LMFDB - Embedded newform 8015.2.a.m.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.89706 q^{2} -1.32001 q^{3} +1.59885 q^{4} +1.00000 q^{5} +2.50414 q^{6} -1.00000 q^{7} +0.761013 q^{8} -1.25758 q^{9} +O(q^{10})$	\(q-1.89706 q^{2} -1.32001 q^{3} +1.59885 q^{4} +1.00000 q^{5} +2.50414 q^{6} -1.00000 q^{7} +0.761013 q^{8} -1.25758 q^{9} -1.89706 q^{10} -4.27013 q^{11} -2.11049 q^{12} +6.67988 q^{13} +1.89706 q^{14} -1.32001 q^{15} -4.64138 q^{16} +3.66894 q^{17} +2.38570 q^{18} -8.31367 q^{19} +1.59885 q^{20} +1.32001 q^{21} +8.10070 q^{22} +4.46641 q^{23} -1.00454 q^{24} +1.00000 q^{25} -12.6722 q^{26} +5.62004 q^{27} -1.59885 q^{28} +2.61057 q^{29} +2.50414 q^{30} -1.94181 q^{31} +7.28297 q^{32} +5.63661 q^{33} -6.96021 q^{34} -1.00000 q^{35} -2.01067 q^{36} -5.68944 q^{37} +15.7715 q^{38} -8.81751 q^{39} +0.761013 q^{40} +8.33873 q^{41} -2.50414 q^{42} -12.2885 q^{43} -6.82728 q^{44} -1.25758 q^{45} -8.47305 q^{46} +4.28551 q^{47} +6.12667 q^{48} +1.00000 q^{49} -1.89706 q^{50} -4.84304 q^{51} +10.6801 q^{52} -0.475367 q^{53} -10.6616 q^{54} -4.27013 q^{55} -0.761013 q^{56} +10.9741 q^{57} -4.95241 q^{58} +7.05293 q^{59} -2.11049 q^{60} +2.30152 q^{61} +3.68373 q^{62} +1.25758 q^{63} -4.53348 q^{64} +6.67988 q^{65} -10.6930 q^{66} +2.86284 q^{67} +5.86608 q^{68} -5.89570 q^{69} +1.89706 q^{70} +5.04155 q^{71} -0.957032 q^{72} -11.5287 q^{73} +10.7932 q^{74} -1.32001 q^{75} -13.2923 q^{76} +4.27013 q^{77} +16.7274 q^{78} +3.32995 q^{79} -4.64138 q^{80} -3.64577 q^{81} -15.8191 q^{82} -15.7266 q^{83} +2.11049 q^{84} +3.66894 q^{85} +23.3120 q^{86} -3.44598 q^{87} -3.24962 q^{88} -4.88159 q^{89} +2.38570 q^{90} -6.67988 q^{91} +7.14110 q^{92} +2.56320 q^{93} -8.12988 q^{94} -8.31367 q^{95} -9.61358 q^{96} +11.4440 q^{97} -1.89706 q^{98} +5.37001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.89706	−1.34143	−0.670713	−	0.741717i	$-0.734012\pi$
$2$	−1.89706	−1.34143	−0.670713	+	0.741717i	$0.734012\pi$
$3$	−1.32001	−0.762108	−0.381054	−	0.924553i	$-0.624439\pi$
$3$	−1.32001	−0.762108	−0.381054	+	0.924553i	$0.624439\pi$
$4$	1.59885	0.799423
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.50414	1.02231
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.761013	0.269059
$9$	−1.25758	−0.419192
$10$	−1.89706	−0.599904
$11$	−4.27013	−1.28749	−0.643746	−	0.765239i	$-0.722621\pi$
$11$	−4.27013	−1.28749	−0.643746	+	0.765239i	$0.722621\pi$
$12$	−2.11049	−0.609247
$13$	6.67988	1.85267	0.926333	−	0.376705i	$-0.122943\pi$
$13$	6.67988	1.85267	0.926333	+	0.376705i	$0.122943\pi$
$14$	1.89706	0.507011
$15$	−1.32001	−0.340825
$16$	−4.64138	−1.16035
$17$	3.66894	0.889849	0.444925	−	0.895568i	$-0.353230\pi$
$17$	3.66894	0.889849	0.444925	+	0.895568i	$0.353230\pi$
$18$	2.38570	0.562315
$19$	−8.31367	−1.90729	−0.953643	−	0.300940i	$-0.902700\pi$
$19$	−8.31367	−1.90729	−0.953643	+	0.300940i	$0.902700\pi$
$20$	1.59885	0.357513
$21$	1.32001	0.288050
$22$	8.10070	1.72708
$23$	4.46641	0.931310	0.465655	−	0.884966i	$-0.345819\pi$
$23$	4.46641	0.931310	0.465655	+	0.884966i	$0.345819\pi$
$24$	−1.00454	−0.205052
$25$	1.00000	0.200000
$26$	−12.6722	−2.48521
$27$	5.62004	1.08158
$28$	−1.59885	−0.302154
$29$	2.61057	0.484771	0.242385	−	0.970180i	$-0.422070\pi$
$29$	2.61057	0.484771	0.242385	+	0.970180i	$0.422070\pi$
$30$	2.50414	0.457191
$31$	−1.94181	−0.348759	−0.174379	−	0.984679i	$-0.555792\pi$
$31$	−1.94181	−0.348759	−0.174379	+	0.984679i	$0.555792\pi$
$32$	7.28297	1.28746
$33$	5.63661	0.981207
$34$	−6.96021	−1.19367
$35$	−1.00000	−0.169031
$36$	−2.01067	−0.335112
$37$	−5.68944	−0.935338	−0.467669	−	0.883904i	$-0.654906\pi$
$37$	−5.68944	−0.935338	−0.467669	+	0.883904i	$0.654906\pi$
$38$	15.7715	2.55848
$39$	−8.81751	−1.41193
$40$	0.761013	0.120327
$41$	8.33873	1.30229	0.651145	−	0.758953i	$-0.274289\pi$
$41$	8.33873	1.30229	0.651145	+	0.758953i	$0.274289\pi$
$42$	−2.50414	−0.386397
$43$	−12.2885	−1.87398	−0.936988	−	0.349362i	$-0.886398\pi$
$43$	−12.2885	−1.87398	−0.936988	+	0.349362i	$0.886398\pi$
$44$	−6.82728	−1.02925
$45$	−1.25758	−0.187468
$46$	−8.47305	−1.24928
$47$	4.28551	0.625106	0.312553	−	0.949900i	$-0.398816\pi$
$47$	4.28551	0.625106	0.312553	+	0.949900i	$0.398816\pi$
$48$	6.12667	0.884308
$49$	1.00000	0.142857
$50$	−1.89706	−0.268285
$51$	−4.84304	−0.678161
$52$	10.6801	1.48106
$53$	−0.475367	−0.0652967	−0.0326483	−	0.999467i	$-0.510394\pi$
$53$	−0.475367	−0.0652967	−0.0326483	+	0.999467i	$0.510394\pi$
$54$	−10.6616	−1.45086
$55$	−4.27013	−0.575784
$56$	−0.761013	−0.101695
$57$	10.9741	1.45356
$58$	−4.95241	−0.650284
$59$	7.05293	0.918213	0.459107	−	0.888381i	$-0.348170\pi$
$59$	7.05293	0.918213	0.459107	+	0.888381i	$0.348170\pi$
$60$	−2.11049	−0.272463
$61$	2.30152	0.294680	0.147340	−	0.989086i	$-0.452929\pi$
$61$	2.30152	0.294680	0.147340	+	0.989086i	$0.452929\pi$
$62$	3.68373	0.467834
$63$	1.25758	0.158440
$64$	−4.53348	−0.566685
$65$	6.67988	0.828538
$66$	−10.6930	−1.31622
$67$	2.86284	0.349751	0.174876	−	0.984591i	$-0.444048\pi$
$67$	2.86284	0.349751	0.174876	+	0.984591i	$0.444048\pi$
$68$	5.86608	0.711366
$69$	−5.89570	−0.709758
$70$	1.89706	0.226742
$71$	5.04155	0.598322	0.299161	−	0.954203i	$-0.403293\pi$
$71$	5.04155	0.598322	0.299161	+	0.954203i	$0.403293\pi$
$72$	−0.957032	−0.112787
$73$	−11.5287	−1.34934	−0.674668	−	0.738121i	$-0.735713\pi$
$73$	−11.5287	−1.34934	−0.674668	+	0.738121i	$0.735713\pi$
$74$	10.7932	1.25469
$75$	−1.32001	−0.152422
$76$	−13.2923	−1.52473
$77$	4.27013	0.486626
$78$	16.7274	1.89400
$79$	3.32995	0.374649	0.187324	−	0.982298i	$-0.440018\pi$
$79$	3.32995	0.374649	0.187324	+	0.982298i	$0.440018\pi$
$80$	−4.64138	−0.518922
$81$	−3.64577	−0.405086
$82$	−15.8191	−1.74693
$83$	−15.7266	−1.72622	−0.863112	−	0.505013i	$-0.831488\pi$
$83$	−15.7266	−1.72622	−0.863112	+	0.505013i	$0.831488\pi$
$84$	2.11049	0.230274
$85$	3.66894	0.397953
$86$	23.3120	2.51380
$87$	−3.44598	−0.369447
$88$	−3.24962	−0.346411
$89$	−4.88159	−0.517448	−0.258724	−	0.965951i	$-0.583302\pi$
$89$	−4.88159	−0.517448	−0.258724	+	0.965951i	$0.583302\pi$
$90$	2.38570	0.251475
$91$	−6.67988	−0.700242
$92$	7.14110	0.744511
$93$	2.56320	0.265792
$94$	−8.12988	−0.838533
$95$	−8.31367	−0.852964
$96$	−9.61358	−0.981182
$97$	11.4440	1.16197	0.580983	−	0.813916i	$-0.302668\pi$
$97$	11.4440	1.16197	0.580983	+	0.813916i	$0.302668\pi$
$98$	−1.89706	−0.191632
$99$	5.37001	0.539706
$100$	1.59885	0.159885
$101$	−9.76565	−0.971719	−0.485859	−	0.874037i	$-0.661493\pi$
$101$	−9.76565	−0.971719	−0.485859	+	0.874037i	$0.661493\pi$
$102$	9.18755	0.909703
$103$	−3.44731	−0.339674	−0.169837	−	0.985472i	$-0.554324\pi$
$103$	−3.44731	−0.339674	−0.169837	+	0.985472i	$0.554324\pi$
$104$	5.08348	0.498476
$105$	1.32001	0.128820
$106$	0.901801	0.0875907
$107$	−15.1976	−1.46921	−0.734603	−	0.678497i	$-0.762631\pi$
$107$	−15.1976	−1.46921	−0.734603	+	0.678497i	$0.762631\pi$
$108$	8.98558	0.864638
$109$	−2.44588	−0.234273	−0.117136	−	0.993116i	$-0.537371\pi$
$109$	−2.44588	−0.234273	−0.117136	+	0.993116i	$0.537371\pi$
$110$	8.10070	0.772372
$111$	7.51011	0.712829
$112$	4.64138	0.438569
$113$	16.7433	1.57508	0.787538	−	0.616266i	$-0.211355\pi$
$113$	16.7433	1.57508	0.787538	+	0.616266i	$0.211355\pi$
$114$	−20.8186	−1.94984
$115$	4.46641	0.416495
$116$	4.17390	0.387537
$117$	−8.40046	−0.776623
$118$	−13.3798	−1.23171
$119$	−3.66894	−0.336331
$120$	−1.00454	−0.0917019
$121$	7.23400	0.657636
$122$	−4.36614	−0.395291
$123$	−11.0072	−0.992485
$124$	−3.10465	−0.278806
$125$	1.00000	0.0894427
$126$	−2.38570	−0.212535
$127$	16.8355	1.49391	0.746953	−	0.664877i	$-0.231516\pi$
$127$	16.8355	1.49391	0.746953	+	0.664877i	$0.231516\pi$
$128$	−5.96564	−0.527293
$129$	16.2209	1.42817
$130$	−12.6722	−1.11142
$131$	−2.43588	−0.212823	−0.106412	−	0.994322i	$-0.533936\pi$
$131$	−2.43588	−0.212823	−0.106412	+	0.994322i	$0.533936\pi$
$132$	9.01207	0.784400
$133$	8.31367	0.720886
$134$	−5.43098	−0.469165
$135$	5.62004	0.483696
$136$	2.79211	0.239422
$137$	13.6639	1.16739	0.583693	−	0.811975i	$-0.301607\pi$
$137$	13.6639	1.16739	0.583693	+	0.811975i	$0.301607\pi$
$138$	11.1845	0.952088
$139$	9.24299	0.783980	0.391990	−	0.919969i	$-0.371787\pi$
$139$	9.24299	0.783980	0.391990	+	0.919969i	$0.371787\pi$
$140$	−1.59885	−0.135127
$141$	−5.65691	−0.476398
$142$	−9.56414	−0.802604
$143$	−28.5240	−2.38529
$144$	5.83689	0.486408
$145$	2.61057	0.216796
$146$	21.8707	1.81003
$147$	−1.32001	−0.108873
$148$	−9.09654	−0.747731
$149$	−18.2824	−1.49775	−0.748876	−	0.662710i	$-0.769406\pi$
$149$	−18.2824	−1.49775	−0.748876	+	0.662710i	$0.769406\pi$
$150$	2.50414	0.204462
$151$	8.96584	0.729630	0.364815	−	0.931080i	$-0.381132\pi$
$151$	8.96584	0.729630	0.364815	+	0.931080i	$0.381132\pi$
$152$	−6.32681	−0.513172
$153$	−4.61397	−0.373018
$154$	−8.10070	−0.652773
$155$	−1.94181	−0.155970
$156$	−14.0978	−1.12873
$157$	11.3997	0.909797	0.454899	−	0.890543i	$-0.349675\pi$
$157$	11.3997	0.909797	0.454899	+	0.890543i	$0.349675\pi$
$158$	−6.31713	−0.502564
$159$	0.627489	0.0497631
$160$	7.28297	0.575769
$161$	−4.46641	−0.352002
$162$	6.91626	0.543393
$163$	22.6807	1.77649	0.888247	−	0.459367i	$-0.151924\pi$
$163$	22.6807	1.77649	0.888247	+	0.459367i	$0.151924\pi$
$164$	13.3323	1.04108
$165$	5.63661	0.438809
$166$	29.8344	2.31560
$167$	−17.3959	−1.34613	−0.673067	−	0.739581i	$-0.735024\pi$
$167$	−17.3959	−1.34613	−0.673067	+	0.739581i	$0.735024\pi$
$168$	1.00454	0.0775023
$169$	31.6209	2.43237
$170$	−6.96021	−0.533824
$171$	10.4551	0.799519
$172$	−19.6474	−1.49810
$173$	−20.2634	−1.54060	−0.770299	−	0.637683i	$-0.779893\pi$
$173$	−20.2634	−1.54060	−0.770299	+	0.637683i	$0.779893\pi$
$174$	6.53723	0.495586
$175$	−1.00000	−0.0755929
$176$	19.8193	1.49394
$177$	−9.30993	−0.699777
$178$	9.26068	0.694118
$179$	−7.63870	−0.570943	−0.285472	−	0.958387i	$-0.592150\pi$
$179$	−7.63870	−0.570943	−0.285472	+	0.958387i	$0.592150\pi$
$180$	−2.01067	−0.149867
$181$	−24.3992	−1.81358	−0.906790	−	0.421583i	$-0.861474\pi$
$181$	−24.3992	−1.81358	−0.906790	+	0.421583i	$0.861474\pi$
$182$	12.6722	0.939323
$183$	−3.03803	−0.224578
$184$	3.39899	0.250577
$185$	−5.68944	−0.418296
$186$	−4.86256	−0.356540
$187$	−15.6669	−1.14567
$188$	6.85187	0.499724
$189$	−5.62004	−0.408798
$190$	15.7715	1.14419
$191$	15.9255	1.15233	0.576166	−	0.817333i	$-0.304548\pi$
$191$	15.9255	1.15233	0.576166	+	0.817333i	$0.304548\pi$
$192$	5.98423	0.431875
$193$	−3.08991	−0.222417	−0.111208	−	0.993797i	$-0.535472\pi$
$193$	−3.08991	−0.222417	−0.111208	+	0.993797i	$0.535472\pi$
$194$	−21.7101	−1.55869
$195$	−8.81751	−0.631435
$196$	1.59885	0.114203
$197$	24.1934	1.72371	0.861854	−	0.507157i	$-0.169303\pi$
$197$	24.1934	1.72371	0.861854	+	0.507157i	$0.169303\pi$
$198$	−10.1872	−0.723976
$199$	−10.2745	−0.728343	−0.364172	−	0.931332i	$-0.618648\pi$
$199$	−10.2745	−0.728343	−0.364172	+	0.931332i	$0.618648\pi$
$200$	0.761013	0.0538118
$201$	−3.77897	−0.266548
$202$	18.5261	1.30349
$203$	−2.61057	−0.183226
$204$	−7.74327	−0.542138
$205$	8.33873	0.582402
$206$	6.53977	0.455647
$207$	−5.61685	−0.390398
$208$	−31.0039	−2.14973
$209$	35.5004	2.45562
$210$	−2.50414	−0.172802
$211$	−4.67557	−0.321879	−0.160940	−	0.986964i	$-0.551452\pi$
$211$	−4.67557	−0.321879	−0.160940	+	0.986964i	$0.551452\pi$
$212$	−0.760039	−0.0521997
$213$	−6.65489	−0.455986
$214$	28.8308	1.97083
$215$	−12.2885	−0.838067
$216$	4.27692	0.291008
$217$	1.94181	0.131818
$218$	4.63999	0.314260
$219$	15.2180	1.02834
$220$	−6.82728	−0.460295
$221$	24.5081	1.64859
$222$	−14.2472	−0.956207
$223$	−2.11945	−0.141929	−0.0709644	−	0.997479i	$-0.522608\pi$
$223$	−2.11945	−0.141929	−0.0709644	+	0.997479i	$0.522608\pi$
$224$	−7.28297	−0.486614
$225$	−1.25758	−0.0838384
$226$	−31.7631	−2.11285
$227$	19.7057	1.30791	0.653957	−	0.756532i	$-0.273108\pi$
$227$	19.7057	1.30791	0.653957	+	0.756532i	$0.273108\pi$
$228$	17.5459	1.16201
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−8.47305	−0.558697
$231$	−5.63661	−0.370862
$232$	1.98668	0.130432
$233$	−16.2231	−1.06281	−0.531405	−	0.847118i	$-0.678336\pi$
$233$	−16.2231	−1.06281	−0.531405	+	0.847118i	$0.678336\pi$
$234$	15.9362	1.04178
$235$	4.28551	0.279556
$236$	11.2766	0.734041
$237$	−4.39557	−0.285523
$238$	6.96021	0.451164
$239$	−24.3285	−1.57368	−0.786839	−	0.617158i	$-0.788284\pi$
$239$	−24.3285	−1.57368	−0.786839	+	0.617158i	$0.788284\pi$
$240$	6.12667	0.395475
$241$	3.66169	0.235870	0.117935	−	0.993021i	$-0.462373\pi$
$241$	3.66169	0.235870	0.117935	+	0.993021i	$0.462373\pi$
$242$	−13.7233	−0.882170
$243$	−12.0477	−0.772858
$244$	3.67978	0.235574
$245$	1.00000	0.0638877
$246$	20.8813	1.33135
$247$	−55.5343	−3.53357
$248$	−1.47774	−0.0938366
$249$	20.7593	1.31557
$250$	−1.89706	−0.119981
$251$	−23.4662	−1.48117	−0.740587	−	0.671961i	$-0.765452\pi$
$251$	−23.4662	−1.48117	−0.740587	+	0.671961i	$0.765452\pi$
$252$	2.01067	0.126660
$253$	−19.0721	−1.19905
$254$	−31.9379	−2.00396
$255$	−4.84304	−0.303283
$256$	20.3842	1.27401
$257$	30.3879	1.89554	0.947772	−	0.318950i	$-0.103330\pi$
$257$	30.3879	1.89554	0.947772	+	0.318950i	$0.103330\pi$
$258$	−30.7721	−1.91579
$259$	5.68944	0.353525
$260$	10.6801	0.662352
$261$	−3.28299	−0.203212
$262$	4.62101	0.285487
$263$	−6.66038	−0.410697	−0.205348	−	0.978689i	$-0.565833\pi$
$263$	−6.66038	−0.410697	−0.205348	+	0.978689i	$0.565833\pi$
$264$	4.28953	0.264002
$265$	−0.475367	−0.0292016
$266$	−15.7715	−0.967016
$267$	6.44374	0.394351
$268$	4.57724	0.279599
$269$	12.7827	0.779378	0.389689	−	0.920947i	$-0.372583\pi$
$269$	12.7827	0.779378	0.389689	+	0.920947i	$0.372583\pi$
$270$	−10.6616	−0.648842
$271$	29.0040	1.76187	0.880933	−	0.473241i	$-0.156916\pi$
$271$	29.0040	1.76187	0.880933	+	0.473241i	$0.156916\pi$
$272$	−17.0290	−1.03253
$273$	8.81751	0.533660
$274$	−25.9213	−1.56596
$275$	−4.27013	−0.257498
$276$	−9.42631	−0.567397
$277$	13.5153	0.812055	0.406028	−	0.913861i	$-0.366914\pi$
$277$	13.5153	0.812055	0.406028	+	0.913861i	$0.366914\pi$
$278$	−17.5345	−1.05165
$279$	2.44197	0.146197
$280$	−0.761013	−0.0454792
$281$	−22.9233	−1.36749	−0.683746	−	0.729721i	$-0.739650\pi$
$281$	−22.9233	−1.36749	−0.683746	+	0.729721i	$0.739650\pi$
$282$	10.7315	0.639052
$283$	−18.4144	−1.09462	−0.547312	−	0.836929i	$-0.684349\pi$
$283$	−18.4144	−1.09462	−0.547312	+	0.836929i	$0.684349\pi$
$284$	8.06066	0.478312
$285$	10.9741	0.650051
$286$	54.1117	3.19969
$287$	−8.33873	−0.492220
$288$	−9.15889	−0.539693
$289$	−3.53886	−0.208168
$290$	−4.95241	−0.290816
$291$	−15.1062	−0.885543
$292$	−18.4327	−1.07869
$293$	−26.6080	−1.55445	−0.777227	−	0.629221i	$-0.783374\pi$
$293$	−26.6080	−1.55445	−0.777227	+	0.629221i	$0.783374\pi$
$294$	2.50414	0.146044
$295$	7.05293	0.410637
$296$	−4.32974	−0.251661
$297$	−23.9983	−1.39252
$298$	34.6828	2.00912
$299$	29.8351	1.72541
$300$	−2.11049	−0.121849
$301$	12.2885	0.708296
$302$	−17.0088	−0.978745
$303$	12.8907	0.740554
$304$	38.5869	2.21311
$305$	2.30152	0.131785
$306$	8.75300	0.500376
$307$	−19.8881	−1.13507	−0.567537	−	0.823348i	$-0.692104\pi$
$307$	−19.8881	−1.13507	−0.567537	+	0.823348i	$0.692104\pi$
$308$	6.82728	0.389020
$309$	4.55048	0.258868
$310$	3.68373	0.209222
$311$	−17.9149	−1.01586	−0.507930	−	0.861398i	$-0.669589\pi$
$311$	−17.9149	−1.01586	−0.507930	+	0.861398i	$0.669589\pi$
$312$	−6.71024	−0.379892
$313$	12.6009	0.712243	0.356121	−	0.934440i	$-0.384099\pi$
$313$	12.6009	0.712243	0.356121	+	0.934440i	$0.384099\pi$
$314$	−21.6260	−1.22043
$315$	1.25758	0.0708564
$316$	5.32408	0.299503
$317$	−0.408604	−0.0229495	−0.0114747	−	0.999934i	$-0.503653\pi$
$317$	−0.408604	−0.0229495	−0.0114747	+	0.999934i	$0.503653\pi$
$318$	−1.19039	−0.0667535
$319$	−11.1475	−0.624138
$320$	−4.53348	−0.253429
$321$	20.0609	1.11969
$322$	8.47305	0.472185
$323$	−30.5024	−1.69720
$324$	−5.82903	−0.323835
$325$	6.67988	0.370533
$326$	−43.0268	−2.38303
$327$	3.22859	0.178541
$328$	6.34588	0.350393
$329$	−4.28551	−0.236268
$330$	−10.6930	−0.588630
$331$	−18.0303	−0.991037	−0.495518	−	0.868598i	$-0.665022\pi$
$331$	−18.0303	−0.991037	−0.495518	+	0.868598i	$0.665022\pi$
$332$	−25.1445	−1.37998
$333$	7.15491	0.392086
$334$	33.0011	1.80574
$335$	2.86284	0.156414
$336$	−6.12667	−0.334237
$337$	1.14623	0.0624392	0.0312196	−	0.999513i	$-0.490061\pi$
$337$	1.14623	0.0624392	0.0312196	+	0.999513i	$0.490061\pi$
$338$	−59.9867	−3.26285
$339$	−22.1013	−1.20038
$340$	5.86608	0.318133
$341$	8.29177	0.449024
$342$	−19.8339	−1.07250
$343$	−1.00000	−0.0539949
$344$	−9.35169	−0.504210
$345$	−5.89570	−0.317414
$346$	38.4409	2.06660
$347$	−27.5656	−1.47980	−0.739900	−	0.672717i	$-0.765127\pi$
$347$	−27.5656	−1.47980	−0.739900	+	0.672717i	$0.765127\pi$
$348$	−5.50959	−0.295345
$349$	26.9794	1.44418	0.722088	−	0.691801i	$-0.243183\pi$
$349$	26.9794	1.44418	0.722088	+	0.691801i	$0.243183\pi$
$350$	1.89706	0.101402
$351$	37.5412	2.00380
$352$	−31.0992	−1.65759
$353$	0.537640	0.0286157	0.0143078	−	0.999898i	$-0.495446\pi$
$353$	0.537640	0.0286157	0.0143078	+	0.999898i	$0.495446\pi$
$354$	17.6615	0.938699
$355$	5.04155	0.267578
$356$	−7.80491	−0.413660
$357$	4.84304	0.256321
$358$	14.4911	0.765878
$359$	−5.51693	−0.291172	−0.145586	−	0.989346i	$-0.546507\pi$
$359$	−5.51693	−0.291172	−0.145586	+	0.989346i	$0.546507\pi$
$360$	−0.957032	−0.0504400
$361$	50.1171	2.63774
$362$	46.2868	2.43278
$363$	−9.54894	−0.501189
$364$	−10.6801	−0.559790
$365$	−11.5287	−0.603441
$366$	5.76334	0.301255
$367$	7.90978	0.412887	0.206444	−	0.978458i	$-0.433811\pi$
$367$	7.90978	0.412887	0.206444	+	0.978458i	$0.433811\pi$
$368$	−20.7303	−1.08064
$369$	−10.4866	−0.545910
$370$	10.7932	0.561113
$371$	0.475367	0.0246798
$372$	4.09817	0.212480
$373$	12.0211	0.622427	0.311214	−	0.950340i	$-0.399264\pi$
$373$	12.0211	0.622427	0.311214	+	0.950340i	$0.399264\pi$
$374$	29.7210	1.53684
$375$	−1.32001	−0.0681650
$376$	3.26133	0.168190
$377$	17.4383	0.898118
$378$	10.6616	0.548372
$379$	31.9837	1.64289	0.821447	−	0.570285i	$-0.193167\pi$
$379$	31.9837	1.64289	0.821447	+	0.570285i	$0.193167\pi$
$380$	−13.2923	−0.681880
$381$	−22.2230	−1.13852
$382$	−30.2117	−1.54577
$383$	−11.8912	−0.607613	−0.303807	−	0.952734i	$-0.598258\pi$
$383$	−11.8912	−0.607613	−0.303807	+	0.952734i	$0.598258\pi$
$384$	7.87470	0.401854
$385$	4.27013	0.217626
$386$	5.86176	0.298356
$387$	15.4537	0.785556
$388$	18.2973	0.928903
$389$	−12.8767	−0.652876	−0.326438	−	0.945219i	$-0.605849\pi$
$389$	−12.8767	−0.652876	−0.326438	+	0.945219i	$0.605849\pi$
$390$	16.7274	0.847023
$391$	16.3870	0.828726
$392$	0.761013	0.0384370
$393$	3.21538	0.162194
$394$	−45.8964	−2.31223
$395$	3.32995	0.167548
$396$	8.58582	0.431454
$397$	−7.14188	−0.358441	−0.179220	−	0.983809i	$-0.557357\pi$
$397$	−7.14188	−0.358441	−0.179220	+	0.983809i	$0.557357\pi$
$398$	19.4915	0.977019
$399$	−10.9741	−0.549393
$400$	−4.64138	−0.232069
$401$	36.6474	1.83008	0.915042	−	0.403359i	$-0.132157\pi$
$401$	36.6474	1.83008	0.915042	+	0.403359i	$0.132157\pi$
$402$	7.16895	0.357555
$403$	−12.9710	−0.646134
$404$	−15.6138	−0.776815
$405$	−3.64577	−0.181160
$406$	4.95241	0.245784
$407$	24.2946	1.20424
$408$	−3.68561	−0.182465
$409$	−11.2138	−0.554485	−0.277243	−	0.960800i	$-0.589421\pi$
$409$	−11.2138	−0.554485	−0.277243	+	0.960800i	$0.589421\pi$
$410$	−15.8191	−0.781249
$411$	−18.0365	−0.889674
$412$	−5.51172	−0.271543
$413$	−7.05293	−0.347052
$414$	10.6555	0.523690
$415$	−15.7266	−0.771990
$416$	48.6494	2.38523
$417$	−12.2008	−0.597477
$418$	−67.3465	−3.29403
$419$	11.3725	0.555585	0.277792	−	0.960641i	$-0.410397\pi$
$419$	11.3725	0.555585	0.277792	+	0.960641i	$0.410397\pi$
$420$	2.11049	0.102981
$421$	−31.2636	−1.52370	−0.761848	−	0.647756i	$-0.775708\pi$
$421$	−31.2636	−1.52370	−0.761848	+	0.647756i	$0.775708\pi$
$422$	8.86985	0.431777
$423$	−5.38935	−0.262039
$424$	−0.361761	−0.0175686
$425$	3.66894	0.177970
$426$	12.6247	0.611671
$427$	−2.30152	−0.111379
$428$	−24.2986	−1.17452
$429$	37.6519	1.81785
$430$	23.3120	1.12421
$431$	37.5377	1.80813	0.904063	−	0.427399i	$-0.140570\pi$
$431$	37.5377	1.80813	0.904063	+	0.427399i	$0.140570\pi$
$432$	−26.0848	−1.25500
$433$	7.86991	0.378204	0.189102	−	0.981957i	$-0.439442\pi$
$433$	7.86991	0.378204	0.189102	+	0.981957i	$0.439442\pi$
$434$	−3.68373	−0.176825
$435$	−3.44598	−0.165222
$436$	−3.91059	−0.187283
$437$	−37.1322	−1.77627
$438$	−28.8696	−1.37944
$439$	26.6791	1.27332	0.636662	−	0.771143i	$-0.280315\pi$
$439$	26.6791	1.27332	0.636662	+	0.771143i	$0.280315\pi$
$440$	−3.24962	−0.154920
$441$	−1.25758	−0.0598846
$442$	−46.4934	−2.21147
$443$	17.3446	0.824069	0.412035	−	0.911168i	$-0.364818\pi$
$443$	17.3446	0.824069	0.412035	+	0.911168i	$0.364818\pi$
$444$	12.0075	0.569852
$445$	−4.88159	−0.231410
$446$	4.02073	0.190387
$447$	24.1329	1.14145
$448$	4.53348	0.214187
$449$	−40.9938	−1.93462	−0.967308	−	0.253605i	$-0.918384\pi$
$449$	−40.9938	−1.93462	−0.967308	+	0.253605i	$0.918384\pi$
$450$	2.38570	0.112463
$451$	−35.6074	−1.67669
$452$	26.7699	1.25915
$453$	−11.8350	−0.556057
$454$	−37.3829	−1.75447
$455$	−6.67988	−0.313158
$456$	8.35145	0.391092
$457$	−22.8093	−1.06697	−0.533487	−	0.845808i	$-0.679119\pi$
$457$	−22.8093	−1.06697	−0.533487	+	0.845808i	$0.679119\pi$
$458$	1.89706	0.0886439
$459$	20.6196	0.962441
$460$	7.14110	0.332955
$461$	14.4044	0.670878	0.335439	−	0.942062i	$-0.391115\pi$
$461$	14.4044	0.670878	0.335439	+	0.942062i	$0.391115\pi$
$462$	10.6930	0.497483
$463$	38.9822	1.81166	0.905828	−	0.423647i	$-0.139250\pi$
$463$	38.9822	1.81166	0.905828	+	0.423647i	$0.139250\pi$
$464$	−12.1167	−0.562502
$465$	2.56320	0.118866
$466$	30.7762	1.42568
$467$	−0.124066	−0.00574108	−0.00287054	−	0.999996i	$-0.500914\pi$
$467$	−0.124066	−0.00574108	−0.00287054	+	0.999996i	$0.500914\pi$
$468$	−13.4311	−0.620851
$469$	−2.86284	−0.132194
$470$	−8.12988	−0.375003
$471$	−15.0477	−0.693363
$472$	5.36737	0.247053
$473$	52.4734	2.41273
$474$	8.33866	0.383008
$475$	−8.31367	−0.381457
$476$	−5.86608	−0.268871
$477$	0.597810	0.0273718
$478$	46.1527	2.11097
$479$	24.0159	1.09731	0.548657	−	0.836047i	$-0.315139\pi$
$479$	24.0159	1.09731	0.548657	+	0.836047i	$0.315139\pi$
$480$	−9.61358	−0.438798
$481$	−38.0048	−1.73287
$482$	−6.94646	−0.316403
$483$	5.89570	0.268263
$484$	11.5660	0.525729
$485$	11.4440	0.519647
$486$	22.8552	1.03673
$487$	−29.7511	−1.34815	−0.674076	−	0.738662i	$-0.735458\pi$
$487$	−29.7511	−1.34815	−0.674076	+	0.738662i	$0.735458\pi$
$488$	1.75149	0.0792862
$489$	−29.9388	−1.35388
$490$	−1.89706	−0.0857006
$491$	−25.6950	−1.15960	−0.579800	−	0.814759i	$-0.696869\pi$
$491$	−25.6950	−1.15960	−0.579800	+	0.814759i	$0.696869\pi$
$492$	−17.5988	−0.793416
$493$	9.57803	0.431373
$494$	105.352	4.74002
$495$	5.37001	0.241364
$496$	9.01267	0.404681
$497$	−5.04155	−0.226144
$498$	−39.3817	−1.76474
$499$	−38.2476	−1.71220	−0.856099	−	0.516811i	$-0.827119\pi$
$499$	−38.2476	−1.71220	−0.856099	+	0.516811i	$0.827119\pi$
$500$	1.59885	0.0715026
$501$	22.9627	1.02590
$502$	44.5169	1.98688
$503$	11.0248	0.491573	0.245787	−	0.969324i	$-0.420954\pi$
$503$	11.0248	0.491573	0.245787	+	0.969324i	$0.420954\pi$
$504$	0.957032	0.0426296
$505$	−9.76565	−0.434566
$506$	36.1810	1.60844
$507$	−41.7398	−1.85373
$508$	26.9173	1.19426
$509$	−4.53964	−0.201216	−0.100608	−	0.994926i	$-0.532079\pi$
$509$	−4.53964	−0.201216	−0.100608	+	0.994926i	$0.532079\pi$
$510$	9.18755	0.406831
$511$	11.5287	0.510001
$512$	−26.7387	−1.18170
$513$	−46.7231	−2.06288
$514$	−57.6477	−2.54273
$515$	−3.44731	−0.151907
$516$	25.9347	1.14171
$517$	−18.2997	−0.804819
$518$	−10.7932	−0.474227
$519$	26.7479	1.17410
$520$	5.08348	0.222925
$521$	9.23555	0.404617	0.202309	−	0.979322i	$-0.435156\pi$
$521$	9.23555	0.404617	0.202309	+	0.979322i	$0.435156\pi$
$522$	6.22804	0.272594
$523$	11.1959	0.489561	0.244781	−	0.969578i	$-0.421284\pi$
$523$	11.1959	0.489561	0.244781	+	0.969578i	$0.421284\pi$
$524$	−3.89459	−0.170136
$525$	1.32001	0.0576099
$526$	12.6352	0.550919
$527$	−7.12438	−0.310343
$528$	−26.1617	−1.13854
$529$	−3.05122	−0.132662
$530$	0.901801	0.0391717
$531$	−8.86960	−0.384908
$532$	13.2923	0.576293
$533$	55.7017	2.41271
$534$	−12.2242	−0.528992
$535$	−15.1976	−0.657049
$536$	2.17866	0.0941037
$537$	10.0832	0.435120
$538$	−24.2497	−1.04548
$539$	−4.27013	−0.183927
$540$	8.98558	0.386678
$541$	17.1692	0.738161	0.369081	−	0.929397i	$-0.379673\pi$
$541$	17.1692	0.738161	0.369081	+	0.929397i	$0.379673\pi$
$542$	−55.0224	−2.36341
$543$	32.2072	1.38214
$544$	26.7208	1.14564
$545$	−2.44588	−0.104770
$546$	−16.7274	−0.715865
$547$	−0.361961	−0.0154763	−0.00773817	−	0.999970i	$-0.502463\pi$
$547$	−0.361961	−0.0154763	−0.00773817	+	0.999970i	$0.502463\pi$
$548$	21.8465	0.933235
$549$	−2.89434	−0.123528
$550$	8.10070	0.345415
$551$	−21.7034	−0.924596
$552$	−4.48670	−0.190967
$553$	−3.32995	−0.141604
$554$	−25.6394	−1.08931
$555$	7.51011	0.318787
$556$	14.7781	0.626732
$557$	13.6146	0.576868	0.288434	−	0.957500i	$-0.406865\pi$
$557$	13.6146	0.576868	0.288434	+	0.957500i	$0.406865\pi$
$558$	−4.63257	−0.196112
$559$	−82.0856	−3.47185
$560$	4.64138	0.196134
$561$	20.6804	0.873127
$562$	43.4870	1.83439
$563$	−25.3291	−1.06749	−0.533747	−	0.845644i	$-0.679217\pi$
$563$	−25.3291	−1.06749	−0.533747	+	0.845644i	$0.679217\pi$
$564$	−9.04453	−0.380844
$565$	16.7433	0.704395
$566$	34.9333	1.46836
$567$	3.64577	0.153108
$568$	3.83669	0.160984
$569$	2.08615	0.0874561	0.0437280	−	0.999043i	$-0.486076\pi$
$569$	2.08615	0.0874561	0.0437280	+	0.999043i	$0.486076\pi$
$570$	−20.8186	−0.871995
$571$	−8.54630	−0.357651	−0.178826	−	0.983881i	$-0.557230\pi$
$571$	−8.54630	−0.357651	−0.178826	+	0.983881i	$0.557230\pi$
$572$	−45.6054	−1.90686
$573$	−21.0219	−0.878201
$574$	15.8191	0.660276
$575$	4.46641	0.186262
$576$	5.70120	0.237550
$577$	21.2429	0.884355	0.442178	−	0.896927i	$-0.354206\pi$
$577$	21.2429	0.884355	0.442178	+	0.896927i	$0.354206\pi$
$578$	6.71344	0.279242
$579$	4.07871	0.169506
$580$	4.17390	0.173312
$581$	15.7266	0.652451
$582$	28.6575	1.18789
$583$	2.02988	0.0840690
$584$	−8.77351	−0.363051
$585$	−8.40046	−0.347316
$586$	50.4770	2.08518
$587$	4.10742	0.169531	0.0847656	−	0.996401i	$-0.472986\pi$
$587$	4.10742	0.169531	0.0847656	+	0.996401i	$0.472986\pi$
$588$	−2.11049	−0.0870352
$589$	16.1435	0.665183
$590$	−13.3798	−0.550840
$591$	−31.9355	−1.31365
$592$	26.4069	1.08532
$593$	25.0587	1.02904	0.514518	−	0.857479i	$-0.327971\pi$
$593$	25.0587	1.02904	0.514518	+	0.857479i	$0.327971\pi$
$594$	45.5263	1.86796
$595$	−3.66894	−0.150412
$596$	−29.2307	−1.19734
$597$	13.5625	0.555076
$598$	−56.5990	−2.31451
$599$	45.3207	1.85175	0.925877	−	0.377825i	$-0.123328\pi$
$599$	45.3207	1.85175	0.925877	+	0.377825i	$0.123328\pi$
$600$	−1.00454	−0.0410103
$601$	−2.63429	−0.107455	−0.0537276	−	0.998556i	$-0.517110\pi$
$601$	−2.63429	−0.107455	−0.0537276	+	0.998556i	$0.517110\pi$
$602$	−23.3120	−0.950127
$603$	−3.60024	−0.146613
$604$	14.3350	0.583283
$605$	7.23400	0.294104
$606$	−24.4546	−0.993398
$607$	30.3686	1.23263	0.616313	−	0.787502i	$-0.288626\pi$
$607$	30.3686	1.23263	0.616313	+	0.787502i	$0.288626\pi$
$608$	−60.5482	−2.45555
$609$	3.44598	0.139638
$610$	−4.36614	−0.176780
$611$	28.6267	1.15811
$612$	−7.37704	−0.298199
$613$	−4.88769	−0.197412	−0.0987059	−	0.995117i	$-0.531470\pi$
$613$	−4.88769	−0.197412	−0.0987059	+	0.995117i	$0.531470\pi$
$614$	37.7290	1.52262
$615$	−11.0072	−0.443853
$616$	3.24962	0.130931
$617$	40.6460	1.63635	0.818174	−	0.574971i	$-0.194987\pi$
$617$	40.6460	1.63635	0.818174	+	0.574971i	$0.194987\pi$
$618$	−8.63255	−0.347252
$619$	−3.17161	−0.127478	−0.0637388	−	0.997967i	$-0.520302\pi$
$619$	−3.17161	−0.127478	−0.0637388	+	0.997967i	$0.520302\pi$
$620$	−3.10465	−0.124686
$621$	25.1014	1.00728
$622$	33.9857	1.36270
$623$	4.88159	0.195577
$624$	40.9254	1.63833
$625$	1.00000	0.0400000
$626$	−23.9046	−0.955421
$627$	−46.8609	−1.87144
$628$	18.2264	0.727313
$629$	−20.8742	−0.832310
$630$	−2.38570	−0.0950486
$631$	29.6709	1.18118	0.590590	−	0.806971i	$-0.298895\pi$
$631$	29.6709	1.18118	0.590590	+	0.806971i	$0.298895\pi$
$632$	2.53414	0.100803
$633$	6.17179	0.245307
$634$	0.775148	0.0307850
$635$	16.8355	0.668095
$636$	1.00326	0.0397818
$637$	6.67988	0.264667
$638$	21.1474	0.837235
$639$	−6.34013	−0.250812
$640$	−5.96564	−0.235813
$641$	46.6544	1.84274	0.921370	−	0.388688i	$-0.127071\pi$
$641$	46.6544	1.84274	0.921370	+	0.388688i	$0.127071\pi$
$642$	−38.0569	−1.50198
$643$	10.2635	0.404752	0.202376	−	0.979308i	$-0.435134\pi$
$643$	10.2635	0.404752	0.202376	+	0.979308i	$0.435134\pi$
$644$	−7.14110	−0.281399
$645$	16.2209	0.638698
$646$	57.8649	2.27666
$647$	−8.62561	−0.339108	−0.169554	−	0.985521i	$-0.554233\pi$
$647$	−8.62561	−0.339108	−0.169554	+	0.985521i	$0.554233\pi$
$648$	−2.77448	−0.108992
$649$	−30.1169	−1.18219
$650$	−12.6722	−0.497043
$651$	−2.56320	−0.100460
$652$	36.2630	1.42017
$653$	12.1068	0.473774	0.236887	−	0.971537i	$-0.423873\pi$
$653$	12.1068	0.473774	0.236887	+	0.971537i	$0.423873\pi$
$654$	−6.12483	−0.239500
$655$	−2.43588	−0.0951775
$656$	−38.7032	−1.51111
$657$	14.4983	0.565631
$658$	8.12988	0.316936
$659$	22.4317	0.873813	0.436907	−	0.899507i	$-0.356074\pi$
$659$	22.4317	0.873813	0.436907	+	0.899507i	$0.356074\pi$
$660$	9.01207	0.350794
$661$	33.0051	1.28375	0.641876	−	0.766809i	$-0.278157\pi$
$661$	33.0051	1.28375	0.641876	+	0.766809i	$0.278157\pi$
$662$	34.2047	1.32940
$663$	−32.3509	−1.25641
$664$	−11.9682	−0.464455
$665$	8.31367	0.322390
$666$	−13.5733	−0.525955
$667$	11.6599	0.451472
$668$	−27.8134	−1.07613
$669$	2.79769	0.108165
$670$	−5.43098	−0.209817
$671$	−9.82780	−0.379398
$672$	9.61358	0.370852
$673$	−14.5490	−0.560822	−0.280411	−	0.959880i	$-0.590471\pi$
$673$	−14.5490	−0.560822	−0.280411	+	0.959880i	$0.590471\pi$
$674$	−2.17447	−0.0837575
$675$	5.62004	0.216315
$676$	50.5569	1.94450
$677$	9.74845	0.374663	0.187332	−	0.982297i	$-0.440016\pi$
$677$	9.74845	0.374663	0.187332	+	0.982297i	$0.440016\pi$
$678$	41.9275	1.61022
$679$	−11.4440	−0.439182
$680$	2.79211	0.107073
$681$	−26.0117	−0.996771
$682$	−15.7300	−0.602333
$683$	−9.72430	−0.372090	−0.186045	−	0.982541i	$-0.559567\pi$
$683$	−9.72430	−0.372090	−0.186045	+	0.982541i	$0.559567\pi$
$684$	16.7161	0.639154
$685$	13.6639	0.522071
$686$	1.89706	0.0724302
$687$	1.32001	0.0503615
$688$	57.0355	2.17446
$689$	−3.17540	−0.120973
$690$	11.1845	0.425787
$691$	11.7121	0.445548	0.222774	−	0.974870i	$-0.428489\pi$
$691$	11.7121	0.445548	0.222774	+	0.974870i	$0.428489\pi$
$692$	−32.3981	−1.23159
$693$	−5.37001	−0.203990
$694$	52.2937	1.98504
$695$	9.24299	0.350607
$696$	−2.62243	−0.0994031
$697$	30.5943	1.15884
$698$	−51.1817	−1.93726
$699$	21.4146	0.809976
$700$	−1.59885	−0.0604307
$701$	33.9656	1.28286	0.641431	−	0.767181i	$-0.278341\pi$
$701$	33.9656	1.28286	0.641431	+	0.767181i	$0.278341\pi$
$702$	−71.2180	−2.68795
$703$	47.3001	1.78396
$704$	19.3585	0.729602
$705$	−5.65691	−0.213052
$706$	−1.01994	−0.0383858
$707$	9.76565	0.367275
$708$	−14.8851	−0.559418
$709$	31.9062	1.19826	0.599131	−	0.800651i	$-0.295513\pi$
$709$	31.9062	1.19826	0.599131	+	0.800651i	$0.295513\pi$
$710$	−9.56414	−0.358936
$711$	−4.18767	−0.157050
$712$	−3.71495	−0.139224
$713$	−8.67290	−0.324803
$714$	−9.18755	−0.343835
$715$	−28.5240	−1.06674
$716$	−12.2131	−0.456425
$717$	32.1138	1.19931
$718$	10.4660	0.390586
$719$	29.6370	1.10527	0.552637	−	0.833422i	$-0.313622\pi$
$719$	29.6370	1.10527	0.552637	+	0.833422i	$0.313622\pi$
$720$	5.83689	0.217528
$721$	3.44731	0.128385
$722$	−95.0752	−3.53833
$723$	−4.83347	−0.179759
$724$	−39.0106	−1.44982
$725$	2.61057	0.0969541
$726$	18.1149	0.672308
$727$	13.4931	0.500432	0.250216	−	0.968190i	$-0.419498\pi$
$727$	13.4931	0.500432	0.250216	+	0.968190i	$0.419498\pi$
$728$	−5.08348	−0.188406
$729$	26.8403	0.994087
$730$	21.8707	0.809472
$731$	−45.0857	−1.66756
$732$	−4.85735	−0.179533
$733$	8.21393	0.303388	0.151694	−	0.988427i	$-0.451527\pi$
$733$	8.21393	0.303388	0.151694	+	0.988427i	$0.451527\pi$
$734$	−15.0054	−0.553858
$735$	−1.32001	−0.0486893
$736$	32.5287	1.19902
$737$	−12.2247	−0.450302
$738$	19.8937	0.732298
$739$	49.6286	1.82562	0.912809	−	0.408387i	$-0.133908\pi$
$739$	49.6286	1.82562	0.912809	+	0.408387i	$0.133908\pi$
$740$	−9.09654	−0.334396
$741$	73.3058	2.69296
$742$	−0.901801	−0.0331062
$743$	50.2872	1.84486	0.922429	−	0.386167i	$-0.126201\pi$
$743$	50.2872	1.84486	0.922429	+	0.386167i	$0.126201\pi$
$744$	1.95063	0.0715136
$745$	−18.2824	−0.669815
$746$	−22.8047	−0.834940
$747$	19.7774	0.723619
$748$	−25.0489	−0.915878
$749$	15.1976	0.555307
$750$	2.50414	0.0914383
$751$	44.8289	1.63583	0.817915	−	0.575339i	$-0.195130\pi$
$751$	44.8289	1.63583	0.817915	+	0.575339i	$0.195130\pi$
$752$	−19.8907	−0.725339
$753$	30.9756	1.12881
$754$	−33.0816	−1.20476
$755$	8.96584	0.326300
$756$	−8.98558	−0.326802
$757$	5.50860	0.200213	0.100107	−	0.994977i	$-0.468082\pi$
$757$	5.50860	0.200213	0.100107	+	0.994977i	$0.468082\pi$
$758$	−60.6752	−2.20382
$759$	25.1754	0.913808
$760$	−6.32681	−0.229498
$761$	18.9523	0.687021	0.343510	−	0.939149i	$-0.388384\pi$
$761$	18.9523	0.687021	0.343510	+	0.939149i	$0.388384\pi$
$762$	42.1584	1.52724
$763$	2.44588	0.0885469
$764$	25.4625	0.921201
$765$	−4.61397	−0.166819
$766$	22.5584	0.815068
$767$	47.1128	1.70114
$768$	−26.9073	−0.970932
$769$	17.3677	0.626296	0.313148	−	0.949704i	$-0.398616\pi$
$769$	17.3677	0.626296	0.313148	+	0.949704i	$0.398616\pi$
$770$	−8.10070	−0.291929
$771$	−40.1123	−1.44461
$772$	−4.94030	−0.177805
$773$	−45.9153	−1.65146	−0.825729	−	0.564066i	$-0.809236\pi$
$773$	−45.9153	−1.65146	−0.825729	+	0.564066i	$0.809236\pi$
$774$	−29.3166	−1.05376
$775$	−1.94181	−0.0697518
$776$	8.70906	0.312637
$777$	−7.51011	−0.269424
$778$	24.4280	0.875785
$779$	−69.3254	−2.48384
$780$	−14.0978	−0.504784
$781$	−21.5281	−0.770335
$782$	−31.0871	−1.11167
$783$	14.6715	0.524317
$784$	−4.64138	−0.165764
$785$	11.3997	0.406874
$786$	−6.09977	−0.217572
$787$	−30.1502	−1.07474	−0.537370	−	0.843347i	$-0.680582\pi$
$787$	−30.1502	−1.07474	−0.537370	+	0.843347i	$0.680582\pi$
$788$	38.6815	1.37797
$789$	8.79176	0.312995
$790$	−6.31713	−0.224753
$791$	−16.7433	−0.595323
$792$	4.08665	0.145213
$793$	15.3739	0.545944
$794$	13.5486	0.480821
$795$	0.627489	0.0222547
$796$	−16.4274	−0.582255
$797$	−9.03981	−0.320206	−0.160103	−	0.987100i	$-0.551183\pi$
$797$	−9.03981	−0.320206	−0.160103	+	0.987100i	$0.551183\pi$
$798$	20.8186	0.736970
$799$	15.7233	0.556250
$800$	7.28297	0.257492
$801$	6.13897	0.216910
$802$	−69.5224	−2.45492
$803$	49.2292	1.73726
$804$	−6.04200	−0.213085
$805$	−4.46641	−0.157420
$806$	24.6069	0.866741
$807$	−16.8733	−0.593970
$808$	−7.43179	−0.261449
$809$	32.6004	1.14617	0.573084	−	0.819497i	$-0.305747\pi$
$809$	32.6004	1.14617	0.573084	+	0.819497i	$0.305747\pi$
$810$	6.91626	0.243013
$811$	2.53557	0.0890357	0.0445179	−	0.999009i	$-0.485825\pi$
$811$	2.53557	0.0890357	0.0445179	+	0.999009i	$0.485825\pi$
$812$	−4.17390	−0.146475
$813$	−38.2855	−1.34273
$814$	−46.0885	−1.61540
$815$	22.6807	0.794472
$816$	22.4784	0.786901
$817$	102.162	3.57421
$818$	21.2732	0.743801
$819$	8.40046	0.293536
$820$	13.3323	0.465586
$821$	23.7993	0.830600	0.415300	−	0.909685i	$-0.363677\pi$
$821$	23.7993	0.830600	0.415300	+	0.909685i	$0.363677\pi$
$822$	34.2163	1.19343
$823$	17.9706	0.626417	0.313209	−	0.949684i	$-0.398596\pi$
$823$	17.9706	0.626417	0.313209	+	0.949684i	$0.398596\pi$
$824$	−2.62345	−0.0913922
$825$	5.63661	0.196241
$826$	13.3798	0.465544
$827$	34.2727	1.19178	0.595889	−	0.803067i	$-0.296800\pi$
$827$	34.2727	1.19178	0.595889	+	0.803067i	$0.296800\pi$
$828$	−8.98047	−0.312093
$829$	−24.1607	−0.839134	−0.419567	−	0.907724i	$-0.637818\pi$
$829$	−24.1607	−0.839134	−0.419567	+	0.907724i	$0.637818\pi$
$830$	29.8344	1.03557
$831$	−17.8403	−0.618874
$832$	−30.2831	−1.04988
$833$	3.66894	0.127121
$834$	23.1457	0.801472
$835$	−17.3959	−0.602010
$836$	56.7597	1.96308
$837$	−10.9130	−0.377210
$838$	−21.5744	−0.745276
$839$	21.1655	0.730714	0.365357	−	0.930867i	$-0.380947\pi$
$839$	21.1655	0.730714	0.365357	+	0.930867i	$0.380947\pi$
$840$	1.00454	0.0346601
$841$	−22.1849	−0.764997
$842$	59.3090	2.04392
$843$	30.2590	1.04218
$844$	−7.47552	−0.257318
$845$	31.6209	1.08779
$846$	10.2239	0.351506
$847$	−7.23400	−0.248563
$848$	2.20636	0.0757667
$849$	24.3072	0.834221
$850$	−6.96021	−0.238733
$851$	−25.4114	−0.871090
$852$	−10.6401	−0.364526
$853$	34.2244	1.17182	0.585911	−	0.810375i	$-0.300737\pi$
$853$	34.2244	1.17182	0.585911	+	0.810375i	$0.300737\pi$
$854$	4.36614	0.149406
$855$	10.4551	0.357556
$856$	−11.5656	−0.395303
$857$	−2.56529	−0.0876287	−0.0438144	−	0.999040i	$-0.513951\pi$
$857$	−2.56529	−0.0876287	−0.0438144	+	0.999040i	$0.513951\pi$
$858$	−71.4280	−2.43851
$859$	54.2604	1.85134	0.925670	−	0.378331i	$-0.123502\pi$
$859$	54.2604	1.85134	0.925670	+	0.378331i	$0.123502\pi$
$860$	−19.6474	−0.669971
$861$	11.0072	0.375124
$862$	−71.2113	−2.42547
$863$	−19.5129	−0.664227	−0.332113	−	0.943239i	$-0.607762\pi$
$863$	−19.5129	−0.664227	−0.332113	+	0.943239i	$0.607762\pi$
$864$	40.9306	1.39249
$865$	−20.2634	−0.688976
$866$	−14.9297	−0.507332
$867$	4.67133	0.158647
$868$	3.10465	0.105379
$869$	−14.2193	−0.482357
$870$	6.53723	0.221633
$871$	19.1234	0.647973
$872$	−1.86135	−0.0630332
$873$	−14.3917	−0.487087
$874$	70.4421	2.38274
$875$	−1.00000	−0.0338062
$876$	24.3313	0.822078
$877$	−6.73691	−0.227489	−0.113745	−	0.993510i	$-0.536285\pi$
$877$	−6.73691	−0.227489	−0.113745	+	0.993510i	$0.536285\pi$
$878$	−50.6119	−1.70807
$879$	35.1227	1.18466
$880$	19.8193	0.668108
$881$	−29.0828	−0.979824	−0.489912	−	0.871772i	$-0.662971\pi$
$881$	−29.0828	−0.979824	−0.489912	+	0.871772i	$0.662971\pi$
$882$	2.38570	0.0803307
$883$	12.7617	0.429465	0.214733	−	0.976673i	$-0.431112\pi$
$883$	12.7617	0.429465	0.214733	+	0.976673i	$0.431112\pi$
$884$	39.1847	1.31792
$885$	−9.30993	−0.312950
$886$	−32.9039	−1.10543
$887$	−1.05298	−0.0353554	−0.0176777	−	0.999844i	$-0.505627\pi$
$887$	−1.05298	−0.0353554	−0.0176777	+	0.999844i	$0.505627\pi$
$888$	5.71530	0.191793
$889$	−16.8355	−0.564643
$890$	9.26068	0.310419
$891$	15.5679	0.521545
$892$	−3.38867	−0.113461
$893$	−35.6283	−1.19226
$894$	−45.7817	−1.53117
$895$	−7.63870	−0.255334
$896$	5.96564	0.199298
$897$	−39.3826	−1.31495
$898$	77.7678	2.59514
$899$	−5.06922	−0.169068
$900$	−2.01067	−0.0670224
$901$	−1.74409	−0.0581042
$902$	67.5495	2.24915
$903$	−16.2209	−0.539798
$904$	12.7419	0.423788
$905$	−24.3992	−0.811057
$906$	22.4517	0.745909
$907$	−8.79195	−0.291932	−0.145966	−	0.989290i	$-0.546629\pi$
$907$	−8.79195	−0.291932	−0.145966	+	0.989290i	$0.546629\pi$
$908$	31.5064	1.04558
$909$	12.2811	0.407337
$910$	12.6722	0.420078
$911$	−42.7355	−1.41589	−0.707944	−	0.706268i	$-0.750377\pi$
$911$	−42.7355	−1.41589	−0.707944	+	0.706268i	$0.750377\pi$
$912$	−50.9351	−1.68663
$913$	67.1548	2.22250
$914$	43.2707	1.43127
$915$	−3.03803	−0.100434
$916$	−1.59885	−0.0528274
$917$	2.43588	0.0804397
$918$	−39.1167	−1.29104
$919$	−36.6966	−1.21051	−0.605254	−	0.796032i	$-0.706929\pi$
$919$	−36.6966	−1.21051	−0.605254	+	0.796032i	$0.706929\pi$
$920$	3.39899	0.112062
$921$	26.2525	0.865049
$922$	−27.3260	−0.899933
$923$	33.6770	1.10849
$924$	−9.01207	−0.296475
$925$	−5.68944	−0.187068
$926$	−73.9516	−2.43020
$927$	4.33526	0.142389
$928$	19.0127	0.624122
$929$	−5.26699	−0.172804	−0.0864022	−	0.996260i	$-0.527537\pi$
$929$	−5.26699	−0.172804	−0.0864022	+	0.996260i	$0.527537\pi$
$930$	−4.86256	−0.159450
$931$	−8.31367	−0.272469
$932$	−25.9382	−0.849636
$933$	23.6478	0.774195
$934$	0.235361	0.00770124
$935$	−15.6669	−0.512361
$936$	−6.39286	−0.208957
$937$	−48.1241	−1.57214	−0.786072	−	0.618135i	$-0.787889\pi$
$937$	−48.1241	−1.57214	−0.786072	+	0.618135i	$0.787889\pi$
$938$	5.43098	0.177328
$939$	−16.6332	−0.542805
$940$	6.85187	0.223483
$941$	12.7062	0.414211	0.207106	−	0.978319i	$-0.433596\pi$
$941$	12.7062	0.414211	0.207106	+	0.978319i	$0.433596\pi$
$942$	28.5465	0.930096
$943$	37.2441	1.21284
$944$	−32.7353	−1.06544
$945$	−5.62004	−0.182820
$946$	−99.5453	−3.23650
$947$	−11.6901	−0.379878	−0.189939	−	0.981796i	$-0.560829\pi$
$947$	−11.6901	−0.379878	−0.189939	+	0.981796i	$0.560829\pi$
$948$	−7.02784	−0.228253
$949$	−77.0106	−2.49987
$950$	15.7715	0.511697
$951$	0.539361	0.0174900
$952$	−2.79211	−0.0904929
$953$	−45.9722	−1.48918	−0.744592	−	0.667520i	$-0.767356\pi$
$953$	−45.9722	−1.48918	−0.744592	+	0.667520i	$0.767356\pi$
$954$	−1.13408	−0.0367173
$955$	15.9255	0.515338
$956$	−38.8975	−1.25804
$957$	14.7148	0.475661
$958$	−45.5597	−1.47197
$959$	−13.6639	−0.441230
$960$	5.98423	0.193140
$961$	−27.2294	−0.878367
$962$	72.0975	2.32452
$963$	19.1121	0.615879
$964$	5.85448	0.188560
$965$	−3.08991	−0.0994678
$966$	−11.1845	−0.359856
$967$	28.7114	0.923296	0.461648	−	0.887063i	$-0.347258\pi$
$967$	28.7114	0.923296	0.461648	+	0.887063i	$0.347258\pi$
$968$	5.50517	0.176943
$969$	40.2634	1.29345
$970$	−21.7101	−0.697068
$971$	18.0656	0.579752	0.289876	−	0.957064i	$-0.406386\pi$
$971$	18.0656	0.579752	0.289876	+	0.957064i	$0.406386\pi$
$972$	−19.2624	−0.617841
$973$	−9.24299	−0.296317
$974$	56.4397	1.80844
$975$	−8.81751	−0.282386
$976$	−10.6823	−0.341931
$977$	17.6273	0.563947	0.281974	−	0.959422i	$-0.409011\pi$
$977$	17.6273	0.563947	0.281974	+	0.959422i	$0.409011\pi$
$978$	56.7958	1.81613
$979$	20.8450	0.666210
$980$	1.59885	0.0510733
$981$	3.07588	0.0982054
$982$	48.7451	1.55552
$983$	12.8787	0.410767	0.205383	−	0.978682i	$-0.434156\pi$
$983$	12.8787	0.410767	0.205383	+	0.978682i	$0.434156\pi$
$984$	−8.37662	−0.267037
$985$	24.1934	0.770866
$986$	−18.1701	−0.578655
$987$	5.65691	0.180061
$988$	−88.7909	−2.82481
$989$	−54.8853	−1.74525
$990$	−10.1872	−0.323772
$991$	−32.8525	−1.04359	−0.521797	−	0.853070i	$-0.674738\pi$
$991$	−32.8525	−1.04359	−0.521797	+	0.853070i	$0.674738\pi$
$992$	−14.1421	−0.449013
$993$	23.8002	0.755276
$994$	9.56414	0.303356
$995$	−10.2745	−0.325725
$996$	33.1910	1.05170
$997$	33.3491	1.05618	0.528088	−	0.849190i	$-0.322909\pi$
$997$	33.3491	1.05618	0.528088	+	0.849190i	$0.322909\pi$
$998$	72.5581	2.29679
$999$	−31.9749	−1.01164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.m.1.12	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.m.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.89706 q^{2} -1.32001 q^{3} +1.59885 q^{4} +1.00000 q^{5} +2.50414 q^{6} -1.00000 q^{7} +0.761013 q^{8} -1.25758 q^{9} +O(q^{10})\)	\(q-1.89706 q^{2} -1.32001 q^{3} +1.59885 q^{4} +1.00000 q^{5} +2.50414 q^{6} -1.00000 q^{7} +0.761013 q^{8} -1.25758 q^{9} -1.89706 q^{10} -4.27013 q^{11} -2.11049 q^{12} +6.67988 q^{13} +1.89706 q^{14} -1.32001 q^{15} -4.64138 q^{16} +3.66894 q^{17} +2.38570 q^{18} -8.31367 q^{19} +1.59885 q^{20} +1.32001 q^{21} +8.10070 q^{22} +4.46641 q^{23} -1.00454 q^{24} +1.00000 q^{25} -12.6722 q^{26} +5.62004 q^{27} -1.59885 q^{28} +2.61057 q^{29} +2.50414 q^{30} -1.94181 q^{31} +7.28297 q^{32} +5.63661 q^{33} -6.96021 q^{34} -1.00000 q^{35} -2.01067 q^{36} -5.68944 q^{37} +15.7715 q^{38} -8.81751 q^{39} +0.761013 q^{40} +8.33873 q^{41} -2.50414 q^{42} -12.2885 q^{43} -6.82728 q^{44} -1.25758 q^{45} -8.47305 q^{46} +4.28551 q^{47} +6.12667 q^{48} +1.00000 q^{49} -1.89706 q^{50} -4.84304 q^{51} +10.6801 q^{52} -0.475367 q^{53} -10.6616 q^{54} -4.27013 q^{55} -0.761013 q^{56} +10.9741 q^{57} -4.95241 q^{58} +7.05293 q^{59} -2.11049 q^{60} +2.30152 q^{61} +3.68373 q^{62} +1.25758 q^{63} -4.53348 q^{64} +6.67988 q^{65} -10.6930 q^{66} +2.86284 q^{67} +5.86608 q^{68} -5.89570 q^{69} +1.89706 q^{70} +5.04155 q^{71} -0.957032 q^{72} -11.5287 q^{73} +10.7932 q^{74} -1.32001 q^{75} -13.2923 q^{76} +4.27013 q^{77} +16.7274 q^{78} +3.32995 q^{79} -4.64138 q^{80} -3.64577 q^{81} -15.8191 q^{82} -15.7266 q^{83} +2.11049 q^{84} +3.66894 q^{85} +23.3120 q^{86} -3.44598 q^{87} -3.24962 q^{88} -4.88159 q^{89} +2.38570 q^{90} -6.67988 q^{91} +7.14110 q^{92} +2.56320 q^{93} -8.12988 q^{94} -8.31367 q^{95} -9.61358 q^{96} +11.4440 q^{97} -1.89706 q^{98} +5.37001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) 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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