LMFDB - Embedded newform 8035.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64032 q^{2} +0.589008 q^{3} +4.97127 q^{4} +1.00000 q^{5} -1.55517 q^{6} +2.76981 q^{7} -7.84509 q^{8} -2.65307 q^{9} +O(q^{10})$	\(q-2.64032 q^{2} +0.589008 q^{3} +4.97127 q^{4} +1.00000 q^{5} -1.55517 q^{6} +2.76981 q^{7} -7.84509 q^{8} -2.65307 q^{9} -2.64032 q^{10} -1.01471 q^{11} +2.92812 q^{12} +3.88182 q^{13} -7.31318 q^{14} +0.589008 q^{15} +10.7710 q^{16} -4.24960 q^{17} +7.00494 q^{18} +3.62386 q^{19} +4.97127 q^{20} +1.63144 q^{21} +2.67916 q^{22} +3.08269 q^{23} -4.62082 q^{24} +1.00000 q^{25} -10.2492 q^{26} -3.32971 q^{27} +13.7695 q^{28} +7.81813 q^{29} -1.55517 q^{30} -8.40048 q^{31} -12.7486 q^{32} -0.597674 q^{33} +11.2203 q^{34} +2.76981 q^{35} -13.1891 q^{36} -9.14909 q^{37} -9.56815 q^{38} +2.28642 q^{39} -7.84509 q^{40} -2.73619 q^{41} -4.30752 q^{42} -5.52356 q^{43} -5.04441 q^{44} -2.65307 q^{45} -8.13927 q^{46} -2.01511 q^{47} +6.34420 q^{48} +0.671862 q^{49} -2.64032 q^{50} -2.50305 q^{51} +19.2975 q^{52} -8.85254 q^{53} +8.79147 q^{54} -1.01471 q^{55} -21.7294 q^{56} +2.13449 q^{57} -20.6423 q^{58} -5.84638 q^{59} +2.92812 q^{60} +7.14772 q^{61} +22.1799 q^{62} -7.34850 q^{63} +12.1184 q^{64} +3.88182 q^{65} +1.57805 q^{66} -6.79784 q^{67} -21.1259 q^{68} +1.81573 q^{69} -7.31318 q^{70} -6.46981 q^{71} +20.8136 q^{72} +10.1509 q^{73} +24.1565 q^{74} +0.589008 q^{75} +18.0152 q^{76} -2.81056 q^{77} -6.03688 q^{78} -12.3626 q^{79} +10.7710 q^{80} +5.99798 q^{81} +7.22441 q^{82} +14.9877 q^{83} +8.11034 q^{84} -4.24960 q^{85} +14.5839 q^{86} +4.60495 q^{87} +7.96051 q^{88} -10.5078 q^{89} +7.00494 q^{90} +10.7519 q^{91} +15.3249 q^{92} -4.94795 q^{93} +5.32054 q^{94} +3.62386 q^{95} -7.50904 q^{96} +9.36197 q^{97} -1.77393 q^{98} +2.69210 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) $ 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * 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 $

$2$	−2.64032	−1.86699	−0.933493	−	0.358596i	$-0.883255\pi$
$2$	−2.64032	−1.86699	−0.933493	+	0.358596i	$0.883255\pi$
$3$	0.589008	0.340064	0.170032	−	0.985439i	$-0.445613\pi$
$3$	0.589008	0.340064	0.170032	+	0.985439i	$0.445613\pi$
$4$	4.97127	2.48563
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.55517	−0.634895
$7$	2.76981	1.04689	0.523445	−	0.852059i	$-0.324646\pi$
$7$	2.76981	1.04689	0.523445	+	0.852059i	$0.324646\pi$
$8$	−7.84509	−2.77366
$9$	−2.65307	−0.884356
$10$	−2.64032	−0.834941
$11$	−1.01471	−0.305947	−0.152974	−	0.988230i	$-0.548885\pi$
$11$	−1.01471	−0.305947	−0.152974	+	0.988230i	$0.548885\pi$
$12$	2.92812	0.845275
$13$	3.88182	1.07662	0.538311	−	0.842746i	$-0.319063\pi$
$13$	3.88182	1.07662	0.538311	+	0.842746i	$0.319063\pi$
$14$	−7.31318	−1.95453
$15$	0.589008	0.152081
$16$	10.7710	2.69274
$17$	−4.24960	−1.03068	−0.515340	−	0.856986i	$-0.672334\pi$
$17$	−4.24960	−1.03068	−0.515340	+	0.856986i	$0.672334\pi$
$18$	7.00494	1.65108
$19$	3.62386	0.831371	0.415686	−	0.909508i	$-0.363542\pi$
$19$	3.62386	0.831371	0.415686	+	0.909508i	$0.363542\pi$
$20$	4.97127	1.11161
$21$	1.63144	0.356010
$22$	2.67916	0.571199
$23$	3.08269	0.642785	0.321392	−	0.946946i	$-0.395849\pi$
$23$	3.08269	0.642785	0.321392	+	0.946946i	$0.395849\pi$
$24$	−4.62082	−0.943222
$25$	1.00000	0.200000
$26$	−10.2492	−2.01004
$27$	−3.32971	−0.640802
$28$	13.7695	2.60219
$29$	7.81813	1.45179	0.725895	−	0.687805i	$-0.241426\pi$
$29$	7.81813	1.45179	0.725895	+	0.687805i	$0.241426\pi$
$30$	−1.55517	−0.283934
$31$	−8.40048	−1.50877	−0.754385	−	0.656432i	$-0.772065\pi$
$31$	−8.40048	−1.50877	−0.754385	+	0.656432i	$0.772065\pi$
$32$	−12.7486	−2.25366
$33$	−0.597674	−0.104042
$34$	11.2203	1.92426
$35$	2.76981	0.468184
$36$	−13.1891	−2.19819
$37$	−9.14909	−1.50410	−0.752051	−	0.659105i	$-0.770935\pi$
$37$	−9.14909	−1.50410	−0.752051	+	0.659105i	$0.770935\pi$
$38$	−9.56815	−1.55216
$39$	2.28642	0.366121
$40$	−7.84509	−1.24042
$41$	−2.73619	−0.427321	−0.213661	−	0.976908i	$-0.568539\pi$
$41$	−2.73619	−0.427321	−0.213661	+	0.976908i	$0.568539\pi$
$42$	−4.30752	−0.664666
$43$	−5.52356	−0.842334	−0.421167	−	0.906983i	$-0.638379\pi$
$43$	−5.52356	−0.842334	−0.421167	+	0.906983i	$0.638379\pi$
$44$	−5.04441	−0.760473
$45$	−2.65307	−0.395496
$46$	−8.13927	−1.20007
$47$	−2.01511	−0.293935	−0.146967	−	0.989141i	$-0.546951\pi$
$47$	−2.01511	−0.293935	−0.146967	+	0.989141i	$0.546951\pi$
$48$	6.34420	0.915706
$49$	0.671862	0.0959803
$50$	−2.64032	−0.373397
$51$	−2.50305	−0.350497
$52$	19.2975	2.67609
$53$	−8.85254	−1.21599	−0.607995	−	0.793941i	$-0.708026\pi$
$53$	−8.85254	−1.21599	−0.607995	+	0.793941i	$0.708026\pi$
$54$	8.79147	1.19637
$55$	−1.01471	−0.136824
$56$	−21.7294	−2.90372
$57$	2.13449	0.282720
$58$	−20.6423	−2.71047
$59$	−5.84638	−0.761134	−0.380567	−	0.924753i	$-0.624271\pi$
$59$	−5.84638	−0.761134	−0.380567	+	0.924753i	$0.624271\pi$
$60$	2.92812	0.378019
$61$	7.14772	0.915172	0.457586	−	0.889165i	$-0.348714\pi$
$61$	7.14772	0.915172	0.457586	+	0.889165i	$0.348714\pi$
$62$	22.1799	2.81685
$63$	−7.34850	−0.925825
$64$	12.1184	1.51480
$65$	3.88182	0.481480
$66$	1.57805	0.194244
$67$	−6.79784	−0.830488	−0.415244	−	0.909710i	$-0.636304\pi$
$67$	−6.79784	−0.830488	−0.415244	+	0.909710i	$0.636304\pi$
$68$	−21.1259	−2.56189
$69$	1.81573	0.218588
$70$	−7.31318	−0.874092
$71$	−6.46981	−0.767825	−0.383913	−	0.923369i	$-0.625424\pi$
$71$	−6.46981	−0.767825	−0.383913	+	0.923369i	$0.625424\pi$
$72$	20.8136	2.45290
$73$	10.1509	1.18807	0.594037	−	0.804438i	$-0.297533\pi$
$73$	10.1509	1.18807	0.594037	+	0.804438i	$0.297533\pi$
$74$	24.1565	2.80814
$75$	0.589008	0.0680128
$76$	18.0152	2.06649
$77$	−2.81056	−0.320293
$78$	−6.03688	−0.683542
$79$	−12.3626	−1.39090	−0.695452	−	0.718573i	$-0.744796\pi$
$79$	−12.3626	−1.39090	−0.695452	+	0.718573i	$0.744796\pi$
$80$	10.7710	1.20423
$81$	5.99798	0.666443
$82$	7.22441	0.797802
$83$	14.9877	1.64512	0.822558	−	0.568682i	$-0.192546\pi$
$83$	14.9877	1.64512	0.822558	+	0.568682i	$0.192546\pi$
$84$	8.11034	0.884911
$85$	−4.24960	−0.460934
$86$	14.5839	1.57263
$87$	4.60495	0.493702
$88$	7.96051	0.848593
$89$	−10.5078	−1.11382	−0.556912	−	0.830572i	$-0.688014\pi$
$89$	−10.5078	−1.11382	−0.556912	+	0.830572i	$0.688014\pi$
$90$	7.00494	0.738386
$91$	10.7519	1.12711
$92$	15.3249	1.59773
$93$	−4.94795	−0.513079
$94$	5.32054	0.548772
$95$	3.62386	0.371801
$96$	−7.50904	−0.766388
$97$	9.36197	0.950564	0.475282	−	0.879834i	$-0.342346\pi$
$97$	9.36197	0.950564	0.475282	+	0.879834i	$0.342346\pi$
$98$	−1.77393	−0.179194
$99$	2.69210	0.270566
$100$	4.97127	0.497127
$101$	−16.2959	−1.62150	−0.810751	−	0.585391i	$-0.800941\pi$
$101$	−16.2959	−1.62150	−0.810751	+	0.585391i	$0.800941\pi$
$102$	6.60885	0.654373
$103$	−4.08039	−0.402053	−0.201026	−	0.979586i	$-0.564428\pi$
$103$	−4.08039	−0.402053	−0.201026	+	0.979586i	$0.564428\pi$
$104$	−30.4532	−2.98618
$105$	1.63144	0.159213
$106$	23.3735	2.27023
$107$	−2.07326	−0.200430	−0.100215	−	0.994966i	$-0.531953\pi$
$107$	−2.07326	−0.200430	−0.100215	+	0.994966i	$0.531953\pi$
$108$	−16.5529	−1.59280
$109$	6.47890	0.620566	0.310283	−	0.950644i	$-0.399576\pi$
$109$	6.47890	0.620566	0.310283	+	0.950644i	$0.399576\pi$
$110$	2.67916	0.255448
$111$	−5.38889	−0.511491
$112$	29.8336	2.81901
$113$	−14.4730	−1.36151	−0.680753	−	0.732513i	$-0.738347\pi$
$113$	−14.4730	−1.36151	−0.680753	+	0.732513i	$0.738347\pi$
$114$	−5.63572	−0.527833
$115$	3.08269	0.287462
$116$	38.8660	3.60862
$117$	−10.2987	−0.952117
$118$	15.4363	1.42103
$119$	−11.7706	−1.07901
$120$	−4.62082	−0.421822
$121$	−9.97036	−0.906396
$122$	−18.8722	−1.70861
$123$	−1.61164	−0.145317
$124$	−41.7610	−3.75025
$125$	1.00000	0.0894427
$126$	19.4024	1.72850
$127$	12.6518	1.12266	0.561332	−	0.827591i	$-0.310289\pi$
$127$	12.6518	1.12266	0.561332	+	0.827591i	$0.310289\pi$
$128$	−6.49918	−0.574452
$129$	−3.25342	−0.286448
$130$	−10.2492	−0.898916
$131$	−13.9680	−1.22039	−0.610193	−	0.792253i	$-0.708908\pi$
$131$	−13.9680	−1.22039	−0.610193	+	0.792253i	$0.708908\pi$
$132$	−2.97120	−0.258610
$133$	10.0374	0.870355
$134$	17.9484	1.55051
$135$	−3.32971	−0.286575
$136$	33.3385	2.85875
$137$	−14.7762	−1.26241	−0.631206	−	0.775615i	$-0.717440\pi$
$137$	−14.7762	−1.26241	−0.631206	+	0.775615i	$0.717440\pi$
$138$	−4.79410	−0.408101
$139$	20.8021	1.76441	0.882206	−	0.470863i	$-0.156057\pi$
$139$	20.8021	1.76441	0.882206	+	0.470863i	$0.156057\pi$
$140$	13.7695	1.16373
$141$	−1.18692	−0.0999566
$142$	17.0823	1.43352
$143$	−3.93893	−0.329389
$144$	−28.5761	−2.38135
$145$	7.81813	0.649261
$146$	−26.8016	−2.21812
$147$	0.395732	0.0326395
$148$	−45.4826	−3.73865
$149$	−17.5967	−1.44158	−0.720789	−	0.693154i	$-0.756220\pi$
$149$	−17.5967	−1.44158	−0.720789	+	0.693154i	$0.756220\pi$
$150$	−1.55517	−0.126979
$151$	0.745080	0.0606337	0.0303169	−	0.999540i	$-0.490348\pi$
$151$	0.745080	0.0606337	0.0303169	+	0.999540i	$0.490348\pi$
$152$	−28.4295	−2.30594
$153$	11.2745	0.911489
$154$	7.42077	0.597983
$155$	−8.40048	−0.674743
$156$	11.3664	0.910042
$157$	13.5472	1.08118	0.540592	−	0.841285i	$-0.318200\pi$
$157$	13.5472	1.08118	0.540592	+	0.841285i	$0.318200\pi$
$158$	32.6412	2.59680
$159$	−5.21422	−0.413514
$160$	−12.7486	−1.00787
$161$	8.53847	0.672926
$162$	−15.8366	−1.24424
$163$	16.7631	1.31299	0.656494	−	0.754332i	$-0.272039\pi$
$163$	16.7631	1.31299	0.656494	+	0.754332i	$0.272039\pi$
$164$	−13.6023	−1.06216
$165$	−0.597674	−0.0465289
$166$	−39.5723	−3.07141
$167$	−15.2388	−1.17921	−0.589606	−	0.807691i	$-0.700717\pi$
$167$	−15.2388	−1.17921	−0.589606	+	0.807691i	$0.700717\pi$
$168$	−12.7988	−0.987450
$169$	2.06849	0.159115
$170$	11.2203	0.860557
$171$	−9.61436	−0.735229
$172$	−27.4591	−2.09374
$173$	−18.1267	−1.37815	−0.689074	−	0.724691i	$-0.741983\pi$
$173$	−18.1267	−1.37815	−0.689074	+	0.724691i	$0.741983\pi$
$174$	−12.1585	−0.921735
$175$	2.76981	0.209378
$176$	−10.9294	−0.823838
$177$	−3.44357	−0.258834
$178$	27.7439	2.07949
$179$	12.7271	0.951266	0.475633	−	0.879644i	$-0.342219\pi$
$179$	12.7271	0.951266	0.475633	+	0.879644i	$0.342219\pi$
$180$	−13.1891	−0.983059
$181$	−13.7829	−1.02448	−0.512238	−	0.858844i	$-0.671183\pi$
$181$	−13.7829	−1.02448	−0.512238	+	0.858844i	$0.671183\pi$
$182$	−28.3884	−2.10429
$183$	4.21007	0.311217
$184$	−24.1840	−1.78287
$185$	−9.14909	−0.672655
$186$	13.0642	0.957910
$187$	4.31212	0.315334
$188$	−10.0177	−0.730614
$189$	−9.22266	−0.670850
$190$	−9.56815	−0.694146
$191$	0.982467	0.0710888	0.0355444	−	0.999368i	$-0.488683\pi$
$191$	0.982467	0.0710888	0.0355444	+	0.999368i	$0.488683\pi$
$192$	7.13784	0.515129
$193$	−6.72220	−0.483874	−0.241937	−	0.970292i	$-0.577783\pi$
$193$	−6.72220	−0.483874	−0.241937	+	0.970292i	$0.577783\pi$
$194$	−24.7186	−1.77469
$195$	2.28642	0.163734
$196$	3.34001	0.238572
$197$	10.0579	0.716595	0.358297	−	0.933608i	$-0.383357\pi$
$197$	10.0579	0.716595	0.358297	+	0.933608i	$0.383357\pi$
$198$	−7.10800	−0.505143
$199$	8.54626	0.605828	0.302914	−	0.953018i	$-0.402040\pi$
$199$	8.54626	0.605828	0.302914	+	0.953018i	$0.402040\pi$
$200$	−7.84509	−0.554732
$201$	−4.00398	−0.282419
$202$	43.0263	3.02732
$203$	21.6548	1.51987
$204$	−12.4433	−0.871208
$205$	−2.73619	−0.191104
$206$	10.7735	0.750626
$207$	−8.17858	−0.568451
$208$	41.8109	2.89907
$209$	−3.67718	−0.254356
$210$	−4.30752	−0.297247
$211$	11.1663	0.768723	0.384362	−	0.923183i	$-0.374422\pi$
$211$	11.1663	0.768723	0.384362	+	0.923183i	$0.374422\pi$
$212$	−44.0083	−3.02251
$213$	−3.81077	−0.261110
$214$	5.47406	0.374199
$215$	−5.52356	−0.376703
$216$	26.1218	1.77737
$217$	−23.2677	−1.57952
$218$	−17.1064	−1.15859
$219$	5.97897	0.404021
$220$	−5.04441	−0.340094
$221$	−16.4962	−1.10965
$222$	14.2284	0.954946
$223$	−7.51301	−0.503108	−0.251554	−	0.967843i	$-0.580942\pi$
$223$	−7.51301	−0.503108	−0.251554	+	0.967843i	$0.580942\pi$
$224$	−35.3113	−2.35933
$225$	−2.65307	−0.176871
$226$	38.2133	2.54191
$227$	2.66336	0.176773	0.0883867	−	0.996086i	$-0.471829\pi$
$227$	2.66336	0.176773	0.0883867	+	0.996086i	$0.471829\pi$
$228$	10.6111	0.702738
$229$	−14.9187	−0.985857	−0.492929	−	0.870070i	$-0.664074\pi$
$229$	−14.9187	−0.985857	−0.492929	+	0.870070i	$0.664074\pi$
$230$	−8.13927	−0.536688
$231$	−1.65544	−0.108920
$232$	−61.3340	−4.02677
$233$	16.4729	1.07918	0.539589	−	0.841929i	$-0.318580\pi$
$233$	16.4729	1.07918	0.539589	+	0.841929i	$0.318580\pi$
$234$	27.1919	1.77759
$235$	−2.01511	−0.131452
$236$	−29.0639	−1.89190
$237$	−7.28169	−0.472996
$238$	31.0781	2.01450
$239$	−5.31567	−0.343842	−0.171921	−	0.985111i	$-0.554997\pi$
$239$	−5.31567	−0.343842	−0.171921	+	0.985111i	$0.554997\pi$
$240$	6.34420	0.409516
$241$	−3.28997	−0.211926	−0.105963	−	0.994370i	$-0.533792\pi$
$241$	−3.28997	−0.211926	−0.105963	+	0.994370i	$0.533792\pi$
$242$	26.3249	1.69223
$243$	13.5220	0.867435
$244$	35.5333	2.27478
$245$	0.671862	0.0429237
$246$	4.25524	0.271304
$247$	14.0672	0.895073
$248$	65.9025	4.18481
$249$	8.82789	0.559445
$250$	−2.64032	−0.166988
$251$	−9.80463	−0.618863	−0.309432	−	0.950922i	$-0.600139\pi$
$251$	−9.80463	−0.618863	−0.309432	+	0.950922i	$0.600139\pi$
$252$	−36.5314	−2.30126
$253$	−3.12804	−0.196658
$254$	−33.4047	−2.09600
$255$	−2.50305	−0.156747
$256$	−7.07689	−0.442306
$257$	0.361265	0.0225351	0.0112676	−	0.999937i	$-0.496413\pi$
$257$	0.361265	0.0225351	0.0112676	+	0.999937i	$0.496413\pi$
$258$	8.59006	0.534794
$259$	−25.3413	−1.57463
$260$	19.2975	1.19678
$261$	−20.7420	−1.28390
$262$	36.8798	2.27844
$263$	−19.7853	−1.22001	−0.610006	−	0.792397i	$-0.708833\pi$
$263$	−19.7853	−1.22001	−0.610006	+	0.792397i	$0.708833\pi$
$264$	4.68881	0.288576
$265$	−8.85254	−0.543807
$266$	−26.5020	−1.62494
$267$	−6.18918	−0.378771
$268$	−33.7939	−2.06429
$269$	−29.3857	−1.79167	−0.895837	−	0.444382i	$-0.853423\pi$
$269$	−29.3857	−1.79167	−0.895837	+	0.444382i	$0.853423\pi$
$270$	8.79147	0.535032
$271$	−15.4266	−0.937101	−0.468551	−	0.883437i	$-0.655224\pi$
$271$	−15.4266	−0.937101	−0.468551	+	0.883437i	$0.655224\pi$
$272$	−45.7724	−2.77536
$273$	6.33296	0.383288
$274$	39.0137	2.35691
$275$	−1.01471	−0.0611894
$276$	9.02648	0.543330
$277$	−6.68146	−0.401450	−0.200725	−	0.979648i	$-0.564330\pi$
$277$	−6.68146	−0.401450	−0.200725	+	0.979648i	$0.564330\pi$
$278$	−54.9242	−3.29413
$279$	22.2870	1.33429
$280$	−21.7294	−1.29858
$281$	7.89154	0.470770	0.235385	−	0.971902i	$-0.424365\pi$
$281$	7.89154	0.470770	0.235385	+	0.971902i	$0.424365\pi$
$282$	3.13384	0.186618
$283$	12.9915	0.772265	0.386132	−	0.922443i	$-0.373811\pi$
$283$	12.9915	0.772265	0.386132	+	0.922443i	$0.373811\pi$
$284$	−32.1632	−1.90853
$285$	2.13449	0.126436
$286$	10.4000	0.614965
$287$	−7.57873	−0.447358
$288$	33.8229	1.99304
$289$	1.05913	0.0623016
$290$	−20.6423	−1.21216
$291$	5.51428	0.323253
$292$	50.4629	2.95312
$293$	22.6520	1.32334	0.661671	−	0.749795i	$-0.269848\pi$
$293$	22.6520	1.32334	0.661671	+	0.749795i	$0.269848\pi$
$294$	−1.04486	−0.0609374
$295$	−5.84638	−0.340389
$296$	71.7754	4.17186
$297$	3.37869	0.196052
$298$	46.4609	2.69141
$299$	11.9664	0.692036
$300$	2.92812	0.169055
$301$	−15.2992	−0.881832
$302$	−1.96725	−0.113202
$303$	−9.59842	−0.551415
$304$	39.0326	2.23867
$305$	7.14772	0.409277
$306$	−29.7682	−1.70174
$307$	−28.8507	−1.64660	−0.823299	−	0.567608i	$-0.807869\pi$
$307$	−28.8507	−1.64660	−0.823299	+	0.567608i	$0.807869\pi$
$308$	−13.9721	−0.796132
$309$	−2.40338	−0.136724
$310$	22.1799	1.25973
$311$	−21.1019	−1.19658	−0.598290	−	0.801280i	$-0.704153\pi$
$311$	−21.1019	−1.19658	−0.598290	+	0.801280i	$0.704153\pi$
$312$	−17.9372	−1.01549
$313$	26.7061	1.50952	0.754760	−	0.656002i	$-0.227754\pi$
$313$	26.7061	1.50952	0.754760	+	0.656002i	$0.227754\pi$
$314$	−35.7689	−2.01856
$315$	−7.34850	−0.414041
$316$	−61.4579	−3.45728
$317$	10.8942	0.611877	0.305939	−	0.952051i	$-0.401030\pi$
$317$	10.8942	0.611877	0.305939	+	0.952051i	$0.401030\pi$
$318$	13.7672	0.772025
$319$	−7.93316	−0.444171
$320$	12.1184	0.677439
$321$	−1.22117	−0.0681590
$322$	−22.5443	−1.25634
$323$	−15.4000	−0.856878
$324$	29.8176	1.65653
$325$	3.88182	0.215324
$326$	−44.2599	−2.45133
$327$	3.81613	0.211032
$328$	21.4657	1.18524
$329$	−5.58149	−0.307717
$330$	1.57805	0.0868687
$331$	−12.6989	−0.697997	−0.348998	−	0.937123i	$-0.613478\pi$
$331$	−12.6989	−0.697997	−0.348998	+	0.937123i	$0.613478\pi$
$332$	74.5079	4.08915
$333$	24.2732	1.33016
$334$	40.2352	2.20157
$335$	−6.79784	−0.371406
$336$	17.5722	0.958644
$337$	12.4896	0.680354	0.340177	−	0.940361i	$-0.389513\pi$
$337$	12.4896	0.680354	0.340177	+	0.940361i	$0.389513\pi$
$338$	−5.46147	−0.297065
$339$	−8.52472	−0.462999
$340$	−21.1259	−1.14571
$341$	8.52407	0.461604
$342$	25.3850	1.37266
$343$	−17.5278	−0.946410
$344$	43.3328	2.33635
$345$	1.81573	0.0977556
$346$	47.8603	2.57298
$347$	−17.7607	−0.953444	−0.476722	−	0.879054i	$-0.658175\pi$
$347$	−17.7607	−0.953444	−0.476722	+	0.879054i	$0.658175\pi$
$348$	22.8924	1.22716
$349$	36.2608	1.94100	0.970499	−	0.241106i	$-0.0775102\pi$
$349$	36.2608	1.94100	0.970499	+	0.241106i	$0.0775102\pi$
$350$	−7.31318	−0.390906
$351$	−12.9253	−0.689902
$352$	12.9362	0.689500
$353$	1.55181	0.0825948	0.0412974	−	0.999147i	$-0.486851\pi$
$353$	1.55181	0.0825948	0.0412974	+	0.999147i	$0.486851\pi$
$354$	9.09211	0.483240
$355$	−6.46981	−0.343382
$356$	−52.2371	−2.76856
$357$	−6.93298	−0.366932
$358$	−33.6035	−1.77600
$359$	9.99302	0.527411	0.263706	−	0.964603i	$-0.415055\pi$
$359$	9.99302	0.527411	0.263706	+	0.964603i	$0.415055\pi$
$360$	20.8136	1.09697
$361$	−5.86761	−0.308822
$362$	36.3912	1.91268
$363$	−5.87263	−0.308233
$364$	53.4506	2.80157
$365$	10.1509	0.531323
$366$	−11.1159	−0.581038
$367$	−19.4694	−1.01629	−0.508147	−	0.861270i	$-0.669669\pi$
$367$	−19.4694	−1.01629	−0.508147	+	0.861270i	$0.669669\pi$
$368$	33.2036	1.73086
$369$	7.25930	0.377904
$370$	24.1565	1.25584
$371$	−24.5199	−1.27301
$372$	−24.5976	−1.27533
$373$	35.9628	1.86208	0.931041	−	0.364914i	$-0.118902\pi$
$373$	35.9628	1.86208	0.931041	+	0.364914i	$0.118902\pi$
$374$	−11.3854	−0.588723
$375$	0.589008	0.0304163
$376$	15.8087	0.815274
$377$	30.3486	1.56303
$378$	24.3507	1.25247
$379$	1.98485	0.101955	0.0509774	−	0.998700i	$-0.483766\pi$
$379$	1.98485	0.101955	0.0509774	+	0.998700i	$0.483766\pi$
$380$	18.0152	0.924160
$381$	7.45201	0.381778
$382$	−2.59402	−0.132722
$383$	24.8445	1.26949	0.634747	−	0.772720i	$-0.281104\pi$
$383$	24.8445	1.26949	0.634747	+	0.772720i	$0.281104\pi$
$384$	−3.82807	−0.195351
$385$	−2.81056	−0.143240
$386$	17.7487	0.903386
$387$	14.6544	0.744924
$388$	46.5409	2.36275
$389$	23.9075	1.21216	0.606080	−	0.795404i	$-0.292741\pi$
$389$	23.9075	1.21216	0.606080	+	0.795404i	$0.292741\pi$
$390$	−6.03688	−0.305689
$391$	−13.1002	−0.662506
$392$	−5.27082	−0.266217
$393$	−8.22724	−0.415010
$394$	−26.5560	−1.33787
$395$	−12.3626	−0.622031
$396$	13.3832	0.672529
$397$	34.6368	1.73837	0.869186	−	0.494486i	$-0.164644\pi$
$397$	34.6368	1.73837	0.869186	+	0.494486i	$0.164644\pi$
$398$	−22.5648	−1.13107
$399$	5.91213	0.295977
$400$	10.7710	0.538549
$401$	−37.3051	−1.86293	−0.931463	−	0.363837i	$-0.881467\pi$
$401$	−37.3051	−1.86293	−0.931463	+	0.363837i	$0.881467\pi$
$402$	10.5718	0.527273
$403$	−32.6091	−1.62438
$404$	−81.0113	−4.03046
$405$	5.99798	0.298042
$406$	−57.1754	−2.83757
$407$	9.28369	0.460176
$408$	19.6367	0.972160
$409$	−9.80158	−0.484657	−0.242328	−	0.970194i	$-0.577911\pi$
$409$	−9.80158	−0.484657	−0.242328	+	0.970194i	$0.577911\pi$
$410$	7.22441	0.356788
$411$	−8.70328	−0.429301
$412$	−20.2847	−0.999356
$413$	−16.1934	−0.796824
$414$	21.5940	1.06129
$415$	14.9877	0.735718
$416$	−49.4877	−2.42634
$417$	12.2526	0.600013
$418$	9.70891	0.474879
$419$	19.9976	0.976945	0.488472	−	0.872579i	$-0.337554\pi$
$419$	19.9976	0.976945	0.488472	+	0.872579i	$0.337554\pi$
$420$	8.11034	0.395744
$421$	8.64416	0.421291	0.210645	−	0.977563i	$-0.432443\pi$
$421$	8.64416	0.421291	0.210645	+	0.977563i	$0.432443\pi$
$422$	−29.4827	−1.43520
$423$	5.34624	0.259943
$424$	69.4489	3.37274
$425$	−4.24960	−0.206136
$426$	10.0616	0.487488
$427$	19.7979	0.958085
$428$	−10.3067	−0.498195
$429$	−2.32006	−0.112014
$430$	14.5839	0.703300
$431$	20.4738	0.986187	0.493094	−	0.869976i	$-0.335866\pi$
$431$	20.4738	0.986187	0.493094	+	0.869976i	$0.335866\pi$
$432$	−35.8642	−1.72552
$433$	31.0238	1.49091	0.745453	−	0.666558i	$-0.232233\pi$
$433$	31.0238	1.49091	0.745453	+	0.666558i	$0.232233\pi$
$434$	61.4342	2.94894
$435$	4.60495	0.220790
$436$	32.2084	1.54250
$437$	11.1712	0.534393
$438$	−15.7864	−0.754302
$439$	−31.0038	−1.47973	−0.739865	−	0.672755i	$-0.765111\pi$
$439$	−31.0038	−1.47973	−0.739865	+	0.672755i	$0.765111\pi$
$440$	7.96051	0.379502
$441$	−1.78250	−0.0848808
$442$	43.5551	2.07171
$443$	−0.103776	−0.00493056	−0.00246528	−	0.999997i	$-0.500785\pi$
$443$	−0.103776	−0.00493056	−0.00246528	+	0.999997i	$0.500785\pi$
$444$	−26.7896	−1.27138
$445$	−10.5078	−0.498117
$446$	19.8367	0.939296
$447$	−10.3646	−0.490229
$448$	33.5657	1.58583
$449$	−40.9882	−1.93435	−0.967176	−	0.254106i	$-0.918219\pi$
$449$	−40.9882	−1.93435	−0.967176	+	0.254106i	$0.918219\pi$
$450$	7.00494	0.330216
$451$	2.77644	0.130738
$452$	−71.9492	−3.38421
$453$	0.438858	0.0206194
$454$	−7.03211	−0.330033
$455$	10.7519	0.504057
$456$	−16.7452	−0.784167
$457$	36.2356	1.69503	0.847516	−	0.530770i	$-0.178097\pi$
$457$	36.2356	1.69503	0.847516	+	0.530770i	$0.178097\pi$
$458$	39.3902	1.84058
$459$	14.1499	0.660462
$460$	15.3249	0.714526
$461$	16.8151	0.783157	0.391578	−	0.920145i	$-0.371929\pi$
$461$	16.8151	0.783157	0.391578	+	0.920145i	$0.371929\pi$
$462$	4.37090	0.203353
$463$	−9.57465	−0.444972	−0.222486	−	0.974936i	$-0.571417\pi$
$463$	−9.57465	−0.444972	−0.222486	+	0.974936i	$0.571417\pi$
$464$	84.2089	3.90930
$465$	−4.94795	−0.229456
$466$	−43.4937	−2.01481
$467$	17.2256	0.797104	0.398552	−	0.917146i	$-0.369513\pi$
$467$	17.2256	0.797104	0.398552	+	0.917146i	$0.369513\pi$
$468$	−51.1977	−2.36662
$469$	−18.8287	−0.869430
$470$	5.32054	0.245418
$471$	7.97942	0.367672
$472$	45.8654	2.11113
$473$	5.60482	0.257710
$474$	19.2260	0.883077
$475$	3.62386	0.166274
$476$	−58.5148	−2.68202
$477$	23.4864	1.07537
$478$	14.0350	0.641948
$479$	5.70954	0.260876	0.130438	−	0.991456i	$-0.458362\pi$
$479$	5.70954	0.260876	0.130438	+	0.991456i	$0.458362\pi$
$480$	−7.50904	−0.342739
$481$	−35.5151	−1.61935
$482$	8.68657	0.395663
$483$	5.02923	0.228838
$484$	−49.5653	−2.25297
$485$	9.36197	0.425105
$486$	−35.7023	−1.61949
$487$	17.3624	0.786767	0.393383	−	0.919375i	$-0.371305\pi$
$487$	17.3624	0.786767	0.393383	+	0.919375i	$0.371305\pi$
$488$	−56.0745	−2.53837
$489$	9.87361	0.446500
$490$	−1.77393	−0.0801379
$491$	35.2685	1.59165	0.795823	−	0.605529i	$-0.207039\pi$
$491$	35.2685	1.59165	0.795823	+	0.605529i	$0.207039\pi$
$492$	−8.01189	−0.361204
$493$	−33.2240	−1.49633
$494$	−37.1418	−1.67109
$495$	2.69210	0.121001
$496$	−90.4814	−4.06273
$497$	−17.9202	−0.803829
$498$	−23.3084	−1.04448
$499$	−27.9677	−1.25200	−0.626002	−	0.779821i	$-0.715310\pi$
$499$	−27.9677	−1.25200	−0.626002	+	0.779821i	$0.715310\pi$
$500$	4.97127	0.222322
$501$	−8.97576	−0.401007
$502$	25.8873	1.15541
$503$	−32.4448	−1.44664	−0.723320	−	0.690513i	$-0.757385\pi$
$503$	−32.4448	−1.44664	−0.723320	+	0.690513i	$0.757385\pi$
$504$	57.6497	2.56792
$505$	−16.2959	−0.725158
$506$	8.25902	0.367158
$507$	1.21836	0.0541092
$508$	62.8954	2.79053
$509$	−25.5757	−1.13362	−0.566811	−	0.823848i	$-0.691823\pi$
$509$	−25.5757	−1.13362	−0.566811	+	0.823848i	$0.691823\pi$
$510$	6.60885	0.292645
$511$	28.1161	1.24378
$512$	31.6836	1.40023
$513$	−12.0664	−0.532744
$514$	−0.953855	−0.0420727
$515$	−4.08039	−0.179803
$516$	−16.1736	−0.712004
$517$	2.04476	0.0899285
$518$	66.9090	2.93981
$519$	−10.6768	−0.468659
$520$	−30.4532	−1.33546
$521$	−18.3979	−0.806027	−0.403013	−	0.915194i	$-0.632037\pi$
$521$	−18.3979	−0.806027	−0.403013	+	0.915194i	$0.632037\pi$
$522$	54.7656	2.39702
$523$	−30.7301	−1.34373	−0.671867	−	0.740672i	$-0.734507\pi$
$523$	−30.7301	−1.34373	−0.671867	+	0.740672i	$0.734507\pi$
$524$	−69.4385	−3.03343
$525$	1.63144	0.0712020
$526$	52.2393	2.27774
$527$	35.6987	1.55506
$528$	−6.43753	−0.280158
$529$	−13.4970	−0.586828
$530$	23.3735	1.01528
$531$	15.5109	0.673114
$532$	49.8987	2.16338
$533$	−10.6214	−0.460063
$534$	16.3414	0.707161
$535$	−2.07326	−0.0896349
$536$	53.3296	2.30349
$537$	7.49635	0.323491
$538$	77.5874	3.34503
$539$	−0.681747	−0.0293649
$540$	−16.5529	−0.712322
$541$	24.1451	1.03808	0.519039	−	0.854750i	$-0.326290\pi$
$541$	24.1451	1.03808	0.519039	+	0.854750i	$0.326290\pi$
$542$	40.7312	1.74955
$543$	−8.11825	−0.348387
$544$	54.1765	2.32280
$545$	6.47890	0.277526
$546$	−16.7210	−0.715593
$547$	−27.6272	−1.18125	−0.590626	−	0.806945i	$-0.701119\pi$
$547$	−27.6272	−1.18125	−0.590626	+	0.806945i	$0.701119\pi$
$548$	−73.4563	−3.13790
$549$	−18.9634	−0.809338
$550$	2.67916	0.114240
$551$	28.3319	1.20698
$552$	−14.2446	−0.606289
$553$	−34.2421	−1.45612
$554$	17.6412	0.749501
$555$	−5.38889	−0.228746
$556$	103.413	4.38568
$557$	17.6444	0.747619	0.373810	−	0.927505i	$-0.378051\pi$
$557$	17.6444	0.747619	0.373810	+	0.927505i	$0.378051\pi$
$558$	−58.8449	−2.49110
$559$	−21.4414	−0.906876
$560$	29.8336	1.26070
$561$	2.53988	0.107234
$562$	−20.8362	−0.878921
$563$	11.4687	0.483348	0.241674	−	0.970357i	$-0.422303\pi$
$563$	11.4687	0.483348	0.241674	+	0.970357i	$0.422303\pi$
$564$	−5.90049	−0.248456
$565$	−14.4730	−0.608884
$566$	−34.3017	−1.44181
$567$	16.6133	0.697693
$568$	50.7562	2.12968
$569$	29.5671	1.23952	0.619760	−	0.784792i	$-0.287230\pi$
$569$	29.5671	1.23952	0.619760	+	0.784792i	$0.287230\pi$
$570$	−5.63572	−0.236054
$571$	−36.5421	−1.52924	−0.764620	−	0.644481i	$-0.777073\pi$
$571$	−36.5421	−1.52924	−0.764620	+	0.644481i	$0.777073\pi$
$572$	−19.5815	−0.818742
$573$	0.578681	0.0241747
$574$	20.0102	0.835212
$575$	3.08269	0.128557
$576$	−32.1509	−1.33962
$577$	−41.0543	−1.70911	−0.854557	−	0.519358i	$-0.826171\pi$
$577$	−41.0543	−1.70911	−0.854557	+	0.519358i	$0.826171\pi$
$578$	−2.79643	−0.116316
$579$	−3.95943	−0.164548
$580$	38.8660	1.61382
$581$	41.5132	1.72226
$582$	−14.5594	−0.603508
$583$	8.98278	0.372029
$584$	−79.6348	−3.29531
$585$	−10.2987	−0.425800
$586$	−59.8083	−2.47066
$587$	−25.9357	−1.07048	−0.535241	−	0.844699i	$-0.679779\pi$
$587$	−25.9357	−1.07048	−0.535241	+	0.844699i	$0.679779\pi$
$588$	1.96729	0.0811298
$589$	−30.4422	−1.25435
$590$	15.4363	0.635502
$591$	5.92418	0.243688
$592$	−98.5447	−4.05016
$593$	−7.18171	−0.294918	−0.147459	−	0.989068i	$-0.547109\pi$
$593$	−7.18171	−0.294918	−0.147459	+	0.989068i	$0.547109\pi$
$594$	−8.92082	−0.366025
$595$	−11.7706	−0.482548
$596$	−87.4780	−3.58324
$597$	5.03382	0.206020
$598$	−31.5951	−1.29202
$599$	9.30391	0.380148	0.190074	−	0.981770i	$-0.439127\pi$
$599$	9.30391	0.380148	0.190074	+	0.981770i	$0.439127\pi$
$600$	−4.62082	−0.188644
$601$	−12.5983	−0.513894	−0.256947	−	0.966426i	$-0.582717\pi$
$601$	−12.5983	−0.513894	−0.256947	+	0.966426i	$0.582717\pi$
$602$	40.3948	1.64637
$603$	18.0351	0.734447
$604$	3.70399	0.150713
$605$	−9.97036	−0.405353
$606$	25.3429	1.02948
$607$	−9.03398	−0.366678	−0.183339	−	0.983050i	$-0.558691\pi$
$607$	−9.03398	−0.366678	−0.183339	+	0.983050i	$0.558691\pi$
$608$	−46.1992	−1.87363
$609$	12.7548	0.516852
$610$	−18.8722	−0.764115
$611$	−7.82230	−0.316456
$612$	56.0485	2.26563
$613$	10.7075	0.432473	0.216236	−	0.976341i	$-0.430622\pi$
$613$	10.7075	0.432473	0.216236	+	0.976341i	$0.430622\pi$
$614$	76.1750	3.07417
$615$	−1.61164	−0.0649875
$616$	22.0491	0.888384
$617$	34.0034	1.36892	0.684462	−	0.729048i	$-0.260037\pi$
$617$	34.0034	1.36892	0.684462	+	0.729048i	$0.260037\pi$
$618$	6.34569	0.255261
$619$	20.1860	0.811345	0.405673	−	0.914018i	$-0.367037\pi$
$619$	20.1860	0.811345	0.405673	+	0.914018i	$0.367037\pi$
$620$	−41.7610	−1.67716
$621$	−10.2644	−0.411898
$622$	55.7158	2.23400
$623$	−29.1046	−1.16605
$624$	24.6270	0.985869
$625$	1.00000	0.0400000
$626$	−70.5126	−2.81825
$627$	−2.16589	−0.0864973
$628$	67.3468	2.68743
$629$	38.8800	1.55025
$630$	19.4024	0.773009
$631$	11.1691	0.444636	0.222318	−	0.974974i	$-0.428638\pi$
$631$	11.1691	0.444636	0.222318	+	0.974974i	$0.428638\pi$
$632$	96.9859	3.85789
$633$	6.57707	0.261415
$634$	−28.7640	−1.14237
$635$	12.6518	0.502071
$636$	−25.9213	−1.02785
$637$	2.60804	0.103334
$638$	20.9460	0.829262
$639$	17.1649	0.679031
$640$	−6.49918	−0.256903
$641$	21.9561	0.867215	0.433608	−	0.901102i	$-0.357240\pi$
$641$	21.9561	0.867215	0.433608	+	0.901102i	$0.357240\pi$
$642$	3.22427	0.127252
$643$	−31.7056	−1.25035	−0.625174	−	0.780486i	$-0.714972\pi$
$643$	−31.7056	−1.25035	−0.625174	+	0.780486i	$0.714972\pi$
$644$	42.4470	1.67265
$645$	−3.25342	−0.128103
$646$	40.6608	1.59978
$647$	25.1697	0.989524	0.494762	−	0.869028i	$-0.335255\pi$
$647$	25.1697	0.989524	0.494762	+	0.869028i	$0.335255\pi$
$648$	−47.0547	−1.84848
$649$	5.93239	0.232867
$650$	−10.2492	−0.402007
$651$	−13.7049	−0.537137
$652$	83.3339	3.26361
$653$	−24.9225	−0.975291	−0.487646	−	0.873042i	$-0.662144\pi$
$653$	−24.9225	−0.975291	−0.487646	+	0.873042i	$0.662144\pi$
$654$	−10.0758	−0.393994
$655$	−13.9680	−0.545773
$656$	−29.4714	−1.15067
$657$	−26.9311	−1.05068
$658$	14.7369	0.574504
$659$	−30.6259	−1.19302	−0.596509	−	0.802607i	$-0.703446\pi$
$659$	−30.6259	−1.19302	−0.596509	+	0.802607i	$0.703446\pi$
$660$	−2.97120	−0.115654
$661$	33.5614	1.30539	0.652694	−	0.757622i	$-0.273639\pi$
$661$	33.5614	1.30539	0.652694	+	0.757622i	$0.273639\pi$
$662$	33.5292	1.30315
$663$	−9.71639	−0.377353
$664$	−117.580	−4.56299
$665$	10.0374	0.389235
$666$	−64.0888	−2.48339
$667$	24.1009	0.933189
$668$	−75.7560	−2.93109
$669$	−4.42522	−0.171089
$670$	17.9484	0.693409
$671$	−7.25288	−0.279994
$672$	−20.7986	−0.802324
$673$	−30.0428	−1.15807	−0.579033	−	0.815304i	$-0.696570\pi$
$673$	−30.0428	−1.15807	−0.579033	+	0.815304i	$0.696570\pi$
$674$	−32.9766	−1.27021
$675$	−3.32971	−0.128160
$676$	10.2830	0.395501
$677$	46.7050	1.79502	0.897510	−	0.440994i	$-0.145374\pi$
$677$	46.7050	1.79502	0.897510	+	0.440994i	$0.145374\pi$
$678$	22.5080	0.864413
$679$	25.9309	0.995137
$680$	33.3385	1.27847
$681$	1.56874	0.0601143
$682$	−22.5062	−0.861808
$683$	43.5937	1.66807	0.834034	−	0.551713i	$-0.186026\pi$
$683$	43.5937	1.66807	0.834034	+	0.551713i	$0.186026\pi$
$684$	−47.7956	−1.82751
$685$	−14.7762	−0.564568
$686$	46.2788	1.76693
$687$	−8.78726	−0.335255
$688$	−59.4941	−2.26819
$689$	−34.3639	−1.30916
$690$	−4.79410	−0.182508
$691$	−24.9143	−0.947785	−0.473893	−	0.880583i	$-0.657152\pi$
$691$	−24.9143	−0.947785	−0.473893	+	0.880583i	$0.657152\pi$
$692$	−90.1128	−3.42557
$693$	7.45662	0.283253
$694$	46.8939	1.78007
$695$	20.8021	0.789069
$696$	−36.1262	−1.36936
$697$	11.6277	0.440431
$698$	−95.7400	−3.62381
$699$	9.70270	0.366990
$700$	13.7695	0.520438
$701$	−7.47160	−0.282199	−0.141099	−	0.989995i	$-0.545064\pi$
$701$	−7.47160	−0.282199	−0.141099	+	0.989995i	$0.545064\pi$
$702$	34.1269	1.28804
$703$	−33.1551	−1.25047
$704$	−12.2967	−0.463449
$705$	−1.18692	−0.0447020
$706$	−4.09728	−0.154203
$707$	−45.1366	−1.69754
$708$	−17.1189	−0.643368
$709$	−44.6388	−1.67645	−0.838223	−	0.545328i	$-0.816405\pi$
$709$	−44.6388	−1.67645	−0.838223	+	0.545328i	$0.816405\pi$
$710$	17.0823	0.641089
$711$	32.7989	1.23005
$712$	82.4346	3.08937
$713$	−25.8961	−0.969815
$714$	18.3053	0.685058
$715$	−3.93893	−0.147307
$716$	63.2697	2.36450
$717$	−3.13097	−0.116928
$718$	−26.3847	−0.984669
$719$	35.3422	1.31804	0.659021	−	0.752125i	$-0.270971\pi$
$719$	35.3422	1.31804	0.659021	+	0.752125i	$0.270971\pi$
$720$	−28.5761	−1.06497
$721$	−11.3019	−0.420905
$722$	15.4923	0.576565
$723$	−1.93782	−0.0720684
$724$	−68.5185	−2.54647
$725$	7.81813	0.290358
$726$	15.5056	0.575466
$727$	40.8357	1.51451	0.757256	−	0.653118i	$-0.226540\pi$
$727$	40.8357	1.51451	0.757256	+	0.653118i	$0.226540\pi$
$728$	−84.3496	−3.12621
$729$	−10.0294	−0.371459
$730$	−26.8016	−0.991972
$731$	23.4729	0.868177
$732$	20.9294	0.773572
$733$	3.52283	0.130119	0.0650594	−	0.997881i	$-0.479276\pi$
$733$	3.52283	0.130119	0.0650594	+	0.997881i	$0.479276\pi$
$734$	51.4054	1.89741
$735$	0.395732	0.0145968
$736$	−39.3000	−1.44862
$737$	6.89785	0.254086
$738$	−19.1668	−0.705541
$739$	−45.3045	−1.66655	−0.833276	−	0.552858i	$-0.813537\pi$
$739$	−45.3045	−1.66655	−0.833276	+	0.552858i	$0.813537\pi$
$740$	−45.4826	−1.67197
$741$	8.28568	0.304382
$742$	64.7402	2.37669
$743$	−28.5275	−1.04657	−0.523286	−	0.852157i	$-0.675294\pi$
$743$	−28.5275	−1.04657	−0.523286	+	0.852157i	$0.675294\pi$
$744$	38.8171	1.42310
$745$	−17.5967	−0.644694
$746$	−94.9531	−3.47648
$747$	−39.7634	−1.45487
$748$	21.4367	0.783804
$749$	−5.74254	−0.209828
$750$	−1.55517	−0.0567867
$751$	−24.1287	−0.880468	−0.440234	−	0.897883i	$-0.645104\pi$
$751$	−24.1287	−0.880468	−0.440234	+	0.897883i	$0.645104\pi$
$752$	−21.7047	−0.791491
$753$	−5.77501	−0.210453
$754$	−80.1298	−2.91815
$755$	0.745080	0.0271162
$756$	−45.8483	−1.66749
$757$	−9.01842	−0.327780	−0.163890	−	0.986479i	$-0.552404\pi$
$757$	−9.01842	−0.327780	−0.163890	+	0.986479i	$0.552404\pi$
$758$	−5.24063	−0.190348
$759$	−1.84244	−0.0668764
$760$	−28.4295	−1.03125
$761$	−21.8524	−0.792149	−0.396074	−	0.918218i	$-0.629628\pi$
$761$	−21.8524	−0.792149	−0.396074	+	0.918218i	$0.629628\pi$
$762$	−19.6757	−0.712774
$763$	17.9454	0.649665
$764$	4.88411	0.176701
$765$	11.2745	0.407630
$766$	−65.5973	−2.37013
$767$	−22.6946	−0.819453
$768$	−4.16835	−0.150412
$769$	8.05025	0.290299	0.145150	−	0.989410i	$-0.453634\pi$
$769$	8.05025	0.290299	0.145150	+	0.989410i	$0.453634\pi$
$770$	7.42077	0.267426
$771$	0.212788	0.00766339
$772$	−33.4178	−1.20273
$773$	−20.5021	−0.737408	−0.368704	−	0.929547i	$-0.620198\pi$
$773$	−20.5021	−0.737408	−0.368704	+	0.929547i	$0.620198\pi$
$774$	−38.6922	−1.39076
$775$	−8.40048	−0.301754
$776$	−73.4455	−2.63654
$777$	−14.9262	−0.535475
$778$	−63.1234	−2.26309
$779$	−9.91558	−0.355262
$780$	11.3664	0.406983
$781$	6.56499	0.234914
$782$	34.5887	1.23689
$783$	−26.0321	−0.930311
$784$	7.23661	0.258450
$785$	13.5472	0.483520
$786$	21.7225	0.774817
$787$	43.1730	1.53895	0.769476	−	0.638676i	$-0.220518\pi$
$787$	43.1730	1.53895	0.769476	+	0.638676i	$0.220518\pi$
$788$	50.0005	1.78119
$789$	−11.6537	−0.414882
$790$	32.6412	1.16132
$791$	−40.0875	−1.42535
$792$	−21.1198	−0.750459
$793$	27.7461	0.985294
$794$	−91.4521	−3.24551
$795$	−5.21422	−0.184929
$796$	42.4858	1.50587
$797$	26.2644	0.930333	0.465166	−	0.885223i	$-0.345995\pi$
$797$	26.2644	0.930333	0.465166	+	0.885223i	$0.345995\pi$
$798$	−15.6099	−0.552584
$799$	8.56343	0.302953
$800$	−12.7486	−0.450731
$801$	27.8779	0.985017
$802$	98.4971	3.47805
$803$	−10.3002	−0.363488
$804$	−19.9049	−0.701991
$805$	8.53847	0.300941
$806$	86.0983	3.03268
$807$	−17.3084	−0.609284
$808$	127.843	4.49749
$809$	19.1042	0.671669	0.335835	−	0.941921i	$-0.390982\pi$
$809$	19.1042	0.671669	0.335835	+	0.941921i	$0.390982\pi$
$810$	−15.8366	−0.556440
$811$	−33.1604	−1.16442	−0.582210	−	0.813039i	$-0.697812\pi$
$811$	−33.1604	−1.16442	−0.582210	+	0.813039i	$0.697812\pi$
$812$	107.652	3.77783
$813$	−9.08642	−0.318675
$814$	−24.5119	−0.859141
$815$	16.7631	0.587186
$816$	−26.9603	−0.943800
$817$	−20.0166	−0.700293
$818$	25.8793	0.904847
$819$	−28.5255	−0.996763
$820$	−13.6023	−0.475014
$821$	23.1278	0.807165	0.403583	−	0.914943i	$-0.367765\pi$
$821$	23.1278	0.807165	0.403583	+	0.914943i	$0.367765\pi$
$822$	22.9794	0.801499
$823$	−29.6807	−1.03460	−0.517302	−	0.855803i	$-0.673064\pi$
$823$	−29.6807	−1.03460	−0.517302	+	0.855803i	$0.673064\pi$
$824$	32.0110	1.11516
$825$	−0.597674	−0.0208083
$826$	42.7556	1.48766
$827$	0.852914	0.0296587	0.0148294	−	0.999890i	$-0.495279\pi$
$827$	0.852914	0.0296587	0.0148294	+	0.999890i	$0.495279\pi$
$828$	−40.6579	−1.41296
$829$	−9.22004	−0.320225	−0.160113	−	0.987099i	$-0.551186\pi$
$829$	−9.22004	−0.320225	−0.160113	+	0.987099i	$0.551186\pi$
$830$	−39.5723	−1.37357
$831$	−3.93544	−0.136519
$832$	47.0414	1.63087
$833$	−2.85515	−0.0989250
$834$	−32.3508	−1.12022
$835$	−15.2388	−0.527359
$836$	−18.2802	−0.632235
$837$	27.9711	0.966823
$838$	−52.7999	−1.82394
$839$	−35.1519	−1.21358	−0.606789	−	0.794863i	$-0.707543\pi$
$839$	−35.1519	−1.21358	−0.606789	+	0.794863i	$0.707543\pi$
$840$	−12.7988	−0.441601
$841$	32.1232	1.10770
$842$	−22.8233	−0.786544
$843$	4.64819	0.160092
$844$	55.5109	1.91076
$845$	2.06849	0.0711583
$846$	−14.1158	−0.485310
$847$	−27.6160	−0.948898
$848$	−95.3505	−3.27435
$849$	7.65211	0.262620
$850$	11.2203	0.384853
$851$	−28.2038	−0.966814
$852$	−18.9444	−0.649023
$853$	−18.5073	−0.633678	−0.316839	−	0.948479i	$-0.602622\pi$
$853$	−18.5073	−0.633678	−0.316839	+	0.948479i	$0.602622\pi$
$854$	−52.2726	−1.78873
$855$	−9.61436	−0.328804
$856$	16.2649	0.555923
$857$	−13.3223	−0.455083	−0.227541	−	0.973768i	$-0.573069\pi$
$857$	−13.3223	−0.455083	−0.227541	+	0.973768i	$0.573069\pi$
$858$	6.12569	0.209128
$859$	47.3037	1.61398	0.806991	−	0.590564i	$-0.201095\pi$
$859$	47.3037	1.61398	0.806991	+	0.590564i	$0.201095\pi$
$860$	−27.4591	−0.936347
$861$	−4.46394	−0.152131
$862$	−54.0572	−1.84120
$863$	26.5961	0.905340	0.452670	−	0.891678i	$-0.350471\pi$
$863$	26.5961	0.905340	0.452670	+	0.891678i	$0.350471\pi$
$864$	42.4491	1.44415
$865$	−18.1267	−0.616327
$866$	−81.9125	−2.78350
$867$	0.623835	0.0211865
$868$	−115.670	−3.92610
$869$	12.5445	0.425543
$870$	−12.1585	−0.412212
$871$	−26.3880	−0.894122
$872$	−50.8276	−1.72124
$873$	−24.8379	−0.840637
$874$	−29.4956	−0.997704
$875$	2.76981	0.0936368
$876$	29.7231	1.00425
$877$	38.1995	1.28990	0.644952	−	0.764223i	$-0.276877\pi$
$877$	38.1995	1.28990	0.644952	+	0.764223i	$0.276877\pi$
$878$	81.8598	2.76264
$879$	13.3422	0.450021
$880$	−10.9294	−0.368431
$881$	−14.7196	−0.495916	−0.247958	−	0.968771i	$-0.579759\pi$
$881$	−14.7196	−0.495916	−0.247958	+	0.968771i	$0.579759\pi$
$882$	4.70635	0.158471
$883$	−10.7176	−0.360675	−0.180338	−	0.983605i	$-0.557719\pi$
$883$	−10.7176	−0.360675	−0.180338	+	0.983605i	$0.557719\pi$
$884$	−82.0069	−2.75819
$885$	−3.44357	−0.115754
$886$	0.274002	0.00920529
$887$	−25.7914	−0.865991	−0.432996	−	0.901396i	$-0.642543\pi$
$887$	−25.7914	−0.865991	−0.432996	+	0.901396i	$0.642543\pi$
$888$	42.2763	1.41870
$889$	35.0431	1.17531
$890$	27.7439	0.929977
$891$	−6.08623	−0.203896
$892$	−37.3492	−1.25054
$893$	−7.30250	−0.244369
$894$	27.3658	0.915251
$895$	12.7271	0.425419
$896$	−18.0015	−0.601389
$897$	7.04833	0.235337
$898$	108.222	3.61141
$899$	−65.6761	−2.19042
$900$	−13.1891	−0.439637
$901$	37.6198	1.25330
$902$	−7.33069	−0.244085
$903$	−9.01137	−0.299879
$904$	113.542	3.77635
$905$	−13.7829	−0.458159
$906$	−1.15872	−0.0384960
$907$	−1.46580	−0.0486713	−0.0243356	−	0.999704i	$-0.507747\pi$
$907$	−1.46580	−0.0486713	−0.0243356	+	0.999704i	$0.507747\pi$
$908$	13.2403	0.439394
$909$	43.2341	1.43399
$910$	−28.3884	−0.941067
$911$	−2.68071	−0.0888159	−0.0444080	−	0.999013i	$-0.514140\pi$
$911$	−2.68071	−0.0888159	−0.0444080	+	0.999013i	$0.514140\pi$
$912$	22.9905	0.761292
$913$	−15.2082	−0.503318
$914$	−95.6735	−3.16460
$915$	4.21007	0.139181
$916$	−74.1650	−2.45048
$917$	−38.6886	−1.27761
$918$	−37.3603	−1.23307
$919$	−8.00900	−0.264193	−0.132096	−	0.991237i	$-0.542171\pi$
$919$	−8.00900	−0.264193	−0.132096	+	0.991237i	$0.542171\pi$
$920$	−24.1840	−0.797322
$921$	−16.9933	−0.559949
$922$	−44.3972	−1.46214
$923$	−25.1146	−0.826657
$924$	−8.22966	−0.270736
$925$	−9.14909	−0.300820
$926$	25.2801	0.830756
$927$	10.8256	0.355558
$928$	−99.6703	−3.27184
$929$	−31.0039	−1.01721	−0.508603	−	0.861001i	$-0.669838\pi$
$929$	−31.0039	−1.01721	−0.508603	+	0.861001i	$0.669838\pi$
$930$	13.0642	0.428391
$931$	2.43474	0.0797953
$932$	81.8914	2.68244
$933$	−12.4292	−0.406914
$934$	−45.4810	−1.48818
$935$	4.31212	0.141022
$936$	80.7944	2.64085
$937$	18.6769	0.610148	0.305074	−	0.952329i	$-0.401319\pi$
$937$	18.6769	0.610148	0.305074	+	0.952329i	$0.401319\pi$
$938$	49.7138	1.62321
$939$	15.7301	0.513333
$940$	−10.0177	−0.326740
$941$	−44.7521	−1.45888	−0.729438	−	0.684047i	$-0.760218\pi$
$941$	−44.7521	−1.45888	−0.729438	+	0.684047i	$0.760218\pi$
$942$	−21.0682	−0.686438
$943$	−8.43482	−0.274676
$944$	−62.9712	−2.04954
$945$	−9.22266	−0.300013
$946$	−14.7985	−0.481141
$947$	12.8578	0.417822	0.208911	−	0.977935i	$-0.433008\pi$
$947$	12.8578	0.417822	0.208911	+	0.977935i	$0.433008\pi$
$948$	−36.1992	−1.17570
$949$	39.4039	1.27911
$950$	−9.56815	−0.310432
$951$	6.41675	0.208077
$952$	92.3414	2.99280
$953$	11.9421	0.386843	0.193422	−	0.981116i	$-0.438041\pi$
$953$	11.9421	0.386843	0.193422	+	0.981116i	$0.438041\pi$
$954$	−62.0115	−2.00770
$955$	0.982467	0.0317919
$956$	−26.4256	−0.854665
$957$	−4.67269	−0.151047
$958$	−15.0750	−0.487051
$959$	−40.9272	−1.32161
$960$	7.13784	0.230373
$961$	39.5680	1.27639
$962$	93.7711	3.02330
$963$	5.50050	0.177251
$964$	−16.3553	−0.526770
$965$	−6.72220	−0.216395
$966$	−13.2788	−0.427237
$967$	−44.6114	−1.43460	−0.717302	−	0.696762i	$-0.754623\pi$
$967$	−44.6114	−1.43460	−0.717302	+	0.696762i	$0.754623\pi$
$968$	78.2184	2.51403
$969$	−9.07072	−0.291393
$970$	−24.7186	−0.793665
$971$	29.1948	0.936907	0.468453	−	0.883488i	$-0.344811\pi$
$971$	29.1948	0.936907	0.468453	+	0.883488i	$0.344811\pi$
$972$	67.2214	2.15613
$973$	57.6180	1.84715
$974$	−45.8423	−1.46888
$975$	2.28642	0.0732241
$976$	76.9880	2.46432
$977$	−5.09982	−0.163158	−0.0815789	−	0.996667i	$-0.525996\pi$
$977$	−5.09982	−0.163158	−0.0815789	+	0.996667i	$0.525996\pi$
$978$	−26.0694	−0.833609
$979$	10.6624	0.340771
$980$	3.34001	0.106693
$981$	−17.1890	−0.548802
$982$	−93.1200	−2.97158
$983$	18.3111	0.584034	0.292017	−	0.956413i	$-0.405674\pi$
$983$	18.3111	0.584034	0.292017	+	0.956413i	$0.405674\pi$
$984$	12.6434	0.403058
$985$	10.0579	0.320471
$986$	87.7218	2.79363
$987$	−3.28754	−0.104644
$988$	69.9317	2.22482
$989$	−17.0274	−0.541440
$990$	−7.10800	−0.225907
$991$	−3.13858	−0.0997001	−0.0498501	−	0.998757i	$-0.515874\pi$
$991$	−3.13858	−0.0997001	−0.0498501	+	0.998757i	$0.515874\pi$
$992$	107.094	3.40025
$993$	−7.47978	−0.237364
$994$	47.3149	1.50074
$995$	8.54626	0.270935
$996$	43.8858	1.39058
$997$	−53.3528	−1.68970	−0.844850	−	0.535004i	$-0.820310\pi$
$997$	−53.3528	−1.68970	−0.844850	+	0.535004i	$0.820310\pi$
$998$	73.8435	2.33747
$999$	30.4638	0.963831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.b.1.5	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.b.1.5	✓	114	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64032 q^{2} +0.589008 q^{3} +4.97127 q^{4} +1.00000 q^{5} -1.55517 q^{6} +2.76981 q^{7} -7.84509 q^{8} -2.65307 q^{9} +O(q^{10})\)	\(q-2.64032 q^{2} +0.589008 q^{3} +4.97127 q^{4} +1.00000 q^{5} -1.55517 q^{6} +2.76981 q^{7} -7.84509 q^{8} -2.65307 q^{9} -2.64032 q^{10} -1.01471 q^{11} +2.92812 q^{12} +3.88182 q^{13} -7.31318 q^{14} +0.589008 q^{15} +10.7710 q^{16} -4.24960 q^{17} +7.00494 q^{18} +3.62386 q^{19} +4.97127 q^{20} +1.63144 q^{21} +2.67916 q^{22} +3.08269 q^{23} -4.62082 q^{24} +1.00000 q^{25} -10.2492 q^{26} -3.32971 q^{27} +13.7695 q^{28} +7.81813 q^{29} -1.55517 q^{30} -8.40048 q^{31} -12.7486 q^{32} -0.597674 q^{33} +11.2203 q^{34} +2.76981 q^{35} -13.1891 q^{36} -9.14909 q^{37} -9.56815 q^{38} +2.28642 q^{39} -7.84509 q^{40} -2.73619 q^{41} -4.30752 q^{42} -5.52356 q^{43} -5.04441 q^{44} -2.65307 q^{45} -8.13927 q^{46} -2.01511 q^{47} +6.34420 q^{48} +0.671862 q^{49} -2.64032 q^{50} -2.50305 q^{51} +19.2975 q^{52} -8.85254 q^{53} +8.79147 q^{54} -1.01471 q^{55} -21.7294 q^{56} +2.13449 q^{57} -20.6423 q^{58} -5.84638 q^{59} +2.92812 q^{60} +7.14772 q^{61} +22.1799 q^{62} -7.34850 q^{63} +12.1184 q^{64} +3.88182 q^{65} +1.57805 q^{66} -6.79784 q^{67} -21.1259 q^{68} +1.81573 q^{69} -7.31318 q^{70} -6.46981 q^{71} +20.8136 q^{72} +10.1509 q^{73} +24.1565 q^{74} +0.589008 q^{75} +18.0152 q^{76} -2.81056 q^{77} -6.03688 q^{78} -12.3626 q^{79} +10.7710 q^{80} +5.99798 q^{81} +7.22441 q^{82} +14.9877 q^{83} +8.11034 q^{84} -4.24960 q^{85} +14.5839 q^{86} +4.60495 q^{87} +7.96051 q^{88} -10.5078 q^{89} +7.00494 q^{90} +10.7519 q^{91} +15.3249 q^{92} -4.94795 q^{93} +5.32054 q^{94} +3.62386 q^{95} -7.50904 q^{96} +9.36197 q^{97} -1.77393 q^{98} +2.69210 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * q^99

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