1.26323
$867$	5.17939	0.175901
$868$	−8.08803	−0.274526
$869$	−32.0693	−1.08788
$870$	5.22133	0.177020
$871$	5.52678	0.187268
$872$	−2.07981	−0.0704313
$873$	−2.62596	−0.0888752
$874$	−1.81657	−0.0614463
$875$	1.00000	0.0338062
$876$	−9.33104	−0.315267
$877$	25.4616	0.859776	0.429888	−	0.902882i	$-0.358553\pi$
$877$	25.4616	0.859776	0.429888	+	0.902882i	$0.358553\pi$
$878$	41.5732	1.40303
$879$	−5.23541	−0.176586
$880$	−12.3624	−0.416737
$881$	10.5426	0.355191	0.177595	−	0.984104i	$-0.443168\pi$
$881$	10.5426	0.355191	0.177595	+	0.984104i	$0.443168\pi$
$882$	6.04704	0.203614
$883$	8.95273	0.301283	0.150642	−	0.988588i	$-0.451866\pi$
$883$	8.95273	0.301283	0.150642	+	0.988588i	$0.451866\pi$
$884$	3.99481	0.134360
$885$	2.72832	0.0917115
$886$	−7.53405	−0.253111
$887$	−20.5514	−0.690049	−0.345025	−	0.938594i	$-0.612129\pi$
$887$	−20.5514	−0.690049	−0.345025	+	0.938594i	$0.612129\pi$
$888$	0.552350	0.0185357
$889$	−9.83617	−0.329894
$890$	15.1631	0.508270
$891$	−31.7399	−1.06333
$892$	−55.6067	−1.86185
$893$	8.38651	0.280644
$894$	16.1373	0.539712
$895$	0.480019	0.0160453
$896$	−5.97162	−0.199498
$897$	0.251530	0.00839833
$898$	67.6437	2.25730
$899$	−26.3862	−0.880029
$900$	−6.84164	−0.228055
$901$	−7.40512	−0.246700
$902$	78.6431	2.61853
$903$	−3.35905	−0.111782
$904$	12.8234	0.426501
$905$	12.5602	0.417517
$906$	−11.2459	−0.373619
$907$	−19.1304	−0.635216	−0.317608	−	0.948222i	$-0.602880\pi$
$907$	−19.1304	−0.635216	−0.317608	+	0.948222i	$0.602880\pi$
$908$	50.5337	1.67702
$909$	2.35062	0.0779652
$910$	3.48925	0.115668
$911$	−11.2310	−0.372098	−0.186049	−	0.982540i	$-0.559568\pi$
$911$	−11.2310	−0.372098	−0.186049	+	0.982540i	$0.559568\pi$
$912$	1.90679	0.0631401
$913$	−63.2966	−2.09481
$914$	7.02430	0.232343
$915$	−3.09927	−0.102459
$916$	−2.36335	−0.0780871
$917$	−11.4936	−0.379553
$918$	4.03963	0.133328
$919$	−47.8043	−1.57692	−0.788459	−	0.615087i	$-0.789121\pi$
$919$	−47.8043	−1.57692	−0.788459	+	0.615087i	$0.789121\pi$
$920$	0.352522	0.0116223
$921$	2.63126	0.0867030
$922$	−78.6609	−2.59056
$923$	−4.16293	−0.137024
$924$	−3.01531	−0.0991963
$925$	2.24479	0.0738082
$926$	73.6354	2.41981
$927$	5.18048	0.170149
$928$	−62.2953	−2.04494
$929$	−24.1473	−0.792248	−0.396124	−	0.918197i	$-0.629645\pi$
$929$	−24.1473	−0.792248	−0.396124	+	0.918197i	$0.629645\pi$
$930$	−2.31758	−0.0759965
$931$	1.87234	0.0613634
$932$	29.5523	0.968019
$933$	8.57953	0.280881
$934$	14.4822	0.473871
$935$	−3.98236	−0.130237
$936$	−3.67015	−0.119963
$937$	−3.92528	−0.128233	−0.0641166	−	0.997942i	$-0.520423\pi$
$937$	−3.92528	−0.128233	−0.0641166	+	0.997942i	$0.520423\pi$
$938$	−6.91130	−0.225662
$939$	9.21986	0.300879
$940$	−10.5858	−0.345271
$941$	47.3148	1.54242	0.771209	−	0.636582i	$-0.219652\pi$
$941$	47.3148	1.54242	0.771209	+	0.636582i	$0.219652\pi$
$942$	13.0482	0.425133
$943$	4.44338	0.144696
$944$	−26.4359	−0.860415
$945$	1.91111	0.0621684
$946$	−85.1748	−2.76927
$947$	9.77097	0.317514	0.158757	−	0.987318i	$-0.449251\pi$
$947$	9.77097	0.317514	0.158757	+	0.987318i	$0.449251\pi$
$948$	−6.24356	−0.202781
$949$	−20.3430	−0.660363
$950$	−3.91106	−0.126892
$951$	−2.90463	−0.0941891
$952$	−0.768025	−0.0248918
$953$	47.1113	1.52608	0.763042	−	0.646349i	$-0.223705\pi$
$953$	47.1113	1.52608	0.763042	+	0.646349i	$0.223705\pi$
$954$	44.2515	1.43270
$955$	−2.37160	−0.0767432
$956$	−22.1309	−0.715763
$957$	−9.83707	−0.317987
$958$	10.1215	0.327012
$959$	4.78289	0.154448
$960$	−3.43479	−0.110857
$961$	−19.2880	−0.622193
$962$	7.83263	0.252534
$963$	48.0197	1.54741
$964$	33.7782	1.08792
$965$	11.5628	0.372218
$966$	−0.314541	−0.0101202
$967$	−2.84170	−0.0913830	−0.0456915	−	0.998956i	$-0.514549\pi$
$967$	−2.84170	−0.0913830	−0.0456915	+	0.998956i	$0.514549\pi$
$968$	−3.40614	−0.109477
$969$	0.614243	0.0197323
$970$	1.89481	0.0608385
$971$	−6.90391	−0.221557	−0.110778	−	0.993845i	$-0.535334\pi$
$971$	−6.90391	−0.221557	−0.110778	+	0.993845i	$0.535334\pi$
$972$	−19.7293	−0.632816
$973$	4.99193	0.160034
$974$	−74.4286	−2.38485
$975$	0.541542	0.0173432
$976$	30.0302	0.961243
$977$	12.1161	0.387628	0.193814	−	0.981038i	$-0.437914\pi$
$977$	12.1161	0.387628	0.193814	+	0.981038i	$0.437914\pi$
$978$	−13.7255	−0.438894
$979$	−28.5676	−0.913026
$980$	−2.36335	−0.0754943
$981$	−7.93283	−0.253276
$982$	−12.2960	−0.392382
$983$	−27.9444	−0.891287	−0.445643	−	0.895211i	$-0.647025\pi$
$983$	−27.9444	−0.891287	−0.445643	+	0.895211i	$0.647025\pi$
$984$	2.35394	0.0750407
$985$	0.472448	0.0150534
$986$	−16.2974	−0.519014
$987$	1.45213	0.0462219
$988$	−7.39152	−0.235156
$989$	−4.81242	−0.153026
$990$	23.7978	0.756345
$991$	−58.2875	−1.85156	−0.925782	−	0.378058i	$-0.876592\pi$
$991$	−58.2875	−1.85156	−0.925782	+	0.378058i	$0.876592\pi$
$992$	27.6509	0.877918
$993$	−9.54892	−0.303026
$994$	5.20578	0.165117
$995$	−7.04925	−0.223476
$996$	−12.3232	−0.390475
$997$	−30.6875	−0.971882	−0.485941	−	0.873992i	$-0.661523\pi$
$997$	−30.6875	−0.971882	−0.485941	+	0.873992i	$0.661523\pi$
$998$	−2.33688	−0.0739727
$999$	4.29004	0.135731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.8	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.8	✓	49	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08886 q^{2} -0.324198 q^{3} +2.36335 q^{4} -1.00000 q^{5} +0.677204 q^{6} -1.00000 q^{7} -0.758978 q^{8} -2.89490 q^{9} +O(q^{10})\)	\(q-2.08886 q^{2} -0.324198 q^{3} +2.36335 q^{4} -1.00000 q^{5} +0.677204 q^{6} -1.00000 q^{7} -0.758978 q^{8} -2.89490 q^{9} +2.08886 q^{10} -3.93545 q^{11} -0.766191 q^{12} -1.67041 q^{13} +2.08886 q^{14} +0.324198 q^{15} -3.14129 q^{16} -1.01192 q^{17} +6.04704 q^{18} +1.87234 q^{19} -2.36335 q^{20} +0.324198 q^{21} +8.22062 q^{22} +0.464469 q^{23} +0.246059 q^{24} +1.00000 q^{25} +3.48925 q^{26} +1.91111 q^{27} -2.36335 q^{28} -7.71012 q^{29} -0.677204 q^{30} +3.42228 q^{31} +8.07968 q^{32} +1.27586 q^{33} +2.11376 q^{34} +1.00000 q^{35} -6.84164 q^{36} +2.24479 q^{37} -3.91106 q^{38} +0.541542 q^{39} +0.758978 q^{40} +9.56656 q^{41} -0.677204 q^{42} -10.3611 q^{43} -9.30084 q^{44} +2.89490 q^{45} -0.970213 q^{46} +4.47916 q^{47} +1.01840 q^{48} +1.00000 q^{49} -2.08886 q^{50} +0.328062 q^{51} -3.94775 q^{52} +7.31789 q^{53} -3.99205 q^{54} +3.93545 q^{55} +0.758978 q^{56} -0.607008 q^{57} +16.1054 q^{58} +8.41562 q^{59} +0.766191 q^{60} -9.55983 q^{61} -7.14867 q^{62} +2.89490 q^{63} -10.5948 q^{64} +1.67041 q^{65} -2.66510 q^{66} -3.30864 q^{67} -2.39152 q^{68} -0.150580 q^{69} -2.08886 q^{70} +2.49216 q^{71} +2.19716 q^{72} +12.1785 q^{73} -4.68906 q^{74} -0.324198 q^{75} +4.42498 q^{76} +3.93545 q^{77} -1.13121 q^{78} +8.14883 q^{79} +3.14129 q^{80} +8.06511 q^{81} -19.9832 q^{82} +16.0837 q^{83} +0.766191 q^{84} +1.01192 q^{85} +21.6429 q^{86} +2.49960 q^{87} +2.98692 q^{88} +7.25905 q^{89} -6.04704 q^{90} +1.67041 q^{91} +1.09770 q^{92} -1.10949 q^{93} -9.35635 q^{94} -1.87234 q^{95} -2.61941 q^{96} +0.907099 q^{97} -2.08886 q^{98} +11.3927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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