LMFDB - Embedded newform 8015.2.a.m.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83785 q^{2} +1.36680 q^{3} +1.37770 q^{4} +1.00000 q^{5} -2.51199 q^{6} -1.00000 q^{7} +1.14369 q^{8} -1.13184 q^{9} +O(q^{10})$	\(q-1.83785 q^{2} +1.36680 q^{3} +1.37770 q^{4} +1.00000 q^{5} -2.51199 q^{6} -1.00000 q^{7} +1.14369 q^{8} -1.13184 q^{9} -1.83785 q^{10} -5.87380 q^{11} +1.88305 q^{12} -0.301110 q^{13} +1.83785 q^{14} +1.36680 q^{15} -4.85734 q^{16} -7.91595 q^{17} +2.08016 q^{18} -1.02660 q^{19} +1.37770 q^{20} -1.36680 q^{21} +10.7952 q^{22} +0.698218 q^{23} +1.56321 q^{24} +1.00000 q^{25} +0.553396 q^{26} -5.64743 q^{27} -1.37770 q^{28} +7.90761 q^{29} -2.51199 q^{30} -10.7353 q^{31} +6.63969 q^{32} -8.02834 q^{33} +14.5483 q^{34} -1.00000 q^{35} -1.55934 q^{36} -2.22845 q^{37} +1.88674 q^{38} -0.411559 q^{39} +1.14369 q^{40} +9.13601 q^{41} +2.51199 q^{42} +1.19933 q^{43} -8.09233 q^{44} -1.13184 q^{45} -1.28322 q^{46} -2.17875 q^{47} -6.63904 q^{48} +1.00000 q^{49} -1.83785 q^{50} -10.8196 q^{51} -0.414840 q^{52} +4.88692 q^{53} +10.3791 q^{54} -5.87380 q^{55} -1.14369 q^{56} -1.40316 q^{57} -14.5330 q^{58} -12.0282 q^{59} +1.88305 q^{60} -12.8748 q^{61} +19.7299 q^{62} +1.13184 q^{63} -2.48808 q^{64} -0.301110 q^{65} +14.7549 q^{66} +4.27626 q^{67} -10.9058 q^{68} +0.954328 q^{69} +1.83785 q^{70} -8.27426 q^{71} -1.29448 q^{72} +9.93905 q^{73} +4.09555 q^{74} +1.36680 q^{75} -1.41434 q^{76} +5.87380 q^{77} +0.756385 q^{78} +3.87387 q^{79} -4.85734 q^{80} -4.32340 q^{81} -16.7906 q^{82} +2.69752 q^{83} -1.88305 q^{84} -7.91595 q^{85} -2.20420 q^{86} +10.8082 q^{87} -6.71783 q^{88} +9.35172 q^{89} +2.08016 q^{90} +0.301110 q^{91} +0.961935 q^{92} -14.6731 q^{93} +4.00422 q^{94} -1.02660 q^{95} +9.07516 q^{96} +0.0705004 q^{97} -1.83785 q^{98} +6.64822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) $ 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.83785	−1.29956	−0.649779	−	0.760123i	$-0.725138\pi$
$2$	−1.83785	−1.29956	−0.649779	+	0.760123i	$0.725138\pi$
$3$	1.36680	0.789125	0.394563	−	0.918869i	$-0.370896\pi$
$3$	1.36680	0.789125	0.394563	+	0.918869i	$0.370896\pi$
$4$	1.37770	0.688850
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.51199	−1.02551
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.14369	0.404357
$9$	−1.13184	−0.377281
$10$	−1.83785	−0.581180
$11$	−5.87380	−1.77102	−0.885508	−	0.464623i	$-0.846190\pi$
$11$	−5.87380	−1.77102	−0.885508	+	0.464623i	$0.846190\pi$
$12$	1.88305	0.543589
$13$	−0.301110	−0.0835130	−0.0417565	−	0.999128i	$-0.513295\pi$
$13$	−0.301110	−0.0835130	−0.0417565	+	0.999128i	$0.513295\pi$
$14$	1.83785	0.491187
$15$	1.36680	0.352908
$16$	−4.85734	−1.21434
$17$	−7.91595	−1.91990	−0.959950	−	0.280171i	$-0.909609\pi$
$17$	−7.91595	−1.91990	−0.959950	+	0.280171i	$0.909609\pi$
$18$	2.08016	0.490299
$19$	−1.02660	−0.235518	−0.117759	−	0.993042i	$-0.537571\pi$
$19$	−1.02660	−0.235518	−0.117759	+	0.993042i	$0.537571\pi$
$20$	1.37770	0.308063
$21$	−1.36680	−0.298261
$22$	10.7952	2.30154
$23$	0.698218	0.145589	0.0727943	−	0.997347i	$-0.476808\pi$
$23$	0.698218	0.145589	0.0727943	+	0.997347i	$0.476808\pi$
$24$	1.56321	0.319088
$25$	1.00000	0.200000
$26$	0.553396	0.108530
$27$	−5.64743	−1.08685
$28$	−1.37770	−0.260361
$29$	7.90761	1.46841	0.734203	−	0.678930i	$-0.237556\pi$
$29$	7.90761	1.46841	0.734203	+	0.678930i	$0.237556\pi$
$30$	−2.51199	−0.458624
$31$	−10.7353	−1.92812	−0.964058	−	0.265693i	$-0.914399\pi$
$31$	−10.7353	−1.92812	−0.964058	+	0.265693i	$0.914399\pi$
$32$	6.63969	1.17374
$33$	−8.02834	−1.39755
$34$	14.5483	2.49502
$35$	−1.00000	−0.169031
$36$	−1.55934	−0.259890
$37$	−2.22845	−0.366354	−0.183177	−	0.983080i	$-0.558638\pi$
$37$	−2.22845	−0.366354	−0.183177	+	0.983080i	$0.558638\pi$
$38$	1.88674	0.306069
$39$	−0.411559	−0.0659022
$40$	1.14369	0.180834
$41$	9.13601	1.42680	0.713402	−	0.700755i	$-0.247153\pi$
$41$	9.13601	1.42680	0.713402	+	0.700755i	$0.247153\pi$
$42$	2.51199	0.387608
$43$	1.19933	0.182897	0.0914483	−	0.995810i	$-0.470850\pi$
$43$	1.19933	0.182897	0.0914483	+	0.995810i	$0.470850\pi$
$44$	−8.09233	−1.21997
$45$	−1.13184	−0.168725
$46$	−1.28322	−0.189201
$47$	−2.17875	−0.317803	−0.158902	−	0.987294i	$-0.550795\pi$
$47$	−2.17875	−0.317803	−0.158902	+	0.987294i	$0.550795\pi$
$48$	−6.63904	−0.958263
$49$	1.00000	0.142857
$50$	−1.83785	−0.259912
$51$	−10.8196	−1.51504
$52$	−0.414840	−0.0575279
$53$	4.88692	0.671270	0.335635	−	0.941992i	$-0.391049\pi$
$53$	4.88692	0.671270	0.335635	+	0.941992i	$0.391049\pi$
$54$	10.3791	1.41242
$55$	−5.87380	−0.792023
$56$	−1.14369	−0.152833
$57$	−1.40316	−0.185853
$58$	−14.5330	−1.90828
$59$	−12.0282	−1.56594	−0.782969	−	0.622061i	$-0.786296\pi$
$59$	−12.0282	−1.56594	−0.782969	+	0.622061i	$0.786296\pi$
$60$	1.88305	0.243100
$61$	−12.8748	−1.64845	−0.824224	−	0.566263i	$-0.808388\pi$
$61$	−12.8748	−1.64845	−0.824224	+	0.566263i	$0.808388\pi$
$62$	19.7299	2.50570
$63$	1.13184	0.142599
$64$	−2.48808	−0.311010
$65$	−0.301110	−0.0373481
$66$	14.7549	1.81620
$67$	4.27626	0.522429	0.261214	−	0.965281i	$-0.415877\pi$
$67$	4.27626	0.522429	0.261214	+	0.965281i	$0.415877\pi$
$68$	−10.9058	−1.32252
$69$	0.954328	0.114888
$70$	1.83785	0.219665
$71$	−8.27426	−0.981974	−0.490987	−	0.871167i	$-0.663364\pi$
$71$	−8.27426	−0.981974	−0.490987	+	0.871167i	$0.663364\pi$
$72$	−1.29448	−0.152556
$73$	9.93905	1.16328	0.581639	−	0.813447i	$-0.302412\pi$
$73$	9.93905	1.16328	0.581639	+	0.813447i	$0.302412\pi$
$74$	4.09555	0.476099
$75$	1.36680	0.157825
$76$	−1.41434	−0.162236
$77$	5.87380	0.669381
$78$	0.756385	0.0856437
$79$	3.87387	0.435844	0.217922	−	0.975966i	$-0.430072\pi$
$79$	3.87387	0.435844	0.217922	+	0.975966i	$0.430072\pi$
$80$	−4.85734	−0.543067
$81$	−4.32340	−0.480377
$82$	−16.7906	−1.85422
$83$	2.69752	0.296091	0.148046	−	0.988981i	$-0.452702\pi$
$83$	2.69752	0.296091	0.148046	+	0.988981i	$0.452702\pi$
$84$	−1.88305	−0.205457
$85$	−7.91595	−0.858606
$86$	−2.20420	−0.237685
$87$	10.8082	1.15876
$88$	−6.71783	−0.716123
$89$	9.35172	0.991281	0.495640	−	0.868528i	$-0.334933\pi$
$89$	9.35172	0.991281	0.495640	+	0.868528i	$0.334933\pi$
$90$	2.08016	0.219268
$91$	0.301110	0.0315649
$92$	0.961935	0.100289
$93$	−14.6731	−1.52152
$94$	4.00422	0.413004
$95$	−1.02660	−0.105327
$96$	9.07516	0.926229
$97$	0.0705004	0.00715824	0.00357912	−	0.999994i	$-0.498861\pi$
$97$	0.0705004	0.00715824	0.00357912	+	0.999994i	$0.498861\pi$
$98$	−1.83785	−0.185651
$99$	6.64822	0.668172
$100$	1.37770	0.137770
$101$	−5.62632	−0.559840	−0.279920	−	0.960023i	$-0.590308\pi$
$101$	−5.62632	−0.559840	−0.279920	+	0.960023i	$0.590308\pi$
$102$	19.8848	1.96888
$103$	6.25350	0.616175	0.308088	−	0.951358i	$-0.400311\pi$
$103$	6.25350	0.616175	0.308088	+	0.951358i	$0.400311\pi$
$104$	−0.344378	−0.0337691
$105$	−1.36680	−0.133387
$106$	−8.98144	−0.872355
$107$	−15.9433	−1.54130	−0.770648	−	0.637261i	$-0.780067\pi$
$107$	−15.9433	−1.54130	−0.770648	+	0.637261i	$0.780067\pi$
$108$	−7.78046	−0.748675
$109$	4.57645	0.438344	0.219172	−	0.975686i	$-0.429664\pi$
$109$	4.57645	0.438344	0.219172	+	0.975686i	$0.429664\pi$
$110$	10.7952	1.02928
$111$	−3.04585	−0.289099
$112$	4.85734	0.458976
$113$	9.41167	0.885375	0.442688	−	0.896676i	$-0.354025\pi$
$113$	9.41167	0.885375	0.442688	+	0.896676i	$0.354025\pi$
$114$	2.57880	0.241527
$115$	0.698218	0.0651092
$116$	10.8943	1.01151
$117$	0.340810	0.0315079
$118$	22.1060	2.03503
$119$	7.91595	0.725654
$120$	1.56321	0.142701
$121$	23.5015	2.13650
$122$	23.6620	2.14225
$123$	12.4871	1.12593
$124$	−14.7900	−1.32818
$125$	1.00000	0.0894427
$126$	−2.08016	−0.185316
$127$	−8.07368	−0.716423	−0.358211	−	0.933640i	$-0.616613\pi$
$127$	−8.07368	−0.716423	−0.358211	+	0.933640i	$0.616613\pi$
$128$	−8.70666	−0.769567
$129$	1.63925	0.144328
$130$	0.553396	0.0485361
$131$	−6.55329	−0.572563	−0.286282	−	0.958145i	$-0.592419\pi$
$131$	−6.55329	−0.572563	−0.286282	+	0.958145i	$0.592419\pi$
$132$	−11.0606	−0.962705
$133$	1.02660	0.0890173
$134$	−7.85914	−0.678926
$135$	−5.64743	−0.486053
$136$	−9.05343	−0.776326
$137$	16.1360	1.37859	0.689295	−	0.724480i	$-0.257920\pi$
$137$	16.1360	1.37859	0.689295	+	0.724480i	$0.257920\pi$
$138$	−1.75391	−0.149303
$139$	18.8567	1.59940	0.799702	−	0.600397i	$-0.204991\pi$
$139$	18.8567	1.59940	0.799702	+	0.600397i	$0.204991\pi$
$140$	−1.37770	−0.116437
$141$	−2.97793	−0.250787
$142$	15.2069	1.27613
$143$	1.76866	0.147903
$144$	5.49775	0.458146
$145$	7.90761	0.656691
$146$	−18.2665	−1.51175
$147$	1.36680	0.112732
$148$	−3.07013	−0.252363
$149$	−14.2755	−1.16950	−0.584748	−	0.811215i	$-0.698807\pi$
$149$	−14.2755	−1.16950	−0.584748	+	0.811215i	$0.698807\pi$
$150$	−2.51199	−0.205103
$151$	17.8176	1.44998	0.724990	−	0.688760i	$-0.241845\pi$
$151$	17.8176	1.44998	0.724990	+	0.688760i	$0.241845\pi$
$152$	−1.17411	−0.0952333
$153$	8.95962	0.724343
$154$	−10.7952	−0.869900
$155$	−10.7353	−0.862280
$156$	−0.567005	−0.0453967
$157$	14.8799	1.18754	0.593772	−	0.804633i	$-0.297638\pi$
$157$	14.8799	1.18754	0.593772	+	0.804633i	$0.297638\pi$
$158$	−7.11959	−0.566404
$159$	6.67947	0.529716
$160$	6.63969	0.524913
$161$	−0.698218	−0.0550273
$162$	7.94576	0.624278
$163$	−18.5798	−1.45528	−0.727641	−	0.685958i	$-0.759383\pi$
$163$	−18.5798	−1.45528	−0.727641	+	0.685958i	$0.759383\pi$
$164$	12.5867	0.982855
$165$	−8.02834	−0.625005
$166$	−4.95764	−0.384788
$167$	11.3984	0.882034	0.441017	−	0.897499i	$-0.354618\pi$
$167$	11.3984	0.882034	0.441017	+	0.897499i	$0.354618\pi$
$168$	−1.56321	−0.120604
$169$	−12.9093	−0.993026
$170$	14.5483	1.11581
$171$	1.16195	0.0888565
$172$	1.65232	0.125988
$173$	15.0871	1.14705	0.573525	−	0.819188i	$-0.305576\pi$
$173$	15.0871	1.14705	0.573525	+	0.819188i	$0.305576\pi$
$174$	−19.8638	−1.50587
$175$	−1.00000	−0.0755929
$176$	28.5310	2.15061
$177$	−16.4402	−1.23572
$178$	−17.1871	−1.28823
$179$	−13.5529	−1.01299	−0.506496	−	0.862242i	$-0.669059\pi$
$179$	−13.5529	−1.01299	−0.506496	+	0.862242i	$0.669059\pi$
$180$	−1.55934	−0.116226
$181$	17.5745	1.30631	0.653153	−	0.757226i	$-0.273446\pi$
$181$	17.5745	1.30631	0.653153	+	0.757226i	$0.273446\pi$
$182$	−0.553396	−0.0410205
$183$	−17.5973	−1.30083
$184$	0.798549	0.0588698
$185$	−2.22845	−0.163839
$186$	26.9669	1.97731
$187$	46.4967	3.40018
$188$	−3.00166	−0.218919
$189$	5.64743	0.410790
$190$	1.88674	0.136878
$191$	0.523404	0.0378722	0.0189361	−	0.999821i	$-0.493972\pi$
$191$	0.523404	0.0378722	0.0189361	+	0.999821i	$0.493972\pi$
$192$	−3.40072	−0.245426
$193$	12.5284	0.901815	0.450908	−	0.892571i	$-0.351100\pi$
$193$	12.5284	0.901815	0.450908	+	0.892571i	$0.351100\pi$
$194$	−0.129569	−0.00930254
$195$	−0.411559	−0.0294724
$196$	1.37770	0.0984072
$197$	3.81899	0.272092	0.136046	−	0.990703i	$-0.456561\pi$
$197$	3.81899	0.272092	0.136046	+	0.990703i	$0.456561\pi$
$198$	−12.2185	−0.868328
$199$	7.28162	0.516180	0.258090	−	0.966121i	$-0.416907\pi$
$199$	7.28162	0.516180	0.258090	+	0.966121i	$0.416907\pi$
$200$	1.14369	0.0808714
$201$	5.84482	0.412262
$202$	10.3404	0.727545
$203$	−7.90761	−0.555005
$204$	−14.9061	−1.04364
$205$	9.13601	0.638086
$206$	−11.4930	−0.800755
$207$	−0.790274	−0.0549279
$208$	1.46260	0.101413
$209$	6.03003	0.417106
$210$	2.51199	0.173343
$211$	−14.6729	−1.01012	−0.505062	−	0.863083i	$-0.668530\pi$
$211$	−14.6729	−1.01012	−0.505062	+	0.863083i	$0.668530\pi$
$212$	6.73271	0.462405
$213$	−11.3093	−0.774901
$214$	29.3014	2.00300
$215$	1.19933	0.0817939
$216$	−6.45893	−0.439475
$217$	10.7353	0.728759
$218$	−8.41084	−0.569654
$219$	13.5847	0.917972
$220$	−8.09233	−0.545585
$221$	2.38357	0.160337
$222$	5.59782	0.375701
$223$	25.1757	1.68589	0.842944	−	0.538001i	$-0.180820\pi$
$223$	25.1757	1.68589	0.842944	+	0.538001i	$0.180820\pi$
$224$	−6.63969	−0.443633
$225$	−1.13184	−0.0754563
$226$	−17.2973	−1.15060
$227$	−9.91258	−0.657921	−0.328961	−	0.944344i	$-0.606698\pi$
$227$	−9.91258	−0.657921	−0.328961	+	0.944344i	$0.606698\pi$
$228$	−1.93313	−0.128025
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−1.28322	−0.0846131
$231$	8.02834	0.528226
$232$	9.04389	0.593760
$233$	16.7277	1.09587	0.547935	−	0.836521i	$-0.315414\pi$
$233$	16.7277	1.09587	0.547935	+	0.836521i	$0.315414\pi$
$234$	−0.626358	−0.0409463
$235$	−2.17875	−0.142126
$236$	−16.5712	−1.07870
$237$	5.29482	0.343935
$238$	−14.5483	−0.943029
$239$	−10.7489	−0.695288	−0.347644	−	0.937627i	$-0.613018\pi$
$239$	−10.7489	−0.695288	−0.347644	+	0.937627i	$0.613018\pi$
$240$	−6.63904	−0.428548
$241$	2.76102	0.177853	0.0889265	−	0.996038i	$-0.471656\pi$
$241$	2.76102	0.177853	0.0889265	+	0.996038i	$0.471656\pi$
$242$	−43.1923	−2.77651
$243$	11.0330	0.707770
$244$	−17.7376	−1.13553
$245$	1.00000	0.0638877
$246$	−22.9495	−1.46321
$247$	0.309119	0.0196688
$248$	−12.2779	−0.779647
$249$	3.68698	0.233653
$250$	−1.83785	−0.116236
$251$	−13.2662	−0.837355	−0.418677	−	0.908135i	$-0.637506\pi$
$251$	−13.2662	−0.837355	−0.418677	+	0.908135i	$0.637506\pi$
$252$	1.55934	0.0982293
$253$	−4.10119	−0.257840
$254$	14.8382	0.931033
$255$	−10.8196	−0.677547
$256$	20.9777	1.31111
$257$	−13.3895	−0.835213	−0.417606	−	0.908628i	$-0.637131\pi$
$257$	−13.3895	−0.835213	−0.417606	+	0.908628i	$0.637131\pi$
$258$	−3.01271	−0.187563
$259$	2.22845	0.138469
$260$	−0.414840	−0.0257273
$261$	−8.95018	−0.554002
$262$	12.0440	0.744079
$263$	−0.969053	−0.0597543	−0.0298772	−	0.999554i	$-0.509512\pi$
$263$	−0.969053	−0.0597543	−0.0298772	+	0.999554i	$0.509512\pi$
$264$	−9.18197	−0.565111
$265$	4.88692	0.300201
$266$	−1.88674	−0.115683
$267$	12.7820	0.782245
$268$	5.89141	0.359875
$269$	15.1465	0.923499	0.461750	−	0.887010i	$-0.347222\pi$
$269$	15.1465	0.923499	0.461750	+	0.887010i	$0.347222\pi$
$270$	10.3791	0.631654
$271$	−8.96915	−0.544837	−0.272419	−	0.962179i	$-0.587824\pi$
$271$	−8.96915	−0.544837	−0.272419	+	0.962179i	$0.587824\pi$
$272$	38.4505	2.33140
$273$	0.411559	0.0249087
$274$	−29.6556	−1.79156
$275$	−5.87380	−0.354203
$276$	1.31478	0.0791403
$277$	−28.9561	−1.73980	−0.869901	−	0.493227i	$-0.835817\pi$
$277$	−28.9561	−1.73980	−0.869901	+	0.493227i	$0.835817\pi$
$278$	−34.6558	−2.07852
$279$	12.1507	0.727442
$280$	−1.14369	−0.0683488
$281$	25.7586	1.53663	0.768314	−	0.640074i	$-0.221096\pi$
$281$	25.7586	1.53663	0.768314	+	0.640074i	$0.221096\pi$
$282$	5.47299	0.325912
$283$	−24.9421	−1.48266	−0.741328	−	0.671143i	$-0.765804\pi$
$283$	−24.9421	−1.48266	−0.741328	+	0.671143i	$0.765804\pi$
$284$	−11.3995	−0.676433
$285$	−1.40316	−0.0831160
$286$	−3.25054	−0.192208
$287$	−9.13601	−0.539282
$288$	−7.51509	−0.442831
$289$	45.6623	2.68602
$290$	−14.5330	−0.853408
$291$	0.0963604	0.00564874
$292$	13.6930	0.801324
$293$	3.59756	0.210172	0.105086	−	0.994463i	$-0.466488\pi$
$293$	3.59756	0.210172	0.105086	+	0.994463i	$0.466488\pi$
$294$	−2.51199	−0.146502
$295$	−12.0282	−0.700309
$296$	−2.54866	−0.148138
$297$	33.1718	1.92483
$298$	26.2363	1.51983
$299$	−0.210241	−0.0121585
$300$	1.88305	0.108718
$301$	−1.19933	−0.0691284
$302$	−32.7462	−1.88433
$303$	−7.69009	−0.441784
$304$	4.98654	0.285998
$305$	−12.8748	−0.737209
$306$	−16.4665	−0.941325
$307$	13.5853	0.775354	0.387677	−	0.921795i	$-0.373278\pi$
$307$	13.5853	0.775354	0.387677	+	0.921795i	$0.373278\pi$
$308$	8.09233	0.461103
$309$	8.54731	0.486239
$310$	19.7299	1.12058
$311$	24.1917	1.37179	0.685893	−	0.727702i	$-0.259412\pi$
$311$	24.1917	1.37179	0.685893	+	0.727702i	$0.259412\pi$
$312$	−0.470698	−0.0266480
$313$	3.36258	0.190064	0.0950321	−	0.995474i	$-0.469705\pi$
$313$	3.36258	0.190064	0.0950321	+	0.995474i	$0.469705\pi$
$314$	−27.3470	−1.54328
$315$	1.13184	0.0637722
$316$	5.33703	0.300231
$317$	−19.5434	−1.09766	−0.548832	−	0.835933i	$-0.684927\pi$
$317$	−19.5434	−1.09766	−0.548832	+	0.835933i	$0.684927\pi$
$318$	−12.2759	−0.688397
$319$	−46.4477	−2.60057
$320$	−2.48808	−0.139088
$321$	−21.7914	−1.21628
$322$	1.28322	0.0715112
$323$	8.12650	0.452171
$324$	−5.95634	−0.330908
$325$	−0.301110	−0.0167026
$326$	34.1469	1.89122
$327$	6.25511	0.345909
$328$	10.4488	0.576939
$329$	2.17875	0.120118
$330$	14.7549	0.812230
$331$	24.7013	1.35771	0.678854	−	0.734273i	$-0.262477\pi$
$331$	24.7013	1.35771	0.678854	+	0.734273i	$0.262477\pi$
$332$	3.71637	0.203962
$333$	2.52225	0.138219
$334$	−20.9486	−1.14625
$335$	4.27626	0.233637
$336$	6.63904	0.362189
$337$	4.28091	0.233196	0.116598	−	0.993179i	$-0.462801\pi$
$337$	4.28091	0.233196	0.116598	+	0.993179i	$0.462801\pi$
$338$	23.7254	1.29049
$339$	12.8639	0.698672
$340$	−10.9058	−0.591451
$341$	63.0569	3.41473
$342$	−2.13549	−0.115474
$343$	−1.00000	−0.0539949
$344$	1.37167	0.0739556
$345$	0.954328	0.0513793
$346$	−27.7278	−1.49066
$347$	−6.61223	−0.354963	−0.177482	−	0.984124i	$-0.556795\pi$
$347$	−6.61223	−0.354963	−0.177482	+	0.984124i	$0.556795\pi$
$348$	14.8904	0.798209
$349$	−33.4548	−1.79080	−0.895398	−	0.445267i	$-0.853109\pi$
$349$	−33.4548	−1.79080	−0.895398	+	0.445267i	$0.853109\pi$
$350$	1.83785	0.0982373
$351$	1.70050	0.0907659
$352$	−39.0002	−2.07872
$353$	−17.1343	−0.911967	−0.455984	−	0.889988i	$-0.650712\pi$
$353$	−17.1343	−0.911967	−0.455984	+	0.889988i	$0.650712\pi$
$354$	30.2147	1.60589
$355$	−8.27426	−0.439152
$356$	12.8839	0.682844
$357$	10.8196	0.572632
$358$	24.9082	1.31644
$359$	25.9699	1.37064	0.685319	−	0.728243i	$-0.259663\pi$
$359$	25.9699	1.37064	0.685319	+	0.728243i	$0.259663\pi$
$360$	−1.29448	−0.0682253
$361$	−17.9461	−0.944531
$362$	−32.2994	−1.69762
$363$	32.1220	1.68597
$364$	0.414840	0.0217435
$365$	9.93905	0.520234
$366$	32.3413	1.69051
$367$	10.2450	0.534783	0.267392	−	0.963588i	$-0.413838\pi$
$367$	10.2450	0.534783	0.267392	+	0.963588i	$0.413838\pi$
$368$	−3.39149	−0.176793
$369$	−10.3405	−0.538307
$370$	4.09555	0.212918
$371$	−4.88692	−0.253716
$372$	−20.2151	−1.04810
$373$	−9.47638	−0.490668	−0.245334	−	0.969439i	$-0.578898\pi$
$373$	−9.47638	−0.490668	−0.245334	+	0.969439i	$0.578898\pi$
$374$	−85.4541	−4.41872
$375$	1.36680	0.0705815
$376$	−2.49182	−0.128506
$377$	−2.38106	−0.122631
$378$	−10.3791	−0.533845
$379$	1.18149	0.0606891	0.0303445	−	0.999539i	$-0.490340\pi$
$379$	1.18149	0.0606891	0.0303445	+	0.999539i	$0.490340\pi$
$380$	−1.41434	−0.0725543
$381$	−11.0351	−0.565347
$382$	−0.961938	−0.0492170
$383$	5.68477	0.290478	0.145239	−	0.989397i	$-0.453605\pi$
$383$	5.68477	0.290478	0.145239	+	0.989397i	$0.453605\pi$
$384$	−11.9003	−0.607285
$385$	5.87380	0.299356
$386$	−23.0254	−1.17196
$387$	−1.35746	−0.0690035
$388$	0.0971285	0.00493095
$389$	28.9858	1.46964	0.734819	−	0.678264i	$-0.237267\pi$
$389$	28.9858	1.46964	0.734819	+	0.678264i	$0.237267\pi$
$390$	0.756385	0.0383010
$391$	−5.52706	−0.279516
$392$	1.14369	0.0577653
$393$	−8.95707	−0.451824
$394$	−7.01874	−0.353599
$395$	3.87387	0.194915
$396$	9.15926	0.460270
$397$	−18.4388	−0.925419	−0.462709	−	0.886510i	$-0.653123\pi$
$397$	−18.4388	−0.925419	−0.462709	+	0.886510i	$0.653123\pi$
$398$	−13.3825	−0.670806
$399$	1.40316	0.0702458
$400$	−4.85734	−0.242867
$401$	−5.99441	−0.299346	−0.149673	−	0.988736i	$-0.547822\pi$
$401$	−5.99441	−0.299346	−0.149673	+	0.988736i	$0.547822\pi$
$402$	−10.7419	−0.535758
$403$	3.23251	0.161023
$404$	−7.75139	−0.385646
$405$	−4.32340	−0.214831
$406$	14.5330	0.721261
$407$	13.0894	0.648820
$408$	−12.3743	−0.612618
$409$	32.4684	1.60546	0.802730	−	0.596343i	$-0.203380\pi$
$409$	32.4684	1.60546	0.802730	+	0.596343i	$0.203380\pi$
$410$	−16.7906	−0.829230
$411$	22.0548	1.08788
$412$	8.61544	0.424452
$413$	12.0282	0.591869
$414$	1.45241	0.0713819
$415$	2.69752	0.132416
$416$	−1.99928	−0.0980227
$417$	25.7734	1.26213
$418$	−11.0823	−0.542053
$419$	−31.6931	−1.54831	−0.774155	−	0.632997i	$-0.781825\pi$
$419$	−31.6931	−1.54831	−0.774155	+	0.632997i	$0.781825\pi$
$420$	−1.88305	−0.0918833
$421$	14.2976	0.696822	0.348411	−	0.937342i	$-0.386721\pi$
$421$	14.2976	0.696822	0.348411	+	0.937342i	$0.386721\pi$
$422$	26.9666	1.31271
$423$	2.46600	0.119901
$424$	5.58915	0.271433
$425$	−7.91595	−0.383980
$426$	20.7848	1.00703
$427$	12.8748	0.623055
$428$	−21.9651	−1.06172
$429$	2.41741	0.116714
$430$	−2.20420	−0.106296
$431$	−19.5193	−0.940212	−0.470106	−	0.882610i	$-0.655784\pi$
$431$	−19.5193	−0.940212	−0.470106	+	0.882610i	$0.655784\pi$
$432$	27.4315	1.31980
$433$	−28.6768	−1.37812	−0.689060	−	0.724704i	$-0.741976\pi$
$433$	−28.6768	−1.37812	−0.689060	+	0.724704i	$0.741976\pi$
$434$	−19.7299	−0.947065
$435$	10.8082	0.518211
$436$	6.30497	0.301954
$437$	−0.716789	−0.0342887
$438$	−24.9667	−1.19296
$439$	33.6881	1.60785	0.803924	−	0.594732i	$-0.202742\pi$
$439$	33.6881	1.60785	0.803924	+	0.594732i	$0.202742\pi$
$440$	−6.71783	−0.320260
$441$	−1.13184	−0.0538973
$442$	−4.38066	−0.208367
$443$	−32.6703	−1.55221	−0.776106	−	0.630603i	$-0.782808\pi$
$443$	−32.6703	−1.55221	−0.776106	+	0.630603i	$0.782808\pi$
$444$	−4.19627	−0.199146
$445$	9.35172	0.443314
$446$	−46.2692	−2.19091
$447$	−19.5119	−0.922880
$448$	2.48808	0.117551
$449$	−20.2572	−0.955997	−0.477999	−	0.878361i	$-0.658638\pi$
$449$	−20.2572	−0.955997	−0.477999	+	0.878361i	$0.658638\pi$
$450$	2.08016	0.0980598
$451$	−53.6631	−2.52690
$452$	12.9665	0.609891
$453$	24.3532	1.14422
$454$	18.2179	0.855007
$455$	0.301110	0.0141163
$456$	−1.60479	−0.0751510
$457$	−5.55927	−0.260052	−0.130026	−	0.991511i	$-0.541506\pi$
$457$	−5.55927	−0.260052	−0.130026	+	0.991511i	$0.541506\pi$
$458$	1.83785	0.0858772
$459$	44.7047	2.08664
$460$	0.961935	0.0448505
$461$	17.0865	0.795797	0.397899	−	0.917429i	$-0.369740\pi$
$461$	17.0865	0.795797	0.397899	+	0.917429i	$0.369740\pi$
$462$	−14.7549	−0.686460
$463$	4.59560	0.213576	0.106788	−	0.994282i	$-0.465943\pi$
$463$	4.59560	0.213576	0.106788	+	0.994282i	$0.465943\pi$
$464$	−38.4100	−1.78314
$465$	−14.6731	−0.680447
$466$	−30.7431	−1.42415
$467$	−33.9793	−1.57237	−0.786187	−	0.617988i	$-0.787948\pi$
$467$	−33.9793	−1.57237	−0.786187	+	0.617988i	$0.787948\pi$
$468$	0.469534	0.0217042
$469$	−4.27626	−0.197460
$470$	4.00422	0.184701
$471$	20.3379	0.937121
$472$	−13.7566	−0.633198
$473$	−7.04464	−0.323913
$474$	−9.73109	−0.446964
$475$	−1.02660	−0.0471035
$476$	10.9058	0.499867
$477$	−5.53123	−0.253258
$478$	19.7549	0.903566
$479$	−12.5069	−0.571456	−0.285728	−	0.958311i	$-0.592235\pi$
$479$	−12.5069	−0.571456	−0.285728	+	0.958311i	$0.592235\pi$
$480$	9.07516	0.414222
$481$	0.671008	0.0305953
$482$	−5.07435	−0.231130
$483$	−0.954328	−0.0434234
$484$	32.3780	1.47173
$485$	0.0705004	0.00320126
$486$	−20.2771	−0.919787
$487$	−5.88320	−0.266593	−0.133297	−	0.991076i	$-0.542556\pi$
$487$	−5.88320	−0.266593	−0.133297	+	0.991076i	$0.542556\pi$
$488$	−14.7248	−0.666562
$489$	−25.3950	−1.14840
$490$	−1.83785	−0.0830257
$491$	9.57425	0.432080	0.216040	−	0.976385i	$-0.430686\pi$
$491$	9.57425	0.432080	0.216040	+	0.976385i	$0.430686\pi$
$492$	17.2035	0.775595
$493$	−62.5962	−2.81919
$494$	−0.568115	−0.0255607
$495$	6.64822	0.298815
$496$	52.1450	2.34138
$497$	8.27426	0.371151
$498$	−6.77613	−0.303646
$499$	25.2927	1.13226	0.566128	−	0.824317i	$-0.308441\pi$
$499$	25.2927	1.13226	0.566128	+	0.824317i	$0.308441\pi$
$500$	1.37770	0.0616126
$501$	15.5794	0.696035
$502$	24.3813	1.08819
$503$	37.1260	1.65537	0.827684	−	0.561194i	$-0.189658\pi$
$503$	37.1260	1.65537	0.827684	+	0.561194i	$0.189658\pi$
$504$	1.29448	0.0576609
$505$	−5.62632	−0.250368
$506$	7.53739	0.335078
$507$	−17.6445	−0.783622
$508$	−11.1231	−0.493508
$509$	36.6185	1.62309	0.811544	−	0.584292i	$-0.198628\pi$
$509$	36.6185	1.62309	0.811544	+	0.584292i	$0.198628\pi$
$510$	19.8848	0.880512
$511$	−9.93905	−0.439678
$512$	−21.1406	−0.934291
$513$	5.79764	0.255972
$514$	24.6079	1.08541
$515$	6.25350	0.275562
$516$	2.25840	0.0994206
$517$	12.7975	0.562835
$518$	−4.09555	−0.179948
$519$	20.6211	0.905166
$520$	−0.344378	−0.0151020
$521$	−11.0751	−0.485209	−0.242604	−	0.970125i	$-0.578002\pi$
$521$	−11.0751	−0.485209	−0.242604	+	0.970125i	$0.578002\pi$
$522$	16.4491	0.719958
$523$	8.16738	0.357135	0.178567	−	0.983928i	$-0.442854\pi$
$523$	8.16738	0.357135	0.178567	+	0.983928i	$0.442854\pi$
$524$	−9.02847	−0.394410
$525$	−1.36680	−0.0596523
$526$	1.78098	0.0776542
$527$	84.9801	3.70179
$528$	38.9964	1.69710
$529$	−22.5125	−0.978804
$530$	−8.98144	−0.390129
$531$	13.6140	0.590799
$532$	1.41434	0.0613196
$533$	−2.75095	−0.119157
$534$	−23.4914	−1.01657
$535$	−15.9433	−0.689289
$536$	4.89074	0.211248
$537$	−18.5242	−0.799377
$538$	−27.8371	−1.20014
$539$	−5.87380	−0.253002
$540$	−7.78046	−0.334818
$541$	3.78663	0.162800	0.0814000	−	0.996682i	$-0.474061\pi$
$541$	3.78663	0.162800	0.0814000	+	0.996682i	$0.474061\pi$
$542$	16.4840	0.708047
$543$	24.0210	1.03084
$544$	−52.5594	−2.25347
$545$	4.57645	0.196034
$546$	−0.756385	−0.0323703
$547$	5.78129	0.247190	0.123595	−	0.992333i	$-0.460558\pi$
$547$	5.78129	0.247190	0.123595	+	0.992333i	$0.460558\pi$
$548$	22.2306	0.949642
$549$	14.5723	0.621929
$550$	10.7952	0.460308
$551$	−8.11793	−0.345836
$552$	1.09146	0.0464556
$553$	−3.87387	−0.164734
$554$	53.2170	2.26097
$555$	−3.04585	−0.129289
$556$	25.9789	1.10175
$557$	−12.9246	−0.547631	−0.273816	−	0.961782i	$-0.588286\pi$
$557$	−12.9246	−0.547631	−0.273816	+	0.961782i	$0.588286\pi$
$558$	−22.3312	−0.945353
$559$	−0.361132	−0.0152742
$560$	4.85734	0.205260
$561$	63.5519	2.68316
$562$	−47.3404	−1.99694
$563$	−35.2921	−1.48739	−0.743693	−	0.668521i	$-0.766928\pi$
$563$	−35.2921	−1.48739	−0.743693	+	0.668521i	$0.766928\pi$
$564$	−4.10269	−0.172754
$565$	9.41167	0.395952
$566$	45.8400	1.92680
$567$	4.32340	0.181566
$568$	−9.46323	−0.397068
$569$	4.21785	0.176821	0.0884106	−	0.996084i	$-0.471821\pi$
$569$	4.21785	0.176821	0.0884106	+	0.996084i	$0.471821\pi$
$570$	2.57880	0.108014
$571$	−0.826933	−0.0346061	−0.0173030	−	0.999850i	$-0.505508\pi$
$571$	−0.826933	−0.0346061	−0.0173030	+	0.999850i	$0.505508\pi$
$572$	2.43668	0.101883
$573$	0.715391	0.0298859
$574$	16.7906	0.700827
$575$	0.698218	0.0291177
$576$	2.81612	0.117338
$577$	−6.30093	−0.262311	−0.131156	−	0.991362i	$-0.541869\pi$
$577$	−6.30093	−0.262311	−0.131156	+	0.991362i	$0.541869\pi$
$578$	−83.9206	−3.49064
$579$	17.1239	0.711645
$580$	10.8943	0.452362
$581$	−2.69752	−0.111912
$582$	−0.177096	−0.00734087
$583$	−28.7048	−1.18883
$584$	11.3672	0.470380
$585$	0.340810	0.0140908
$586$	−6.61179	−0.273130
$587$	−12.6304	−0.521313	−0.260656	−	0.965432i	$-0.583939\pi$
$587$	−12.6304	−0.521313	−0.260656	+	0.965432i	$0.583939\pi$
$588$	1.88305	0.0776556
$589$	11.0208	0.454105
$590$	22.1060	0.910091
$591$	5.21982	0.214715
$592$	10.8243	0.444877
$593$	−35.4508	−1.45579	−0.727895	−	0.685688i	$-0.759501\pi$
$593$	−35.4508	−1.45579	−0.727895	+	0.685688i	$0.759501\pi$
$594$	−60.9649	−2.50142
$595$	7.91595	0.324522
$596$	−19.6674	−0.805608
$597$	9.95255	0.407331
$598$	0.386391	0.0158007
$599$	−23.9988	−0.980566	−0.490283	−	0.871563i	$-0.663107\pi$
$599$	−23.9988	−0.980566	−0.490283	+	0.871563i	$0.663107\pi$
$600$	1.56321	0.0638177
$601$	37.1382	1.51490	0.757450	−	0.652894i	$-0.226445\pi$
$601$	37.1382	1.51490	0.757450	+	0.652894i	$0.226445\pi$
$602$	2.20420	0.0898364
$603$	−4.84006	−0.197103
$604$	24.5474	0.998818
$605$	23.5015	0.955472
$606$	14.1332	0.574124
$607$	41.6830	1.69186	0.845931	−	0.533293i	$-0.179046\pi$
$607$	41.6830	1.69186	0.845931	+	0.533293i	$0.179046\pi$
$608$	−6.81629	−0.276437
$609$	−10.8082	−0.437969
$610$	23.6620	0.958045
$611$	0.656044	0.0265407
$612$	12.3437	0.498964
$613$	23.1323	0.934305	0.467152	−	0.884177i	$-0.345280\pi$
$613$	23.1323	0.934305	0.467152	+	0.884177i	$0.345280\pi$
$614$	−24.9678	−1.00762
$615$	12.4871	0.503530
$616$	6.71783	0.270669
$617$	−23.5788	−0.949245	−0.474622	−	0.880189i	$-0.657415\pi$
$617$	−23.5788	−0.949245	−0.474622	+	0.880189i	$0.657415\pi$
$618$	−15.7087	−0.631896
$619$	2.56932	0.103270	0.0516349	−	0.998666i	$-0.483557\pi$
$619$	2.56932	0.103270	0.0516349	+	0.998666i	$0.483557\pi$
$620$	−14.7900	−0.593981
$621$	−3.94314	−0.158233
$622$	−44.4608	−1.78271
$623$	−9.35172	−0.374669
$624$	1.99908	0.0800274
$625$	1.00000	0.0400000
$626$	−6.17992	−0.246999
$627$	8.24187	0.329149
$628$	20.5000	0.818040
$629$	17.6403	0.703364
$630$	−2.08016	−0.0828756
$631$	26.2694	1.04577	0.522884	−	0.852404i	$-0.324856\pi$
$631$	26.2694	1.04577	0.522884	+	0.852404i	$0.324856\pi$
$632$	4.43052	0.176237
$633$	−20.0550	−0.797115
$634$	35.9178	1.42648
$635$	−8.07368	−0.320394
$636$	9.20231	0.364895
$637$	−0.301110	−0.0119304
$638$	85.3640	3.37959
$639$	9.36518	0.370481
$640$	−8.70666	−0.344161
$641$	29.9653	1.18356	0.591779	−	0.806101i	$-0.298426\pi$
$641$	29.9653	1.18356	0.591779	+	0.806101i	$0.298426\pi$
$642$	40.0493	1.58062
$643$	−33.9642	−1.33942	−0.669708	−	0.742624i	$-0.733581\pi$
$643$	−33.9642	−1.33942	−0.669708	+	0.742624i	$0.733581\pi$
$644$	−0.961935	−0.0379056
$645$	1.63925	0.0645456
$646$	−14.9353	−0.587622
$647$	−3.13672	−0.123317	−0.0616585	−	0.998097i	$-0.519639\pi$
$647$	−3.13672	−0.123317	−0.0616585	+	0.998097i	$0.519639\pi$
$648$	−4.94465	−0.194244
$649$	70.6512	2.77330
$650$	0.553396	0.0217060
$651$	14.6731	0.575082
$652$	−25.5974	−1.00247
$653$	−3.76135	−0.147193	−0.0735965	−	0.997288i	$-0.523448\pi$
$653$	−3.76135	−0.147193	−0.0735965	+	0.997288i	$0.523448\pi$
$654$	−11.4960	−0.449528
$655$	−6.55329	−0.256058
$656$	−44.3767	−1.73262
$657$	−11.2495	−0.438883
$658$	−4.00422	−0.156101
$659$	−22.8876	−0.891574	−0.445787	−	0.895139i	$-0.647076\pi$
$659$	−22.8876	−0.891574	−0.445787	+	0.895139i	$0.647076\pi$
$660$	−11.0606	−0.430535
$661$	−30.9467	−1.20369	−0.601843	−	0.798615i	$-0.705567\pi$
$661$	−30.9467	−1.20369	−0.601843	+	0.798615i	$0.705567\pi$
$662$	−45.3974	−1.76442
$663$	3.25788	0.126526
$664$	3.08514	0.119727
$665$	1.02660	0.0398098
$666$	−4.63553	−0.179623
$667$	5.52124	0.213783
$668$	15.7036	0.607589
$669$	34.4102	1.33038
$670$	−7.85914	−0.303625
$671$	75.6239	2.91943
$672$	−9.07516	−0.350082
$673$	−1.80199	−0.0694616	−0.0347308	−	0.999397i	$-0.511057\pi$
$673$	−1.80199	−0.0694616	−0.0347308	+	0.999397i	$0.511057\pi$
$674$	−7.86768	−0.303052
$675$	−5.64743	−0.217369
$676$	−17.7852	−0.684046
$677$	−4.51874	−0.173669	−0.0868347	−	0.996223i	$-0.527675\pi$
$677$	−4.51874	−0.173669	−0.0868347	+	0.996223i	$0.527675\pi$
$678$	−23.6420	−0.907965
$679$	−0.0705004	−0.00270556
$680$	−9.05343	−0.347183
$681$	−13.5486	−0.519182
$682$	−115.889	−4.43763
$683$	20.3109	0.777176	0.388588	−	0.921412i	$-0.372963\pi$
$683$	20.3109	0.777176	0.388588	+	0.921412i	$0.372963\pi$
$684$	1.60082	0.0612088
$685$	16.1360	0.616525
$686$	1.83785	0.0701695
$687$	−1.36680	−0.0521469
$688$	−5.82557	−0.222098
$689$	−1.47150	−0.0560598
$690$	−1.75391	−0.0667704
$691$	23.5400	0.895502	0.447751	−	0.894158i	$-0.352225\pi$
$691$	23.5400	0.895502	0.447751	+	0.894158i	$0.352225\pi$
$692$	20.7855	0.790146
$693$	−6.64822	−0.252545
$694$	12.1523	0.461295
$695$	18.8567	0.715276
$696$	12.3612	0.468551
$697$	−72.3202	−2.73932
$698$	61.4850	2.32724
$699$	22.8635	0.864778
$700$	−1.37770	−0.0520722
$701$	23.4587	0.886024	0.443012	−	0.896516i	$-0.353910\pi$
$701$	23.4587	0.886024	0.443012	+	0.896516i	$0.353910\pi$
$702$	−3.12526	−0.117955
$703$	2.28772	0.0862829
$704$	14.6145	0.550803
$705$	−2.97793	−0.112155
$706$	31.4903	1.18515
$707$	5.62632	0.211600
$708$	−22.6497	−0.851227
$709$	−9.19983	−0.345507	−0.172753	−	0.984965i	$-0.555266\pi$
$709$	−9.19983	−0.345507	−0.172753	+	0.984965i	$0.555266\pi$
$710$	15.2069	0.570704
$711$	−4.38461	−0.164436
$712$	10.6955	0.400832
$713$	−7.49558	−0.280712
$714$	−19.8848	−0.744168
$715$	1.76866	0.0661442
$716$	−18.6718	−0.697799
$717$	−14.6916	−0.548669
$718$	−47.7288	−1.78122
$719$	−30.0189	−1.11951	−0.559757	−	0.828657i	$-0.689106\pi$
$719$	−30.0189	−1.11951	−0.559757	+	0.828657i	$0.689106\pi$
$720$	5.49775	0.204889
$721$	−6.25350	−0.232892
$722$	32.9823	1.22747
$723$	3.77378	0.140348
$724$	24.2124	0.899849
$725$	7.90761	0.293681
$726$	−59.0354	−2.19101
$727$	−11.6486	−0.432021	−0.216011	−	0.976391i	$-0.569305\pi$
$727$	−11.6486	−0.432021	−0.216011	+	0.976391i	$0.569305\pi$
$728$	0.344378	0.0127635
$729$	28.0502	1.03890
$730$	−18.2665	−0.676073
$731$	−9.49387	−0.351143
$732$	−24.2439	−0.896079
$733$	9.60610	0.354809	0.177405	−	0.984138i	$-0.443230\pi$
$733$	9.60610	0.354809	0.177405	+	0.984138i	$0.443230\pi$
$734$	−18.8287	−0.694982
$735$	1.36680	0.0504154
$736$	4.63595	0.170883
$737$	−25.1179	−0.925230
$738$	19.0044	0.699561
$739$	23.3884	0.860357	0.430179	−	0.902744i	$-0.358451\pi$
$739$	23.3884	0.860357	0.430179	+	0.902744i	$0.358451\pi$
$740$	−3.07013	−0.112860
$741$	0.422506	0.0155211
$742$	8.98144	0.329719
$743$	−32.2222	−1.18212	−0.591060	−	0.806628i	$-0.701290\pi$
$743$	−32.2222	−1.18212	−0.591060	+	0.806628i	$0.701290\pi$
$744$	−16.7815	−0.615239
$745$	−14.2755	−0.523015
$746$	17.4162	0.637652
$747$	−3.05317	−0.111710
$748$	64.0585	2.34221
$749$	15.9433	0.582555
$750$	−2.51199	−0.0917247
$751$	0.550988	0.0201058	0.0100529	−	0.999949i	$-0.496800\pi$
$751$	0.550988	0.0201058	0.0100529	+	0.999949i	$0.496800\pi$
$752$	10.5829	0.385920
$753$	−18.1323	−0.660778
$754$	4.37604	0.159366
$755$	17.8176	0.648450
$756$	7.78046	0.282973
$757$	−13.6055	−0.494500	−0.247250	−	0.968952i	$-0.579527\pi$
$757$	−13.6055	−0.494500	−0.247250	+	0.968952i	$0.579527\pi$
$758$	−2.17140	−0.0788689
$759$	−5.60553	−0.203468
$760$	−1.17411	−0.0425896
$761$	8.26796	0.299713	0.149857	−	0.988708i	$-0.452119\pi$
$761$	8.26796	0.299713	0.149857	+	0.988708i	$0.452119\pi$
$762$	20.2810	0.734702
$763$	−4.57645	−0.165679
$764$	0.721093	0.0260882
$765$	8.95962	0.323936
$766$	−10.4478	−0.377493
$767$	3.62181	0.130776
$768$	28.6724	1.03463
$769$	−13.7990	−0.497606	−0.248803	−	0.968554i	$-0.580037\pi$
$769$	−13.7990	−0.497606	−0.248803	+	0.968554i	$0.580037\pi$
$770$	−10.7952	−0.389031
$771$	−18.3008	−0.659088
$772$	17.2604	0.621215
$773$	2.51463	0.0904451	0.0452225	−	0.998977i	$-0.485600\pi$
$773$	2.51463	0.0904451	0.0452225	+	0.998977i	$0.485600\pi$
$774$	2.49481	0.0896740
$775$	−10.7353	−0.385623
$776$	0.0806310	0.00289448
$777$	3.04585	0.109269
$778$	−53.2716	−1.90988
$779$	−9.37901	−0.336038
$780$	−0.567005	−0.0203020
$781$	48.6013	1.73909
$782$	10.1579	0.363247
$783$	−44.6576	−1.59593
$784$	−4.85734	−0.173477
$785$	14.8799	0.531086
$786$	16.4618	0.587172
$787$	35.0681	1.25004	0.625021	−	0.780608i	$-0.285091\pi$
$787$	35.0681	1.25004	0.625021	+	0.780608i	$0.285091\pi$
$788$	5.26143	0.187431
$789$	−1.32451	−0.0471537
$790$	−7.11959	−0.253304
$791$	−9.41167	−0.334640
$792$	7.60354	0.270180
$793$	3.87673	0.137667
$794$	33.8879	1.20264
$795$	6.67947	0.236896
$796$	10.0319	0.355571
$797$	−55.7412	−1.97445	−0.987226	−	0.159323i	$-0.949069\pi$
$797$	−55.7412	−1.97445	−0.987226	+	0.159323i	$0.949069\pi$
$798$	−2.57880	−0.0912885
$799$	17.2469	0.610151
$800$	6.63969	0.234748
$801$	−10.5847	−0.373992
$802$	11.0168	0.389018
$803$	−58.3800	−2.06018
$804$	8.05241	0.283987
$805$	−0.698218	−0.0246090
$806$	−5.94087	−0.209258
$807$	20.7023	0.728757
$808$	−6.43480	−0.226375
$809$	−37.1410	−1.30581	−0.652903	−	0.757441i	$-0.726449\pi$
$809$	−37.1410	−1.30581	−0.652903	+	0.757441i	$0.726449\pi$
$810$	7.94576	0.279186
$811$	0.427125	0.0149984	0.00749919	−	0.999972i	$-0.497613\pi$
$811$	0.427125	0.0149984	0.00749919	+	0.999972i	$0.497613\pi$
$812$	−10.8943	−0.382315
$813$	−12.2591	−0.429945
$814$	−24.0565	−0.843178
$815$	−18.5798	−0.650822
$816$	52.5543	1.83977
$817$	−1.23123	−0.0430754
$818$	−59.6721	−2.08639
$819$	−0.340810	−0.0119089
$820$	12.5867	0.439546
$821$	−27.8894	−0.973349	−0.486674	−	0.873584i	$-0.661790\pi$
$821$	−27.8894	−0.973349	−0.486674	+	0.873584i	$0.661790\pi$
$822$	−40.5334	−1.41376
$823$	−15.2988	−0.533284	−0.266642	−	0.963796i	$-0.585914\pi$
$823$	−15.2988	−0.533284	−0.266642	+	0.963796i	$0.585914\pi$
$824$	7.15209	0.249155
$825$	−8.02834	−0.279511
$826$	−22.1060	−0.769168
$827$	52.7446	1.83411	0.917055	−	0.398760i	$-0.130559\pi$
$827$	52.7446	1.83411	0.917055	+	0.398760i	$0.130559\pi$
$828$	−1.08876	−0.0378371
$829$	40.8180	1.41767	0.708834	−	0.705376i	$-0.249222\pi$
$829$	40.8180	1.41767	0.708834	+	0.705376i	$0.249222\pi$
$830$	−4.95764	−0.172082
$831$	−39.5773	−1.37292
$832$	0.749186	0.0259733
$833$	−7.91595	−0.274271
$834$	−47.3678	−1.64021
$835$	11.3984	0.394457
$836$	8.30757	0.287323
$837$	60.6268	2.09557
$838$	58.2472	2.01212
$839$	1.79166	0.0618551	0.0309276	−	0.999522i	$-0.490154\pi$
$839$	1.79166	0.0618551	0.0309276	+	0.999522i	$0.490154\pi$
$840$	−1.56321	−0.0539358
$841$	33.5302	1.15622
$842$	−26.2769	−0.905561
$843$	35.2069	1.21259
$844$	−20.2149	−0.695824
$845$	−12.9093	−0.444095
$846$	−4.53215	−0.155819
$847$	−23.5015	−0.807521
$848$	−23.7375	−0.815148
$849$	−34.0910	−1.17000
$850$	14.5483	0.499004
$851$	−1.55594	−0.0533370
$852$	−15.5808	−0.533790
$853$	48.5804	1.66336	0.831681	−	0.555253i	$-0.187379\pi$
$853$	48.5804	1.66336	0.831681	+	0.555253i	$0.187379\pi$
$854$	−23.6620	−0.809696
$855$	1.16195	0.0397378
$856$	−18.2343	−0.623234
$857$	35.7509	1.22123	0.610614	−	0.791928i	$-0.290923\pi$
$857$	35.7509	1.22123	0.610614	+	0.791928i	$0.290923\pi$
$858$	−4.44285	−0.151676
$859$	47.4553	1.61916	0.809578	−	0.587013i	$-0.199696\pi$
$859$	47.4553	1.61916	0.809578	+	0.587013i	$0.199696\pi$
$860$	1.65232	0.0563437
$861$	−12.4871	−0.425561
$862$	35.8736	1.22186
$863$	−31.1653	−1.06088	−0.530440	−	0.847723i	$-0.677973\pi$
$863$	−31.1653	−1.06088	−0.530440	+	0.847723i	$0.677973\pi$
$864$	−37.4971	−1.27568
$865$	15.0871	0.512976
$866$	52.7037	1.79095
$867$	62.4115	2.11960
$868$	14.7900	0.502006
$869$	−22.7543	−0.771887
$870$	−19.8638	−0.673446
$871$	−1.28763	−0.0436296
$872$	5.23406	0.177248
$873$	−0.0797955	−0.00270067
$874$	1.31735	0.0445601
$875$	−1.00000	−0.0338062
$876$	18.7157	0.632345
$877$	−43.4464	−1.46708	−0.733541	−	0.679646i	$-0.762134\pi$
$877$	−43.4464	−1.46708	−0.733541	+	0.679646i	$0.762134\pi$
$878$	−61.9138	−2.08949
$879$	4.91716	0.165852
$880$	28.5310	0.961781
$881$	−14.4092	−0.485457	−0.242728	−	0.970094i	$-0.578042\pi$
$881$	−14.4092	−0.485457	−0.242728	+	0.970094i	$0.578042\pi$
$882$	2.08016	0.0700427
$883$	55.2090	1.85793	0.928966	−	0.370165i	$-0.120699\pi$
$883$	55.2090	1.85793	0.928966	+	0.370165i	$0.120699\pi$
$884$	3.28385	0.110448
$885$	−16.4402	−0.552631
$886$	60.0431	2.01719
$887$	42.1851	1.41644	0.708219	−	0.705993i	$-0.249499\pi$
$887$	42.1851	1.41644	0.708219	+	0.705993i	$0.249499\pi$
$888$	−3.48352	−0.116899
$889$	8.07368	0.270782
$890$	−17.1871	−0.576112
$891$	25.3948	0.850756
$892$	34.6845	1.16132
$893$	2.23670	0.0748483
$894$	35.8599	1.19934
$895$	−13.5529	−0.453024
$896$	8.70666	0.290869
$897$	−0.287358	−0.00959460
$898$	37.2298	1.24237
$899$	−84.8905	−2.83126
$900$	−1.55934	−0.0519781
$901$	−38.6846	−1.28877
$902$	98.6248	3.28385
$903$	−1.63925	−0.0545510
$904$	10.7641	0.358008
$905$	17.5745	0.584198
$906$	−44.7577	−1.48697
$907$	−14.7348	−0.489262	−0.244631	−	0.969616i	$-0.578667\pi$
$907$	−14.7348	−0.489262	−0.244631	+	0.969616i	$0.578667\pi$
$908$	−13.6566	−0.453209
$909$	6.36812	0.211217
$910$	−0.553396	−0.0183449
$911$	0.0191120	0.000633209 0	0.000316604	−	1.00000i	$-0.499899\pi$
$911$	0.0191120	0.000633209 0	0.000316604		1.00000i	$0.499899\pi$
$912$	6.81563	0.225688
$913$	−15.8447	−0.524382
$914$	10.2171	0.337952
$915$	−17.5973	−0.581750
$916$	−1.37770	−0.0455205
$917$	6.55329	0.216409
$918$	−82.1607	−2.71171
$919$	−26.2423	−0.865653	−0.432826	−	0.901477i	$-0.642484\pi$
$919$	−26.2423	−0.865653	−0.432826	+	0.901477i	$0.642484\pi$
$920$	0.798549	0.0263274
$921$	18.5684	0.611851
$922$	−31.4024	−1.03418
$923$	2.49147	0.0820076
$924$	11.0606	0.363868
$925$	−2.22845	−0.0732709
$926$	−8.44604	−0.277554
$927$	−7.07798	−0.232471
$928$	52.5040	1.72353
$929$	24.8797	0.816276	0.408138	−	0.912920i	$-0.366178\pi$
$929$	24.8797	0.816276	0.408138	+	0.912920i	$0.366178\pi$
$930$	26.9669	0.884279
$931$	−1.02660	−0.0336454
$932$	23.0458	0.754890
$933$	33.0653	1.08251
$934$	62.4489	2.04339
$935$	46.4967	1.52060
$936$	0.389783	0.0127404
$937$	−41.2988	−1.34917	−0.674587	−	0.738195i	$-0.735678\pi$
$937$	−41.2988	−1.34917	−0.674587	+	0.738195i	$0.735678\pi$
$938$	7.85914	0.256610
$939$	4.59599	0.149984
$940$	−3.00166	−0.0979035
$941$	−1.85238	−0.0603860	−0.0301930	−	0.999544i	$-0.509612\pi$
$941$	−1.85238	−0.0603860	−0.0301930	+	0.999544i	$0.509612\pi$
$942$	−37.3780	−1.21784
$943$	6.37893	0.207726
$944$	58.4251	1.90157
$945$	5.64743	0.183711
$946$	12.9470	0.420944
$947$	9.33035	0.303196	0.151598	−	0.988442i	$-0.451558\pi$
$947$	9.33035	0.303196	0.151598	+	0.988442i	$0.451558\pi$
$948$	7.29467	0.236920
$949$	−2.99275	−0.0971488
$950$	1.88674	0.0612138
$951$	−26.7120	−0.866194
$952$	9.05343	0.293423
$953$	−31.4986	−1.02034	−0.510169	−	0.860074i	$-0.670417\pi$
$953$	−31.4986	−1.02034	−0.510169	+	0.860074i	$0.670417\pi$
$954$	10.1656	0.329123
$955$	0.523404	0.0169369
$956$	−14.8087	−0.478949
$957$	−63.4849	−2.05218
$958$	22.9859	0.742640
$959$	−16.1360	−0.521058
$960$	−3.40072	−0.109758
$961$	84.2465	2.71763
$962$	−1.23321	−0.0397604
$963$	18.0453	0.581502
$964$	3.80386	0.122514
$965$	12.5284	0.403304
$966$	1.75391	0.0564313
$967$	23.1089	0.743133	0.371566	−	0.928406i	$-0.378821\pi$
$967$	23.1089	0.743133	0.371566	+	0.928406i	$0.378821\pi$
$968$	26.8785	0.863909
$969$	11.1073	0.356819
$970$	−0.129569	−0.00416022
$971$	23.8820	0.766409	0.383205	−	0.923663i	$-0.374820\pi$
$971$	23.8820	0.766409	0.383205	+	0.923663i	$0.374820\pi$
$972$	15.2002	0.487547
$973$	−18.8567	−0.604518
$974$	10.8124	0.346453
$975$	−0.411559	−0.0131804
$976$	62.5373	2.00177
$977$	18.4585	0.590540	0.295270	−	0.955414i	$-0.404590\pi$
$977$	18.4585	0.590540	0.295270	+	0.955414i	$0.404590\pi$
$978$	46.6722	1.49241
$979$	−54.9301	−1.75557
$980$	1.37770	0.0440090
$981$	−5.17983	−0.165379
$982$	−17.5960	−0.561513
$983$	23.9496	0.763873	0.381936	−	0.924189i	$-0.375257\pi$
$983$	23.9496	0.763873	0.381936	+	0.924189i	$0.375257\pi$
$984$	14.2815	0.455277
$985$	3.81899	0.121683
$986$	115.043	3.66370
$987$	2.97793	0.0947884
$988$	0.425874	0.0135488
$989$	0.837396	0.0266277
$990$	−12.2185	−0.388328
$991$	−24.9815	−0.793562	−0.396781	−	0.917913i	$-0.629873\pi$
$991$	−24.9815	−0.793562	−0.396781	+	0.917913i	$0.629873\pi$
$992$	−71.2790	−2.26311
$993$	33.7619	1.07140
$994$	−15.2069	−0.482333
$995$	7.28162	0.230843
$996$	5.07956	0.160952
$997$	−4.69016	−0.148539	−0.0742694	−	0.997238i	$-0.523662\pi$
$997$	−4.69016	−0.148539	−0.0742694	+	0.997238i	$0.523662\pi$
$998$	−46.4842	−1.47143
$999$	12.5850	0.398171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.13	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.13	✓	67	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83785 q^{2} +1.36680 q^{3} +1.37770 q^{4} +1.00000 q^{5} -2.51199 q^{6} -1.00000 q^{7} +1.14369 q^{8} -1.13184 q^{9} +O(q^{10})\)	\(q-1.83785 q^{2} +1.36680 q^{3} +1.37770 q^{4} +1.00000 q^{5} -2.51199 q^{6} -1.00000 q^{7} +1.14369 q^{8} -1.13184 q^{9} -1.83785 q^{10} -5.87380 q^{11} +1.88305 q^{12} -0.301110 q^{13} +1.83785 q^{14} +1.36680 q^{15} -4.85734 q^{16} -7.91595 q^{17} +2.08016 q^{18} -1.02660 q^{19} +1.37770 q^{20} -1.36680 q^{21} +10.7952 q^{22} +0.698218 q^{23} +1.56321 q^{24} +1.00000 q^{25} +0.553396 q^{26} -5.64743 q^{27} -1.37770 q^{28} +7.90761 q^{29} -2.51199 q^{30} -10.7353 q^{31} +6.63969 q^{32} -8.02834 q^{33} +14.5483 q^{34} -1.00000 q^{35} -1.55934 q^{36} -2.22845 q^{37} +1.88674 q^{38} -0.411559 q^{39} +1.14369 q^{40} +9.13601 q^{41} +2.51199 q^{42} +1.19933 q^{43} -8.09233 q^{44} -1.13184 q^{45} -1.28322 q^{46} -2.17875 q^{47} -6.63904 q^{48} +1.00000 q^{49} -1.83785 q^{50} -10.8196 q^{51} -0.414840 q^{52} +4.88692 q^{53} +10.3791 q^{54} -5.87380 q^{55} -1.14369 q^{56} -1.40316 q^{57} -14.5330 q^{58} -12.0282 q^{59} +1.88305 q^{60} -12.8748 q^{61} +19.7299 q^{62} +1.13184 q^{63} -2.48808 q^{64} -0.301110 q^{65} +14.7549 q^{66} +4.27626 q^{67} -10.9058 q^{68} +0.954328 q^{69} +1.83785 q^{70} -8.27426 q^{71} -1.29448 q^{72} +9.93905 q^{73} +4.09555 q^{74} +1.36680 q^{75} -1.41434 q^{76} +5.87380 q^{77} +0.756385 q^{78} +3.87387 q^{79} -4.85734 q^{80} -4.32340 q^{81} -16.7906 q^{82} +2.69752 q^{83} -1.88305 q^{84} -7.91595 q^{85} -2.20420 q^{86} +10.8082 q^{87} -6.71783 q^{88} +9.35172 q^{89} +2.08016 q^{90} +0.301110 q^{91} +0.961935 q^{92} -14.6731 q^{93} +4.00422 q^{94} -1.02660 q^{95} +9.07516 q^{96} +0.0705004 q^{97} -1.83785 q^{98} +6.64822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 67 * q + 3 * q^2 + 73 * q^4 + 67 * q^5 + 17 * q^6 - 67 * q^7 + 12 * q^8 + 97 * q^9 + 3 * q^10 + 11 * q^11 + 9 * q^12 + 19 * q^13 - 3 * q^14 + 93 * q^16 + 7 * q^17 + 9 * q^18 + 36 * q^19 + 73 * q^20 - 8 * q^22 - 2 * q^23 + 37 * q^24 + 67 * q^25 + 39 * q^26 + 6 * q^27 - 73 * q^28 + 56 * q^29 + 17 * q^30 + 63 * q^31 + 27 * q^32 + 51 * q^33 + 55 * q^34 - 67 * q^35 + 148 * q^36 + 28 * q^37 + 10 * q^38 + 7 * q^39 + 12 * q^40 + 84 * q^41 - 17 * q^42 - 11 * q^43 + 41 * q^44 + 97 * q^45 + 17 * q^46 - 10 * q^47 + 10 * q^48 + 67 * q^49 + 3 * q^50 - q^51 + 49 * q^52 + 3 * q^53 + 20 * q^54 + 11 * q^55 - 12 * q^56 + 45 * q^57 + 22 * q^58 + 80 * q^59 + 9 * q^60 + 64 * q^61 - 37 * q^62 - 97 * q^63 + 110 * q^64 + 19 * q^65 + 75 * q^66 + 22 * q^67 + 7 * q^68 + 107 * q^69 - 3 * q^70 + 24 * q^71 + 72 * q^72 + 83 * q^73 + 52 * q^74 + 115 * q^76 - 11 * q^77 - 70 * q^78 - 32 * q^79 + 93 * q^80 + 183 * q^81 + 56 * q^82 - 58 * q^83 - 9 * q^84 + 7 * q^85 + 51 * q^86 + 20 * q^87 - 5 * q^88 + 129 * q^89 + 9 * q^90 - 19 * q^91 - 37 * q^92 + 33 * q^93 + 89 * q^94 + 36 * q^95 + 129 * q^96 + 126 * q^97 + 3 * q^98 - 27 * q^99

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