LMFDB - Embedded newform 8005.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68284 q^{2} +2.48419 q^{3} +5.19763 q^{4} +1.00000 q^{5} -6.66470 q^{6} +0.389624 q^{7} -8.57874 q^{8} +3.17122 q^{9} +O(q^{10})$	\(q-2.68284 q^{2} +2.48419 q^{3} +5.19763 q^{4} +1.00000 q^{5} -6.66470 q^{6} +0.389624 q^{7} -8.57874 q^{8} +3.17122 q^{9} -2.68284 q^{10} -0.726629 q^{11} +12.9119 q^{12} -0.929729 q^{13} -1.04530 q^{14} +2.48419 q^{15} +12.6201 q^{16} -4.73623 q^{17} -8.50787 q^{18} +4.56139 q^{19} +5.19763 q^{20} +0.967902 q^{21} +1.94943 q^{22} -2.76946 q^{23} -21.3113 q^{24} +1.00000 q^{25} +2.49431 q^{26} +0.425338 q^{27} +2.02512 q^{28} +1.93541 q^{29} -6.66470 q^{30} +1.26449 q^{31} -16.7003 q^{32} -1.80509 q^{33} +12.7065 q^{34} +0.389624 q^{35} +16.4828 q^{36} -7.24064 q^{37} -12.2375 q^{38} -2.30963 q^{39} -8.57874 q^{40} +0.791917 q^{41} -2.59673 q^{42} +2.83859 q^{43} -3.77675 q^{44} +3.17122 q^{45} +7.43001 q^{46} -9.75978 q^{47} +31.3508 q^{48} -6.84819 q^{49} -2.68284 q^{50} -11.7657 q^{51} -4.83239 q^{52} -7.50251 q^{53} -1.14111 q^{54} -0.726629 q^{55} -3.34249 q^{56} +11.3314 q^{57} -5.19241 q^{58} +6.90779 q^{59} +12.9119 q^{60} -11.3541 q^{61} -3.39241 q^{62} +1.23558 q^{63} +19.5640 q^{64} -0.929729 q^{65} +4.84276 q^{66} -1.77906 q^{67} -24.6172 q^{68} -6.87986 q^{69} -1.04530 q^{70} -11.5702 q^{71} -27.2051 q^{72} +1.36668 q^{73} +19.4255 q^{74} +2.48419 q^{75} +23.7084 q^{76} -0.283112 q^{77} +6.19636 q^{78} +6.15982 q^{79} +12.6201 q^{80} -8.45703 q^{81} -2.12459 q^{82} -11.4113 q^{83} +5.03080 q^{84} -4.73623 q^{85} -7.61548 q^{86} +4.80794 q^{87} +6.23356 q^{88} -5.17840 q^{89} -8.50787 q^{90} -0.362245 q^{91} -14.3946 q^{92} +3.14123 q^{93} +26.1839 q^{94} +4.56139 q^{95} -41.4868 q^{96} -13.7583 q^{97} +18.3726 q^{98} -2.30430 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) $ 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.68284	−1.89705	−0.948527	−	0.316695i	$-0.897427\pi$
$2$	−2.68284	−1.89705	−0.948527	+	0.316695i	$0.897427\pi$
$3$	2.48419	1.43425	0.717125	−	0.696945i	$-0.245458\pi$
$3$	2.48419	1.43425	0.717125	+	0.696945i	$0.245458\pi$
$4$	5.19763	2.59882
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.66470	−2.72085
$7$	0.389624	0.147264	0.0736321	−	0.997285i	$-0.476541\pi$
$7$	0.389624	0.147264	0.0736321	+	0.997285i	$0.476541\pi$
$8$	−8.57874	−3.03304
$9$	3.17122	1.05707
$10$	−2.68284	−0.848389
$11$	−0.726629	−0.219087	−0.109543	−	0.993982i	$-0.534939\pi$
$11$	−0.726629	−0.219087	−0.109543	+	0.993982i	$0.534939\pi$
$12$	12.9119	3.72735
$13$	−0.929729	−0.257860	−0.128930	−	0.991654i	$-0.541154\pi$
$13$	−0.929729	−0.257860	−0.128930	+	0.991654i	$0.541154\pi$
$14$	−1.04530	−0.279368
$15$	2.48419	0.641416
$16$	12.6201	3.15503
$17$	−4.73623	−1.14870	−0.574352	−	0.818608i	$-0.694746\pi$
$17$	−4.73623	−1.14870	−0.574352	+	0.818608i	$0.694746\pi$
$18$	−8.50787	−2.00532
$19$	4.56139	1.04645	0.523227	−	0.852193i	$-0.324728\pi$
$19$	4.56139	1.04645	0.523227	+	0.852193i	$0.324728\pi$
$20$	5.19763	1.16223
$21$	0.967902	0.211214
$22$	1.94943	0.415620
$23$	−2.76946	−0.577471	−0.288736	−	0.957409i	$-0.593235\pi$
$23$	−2.76946	−0.577471	−0.288736	+	0.957409i	$0.593235\pi$
$24$	−21.3113	−4.35014
$25$	1.00000	0.200000
$26$	2.49431	0.489175
$27$	0.425338	0.0818564
$28$	2.02512	0.382712
$29$	1.93541	0.359397	0.179699	−	0.983722i	$-0.442488\pi$
$29$	1.93541	0.359397	0.179699	+	0.983722i	$0.442488\pi$
$30$	−6.66470	−1.21680
$31$	1.26449	0.227108	0.113554	−	0.993532i	$-0.463776\pi$
$31$	1.26449	0.227108	0.113554	+	0.993532i	$0.463776\pi$
$32$	−16.7003	−2.95222
$33$	−1.80509	−0.314225
$34$	12.7065	2.17915
$35$	0.389624	0.0658585
$36$	16.4828	2.74714
$37$	−7.24064	−1.19035	−0.595177	−	0.803594i	$-0.702918\pi$
$37$	−7.24064	−1.19035	−0.595177	+	0.803594i	$0.702918\pi$
$38$	−12.2375	−1.98518
$39$	−2.30963	−0.369836
$40$	−8.57874	−1.35642
$41$	0.791917	0.123677	0.0618384	−	0.998086i	$-0.480304\pi$
$41$	0.791917	0.123677	0.0618384	+	0.998086i	$0.480304\pi$
$42$	−2.59673	−0.400684
$43$	2.83859	0.432881	0.216440	−	0.976296i	$-0.430555\pi$
$43$	2.83859	0.432881	0.216440	+	0.976296i	$0.430555\pi$
$44$	−3.77675	−0.569367
$45$	3.17122	0.472737
$46$	7.43001	1.09549
$47$	−9.75978	−1.42361	−0.711805	−	0.702377i	$-0.752122\pi$
$47$	−9.75978	−1.42361	−0.711805	+	0.702377i	$0.752122\pi$
$48$	31.3508	4.52510
$49$	−6.84819	−0.978313
$50$	−2.68284	−0.379411
$51$	−11.7657	−1.64753
$52$	−4.83239	−0.670132
$53$	−7.50251	−1.03055	−0.515275	−	0.857025i	$-0.672310\pi$
$53$	−7.50251	−1.03055	−0.515275	+	0.857025i	$0.672310\pi$
$54$	−1.14111	−0.155286
$55$	−0.726629	−0.0979787
$56$	−3.34249	−0.446658
$57$	11.3314	1.50088
$58$	−5.19241	−0.681796
$59$	6.90779	0.899317	0.449659	−	0.893201i	$-0.351546\pi$
$59$	6.90779	0.899317	0.449659	+	0.893201i	$0.351546\pi$
$60$	12.9119	1.66692
$61$	−11.3541	−1.45374	−0.726869	−	0.686777i	$-0.759025\pi$
$61$	−11.3541	−1.45374	−0.726869	+	0.686777i	$0.759025\pi$
$62$	−3.39241	−0.430837
$63$	1.23558	0.155669
$64$	19.5640	2.44550
$65$	−0.929729	−0.115319
$66$	4.84276	0.596103
$67$	−1.77906	−0.217347	−0.108674	−	0.994077i	$-0.534660\pi$
$67$	−1.77906	−0.217347	−0.108674	+	0.994077i	$0.534660\pi$
$68$	−24.6172	−2.98527
$69$	−6.87986	−0.828238
$70$	−1.04530	−0.124937
$71$	−11.5702	−1.37313	−0.686563	−	0.727070i	$-0.740881\pi$
$71$	−11.5702	−1.37313	−0.686563	+	0.727070i	$0.740881\pi$
$72$	−27.2051	−3.20615
$73$	1.36668	0.159958	0.0799788	−	0.996797i	$-0.474515\pi$
$73$	1.36668	0.159958	0.0799788	+	0.996797i	$0.474515\pi$
$74$	19.4255	2.25817
$75$	2.48419	0.286850
$76$	23.7084	2.71954
$77$	−0.283112	−0.0322636
$78$	6.19636	0.701600
$79$	6.15982	0.693034	0.346517	−	0.938044i	$-0.387364\pi$
$79$	6.15982	0.693034	0.346517	+	0.938044i	$0.387364\pi$
$80$	12.6201	1.41097
$81$	−8.45703	−0.939670
$82$	−2.12459	−0.234622
$83$	−11.4113	−1.25255	−0.626276	−	0.779601i	$-0.715422\pi$
$83$	−11.4113	−1.25255	−0.626276	+	0.779601i	$0.715422\pi$
$84$	5.03080	0.548905
$85$	−4.73623	−0.513716
$86$	−7.61548	−0.821198
$87$	4.80794	0.515465
$88$	6.23356	0.664500
$89$	−5.17840	−0.548909	−0.274455	−	0.961600i	$-0.588497\pi$
$89$	−5.17840	−0.548909	−0.274455	+	0.961600i	$0.588497\pi$
$90$	−8.50787	−0.896808
$91$	−0.362245	−0.0379736
$92$	−14.3946	−1.50074
$93$	3.14123	0.325730
$94$	26.1839	2.70067
$95$	4.56139	0.467989
$96$	−41.4868	−4.23423
$97$	−13.7583	−1.39695	−0.698473	−	0.715636i	$-0.746137\pi$
$97$	−13.7583	−1.39695	−0.698473	+	0.715636i	$0.746137\pi$
$98$	18.3726	1.85591
$99$	−2.30430	−0.231591
$100$	5.19763	0.519763
$101$	−4.64579	−0.462273	−0.231137	−	0.972921i	$-0.574244\pi$
$101$	−4.64579	−0.462273	−0.231137	+	0.972921i	$0.574244\pi$
$102$	31.5655	3.12545
$103$	6.61827	0.652117	0.326059	−	0.945350i	$-0.394279\pi$
$103$	6.61827	0.652117	0.326059	+	0.945350i	$0.394279\pi$
$104$	7.97590	0.782102
$105$	0.967902	0.0944576
$106$	20.1280	1.95501
$107$	−1.63346	−0.157913	−0.0789564	−	0.996878i	$-0.525159\pi$
$107$	−1.63346	−0.157913	−0.0789564	+	0.996878i	$0.525159\pi$
$108$	2.21075	0.212730
$109$	16.6143	1.59136	0.795682	−	0.605715i	$-0.207113\pi$
$109$	16.6143	1.59136	0.795682	+	0.605715i	$0.207113\pi$
$110$	1.94943	0.185871
$111$	−17.9872	−1.70727
$112$	4.91711	0.464623
$113$	3.94269	0.370897	0.185449	−	0.982654i	$-0.440626\pi$
$113$	3.94269	0.370897	0.185449	+	0.982654i	$0.440626\pi$
$114$	−30.4003	−2.84725
$115$	−2.76946	−0.258253
$116$	10.0596	0.934007
$117$	−2.94837	−0.272577
$118$	−18.5325	−1.70605
$119$	−1.84535	−0.169163
$120$	−21.3113	−1.94544
$121$	−10.4720	−0.952001
$122$	30.4611	2.75782
$123$	1.96728	0.177383
$124$	6.57233	0.590213
$125$	1.00000	0.0894427
$126$	−3.31487	−0.295312
$127$	9.54493	0.846976	0.423488	−	0.905902i	$-0.360806\pi$
$127$	9.54493	0.846976	0.423488	+	0.905902i	$0.360806\pi$
$128$	−19.0865	−1.68702
$129$	7.05160	0.620859
$130$	2.49431	0.218766
$131$	−4.51674	−0.394629	−0.197315	−	0.980340i	$-0.563222\pi$
$131$	−4.51674	−0.394629	−0.197315	+	0.980340i	$0.563222\pi$
$132$	−9.38218	−0.816614
$133$	1.77723	0.154105
$134$	4.77294	0.412319
$135$	0.425338	0.0366073
$136$	40.6309	3.48407
$137$	−8.98458	−0.767605	−0.383802	−	0.923415i	$-0.625386\pi$
$137$	−8.98458	−0.767605	−0.383802	+	0.923415i	$0.625386\pi$
$138$	18.4576	1.57121
$139$	4.45093	0.377523	0.188761	−	0.982023i	$-0.439553\pi$
$139$	4.45093	0.377523	0.188761	+	0.982023i	$0.439553\pi$
$140$	2.02512	0.171154
$141$	−24.2452	−2.04181
$142$	31.0409	2.60490
$143$	0.675568	0.0564939
$144$	40.0212	3.33510
$145$	1.93541	0.160727
$146$	−3.66658	−0.303448
$147$	−17.0122	−1.40315
$148$	−37.6342	−3.09351
$149$	9.11405	0.746652	0.373326	−	0.927700i	$-0.378217\pi$
$149$	9.11405	0.746652	0.373326	+	0.927700i	$0.378217\pi$
$150$	−6.66470	−0.544170
$151$	−10.2757	−0.836228	−0.418114	−	0.908395i	$-0.637309\pi$
$151$	−10.2757	−0.836228	−0.418114	+	0.908395i	$0.637309\pi$
$152$	−39.1310	−3.17394
$153$	−15.0196	−1.21426
$154$	0.759545	0.0612059
$155$	1.26449	0.101566
$156$	−12.0046	−0.961137
$157$	23.0088	1.83630	0.918152	−	0.396228i	$-0.129681\pi$
$157$	23.0088	1.83630	0.918152	+	0.396228i	$0.129681\pi$
$158$	−16.5258	−1.31472
$159$	−18.6377	−1.47807
$160$	−16.7003	−1.32027
$161$	−1.07905	−0.0850408
$162$	22.6889	1.78261
$163$	16.4215	1.28623	0.643114	−	0.765770i	$-0.277642\pi$
$163$	16.4215	1.28623	0.643114	+	0.765770i	$0.277642\pi$
$164$	4.11610	0.321413
$165$	−1.80509	−0.140526
$166$	30.6147	2.37616
$167$	−0.971160	−0.0751507	−0.0375753	−	0.999294i	$-0.511963\pi$
$167$	−0.971160	−0.0751507	−0.0375753	+	0.999294i	$0.511963\pi$
$168$	−8.30338	−0.640620
$169$	−12.1356	−0.933508
$170$	12.7065	0.974548
$171$	14.4652	1.10618
$172$	14.7539	1.12498
$173$	12.0342	0.914947	0.457473	−	0.889223i	$-0.348755\pi$
$173$	12.0342	0.914947	0.457473	+	0.889223i	$0.348755\pi$
$174$	−12.8989	−0.977866
$175$	0.389624	0.0294528
$176$	−9.17015	−0.691226
$177$	17.1603	1.28985
$178$	13.8928	1.04131
$179$	16.4209	1.22735	0.613676	−	0.789558i	$-0.289690\pi$
$179$	16.4209	1.22735	0.613676	+	0.789558i	$0.289690\pi$
$180$	16.4828	1.22856
$181$	−2.65182	−0.197108	−0.0985540	−	0.995132i	$-0.531422\pi$
$181$	−2.65182	−0.197108	−0.0985540	+	0.995132i	$0.531422\pi$
$182$	0.971846	0.0720380
$183$	−28.2057	−2.08502
$184$	23.7584	1.75150
$185$	−7.24064	−0.532343
$186$	−8.42741	−0.617928
$187$	3.44148	0.251666
$188$	−50.7277	−3.69970
$189$	0.165722	0.0120545
$190$	−12.2375	−0.887800
$191$	17.6554	1.27750	0.638748	−	0.769416i	$-0.279453\pi$
$191$	17.6554	1.27750	0.638748	+	0.769416i	$0.279453\pi$
$192$	48.6007	3.50746
$193$	−9.94885	−0.716134	−0.358067	−	0.933696i	$-0.616564\pi$
$193$	−9.94885	−0.716134	−0.358067	+	0.933696i	$0.616564\pi$
$194$	36.9114	2.65008
$195$	−2.30963	−0.165396
$196$	−35.5944	−2.54246
$197$	−14.8842	−1.06046	−0.530228	−	0.847855i	$-0.677894\pi$
$197$	−14.8842	−1.06046	−0.530228	+	0.847855i	$0.677894\pi$
$198$	6.18207	0.439340
$199$	−12.0736	−0.855875	−0.427937	−	0.903808i	$-0.640760\pi$
$199$	−12.0736	−0.855875	−0.427937	+	0.903808i	$0.640760\pi$
$200$	−8.57874	−0.606608
$201$	−4.41953	−0.311730
$202$	12.4639	0.876957
$203$	0.754084	0.0529263
$204$	−61.1538	−4.28163
$205$	0.791917	0.0553099
$206$	−17.7558	−1.23710
$207$	−8.78255	−0.610429
$208$	−11.7333	−0.813558
$209$	−3.31444	−0.229265
$210$	−2.59673	−0.179191
$211$	−1.52943	−0.105290	−0.0526452	−	0.998613i	$-0.516765\pi$
$211$	−1.52943	−0.105290	−0.0526452	+	0.998613i	$0.516765\pi$
$212$	−38.9953	−2.67821
$213$	−28.7425	−1.96941
$214$	4.38232	0.299569
$215$	2.83859	0.193590
$216$	−3.64886	−0.248274
$217$	0.492674	0.0334449
$218$	−44.5736	−3.01890
$219$	3.39509	0.229419
$220$	−3.77675	−0.254629
$221$	4.40341	0.296205
$222$	48.2567	3.23878
$223$	21.4376	1.43557	0.717783	−	0.696267i	$-0.245157\pi$
$223$	21.4376	1.43557	0.717783	+	0.696267i	$0.245157\pi$
$224$	−6.50684	−0.434757
$225$	3.17122	0.211415
$226$	−10.5776	−0.703613
$227$	−3.37272	−0.223856	−0.111928	−	0.993716i	$-0.535703\pi$
$227$	−3.37272	−0.223856	−0.111928	+	0.993716i	$0.535703\pi$
$228$	58.8963	3.90050
$229$	−17.8215	−1.17768	−0.588840	−	0.808250i	$-0.700415\pi$
$229$	−17.8215	−1.17768	−0.588840	+	0.808250i	$0.700415\pi$
$230$	7.43001	0.489920
$231$	−0.703306	−0.0462741
$232$	−16.6034	−1.09007
$233$	−15.3859	−1.00797	−0.503983	−	0.863714i	$-0.668132\pi$
$233$	−15.3859	−1.00797	−0.503983	+	0.863714i	$0.668132\pi$
$234$	7.91002	0.517094
$235$	−9.75978	−0.636658
$236$	35.9041	2.33716
$237$	15.3022	0.993984
$238$	4.95078	0.320911
$239$	−13.9051	−0.899447	−0.449723	−	0.893168i	$-0.648477\pi$
$239$	−13.9051	−0.899447	−0.449723	+	0.893168i	$0.648477\pi$
$240$	31.3508	2.02369
$241$	13.2015	0.850386	0.425193	−	0.905103i	$-0.360206\pi$
$241$	13.2015	0.850386	0.425193	+	0.905103i	$0.360206\pi$
$242$	28.0947	1.80600
$243$	−22.2849	−1.42958
$244$	−59.0142	−3.77800
$245$	−6.84819	−0.437515
$246$	−5.27789	−0.336506
$247$	−4.24086	−0.269839
$248$	−10.8477	−0.688829
$249$	−28.3479	−1.79647
$250$	−2.68284	−0.169678
$251$	3.71123	0.234251	0.117125	−	0.993117i	$-0.462632\pi$
$251$	3.71123	0.234251	0.117125	+	0.993117i	$0.462632\pi$
$252$	6.42211	0.404555
$253$	2.01237	0.126516
$254$	−25.6075	−1.60676
$255$	−11.7657	−0.736797
$256$	12.0780	0.754874
$257$	−18.5467	−1.15691	−0.578455	−	0.815714i	$-0.696344\pi$
$257$	−18.5467	−1.15691	−0.578455	+	0.815714i	$0.696344\pi$
$258$	−18.9183	−1.17780
$259$	−2.82113	−0.175297
$260$	−4.83239	−0.299692
$261$	6.13762	0.379909
$262$	12.1177	0.748633
$263$	−1.71482	−0.105741	−0.0528703	−	0.998601i	$-0.516837\pi$
$263$	−1.71482	−0.105741	−0.0528703	+	0.998601i	$0.516837\pi$
$264$	15.4854	0.953059
$265$	−7.50251	−0.460876
$266$	−4.76802	−0.292346
$267$	−12.8641	−0.787273
$268$	−9.24691	−0.564845
$269$	−17.4751	−1.06547	−0.532736	−	0.846281i	$-0.678836\pi$
$269$	−17.4751	−1.06547	−0.532736	+	0.846281i	$0.678836\pi$
$270$	−1.14111	−0.0694460
$271$	−16.3023	−0.990293	−0.495146	−	0.868810i	$-0.664886\pi$
$271$	−16.3023	−0.990293	−0.495146	+	0.868810i	$0.664886\pi$
$272$	−59.7718	−3.62420
$273$	−0.899887	−0.0544636
$274$	24.1042	1.45619
$275$	−0.726629	−0.0438174
$276$	−35.7590	−2.15244
$277$	−6.94525	−0.417300	−0.208650	−	0.977990i	$-0.566907\pi$
$277$	−6.94525	−0.417300	−0.208650	+	0.977990i	$0.566907\pi$
$278$	−11.9411	−0.716182
$279$	4.00996	0.240070
$280$	−3.34249	−0.199752
$281$	13.0948	0.781172	0.390586	−	0.920566i	$-0.372272\pi$
$281$	13.0948	0.781172	0.390586	+	0.920566i	$0.372272\pi$
$282$	65.0459	3.87343
$283$	−23.4988	−1.39686	−0.698429	−	0.715680i	$-0.746117\pi$
$283$	−23.4988	−1.39686	−0.698429	+	0.715680i	$0.746117\pi$
$284$	−60.1375	−3.56850
$285$	11.3314	0.671213
$286$	−1.81244	−0.107172
$287$	0.308550	0.0182131
$288$	−52.9603	−3.12071
$289$	5.43186	0.319521
$290$	−5.19241	−0.304909
$291$	−34.1783	−2.00357
$292$	7.10349	0.415700
$293$	4.53626	0.265011	0.132505	−	0.991182i	$-0.457698\pi$
$293$	4.53626	0.265011	0.132505	+	0.991182i	$0.457698\pi$
$294$	45.6411	2.66184
$295$	6.90779	0.402187
$296$	62.1156	3.61040
$297$	−0.309063	−0.0179337
$298$	−24.4515	−1.41644
$299$	2.57484	0.148907
$300$	12.9119	0.745470
$301$	1.10598	0.0637478
$302$	27.5682	1.58637
$303$	−11.5410	−0.663015
$304$	57.5653	3.30160
$305$	−11.3541	−0.650131
$306$	40.2952	2.30352
$307$	16.2270	0.926121	0.463061	−	0.886327i	$-0.346751\pi$
$307$	16.2270	0.926121	0.463061	+	0.886327i	$0.346751\pi$
$308$	−1.47151	−0.0838473
$309$	16.4411	0.935299
$310$	−3.39241	−0.192676
$311$	−8.79555	−0.498750	−0.249375	−	0.968407i	$-0.580225\pi$
$311$	−8.79555	−0.498750	−0.249375	+	0.968407i	$0.580225\pi$
$312$	19.8137	1.12173
$313$	−27.7369	−1.56778	−0.783891	−	0.620898i	$-0.786768\pi$
$313$	−27.7369	−1.56778	−0.783891	+	0.620898i	$0.786768\pi$
$314$	−61.7290	−3.48357
$315$	1.23558	0.0696172
$316$	32.0165	1.80107
$317$	3.95276	0.222009	0.111005	−	0.993820i	$-0.464593\pi$
$317$	3.95276	0.222009	0.111005	+	0.993820i	$0.464593\pi$
$318$	50.0020	2.80397
$319$	−1.40633	−0.0787392
$320$	19.5640	1.09366
$321$	−4.05784	−0.226487
$322$	2.89491	0.161327
$323$	−21.6038	−1.20207
$324$	−43.9565	−2.44203
$325$	−0.929729	−0.0515721
$326$	−44.0562	−2.44005
$327$	41.2732	2.28241
$328$	−6.79365	−0.375117
$329$	−3.80265	−0.209647
$330$	4.84276	0.266585
$331$	−4.41712	−0.242787	−0.121393	−	0.992604i	$-0.538736\pi$
$331$	−4.41712	−0.242787	−0.121393	+	0.992604i	$0.538736\pi$
$332$	−59.3117	−3.25515
$333$	−22.9617	−1.25829
$334$	2.60547	0.142565
$335$	−1.77906	−0.0972005
$336$	12.2150	0.666385
$337$	10.8230	0.589568	0.294784	−	0.955564i	$-0.404752\pi$
$337$	10.8230	0.589568	0.294784	+	0.955564i	$0.404752\pi$
$338$	32.5579	1.77092
$339$	9.79442	0.531960
$340$	−24.6172	−1.33505
$341$	−0.918812	−0.0497564
$342$	−38.8077	−2.09848
$343$	−5.39559	−0.291335
$344$	−24.3515	−1.31295
$345$	−6.87986	−0.370399
$346$	−32.2860	−1.73570
$347$	−10.3268	−0.554372	−0.277186	−	0.960816i	$-0.589402\pi$
$347$	−10.3268	−0.554372	−0.277186	+	0.960816i	$0.589402\pi$
$348$	24.9899	1.33960
$349$	34.3739	1.83999	0.919995	−	0.391929i	$-0.128192\pi$
$349$	34.3739	1.83999	0.919995	+	0.391929i	$0.128192\pi$
$350$	−1.04530	−0.0558736
$351$	−0.395449	−0.0211075
$352$	12.1349	0.646794
$353$	−13.9950	−0.744878	−0.372439	−	0.928057i	$-0.621478\pi$
$353$	−13.9950	−0.744878	−0.372439	+	0.928057i	$0.621478\pi$
$354$	−46.0383	−2.44691
$355$	−11.5702	−0.614081
$356$	−26.9154	−1.42651
$357$	−4.58421	−0.242622
$358$	−44.0545	−2.32835
$359$	34.7895	1.83612	0.918059	−	0.396444i	$-0.129756\pi$
$359$	34.7895	1.83612	0.918059	+	0.396444i	$0.129756\pi$
$360$	−27.2051	−1.43383
$361$	1.80628	0.0950673
$362$	7.11440	0.373925
$363$	−26.0145	−1.36541
$364$	−1.88282	−0.0986864
$365$	1.36668	0.0715352
$366$	75.6713	3.95540
$367$	10.1809	0.531437	0.265718	−	0.964051i	$-0.414391\pi$
$367$	10.1809	0.531437	0.265718	+	0.964051i	$0.414391\pi$
$368$	−34.9509	−1.82194
$369$	2.51134	0.130735
$370$	19.4255	1.00988
$371$	−2.92316	−0.151763
$372$	16.3269	0.846512
$373$	13.6646	0.707526	0.353763	−	0.935335i	$-0.384902\pi$
$373$	13.6646	0.707526	0.353763	+	0.935335i	$0.384902\pi$
$374$	−9.23295	−0.477424
$375$	2.48419	0.128283
$376$	83.7266	4.31787
$377$	−1.79941	−0.0926743
$378$	−0.444606	−0.0228681
$379$	24.6950	1.26850	0.634249	−	0.773129i	$-0.281309\pi$
$379$	24.6950	1.26850	0.634249	+	0.773129i	$0.281309\pi$
$380$	23.7084	1.21622
$381$	23.7115	1.21477
$382$	−47.3665	−2.42348
$383$	−13.3189	−0.680564	−0.340282	−	0.940323i	$-0.610523\pi$
$383$	−13.3189	−0.680564	−0.340282	+	0.940323i	$0.610523\pi$
$384$	−47.4145	−2.41961
$385$	−0.283112	−0.0144287
$386$	26.6912	1.35855
$387$	9.00178	0.457586
$388$	−71.5107	−3.63041
$389$	−29.2086	−1.48094	−0.740468	−	0.672092i	$-0.765396\pi$
$389$	−29.2086	−1.48094	−0.740468	+	0.672092i	$0.765396\pi$
$390$	6.19636	0.313765
$391$	13.1168	0.663344
$392$	58.7489	2.96727
$393$	−11.2205	−0.565997
$394$	39.9320	2.01174
$395$	6.15982	0.309934
$396$	−11.9769	−0.601862
$397$	−0.00725866	−0.000364301 0	−0.000182151	−	1.00000i	$-0.500058\pi$
$397$	−0.00725866	−0.000364301 0	−0.000182151		1.00000i	$0.500058\pi$
$398$	32.3915	1.62364
$399$	4.41498	0.221025
$400$	12.6201	0.631006
$401$	13.7906	0.688670	0.344335	−	0.938847i	$-0.388104\pi$
$401$	13.7906	0.688670	0.344335	+	0.938847i	$0.388104\pi$
$402$	11.8569	0.591369
$403$	−1.17563	−0.0585622
$404$	−24.1471	−1.20136
$405$	−8.45703	−0.420233
$406$	−2.02309	−0.100404
$407$	5.26126	0.260791
$408$	100.935	4.99703
$409$	−11.7458	−0.580794	−0.290397	−	0.956906i	$-0.593787\pi$
$409$	−11.7458	−0.580794	−0.290397	+	0.956906i	$0.593787\pi$
$410$	−2.12459	−0.104926
$411$	−22.3194	−1.10094
$412$	34.3993	1.69473
$413$	2.69144	0.132437
$414$	23.5622	1.15802
$415$	−11.4113	−0.560158
$416$	15.5268	0.761262
$417$	11.0570	0.541462
$418$	8.89211	0.434927
$419$	5.72654	0.279760	0.139880	−	0.990168i	$-0.455328\pi$
$419$	5.72654	0.279760	0.139880	+	0.990168i	$0.455328\pi$
$420$	5.03080	0.245478
$421$	13.1416	0.640484	0.320242	−	0.947336i	$-0.396236\pi$
$421$	13.1416	0.640484	0.320242	+	0.947336i	$0.396236\pi$
$422$	4.10322	0.199742
$423$	−30.9504	−1.50486
$424$	64.3621	3.12570
$425$	−4.73623	−0.229741
$426$	77.1116	3.73607
$427$	−4.42381	−0.214083
$428$	−8.49014	−0.410387
$429$	1.67824	0.0810263
$430$	−7.61548	−0.367251
$431$	36.1086	1.73929	0.869644	−	0.493680i	$-0.164348\pi$
$431$	36.1086	1.73929	0.869644	+	0.493680i	$0.164348\pi$
$432$	5.36782	0.258259
$433$	1.27441	0.0612444	0.0306222	−	0.999531i	$-0.490251\pi$
$433$	1.27441	0.0612444	0.0306222	+	0.999531i	$0.490251\pi$
$434$	−1.32177	−0.0634468
$435$	4.80794	0.230523
$436$	86.3552	4.13566
$437$	−12.6326	−0.604298
$438$	−9.10850	−0.435221
$439$	−31.9713	−1.52591	−0.762954	−	0.646453i	$-0.776252\pi$
$439$	−31.9713	−1.52591	−0.762954	+	0.646453i	$0.776252\pi$
$440$	6.23356	0.297173
$441$	−21.7171	−1.03415
$442$	−11.8136	−0.561918
$443$	15.3763	0.730551	0.365276	−	0.930899i	$-0.380975\pi$
$443$	15.3763	0.730551	0.365276	+	0.930899i	$0.380975\pi$
$444$	−93.4907	−4.43687
$445$	−5.17840	−0.245480
$446$	−57.5136	−2.72335
$447$	22.6411	1.07089
$448$	7.62261	0.360134
$449$	−21.9072	−1.03386	−0.516932	−	0.856026i	$-0.672926\pi$
$449$	−21.9072	−1.03386	−0.516932	+	0.856026i	$0.672926\pi$
$450$	−8.50787	−0.401065
$451$	−0.575430	−0.0270960
$452$	20.4927	0.963894
$453$	−25.5269	−1.19936
$454$	9.04848	0.424666
$455$	−0.362245	−0.0169823
$456$	−97.2089	−4.55222
$457$	11.7638	0.550289	0.275145	−	0.961403i	$-0.411274\pi$
$457$	11.7638	0.550289	0.275145	+	0.961403i	$0.411274\pi$
$458$	47.8123	2.23412
$459$	−2.01450	−0.0940287
$460$	−14.3946	−0.671152
$461$	−5.43228	−0.253006	−0.126503	−	0.991966i	$-0.540375\pi$
$461$	−5.43228	−0.253006	−0.126503	+	0.991966i	$0.540375\pi$
$462$	1.88686	0.0877846
$463$	−18.7200	−0.869992	−0.434996	−	0.900432i	$-0.643250\pi$
$463$	−18.7200	−0.869992	−0.434996	+	0.900432i	$0.643250\pi$
$464$	24.4252	1.13391
$465$	3.14123	0.145671
$466$	41.2780	1.91216
$467$	11.1703	0.516901	0.258450	−	0.966025i	$-0.416788\pi$
$467$	11.1703	0.516901	0.258450	+	0.966025i	$0.416788\pi$
$468$	−15.3246	−0.708378
$469$	−0.693166	−0.0320074
$470$	26.1839	1.20777
$471$	57.1584	2.63372
$472$	−59.2601	−2.72767
$473$	−2.06260	−0.0948385
$474$	−41.0533	−1.88564
$475$	4.56139	0.209291
$476$	−9.59145	−0.439623
$477$	−23.7921	−1.08937
$478$	37.3052	1.70630
$479$	3.38428	0.154632	0.0773158	−	0.997007i	$-0.475365\pi$
$479$	3.38428	0.154632	0.0773158	+	0.997007i	$0.475365\pi$
$480$	−41.4868	−1.89360
$481$	6.73184	0.306945
$482$	−35.4176	−1.61323
$483$	−2.68056	−0.121970
$484$	−54.4297	−2.47408
$485$	−13.7583	−0.624733
$486$	59.7869	2.71199
$487$	9.29297	0.421105	0.210552	−	0.977583i	$-0.432474\pi$
$487$	9.29297	0.421105	0.210552	+	0.977583i	$0.432474\pi$
$488$	97.4034	4.40925
$489$	40.7941	1.84477
$490$	18.3726	0.829990
$491$	−19.7833	−0.892809	−0.446404	−	0.894831i	$-0.647296\pi$
$491$	−19.7833	−0.892809	−0.446404	+	0.894831i	$0.647296\pi$
$492$	10.2252	0.460987
$493$	−9.16656	−0.412841
$494$	11.3775	0.511900
$495$	−2.30430	−0.103571
$496$	15.9580	0.716533
$497$	−4.50802	−0.202212
$498$	76.0528	3.40801
$499$	−21.7003	−0.971437	−0.485718	−	0.874115i	$-0.661442\pi$
$499$	−21.7003	−0.971437	−0.485718	+	0.874115i	$0.661442\pi$
$500$	5.19763	0.232445
$501$	−2.41255	−0.107785
$502$	−9.95664	−0.444387
$503$	10.8914	0.485625	0.242812	−	0.970073i	$-0.421930\pi$
$503$	10.8914	0.485625	0.242812	+	0.970073i	$0.421930\pi$
$504$	−10.5997	−0.472150
$505$	−4.64579	−0.206735
$506$	−5.39886	−0.240009
$507$	−30.1472	−1.33888
$508$	49.6110	2.20113
$509$	30.6925	1.36042	0.680210	−	0.733017i	$-0.261889\pi$
$509$	30.6925	1.36042	0.680210	+	0.733017i	$0.261889\pi$
$510$	31.5655	1.39774
$511$	0.532491	0.0235560
$512$	5.76966	0.254985
$513$	1.94013	0.0856590
$514$	49.7578	2.19472
$515$	6.61827	0.291636
$516$	36.6516	1.61350
$517$	7.09174	0.311894
$518$	7.56864	0.332547
$519$	29.8954	1.31226
$520$	7.97590	0.349767
$521$	−28.1820	−1.23467	−0.617337	−	0.786699i	$-0.711789\pi$
$521$	−28.1820	−1.23467	−0.617337	+	0.786699i	$0.711789\pi$
$522$	−16.4662	−0.720708
$523$	8.54004	0.373430	0.186715	−	0.982414i	$-0.440216\pi$
$523$	8.54004	0.373430	0.186715	+	0.982414i	$0.440216\pi$
$524$	−23.4764	−1.02557
$525$	0.967902	0.0422427
$526$	4.60060	0.200596
$527$	−5.98889	−0.260880
$528$	−22.7804	−0.991391
$529$	−15.3301	−0.666527
$530$	20.1280	0.874306
$531$	21.9061	0.950644
$532$	9.23738	0.400491
$533$	−0.736269	−0.0318913
$534$	34.5125	1.49350
$535$	−1.63346	−0.0706208
$536$	15.2621	0.659223
$537$	40.7926	1.76033
$538$	46.8828	2.02126
$539$	4.97610	0.214336
$540$	2.21075	0.0951356
$541$	39.0161	1.67743	0.838717	−	0.544568i	$-0.183306\pi$
$541$	39.0161	1.67743	0.838717	+	0.544568i	$0.183306\pi$
$542$	43.7364	1.87864
$543$	−6.58763	−0.282702
$544$	79.0964	3.39123
$545$	16.6143	0.711680
$546$	2.41425	0.103320
$547$	−28.7572	−1.22957	−0.614784	−	0.788695i	$-0.710757\pi$
$547$	−28.7572	−1.22957	−0.614784	+	0.788695i	$0.710757\pi$
$548$	−46.6986	−1.99486
$549$	−36.0062	−1.53671
$550$	1.94943	0.0831240
$551$	8.82818	0.376093
$552$	59.0206	2.51208
$553$	2.40002	0.102059
$554$	18.6330	0.791640
$555$	−17.9872	−0.763513
$556$	23.1343	0.981113
$557$	−1.77114	−0.0750455	−0.0375228	−	0.999296i	$-0.511947\pi$
$557$	−1.77114	−0.0750455	−0.0375228	+	0.999296i	$0.511947\pi$
$558$	−10.7581	−0.455426
$559$	−2.63912	−0.111623
$560$	4.91711	0.207786
$561$	8.54931	0.360952
$562$	−35.1313	−1.48193
$563$	0.465016	0.0195981	0.00979905	−	0.999952i	$-0.496881\pi$
$563$	0.465016	0.0195981	0.00979905	+	0.999952i	$0.496881\pi$
$564$	−126.018	−5.30629
$565$	3.94269	0.165870
$566$	63.0435	2.64991
$567$	−3.29506	−0.138380
$568$	99.2575	4.16475
$569$	−26.0478	−1.09198	−0.545989	−	0.837792i	$-0.683846\pi$
$569$	−26.0478	−1.09198	−0.545989	+	0.837792i	$0.683846\pi$
$570$	−30.4003	−1.27333
$571$	20.0065	0.837246	0.418623	−	0.908160i	$-0.362513\pi$
$571$	20.0065	0.837246	0.418623	+	0.908160i	$0.362513\pi$
$572$	3.51136	0.146817
$573$	43.8593	1.83225
$574$	−0.827791	−0.0345513
$575$	−2.76946	−0.115494
$576$	62.0417	2.58507
$577$	25.6203	1.06659	0.533294	−	0.845930i	$-0.320954\pi$
$577$	25.6203	1.06659	0.533294	+	0.845930i	$0.320954\pi$
$578$	−14.5728	−0.606150
$579$	−24.7149	−1.02711
$580$	10.0596	0.417701
$581$	−4.44612	−0.184456
$582$	91.6950	3.80088
$583$	5.45154	0.225780
$584$	−11.7244	−0.485158
$585$	−2.94837	−0.121900
$586$	−12.1701	−0.502740
$587$	40.0438	1.65279	0.826393	−	0.563094i	$-0.190389\pi$
$587$	40.0438	1.65279	0.826393	+	0.563094i	$0.190389\pi$
$588$	−88.4234	−3.64652
$589$	5.76781	0.237658
$590$	−18.5325	−0.762971
$591$	−36.9753	−1.52096
$592$	−91.3778	−3.75561
$593$	−17.3763	−0.713561	−0.356780	−	0.934188i	$-0.616126\pi$
$593$	−17.3763	−0.713561	−0.356780	+	0.934188i	$0.616126\pi$
$594$	0.829167	0.0340211
$595$	−1.84535	−0.0756520
$596$	47.3715	1.94041
$597$	−29.9932	−1.22754
$598$	−6.90789	−0.282485
$599$	−7.72616	−0.315682	−0.157841	−	0.987465i	$-0.550453\pi$
$599$	−7.72616	−0.315682	−0.157841	+	0.987465i	$0.550453\pi$
$600$	−21.3113	−0.870028
$601$	19.3402	0.788903	0.394451	−	0.918917i	$-0.370935\pi$
$601$	19.3402	0.788903	0.394451	+	0.918917i	$0.370935\pi$
$602$	−2.96718	−0.120933
$603$	−5.64179	−0.229752
$604$	−53.4095	−2.17320
$605$	−10.4720	−0.425748
$606$	30.9627	1.25778
$607$	−11.7001	−0.474893	−0.237446	−	0.971401i	$-0.576310\pi$
$607$	−11.7001	−0.474893	−0.237446	+	0.971401i	$0.576310\pi$
$608$	−76.1766	−3.08937
$609$	1.87329	0.0759096
$610$	30.4611	1.23333
$611$	9.07395	0.367093
$612$	−78.0664	−3.15565
$613$	30.8575	1.24632	0.623162	−	0.782093i	$-0.285848\pi$
$613$	30.8575	1.24632	0.623162	+	0.782093i	$0.285848\pi$
$614$	−43.5343	−1.75690
$615$	1.96728	0.0793282
$616$	2.42875	0.0978570
$617$	−11.9570	−0.481371	−0.240686	−	0.970603i	$-0.577372\pi$
$617$	−11.9570	−0.481371	−0.240686	+	0.970603i	$0.577372\pi$
$618$	−44.1087	−1.77431
$619$	−24.8557	−0.999033	−0.499517	−	0.866304i	$-0.666489\pi$
$619$	−24.8557	−0.999033	−0.499517	+	0.866304i	$0.666489\pi$
$620$	6.57233	0.263951
$621$	−1.17796	−0.0472697
$622$	23.5971	0.946156
$623$	−2.01763	−0.0808346
$624$	−29.1478	−1.16685
$625$	1.00000	0.0400000
$626$	74.4137	2.97417
$627$	−8.23371	−0.328823
$628$	119.591	4.77222
$629$	34.2934	1.36737
$630$	−3.31487	−0.132068
$631$	27.9840	1.11402	0.557012	−	0.830505i	$-0.311948\pi$
$631$	27.9840	1.11402	0.557012	+	0.830505i	$0.311948\pi$
$632$	−52.8435	−2.10200
$633$	−3.79940	−0.151013
$634$	−10.6046	−0.421164
$635$	9.54493	0.378779
$636$	−96.8719	−3.84122
$637$	6.36696	0.252268
$638$	3.77295	0.149373
$639$	−36.6915	−1.45149
$640$	−19.0865	−0.754459
$641$	4.10918	0.162303	0.0811513	−	0.996702i	$-0.474140\pi$
$641$	4.10918	0.162303	0.0811513	+	0.996702i	$0.474140\pi$
$642$	10.8865	0.429657
$643$	−14.7970	−0.583536	−0.291768	−	0.956489i	$-0.594244\pi$
$643$	−14.7970	−0.583536	−0.291768	+	0.956489i	$0.594244\pi$
$644$	−5.60849	−0.221006
$645$	7.05160	0.277657
$646$	57.9595	2.28039
$647$	−9.79044	−0.384902	−0.192451	−	0.981307i	$-0.561644\pi$
$647$	−9.79044	−0.384902	−0.192451	+	0.981307i	$0.561644\pi$
$648$	72.5507	2.85006
$649$	−5.01940	−0.197029
$650$	2.49431	0.0978351
$651$	1.22390	0.0479683
$652$	85.3528	3.34267
$653$	−21.7370	−0.850636	−0.425318	−	0.905044i	$-0.639838\pi$
$653$	−21.7370	−0.850636	−0.425318	+	0.905044i	$0.639838\pi$
$654$	−110.729	−4.32986
$655$	−4.51674	−0.176484
$656$	9.99410	0.390204
$657$	4.33404	0.169087
$658$	10.2019	0.397711
$659$	32.8558	1.27988	0.639941	−	0.768424i	$-0.278959\pi$
$659$	32.8558	1.27988	0.639941	+	0.768424i	$0.278959\pi$
$660$	−9.38218	−0.365201
$661$	−36.5138	−1.42022	−0.710111	−	0.704090i	$-0.751355\pi$
$661$	−36.5138	−1.42022	−0.710111	+	0.704090i	$0.751355\pi$
$662$	11.8504	0.460580
$663$	10.9389	0.424833
$664$	97.8945	3.79904
$665$	1.77723	0.0689180
$666$	61.6025	2.38705
$667$	−5.36004	−0.207542
$668$	−5.04774	−0.195303
$669$	53.2551	2.05896
$670$	4.77294	0.184395
$671$	8.25018	0.318495
$672$	−16.1643	−0.623550
$673$	19.1217	0.737085	0.368543	−	0.929611i	$-0.379857\pi$
$673$	19.1217	0.737085	0.368543	+	0.929611i	$0.379857\pi$
$674$	−29.0365	−1.11844
$675$	0.425338	0.0163713
$676$	−63.0764	−2.42602
$677$	−29.7350	−1.14281	−0.571404	−	0.820669i	$-0.693601\pi$
$677$	−29.7350	−1.14281	−0.571404	+	0.820669i	$0.693601\pi$
$678$	−26.2769	−1.00916
$679$	−5.36058	−0.205720
$680$	40.6309	1.55812
$681$	−8.37850	−0.321065
$682$	2.46503	0.0943907
$683$	13.0911	0.500918	0.250459	−	0.968127i	$-0.419419\pi$
$683$	13.0911	0.500918	0.250459	+	0.968127i	$0.419419\pi$
$684$	75.1846	2.87476
$685$	−8.98458	−0.343283
$686$	14.4755	0.552678
$687$	−44.2721	−1.68909
$688$	35.8233	1.36575
$689$	6.97530	0.265738
$690$	18.4576	0.702668
$691$	6.11970	0.232804	0.116402	−	0.993202i	$-0.462864\pi$
$691$	6.11970	0.232804	0.116402	+	0.993202i	$0.462864\pi$
$692$	62.5496	2.37778
$693$	−0.897811	−0.0341050
$694$	27.7052	1.05167
$695$	4.45093	0.168833
$696$	−41.2461	−1.56343
$697$	−3.75070	−0.142068
$698$	−92.2196	−3.49056
$699$	−38.2216	−1.44567
$700$	2.02512	0.0765425
$701$	−13.7209	−0.518232	−0.259116	−	0.965846i	$-0.583431\pi$
$701$	−13.7209	−0.518232	−0.259116	+	0.965846i	$0.583431\pi$
$702$	1.06093	0.0400421
$703$	−33.0274	−1.24565
$704$	−14.2158	−0.535777
$705$	−24.2452	−0.913126
$706$	37.5463	1.41307
$707$	−1.81011	−0.0680762
$708$	89.1928	3.35207
$709$	36.1791	1.35874	0.679368	−	0.733798i	$-0.262254\pi$
$709$	36.1791	1.35874	0.679368	+	0.733798i	$0.262254\pi$
$710$	31.0409	1.16494
$711$	19.5341	0.732588
$712$	44.4241	1.66487
$713$	−3.50194	−0.131149
$714$	12.2987	0.460267
$715$	0.675568	0.0252648
$716$	85.3496	3.18966
$717$	−34.5430	−1.29003
$718$	−93.3346	−3.48322
$719$	40.7328	1.51908	0.759538	−	0.650463i	$-0.225425\pi$
$719$	40.7328	1.51908	0.759538	+	0.650463i	$0.225425\pi$
$720$	40.0212	1.49150
$721$	2.57864	0.0960335
$722$	−4.84596	−0.180348
$723$	32.7952	1.21967
$724$	−13.7832	−0.512248
$725$	1.93541	0.0718794
$726$	69.7928	2.59025
$727$	−6.15837	−0.228401	−0.114201	−	0.993458i	$-0.536431\pi$
$727$	−6.15837	−0.228401	−0.114201	+	0.993458i	$0.536431\pi$
$728$	3.10761	0.115176
$729$	−29.9890	−1.11070
$730$	−3.66658	−0.135706
$731$	−13.4442	−0.497252
$732$	−146.603	−5.41859
$733$	−49.7160	−1.83630	−0.918151	−	0.396230i	$-0.870318\pi$
$733$	−49.7160	−1.83630	−0.918151	+	0.396230i	$0.870318\pi$
$734$	−27.3136	−1.00816
$735$	−17.0122	−0.627506
$736$	46.2507	1.70483
$737$	1.29272	0.0476179
$738$	−6.73753	−0.248012
$739$	−16.0582	−0.590710	−0.295355	−	0.955388i	$-0.595438\pi$
$739$	−16.0582	−0.590710	−0.295355	+	0.955388i	$0.595438\pi$
$740$	−37.6342	−1.38346
$741$	−10.5351	−0.387017
$742$	7.84237	0.287903
$743$	−22.5903	−0.828757	−0.414378	−	0.910105i	$-0.636001\pi$
$743$	−22.5903	−0.828757	−0.414378	+	0.910105i	$0.636001\pi$
$744$	−26.9478	−0.987953
$745$	9.11405	0.333913
$746$	−36.6599	−1.34222
$747$	−36.1877	−1.32404
$748$	17.8876	0.654034
$749$	−0.636437	−0.0232549
$750$	−6.66470	−0.243360
$751$	−0.762503	−0.0278241	−0.0139121	−	0.999903i	$-0.504428\pi$
$751$	−0.762503	−0.0278241	−0.0139121	+	0.999903i	$0.504428\pi$
$752$	−123.170	−4.49153
$753$	9.21942	0.335974
$754$	4.82753	0.175808
$755$	−10.2757	−0.373972
$756$	0.861362	0.0313274
$757$	−19.0599	−0.692745	−0.346372	−	0.938097i	$-0.612587\pi$
$757$	−19.0599	−0.692745	−0.346372	+	0.938097i	$0.612587\pi$
$758$	−66.2528	−2.40641
$759$	4.99911	0.181456
$760$	−39.1310	−1.41943
$761$	7.31884	0.265308	0.132654	−	0.991162i	$-0.457650\pi$
$761$	7.31884	0.265308	0.132654	+	0.991162i	$0.457650\pi$
$762$	−63.6140	−2.30449
$763$	6.47334	0.234351
$764$	91.7660	3.31998
$765$	−15.0196	−0.543035
$766$	35.7325	1.29107
$767$	−6.42237	−0.231898
$768$	30.0040	1.08268
$769$	2.90707	0.104832	0.0524159	−	0.998625i	$-0.483308\pi$
$769$	2.90707	0.104832	0.0524159	+	0.998625i	$0.483308\pi$
$770$	0.759545	0.0273721
$771$	−46.0736	−1.65930
$772$	−51.7105	−1.86110
$773$	−28.0020	−1.00716	−0.503580	−	0.863948i	$-0.667984\pi$
$773$	−28.0020	−1.00716	−0.503580	+	0.863948i	$0.667984\pi$
$774$	−24.1503	−0.868066
$775$	1.26449	0.0454216
$776$	118.029	4.23700
$777$	−7.00824	−0.251419
$778$	78.3621	2.80942
$779$	3.61224	0.129422
$780$	−12.0046	−0.429833
$781$	8.40722	0.300834
$782$	−35.1902	−1.25840
$783$	0.823205	0.0294189
$784$	−86.4250	−3.08661
$785$	23.0088	0.821220
$786$	30.1027	1.07373
$787$	−3.33877	−0.119014	−0.0595072	−	0.998228i	$-0.518953\pi$
$787$	−3.33877	−0.119014	−0.0595072	+	0.998228i	$0.518953\pi$
$788$	−77.3627	−2.75593
$789$	−4.25995	−0.151658
$790$	−16.5258	−0.587962
$791$	1.53617	0.0546199
$792$	19.7680	0.702425
$793$	10.5562	0.374861
$794$	0.0194738	0.000691100 0
$795$	−18.6377	−0.661011
$796$	−62.7541	−2.22426
$797$	−3.99041	−0.141348	−0.0706738	−	0.997499i	$-0.522515\pi$
$797$	−3.99041	−0.141348	−0.0706738	+	0.997499i	$0.522515\pi$
$798$	−11.8447	−0.419297
$799$	46.2245	1.63531
$800$	−16.7003	−0.590445
$801$	−16.4218	−0.580237
$802$	−36.9980	−1.30645
$803$	−0.993068	−0.0350446
$804$	−22.9711	−0.810129
$805$	−1.07905	−0.0380314
$806$	3.15402	0.111096
$807$	−43.4114	−1.52815
$808$	39.8550	1.40209
$809$	8.79737	0.309299	0.154649	−	0.987969i	$-0.450575\pi$
$809$	8.79737	0.309299	0.154649	+	0.987969i	$0.450575\pi$
$810$	22.6889	0.797205
$811$	46.8043	1.64352	0.821761	−	0.569832i	$-0.192992\pi$
$811$	46.8043	1.64352	0.821761	+	0.569832i	$0.192992\pi$
$812$	3.91945	0.137546
$813$	−40.4980	−1.42033
$814$	−14.1151	−0.494735
$815$	16.4215	0.575219
$816$	−148.485	−5.19800
$817$	12.9479	0.452990
$818$	31.5122	1.10180
$819$	−1.14876	−0.0401408
$820$	4.11610	0.143740
$821$	24.2853	0.847562	0.423781	−	0.905765i	$-0.360703\pi$
$821$	24.2853	0.847562	0.423781	+	0.905765i	$0.360703\pi$
$822$	59.8795	2.08854
$823$	−14.9347	−0.520590	−0.260295	−	0.965529i	$-0.583820\pi$
$823$	−14.9347	−0.520590	−0.260295	+	0.965529i	$0.583820\pi$
$824$	−56.7764	−1.97790
$825$	−1.80509	−0.0628451
$826$	−7.22071	−0.251241
$827$	19.7252	0.685911	0.342956	−	0.939352i	$-0.388572\pi$
$827$	19.7252	0.685911	0.342956	+	0.939352i	$0.388572\pi$
$828$	−45.6485	−1.58639
$829$	−51.8372	−1.80038	−0.900191	−	0.435496i	$-0.856573\pi$
$829$	−51.8372	−1.80038	−0.900191	+	0.435496i	$0.856573\pi$
$830$	30.6147	1.06265
$831$	−17.2534	−0.598512
$832$	−18.1892	−0.630598
$833$	32.4346	1.12379
$834$	−29.6641	−1.02718
$835$	−0.971160	−0.0336084
$836$	−17.2272	−0.595816
$837$	0.537834	0.0185903
$838$	−15.3634	−0.530720
$839$	−33.4189	−1.15375	−0.576875	−	0.816832i	$-0.695728\pi$
$839$	−33.4189	−1.15375	−0.576875	+	0.816832i	$0.695728\pi$
$840$	−8.30338	−0.286494
$841$	−25.2542	−0.870834
$842$	−35.2569	−1.21503
$843$	32.5301	1.12040
$844$	−7.94942	−0.273630
$845$	−12.1356	−0.417477
$846$	83.0349	2.85480
$847$	−4.08015	−0.140196
$848$	−94.6826	−3.25142
$849$	−58.3755	−2.00344
$850$	12.7065	0.435831
$851$	20.0526	0.687396
$852$	−149.393	−5.11813
$853$	−25.3997	−0.869670	−0.434835	−	0.900510i	$-0.643193\pi$
$853$	−25.3997	−0.869670	−0.434835	+	0.900510i	$0.643193\pi$
$854$	11.8684	0.406128
$855$	14.4652	0.494698
$856$	14.0131	0.478957
$857$	4.65859	0.159134	0.0795672	−	0.996830i	$-0.474646\pi$
$857$	4.65859	0.159134	0.0795672	+	0.996830i	$0.474646\pi$
$858$	−4.50246	−0.153711
$859$	47.3396	1.61521	0.807603	−	0.589727i	$-0.200765\pi$
$859$	47.3396	1.61521	0.807603	+	0.589727i	$0.200765\pi$
$860$	14.7539	0.503105
$861$	0.766499	0.0261222
$862$	−96.8735	−3.29952
$863$	2.49495	0.0849290	0.0424645	−	0.999098i	$-0.486479\pi$
$863$	2.49495	0.0849290	0.0424645	+	0.999098i	$0.486479\pi$
$864$	−7.10327	−0.241658
$865$	12.0342	0.409177
$866$	−3.41905	−0.116184
$867$	13.4938	0.458274
$868$	2.56074	0.0869171
$869$	−4.47591	−0.151835
$870$	−12.8989	−0.437315
$871$	1.65405	0.0560452
$872$	−142.530	−4.82667
$873$	−43.6306	−1.47667
$874$	33.8912	1.14639
$875$	0.389624	0.0131717
$876$	17.6465	0.596218
$877$	24.8039	0.837568	0.418784	−	0.908086i	$-0.362457\pi$
$877$	24.8039	0.837568	0.418784	+	0.908086i	$0.362457\pi$
$878$	85.7740	2.89473
$879$	11.2689	0.380092
$880$	−9.17015	−0.309126
$881$	−20.1300	−0.678196	−0.339098	−	0.940751i	$-0.610122\pi$
$881$	−20.1300	−0.678196	−0.339098	+	0.940751i	$0.610122\pi$
$882$	58.2635	1.96184
$883$	−24.4940	−0.824290	−0.412145	−	0.911118i	$-0.635220\pi$
$883$	−24.4940	−0.824290	−0.412145	+	0.911118i	$0.635220\pi$
$884$	22.8873	0.769783
$885$	17.1603	0.576836
$886$	−41.2522	−1.38590
$887$	−34.0128	−1.14204	−0.571018	−	0.820937i	$-0.693452\pi$
$887$	−34.0128	−1.14204	−0.571018	+	0.820937i	$0.693452\pi$
$888$	154.307	5.17821
$889$	3.71894	0.124729
$890$	13.8928	0.465688
$891$	6.14513	0.205869
$892$	111.425	3.73077
$893$	−44.5181	−1.48974
$894$	−60.7424	−2.03153
$895$	16.4209	0.548889
$896$	−7.43655	−0.248438
$897$	6.39641	0.213570
$898$	58.7735	1.96130
$899$	2.44730	0.0816221
$900$	16.4828	0.549428
$901$	35.5336	1.18380
$902$	1.54379	0.0514025
$903$	2.74748	0.0914303
$904$	−33.8233	−1.12495
$905$	−2.65182	−0.0881494
$906$	68.4847	2.27525
$907$	−44.1531	−1.46608	−0.733040	−	0.680186i	$-0.761899\pi$
$907$	−44.1531	−1.46608	−0.733040	+	0.680186i	$0.761899\pi$
$908$	−17.5302	−0.581759
$909$	−14.7328	−0.488656
$910$	0.971846	0.0322164
$911$	28.2448	0.935790	0.467895	−	0.883784i	$-0.345012\pi$
$911$	28.2448	0.935790	0.467895	+	0.883784i	$0.345012\pi$
$912$	143.003	4.73531
$913$	8.29178	0.274418
$914$	−31.5605	−1.04393
$915$	−28.2057	−0.932450
$916$	−92.6298	−3.06058
$917$	−1.75983	−0.0581147
$918$	5.40458	0.178378
$919$	53.9675	1.78022	0.890112	−	0.455742i	$-0.150626\pi$
$919$	53.9675	1.78022	0.890112	+	0.455742i	$0.150626\pi$
$920$	23.7584	0.783293
$921$	40.3109	1.32829
$922$	14.5739	0.479967
$923$	10.7571	0.354075
$924$	−3.65553	−0.120258
$925$	−7.24064	−0.238071
$926$	50.2227	1.65042
$927$	20.9880	0.689335
$928$	−32.3220	−1.06102
$929$	15.9479	0.523235	0.261617	−	0.965172i	$-0.415744\pi$
$929$	15.9479	0.523235	0.261617	+	0.965172i	$0.415744\pi$
$930$	−8.42741	−0.276346
$931$	−31.2373	−1.02376
$932$	−79.9704	−2.61952
$933$	−21.8499	−0.715332
$934$	−29.9682	−0.980589
$935$	3.44148	0.112548
$936$	25.2933	0.826738
$937$	40.6823	1.32903	0.664517	−	0.747273i	$-0.268637\pi$
$937$	40.6823	1.32903	0.664517	+	0.747273i	$0.268637\pi$
$938$	1.85965	0.0607198
$939$	−68.9038	−2.24859
$940$	−50.7277	−1.65456
$941$	14.0863	0.459200	0.229600	−	0.973285i	$-0.426258\pi$
$941$	14.0863	0.459200	0.229600	+	0.973285i	$0.426258\pi$
$942$	−153.347	−4.99631
$943$	−2.19318	−0.0714198
$944$	87.1771	2.83737
$945$	0.165722	0.00539094
$946$	5.53363	0.179914
$947$	−14.5737	−0.473583	−0.236791	−	0.971561i	$-0.576096\pi$
$947$	−14.5737	−0.473583	−0.236791	+	0.971561i	$0.576096\pi$
$948$	79.5352	2.58318
$949$	−1.27064	−0.0412467
$950$	−12.2375	−0.397036
$951$	9.81943	0.318417
$952$	15.8308	0.513078
$953$	−20.0719	−0.650193	−0.325097	−	0.945681i	$-0.605397\pi$
$953$	−20.0719	−0.650193	−0.325097	+	0.945681i	$0.605397\pi$
$954$	63.8304	2.06659
$955$	17.6554	0.571314
$956$	−72.2737	−2.33750
$957$	−3.49359	−0.112932
$958$	−9.07948	−0.293345
$959$	−3.50061	−0.113041
$960$	48.6007	1.56858
$961$	−29.4011	−0.948422
$962$	−18.0604	−0.582292
$963$	−5.18007	−0.166925
$964$	68.6168	2.21000
$965$	−9.94885	−0.320265
$966$	7.19152	0.231383
$967$	−34.7763	−1.11833	−0.559165	−	0.829056i	$-0.688878\pi$
$967$	−34.7763	−1.11833	−0.559165	+	0.829056i	$0.688878\pi$
$968$	89.8366	2.88746
$969$	−53.6680	−1.72406
$970$	36.9114	1.18515
$971$	−27.6001	−0.885728	−0.442864	−	0.896589i	$-0.646038\pi$
$971$	−27.6001	−0.885728	−0.442864	+	0.896589i	$0.646038\pi$
$972$	−115.829	−3.71521
$973$	1.73419	0.0555956
$974$	−24.9316	−0.798859
$975$	−2.30963	−0.0739673
$976$	−143.290	−4.58659
$977$	−32.0367	−1.02494	−0.512472	−	0.858704i	$-0.671270\pi$
$977$	−32.0367	−1.02494	−0.512472	+	0.858704i	$0.671270\pi$
$978$	−109.444	−3.49964
$979$	3.76278	0.120259
$980$	−35.5944	−1.13702
$981$	52.6876	1.68219
$982$	53.0755	1.69371
$983$	41.4151	1.32094	0.660469	−	0.750853i	$-0.270357\pi$
$983$	41.4151	1.32094	0.660469	+	0.750853i	$0.270357\pi$
$984$	−16.8768	−0.538011
$985$	−14.8842	−0.474250
$986$	24.5924	0.783182
$987$	−9.44651	−0.300686
$988$	−22.0424	−0.701263
$989$	−7.86134	−0.249976
$990$	6.18207	0.196479
$991$	−17.3410	−0.550854	−0.275427	−	0.961322i	$-0.588819\pi$
$991$	−17.3410	−0.550854	−0.275427	+	0.961322i	$0.588819\pi$
$992$	−21.1173	−0.670474
$993$	−10.9730	−0.348217
$994$	12.0943	0.383608
$995$	−12.0736	−0.382759
$996$	−147.342	−4.66870
$997$	14.4361	0.457196	0.228598	−	0.973521i	$-0.426586\pi$
$997$	14.4361	0.457196	0.228598	+	0.973521i	$0.426586\pi$
$998$	58.2183	1.84287
$999$	−3.07972	−0.0974381

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.e.1.6	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.e.1.6	✓	126	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68284 q^{2} +2.48419 q^{3} +5.19763 q^{4} +1.00000 q^{5} -6.66470 q^{6} +0.389624 q^{7} -8.57874 q^{8} +3.17122 q^{9} +O(q^{10})\)	\(q-2.68284 q^{2} +2.48419 q^{3} +5.19763 q^{4} +1.00000 q^{5} -6.66470 q^{6} +0.389624 q^{7} -8.57874 q^{8} +3.17122 q^{9} -2.68284 q^{10} -0.726629 q^{11} +12.9119 q^{12} -0.929729 q^{13} -1.04530 q^{14} +2.48419 q^{15} +12.6201 q^{16} -4.73623 q^{17} -8.50787 q^{18} +4.56139 q^{19} +5.19763 q^{20} +0.967902 q^{21} +1.94943 q^{22} -2.76946 q^{23} -21.3113 q^{24} +1.00000 q^{25} +2.49431 q^{26} +0.425338 q^{27} +2.02512 q^{28} +1.93541 q^{29} -6.66470 q^{30} +1.26449 q^{31} -16.7003 q^{32} -1.80509 q^{33} +12.7065 q^{34} +0.389624 q^{35} +16.4828 q^{36} -7.24064 q^{37} -12.2375 q^{38} -2.30963 q^{39} -8.57874 q^{40} +0.791917 q^{41} -2.59673 q^{42} +2.83859 q^{43} -3.77675 q^{44} +3.17122 q^{45} +7.43001 q^{46} -9.75978 q^{47} +31.3508 q^{48} -6.84819 q^{49} -2.68284 q^{50} -11.7657 q^{51} -4.83239 q^{52} -7.50251 q^{53} -1.14111 q^{54} -0.726629 q^{55} -3.34249 q^{56} +11.3314 q^{57} -5.19241 q^{58} +6.90779 q^{59} +12.9119 q^{60} -11.3541 q^{61} -3.39241 q^{62} +1.23558 q^{63} +19.5640 q^{64} -0.929729 q^{65} +4.84276 q^{66} -1.77906 q^{67} -24.6172 q^{68} -6.87986 q^{69} -1.04530 q^{70} -11.5702 q^{71} -27.2051 q^{72} +1.36668 q^{73} +19.4255 q^{74} +2.48419 q^{75} +23.7084 q^{76} -0.283112 q^{77} +6.19636 q^{78} +6.15982 q^{79} +12.6201 q^{80} -8.45703 q^{81} -2.12459 q^{82} -11.4113 q^{83} +5.03080 q^{84} -4.73623 q^{85} -7.61548 q^{86} +4.80794 q^{87} +6.23356 q^{88} -5.17840 q^{89} -8.50787 q^{90} -0.362245 q^{91} -14.3946 q^{92} +3.14123 q^{93} +26.1839 q^{94} +4.56139 q^{95} -41.4868 q^{96} -13.7583 q^{97} +18.3726 q^{98} -2.30430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * q^99

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