LMFDB - Embedded newform 8015.2.a.k.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.12638 q^{2} -2.96921 q^{3} -0.731259 q^{4} -1.00000 q^{5} +3.34447 q^{6} -1.00000 q^{7} +3.07645 q^{8} +5.81619 q^{9} +O(q^{10})$	\(q-1.12638 q^{2} -2.96921 q^{3} -0.731259 q^{4} -1.00000 q^{5} +3.34447 q^{6} -1.00000 q^{7} +3.07645 q^{8} +5.81619 q^{9} +1.12638 q^{10} +0.347433 q^{11} +2.17126 q^{12} +0.620759 q^{13} +1.12638 q^{14} +2.96921 q^{15} -2.00274 q^{16} -4.61287 q^{17} -6.55126 q^{18} +6.12046 q^{19} +0.731259 q^{20} +2.96921 q^{21} -0.391344 q^{22} -3.99956 q^{23} -9.13460 q^{24} +1.00000 q^{25} -0.699213 q^{26} -8.36183 q^{27} +0.731259 q^{28} +5.05567 q^{29} -3.34447 q^{30} -0.592469 q^{31} -3.89704 q^{32} -1.03160 q^{33} +5.19586 q^{34} +1.00000 q^{35} -4.25314 q^{36} +1.86732 q^{37} -6.89399 q^{38} -1.84316 q^{39} -3.07645 q^{40} +3.62256 q^{41} -3.34447 q^{42} -7.36357 q^{43} -0.254064 q^{44} -5.81619 q^{45} +4.50504 q^{46} +4.51743 q^{47} +5.94656 q^{48} +1.00000 q^{49} -1.12638 q^{50} +13.6966 q^{51} -0.453935 q^{52} -9.04895 q^{53} +9.41864 q^{54} -0.347433 q^{55} -3.07645 q^{56} -18.1729 q^{57} -5.69463 q^{58} -8.35068 q^{59} -2.17126 q^{60} -9.76483 q^{61} +0.667348 q^{62} -5.81619 q^{63} +8.39504 q^{64} -0.620759 q^{65} +1.16198 q^{66} -7.79286 q^{67} +3.37320 q^{68} +11.8755 q^{69} -1.12638 q^{70} +5.96316 q^{71} +17.8932 q^{72} -4.56124 q^{73} -2.10332 q^{74} -2.96921 q^{75} -4.47564 q^{76} -0.347433 q^{77} +2.07611 q^{78} +3.88708 q^{79} +2.00274 q^{80} +7.37946 q^{81} -4.08040 q^{82} +11.9211 q^{83} -2.17126 q^{84} +4.61287 q^{85} +8.29421 q^{86} -15.0113 q^{87} +1.06886 q^{88} -12.9761 q^{89} +6.55126 q^{90} -0.620759 q^{91} +2.92472 q^{92} +1.75916 q^{93} -5.08836 q^{94} -6.12046 q^{95} +11.5711 q^{96} +0.583558 q^{97} -1.12638 q^{98} +2.02074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.12638	−0.796474	−0.398237	−	0.917283i	$-0.630378\pi$
$2$	−1.12638	−0.796474	−0.398237	+	0.917283i	$0.630378\pi$
$3$	−2.96921	−1.71427	−0.857136	−	0.515090i	$-0.827758\pi$
$3$	−2.96921	−1.71427	−0.857136	+	0.515090i	$0.827758\pi$
$4$	−0.731259	−0.365629
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.34447	1.36537
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.07645	1.08769
$9$	5.81619	1.93873
$10$	1.12638	0.356194
$11$	0.347433	0.104755	0.0523776	−	0.998627i	$-0.483320\pi$
$11$	0.347433	0.104755	0.0523776	+	0.998627i	$0.483320\pi$
$12$	2.17126	0.626788
$13$	0.620759	0.172167	0.0860837	−	0.996288i	$-0.472565\pi$
$13$	0.620759	0.172167	0.0860837	+	0.996288i	$0.472565\pi$
$14$	1.12638	0.301039
$15$	2.96921	0.766646
$16$	−2.00274	−0.500686
$17$	−4.61287	−1.11878	−0.559392	−	0.828903i	$-0.688965\pi$
$17$	−4.61287	−1.11878	−0.559392	+	0.828903i	$0.688965\pi$
$18$	−6.55126	−1.54415
$19$	6.12046	1.40413	0.702065	−	0.712113i	$-0.252261\pi$
$19$	6.12046	1.40413	0.702065	+	0.712113i	$0.252261\pi$
$20$	0.731259	0.163514
$21$	2.96921	0.647934
$22$	−0.391344	−0.0834347
$23$	−3.99956	−0.833967	−0.416983	−	0.908914i	$-0.636913\pi$
$23$	−3.99956	−0.833967	−0.416983	+	0.908914i	$0.636913\pi$
$24$	−9.13460	−1.86459
$25$	1.00000	0.200000
$26$	−0.699213	−0.137127
$27$	−8.36183	−1.60924
$28$	0.731259	0.138195
$29$	5.05567	0.938815	0.469408	−	0.882982i	$-0.344468\pi$
$29$	5.05567	0.938815	0.469408	+	0.882982i	$0.344468\pi$
$30$	−3.34447	−0.610613
$31$	−0.592469	−0.106411	−0.0532053	−	0.998584i	$-0.516944\pi$
$31$	−0.592469	−0.106411	−0.0532053	+	0.998584i	$0.516944\pi$
$32$	−3.89704	−0.688905
$33$	−1.03160	−0.179579
$34$	5.19586	0.891083
$35$	1.00000	0.169031
$36$	−4.25314	−0.708856
$37$	1.86732	0.306985	0.153493	−	0.988150i	$-0.450948\pi$
$37$	1.86732	0.306985	0.153493	+	0.988150i	$0.450948\pi$
$38$	−6.89399	−1.11835
$39$	−1.84316	−0.295142
$40$	−3.07645	−0.486429
$41$	3.62256	0.565749	0.282874	−	0.959157i	$-0.408712\pi$
$41$	3.62256	0.565749	0.282874	+	0.959157i	$0.408712\pi$
$42$	−3.34447	−0.516062
$43$	−7.36357	−1.12293	−0.561467	−	0.827499i	$-0.689763\pi$
$43$	−7.36357	−1.12293	−0.561467	+	0.827499i	$0.689763\pi$
$44$	−0.254064	−0.0383016
$45$	−5.81619	−0.867026
$46$	4.50504	0.664233
$47$	4.51743	0.658935	0.329467	−	0.944167i	$-0.393131\pi$
$47$	4.51743	0.658935	0.329467	+	0.944167i	$0.393131\pi$
$48$	5.94656	0.858311
$49$	1.00000	0.142857
$50$	−1.12638	−0.159295
$51$	13.6966	1.91790
$52$	−0.453935	−0.0629495
$53$	−9.04895	−1.24297	−0.621484	−	0.783427i	$-0.713470\pi$
$53$	−9.04895	−1.24297	−0.621484	+	0.783427i	$0.713470\pi$
$54$	9.41864	1.28171
$55$	−0.347433	−0.0468479
$56$	−3.07645	−0.411107
$57$	−18.1729	−2.40706
$58$	−5.69463	−0.747742
$59$	−8.35068	−1.08717	−0.543583	−	0.839356i	$-0.682933\pi$
$59$	−8.35068	−1.08717	−0.543583	+	0.839356i	$0.682933\pi$
$60$	−2.17126	−0.280308
$61$	−9.76483	−1.25026	−0.625129	−	0.780521i	$-0.714954\pi$
$61$	−9.76483	−1.25026	−0.625129	+	0.780521i	$0.714954\pi$
$62$	0.667348	0.0847532
$63$	−5.81619	−0.732770
$64$	8.39504	1.04938
$65$	−0.620759	−0.0769956
$66$	1.16198	0.143030
$67$	−7.79286	−0.952050	−0.476025	−	0.879432i	$-0.657923\pi$
$67$	−7.79286	−0.952050	−0.476025	+	0.879432i	$0.657923\pi$
$68$	3.37320	0.409061
$69$	11.8755	1.42965
$70$	−1.12638	−0.134629
$71$	5.96316	0.707697	0.353848	−	0.935303i	$-0.384873\pi$
$71$	5.96316	0.707697	0.353848	+	0.935303i	$0.384873\pi$
$72$	17.8932	2.10873
$73$	−4.56124	−0.533852	−0.266926	−	0.963717i	$-0.586008\pi$
$73$	−4.56124	−0.533852	−0.266926	+	0.963717i	$0.586008\pi$
$74$	−2.10332	−0.244506
$75$	−2.96921	−0.342854
$76$	−4.47564	−0.513391
$77$	−0.347433	−0.0395937
$78$	2.07611	0.235073
$79$	3.88708	0.437331	0.218665	−	0.975800i	$-0.429830\pi$
$79$	3.88708	0.437331	0.218665	+	0.975800i	$0.429830\pi$
$80$	2.00274	0.223913
$81$	7.37946	0.819940
$82$	−4.08040	−0.450604
$83$	11.9211	1.30851	0.654253	−	0.756276i	$-0.272983\pi$
$83$	11.9211	1.30851	0.654253	+	0.756276i	$0.272983\pi$
$84$	−2.17126	−0.236904
$85$	4.61287	0.500336
$86$	8.29421	0.894388
$87$	−15.0113	−1.60938
$88$	1.06886	0.113941
$89$	−12.9761	−1.37546	−0.687730	−	0.725967i	$-0.741393\pi$
$89$	−12.9761	−1.37546	−0.687730	+	0.725967i	$0.741393\pi$
$90$	6.55126	0.690563
$91$	−0.620759	−0.0650732
$92$	2.92472	0.304923
$93$	1.75916	0.182417
$94$	−5.08836	−0.524824
$95$	−6.12046	−0.627946
$96$	11.5711	1.18097
$97$	0.583558	0.0592513	0.0296256	−	0.999561i	$-0.490568\pi$
$97$	0.583558	0.0592513	0.0296256	+	0.999561i	$0.490568\pi$
$98$	−1.12638	−0.113782
$99$	2.02074	0.203092
$100$	−0.731259	−0.0731259
$101$	10.6589	1.06060	0.530299	−	0.847811i	$-0.322080\pi$
$101$	10.6589	1.06060	0.530299	+	0.847811i	$0.322080\pi$
$102$	−15.4276	−1.52756
$103$	−12.8929	−1.27037	−0.635185	−	0.772360i	$-0.719076\pi$
$103$	−12.8929	−1.27037	−0.635185	+	0.772360i	$0.719076\pi$
$104$	1.90973	0.187265
$105$	−2.96921	−0.289765
$106$	10.1926	0.989992
$107$	12.2370	1.18300	0.591499	−	0.806305i	$-0.298536\pi$
$107$	12.2370	1.18300	0.591499	+	0.806305i	$0.298536\pi$
$108$	6.11467	0.588384
$109$	−11.5958	−1.11068	−0.555339	−	0.831624i	$-0.687411\pi$
$109$	−11.5958	−1.11068	−0.555339	+	0.831624i	$0.687411\pi$
$110$	0.391344	0.0373131
$111$	−5.54446	−0.526256
$112$	2.00274	0.189241
$113$	13.2084	1.24254	0.621270	−	0.783596i	$-0.286617\pi$
$113$	13.2084	1.24254	0.621270	+	0.783596i	$0.286617\pi$
$114$	20.4697	1.91716
$115$	3.99956	0.372961
$116$	−3.69701	−0.343258
$117$	3.61045	0.333786
$118$	9.40607	0.865899
$119$	4.61287	0.422861
$120$	9.13460	0.833871
$121$	−10.8793	−0.989026
$122$	10.9989	0.995798
$123$	−10.7561	−0.969848
$124$	0.433248	0.0389068
$125$	−1.00000	−0.0894427
$126$	6.55126	0.583633
$127$	12.7684	1.13301	0.566507	−	0.824057i	$-0.308295\pi$
$127$	12.7684	1.13301	0.566507	+	0.824057i	$0.308295\pi$
$128$	−1.66197	−0.146899
$129$	21.8640	1.92501
$130$	0.699213	0.0613250
$131$	−8.44772	−0.738081	−0.369040	−	0.929413i	$-0.620314\pi$
$131$	−8.44772	−0.738081	−0.369040	+	0.929413i	$0.620314\pi$
$132$	0.754368	0.0656593
$133$	−6.12046	−0.530711
$134$	8.77776	0.758283
$135$	8.36183	0.719672
$136$	−14.1912	−1.21689
$137$	11.0670	0.945516	0.472758	−	0.881192i	$-0.343259\pi$
$137$	11.0670	0.945516	0.472758	+	0.881192i	$0.343259\pi$
$138$	−13.3764	−1.13868
$139$	14.3863	1.22023	0.610115	−	0.792313i	$-0.291123\pi$
$139$	14.3863	1.22023	0.610115	+	0.792313i	$0.291123\pi$
$140$	−0.731259	−0.0618027
$141$	−13.4132	−1.12959
$142$	−6.71681	−0.563662
$143$	0.215672	0.0180354
$144$	−11.6483	−0.970694
$145$	−5.05567	−0.419851
$146$	5.13770	0.425199
$147$	−2.96921	−0.244896
$148$	−1.36549	−0.112243
$149$	6.77476	0.555010	0.277505	−	0.960724i	$-0.410493\pi$
$149$	6.77476	0.555010	0.277505	+	0.960724i	$0.410493\pi$
$150$	3.34447	0.273075
$151$	17.4909	1.42339	0.711695	−	0.702489i	$-0.247928\pi$
$151$	17.4909	1.42339	0.711695	+	0.702489i	$0.247928\pi$
$152$	18.8293	1.52726
$153$	−26.8293	−2.16902
$154$	0.391344	0.0315354
$155$	0.592469	0.0475883
$156$	1.34783	0.107913
$157$	10.7276	0.856158	0.428079	−	0.903741i	$-0.359190\pi$
$157$	10.7276	0.856158	0.428079	+	0.903741i	$0.359190\pi$
$158$	−4.37834	−0.348322
$159$	26.8682	2.13079
$160$	3.89704	0.308088
$161$	3.99956	0.315210
$162$	−8.31210	−0.653060
$163$	3.49826	0.274005	0.137002	−	0.990571i	$-0.456253\pi$
$163$	3.49826	0.274005	0.137002	+	0.990571i	$0.456253\pi$
$164$	−2.64903	−0.206854
$165$	1.03160	0.0803101
$166$	−13.4277	−1.04219
$167$	−9.94343	−0.769446	−0.384723	−	0.923032i	$-0.625703\pi$
$167$	−9.94343	−0.769446	−0.384723	+	0.923032i	$0.625703\pi$
$168$	9.13460	0.704750
$169$	−12.6147	−0.970358
$170$	−5.19586	−0.398504
$171$	35.5977	2.72223
$172$	5.38468	0.410578
$173$	21.3058	1.61985	0.809924	−	0.586534i	$-0.199508\pi$
$173$	21.3058	1.61985	0.809924	+	0.586534i	$0.199508\pi$
$174$	16.9085	1.28183
$175$	−1.00000	−0.0755929
$176$	−0.695820	−0.0524494
$177$	24.7949	1.86370
$178$	14.6160	1.09552
$179$	11.0534	0.826174	0.413087	−	0.910692i	$-0.364451\pi$
$179$	11.0534	0.826174	0.413087	+	0.910692i	$0.364451\pi$
$180$	4.25314	0.317010
$181$	−3.98881	−0.296486	−0.148243	−	0.988951i	$-0.547362\pi$
$181$	−3.98881	−0.296486	−0.148243	+	0.988951i	$0.547362\pi$
$182$	0.699213	0.0518291
$183$	28.9938	2.14328
$184$	−12.3044	−0.907095
$185$	−1.86732	−0.137288
$186$	−1.98149	−0.145290
$187$	−1.60266	−0.117198
$188$	−3.30341	−0.240926
$189$	8.36183	0.608234
$190$	6.89399	0.500143
$191$	6.24288	0.451719	0.225859	−	0.974160i	$-0.427481\pi$
$191$	6.24288	0.451719	0.225859	+	0.974160i	$0.427481\pi$
$192$	−24.9266	−1.79892
$193$	16.0370	1.15437	0.577186	−	0.816613i	$-0.304151\pi$
$193$	16.0370	1.15437	0.577186	+	0.816613i	$0.304151\pi$
$194$	−0.657310	−0.0471921
$195$	1.84316	0.131991
$196$	−0.731259	−0.0522328
$197$	−22.8112	−1.62523	−0.812616	−	0.582799i	$-0.801958\pi$
$197$	−22.8112	−1.62523	−0.812616	+	0.582799i	$0.801958\pi$
$198$	−2.27613	−0.161757
$199$	3.45333	0.244800	0.122400	−	0.992481i	$-0.460941\pi$
$199$	3.45333	0.244800	0.122400	+	0.992481i	$0.460941\pi$
$200$	3.07645	0.217538
$201$	23.1386	1.63207
$202$	−12.0060	−0.844739
$203$	−5.05567	−0.354839
$204$	−10.0157	−0.701241
$205$	−3.62256	−0.253011
$206$	14.5223	1.01182
$207$	−23.2622	−1.61683
$208$	−1.24322	−0.0862018
$209$	2.12645	0.147090
$210$	3.34447	0.230790
$211$	15.3384	1.05594	0.527968	−	0.849264i	$-0.322954\pi$
$211$	15.3384	1.05594	0.527968	+	0.849264i	$0.322954\pi$
$212$	6.61712	0.454466
$213$	−17.7059	−1.21318
$214$	−13.7836	−0.942228
$215$	7.36357	0.502191
$216$	−25.7247	−1.75035
$217$	0.592469	0.0402194
$218$	13.0613	0.884626
$219$	13.5432	0.915168
$220$	0.254064	0.0171290
$221$	−2.86348	−0.192618
$222$	6.24519	0.419149
$223$	17.2214	1.15323	0.576615	−	0.817016i	$-0.304373\pi$
$223$	17.2214	1.15323	0.576615	+	0.817016i	$0.304373\pi$
$224$	3.89704	0.260382
$225$	5.81619	0.387746
$226$	−14.8777	−0.989651
$227$	−17.5920	−1.16762	−0.583812	−	0.811889i	$-0.698440\pi$
$227$	−17.5920	−1.16762	−0.583812	+	0.811889i	$0.698440\pi$
$228$	13.2891	0.880093
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−4.50504	−0.297054
$231$	1.03160	0.0678744
$232$	15.5535	1.02114
$233$	21.8794	1.43337	0.716683	−	0.697399i	$-0.245659\pi$
$233$	21.8794	1.43337	0.716683	+	0.697399i	$0.245659\pi$
$234$	−4.06675	−0.265852
$235$	−4.51743	−0.294685
$236$	6.10651	0.397500
$237$	−11.5415	−0.749704
$238$	−5.19586	−0.336798
$239$	0.953943	0.0617055	0.0308527	−	0.999524i	$-0.490178\pi$
$239$	0.953943	0.0617055	0.0308527	+	0.999524i	$0.490178\pi$
$240$	−5.94656	−0.383849
$241$	8.27432	0.532996	0.266498	−	0.963836i	$-0.414133\pi$
$241$	8.27432	0.532996	0.266498	+	0.963836i	$0.414133\pi$
$242$	12.2543	0.787734
$243$	3.17438	0.203636
$244$	7.14062	0.457131
$245$	−1.00000	−0.0638877
$246$	12.1155	0.772458
$247$	3.79933	0.241746
$248$	−1.82270	−0.115742
$249$	−35.3961	−2.24314
$250$	1.12638	0.0712388
$251$	17.1442	1.08213	0.541065	−	0.840981i	$-0.318021\pi$
$251$	17.1442	1.08213	0.541065	+	0.840981i	$0.318021\pi$
$252$	4.25314	0.267922
$253$	−1.38958	−0.0873623
$254$	−14.3821	−0.902415
$255$	−13.6966	−0.857711
$256$	−14.9181	−0.932379
$257$	−15.1388	−0.944333	−0.472166	−	0.881509i	$-0.656528\pi$
$257$	−15.1388	−0.944333	−0.472166	+	0.881509i	$0.656528\pi$
$258$	−24.6272	−1.53322
$259$	−1.86732	−0.116030
$260$	0.453935	0.0281519
$261$	29.4047	1.82011
$262$	9.51538	0.587862
$263$	12.8492	0.792316	0.396158	−	0.918182i	$-0.370343\pi$
$263$	12.8492	0.792316	0.396158	+	0.918182i	$0.370343\pi$
$264$	−3.17367	−0.195326
$265$	9.04895	0.555872
$266$	6.89399	0.422698
$267$	38.5286	2.35791
$268$	5.69860	0.348097
$269$	−11.5859	−0.706408	−0.353204	−	0.935546i	$-0.614908\pi$
$269$	−11.5859	−0.706408	−0.353204	+	0.935546i	$0.614908\pi$
$270$	−9.41864	−0.573200
$271$	−0.661225	−0.0401666	−0.0200833	−	0.999798i	$-0.506393\pi$
$271$	−0.661225	−0.0401666	−0.0200833	+	0.999798i	$0.506393\pi$
$272$	9.23838	0.560159
$273$	1.84316	0.111553
$274$	−12.4657	−0.753078
$275$	0.347433	0.0209510
$276$	−8.68408	−0.522720
$277$	15.5447	0.933993	0.466996	−	0.884259i	$-0.345336\pi$
$277$	15.5447	0.933993	0.466996	+	0.884259i	$0.345336\pi$
$278$	−16.2045	−0.971881
$279$	−3.44591	−0.206301
$280$	3.07645	0.183853
$281$	−13.7280	−0.818946	−0.409473	−	0.912322i	$-0.634287\pi$
$281$	−13.7280	−0.818946	−0.409473	+	0.912322i	$0.634287\pi$
$282$	15.1084	0.899692
$283$	−29.6359	−1.76167	−0.880837	−	0.473419i	$-0.843020\pi$
$283$	−29.6359	−1.76167	−0.880837	+	0.473419i	$0.843020\pi$
$284$	−4.36061	−0.258755
$285$	18.1729	1.07647
$286$	−0.242930	−0.0143647
$287$	−3.62256	−0.213833
$288$	−22.6659	−1.33560
$289$	4.27854	0.251679
$290$	5.69463	0.334400
$291$	−1.73270	−0.101573
$292$	3.33544	0.195192
$293$	−28.9032	−1.68854	−0.844271	−	0.535916i	$-0.819966\pi$
$293$	−28.9032	−1.68854	−0.844271	+	0.535916i	$0.819966\pi$
$294$	3.34447	0.195053
$295$	8.35068	0.486195
$296$	5.74471	0.333904
$297$	−2.90518	−0.168576
$298$	−7.63098	−0.442051
$299$	−2.48276	−0.143582
$300$	2.17126	0.125358
$301$	7.36357	0.424429
$302$	−19.7015	−1.13369
$303$	−31.6484	−1.81815
$304$	−12.2577	−0.703028
$305$	9.76483	0.559132
$306$	30.2201	1.72757
$307$	−32.0747	−1.83060	−0.915301	−	0.402771i	$-0.868047\pi$
$307$	−32.0747	−1.83060	−0.915301	+	0.402771i	$0.868047\pi$
$308$	0.254064	0.0144766
$309$	38.2815	2.17776
$310$	−0.667348	−0.0379028
$311$	30.3303	1.71987	0.859936	−	0.510401i	$-0.170503\pi$
$311$	30.3303	1.71987	0.859936	+	0.510401i	$0.170503\pi$
$312$	−5.67039	−0.321022
$313$	−21.1379	−1.19478	−0.597391	−	0.801950i	$-0.703796\pi$
$313$	−21.1379	−1.19478	−0.597391	+	0.801950i	$0.703796\pi$
$314$	−12.0834	−0.681908
$315$	5.81619	0.327705
$316$	−2.84246	−0.159901
$317$	−13.5294	−0.759884	−0.379942	−	0.925010i	$-0.624056\pi$
$317$	−13.5294	−0.759884	−0.379942	+	0.925010i	$0.624056\pi$
$318$	−30.2639	−1.69712
$319$	1.75651	0.0983457
$320$	−8.39504	−0.469297
$321$	−36.3343	−2.02798
$322$	−4.50504	−0.251056
$323$	−28.2329	−1.57092
$324$	−5.39629	−0.299794
$325$	0.620759	0.0344335
$326$	−3.94038	−0.218237
$327$	34.4304	1.90400
$328$	11.1446	0.615358
$329$	−4.51743	−0.249054
$330$	−1.16198	−0.0639649
$331$	21.2308	1.16695	0.583474	−	0.812131i	$-0.301693\pi$
$331$	21.2308	1.16695	0.583474	+	0.812131i	$0.301693\pi$
$332$	−8.71738	−0.478428
$333$	10.8607	0.595161
$334$	11.2001	0.612843
$335$	7.79286	0.425770
$336$	−5.94656	−0.324411
$337$	3.86629	0.210610	0.105305	−	0.994440i	$-0.466418\pi$
$337$	3.86629	0.210610	0.105305	+	0.994440i	$0.466418\pi$
$338$	14.2090	0.772865
$339$	−39.2184	−2.13005
$340$	−3.37320	−0.182937
$341$	−0.205844	−0.0111471
$342$	−40.0967	−2.16818
$343$	−1.00000	−0.0539949
$344$	−22.6536	−1.22140
$345$	−11.8755	−0.639357
$346$	−23.9985	−1.29017
$347$	−25.7648	−1.38313	−0.691564	−	0.722315i	$-0.743078\pi$
$347$	−25.7648	−1.38313	−0.691564	+	0.722315i	$0.743078\pi$
$348$	10.9772	0.588438
$349$	−20.8363	−1.11534	−0.557671	−	0.830062i	$-0.688305\pi$
$349$	−20.8363	−1.11534	−0.557671	+	0.830062i	$0.688305\pi$
$350$	1.12638	0.0602078
$351$	−5.19068	−0.277058
$352$	−1.35396	−0.0721663
$353$	−17.5441	−0.933779	−0.466890	−	0.884316i	$-0.654625\pi$
$353$	−17.5441	−0.933779	−0.466890	+	0.884316i	$0.654625\pi$
$354$	−27.9286	−1.48439
$355$	−5.96316	−0.316492
$356$	9.48886	0.502909
$357$	−13.6966	−0.724898
$358$	−12.4504	−0.658026
$359$	12.3865	0.653735	0.326868	−	0.945070i	$-0.394007\pi$
$359$	12.3865	0.653735	0.326868	+	0.945070i	$0.394007\pi$
$360$	−17.8932	−0.943054
$361$	18.4601	0.971582
$362$	4.49294	0.236143
$363$	32.3029	1.69546
$364$	0.453935	0.0237927
$365$	4.56124	0.238746
$366$	−32.6581	−1.70707
$367$	−20.8076	−1.08615	−0.543073	−	0.839685i	$-0.682739\pi$
$367$	−20.8076	−1.08615	−0.543073	+	0.839685i	$0.682739\pi$
$368$	8.01010	0.417555
$369$	21.0695	1.09683
$370$	2.10332	0.109346
$371$	9.04895	0.469798
$372$	−1.28640	−0.0666969
$373$	11.6780	0.604666	0.302333	−	0.953202i	$-0.402234\pi$
$373$	11.6780	0.604666	0.302333	+	0.953202i	$0.402234\pi$
$374$	1.80522	0.0933455
$375$	2.96921	0.153329
$376$	13.8976	0.716716
$377$	3.13835	0.161633
$378$	−9.41864	−0.484442
$379$	17.3144	0.889381	0.444690	−	0.895684i	$-0.353314\pi$
$379$	17.3144	0.889381	0.444690	+	0.895684i	$0.353314\pi$
$380$	4.47564	0.229596
$381$	−37.9120	−1.94229
$382$	−7.03188	−0.359782
$383$	−13.2243	−0.675728	−0.337864	−	0.941195i	$-0.609704\pi$
$383$	−13.2243	−0.675728	−0.337864	+	0.941195i	$0.609704\pi$
$384$	4.93474	0.251825
$385$	0.347433	0.0177069
$386$	−18.0639	−0.919427
$387$	−42.8279	−2.17706
$388$	−0.426732	−0.0216640
$389$	31.0974	1.57670	0.788351	−	0.615225i	$-0.210935\pi$
$389$	31.0974	1.57670	0.788351	+	0.615225i	$0.210935\pi$
$390$	−2.07611	−0.105128
$391$	18.4494	0.933029
$392$	3.07645	0.155384
$393$	25.0830	1.26527
$394$	25.6942	1.29446
$395$	−3.88708	−0.195580
$396$	−1.47768	−0.0742563
$397$	3.59568	0.180462	0.0902311	−	0.995921i	$-0.471239\pi$
$397$	3.59568	0.180462	0.0902311	+	0.995921i	$0.471239\pi$
$398$	−3.88978	−0.194977
$399$	18.1729	0.909784
$400$	−2.00274	−0.100137
$401$	35.2851	1.76205	0.881026	−	0.473067i	$-0.156853\pi$
$401$	35.2851	1.76205	0.881026	+	0.473067i	$0.156853\pi$
$402$	−26.0630	−1.29990
$403$	−0.367780	−0.0183204
$404$	−7.79440	−0.387786
$405$	−7.37946	−0.366688
$406$	5.69463	0.282620
$407$	0.648769	0.0321583
$408$	42.1367	2.08608
$409$	21.2120	1.04887	0.524433	−	0.851452i	$-0.324277\pi$
$409$	21.2120	1.04887	0.524433	+	0.851452i	$0.324277\pi$
$410$	4.08040	0.201516
$411$	−32.8601	−1.62087
$412$	9.42801	0.464485
$413$	8.35068	0.410910
$414$	26.2022	1.28777
$415$	−11.9211	−0.585182
$416$	−2.41912	−0.118607
$417$	−42.7159	−2.09181
$418$	−2.39520	−0.117153
$419$	2.17975	0.106488	0.0532439	−	0.998582i	$-0.483044\pi$
$419$	2.17975	0.106488	0.0532439	+	0.998582i	$0.483044\pi$
$420$	2.17126	0.105947
$421$	−14.0323	−0.683894	−0.341947	−	0.939719i	$-0.611086\pi$
$421$	−14.0323	−0.683894	−0.341947	+	0.939719i	$0.611086\pi$
$422$	−17.2769	−0.841026
$423$	26.2742	1.27750
$424$	−27.8386	−1.35196
$425$	−4.61287	−0.223757
$426$	19.9436	0.966270
$427$	9.76483	0.472553
$428$	−8.94844	−0.432539
$429$	−0.640376	−0.0309176
$430$	−8.29421	−0.399982
$431$	−0.126926	−0.00611382	−0.00305691	−	0.999995i	$-0.500973\pi$
$431$	−0.126926	−0.00611382	−0.00305691	+	0.999995i	$0.500973\pi$
$432$	16.7466	0.805721
$433$	16.2223	0.779596	0.389798	−	0.920900i	$-0.372545\pi$
$433$	16.2223	0.779596	0.389798	+	0.920900i	$0.372545\pi$
$434$	−0.667348	−0.0320337
$435$	15.0113	0.719739
$436$	8.47954	0.406096
$437$	−24.4792	−1.17100
$438$	−15.2549	−0.728907
$439$	−22.7758	−1.08703	−0.543514	−	0.839400i	$-0.682906\pi$
$439$	−22.7758	−1.08703	−0.543514	+	0.839400i	$0.682906\pi$
$440$	−1.06886	−0.0509559
$441$	5.81619	0.276961
$442$	3.22538	0.153415
$443$	29.2175	1.38817	0.694083	−	0.719895i	$-0.255810\pi$
$443$	29.2175	1.38817	0.694083	+	0.719895i	$0.255810\pi$
$444$	4.05443	0.192415
$445$	12.9761	0.615124
$446$	−19.3979	−0.918517
$447$	−20.1157	−0.951438
$448$	−8.39504	−0.396629
$449$	−33.7692	−1.59367	−0.796834	−	0.604198i	$-0.793493\pi$
$449$	−33.7692	−1.59367	−0.796834	+	0.604198i	$0.793493\pi$
$450$	−6.55126	−0.308829
$451$	1.25860	0.0592651
$452$	−9.65875	−0.454310
$453$	−51.9341	−2.44008
$454$	19.8154	0.929983
$455$	0.620759	0.0291016
$456$	−55.9080	−2.61813
$457$	−8.03562	−0.375890	−0.187945	−	0.982180i	$-0.560183\pi$
$457$	−8.03562	−0.375890	−0.187945	+	0.982180i	$0.560183\pi$
$458$	1.12638	0.0526325
$459$	38.5720	1.80039
$460$	−2.92472	−0.136366
$461$	−0.738599	−0.0344000	−0.0172000	−	0.999852i	$-0.505475\pi$
$461$	−0.738599	−0.0344000	−0.0172000	+	0.999852i	$0.505475\pi$
$462$	−1.16198	−0.0540602
$463$	−28.9615	−1.34596	−0.672979	−	0.739662i	$-0.734985\pi$
$463$	−28.9615	−1.34596	−0.672979	+	0.739662i	$0.734985\pi$
$464$	−10.1252	−0.470051
$465$	−1.75916	−0.0815792
$466$	−24.6446	−1.14164
$467$	−10.9715	−0.507699	−0.253850	−	0.967244i	$-0.581697\pi$
$467$	−10.9715	−0.507699	−0.253850	+	0.967244i	$0.581697\pi$
$468$	−2.64017	−0.122042
$469$	7.79286	0.359841
$470$	5.08836	0.234709
$471$	−31.8526	−1.46769
$472$	−25.6904	−1.18250
$473$	−2.55835	−0.117633
$474$	13.0002	0.597119
$475$	6.12046	0.280826
$476$	−3.37320	−0.154610
$477$	−52.6304	−2.40978
$478$	−1.07451	−0.0491468
$479$	0.961216	0.0439191	0.0219595	−	0.999759i	$-0.493010\pi$
$479$	0.961216	0.0439191	0.0219595	+	0.999759i	$0.493010\pi$
$480$	−11.5711	−0.528146
$481$	1.15915	0.0528529
$482$	−9.32006	−0.424517
$483$	−11.8755	−0.540355
$484$	7.95558	0.361617
$485$	−0.583558	−0.0264980
$486$	−3.57557	−0.162191
$487$	−2.64835	−0.120008	−0.0600040	−	0.998198i	$-0.519111\pi$
$487$	−2.64835	−0.120008	−0.0600040	+	0.998198i	$0.519111\pi$
$488$	−30.0410	−1.35989
$489$	−10.3870	−0.469718
$490$	1.12638	0.0508848
$491$	17.7582	0.801417	0.400709	−	0.916206i	$-0.368764\pi$
$491$	17.7582	0.801417	0.400709	+	0.916206i	$0.368764\pi$
$492$	7.86552	0.354605
$493$	−23.3211	−1.05033
$494$	−4.27951	−0.192544
$495$	−2.02074	−0.0908254
$496$	1.18656	0.0532783
$497$	−5.96316	−0.267484
$498$	39.8696	1.78660
$499$	−22.0498	−0.987083	−0.493542	−	0.869722i	$-0.664298\pi$
$499$	−22.0498	−0.987083	−0.493542	+	0.869722i	$0.664298\pi$
$500$	0.731259	0.0327029
$501$	29.5241	1.31904
$502$	−19.3109	−0.861888
$503$	−29.9078	−1.33352	−0.666762	−	0.745271i	$-0.732320\pi$
$503$	−29.9078	−1.33352	−0.666762	+	0.745271i	$0.732320\pi$
$504$	−17.8932	−0.797026
$505$	−10.6589	−0.474314
$506$	1.56520	0.0695818
$507$	37.4555	1.66346
$508$	−9.33701	−0.414263
$509$	−37.9896	−1.68386	−0.841930	−	0.539587i	$-0.818581\pi$
$509$	−37.9896	−1.68386	−0.841930	+	0.539587i	$0.818581\pi$
$510$	15.4276	0.683145
$511$	4.56124	0.201777
$512$	20.1274	0.889515
$513$	−51.1783	−2.25958
$514$	17.0521	0.752136
$515$	12.8929	0.568127
$516$	−15.9882	−0.703842
$517$	1.56951	0.0690268
$518$	2.10332	0.0924145
$519$	−63.2613	−2.77686
$520$	−1.90973	−0.0837472
$521$	9.83937	0.431071	0.215535	−	0.976496i	$-0.430850\pi$
$521$	9.83937	0.431071	0.215535	+	0.976496i	$0.430850\pi$
$522$	−33.1210	−1.44967
$523$	43.7582	1.91341	0.956705	−	0.291059i	$-0.0940075\pi$
$523$	43.7582	1.91341	0.956705	+	0.291059i	$0.0940075\pi$
$524$	6.17747	0.269864
$525$	2.96921	0.129587
$526$	−14.4731	−0.631059
$527$	2.73298	0.119050
$528$	2.06603	0.0899125
$529$	−7.00350	−0.304500
$530$	−10.1926	−0.442738
$531$	−48.5691	−2.10772
$532$	4.47564	0.194044
$533$	2.24874	0.0974036
$534$	−43.3980	−1.87802
$535$	−12.2370	−0.529053
$536$	−23.9743	−1.03553
$537$	−32.8200	−1.41629
$538$	13.0502	0.562635
$539$	0.347433	0.0149650
$540$	−6.11467	−0.263133
$541$	17.0987	0.735132	0.367566	−	0.929997i	$-0.380191\pi$
$541$	17.0987	0.735132	0.367566	+	0.929997i	$0.380191\pi$
$542$	0.744793	0.0319916
$543$	11.8436	0.508258
$544$	17.9765	0.770736
$545$	11.5958	0.496710
$546$	−2.07611	−0.0888492
$547$	−23.1939	−0.991700	−0.495850	−	0.868408i	$-0.665143\pi$
$547$	−23.1939	−0.991700	−0.495850	+	0.868408i	$0.665143\pi$
$548$	−8.09282	−0.345708
$549$	−56.7941	−2.42391
$550$	−0.391344	−0.0166869
$551$	30.9431	1.31822
$552$	36.5344	1.55501
$553$	−3.88708	−0.165295
$554$	−17.5093	−0.743901
$555$	5.54446	0.235349
$556$	−10.5201	−0.446152
$557$	11.5939	0.491251	0.245625	−	0.969365i	$-0.421007\pi$
$557$	11.5939	0.491251	0.245625	+	0.969365i	$0.421007\pi$
$558$	3.88142	0.164314
$559$	−4.57100	−0.193333
$560$	−2.00274	−0.0846313
$561$	4.75864	0.200910
$562$	15.4630	0.652269
$563$	29.5033	1.24341	0.621707	−	0.783250i	$-0.286439\pi$
$563$	29.5033	1.24341	0.621707	+	0.783250i	$0.286439\pi$
$564$	9.80851	0.413013
$565$	−13.2084	−0.555681
$566$	33.3815	1.40313
$567$	−7.37946	−0.309908
$568$	18.3453	0.769754
$569$	−13.8237	−0.579518	−0.289759	−	0.957100i	$-0.593575\pi$
$569$	−13.8237	−0.579518	−0.289759	+	0.957100i	$0.593575\pi$
$570$	−20.4697	−0.857381
$571$	0.608059	0.0254465	0.0127232	−	0.999919i	$-0.495950\pi$
$571$	0.608059	0.0254465	0.0127232	+	0.999919i	$0.495950\pi$
$572$	−0.157712	−0.00659428
$573$	−18.5364	−0.774369
$574$	4.08040	0.170312
$575$	−3.99956	−0.166793
$576$	48.8271	2.03446
$577$	18.6369	0.775862	0.387931	−	0.921688i	$-0.373190\pi$
$577$	18.6369	0.775862	0.387931	+	0.921688i	$0.373190\pi$
$578$	−4.81928	−0.200455
$579$	−47.6173	−1.97891
$580$	3.69701	0.153510
$581$	−11.9211	−0.494569
$582$	1.95169	0.0809001
$583$	−3.14391	−0.130207
$584$	−14.0324	−0.580665
$585$	−3.61045	−0.149274
$586$	32.5561	1.34488
$587$	14.9884	0.618637	0.309319	−	0.950958i	$-0.399899\pi$
$587$	14.9884	0.618637	0.309319	+	0.950958i	$0.399899\pi$
$588$	2.17126	0.0895412
$589$	−3.62618	−0.149414
$590$	−9.40607	−0.387242
$591$	67.7312	2.78609
$592$	−3.73976	−0.153703
$593$	−28.7402	−1.18022	−0.590110	−	0.807323i	$-0.700916\pi$
$593$	−28.7402	−1.18022	−0.590110	+	0.807323i	$0.700916\pi$
$594$	3.27235	0.134266
$595$	−4.61287	−0.189109
$596$	−4.95410	−0.202928
$597$	−10.2537	−0.419654
$598$	2.79655	0.114359
$599$	24.1102	0.985117	0.492558	−	0.870279i	$-0.336062\pi$
$599$	24.1102	0.985117	0.492558	+	0.870279i	$0.336062\pi$
$600$	−9.13460	−0.372919
$601$	−6.89229	−0.281142	−0.140571	−	0.990071i	$-0.544894\pi$
$601$	−6.89229	−0.281142	−0.140571	+	0.990071i	$0.544894\pi$
$602$	−8.29421	−0.338047
$603$	−45.3247	−1.84577
$604$	−12.7904	−0.520433
$605$	10.8793	0.442306
$606$	35.6483	1.44811
$607$	5.17031	0.209856	0.104928	−	0.994480i	$-0.466539\pi$
$607$	5.17031	0.209856	0.104928	+	0.994480i	$0.466539\pi$
$608$	−23.8517	−0.967313
$609$	15.0113	0.608290
$610$	−10.9989	−0.445334
$611$	2.80423	0.113447
$612$	19.6192	0.793057
$613$	−9.88169	−0.399118	−0.199559	−	0.979886i	$-0.563951\pi$
$613$	−9.88169	−0.399118	−0.199559	+	0.979886i	$0.563951\pi$
$614$	36.1285	1.45803
$615$	10.7561	0.433729
$616$	−1.06886	−0.0430656
$617$	−3.95373	−0.159171	−0.0795855	−	0.996828i	$-0.525360\pi$
$617$	−3.95373	−0.159171	−0.0795855	+	0.996828i	$0.525360\pi$
$618$	−43.1197	−1.73453
$619$	−31.4139	−1.26263	−0.631315	−	0.775526i	$-0.717485\pi$
$619$	−31.4139	−1.26263	−0.631315	+	0.775526i	$0.717485\pi$
$620$	−0.433248	−0.0173997
$621$	33.4437	1.34205
$622$	−34.1635	−1.36983
$623$	12.9761	0.519875
$624$	3.69138	0.147773
$625$	1.00000	0.0400000
$626$	23.8093	0.951613
$627$	−6.31388	−0.252152
$628$	−7.84468	−0.313037
$629$	−8.61369	−0.343450
$630$	−6.55126	−0.261008
$631$	5.36819	0.213704	0.106852	−	0.994275i	$-0.465923\pi$
$631$	5.36819	0.213704	0.106852	+	0.994275i	$0.465923\pi$
$632$	11.9584	0.475679
$633$	−45.5428	−1.81016
$634$	15.2393	0.605228
$635$	−12.7684	−0.506699
$636$	−19.6476	−0.779078
$637$	0.620759	0.0245954
$638$	−1.97851	−0.0783298
$639$	34.6828	1.37203
$640$	1.66197	0.0656953
$641$	14.3692	0.567548	0.283774	−	0.958891i	$-0.408414\pi$
$641$	14.3692	0.567548	0.283774	+	0.958891i	$0.408414\pi$
$642$	40.9264	1.61523
$643$	8.37940	0.330451	0.165226	−	0.986256i	$-0.447165\pi$
$643$	8.37940	0.330451	0.165226	+	0.986256i	$0.447165\pi$
$644$	−2.92472	−0.115250
$645$	−21.8640	−0.860893
$646$	31.8011	1.25120
$647$	−46.2529	−1.81839	−0.909194	−	0.416372i	$-0.863301\pi$
$647$	−46.2529	−1.81839	−0.909194	+	0.416372i	$0.863301\pi$
$648$	22.7025	0.891839
$649$	−2.90131	−0.113886
$650$	−0.699213	−0.0274254
$651$	−1.75916	−0.0689470
$652$	−2.55813	−0.100184
$653$	16.7756	0.656480	0.328240	−	0.944594i	$-0.393545\pi$
$653$	16.7756	0.656480	0.328240	+	0.944594i	$0.393545\pi$
$654$	−38.7818	−1.51649
$655$	8.44772	0.330080
$656$	−7.25506	−0.283262
$657$	−26.5290	−1.03499
$658$	5.08836	0.198365
$659$	21.6249	0.842387	0.421194	−	0.906971i	$-0.361611\pi$
$659$	21.6249	0.842387	0.421194	+	0.906971i	$0.361611\pi$
$660$	−0.754368	−0.0293637
$661$	−39.6495	−1.54219	−0.771094	−	0.636721i	$-0.780290\pi$
$661$	−39.6495	−1.54219	−0.771094	+	0.636721i	$0.780290\pi$
$662$	−23.9140	−0.929444
$663$	8.50225	0.330200
$664$	36.6745	1.42325
$665$	6.12046	0.237341
$666$	−12.2333	−0.474030
$667$	−20.2205	−0.782940
$668$	7.27122	0.281332
$669$	−51.1339	−1.97695
$670$	−8.77776	−0.339114
$671$	−3.39263	−0.130971
$672$	−11.5711	−0.446365
$673$	9.49184	0.365883	0.182942	−	0.983124i	$-0.441438\pi$
$673$	9.49184	0.365883	0.182942	+	0.983124i	$0.441438\pi$
$674$	−4.35493	−0.167746
$675$	−8.36183	−0.321847
$676$	9.22458	0.354792
$677$	31.6521	1.21649	0.608244	−	0.793750i	$-0.291874\pi$
$677$	31.6521	1.21649	0.608244	+	0.793750i	$0.291874\pi$
$678$	44.1750	1.69653
$679$	−0.583558	−0.0223949
$680$	14.1912	0.544209
$681$	52.2344	2.00163
$682$	0.231859	0.00887834
$683$	40.2769	1.54115	0.770576	−	0.637349i	$-0.219969\pi$
$683$	40.2769	1.54115	0.770576	+	0.637349i	$0.219969\pi$
$684$	−26.0312	−0.995327
$685$	−11.0670	−0.422847
$686$	1.12638	0.0430055
$687$	2.96921	0.113282
$688$	14.7473	0.562237
$689$	−5.61721	−0.213999
$690$	13.3764	0.509231
$691$	49.9840	1.90148	0.950741	−	0.309986i	$-0.100324\pi$
$691$	49.9840	1.90148	0.950741	+	0.309986i	$0.100324\pi$
$692$	−15.5800	−0.592264
$693$	−2.02074	−0.0767615
$694$	29.0211	1.10163
$695$	−14.3863	−0.545703
$696$	−46.1816	−1.75051
$697$	−16.7104	−0.632951
$698$	23.4697	0.888340
$699$	−64.9644	−2.45718
$700$	0.731259	0.0276390
$701$	−21.8470	−0.825149	−0.412574	−	0.910924i	$-0.635370\pi$
$701$	−21.8470	−0.825149	−0.412574	+	0.910924i	$0.635370\pi$
$702$	5.84670	0.220670
$703$	11.4289	0.431048
$704$	2.91672	0.109928
$705$	13.4132	0.505170
$706$	19.7614	0.743731
$707$	−10.6589	−0.400869
$708$	−18.1315	−0.681423
$709$	42.3738	1.59138	0.795690	−	0.605704i	$-0.207108\pi$
$709$	42.3738	1.59138	0.795690	+	0.605704i	$0.207108\pi$
$710$	6.71681	0.252077
$711$	22.6080	0.847865
$712$	−39.9202	−1.49607
$713$	2.36962	0.0887429
$714$	15.4276	0.577363
$715$	−0.215672	−0.00806569
$716$	−8.08293	−0.302073
$717$	−2.83245	−0.105780
$718$	−13.9520	−0.520683
$719$	−6.67004	−0.248751	−0.124375	−	0.992235i	$-0.539693\pi$
$719$	−6.67004	−0.248751	−0.124375	+	0.992235i	$0.539693\pi$
$720$	11.6483	0.434107
$721$	12.8929	0.480155
$722$	−20.7931	−0.773840
$723$	−24.5682	−0.913699
$724$	2.91685	0.108404
$725$	5.05567	0.187763
$726$	−36.3854	−1.35039
$727$	−29.9139	−1.10945	−0.554723	−	0.832035i	$-0.687176\pi$
$727$	−29.9139	−1.10945	−0.554723	+	0.832035i	$0.687176\pi$
$728$	−1.90973	−0.0707793
$729$	−31.5638	−1.16903
$730$	−5.13770	−0.190155
$731$	33.9672	1.25632
$732$	−21.2020	−0.783647
$733$	23.2685	0.859442	0.429721	−	0.902962i	$-0.358612\pi$
$733$	23.2685	0.859442	0.429721	+	0.902962i	$0.358612\pi$
$734$	23.4373	0.865087
$735$	2.96921	0.109521
$736$	15.5864	0.574524
$737$	−2.70750	−0.0997321
$738$	−23.7323	−0.873599
$739$	−40.3621	−1.48474	−0.742371	−	0.669989i	$-0.766299\pi$
$739$	−40.3621	−1.48474	−0.742371	+	0.669989i	$0.766299\pi$
$740$	1.36549	0.0501965
$741$	−11.2810	−0.414418
$742$	−10.1926	−0.374182
$743$	43.7859	1.60635	0.803175	−	0.595743i	$-0.203142\pi$
$743$	43.7859	1.60635	0.803175	+	0.595743i	$0.203142\pi$
$744$	5.41197	0.198412
$745$	−6.77476	−0.248208
$746$	−13.1540	−0.481601
$747$	69.3351	2.53684
$748$	1.17196	0.0428512
$749$	−12.2370	−0.447132
$750$	−3.34447	−0.122123
$751$	9.69213	0.353671	0.176835	−	0.984240i	$-0.443414\pi$
$751$	9.69213	0.353671	0.176835	+	0.984240i	$0.443414\pi$
$752$	−9.04725	−0.329919
$753$	−50.9046	−1.85507
$754$	−3.53499	−0.128737
$755$	−17.4909	−0.636559
$756$	−6.11467	−0.222388
$757$	−15.4689	−0.562226	−0.281113	−	0.959675i	$-0.590704\pi$
$757$	−15.4689	−0.562226	−0.281113	+	0.959675i	$0.590704\pi$
$758$	−19.5027	−0.708369
$759$	4.12596	0.149763
$760$	−18.8293	−0.683010
$761$	26.7164	0.968469	0.484234	−	0.874938i	$-0.339098\pi$
$761$	26.7164	0.968469	0.484234	+	0.874938i	$0.339098\pi$
$762$	42.7035	1.54699
$763$	11.5958	0.419797
$764$	−4.56516	−0.165162
$765$	26.8293	0.970015
$766$	14.8956	0.538200
$767$	−5.18376	−0.187175
$768$	44.2948	1.59835
$769$	−15.0401	−0.542361	−0.271180	−	0.962529i	$-0.587414\pi$
$769$	−15.0401	−0.542361	−0.271180	+	0.962529i	$0.587414\pi$
$770$	−0.391344	−0.0141030
$771$	44.9502	1.61884
$772$	−11.7272	−0.422072
$773$	8.23856	0.296321	0.148160	−	0.988963i	$-0.452665\pi$
$773$	8.23856	0.296321	0.148160	+	0.988963i	$0.452665\pi$
$774$	48.2407	1.73397
$775$	−0.592469	−0.0212821
$776$	1.79528	0.0644469
$777$	5.54446	0.198906
$778$	−35.0277	−1.25580
$779$	22.1718	0.794385
$780$	−1.34783	−0.0482600
$781$	2.07180	0.0741349
$782$	−20.7812	−0.743133
$783$	−42.2747	−1.51077
$784$	−2.00274	−0.0715265
$785$	−10.7276	−0.382886
$786$	−28.2531	−1.00776
$787$	−7.43330	−0.264969	−0.132484	−	0.991185i	$-0.542295\pi$
$787$	−7.43330	−0.264969	−0.132484	+	0.991185i	$0.542295\pi$
$788$	16.6809	0.594233
$789$	−38.1519	−1.35824
$790$	4.37834	0.155775
$791$	−13.2084	−0.469636
$792$	6.21669	0.220901
$793$	−6.06160	−0.215254
$794$	−4.05012	−0.143733
$795$	−26.8682	−0.952917
$796$	−2.52528	−0.0895062
$797$	20.2242	0.716377	0.358188	−	0.933649i	$-0.383395\pi$
$797$	20.2242	0.716377	0.358188	+	0.933649i	$0.383395\pi$
$798$	−20.4697	−0.724619
$799$	−20.8383	−0.737206
$800$	−3.89704	−0.137781
$801$	−75.4712	−2.66664
$802$	−39.7445	−1.40343
$803$	−1.58473	−0.0559238
$804$	−16.9203	−0.596734
$805$	−3.99956	−0.140966
$806$	0.414262	0.0145918
$807$	34.4011	1.21097
$808$	32.7915	1.15360
$809$	−33.9525	−1.19371	−0.596853	−	0.802351i	$-0.703582\pi$
$809$	−33.9525	−1.19371	−0.596853	+	0.802351i	$0.703582\pi$
$810$	8.31210	0.292057
$811$	2.53544	0.0890314	0.0445157	−	0.999009i	$-0.485826\pi$
$811$	2.53544	0.0890314	0.0445157	+	0.999009i	$0.485826\pi$
$812$	3.69701	0.129739
$813$	1.96331	0.0688564
$814$	−0.730763	−0.0256132
$815$	−3.49826	−0.122539
$816$	−27.4307	−0.960265
$817$	−45.0685	−1.57675
$818$	−23.8929	−0.835394
$819$	−3.61045	−0.126159
$820$	2.64903	0.0925081
$821$	23.6286	0.824642	0.412321	−	0.911039i	$-0.364718\pi$
$821$	23.6286	0.824642	0.412321	+	0.911039i	$0.364718\pi$
$822$	37.0131	1.29098
$823$	18.3803	0.640695	0.320348	−	0.947300i	$-0.396200\pi$
$823$	18.3803	0.640695	0.320348	+	0.947300i	$0.396200\pi$
$824$	−39.6642	−1.38177
$825$	−1.03160	−0.0359158
$826$	−9.40607	−0.327279
$827$	−8.37919	−0.291373	−0.145687	−	0.989331i	$-0.546539\pi$
$827$	−8.37919	−0.291373	−0.145687	+	0.989331i	$0.546539\pi$
$828$	17.0107	0.591162
$829$	4.86924	0.169116	0.0845579	−	0.996419i	$-0.473052\pi$
$829$	4.86924	0.169116	0.0845579	+	0.996419i	$0.473052\pi$
$830$	13.4277	0.466082
$831$	−46.1555	−1.60112
$832$	5.21130	0.180669
$833$	−4.61287	−0.159826
$834$	48.1145	1.66607
$835$	9.94343	0.344107
$836$	−1.55499	−0.0537804
$837$	4.95413	0.171240
$838$	−2.45524	−0.0848148
$839$	−17.2439	−0.595326	−0.297663	−	0.954671i	$-0.596207\pi$
$839$	−17.2439	−0.595326	−0.297663	+	0.954671i	$0.596207\pi$
$840$	−9.13460	−0.315174
$841$	−3.44016	−0.118626
$842$	15.8058	0.544704
$843$	40.7614	1.40390
$844$	−11.2163	−0.386081
$845$	12.6147	0.433957
$846$	−29.5948	−1.01749
$847$	10.8793	0.373817
$848$	18.1227	0.622337
$849$	87.9952	3.01999
$850$	5.19586	0.178217
$851$	−7.46846	−0.256016
$852$	12.9476	0.443576
$853$	−15.5611	−0.532803	−0.266402	−	0.963862i	$-0.585835\pi$
$853$	−15.5611	−0.532803	−0.266402	+	0.963862i	$0.585835\pi$
$854$	−10.9989	−0.376376
$855$	−35.5977	−1.21742
$856$	37.6466	1.28673
$857$	9.30104	0.317718	0.158859	−	0.987301i	$-0.449219\pi$
$857$	9.30104	0.317718	0.158859	+	0.987301i	$0.449219\pi$
$858$	0.721309	0.0246251
$859$	−32.9720	−1.12499	−0.562496	−	0.826800i	$-0.690159\pi$
$859$	−32.9720	−1.12499	−0.562496	+	0.826800i	$0.690159\pi$
$860$	−5.38468	−0.183616
$861$	10.7561	0.366568
$862$	0.142968	0.00486950
$863$	−24.0170	−0.817550	−0.408775	−	0.912635i	$-0.634044\pi$
$863$	−24.0170	−0.817550	−0.408775	+	0.912635i	$0.634044\pi$
$864$	32.5864	1.10861
$865$	−21.3058	−0.724418
$866$	−18.2726	−0.620928
$867$	−12.7039	−0.431446
$868$	−0.433248	−0.0147054
$869$	1.35050	0.0458126
$870$	−16.9085	−0.573253
$871$	−4.83749	−0.163912
$872$	−35.6739	−1.20807
$873$	3.39408	0.114872
$874$	27.5730	0.932669
$875$	1.00000	0.0338062
$876$	−9.90362	−0.334612
$877$	−26.5245	−0.895668	−0.447834	−	0.894117i	$-0.647804\pi$
$877$	−26.5245	−0.895668	−0.447834	+	0.894117i	$0.647804\pi$
$878$	25.6542	0.865789
$879$	85.8195	2.89462
$880$	0.695820	0.0234561
$881$	2.63678	0.0888353	0.0444177	−	0.999013i	$-0.485857\pi$
$881$	2.63678	0.0888353	0.0444177	+	0.999013i	$0.485857\pi$
$882$	−6.55126	−0.220592
$883$	34.0829	1.14698	0.573490	−	0.819212i	$-0.305589\pi$
$883$	34.0829	1.14698	0.573490	+	0.819212i	$0.305589\pi$
$884$	2.09394	0.0704269
$885$	−24.7949	−0.833471
$886$	−32.9101	−1.10564
$887$	39.7189	1.33363	0.666815	−	0.745223i	$-0.267657\pi$
$887$	39.7189	1.33363	0.666815	+	0.745223i	$0.267657\pi$
$888$	−17.0572	−0.572403
$889$	−12.7684	−0.428239
$890$	−14.6160	−0.489930
$891$	2.56387	0.0858929
$892$	−12.5933	−0.421655
$893$	27.6488	0.925230
$894$	22.6580	0.757795
$895$	−11.0534	−0.369476
$896$	1.66197	0.0555226
$897$	7.37184	0.246138
$898$	38.0371	1.26931
$899$	−2.99533	−0.0998999
$900$	−4.25314	−0.141771
$901$	41.7416	1.39061
$902$	−1.41767	−0.0472031
$903$	−21.8640	−0.727587
$904$	40.6349	1.35150
$905$	3.98881	0.132593
$906$	58.4978	1.94346
$907$	−5.64192	−0.187337	−0.0936684	−	0.995603i	$-0.529859\pi$
$907$	−5.64192	−0.187337	−0.0936684	+	0.995603i	$0.529859\pi$
$908$	12.8643	0.426918
$909$	61.9940	2.05621
$910$	−0.699213	−0.0231787
$911$	2.15157	0.0712846	0.0356423	−	0.999365i	$-0.488652\pi$
$911$	2.15157	0.0712846	0.0356423	+	0.999365i	$0.488652\pi$
$912$	36.3957	1.20518
$913$	4.14177	0.137073
$914$	9.05119	0.299387
$915$	−28.9938	−0.958505
$916$	0.731259	0.0241615
$917$	8.44772	0.278968
$918$	−43.4469	−1.43396
$919$	−24.2770	−0.800826	−0.400413	−	0.916335i	$-0.631133\pi$
$919$	−24.2770	−0.800826	−0.400413	+	0.916335i	$0.631133\pi$
$920$	12.3044	0.405665
$921$	95.2365	3.13815
$922$	0.831946	0.0273987
$923$	3.70168	0.121842
$924$	−0.754368	−0.0248169
$925$	1.86732	0.0613971
$926$	32.6218	1.07202
$927$	−74.9872	−2.46290
$928$	−19.7021	−0.646754
$929$	−31.3650	−1.02905	−0.514526	−	0.857475i	$-0.672032\pi$
$929$	−31.3650	−1.02905	−0.514526	+	0.857475i	$0.672032\pi$
$930$	1.98149	0.0649757
$931$	6.12046	0.200590
$932$	−15.9995	−0.524081
$933$	−90.0569	−2.94833
$934$	12.3581	0.404369
$935$	1.60266	0.0524127
$936$	11.1073	0.363055
$937$	−7.68807	−0.251158	−0.125579	−	0.992084i	$-0.540079\pi$
$937$	−7.68807	−0.251158	−0.125579	+	0.992084i	$0.540079\pi$
$938$	−8.77776	−0.286604
$939$	62.7627	2.04818
$940$	3.30341	0.107745
$941$	−48.7990	−1.59080	−0.795401	−	0.606084i	$-0.792740\pi$
$941$	−48.7990	−1.59080	−0.795401	+	0.606084i	$0.792740\pi$
$942$	35.8782	1.16898
$943$	−14.4887	−0.471816
$944$	16.7243	0.544328
$945$	−8.36183	−0.272011
$946$	2.88169	0.0936917
$947$	7.10361	0.230836	0.115418	−	0.993317i	$-0.463179\pi$
$947$	7.10361	0.230836	0.115418	+	0.993317i	$0.463179\pi$
$948$	8.43985	0.274114
$949$	−2.83143	−0.0919120
$950$	−6.89399	−0.223671
$951$	40.1714	1.30265
$952$	14.1912	0.459941
$953$	13.5951	0.440388	0.220194	−	0.975456i	$-0.429331\pi$
$953$	13.5951	0.440388	0.220194	+	0.975456i	$0.429331\pi$
$954$	59.2820	1.91933
$955$	−6.24288	−0.202015
$956$	−0.697580	−0.0225613
$957$	−5.21544	−0.168591
$958$	−1.08270	−0.0349804
$959$	−11.0670	−0.357371
$960$	24.9266	0.804503
$961$	−30.6490	−0.988677
$962$	−1.30565	−0.0420960
$963$	71.1729	2.29351
$964$	−6.05067	−0.194879
$965$	−16.0370	−0.516251
$966$	13.3764	0.430379
$967$	9.83795	0.316367	0.158184	−	0.987410i	$-0.449436\pi$
$967$	9.83795	0.316367	0.158184	+	0.987410i	$0.449436\pi$
$968$	−33.4696	−1.07575
$969$	83.8292	2.69298
$970$	0.657310	0.0211050
$971$	−29.3220	−0.940986	−0.470493	−	0.882404i	$-0.655924\pi$
$971$	−29.3220	−0.940986	−0.470493	+	0.882404i	$0.655924\pi$
$972$	−2.32129	−0.0744555
$973$	−14.3863	−0.461204
$974$	2.98305	0.0955832
$975$	−1.84316	−0.0590284
$976$	19.5564	0.625986
$977$	−32.0296	−1.02472	−0.512359	−	0.858772i	$-0.671228\pi$
$977$	−32.0296	−1.02472	−0.512359	+	0.858772i	$0.671228\pi$
$978$	11.6998	0.374118
$979$	−4.50832	−0.144087
$980$	0.731259	0.0233592
$981$	−67.4434	−2.15330
$982$	−20.0026	−0.638308
$983$	38.5885	1.23078	0.615391	−	0.788222i	$-0.288998\pi$
$983$	38.5885	1.23078	0.615391	+	0.788222i	$0.288998\pi$
$984$	−33.0907	−1.05489
$985$	22.8112	0.726826
$986$	26.2686	0.836562
$987$	13.4132	0.426946
$988$	−2.77829	−0.0883893
$989$	29.4511	0.936489
$990$	2.27613	0.0723401
$991$	−45.5298	−1.44630	−0.723152	−	0.690689i	$-0.757307\pi$
$991$	−45.5298	−1.44630	−0.723152	+	0.690689i	$0.757307\pi$
$992$	2.30887	0.0733068
$993$	−63.0385	−2.00047
$994$	6.71681	0.213044
$995$	−3.45333	−0.109478
$996$	25.8837	0.820156
$997$	−40.0608	−1.26874	−0.634369	−	0.773030i	$-0.718740\pi$
$997$	−40.0608	−1.26874	−0.634369	+	0.773030i	$0.718740\pi$
$998$	24.8365	0.786186
$999$	−15.6142	−0.494012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.17	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.12638 q^{2} -2.96921 q^{3} -0.731259 q^{4} -1.00000 q^{5} +3.34447 q^{6} -1.00000 q^{7} +3.07645 q^{8} +5.81619 q^{9} +O(q^{10})\)	\(q-1.12638 q^{2} -2.96921 q^{3} -0.731259 q^{4} -1.00000 q^{5} +3.34447 q^{6} -1.00000 q^{7} +3.07645 q^{8} +5.81619 q^{9} +1.12638 q^{10} +0.347433 q^{11} +2.17126 q^{12} +0.620759 q^{13} +1.12638 q^{14} +2.96921 q^{15} -2.00274 q^{16} -4.61287 q^{17} -6.55126 q^{18} +6.12046 q^{19} +0.731259 q^{20} +2.96921 q^{21} -0.391344 q^{22} -3.99956 q^{23} -9.13460 q^{24} +1.00000 q^{25} -0.699213 q^{26} -8.36183 q^{27} +0.731259 q^{28} +5.05567 q^{29} -3.34447 q^{30} -0.592469 q^{31} -3.89704 q^{32} -1.03160 q^{33} +5.19586 q^{34} +1.00000 q^{35} -4.25314 q^{36} +1.86732 q^{37} -6.89399 q^{38} -1.84316 q^{39} -3.07645 q^{40} +3.62256 q^{41} -3.34447 q^{42} -7.36357 q^{43} -0.254064 q^{44} -5.81619 q^{45} +4.50504 q^{46} +4.51743 q^{47} +5.94656 q^{48} +1.00000 q^{49} -1.12638 q^{50} +13.6966 q^{51} -0.453935 q^{52} -9.04895 q^{53} +9.41864 q^{54} -0.347433 q^{55} -3.07645 q^{56} -18.1729 q^{57} -5.69463 q^{58} -8.35068 q^{59} -2.17126 q^{60} -9.76483 q^{61} +0.667348 q^{62} -5.81619 q^{63} +8.39504 q^{64} -0.620759 q^{65} +1.16198 q^{66} -7.79286 q^{67} +3.37320 q^{68} +11.8755 q^{69} -1.12638 q^{70} +5.96316 q^{71} +17.8932 q^{72} -4.56124 q^{73} -2.10332 q^{74} -2.96921 q^{75} -4.47564 q^{76} -0.347433 q^{77} +2.07611 q^{78} +3.88708 q^{79} +2.00274 q^{80} +7.37946 q^{81} -4.08040 q^{82} +11.9211 q^{83} -2.17126 q^{84} +4.61287 q^{85} +8.29421 q^{86} -15.0113 q^{87} +1.06886 q^{88} -12.9761 q^{89} +6.55126 q^{90} -0.620759 q^{91} +2.92472 q^{92} +1.75916 q^{93} -5.08836 q^{94} -6.12046 q^{95} +11.5711 q^{96} +0.583558 q^{97} -1.12638 q^{98} +2.02074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 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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