LMFDB - Embedded newform 8023.2.a.d.1.92

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:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.92
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)

$f(q)$	$=$	$q+0.507854 q^{2} +0.536158 q^{3} -1.74208 q^{4} +0.419130 q^{5} +0.272290 q^{6} +3.10387 q^{7} -1.90043 q^{8} -2.71253 q^{9} +O(q^{10})$	\(q+0.507854 q^{2} +0.536158 q^{3} -1.74208 q^{4} +0.419130 q^{5} +0.272290 q^{6} +3.10387 q^{7} -1.90043 q^{8} -2.71253 q^{9} +0.212857 q^{10} -3.41587 q^{11} -0.934032 q^{12} -5.87544 q^{13} +1.57631 q^{14} +0.224720 q^{15} +2.51903 q^{16} +0.603523 q^{17} -1.37757 q^{18} -8.10679 q^{19} -0.730159 q^{20} +1.66416 q^{21} -1.73476 q^{22} -0.362738 q^{23} -1.01893 q^{24} -4.82433 q^{25} -2.98386 q^{26} -3.06282 q^{27} -5.40720 q^{28} -4.79981 q^{29} +0.114125 q^{30} +7.17926 q^{31} +5.08016 q^{32} -1.83144 q^{33} +0.306502 q^{34} +1.30092 q^{35} +4.72546 q^{36} +4.14842 q^{37} -4.11707 q^{38} -3.15016 q^{39} -0.796528 q^{40} +10.9405 q^{41} +0.845152 q^{42} -9.19286 q^{43} +5.95073 q^{44} -1.13690 q^{45} -0.184218 q^{46} -0.845314 q^{47} +1.35060 q^{48} +2.63399 q^{49} -2.45006 q^{50} +0.323584 q^{51} +10.2355 q^{52} +9.41639 q^{53} -1.55547 q^{54} -1.43169 q^{55} -5.89869 q^{56} -4.34652 q^{57} -2.43761 q^{58} +4.05216 q^{59} -0.391481 q^{60} +3.37305 q^{61} +3.64602 q^{62} -8.41935 q^{63} -2.45807 q^{64} -2.46257 q^{65} -0.930106 q^{66} +7.24797 q^{67} -1.05139 q^{68} -0.194485 q^{69} +0.660679 q^{70} +1.00000 q^{71} +5.15499 q^{72} +6.44522 q^{73} +2.10679 q^{74} -2.58660 q^{75} +14.1227 q^{76} -10.6024 q^{77} -1.59982 q^{78} +5.45270 q^{79} +1.05580 q^{80} +6.49545 q^{81} +5.55619 q^{82} -9.52304 q^{83} -2.89911 q^{84} +0.252954 q^{85} -4.66863 q^{86} -2.57346 q^{87} +6.49162 q^{88} +9.97735 q^{89} -0.577381 q^{90} -18.2366 q^{91} +0.631920 q^{92} +3.84922 q^{93} -0.429296 q^{94} -3.39780 q^{95} +2.72377 q^{96} +16.7461 q^{97} +1.33768 q^{98} +9.26566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	0.507854	0.359107	0.179554	−	0.983748i	$-0.442535\pi$
$2$	0.507854	0.359107	0.179554	+	0.983748i	$0.442535\pi$
$3$	0.536158	0.309551	0.154775	−	0.987950i	$-0.450535\pi$
$3$	0.536158	0.309551	0.154775	+	0.987950i	$0.450535\pi$
$4$	−1.74208	−0.871042
$5$	0.419130	0.187440	0.0937202	−	0.995599i	$-0.470124\pi$
$5$	0.419130	0.187440	0.0937202	+	0.995599i	$0.470124\pi$
$6$	0.272290	0.111162
$7$	3.10387	1.17315	0.586576	−	0.809894i	$-0.300476\pi$
$7$	3.10387	1.17315	0.586576	+	0.809894i	$0.300476\pi$
$8$	−1.90043	−0.671904
$9$	−2.71253	−0.904178
$10$	0.212857	0.0673112
$11$	−3.41587	−1.02992	−0.514961	−	0.857213i	$-0.672194\pi$
$11$	−3.41587	−1.02992	−0.514961	+	0.857213i	$0.672194\pi$
$12$	−0.934032	−0.269632
$13$	−5.87544	−1.62955	−0.814776	−	0.579775i	$-0.803140\pi$
$13$	−5.87544	−1.62955	−0.814776	+	0.579775i	$0.803140\pi$
$14$	1.57631	0.421287
$15$	0.224720	0.0580224
$16$	2.51903	0.629756
$17$	0.603523	0.146376	0.0731879	−	0.997318i	$-0.476683\pi$
$17$	0.603523	0.146376	0.0731879	+	0.997318i	$0.476683\pi$
$18$	−1.37757	−0.324697
$19$	−8.10679	−1.85983	−0.929913	−	0.367779i	$-0.880118\pi$
$19$	−8.10679	−1.85983	−0.929913	+	0.367779i	$0.880118\pi$
$20$	−0.730159	−0.163269
$21$	1.66416	0.363150
$22$	−1.73476	−0.369852
$23$	−0.362738	−0.0756361	−0.0378180	−	0.999285i	$-0.512041\pi$
$23$	−0.362738	−0.0756361	−0.0378180	+	0.999285i	$0.512041\pi$
$24$	−1.01893	−0.207989
$25$	−4.82433	−0.964866
$26$	−2.98386	−0.585184
$27$	−3.06282	−0.589440
$28$	−5.40720	−1.02186
$29$	−4.79981	−0.891303	−0.445651	−	0.895207i	$-0.647028\pi$
$29$	−4.79981	−0.891303	−0.445651	+	0.895207i	$0.647028\pi$
$30$	0.114125	0.0208362
$31$	7.17926	1.28943	0.644716	−	0.764422i	$-0.276975\pi$
$31$	7.17926	1.28943	0.644716	+	0.764422i	$0.276975\pi$
$32$	5.08016	0.898054
$33$	−1.83144	−0.318813
$34$	0.306502	0.0525646
$35$	1.30092	0.219896
$36$	4.72546	0.787577
$37$	4.14842	0.681995	0.340998	−	0.940064i	$-0.389235\pi$
$37$	4.14842	0.681995	0.340998	+	0.940064i	$0.389235\pi$
$38$	−4.11707	−0.667877
$39$	−3.15016	−0.504429
$40$	−0.796528	−0.125942
$41$	10.9405	1.70862	0.854311	−	0.519762i	$-0.173979\pi$
$41$	10.9405	1.70862	0.854311	+	0.519762i	$0.173979\pi$
$42$	0.845152	0.130410
$43$	−9.19286	−1.40190	−0.700949	−	0.713211i	$-0.747240\pi$
$43$	−9.19286	−1.40190	−0.700949	+	0.713211i	$0.747240\pi$
$44$	5.95073	0.897106
$45$	−1.13690	−0.169480
$46$	−0.184218	−0.0271615
$47$	−0.845314	−0.123302	−0.0616509	−	0.998098i	$-0.519637\pi$
$47$	−0.845314	−0.123302	−0.0616509	+	0.998098i	$0.519637\pi$
$48$	1.35060	0.194942
$49$	2.63399	0.376284
$50$	−2.45006	−0.346490
$51$	0.323584	0.0453108
$52$	10.2355	1.41941
$53$	9.41639	1.29344	0.646720	−	0.762727i	$-0.276140\pi$
$53$	9.41639	1.29344	0.646720	+	0.762727i	$0.276140\pi$
$54$	−1.55547	−0.211672
$55$	−1.43169	−0.193049
$56$	−5.89869	−0.788246
$57$	−4.34652	−0.575711
$58$	−2.43761	−0.320073
$59$	4.05216	0.527546	0.263773	−	0.964585i	$-0.415033\pi$
$59$	4.05216	0.527546	0.263773	+	0.964585i	$0.415033\pi$
$60$	−0.391481	−0.0505399
$61$	3.37305	0.431874	0.215937	−	0.976407i	$-0.430719\pi$
$61$	3.37305	0.431874	0.215937	+	0.976407i	$0.430719\pi$
$62$	3.64602	0.463045
$63$	−8.41935	−1.06074
$64$	−2.45807	−0.307259
$65$	−2.46257	−0.305444
$66$	−0.930106	−0.114488
$67$	7.24797	0.885480	0.442740	−	0.896650i	$-0.354006\pi$
$67$	7.24797	0.885480	0.442740	+	0.896650i	$0.354006\pi$
$68$	−1.05139	−0.127499
$69$	−0.194485	−0.0234132
$70$	0.660679	0.0789662
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	5.15499	0.607521
$73$	6.44522	0.754356	0.377178	−	0.926141i	$-0.376895\pi$
$73$	6.44522	0.754356	0.377178	+	0.926141i	$0.376895\pi$
$74$	2.10679	0.244909
$75$	−2.58660	−0.298675
$76$	14.1227	1.61999
$77$	−10.6024	−1.20825
$78$	−1.59982	−0.181144
$79$	5.45270	0.613477	0.306739	−	0.951794i	$-0.400762\pi$
$79$	5.45270	0.613477	0.306739	+	0.951794i	$0.400762\pi$
$80$	1.05580	0.118042
$81$	6.49545	0.721717
$82$	5.55619	0.613578
$83$	−9.52304	−1.04529	−0.522645	−	0.852551i	$-0.675055\pi$
$83$	−9.52304	−1.04529	−0.522645	+	0.852551i	$0.675055\pi$
$84$	−2.89911	−0.316319
$85$	0.252954	0.0274367
$86$	−4.66863	−0.503432
$87$	−2.57346	−0.275904
$88$	6.49162	0.692009
$89$	9.97735	1.05760	0.528799	−	0.848747i	$-0.322643\pi$
$89$	9.97735	1.05760	0.528799	+	0.848747i	$0.322643\pi$
$90$	−0.577381	−0.0608613
$91$	−18.2366	−1.91171
$92$	0.631920	0.0658822
$93$	3.84922	0.399145
$94$	−0.429296	−0.0442785
$95$	−3.39780	−0.348607
$96$	2.72377	0.277994
$97$	16.7461	1.70031	0.850155	−	0.526532i	$-0.176508\pi$
$97$	16.7461	1.70031	0.850155	+	0.526532i	$0.176508\pi$
$98$	1.33768	0.135126
$99$	9.26566	0.931233
$100$	8.40439	0.840439
$101$	−5.63004	−0.560210	−0.280105	−	0.959969i	$-0.590369\pi$
$101$	−5.63004	−0.560210	−0.280105	+	0.959969i	$0.590369\pi$
$102$	0.164333	0.0162714
$103$	3.58362	0.353105	0.176552	−	0.984291i	$-0.443506\pi$
$103$	3.58362	0.353105	0.176552	+	0.984291i	$0.443506\pi$
$104$	11.1659	1.09490
$105$	0.697500	0.0680690
$106$	4.78215	0.464484
$107$	12.6345	1.22142	0.610710	−	0.791855i	$-0.290884\pi$
$107$	12.6345	1.22142	0.610710	+	0.791855i	$0.290884\pi$
$108$	5.33569	0.513427
$109$	12.7112	1.21751	0.608757	−	0.793356i	$-0.291668\pi$
$109$	12.7112	1.21751	0.608757	+	0.793356i	$0.291668\pi$
$110$	−0.727090	−0.0693253
$111$	2.22421	0.211112
$112$	7.81872	0.738800
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−2.20740	−0.206742
$115$	−0.152034	−0.0141773
$116$	8.36168	0.776362
$117$	15.9373	1.47341
$118$	2.05790	0.189445
$119$	1.87325	0.171721
$120$	−0.427065	−0.0389855
$121$	0.668142	0.0607402
$122$	1.71302	0.155089
$123$	5.86585	0.528906
$124$	−12.5069	−1.12315
$125$	−4.11767	−0.368295
$126$	−4.27580	−0.380919
$127$	5.55140	0.492607	0.246304	−	0.969193i	$-0.420784\pi$
$127$	5.55140	0.492607	0.246304	+	0.969193i	$0.420784\pi$
$128$	−11.4087	−1.00839
$129$	−4.92882	−0.433959
$130$	−1.25063	−0.109687
$131$	4.85533	0.424212	0.212106	−	0.977247i	$-0.431968\pi$
$131$	4.85533	0.424212	0.212106	+	0.977247i	$0.431968\pi$
$132$	3.19053	0.277700
$133$	−25.1624	−2.18186
$134$	3.68091	0.317982
$135$	−1.28372	−0.110485
$136$	−1.14695	−0.0983506
$137$	−7.89368	−0.674403	−0.337201	−	0.941433i	$-0.609480\pi$
$137$	−7.89368	−0.674403	−0.337201	+	0.941433i	$0.609480\pi$
$138$	−0.0987699	−0.00840785
$139$	6.55518	0.556003	0.278002	−	0.960581i	$-0.410328\pi$
$139$	6.55518	0.556003	0.278002	+	0.960581i	$0.410328\pi$
$140$	−2.26632	−0.191539
$141$	−0.453222	−0.0381682
$142$	0.507854	0.0426182
$143$	20.0697	1.67831
$144$	−6.83294	−0.569412
$145$	−2.01174	−0.167066
$146$	3.27323	0.270895
$147$	1.41223	0.116479
$148$	−7.22689	−0.594047
$149$	−3.20829	−0.262834	−0.131417	−	0.991327i	$-0.541953\pi$
$149$	−3.20829	−0.262834	−0.131417	+	0.991327i	$0.541953\pi$
$150$	−1.31362	−0.107256
$151$	−4.62261	−0.376183	−0.188091	−	0.982152i	$-0.560230\pi$
$151$	−4.62261	−0.376183	−0.188091	+	0.982152i	$0.560230\pi$
$152$	15.4064	1.24963
$153$	−1.63708	−0.132350
$154$	−5.38447	−0.433893
$155$	3.00904	0.241692
$156$	5.48785	0.439379
$157$	9.72649	0.776259	0.388129	−	0.921605i	$-0.373121\pi$
$157$	9.72649	0.776259	0.388129	+	0.921605i	$0.373121\pi$
$158$	2.76918	0.220304
$159$	5.04867	0.400386
$160$	2.12925	0.168332
$161$	−1.12589	−0.0887326
$162$	3.29874	0.259174
$163$	12.7494	0.998606	0.499303	−	0.866427i	$-0.333589\pi$
$163$	12.7494	0.998606	0.499303	+	0.866427i	$0.333589\pi$
$164$	−19.0593	−1.48828
$165$	−0.767612	−0.0597585
$166$	−4.83631	−0.375371
$167$	−19.8328	−1.53471	−0.767353	−	0.641225i	$-0.778427\pi$
$167$	−19.8328	−1.53471	−0.767353	+	0.641225i	$0.778427\pi$
$168$	−3.16263	−0.244002
$169$	21.5207	1.65544
$170$	0.128464	0.00985273
$171$	21.9900	1.68161
$172$	16.0147	1.22111
$173$	−2.28795	−0.173950	−0.0869748	−	0.996211i	$-0.527720\pi$
$173$	−2.28795	−0.173950	−0.0869748	+	0.996211i	$0.527720\pi$
$174$	−1.30694	−0.0990789
$175$	−14.9741	−1.13193
$176$	−8.60465	−0.648600
$177$	2.17260	0.163302
$178$	5.06704	0.379791
$179$	−8.90322	−0.665458	−0.332729	−	0.943022i	$-0.607969\pi$
$179$	−8.90322	−0.665458	−0.332729	+	0.943022i	$0.607969\pi$
$180$	1.98058	0.147624
$181$	−22.8327	−1.69714	−0.848570	−	0.529082i	$-0.822536\pi$
$181$	−22.8327	−1.69714	−0.848570	+	0.529082i	$0.822536\pi$
$182$	−9.26152	−0.686509
$183$	1.80848	0.133687
$184$	0.689359	0.0508202
$185$	1.73872	0.127834
$186$	1.95484	0.143336
$187$	−2.06155	−0.150756
$188$	1.47261	0.107401
$189$	−9.50659	−0.691502
$190$	−1.72559	−0.125187
$191$	−5.57592	−0.403460	−0.201730	−	0.979441i	$-0.564656\pi$
$191$	−5.57592	−0.403460	−0.201730	+	0.979441i	$0.564656\pi$
$192$	−1.31791	−0.0951122
$193$	−11.9882	−0.862932	−0.431466	−	0.902129i	$-0.642004\pi$
$193$	−11.9882	−0.862932	−0.431466	+	0.902129i	$0.642004\pi$
$194$	8.50459	0.610594
$195$	−1.32033	−0.0945505
$196$	−4.58863	−0.327759
$197$	13.0509	0.929835	0.464917	−	0.885354i	$-0.346084\pi$
$197$	13.0509	0.929835	0.464917	+	0.885354i	$0.346084\pi$
$198$	4.70560	0.334413
$199$	−18.8225	−1.33429	−0.667144	−	0.744929i	$-0.732484\pi$
$199$	−18.8225	−1.33429	−0.667144	+	0.744929i	$0.732484\pi$
$200$	9.16832	0.648298
$201$	3.88605	0.274101
$202$	−2.85924	−0.201175
$203$	−14.8980	−1.04563
$204$	−0.563710	−0.0394676
$205$	4.58550	0.320265
$206$	1.81996	0.126802
$207$	0.983939	0.0683885
$208$	−14.8004	−1.02622
$209$	27.6917	1.91548
$210$	0.354228	0.0244441
$211$	−14.1765	−0.975953	−0.487976	−	0.872857i	$-0.662265\pi$
$211$	−14.1765	−0.975953	−0.487976	+	0.872857i	$0.662265\pi$
$212$	−16.4041	−1.12664
$213$	0.536158	0.0367369
$214$	6.41646	0.438620
$215$	−3.85300	−0.262772
$216$	5.82068	0.396047
$217$	22.2835	1.51270
$218$	6.45545	0.437218
$219$	3.45566	0.233512
$220$	2.49413	0.168154
$221$	−3.54596	−0.238527
$222$	1.12957	0.0758119
$223$	26.5044	1.77487	0.887433	−	0.460936i	$-0.152486\pi$
$223$	26.5044	1.77487	0.887433	+	0.460936i	$0.152486\pi$
$224$	15.7681	1.05355
$225$	13.0862	0.872411
$226$	−0.507854	−0.0337820
$227$	−17.0087	−1.12890	−0.564452	−	0.825466i	$-0.690913\pi$
$227$	−17.0087	−1.12890	−0.564452	+	0.825466i	$0.690913\pi$
$228$	7.57201	0.501468
$229$	16.8623	1.11429	0.557146	−	0.830415i	$-0.311896\pi$
$229$	16.8623	1.11429	0.557146	+	0.830415i	$0.311896\pi$
$230$	−0.0772112	−0.00509116
$231$	−5.68456	−0.374016
$232$	9.12172	0.598870
$233$	−9.80971	−0.642655	−0.321328	−	0.946968i	$-0.604129\pi$
$233$	−9.80971	−0.642655	−0.321328	+	0.946968i	$0.604129\pi$
$234$	8.09384	0.529111
$235$	−0.354296	−0.0231117
$236$	−7.05920	−0.459515
$237$	2.92351	0.189902
$238$	0.951340	0.0616662
$239$	−4.06337	−0.262838	−0.131419	−	0.991327i	$-0.541953\pi$
$239$	−4.06337	−0.262838	−0.131419	+	0.991327i	$0.541953\pi$
$240$	0.566075	0.0365400
$241$	−18.0112	−1.16020	−0.580100	−	0.814545i	$-0.696987\pi$
$241$	−18.0112	−1.16020	−0.580100	+	0.814545i	$0.696987\pi$
$242$	0.339319	0.0218122
$243$	12.6710	0.812848
$244$	−5.87613	−0.376181
$245$	1.10398	0.0705308
$246$	2.97899	0.189934
$247$	47.6310	3.03068
$248$	−13.6437	−0.866376
$249$	−5.10585	−0.323570
$250$	−2.09117	−0.132257
$251$	−21.9145	−1.38323	−0.691615	−	0.722267i	$-0.743100\pi$
$251$	−21.9145	−1.38323	−0.691615	+	0.722267i	$0.743100\pi$
$252$	14.6672	0.923947
$253$	1.23906	0.0778993
$254$	2.81930	0.176899
$255$	0.135623	0.00849307
$256$	−0.877800	−0.0548625
$257$	−4.59600	−0.286691	−0.143345	−	0.989673i	$-0.545786\pi$
$257$	−4.59600	−0.286691	−0.143345	+	0.989673i	$0.545786\pi$
$258$	−2.50312	−0.155838
$259$	12.8761	0.800084
$260$	4.29000	0.266055
$261$	13.0197	0.805897
$262$	2.46580	0.152338
$263$	−17.6974	−1.09127	−0.545635	−	0.838023i	$-0.683712\pi$
$263$	−17.6974	−1.09127	−0.545635	+	0.838023i	$0.683712\pi$
$264$	3.48054	0.214212
$265$	3.94669	0.242443
$266$	−12.7788	−0.783521
$267$	5.34944	0.327380
$268$	−12.6266	−0.771290
$269$	−0.604890	−0.0368808	−0.0184404	−	0.999830i	$-0.505870\pi$
$269$	−0.604890	−0.0368808	−0.0184404	+	0.999830i	$0.505870\pi$
$270$	−0.651942	−0.0396759
$271$	8.39604	0.510023	0.255011	−	0.966938i	$-0.417921\pi$
$271$	8.39604	0.510023	0.255011	+	0.966938i	$0.417921\pi$
$272$	1.52029	0.0921811
$273$	−9.77768	−0.591772
$274$	−4.00884	−0.242183
$275$	16.4793	0.993737
$276$	0.338809	0.0203939
$277$	27.8780	1.67503	0.837513	−	0.546418i	$-0.184009\pi$
$277$	27.8780	1.67503	0.837513	+	0.546418i	$0.184009\pi$
$278$	3.32908	0.199665
$279$	−19.4740	−1.16588
$280$	−2.47232	−0.147749
$281$	1.52045	0.0907025	0.0453512	−	0.998971i	$-0.485559\pi$
$281$	1.52045	0.0907025	0.0453512	+	0.998971i	$0.485559\pi$
$282$	−0.230171	−0.0137065
$283$	1.07118	0.0636749	0.0318374	−	0.999493i	$-0.489864\pi$
$283$	1.07118	0.0636749	0.0318374	+	0.999493i	$0.489864\pi$
$284$	−1.74208	−0.103374
$285$	−1.82176	−0.107912
$286$	10.1925	0.602694
$287$	33.9579	2.00447
$288$	−13.7801	−0.812001
$289$	−16.6358	−0.978574
$290$	−1.02167	−0.0599947
$291$	8.97856	0.526333
$292$	−11.2281	−0.657076
$293$	2.82397	0.164978	0.0824890	−	0.996592i	$-0.473713\pi$
$293$	2.82397	0.164978	0.0824890	+	0.996592i	$0.473713\pi$
$294$	0.717209	0.0418285
$295$	1.69838	0.0988834
$296$	−7.88378	−0.458236
$297$	10.4622	0.607078
$298$	−1.62934	−0.0943854
$299$	2.13124	0.123253
$300$	4.50608	0.260159
$301$	−28.5334	−1.64464
$302$	−2.34761	−0.135090
$303$	−3.01859	−0.173413
$304$	−20.4212	−1.17124
$305$	1.41374	0.0809507
$306$	−0.831396	−0.0475278
$307$	2.96045	0.168962	0.0844809	−	0.996425i	$-0.473077\pi$
$307$	2.96045	0.168962	0.0844809	+	0.996425i	$0.473077\pi$
$308$	18.4703	1.05244
$309$	1.92139	0.109304
$310$	1.52815	0.0867933
$311$	−15.7252	−0.891693	−0.445846	−	0.895110i	$-0.647097\pi$
$311$	−15.7252	−0.891693	−0.445846	+	0.895110i	$0.647097\pi$
$312$	5.98667	0.338928
$313$	16.3640	0.924949	0.462475	−	0.886633i	$-0.346962\pi$
$313$	16.3640	0.924949	0.462475	+	0.886633i	$0.346962\pi$
$314$	4.93964	0.278760
$315$	−3.52880	−0.198825
$316$	−9.49907	−0.534364
$317$	−26.1483	−1.46863	−0.734317	−	0.678806i	$-0.762498\pi$
$317$	−26.1483	−1.46863	−0.734317	+	0.678806i	$0.762498\pi$
$318$	2.56399	0.143781
$319$	16.3955	0.917973
$320$	−1.03025	−0.0575927
$321$	6.77406	0.378091
$322$	−0.571788	−0.0318645
$323$	−4.89264	−0.272234
$324$	−11.3156	−0.628646
$325$	28.3450	1.57230
$326$	6.47481	0.358607
$327$	6.81522	0.376883
$328$	−20.7917	−1.14803
$329$	−2.62374	−0.144652
$330$	−0.389835	−0.0214597
$331$	18.1635	0.998357	0.499179	−	0.866499i	$-0.333635\pi$
$331$	18.1635	0.998357	0.499179	+	0.866499i	$0.333635\pi$
$332$	16.5899	0.910491
$333$	−11.2527	−0.616645
$334$	−10.0722	−0.551124
$335$	3.03784	0.165975
$336$	4.19207	0.228696
$337$	−29.8388	−1.62542	−0.812712	−	0.582666i	$-0.802010\pi$
$337$	−29.8388	−1.62542	−0.812712	+	0.582666i	$0.802010\pi$
$338$	10.9294	0.594481
$339$	−0.536158	−0.0291201
$340$	−0.440668	−0.0238986
$341$	−24.5234	−1.32802
$342$	11.1677	0.603880
$343$	−13.5515	−0.731713
$344$	17.4704	0.941942
$345$	−0.0815143	−0.00438858
$346$	−1.16194	−0.0624665
$347$	19.2999	1.03607	0.518036	−	0.855359i	$-0.326663\pi$
$347$	19.2999	1.03607	0.518036	+	0.855359i	$0.326663\pi$
$348$	4.48318	0.240324
$349$	7.23084	0.387058	0.193529	−	0.981095i	$-0.438007\pi$
$349$	7.23084	0.387058	0.193529	+	0.981095i	$0.438007\pi$
$350$	−7.60465	−0.406485
$351$	17.9954	0.960524
$352$	−17.3532	−0.924926
$353$	−12.4832	−0.664414	−0.332207	−	0.943207i	$-0.607793\pi$
$353$	−12.4832	−0.664414	−0.332207	+	0.943207i	$0.607793\pi$
$354$	1.10336	0.0586430
$355$	0.419130	0.0222451
$356$	−17.3814	−0.921212
$357$	1.00436	0.0531564
$358$	−4.52154	−0.238971
$359$	37.5622	1.98245	0.991227	−	0.132168i	$-0.0421939\pi$
$359$	37.5622	1.98245	0.991227	+	0.132168i	$0.0421939\pi$
$360$	2.16061	0.113874
$361$	46.7201	2.45895
$362$	−11.5957	−0.609455
$363$	0.358230	0.0188022
$364$	31.7696	1.66518
$365$	2.70138	0.141397
$366$	0.918447	0.0480080
$367$	29.4173	1.53557	0.767784	−	0.640708i	$-0.221359\pi$
$367$	29.4173	1.53557	0.767784	+	0.640708i	$0.221359\pi$
$368$	−0.913746	−0.0476323
$369$	−29.6765	−1.54490
$370$	0.883018	0.0459059
$371$	29.2272	1.51740
$372$	−6.70566	−0.347672
$373$	16.7430	0.866919	0.433460	−	0.901173i	$-0.357293\pi$
$373$	16.7430	0.866919	0.433460	+	0.901173i	$0.357293\pi$
$374$	−1.04697	−0.0541374
$375$	−2.20772	−0.114006
$376$	1.60646	0.0828470
$377$	28.2010	1.45243
$378$	−4.82796	−0.248323
$379$	−17.3764	−0.892565	−0.446282	−	0.894892i	$-0.647252\pi$
$379$	−17.3764	−0.892565	−0.446282	+	0.894892i	$0.647252\pi$
$380$	5.91925	0.303651
$381$	2.97643	0.152487
$382$	−2.83176	−0.144885
$383$	27.0468	1.38203	0.691014	−	0.722842i	$-0.257164\pi$
$383$	27.0468	1.38203	0.691014	+	0.722842i	$0.257164\pi$
$384$	−6.11685	−0.312149
$385$	−4.44378	−0.226476
$386$	−6.08828	−0.309885
$387$	24.9360	1.26757
$388$	−29.1731	−1.48104
$389$	35.5143	1.80064	0.900322	−	0.435224i	$-0.143331\pi$
$389$	35.5143	1.80064	0.900322	+	0.435224i	$0.143331\pi$
$390$	−0.670533	−0.0339538
$391$	−0.218921	−0.0110713
$392$	−5.00572	−0.252827
$393$	2.60322	0.131315
$394$	6.62793	0.333910
$395$	2.28539	0.114990
$396$	−16.1416	−0.811144
$397$	−13.1671	−0.660839	−0.330420	−	0.943834i	$-0.607190\pi$
$397$	−13.1671	−0.660839	−0.330420	+	0.943834i	$0.607190\pi$
$398$	−9.55906	−0.479152
$399$	−13.4910	−0.675396
$400$	−12.1526	−0.607631
$401$	33.1510	1.65548	0.827741	−	0.561110i	$-0.189626\pi$
$401$	33.1510	1.65548	0.827741	+	0.561110i	$0.189626\pi$
$402$	1.97355	0.0984317
$403$	−42.1813	−2.10120
$404$	9.80800	0.487966
$405$	2.72244	0.135279
$406$	−7.56600	−0.375494
$407$	−14.1704	−0.702402
$408$	−0.614949	−0.0304445
$409$	10.0075	0.494838	0.247419	−	0.968909i	$-0.420418\pi$
$409$	10.0075	0.494838	0.247419	+	0.968909i	$0.420418\pi$
$410$	2.32876	0.115009
$411$	−4.23226	−0.208762
$412$	−6.24297	−0.307569
$413$	12.5774	0.618891
$414$	0.499698	0.0245588
$415$	−3.99139	−0.195929
$416$	−29.8482	−1.46343
$417$	3.51461	0.172111
$418$	14.0634	0.687861
$419$	1.59964	0.0781476	0.0390738	−	0.999236i	$-0.487559\pi$
$419$	1.59964	0.0781476	0.0390738	+	0.999236i	$0.487559\pi$
$420$	−1.21510	−0.0592910
$421$	−37.8824	−1.84628	−0.923138	−	0.384469i	$-0.874384\pi$
$421$	−37.8824	−1.84628	−0.923138	+	0.384469i	$0.874384\pi$
$422$	−7.19961	−0.350471
$423$	2.29294	0.111487
$424$	−17.8952	−0.869069
$425$	−2.91159	−0.141233
$426$	0.272290	0.0131925
$427$	10.4695	0.506654
$428$	−22.0103	−1.06391
$429$	10.7605	0.519523
$430$	−1.95676	−0.0943635
$431$	36.2363	1.74544	0.872722	−	0.488218i	$-0.162353\pi$
$431$	36.2363	1.74544	0.872722	+	0.488218i	$0.162353\pi$
$432$	−7.71532	−0.371204
$433$	−13.4167	−0.644764	−0.322382	−	0.946610i	$-0.604484\pi$
$433$	−13.4167	−0.644764	−0.322382	+	0.946610i	$0.604484\pi$
$434$	11.3167	0.543221
$435$	−1.07861	−0.0517155
$436$	−22.1440	−1.06051
$437$	2.94064	0.140670
$438$	1.75497	0.0838557
$439$	−12.9478	−0.617963	−0.308981	−	0.951068i	$-0.599988\pi$
$439$	−12.9478	−0.617963	−0.308981	+	0.951068i	$0.599988\pi$
$440$	2.72083	0.129711
$441$	−7.14478	−0.340228
$442$	−1.80083	−0.0856568
$443$	−10.3775	−0.493050	−0.246525	−	0.969136i	$-0.579289\pi$
$443$	−10.3775	−0.493050	−0.246525	+	0.969136i	$0.579289\pi$
$444$	−3.87475	−0.183888
$445$	4.18180	0.198236
$446$	13.4604	0.637367
$447$	−1.72015	−0.0813603
$448$	−7.62952	−0.360461
$449$	−36.3694	−1.71638	−0.858189	−	0.513334i	$-0.828410\pi$
$449$	−36.3694	−1.71638	−0.858189	+	0.513334i	$0.828410\pi$
$450$	6.64586	0.313289
$451$	−37.3714	−1.75975
$452$	1.74208	0.0819407
$453$	−2.47845	−0.116448
$454$	−8.63792	−0.405398
$455$	−7.64349	−0.358332
$456$	8.26027	0.386823
$457$	−23.6515	−1.10637	−0.553185	−	0.833059i	$-0.686588\pi$
$457$	−23.6515	−1.10637	−0.553185	+	0.833059i	$0.686588\pi$
$458$	8.56359	0.400150
$459$	−1.84848	−0.0862798
$460$	0.264856	0.0123490
$461$	3.58041	0.166756	0.0833781	−	0.996518i	$-0.473429\pi$
$461$	3.58041	0.166756	0.0833781	+	0.996518i	$0.473429\pi$
$462$	−2.88693	−0.134312
$463$	−28.5621	−1.32739	−0.663696	−	0.748002i	$-0.731013\pi$
$463$	−28.5621	−1.32739	−0.663696	+	0.748002i	$0.731013\pi$
$464$	−12.0909	−0.561304
$465$	1.61332	0.0748159
$466$	−4.98190	−0.230782
$467$	−26.8745	−1.24361	−0.621803	−	0.783174i	$-0.713599\pi$
$467$	−26.8745	−1.24361	−0.621803	+	0.783174i	$0.713599\pi$
$468$	−27.7642	−1.28340
$469$	22.4967	1.03880
$470$	−0.179931	−0.00829959
$471$	5.21494	0.240292
$472$	−7.70085	−0.354460
$473$	31.4016	1.44385
$474$	1.48472	0.0681953
$475$	39.1099	1.79448
$476$	−3.26337	−0.149576
$477$	−25.5423	−1.16950
$478$	−2.06360	−0.0943869
$479$	14.7460	0.673760	0.336880	−	0.941548i	$-0.390628\pi$
$479$	14.7460	0.673760	0.336880	+	0.941548i	$0.390628\pi$
$480$	1.14161	0.0521072
$481$	−24.3737	−1.11135
$482$	−9.14704	−0.416636
$483$	−0.603655	−0.0274672
$484$	−1.16396	−0.0529073
$485$	7.01879	0.318707
$486$	6.43504	0.291900
$487$	22.0700	1.00009	0.500043	−	0.866001i	$-0.333318\pi$
$487$	22.0700	1.00009	0.500043	+	0.866001i	$0.333318\pi$
$488$	−6.41025	−0.290178
$489$	6.83567	0.309119
$490$	0.560662	0.0253281
$491$	−6.57304	−0.296637	−0.148319	−	0.988940i	$-0.547386\pi$
$491$	−6.57304	−0.296637	−0.148319	+	0.988940i	$0.547386\pi$
$492$	−10.2188	−0.460699
$493$	−2.89680	−0.130465
$494$	24.1896	1.08834
$495$	3.88351	0.174551
$496$	18.0847	0.812029
$497$	3.10387	0.139227
$498$	−2.59303	−0.116196
$499$	13.7799	0.616871	0.308435	−	0.951245i	$-0.400195\pi$
$499$	13.7799	0.616871	0.308435	+	0.951245i	$0.400195\pi$
$500$	7.17332	0.320801
$501$	−10.6335	−0.475070
$502$	−11.1294	−0.496727
$503$	37.3061	1.66339	0.831697	−	0.555229i	$-0.187369\pi$
$503$	37.3061	1.66339	0.831697	+	0.555229i	$0.187369\pi$
$504$	16.0004	0.712715
$505$	−2.35972	−0.105006
$506$	0.629264	0.0279742
$507$	11.5385	0.512444
$508$	−9.67101	−0.429082
$509$	4.72602	0.209477	0.104739	−	0.994500i	$-0.466599\pi$
$509$	4.72602	0.209477	0.104739	+	0.994500i	$0.466599\pi$
$510$	0.0688769	0.00304992
$511$	20.0051	0.884974
$512$	22.3715	0.988692
$513$	24.8297	1.09626
$514$	−2.33410	−0.102953
$515$	1.50200	0.0661861
$516$	8.58643	0.377996
$517$	2.88748	0.126991
$518$	6.53919	0.287316
$519$	−1.22670	−0.0538462
$520$	4.67995	0.205229
$521$	2.63533	0.115456	0.0577281	−	0.998332i	$-0.481614\pi$
$521$	2.63533	0.115456	0.0577281	+	0.998332i	$0.481614\pi$
$522$	6.61209	0.289403
$523$	−16.0081	−0.699986	−0.349993	−	0.936752i	$-0.613816\pi$
$523$	−16.0081	−0.699986	−0.349993	+	0.936752i	$0.613816\pi$
$524$	−8.45839	−0.369507
$525$	−8.02847	−0.350391
$526$	−8.98771	−0.391883
$527$	4.33285	0.188742
$528$	−4.61345	−0.200775
$529$	−22.8684	−0.994279
$530$	2.00434	0.0870631
$531$	−10.9916	−0.476995
$532$	43.8350	1.90049
$533$	−64.2803	−2.78429
$534$	2.71673	0.117565
$535$	5.29548	0.228943
$536$	−13.7743	−0.594958
$537$	−4.77353	−0.205993
$538$	−0.307196	−0.0132442
$539$	−8.99735	−0.387543
$540$	2.23635	0.0962370
$541$	5.64063	0.242510	0.121255	−	0.992621i	$-0.461308\pi$
$541$	5.64063	0.242510	0.121255	+	0.992621i	$0.461308\pi$
$542$	4.26396	0.183153
$543$	−12.2419	−0.525351
$544$	3.06599	0.131453
$545$	5.32765	0.228212
$546$	−4.96563	−0.212510
$547$	22.8787	0.978222	0.489111	−	0.872221i	$-0.337321\pi$
$547$	22.8787	0.978222	0.489111	+	0.872221i	$0.337321\pi$
$548$	13.7515	0.587433
$549$	−9.14950	−0.390491
$550$	8.36906	0.356858
$551$	38.9111	1.65767
$552$	0.369605	0.0157314
$553$	16.9245	0.719702
$554$	14.1579	0.601514
$555$	0.932230	0.0395710
$556$	−11.4197	−0.484302
$557$	32.3412	1.37034	0.685171	−	0.728382i	$-0.259727\pi$
$557$	32.3412	1.37034	0.685171	+	0.728382i	$0.259727\pi$
$558$	−9.88995	−0.418675
$559$	54.0121	2.28447
$560$	3.27706	0.138481
$561$	−1.10532	−0.0466666
$562$	0.772167	0.0325719
$563$	22.0756	0.930375	0.465187	−	0.885212i	$-0.345987\pi$
$563$	22.0756	0.930375	0.465187	+	0.885212i	$0.345987\pi$
$564$	0.789551	0.0332461
$565$	−0.419130	−0.0176329
$566$	0.544002	0.0228661
$567$	20.1610	0.846683
$568$	−1.90043	−0.0797404
$569$	20.1068	0.842922	0.421461	−	0.906847i	$-0.361517\pi$
$569$	20.1068	0.842922	0.421461	+	0.906847i	$0.361517\pi$
$570$	−0.925186	−0.0387518
$571$	−10.6814	−0.447004	−0.223502	−	0.974703i	$-0.571749\pi$
$571$	−10.6814	−0.447004	−0.223502	+	0.974703i	$0.571749\pi$
$572$	−34.9631	−1.46188
$573$	−2.98958	−0.124891
$574$	17.2457	0.719820
$575$	1.74997	0.0729787
$576$	6.66760	0.277817
$577$	12.9469	0.538985	0.269493	−	0.963002i	$-0.413144\pi$
$577$	12.9469	0.538985	0.269493	+	0.963002i	$0.413144\pi$
$578$	−8.44854	−0.351413
$579$	−6.42759	−0.267121
$580$	3.50463	0.145522
$581$	−29.5582	−1.22628
$582$	4.55980	0.189010
$583$	−32.1651	−1.33214
$584$	−12.2487	−0.506855
$585$	6.67980	0.276176
$586$	1.43416	0.0592447
$587$	−5.39214	−0.222557	−0.111279	−	0.993789i	$-0.535495\pi$
$587$	−5.39214	−0.222557	−0.111279	+	0.993789i	$0.535495\pi$
$588$	−2.46023	−0.101458
$589$	−58.2008	−2.39812
$590$	0.862529	0.0355097
$591$	6.99732	0.287831
$592$	10.4500	0.429491
$593$	35.1742	1.44443	0.722216	−	0.691667i	$-0.243123\pi$
$593$	35.1742	1.44443	0.722216	+	0.691667i	$0.243123\pi$
$594$	5.31326	0.218006
$595$	0.785136	0.0321875
$596$	5.58911	0.228939
$597$	−10.0918	−0.413030
$598$	1.08236	0.0442610
$599$	8.91300	0.364175	0.182088	−	0.983282i	$-0.441715\pi$
$599$	8.91300	0.364175	0.182088	+	0.983282i	$0.441715\pi$
$600$	4.91566	0.200681
$601$	−15.5590	−0.634665	−0.317332	−	0.948314i	$-0.602787\pi$
$601$	−15.5590	−0.634665	−0.317332	+	0.948314i	$0.602787\pi$
$602$	−14.4908	−0.590601
$603$	−19.6604	−0.800632
$604$	8.05298	0.327671
$605$	0.280038	0.0113852
$606$	−1.53300	−0.0622740
$607$	28.9455	1.17486	0.587430	−	0.809275i	$-0.300140\pi$
$607$	28.9455	1.17486	0.587430	+	0.809275i	$0.300140\pi$
$608$	−41.1838	−1.67023
$609$	−7.98767	−0.323677
$610$	0.717975	0.0290700
$611$	4.96659	0.200927
$612$	2.85193	0.115282
$613$	17.3233	0.699683	0.349842	−	0.936809i	$-0.386235\pi$
$613$	17.3233	0.699683	0.349842	+	0.936809i	$0.386235\pi$
$614$	1.50348	0.0606754
$615$	2.45855	0.0991383
$616$	20.1491	0.811832
$617$	−12.5176	−0.503941	−0.251970	−	0.967735i	$-0.581079\pi$
$617$	−12.5176	−0.503941	−0.251970	+	0.967735i	$0.581079\pi$
$618$	0.975784	0.0392518
$619$	11.6283	0.467382	0.233691	−	0.972311i	$-0.424920\pi$
$619$	11.6283	0.467382	0.233691	+	0.972311i	$0.424920\pi$
$620$	−5.24200	−0.210524
$621$	1.11100	0.0445829
$622$	−7.98609	−0.320213
$623$	30.9684	1.24072
$624$	−7.93534	−0.317668
$625$	22.3958	0.895833
$626$	8.31054	0.332156
$627$	14.8471	0.592938
$628$	−16.9444	−0.676154
$629$	2.50366	0.0998276
$630$	−1.79211	−0.0713995
$631$	10.1648	0.404655	0.202328	−	0.979318i	$-0.435149\pi$
$631$	10.1648	0.404655	0.202328	+	0.979318i	$0.435149\pi$
$632$	−10.3625	−0.412198
$633$	−7.60086	−0.302107
$634$	−13.2795	−0.527397
$635$	2.32676	0.0923345
$636$	−8.79521	−0.348753
$637$	−15.4758	−0.613175
$638$	8.32653	0.329651
$639$	−2.71253	−0.107306
$640$	−4.78171	−0.189014
$641$	18.4809	0.729950	0.364975	−	0.931017i	$-0.381077\pi$
$641$	18.4809	0.729950	0.364975	+	0.931017i	$0.381077\pi$
$642$	3.44024	0.135775
$643$	10.0423	0.396029	0.198014	−	0.980199i	$-0.436551\pi$
$643$	10.0423	0.396029	0.198014	+	0.980199i	$0.436551\pi$
$644$	1.96140	0.0772898
$645$	−2.06582	−0.0813414
$646$	−2.48475	−0.0977610
$647$	21.9525	0.863044	0.431522	−	0.902103i	$-0.357977\pi$
$647$	21.9525	0.863044	0.431522	+	0.902103i	$0.357977\pi$
$648$	−12.3442	−0.484925
$649$	−13.8416	−0.543331
$650$	14.3951	0.564624
$651$	11.9475	0.468258
$652$	−22.2104	−0.869828
$653$	−14.7991	−0.579135	−0.289567	−	0.957158i	$-0.593511\pi$
$653$	−14.7991	−0.579135	−0.289567	+	0.957158i	$0.593511\pi$
$654$	3.46114	0.135341
$655$	2.03501	0.0795145
$656$	27.5595	1.07602
$657$	−17.4829	−0.682072
$658$	−1.33248	−0.0519454
$659$	28.2342	1.09985	0.549923	−	0.835215i	$-0.314657\pi$
$659$	28.2342	1.09985	0.549923	+	0.835215i	$0.314657\pi$
$660$	1.33725	0.0520522
$661$	−32.9320	−1.28091	−0.640454	−	0.767997i	$-0.721254\pi$
$661$	−32.9320	−1.28091	−0.640454	+	0.767997i	$0.721254\pi$
$662$	9.22442	0.358517
$663$	−1.90119	−0.0738363
$664$	18.0979	0.702335
$665$	−10.5463	−0.408968
$666$	−5.71474	−0.221442
$667$	1.74107	0.0674147
$668$	34.5504	1.33679
$669$	14.2106	0.549412
$670$	1.54278	0.0596027
$671$	−11.5219	−0.444797
$672$	8.45422	0.326129
$673$	31.0994	1.19879	0.599396	−	0.800453i	$-0.295407\pi$
$673$	31.0994	1.19879	0.599396	+	0.800453i	$0.295407\pi$
$674$	−15.1538	−0.583701
$675$	14.7761	0.568731
$676$	−37.4910	−1.44196
$677$	−8.18778	−0.314682	−0.157341	−	0.987544i	$-0.550292\pi$
$677$	−8.18778	−0.314682	−0.157341	+	0.987544i	$0.550292\pi$
$678$	−0.272290	−0.0104572
$679$	51.9777	1.99472
$680$	−0.480723	−0.0184349
$681$	−9.11933	−0.349453
$682$	−12.4543	−0.476900
$683$	−4.02951	−0.154185	−0.0770924	−	0.997024i	$-0.524564\pi$
$683$	−4.02951	−0.154185	−0.0770924	+	0.997024i	$0.524564\pi$
$684$	−38.3084	−1.46476
$685$	−3.30848	−0.126410
$686$	−6.88219	−0.262763
$687$	9.04085	0.344930
$688$	−23.1571	−0.882854
$689$	−55.3254	−2.10773
$690$	−0.0413974	−0.00157597
$691$	−13.6532	−0.519394	−0.259697	−	0.965690i	$-0.583623\pi$
$691$	−13.6532	−0.519394	−0.259697	+	0.965690i	$0.583623\pi$
$692$	3.98580	0.151517
$693$	28.7594	1.09248
$694$	9.80153	0.372061
$695$	2.74747	0.104217
$696$	4.89068	0.185381
$697$	6.60286	0.250101
$698$	3.67221	0.138995
$699$	−5.25955	−0.198935
$700$	26.0861	0.985962
$701$	48.5638	1.83423	0.917115	−	0.398622i	$-0.130511\pi$
$701$	48.5638	1.83423	0.917115	+	0.398622i	$0.130511\pi$
$702$	9.13904	0.344931
$703$	−33.6304	−1.26839
$704$	8.39644	0.316453
$705$	−0.189959	−0.00715426
$706$	−6.33964	−0.238596
$707$	−17.4749	−0.657211
$708$	−3.78484	−0.142243
$709$	19.0970	0.717204	0.358602	−	0.933491i	$-0.383254\pi$
$709$	19.0970	0.717204	0.358602	+	0.933491i	$0.383254\pi$
$710$	0.212857	0.00798837
$711$	−14.7907	−0.554693
$712$	−18.9613	−0.710604
$713$	−2.60419	−0.0975277
$714$	0.510068	0.0190888
$715$	8.41181	0.314584
$716$	15.5102	0.579642
$717$	−2.17861	−0.0813616
$718$	19.0761	0.711914
$719$	46.7103	1.74200	0.871000	−	0.491282i	$-0.163472\pi$
$719$	46.7103	1.74200	0.871000	+	0.491282i	$0.163472\pi$
$720$	−2.86389	−0.106731
$721$	11.1231	0.414245
$722$	23.7270	0.883028
$723$	−9.65682	−0.359141
$724$	39.7765	1.47828
$725$	23.1559	0.859988
$726$	0.181928	0.00675199
$727$	−29.7247	−1.10243	−0.551213	−	0.834364i	$-0.685835\pi$
$727$	−29.7247	−1.10243	−0.551213	+	0.834364i	$0.685835\pi$
$728$	34.6574	1.28449
$729$	−12.6927	−0.470099
$730$	1.37191	0.0507766
$731$	−5.54810	−0.205204
$732$	−3.15053	−0.116447
$733$	1.64493	0.0607569	0.0303785	−	0.999538i	$-0.490329\pi$
$733$	1.64493	0.0607569	0.0303785	+	0.999538i	$0.490329\pi$
$734$	14.9397	0.551434
$735$	0.591909	0.0218329
$736$	−1.84277	−0.0679253
$737$	−24.7581	−0.911976
$738$	−15.0714	−0.554784
$739$	−14.6935	−0.540510	−0.270255	−	0.962789i	$-0.587108\pi$
$739$	−14.6935	−0.540510	−0.270255	+	0.962789i	$0.587108\pi$
$740$	−3.02900	−0.111348
$741$	25.5377	0.938151
$742$	14.8432	0.544910
$743$	−13.1203	−0.481337	−0.240669	−	0.970607i	$-0.577367\pi$
$743$	−13.1203	−0.481337	−0.240669	+	0.970607i	$0.577367\pi$
$744$	−7.31518	−0.268187
$745$	−1.34469	−0.0492656
$746$	8.50300	0.311317
$747$	25.8316	0.945128
$748$	3.59140	0.131315
$749$	39.2157	1.43291
$750$	−1.12120	−0.0409404
$751$	18.9523	0.691578	0.345789	−	0.938312i	$-0.387611\pi$
$751$	18.9523	0.691578	0.345789	+	0.938312i	$0.387611\pi$
$752$	−2.12937	−0.0776501
$753$	−11.7496	−0.428180
$754$	14.3220	0.521576
$755$	−1.93747	−0.0705119
$756$	16.5613	0.602328
$757$	52.7594	1.91757	0.958787	−	0.284125i	$-0.0917031\pi$
$757$	52.7594	1.91757	0.958787	+	0.284125i	$0.0917031\pi$
$758$	−8.82467	−0.320526
$759$	0.664334	0.0241138
$760$	6.45729	0.234230
$761$	4.87577	0.176746	0.0883732	−	0.996087i	$-0.471833\pi$
$761$	4.87577	0.176746	0.0883732	+	0.996087i	$0.471833\pi$
$762$	1.51159	0.0547592
$763$	39.4539	1.42833
$764$	9.71373	0.351430
$765$	−0.686147	−0.0248077
$766$	13.7358	0.496296
$767$	−23.8082	−0.859664
$768$	−0.470639	−0.0169827
$769$	−2.23681	−0.0806616	−0.0403308	−	0.999186i	$-0.512841\pi$
$769$	−2.23681	−0.0806616	−0.0403308	+	0.999186i	$0.512841\pi$
$770$	−2.25679	−0.0813291
$771$	−2.46418	−0.0887453
$772$	20.8845	0.751650
$773$	13.7573	0.494817	0.247408	−	0.968911i	$-0.420421\pi$
$773$	13.7573	0.494817	0.247408	+	0.968911i	$0.420421\pi$
$774$	12.6638	0.455192
$775$	−34.6351	−1.24413
$776$	−31.8249	−1.14245
$777$	6.90364	0.247667
$778$	18.0361	0.646624
$779$	−88.6926	−3.17774
$780$	2.30012	0.0823575
$781$	−3.41587	−0.122229
$782$	−0.111180	−0.00397578
$783$	14.7010	0.525370
$784$	6.63508	0.236967
$785$	4.07666	0.145502
$786$	1.32206	0.0471562
$787$	−38.3267	−1.36620	−0.683099	−	0.730326i	$-0.739368\pi$
$787$	−38.3267	−1.36620	−0.683099	+	0.730326i	$0.739368\pi$
$788$	−22.7357	−0.809925
$789$	−9.48862	−0.337804
$790$	1.16064	0.0412939
$791$	−3.10387	−0.110361
$792$	−17.6088	−0.625700
$793$	−19.8181	−0.703762
$794$	−6.68698	−0.237312
$795$	2.11605	0.0750485
$796$	32.7903	1.16222
$797$	35.8306	1.26918	0.634592	−	0.772847i	$-0.281168\pi$
$797$	35.8306	1.26918	0.634592	+	0.772847i	$0.281168\pi$
$798$	−6.85147	−0.242539
$799$	−0.510167	−0.0180484
$800$	−24.5084	−0.866502
$801$	−27.0639	−0.956256
$802$	16.8359	0.594495
$803$	−22.0160	−0.776928
$804$	−6.76983	−0.238754
$805$	−0.471894	−0.0166321
$806$	−21.4219	−0.754555
$807$	−0.324317	−0.0114165
$808$	10.6995	0.376407
$809$	3.30123	0.116065	0.0580325	−	0.998315i	$-0.481517\pi$
$809$	3.30123	0.116065	0.0580325	+	0.998315i	$0.481517\pi$
$810$	1.38260	0.0485796
$811$	−9.78363	−0.343550	−0.171775	−	0.985136i	$-0.554950\pi$
$811$	−9.78363	−0.343550	−0.171775	+	0.985136i	$0.554950\pi$
$812$	25.9535	0.910791
$813$	4.50160	0.157878
$814$	−7.19651	−0.252238
$815$	5.34363	0.187179
$816$	0.815115	0.0285347
$817$	74.5246	2.60729
$818$	5.08234	0.177700
$819$	49.4673	1.72853
$820$	−7.98832	−0.278964
$821$	46.7735	1.63241	0.816203	−	0.577765i	$-0.196075\pi$
$821$	46.7735	1.63241	0.816203	+	0.577765i	$0.196075\pi$
$822$	−2.14937	−0.0749679
$823$	12.6654	0.441487	0.220743	−	0.975332i	$-0.429152\pi$
$823$	12.6654	0.441487	0.220743	+	0.975332i	$0.429152\pi$
$824$	−6.81043	−0.237253
$825$	8.83549	0.307612
$826$	6.38746	0.222248
$827$	−14.7505	−0.512924	−0.256462	−	0.966554i	$-0.582557\pi$
$827$	−14.7505	−0.512924	−0.256462	+	0.966554i	$0.582557\pi$
$828$	−1.71411	−0.0595693
$829$	−14.9737	−0.520057	−0.260028	−	0.965601i	$-0.583732\pi$
$829$	−14.9737	−0.520057	−0.260028	+	0.965601i	$0.583732\pi$
$830$	−2.02704	−0.0703597
$831$	14.9470	0.518506
$832$	14.4422	0.500694
$833$	1.58967	0.0550789
$834$	1.78491	0.0618064
$835$	−8.31250	−0.287666
$836$	−48.2413	−1.66846
$837$	−21.9888	−0.760043
$838$	0.812385	0.0280634
$839$	54.0438	1.86580	0.932899	−	0.360137i	$-0.117270\pi$
$839$	54.0438	1.86580	0.932899	+	0.360137i	$0.117270\pi$
$840$	−1.32555	−0.0457359
$841$	−5.96179	−0.205579
$842$	−19.2387	−0.663011
$843$	0.815201	0.0280770
$844$	24.6967	0.850096
$845$	9.01998	0.310297
$846$	1.16448	0.0400357
$847$	2.07382	0.0712574
$848$	23.7201	0.814553
$849$	0.574320	0.0197106
$850$	−1.47866	−0.0507178
$851$	−1.50479	−0.0515835
$852$	−0.934032	−0.0319994
$853$	2.12885	0.0728906	0.0364453	−	0.999336i	$-0.488397\pi$
$853$	2.12885	0.0728906	0.0364453	+	0.999336i	$0.488397\pi$
$854$	5.31697	0.181943
$855$	9.21664	0.315203
$856$	−24.0109	−0.820677
$857$	−2.77557	−0.0948116	−0.0474058	−	0.998876i	$-0.515095\pi$
$857$	−2.77557	−0.0948116	−0.0474058	+	0.998876i	$0.515095\pi$
$858$	5.46478	0.186564
$859$	21.0562	0.718429	0.359215	−	0.933255i	$-0.383045\pi$
$859$	21.0562	0.718429	0.359215	+	0.933255i	$0.383045\pi$
$860$	6.71225	0.228886
$861$	18.2068	0.620486
$862$	18.4028	0.626801
$863$	−45.6457	−1.55380	−0.776899	−	0.629626i	$-0.783208\pi$
$863$	−45.6457	−1.55380	−0.776899	+	0.629626i	$0.783208\pi$
$864$	−15.5596	−0.529349
$865$	−0.958947	−0.0326052
$866$	−6.81371	−0.231539
$867$	−8.91939	−0.302918
$868$	−38.8197	−1.31763
$869$	−18.6257	−0.631834
$870$	−0.547778	−0.0185714
$871$	−42.5850	−1.44294
$872$	−24.1568	−0.818054
$873$	−45.4244	−1.53738
$874$	1.49342	0.0505156
$875$	−12.7807	−0.432066
$876$	−6.02004	−0.203398
$877$	−30.8221	−1.04079	−0.520394	−	0.853926i	$-0.674215\pi$
$877$	−30.8221	−1.04079	−0.520394	+	0.853926i	$0.674215\pi$
$878$	−6.57557	−0.221915
$879$	1.51409	0.0510691
$880$	−3.60647	−0.121574
$881$	10.9419	0.368642	0.184321	−	0.982866i	$-0.440991\pi$
$881$	10.9419	0.368642	0.184321	+	0.982866i	$0.440991\pi$
$882$	−3.62851	−0.122178
$883$	−40.8170	−1.37360	−0.686800	−	0.726846i	$-0.740985\pi$
$883$	−40.8170	−1.37360	−0.686800	+	0.726846i	$0.740985\pi$
$884$	6.17736	0.207767
$885$	0.910599	0.0306095
$886$	−5.27026	−0.177058
$887$	34.4731	1.15749	0.578747	−	0.815507i	$-0.303542\pi$
$887$	34.4731	1.15749	0.578747	+	0.815507i	$0.303542\pi$
$888$	−4.22695	−0.141847
$889$	17.2308	0.577903
$890$	2.12375	0.0711881
$891$	−22.1876	−0.743312
$892$	−46.1729	−1.54598
$893$	6.85279	0.229320
$894$	−0.873586	−0.0292171
$895$	−3.73160	−0.124734
$896$	−35.4110	−1.18300
$897$	1.14268	0.0381531
$898$	−18.4703	−0.616363
$899$	−34.4591	−1.14928
$900$	−22.7972	−0.759907
$901$	5.68301	0.189328
$902$	−18.9792	−0.631938
$903$	−15.2984	−0.509099
$904$	1.90043	0.0632075
$905$	−9.56986	−0.318113
$906$	−1.25869	−0.0418172
$907$	−18.1140	−0.601466	−0.300733	−	0.953708i	$-0.597231\pi$
$907$	−18.1140	−0.601466	−0.300733	+	0.953708i	$0.597231\pi$
$908$	29.6305	0.983323
$909$	15.2717	0.506529
$910$	−3.88178	−0.128680
$911$	−1.80172	−0.0596935	−0.0298467	−	0.999554i	$-0.509502\pi$
$911$	−1.80172	−0.0596935	−0.0298467	+	0.999554i	$0.509502\pi$
$912$	−10.9490	−0.362558
$913$	32.5294	1.07657
$914$	−12.0115	−0.397305
$915$	0.757990	0.0250584
$916$	−29.3755	−0.970595
$917$	15.0703	0.497665
$918$	−0.938759	−0.0309837
$919$	14.6616	0.483643	0.241822	−	0.970321i	$-0.422255\pi$
$919$	14.6616	0.483643	0.241822	+	0.970321i	$0.422255\pi$
$920$	0.288931	0.00952577
$921$	1.58727	0.0523023
$922$	1.81833	0.0598834
$923$	−5.87544	−0.193392
$924$	9.90298	0.325784
$925$	−20.0133	−0.658034
$926$	−14.5054	−0.476676
$927$	−9.72070	−0.319270
$928$	−24.3838	−0.800439
$929$	−31.4715	−1.03255	−0.516273	−	0.856424i	$-0.672681\pi$
$929$	−31.4715	−1.03255	−0.516273	+	0.856424i	$0.672681\pi$
$930$	0.819331	0.0268669
$931$	−21.3532	−0.699823
$932$	17.0893	0.559780
$933$	−8.43117	−0.276024
$934$	−13.6483	−0.446587
$935$	−0.864058	−0.0282577
$936$	−30.2878	−0.989988
$937$	1.19447	0.0390216	0.0195108	−	0.999810i	$-0.493789\pi$
$937$	1.19447	0.0390216	0.0195108	+	0.999810i	$0.493789\pi$
$938$	11.4251	0.373041
$939$	8.77370	0.286319
$940$	0.617214	0.0201313
$941$	28.9029	0.942208	0.471104	−	0.882078i	$-0.343856\pi$
$941$	28.9029	0.942208	0.471104	+	0.882078i	$0.343856\pi$
$942$	2.64843	0.0862904
$943$	−3.96854	−0.129234
$944$	10.2075	0.332225
$945$	−3.98449	−0.129616
$946$	15.9474	0.518495
$947$	−56.5449	−1.83746	−0.918732	−	0.394882i	$-0.870786\pi$
$947$	−56.5449	−1.83746	−0.918732	+	0.394882i	$0.870786\pi$
$948$	−5.09300	−0.165413
$949$	−37.8685	−1.22926
$950$	19.8621	0.644412
$951$	−14.0196	−0.454617
$952$	−3.55999	−0.115380
$953$	−25.1335	−0.814155	−0.407077	−	0.913394i	$-0.633452\pi$
$953$	−25.1335	−0.814155	−0.407077	+	0.913394i	$0.633452\pi$
$954$	−12.9718	−0.419976
$955$	−2.33703	−0.0756247
$956$	7.07874	0.228943
$957$	8.79059	0.284159
$958$	7.48880	0.241952
$959$	−24.5009	−0.791176
$960$	−0.552376	−0.0178279
$961$	20.5418	0.662637
$962$	−12.3783	−0.399093
$963$	−34.2714	−1.10438
$964$	31.3770	1.01058
$965$	−5.02463	−0.161748
$966$	−0.306569	−0.00986368
$967$	16.3233	0.524923	0.262461	−	0.964942i	$-0.415466\pi$
$967$	16.3233	0.524923	0.262461	+	0.964942i	$0.415466\pi$
$968$	−1.26976	−0.0408116
$969$	−2.62323	−0.0842701
$970$	3.56452	0.114450
$971$	26.9048	0.863417	0.431708	−	0.902013i	$-0.357911\pi$
$971$	26.9048	0.863417	0.431708	+	0.902013i	$0.357911\pi$
$972$	−22.0740	−0.708025
$973$	20.3464	0.652276
$974$	11.2083	0.359138
$975$	15.1974	0.486707
$976$	8.49679	0.271976
$977$	29.8829	0.956037	0.478019	−	0.878350i	$-0.341355\pi$
$977$	29.8829	0.956037	0.478019	+	0.878350i	$0.341355\pi$
$978$	3.47152	0.111007
$979$	−34.0813	−1.08924
$980$	−1.92323	−0.0614353
$981$	−34.4796	−1.10085
$982$	−3.33815	−0.106525
$983$	−13.4441	−0.428800	−0.214400	−	0.976746i	$-0.568780\pi$
$983$	−13.4441	−0.428800	−0.214400	+	0.976746i	$0.568780\pi$
$984$	−11.1476	−0.355374
$985$	5.47000	0.174289
$986$	−1.47115	−0.0468510
$987$	−1.40674	−0.0447770
$988$	−82.9771	−2.63985
$989$	3.33460	0.106034
$990$	1.97226	0.0626824
$991$	43.9352	1.39565	0.697824	−	0.716269i	$-0.254152\pi$
$991$	43.9352	1.39565	0.697824	+	0.716269i	$0.254152\pi$
$992$	36.4718	1.15798
$993$	9.73851	0.309042
$994$	1.57631	0.0499976
$995$	−7.88905	−0.250100
$996$	8.89482	0.281843
$997$	26.6770	0.844870	0.422435	−	0.906393i	$-0.361175\pi$
$997$	26.6770	0.844870	0.422435	+	0.906393i	$0.361175\pi$
$998$	6.99815	0.221523
$999$	−12.7059	−0.401995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.92	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.92	✓	165	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)

\(f(q)\)	\(=\)	\(q+0.507854 q^{2} +0.536158 q^{3} -1.74208 q^{4} +0.419130 q^{5} +0.272290 q^{6} +3.10387 q^{7} -1.90043 q^{8} -2.71253 q^{9} +O(q^{10})\)	\(q+0.507854 q^{2} +0.536158 q^{3} -1.74208 q^{4} +0.419130 q^{5} +0.272290 q^{6} +3.10387 q^{7} -1.90043 q^{8} -2.71253 q^{9} +0.212857 q^{10} -3.41587 q^{11} -0.934032 q^{12} -5.87544 q^{13} +1.57631 q^{14} +0.224720 q^{15} +2.51903 q^{16} +0.603523 q^{17} -1.37757 q^{18} -8.10679 q^{19} -0.730159 q^{20} +1.66416 q^{21} -1.73476 q^{22} -0.362738 q^{23} -1.01893 q^{24} -4.82433 q^{25} -2.98386 q^{26} -3.06282 q^{27} -5.40720 q^{28} -4.79981 q^{29} +0.114125 q^{30} +7.17926 q^{31} +5.08016 q^{32} -1.83144 q^{33} +0.306502 q^{34} +1.30092 q^{35} +4.72546 q^{36} +4.14842 q^{37} -4.11707 q^{38} -3.15016 q^{39} -0.796528 q^{40} +10.9405 q^{41} +0.845152 q^{42} -9.19286 q^{43} +5.95073 q^{44} -1.13690 q^{45} -0.184218 q^{46} -0.845314 q^{47} +1.35060 q^{48} +2.63399 q^{49} -2.45006 q^{50} +0.323584 q^{51} +10.2355 q^{52} +9.41639 q^{53} -1.55547 q^{54} -1.43169 q^{55} -5.89869 q^{56} -4.34652 q^{57} -2.43761 q^{58} +4.05216 q^{59} -0.391481 q^{60} +3.37305 q^{61} +3.64602 q^{62} -8.41935 q^{63} -2.45807 q^{64} -2.46257 q^{65} -0.930106 q^{66} +7.24797 q^{67} -1.05139 q^{68} -0.194485 q^{69} +0.660679 q^{70} +1.00000 q^{71} +5.15499 q^{72} +6.44522 q^{73} +2.10679 q^{74} -2.58660 q^{75} +14.1227 q^{76} -10.6024 q^{77} -1.59982 q^{78} +5.45270 q^{79} +1.05580 q^{80} +6.49545 q^{81} +5.55619 q^{82} -9.52304 q^{83} -2.89911 q^{84} +0.252954 q^{85} -4.66863 q^{86} -2.57346 q^{87} +6.49162 q^{88} +9.97735 q^{89} -0.577381 q^{90} -18.2366 q^{91} +0.631920 q^{92} +3.84922 q^{93} -0.429296 q^{94} -3.39780 q^{95} +2.72377 q^{96} +16.7461 q^{97} +1.33768 q^{98} +9.26566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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