LMFDB - Embedded newform 8005.2.a.e.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.65121 q^{2} +2.20817 q^{3} +5.02889 q^{4} +1.00000 q^{5} -5.85432 q^{6} +1.13274 q^{7} -8.03022 q^{8} +1.87603 q^{9} +O(q^{10})$	\(q-2.65121 q^{2} +2.20817 q^{3} +5.02889 q^{4} +1.00000 q^{5} -5.85432 q^{6} +1.13274 q^{7} -8.03022 q^{8} +1.87603 q^{9} -2.65121 q^{10} +6.16661 q^{11} +11.1047 q^{12} -5.14959 q^{13} -3.00312 q^{14} +2.20817 q^{15} +11.2320 q^{16} +4.03839 q^{17} -4.97373 q^{18} -7.09141 q^{19} +5.02889 q^{20} +2.50128 q^{21} -16.3490 q^{22} -5.66418 q^{23} -17.7321 q^{24} +1.00000 q^{25} +13.6526 q^{26} -2.48193 q^{27} +5.69642 q^{28} -3.26369 q^{29} -5.85432 q^{30} -0.590389 q^{31} -13.7179 q^{32} +13.6169 q^{33} -10.7066 q^{34} +1.13274 q^{35} +9.43434 q^{36} -4.80612 q^{37} +18.8008 q^{38} -11.3712 q^{39} -8.03022 q^{40} +3.69383 q^{41} -6.63141 q^{42} -2.94999 q^{43} +31.0113 q^{44} +1.87603 q^{45} +15.0169 q^{46} -1.40841 q^{47} +24.8022 q^{48} -5.71690 q^{49} -2.65121 q^{50} +8.91747 q^{51} -25.8968 q^{52} -7.83931 q^{53} +6.58011 q^{54} +6.16661 q^{55} -9.09614 q^{56} -15.6591 q^{57} +8.65270 q^{58} -11.5832 q^{59} +11.1047 q^{60} +10.8205 q^{61} +1.56524 q^{62} +2.12505 q^{63} +13.9049 q^{64} -5.14959 q^{65} -36.1013 q^{66} -12.2099 q^{67} +20.3087 q^{68} -12.5075 q^{69} -3.00312 q^{70} -6.17768 q^{71} -15.0649 q^{72} -1.36244 q^{73} +12.7420 q^{74} +2.20817 q^{75} -35.6619 q^{76} +6.98516 q^{77} +30.1474 q^{78} -0.124690 q^{79} +11.2320 q^{80} -11.1086 q^{81} -9.79310 q^{82} -9.52835 q^{83} +12.5787 q^{84} +4.03839 q^{85} +7.82103 q^{86} -7.20678 q^{87} -49.5193 q^{88} +6.33020 q^{89} -4.97373 q^{90} -5.83314 q^{91} -28.4846 q^{92} -1.30368 q^{93} +3.73398 q^{94} -7.09141 q^{95} -30.2914 q^{96} +14.1253 q^{97} +15.1567 q^{98} +11.5687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65121	−1.87469	−0.937343	−	0.348408i	$-0.886722\pi$
$2$	−2.65121	−1.87469	−0.937343	+	0.348408i	$0.886722\pi$
$3$	2.20817	1.27489	0.637444	−	0.770496i	$-0.279992\pi$
$3$	2.20817	1.27489	0.637444	+	0.770496i	$0.279992\pi$
$4$	5.02889	2.51445
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.85432	−2.39002
$7$	1.13274	0.428135	0.214067	−	0.976819i	$-0.431329\pi$
$7$	1.13274	0.428135	0.214067	+	0.976819i	$0.431329\pi$
$8$	−8.03022	−2.83911
$9$	1.87603	0.625342
$10$	−2.65121	−0.838385
$11$	6.16661	1.85930	0.929652	−	0.368439i	$-0.120108\pi$
$11$	6.16661	1.85930	0.929652	+	0.368439i	$0.120108\pi$
$12$	11.1047	3.20564
$13$	−5.14959	−1.42824	−0.714120	−	0.700023i	$-0.753173\pi$
$13$	−5.14959	−1.42824	−0.714120	+	0.700023i	$0.753173\pi$
$14$	−3.00312	−0.802618
$15$	2.20817	0.570148
$16$	11.2320	2.80800
$17$	4.03839	0.979454	0.489727	−	0.871876i	$-0.337096\pi$
$17$	4.03839	0.979454	0.489727	+	0.871876i	$0.337096\pi$
$18$	−4.97373	−1.17232
$19$	−7.09141	−1.62688	−0.813440	−	0.581649i	$-0.802408\pi$
$19$	−7.09141	−1.62688	−0.813440	+	0.581649i	$0.802408\pi$
$20$	5.02889	1.12450
$21$	2.50128	0.545824
$22$	−16.3490	−3.48561
$23$	−5.66418	−1.18106	−0.590532	−	0.807015i	$-0.701082\pi$
$23$	−5.66418	−1.18106	−0.590532	+	0.807015i	$0.701082\pi$
$24$	−17.7321	−3.61955
$25$	1.00000	0.200000
$26$	13.6526	2.67750
$27$	−2.48193	−0.477648
$28$	5.69642	1.07652
$29$	−3.26369	−0.606051	−0.303026	−	0.952982i	$-0.597997\pi$
$29$	−3.26369	−0.606051	−0.303026	+	0.952982i	$0.597997\pi$
$30$	−5.85432	−1.06885
$31$	−0.590389	−0.106037	−0.0530185	−	0.998594i	$-0.516884\pi$
$31$	−0.590389	−0.106037	−0.0530185	+	0.998594i	$0.516884\pi$
$32$	−13.7179	−2.42500
$33$	13.6169	2.37041
$34$	−10.7066	−1.83617
$35$	1.13274	0.191468
$36$	9.43434	1.57239
$37$	−4.80612	−0.790122	−0.395061	−	0.918655i	$-0.629277\pi$
$37$	−4.80612	−0.790122	−0.395061	+	0.918655i	$0.629277\pi$
$38$	18.8008	3.04989
$39$	−11.3712	−1.82085
$40$	−8.03022	−1.26969
$41$	3.69383	0.576879	0.288439	−	0.957498i	$-0.406864\pi$
$41$	3.69383	0.576879	0.288439	+	0.957498i	$0.406864\pi$
$42$	−6.63141	−1.02325
$43$	−2.94999	−0.449869	−0.224935	−	0.974374i	$-0.572217\pi$
$43$	−2.94999	−0.449869	−0.224935	+	0.974374i	$0.572217\pi$
$44$	31.0113	4.67512
$45$	1.87603	0.279661
$46$	15.0169	2.21412
$47$	−1.40841	−0.205438	−0.102719	−	0.994710i	$-0.532754\pi$
$47$	−1.40841	−0.205438	−0.102719	+	0.994710i	$0.532754\pi$
$48$	24.8022	3.57989
$49$	−5.71690	−0.816701
$50$	−2.65121	−0.374937
$51$	8.91747	1.24870
$52$	−25.8968	−3.59124
$53$	−7.83931	−1.07681	−0.538406	−	0.842686i	$-0.680973\pi$
$53$	−7.83931	−1.07681	−0.538406	+	0.842686i	$0.680973\pi$
$54$	6.58011	0.895439
$55$	6.16661	0.831506
$56$	−9.09614	−1.21552
$57$	−15.6591	−2.07409
$58$	8.65270	1.13616
$59$	−11.5832	−1.50801	−0.754004	−	0.656869i	$-0.771880\pi$
$59$	−11.5832	−1.50801	−0.754004	+	0.656869i	$0.771880\pi$
$60$	11.1047	1.43361
$61$	10.8205	1.38542	0.692709	−	0.721217i	$-0.256417\pi$
$61$	10.8205	1.38542	0.692709	+	0.721217i	$0.256417\pi$
$62$	1.56524	0.198786
$63$	2.12505	0.267731
$64$	13.9049	1.73812
$65$	−5.14959	−0.638728
$66$	−36.1013	−4.44377
$67$	−12.2099	−1.49168	−0.745839	−	0.666126i	$-0.767951\pi$
$67$	−12.2099	−1.49168	−0.745839	+	0.666126i	$0.767951\pi$
$68$	20.3087	2.46279
$69$	−12.5075	−1.50572
$70$	−3.00312	−0.358942
$71$	−6.17768	−0.733155	−0.366578	−	0.930387i	$-0.619471\pi$
$71$	−6.17768	−0.733155	−0.366578	+	0.930387i	$0.619471\pi$
$72$	−15.0649	−1.77542
$73$	−1.36244	−0.159461	−0.0797306	−	0.996816i	$-0.525406\pi$
$73$	−1.36244	−0.159461	−0.0797306	+	0.996816i	$0.525406\pi$
$74$	12.7420	1.48123
$75$	2.20817	0.254978
$76$	−35.6619	−4.09071
$77$	6.98516	0.796033
$78$	30.1474	3.41352
$79$	−0.124690	−0.0140287	−0.00701434	−	0.999975i	$-0.502233\pi$
$79$	−0.124690	−0.0140287	−0.00701434	+	0.999975i	$0.502233\pi$
$80$	11.2320	1.25577
$81$	−11.1086	−1.23429
$82$	−9.79310	−1.08147
$83$	−9.52835	−1.04587	−0.522936	−	0.852372i	$-0.675163\pi$
$83$	−9.52835	−1.04587	−0.522936	+	0.852372i	$0.675163\pi$
$84$	12.5787	1.37245
$85$	4.03839	0.438025
$86$	7.82103	0.843364
$87$	−7.20678	−0.772648
$88$	−49.5193	−5.27877
$89$	6.33020	0.671000	0.335500	−	0.942040i	$-0.391095\pi$
$89$	6.33020	0.671000	0.335500	+	0.942040i	$0.391095\pi$
$90$	−4.97373	−0.524277
$91$	−5.83314	−0.611480
$92$	−28.4846	−2.96972
$93$	−1.30368	−0.135185
$94$	3.73398	0.385131
$95$	−7.09141	−0.727563
$96$	−30.2914	−3.09161
$97$	14.1253	1.43421	0.717104	−	0.696966i	$-0.245467\pi$
$97$	14.1253	1.43421	0.717104	+	0.696966i	$0.245467\pi$
$98$	15.1567	1.53106
$99$	11.5687	1.16270
$100$	5.02889	0.502889
$101$	−5.51925	−0.549186	−0.274593	−	0.961561i	$-0.588543\pi$
$101$	−5.51925	−0.549186	−0.274593	+	0.961561i	$0.588543\pi$
$102$	−23.6421	−2.34091
$103$	2.42921	0.239357	0.119679	−	0.992813i	$-0.461814\pi$
$103$	2.42921	0.239357	0.119679	+	0.992813i	$0.461814\pi$
$104$	41.3524	4.05494
$105$	2.50128	0.244100
$106$	20.7836	2.01868
$107$	−0.0780864	−0.00754890	−0.00377445	−	0.999993i	$-0.501201\pi$
$107$	−0.0780864	−0.00754890	−0.00377445	+	0.999993i	$0.501201\pi$
$108$	−12.4814	−1.20102
$109$	−8.56848	−0.820712	−0.410356	−	0.911925i	$-0.634596\pi$
$109$	−8.56848	−0.820712	−0.410356	+	0.911925i	$0.634596\pi$
$110$	−16.3490	−1.55881
$111$	−10.6127	−1.00732
$112$	12.7229	1.20220
$113$	−19.7247	−1.85554	−0.927772	−	0.373148i	$-0.878278\pi$
$113$	−19.7247	−1.85554	−0.927772	+	0.373148i	$0.878278\pi$
$114$	41.5154	3.88827
$115$	−5.66418	−0.528188
$116$	−16.4127	−1.52388
$117$	−9.66077	−0.893138
$118$	30.7095	2.82704
$119$	4.57444	0.419339
$120$	−17.7321	−1.61871
$121$	27.0271	2.45701
$122$	−28.6873	−2.59722
$123$	8.15661	0.735457
$124$	−2.96900	−0.266624
$125$	1.00000	0.0894427
$126$	−5.63394	−0.501911
$127$	−12.2242	−1.08472	−0.542359	−	0.840147i	$-0.682469\pi$
$127$	−12.2242	−1.08472	−0.542359	+	0.840147i	$0.682469\pi$
$128$	−9.42912	−0.833424
$129$	−6.51409	−0.573533
$130$	13.6526	1.19742
$131$	−13.0101	−1.13670	−0.568350	−	0.822787i	$-0.692418\pi$
$131$	−13.0101	−1.13670	−0.568350	+	0.822787i	$0.692418\pi$
$132$	68.4782	5.96026
$133$	−8.03271	−0.696524
$134$	32.3710	2.79643
$135$	−2.48193	−0.213610
$136$	−32.4292	−2.78078
$137$	8.61369	0.735917	0.367958	−	0.929842i	$-0.380057\pi$
$137$	8.61369	0.735917	0.367958	+	0.929842i	$0.380057\pi$
$138$	33.1599	2.82276
$139$	15.7763	1.33813	0.669065	−	0.743204i	$-0.266695\pi$
$139$	15.7763	1.33813	0.669065	+	0.743204i	$0.266695\pi$
$140$	5.69642	0.481436
$141$	−3.11001	−0.261910
$142$	16.3783	1.37444
$143$	−31.7556	−2.65553
$144$	21.0715	1.75596
$145$	−3.26369	−0.271034
$146$	3.61210	0.298940
$147$	−12.6239	−1.04120
$148$	−24.1695	−1.98672
$149$	4.10854	0.336585	0.168292	−	0.985737i	$-0.446175\pi$
$149$	4.10854	0.336585	0.168292	+	0.985737i	$0.446175\pi$
$150$	−5.85432	−0.478003
$151$	12.5997	1.02535	0.512674	−	0.858583i	$-0.328655\pi$
$151$	12.5997	1.02535	0.512674	+	0.858583i	$0.328655\pi$
$152$	56.9456	4.61890
$153$	7.57613	0.612494
$154$	−18.5191	−1.49231
$155$	−0.590389	−0.0474212
$156$	−57.1845	−4.57843
$157$	5.07286	0.404858	0.202429	−	0.979297i	$-0.435116\pi$
$157$	5.07286	0.404858	0.202429	+	0.979297i	$0.435116\pi$
$158$	0.330578	0.0262994
$159$	−17.3105	−1.37282
$160$	−13.7179	−1.08449
$161$	−6.41603	−0.505654
$162$	29.4512	2.31391
$163$	−19.1402	−1.49918	−0.749589	−	0.661904i	$-0.769749\pi$
$163$	−19.1402	−1.49918	−0.749589	+	0.661904i	$0.769749\pi$
$164$	18.5759	1.45053
$165$	13.6169	1.06008
$166$	25.2616	1.96068
$167$	17.8039	1.37771	0.688854	−	0.724900i	$-0.258114\pi$
$167$	17.8039	1.37771	0.688854	+	0.724900i	$0.258114\pi$
$168$	−20.0859	−1.54966
$169$	13.5183	1.03987
$170$	−10.7066	−0.821160
$171$	−13.3037	−1.01736
$172$	−14.8352	−1.13117
$173$	22.4717	1.70849	0.854246	−	0.519869i	$-0.174019\pi$
$173$	22.4717	1.70849	0.854246	+	0.519869i	$0.174019\pi$
$174$	19.1067	1.44847
$175$	1.13274	0.0856270
$176$	69.2634	5.22092
$177$	−25.5778	−1.92254
$178$	−16.7827	−1.25791
$179$	−25.6220	−1.91508	−0.957538	−	0.288306i	$-0.906908\pi$
$179$	−25.6220	−1.91508	−0.957538	+	0.288306i	$0.906908\pi$
$180$	9.43434	0.703194
$181$	7.00251	0.520492	0.260246	−	0.965542i	$-0.416196\pi$
$181$	7.00251	0.520492	0.260246	+	0.965542i	$0.416196\pi$
$182$	15.4649	1.14633
$183$	23.8934	1.76625
$184$	45.4846	3.35317
$185$	−4.80612	−0.353353
$186$	3.45633	0.253430
$187$	24.9032	1.82110
$188$	−7.08274	−0.516562
$189$	−2.81138	−0.204498
$190$	18.8008	1.36395
$191$	7.92623	0.573522	0.286761	−	0.958002i	$-0.407421\pi$
$191$	7.92623	0.573522	0.286761	+	0.958002i	$0.407421\pi$
$192$	30.7045	2.21591
$193$	−12.0373	−0.866467	−0.433233	−	0.901282i	$-0.642627\pi$
$193$	−12.0373	−0.866467	−0.433233	+	0.901282i	$0.642627\pi$
$194$	−37.4491	−2.68869
$195$	−11.3712	−0.814308
$196$	−28.7497	−2.05355
$197$	−10.6338	−0.757630	−0.378815	−	0.925472i	$-0.623668\pi$
$197$	−10.6338	−0.757630	−0.378815	+	0.925472i	$0.623668\pi$
$198$	−30.6711	−2.17970
$199$	3.66869	0.260067	0.130033	−	0.991510i	$-0.458492\pi$
$199$	3.66869	0.260067	0.130033	+	0.991510i	$0.458492\pi$
$200$	−8.03022	−0.567823
$201$	−26.9616	−1.90172
$202$	14.6327	1.02955
$203$	−3.69690	−0.259472
$204$	44.8450	3.13978
$205$	3.69383	0.257988
$206$	−6.44033	−0.448719
$207$	−10.6261	−0.738568
$208$	−57.8402	−4.01050
$209$	−43.7300	−3.02487
$210$	−6.63141	−0.457611
$211$	−2.14630	−0.147757	−0.0738786	−	0.997267i	$-0.523538\pi$
$211$	−2.14630	−0.147757	−0.0738786	+	0.997267i	$0.523538\pi$
$212$	−39.4231	−2.70759
$213$	−13.6414	−0.934692
$214$	0.207023	0.0141518
$215$	−2.94999	−0.201188
$216$	19.9305	1.35610
$217$	−0.668756	−0.0453981
$218$	22.7168	1.53858
$219$	−3.00849	−0.203295
$220$	31.0113	2.09078
$221$	−20.7961	−1.39890
$222$	28.1366	1.88840
$223$	−7.54419	−0.505196	−0.252598	−	0.967571i	$-0.581285\pi$
$223$	−7.54419	−0.505196	−0.252598	+	0.967571i	$0.581285\pi$
$224$	−15.5388	−1.03823
$225$	1.87603	0.125068
$226$	52.2942	3.47856
$227$	−18.2193	−1.20926	−0.604630	−	0.796507i	$-0.706679\pi$
$227$	−18.2193	−1.20926	−0.604630	+	0.796507i	$0.706679\pi$
$228$	−78.7477	−5.21519
$229$	23.0763	1.52492	0.762461	−	0.647034i	$-0.223991\pi$
$229$	23.0763	1.52492	0.762461	+	0.647034i	$0.223991\pi$
$230$	15.0169	0.990186
$231$	15.4244	1.01485
$232$	26.2081	1.72065
$233$	10.0104	0.655803	0.327902	−	0.944712i	$-0.393659\pi$
$233$	10.0104	0.655803	0.327902	+	0.944712i	$0.393659\pi$
$234$	25.6127	1.67435
$235$	−1.40841	−0.0918745
$236$	−58.2509	−3.79181
$237$	−0.275336	−0.0178850
$238$	−12.1278	−0.786128
$239$	−5.26543	−0.340592	−0.170296	−	0.985393i	$-0.554472\pi$
$239$	−5.26543	−0.340592	−0.170296	+	0.985393i	$0.554472\pi$
$240$	24.8022	1.60097
$241$	16.1239	1.03863	0.519317	−	0.854582i	$-0.326187\pi$
$241$	16.1239	1.03863	0.519317	+	0.854582i	$0.326187\pi$
$242$	−71.6545	−4.60613
$243$	−17.0839	−1.09593
$244$	54.4150	3.48356
$245$	−5.71690	−0.365240
$246$	−21.6249	−1.37875
$247$	36.5179	2.32358
$248$	4.74095	0.301051
$249$	−21.0402	−1.33337
$250$	−2.65121	−0.167677
$251$	−21.2144	−1.33904	−0.669522	−	0.742792i	$-0.733501\pi$
$251$	−21.2144	−1.33904	−0.669522	+	0.742792i	$0.733501\pi$
$252$	10.6866	0.673195
$253$	−34.9288	−2.19596
$254$	32.4088	2.03351
$255$	8.91747	0.558434
$256$	−2.81136	−0.175710
$257$	2.90055	0.180931	0.0904655	−	0.995900i	$-0.471165\pi$
$257$	2.90055	0.180931	0.0904655	+	0.995900i	$0.471165\pi$
$258$	17.2702	1.07519
$259$	−5.44408	−0.338279
$260$	−25.8968	−1.60605
$261$	−6.12276	−0.378989
$262$	34.4925	2.13096
$263$	−18.5999	−1.14692	−0.573460	−	0.819234i	$-0.694399\pi$
$263$	−18.5999	−1.14692	−0.573460	+	0.819234i	$0.694399\pi$
$264$	−109.347	−6.72985
$265$	−7.83931	−0.481565
$266$	21.2964	1.30576
$267$	13.9782	0.855451
$268$	−61.4024	−3.75075
$269$	−1.29468	−0.0789379	−0.0394689	−	0.999221i	$-0.512567\pi$
$269$	−1.29468	−0.0789379	−0.0394689	+	0.999221i	$0.512567\pi$
$270$	6.58011	0.400453
$271$	1.05833	0.0642889	0.0321444	−	0.999483i	$-0.489766\pi$
$271$	1.05833	0.0642889	0.0321444	+	0.999483i	$0.489766\pi$
$272$	45.3592	2.75031
$273$	−12.8806	−0.779569
$274$	−22.8367	−1.37961
$275$	6.16661	0.371861
$276$	−62.8988	−3.78606
$277$	2.53013	0.152021	0.0760103	−	0.997107i	$-0.475782\pi$
$277$	2.53013	0.152021	0.0760103	+	0.997107i	$0.475782\pi$
$278$	−41.8263	−2.50857
$279$	−1.10758	−0.0663093
$280$	−9.09614	−0.543599
$281$	−1.86557	−0.111291	−0.0556454	−	0.998451i	$-0.517722\pi$
$281$	−1.86557	−0.111291	−0.0556454	+	0.998451i	$0.517722\pi$
$282$	8.24528	0.490999
$283$	7.04029	0.418502	0.209251	−	0.977862i	$-0.432897\pi$
$283$	7.04029	0.418502	0.209251	+	0.977862i	$0.432897\pi$
$284$	−31.0669	−1.84348
$285$	−15.6591	−0.927562
$286$	84.1905	4.97829
$287$	4.18414	0.246982
$288$	−25.7351	−1.51645
$289$	−0.691374	−0.0406691
$290$	8.65270	0.508104
$291$	31.1911	1.82846
$292$	−6.85155	−0.400957
$293$	−19.7871	−1.15598	−0.577988	−	0.816045i	$-0.696162\pi$
$293$	−19.7871	−1.15598	−0.577988	+	0.816045i	$0.696162\pi$
$294$	33.4686	1.95193
$295$	−11.5832	−0.674402
$296$	38.5943	2.24325
$297$	−15.3051	−0.888092
$298$	−10.8926	−0.630991
$299$	29.1682	1.68684
$300$	11.1047	0.641128
$301$	−3.34157	−0.192605
$302$	−33.4044	−1.92221
$303$	−12.1874	−0.700151
$304$	−79.6506	−4.56828
$305$	10.8205	0.619578
$306$	−20.0859	−1.14823
$307$	−27.7797	−1.58547	−0.792734	−	0.609567i	$-0.791343\pi$
$307$	−27.7797	−1.58547	−0.792734	+	0.609567i	$0.791343\pi$
$308$	35.1276	2.00158
$309$	5.36411	0.305154
$310$	1.56524	0.0888998
$311$	−1.94415	−0.110243	−0.0551213	−	0.998480i	$-0.517555\pi$
$311$	−1.94415	−0.110243	−0.0551213	+	0.998480i	$0.517555\pi$
$312$	91.3132	5.16959
$313$	−10.1205	−0.572046	−0.286023	−	0.958223i	$-0.592333\pi$
$313$	−10.1205	−0.572046	−0.286023	+	0.958223i	$0.592333\pi$
$314$	−13.4492	−0.758982
$315$	2.12505	0.119733
$316$	−0.627051	−0.0352744
$317$	13.3426	0.749394	0.374697	−	0.927147i	$-0.377747\pi$
$317$	13.3426	0.749394	0.374697	+	0.927147i	$0.377747\pi$
$318$	45.8938	2.57360
$319$	−20.1259	−1.12683
$320$	13.9049	0.777310
$321$	−0.172428	−0.00962401
$322$	17.0102	0.947943
$323$	−28.6379	−1.59346
$324$	−55.8640	−3.10356
$325$	−5.14959	−0.285648
$326$	50.7447	2.81049
$327$	−18.9207	−1.04632
$328$	−29.6623	−1.63782
$329$	−1.59536	−0.0879550
$330$	−36.1013	−1.98731
$331$	−3.89114	−0.213876	−0.106938	−	0.994266i	$-0.534105\pi$
$331$	−3.89114	−0.213876	−0.106938	+	0.994266i	$0.534105\pi$
$332$	−47.9171	−2.62979
$333$	−9.01641	−0.494096
$334$	−47.2018	−2.58277
$335$	−12.2099	−0.667099
$336$	28.0944	1.53267
$337$	5.16115	0.281146	0.140573	−	0.990070i	$-0.455106\pi$
$337$	5.16115	0.281146	0.140573	+	0.990070i	$0.455106\pi$
$338$	−35.8398	−1.94943
$339$	−43.5555	−2.36561
$340$	20.3087	1.10139
$341$	−3.64070	−0.197155
$342$	35.2708	1.90722
$343$	−14.4049	−0.777793
$344$	23.6891	1.27723
$345$	−12.5075	−0.673380
$346$	−59.5771	−3.20289
$347$	27.1393	1.45691	0.728456	−	0.685093i	$-0.240238\pi$
$347$	27.1393	1.45691	0.728456	+	0.685093i	$0.240238\pi$
$348$	−36.2421	−1.94278
$349$	13.9790	0.748277	0.374138	−	0.927373i	$-0.377939\pi$
$349$	13.9790	0.748277	0.374138	+	0.927373i	$0.377939\pi$
$350$	−3.00312	−0.160524
$351$	12.7809	0.682195
$352$	−84.5929	−4.50882
$353$	12.2636	0.652726	0.326363	−	0.945244i	$-0.394177\pi$
$353$	12.2636	0.652726	0.326363	+	0.945244i	$0.394177\pi$
$354$	67.8120	3.60417
$355$	−6.17768	−0.327877
$356$	31.8339	1.68719
$357$	10.1012	0.534610
$358$	67.9291	3.59017
$359$	30.0859	1.58787	0.793936	−	0.608002i	$-0.208029\pi$
$359$	30.0859	1.58787	0.793936	+	0.608002i	$0.208029\pi$
$360$	−15.0649	−0.793990
$361$	31.2881	1.64674
$362$	−18.5651	−0.975760
$363$	59.6806	3.13242
$364$	−29.3343	−1.53753
$365$	−1.36244	−0.0713132
$366$	−63.3465	−3.31117
$367$	34.8184	1.81750	0.908752	−	0.417337i	$-0.137037\pi$
$367$	34.8184	1.81750	0.908752	+	0.417337i	$0.137037\pi$
$368$	−63.6200	−3.31642
$369$	6.92972	0.360747
$370$	12.7420	0.662426
$371$	−8.87989	−0.461021
$372$	−6.55607	−0.339916
$373$	30.4808	1.57824	0.789118	−	0.614242i	$-0.210538\pi$
$373$	30.4808	1.57824	0.789118	+	0.614242i	$0.210538\pi$
$374$	−66.0236	−3.41400
$375$	2.20817	0.114030
$376$	11.3098	0.583261
$377$	16.8067	0.865587
$378$	7.45354	0.383369
$379$	8.26501	0.424545	0.212273	−	0.977211i	$-0.431914\pi$
$379$	8.26501	0.424545	0.212273	+	0.977211i	$0.431914\pi$
$380$	−35.6619	−1.82942
$381$	−26.9930	−1.38290
$382$	−21.0141	−1.07517
$383$	27.9416	1.42775	0.713874	−	0.700274i	$-0.246939\pi$
$383$	27.9416	1.42775	0.713874	+	0.700274i	$0.246939\pi$
$384$	−20.8211	−1.06252
$385$	6.98516	0.355997
$386$	31.9135	1.62435
$387$	−5.53426	−0.281322
$388$	71.0347	3.60624
$389$	38.7093	1.96264	0.981321	−	0.192380i	$-0.0616206\pi$
$389$	38.7093	1.96264	0.981321	+	0.192380i	$0.0616206\pi$
$390$	30.1474	1.52657
$391$	−22.8742	−1.15680
$392$	45.9080	2.31871
$393$	−28.7286	−1.44917
$394$	28.1925	1.42032
$395$	−0.124690	−0.00627382
$396$	58.1779	2.92355
$397$	19.6157	0.984483	0.492242	−	0.870459i	$-0.336178\pi$
$397$	19.6157	0.984483	0.492242	+	0.870459i	$0.336178\pi$
$398$	−9.72646	−0.487543
$399$	−17.7376	−0.887991
$400$	11.2320	0.561600
$401$	−22.4897	−1.12308	−0.561542	−	0.827448i	$-0.689792\pi$
$401$	−22.4897	−1.12308	−0.561542	+	0.827448i	$0.689792\pi$
$402$	71.4808	3.56514
$403$	3.04026	0.151446
$404$	−27.7557	−1.38090
$405$	−11.1086	−0.551991
$406$	9.80125	0.486428
$407$	−29.6375	−1.46908
$408$	−71.6093	−3.54519
$409$	28.5166	1.41006	0.705029	−	0.709179i	$-0.250934\pi$
$409$	28.5166	1.41006	0.705029	+	0.709179i	$0.250934\pi$
$410$	−9.79310	−0.483647
$411$	19.0205	0.938212
$412$	12.2162	0.601851
$413$	−13.1208	−0.645631
$414$	28.1721	1.38458
$415$	−9.52835	−0.467728
$416$	70.6415	3.46348
$417$	34.8368	1.70597
$418$	115.937	5.67067
$419$	−26.8980	−1.31405	−0.657027	−	0.753867i	$-0.728186\pi$
$419$	−26.8980	−1.31405	−0.657027	+	0.753867i	$0.728186\pi$
$420$	12.5787	0.613777
$421$	−14.3715	−0.700426	−0.350213	−	0.936670i	$-0.613891\pi$
$421$	−14.3715	−0.700426	−0.350213	+	0.936670i	$0.613891\pi$
$422$	5.69028	0.276998
$423$	−2.64221	−0.128469
$424$	62.9514	3.05719
$425$	4.03839	0.195891
$426$	36.1661	1.75225
$427$	12.2568	0.593146
$428$	−0.392688	−0.0189813
$429$	−70.1217	−3.38551
$430$	7.82103	0.377164
$431$	−20.3435	−0.979912	−0.489956	−	0.871747i	$-0.662987\pi$
$431$	−20.3435	−0.979912	−0.489956	+	0.871747i	$0.662987\pi$
$432$	−27.8770	−1.34123
$433$	15.5296	0.746306	0.373153	−	0.927770i	$-0.378277\pi$
$433$	15.5296	0.746306	0.373153	+	0.927770i	$0.378277\pi$
$434$	1.77301	0.0851072
$435$	−7.20678	−0.345539
$436$	−43.0900	−2.06364
$437$	40.1670	1.92145
$438$	7.97614	0.381115
$439$	16.3792	0.781736	0.390868	−	0.920447i	$-0.372175\pi$
$439$	16.3792	0.781736	0.390868	+	0.920447i	$0.372175\pi$
$440$	−49.5193	−2.36074
$441$	−10.7251	−0.510717
$442$	55.1347	2.62249
$443$	−2.86067	−0.135915	−0.0679573	−	0.997688i	$-0.521648\pi$
$443$	−2.86067	−0.135915	−0.0679573	+	0.997688i	$0.521648\pi$
$444$	−53.3704	−2.53285
$445$	6.33020	0.300080
$446$	20.0012	0.947085
$447$	9.07237	0.429108
$448$	15.7507	0.744149
$449$	2.25904	0.106611	0.0533054	−	0.998578i	$-0.483024\pi$
$449$	2.25904	0.106611	0.0533054	+	0.998578i	$0.483024\pi$
$450$	−4.97373	−0.234464
$451$	22.7784	1.07259
$452$	−99.1934	−4.66567
$453$	27.8223	1.30720
$454$	48.3032	2.26698
$455$	−5.83314	−0.273462
$456$	125.746	5.88858
$457$	−4.33313	−0.202695	−0.101348	−	0.994851i	$-0.532315\pi$
$457$	−4.33313	−0.202695	−0.101348	+	0.994851i	$0.532315\pi$
$458$	−61.1799	−2.85875
$459$	−10.0230	−0.467834
$460$	−28.4846	−1.32810
$461$	19.2717	0.897575	0.448787	−	0.893639i	$-0.351856\pi$
$461$	19.2717	0.897575	0.448787	+	0.893639i	$0.351856\pi$
$462$	−40.8934	−1.90253
$463$	−19.5181	−0.907084	−0.453542	−	0.891235i	$-0.649840\pi$
$463$	−19.5181	−0.907084	−0.453542	+	0.891235i	$0.649840\pi$
$464$	−36.6577	−1.70179
$465$	−1.30368	−0.0604567
$466$	−26.5396	−1.22943
$467$	−37.4251	−1.73183	−0.865913	−	0.500194i	$-0.833262\pi$
$467$	−37.4251	−1.73183	−0.865913	+	0.500194i	$0.833262\pi$
$468$	−48.5830	−2.24575
$469$	−13.8306	−0.638640
$470$	3.73398	0.172236
$471$	11.2018	0.516149
$472$	93.0160	4.28141
$473$	−18.1914	−0.836444
$474$	0.729973	0.0335288
$475$	−7.09141	−0.325376
$476$	23.0044	1.05440
$477$	−14.7067	−0.673376
$478$	13.9597	0.638504
$479$	31.1051	1.42123	0.710615	−	0.703581i	$-0.248417\pi$
$479$	31.1051	1.42123	0.710615	+	0.703581i	$0.248417\pi$
$480$	−30.2914	−1.38261
$481$	24.7496	1.12848
$482$	−42.7478	−1.94711
$483$	−14.1677	−0.644653
$484$	135.917	6.17803
$485$	14.1253	0.641397
$486$	45.2930	2.05453
$487$	−7.56183	−0.342659	−0.171330	−	0.985214i	$-0.554806\pi$
$487$	−7.56183	−0.342659	−0.171330	+	0.985214i	$0.554806\pi$
$488$	−86.8907	−3.93336
$489$	−42.2649	−1.91129
$490$	15.1567	0.684709
$491$	−27.1842	−1.22681	−0.613403	−	0.789770i	$-0.710200\pi$
$491$	−27.1842	−1.22681	−0.613403	+	0.789770i	$0.710200\pi$
$492$	41.0187	1.84927
$493$	−13.1800	−0.593600
$494$	−96.8164	−4.35598
$495$	11.5687	0.519976
$496$	−6.63124	−0.297752
$497$	−6.99769	−0.313889
$498$	55.7820	2.49965
$499$	−15.0420	−0.673372	−0.336686	−	0.941617i	$-0.609306\pi$
$499$	−15.0420	−0.673372	−0.336686	+	0.941617i	$0.609306\pi$
$500$	5.02889	0.224899
$501$	39.3141	1.75642
$502$	56.2439	2.51029
$503$	38.6539	1.72349	0.861745	−	0.507342i	$-0.169372\pi$
$503$	38.6539	1.72349	0.861745	+	0.507342i	$0.169372\pi$
$504$	−17.0646	−0.760118
$505$	−5.51925	−0.245603
$506$	92.6035	4.11673
$507$	29.8508	1.32572
$508$	−61.4740	−2.72747
$509$	−18.8927	−0.837402	−0.418701	−	0.908124i	$-0.637514\pi$
$509$	−18.8927	−0.837402	−0.418701	+	0.908124i	$0.637514\pi$
$510$	−23.6421	−1.04689
$511$	−1.54328	−0.0682709
$512$	26.3117	1.16282
$513$	17.6004	0.777075
$514$	−7.68995	−0.339189
$515$	2.42921	0.107044
$516$	−32.7587	−1.44212
$517$	−8.68512	−0.381971
$518$	14.4334	0.634166
$519$	49.6214	2.17814
$520$	41.3524	1.81342
$521$	2.88583	0.126430	0.0632152	−	0.998000i	$-0.479865\pi$
$521$	2.88583	0.126430	0.0632152	+	0.998000i	$0.479865\pi$
$522$	16.2327	0.710486
$523$	−18.7790	−0.821150	−0.410575	−	0.911827i	$-0.634672\pi$
$523$	−18.7790	−0.821150	−0.410575	+	0.911827i	$0.634672\pi$
$524$	−65.4266	−2.85817
$525$	2.50128	0.109165
$526$	49.3122	2.15011
$527$	−2.38422	−0.103858
$528$	152.945	6.65610
$529$	9.08294	0.394910
$530$	20.7836	0.902783
$531$	−21.7304	−0.943021
$532$	−40.3957	−1.75137
$533$	−19.0217	−0.823922
$534$	−37.0590	−1.60370
$535$	−0.0780864	−0.00337597
$536$	98.0484	4.23504
$537$	−56.5777	−2.44151
$538$	3.43246	0.147984
$539$	−35.2539	−1.51849
$540$	−12.4814	−0.537112
$541$	15.0365	0.646468	0.323234	−	0.946319i	$-0.395230\pi$
$541$	15.0365	0.646468	0.323234	+	0.946319i	$0.395230\pi$
$542$	−2.80585	−0.120521
$543$	15.4627	0.663570
$544$	−55.3982	−2.37518
$545$	−8.56848	−0.367034
$546$	34.1491	1.46145
$547$	13.7565	0.588184	0.294092	−	0.955777i	$-0.404983\pi$
$547$	13.7565	0.588184	0.294092	+	0.955777i	$0.404983\pi$
$548$	43.3173	1.85042
$549$	20.2995	0.866360
$550$	−16.3490	−0.697122
$551$	23.1441	0.985973
$552$	100.438	4.27492
$553$	−0.141241	−0.00600617
$554$	−6.70789	−0.284991
$555$	−10.6127	−0.450486
$556$	79.3374	3.36466
$557$	7.12997	0.302107	0.151053	−	0.988526i	$-0.451733\pi$
$557$	7.12997	0.302107	0.151053	+	0.988526i	$0.451733\pi$
$558$	2.93643	0.124309
$559$	15.1912	0.642521
$560$	12.7229	0.537641
$561$	54.9906	2.32170
$562$	4.94602	0.208635
$563$	−20.2611	−0.853904	−0.426952	−	0.904274i	$-0.640413\pi$
$563$	−20.2611	−0.853904	−0.426952	+	0.904274i	$0.640413\pi$
$564$	−15.6399	−0.658559
$565$	−19.7247	−0.829824
$566$	−18.6653	−0.784560
$567$	−12.5831	−0.528442
$568$	49.6081	2.08151
$569$	38.4241	1.61082	0.805411	−	0.592716i	$-0.201945\pi$
$569$	38.4241	1.61082	0.805411	+	0.592716i	$0.201945\pi$
$570$	41.5154	1.73889
$571$	21.5928	0.903630	0.451815	−	0.892112i	$-0.350777\pi$
$571$	21.5928	0.903630	0.451815	+	0.892112i	$0.350777\pi$
$572$	−159.695	−6.67720
$573$	17.5025	0.731177
$574$	−11.0930	−0.463014
$575$	−5.66418	−0.236213
$576$	26.0860	1.08692
$577$	−17.2363	−0.717556	−0.358778	−	0.933423i	$-0.616807\pi$
$577$	−17.2363	−0.717556	−0.358778	+	0.933423i	$0.616807\pi$
$578$	1.83298	0.0762417
$579$	−26.5805	−1.10465
$580$	−16.4127	−0.681502
$581$	−10.7931	−0.447774
$582$	−82.6941	−3.42778
$583$	−48.3420	−2.00212
$584$	10.9407	0.452728
$585$	−9.66077	−0.399424
$586$	52.4597	2.16709
$587$	17.7648	0.733231	0.366615	−	0.930373i	$-0.380517\pi$
$587$	17.7648	0.733231	0.366615	+	0.930373i	$0.380517\pi$
$588$	−63.4843	−2.61805
$589$	4.18669	0.172509
$590$	30.7095	1.26429
$591$	−23.4814	−0.965894
$592$	−53.9823	−2.21866
$593$	−20.2694	−0.832363	−0.416182	−	0.909281i	$-0.636632\pi$
$593$	−20.2694	−0.832363	−0.416182	+	0.909281i	$0.636632\pi$
$594$	40.5770	1.66489
$595$	4.57444	0.187534
$596$	20.6614	0.846325
$597$	8.10110	0.331556
$598$	−77.3310	−3.16230
$599$	2.33504	0.0954070	0.0477035	−	0.998862i	$-0.484810\pi$
$599$	2.33504	0.0954070	0.0477035	+	0.998862i	$0.484810\pi$
$600$	−17.7321	−0.723911
$601$	−41.3762	−1.68777	−0.843885	−	0.536524i	$-0.819737\pi$
$601$	−41.3762	−1.68777	−0.843885	+	0.536524i	$0.819737\pi$
$602$	8.85918	0.361073
$603$	−22.9061	−0.932809
$604$	63.3625	2.57818
$605$	27.0271	1.09881
$606$	32.3114	1.31256
$607$	16.2448	0.659354	0.329677	−	0.944094i	$-0.393060\pi$
$607$	16.2448	0.659354	0.329677	+	0.944094i	$0.393060\pi$
$608$	97.2791	3.94519
$609$	−8.16340	−0.330798
$610$	−28.6873	−1.16151
$611$	7.25274	0.293414
$612$	38.0996	1.54008
$613$	−4.13234	−0.166904	−0.0834519	−	0.996512i	$-0.526594\pi$
$613$	−4.13234	−0.166904	−0.0834519	+	0.996512i	$0.526594\pi$
$614$	73.6496	2.97226
$615$	8.15661	0.328906
$616$	−56.0924	−2.26003
$617$	9.64148	0.388152	0.194076	−	0.980987i	$-0.437829\pi$
$617$	9.64148	0.388152	0.194076	+	0.980987i	$0.437829\pi$
$618$	−14.2214	−0.572067
$619$	30.8115	1.23842	0.619209	−	0.785226i	$-0.287453\pi$
$619$	30.8115	1.23842	0.619209	+	0.785226i	$0.287453\pi$
$620$	−2.96900	−0.119238
$621$	14.0581	0.564132
$622$	5.15434	0.206670
$623$	7.17046	0.287279
$624$	−127.721	−5.11294
$625$	1.00000	0.0400000
$626$	26.8316	1.07241
$627$	−96.5633	−3.85637
$628$	25.5109	1.01800
$629$	−19.4090	−0.773888
$630$	−5.63394	−0.224461
$631$	−3.08483	−0.122805	−0.0614026	−	0.998113i	$-0.519557\pi$
$631$	−3.08483	−0.122805	−0.0614026	+	0.998113i	$0.519557\pi$
$632$	1.00129	0.0398290
$633$	−4.73939	−0.188374
$634$	−35.3739	−1.40488
$635$	−12.2242	−0.485101
$636$	−87.0529	−3.45187
$637$	29.4397	1.16644
$638$	53.3579	2.11246
$639$	−11.5895	−0.458473
$640$	−9.42912	−0.372719
$641$	10.8842	0.429901	0.214951	−	0.976625i	$-0.431041\pi$
$641$	10.8842	0.429901	0.214951	+	0.976625i	$0.431041\pi$
$642$	0.457143	0.0180420
$643$	−6.89704	−0.271993	−0.135996	−	0.990709i	$-0.543424\pi$
$643$	−6.89704	−0.271993	−0.135996	+	0.990709i	$0.543424\pi$
$644$	−32.2656	−1.27144
$645$	−6.51409	−0.256492
$646$	75.9250	2.98723
$647$	−19.2155	−0.755440	−0.377720	−	0.925920i	$-0.623292\pi$
$647$	−19.2155	−0.755440	−0.377720	+	0.925920i	$0.623292\pi$
$648$	89.2046	3.50429
$649$	−71.4293	−2.80385
$650$	13.6526	0.535500
$651$	−1.47673	−0.0578776
$652$	−96.2542	−3.76960
$653$	−22.6603	−0.886766	−0.443383	−	0.896332i	$-0.646222\pi$
$653$	−22.6603	−0.886766	−0.443383	+	0.896332i	$0.646222\pi$
$654$	50.1627	1.96152
$655$	−13.0101	−0.508348
$656$	41.4890	1.61988
$657$	−2.55597	−0.0997177
$658$	4.22963	0.164888
$659$	26.4558	1.03057	0.515286	−	0.857018i	$-0.327686\pi$
$659$	26.4558	1.03057	0.515286	+	0.857018i	$0.327686\pi$
$660$	68.4782	2.66551
$661$	29.7440	1.15691	0.578454	−	0.815715i	$-0.303656\pi$
$661$	29.7440	1.15691	0.578454	+	0.815715i	$0.303656\pi$
$662$	10.3162	0.400951
$663$	−45.9213	−1.78344
$664$	76.5148	2.96935
$665$	−8.03271	−0.311495
$666$	23.9044	0.926275
$667$	18.4861	0.715785
$668$	89.5340	3.46417
$669$	−16.6589	−0.644069
$670$	32.3710	1.25060
$671$	66.7256	2.57591
$672$	−34.3123	−1.32363
$673$	37.9662	1.46349	0.731744	−	0.681580i	$-0.238707\pi$
$673$	37.9662	1.46349	0.731744	+	0.681580i	$0.238707\pi$
$674$	−13.6833	−0.527060
$675$	−2.48193	−0.0955295
$676$	67.9822	2.61470
$677$	−33.7882	−1.29859	−0.649293	−	0.760539i	$-0.724935\pi$
$677$	−33.7882	−1.29859	−0.649293	+	0.760539i	$0.724935\pi$
$678$	115.475	4.43478
$679$	16.0003	0.614035
$680$	−32.4292	−1.24360
$681$	−40.2314	−1.54167
$682$	9.65225	0.369604
$683$	23.8340	0.911985	0.455992	−	0.889984i	$-0.349284\pi$
$683$	23.8340	0.911985	0.455992	+	0.889984i	$0.349284\pi$
$684$	−66.9027	−2.55809
$685$	8.61369	0.329112
$686$	38.1904	1.45812
$687$	50.9564	1.94411
$688$	−33.1343	−1.26323
$689$	40.3693	1.53795
$690$	33.1599	1.26238
$691$	28.9798	1.10244	0.551221	−	0.834359i	$-0.314162\pi$
$691$	28.9798	1.10244	0.551221	+	0.834359i	$0.314162\pi$
$692$	113.008	4.29591
$693$	13.1043	0.497793
$694$	−71.9518	−2.73125
$695$	15.7763	0.598430
$696$	57.8721	2.19364
$697$	14.9171	0.565027
$698$	−37.0611	−1.40278
$699$	22.1047	0.836076
$700$	5.69642	0.215305
$701$	−31.2490	−1.18026	−0.590130	−	0.807308i	$-0.700923\pi$
$701$	−31.2490	−1.18026	−0.590130	+	0.807308i	$0.700923\pi$
$702$	−33.8849	−1.27890
$703$	34.0822	1.28543
$704$	85.7464	3.23169
$705$	−3.11001	−0.117130
$706$	−32.5134	−1.22366
$707$	−6.25186	−0.235126
$708$	−128.628	−4.83413
$709$	7.65967	0.287665	0.143832	−	0.989602i	$-0.454057\pi$
$709$	7.65967	0.287665	0.143832	+	0.989602i	$0.454057\pi$
$710$	16.3783	0.614667
$711$	−0.233921	−0.00877272
$712$	−50.8329	−1.90505
$713$	3.34407	0.125236
$714$	−26.7803	−1.00223
$715$	−31.7556	−1.18759
$716$	−128.850	−4.81536
$717$	−11.6270	−0.434217
$718$	−79.7639	−2.97676
$719$	−12.4646	−0.464849	−0.232425	−	0.972614i	$-0.574666\pi$
$719$	−12.4646	−0.464849	−0.232425	+	0.972614i	$0.574666\pi$
$720$	21.0715	0.785289
$721$	2.75166	0.102477
$722$	−82.9511	−3.08712
$723$	35.6044	1.32414
$724$	35.2149	1.30875
$725$	−3.26369	−0.121210
$726$	−158.225	−5.87230
$727$	51.6908	1.91711	0.958553	−	0.284913i	$-0.0919648\pi$
$727$	51.6908	1.91711	0.958553	+	0.284913i	$0.0919648\pi$
$728$	46.8414	1.73606
$729$	−4.39844	−0.162905
$730$	3.61210	0.133690
$731$	−11.9132	−0.440626
$732$	120.158	4.44115
$733$	28.0202	1.03495	0.517475	−	0.855698i	$-0.326872\pi$
$733$	28.0202	1.03495	0.517475	+	0.855698i	$0.326872\pi$
$734$	−92.3106	−3.40725
$735$	−12.6239	−0.465640
$736$	77.7005	2.86408
$737$	−75.2938	−2.77348
$738$	−18.3721	−0.676287
$739$	0.343705	0.0126434	0.00632169	−	0.999980i	$-0.497988\pi$
$739$	0.343705	0.0126434	0.00632169	+	0.999980i	$0.497988\pi$
$740$	−24.1695	−0.888488
$741$	80.6377	2.96230
$742$	23.5424	0.864269
$743$	50.9885	1.87059	0.935294	−	0.353872i	$-0.115135\pi$
$743$	50.9885	1.87059	0.935294	+	0.353872i	$0.115135\pi$
$744$	10.4688	0.383806
$745$	4.10854	0.150525
$746$	−80.8109	−2.95870
$747$	−17.8754	−0.654027
$748$	125.236	4.57907
$749$	−0.0884515	−0.00323195
$750$	−5.85432	−0.213770
$751$	29.5681	1.07896	0.539478	−	0.841999i	$-0.318621\pi$
$751$	29.5681	1.07896	0.539478	+	0.841999i	$0.318621\pi$
$752$	−15.8192	−0.576869
$753$	−46.8451	−1.70713
$754$	−44.5579	−1.62270
$755$	12.5997	0.458550
$756$	−14.1381	−0.514198
$757$	−41.8887	−1.52247	−0.761236	−	0.648475i	$-0.775407\pi$
$757$	−41.8887	−1.52247	−0.761236	+	0.648475i	$0.775407\pi$
$758$	−21.9122	−0.795889
$759$	−77.1288	−2.79960
$760$	56.9456	2.06563
$761$	1.94920	0.0706586	0.0353293	−	0.999376i	$-0.488752\pi$
$761$	1.94920	0.0706586	0.0353293	+	0.999376i	$0.488752\pi$
$762$	71.5641	2.59250
$763$	−9.70585	−0.351375
$764$	39.8602	1.44209
$765$	7.57613	0.273916
$766$	−74.0789	−2.67658
$767$	59.6490	2.15380
$768$	−6.20796	−0.224011
$769$	−38.2791	−1.38038	−0.690190	−	0.723628i	$-0.742473\pi$
$769$	−38.2791	−1.38038	−0.690190	+	0.723628i	$0.742473\pi$
$770$	−18.5191	−0.667382
$771$	6.40491	0.230667
$772$	−60.5345	−2.17868
$773$	12.7451	0.458409	0.229204	−	0.973378i	$-0.426388\pi$
$773$	12.7451	0.458409	0.229204	+	0.973378i	$0.426388\pi$
$774$	14.6725	0.527390
$775$	−0.590389	−0.0212074
$776$	−113.429	−4.07188
$777$	−12.0215	−0.431268
$778$	−102.626	−3.67934
$779$	−26.1944	−0.938513
$780$	−57.1845	−2.04753
$781$	−38.0954	−1.36316
$782$	60.6442	2.16863
$783$	8.10024	0.289479
$784$	−64.2122	−2.29329
$785$	5.07286	0.181058
$786$	76.1654	2.71673
$787$	−34.5902	−1.23301	−0.616504	−	0.787352i	$-0.711451\pi$
$787$	−34.5902	−1.23301	−0.616504	+	0.787352i	$0.711451\pi$
$788$	−53.4765	−1.90502
$789$	−41.0718	−1.46219
$790$	0.330578	0.0117614
$791$	−22.3429	−0.794423
$792$	−92.8995	−3.30104
$793$	−55.7210	−1.97871
$794$	−52.0052	−1.84560
$795$	−17.3105	−0.613942
$796$	18.4495	0.653924
$797$	−52.4168	−1.85670	−0.928349	−	0.371709i	$-0.878772\pi$
$797$	−52.4168	−1.85670	−0.928349	+	0.371709i	$0.878772\pi$
$798$	47.0261	1.66470
$799$	−5.68771	−0.201217
$800$	−13.7179	−0.485000
$801$	11.8756	0.419604
$802$	59.6249	2.10543
$803$	−8.40162	−0.296487
$804$	−135.587	−4.78179
$805$	−6.41603	−0.226136
$806$	−8.06036	−0.283914
$807$	−2.85887	−0.100637
$808$	44.3208	1.55920
$809$	−23.8675	−0.839137	−0.419569	−	0.907724i	$-0.637819\pi$
$809$	−23.8675	−0.839137	−0.419569	+	0.907724i	$0.637819\pi$
$810$	29.4512	1.03481
$811$	46.4678	1.63170	0.815852	−	0.578261i	$-0.196269\pi$
$811$	46.4678	1.63170	0.815852	+	0.578261i	$0.196269\pi$
$812$	−18.5913	−0.652428
$813$	2.33697	0.0819612
$814$	78.5751	2.75406
$815$	−19.1402	−0.670453
$816$	100.161	3.50633
$817$	20.9196	0.731883
$818$	−75.6035	−2.64341
$819$	−10.9431	−0.382384
$820$	18.5759	0.648698
$821$	−1.16989	−0.0408295	−0.0204148	−	0.999792i	$-0.506499\pi$
$821$	−1.16989	−0.0408295	−0.0204148	+	0.999792i	$0.506499\pi$
$822$	−50.4273	−1.75885
$823$	34.3585	1.19766	0.598830	−	0.800876i	$-0.295632\pi$
$823$	34.3585	1.19766	0.598830	+	0.800876i	$0.295632\pi$
$824$	−19.5071	−0.679562
$825$	13.6169	0.474081
$826$	34.7859	1.21036
$827$	3.90270	0.135710	0.0678551	−	0.997695i	$-0.478384\pi$
$827$	3.90270	0.135710	0.0678551	+	0.997695i	$0.478384\pi$
$828$	−53.4378	−1.85709
$829$	−23.3196	−0.809922	−0.404961	−	0.914334i	$-0.632715\pi$
$829$	−23.3196	−0.809922	−0.404961	+	0.914334i	$0.632715\pi$
$830$	25.2616	0.876843
$831$	5.58695	0.193809
$832$	−71.6048	−2.48245
$833$	−23.0871	−0.799921
$834$	−92.3596	−3.19815
$835$	17.8039	0.616130
$836$	−219.913	−7.60587
$837$	1.46530	0.0506483
$838$	71.3121	2.46344
$839$	38.3575	1.32425	0.662123	−	0.749395i	$-0.269656\pi$
$839$	38.3575	1.32425	0.662123	+	0.749395i	$0.269656\pi$
$840$	−20.0859	−0.693028
$841$	−18.3484	−0.632702
$842$	38.1019	1.31308
$843$	−4.11951	−0.141883
$844$	−10.7935	−0.371528
$845$	13.5183	0.465044
$846$	7.00505	0.240839
$847$	30.6147	1.05193
$848$	−88.0511	−3.02369
$849$	15.5462	0.533544
$850$	−10.7066	−0.367234
$851$	27.2227	0.933184
$852$	−68.6011	−2.35023
$853$	14.7161	0.503869	0.251934	−	0.967744i	$-0.418933\pi$
$853$	14.7161	0.503869	0.251934	+	0.967744i	$0.418933\pi$
$854$	−32.4952	−1.11196
$855$	−13.3037	−0.454976
$856$	0.627051	0.0214322
$857$	−47.8200	−1.63350	−0.816750	−	0.576992i	$-0.804226\pi$
$857$	−47.8200	−1.63350	−0.816750	+	0.576992i	$0.804226\pi$
$858$	185.907	6.34677
$859$	−40.4213	−1.37916	−0.689579	−	0.724211i	$-0.742204\pi$
$859$	−40.4213	−1.37916	−0.689579	+	0.724211i	$0.742204\pi$
$860$	−14.8352	−0.505876
$861$	9.23930	0.314875
$862$	53.9348	1.83703
$863$	−8.89484	−0.302784	−0.151392	−	0.988474i	$-0.548376\pi$
$863$	−8.89484	−0.302784	−0.151392	+	0.988474i	$0.548376\pi$
$864$	34.0468	1.15830
$865$	22.4717	0.764061
$866$	−41.1722	−1.39909
$867$	−1.52667	−0.0518486
$868$	−3.36310	−0.114151
$869$	−0.768913	−0.0260836
$870$	19.1067	0.647777
$871$	62.8761	2.13048
$872$	68.8069	2.33009
$873$	26.4994	0.896870
$874$	−106.491	−3.60211
$875$	1.13274	0.0382935
$876$	−15.1294	−0.511175
$877$	−31.4911	−1.06338	−0.531689	−	0.846940i	$-0.678442\pi$
$877$	−31.4911	−1.06338	−0.531689	+	0.846940i	$0.678442\pi$
$878$	−43.4246	−1.46551
$879$	−43.6934	−1.47374
$880$	69.2634	2.33487
$881$	16.9332	0.570495	0.285248	−	0.958454i	$-0.407924\pi$
$881$	16.9332	0.570495	0.285248	+	0.958454i	$0.407924\pi$
$882$	28.4343	0.957434
$883$	−36.3206	−1.22229	−0.611143	−	0.791520i	$-0.709290\pi$
$883$	−36.3206	−1.22229	−0.611143	+	0.791520i	$0.709290\pi$
$884$	−104.581	−3.51745
$885$	−25.5778	−0.859788
$886$	7.58423	0.254797
$887$	−11.7492	−0.394498	−0.197249	−	0.980353i	$-0.563201\pi$
$887$	−11.7492	−0.394498	−0.197249	+	0.980353i	$0.563201\pi$
$888$	85.2228	2.85989
$889$	−13.8468	−0.464406
$890$	−16.7827	−0.562556
$891$	−68.5025	−2.29492
$892$	−37.9389	−1.27029
$893$	9.98761	0.334222
$894$	−24.0527	−0.804444
$895$	−25.6220	−0.856448
$896$	−10.6807	−0.356818
$897$	64.4085	2.15054
$898$	−5.98918	−0.199862
$899$	1.92684	0.0642638
$900$	9.43434	0.314478
$901$	−31.6582	−1.05469
$902$	−60.3903	−2.01078
$903$	−7.37876	−0.245550
$904$	158.394	5.26810
$905$	7.00251	0.232771
$906$	−73.7626	−2.45060
$907$	−9.36294	−0.310891	−0.155446	−	0.987844i	$-0.549681\pi$
$907$	−9.36294	−0.310891	−0.155446	+	0.987844i	$0.549681\pi$
$908$	−91.6231	−3.04062
$909$	−10.3542	−0.343429
$910$	15.4649	0.512655
$911$	−14.0949	−0.466984	−0.233492	−	0.972359i	$-0.575015\pi$
$911$	−14.0949	−0.466984	−0.233492	+	0.972359i	$0.575015\pi$
$912$	−175.882	−5.82405
$913$	−58.7576	−1.94459
$914$	11.4880	0.379990
$915$	23.8934	0.789893
$916$	116.048	3.83434
$917$	−14.7371	−0.486661
$918$	26.5731	0.877042
$919$	7.54217	0.248793	0.124397	−	0.992233i	$-0.460300\pi$
$919$	7.54217	0.248793	0.124397	+	0.992233i	$0.460300\pi$
$920$	45.4846	1.49958
$921$	−61.3423	−2.02130
$922$	−51.0934	−1.68267
$923$	31.8125	1.04712
$924$	77.5679	2.55180
$925$	−4.80612	−0.158024
$926$	51.7466	1.70050
$927$	4.55726	0.149680
$928$	44.7708	1.46968
$929$	−6.47102	−0.212307	−0.106154	−	0.994350i	$-0.533854\pi$
$929$	−6.47102	−0.212307	−0.106154	+	0.994350i	$0.533854\pi$
$930$	3.45633	0.113337
$931$	40.5409	1.32867
$932$	50.3413	1.64898
$933$	−4.29302	−0.140547
$934$	99.2216	3.24663
$935$	24.9032	0.814422
$936$	77.5781	2.53572
$937$	40.2500	1.31491	0.657455	−	0.753494i	$-0.271633\pi$
$937$	40.2500	1.31491	0.657455	+	0.753494i	$0.271633\pi$
$938$	36.6679	1.19725
$939$	−22.3479	−0.729295
$940$	−7.08274	−0.231014
$941$	11.6166	0.378691	0.189346	−	0.981911i	$-0.439363\pi$
$941$	11.6166	0.378691	0.189346	+	0.981911i	$0.439363\pi$
$942$	−29.6982	−0.967618
$943$	−20.9225	−0.681331
$944$	−130.103	−4.23449
$945$	−2.81138	−0.0914541
$946$	48.2293	1.56807
$947$	−10.3049	−0.334864	−0.167432	−	0.985884i	$-0.553547\pi$
$947$	−10.3049	−0.334864	−0.167432	+	0.985884i	$0.553547\pi$
$948$	−1.38464	−0.0449709
$949$	7.01599	0.227749
$950$	18.8008	0.609978
$951$	29.4627	0.955394
$952$	−36.7338	−1.19055
$953$	−24.0930	−0.780450	−0.390225	−	0.920720i	$-0.627603\pi$
$953$	−24.0930	−0.780450	−0.390225	+	0.920720i	$0.627603\pi$
$954$	38.9906	1.26237
$955$	7.92623	0.256487
$956$	−26.4793	−0.856402
$957$	−44.4414	−1.43659
$958$	−82.4661	−2.66436
$959$	9.75705	0.315072
$960$	30.7045	0.990984
$961$	−30.6514	−0.988756
$962$	−65.6162	−2.11555
$963$	−0.146492	−0.00472064
$964$	81.0855	2.61159
$965$	−12.0373	−0.387496
$966$	37.5615	1.20852
$967$	−58.3455	−1.87627	−0.938133	−	0.346275i	$-0.887446\pi$
$967$	−58.3455	−1.87627	−0.938133	+	0.346275i	$0.887446\pi$
$968$	−217.034	−6.97574
$969$	−63.2374	−2.03148
$970$	−37.4491	−1.20242
$971$	−6.19216	−0.198716	−0.0993580	−	0.995052i	$-0.531679\pi$
$971$	−6.19216	−0.198716	−0.0993580	+	0.995052i	$0.531679\pi$
$972$	−85.9133	−2.75567
$973$	17.8704	0.572900
$974$	20.0480	0.642378
$975$	−11.3712	−0.364170
$976$	121.535	3.89025
$977$	−37.4645	−1.19860	−0.599298	−	0.800526i	$-0.704554\pi$
$977$	−37.4645	−1.19860	−0.599298	+	0.800526i	$0.704554\pi$
$978$	112.053	3.58306
$979$	39.0359	1.24759
$980$	−28.7497	−0.918376
$981$	−16.0747	−0.513226
$982$	72.0709	2.29988
$983$	−39.9677	−1.27477	−0.637385	−	0.770545i	$-0.719984\pi$
$983$	−39.9677	−1.27477	−0.637385	+	0.770545i	$0.719984\pi$
$984$	−65.4994	−2.08804
$985$	−10.6338	−0.338822
$986$	34.9430	1.11281
$987$	−3.52283	−0.112133
$988$	183.645	5.84251
$989$	16.7093	0.531324
$990$	−30.6711	−0.974791
$991$	−25.8106	−0.819900	−0.409950	−	0.912108i	$-0.634454\pi$
$991$	−25.8106	−0.819900	−0.409950	+	0.912108i	$0.634454\pi$
$992$	8.09888	0.257140
$993$	−8.59231	−0.272669
$994$	18.5523	0.588444
$995$	3.66869	0.116305
$996$	−105.809	−3.35269
$997$	−44.1353	−1.39778	−0.698890	−	0.715229i	$-0.746322\pi$
$997$	−44.1353	−1.39778	−0.698890	+	0.715229i	$0.746322\pi$
$998$	39.8794	1.26236
$999$	11.9285	0.377400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.e.1.7	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.e.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.65121 q^{2} +2.20817 q^{3} +5.02889 q^{4} +1.00000 q^{5} -5.85432 q^{6} +1.13274 q^{7} -8.03022 q^{8} +1.87603 q^{9} +O(q^{10})\)	\(q-2.65121 q^{2} +2.20817 q^{3} +5.02889 q^{4} +1.00000 q^{5} -5.85432 q^{6} +1.13274 q^{7} -8.03022 q^{8} +1.87603 q^{9} -2.65121 q^{10} +6.16661 q^{11} +11.1047 q^{12} -5.14959 q^{13} -3.00312 q^{14} +2.20817 q^{15} +11.2320 q^{16} +4.03839 q^{17} -4.97373 q^{18} -7.09141 q^{19} +5.02889 q^{20} +2.50128 q^{21} -16.3490 q^{22} -5.66418 q^{23} -17.7321 q^{24} +1.00000 q^{25} +13.6526 q^{26} -2.48193 q^{27} +5.69642 q^{28} -3.26369 q^{29} -5.85432 q^{30} -0.590389 q^{31} -13.7179 q^{32} +13.6169 q^{33} -10.7066 q^{34} +1.13274 q^{35} +9.43434 q^{36} -4.80612 q^{37} +18.8008 q^{38} -11.3712 q^{39} -8.03022 q^{40} +3.69383 q^{41} -6.63141 q^{42} -2.94999 q^{43} +31.0113 q^{44} +1.87603 q^{45} +15.0169 q^{46} -1.40841 q^{47} +24.8022 q^{48} -5.71690 q^{49} -2.65121 q^{50} +8.91747 q^{51} -25.8968 q^{52} -7.83931 q^{53} +6.58011 q^{54} +6.16661 q^{55} -9.09614 q^{56} -15.6591 q^{57} +8.65270 q^{58} -11.5832 q^{59} +11.1047 q^{60} +10.8205 q^{61} +1.56524 q^{62} +2.12505 q^{63} +13.9049 q^{64} -5.14959 q^{65} -36.1013 q^{66} -12.2099 q^{67} +20.3087 q^{68} -12.5075 q^{69} -3.00312 q^{70} -6.17768 q^{71} -15.0649 q^{72} -1.36244 q^{73} +12.7420 q^{74} +2.20817 q^{75} -35.6619 q^{76} +6.98516 q^{77} +30.1474 q^{78} -0.124690 q^{79} +11.2320 q^{80} -11.1086 q^{81} -9.79310 q^{82} -9.52835 q^{83} +12.5787 q^{84} +4.03839 q^{85} +7.82103 q^{86} -7.20678 q^{87} -49.5193 q^{88} +6.33020 q^{89} -4.97373 q^{90} -5.83314 q^{91} -28.4846 q^{92} -1.30368 q^{93} +3.73398 q^{94} -7.09141 q^{95} -30.2914 q^{96} +14.1253 q^{97} +15.1567 q^{98} +11.5687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) 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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