LMFDB - Embedded newform 8003.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9042767376$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41716 q^{2} -1.38399 q^{3} +3.84266 q^{4} +1.63498 q^{5} +3.34533 q^{6} -3.98295 q^{7} -4.45401 q^{8} -1.08457 q^{9} +O(q^{10})$	\(q-2.41716 q^{2} -1.38399 q^{3} +3.84266 q^{4} +1.63498 q^{5} +3.34533 q^{6} -3.98295 q^{7} -4.45401 q^{8} -1.08457 q^{9} -3.95202 q^{10} +3.77197 q^{11} -5.31821 q^{12} -0.915163 q^{13} +9.62743 q^{14} -2.26280 q^{15} +3.08073 q^{16} +2.97669 q^{17} +2.62157 q^{18} +5.78926 q^{19} +6.28269 q^{20} +5.51237 q^{21} -9.11745 q^{22} -4.09109 q^{23} +6.16431 q^{24} -2.32683 q^{25} +2.21209 q^{26} +5.65301 q^{27} -15.3051 q^{28} -2.59173 q^{29} +5.46956 q^{30} +8.51302 q^{31} +1.46140 q^{32} -5.22038 q^{33} -7.19513 q^{34} -6.51206 q^{35} -4.16762 q^{36} -1.46789 q^{37} -13.9936 q^{38} +1.26658 q^{39} -7.28223 q^{40} +2.34134 q^{41} -13.3243 q^{42} -11.1388 q^{43} +14.4944 q^{44} -1.77325 q^{45} +9.88882 q^{46} -12.8765 q^{47} -4.26370 q^{48} +8.86389 q^{49} +5.62432 q^{50} -4.11971 q^{51} -3.51666 q^{52} -1.00000 q^{53} -13.6642 q^{54} +6.16711 q^{55} +17.7401 q^{56} -8.01229 q^{57} +6.26462 q^{58} -9.03203 q^{59} -8.69519 q^{60} +1.34872 q^{61} -20.5773 q^{62} +4.31977 q^{63} -9.69391 q^{64} -1.49628 q^{65} +12.6185 q^{66} +4.57214 q^{67} +11.4384 q^{68} +5.66203 q^{69} +15.7407 q^{70} +3.64013 q^{71} +4.83067 q^{72} -5.63539 q^{73} +3.54812 q^{74} +3.22031 q^{75} +22.2462 q^{76} -15.0236 q^{77} -3.06152 q^{78} +15.6324 q^{79} +5.03694 q^{80} -4.57002 q^{81} -5.65939 q^{82} -4.47647 q^{83} +21.1822 q^{84} +4.86684 q^{85} +26.9243 q^{86} +3.58693 q^{87} -16.8004 q^{88} +6.18881 q^{89} +4.28622 q^{90} +3.64505 q^{91} -15.7207 q^{92} -11.7820 q^{93} +31.1245 q^{94} +9.46535 q^{95} -2.02257 q^{96} +7.86088 q^{97} -21.4254 q^{98} -4.09095 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * 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 $

$2$	−2.41716	−1.70919	−0.854595	−	0.519295i	$-0.826195\pi$
$2$	−2.41716	−1.70919	−0.854595	+	0.519295i	$0.826195\pi$
$3$	−1.38399	−0.799048	−0.399524	−	0.916723i	$-0.630825\pi$
$3$	−1.38399	−0.799048	−0.399524	+	0.916723i	$0.630825\pi$
$4$	3.84266	1.92133
$5$	1.63498	0.731187	0.365593	−	0.930775i	$-0.380866\pi$
$5$	1.63498	0.731187	0.365593	+	0.930775i	$0.380866\pi$
$6$	3.34533	1.36573
$7$	−3.98295	−1.50541	−0.752707	−	0.658356i	$-0.771252\pi$
$7$	−3.98295	−1.50541	−0.752707	+	0.658356i	$0.771252\pi$
$8$	−4.45401	−1.57473
$9$	−1.08457	−0.361522
$10$	−3.95202	−1.24974
$11$	3.77197	1.13729	0.568646	−	0.822582i	$-0.307468\pi$
$11$	3.77197	1.13729	0.568646	+	0.822582i	$0.307468\pi$
$12$	−5.31821	−1.53524
$13$	−0.915163	−0.253820	−0.126910	−	0.991914i	$-0.540506\pi$
$13$	−0.915163	−0.253820	−0.126910	+	0.991914i	$0.540506\pi$
$14$	9.62743	2.57304
$15$	−2.26280	−0.584254
$16$	3.08073	0.770182
$17$	2.97669	0.721953	0.360976	−	0.932575i	$-0.382443\pi$
$17$	2.97669	0.721953	0.360976	+	0.932575i	$0.382443\pi$
$18$	2.62157	0.617910
$19$	5.78926	1.32815	0.664074	−	0.747667i	$-0.268826\pi$
$19$	5.78926	1.32815	0.664074	+	0.747667i	$0.268826\pi$
$20$	6.28269	1.40485
$21$	5.51237	1.20290
$22$	−9.11745	−1.94385
$23$	−4.09109	−0.853051	−0.426526	−	0.904476i	$-0.640263\pi$
$23$	−4.09109	−0.853051	−0.426526	+	0.904476i	$0.640263\pi$
$24$	6.16431	1.25829
$25$	−2.32683	−0.465366
$26$	2.21209	0.433827
$27$	5.65301	1.08792
$28$	−15.3051	−2.89240
$29$	−2.59173	−0.481272	−0.240636	−	0.970615i	$-0.577356\pi$
$29$	−2.59173	−0.481272	−0.240636	+	0.970615i	$0.577356\pi$
$30$	5.46956	0.998600
$31$	8.51302	1.52898	0.764492	−	0.644633i	$-0.222990\pi$
$31$	8.51302	1.52898	0.764492	+	0.644633i	$0.222990\pi$
$32$	1.46140	0.258342
$33$	−5.22038	−0.908751
$34$	−7.19513	−1.23395
$35$	−6.51206	−1.10074
$36$	−4.16762	−0.694604
$37$	−1.46789	−0.241319	−0.120660	−	0.992694i	$-0.538501\pi$
$37$	−1.46789	−0.241319	−0.120660	+	0.992694i	$0.538501\pi$
$38$	−13.9936	−2.27006
$39$	1.26658	0.202815
$40$	−7.28223	−1.15142
$41$	2.34134	0.365656	0.182828	−	0.983145i	$-0.441475\pi$
$41$	2.34134	0.365656	0.182828	+	0.983145i	$0.441475\pi$
$42$	−13.3243	−2.05598
$43$	−11.1388	−1.69865	−0.849327	−	0.527867i	$-0.822992\pi$
$43$	−11.1388	−1.69865	−0.849327	+	0.527867i	$0.822992\pi$
$44$	14.4944	2.18511
$45$	−1.77325	−0.264340
$46$	9.88882	1.45803
$47$	−12.8765	−1.87822	−0.939112	−	0.343610i	$-0.888350\pi$
$47$	−12.8765	−1.87822	−0.939112	+	0.343610i	$0.888350\pi$
$48$	−4.26370	−0.615413
$49$	8.86389	1.26627
$50$	5.62432	0.795398
$51$	−4.11971	−0.576875
$52$	−3.51666	−0.487673
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−13.6642	−1.85947
$55$	6.16711	0.831573
$56$	17.7401	2.37062
$57$	−8.01229	−1.06125
$58$	6.26462	0.822585
$59$	−9.03203	−1.17587	−0.587935	−	0.808908i	$-0.700059\pi$
$59$	−9.03203	−1.17587	−0.587935	+	0.808908i	$0.700059\pi$
$60$	−8.69519	−1.12254
$61$	1.34872	0.172686	0.0863431	−	0.996265i	$-0.472482\pi$
$61$	1.34872	0.172686	0.0863431	+	0.996265i	$0.472482\pi$
$62$	−20.5773	−2.61332
$63$	4.31977	0.544240
$64$	−9.69391	−1.21174
$65$	−1.49628	−0.185590
$66$	12.6185	1.55323
$67$	4.57214	0.558575	0.279288	−	0.960207i	$-0.409902\pi$
$67$	4.57214	0.558575	0.279288	+	0.960207i	$0.409902\pi$
$68$	11.4384	1.38711
$69$	5.66203	0.681629
$70$	15.7407	1.88137
$71$	3.64013	0.432003	0.216002	−	0.976393i	$-0.430698\pi$
$71$	3.64013	0.432003	0.216002	+	0.976393i	$0.430698\pi$
$72$	4.83067	0.569300
$73$	−5.63539	−0.659573	−0.329786	−	0.944056i	$-0.606977\pi$
$73$	−5.63539	−0.659573	−0.329786	+	0.944056i	$0.606977\pi$
$74$	3.54812	0.412460
$75$	3.22031	0.371850
$76$	22.2462	2.55181
$77$	−15.0236	−1.71209
$78$	−3.06152	−0.346649
$79$	15.6324	1.75878	0.879389	−	0.476104i	$-0.157951\pi$
$79$	15.6324	1.75878	0.879389	+	0.476104i	$0.157951\pi$
$80$	5.03694	0.563147
$81$	−4.57002	−0.507780
$82$	−5.65939	−0.624975
$83$	−4.47647	−0.491357	−0.245678	−	0.969351i	$-0.579011\pi$
$83$	−4.47647	−0.491357	−0.245678	+	0.969351i	$0.579011\pi$
$84$	21.1822	2.31116
$85$	4.86684	0.527882
$86$	26.9243	2.90332
$87$	3.58693	0.384559
$88$	−16.8004	−1.79093
$89$	6.18881	0.656013	0.328006	−	0.944676i	$-0.393623\pi$
$89$	6.18881	0.656013	0.328006	+	0.944676i	$0.393623\pi$
$90$	4.28622	0.451808
$91$	3.64505	0.382105
$92$	−15.7207	−1.63899
$93$	−11.7820	−1.22173
$94$	31.1245	3.21024
$95$	9.46535	0.971124
$96$	−2.02257	−0.206428
$97$	7.86088	0.798151	0.399076	−	0.916918i	$-0.369331\pi$
$97$	7.86088	0.798151	0.399076	+	0.916918i	$0.369331\pi$
$98$	−21.4254	−2.16430
$99$	−4.09095	−0.411156
$100$	−8.94122	−0.894122
$101$	−0.368282	−0.0366455	−0.0183227	−	0.999832i	$-0.505833\pi$
$101$	−0.368282	−0.0366455	−0.0183227	+	0.999832i	$0.505833\pi$
$102$	9.95800	0.985989
$103$	6.21988	0.612862	0.306431	−	0.951893i	$-0.400865\pi$
$103$	6.21988	0.612862	0.306431	+	0.951893i	$0.400865\pi$
$104$	4.07614	0.399699
$105$	9.01263	0.879543
$106$	2.41716	0.234775
$107$	0.700217	0.0676926	0.0338463	−	0.999427i	$-0.489224\pi$
$107$	0.700217	0.0676926	0.0338463	+	0.999427i	$0.489224\pi$
$108$	21.7226	2.09026
$109$	2.42746	0.232509	0.116254	−	0.993219i	$-0.462911\pi$
$109$	2.42746	0.232509	0.116254	+	0.993219i	$0.462911\pi$
$110$	−14.9069	−1.42132
$111$	2.03154	0.192826
$112$	−12.2704	−1.15944
$113$	7.25651	0.682635	0.341318	−	0.939948i	$-0.389127\pi$
$113$	7.25651	0.682635	0.341318	+	0.939948i	$0.389127\pi$
$114$	19.3670	1.81388
$115$	−6.68886	−0.623740
$116$	−9.95914	−0.924683
$117$	0.992555	0.0917617
$118$	21.8319	2.00979
$119$	−11.8560	−1.08684
$120$	10.0786	0.920042
$121$	3.22775	0.293432
$122$	−3.26008	−0.295154
$123$	−3.24039	−0.292176
$124$	32.7127	2.93768
$125$	−11.9792	−1.07146
$126$	−10.4416	−0.930210
$127$	−13.3065	−1.18076	−0.590381	−	0.807125i	$-0.701022\pi$
$127$	−13.3065	−1.18076	−0.590381	+	0.807125i	$0.701022\pi$
$128$	20.5089	1.81275
$129$	15.4160	1.35731
$130$	3.61674	0.317209
$131$	−3.05257	−0.266704	−0.133352	−	0.991069i	$-0.542574\pi$
$131$	−3.05257	−0.266704	−0.133352	+	0.991069i	$0.542574\pi$
$132$	−20.0601	−1.74601
$133$	−23.0583	−1.99941
$134$	−11.0516	−0.954712
$135$	9.24257	0.795474
$136$	−13.2582	−1.13688
$137$	4.02836	0.344166	0.172083	−	0.985082i	$-0.444950\pi$
$137$	4.02836	0.344166	0.172083	+	0.985082i	$0.444950\pi$
$138$	−13.6860	−1.16503
$139$	−8.78329	−0.744989	−0.372495	−	0.928034i	$-0.621497\pi$
$139$	−8.78329	−0.744989	−0.372495	+	0.928034i	$0.621497\pi$
$140$	−25.0236	−2.11488
$141$	17.8209	1.50079
$142$	−8.79876	−0.738376
$143$	−3.45197	−0.288668
$144$	−3.34125	−0.278438
$145$	−4.23743	−0.351900
$146$	13.6216	1.12734
$147$	−12.2675	−1.01181
$148$	−5.64059	−0.463654
$149$	−10.7964	−0.884478	−0.442239	−	0.896897i	$-0.645816\pi$
$149$	−10.7964	−0.884478	−0.442239	+	0.896897i	$0.645816\pi$
$150$	−7.78401	−0.635562
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−25.7854	−2.09147
$153$	−3.22842	−0.261002
$154$	36.3144	2.92629
$155$	13.9186	1.11797
$156$	4.86703	0.389674
$157$	22.4632	1.79276	0.896379	−	0.443289i	$-0.146188\pi$
$157$	22.4632	1.79276	0.896379	+	0.443289i	$0.146188\pi$
$158$	−37.7859	−3.00609
$159$	1.38399	0.109758
$160$	2.38937	0.188896
$161$	16.2946	1.28419
$162$	11.0465	0.867892
$163$	−6.05993	−0.474650	−0.237325	−	0.971430i	$-0.576271\pi$
$163$	−6.05993	−0.474650	−0.237325	+	0.971430i	$0.576271\pi$
$164$	8.99697	0.702546
$165$	−8.53523	−0.664467
$166$	10.8203	0.839822
$167$	25.7728	1.99436	0.997181	−	0.0750270i	$-0.0239043\pi$
$167$	25.7728	1.99436	0.997181	+	0.0750270i	$0.0239043\pi$
$168$	−24.5521	−1.89424
$169$	−12.1625	−0.935575
$170$	−11.7639	−0.902251
$171$	−6.27884	−0.480155
$172$	−42.8027	−3.26368
$173$	−4.00816	−0.304735	−0.152368	−	0.988324i	$-0.548690\pi$
$173$	−4.00816	−0.304735	−0.152368	+	0.988324i	$0.548690\pi$
$174$	−8.67019	−0.657285
$175$	9.26764	0.700568
$176$	11.6204	0.875922
$177$	12.5003	0.939577
$178$	−14.9593	−1.12125
$179$	−3.22255	−0.240865	−0.120432	−	0.992722i	$-0.538428\pi$
$179$	−3.22255	−0.240865	−0.120432	+	0.992722i	$0.538428\pi$
$180$	−6.81399	−0.507885
$181$	−5.83918	−0.434023	−0.217012	−	0.976169i	$-0.569631\pi$
$181$	−5.83918	−0.434023	−0.217012	+	0.976169i	$0.569631\pi$
$182$	−8.81066	−0.653090
$183$	−1.86662	−0.137985
$184$	18.2218	1.34333
$185$	−2.39997	−0.176449
$186$	28.4789	2.08817
$187$	11.2280	0.821071
$188$	−49.4799	−3.60869
$189$	−22.5156	−1.63777
$190$	−22.8793	−1.65984
$191$	9.71456	0.702921	0.351460	−	0.936203i	$-0.385685\pi$
$191$	9.71456	0.702921	0.351460	+	0.936203i	$0.385685\pi$
$192$	13.4163	0.968237
$193$	10.6698	0.768028	0.384014	−	0.923327i	$-0.374541\pi$
$193$	10.6698	0.768028	0.384014	+	0.923327i	$0.374541\pi$
$194$	−19.0010	−1.36419
$195$	2.07083	0.148295
$196$	34.0609	2.43292
$197$	−16.3821	−1.16717	−0.583587	−	0.812051i	$-0.698351\pi$
$197$	−16.3821	−1.16717	−0.583587	+	0.812051i	$0.698351\pi$
$198$	9.88848	0.702744
$199$	2.20043	0.155984	0.0779921	−	0.996954i	$-0.475149\pi$
$199$	2.20043	0.155984	0.0779921	+	0.996954i	$0.475149\pi$
$200$	10.3637	0.732825
$201$	−6.32780	−0.446329
$202$	0.890198	0.0626341
$203$	10.3227	0.724513
$204$	−15.8307	−1.10837
$205$	3.82805	0.267363
$206$	−15.0344	−1.04750
$207$	4.43706	0.308397
$208$	−2.81937	−0.195488
$209$	21.8369	1.51049
$210$	−21.7850	−1.50331
$211$	−17.4754	−1.20306	−0.601529	−	0.798851i	$-0.705441\pi$
$211$	−17.4754	−1.20306	−0.601529	+	0.798851i	$0.705441\pi$
$212$	−3.84266	−0.263915
$213$	−5.03790	−0.345191
$214$	−1.69254	−0.115699
$215$	−18.2118	−1.24203
$216$	−25.1785	−1.71318
$217$	−33.9069	−2.30175
$218$	−5.86757	−0.397402
$219$	7.79934	0.527030
$220$	23.6981	1.59773
$221$	−2.72415	−0.183246
$222$	−4.91056	−0.329575
$223$	8.61755	0.577074	0.288537	−	0.957469i	$-0.406831\pi$
$223$	8.61755	0.577074	0.288537	+	0.957469i	$0.406831\pi$
$224$	−5.82070	−0.388912
$225$	2.52360	0.168240
$226$	−17.5401	−1.16675
$227$	22.0292	1.46213	0.731065	−	0.682307i	$-0.239023\pi$
$227$	22.0292	1.46213	0.731065	+	0.682307i	$0.239023\pi$
$228$	−30.7885	−2.03902
$229$	7.83327	0.517637	0.258818	−	0.965926i	$-0.416667\pi$
$229$	7.83327	0.517637	0.258818	+	0.965926i	$0.416667\pi$
$230$	16.1681	1.06609
$231$	20.7925	1.36805
$232$	11.5436	0.757873
$233$	−9.62780	−0.630738	−0.315369	−	0.948969i	$-0.602128\pi$
$233$	−9.62780	−0.630738	−0.315369	+	0.948969i	$0.602128\pi$
$234$	−2.39916	−0.156838
$235$	−21.0528	−1.37333
$236$	−34.7070	−2.25924
$237$	−21.6351	−1.40535
$238$	28.6578	1.85761
$239$	−9.11876	−0.589844	−0.294922	−	0.955521i	$-0.595294\pi$
$239$	−9.11876	−0.589844	−0.294922	+	0.955521i	$0.595294\pi$
$240$	−6.97109	−0.449982
$241$	6.53291	0.420822	0.210411	−	0.977613i	$-0.432520\pi$
$241$	6.53291	0.420822	0.210411	+	0.977613i	$0.432520\pi$
$242$	−7.80200	−0.501531
$243$	−10.6342	−0.682181
$244$	5.18269	0.331788
$245$	14.4923	0.925880
$246$	7.83255	0.499385
$247$	−5.29811	−0.337111
$248$	−37.9171	−2.40774
$249$	6.19540	0.392618
$250$	28.9558	1.83132
$251$	17.3455	1.09484	0.547420	−	0.836858i	$-0.315610\pi$
$251$	17.3455	1.09484	0.547420	+	0.836858i	$0.315610\pi$
$252$	16.5994	1.04567
$253$	−15.4315	−0.970168
$254$	32.1639	2.01815
$255$	−6.73566	−0.421803
$256$	−30.1855	−1.88659
$257$	−5.01817	−0.313025	−0.156512	−	0.987676i	$-0.550025\pi$
$257$	−5.01817	−0.313025	−0.156512	+	0.987676i	$0.550025\pi$
$258$	−37.2630	−2.31989
$259$	5.84652	0.363285
$260$	−5.74968	−0.356580
$261$	2.81090	0.173990
$262$	7.37855	0.455848
$263$	25.2743	1.55848	0.779241	−	0.626724i	$-0.215605\pi$
$263$	25.2743	1.55848	0.779241	+	0.626724i	$0.215605\pi$
$264$	23.2516	1.43104
$265$	−1.63498	−0.100436
$266$	55.7357	3.41737
$267$	−8.56526	−0.524186
$268$	17.5692	1.07321
$269$	−12.5595	−0.765766	−0.382883	−	0.923797i	$-0.625069\pi$
$269$	−12.5595	−0.765766	−0.382883	+	0.923797i	$0.625069\pi$
$270$	−22.3408	−1.35962
$271$	−3.00930	−0.182802	−0.0914011	−	0.995814i	$-0.529135\pi$
$271$	−3.00930	−0.182802	−0.0914011	+	0.995814i	$0.529135\pi$
$272$	9.17037	0.556035
$273$	−5.04472	−0.305320
$274$	−9.73718	−0.588245
$275$	−8.77673	−0.529256
$276$	21.7573	1.30963
$277$	−25.0390	−1.50445	−0.752225	−	0.658906i	$-0.771019\pi$
$277$	−25.0390	−1.50445	−0.752225	+	0.658906i	$0.771019\pi$
$278$	21.2306	1.27333
$279$	−9.23293	−0.552761
$280$	29.0048	1.73337
$281$	4.59917	0.274364	0.137182	−	0.990546i	$-0.456196\pi$
$281$	4.59917	0.274364	0.137182	+	0.990546i	$0.456196\pi$
$282$	−43.0760	−2.56514
$283$	28.6117	1.70079	0.850395	−	0.526145i	$-0.176363\pi$
$283$	28.6117	1.70079	0.850395	+	0.526145i	$0.176363\pi$
$284$	13.9878	0.830022
$285$	−13.1000	−0.775975
$286$	8.34395	0.493388
$287$	−9.32543	−0.550463
$288$	−1.58499	−0.0933964
$289$	−8.13933	−0.478784
$290$	10.2426	0.601464
$291$	−10.8794	−0.637761
$292$	−21.6549	−1.26726
$293$	−3.64687	−0.213052	−0.106526	−	0.994310i	$-0.533973\pi$
$293$	−3.64687	−0.213052	−0.106526	+	0.994310i	$0.533973\pi$
$294$	29.6526	1.72938
$295$	−14.7672	−0.859781
$296$	6.53798	0.380012
$297$	21.3230	1.23728
$298$	26.0967	1.51174
$299$	3.74401	0.216522
$300$	12.3746	0.714446
$301$	44.3654	2.55718
$302$	2.41716	0.139092
$303$	0.509700	0.0292815
$304$	17.8351	1.02292
$305$	2.20514	0.126266
$306$	7.80360	0.446102
$307$	−3.22369	−0.183986	−0.0919929	−	0.995760i	$-0.529324\pi$
$307$	−3.22369	−0.183986	−0.0919929	+	0.995760i	$0.529324\pi$
$308$	−57.7305	−3.28950
$309$	−8.60826	−0.489707
$310$	−33.6436	−1.91083
$311$	−13.5724	−0.769621	−0.384811	−	0.922996i	$-0.625733\pi$
$311$	−13.5724	−0.769621	−0.384811	+	0.922996i	$0.625733\pi$
$312$	−5.64135	−0.319379
$313$	−13.3008	−0.751807	−0.375904	−	0.926659i	$-0.622668\pi$
$313$	−13.3008	−0.751807	−0.375904	+	0.926659i	$0.622668\pi$
$314$	−54.2971	−3.06416
$315$	7.06276	0.397941
$316$	60.0699	3.37919
$317$	15.9615	0.896488	0.448244	−	0.893911i	$-0.352050\pi$
$317$	15.9615	0.896488	0.448244	+	0.893911i	$0.352050\pi$
$318$	−3.34533	−0.187597
$319$	−9.77592	−0.547346
$320$	−15.8494	−0.886007
$321$	−0.969095	−0.0540896
$322$	−39.3867	−2.19493
$323$	17.2328	0.958860
$324$	−17.5610	−0.975613
$325$	2.12943	0.118119
$326$	14.6478	0.811267
$327$	−3.35959	−0.185786
$328$	−10.4283	−0.575809
$329$	51.2863	2.82750
$330$	20.6310	1.13570
$331$	−9.78829	−0.538013	−0.269007	−	0.963138i	$-0.586695\pi$
$331$	−9.78829	−0.538013	−0.269007	+	0.963138i	$0.586695\pi$
$332$	−17.2016	−0.944059
$333$	1.59202	0.0872422
$334$	−62.2971	−3.40875
$335$	7.47537	0.408423
$336$	16.9821	0.926450
$337$	−15.9058	−0.866443	−0.433221	−	0.901288i	$-0.642623\pi$
$337$	−15.9058	−0.866443	−0.433221	+	0.901288i	$0.642623\pi$
$338$	29.3987	1.59908
$339$	−10.0430	−0.545458
$340$	18.7016	1.01424
$341$	32.1109	1.73890
$342$	15.1770	0.820676
$343$	−7.42377	−0.400846
$344$	49.6124	2.67492
$345$	9.25733	0.498398
$346$	9.68837	0.520850
$347$	−12.2218	−0.656098	−0.328049	−	0.944661i	$-0.606391\pi$
$347$	−12.2218	−0.656098	−0.328049	+	0.944661i	$0.606391\pi$
$348$	13.7834	0.738866
$349$	19.0876	1.02174	0.510868	−	0.859659i	$-0.329324\pi$
$349$	19.0876	1.02174	0.510868	+	0.859659i	$0.329324\pi$
$350$	−22.4014	−1.19740
$351$	−5.17342	−0.276137
$352$	5.51237	0.293810
$353$	−7.52709	−0.400627	−0.200313	−	0.979732i	$-0.564196\pi$
$353$	−7.52709	−0.400627	−0.200313	+	0.979732i	$0.564196\pi$
$354$	−30.2151	−1.60592
$355$	5.95155	0.315875
$356$	23.7815	1.26042
$357$	16.4086	0.868435
$358$	7.78943	0.411684
$359$	18.9712	1.00126	0.500631	−	0.865661i	$-0.333101\pi$
$359$	18.9712	1.00126	0.500631	+	0.865661i	$0.333101\pi$
$360$	7.89806	0.416265
$361$	14.5155	0.763975
$362$	14.1142	0.741828
$363$	−4.46719	−0.234466
$364$	14.0067	0.734150
$365$	−9.21378	−0.482271
$366$	4.51192	0.235842
$367$	−9.85226	−0.514284	−0.257142	−	0.966374i	$-0.582781\pi$
$367$	−9.85226	−0.514284	−0.257142	+	0.966374i	$0.582781\pi$
$368$	−12.6035	−0.657005
$369$	−2.53934	−0.132193
$370$	5.80111	0.301585
$371$	3.98295	0.206784
$372$	−45.2741	−2.34735
$373$	9.68880	0.501667	0.250833	−	0.968030i	$-0.419295\pi$
$373$	9.68880	0.501667	0.250833	+	0.968030i	$0.419295\pi$
$374$	−27.1398	−1.40337
$375$	16.5792	0.856145
$376$	57.3519	2.95770
$377$	2.37185	0.122157
$378$	54.4239	2.79926
$379$	15.7389	0.808454	0.404227	−	0.914659i	$-0.367541\pi$
$379$	15.7389	0.808454	0.404227	+	0.914659i	$0.367541\pi$
$380$	36.3721	1.86585
$381$	18.4161	0.943485
$382$	−23.4816	−1.20143
$383$	11.3510	0.580011	0.290006	−	0.957025i	$-0.406343\pi$
$383$	11.3510	0.580011	0.290006	+	0.957025i	$0.406343\pi$
$384$	−28.3842	−1.44847
$385$	−24.5633	−1.25186
$386$	−25.7906	−1.31271
$387$	12.0808	0.614101
$388$	30.2067	1.53351
$389$	−14.6443	−0.742497	−0.371248	−	0.928534i	$-0.621070\pi$
$389$	−14.6443	−0.742497	−0.371248	+	0.928534i	$0.621070\pi$
$390$	−5.00554	−0.253465
$391$	−12.1779	−0.615863
$392$	−39.4798	−1.99403
$393$	4.22473	0.213110
$394$	39.5981	1.99492
$395$	25.5587	1.28600
$396$	−15.7201	−0.789967
$397$	14.9090	0.748259	0.374130	−	0.927376i	$-0.377942\pi$
$397$	14.9090	0.748259	0.374130	+	0.927376i	$0.377942\pi$
$398$	−5.31878	−0.266607
$399$	31.9125	1.59763
$400$	−7.16833	−0.358416
$401$	1.59608	0.0797046	0.0398523	−	0.999206i	$-0.487311\pi$
$401$	1.59608	0.0797046	0.0398523	+	0.999206i	$0.487311\pi$
$402$	15.2953	0.762861
$403$	−7.79080	−0.388087
$404$	−1.41519	−0.0704081
$405$	−7.47190	−0.371282
$406$	−24.9517	−1.23833
$407$	−5.53682	−0.274450
$408$	18.3492	0.908423
$409$	−24.0325	−1.18833	−0.594165	−	0.804343i	$-0.702517\pi$
$409$	−24.0325	−1.18833	−0.594165	+	0.804343i	$0.702517\pi$
$410$	−9.25301	−0.456974
$411$	−5.57521	−0.275005
$412$	23.9009	1.17751
$413$	35.9741	1.77017
$414$	−10.7251	−0.527109
$415$	−7.31896	−0.359274
$416$	−1.33742	−0.0655725
$417$	12.1560	0.595282
$418$	−52.7833	−2.58172
$419$	−3.90937	−0.190985	−0.0954926	−	0.995430i	$-0.530443\pi$
$419$	−3.90937	−0.190985	−0.0954926	+	0.995430i	$0.530443\pi$
$420$	34.6325	1.68989
$421$	−26.7436	−1.30340	−0.651702	−	0.758475i	$-0.725945\pi$
$421$	−26.7436	−1.30340	−0.651702	+	0.758475i	$0.725945\pi$
$422$	42.2409	2.05625
$423$	13.9654	0.679020
$424$	4.45401	0.216306
$425$	−6.92624	−0.335972
$426$	12.1774	0.589998
$427$	−5.37190	−0.259964
$428$	2.69070	0.130060
$429$	4.77749	0.230660
$430$	44.0208	2.12287
$431$	19.9942	0.963085	0.481542	−	0.876423i	$-0.340077\pi$
$431$	19.9942	0.963085	0.481542	+	0.876423i	$0.340077\pi$
$432$	17.4154	0.837898
$433$	−21.6850	−1.04212	−0.521058	−	0.853521i	$-0.674462\pi$
$433$	−21.6850	−1.04212	−0.521058	+	0.853521i	$0.674462\pi$
$434$	81.9585	3.93413
$435$	5.86457	0.281185
$436$	9.32792	0.446727
$437$	−23.6844	−1.13298
$438$	−18.8522	−0.900795
$439$	8.46045	0.403795	0.201898	−	0.979407i	$-0.435289\pi$
$439$	8.46045	0.403795	0.201898	+	0.979407i	$0.435289\pi$
$440$	−27.4684	−1.30950
$441$	−9.61347	−0.457784
$442$	6.58471	0.313203
$443$	8.06860	0.383351	0.191675	−	0.981458i	$-0.438608\pi$
$443$	8.06860	0.383351	0.191675	+	0.981458i	$0.438608\pi$
$444$	7.80653	0.370482
$445$	10.1186	0.479668
$446$	−20.8300	−0.986329
$447$	14.9422	0.706741
$448$	38.6103	1.82417
$449$	25.3021	1.19408	0.597040	−	0.802212i	$-0.296344\pi$
$449$	25.3021	1.19408	0.597040	+	0.802212i	$0.296344\pi$
$450$	−6.09994	−0.287554
$451$	8.83146	0.415857
$452$	27.8843	1.31157
$453$	1.38399	0.0650256
$454$	−53.2482	−2.49906
$455$	5.95959	0.279390
$456$	35.6868	1.67119
$457$	8.51913	0.398508	0.199254	−	0.979948i	$-0.436148\pi$
$457$	8.51913	0.398508	0.199254	+	0.979948i	$0.436148\pi$
$458$	−18.9343	−0.884740
$459$	16.8272	0.785428
$460$	−25.7030	−1.19841
$461$	8.48556	0.395212	0.197606	−	0.980282i	$-0.436683\pi$
$461$	8.48556	0.395212	0.197606	+	0.980282i	$0.436683\pi$
$462$	−50.2588	−2.33825
$463$	5.16705	0.240133	0.120067	−	0.992766i	$-0.461689\pi$
$463$	5.16705	0.240133	0.120067	+	0.992766i	$0.461689\pi$
$464$	−7.98441	−0.370667
$465$	−19.2633	−0.893314
$466$	23.2719	1.07805
$467$	31.6688	1.46546	0.732728	−	0.680522i	$-0.238247\pi$
$467$	31.6688	1.46546	0.732728	+	0.680522i	$0.238247\pi$
$468$	3.81405	0.176305
$469$	−18.2106	−0.840887
$470$	50.8880	2.34729
$471$	−31.0889	−1.43250
$472$	40.2287	1.85168
$473$	−42.0153	−1.93186
$474$	52.2954	2.40201
$475$	−13.4706	−0.618074
$476$	−45.5586	−2.08817
$477$	1.08457	0.0496589
$478$	22.0415	1.00816
$479$	8.84548	0.404160	0.202080	−	0.979369i	$-0.435230\pi$
$479$	8.84548	0.404160	0.202080	+	0.979369i	$0.435230\pi$
$480$	−3.30687	−0.150937
$481$	1.34335	0.0612517
$482$	−15.7911	−0.719264
$483$	−22.5516	−1.02613
$484$	12.4032	0.563780
$485$	12.8524	0.583598
$486$	25.7045	1.16598
$487$	−13.7042	−0.620995	−0.310497	−	0.950574i	$-0.600496\pi$
$487$	−13.7042	−0.620995	−0.310497	+	0.950574i	$0.600496\pi$
$488$	−6.00722	−0.271934
$489$	8.38689	0.379268
$490$	−35.0302	−1.58250
$491$	−38.3817	−1.73214	−0.866071	−	0.499920i	$-0.833363\pi$
$491$	−38.3817	−1.73214	−0.866071	+	0.499920i	$0.833363\pi$
$492$	−12.4517	−0.561368
$493$	−7.71477	−0.347456
$494$	12.8064	0.576187
$495$	−6.68864	−0.300632
$496$	26.2263	1.17760
$497$	−14.4984	−0.650344
$498$	−14.9753	−0.671058
$499$	−36.7846	−1.64671	−0.823353	−	0.567529i	$-0.807899\pi$
$499$	−36.7846	−1.64671	−0.823353	+	0.567529i	$0.807899\pi$
$500$	−46.0322	−2.05862
$501$	−35.6694	−1.59359
$502$	−41.9269	−1.87129
$503$	−5.91854	−0.263895	−0.131947	−	0.991257i	$-0.542123\pi$
$503$	−5.91854	−0.263895	−0.131947	+	0.991257i	$0.542123\pi$
$504$	−19.2403	−0.857031
$505$	−0.602136	−0.0267947
$506$	37.3003	1.65820
$507$	16.8328	0.747570
$508$	−51.1324	−2.26863
$509$	0.239785	0.0106283	0.00531414	−	0.999986i	$-0.498308\pi$
$509$	0.239785	0.0106283	0.00531414	+	0.999986i	$0.498308\pi$
$510$	16.2812	0.720942
$511$	22.4455	0.992930
$512$	31.9454	1.41180
$513$	32.7267	1.44492
$514$	12.1297	0.535019
$515$	10.1694	0.448117
$516$	59.2386	2.60783
$517$	−48.5696	−2.13609
$518$	−14.1320	−0.620923
$519$	5.54727	0.243498
$520$	6.66443	0.292254
$521$	3.17983	0.139311	0.0696555	−	0.997571i	$-0.477810\pi$
$521$	3.17983	0.139311	0.0696555	+	0.997571i	$0.477810\pi$
$522$	−6.79440	−0.297383
$523$	−31.4780	−1.37643	−0.688217	−	0.725505i	$-0.741606\pi$
$523$	−31.4780	−1.37643	−0.688217	+	0.725505i	$0.741606\pi$
$524$	−11.7300	−0.512427
$525$	−12.8263	−0.559787
$526$	−61.0921	−2.66374
$527$	25.3406	1.10385
$528$	−16.0826	−0.699904
$529$	−6.26299	−0.272304
$530$	3.95202	0.171665
$531$	9.79583	0.425103
$532$	−88.6054	−3.84153
$533$	−2.14271	−0.0928109
$534$	20.7036	0.895933
$535$	1.14484	0.0494959
$536$	−20.3643	−0.879606
$537$	4.45999	0.192463
$538$	30.3583	1.30884
$539$	33.4343	1.44012
$540$	35.5161	1.52837
$541$	2.14069	0.0920354	0.0460177	−	0.998941i	$-0.485347\pi$
$541$	2.14069	0.0920354	0.0460177	+	0.998941i	$0.485347\pi$
$542$	7.27397	0.312444
$543$	8.08138	0.346805
$544$	4.35014	0.186511
$545$	3.96886	0.170007
$546$	12.1939	0.521850
$547$	−28.0229	−1.19817	−0.599086	−	0.800685i	$-0.704469\pi$
$547$	−28.0229	−1.19817	−0.599086	+	0.800685i	$0.704469\pi$
$548$	15.4796	0.661257
$549$	−1.46278	−0.0624299
$550$	21.2148	0.904600
$551$	−15.0042	−0.639200
$552$	−25.2188	−1.07338
$553$	−62.2629	−2.64769
$554$	60.5234	2.57139
$555$	3.32154	0.140991
$556$	−33.7512	−1.43137
$557$	−29.5015	−1.25002	−0.625010	−	0.780617i	$-0.714905\pi$
$557$	−29.5015	−1.25002	−0.625010	+	0.780617i	$0.714905\pi$
$558$	22.3175	0.944774
$559$	10.1938	0.431153
$560$	−20.0619	−0.847769
$561$	−15.5394	−0.656075
$562$	−11.1169	−0.468940
$563$	7.90008	0.332949	0.166474	−	0.986046i	$-0.446762\pi$
$563$	7.90008	0.332949	0.166474	+	0.986046i	$0.446762\pi$
$564$	68.4798	2.88352
$565$	11.8643	0.499134
$566$	−69.1591	−2.90697
$567$	18.2021	0.764418
$568$	−16.2132	−0.680289
$569$	−20.1934	−0.846553	−0.423276	−	0.906001i	$-0.639120\pi$
$569$	−20.1934	−0.846553	−0.423276	+	0.906001i	$0.639120\pi$
$570$	31.6647	1.32629
$571$	−5.92942	−0.248139	−0.124069	−	0.992274i	$-0.539595\pi$
$571$	−5.92942	−0.248139	−0.124069	+	0.992274i	$0.539595\pi$
$572$	−13.2647	−0.554627
$573$	−13.4449	−0.561668
$574$	22.5411	0.940846
$575$	9.51926	0.396981
$576$	10.5137	0.438070
$577$	−27.0196	−1.12484	−0.562421	−	0.826851i	$-0.690130\pi$
$577$	−27.0196	−1.12484	−0.562421	+	0.826851i	$0.690130\pi$
$578$	19.6741	0.818333
$579$	−14.7669	−0.613692
$580$	−16.2830	−0.676116
$581$	17.8296	0.739695
$582$	26.2972	1.09006
$583$	−3.77197	−0.156219
$584$	25.1001	1.03865
$585$	1.62281	0.0670950
$586$	8.81506	0.364147
$587$	43.3296	1.78840	0.894201	−	0.447665i	$-0.147744\pi$
$587$	43.3296	1.78840	0.894201	+	0.447665i	$0.147744\pi$
$588$	−47.1400	−1.94402
$589$	49.2841	2.03072
$590$	35.6947	1.46953
$591$	22.6727	0.932628
$592$	−4.52216	−0.185860
$593$	−3.21606	−0.132068	−0.0660338	−	0.997817i	$-0.521035\pi$
$593$	−3.21606	−0.132068	−0.0660338	+	0.997817i	$0.521035\pi$
$594$	−51.5410	−2.11475
$595$	−19.3844	−0.794681
$596$	−41.4871	−1.69938
$597$	−3.04537	−0.124639
$598$	−9.04988	−0.370077
$599$	18.8454	0.770000	0.385000	−	0.922916i	$-0.374201\pi$
$599$	18.8454	0.770000	0.385000	+	0.922916i	$0.374201\pi$
$600$	−14.3433	−0.585563
$601$	−13.3998	−0.546590	−0.273295	−	0.961930i	$-0.588114\pi$
$601$	−13.3998	−0.546590	−0.273295	+	0.961930i	$0.588114\pi$
$602$	−107.238	−4.37070
$603$	−4.95879	−0.201937
$604$	−3.84266	−0.156356
$605$	5.27732	0.214554
$606$	−1.23203	−0.0500476
$607$	45.9041	1.86319	0.931594	−	0.363500i	$-0.118418\pi$
$607$	45.9041	1.86319	0.931594	+	0.363500i	$0.118418\pi$
$608$	8.46045	0.343117
$609$	−14.2866	−0.578921
$610$	−5.33018	−0.215813
$611$	11.7841	0.476732
$612$	−12.4057	−0.501471
$613$	31.4026	1.26834	0.634169	−	0.773195i	$-0.281342\pi$
$613$	31.4026	1.26834	0.634169	+	0.773195i	$0.281342\pi$
$614$	7.79218	0.314467
$615$	−5.29799	−0.213636
$616$	66.9151	2.69609
$617$	14.5913	0.587423	0.293711	−	0.955894i	$-0.405110\pi$
$617$	14.5913	0.587423	0.293711	+	0.955894i	$0.405110\pi$
$618$	20.8075	0.837002
$619$	2.31345	0.0929854	0.0464927	−	0.998919i	$-0.485196\pi$
$619$	2.31345	0.0929854	0.0464927	+	0.998919i	$0.485196\pi$
$620$	53.4847	2.14800
$621$	−23.1270	−0.928053
$622$	32.8067	1.31543
$623$	−24.6497	−0.987570
$624$	3.90198	0.156204
$625$	−7.95173	−0.318069
$626$	32.1502	1.28498
$627$	−30.2221	−1.20695
$628$	86.3185	3.44448
$629$	−4.36944	−0.174221
$630$	−17.0718	−0.680157
$631$	−28.4395	−1.13216	−0.566080	−	0.824350i	$-0.691541\pi$
$631$	−28.4395	−1.13216	−0.566080	+	0.824350i	$0.691541\pi$
$632$	−69.6267	−2.76960
$633$	24.1858	0.961301
$634$	−38.5816	−1.53227
$635$	−21.7559	−0.863357
$636$	5.31821	0.210881
$637$	−8.11190	−0.321405
$638$	23.6300	0.935519
$639$	−3.94796	−0.156179
$640$	33.5317	1.32546
$641$	−46.8720	−1.85133	−0.925667	−	0.378340i	$-0.876495\pi$
$641$	−46.8720	−1.85133	−0.925667	+	0.378340i	$0.876495\pi$
$642$	2.34246	0.0924494
$643$	−23.4527	−0.924886	−0.462443	−	0.886649i	$-0.653027\pi$
$643$	−23.4527	−0.924886	−0.462443	+	0.886649i	$0.653027\pi$
$644$	62.6147	2.46736
$645$	25.2050	0.992445
$646$	−41.6545	−1.63887
$647$	29.5807	1.16294	0.581468	−	0.813569i	$-0.302479\pi$
$647$	29.5807	1.16294	0.581468	+	0.813569i	$0.302479\pi$
$648$	20.3549	0.799616
$649$	−34.0685	−1.33731
$650$	−5.14716	−0.201888
$651$	46.9269	1.83921
$652$	−23.2862	−0.911960
$653$	−8.87991	−0.347498	−0.173749	−	0.984790i	$-0.555588\pi$
$653$	−8.87991	−0.347498	−0.173749	+	0.984790i	$0.555588\pi$
$654$	8.12067	0.317543
$655$	−4.99090	−0.195011
$656$	7.21303	0.281621
$657$	6.11196	0.238450
$658$	−123.967	−4.83274
$659$	20.5142	0.799118	0.399559	−	0.916707i	$-0.369163\pi$
$659$	20.5142	0.799118	0.399559	+	0.916707i	$0.369163\pi$
$660$	−32.7980	−1.27666
$661$	26.8031	1.04252	0.521260	−	0.853398i	$-0.325462\pi$
$661$	26.8031	1.04252	0.521260	+	0.853398i	$0.325462\pi$
$662$	23.6599	0.919567
$663$	3.77021	0.146423
$664$	19.9382	0.773754
$665$	−37.7000	−1.46194
$666$	−3.84817	−0.149113
$667$	10.6030	0.410549
$668$	99.0364	3.83183
$669$	−11.9266	−0.461110
$670$	−18.0692	−0.698073
$671$	5.08734	0.196395
$672$	8.05580	0.310759
$673$	−15.8695	−0.611724	−0.305862	−	0.952076i	$-0.598945\pi$
$673$	−15.8695	−0.611724	−0.305862	+	0.952076i	$0.598945\pi$
$674$	38.4468	1.48092
$675$	−13.1536	−0.506281
$676$	−46.7363	−1.79755
$677$	−35.0648	−1.34765	−0.673826	−	0.738890i	$-0.735350\pi$
$677$	−35.0648	−1.34765	−0.673826	+	0.738890i	$0.735350\pi$
$678$	24.2754	0.932292
$679$	−31.3095	−1.20155
$680$	−21.6769	−0.831272
$681$	−30.4883	−1.16831
$682$	−77.6171	−2.97211
$683$	−4.38314	−0.167716	−0.0838581	−	0.996478i	$-0.526724\pi$
$683$	−4.38314	−0.167716	−0.0838581	+	0.996478i	$0.526724\pi$
$684$	−24.1274	−0.922536
$685$	6.58630	0.251650
$686$	17.9444	0.685122
$687$	−10.8412	−0.413617
$688$	−34.3157	−1.30827
$689$	0.915163	0.0348649
$690$	−22.3765	−0.851857
$691$	36.4667	1.38726	0.693630	−	0.720332i	$-0.256010\pi$
$691$	36.4667	1.38726	0.693630	+	0.720332i	$0.256010\pi$
$692$	−15.4020	−0.585497
$693$	16.2941	0.618960
$694$	29.5419	1.12140
$695$	−14.3605	−0.544726
$696$	−15.9762	−0.605577
$697$	6.96943	0.263986
$698$	−46.1378	−1.74634
$699$	13.3248	0.503990
$700$	35.6124	1.34602
$701$	−21.7976	−0.823284	−0.411642	−	0.911346i	$-0.635045\pi$
$701$	−21.7976	−0.823284	−0.411642	+	0.911346i	$0.635045\pi$
$702$	12.5050	0.471970
$703$	−8.49798	−0.320507
$704$	−36.5651	−1.37810
$705$	29.1369	1.09736
$706$	18.1942	0.684747
$707$	1.46685	0.0551666
$708$	48.0343	1.80524
$709$	−16.7299	−0.628303	−0.314151	−	0.949373i	$-0.601720\pi$
$709$	−16.7299	−0.628303	−0.314151	+	0.949373i	$0.601720\pi$
$710$	−14.3858	−0.539891
$711$	−16.9543	−0.635837
$712$	−27.5650	−1.03304
$713$	−34.8275	−1.30430
$714$	−39.6622	−1.48432
$715$	−5.64391	−0.211070
$716$	−12.3832	−0.462781
$717$	12.6203	0.471313
$718$	−45.8564	−1.71135
$719$	−42.8163	−1.59678	−0.798389	−	0.602142i	$-0.794314\pi$
$719$	−42.8163	−1.59678	−0.798389	+	0.602142i	$0.794314\pi$
$720$	−5.46290	−0.203590
$721$	−24.7734	−0.922611
$722$	−35.0864	−1.30578
$723$	−9.04149	−0.336257
$724$	−22.4380	−0.833902
$725$	6.03051	0.223967
$726$	10.7979	0.400748
$727$	−40.7249	−1.51040	−0.755201	−	0.655493i	$-0.772461\pi$
$727$	−40.7249	−1.51040	−0.755201	+	0.655493i	$0.772461\pi$
$728$	−16.2351	−0.601712
$729$	28.4276	1.05288
$730$	22.2712	0.824293
$731$	−33.1568	−1.22635
$732$	−7.17280	−0.265114
$733$	24.4080	0.901529	0.450764	−	0.892643i	$-0.351151\pi$
$733$	24.4080	0.901529	0.450764	+	0.892643i	$0.351151\pi$
$734$	23.8145	0.879009
$735$	−20.0572	−0.739822
$736$	−5.97874	−0.220379
$737$	17.2460	0.635263
$738$	6.13798	0.225942
$739$	−45.2432	−1.66430	−0.832149	−	0.554551i	$-0.812890\pi$
$739$	−45.2432	−1.66430	−0.832149	+	0.554551i	$0.812890\pi$
$740$	−9.22227	−0.339018
$741$	7.33255	0.269368
$742$	−9.62743	−0.353434
$743$	−30.4294	−1.11635	−0.558173	−	0.829725i	$-0.688497\pi$
$743$	−30.4294	−1.11635	−0.558173	+	0.829725i	$0.688497\pi$
$744$	52.4769	1.92390
$745$	−17.6520	−0.646719
$746$	−23.4194	−0.857444
$747$	4.85503	0.177636
$748$	43.1453	1.57755
$749$	−2.78893	−0.101905
$750$	−40.0745	−1.46331
$751$	−49.4718	−1.80525	−0.902627	−	0.430424i	$-0.858364\pi$
$751$	−49.4718	−1.80525	−0.902627	+	0.430424i	$0.858364\pi$
$752$	−39.6689	−1.44658
$753$	−24.0061	−0.874829
$754$	−5.73315	−0.208789
$755$	−1.63498	−0.0595031
$756$	−86.5200	−3.14670
$757$	−16.4969	−0.599589	−0.299794	−	0.954004i	$-0.596918\pi$
$757$	−16.4969	−0.599589	−0.299794	+	0.954004i	$0.596918\pi$
$758$	−38.0435	−1.38180
$759$	21.3570	0.775211
$760$	−42.1587	−1.52926
$761$	36.5717	1.32572	0.662861	−	0.748743i	$-0.269342\pi$
$761$	36.5717	1.32572	0.662861	+	0.748743i	$0.269342\pi$
$762$	−44.5146	−1.61260
$763$	−9.66847	−0.350022
$764$	37.3298	1.35054
$765$	−5.27841	−0.190841
$766$	−27.4373	−0.991350
$767$	8.26578	0.298460
$768$	41.7765	1.50748
$769$	6.05562	0.218371	0.109186	−	0.994021i	$-0.465176\pi$
$769$	6.05562	0.218371	0.109186	+	0.994021i	$0.465176\pi$
$770$	59.3734	2.13967
$771$	6.94510	0.250122
$772$	41.0004	1.47564
$773$	−42.7471	−1.53751	−0.768753	−	0.639546i	$-0.779122\pi$
$773$	−42.7471	−1.53751	−0.768753	+	0.639546i	$0.779122\pi$
$774$	−29.2012	−1.04962
$775$	−19.8083	−0.711537
$776$	−35.0124	−1.25687
$777$	−8.09153	−0.290282
$778$	35.3977	1.26907
$779$	13.5546	0.485645
$780$	7.95752	0.284925
$781$	13.7304	0.491314
$782$	29.4359	1.05263
$783$	−14.6511	−0.523586
$784$	27.3072	0.975258
$785$	36.7270	1.31084
$786$	−10.2119	−0.364245
$787$	20.9093	0.745335	0.372667	−	0.927965i	$-0.378443\pi$
$787$	20.9093	0.745335	0.372667	+	0.927965i	$0.378443\pi$
$788$	−62.9508	−2.24253
$789$	−34.9795	−1.24530
$790$	−61.7793	−2.19801
$791$	−28.9023	−1.02765
$792$	18.2211	0.647460
$793$	−1.23430	−0.0438313
$794$	−36.0373	−1.27892
$795$	2.26280	0.0802534
$796$	8.45550	0.299697
$797$	5.55691	0.196836	0.0984179	−	0.995145i	$-0.468622\pi$
$797$	5.55691	0.196836	0.0984179	+	0.995145i	$0.468622\pi$
$798$	−77.1377	−2.73065
$799$	−38.3292	−1.35599
$800$	−3.40044	−0.120224
$801$	−6.71218	−0.237163
$802$	−3.85799	−0.136230
$803$	−21.2565	−0.750127
$804$	−24.3156	−0.857545
$805$	26.6414	0.938986
$806$	18.8316	0.663315
$807$	17.3822	0.611883
$808$	1.64033	0.0577067
$809$	2.42037	0.0850957	0.0425478	−	0.999094i	$-0.486453\pi$
$809$	2.42037	0.0850957	0.0425478	+	0.999094i	$0.486453\pi$
$810$	18.0608	0.634591
$811$	15.3009	0.537288	0.268644	−	0.963240i	$-0.413425\pi$
$811$	15.3009	0.537288	0.268644	+	0.963240i	$0.413425\pi$
$812$	39.6667	1.39203
$813$	4.16485	0.146068
$814$	13.3834	0.469087
$815$	−9.90788	−0.347058
$816$	−12.6917	−0.444299
$817$	−64.4855	−2.25606
$818$	58.0903	2.03108
$819$	−3.95329	−0.138139
$820$	14.7099	0.513692
$821$	4.32367	0.150897	0.0754486	−	0.997150i	$-0.475961\pi$
$821$	4.32367	0.150897	0.0754486	+	0.997150i	$0.475961\pi$
$822$	13.4762	0.470036
$823$	−24.2140	−0.844045	−0.422023	−	0.906585i	$-0.638680\pi$
$823$	−24.2140	−0.844045	−0.422023	+	0.906585i	$0.638680\pi$
$824$	−27.7034	−0.965093
$825$	12.1469	0.422901
$826$	−86.9552	−3.02556
$827$	4.11769	0.143186	0.0715931	−	0.997434i	$-0.477192\pi$
$827$	4.11769	0.143186	0.0715931	+	0.997434i	$0.477192\pi$
$828$	17.0501	0.592532
$829$	−45.8257	−1.59159	−0.795796	−	0.605564i	$-0.792948\pi$
$829$	−45.8257	−1.59159	−0.795796	+	0.605564i	$0.792948\pi$
$830$	17.6911	0.614067
$831$	34.6538	1.20213
$832$	8.87150	0.307564
$833$	26.3850	0.914187
$834$	−29.3830	−1.01745
$835$	42.1382	1.45825
$836$	83.9119	2.90215
$837$	48.1242	1.66341
$838$	9.44957	0.326430
$839$	−49.6182	−1.71301	−0.856506	−	0.516137i	$-0.827369\pi$
$839$	−49.6182	−1.71301	−0.856506	+	0.516137i	$0.827369\pi$
$840$	−40.1424	−1.38504
$841$	−22.2829	−0.768377
$842$	64.6436	2.22777
$843$	−6.36522	−0.219230
$844$	−67.1521	−2.31147
$845$	−19.8855	−0.684080
$846$	−33.7565	−1.16057
$847$	−12.8560	−0.441737
$848$	−3.08073	−0.105793
$849$	−39.5984	−1.35901
$850$	16.7418	0.574240
$851$	6.00525	0.205857
$852$	−19.3590	−0.663227
$853$	−44.5214	−1.52438	−0.762192	−	0.647351i	$-0.775877\pi$
$853$	−44.5214	−1.52438	−0.762192	+	0.647351i	$0.775877\pi$
$854$	12.9847	0.444328
$855$	−10.2658	−0.351083
$856$	−3.11877	−0.106598
$857$	−26.1115	−0.891953	−0.445977	−	0.895045i	$-0.647144\pi$
$857$	−26.1115	−0.891953	−0.445977	+	0.895045i	$0.647144\pi$
$858$	−11.5480	−0.394241
$859$	−18.3390	−0.625719	−0.312860	−	0.949799i	$-0.601287\pi$
$859$	−18.3390	−0.625719	−0.312860	+	0.949799i	$0.601287\pi$
$860$	−69.9817	−2.38636
$861$	12.9063	0.439846
$862$	−48.3291	−1.64609
$863$	−37.4770	−1.27573	−0.637867	−	0.770147i	$-0.720183\pi$
$863$	−37.4770	−1.27573	−0.637867	+	0.770147i	$0.720183\pi$
$864$	8.26133	0.281056
$865$	−6.55328	−0.222818
$866$	52.4162	1.78117
$867$	11.2648	0.382572
$868$	−130.293	−4.42243
$869$	58.9648	2.00024
$870$	−14.1756	−0.480598
$871$	−4.18425	−0.141778
$872$	−10.8119	−0.366139
$873$	−8.52564	−0.288549
$874$	57.2489	1.93647
$875$	47.7127	1.61298
$876$	29.9702	1.01260
$877$	−4.38994	−0.148238	−0.0741188	−	0.997249i	$-0.523614\pi$
$877$	−4.38994	−0.148238	−0.0741188	+	0.997249i	$0.523614\pi$
$878$	−20.4503	−0.690163
$879$	5.04723	0.170239
$880$	18.9992	0.640463
$881$	1.04419	0.0351796	0.0175898	−	0.999845i	$-0.494401\pi$
$881$	1.04419	0.0351796	0.0175898	+	0.999845i	$0.494401\pi$
$882$	23.2373	0.782441
$883$	−7.75537	−0.260989	−0.130495	−	0.991449i	$-0.541656\pi$
$883$	−7.75537	−0.260989	−0.130495	+	0.991449i	$0.541656\pi$
$884$	−10.4680	−0.352077
$885$	20.4377	0.687006
$886$	−19.5031	−0.655220
$887$	10.7999	0.362624	0.181312	−	0.983426i	$-0.441966\pi$
$887$	10.7999	0.362624	0.181312	+	0.983426i	$0.441966\pi$
$888$	−9.04851	−0.303648
$889$	52.9991	1.77753
$890$	−24.4583	−0.819844
$891$	−17.2380	−0.577494
$892$	33.1144	1.10875
$893$	−74.5452	−2.49456
$894$	−36.1176	−1.20795
$895$	−5.26882	−0.176117
$896$	−81.6860	−2.72894
$897$	−5.18168	−0.173011
$898$	−61.1592	−2.04091
$899$	−22.0634	−0.735857
$900$	9.69734	0.323245
$901$	−2.97669	−0.0991678
$902$	−21.3470	−0.710779
$903$	−61.4013	−2.04331
$904$	−32.3206	−1.07497
$905$	−9.54697	−0.317352
$906$	−3.34533	−0.111141
$907$	31.1281	1.03359	0.516796	−	0.856108i	$-0.327124\pi$
$907$	31.1281	1.03359	0.516796	+	0.856108i	$0.327124\pi$
$908$	84.6509	2.80924
$909$	0.399427	0.0132481
$910$	−14.4053	−0.477531
$911$	18.5023	0.613008	0.306504	−	0.951869i	$-0.400841\pi$
$911$	18.5023	0.613008	0.306504	+	0.951869i	$0.400841\pi$
$912$	−24.6837	−0.817359
$913$	−16.8851	−0.558816
$914$	−20.5921	−0.681126
$915$	−3.05190	−0.100893
$916$	30.1006	0.994552
$917$	12.1582	0.401500
$918$	−40.6741	−1.34245
$919$	−45.5882	−1.50382	−0.751908	−	0.659268i	$-0.770866\pi$
$919$	−45.5882	−1.50382	−0.751908	+	0.659268i	$0.770866\pi$
$920$	29.7923	0.982222
$921$	4.46157	0.147014
$922$	−20.5110	−0.675492
$923$	−3.33131	−0.109651
$924$	79.8985	2.62847
$925$	3.41552	0.112302
$926$	−12.4896	−0.410433
$927$	−6.74587	−0.221563
$928$	−3.78756	−0.124333
$929$	13.4186	0.440251	0.220125	−	0.975472i	$-0.429353\pi$
$929$	13.4186	0.440251	0.220125	+	0.975472i	$0.429353\pi$
$930$	46.5625	1.52684
$931$	51.3153	1.68179
$932$	−36.9964	−1.21186
$933$	18.7841	0.614964
$934$	−76.5485	−2.50474
$935$	18.3576	0.600356
$936$	−4.42085	−0.144500
$937$	−34.9653	−1.14227	−0.571134	−	0.820857i	$-0.693496\pi$
$937$	−34.9653	−1.14227	−0.571134	+	0.820857i	$0.693496\pi$
$938$	44.0179	1.43724
$939$	18.4082	0.600730
$940$	−80.8988	−2.63863
$941$	−29.3230	−0.955902	−0.477951	−	0.878386i	$-0.658620\pi$
$941$	−29.3230	−0.955902	−0.477951	+	0.878386i	$0.658620\pi$
$942$	75.1468	2.44841
$943$	−9.57863	−0.311923
$944$	−27.8252	−0.905634
$945$	−36.8127	−1.19752
$946$	101.558	3.30192
$947$	−0.132313	−0.00429959	−0.00214980	−	0.999998i	$-0.500684\pi$
$947$	−0.132313	−0.00429959	−0.00214980	+	0.999998i	$0.500684\pi$
$948$	−83.1362	−2.70014
$949$	5.15730	0.167413
$950$	32.5606	1.05641
$951$	−22.0906	−0.716337
$952$	52.8067	1.71148
$953$	−59.8694	−1.93936	−0.969680	−	0.244379i	$-0.921416\pi$
$953$	−59.8694	−1.93936	−0.969680	+	0.244379i	$0.921416\pi$
$954$	−2.62157	−0.0848765
$955$	15.8831	0.513967
$956$	−35.0403	−1.13329
$957$	13.5298	0.437356
$958$	−21.3809	−0.690787
$959$	−16.0447	−0.518112
$960$	21.9354	0.707962
$961$	41.4715	1.33779
$962$	−3.24710	−0.104691
$963$	−0.759432	−0.0244724
$964$	25.1038	0.808538
$965$	17.4449	0.561572
$966$	54.5108	1.75386
$967$	−34.2593	−1.10170	−0.550852	−	0.834603i	$-0.685697\pi$
$967$	−34.2593	−1.10170	−0.550852	+	0.834603i	$0.685697\pi$
$968$	−14.3764	−0.462076
$969$	−23.8501	−0.766175
$970$	−31.0663	−0.997480
$971$	27.2510	0.874525	0.437263	−	0.899334i	$-0.355948\pi$
$971$	27.2510	0.874525	0.437263	+	0.899334i	$0.355948\pi$
$972$	−40.8635	−1.31070
$973$	34.9834	1.12152
$974$	33.1252	1.06140
$975$	−2.94711	−0.0943830
$976$	4.15505	0.133000
$977$	−19.1638	−0.613104	−0.306552	−	0.951854i	$-0.599175\pi$
$977$	−19.1638	−0.613104	−0.306552	+	0.951854i	$0.599175\pi$
$978$	−20.2725	−0.648241
$979$	23.3440	0.746078
$980$	55.6891	1.77892
$981$	−2.63275	−0.0840571
$982$	92.7748	2.96056
$983$	−33.6066	−1.07188	−0.535942	−	0.844255i	$-0.680043\pi$
$983$	−33.6066	−1.07188	−0.535942	+	0.844255i	$0.680043\pi$
$984$	14.4327	0.460099
$985$	−26.7844	−0.853423
$986$	18.6478	0.593868
$987$	−70.9798	−2.25931
$988$	−20.3589	−0.647702
$989$	45.5699	1.44904
$990$	16.1675	0.513837
$991$	−17.5259	−0.556727	−0.278364	−	0.960476i	$-0.589792\pi$
$991$	−17.5259	−0.556727	−0.278364	+	0.960476i	$0.589792\pi$
$992$	12.4410	0.395001
$993$	13.5469	0.429898
$994$	35.0450	1.11156
$995$	3.59766	0.114054
$996$	23.8068	0.754348
$997$	−8.00286	−0.253453	−0.126727	−	0.991938i	$-0.540447\pi$
$997$	−8.00286	−0.253453	−0.126727	+	0.991938i	$0.540447\pi$
$998$	88.9143	2.81453
$999$	−8.29797	−0.262536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.14	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.14	✓	153	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41716 q^{2} -1.38399 q^{3} +3.84266 q^{4} +1.63498 q^{5} +3.34533 q^{6} -3.98295 q^{7} -4.45401 q^{8} -1.08457 q^{9} +O(q^{10})\)	\(q-2.41716 q^{2} -1.38399 q^{3} +3.84266 q^{4} +1.63498 q^{5} +3.34533 q^{6} -3.98295 q^{7} -4.45401 q^{8} -1.08457 q^{9} -3.95202 q^{10} +3.77197 q^{11} -5.31821 q^{12} -0.915163 q^{13} +9.62743 q^{14} -2.26280 q^{15} +3.08073 q^{16} +2.97669 q^{17} +2.62157 q^{18} +5.78926 q^{19} +6.28269 q^{20} +5.51237 q^{21} -9.11745 q^{22} -4.09109 q^{23} +6.16431 q^{24} -2.32683 q^{25} +2.21209 q^{26} +5.65301 q^{27} -15.3051 q^{28} -2.59173 q^{29} +5.46956 q^{30} +8.51302 q^{31} +1.46140 q^{32} -5.22038 q^{33} -7.19513 q^{34} -6.51206 q^{35} -4.16762 q^{36} -1.46789 q^{37} -13.9936 q^{38} +1.26658 q^{39} -7.28223 q^{40} +2.34134 q^{41} -13.3243 q^{42} -11.1388 q^{43} +14.4944 q^{44} -1.77325 q^{45} +9.88882 q^{46} -12.8765 q^{47} -4.26370 q^{48} +8.86389 q^{49} +5.62432 q^{50} -4.11971 q^{51} -3.51666 q^{52} -1.00000 q^{53} -13.6642 q^{54} +6.16711 q^{55} +17.7401 q^{56} -8.01229 q^{57} +6.26462 q^{58} -9.03203 q^{59} -8.69519 q^{60} +1.34872 q^{61} -20.5773 q^{62} +4.31977 q^{63} -9.69391 q^{64} -1.49628 q^{65} +12.6185 q^{66} +4.57214 q^{67} +11.4384 q^{68} +5.66203 q^{69} +15.7407 q^{70} +3.64013 q^{71} +4.83067 q^{72} -5.63539 q^{73} +3.54812 q^{74} +3.22031 q^{75} +22.2462 q^{76} -15.0236 q^{77} -3.06152 q^{78} +15.6324 q^{79} +5.03694 q^{80} -4.57002 q^{81} -5.65939 q^{82} -4.47647 q^{83} +21.1822 q^{84} +4.86684 q^{85} +26.9243 q^{86} +3.58693 q^{87} -16.8004 q^{88} +6.18881 q^{89} +4.28622 q^{90} +3.64505 q^{91} -15.7207 q^{92} -11.7820 q^{93} +31.1245 q^{94} +9.46535 q^{95} -2.02257 q^{96} +7.86088 q^{97} -21.4254 q^{98} -4.09095 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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