LMFDB - Embedded newform 8023.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79904 q^{2} -0.951830 q^{3} +5.83462 q^{4} +2.72456 q^{5} +2.66421 q^{6} +1.55879 q^{7} -10.7333 q^{8} -2.09402 q^{9} +O(q^{10})$	\(q-2.79904 q^{2} -0.951830 q^{3} +5.83462 q^{4} +2.72456 q^{5} +2.66421 q^{6} +1.55879 q^{7} -10.7333 q^{8} -2.09402 q^{9} -7.62616 q^{10} +4.52022 q^{11} -5.55357 q^{12} -4.81472 q^{13} -4.36313 q^{14} -2.59332 q^{15} +18.3736 q^{16} +4.93209 q^{17} +5.86124 q^{18} -6.45811 q^{19} +15.8968 q^{20} -1.48371 q^{21} -12.6523 q^{22} -0.588724 q^{23} +10.2162 q^{24} +2.42324 q^{25} +13.4766 q^{26} +4.84864 q^{27} +9.09497 q^{28} -7.40239 q^{29} +7.25881 q^{30} +4.71218 q^{31} -29.9618 q^{32} -4.30249 q^{33} -13.8051 q^{34} +4.24703 q^{35} -12.2178 q^{36} -9.59806 q^{37} +18.0765 q^{38} +4.58280 q^{39} -29.2434 q^{40} +3.80683 q^{41} +4.15296 q^{42} -3.38931 q^{43} +26.3738 q^{44} -5.70528 q^{45} +1.64786 q^{46} -2.11515 q^{47} -17.4885 q^{48} -4.57016 q^{49} -6.78273 q^{50} -4.69451 q^{51} -28.0921 q^{52} +7.56236 q^{53} -13.5715 q^{54} +12.3156 q^{55} -16.7309 q^{56} +6.14702 q^{57} +20.7196 q^{58} -0.485115 q^{59} -15.1310 q^{60} +11.8614 q^{61} -13.1896 q^{62} -3.26414 q^{63} +47.1172 q^{64} -13.1180 q^{65} +12.0428 q^{66} -1.53815 q^{67} +28.7769 q^{68} +0.560365 q^{69} -11.8876 q^{70} -1.00000 q^{71} +22.4756 q^{72} +9.26795 q^{73} +26.8653 q^{74} -2.30651 q^{75} -37.6806 q^{76} +7.04610 q^{77} -12.8274 q^{78} +1.69346 q^{79} +50.0599 q^{80} +1.66697 q^{81} -10.6555 q^{82} -14.2688 q^{83} -8.65687 q^{84} +13.4378 q^{85} +9.48681 q^{86} +7.04582 q^{87} -48.5167 q^{88} -4.19505 q^{89} +15.9693 q^{90} -7.50516 q^{91} -3.43498 q^{92} -4.48519 q^{93} +5.92038 q^{94} -17.5955 q^{95} +28.5186 q^{96} +16.9329 q^{97} +12.7921 q^{98} -9.46544 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.79904	−1.97922	−0.989610	−	0.143779i	$-0.954075\pi$
$2$	−2.79904	−1.97922	−0.989610	+	0.143779i	$0.954075\pi$
$3$	−0.951830	−0.549540	−0.274770	−	0.961510i	$-0.588602\pi$
$3$	−0.951830	−0.549540	−0.274770	+	0.961510i	$0.588602\pi$
$4$	5.83462	2.91731
$5$	2.72456	1.21846	0.609231	−	0.792993i	$-0.291478\pi$
$5$	2.72456	1.21846	0.609231	+	0.792993i	$0.291478\pi$
$6$	2.66421	1.08766
$7$	1.55879	0.589169	0.294584	−	0.955625i	$-0.404819\pi$
$7$	1.55879	0.589169	0.294584	+	0.955625i	$0.404819\pi$
$8$	−10.7333	−3.79478
$9$	−2.09402	−0.698006
$10$	−7.62616	−2.41160
$11$	4.52022	1.36290	0.681450	−	0.731865i	$-0.261350\pi$
$11$	4.52022	1.36290	0.681450	+	0.731865i	$0.261350\pi$
$12$	−5.55357	−1.60318
$13$	−4.81472	−1.33536	−0.667682	−	0.744447i	$-0.732713\pi$
$13$	−4.81472	−1.33536	−0.667682	+	0.744447i	$0.732713\pi$
$14$	−4.36313	−1.16609
$15$	−2.59332	−0.669593
$16$	18.3736	4.59339
$17$	4.93209	1.19621	0.598104	−	0.801419i	$-0.295921\pi$
$17$	4.93209	1.19621	0.598104	+	0.801419i	$0.295921\pi$
$18$	5.86124	1.38151
$19$	−6.45811	−1.48159	−0.740796	−	0.671730i	$-0.765551\pi$
$19$	−6.45811	−1.48159	−0.740796	+	0.671730i	$0.765551\pi$
$20$	15.8968	3.55463
$21$	−1.48371	−0.323772
$22$	−12.6523	−2.69748
$23$	−0.588724	−0.122757	−0.0613787	−	0.998115i	$-0.519550\pi$
$23$	−0.588724	−0.122757	−0.0613787	+	0.998115i	$0.519550\pi$
$24$	10.2162	2.08538
$25$	2.42324	0.484647
$26$	13.4766	2.64298
$27$	4.84864	0.933122
$28$	9.09497	1.71879
$29$	−7.40239	−1.37459	−0.687295	−	0.726379i	$-0.741202\pi$
$29$	−7.40239	−1.37459	−0.687295	+	0.726379i	$0.741202\pi$
$30$	7.25881	1.32527
$31$	4.71218	0.846332	0.423166	−	0.906052i	$-0.360919\pi$
$31$	4.71218	0.846332	0.423166	+	0.906052i	$0.360919\pi$
$32$	−29.9618	−5.29655
$33$	−4.30249	−0.748967
$34$	−13.8051	−2.36756
$35$	4.24703	0.717879
$36$	−12.2178	−2.03630
$37$	−9.59806	−1.57791	−0.788955	−	0.614451i	$-0.789378\pi$
$37$	−9.59806	−1.57791	−0.788955	+	0.614451i	$0.789378\pi$
$38$	18.0765	2.93239
$39$	4.58280	0.733835
$40$	−29.2434	−4.62379
$41$	3.80683	0.594527	0.297264	−	0.954795i	$-0.403926\pi$
$41$	3.80683	0.594527	0.297264	+	0.954795i	$0.403926\pi$
$42$	4.15296	0.640815
$43$	−3.38931	−0.516865	−0.258432	−	0.966029i	$-0.583206\pi$
$43$	−3.38931	−0.516865	−0.258432	+	0.966029i	$0.583206\pi$
$44$	26.3738	3.97600
$45$	−5.70528	−0.850493
$46$	1.64786	0.242964
$47$	−2.11515	−0.308526	−0.154263	−	0.988030i	$-0.549300\pi$
$47$	−2.11515	−0.308526	−0.154263	+	0.988030i	$0.549300\pi$
$48$	−17.4885	−2.52425
$49$	−4.57016	−0.652880
$50$	−6.78273	−0.959224
$51$	−4.69451	−0.657363
$52$	−28.0921	−3.89567
$53$	7.56236	1.03877	0.519385	−	0.854540i	$-0.326161\pi$
$53$	7.56236	1.03877	0.519385	+	0.854540i	$0.326161\pi$
$54$	−13.5715	−1.84685
$55$	12.3156	1.66064
$56$	−16.7309	−2.23577
$57$	6.14702	0.814193
$58$	20.7196	2.72061
$59$	−0.485115	−0.0631566	−0.0315783	−	0.999501i	$-0.510053\pi$
$59$	−0.485115	−0.0631566	−0.0315783	+	0.999501i	$0.510053\pi$
$60$	−15.1310	−1.95341
$61$	11.8614	1.51869	0.759345	−	0.650688i	$-0.225519\pi$
$61$	11.8614	1.51869	0.759345	+	0.650688i	$0.225519\pi$
$62$	−13.1896	−1.67508
$63$	−3.26414	−0.411244
$64$	47.1172	5.88965
$65$	−13.1180	−1.62709
$66$	12.0428	1.48237
$67$	−1.53815	−0.187915	−0.0939575	−	0.995576i	$-0.529952\pi$
$67$	−1.53815	−0.187915	−0.0939575	+	0.995576i	$0.529952\pi$
$68$	28.7769	3.48971
$69$	0.560365	0.0674601
$70$	−11.8876	−1.42084
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	22.4756	2.64878
$73$	9.26795	1.08473	0.542366	−	0.840143i	$-0.317529\pi$
$73$	9.26795	1.08473	0.542366	+	0.840143i	$0.317529\pi$
$74$	26.8653	3.12303
$75$	−2.30651	−0.266333
$76$	−37.6806	−4.32226
$77$	7.04610	0.802978
$78$	−12.8274	−1.45242
$79$	1.69346	0.190529	0.0952647	−	0.995452i	$-0.469630\pi$
$79$	1.69346	0.190529	0.0952647	+	0.995452i	$0.469630\pi$
$80$	50.0599	5.59687
$81$	1.66697	0.185219
$82$	−10.6555	−1.17670
$83$	−14.2688	−1.56621	−0.783104	−	0.621891i	$-0.786365\pi$
$83$	−14.2688	−1.56621	−0.783104	+	0.621891i	$0.786365\pi$
$84$	−8.65687	−0.944542
$85$	13.4378	1.45753
$86$	9.48681	1.02299
$87$	7.04582	0.755391
$88$	−48.5167	−5.17190
$89$	−4.19505	−0.444675	−0.222337	−	0.974970i	$-0.571369\pi$
$89$	−4.19505	−0.444675	−0.222337	+	0.974970i	$0.571369\pi$
$90$	15.9693	1.68331
$91$	−7.50516	−0.786754
$92$	−3.43498	−0.358122
$93$	−4.48519	−0.465093
$94$	5.92038	0.610640
$95$	−17.5955	−1.80526
$96$	28.5186	2.91066
$97$	16.9329	1.71927	0.859636	−	0.510908i	$-0.170691\pi$
$97$	16.9329	1.71927	0.859636	+	0.510908i	$0.170691\pi$
$98$	12.7921	1.29219
$99$	−9.46544	−0.951312
$100$	14.1387	1.41387
$101$	3.60427	0.358638	0.179319	−	0.983791i	$-0.442611\pi$
$101$	3.60427	0.358638	0.179319	+	0.983791i	$0.442611\pi$
$102$	13.1401	1.30107
$103$	7.52131	0.741097	0.370548	−	0.928813i	$-0.379170\pi$
$103$	7.52131	0.741097	0.370548	+	0.928813i	$0.379170\pi$
$104$	51.6776	5.06741
$105$	−4.04245	−0.394503
$106$	−21.1674	−2.05595
$107$	7.78789	0.752884	0.376442	−	0.926440i	$-0.377147\pi$
$107$	7.78789	0.752884	0.376442	+	0.926440i	$0.377147\pi$
$108$	28.2900	2.72221
$109$	−6.68192	−0.640012	−0.320006	−	0.947416i	$-0.603685\pi$
$109$	−6.68192	−0.640012	−0.320006	+	0.947416i	$0.603685\pi$
$110$	−34.4719	−3.28677
$111$	9.13572	0.867124
$112$	28.6406	2.70628
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−17.2058	−1.61147
$115$	−1.60401	−0.149575
$116$	−43.1901	−4.01010
$117$	10.0821	0.932092
$118$	1.35786	0.125001
$119$	7.68811	0.704768
$120$	27.8348	2.54096
$121$	9.43243	0.857494
$122$	−33.2004	−3.00582
$123$	−3.62346	−0.326716
$124$	27.4938	2.46901
$125$	−7.02055	−0.627937
$126$	9.13647	0.813941
$127$	−10.6704	−0.946848	−0.473424	−	0.880835i	$-0.656982\pi$
$127$	−10.6704	−0.946848	−0.473424	+	0.880835i	$0.656982\pi$
$128$	−71.9592	−6.36035
$129$	3.22605	0.284038
$130$	36.7178	3.22037
$131$	−17.7640	−1.55205	−0.776026	−	0.630701i	$-0.782767\pi$
$131$	−17.7640	−1.55205	−0.776026	+	0.630701i	$0.782767\pi$
$132$	−25.1034	−2.18497
$133$	−10.0669	−0.872907
$134$	4.30534	0.371925
$135$	13.2104	1.13697
$136$	−52.9374	−4.53934
$137$	−13.2043	−1.12812	−0.564061	−	0.825733i	$-0.690762\pi$
$137$	−13.2043	−1.12812	−0.564061	+	0.825733i	$0.690762\pi$
$138$	−1.56848	−0.133518
$139$	14.0241	1.18951	0.594754	−	0.803908i	$-0.297249\pi$
$139$	14.0241	1.18951	0.594754	+	0.803908i	$0.297249\pi$
$140$	24.7798	2.09428
$141$	2.01326	0.169547
$142$	2.79904	0.234890
$143$	−21.7636	−1.81997
$144$	−38.4746	−3.20622
$145$	−20.1683	−1.67488
$146$	−25.9414	−2.14692
$147$	4.35002	0.358783
$148$	−56.0010	−4.60326
$149$	18.7475	1.53586	0.767928	−	0.640537i	$-0.221288\pi$
$149$	18.7475	1.53586	0.767928	+	0.640537i	$0.221288\pi$
$150$	6.45601	0.527131
$151$	−10.2197	−0.831671	−0.415836	−	0.909440i	$-0.636511\pi$
$151$	−10.2197	−0.831671	−0.415836	+	0.909440i	$0.636511\pi$
$152$	69.3165	5.62231
$153$	−10.3279	−0.834960
$154$	−19.7223	−1.58927
$155$	12.8386	1.03122
$156$	26.7389	2.14082
$157$	2.27234	0.181352	0.0906761	−	0.995880i	$-0.471097\pi$
$157$	2.27234	0.181352	0.0906761	+	0.995880i	$0.471097\pi$
$158$	−4.74007	−0.377099
$159$	−7.19809	−0.570845
$160$	−81.6328	−6.45364
$161$	−0.917699	−0.0723248
$162$	−4.66592	−0.366589
$163$	−18.6264	−1.45893	−0.729465	−	0.684019i	$-0.760231\pi$
$163$	−18.6264	−1.45893	−0.729465	+	0.684019i	$0.760231\pi$
$164$	22.2114	1.73442
$165$	−11.7224	−0.912587
$166$	39.9390	3.09987
$167$	−23.1945	−1.79484	−0.897422	−	0.441173i	$-0.854563\pi$
$167$	−23.1945	−1.79484	−0.897422	+	0.441173i	$0.854563\pi$
$168$	15.9250	1.22864
$169$	10.1815	0.783195
$170$	−37.6129	−2.88478
$171$	13.5234	1.03416
$172$	−19.7753	−1.50785
$173$	−18.9370	−1.43975	−0.719876	−	0.694103i	$-0.755801\pi$
$173$	−18.9370	−1.43975	−0.719876	+	0.694103i	$0.755801\pi$
$174$	−19.7215	−1.49509
$175$	3.77733	0.285539
$176$	83.0526	6.26033
$177$	0.461747	0.0347070
$178$	11.7421	0.880109
$179$	−10.2103	−0.763153	−0.381577	−	0.924337i	$-0.624619\pi$
$179$	−10.2103	−0.763153	−0.381577	+	0.924337i	$0.624619\pi$
$180$	−33.2882	−2.48115
$181$	3.78721	0.281501	0.140751	−	0.990045i	$-0.455048\pi$
$181$	3.78721	0.281501	0.140751	+	0.990045i	$0.455048\pi$
$182$	21.0072	1.55716
$183$	−11.2900	−0.834580
$184$	6.31892	0.465837
$185$	−26.1505	−1.92262
$186$	12.5542	0.920521
$187$	22.2942	1.63031
$188$	−12.3411	−0.900065
$189$	7.55804	0.549766
$190$	49.2505	3.57301
$191$	17.7306	1.28294	0.641471	−	0.767147i	$-0.278324\pi$
$191$	17.7306	1.28294	0.641471	+	0.767147i	$0.278324\pi$
$192$	−44.8476	−3.23659
$193$	−6.63178	−0.477366	−0.238683	−	0.971098i	$-0.576716\pi$
$193$	−6.63178	−0.477366	−0.238683	+	0.971098i	$0.576716\pi$
$194$	−47.3957	−3.40282
$195$	12.4861	0.894149
$196$	−26.6652	−1.90465
$197$	−26.1932	−1.86619	−0.933094	−	0.359633i	$-0.882902\pi$
$197$	−26.1932	−1.86619	−0.933094	+	0.359633i	$0.882902\pi$
$198$	26.4941	1.88286
$199$	−5.79633	−0.410891	−0.205445	−	0.978669i	$-0.565864\pi$
$199$	−5.79633	−0.410891	−0.205445	+	0.978669i	$0.565864\pi$
$200$	−26.0092	−1.83913
$201$	1.46406	0.103267
$202$	−10.0885	−0.709824
$203$	−11.5388	−0.809865
$204$	−27.3907	−1.91773
$205$	10.3719	0.724408
$206$	−21.0524	−1.46679
$207$	1.23280	0.0856854
$208$	−88.4636	−6.13385
$209$	−29.1921	−2.01926
$210$	11.3150	0.780808
$211$	21.4352	1.47566	0.737830	−	0.674987i	$-0.235851\pi$
$211$	21.4352	1.47566	0.737830	+	0.674987i	$0.235851\pi$
$212$	44.1235	3.03042
$213$	0.951830	0.0652183
$214$	−21.7986	−1.49012
$215$	−9.23438	−0.629779
$216$	−52.0417	−3.54099
$217$	7.34531	0.498632
$218$	18.7029	1.26672
$219$	−8.82152	−0.596103
$220$	71.8570	4.84460
$221$	−23.7466	−1.59737
$222$	−25.5712	−1.71623
$223$	−7.28428	−0.487791	−0.243896	−	0.969801i	$-0.578425\pi$
$223$	−7.28428	−0.487791	−0.243896	+	0.969801i	$0.578425\pi$
$224$	−46.7043	−3.12056
$225$	−5.07430	−0.338287
$226$	2.79904	0.186189
$227$	−0.774392	−0.0513982	−0.0256991	−	0.999670i	$-0.508181\pi$
$227$	−0.774392	−0.0513982	−0.0256991	+	0.999670i	$0.508181\pi$
$228$	35.8655	2.37525
$229$	3.83151	0.253193	0.126597	−	0.991954i	$-0.459595\pi$
$229$	3.83151	0.253193	0.126597	+	0.991954i	$0.459595\pi$
$230$	4.48970	0.296042
$231$	−6.70669	−0.441268
$232$	79.4518	5.21626
$233$	−22.4638	−1.47165	−0.735825	−	0.677171i	$-0.763206\pi$
$233$	−22.4638	−1.47165	−0.735825	+	0.677171i	$0.763206\pi$
$234$	−28.2202	−1.84481
$235$	−5.76285	−0.375927
$236$	−2.83046	−0.184247
$237$	−1.61189	−0.104703
$238$	−21.5193	−1.39489
$239$	−8.61463	−0.557234	−0.278617	−	0.960402i	$-0.589876\pi$
$239$	−8.61463	−0.557234	−0.278617	+	0.960402i	$0.589876\pi$
$240$	−47.6485	−3.07570
$241$	13.2008	0.850341	0.425171	−	0.905113i	$-0.360214\pi$
$241$	13.2008	0.850341	0.425171	+	0.905113i	$0.360214\pi$
$242$	−26.4017	−1.69717
$243$	−16.1326	−1.03491
$244$	69.2065	4.43049
$245$	−12.4517	−0.795509
$246$	10.1422	0.646643
$247$	31.0940	1.97846
$248$	−50.5770	−3.21164
$249$	13.5815	0.860693
$250$	19.6508	1.24283
$251$	19.2217	1.21327	0.606633	−	0.794982i	$-0.292520\pi$
$251$	19.2217	1.21327	0.606633	+	0.794982i	$0.292520\pi$
$252$	−19.0450	−1.19973
$253$	−2.66116	−0.167306
$254$	29.8670	1.87402
$255$	−12.7905	−0.800972
$256$	107.182	6.69889
$257$	−28.6703	−1.78840	−0.894202	−	0.447663i	$-0.852257\pi$
$257$	−28.6703	−1.78840	−0.894202	+	0.447663i	$0.852257\pi$
$258$	−9.02983	−0.562173
$259$	−14.9614	−0.929656
$260$	−76.5386	−4.74672
$261$	15.5007	0.959472
$262$	49.7223	3.07185
$263$	−4.38944	−0.270665	−0.135332	−	0.990800i	$-0.543210\pi$
$263$	−4.38944	−0.270665	−0.135332	+	0.990800i	$0.543210\pi$
$264$	46.1797	2.84216
$265$	20.6041	1.26570
$266$	28.1775	1.72768
$267$	3.99298	0.244366
$268$	−8.97452	−0.548206
$269$	2.28116	0.139085	0.0695423	−	0.997579i	$-0.477846\pi$
$269$	2.28116	0.139085	0.0695423	+	0.997579i	$0.477846\pi$
$270$	−36.9765	−2.25032
$271$	−28.3719	−1.72347	−0.861736	−	0.507357i	$-0.830622\pi$
$271$	−28.3719	−1.72347	−0.861736	+	0.507357i	$0.830622\pi$
$272$	90.6201	5.49465
$273$	7.14364	0.432353
$274$	36.9594	2.23280
$275$	10.9536	0.660525
$276$	3.26952	0.196802
$277$	−9.90508	−0.595139	−0.297569	−	0.954700i	$-0.596176\pi$
$277$	−9.90508	−0.595139	−0.297569	+	0.954700i	$0.596176\pi$
$278$	−39.2540	−2.35430
$279$	−9.86738	−0.590745
$280$	−45.5845	−2.72419
$281$	22.5145	1.34310	0.671550	−	0.740959i	$-0.265629\pi$
$281$	22.5145	1.34310	0.671550	+	0.740959i	$0.265629\pi$
$282$	−5.63519	−0.335571
$283$	−12.9633	−0.770588	−0.385294	−	0.922794i	$-0.625900\pi$
$283$	−12.9633	−0.770588	−0.385294	+	0.922794i	$0.625900\pi$
$284$	−5.83462	−0.346221
$285$	16.7479	0.992062
$286$	60.9172	3.60211
$287$	5.93406	0.350277
$288$	62.7406	3.69703
$289$	7.32551	0.430912
$290$	56.4518	3.31496
$291$	−16.1172	−0.944807
$292$	54.0750	3.16450
$293$	−5.78203	−0.337790	−0.168895	−	0.985634i	$-0.554020\pi$
$293$	−5.78203	−0.337790	−0.168895	+	0.985634i	$0.554020\pi$
$294$	−12.1759	−0.710111
$295$	−1.32173	−0.0769538
$296$	103.018	5.98782
$297$	21.9170	1.27175
$298$	−52.4750	−3.03980
$299$	2.83454	0.163926
$300$	−13.4576	−0.776976
$301$	−5.28323	−0.304521
$302$	28.6055	1.64606
$303$	−3.43065	−0.197086
$304$	−118.658	−6.80553
$305$	32.3170	1.85046
$306$	28.9082	1.65257
$307$	9.45478	0.539613	0.269806	−	0.962915i	$-0.413040\pi$
$307$	9.45478	0.539613	0.269806	+	0.962915i	$0.413040\pi$
$308$	41.1113	2.34253
$309$	−7.15901	−0.407262
$310$	−35.9358	−2.04102
$311$	−0.299660	−0.0169922	−0.00849609	−	0.999964i	$-0.502704\pi$
$311$	−0.299660	−0.0169922	−0.00849609	+	0.999964i	$0.502704\pi$
$312$	−49.1883	−2.78474
$313$	21.1267	1.19415	0.597077	−	0.802184i	$-0.296329\pi$
$313$	21.1267	1.19415	0.597077	+	0.802184i	$0.296329\pi$
$314$	−6.36036	−0.358936
$315$	−8.89336	−0.501084
$316$	9.88071	0.555833
$317$	17.0324	0.956635	0.478318	−	0.878187i	$-0.341247\pi$
$317$	17.0324	0.956635	0.478318	+	0.878187i	$0.341247\pi$
$318$	20.1477	1.12983
$319$	−33.4605	−1.87343
$320$	128.374	7.17630
$321$	−7.41275	−0.413740
$322$	2.56868	0.143147
$323$	−31.8520	−1.77229
$324$	9.72614	0.540341
$325$	−11.6672	−0.647180
$326$	52.1359	2.88754
$327$	6.36005	0.351712
$328$	−40.8597	−2.25610
$329$	−3.29708	−0.181774
$330$	32.8114	1.80621
$331$	−18.6341	−1.02422	−0.512112	−	0.858918i	$-0.671137\pi$
$331$	−18.6341	−1.02422	−0.512112	+	0.858918i	$0.671137\pi$
$332$	−83.2532	−4.56911
$333$	20.0985	1.10139
$334$	64.9223	3.55239
$335$	−4.19078	−0.228967
$336$	−27.2610	−1.48721
$337$	−0.878329	−0.0478456	−0.0239228	−	0.999714i	$-0.507616\pi$
$337$	−0.878329	−0.0478456	−0.0239228	+	0.999714i	$0.507616\pi$
$338$	−28.4985	−1.55012
$339$	0.951830	0.0516963
$340$	78.4044	4.25207
$341$	21.3001	1.15346
$342$	−37.8525	−2.04683
$343$	−18.0355	−0.973825
$344$	36.3783	1.96139
$345$	1.52675	0.0821975
$346$	53.0053	2.84958
$347$	1.55446	0.0834477	0.0417239	−	0.999129i	$-0.486715\pi$
$347$	1.55446	0.0834477	0.0417239	+	0.999129i	$0.486715\pi$
$348$	41.1097	2.20371
$349$	−10.4934	−0.561700	−0.280850	−	0.959752i	$-0.590616\pi$
$349$	−10.4934	−0.561700	−0.280850	+	0.959752i	$0.590616\pi$
$350$	−10.5729	−0.565145
$351$	−23.3449	−1.24606
$352$	−135.434	−7.21866
$353$	−19.9786	−1.06335	−0.531677	−	0.846947i	$-0.678438\pi$
$353$	−19.9786	−1.06335	−0.531677	+	0.846947i	$0.678438\pi$
$354$	−1.29245	−0.0686929
$355$	−2.72456	−0.144605
$356$	−24.4765	−1.29725
$357$	−7.31778	−0.387298
$358$	28.5790	1.51045
$359$	−14.7281	−0.777318	−0.388659	−	0.921382i	$-0.627062\pi$
$359$	−14.7281	−0.777318	−0.388659	+	0.921382i	$0.627062\pi$
$360$	61.2363	3.22743
$361$	22.7071	1.19511
$362$	−10.6006	−0.557153
$363$	−8.97808	−0.471227
$364$	−43.7898	−2.29521
$365$	25.2511	1.32170
$366$	31.6011	1.65182
$367$	−21.7557	−1.13564	−0.567820	−	0.823153i	$-0.692213\pi$
$367$	−21.7557	−1.13564	−0.567820	+	0.823153i	$0.692213\pi$
$368$	−10.8170	−0.563873
$369$	−7.97157	−0.414984
$370$	73.1963	3.80529
$371$	11.7882	0.612011
$372$	−26.1694	−1.35682
$373$	12.0515	0.624004	0.312002	−	0.950081i	$-0.399000\pi$
$373$	12.0515	0.624004	0.312002	+	0.950081i	$0.399000\pi$
$374$	−62.4022	−3.22674
$375$	6.68237	0.345076
$376$	22.7024	1.17079
$377$	35.6404	1.83558
$378$	−21.1552	−1.08811
$379$	24.9294	1.28054	0.640268	−	0.768151i	$-0.278823\pi$
$379$	24.9294	1.28054	0.640268	+	0.768151i	$0.278823\pi$
$380$	−102.663	−5.26651
$381$	10.1564	0.520330
$382$	−49.6287	−2.53922
$383$	−18.3164	−0.935925	−0.467963	−	0.883748i	$-0.655012\pi$
$383$	−18.3164	−0.935925	−0.467963	+	0.883748i	$0.655012\pi$
$384$	68.4929	3.49527
$385$	19.1975	0.978397
$386$	18.5626	0.944812
$387$	7.09728	0.360775
$388$	98.7968	5.01565
$389$	−1.38101	−0.0700199	−0.0350099	−	0.999387i	$-0.511146\pi$
$389$	−1.38101	−0.0700199	−0.0350099	+	0.999387i	$0.511146\pi$
$390$	−34.9491	−1.76972
$391$	−2.90364	−0.146843
$392$	49.0527	2.47754
$393$	16.9084	0.852914
$394$	73.3158	3.69359
$395$	4.61394	0.232153
$396$	−55.2272	−2.77527
$397$	21.9907	1.10368	0.551841	−	0.833950i	$-0.313926\pi$
$397$	21.9907	1.10368	0.551841	+	0.833950i	$0.313926\pi$
$398$	16.2241	0.813243
$399$	9.58194	0.479697
$400$	44.5235	2.22617
$401$	−32.5599	−1.62597	−0.812983	−	0.582288i	$-0.802158\pi$
$401$	−32.5599	−1.62597	−0.812983	+	0.582288i	$0.802158\pi$
$402$	−4.09796	−0.204387
$403$	−22.6878	−1.13016
$404$	21.0295	1.04626
$405$	4.54177	0.225682
$406$	32.2976	1.60290
$407$	−43.3854	−2.15053
$408$	50.3874	2.49455
$409$	−32.5465	−1.60932	−0.804660	−	0.593736i	$-0.797652\pi$
$409$	−32.5465	−1.60932	−0.804660	+	0.593736i	$0.797652\pi$
$410$	−29.0315	−1.43376
$411$	12.5683	0.619948
$412$	43.8840	2.16201
$413$	−0.756194	−0.0372099
$414$	−3.45065	−0.169590
$415$	−38.8763	−1.90836
$416$	144.258	7.07282
$417$	−13.3486	−0.653682
$418$	81.7098	3.99656
$419$	34.5682	1.68877	0.844384	−	0.535738i	$-0.179966\pi$
$419$	34.5682	1.68877	0.844384	+	0.535738i	$0.179966\pi$
$420$	−23.5862	−1.15089
$421$	−0.364949	−0.0177865	−0.00889325	−	0.999960i	$-0.502831\pi$
$421$	−0.364949	−0.0177865	−0.00889325	+	0.999960i	$0.502831\pi$
$422$	−59.9979	−2.92065
$423$	4.42916	0.215353
$424$	−81.1688	−3.94190
$425$	11.9516	0.579739
$426$	−2.66421	−0.129081
$427$	18.4894	0.894765
$428$	45.4394	2.19640
$429$	20.7153	1.00014
$430$	25.8474	1.24647
$431$	−17.8486	−0.859736	−0.429868	−	0.902892i	$-0.641440\pi$
$431$	−17.8486	−0.859736	−0.429868	+	0.902892i	$0.641440\pi$
$432$	89.0868	4.28619
$433$	−30.9228	−1.48605	−0.743027	−	0.669262i	$-0.766610\pi$
$433$	−30.9228	−1.48605	−0.743027	+	0.669262i	$0.766610\pi$
$434$	−20.5598	−0.986903
$435$	19.1968	0.920415
$436$	−38.9865	−1.86711
$437$	3.80204	0.181876
$438$	24.6918	1.17982
$439$	35.1753	1.67882	0.839412	−	0.543495i	$-0.182899\pi$
$439$	35.1753	1.67882	0.839412	+	0.543495i	$0.182899\pi$
$440$	−132.187	−6.30176
$441$	9.57000	0.455714
$442$	66.4678	3.16155
$443$	8.21427	0.390272	0.195136	−	0.980776i	$-0.437485\pi$
$443$	8.21427	0.390272	0.195136	+	0.980776i	$0.437485\pi$
$444$	53.3035	2.52967
$445$	−11.4297	−0.541819
$446$	20.3890	0.965446
$447$	−17.8444	−0.844013
$448$	73.4460	3.47000
$449$	−5.35415	−0.252678	−0.126339	−	0.991987i	$-0.540323\pi$
$449$	−5.35415	−0.252678	−0.126339	+	0.991987i	$0.540323\pi$
$450$	14.2032	0.669544
$451$	17.2077	0.810280
$452$	−5.83462	−0.274437
$453$	9.72746	0.457036
$454$	2.16755	0.101728
$455$	−20.4483	−0.958630
$456$	−65.9776	−3.08968
$457$	5.39398	0.252320	0.126160	−	0.992010i	$-0.459735\pi$
$457$	5.39398	0.252320	0.126160	+	0.992010i	$0.459735\pi$
$458$	−10.7245	−0.501125
$459$	23.9139	1.11621
$460$	−9.35882	−0.436357
$461$	−14.9094	−0.694401	−0.347200	−	0.937791i	$-0.612868\pi$
$461$	−14.9094	−0.694401	−0.347200	+	0.937791i	$0.612868\pi$
$462$	18.7723	0.873366
$463$	30.7873	1.43081	0.715405	−	0.698710i	$-0.246242\pi$
$463$	30.7873	1.43081	0.715405	+	0.698710i	$0.246242\pi$
$464$	−136.008	−6.31403
$465$	−12.2202	−0.566697
$466$	62.8770	2.91272
$467$	15.3885	0.712096	0.356048	−	0.934468i	$-0.384124\pi$
$467$	15.3885	0.712096	0.356048	+	0.934468i	$0.384124\pi$
$468$	58.8253	2.71920
$469$	−2.39766	−0.110714
$470$	16.1304	0.744041
$471$	−2.16288	−0.0996603
$472$	5.20686	0.239665
$473$	−15.3204	−0.704434
$474$	4.51174	0.207231
$475$	−15.6495	−0.718049
$476$	44.8572	2.05603
$477$	−15.8357	−0.725068
$478$	24.1127	1.10289
$479$	31.2711	1.42881	0.714407	−	0.699731i	$-0.246697\pi$
$479$	31.2711	1.42881	0.714407	+	0.699731i	$0.246697\pi$
$480$	77.7006	3.54653
$481$	46.2120	2.10708
$482$	−36.9497	−1.68301
$483$	0.873494	0.0397454
$484$	55.0347	2.50158
$485$	46.1346	2.09486
$486$	45.1558	2.04831
$487$	−28.2574	−1.28047	−0.640233	−	0.768181i	$-0.721162\pi$
$487$	−28.2574	−1.28047	−0.640233	+	0.768181i	$0.721162\pi$
$488$	−127.311	−5.76309
$489$	17.7291	0.801739
$490$	34.8528	1.57449
$491$	−24.1233	−1.08867	−0.544335	−	0.838868i	$-0.683218\pi$
$491$	−24.1233	−1.08867	−0.544335	+	0.838868i	$0.683218\pi$
$492$	−21.1415	−0.953132
$493$	−36.5093	−1.64429
$494$	−87.0333	−3.91581
$495$	−25.7892	−1.15914
$496$	86.5795	3.88753
$497$	−1.55879	−0.0699215
$498$	−38.0152	−1.70350
$499$	24.8489	1.11239	0.556195	−	0.831052i	$-0.312261\pi$
$499$	24.8489	1.11239	0.556195	+	0.831052i	$0.312261\pi$
$500$	−40.9623	−1.83189
$501$	22.0772	0.986338
$502$	−53.8024	−2.40132
$503$	16.9000	0.753532	0.376766	−	0.926308i	$-0.377036\pi$
$503$	16.9000	0.753532	0.376766	+	0.926308i	$0.377036\pi$
$504$	35.0349	1.56058
$505$	9.82005	0.436987
$506$	7.44870	0.331135
$507$	−9.69110	−0.430397
$508$	−62.2579	−2.76225
$509$	6.06807	0.268962	0.134481	−	0.990916i	$-0.457063\pi$
$509$	6.06807	0.268962	0.134481	+	0.990916i	$0.457063\pi$
$510$	35.8011	1.58530
$511$	14.4468	0.639090
$512$	−156.089	−6.89822
$513$	−31.3130	−1.38250
$514$	80.2493	3.53965
$515$	20.4923	0.902997
$516$	18.8228	0.828626
$517$	−9.56093	−0.420489
$518$	41.8775	1.83999
$519$	18.0248	0.791200
$520$	140.799	6.17444
$521$	−1.40716	−0.0616487	−0.0308243	−	0.999525i	$-0.509813\pi$
$521$	−1.40716	−0.0616487	−0.0308243	+	0.999525i	$0.509813\pi$
$522$	−43.3872	−1.89901
$523$	12.8262	0.560851	0.280425	−	0.959876i	$-0.409524\pi$
$523$	12.8262	0.560851	0.280425	+	0.959876i	$0.409524\pi$
$524$	−103.646	−4.52782
$525$	−3.59537	−0.156915
$526$	12.2862	0.535705
$527$	23.2409	1.01239
$528$	−79.0520	−3.44030
$529$	−22.6534	−0.984931
$530$	−57.6718	−2.50510
$531$	1.01584	0.0440837
$532$	−58.7363	−2.54654
$533$	−18.3288	−0.793910
$534$	−11.1765	−0.483655
$535$	21.2186	0.917360
$536$	16.5094	0.713096
$537$	9.71847	0.419383
$538$	−6.38505	−0.275279
$539$	−20.6582	−0.889810
$540$	77.0778	3.31690
$541$	−7.38366	−0.317448	−0.158724	−	0.987323i	$-0.550738\pi$
$541$	−7.38366	−0.317448	−0.158724	+	0.987323i	$0.550738\pi$
$542$	79.4141	3.41113
$543$	−3.60478	−0.154696
$544$	−147.774	−6.33577
$545$	−18.2053	−0.779829
$546$	−19.9953	−0.855721
$547$	20.7782	0.888412	0.444206	−	0.895925i	$-0.353486\pi$
$547$	20.7782	0.888412	0.444206	+	0.895925i	$0.353486\pi$
$548$	−77.0423	−3.29108
$549$	−24.8379	−1.06006
$550$	−30.6595	−1.30732
$551$	47.8054	2.03658
$552$	−6.01454	−0.255996
$553$	2.63976	0.112254
$554$	27.7247	1.17791
$555$	24.8908	1.05656
$556$	81.8253	3.47017
$557$	38.4553	1.62941	0.814703	−	0.579879i	$-0.196900\pi$
$557$	38.4553	1.62941	0.814703	+	0.579879i	$0.196900\pi$
$558$	27.6192	1.16921
$559$	16.3186	0.690202
$560$	78.0331	3.29750
$561$	−21.2203	−0.895920
$562$	−63.0189	−2.65829
$563$	−16.6860	−0.703229	−0.351615	−	0.936145i	$-0.614367\pi$
$563$	−16.6860	−0.703229	−0.351615	+	0.936145i	$0.614367\pi$
$564$	11.7466	0.494622
$565$	−2.72456	−0.114623
$566$	36.2848	1.52516
$567$	2.59846	0.109125
$568$	10.7333	0.450357
$569$	−41.0491	−1.72087	−0.860433	−	0.509563i	$-0.829807\pi$
$569$	−41.0491	−1.72087	−0.860433	+	0.509563i	$0.829807\pi$
$570$	−46.8781	−1.96351
$571$	−31.3959	−1.31388	−0.656938	−	0.753945i	$-0.728149\pi$
$571$	−31.3959	−1.31388	−0.656938	+	0.753945i	$0.728149\pi$
$572$	−126.982	−5.30940
$573$	−16.8765	−0.705027
$574$	−16.6097	−0.693275
$575$	−1.42662	−0.0594941
$576$	−98.6642	−4.11101
$577$	−35.2447	−1.46726	−0.733629	−	0.679550i	$-0.762175\pi$
$577$	−35.2447	−1.46726	−0.733629	+	0.679550i	$0.762175\pi$
$578$	−20.5044	−0.852870
$579$	6.31233	0.262331
$580$	−117.674	−4.88616
$581$	−22.2422	−0.922761
$582$	45.1127	1.86998
$583$	34.1836	1.41574
$584$	−99.4753	−4.11632
$585$	27.4693	1.13572
$586$	16.1841	0.668561
$587$	7.02358	0.289894	0.144947	−	0.989439i	$-0.453699\pi$
$587$	7.02358	0.289894	0.144947	+	0.989439i	$0.453699\pi$
$588$	25.3807	1.04668
$589$	−30.4317	−1.25392
$590$	3.69956	0.152309
$591$	24.9315	1.02554
$592$	−176.350	−7.24796
$593$	0.588708	0.0241754	0.0120877	−	0.999927i	$-0.496152\pi$
$593$	0.588708	0.0241754	0.0120877	+	0.999927i	$0.496152\pi$
$594$	−61.3464	−2.51707
$595$	20.9467	0.858732
$596$	109.385	4.48057
$597$	5.51712	0.225801
$598$	−7.93399	−0.324445
$599$	−25.6346	−1.04740	−0.523702	−	0.851902i	$-0.675449\pi$
$599$	−25.6346	−1.04740	−0.523702	+	0.851902i	$0.675449\pi$
$600$	24.7564	1.01067
$601$	15.1624	0.618486	0.309243	−	0.950983i	$-0.399924\pi$
$601$	15.1624	0.618486	0.309243	+	0.950983i	$0.399924\pi$
$602$	14.7880	0.602713
$603$	3.22091	0.131166
$604$	−59.6283	−2.42624
$605$	25.6992	1.04482
$606$	9.60253	0.390076
$607$	2.47771	0.100567	0.0502835	−	0.998735i	$-0.483987\pi$
$607$	2.47771	0.100567	0.0502835	+	0.998735i	$0.483987\pi$
$608$	193.497	7.84732
$609$	10.9830	0.445053
$610$	−90.4565	−3.66248
$611$	10.1838	0.411994
$612$	−60.2593	−2.43584
$613$	−30.1231	−1.21666	−0.608330	−	0.793684i	$-0.708160\pi$
$613$	−30.1231	−1.21666	−0.608330	+	0.793684i	$0.708160\pi$
$614$	−26.4643	−1.06801
$615$	−9.87233	−0.398091
$616$	−75.6276	−3.04712
$617$	3.17681	0.127894	0.0639468	−	0.997953i	$-0.479631\pi$
$617$	3.17681	0.127894	0.0639468	+	0.997953i	$0.479631\pi$
$618$	20.0384	0.806061
$619$	44.6994	1.79662	0.898311	−	0.439360i	$-0.144795\pi$
$619$	44.6994	1.79662	0.898311	+	0.439360i	$0.144795\pi$
$620$	74.9084	3.00840
$621$	−2.85451	−0.114548
$622$	0.838761	0.0336312
$623$	−6.53922	−0.261988
$624$	84.2023	3.37079
$625$	−31.2441	−1.24976
$626$	−59.1346	−2.36349
$627$	27.7859	1.10966
$628$	13.2582	0.529061
$629$	−47.3385	−1.88751
$630$	24.8929	0.991756
$631$	−22.7524	−0.905758	−0.452879	−	0.891572i	$-0.649603\pi$
$631$	−22.7524	−0.905758	−0.452879	+	0.891572i	$0.649603\pi$
$632$	−18.1764	−0.723017
$633$	−20.4027	−0.810933
$634$	−47.6744	−1.89339
$635$	−29.0722	−1.15370
$636$	−41.9981	−1.66533
$637$	22.0041	0.871832
$638$	93.6572	3.70792
$639$	2.09402	0.0828381
$640$	−196.057	−7.74984
$641$	−20.3231	−0.802714	−0.401357	−	0.915922i	$-0.631461\pi$
$641$	−20.3231	−0.802714	−0.401357	+	0.915922i	$0.631461\pi$
$642$	20.7486	0.818882
$643$	6.90125	0.272159	0.136079	−	0.990698i	$-0.456550\pi$
$643$	6.90125	0.272159	0.136079	+	0.990698i	$0.456550\pi$
$644$	−5.35443	−0.210994
$645$	8.78956	0.346089
$646$	89.1549	3.50775
$647$	−2.92065	−0.114822	−0.0574112	−	0.998351i	$-0.518285\pi$
$647$	−2.92065	−0.114822	−0.0574112	+	0.998351i	$0.518285\pi$
$648$	−17.8920	−0.702865
$649$	−2.19283	−0.0860760
$650$	32.6570	1.28091
$651$	−6.99149	−0.274018
$652$	−108.678	−4.25615
$653$	2.59117	0.101400	0.0507002	−	0.998714i	$-0.483855\pi$
$653$	2.59117	0.101400	0.0507002	+	0.998714i	$0.483855\pi$
$654$	−17.8020	−0.696115
$655$	−48.3992	−1.89111
$656$	69.9450	2.73089
$657$	−19.4073	−0.757149
$658$	9.22865	0.359770
$659$	−35.4851	−1.38230	−0.691152	−	0.722710i	$-0.742896\pi$
$659$	−35.4851	−1.38230	−0.691152	+	0.722710i	$0.742896\pi$
$660$	−68.3957	−2.66230
$661$	16.9763	0.660303	0.330152	−	0.943928i	$-0.392900\pi$
$661$	16.9763	0.660303	0.330152	+	0.943928i	$0.392900\pi$
$662$	52.1577	2.02717
$663$	22.6028	0.877819
$664$	153.151	5.94341
$665$	−27.4278	−1.06360
$666$	−56.2565	−2.17990
$667$	4.35796	0.168741
$668$	−135.331	−5.23612
$669$	6.93340	0.268061
$670$	11.7302	0.453176
$671$	53.6160	2.06982
$672$	44.4546	1.71487
$673$	3.46985	0.133753	0.0668765	−	0.997761i	$-0.478697\pi$
$673$	3.46985	0.133753	0.0668765	+	0.997761i	$0.478697\pi$
$674$	2.45848	0.0946970
$675$	11.7494	0.452235
$676$	59.4054	2.28482
$677$	47.3242	1.81882	0.909409	−	0.415903i	$-0.136534\pi$
$677$	47.3242	1.81882	0.909409	+	0.415903i	$0.136534\pi$
$678$	−2.66421	−0.102318
$679$	26.3948	1.01294
$680$	−144.231	−5.53101
$681$	0.737090	0.0282453
$682$	−59.6198	−2.28296
$683$	−13.9532	−0.533904	−0.266952	−	0.963710i	$-0.586017\pi$
$683$	−13.9532	−0.533904	−0.266952	+	0.963710i	$0.586017\pi$
$684$	78.9039	3.01697
$685$	−35.9760	−1.37457
$686$	50.4821	1.92741
$687$	−3.64695	−0.139140
$688$	−62.2737	−2.37416
$689$	−36.4107	−1.38714
$690$	−4.27343	−0.162687
$691$	44.1286	1.67873	0.839365	−	0.543568i	$-0.182927\pi$
$691$	44.1286	1.67873	0.839365	+	0.543568i	$0.182927\pi$
$692$	−110.490	−4.20020
$693$	−14.7547	−0.560483
$694$	−4.35099	−0.165161
$695$	38.2095	1.44937
$696$	−75.6246	−2.86654
$697$	18.7756	0.711178
$698$	29.3715	1.11173
$699$	21.3817	0.808730
$700$	22.0393	0.833006
$701$	10.7832	0.407276	0.203638	−	0.979046i	$-0.434723\pi$
$701$	10.7832	0.407276	0.203638	+	0.979046i	$0.434723\pi$
$702$	65.3432	2.46622
$703$	61.9853	2.33782
$704$	212.980	8.02699
$705$	5.48525	0.206587
$706$	55.9210	2.10461
$707$	5.61831	0.211298
$708$	2.69412	0.101251
$709$	30.7319	1.15416	0.577080	−	0.816687i	$-0.304192\pi$
$709$	30.7319	1.15416	0.577080	+	0.816687i	$0.304192\pi$
$710$	7.62616	0.286205
$711$	−3.54614	−0.132991
$712$	45.0266	1.68744
$713$	−2.77417	−0.103894
$714$	20.4828	0.766548
$715$	−59.2963	−2.21756
$716$	−59.5732	−2.22636
$717$	8.19967	0.306222
$718$	41.2245	1.53848
$719$	32.1913	1.20053	0.600267	−	0.799800i	$-0.295061\pi$
$719$	32.1913	1.20053	0.600267	+	0.799800i	$0.295061\pi$
$720$	−104.826	−3.90665
$721$	11.7242	0.436631
$722$	−63.5582	−2.36539
$723$	−12.5650	−0.467296
$724$	22.0969	0.821227
$725$	−17.9377	−0.666191
$726$	25.1300	0.932661
$727$	−21.6385	−0.802529	−0.401265	−	0.915962i	$-0.631429\pi$
$727$	−21.6385	−0.802529	−0.401265	+	0.915962i	$0.631429\pi$
$728$	80.5548	2.98556
$729$	10.3546	0.383503
$730$	−70.6788	−2.61594
$731$	−16.7164	−0.618277
$732$	−65.8728	−2.43473
$733$	28.6036	1.05650	0.528248	−	0.849090i	$-0.322849\pi$
$733$	28.6036	1.05650	0.528248	+	0.849090i	$0.322849\pi$
$734$	60.8951	2.24768
$735$	11.8519	0.437164
$736$	17.6392	0.650191
$737$	−6.95278	−0.256109
$738$	22.3127	0.821344
$739$	−29.2269	−1.07513	−0.537564	−	0.843223i	$-0.680655\pi$
$739$	−29.2269	−1.07513	−0.537564	+	0.843223i	$0.680655\pi$
$740$	−152.578	−5.60889
$741$	−29.5962	−1.08724
$742$	−32.9955	−1.21130
$743$	−3.07880	−0.112950	−0.0564751	−	0.998404i	$-0.517986\pi$
$743$	−3.07880	−0.112950	−0.0564751	+	0.998404i	$0.517986\pi$
$744$	48.1407	1.76492
$745$	51.0787	1.87138
$746$	−33.7327	−1.23504
$747$	29.8792	1.09322
$748$	130.078	4.75612
$749$	12.1397	0.443576
$750$	−18.7042	−0.682982
$751$	−28.3789	−1.03556	−0.517780	−	0.855514i	$-0.673241\pi$
$751$	−28.3789	−1.03556	−0.517780	+	0.855514i	$0.673241\pi$
$752$	−38.8628	−1.41718
$753$	−18.2958	−0.666738
$754$	−99.7590	−3.63301
$755$	−27.8443	−1.01336
$756$	44.0983	1.60384
$757$	5.51550	0.200464	0.100232	−	0.994964i	$-0.468041\pi$
$757$	5.51550	0.200464	0.100232	+	0.994964i	$0.468041\pi$
$758$	−69.7783	−2.53446
$759$	2.53298	0.0919413
$760$	188.857	6.85057
$761$	−42.0455	−1.52415	−0.762074	−	0.647490i	$-0.775819\pi$
$761$	−42.0455	−1.52415	−0.762074	+	0.647490i	$0.775819\pi$
$762$	−28.4283	−1.02985
$763$	−10.4157	−0.377075
$764$	103.451	3.74274
$765$	−28.1390	−1.01737
$766$	51.2684	1.85240
$767$	2.33569	0.0843370
$768$	−102.019	−3.68130
$769$	−51.2803	−1.84921	−0.924607	−	0.380923i	$-0.875606\pi$
$769$	−51.2803	−1.84921	−0.924607	+	0.380923i	$0.875606\pi$
$770$	−53.7347	−1.93646
$771$	27.2893	0.982799
$772$	−38.6939	−1.39262
$773$	−19.7305	−0.709656	−0.354828	−	0.934932i	$-0.615461\pi$
$773$	−19.7305	−0.709656	−0.354828	+	0.934932i	$0.615461\pi$
$774$	−19.8656	−0.714053
$775$	11.4187	0.410172
$776$	−181.745	−6.52425
$777$	14.2407	0.510883
$778$	3.86550	0.138585
$779$	−24.5849	−0.880846
$780$	72.8518	2.60851
$781$	−4.52022	−0.161746
$782$	8.12740	0.290635
$783$	−35.8915	−1.28266
$784$	−83.9701	−2.99893
$785$	6.19112	0.220971
$786$	−47.3272	−1.68810
$787$	−1.76911	−0.0630620	−0.0315310	−	0.999503i	$-0.510038\pi$
$787$	−1.76911	−0.0630620	−0.0315310	+	0.999503i	$0.510038\pi$
$788$	−152.827	−5.44425
$789$	4.17801	0.148741
$790$	−12.9146	−0.459481
$791$	−1.55879	−0.0554243
$792$	101.595	3.61002
$793$	−57.1091	−2.02800
$794$	−61.5528	−2.18443
$795$	−19.6116	−0.695553
$796$	−33.8194	−1.19870
$797$	−37.9826	−1.34541	−0.672707	−	0.739909i	$-0.734869\pi$
$797$	−37.9826	−1.34541	−0.672707	+	0.739909i	$0.734869\pi$
$798$	−26.8202	−0.949426
$799$	−10.4321	−0.369061
$800$	−72.6046	−2.56696
$801$	8.78452	0.310386
$802$	91.1365	3.21814
$803$	41.8932	1.47838
$804$	8.54222	0.301261
$805$	−2.50033	−0.0881250
$806$	63.5041	2.23684
$807$	−2.17127	−0.0764325
$808$	−38.6855	−1.36095
$809$	−25.7544	−0.905475	−0.452738	−	0.891644i	$-0.649553\pi$
$809$	−25.7544	−0.905475	−0.452738	+	0.891644i	$0.649553\pi$
$810$	−12.7126	−0.446674
$811$	16.1452	0.566935	0.283468	−	0.958982i	$-0.408515\pi$
$811$	16.1452	0.566935	0.283468	+	0.958982i	$0.408515\pi$
$812$	−67.3245	−2.36263
$813$	27.0053	0.947116
$814$	121.437	4.25638
$815$	−50.7487	−1.77765
$816$	−86.2549	−3.01953
$817$	21.8885	0.765782
$818$	91.0989	3.18520
$819$	15.7159	0.549160
$820$	60.5164	2.11332
$821$	29.6913	1.03623	0.518117	−	0.855310i	$-0.326633\pi$
$821$	29.6913	1.03623	0.518117	+	0.855310i	$0.326633\pi$
$822$	−35.1791	−1.22701
$823$	−6.58582	−0.229567	−0.114784	−	0.993391i	$-0.536617\pi$
$823$	−6.58582	−0.229567	−0.114784	+	0.993391i	$0.536617\pi$
$824$	−80.7281	−2.81230
$825$	−10.4259	−0.362985
$826$	2.11662	0.0736465
$827$	−7.11821	−0.247525	−0.123762	−	0.992312i	$-0.539496\pi$
$827$	−7.11821	−0.247525	−0.123762	+	0.992312i	$0.539496\pi$
$828$	7.19291	0.249971
$829$	−16.4817	−0.572433	−0.286217	−	0.958165i	$-0.592398\pi$
$829$	−16.4817	−0.572433	−0.286217	+	0.958165i	$0.592398\pi$
$830$	108.816	3.77707
$831$	9.42796	0.327052
$832$	−226.856	−7.86482
$833$	−22.5404	−0.780980
$834$	37.3632	1.29378
$835$	−63.1949	−2.18695
$836$	−170.325	−5.89081
$837$	22.8477	0.789730
$838$	−96.7579	−3.34244
$839$	−29.1410	−1.00606	−0.503029	−	0.864269i	$-0.667781\pi$
$839$	−29.1410	−1.00606	−0.503029	+	0.864269i	$0.667781\pi$
$840$	43.3887	1.49705
$841$	25.7954	0.889496
$842$	1.02151	0.0352034
$843$	−21.4299	−0.738087
$844$	125.066	4.30496
$845$	27.7402	0.954293
$846$	−12.3974	−0.426231
$847$	14.7032	0.505209
$848$	138.948	4.77148
$849$	12.3389	0.423469
$850$	−33.4531	−1.14743
$851$	5.65060	0.193700
$852$	5.55357	0.190262
$853$	−57.0947	−1.95489	−0.977443	−	0.211199i	$-0.932263\pi$
$853$	−57.0947	−1.95489	−0.977443	+	0.211199i	$0.932263\pi$
$854$	−51.7526	−1.77094
$855$	36.8453	1.26008
$856$	−83.5894	−2.85703
$857$	6.64210	0.226890	0.113445	−	0.993544i	$-0.463811\pi$
$857$	6.64210	0.226890	0.113445	+	0.993544i	$0.463811\pi$
$858$	−57.9829	−1.97950
$859$	−5.22720	−0.178350	−0.0891748	−	0.996016i	$-0.528423\pi$
$859$	−5.22720	−0.178350	−0.0891748	+	0.996016i	$0.528423\pi$
$860$	−53.8791	−1.83726
$861$	−5.64822	−0.192491
$862$	49.9589	1.70161
$863$	29.1300	0.991595	0.495798	−	0.868438i	$-0.334876\pi$
$863$	29.1300	0.991595	0.495798	+	0.868438i	$0.334876\pi$
$864$	−145.274	−4.94233
$865$	−51.5950	−1.75428
$866$	86.5540	2.94123
$867$	−6.97264	−0.236803
$868$	42.8571	1.45467
$869$	7.65483	0.259672
$870$	−53.7325	−1.82170
$871$	7.40576	0.250935
$872$	71.7187	2.42870
$873$	−35.4577	−1.20006
$874$	−10.6421	−0.359973
$875$	−10.9436	−0.369961
$876$	−51.4702	−1.73902
$877$	−46.0981	−1.55662	−0.778311	−	0.627879i	$-0.783923\pi$
$877$	−46.0981	−1.55662	−0.778311	+	0.627879i	$0.783923\pi$
$878$	−98.4570	−3.32276
$879$	5.50352	0.185629
$880$	226.282	7.62797
$881$	−35.3559	−1.19117	−0.595585	−	0.803292i	$-0.703080\pi$
$881$	−35.3559	−1.19117	−0.595585	+	0.803292i	$0.703080\pi$
$882$	−26.7868	−0.901959
$883$	2.32888	0.0783730	0.0391865	−	0.999232i	$-0.487523\pi$
$883$	2.32888	0.0783730	0.0391865	+	0.999232i	$0.487523\pi$
$884$	−138.553	−4.66003
$885$	1.25806	0.0422892
$886$	−22.9921	−0.772433
$887$	−22.8493	−0.767205	−0.383602	−	0.923498i	$-0.625317\pi$
$887$	−22.8493	−0.767205	−0.383602	+	0.923498i	$0.625317\pi$
$888$	−98.0560	−3.29055
$889$	−16.6330	−0.557853
$890$	31.9921	1.07238
$891$	7.53508	0.252435
$892$	−42.5010	−1.42304
$893$	13.6598	0.457109
$894$	49.9473	1.67049
$895$	−27.8186	−0.929873
$896$	−112.170	−3.74732
$897$	−2.69800	−0.0900837
$898$	14.9865	0.500105
$899$	−34.8814	−1.16336
$900$	−29.6066	−0.986888
$901$	37.2983	1.24258
$902$	−48.1651	−1.60372
$903$	5.02874	0.167346
$904$	10.7333	0.356983
$905$	10.3185	0.342998
$906$	−27.2276	−0.904575
$907$	40.7286	1.35237	0.676186	−	0.736731i	$-0.263632\pi$
$907$	40.7286	1.35237	0.676186	+	0.736731i	$0.263632\pi$
$908$	−4.51828	−0.149944
$909$	−7.54741	−0.250332
$910$	57.2355	1.89734
$911$	5.42463	0.179726	0.0898629	−	0.995954i	$-0.471357\pi$
$911$	5.42463	0.179726	0.0898629	+	0.995954i	$0.471357\pi$
$912$	112.943	3.73991
$913$	−64.4983	−2.13458
$914$	−15.0979	−0.499396
$915$	−30.7603	−1.01690
$916$	22.3554	0.738643
$917$	−27.6905	−0.914421
$918$	−66.9361	−2.20922
$919$	18.1092	0.597366	0.298683	−	0.954352i	$-0.403453\pi$
$919$	18.1092	0.597366	0.298683	+	0.954352i	$0.403453\pi$
$920$	17.2163	0.567605
$921$	−8.99935	−0.296539
$922$	41.7320	1.37437
$923$	4.81472	0.158478
$924$	−39.1310	−1.28732
$925$	−23.2584	−0.764730
$926$	−86.1750	−2.83189
$927$	−15.7498	−0.517290
$928$	221.789	7.28058
$929$	21.8749	0.717692	0.358846	−	0.933397i	$-0.383170\pi$
$929$	21.8749	0.717692	0.358846	+	0.933397i	$0.383170\pi$
$930$	34.2048	1.12162
$931$	29.5146	0.967301
$932$	−131.068	−4.29326
$933$	0.285226	0.00933787
$934$	−43.0731	−1.40939
$935$	60.7418	1.98647
$936$	−108.214	−3.53708
$937$	−3.82510	−0.124961	−0.0624803	−	0.998046i	$-0.519901\pi$
$937$	−3.82510	−0.124961	−0.0624803	+	0.998046i	$0.519901\pi$
$938$	6.71114	0.219127
$939$	−20.1091	−0.656235
$940$	−33.6240	−1.09669
$941$	36.1146	1.17730	0.588652	−	0.808387i	$-0.299659\pi$
$941$	36.1146	1.17730	0.588652	+	0.808387i	$0.299659\pi$
$942$	6.05399	0.197250
$943$	−2.24117	−0.0729826
$944$	−8.91329	−0.290103
$945$	20.5923	0.669869
$946$	42.8825	1.39423
$947$	4.53975	0.147522	0.0737610	−	0.997276i	$-0.476500\pi$
$947$	4.53975	0.147522	0.0737610	+	0.997276i	$0.476500\pi$
$948$	−9.40476	−0.305452
$949$	−44.6226	−1.44851
$950$	43.8036	1.42118
$951$	−16.2120	−0.525709
$952$	−82.5185	−2.67444
$953$	3.20087	0.103686	0.0518432	−	0.998655i	$-0.483490\pi$
$953$	3.20087	0.103686	0.0518432	+	0.998655i	$0.483490\pi$
$954$	44.3248	1.43507
$955$	48.3081	1.56322
$956$	−50.2631	−1.62563
$957$	31.8487	1.02952
$958$	−87.5291	−2.82794
$959$	−20.5828	−0.664654
$960$	−122.190	−3.94366
$961$	−8.79540	−0.283723
$962$	−129.349	−4.17038
$963$	−16.3080	−0.525518
$964$	77.0219	2.48071
$965$	−18.0687	−0.581652
$966$	−2.44494	−0.0786648
$967$	−19.5764	−0.629535	−0.314768	−	0.949169i	$-0.601927\pi$
$967$	−19.5764	−0.629535	−0.314768	+	0.949169i	$0.601927\pi$
$968$	−101.241	−3.25400
$969$	30.3177	0.973944
$970$	−129.133	−4.14620
$971$	31.7144	1.01776	0.508881	−	0.860837i	$-0.330059\pi$
$971$	31.7144	1.01776	0.508881	+	0.860837i	$0.330059\pi$
$972$	−94.1276	−3.01914
$973$	21.8607	0.700821
$974$	79.0936	2.53432
$975$	11.1052	0.355651
$976$	217.935	6.97594
$977$	−18.4518	−0.590326	−0.295163	−	0.955447i	$-0.595374\pi$
$977$	−18.4518	−0.590326	−0.295163	+	0.955447i	$0.595374\pi$
$978$	−49.6246	−1.58682
$979$	−18.9626	−0.606047
$980$	−72.6509	−2.32075
$981$	13.9921	0.446732
$982$	67.5221	2.15472
$983$	16.7406	0.533941	0.266970	−	0.963705i	$-0.413977\pi$
$983$	16.7406	0.533941	0.266970	+	0.963705i	$0.413977\pi$
$984$	38.8915	1.23982
$985$	−71.3650	−2.27388
$986$	102.191	3.25442
$987$	3.13826	0.0998919
$988$	181.422	5.77179
$989$	1.99537	0.0634490
$990$	72.1849	2.29419
$991$	5.27862	0.167681	0.0838405	−	0.996479i	$-0.473281\pi$
$991$	5.27862	0.167681	0.0838405	+	0.996479i	$0.473281\pi$
$992$	−141.185	−4.48264
$993$	17.7365	0.562852
$994$	4.36313	0.138390
$995$	−15.7925	−0.500654
$996$	79.2430	2.51091
$997$	4.99832	0.158298	0.0791491	−	0.996863i	$-0.474780\pi$
$997$	4.99832	0.158298	0.0791491	+	0.996863i	$0.474780\pi$
$998$	−69.5531	−2.20166
$999$	−46.5375	−1.47238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.1	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.1	✓	158	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79904 q^{2} -0.951830 q^{3} +5.83462 q^{4} +2.72456 q^{5} +2.66421 q^{6} +1.55879 q^{7} -10.7333 q^{8} -2.09402 q^{9} +O(q^{10})\)	\(q-2.79904 q^{2} -0.951830 q^{3} +5.83462 q^{4} +2.72456 q^{5} +2.66421 q^{6} +1.55879 q^{7} -10.7333 q^{8} -2.09402 q^{9} -7.62616 q^{10} +4.52022 q^{11} -5.55357 q^{12} -4.81472 q^{13} -4.36313 q^{14} -2.59332 q^{15} +18.3736 q^{16} +4.93209 q^{17} +5.86124 q^{18} -6.45811 q^{19} +15.8968 q^{20} -1.48371 q^{21} -12.6523 q^{22} -0.588724 q^{23} +10.2162 q^{24} +2.42324 q^{25} +13.4766 q^{26} +4.84864 q^{27} +9.09497 q^{28} -7.40239 q^{29} +7.25881 q^{30} +4.71218 q^{31} -29.9618 q^{32} -4.30249 q^{33} -13.8051 q^{34} +4.24703 q^{35} -12.2178 q^{36} -9.59806 q^{37} +18.0765 q^{38} +4.58280 q^{39} -29.2434 q^{40} +3.80683 q^{41} +4.15296 q^{42} -3.38931 q^{43} +26.3738 q^{44} -5.70528 q^{45} +1.64786 q^{46} -2.11515 q^{47} -17.4885 q^{48} -4.57016 q^{49} -6.78273 q^{50} -4.69451 q^{51} -28.0921 q^{52} +7.56236 q^{53} -13.5715 q^{54} +12.3156 q^{55} -16.7309 q^{56} +6.14702 q^{57} +20.7196 q^{58} -0.485115 q^{59} -15.1310 q^{60} +11.8614 q^{61} -13.1896 q^{62} -3.26414 q^{63} +47.1172 q^{64} -13.1180 q^{65} +12.0428 q^{66} -1.53815 q^{67} +28.7769 q^{68} +0.560365 q^{69} -11.8876 q^{70} -1.00000 q^{71} +22.4756 q^{72} +9.26795 q^{73} +26.8653 q^{74} -2.30651 q^{75} -37.6806 q^{76} +7.04610 q^{77} -12.8274 q^{78} +1.69346 q^{79} +50.0599 q^{80} +1.66697 q^{81} -10.6555 q^{82} -14.2688 q^{83} -8.65687 q^{84} +13.4378 q^{85} +9.48681 q^{86} +7.04582 q^{87} -48.5167 q^{88} -4.19505 q^{89} +15.9693 q^{90} -7.50516 q^{91} -3.43498 q^{92} -4.48519 q^{93} +5.92038 q^{94} -17.5955 q^{95} +28.5186 q^{96} +16.9329 q^{97} +12.7921 q^{98} -9.46544 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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