LMFDB - Embedded newform 8003.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49180 q^{2} +1.26406 q^{3} +4.20905 q^{4} -3.18748 q^{5} -3.14979 q^{6} +4.16576 q^{7} -5.50450 q^{8} -1.40214 q^{9} +O(q^{10})$	\(q-2.49180 q^{2} +1.26406 q^{3} +4.20905 q^{4} -3.18748 q^{5} -3.14979 q^{6} +4.16576 q^{7} -5.50450 q^{8} -1.40214 q^{9} +7.94255 q^{10} +4.10364 q^{11} +5.32050 q^{12} -2.81118 q^{13} -10.3802 q^{14} -4.02918 q^{15} +5.29800 q^{16} -5.22651 q^{17} +3.49386 q^{18} +4.32766 q^{19} -13.4163 q^{20} +5.26579 q^{21} -10.2254 q^{22} -2.96556 q^{23} -6.95804 q^{24} +5.16002 q^{25} +7.00490 q^{26} -5.56459 q^{27} +17.5339 q^{28} +0.134462 q^{29} +10.0399 q^{30} -2.32765 q^{31} -2.19253 q^{32} +5.18726 q^{33} +13.0234 q^{34} -13.2783 q^{35} -5.90169 q^{36} -3.13194 q^{37} -10.7837 q^{38} -3.55351 q^{39} +17.5455 q^{40} -0.709502 q^{41} -13.1213 q^{42} +2.15254 q^{43} +17.2724 q^{44} +4.46931 q^{45} +7.38958 q^{46} +5.65906 q^{47} +6.69701 q^{48} +10.3536 q^{49} -12.8577 q^{50} -6.60663 q^{51} -11.8324 q^{52} -1.00000 q^{53} +13.8658 q^{54} -13.0803 q^{55} -22.9304 q^{56} +5.47044 q^{57} -0.335053 q^{58} -13.8862 q^{59} -16.9590 q^{60} +2.60754 q^{61} +5.80002 q^{62} -5.84100 q^{63} -5.13266 q^{64} +8.96059 q^{65} -12.9256 q^{66} +7.18915 q^{67} -21.9986 q^{68} -3.74866 q^{69} +33.0868 q^{70} -11.1229 q^{71} +7.71811 q^{72} +6.14128 q^{73} +7.80416 q^{74} +6.52260 q^{75} +18.2154 q^{76} +17.0948 q^{77} +8.85463 q^{78} +10.3746 q^{79} -16.8873 q^{80} -2.82756 q^{81} +1.76793 q^{82} -4.78580 q^{83} +22.1640 q^{84} +16.6594 q^{85} -5.36369 q^{86} +0.169969 q^{87} -22.5885 q^{88} -0.627918 q^{89} -11.1366 q^{90} -11.7107 q^{91} -12.4822 q^{92} -2.94229 q^{93} -14.1012 q^{94} -13.7943 q^{95} -2.77150 q^{96} -9.52135 q^{97} -25.7990 q^{98} -5.75389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.49180	−1.76197	−0.880983	−	0.473148i	$-0.843118\pi$
$2$	−2.49180	−1.76197	−0.880983	+	0.473148i	$0.843118\pi$
$3$	1.26406	0.729807	0.364904	−	0.931045i	$-0.381102\pi$
$3$	1.26406	0.729807	0.364904	+	0.931045i	$0.381102\pi$
$4$	4.20905	2.10452
$5$	−3.18748	−1.42548	−0.712742	−	0.701426i	$-0.752547\pi$
$5$	−3.18748	−1.42548	−0.712742	+	0.701426i	$0.752547\pi$
$6$	−3.14979	−1.28590
$7$	4.16576	1.57451	0.787255	−	0.616628i	$-0.211502\pi$
$7$	4.16576	1.57451	0.787255	+	0.616628i	$0.211502\pi$
$8$	−5.50450	−1.94614
$9$	−1.40214	−0.467381
$10$	7.94255	2.51165
$11$	4.10364	1.23729	0.618647	−	0.785669i	$-0.287681\pi$
$11$	4.10364	1.23729	0.618647	+	0.785669i	$0.287681\pi$
$12$	5.32050	1.53590
$13$	−2.81118	−0.779682	−0.389841	−	0.920882i	$-0.627470\pi$
$13$	−2.81118	−0.779682	−0.389841	+	0.920882i	$0.627470\pi$
$14$	−10.3802	−2.77423
$15$	−4.02918	−1.04033
$16$	5.29800	1.32450
$17$	−5.22651	−1.26761	−0.633807	−	0.773491i	$-0.718509\pi$
$17$	−5.22651	−1.26761	−0.633807	+	0.773491i	$0.718509\pi$
$18$	3.49386	0.823510
$19$	4.32766	0.992834	0.496417	−	0.868084i	$-0.334649\pi$
$19$	4.32766	0.992834	0.496417	+	0.868084i	$0.334649\pi$
$20$	−13.4163	−2.99997
$21$	5.26579	1.14909
$22$	−10.2254	−2.18007
$23$	−2.96556	−0.618363	−0.309181	−	0.951003i	$-0.600055\pi$
$23$	−2.96556	−0.618363	−0.309181	+	0.951003i	$0.600055\pi$
$24$	−6.95804	−1.42030
$25$	5.16002	1.03200
$26$	7.00490	1.37377
$27$	−5.56459	−1.07091
$28$	17.5339	3.31360
$29$	0.134462	0.0249690	0.0124845	−	0.999922i	$-0.496026\pi$
$29$	0.134462	0.0249690	0.0124845	+	0.999922i	$0.496026\pi$
$30$	10.0399	1.83302
$31$	−2.32765	−0.418058	−0.209029	−	0.977909i	$-0.567030\pi$
$31$	−2.32765	−0.418058	−0.209029	+	0.977909i	$0.567030\pi$
$32$	−2.19253	−0.387589
$33$	5.18726	0.902986
$34$	13.0234	2.23349
$35$	−13.2783	−2.24444
$36$	−5.90169	−0.983616
$37$	−3.13194	−0.514888	−0.257444	−	0.966293i	$-0.582880\pi$
$37$	−3.13194	−0.514888	−0.257444	+	0.966293i	$0.582880\pi$
$38$	−10.7837	−1.74934
$39$	−3.55351	−0.569018
$40$	17.5455	2.77418
$41$	−0.709502	−0.110806	−0.0554028	−	0.998464i	$-0.517644\pi$
$41$	−0.709502	−0.110806	−0.0554028	+	0.998464i	$0.517644\pi$
$42$	−13.1213	−2.02466
$43$	2.15254	0.328259	0.164129	−	0.986439i	$-0.447519\pi$
$43$	2.15254	0.328259	0.164129	+	0.986439i	$0.447519\pi$
$44$	17.2724	2.60391
$45$	4.46931	0.666245
$46$	7.38958	1.08953
$47$	5.65906	0.825458	0.412729	−	0.910854i	$-0.364576\pi$
$47$	5.65906	0.825458	0.412729	+	0.910854i	$0.364576\pi$
$48$	6.69701	0.966630
$49$	10.3536	1.47908
$50$	−12.8577	−1.81836
$51$	−6.60663	−0.925114
$52$	−11.8324	−1.64086
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	13.8658	1.88690
$55$	−13.0803	−1.76374
$56$	−22.9304	−3.06421
$57$	5.47044	0.724578
$58$	−0.335053	−0.0439946
$59$	−13.8862	−1.80783	−0.903913	−	0.427716i	$-0.859318\pi$
$59$	−13.8862	−1.80783	−0.903913	+	0.427716i	$0.859318\pi$
$60$	−16.9590	−2.18940
$61$	2.60754	0.333862	0.166931	−	0.985969i	$-0.446614\pi$
$61$	2.60754	0.333862	0.166931	+	0.985969i	$0.446614\pi$
$62$	5.80002	0.736604
$63$	−5.84100	−0.735897
$64$	−5.13266	−0.641582
$65$	8.96059	1.11142
$66$	−12.9256	−1.59103
$67$	7.18915	0.878294	0.439147	−	0.898415i	$-0.355281\pi$
$67$	7.18915	0.878294	0.439147	+	0.898415i	$0.355281\pi$
$68$	−21.9986	−2.66773
$69$	−3.74866	−0.451286
$70$	33.0868	3.95463
$71$	−11.1229	−1.32004	−0.660022	−	0.751247i	$-0.729453\pi$
$71$	−11.1229	−1.32004	−0.660022	+	0.751247i	$0.729453\pi$
$72$	7.71811	0.909587
$73$	6.14128	0.718782	0.359391	−	0.933187i	$-0.382984\pi$
$73$	6.14128	0.718782	0.359391	+	0.933187i	$0.382984\pi$
$74$	7.80416	0.907215
$75$	6.52260	0.753165
$76$	18.2154	2.08944
$77$	17.0948	1.94813
$78$	8.85463	1.00259
$79$	10.3746	1.16723	0.583614	−	0.812031i	$-0.301638\pi$
$79$	10.3746	1.16723	0.583614	+	0.812031i	$0.301638\pi$
$80$	−16.8873	−1.88805
$81$	−2.82756	−0.314173
$82$	1.76793	0.195236
$83$	−4.78580	−0.525310	−0.262655	−	0.964890i	$-0.584598\pi$
$83$	−4.78580	−0.525310	−0.262655	+	0.964890i	$0.584598\pi$
$84$	22.1640	2.41829
$85$	16.6594	1.80696
$86$	−5.36369	−0.578381
$87$	0.169969	0.0182226
$88$	−22.5885	−2.40794
$89$	−0.627918	−0.0665592	−0.0332796	−	0.999446i	$-0.510595\pi$
$89$	−0.627918	−0.0665592	−0.0332796	+	0.999446i	$0.510595\pi$
$90$	−11.1366	−1.17390
$91$	−11.7107	−1.22762
$92$	−12.4822	−1.30136
$93$	−2.94229	−0.305102
$94$	−14.1012	−1.45443
$95$	−13.7943	−1.41527
$96$	−2.77150	−0.282865
$97$	−9.52135	−0.966747	−0.483374	−	0.875414i	$-0.660589\pi$
$97$	−9.52135	−0.966747	−0.483374	+	0.875414i	$0.660589\pi$
$98$	−25.7990	−2.60609
$99$	−5.75389	−0.578288
$100$	21.7188	2.17188
$101$	17.6646	1.75770	0.878848	−	0.477102i	$-0.158313\pi$
$101$	17.6646	1.75770	0.878848	+	0.477102i	$0.158313\pi$
$102$	16.4624	1.63002
$103$	12.3226	1.21418	0.607090	−	0.794633i	$-0.292337\pi$
$103$	12.3226	1.21418	0.607090	+	0.794633i	$0.292337\pi$
$104$	15.4742	1.51737
$105$	−16.7846	−1.63801
$106$	2.49180	0.242025
$107$	14.6702	1.41822	0.709110	−	0.705098i	$-0.249097\pi$
$107$	14.6702	1.41822	0.709110	+	0.705098i	$0.249097\pi$
$108$	−23.4216	−2.25375
$109$	4.09509	0.392238	0.196119	−	0.980580i	$-0.437166\pi$
$109$	4.09509	0.392238	0.196119	+	0.980580i	$0.437166\pi$
$110$	32.5934	3.10765
$111$	−3.95897	−0.375769
$112$	22.0702	2.08544
$113$	7.60429	0.715352	0.357676	−	0.933846i	$-0.383569\pi$
$113$	7.60429	0.715352	0.357676	+	0.933846i	$0.383569\pi$
$114$	−13.6312	−1.27668
$115$	9.45267	0.881466
$116$	0.565959	0.0525479
$117$	3.94169	0.364409
$118$	34.6015	3.18533
$119$	−21.7724	−1.99587
$120$	22.1786	2.02462
$121$	5.83985	0.530895
$122$	−6.49747	−0.588253
$123$	−0.896855	−0.0808667
$124$	−9.79718	−0.879813
$125$	−0.510075	−0.0456225
$126$	14.5546	1.29663
$127$	−5.15412	−0.457354	−0.228677	−	0.973502i	$-0.573440\pi$
$127$	−5.15412	−0.457354	−0.228677	+	0.973502i	$0.573440\pi$
$128$	17.1746	1.51803
$129$	2.72094	0.239566
$130$	−22.3280	−1.95829
$131$	0.813284	0.0710570	0.0355285	−	0.999369i	$-0.488689\pi$
$131$	0.813284	0.0710570	0.0355285	+	0.999369i	$0.488689\pi$
$132$	21.8334	1.90036
$133$	18.0280	1.56323
$134$	−17.9139	−1.54752
$135$	17.7370	1.52656
$136$	28.7693	2.46695
$137$	11.1819	0.955338	0.477669	−	0.878540i	$-0.341482\pi$
$137$	11.1819	0.955338	0.477669	+	0.878540i	$0.341482\pi$
$138$	9.34090	0.795150
$139$	7.44775	0.631710	0.315855	−	0.948807i	$-0.397709\pi$
$139$	7.44775	0.631710	0.315855	+	0.948807i	$0.397709\pi$
$140$	−55.8889	−4.72348
$141$	7.15340	0.602425
$142$	27.7160	2.32587
$143$	−11.5361	−0.964696
$144$	−7.42856	−0.619047
$145$	−0.428596	−0.0355930
$146$	−15.3028	−1.26647
$147$	13.0876	1.07944
$148$	−13.1825	−1.08359
$149$	−7.58476	−0.621368	−0.310684	−	0.950513i	$-0.600558\pi$
$149$	−7.58476	−0.621368	−0.310684	+	0.950513i	$0.600558\pi$
$150$	−16.2530	−1.32705
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−23.8216	−1.93219
$153$	7.32832	0.592459
$154$	−42.5967	−3.43254
$155$	7.41933	0.595935
$156$	−14.9569	−1.19751
$157$	−12.5367	−1.00053	−0.500267	−	0.865871i	$-0.666765\pi$
$157$	−12.5367	−1.00053	−0.500267	+	0.865871i	$0.666765\pi$
$158$	−25.8513	−2.05662
$159$	−1.26406	−0.100247
$160$	6.98865	0.552501
$161$	−12.3538	−0.973618
$162$	7.04570	0.553563
$163$	8.33588	0.652916	0.326458	−	0.945212i	$-0.394145\pi$
$163$	8.33588	0.652916	0.326458	+	0.945212i	$0.394145\pi$
$164$	−2.98633	−0.233193
$165$	−16.5343	−1.28719
$166$	11.9252	0.925578
$167$	2.19756	0.170053	0.0850263	−	0.996379i	$-0.472903\pi$
$167$	2.19756	0.170053	0.0850263	+	0.996379i	$0.472903\pi$
$168$	−28.9855	−2.23628
$169$	−5.09725	−0.392096
$170$	−41.5118	−3.18381
$171$	−6.06801	−0.464032
$172$	9.06014	0.690829
$173$	16.7651	1.27463	0.637315	−	0.770603i	$-0.280045\pi$
$173$	16.7651	1.27463	0.637315	+	0.770603i	$0.280045\pi$
$174$	−0.423528	−0.0321076
$175$	21.4954	1.62490
$176$	21.7411	1.63880
$177$	−17.5530	−1.31936
$178$	1.56464	0.117275
$179$	−3.90391	−0.291792	−0.145896	−	0.989300i	$-0.546606\pi$
$179$	−3.90391	−0.291792	−0.145896	+	0.989300i	$0.546606\pi$
$180$	18.8115	1.40213
$181$	6.81301	0.506407	0.253204	−	0.967413i	$-0.418516\pi$
$181$	6.81301	0.506407	0.253204	+	0.967413i	$0.418516\pi$
$182$	29.1807	2.16302
$183$	3.29610	0.243655
$184$	16.3239	1.20342
$185$	9.98299	0.733964
$186$	7.33159	0.537579
$187$	−21.4477	−1.56841
$188$	23.8192	1.73720
$189$	−23.1808	−1.68615
$190$	34.3727	2.49366
$191$	−12.8363	−0.928801	−0.464401	−	0.885625i	$-0.653730\pi$
$191$	−12.8363	−0.928801	−0.464401	+	0.885625i	$0.653730\pi$
$192$	−6.48800	−0.468231
$193$	15.6298	1.12506	0.562528	−	0.826778i	$-0.309829\pi$
$193$	15.6298	1.12506	0.562528	+	0.826778i	$0.309829\pi$
$194$	23.7253	1.70338
$195$	11.3268	0.811126
$196$	43.5787	3.11276
$197$	10.8051	0.769833	0.384916	−	0.922951i	$-0.374230\pi$
$197$	10.8051	0.769833	0.384916	+	0.922951i	$0.374230\pi$
$198$	14.3375	1.01892
$199$	6.76148	0.479309	0.239654	−	0.970858i	$-0.422966\pi$
$199$	6.76148	0.479309	0.239654	+	0.970858i	$0.422966\pi$
$200$	−28.4034	−2.00842
$201$	9.08754	0.640985
$202$	−44.0167	−3.09700
$203$	0.560138	0.0393140
$204$	−27.8077	−1.94693
$205$	2.26152	0.157952
$206$	−30.7053	−2.13934
$207$	4.15815	0.289011
$208$	−14.8936	−1.03269
$209$	17.7592	1.22843
$210$	41.8238	2.88611
$211$	−13.3505	−0.919084	−0.459542	−	0.888156i	$-0.651987\pi$
$211$	−13.3505	−0.919084	−0.459542	+	0.888156i	$0.651987\pi$
$212$	−4.20905	−0.289079
$213$	−14.0600	−0.963377
$214$	−36.5551	−2.49885
$215$	−6.86117	−0.467928
$216$	30.6303	2.08413
$217$	−9.69642	−0.658236
$218$	−10.2041	−0.691111
$219$	7.76296	0.524572
$220$	−55.0555	−3.71184
$221$	14.6927	0.988336
$222$	9.86495	0.662092
$223$	13.9086	0.931389	0.465694	−	0.884946i	$-0.345805\pi$
$223$	13.9086	0.931389	0.465694	+	0.884946i	$0.345805\pi$
$224$	−9.13357	−0.610262
$225$	−7.23510	−0.482340
$226$	−18.9483	−1.26043
$227$	−26.1232	−1.73386	−0.866928	−	0.498434i	$-0.833909\pi$
$227$	−26.1232	−1.73386	−0.866928	+	0.498434i	$0.833909\pi$
$228$	23.0254	1.52489
$229$	−26.1587	−1.72862	−0.864309	−	0.502961i	$-0.832244\pi$
$229$	−26.1587	−1.72862	−0.864309	+	0.502961i	$0.832244\pi$
$230$	−23.5541	−1.55311
$231$	21.6089	1.42176
$232$	−0.740148	−0.0485931
$233$	−8.08685	−0.529787	−0.264893	−	0.964278i	$-0.585337\pi$
$233$	−8.08685	−0.529787	−0.264893	+	0.964278i	$0.585337\pi$
$234$	−9.82188	−0.642076
$235$	−18.0381	−1.17668
$236$	−58.4476	−3.80461
$237$	13.1141	0.851852
$238$	54.2523	3.51666
$239$	−9.17856	−0.593712	−0.296856	−	0.954922i	$-0.595938\pi$
$239$	−9.17856	−0.593712	−0.296856	+	0.954922i	$0.595938\pi$
$240$	−21.3466	−1.37792
$241$	−5.75828	−0.370923	−0.185462	−	0.982651i	$-0.559378\pi$
$241$	−5.75828	−0.370923	−0.185462	+	0.982651i	$0.559378\pi$
$242$	−14.5517	−0.935420
$243$	13.1196	0.841620
$244$	10.9753	0.702620
$245$	−33.0018	−2.10841
$246$	2.23478	0.142484
$247$	−12.1659	−0.774095
$248$	12.8125	0.813597
$249$	−6.04956	−0.383375
$250$	1.27100	0.0803853
$251$	13.2244	0.834718	0.417359	−	0.908742i	$-0.362956\pi$
$251$	13.2244	0.834718	0.417359	+	0.908742i	$0.362956\pi$
$252$	−24.5851	−1.54871
$253$	−12.1696	−0.765096
$254$	12.8430	0.805843
$255$	21.0585	1.31874
$256$	−32.5303	−2.03314
$257$	12.5160	0.780725	0.390363	−	0.920661i	$-0.372350\pi$
$257$	12.5160	0.780725	0.390363	+	0.920661i	$0.372350\pi$
$258$	−6.78004	−0.422107
$259$	−13.0469	−0.810696
$260$	37.7156	2.33902
$261$	−0.188536	−0.0116701
$262$	−2.02654	−0.125200
$263$	3.01417	0.185862	0.0929308	−	0.995673i	$-0.470376\pi$
$263$	3.01417	0.185862	0.0929308	+	0.995673i	$0.470376\pi$
$264$	−28.5533	−1.75733
$265$	3.18748	0.195805
$266$	−44.9222	−2.75435
$267$	−0.793728	−0.0485754
$268$	30.2595	1.84839
$269$	−8.44611	−0.514968	−0.257484	−	0.966283i	$-0.582894\pi$
$269$	−8.44611	−0.514968	−0.257484	+	0.966283i	$0.582894\pi$
$270$	−44.1970	−2.68975
$271$	12.0600	0.732591	0.366295	−	0.930499i	$-0.380626\pi$
$271$	12.0600	0.732591	0.366295	+	0.930499i	$0.380626\pi$
$272$	−27.6900	−1.67895
$273$	−14.8031	−0.895924
$274$	−27.8631	−1.68327
$275$	21.1749	1.27689
$276$	−15.7783	−0.949742
$277$	21.1705	1.27201	0.636005	−	0.771685i	$-0.280586\pi$
$277$	21.1705	1.27201	0.636005	+	0.771685i	$0.280586\pi$
$278$	−18.5583	−1.11305
$279$	3.26370	0.195392
$280$	73.0903	4.36798
$281$	18.6566	1.11296	0.556479	−	0.830862i	$-0.312152\pi$
$281$	18.6566	1.11296	0.556479	+	0.830862i	$0.312152\pi$
$282$	−17.8248	−1.06145
$283$	16.1998	0.962975	0.481488	−	0.876453i	$-0.340097\pi$
$283$	16.1998	0.962975	0.481488	+	0.876453i	$0.340097\pi$
$284$	−46.8168	−2.77806
$285$	−17.4369	−1.03287
$286$	28.7456	1.69976
$287$	−2.95562	−0.174465
$288$	3.07425	0.181152
$289$	10.3164	0.606845
$290$	1.06797	0.0627136
$291$	−12.0356	−0.705539
$292$	25.8489	1.51269
$293$	10.5898	0.618662	0.309331	−	0.950954i	$-0.399895\pi$
$293$	10.5898	0.618662	0.309331	+	0.950954i	$0.399895\pi$
$294$	−32.6116	−1.90195
$295$	44.2619	2.57703
$296$	17.2398	1.00204
$297$	−22.8351	−1.32502
$298$	18.8997	1.09483
$299$	8.33674	0.482126
$300$	27.4539	1.58505
$301$	8.96696	0.516847
$302$	−2.49180	−0.143387
$303$	22.3292	1.28278
$304$	22.9280	1.31501
$305$	−8.31149	−0.475915
$306$	−18.2607	−1.04389
$307$	6.18948	0.353252	0.176626	−	0.984278i	$-0.443482\pi$
$307$	6.18948	0.353252	0.176626	+	0.984278i	$0.443482\pi$
$308$	71.9528	4.09989
$309$	15.5765	0.886117
$310$	−18.4875	−1.05002
$311$	−10.9586	−0.621405	−0.310703	−	0.950507i	$-0.600564\pi$
$311$	−10.9586	−0.621405	−0.310703	+	0.950507i	$0.600564\pi$
$312$	19.5603	1.10739
$313$	11.0319	0.623562	0.311781	−	0.950154i	$-0.399075\pi$
$313$	11.0319	0.623562	0.311781	+	0.950154i	$0.399075\pi$
$314$	31.2388	1.76291
$315$	18.6181	1.04901
$316$	43.6670	2.45646
$317$	16.6097	0.932892	0.466446	−	0.884550i	$-0.345534\pi$
$317$	16.6097	0.932892	0.466446	+	0.884550i	$0.345534\pi$
$318$	3.14979	0.176631
$319$	0.551785	0.0308940
$320$	16.3602	0.914565
$321$	18.5440	1.03503
$322$	30.7832	1.71548
$323$	−22.6186	−1.25853
$324$	−11.9013	−0.661185
$325$	−14.5058	−0.804636
$326$	−20.7713	−1.15042
$327$	5.17645	0.286258
$328$	3.90546	0.215643
$329$	23.5743	1.29969
$330$	41.2001	2.26799
$331$	−8.51012	−0.467758	−0.233879	−	0.972266i	$-0.575142\pi$
$331$	−8.51012	−0.467758	−0.233879	+	0.972266i	$0.575142\pi$
$332$	−20.1437	−1.10553
$333$	4.39143	0.240649
$334$	−5.47588	−0.299627
$335$	−22.9153	−1.25199
$336$	27.8981	1.52197
$337$	20.5446	1.11913	0.559567	−	0.828785i	$-0.310968\pi$
$337$	20.5446	1.11913	0.559567	+	0.828785i	$0.310968\pi$
$338$	12.7013	0.690860
$339$	9.61231	0.522069
$340$	70.1202	3.80280
$341$	−9.55182	−0.517260
$342$	15.1202	0.817609
$343$	13.9702	0.754319
$344$	−11.8487	−0.638836
$345$	11.9488	0.643300
$346$	−41.7753	−2.24586
$347$	−7.43683	−0.399230	−0.199615	−	0.979874i	$-0.563969\pi$
$347$	−7.43683	−0.399230	−0.199615	+	0.979874i	$0.563969\pi$
$348$	0.715408	0.0383499
$349$	29.2579	1.56614	0.783069	−	0.621935i	$-0.213653\pi$
$349$	29.2579	1.56614	0.783069	+	0.621935i	$0.213653\pi$
$350$	−53.5622	−2.86302
$351$	15.6431	0.834966
$352$	−8.99736	−0.479561
$353$	−2.38165	−0.126763	−0.0633813	−	0.997989i	$-0.520188\pi$
$353$	−2.38165	−0.126763	−0.0633813	+	0.997989i	$0.520188\pi$
$354$	43.7385	2.32468
$355$	35.4540	1.88170
$356$	−2.64294	−0.140076
$357$	−27.5217	−1.45660
$358$	9.72774	0.514127
$359$	15.8310	0.835527	0.417763	−	0.908556i	$-0.362814\pi$
$359$	15.8310	0.835527	0.417763	+	0.908556i	$0.362814\pi$
$360$	−24.6013	−1.29660
$361$	−0.271326	−0.0142803
$362$	−16.9766	−0.892272
$363$	7.38194	0.387451
$364$	−49.2910	−2.58355
$365$	−19.5752	−1.02461
$366$	−8.21321	−0.429311
$367$	23.4348	1.22329	0.611644	−	0.791133i	$-0.290509\pi$
$367$	23.4348	1.22329	0.611644	+	0.791133i	$0.290509\pi$
$368$	−15.7116	−0.819021
$369$	0.994824	0.0517885
$370$	−24.8756	−1.29322
$371$	−4.16576	−0.216276
$372$	−12.3843	−0.642094
$373$	−11.1955	−0.579679	−0.289840	−	0.957075i	$-0.593602\pi$
$373$	−11.1955	−0.579679	−0.289840	+	0.957075i	$0.593602\pi$
$374$	53.4433	2.76349
$375$	−0.644767	−0.0332956
$376$	−31.1503	−1.60645
$377$	−0.377998	−0.0194679
$378$	57.7617	2.97094
$379$	4.03176	0.207098	0.103549	−	0.994624i	$-0.466980\pi$
$379$	4.03176	0.207098	0.103549	+	0.994624i	$0.466980\pi$
$380$	−58.0611	−2.97847
$381$	−6.51514	−0.333781
$382$	31.9854	1.63652
$383$	24.5794	1.25595	0.627975	−	0.778234i	$-0.283884\pi$
$383$	24.5794	1.25595	0.627975	+	0.778234i	$0.283884\pi$
$384$	21.7098	1.10787
$385$	−54.4893	−2.77703
$386$	−38.9462	−1.98231
$387$	−3.01817	−0.153422
$388$	−40.0759	−2.03454
$389$	−21.4147	−1.08577	−0.542884	−	0.839808i	$-0.682668\pi$
$389$	−21.4147	−1.08577	−0.542884	+	0.839808i	$0.682668\pi$
$390$	−28.2240	−1.42918
$391$	15.4995	0.783845
$392$	−56.9913	−2.87849
$393$	1.02804	0.0518579
$394$	−26.9242	−1.35642
$395$	−33.0687	−1.66387
$396$	−24.2184	−1.21702
$397$	−18.7397	−0.940520	−0.470260	−	0.882528i	$-0.655840\pi$
$397$	−18.7397	−0.940520	−0.470260	+	0.882528i	$0.655840\pi$
$398$	−16.8482	−0.844526
$399$	22.7886	1.14085
$400$	27.3378	1.36689
$401$	−8.68392	−0.433654	−0.216827	−	0.976210i	$-0.569571\pi$
$401$	−8.68392	−0.433654	−0.216827	+	0.976210i	$0.569571\pi$
$402$	−22.6443	−1.12939
$403$	6.54344	0.325952
$404$	74.3513	3.69912
$405$	9.01279	0.447849
$406$	−1.39575	−0.0692699
$407$	−12.8524	−0.637067
$408$	36.3662	1.80040
$409$	−5.13024	−0.253674	−0.126837	−	0.991924i	$-0.540483\pi$
$409$	−5.13024	−0.253674	−0.126837	+	0.991924i	$0.540483\pi$
$410$	−5.63526	−0.278305
$411$	14.1347	0.697213
$412$	51.8663	2.55527
$413$	−57.8465	−2.84644
$414$	−10.3613	−0.509228
$415$	15.2546	0.748821
$416$	6.16361	0.302196
$417$	9.41443	0.461026
$418$	−44.2522	−2.16445
$419$	−7.99070	−0.390371	−0.195186	−	0.980766i	$-0.562531\pi$
$419$	−7.99070	−0.390371	−0.195186	+	0.980766i	$0.562531\pi$
$420$	−70.6472	−3.44723
$421$	−33.6184	−1.63846	−0.819231	−	0.573464i	$-0.805599\pi$
$421$	−33.6184	−1.63846	−0.819231	+	0.573464i	$0.805599\pi$
$422$	33.2667	1.61940
$423$	−7.93481	−0.385804
$424$	5.50450	0.267322
$425$	−26.9689	−1.30818
$426$	35.0347	1.69744
$427$	10.8624	0.525669
$428$	61.7475	2.98468
$429$	−14.5823	−0.704042
$430$	17.0966	0.824473
$431$	23.5648	1.13508	0.567539	−	0.823347i	$-0.307896\pi$
$431$	23.5648	1.13508	0.567539	+	0.823347i	$0.307896\pi$
$432$	−29.4812	−1.41841
$433$	−8.70169	−0.418177	−0.209088	−	0.977897i	$-0.567050\pi$
$433$	−8.70169	−0.418177	−0.209088	+	0.977897i	$0.567050\pi$
$434$	24.1615	1.15979
$435$	−0.541772	−0.0259760
$436$	17.2364	0.825475
$437$	−12.8340	−0.613932
$438$	−19.3437	−0.924279
$439$	32.2037	1.53700	0.768500	−	0.639849i	$-0.221003\pi$
$439$	32.2037	1.53700	0.768500	+	0.639849i	$0.221003\pi$
$440$	72.0003	3.43248
$441$	−14.5172	−0.691295
$442$	−36.6111	−1.74141
$443$	−0.974585	−0.0463039	−0.0231520	−	0.999732i	$-0.507370\pi$
$443$	−0.974585	−0.0463039	−0.0231520	+	0.999732i	$0.507370\pi$
$444$	−16.6635	−0.790815
$445$	2.00148	0.0948791
$446$	−34.6574	−1.64108
$447$	−9.58761	−0.453479
$448$	−21.3814	−1.01018
$449$	−13.5707	−0.640443	−0.320221	−	0.947343i	$-0.603757\pi$
$449$	−13.5707	−0.640443	−0.320221	+	0.947343i	$0.603757\pi$
$450$	18.0284	0.849867
$451$	−2.91154	−0.137099
$452$	32.0068	1.50548
$453$	1.26406	0.0593909
$454$	65.0936	3.05500
$455$	37.3277	1.74995
$456$	−30.1121	−1.41013
$457$	−14.4128	−0.674203	−0.337101	−	0.941468i	$-0.609447\pi$
$457$	−14.4128	−0.674203	−0.337101	+	0.941468i	$0.609447\pi$
$458$	65.1823	3.04577
$459$	29.0834	1.35749
$460$	39.7868	1.85507
$461$	14.7973	0.689178	0.344589	−	0.938754i	$-0.388018\pi$
$461$	14.7973	0.689178	0.344589	+	0.938754i	$0.388018\pi$
$462$	−53.8449	−2.50509
$463$	−35.3938	−1.64489	−0.822445	−	0.568845i	$-0.807391\pi$
$463$	−35.3938	−1.64489	−0.822445	+	0.568845i	$0.807391\pi$
$464$	0.712381	0.0330715
$465$	9.37850	0.434917
$466$	20.1508	0.933467
$467$	−18.4797	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$467$	−18.4797	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$468$	16.5907	0.766908
$469$	29.9483	1.38288
$470$	44.9473	2.07327
$471$	−15.8471	−0.730197
$472$	76.4365	3.51827
$473$	8.83324	0.406153
$474$	−32.6776	−1.50093
$475$	22.3309	1.02461
$476$	−91.6410	−4.20036
$477$	1.40214	0.0641998
$478$	22.8711	1.04610
$479$	21.2658	0.971659	0.485830	−	0.874054i	$-0.338518\pi$
$479$	21.2658	0.971659	0.485830	+	0.874054i	$0.338518\pi$
$480$	8.83409	0.403219
$481$	8.80446	0.401449
$482$	14.3485	0.653554
$483$	−15.6160	−0.710554
$484$	24.5802	1.11728
$485$	30.3491	1.37808
$486$	−32.6913	−1.48291
$487$	0.153923	0.00697490	0.00348745	−	0.999994i	$-0.498890\pi$
$487$	0.153923	0.00697490	0.00348745	+	0.999994i	$0.498890\pi$
$488$	−14.3532	−0.649740
$489$	10.5371	0.476503
$490$	82.2338	3.71494
$491$	−2.95347	−0.133288	−0.0666440	−	0.997777i	$-0.521229\pi$
$491$	−2.95347	−0.133288	−0.0666440	+	0.997777i	$0.521229\pi$
$492$	−3.77491	−0.170186
$493$	−0.702768	−0.0316511
$494$	30.3148	1.36393
$495$	18.3404	0.824340
$496$	−12.3319	−0.553717
$497$	−46.3353	−2.07842
$498$	15.0743	0.675494
$499$	−17.8334	−0.798335	−0.399167	−	0.916878i	$-0.630701\pi$
$499$	−17.8334	−0.798335	−0.399167	+	0.916878i	$0.630701\pi$
$500$	−2.14693	−0.0960137
$501$	2.77786	0.124106
$502$	−32.9526	−1.47075
$503$	−3.88433	−0.173194	−0.0865970	−	0.996243i	$-0.527599\pi$
$503$	−3.88433	−0.173194	−0.0865970	+	0.996243i	$0.527599\pi$
$504$	32.1518	1.43215
$505$	−56.3056	−2.50557
$506$	30.3242	1.34807
$507$	−6.44324	−0.286154
$508$	−21.6940	−0.962514
$509$	29.1538	1.29222	0.646109	−	0.763245i	$-0.276395\pi$
$509$	29.1538	1.29222	0.646109	+	0.763245i	$0.276395\pi$
$510$	−52.4735	−2.32357
$511$	25.5831	1.13173
$512$	46.7097	2.06429
$513$	−24.0817	−1.06323
$514$	−31.1873	−1.37561
$515$	−39.2780	−1.73079
$516$	11.4526	0.504172
$517$	23.2227	1.02133
$518$	32.5103	1.42842
$519$	21.1922	0.930235
$520$	−49.3236	−2.16298
$521$	−25.3515	−1.11067	−0.555335	−	0.831627i	$-0.687410\pi$
$521$	−25.3515	−1.11067	−0.555335	+	0.831627i	$0.687410\pi$
$522$	0.469792	0.0205623
$523$	−36.8932	−1.61323	−0.806613	−	0.591080i	$-0.798702\pi$
$523$	−36.8932	−1.61323	−0.806613	+	0.591080i	$0.798702\pi$
$524$	3.42315	0.149541
$525$	27.1716	1.18587
$526$	−7.51069	−0.327482
$527$	12.1655	0.529936
$528$	27.4821	1.19600
$529$	−14.2054	−0.617628
$530$	−7.94255	−0.345002
$531$	19.4704	0.844944
$532$	75.8808	3.28985
$533$	1.99454	0.0863932
$534$	1.97781	0.0855882
$535$	−46.7609	−2.02165
$536$	−39.5727	−1.70928
$537$	−4.93478	−0.212952
$538$	21.0460	0.907357
$539$	42.4873	1.83006
$540$	74.6560	3.21268
$541$	−31.7376	−1.36451	−0.682254	−	0.731116i	$-0.739000\pi$
$541$	−31.7376	−1.36451	−0.682254	+	0.731116i	$0.739000\pi$
$542$	−30.0510	−1.29080
$543$	8.61208	0.369580
$544$	11.4593	0.491313
$545$	−13.0530	−0.559129
$546$	36.8863	1.57859
$547$	9.95062	0.425458	0.212729	−	0.977111i	$-0.431765\pi$
$547$	9.95062	0.425458	0.212729	+	0.977111i	$0.431765\pi$
$548$	47.0654	2.01053
$549$	−3.65615	−0.156041
$550$	−52.7635	−2.24984
$551$	0.581908	0.0247901
$552$	20.6345	0.878263
$553$	43.2179	1.83781
$554$	−52.7525	−2.24124
$555$	12.6191	0.535653
$556$	31.3480	1.32945
$557$	−4.37679	−0.185451	−0.0927254	−	0.995692i	$-0.529558\pi$
$557$	−4.37679	−0.185451	−0.0927254	+	0.995692i	$0.529558\pi$
$558$	−8.13247	−0.344275
$559$	−6.05118	−0.255938
$560$	−70.3483	−2.97276
$561$	−27.1112	−1.14464
$562$	−46.4884	−1.96099
$563$	29.1109	1.22688	0.613438	−	0.789743i	$-0.289786\pi$
$563$	29.1109	1.22688	0.613438	+	0.789743i	$0.289786\pi$
$564$	30.1090	1.26782
$565$	−24.2385	−1.01972
$566$	−40.3665	−1.69673
$567$	−11.7789	−0.494669
$568$	61.2259	2.56898
$569$	39.6007	1.66015	0.830074	−	0.557653i	$-0.188298\pi$
$569$	39.6007	1.66015	0.830074	+	0.557653i	$0.188298\pi$
$570$	43.4492	1.81989
$571$	32.1103	1.34378	0.671888	−	0.740653i	$-0.265484\pi$
$571$	32.1103	1.34378	0.671888	+	0.740653i	$0.265484\pi$
$572$	−48.5559	−2.03023
$573$	−16.2259	−0.677846
$574$	7.36480	0.307401
$575$	−15.3024	−0.638153
$576$	7.19672	0.299863
$577$	2.56038	0.106590	0.0532949	−	0.998579i	$-0.483028\pi$
$577$	2.56038	0.106590	0.0532949	+	0.998579i	$0.483028\pi$
$578$	−25.7063	−1.06924
$579$	19.7570	0.821074
$580$	−1.80398	−0.0749063
$581$	−19.9365	−0.827106
$582$	29.9903	1.24314
$583$	−4.10364	−0.169955
$584$	−33.8047	−1.39885
$585$	−12.5640	−0.519459
$586$	−26.3876	−1.09006
$587$	19.0670	0.786979	0.393489	−	0.919329i	$-0.371268\pi$
$587$	19.0670	0.786979	0.393489	+	0.919329i	$0.371268\pi$
$588$	55.0862	2.27172
$589$	−10.0733	−0.415062
$590$	−110.292	−4.54063
$591$	13.6584	0.561830
$592$	−16.5930	−0.681969
$593$	40.4771	1.66219	0.831097	−	0.556127i	$-0.187713\pi$
$593$	40.4771	1.66219	0.831097	+	0.556127i	$0.187713\pi$
$594$	56.9003	2.33465
$595$	69.3990	2.84508
$596$	−31.9246	−1.30768
$597$	8.54694	0.349803
$598$	−20.7735	−0.849490
$599$	28.5911	1.16820	0.584101	−	0.811681i	$-0.301447\pi$
$599$	28.5911	1.16820	0.584101	+	0.811681i	$0.301447\pi$
$600$	−35.9036	−1.46576
$601$	44.4009	1.81115	0.905574	−	0.424188i	$-0.139440\pi$
$601$	44.4009	1.81115	0.905574	+	0.424188i	$0.139440\pi$
$602$	−22.3438	−0.910667
$603$	−10.0802	−0.410498
$604$	4.20905	0.171264
$605$	−18.6144	−0.756783
$606$	−55.6398	−2.26021
$607$	24.0745	0.977156	0.488578	−	0.872520i	$-0.337516\pi$
$607$	24.0745	0.977156	0.488578	+	0.872520i	$0.337516\pi$
$608$	−9.48854	−0.384811
$609$	0.708050	0.0286916
$610$	20.7105	0.838545
$611$	−15.9086	−0.643595
$612$	30.8452	1.24685
$613$	−48.4394	−1.95645	−0.978225	−	0.207548i	$-0.933452\pi$
$613$	−48.4394	−1.95645	−0.978225	+	0.207548i	$0.933452\pi$
$614$	−15.4229	−0.622419
$615$	2.85871	0.115274
$616$	−94.0983	−3.79133
$617$	42.9999	1.73111	0.865555	−	0.500814i	$-0.166966\pi$
$617$	42.9999	1.73111	0.865555	+	0.500814i	$0.166966\pi$
$618$	−38.8135	−1.56131
$619$	−23.9449	−0.962425	−0.481213	−	0.876604i	$-0.659803\pi$
$619$	−23.9449	−0.962425	−0.481213	+	0.876604i	$0.659803\pi$
$620$	31.2283	1.25416
$621$	16.5021	0.662208
$622$	27.3066	1.09489
$623$	−2.61576	−0.104798
$624$	−18.8265	−0.753664
$625$	−24.1743	−0.966971
$626$	−27.4893	−1.09869
$627$	22.4487	0.896515
$628$	−52.7674	−2.10565
$629$	16.3691	0.652679
$630$	−46.3924	−1.84832
$631$	12.4916	0.497281	0.248641	−	0.968596i	$-0.420016\pi$
$631$	12.4916	0.497281	0.248641	+	0.968596i	$0.420016\pi$
$632$	−57.1067	−2.27158
$633$	−16.8758	−0.670754
$634$	−41.3879	−1.64372
$635$	16.4287	0.651951
$636$	−5.32050	−0.210972
$637$	−29.1058	−1.15321
$638$	−1.37494	−0.0544342
$639$	15.5959	0.616964
$640$	−54.7437	−2.16393
$641$	−45.9442	−1.81469	−0.907344	−	0.420389i	$-0.861894\pi$
$641$	−45.9442	−1.81469	−0.907344	+	0.420389i	$0.861894\pi$
$642$	−46.2080	−1.82368
$643$	2.45027	0.0966291	0.0483146	−	0.998832i	$-0.484615\pi$
$643$	2.45027	0.0966291	0.0483146	+	0.998832i	$0.484615\pi$
$644$	−51.9979	−2.04900
$645$	−8.67295	−0.341497
$646$	56.3609	2.21749
$647$	−33.9834	−1.33603	−0.668013	−	0.744150i	$-0.732855\pi$
$647$	−33.9834	−1.33603	−0.668013	+	0.744150i	$0.732855\pi$
$648$	15.5643	0.611424
$649$	−56.9838	−2.23681
$650$	36.1454	1.41774
$651$	−12.2569	−0.480385
$652$	35.0861	1.37408
$653$	−23.0437	−0.901770	−0.450885	−	0.892582i	$-0.648892\pi$
$653$	−23.0437	−0.901770	−0.450885	+	0.892582i	$0.648892\pi$
$654$	−12.8987	−0.504377
$655$	−2.59233	−0.101291
$656$	−3.75894	−0.146762
$657$	−8.61096	−0.335945
$658$	−58.7423	−2.29001
$659$	−6.76293	−0.263446	−0.131723	−	0.991287i	$-0.542051\pi$
$659$	−6.76293	−0.263446	−0.131723	+	0.991287i	$0.542051\pi$
$660$	−69.5936	−2.70893
$661$	14.8145	0.576216	0.288108	−	0.957598i	$-0.406974\pi$
$661$	14.8145	0.576216	0.288108	+	0.957598i	$0.406974\pi$
$662$	21.2055	0.824174
$663$	18.5725	0.721295
$664$	26.3435	1.02232
$665$	−57.4639	−2.22836
$666$	−10.9426	−0.424015
$667$	−0.398757	−0.0154399
$668$	9.24965	0.357880
$669$	17.5814	0.679734
$670$	57.1002	2.20597
$671$	10.7004	0.413085
$672$	−11.5454	−0.445374
$673$	30.1769	1.16323	0.581617	−	0.813463i	$-0.302420\pi$
$673$	30.1769	1.16323	0.581617	+	0.813463i	$0.302420\pi$
$674$	−51.1928	−1.97187
$675$	−28.7134	−1.10518
$676$	−21.4546	−0.825175
$677$	0.900879	0.0346236	0.0173118	−	0.999850i	$-0.494489\pi$
$677$	0.900879	0.0346236	0.0173118	+	0.999850i	$0.494489\pi$
$678$	−23.9519	−0.919867
$679$	−39.6637	−1.52215
$680$	−91.7016	−3.51660
$681$	−33.0213	−1.26538
$682$	23.8012	0.911395
$683$	−16.6953	−0.638827	−0.319413	−	0.947615i	$-0.603486\pi$
$683$	−16.6953	−0.638827	−0.319413	+	0.947615i	$0.603486\pi$
$684$	−25.5406	−0.976567
$685$	−35.6422	−1.36182
$686$	−34.8109	−1.32909
$687$	−33.0663	−1.26156
$688$	11.4041	0.434779
$689$	2.81118	0.107098
$690$	−29.7739	−1.13347
$691$	37.7331	1.43543	0.717717	−	0.696335i	$-0.245187\pi$
$691$	37.7331	1.43543	0.717717	+	0.696335i	$0.245187\pi$
$692$	70.5653	2.68249
$693$	−23.9693	−0.910520
$694$	18.5311	0.703430
$695$	−23.7396	−0.900492
$696$	−0.935594	−0.0354636
$697$	3.70822	0.140459
$698$	−72.9047	−2.75948
$699$	−10.2223	−0.386642
$700$	90.4754	3.41965
$701$	−22.9477	−0.866721	−0.433361	−	0.901221i	$-0.642672\pi$
$701$	−22.9477	−0.866721	−0.433361	+	0.901221i	$0.642672\pi$
$702$	−38.9794	−1.47118
$703$	−13.5540	−0.511198
$704$	−21.0626	−0.793825
$705$	−22.8013	−0.858748
$706$	5.93459	0.223351
$707$	73.5866	2.76751
$708$	−73.8815	−2.77664
$709$	31.7281	1.19157	0.595787	−	0.803143i	$-0.296840\pi$
$709$	31.7281	1.19157	0.595787	+	0.803143i	$0.296840\pi$
$710$	−88.3441	−3.31549
$711$	−14.5466	−0.545541
$712$	3.45638	0.129533
$713$	6.90278	0.258511
$714$	68.5784	2.56648
$715$	36.7710	1.37516
$716$	−16.4317	−0.614083
$717$	−11.6023	−0.433295
$718$	−39.4476	−1.47217
$719$	38.6189	1.44024	0.720121	−	0.693849i	$-0.244086\pi$
$719$	38.6189	1.44024	0.720121	+	0.693849i	$0.244086\pi$
$720$	23.6784	0.882441
$721$	51.3329	1.91174
$722$	0.676089	0.0251614
$723$	−7.27883	−0.270703
$724$	28.6763	1.06575
$725$	0.693829	0.0257682
$726$	−18.3943	−0.682676
$727$	−39.7665	−1.47486	−0.737429	−	0.675425i	$-0.763960\pi$
$727$	−39.7665	−1.47486	−0.737429	+	0.675425i	$0.763960\pi$
$728$	64.4617	2.38911
$729$	25.0666	0.928393
$730$	48.7774	1.80533
$731$	−11.2503	−0.416106
$732$	13.8734	0.512777
$733$	31.9318	1.17943	0.589714	−	0.807612i	$-0.299240\pi$
$733$	31.9318	1.17943	0.589714	+	0.807612i	$0.299240\pi$
$734$	−58.3948	−2.15539
$735$	−41.7164	−1.53873
$736$	6.50209	0.239670
$737$	29.5017	1.08671
$738$	−2.47890	−0.0912496
$739$	35.8263	1.31789	0.658945	−	0.752191i	$-0.271003\pi$
$739$	35.8263	1.31789	0.658945	+	0.752191i	$0.271003\pi$
$740$	42.0189	1.54465
$741$	−15.3784	−0.564940
$742$	10.3802	0.381070
$743$	39.3413	1.44329	0.721647	−	0.692261i	$-0.243385\pi$
$743$	39.3413	1.44329	0.721647	+	0.692261i	$0.243385\pi$
$744$	16.1959	0.593769
$745$	24.1763	0.885750
$746$	27.8968	1.02138
$747$	6.71038	0.245520
$748$	−90.2744	−3.30076
$749$	61.1125	2.23300
$750$	1.60663	0.0586658
$751$	35.8871	1.30954	0.654769	−	0.755829i	$-0.272766\pi$
$751$	35.8871	1.30954	0.654769	+	0.755829i	$0.272766\pi$
$752$	29.9817	1.09332
$753$	16.7165	0.609183
$754$	0.941895	0.0343018
$755$	−3.18748	−0.116004
$756$	−97.5689	−3.54855
$757$	36.0322	1.30961	0.654807	−	0.755796i	$-0.272750\pi$
$757$	36.0322	1.30961	0.654807	+	0.755796i	$0.272750\pi$
$758$	−10.0463	−0.364899
$759$	−15.3831	−0.558373
$760$	75.9310	2.75431
$761$	−26.9295	−0.976194	−0.488097	−	0.872790i	$-0.662309\pi$
$761$	−26.9295	−0.976194	−0.488097	+	0.872790i	$0.662309\pi$
$762$	16.2344	0.588110
$763$	17.0592	0.617583
$764$	−54.0286	−1.95468
$765$	−23.3589	−0.844541
$766$	−61.2469	−2.21294
$767$	39.0366	1.40953
$768$	−41.1203	−1.48380
$769$	−8.52525	−0.307428	−0.153714	−	0.988115i	$-0.549123\pi$
$769$	−8.52525	−0.307428	−0.153714	+	0.988115i	$0.549123\pi$
$770$	135.776	4.89303
$771$	15.8210	0.569779
$772$	65.7865	2.36771
$773$	19.6527	0.706860	0.353430	−	0.935461i	$-0.385015\pi$
$773$	19.6527	0.706860	0.353430	+	0.935461i	$0.385015\pi$
$774$	7.52066	0.270325
$775$	−12.0107	−0.431438
$776$	52.4103	1.88142
$777$	−16.4921	−0.591652
$778$	53.3611	1.91309
$779$	−3.07049	−0.110012
$780$	47.6749	1.70703
$781$	−45.6443	−1.63328
$782$	−38.6217	−1.38111
$783$	−0.748228	−0.0267395
$784$	54.8532	1.95904
$785$	39.9604	1.42625
$786$	−2.56167	−0.0913719
$787$	31.7575	1.13203	0.566016	−	0.824394i	$-0.308484\pi$
$787$	31.7575	1.13203	0.566016	+	0.824394i	$0.308484\pi$
$788$	45.4793	1.62013
$789$	3.81010	0.135643
$790$	82.4004	2.93167
$791$	31.6777	1.12633
$792$	31.6723	1.12543
$793$	−7.33028	−0.260306
$794$	46.6956	1.65717
$795$	4.02918	0.142900
$796$	28.4594	1.00872
$797$	30.1618	1.06838	0.534192	−	0.845363i	$-0.320616\pi$
$797$	30.1618	1.06838	0.534192	+	0.845363i	$0.320616\pi$
$798$	−56.7844	−2.01015
$799$	−29.5771	−1.04636
$800$	−11.3135	−0.399993
$801$	0.880432	0.0311085
$802$	21.6386	0.764085
$803$	25.2016	0.889344
$804$	38.2499	1.34897
$805$	39.3776	1.38788
$806$	−16.3049	−0.574317
$807$	−10.6764	−0.375828
$808$	−97.2350	−3.42071
$809$	−29.1829	−1.02602	−0.513008	−	0.858384i	$-0.671469\pi$
$809$	−29.1829	−1.02602	−0.513008	+	0.858384i	$0.671469\pi$
$810$	−22.4580	−0.789095
$811$	28.3849	0.996727	0.498364	−	0.866968i	$-0.333934\pi$
$811$	28.3849	0.996727	0.498364	+	0.866968i	$0.333934\pi$
$812$	2.35765	0.0827373
$813$	15.2446	0.534650
$814$	32.0254	1.12249
$815$	−26.5704	−0.930722
$816$	−35.0019	−1.22531
$817$	9.31546	0.325907
$818$	12.7835	0.446965
$819$	16.4201	0.573766
$820$	9.51886	0.332413
$821$	−48.3636	−1.68790	−0.843951	−	0.536420i	$-0.819776\pi$
$821$	−48.3636	−1.68790	−0.843951	+	0.536420i	$0.819776\pi$
$822$	−35.2208	−1.22847
$823$	16.2186	0.565346	0.282673	−	0.959216i	$-0.408779\pi$
$823$	16.2186	0.565346	0.282673	+	0.959216i	$0.408779\pi$
$824$	−67.8296	−2.36296
$825$	26.7664	0.931886
$826$	144.142	5.01533
$827$	−38.9798	−1.35546	−0.677731	−	0.735310i	$-0.737036\pi$
$827$	−38.9798	−1.35546	−0.677731	+	0.735310i	$0.737036\pi$
$828$	17.5018	0.608231
$829$	28.4786	0.989104	0.494552	−	0.869148i	$-0.335332\pi$
$829$	28.4786	0.989104	0.494552	+	0.869148i	$0.335332\pi$
$830$	−38.0115	−1.31940
$831$	26.7608	0.928322
$832$	14.4288	0.500230
$833$	−54.1130	−1.87491
$834$	−23.4588	−0.812313
$835$	−7.00469	−0.242407
$836$	74.7492	2.58526
$837$	12.9524	0.447700
$838$	19.9112	0.687821
$839$	1.61826	0.0558687	0.0279344	−	0.999610i	$-0.491107\pi$
$839$	1.61826	0.0558687	0.0279344	+	0.999610i	$0.491107\pi$
$840$	92.3908	3.18778
$841$	−28.9819	−0.999377
$842$	83.7703	2.88691
$843$	23.5831	0.812245
$844$	−56.1928	−1.93424
$845$	16.2474	0.558926
$846$	19.7719	0.679773
$847$	24.3274	0.835900
$848$	−5.29800	−0.181934
$849$	20.4775	0.702786
$850$	67.2010	2.30498
$851$	9.28797	0.318387
$852$	−59.1794	−2.02745
$853$	39.3926	1.34878	0.674389	−	0.738376i	$-0.264407\pi$
$853$	39.3926	1.34878	0.674389	+	0.738376i	$0.264407\pi$
$854$	−27.0669	−0.926210
$855$	19.3417	0.661471
$856$	−80.7520	−2.76005
$857$	−11.3883	−0.389018	−0.194509	−	0.980901i	$-0.562311\pi$
$857$	−11.3883	−0.389018	−0.194509	+	0.980901i	$0.562311\pi$
$858$	36.3362	1.24050
$859$	−18.5054	−0.631396	−0.315698	−	0.948860i	$-0.602239\pi$
$859$	−18.5054	−0.631396	−0.315698	+	0.948860i	$0.602239\pi$
$860$	−28.8790	−0.984766
$861$	−3.73609	−0.127325
$862$	−58.7187	−1.99997
$863$	−15.4435	−0.525703	−0.262851	−	0.964836i	$-0.584663\pi$
$863$	−15.4435	−0.525703	−0.262851	+	0.964836i	$0.584663\pi$
$864$	12.2005	0.415071
$865$	−53.4386	−1.81697
$866$	21.6829	0.736813
$867$	13.0405	0.442880
$868$	−40.8127	−1.38527
$869$	42.5734	1.44420
$870$	1.34999	0.0457688
$871$	−20.2100	−0.684790
$872$	−22.5414	−0.763349
$873$	13.3503	0.451840
$874$	31.9796	1.08173
$875$	−2.12485	−0.0718331
$876$	32.6747	1.10398
$877$	28.0432	0.946952	0.473476	−	0.880807i	$-0.342999\pi$
$877$	28.0432	0.946952	0.473476	+	0.880807i	$0.342999\pi$
$878$	−80.2452	−2.70814
$879$	13.3862	0.451504
$880$	−69.2992	−2.33608
$881$	22.2709	0.750326	0.375163	−	0.926959i	$-0.377587\pi$
$881$	22.2709	0.750326	0.375163	+	0.926959i	$0.377587\pi$
$882$	36.1739	1.21804
$883$	12.6402	0.425377	0.212689	−	0.977120i	$-0.431778\pi$
$883$	12.6402	0.425377	0.212689	+	0.977120i	$0.431778\pi$
$884$	61.8422	2.07998
$885$	55.9498	1.88073
$886$	2.42847	0.0815859
$887$	3.62958	0.121869	0.0609347	−	0.998142i	$-0.480592\pi$
$887$	3.62958	0.121869	0.0609347	+	0.998142i	$0.480592\pi$
$888$	21.7922	0.731297
$889$	−21.4708	−0.720109
$890$	−4.98727	−0.167174
$891$	−11.6033	−0.388724
$892$	58.5420	1.96013
$893$	24.4905	0.819543
$894$	23.8904	0.799014
$895$	12.4436	0.415944
$896$	71.5453	2.39016
$897$	10.5382	0.351859
$898$	33.8155	1.12844
$899$	−0.312981	−0.0104385
$900$	−30.4529	−1.01510
$901$	5.22651	0.174120
$902$	7.25497	0.241564
$903$	11.3348	0.377199
$904$	−41.8578	−1.39217
$905$	−21.7163	−0.721875
$906$	−3.14979	−0.104645
$907$	−19.2521	−0.639255	−0.319628	−	0.947543i	$-0.603558\pi$
$907$	−19.2521	−0.639255	−0.319628	+	0.947543i	$0.603558\pi$
$908$	−109.954	−3.64894
$909$	−24.7684	−0.821515
$910$	−93.0130	−3.08335
$911$	−1.19834	−0.0397029	−0.0198515	−	0.999803i	$-0.506319\pi$
$911$	−1.19834	−0.0397029	−0.0198515	+	0.999803i	$0.506319\pi$
$912$	28.9824	0.959703
$913$	−19.6392	−0.649963
$914$	35.9138	1.18792
$915$	−10.5062	−0.347326
$916$	−110.103	−3.63792
$917$	3.38795	0.111880
$918$	−72.4698	−2.39186
$919$	5.45436	0.179923	0.0899614	−	0.995945i	$-0.471326\pi$
$919$	5.45436	0.179923	0.0899614	+	0.995945i	$0.471326\pi$
$920$	−52.0322	−1.71545
$921$	7.82389	0.257806
$922$	−36.8718	−1.21431
$923$	31.2685	1.02921
$924$	90.9529	2.99213
$925$	−16.1609	−0.531367
$926$	88.1942	2.89824
$927$	−17.2780	−0.567485
$928$	−0.294813	−0.00967771
$929$	−21.3826	−0.701542	−0.350771	−	0.936461i	$-0.614080\pi$
$929$	−21.3826	−0.701542	−0.350771	+	0.936461i	$0.614080\pi$
$930$	−23.3693	−0.766310
$931$	44.8068	1.46848
$932$	−34.0379	−1.11495
$933$	−13.8524	−0.453506
$934$	46.0476	1.50672
$935$	68.3641	2.23574
$936$	−21.6970	−0.709189
$937$	−1.25136	−0.0408803	−0.0204401	−	0.999791i	$-0.506507\pi$
$937$	−1.25136	−0.0408803	−0.0204401	+	0.999791i	$0.506507\pi$
$938$	−74.6250	−2.43659
$939$	13.9451	0.455080
$940$	−75.9234	−2.47635
$941$	−38.3328	−1.24961	−0.624806	−	0.780780i	$-0.714822\pi$
$941$	−38.3328	−1.24961	−0.624806	+	0.780780i	$0.714822\pi$
$942$	39.4878	1.28658
$943$	2.10407	0.0685181
$944$	−73.5689	−2.39447
$945$	73.8882	2.40358
$946$	−22.0106	−0.715627
$947$	34.7326	1.12866	0.564329	−	0.825550i	$-0.309135\pi$
$947$	34.7326	1.12866	0.564329	+	0.825550i	$0.309135\pi$
$948$	55.1979	1.79274
$949$	−17.2643	−0.560422
$950$	−55.6439	−1.80533
$951$	20.9957	0.680831
$952$	119.846	3.88424
$953$	−20.0005	−0.647878	−0.323939	−	0.946078i	$-0.605007\pi$
$953$	−20.0005	−0.647878	−0.323939	+	0.946078i	$0.605007\pi$
$954$	−3.49386	−0.113118
$955$	40.9154	1.32399
$956$	−38.6330	−1.24948
$957$	0.697491	0.0225467
$958$	−52.9900	−1.71203
$959$	46.5813	1.50419
$960$	20.6804	0.667456
$961$	−25.5821	−0.825228
$962$	−21.9389	−0.707339
$963$	−20.5697	−0.662849
$964$	−24.2369	−0.780617
$965$	−49.8196	−1.60375
$966$	38.9119	1.25197
$967$	−1.84170	−0.0592252	−0.0296126	−	0.999561i	$-0.509427\pi$
$967$	−1.84170	−0.0592252	−0.0296126	+	0.999561i	$0.509427\pi$
$968$	−32.1455	−1.03319
$969$	−28.5913	−0.918485
$970$	−75.6238	−2.42813
$971$	40.6756	1.30534	0.652671	−	0.757642i	$-0.273649\pi$
$971$	40.6756	1.30534	0.652671	+	0.757642i	$0.273649\pi$
$972$	55.2208	1.77121
$973$	31.0256	0.994634
$974$	−0.383544	−0.0122895
$975$	−18.3362	−0.587229
$976$	13.8148	0.442200
$977$	47.3886	1.51610	0.758048	−	0.652199i	$-0.226153\pi$
$977$	47.3886	1.51610	0.758048	+	0.652199i	$0.226153\pi$
$978$	−26.2562	−0.839582
$979$	−2.57675	−0.0823533
$980$	−138.906	−4.43720
$981$	−5.74190	−0.183325
$982$	7.35943	0.234849
$983$	57.8968	1.84662	0.923310	−	0.384055i	$-0.125473\pi$
$983$	57.8968	1.84662	0.923310	+	0.384055i	$0.125473\pi$
$984$	4.93674	0.157378
$985$	−34.4411	−1.09738
$986$	1.75116	0.0557682
$987$	29.7994	0.948525
$988$	−51.2067	−1.62910
$989$	−6.38349	−0.202983
$990$	−45.7006	−1.45246
$991$	20.6340	0.655462	0.327731	−	0.944771i	$-0.393716\pi$
$991$	20.6340	0.655462	0.327731	+	0.944771i	$0.393716\pi$
$992$	5.10344	0.162034
$993$	−10.7573	−0.341373
$994$	115.458	3.66211
$995$	−21.5521	−0.683247
$996$	−25.4629	−0.806822
$997$	61.6139	1.95133	0.975666	−	0.219260i	$-0.0703644\pi$
$997$	61.6139	1.95133	0.975666	+	0.219260i	$0.0703644\pi$
$998$	44.4373	1.40664
$999$	17.4280	0.551396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.14	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.14	✓	172	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49180 q^{2} +1.26406 q^{3} +4.20905 q^{4} -3.18748 q^{5} -3.14979 q^{6} +4.16576 q^{7} -5.50450 q^{8} -1.40214 q^{9} +O(q^{10})\)	\(q-2.49180 q^{2} +1.26406 q^{3} +4.20905 q^{4} -3.18748 q^{5} -3.14979 q^{6} +4.16576 q^{7} -5.50450 q^{8} -1.40214 q^{9} +7.94255 q^{10} +4.10364 q^{11} +5.32050 q^{12} -2.81118 q^{13} -10.3802 q^{14} -4.02918 q^{15} +5.29800 q^{16} -5.22651 q^{17} +3.49386 q^{18} +4.32766 q^{19} -13.4163 q^{20} +5.26579 q^{21} -10.2254 q^{22} -2.96556 q^{23} -6.95804 q^{24} +5.16002 q^{25} +7.00490 q^{26} -5.56459 q^{27} +17.5339 q^{28} +0.134462 q^{29} +10.0399 q^{30} -2.32765 q^{31} -2.19253 q^{32} +5.18726 q^{33} +13.0234 q^{34} -13.2783 q^{35} -5.90169 q^{36} -3.13194 q^{37} -10.7837 q^{38} -3.55351 q^{39} +17.5455 q^{40} -0.709502 q^{41} -13.1213 q^{42} +2.15254 q^{43} +17.2724 q^{44} +4.46931 q^{45} +7.38958 q^{46} +5.65906 q^{47} +6.69701 q^{48} +10.3536 q^{49} -12.8577 q^{50} -6.60663 q^{51} -11.8324 q^{52} -1.00000 q^{53} +13.8658 q^{54} -13.0803 q^{55} -22.9304 q^{56} +5.47044 q^{57} -0.335053 q^{58} -13.8862 q^{59} -16.9590 q^{60} +2.60754 q^{61} +5.80002 q^{62} -5.84100 q^{63} -5.13266 q^{64} +8.96059 q^{65} -12.9256 q^{66} +7.18915 q^{67} -21.9986 q^{68} -3.74866 q^{69} +33.0868 q^{70} -11.1229 q^{71} +7.71811 q^{72} +6.14128 q^{73} +7.80416 q^{74} +6.52260 q^{75} +18.2154 q^{76} +17.0948 q^{77} +8.85463 q^{78} +10.3746 q^{79} -16.8873 q^{80} -2.82756 q^{81} +1.76793 q^{82} -4.78580 q^{83} +22.1640 q^{84} +16.6594 q^{85} -5.36369 q^{86} +0.169969 q^{87} -22.5885 q^{88} -0.627918 q^{89} -11.1366 q^{90} -11.7107 q^{91} -12.4822 q^{92} -2.94229 q^{93} -14.1012 q^{94} -13.7943 q^{95} -2.77150 q^{96} -9.52135 q^{97} -25.7990 q^{98} -5.75389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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