LMFDB - Embedded newform 8005.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, 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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59696 q^{2} -3.31155 q^{3} +4.74420 q^{4} +1.00000 q^{5} +8.59996 q^{6} +3.53678 q^{7} -7.12657 q^{8} +7.96636 q^{9} +O(q^{10})$	\(q-2.59696 q^{2} -3.31155 q^{3} +4.74420 q^{4} +1.00000 q^{5} +8.59996 q^{6} +3.53678 q^{7} -7.12657 q^{8} +7.96636 q^{9} -2.59696 q^{10} +2.84557 q^{11} -15.7107 q^{12} -7.02535 q^{13} -9.18486 q^{14} -3.31155 q^{15} +9.01902 q^{16} -2.09585 q^{17} -20.6883 q^{18} +3.52030 q^{19} +4.74420 q^{20} -11.7122 q^{21} -7.38983 q^{22} -7.63786 q^{23} +23.6000 q^{24} +1.00000 q^{25} +18.2445 q^{26} -16.4464 q^{27} +16.7792 q^{28} +7.00072 q^{29} +8.59996 q^{30} -4.53762 q^{31} -9.16889 q^{32} -9.42324 q^{33} +5.44285 q^{34} +3.53678 q^{35} +37.7940 q^{36} +4.77736 q^{37} -9.14208 q^{38} +23.2648 q^{39} -7.12657 q^{40} -9.15368 q^{41} +30.4161 q^{42} +7.57103 q^{43} +13.4999 q^{44} +7.96636 q^{45} +19.8352 q^{46} +10.4500 q^{47} -29.8669 q^{48} +5.50878 q^{49} -2.59696 q^{50} +6.94052 q^{51} -33.3296 q^{52} -1.07649 q^{53} +42.7105 q^{54} +2.84557 q^{55} -25.2051 q^{56} -11.6577 q^{57} -18.1806 q^{58} -3.09909 q^{59} -15.7107 q^{60} -8.36197 q^{61} +11.7840 q^{62} +28.1752 q^{63} +5.77319 q^{64} -7.02535 q^{65} +24.4718 q^{66} +13.6241 q^{67} -9.94314 q^{68} +25.2932 q^{69} -9.18486 q^{70} -1.13427 q^{71} -56.7729 q^{72} +1.96606 q^{73} -12.4066 q^{74} -3.31155 q^{75} +16.7010 q^{76} +10.0641 q^{77} -60.4177 q^{78} -6.74175 q^{79} +9.01902 q^{80} +30.5638 q^{81} +23.7717 q^{82} -8.71869 q^{83} -55.5650 q^{84} -2.09585 q^{85} -19.6617 q^{86} -23.1832 q^{87} -20.2792 q^{88} -11.8689 q^{89} -20.6883 q^{90} -24.8471 q^{91} -36.2355 q^{92} +15.0266 q^{93} -27.1382 q^{94} +3.52030 q^{95} +30.3632 q^{96} +3.55962 q^{97} -14.3061 q^{98} +22.6688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) $ 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * 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 $

$2$	−2.59696	−1.83633	−0.918164	−	0.396201i	$-0.870328\pi$
$2$	−2.59696	−1.83633	−0.918164	+	0.396201i	$0.870328\pi$
$3$	−3.31155	−1.91192	−0.955962	−	0.293490i	$-0.905183\pi$
$3$	−3.31155	−1.91192	−0.955962	+	0.293490i	$0.905183\pi$
$4$	4.74420	2.37210
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	8.59996	3.51092
$7$	3.53678	1.33678	0.668388	−	0.743813i	$-0.266985\pi$
$7$	3.53678	1.33678	0.668388	+	0.743813i	$0.266985\pi$
$8$	−7.12657	−2.51962
$9$	7.96636	2.65545
$10$	−2.59696	−0.821231
$11$	2.84557	0.857971	0.428986	−	0.903311i	$-0.358871\pi$
$11$	2.84557	0.857971	0.428986	+	0.903311i	$0.358871\pi$
$12$	−15.7107	−4.53527
$13$	−7.02535	−1.94848	−0.974240	−	0.225513i	$-0.927594\pi$
$13$	−7.02535	−1.94848	−0.974240	+	0.225513i	$0.927594\pi$
$14$	−9.18486	−2.45476
$15$	−3.31155	−0.855039
$16$	9.01902	2.25476
$17$	−2.09585	−0.508319	−0.254160	−	0.967162i	$-0.581799\pi$
$17$	−2.09585	−0.508319	−0.254160	+	0.967162i	$0.581799\pi$
$18$	−20.6883	−4.87628
$19$	3.52030	0.807613	0.403806	−	0.914844i	$-0.367687\pi$
$19$	3.52030	0.807613	0.403806	+	0.914844i	$0.367687\pi$
$20$	4.74420	1.06084
$21$	−11.7122	−2.55581
$22$	−7.38983	−1.57552
$23$	−7.63786	−1.59260	−0.796302	−	0.604899i	$-0.793213\pi$
$23$	−7.63786	−1.59260	−0.796302	+	0.604899i	$0.793213\pi$
$24$	23.6000	4.81733
$25$	1.00000	0.200000
$26$	18.2445	3.57805
$27$	−16.4464	−3.16510
$28$	16.7792	3.17096
$29$	7.00072	1.30000	0.650000	−	0.759934i	$-0.274769\pi$
$29$	7.00072	1.30000	0.650000	+	0.759934i	$0.274769\pi$
$30$	8.59996	1.57013
$31$	−4.53762	−0.814981	−0.407490	−	0.913209i	$-0.633596\pi$
$31$	−4.53762	−0.814981	−0.407490	+	0.913209i	$0.633596\pi$
$32$	−9.16889	−1.62085
$33$	−9.42324	−1.64038
$34$	5.44285	0.933440
$35$	3.53678	0.597824
$36$	37.7940	6.29900
$37$	4.77736	0.785393	0.392697	−	0.919668i	$-0.371542\pi$
$37$	4.77736	0.785393	0.392697	+	0.919668i	$0.371542\pi$
$38$	−9.14208	−1.48304
$39$	23.2648	3.72535
$40$	−7.12657	−1.12681
$41$	−9.15368	−1.42956	−0.714782	−	0.699347i	$-0.753474\pi$
$41$	−9.15368	−1.42956	−0.714782	+	0.699347i	$0.753474\pi$
$42$	30.4161	4.69331
$43$	7.57103	1.15457	0.577285	−	0.816542i	$-0.304112\pi$
$43$	7.57103	1.15457	0.577285	+	0.816542i	$0.304112\pi$
$44$	13.4999	2.03519
$45$	7.96636	1.18756
$46$	19.8352	2.92454
$47$	10.4500	1.52429	0.762144	−	0.647408i	$-0.224147\pi$
$47$	10.4500	1.52429	0.762144	+	0.647408i	$0.224147\pi$
$48$	−29.8669	−4.31092
$49$	5.50878	0.786968
$50$	−2.59696	−0.367266
$51$	6.94052	0.971868
$52$	−33.3296	−4.62199
$53$	−1.07649	−0.147867	−0.0739334	−	0.997263i	$-0.523555\pi$
$53$	−1.07649	−0.147867	−0.0739334	+	0.997263i	$0.523555\pi$
$54$	42.7105	5.81217
$55$	2.84557	0.383696
$56$	−25.2051	−3.36817
$57$	−11.6577	−1.54409
$58$	−18.1806	−2.38723
$59$	−3.09909	−0.403468	−0.201734	−	0.979440i	$-0.564658\pi$
$59$	−3.09909	−0.403468	−0.201734	+	0.979440i	$0.564658\pi$
$60$	−15.7107	−2.02824
$61$	−8.36197	−1.07064	−0.535320	−	0.844649i	$-0.679809\pi$
$61$	−8.36197	−1.07064	−0.535320	+	0.844649i	$0.679809\pi$
$62$	11.7840	1.49657
$63$	28.1752	3.54975
$64$	5.77319	0.721649
$65$	−7.02535	−0.871387
$66$	24.4718	3.01227
$67$	13.6241	1.66445	0.832227	−	0.554435i	$-0.187066\pi$
$67$	13.6241	1.66445	0.832227	+	0.554435i	$0.187066\pi$
$68$	−9.94314	−1.20578
$69$	25.2932	3.04494
$70$	−9.18486	−1.09780
$71$	−1.13427	−0.134613	−0.0673063	−	0.997732i	$-0.521440\pi$
$71$	−1.13427	−0.134613	−0.0673063	+	0.997732i	$0.521440\pi$
$72$	−56.7729	−6.69075
$73$	1.96606	0.230110	0.115055	−	0.993359i	$-0.463296\pi$
$73$	1.96606	0.230110	0.115055	+	0.993359i	$0.463296\pi$
$74$	−12.4066	−1.44224
$75$	−3.31155	−0.382385
$76$	16.7010	1.91574
$77$	10.0641	1.14691
$78$	−60.4177	−6.84096
$79$	−6.74175	−0.758506	−0.379253	−	0.925293i	$-0.623819\pi$
$79$	−6.74175	−0.758506	−0.379253	+	0.925293i	$0.623819\pi$
$80$	9.01902	1.00836
$81$	30.5638	3.39598
$82$	23.7717	2.62515
$83$	−8.71869	−0.957001	−0.478500	−	0.878087i	$-0.658819\pi$
$83$	−8.71869	−0.957001	−0.478500	+	0.878087i	$0.658819\pi$
$84$	−55.5650	−6.06264
$85$	−2.09585	−0.227327
$86$	−19.6617	−2.12017
$87$	−23.1832	−2.48550
$88$	−20.2792	−2.16176
$89$	−11.8689	−1.25810	−0.629048	−	0.777366i	$-0.716555\pi$
$89$	−11.8689	−1.25810	−0.629048	+	0.777366i	$0.716555\pi$
$90$	−20.6883	−2.18074
$91$	−24.8471	−2.60468
$92$	−36.2355	−3.77781
$93$	15.0266	1.55818
$94$	−27.1382	−2.79909
$95$	3.52030	0.361175
$96$	30.3632	3.09894
$97$	3.55962	0.361425	0.180712	−	0.983536i	$-0.442160\pi$
$97$	3.55962	0.361425	0.180712	+	0.983536i	$0.442160\pi$
$98$	−14.3061	−1.44513
$99$	22.6688	2.27830
$100$	4.74420	0.474420
$101$	3.22729	0.321127	0.160564	−	0.987025i	$-0.448669\pi$
$101$	3.22729	0.321127	0.160564	+	0.987025i	$0.448669\pi$
$102$	−18.0243	−1.78467
$103$	5.41867	0.533917	0.266959	−	0.963708i	$-0.413981\pi$
$103$	5.41867	0.533917	0.266959	+	0.963708i	$0.413981\pi$
$104$	50.0666	4.90944
$105$	−11.7122	−1.14299
$106$	2.79559	0.271532
$107$	−4.30229	−0.415918	−0.207959	−	0.978138i	$-0.566682\pi$
$107$	−4.30229	−0.415918	−0.207959	+	0.978138i	$0.566682\pi$
$108$	−78.0248	−7.50794
$109$	1.61827	0.155002	0.0775011	−	0.996992i	$-0.475306\pi$
$109$	1.61827	0.155002	0.0775011	+	0.996992i	$0.475306\pi$
$110$	−7.38983	−0.704592
$111$	−15.8205	−1.50161
$112$	31.8983	3.01410
$113$	8.57729	0.806884	0.403442	−	0.915005i	$-0.367814\pi$
$113$	8.57729	0.806884	0.403442	+	0.915005i	$0.367814\pi$
$114$	30.2745	2.83546
$115$	−7.63786	−0.712234
$116$	33.2128	3.08373
$117$	−55.9665	−5.17410
$118$	8.04822	0.740899
$119$	−7.41256	−0.679508
$120$	23.6000	2.15438
$121$	−2.90274	−0.263885
$122$	21.7157	1.96605
$123$	30.3129	2.73322
$124$	−21.5274	−1.93322
$125$	1.00000	0.0894427
$126$	−73.1699	−6.51850
$127$	8.03259	0.712777	0.356389	−	0.934338i	$-0.384008\pi$
$127$	8.03259	0.712777	0.356389	+	0.934338i	$0.384008\pi$
$128$	3.34503	0.295662
$129$	−25.0718	−2.20745
$130$	18.2445	1.60015
$131$	−13.5229	−1.18150	−0.590751	−	0.806854i	$-0.701169\pi$
$131$	−13.5229	−1.18150	−0.590751	+	0.806854i	$0.701169\pi$
$132$	−44.7057	−3.89113
$133$	12.4505	1.07960
$134$	−35.3813	−3.05648
$135$	−16.4464	−1.41548
$136$	14.9363	1.28077
$137$	−13.4440	−1.14860	−0.574299	−	0.818646i	$-0.694725\pi$
$137$	−13.4440	−1.14860	−0.574299	+	0.818646i	$0.694725\pi$
$138$	−65.6853	−5.59150
$139$	−7.28321	−0.617754	−0.308877	−	0.951102i	$-0.599953\pi$
$139$	−7.28321	−0.617754	−0.308877	+	0.951102i	$0.599953\pi$
$140$	16.7792	1.41810
$141$	−34.6057	−2.91432
$142$	2.94564	0.247193
$143$	−19.9911	−1.67174
$144$	71.8488	5.98740
$145$	7.00072	0.581378
$146$	−5.10577	−0.422557
$147$	−18.2426	−1.50462
$148$	22.6647	1.86303
$149$	6.43969	0.527560	0.263780	−	0.964583i	$-0.415031\pi$
$149$	6.43969	0.527560	0.263780	+	0.964583i	$0.415031\pi$
$150$	8.59996	0.702184
$151$	−5.43402	−0.442214	−0.221107	−	0.975250i	$-0.570967\pi$
$151$	−5.43402	−0.442214	−0.221107	+	0.975250i	$0.570967\pi$
$152$	−25.0877	−2.03488
$153$	−16.6963	−1.34982
$154$	−26.1362	−2.10611
$155$	−4.53762	−0.364470
$156$	110.373	8.83689
$157$	12.4603	0.994443	0.497221	−	0.867624i	$-0.334354\pi$
$157$	12.4603	0.994443	0.497221	+	0.867624i	$0.334354\pi$
$158$	17.5080	1.39287
$159$	3.56484	0.282710
$160$	−9.16889	−0.724864
$161$	−27.0134	−2.12895
$162$	−79.3731	−6.23614
$163$	−11.0224	−0.863345	−0.431672	−	0.902030i	$-0.642076\pi$
$163$	−11.0224	−0.863345	−0.431672	+	0.902030i	$0.642076\pi$
$164$	−43.4269	−3.39107
$165$	−9.42324	−0.733598
$166$	22.6421	1.75737
$167$	15.7805	1.22113	0.610564	−	0.791967i	$-0.290943\pi$
$167$	15.7805	1.22113	0.610564	+	0.791967i	$0.290943\pi$
$168$	83.4679	6.43969
$169$	36.3555	2.79658
$170$	5.44285	0.417447
$171$	28.0440	2.14458
$172$	35.9185	2.73876
$173$	8.65822	0.658273	0.329136	−	0.944282i	$-0.393242\pi$
$173$	8.65822	0.658273	0.329136	+	0.944282i	$0.393242\pi$
$174$	60.2059	4.56420
$175$	3.53678	0.267355
$176$	25.6642	1.93452
$177$	10.2628	0.771399
$178$	30.8229	2.31028
$179$	−23.5453	−1.75986	−0.879928	−	0.475107i	$-0.842409\pi$
$179$	−23.5453	−1.75986	−0.879928	+	0.475107i	$0.842409\pi$
$180$	37.7940	2.81700
$181$	−13.1572	−0.977970	−0.488985	−	0.872292i	$-0.662633\pi$
$181$	−13.1572	−0.977970	−0.488985	+	0.872292i	$0.662633\pi$
$182$	64.5268	4.78305
$183$	27.6911	2.04698
$184$	54.4318	4.01276
$185$	4.77736	0.351239
$186$	−39.0234	−2.86133
$187$	−5.96390	−0.436123
$188$	49.5768	3.61576
$189$	−58.1671	−4.23103
$190$	−9.14208	−0.663236
$191$	−14.5954	−1.05608	−0.528042	−	0.849218i	$-0.677074\pi$
$191$	−14.5954	−1.05608	−0.528042	+	0.849218i	$0.677074\pi$
$192$	−19.1182	−1.37974
$193$	−24.4539	−1.76023	−0.880115	−	0.474761i	$-0.842535\pi$
$193$	−24.4539	−1.76023	−0.880115	+	0.474761i	$0.842535\pi$
$194$	−9.24420	−0.663695
$195$	23.2648	1.66603
$196$	26.1347	1.86677
$197$	−8.43338	−0.600853	−0.300427	−	0.953805i	$-0.597129\pi$
$197$	−8.43338	−0.600853	−0.300427	+	0.953805i	$0.597129\pi$
$198$	−58.8700	−4.18371
$199$	23.3546	1.65557	0.827783	−	0.561048i	$-0.189602\pi$
$199$	23.3546	1.65557	0.827783	+	0.561048i	$0.189602\pi$
$200$	−7.12657	−0.503925
$201$	−45.1170	−3.18231
$202$	−8.38114	−0.589695
$203$	24.7600	1.73781
$204$	32.9272	2.30537
$205$	−9.15368	−0.639321
$206$	−14.0721	−0.980447
$207$	−60.8460	−4.22909
$208$	−63.3618	−4.39335
$209$	10.0173	0.692909
$210$	30.4161	2.09891
$211$	10.1365	0.697825	0.348913	−	0.937155i	$-0.386551\pi$
$211$	10.1365	0.697825	0.348913	+	0.937155i	$0.386551\pi$
$212$	−5.10706	−0.350755
$213$	3.75618	0.257369
$214$	11.1729	0.763761
$215$	7.57103	0.516340
$216$	117.206	7.97487
$217$	−16.0485	−1.08945
$218$	−4.20259	−0.284635
$219$	−6.51070	−0.439952
$220$	13.4999	0.910166
$221$	14.7241	0.990450
$222$	41.0851	2.75745
$223$	−12.9058	−0.864233	−0.432117	−	0.901818i	$-0.642233\pi$
$223$	−12.9058	−0.864233	−0.432117	+	0.901818i	$0.642233\pi$
$224$	−32.4283	−2.16671
$225$	7.96636	0.531091
$226$	−22.2749	−1.48170
$227$	−14.9185	−0.990176	−0.495088	−	0.868843i	$-0.664864\pi$
$227$	−14.9185	−0.990176	−0.495088	+	0.868843i	$0.664864\pi$
$228$	−55.3062	−3.66275
$229$	22.6122	1.49426	0.747129	−	0.664679i	$-0.231432\pi$
$229$	22.6122	1.49426	0.747129	+	0.664679i	$0.231432\pi$
$230$	19.8352	1.30790
$231$	−33.3279	−2.19281
$232$	−49.8911	−3.27551
$233$	19.6952	1.29028	0.645138	−	0.764066i	$-0.276800\pi$
$233$	19.6952	1.29028	0.645138	+	0.764066i	$0.276800\pi$
$234$	145.343	9.50134
$235$	10.4500	0.681682
$236$	−14.7027	−0.957065
$237$	22.3256	1.45021
$238$	19.2501	1.24780
$239$	19.0419	1.23172	0.615858	−	0.787857i	$-0.288810\pi$
$239$	19.0419	1.23172	0.615858	+	0.787857i	$0.288810\pi$
$240$	−29.8669	−1.92790
$241$	−4.18969	−0.269882	−0.134941	−	0.990854i	$-0.543084\pi$
$241$	−4.18969	−0.269882	−0.134941	+	0.990854i	$0.543084\pi$
$242$	7.53829	0.484580
$243$	−51.8746	−3.32776
$244$	−39.6709	−2.53967
$245$	5.50878	0.351943
$246$	−78.7213	−5.01909
$247$	−24.7313	−1.57362
$248$	32.3377	2.05345
$249$	28.8724	1.82971
$250$	−2.59696	−0.164246
$251$	−26.8537	−1.69499	−0.847496	−	0.530802i	$-0.821891\pi$
$251$	−26.8537	−1.69499	−0.847496	+	0.530802i	$0.821891\pi$
$252$	133.669	8.42035
$253$	−21.7341	−1.36641
$254$	−20.8603	−1.30889
$255$	6.94052	0.434632
$256$	−20.2333	−1.26458
$257$	−11.0813	−0.691229	−0.345615	−	0.938377i	$-0.612330\pi$
$257$	−11.0813	−0.691229	−0.345615	+	0.938377i	$0.612330\pi$
$258$	65.1105	4.05361
$259$	16.8964	1.04989
$260$	−33.3296	−2.06702
$261$	55.7703	3.45209
$262$	35.1185	2.16963
$263$	6.36193	0.392293	0.196147	−	0.980575i	$-0.437157\pi$
$263$	6.36193	0.392293	0.196147	+	0.980575i	$0.437157\pi$
$264$	67.1554	4.13313
$265$	−1.07649	−0.0661280
$266$	−32.3335	−1.98249
$267$	39.3043	2.40539
$268$	64.6356	3.94825
$269$	−18.5052	−1.12828	−0.564140	−	0.825679i	$-0.690792\pi$
$269$	−18.5052	−1.12828	−0.564140	+	0.825679i	$0.690792\pi$
$270$	42.7105	2.59928
$271$	8.04395	0.488635	0.244318	−	0.969695i	$-0.421436\pi$
$271$	8.04395	0.488635	0.244318	+	0.969695i	$0.421436\pi$
$272$	−18.9025	−1.14614
$273$	82.2823	4.97995
$274$	34.9135	2.10920
$275$	2.84557	0.171594
$276$	119.996	7.22290
$277$	−9.26583	−0.556730	−0.278365	−	0.960475i	$-0.589792\pi$
$277$	−9.26583	−0.556730	−0.278365	+	0.960475i	$0.589792\pi$
$278$	18.9142	1.13440
$279$	−36.1483	−2.16414
$280$	−25.2051	−1.50629
$281$	19.4397	1.15967	0.579837	−	0.814732i	$-0.303116\pi$
$281$	19.4397	1.15967	0.579837	+	0.814732i	$0.303116\pi$
$282$	89.8695	5.35165
$283$	−23.8995	−1.42068	−0.710340	−	0.703858i	$-0.751459\pi$
$283$	−23.8995	−1.42068	−0.710340	+	0.703858i	$0.751459\pi$
$284$	−5.38118	−0.319314
$285$	−11.6577	−0.690540
$286$	51.9161	3.06986
$287$	−32.3745	−1.91101
$288$	−73.0427	−4.30408
$289$	−12.6074	−0.741612
$290$	−18.1806	−1.06760
$291$	−11.7879	−0.691017
$292$	9.32737	0.545843
$293$	−19.0789	−1.11460	−0.557299	−	0.830312i	$-0.688162\pi$
$293$	−19.0789	−1.11460	−0.557299	+	0.830312i	$0.688162\pi$
$294$	47.3753	2.76298
$295$	−3.09909	−0.180436
$296$	−34.0462	−1.97890
$297$	−46.7992	−2.71557
$298$	−16.7236	−0.968773
$299$	53.6586	3.10316
$300$	−15.7107	−0.907055
$301$	26.7770	1.54340
$302$	14.1119	0.812050
$303$	−10.6873	−0.613971
$304$	31.7497	1.82097
$305$	−8.36197	−0.478805
$306$	43.3597	2.47871
$307$	27.6266	1.57673	0.788367	−	0.615206i	$-0.210927\pi$
$307$	27.6266	1.57673	0.788367	+	0.615206i	$0.210927\pi$
$308$	47.7463	2.72060
$309$	−17.9442	−1.02081
$310$	11.7840	0.669287
$311$	−5.39720	−0.306047	−0.153024	−	0.988223i	$-0.548901\pi$
$311$	−5.39720	−0.306047	−0.153024	+	0.988223i	$0.548901\pi$
$312$	−165.798	−9.38647
$313$	29.7195	1.67984	0.839922	−	0.542706i	$-0.182600\pi$
$313$	29.7195	1.67984	0.839922	+	0.542706i	$0.182600\pi$
$314$	−32.3590	−1.82612
$315$	28.1752	1.58749
$316$	−31.9842	−1.79925
$317$	−27.1023	−1.52222	−0.761110	−	0.648623i	$-0.775345\pi$
$317$	−27.1023	−1.52222	−0.761110	+	0.648623i	$0.775345\pi$
$318$	−9.25774	−0.519148
$319$	19.9210	1.11536
$320$	5.77319	0.322731
$321$	14.2472	0.795203
$322$	70.1527	3.90946
$323$	−7.37804	−0.410525
$324$	145.001	8.05561
$325$	−7.02535	−0.389696
$326$	28.6248	1.58538
$327$	−5.35899	−0.296353
$328$	65.2344	3.60197
$329$	36.9593	2.03763
$330$	24.4718	1.34713
$331$	22.4854	1.23591	0.617954	−	0.786214i	$-0.287962\pi$
$331$	22.4854	1.23591	0.617954	+	0.786214i	$0.287962\pi$
$332$	−41.3632	−2.27010
$333$	38.0582	2.08558
$334$	−40.9812	−2.24239
$335$	13.6241	0.744366
$336$	−105.633	−5.76273
$337$	21.9472	1.19554	0.597770	−	0.801668i	$-0.296054\pi$
$337$	21.9472	1.19554	0.597770	+	0.801668i	$0.296054\pi$
$338$	−94.4137	−5.13543
$339$	−28.4041	−1.54270
$340$	−9.94314	−0.539243
$341$	−12.9121	−0.699230
$342$	−72.8291	−3.93815
$343$	−5.27412	−0.284776
$344$	−53.9555	−2.90908
$345$	25.2932	1.36174
$346$	−22.4851	−1.20880
$347$	−20.7631	−1.11462	−0.557310	−	0.830304i	$-0.688167\pi$
$347$	−20.7631	−1.11462	−0.557310	+	0.830304i	$0.688167\pi$
$348$	−109.986	−5.89586
$349$	0.649970	0.0347921	0.0173961	−	0.999849i	$-0.494462\pi$
$349$	0.649970	0.0347921	0.0173961	+	0.999849i	$0.494462\pi$
$350$	−9.18486	−0.490951
$351$	115.541	6.16714
$352$	−26.0907	−1.39064
$353$	−9.74908	−0.518891	−0.259446	−	0.965758i	$-0.583540\pi$
$353$	−9.74908	−0.518891	−0.259446	+	0.965758i	$0.583540\pi$
$354$	−26.6521	−1.41654
$355$	−1.13427	−0.0602005
$356$	−56.3082	−2.98433
$357$	24.5471	1.29917
$358$	61.1461	3.23167
$359$	8.08807	0.426872	0.213436	−	0.976957i	$-0.431535\pi$
$359$	8.08807	0.426872	0.213436	+	0.976957i	$0.431535\pi$
$360$	−56.7729	−2.99219
$361$	−6.60747	−0.347762
$362$	34.1688	1.79587
$363$	9.61256	0.504529
$364$	−117.879	−6.17856
$365$	1.96606	0.102908
$366$	−71.9126	−3.75893
$367$	14.1994	0.741201	0.370600	−	0.928792i	$-0.379152\pi$
$367$	14.1994	0.741201	0.370600	+	0.928792i	$0.379152\pi$
$368$	−68.8860	−3.59093
$369$	−72.9215	−3.79614
$370$	−12.4066	−0.644989
$371$	−3.80729	−0.197665
$372$	71.2890	3.69616
$373$	−12.7843	−0.661946	−0.330973	−	0.943640i	$-0.607377\pi$
$373$	−12.7843	−0.661946	−0.330973	+	0.943640i	$0.607377\pi$
$374$	15.4880	0.800865
$375$	−3.31155	−0.171008
$376$	−74.4726	−3.84063
$377$	−49.1825	−2.53303
$378$	151.058	7.76956
$379$	12.2792	0.630740	0.315370	−	0.948969i	$-0.397871\pi$
$379$	12.2792	0.630740	0.315370	+	0.948969i	$0.397871\pi$
$380$	16.7010	0.856744
$381$	−26.6003	−1.36278
$382$	37.9036	1.93932
$383$	−12.9119	−0.659768	−0.329884	−	0.944022i	$-0.607010\pi$
$383$	−12.9119	−0.659768	−0.329884	+	0.944022i	$0.607010\pi$
$384$	−11.0772	−0.565283
$385$	10.0641	0.512916
$386$	63.5058	3.23236
$387$	60.3136	3.06591
$388$	16.8876	0.857336
$389$	−17.6171	−0.893223	−0.446611	−	0.894728i	$-0.647369\pi$
$389$	−17.6171	−0.893223	−0.446611	+	0.894728i	$0.647369\pi$
$390$	−60.4177	−3.05937
$391$	16.0078	0.809551
$392$	−39.2587	−1.98286
$393$	44.7818	2.25894
$394$	21.9011	1.10336
$395$	−6.74175	−0.339214
$396$	107.545	5.40436
$397$	2.52203	0.126577	0.0632885	−	0.997995i	$-0.479841\pi$
$397$	2.52203	0.126577	0.0632885	+	0.997995i	$0.479841\pi$
$398$	−60.6511	−3.04016
$399$	−41.2305	−2.06411
$400$	9.01902	0.450951
$401$	39.0563	1.95038	0.975189	−	0.221373i	$-0.0710538\pi$
$401$	39.0563	1.95038	0.975189	+	0.221373i	$0.0710538\pi$
$402$	117.167	5.84376
$403$	31.8784	1.58797
$404$	15.3109	0.761746
$405$	30.5638	1.51873
$406$	−64.3006	−3.19119
$407$	13.5943	0.673845
$408$	−49.4621	−2.44874
$409$	−7.54704	−0.373177	−0.186588	−	0.982438i	$-0.559743\pi$
$409$	−7.54704	−0.373177	−0.186588	+	0.982438i	$0.559743\pi$
$410$	23.7717	1.17400
$411$	44.5204	2.19603
$412$	25.7072	1.26651
$413$	−10.9608	−0.539345
$414$	158.015	7.76599
$415$	−8.71869	−0.427984
$416$	64.4146	3.15819
$417$	24.1187	1.18110
$418$	−26.0144	−1.27241
$419$	−24.7263	−1.20796	−0.603981	−	0.796999i	$-0.706420\pi$
$419$	−24.7263	−1.20796	−0.603981	+	0.796999i	$0.706420\pi$
$420$	−55.5650	−2.71130
$421$	−32.3834	−1.57827	−0.789134	−	0.614221i	$-0.789471\pi$
$421$	−32.3834	−1.57827	−0.789134	+	0.614221i	$0.789471\pi$
$422$	−26.3241	−1.28144
$423$	83.2484	4.04768
$424$	7.67166	0.372569
$425$	−2.09585	−0.101664
$426$	−9.75464	−0.472614
$427$	−29.5744	−1.43121
$428$	−20.4109	−0.986598
$429$	66.2015	3.19624
$430$	−19.6617	−0.948169
$431$	10.8757	0.523864	0.261932	−	0.965086i	$-0.415640\pi$
$431$	10.8757	0.523864	0.261932	+	0.965086i	$0.415640\pi$
$432$	−148.330	−7.13653
$433$	21.9202	1.05342	0.526708	−	0.850046i	$-0.323426\pi$
$433$	21.9202	1.05342	0.526708	+	0.850046i	$0.323426\pi$
$434$	41.6774	2.00058
$435$	−23.1832	−1.11155
$436$	7.67740	0.367681
$437$	−26.8876	−1.28621
$438$	16.9080	0.807896
$439$	−3.75166	−0.179057	−0.0895284	−	0.995984i	$-0.528536\pi$
$439$	−3.75166	−0.179057	−0.0895284	+	0.995984i	$0.528536\pi$
$440$	−20.2792	−0.966771
$441$	43.8849	2.08976
$442$	−38.2379	−1.81879
$443$	−23.0480	−1.09504	−0.547522	−	0.836791i	$-0.684429\pi$
$443$	−23.0480	−1.09504	−0.547522	+	0.836791i	$0.684429\pi$
$444$	−75.0554	−3.56197
$445$	−11.8689	−0.562638
$446$	33.5157	1.58702
$447$	−21.3254	−1.00866
$448$	20.4185	0.964683
$449$	−6.36031	−0.300162	−0.150081	−	0.988674i	$-0.547953\pi$
$449$	−6.36031	−0.300162	−0.150081	+	0.988674i	$0.547953\pi$
$450$	−20.6883	−0.975257
$451$	−26.0474	−1.22653
$452$	40.6924	1.91401
$453$	17.9950	0.845480
$454$	38.7428	1.81829
$455$	−24.8471	−1.16485
$456$	83.0791	3.89054
$457$	29.5578	1.38265	0.691327	−	0.722542i	$-0.257026\pi$
$457$	29.5578	1.38265	0.691327	+	0.722542i	$0.257026\pi$
$458$	−58.7230	−2.74395
$459$	34.4692	1.60888
$460$	−36.2355	−1.68949
$461$	20.0313	0.932951	0.466476	−	0.884534i	$-0.345524\pi$
$461$	20.0313	0.932951	0.466476	+	0.884534i	$0.345524\pi$
$462$	86.5512	4.02673
$463$	−40.5687	−1.88539	−0.942695	−	0.333657i	$-0.891717\pi$
$463$	−40.5687	−1.88539	−0.942695	+	0.333657i	$0.891717\pi$
$464$	63.1396	2.93118
$465$	15.0266	0.696840
$466$	−51.1476	−2.36937
$467$	20.9252	0.968302	0.484151	−	0.874985i	$-0.339129\pi$
$467$	20.9252	0.968302	0.484151	+	0.874985i	$0.339129\pi$
$468$	−265.516	−12.2735
$469$	48.1855	2.22500
$470$	−27.1382	−1.25179
$471$	−41.2630	−1.90130
$472$	22.0859	1.01659
$473$	21.5439	0.990589
$474$	−57.9788	−2.66305
$475$	3.52030	0.161523
$476$	−35.1667	−1.61186
$477$	−8.57568	−0.392653
$478$	−49.4509	−2.26183
$479$	8.48147	0.387528	0.193764	−	0.981048i	$-0.437930\pi$
$479$	8.48147	0.387528	0.193764	+	0.981048i	$0.437930\pi$
$480$	30.3632	1.38589
$481$	−33.5626	−1.53032
$482$	10.8805	0.495592
$483$	89.4562	4.07040
$484$	−13.7712	−0.625962
$485$	3.55962	0.161634
$486$	134.716	6.11086
$487$	−29.5925	−1.34096	−0.670482	−	0.741926i	$-0.733913\pi$
$487$	−29.5925	−1.34096	−0.670482	+	0.741926i	$0.733913\pi$
$488$	59.5922	2.69761
$489$	36.5014	1.65065
$490$	−14.3061	−0.646282
$491$	24.9633	1.12658	0.563289	−	0.826260i	$-0.309536\pi$
$491$	24.9633	1.12658	0.563289	+	0.826260i	$0.309536\pi$
$492$	143.810	6.48347
$493$	−14.6725	−0.660815
$494$	64.2263	2.88968
$495$	22.6688	1.01889
$496$	−40.9249	−1.83758
$497$	−4.01164	−0.179947
$498$	−74.9804	−3.35995
$499$	27.1542	1.21559	0.607794	−	0.794095i	$-0.292055\pi$
$499$	27.1542	1.21559	0.607794	+	0.794095i	$0.292055\pi$
$500$	4.74420	0.212167
$501$	−52.2578	−2.33471
$502$	69.7380	3.11256
$503$	−25.0191	−1.11554	−0.557772	−	0.829994i	$-0.688344\pi$
$503$	−25.0191	−1.11554	−0.557772	+	0.829994i	$0.688344\pi$
$504$	−200.793	−8.94402
$505$	3.22729	0.143613
$506$	56.4425	2.50917
$507$	−120.393	−5.34684
$508$	38.1082	1.69078
$509$	−29.4634	−1.30594	−0.652971	−	0.757383i	$-0.726478\pi$
$509$	−29.4634	−1.30594	−0.652971	+	0.757383i	$0.726478\pi$
$510$	−18.0243	−0.798128
$511$	6.95350	0.307605
$512$	45.8550	2.02652
$513$	−57.8962	−2.55618
$514$	28.7776	1.26932
$515$	5.41867	0.238775
$516$	−118.946	−5.23630
$517$	29.7362	1.30780
$518$	−43.8794	−1.92795
$519$	−28.6721	−1.25857
$520$	50.0666	2.19557
$521$	6.86759	0.300875	0.150437	−	0.988620i	$-0.451932\pi$
$521$	6.86759	0.300875	0.150437	+	0.988620i	$0.451932\pi$
$522$	−144.833	−6.33917
$523$	−40.9590	−1.79101	−0.895506	−	0.445049i	$-0.853186\pi$
$523$	−40.9590	−1.79101	−0.895506	+	0.445049i	$0.853186\pi$
$524$	−64.1554	−2.80264
$525$	−11.7122	−0.511163
$526$	−16.5217	−0.720379
$527$	9.51019	0.414270
$528$	−84.9884	−3.69865
$529$	35.3369	1.53639
$530$	2.79559	0.121433
$531$	−24.6885	−1.07139
$532$	59.0677	2.56091
$533$	64.3078	2.78548
$534$	−102.072	−4.41708
$535$	−4.30229	−0.186004
$536$	−97.0934	−4.19380
$537$	77.9713	3.36471
$538$	48.0572	2.07189
$539$	15.6756	0.675196
$540$	−78.0248	−3.35765
$541$	−0.273501	−0.0117587	−0.00587936	−	0.999983i	$-0.501871\pi$
$541$	−0.273501	−0.0117587	−0.00587936	+	0.999983i	$0.501871\pi$
$542$	−20.8898	−0.897294
$543$	43.5709	1.86980
$544$	19.2167	0.823907
$545$	1.61827	0.0693191
$546$	−213.684	−9.14482
$547$	1.46427	0.0626077	0.0313038	−	0.999510i	$-0.490034\pi$
$547$	1.46427	0.0626077	0.0313038	+	0.999510i	$0.490034\pi$
$548$	−63.7810	−2.72459
$549$	−66.6145	−2.84304
$550$	−7.38983	−0.315103
$551$	24.6446	1.04990
$552$	−180.254	−7.67210
$553$	−23.8440	−1.01395
$554$	24.0630	1.02234
$555$	−15.8205	−0.671541
$556$	−34.5530	−1.46537
$557$	12.4265	0.526528	0.263264	−	0.964724i	$-0.415201\pi$
$557$	12.4265	0.526528	0.263264	+	0.964724i	$0.415201\pi$
$558$	93.8758	3.97408
$559$	−53.1891	−2.24966
$560$	31.8983	1.34795
$561$	19.7497	0.833835
$562$	−50.4841	−2.12954
$563$	−34.6722	−1.46126	−0.730630	−	0.682774i	$-0.760773\pi$
$563$	−34.6722	−1.46126	−0.730630	+	0.682774i	$0.760773\pi$
$564$	−164.176	−6.91306
$565$	8.57729	0.360849
$566$	62.0662	2.60884
$567$	108.097	4.53967
$568$	8.08342	0.339173
$569$	−27.9353	−1.17111	−0.585554	−	0.810633i	$-0.699123\pi$
$569$	−27.9353	−1.17111	−0.585554	+	0.810633i	$0.699123\pi$
$570$	30.2745	1.26806
$571$	−23.4474	−0.981241	−0.490621	−	0.871373i	$-0.663230\pi$
$571$	−23.4474	−0.981241	−0.490621	+	0.871373i	$0.663230\pi$
$572$	−94.8418	−3.96553
$573$	48.3333	2.01915
$574$	84.0753	3.50923
$575$	−7.63786	−0.318521
$576$	45.9914	1.91631
$577$	29.0443	1.20913	0.604566	−	0.796555i	$-0.293347\pi$
$577$	29.0443	1.20913	0.604566	+	0.796555i	$0.293347\pi$
$578$	32.7409	1.36184
$579$	80.9803	3.36543
$580$	33.2128	1.37909
$581$	−30.8360	−1.27929
$582$	30.6126	1.26893
$583$	−3.06322	−0.126865
$584$	−14.0113	−0.579790
$585$	−55.9665	−2.31393
$586$	49.5470	2.04677
$587$	−31.9357	−1.31813	−0.659064	−	0.752087i	$-0.729047\pi$
$587$	−31.9357	−1.31813	−0.659064	+	0.752087i	$0.729047\pi$
$588$	−86.5465	−3.56912
$589$	−15.9738	−0.658189
$590$	8.04822	0.331340
$591$	27.9276	1.14879
$592$	43.0871	1.77087
$593$	−16.6617	−0.684215	−0.342108	−	0.939661i	$-0.611141\pi$
$593$	−16.6617	−0.684215	−0.342108	+	0.939661i	$0.611141\pi$
$594$	121.536	4.98667
$595$	−7.41256	−0.303885
$596$	30.5512	1.25143
$597$	−77.3401	−3.16532
$598$	−139.349	−5.69841
$599$	33.2254	1.35755	0.678776	−	0.734345i	$-0.262511\pi$
$599$	33.2254	1.35755	0.678776	+	0.734345i	$0.262511\pi$
$600$	23.6000	0.963466
$601$	30.4100	1.24045	0.620226	−	0.784423i	$-0.287041\pi$
$601$	30.4100	1.24045	0.620226	+	0.784423i	$0.287041\pi$
$602$	−69.5388	−2.83419
$603$	108.535	4.41988
$604$	−25.7801	−1.04898
$605$	−2.90274	−0.118013
$606$	27.7546	1.12745
$607$	4.60702	0.186993	0.0934965	−	0.995620i	$-0.470196\pi$
$607$	4.60702	0.186993	0.0934965	+	0.995620i	$0.470196\pi$
$608$	−32.2773	−1.30902
$609$	−81.9939	−3.32256
$610$	21.7157	0.879243
$611$	−73.4148	−2.97005
$612$	−79.2107	−3.20190
$613$	−15.8128	−0.638675	−0.319337	−	0.947641i	$-0.603460\pi$
$613$	−15.8128	−0.638675	−0.319337	+	0.947641i	$0.603460\pi$
$614$	−71.7452	−2.89540
$615$	30.3129	1.22233
$616$	−71.7228	−2.88979
$617$	7.09780	0.285747	0.142873	−	0.989741i	$-0.454366\pi$
$617$	7.09780	0.285747	0.142873	+	0.989741i	$0.454366\pi$
$618$	46.6003	1.87454
$619$	−7.53627	−0.302908	−0.151454	−	0.988464i	$-0.548396\pi$
$619$	−7.53627	−0.302908	−0.151454	+	0.988464i	$0.548396\pi$
$620$	−21.5274	−0.864560
$621$	125.615	5.04076
$622$	14.0163	0.562003
$623$	−41.9775	−1.68179
$624$	209.826	8.39975
$625$	1.00000	0.0400000
$626$	−77.1803	−3.08475
$627$	−33.1727	−1.32479
$628$	59.1143	2.35892
$629$	−10.0126	−0.399230
$630$	−73.1699	−2.91516
$631$	−35.0552	−1.39553	−0.697763	−	0.716329i	$-0.745821\pi$
$631$	−35.0552	−1.39553	−0.697763	+	0.716329i	$0.745821\pi$
$632$	48.0456	1.91115
$633$	−33.5675	−1.33419
$634$	70.3837	2.79529
$635$	8.03259	0.318764
$636$	16.9123	0.670616
$637$	−38.7011	−1.53339
$638$	−51.7341	−2.04817
$639$	−9.03597	−0.357457
$640$	3.34503	0.132224
$641$	37.0109	1.46184	0.730920	−	0.682463i	$-0.239091\pi$
$641$	37.0109	1.46184	0.730920	+	0.682463i	$0.239091\pi$
$642$	−36.9995	−1.46025
$643$	−33.7889	−1.33250	−0.666252	−	0.745726i	$-0.732103\pi$
$643$	−33.7889	−1.33250	−0.666252	+	0.745726i	$0.732103\pi$
$644$	−128.157	−5.05009
$645$	−25.0718	−0.987203
$646$	19.1605	0.753858
$647$	−31.2585	−1.22890	−0.614450	−	0.788956i	$-0.710622\pi$
$647$	−31.2585	−1.22890	−0.614450	+	0.788956i	$0.710622\pi$
$648$	−217.815	−8.55660
$649$	−8.81868	−0.346164
$650$	18.2445	0.715610
$651$	53.1456	2.08294
$652$	−52.2927	−2.04794
$653$	6.62272	0.259167	0.129584	−	0.991568i	$-0.458636\pi$
$653$	6.62272	0.259167	0.129584	+	0.991568i	$0.458636\pi$
$654$	13.9171	0.544201
$655$	−13.5229	−0.528384
$656$	−82.5573	−3.22332
$657$	15.6623	0.611046
$658$	−95.9817	−3.74176
$659$	−8.97294	−0.349536	−0.174768	−	0.984610i	$-0.555918\pi$
$659$	−8.97294	−0.349536	−0.174768	+	0.984610i	$0.555918\pi$
$660$	−44.7057	−1.74017
$661$	36.7229	1.42836	0.714178	−	0.699964i	$-0.246800\pi$
$661$	36.7229	1.42836	0.714178	+	0.699964i	$0.246800\pi$
$662$	−58.3936	−2.26953
$663$	−48.7596	−1.89367
$664$	62.1344	2.41128
$665$	12.4505	0.482810
$666$	−98.8356	−3.82980
$667$	−53.4705	−2.07039
$668$	74.8656	2.89664
$669$	42.7381	1.65235
$670$	−35.3813	−1.36690
$671$	−23.7946	−0.918579
$672$	107.388	4.14258
$673$	34.0979	1.31438	0.657189	−	0.753726i	$-0.271745\pi$
$673$	34.0979	1.31438	0.657189	+	0.753726i	$0.271745\pi$
$674$	−56.9960	−2.19540
$675$	−16.4464	−0.633021
$676$	172.478	6.63375
$677$	−43.4177	−1.66868	−0.834338	−	0.551253i	$-0.814150\pi$
$677$	−43.4177	−1.66868	−0.834338	+	0.551253i	$0.814150\pi$
$678$	73.7644	2.83290
$679$	12.5896	0.483144
$680$	14.9363	0.572779
$681$	49.4034	1.89314
$682$	33.5322	1.28402
$683$	19.9267	0.762474	0.381237	−	0.924477i	$-0.375498\pi$
$683$	19.9267	0.762474	0.381237	+	0.924477i	$0.375498\pi$
$684$	133.046	5.08715
$685$	−13.4440	−0.513668
$686$	13.6967	0.522941
$687$	−74.8815	−2.85691
$688$	68.2833	2.60328
$689$	7.56269	0.288115
$690$	−65.6853	−2.50060
$691$	−20.1022	−0.764724	−0.382362	−	0.924013i	$-0.624889\pi$
$691$	−20.1022	−0.764724	−0.382362	+	0.924013i	$0.624889\pi$
$692$	41.0763	1.56149
$693$	80.1746	3.04558
$694$	53.9209	2.04681
$695$	−7.28321	−0.276268
$696$	165.217	6.26253
$697$	19.1848	0.726675
$698$	−1.68795	−0.0638897
$699$	−65.2217	−2.46691
$700$	16.7792	0.634193
$701$	13.6036	0.513800	0.256900	−	0.966438i	$-0.417299\pi$
$701$	13.6036	0.513800	0.256900	+	0.966438i	$0.417299\pi$
$702$	−300.056	−11.3249
$703$	16.8178	0.634294
$704$	16.4280	0.619154
$705$	−34.6057	−1.30332
$706$	25.3180	0.952855
$707$	11.4142	0.429275
$708$	48.6888	1.82984
$709$	−48.4911	−1.82112	−0.910561	−	0.413374i	$-0.864350\pi$
$709$	−48.4911	−1.82112	−0.910561	+	0.413374i	$0.864350\pi$
$710$	2.94564	0.110548
$711$	−53.7072	−2.01418
$712$	84.5843	3.16993
$713$	34.6577	1.29794
$714$	−63.7477	−2.38570
$715$	−19.9911	−0.747625
$716$	−111.703	−4.17455
$717$	−63.0581	−2.35495
$718$	−21.0044	−0.783876
$719$	11.9850	0.446967	0.223483	−	0.974708i	$-0.428257\pi$
$719$	11.9850	0.446967	0.223483	+	0.974708i	$0.428257\pi$
$720$	71.8488	2.67765
$721$	19.1646	0.713728
$722$	17.1593	0.638604
$723$	13.8744	0.515994
$724$	−62.4206	−2.31984
$725$	7.00072	0.260000
$726$	−24.9634	−0.926480
$727$	31.0004	1.14974	0.574871	−	0.818244i	$-0.305052\pi$
$727$	31.0004	1.14974	0.574871	+	0.818244i	$0.305052\pi$
$728$	177.074	6.56281
$729$	80.0939	2.96644
$730$	−5.10577	−0.188973
$731$	−15.8678	−0.586891
$732$	131.372	4.85565
$733$	43.7371	1.61547	0.807734	−	0.589547i	$-0.200694\pi$
$733$	43.7371	1.61547	0.807734	+	0.589547i	$0.200694\pi$
$734$	−36.8752	−1.36109
$735$	−18.2426	−0.672888
$736$	70.0307	2.58137
$737$	38.7684	1.42805
$738$	189.374	6.97096
$739$	12.1047	0.445277	0.222638	−	0.974901i	$-0.428533\pi$
$739$	12.1047	0.445277	0.222638	+	0.974901i	$0.428533\pi$
$740$	22.6647	0.833173
$741$	81.8991	3.00864
$742$	9.88738	0.362977
$743$	−16.7126	−0.613126	−0.306563	−	0.951850i	$-0.599179\pi$
$743$	−16.7126	−0.613126	−0.306563	+	0.951850i	$0.599179\pi$
$744$	−107.088	−3.92603
$745$	6.43969	0.235932
$746$	33.2003	1.21555
$747$	−69.4562	−2.54127
$748$	−28.2939	−1.03453
$749$	−15.2162	−0.555988
$750$	8.59996	0.314026
$751$	−9.16401	−0.334399	−0.167200	−	0.985923i	$-0.553472\pi$
$751$	−9.16401	−0.334399	−0.167200	+	0.985923i	$0.553472\pi$
$752$	94.2487	3.43690
$753$	88.9274	3.24070
$754$	127.725	4.65147
$755$	−5.43402	−0.197764
$756$	−275.956	−10.0364
$757$	4.60812	0.167485	0.0837424	−	0.996487i	$-0.473313\pi$
$757$	4.60812	0.167485	0.0837424	+	0.996487i	$0.473313\pi$
$758$	−31.8886	−1.15825
$759$	71.9734	2.61247
$760$	−25.0877	−0.910026
$761$	2.65225	0.0961438	0.0480719	−	0.998844i	$-0.484692\pi$
$761$	2.65225	0.0961438	0.0480719	+	0.998844i	$0.484692\pi$
$762$	69.0800	2.50250
$763$	5.72346	0.207203
$764$	−69.2434	−2.50514
$765$	−16.6963	−0.603657
$766$	33.5317	1.21155
$767$	21.7722	0.786149
$768$	67.0036	2.41778
$769$	3.62501	0.130721	0.0653605	−	0.997862i	$-0.479180\pi$
$769$	3.62501	0.130721	0.0653605	+	0.997862i	$0.479180\pi$
$770$	−26.1362	−0.941882
$771$	36.6961	1.32158
$772$	−116.014	−4.17544
$773$	−12.6784	−0.456011	−0.228006	−	0.973660i	$-0.573220\pi$
$773$	−12.6784	−0.456011	−0.228006	+	0.973660i	$0.573220\pi$
$774$	−156.632	−5.63002
$775$	−4.53762	−0.162996
$776$	−25.3679	−0.910655
$777$	−55.9534	−2.00732
$778$	45.7509	1.64025
$779$	−32.2237	−1.15453
$780$	110.373	3.95198
$781$	−3.22763	−0.115494
$782$	−41.5717	−1.48660
$783$	−115.136	−4.11464
$784$	49.6838	1.77442
$785$	12.4603	0.444728
$786$	−116.297	−4.14816
$787$	32.6883	1.16521	0.582606	−	0.812755i	$-0.302033\pi$
$787$	32.6883	1.16521	0.582606	+	0.812755i	$0.302033\pi$
$788$	−40.0096	−1.42528
$789$	−21.0678	−0.750035
$790$	17.5080	0.622908
$791$	30.3359	1.07862
$792$	−161.551	−5.74047
$793$	58.7457	2.08612
$794$	−6.54960	−0.232437
$795$	3.56484	0.126432
$796$	110.799	3.92717
$797$	27.5028	0.974198	0.487099	−	0.873347i	$-0.338055\pi$
$797$	27.5028	0.974198	0.487099	+	0.873347i	$0.338055\pi$
$798$	107.074	3.79038
$799$	−21.9017	−0.774825
$800$	−9.16889	−0.324169
$801$	−94.5516	−3.34082
$802$	−101.428	−3.58153
$803$	5.59455	0.197427
$804$	−214.044	−7.54875
$805$	−27.0134	−0.952097
$806$	−82.7868	−2.91604
$807$	61.2808	2.15719
$808$	−22.9995	−0.809120
$809$	14.1147	0.496245	0.248122	−	0.968729i	$-0.420186\pi$
$809$	14.1147	0.496245	0.248122	+	0.968729i	$0.420186\pi$
$810$	−79.3731	−2.78889
$811$	−8.26894	−0.290362	−0.145181	−	0.989405i	$-0.546376\pi$
$811$	−8.26894	−0.290362	−0.145181	+	0.989405i	$0.546376\pi$
$812$	117.466	4.12226
$813$	−26.6379	−0.934234
$814$	−35.3039	−1.23740
$815$	−11.0224	−0.386099
$816$	62.5967	2.19132
$817$	26.6523	0.932446
$818$	19.5993	0.685275
$819$	−197.941	−6.91661
$820$	−43.4269	−1.51653
$821$	3.15949	0.110267	0.0551334	−	0.998479i	$-0.482442\pi$
$821$	3.15949	0.110267	0.0551334	+	0.998479i	$0.482442\pi$
$822$	−115.618	−4.03263
$823$	−43.4397	−1.51421	−0.757106	−	0.653292i	$-0.773387\pi$
$823$	−43.4397	−1.51421	−0.757106	+	0.653292i	$0.773387\pi$
$824$	−38.6165	−1.34527
$825$	−9.42324	−0.328075
$826$	28.4647	0.990415
$827$	24.6107	0.855799	0.427900	−	0.903826i	$-0.359254\pi$
$827$	24.6107	0.855799	0.427900	+	0.903826i	$0.359254\pi$
$828$	−288.665	−10.0318
$829$	22.3975	0.777896	0.388948	−	0.921260i	$-0.372839\pi$
$829$	22.3975	0.777896	0.388948	+	0.921260i	$0.372839\pi$
$830$	22.6421	0.785918
$831$	30.6843	1.06443
$832$	−40.5587	−1.40612
$833$	−11.5456	−0.400031
$834$	−62.6353	−2.16888
$835$	15.7805	0.546105
$836$	47.5239	1.64365
$837$	74.6273	2.57950
$838$	64.2133	2.21821
$839$	1.90275	0.0656903	0.0328452	−	0.999460i	$-0.489543\pi$
$839$	1.90275	0.0656903	0.0328452	+	0.999460i	$0.489543\pi$
$840$	83.4679	2.87992
$841$	20.0101	0.690002
$842$	84.0983	2.89822
$843$	−64.3755	−2.21721
$844$	48.0896	1.65531
$845$	36.3555	1.25067
$846$	−216.193	−7.43286
$847$	−10.2663	−0.352755
$848$	−9.70885	−0.333403
$849$	79.1445	2.71623
$850$	5.44285	0.186688
$851$	−36.4888	−1.25082
$852$	17.8200	0.610505
$853$	19.1535	0.655805	0.327903	−	0.944712i	$-0.393658\pi$
$853$	19.1535	0.655805	0.327903	+	0.944712i	$0.393658\pi$
$854$	76.8035	2.62816
$855$	28.0440	0.959085
$856$	30.6606	1.04796
$857$	41.2303	1.40840	0.704200	−	0.710001i	$-0.251306\pi$
$857$	41.2303	1.40840	0.704200	+	0.710001i	$0.251306\pi$
$858$	−171.923	−5.86934
$859$	29.1332	0.994012	0.497006	−	0.867747i	$-0.334433\pi$
$859$	29.1332	0.994012	0.497006	+	0.867747i	$0.334433\pi$
$860$	35.9185	1.22481
$861$	107.210	3.65370
$862$	−28.2438	−0.961986
$863$	−56.4457	−1.92143	−0.960716	−	0.277533i	$-0.910483\pi$
$863$	−56.4457	−1.92143	−0.960716	+	0.277533i	$0.910483\pi$
$864$	150.795	5.13015
$865$	8.65822	0.294388
$866$	−56.9258	−1.93442
$867$	41.7500	1.41791
$868$	−76.1375	−2.58427
$869$	−19.1841	−0.650776
$870$	60.2059	2.04117
$871$	−95.7143	−3.24315
$872$	−11.5327	−0.390547
$873$	28.3572	0.959747
$874$	69.8260	2.36190
$875$	3.53678	0.119565
$876$	−30.8880	−1.04361
$877$	20.4640	0.691020	0.345510	−	0.938415i	$-0.387706\pi$
$877$	20.4640	0.691020	0.345510	+	0.938415i	$0.387706\pi$
$878$	9.74290	0.328807
$879$	63.1806	2.13103
$880$	25.6642	0.865142
$881$	11.3384	0.381999	0.191000	−	0.981590i	$-0.438827\pi$
$881$	11.3384	0.381999	0.191000	+	0.981590i	$0.438827\pi$
$882$	−113.967	−3.83748
$883$	−1.10406	−0.0371546	−0.0185773	−	0.999827i	$-0.505914\pi$
$883$	−1.10406	−0.0371546	−0.0185773	+	0.999827i	$0.505914\pi$
$884$	69.8540	2.34945
$885$	10.2628	0.344980
$886$	59.8547	2.01086
$887$	−6.32987	−0.212536	−0.106268	−	0.994338i	$-0.533890\pi$
$887$	−6.32987	−0.212536	−0.106268	+	0.994338i	$0.533890\pi$
$888$	112.746	3.78350
$889$	28.4095	0.952823
$890$	30.8229	1.03319
$891$	86.9715	2.91366
$892$	−61.2275	−2.05005
$893$	36.7871	1.23103
$894$	55.3811	1.85222
$895$	−23.5453	−0.787032
$896$	11.8306	0.395234
$897$	−177.693	−5.93300
$898$	16.5175	0.551195
$899$	−31.7666	−1.05948
$900$	37.7940	1.25980
$901$	2.25616	0.0751635
$902$	67.6441	2.25230
$903$	−88.6734	−2.95087
$904$	−61.1267	−2.03304
$905$	−13.1572	−0.437362
$906$	−46.7323	−1.55258
$907$	34.3288	1.13987	0.569935	−	0.821690i	$-0.306969\pi$
$907$	34.3288	1.13987	0.569935	+	0.821690i	$0.306969\pi$
$908$	−70.7763	−2.34880
$909$	25.7098	0.852739
$910$	64.5268	2.13904
$911$	15.1257	0.501136	0.250568	−	0.968099i	$-0.419383\pi$
$911$	15.1257	0.501136	0.250568	+	0.968099i	$0.419383\pi$
$912$	−105.141	−3.48156
$913$	−24.8096	−0.821079
$914$	−76.7604	−2.53901
$915$	27.6911	0.915439
$916$	107.277	3.54453
$917$	−47.8275	−1.57940
$918$	−89.5150	−2.95444
$919$	−36.2432	−1.19555	−0.597776	−	0.801663i	$-0.703949\pi$
$919$	−36.2432	−1.19555	−0.597776	+	0.801663i	$0.703949\pi$
$920$	54.4318	1.79456
$921$	−91.4869	−3.01459
$922$	−52.0205	−1.71320
$923$	7.96861	0.262290
$924$	−158.114	−5.20157
$925$	4.77736	0.157079
$926$	105.355	3.46219
$927$	43.1671	1.41779
$928$	−64.1888	−2.10710
$929$	−3.21352	−0.105432	−0.0527161	−	0.998610i	$-0.516788\pi$
$929$	−3.21352	−0.105432	−0.0527161	+	0.998610i	$0.516788\pi$
$930$	−39.0234	−1.27963
$931$	19.3926	0.635566
$932$	93.4380	3.06066
$933$	17.8731	0.585139
$934$	−54.3418	−1.77812
$935$	−5.96390	−0.195040
$936$	398.849	13.0368
$937$	24.8118	0.810566	0.405283	−	0.914191i	$-0.367173\pi$
$937$	24.8118	0.810566	0.405283	+	0.914191i	$0.367173\pi$
$938$	−125.136	−4.08583
$939$	−98.4176	−3.21174
$940$	49.5768	1.61702
$941$	−31.3703	−1.02264	−0.511321	−	0.859390i	$-0.670844\pi$
$941$	−31.3703	−1.02264	−0.511321	+	0.859390i	$0.670844\pi$
$942$	107.158	3.49141
$943$	69.9145	2.27673
$944$	−27.9508	−0.909721
$945$	−58.1671	−1.89217
$946$	−55.9486	−1.81905
$947$	−33.8371	−1.09956	−0.549779	−	0.835310i	$-0.685288\pi$
$947$	−33.8371	−1.09956	−0.549779	+	0.835310i	$0.685288\pi$
$948$	105.917	3.44003
$949$	−13.8122	−0.448364
$950$	−9.14208	−0.296608
$951$	89.7508	2.91037
$952$	52.8262	1.71211
$953$	−17.2395	−0.558443	−0.279221	−	0.960227i	$-0.590076\pi$
$953$	−17.2395	−0.558443	−0.279221	+	0.960227i	$0.590076\pi$
$954$	22.2707	0.721040
$955$	−14.5954	−0.472296
$956$	90.3383	2.92175
$957$	−65.9695	−2.13249
$958$	−22.0260	−0.711629
$959$	−47.5484	−1.53542
$960$	−19.1182	−0.617038
$961$	−10.4100	−0.335806
$962$	87.1607	2.81017
$963$	−34.2736	−1.10445
$964$	−19.8767	−0.640187
$965$	−24.4539	−0.787199
$966$	−232.314	−7.47459
$967$	−3.95296	−0.127119	−0.0635593	−	0.997978i	$-0.520245\pi$
$967$	−3.95296	−0.127119	−0.0635593	+	0.997978i	$0.520245\pi$
$968$	20.6866	0.664892
$969$	24.4327	0.784893
$970$	−9.24420	−0.296813
$971$	−39.3781	−1.26370	−0.631852	−	0.775089i	$-0.717705\pi$
$971$	−39.3781	−1.26370	−0.631852	+	0.775089i	$0.717705\pi$
$972$	−246.104	−7.89378
$973$	−25.7591	−0.825798
$974$	76.8505	2.46245
$975$	23.2648	0.745069
$976$	−75.4168	−2.41403
$977$	−4.76215	−0.152355	−0.0761774	−	0.997094i	$-0.524272\pi$
$977$	−4.76215	−0.152355	−0.0761774	+	0.997094i	$0.524272\pi$
$978$	−94.7926	−3.03113
$979$	−33.7737	−1.07941
$980$	26.1347	0.834843
$981$	12.8917	0.411602
$982$	−64.8287	−2.06877
$983$	−52.0129	−1.65895	−0.829476	−	0.558542i	$-0.811361\pi$
$983$	−52.0129	−1.65895	−0.829476	+	0.558542i	$0.811361\pi$
$984$	−216.027	−6.88669
$985$	−8.43338	−0.268710
$986$	38.1038	1.21347
$987$	−122.392	−3.89580
$988$	−117.330	−3.73278
$989$	−57.8265	−1.83877
$990$	−58.8700	−1.87101
$991$	59.4824	1.88952	0.944760	−	0.327762i	$-0.106294\pi$
$991$	59.4824	1.88952	0.944760	+	0.327762i	$0.106294\pi$
$992$	41.6050	1.32096
$993$	−74.4615	−2.36296
$994$	10.4181	0.330441
$995$	23.3546	0.740392
$996$	136.976	4.34026
$997$	−38.7955	−1.22867	−0.614333	−	0.789047i	$-0.710575\pi$
$997$	−38.7955	−1.22867	−0.614333	+	0.789047i	$0.710575\pi$
$998$	−70.5183	−2.23222
$999$	−78.5702	−2.48585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.e.1.9	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.e.1.9	✓	126	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59696 q^{2} -3.31155 q^{3} +4.74420 q^{4} +1.00000 q^{5} +8.59996 q^{6} +3.53678 q^{7} -7.12657 q^{8} +7.96636 q^{9} +O(q^{10})\)	\(q-2.59696 q^{2} -3.31155 q^{3} +4.74420 q^{4} +1.00000 q^{5} +8.59996 q^{6} +3.53678 q^{7} -7.12657 q^{8} +7.96636 q^{9} -2.59696 q^{10} +2.84557 q^{11} -15.7107 q^{12} -7.02535 q^{13} -9.18486 q^{14} -3.31155 q^{15} +9.01902 q^{16} -2.09585 q^{17} -20.6883 q^{18} +3.52030 q^{19} +4.74420 q^{20} -11.7122 q^{21} -7.38983 q^{22} -7.63786 q^{23} +23.6000 q^{24} +1.00000 q^{25} +18.2445 q^{26} -16.4464 q^{27} +16.7792 q^{28} +7.00072 q^{29} +8.59996 q^{30} -4.53762 q^{31} -9.16889 q^{32} -9.42324 q^{33} +5.44285 q^{34} +3.53678 q^{35} +37.7940 q^{36} +4.77736 q^{37} -9.14208 q^{38} +23.2648 q^{39} -7.12657 q^{40} -9.15368 q^{41} +30.4161 q^{42} +7.57103 q^{43} +13.4999 q^{44} +7.96636 q^{45} +19.8352 q^{46} +10.4500 q^{47} -29.8669 q^{48} +5.50878 q^{49} -2.59696 q^{50} +6.94052 q^{51} -33.3296 q^{52} -1.07649 q^{53} +42.7105 q^{54} +2.84557 q^{55} -25.2051 q^{56} -11.6577 q^{57} -18.1806 q^{58} -3.09909 q^{59} -15.7107 q^{60} -8.36197 q^{61} +11.7840 q^{62} +28.1752 q^{63} +5.77319 q^{64} -7.02535 q^{65} +24.4718 q^{66} +13.6241 q^{67} -9.94314 q^{68} +25.2932 q^{69} -9.18486 q^{70} -1.13427 q^{71} -56.7729 q^{72} +1.96606 q^{73} -12.4066 q^{74} -3.31155 q^{75} +16.7010 q^{76} +10.0641 q^{77} -60.4177 q^{78} -6.74175 q^{79} +9.01902 q^{80} +30.5638 q^{81} +23.7717 q^{82} -8.71869 q^{83} -55.5650 q^{84} -2.09585 q^{85} -19.6617 q^{86} -23.1832 q^{87} -20.2792 q^{88} -11.8689 q^{89} -20.6883 q^{90} -24.8471 q^{91} -36.2355 q^{92} +15.0266 q^{93} -27.1382 q^{94} +3.52030 q^{95} +30.3632 q^{96} +3.55962 q^{97} -14.3061 q^{98} +22.6688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * q^99

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