LMFDB - Embedded newform 8003.2.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.54449 q^{2} -2.75216 q^{3} +4.47442 q^{4} -0.0821866 q^{5} +7.00285 q^{6} -2.51361 q^{7} -6.29612 q^{8} +4.57441 q^{9} +O(q^{10})$	\(q-2.54449 q^{2} -2.75216 q^{3} +4.47442 q^{4} -0.0821866 q^{5} +7.00285 q^{6} -2.51361 q^{7} -6.29612 q^{8} +4.57441 q^{9} +0.209123 q^{10} -4.33563 q^{11} -12.3143 q^{12} -6.03114 q^{13} +6.39585 q^{14} +0.226191 q^{15} +7.07156 q^{16} -4.63559 q^{17} -11.6395 q^{18} +1.23205 q^{19} -0.367737 q^{20} +6.91787 q^{21} +11.0320 q^{22} -8.79311 q^{23} +17.3280 q^{24} -4.99325 q^{25} +15.3462 q^{26} -4.33303 q^{27} -11.2469 q^{28} -3.61276 q^{29} -0.575540 q^{30} -6.33205 q^{31} -5.40126 q^{32} +11.9324 q^{33} +11.7952 q^{34} +0.206585 q^{35} +20.4678 q^{36} +2.98659 q^{37} -3.13494 q^{38} +16.5987 q^{39} +0.517457 q^{40} +11.0158 q^{41} -17.6024 q^{42} -0.747991 q^{43} -19.3994 q^{44} -0.375955 q^{45} +22.3740 q^{46} +4.74881 q^{47} -19.4621 q^{48} -0.681756 q^{49} +12.7052 q^{50} +12.7579 q^{51} -26.9858 q^{52} -1.00000 q^{53} +11.0254 q^{54} +0.356331 q^{55} +15.8260 q^{56} -3.39081 q^{57} +9.19262 q^{58} +15.0256 q^{59} +1.01207 q^{60} -8.06472 q^{61} +16.1118 q^{62} -11.4983 q^{63} -0.399679 q^{64} +0.495679 q^{65} -30.3618 q^{66} +1.53748 q^{67} -20.7415 q^{68} +24.2001 q^{69} -0.525653 q^{70} +10.6166 q^{71} -28.8010 q^{72} +0.140557 q^{73} -7.59933 q^{74} +13.7422 q^{75} +5.51272 q^{76} +10.8981 q^{77} -42.2352 q^{78} +9.74079 q^{79} -0.581188 q^{80} -1.79800 q^{81} -28.0295 q^{82} +7.93714 q^{83} +30.9534 q^{84} +0.380983 q^{85} +1.90325 q^{86} +9.94291 q^{87} +27.2977 q^{88} -1.05875 q^{89} +0.956613 q^{90} +15.1600 q^{91} -39.3440 q^{92} +17.4268 q^{93} -12.0833 q^{94} -0.101258 q^{95} +14.8652 q^{96} +8.11423 q^{97} +1.73472 q^{98} -19.8330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54449	−1.79922	−0.899612	−	0.436690i	$-0.856151\pi$
$2$	−2.54449	−1.79922	−0.899612	+	0.436690i	$0.856151\pi$
$3$	−2.75216	−1.58896	−0.794481	−	0.607288i	$-0.792257\pi$
$3$	−2.75216	−1.58896	−0.794481	+	0.607288i	$0.792257\pi$
$4$	4.47442	2.23721
$5$	−0.0821866	−0.0367550	−0.0183775	−	0.999831i	$-0.505850\pi$
$5$	−0.0821866	−0.0367550	−0.0183775	+	0.999831i	$0.505850\pi$
$6$	7.00285	2.85890
$7$	−2.51361	−0.950056	−0.475028	−	0.879971i	$-0.657562\pi$
$7$	−2.51361	−0.950056	−0.475028	+	0.879971i	$0.657562\pi$
$8$	−6.29612	−2.22601
$9$	4.57441	1.52480
$10$	0.209123	0.0661304
$11$	−4.33563	−1.30724	−0.653621	−	0.756822i	$-0.726751\pi$
$11$	−4.33563	−1.30724	−0.653621	+	0.756822i	$0.726751\pi$
$12$	−12.3143	−3.55484
$13$	−6.03114	−1.67274	−0.836369	−	0.548166i	$-0.815326\pi$
$13$	−6.03114	−1.67274	−0.836369	+	0.548166i	$0.815326\pi$
$14$	6.39585	1.70936
$15$	0.226191	0.0584023
$16$	7.07156	1.76789
$17$	−4.63559	−1.12429	−0.562147	−	0.827037i	$-0.690025\pi$
$17$	−4.63559	−1.12429	−0.562147	+	0.827037i	$0.690025\pi$
$18$	−11.6395	−2.74346
$19$	1.23205	0.282652	0.141326	−	0.989963i	$-0.454863\pi$
$19$	1.23205	0.282652	0.141326	+	0.989963i	$0.454863\pi$
$20$	−0.367737	−0.0822285
$21$	6.91787	1.50960
$22$	11.0320	2.35202
$23$	−8.79311	−1.83349	−0.916745	−	0.399473i	$-0.869193\pi$
$23$	−8.79311	−1.83349	−0.916745	+	0.399473i	$0.869193\pi$
$24$	17.3280	3.53705
$25$	−4.99325	−0.998649
$26$	15.3462	3.00963
$27$	−4.33303	−0.833893
$28$	−11.2469	−2.12547
$29$	−3.61276	−0.670873	−0.335436	−	0.942063i	$-0.608884\pi$
$29$	−3.61276	−0.670873	−0.335436	+	0.942063i	$0.608884\pi$
$30$	−0.575540	−0.105079
$31$	−6.33205	−1.13727	−0.568635	−	0.822590i	$-0.692528\pi$
$31$	−6.33205	−1.13727	−0.568635	+	0.822590i	$0.692528\pi$
$32$	−5.40126	−0.954817
$33$	11.9324	2.07716
$34$	11.7952	2.02286
$35$	0.206585	0.0349193
$36$	20.4678	3.41130
$37$	2.98659	0.490992	0.245496	−	0.969398i	$-0.421049\pi$
$37$	2.98659	0.490992	0.245496	+	0.969398i	$0.421049\pi$
$38$	−3.13494	−0.508555
$39$	16.5987	2.65792
$40$	0.517457	0.0818171
$41$	11.0158	1.72038	0.860189	−	0.509976i	$-0.170346\pi$
$41$	11.0158	1.72038	0.860189	+	0.509976i	$0.170346\pi$
$42$	−17.6024	−2.71612
$43$	−0.747991	−0.114068	−0.0570338	−	0.998372i	$-0.518164\pi$
$43$	−0.747991	−0.114068	−0.0570338	+	0.998372i	$0.518164\pi$
$44$	−19.3994	−2.92457
$45$	−0.375955	−0.0560441
$46$	22.3740	3.29886
$47$	4.74881	0.692685	0.346343	−	0.938108i	$-0.387424\pi$
$47$	4.74881	0.692685	0.346343	+	0.938108i	$0.387424\pi$
$48$	−19.4621	−2.80911
$49$	−0.681756	−0.0973937
$50$	12.7052	1.79679
$51$	12.7579	1.78646
$52$	−26.9858	−3.74226
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	11.0254	1.50036
$55$	0.356331	0.0480476
$56$	15.8260	2.11484
$57$	−3.39081	−0.449124
$58$	9.19262	1.20705
$59$	15.0256	1.95617	0.978086	−	0.208203i	$-0.0667616\pi$
$59$	15.0256	1.95617	0.978086	+	0.208203i	$0.0667616\pi$
$60$	1.01207	0.130658
$61$	−8.06472	−1.03258	−0.516291	−	0.856413i	$-0.672688\pi$
$61$	−8.06472	−1.03258	−0.516291	+	0.856413i	$0.672688\pi$
$62$	16.1118	2.04620
$63$	−11.4983	−1.44865
$64$	−0.399679	−0.0499599
$65$	0.495679	0.0614814
$66$	−30.3618	−3.73728
$67$	1.53748	0.187833	0.0939166	−	0.995580i	$-0.470061\pi$
$67$	1.53748	0.187833	0.0939166	+	0.995580i	$0.470061\pi$
$68$	−20.7415	−2.51528
$69$	24.2001	2.91335
$70$	−0.525653	−0.0628276
$71$	10.6166	1.25996	0.629978	−	0.776613i	$-0.283064\pi$
$71$	10.6166	1.25996	0.629978	+	0.776613i	$0.283064\pi$
$72$	−28.8010	−3.39423
$73$	0.140557	0.0164510	0.00822550	−	0.999966i	$-0.497382\pi$
$73$	0.140557	0.0164510	0.00822550	+	0.999966i	$0.497382\pi$
$74$	−7.59933	−0.883404
$75$	13.7422	1.58682
$76$	5.51272	0.632352
$77$	10.8981	1.24195
$78$	−42.2352	−4.78219
$79$	9.74079	1.09592	0.547962	−	0.836503i	$-0.315404\pi$
$79$	9.74079	1.09592	0.547962	+	0.836503i	$0.315404\pi$
$80$	−0.581188	−0.0649788
$81$	−1.79800	−0.199778
$82$	−28.0295	−3.09535
$83$	7.93714	0.871214	0.435607	−	0.900137i	$-0.356534\pi$
$83$	7.93714	0.871214	0.435607	+	0.900137i	$0.356534\pi$
$84$	30.9534	3.37730
$85$	0.380983	0.0413234
$86$	1.90325	0.205233
$87$	9.94291	1.06599
$88$	27.2977	2.90994
$89$	−1.05875	−0.112228	−0.0561138	−	0.998424i	$-0.517871\pi$
$89$	−1.05875	−0.112228	−0.0561138	+	0.998424i	$0.517871\pi$
$90$	0.956613	0.100836
$91$	15.1600	1.58920
$92$	−39.3440	−4.10190
$93$	17.4268	1.80708
$94$	−12.0833	−1.24630
$95$	−0.101258	−0.0103889
$96$	14.8652	1.51717
$97$	8.11423	0.823875	0.411938	−	0.911212i	$-0.364852\pi$
$97$	8.11423	0.823875	0.411938	+	0.911212i	$0.364852\pi$
$98$	1.73472	0.175233
$99$	−19.8330	−1.99329
$100$	−22.3419	−2.23419
$101$	−2.76688	−0.275315	−0.137658	−	0.990480i	$-0.543957\pi$
$101$	−2.76688	−0.275315	−0.137658	+	0.990480i	$0.543957\pi$
$102$	−32.4623	−3.21425
$103$	12.4584	1.22756	0.613782	−	0.789475i	$-0.289647\pi$
$103$	12.4584	1.22756	0.613782	+	0.789475i	$0.289647\pi$
$104$	37.9728	3.72354
$105$	−0.568556	−0.0554854
$106$	2.54449	0.247142
$107$	−9.01422	−0.871437	−0.435719	−	0.900083i	$-0.643506\pi$
$107$	−9.01422	−0.871437	−0.435719	+	0.900083i	$0.643506\pi$
$108$	−19.3878	−1.86559
$109$	0.0571811	0.00547696	0.00273848	−	0.999996i	$-0.499128\pi$
$109$	0.0571811	0.00547696	0.00273848	+	0.999996i	$0.499128\pi$
$110$	−0.906679	−0.0864485
$111$	−8.21958	−0.780168
$112$	−17.7752	−1.67959
$113$	−3.77611	−0.355226	−0.177613	−	0.984100i	$-0.556838\pi$
$113$	−3.77611	−0.355226	−0.177613	+	0.984100i	$0.556838\pi$
$114$	8.62788	0.808075
$115$	0.722676	0.0673899
$116$	−16.1650	−1.50088
$117$	−27.5889	−2.55060
$118$	−38.2325	−3.51959
$119$	11.6521	1.06814
$120$	−1.42413	−0.130004
$121$	7.79771	0.708882
$122$	20.5206	1.85785
$123$	−30.3173	−2.73362
$124$	−28.3322	−2.54431
$125$	0.821311	0.0734603
$126$	29.2573	2.60644
$127$	−18.1415	−1.60979	−0.804897	−	0.593414i	$-0.797780\pi$
$127$	−18.1415	−1.60979	−0.804897	+	0.593414i	$0.797780\pi$
$128$	11.8195	1.04471
$129$	2.05859	0.181249
$130$	−1.26125	−0.110619
$131$	10.4895	0.916469	0.458234	−	0.888831i	$-0.348482\pi$
$131$	10.4895	0.916469	0.458234	+	0.888831i	$0.348482\pi$
$132$	53.3904	4.64704
$133$	−3.09690	−0.268535
$134$	−3.91210	−0.337954
$135$	0.356117	0.0306497
$136$	29.1862	2.50270
$137$	10.0206	0.856116	0.428058	−	0.903751i	$-0.359198\pi$
$137$	10.0206	0.856116	0.428058	+	0.903751i	$0.359198\pi$
$138$	−61.5768	−5.24177
$139$	−1.80560	−0.153149	−0.0765745	−	0.997064i	$-0.524398\pi$
$139$	−1.80560	−0.153149	−0.0765745	+	0.997064i	$0.524398\pi$
$140$	0.924348	0.0781217
$141$	−13.0695	−1.10065
$142$	−27.0138	−2.26694
$143$	26.1488	2.18667
$144$	32.3482	2.69569
$145$	0.296921	0.0246579
$146$	−0.357647	−0.0295990
$147$	1.87631	0.154755
$148$	13.3632	1.09845
$149$	−11.5656	−0.947494	−0.473747	−	0.880661i	$-0.657099\pi$
$149$	−11.5656	−0.947494	−0.473747	+	0.880661i	$0.657099\pi$
$150$	−34.9669	−2.85504
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−7.75715	−0.629188
$153$	−21.2051	−1.71433
$154$	−27.7301	−2.23455
$155$	0.520410	0.0418003
$156$	74.2695	5.94632
$157$	−21.3893	−1.70705	−0.853525	−	0.521052i	$-0.825540\pi$
$157$	−21.3893	−1.70705	−0.853525	+	0.521052i	$0.825540\pi$
$158$	−24.7853	−1.97181
$159$	2.75216	0.218261
$160$	0.443911	0.0350943
$161$	22.1025	1.74192
$162$	4.57500	0.359446
$163$	−6.07776	−0.476047	−0.238023	−	0.971259i	$-0.576499\pi$
$163$	−6.07776	−0.476047	−0.238023	+	0.971259i	$0.576499\pi$
$164$	49.2892	3.84884
$165$	−0.980681	−0.0763459
$166$	−20.1960	−1.56751
$167$	5.43525	0.420592	0.210296	−	0.977638i	$-0.432557\pi$
$167$	5.43525	0.420592	0.210296	+	0.977638i	$0.432557\pi$
$168$	−43.5557	−3.36040
$169$	23.3747	1.79805
$170$	−0.969406	−0.0743501
$171$	5.63591	0.430989
$172$	−3.34682	−0.255193
$173$	−12.0989	−0.919864	−0.459932	−	0.887954i	$-0.652126\pi$
$173$	−12.0989	−0.919864	−0.459932	+	0.887954i	$0.652126\pi$
$174$	−25.2996	−1.91796
$175$	12.5511	0.948772
$176$	−30.6597	−2.31106
$177$	−41.3530	−3.10828
$178$	2.69398	0.201922
$179$	−12.9739	−0.969713	−0.484856	−	0.874594i	$-0.661128\pi$
$179$	−12.9739	−0.969713	−0.484856	+	0.874594i	$0.661128\pi$
$180$	−1.68218	−0.125382
$181$	1.53497	0.114093	0.0570466	−	0.998372i	$-0.481832\pi$
$181$	1.53497	0.114093	0.0570466	+	0.998372i	$0.481832\pi$
$182$	−38.5743	−2.85932
$183$	22.1955	1.64073
$184$	55.3625	4.08137
$185$	−0.245457	−0.0180464
$186$	−44.3424	−3.25134
$187$	20.0982	1.46973
$188$	21.2481	1.54968
$189$	10.8916	0.792245
$190$	0.257650	0.0186919
$191$	−10.0634	−0.728159	−0.364079	−	0.931368i	$-0.618616\pi$
$191$	−10.0634	−0.728159	−0.364079	+	0.931368i	$0.618616\pi$
$192$	1.09998	0.0793844
$193$	1.53965	0.110827	0.0554133	−	0.998464i	$-0.482352\pi$
$193$	1.53965	0.110827	0.0554133	+	0.998464i	$0.482352\pi$
$194$	−20.6466	−1.48234
$195$	−1.36419	−0.0976917
$196$	−3.05046	−0.217890
$197$	21.5930	1.53843	0.769217	−	0.638987i	$-0.220646\pi$
$197$	21.5930	1.53843	0.769217	+	0.638987i	$0.220646\pi$
$198$	50.4647	3.58637
$199$	9.94310	0.704847	0.352424	−	0.935841i	$-0.385358\pi$
$199$	9.94310	0.704847	0.352424	+	0.935841i	$0.385358\pi$
$200$	31.4381	2.22301
$201$	−4.23140	−0.298460
$202$	7.04030	0.495354
$203$	9.08108	0.637367
$204$	57.0841	3.99669
$205$	−0.905350	−0.0632324
$206$	−31.7003	−2.20866
$207$	−40.2233	−2.79571
$208$	−42.6496	−2.95722
$209$	−5.34173	−0.369495
$210$	1.44668	0.0998307
$211$	12.5417	0.863404	0.431702	−	0.902016i	$-0.357913\pi$
$211$	12.5417	0.863404	0.431702	+	0.902016i	$0.357913\pi$
$212$	−4.47442	−0.307304
$213$	−29.2186	−2.00202
$214$	22.9366	1.56791
$215$	0.0614748	0.00419255
$216$	27.2813	1.85626
$217$	15.9163	1.08047
$218$	−0.145497	−0.00985428
$219$	−0.386837	−0.0261400
$220$	1.59437	0.107493
$221$	27.9579	1.88065
$222$	20.9146	1.40370
$223$	−0.124446	−0.00833353	−0.00416677	−	0.999991i	$-0.501326\pi$
$223$	−0.124446	−0.00833353	−0.00416677	+	0.999991i	$0.501326\pi$
$224$	13.5767	0.907130
$225$	−22.8412	−1.52274
$226$	9.60825	0.639131
$227$	12.9103	0.856888	0.428444	−	0.903568i	$-0.359062\pi$
$227$	12.9103	0.856888	0.428444	+	0.903568i	$0.359062\pi$
$228$	−15.1719	−1.00478
$229$	−25.7767	−1.70338	−0.851688	−	0.524050i	$-0.824421\pi$
$229$	−25.7767	−1.70338	−0.851688	+	0.524050i	$0.824421\pi$
$230$	−1.83884	−0.121249
$231$	−29.9934	−1.97342
$232$	22.7464	1.49337
$233$	−3.43074	−0.224755	−0.112378	−	0.993666i	$-0.535847\pi$
$233$	−3.43074	−0.224755	−0.112378	+	0.993666i	$0.535847\pi$
$234$	70.1997	4.58910
$235$	−0.390288	−0.0254596
$236$	67.2309	4.37636
$237$	−26.8083	−1.74138
$238$	−29.6485	−1.92183
$239$	27.0614	1.75046	0.875228	−	0.483711i	$-0.160711\pi$
$239$	27.0614	1.75046	0.875228	+	0.483711i	$0.160711\pi$
$240$	1.59952	0.103249
$241$	−11.8479	−0.763188	−0.381594	−	0.924330i	$-0.624625\pi$
$241$	−11.8479	−0.763188	−0.381594	+	0.924330i	$0.624625\pi$
$242$	−19.8412	−1.27544
$243$	17.9475	1.15133
$244$	−36.0849	−2.31010
$245$	0.0560312	0.00357970
$246$	77.1419	4.91839
$247$	−7.43069	−0.472803
$248$	39.8673	2.53158
$249$	−21.8443	−1.38433
$250$	−2.08981	−0.132171
$251$	−15.4632	−0.976027	−0.488014	−	0.872836i	$-0.662278\pi$
$251$	−15.4632	−0.976027	−0.488014	+	0.872836i	$0.662278\pi$
$252$	−51.4481	−3.24093
$253$	38.1237	2.39682
$254$	46.1607	2.89638
$255$	−1.04853	−0.0656614
$256$	−29.2752	−1.82970
$257$	−19.7042	−1.22912	−0.614558	−	0.788872i	$-0.710666\pi$
$257$	−19.7042	−1.22912	−0.614558	+	0.788872i	$0.710666\pi$
$258$	−5.23807	−0.326108
$259$	−7.50712	−0.466470
$260$	2.21787	0.137547
$261$	−16.5262	−1.02295
$262$	−26.6903	−1.64893
$263$	−1.81497	−0.111916	−0.0559578	−	0.998433i	$-0.517821\pi$
$263$	−1.81497	−0.111916	−0.0559578	+	0.998433i	$0.517821\pi$
$264$	−75.1276	−4.62379
$265$	0.0821866	0.00504868
$266$	7.88003	0.483155
$267$	2.91386	0.178325
$268$	6.87933	0.420222
$269$	−10.4110	−0.634767	−0.317384	−	0.948297i	$-0.602804\pi$
$269$	−10.4110	−0.634767	−0.317384	+	0.948297i	$0.602804\pi$
$270$	−0.906136	−0.0551457
$271$	−0.454510	−0.0276095	−0.0138048	−	0.999905i	$-0.504394\pi$
$271$	−0.454510	−0.0276095	−0.0138048	+	0.999905i	$0.504394\pi$
$272$	−32.7808	−1.98763
$273$	−41.7227	−2.52517
$274$	−25.4972	−1.54034
$275$	21.6489	1.30548
$276$	108.281	6.51776
$277$	9.13852	0.549080	0.274540	−	0.961576i	$-0.411474\pi$
$277$	9.13852	0.549080	0.274540	+	0.961576i	$0.411474\pi$
$278$	4.59432	0.275549
$279$	−28.9654	−1.73411
$280$	−1.30068	−0.0777308
$281$	22.9703	1.37030	0.685148	−	0.728404i	$-0.259738\pi$
$281$	22.9703	1.37030	0.685148	+	0.728404i	$0.259738\pi$
$282$	33.2552	1.98032
$283$	7.83880	0.465968	0.232984	−	0.972481i	$-0.425151\pi$
$283$	7.83880	0.465968	0.232984	+	0.972481i	$0.425151\pi$
$284$	47.5030	2.81879
$285$	0.278679	0.0165075
$286$	−66.5354	−3.93432
$287$	−27.6894	−1.63446
$288$	−24.7076	−1.45591
$289$	4.48866	0.264039
$290$	−0.755511	−0.0443651
$291$	−22.3317	−1.30911
$292$	0.628912	0.0368043
$293$	5.44982	0.318382	0.159191	−	0.987248i	$-0.449111\pi$
$293$	5.44982	0.318382	0.159191	+	0.987248i	$0.449111\pi$
$294$	−4.77423	−0.278439
$295$	−1.23491	−0.0718990
$296$	−18.8039	−1.09295
$297$	18.7864	1.09010
$298$	29.4286	1.70475
$299$	53.0325	3.06695
$300$	61.4885	3.55004
$301$	1.88016	0.108371
$302$	2.54449	0.146419
$303$	7.61492	0.437465
$304$	8.71254	0.499698
$305$	0.662812	0.0379525
$306$	53.9560	3.08446
$307$	−10.1468	−0.579109	−0.289554	−	0.957162i	$-0.593507\pi$
$307$	−10.1468	−0.579109	−0.289554	+	0.957162i	$0.593507\pi$
$308$	48.7626	2.77851
$309$	−34.2876	−1.95055
$310$	−1.32418	−0.0752081
$311$	16.3459	0.926894	0.463447	−	0.886125i	$-0.346613\pi$
$311$	16.3459	0.926894	0.463447	+	0.886125i	$0.346613\pi$
$312$	−104.507	−5.91657
$313$	−25.5288	−1.44297	−0.721487	−	0.692428i	$-0.756541\pi$
$313$	−25.5288	−1.44297	−0.721487	+	0.692428i	$0.756541\pi$
$314$	54.4247	3.07137
$315$	0.945005	0.0532450
$316$	43.5843	2.45181
$317$	0.404252	0.0227050	0.0113525	−	0.999936i	$-0.496386\pi$
$317$	0.404252	0.0227050	0.0113525	+	0.999936i	$0.496386\pi$
$318$	−7.00285	−0.392700
$319$	15.6636	0.876993
$320$	0.0328483	0.00183627
$321$	24.8086	1.38468
$322$	−56.2394	−3.13410
$323$	−5.71129	−0.317784
$324$	−8.04502	−0.446946
$325$	30.1150	1.67048
$326$	15.4648	0.856514
$327$	−0.157372	−0.00870269
$328$	−69.3567	−3.82958
$329$	−11.9367	−0.658089
$330$	2.49533	0.137363
$331$	23.6570	1.30031	0.650153	−	0.759803i	$-0.274705\pi$
$331$	23.6570	1.30031	0.650153	+	0.759803i	$0.274705\pi$
$332$	35.5141	1.94909
$333$	13.6619	0.748666
$334$	−13.8299	−0.756740
$335$	−0.126360	−0.00690380
$336$	48.9202	2.66881
$337$	1.17881	0.0642137	0.0321069	−	0.999484i	$-0.489778\pi$
$337$	1.17881	0.0642137	0.0321069	+	0.999484i	$0.489778\pi$
$338$	−59.4766	−3.23510
$339$	10.3925	0.564441
$340$	1.70468	0.0924490
$341$	27.4534	1.48669
$342$	−14.3405	−0.775446
$343$	19.3090	1.04259
$344$	4.70944	0.253916
$345$	−1.98892	−0.107080
$346$	30.7856	1.65504
$347$	5.11097	0.274371	0.137186	−	0.990545i	$-0.456194\pi$
$347$	5.11097	0.274371	0.137186	+	0.990545i	$0.456194\pi$
$348$	44.4887	2.38485
$349$	22.5638	1.20781	0.603906	−	0.797055i	$-0.293610\pi$
$349$	22.5638	1.20781	0.603906	+	0.797055i	$0.293610\pi$
$350$	−31.9361	−1.70705
$351$	26.1332	1.39488
$352$	23.4179	1.24818
$353$	31.8014	1.69262	0.846309	−	0.532692i	$-0.178819\pi$
$353$	31.8014	1.69262	0.846309	+	0.532692i	$0.178819\pi$
$354$	105.222	5.59250
$355$	−0.872541	−0.0463097
$356$	−4.73730	−0.251076
$357$	−32.0684	−1.69724
$358$	33.0119	1.74473
$359$	−32.3931	−1.70964	−0.854820	−	0.518925i	$-0.826332\pi$
$359$	−32.3931	−1.70964	−0.854820	+	0.518925i	$0.826332\pi$
$360$	2.36706	0.124755
$361$	−17.4820	−0.920108
$362$	−3.90570	−0.205279
$363$	−21.4606	−1.12639
$364$	67.8319	3.55536
$365$	−0.0115519	−0.000604656 0
$366$	−56.4760	−2.95205
$367$	2.80775	0.146563	0.0732817	−	0.997311i	$-0.476653\pi$
$367$	2.80775	0.146563	0.0732817	+	0.997311i	$0.476653\pi$
$368$	−62.1810	−3.24141
$369$	50.3907	2.62324
$370$	0.624563	0.0324695
$371$	2.51361	0.130500
$372$	77.9750	4.04281
$373$	27.7629	1.43751	0.718754	−	0.695264i	$-0.244713\pi$
$373$	27.7629	1.43751	0.718754	+	0.695264i	$0.244713\pi$
$374$	−51.1396	−2.64437
$375$	−2.26038	−0.116726
$376$	−29.8991	−1.54193
$377$	21.7891	1.12220
$378$	−27.7135	−1.42543
$379$	15.3066	0.786246	0.393123	−	0.919486i	$-0.371395\pi$
$379$	15.3066	0.786246	0.393123	+	0.919486i	$0.371395\pi$
$380$	−0.453071	−0.0232421
$381$	49.9283	2.55790
$382$	25.6061	1.31012
$383$	7.84978	0.401105	0.200552	−	0.979683i	$-0.435726\pi$
$383$	7.84978	0.401105	0.200552	+	0.979683i	$0.435726\pi$
$384$	−32.5292	−1.66000
$385$	−0.895677	−0.0456479
$386$	−3.91762	−0.199402
$387$	−3.42162	−0.173931
$388$	36.3064	1.84318
$389$	−2.75006	−0.139433	−0.0697167	−	0.997567i	$-0.522210\pi$
$389$	−2.75006	−0.139433	−0.0697167	+	0.997567i	$0.522210\pi$
$390$	3.47117	0.175769
$391$	40.7612	2.06138
$392$	4.29242	0.216800
$393$	−28.8687	−1.45624
$394$	−54.9430	−2.76799
$395$	−0.800562	−0.0402807
$396$	−88.7409	−4.45940
$397$	−20.2299	−1.01531	−0.507655	−	0.861561i	$-0.669487\pi$
$397$	−20.2299	−1.01531	−0.507655	+	0.861561i	$0.669487\pi$
$398$	−25.3001	−1.26818
$399$	8.52318	0.426693
$400$	−35.3100	−1.76550
$401$	−16.4144	−0.819696	−0.409848	−	0.912154i	$-0.634418\pi$
$401$	−16.4144	−0.819696	−0.409848	+	0.912154i	$0.634418\pi$
$402$	10.7667	0.536996
$403$	38.1895	1.90236
$404$	−12.3802	−0.615937
$405$	0.147772	0.00734284
$406$	−23.1067	−1.14677
$407$	−12.9487	−0.641845
$408$	−80.3252	−3.97669
$409$	−21.3334	−1.05487	−0.527434	−	0.849596i	$-0.676846\pi$
$409$	−21.3334	−1.05487	−0.527434	+	0.849596i	$0.676846\pi$
$410$	2.30365	0.113769
$411$	−27.5783	−1.36034
$412$	55.7441	2.74632
$413$	−37.7686	−1.85847
$414$	102.348	5.03011
$415$	−0.652327	−0.0320214
$416$	32.5758	1.59716
$417$	4.96931	0.243348
$418$	13.5920	0.664804
$419$	20.4484	0.998970	0.499485	−	0.866323i	$-0.333523\pi$
$419$	20.4484	0.998970	0.499485	+	0.866323i	$0.333523\pi$
$420$	−2.54396	−0.124132
$421$	−16.7493	−0.816311	−0.408156	−	0.912912i	$-0.633828\pi$
$421$	−16.7493	−0.816311	−0.408156	+	0.912912i	$0.633828\pi$
$422$	−31.9121	−1.55346
$423$	21.7230	1.05621
$424$	6.29612	0.305767
$425$	23.1466	1.12278
$426$	74.3463	3.60209
$427$	20.2716	0.981011
$428$	−40.3334	−1.94959
$429$	−71.9659	−3.47454
$430$	−0.156422	−0.00754334
$431$	22.6048	1.08884	0.544418	−	0.838814i	$-0.316751\pi$
$431$	22.6048	1.08884	0.544418	+	0.838814i	$0.316751\pi$
$432$	−30.6413	−1.47423
$433$	17.3449	0.833541	0.416770	−	0.909012i	$-0.363162\pi$
$433$	17.3449	0.833541	0.416770	+	0.909012i	$0.363162\pi$
$434$	−40.4989	−1.94401
$435$	−0.817174	−0.0391805
$436$	0.255852	0.0122531
$437$	−10.8336	−0.518240
$438$	0.984302	0.0470318
$439$	14.7166	0.702383	0.351191	−	0.936304i	$-0.385777\pi$
$439$	14.7166	0.702383	0.351191	+	0.936304i	$0.385777\pi$
$440$	−2.24350	−0.106955
$441$	−3.11863	−0.148506
$442$	−71.1385	−3.38371
$443$	20.6598	0.981576	0.490788	−	0.871279i	$-0.336709\pi$
$443$	20.6598	0.981576	0.490788	+	0.871279i	$0.336709\pi$
$444$	−36.7778	−1.74540
$445$	0.0870152	0.00412492
$446$	0.316652	0.0149939
$447$	31.8305	1.50553
$448$	1.00464	0.0474647
$449$	2.46837	0.116489	0.0582447	−	0.998302i	$-0.481450\pi$
$449$	2.46837	0.116489	0.0582447	+	0.998302i	$0.481450\pi$
$450$	58.1190	2.73976
$451$	−47.7604	−2.24895
$452$	−16.8959	−0.794715
$453$	2.75216	0.129308
$454$	−32.8502	−1.54173
$455$	−1.24595	−0.0584108
$456$	21.3490	0.999756
$457$	3.60533	0.168650	0.0843251	−	0.996438i	$-0.473127\pi$
$457$	3.60533	0.168650	0.0843251	+	0.996438i	$0.473127\pi$
$458$	65.5886	3.06475
$459$	20.0862	0.937541
$460$	3.23355	0.150765
$461$	25.7420	1.19893	0.599463	−	0.800403i	$-0.295381\pi$
$461$	25.7420	1.19893	0.599463	+	0.800403i	$0.295381\pi$
$462$	76.3177	3.55062
$463$	−19.7761	−0.919072	−0.459536	−	0.888159i	$-0.651984\pi$
$463$	−19.7761	−0.919072	−0.459536	+	0.888159i	$0.651984\pi$
$464$	−25.5479	−1.18603
$465$	−1.43225	−0.0664192
$466$	8.72948	0.404385
$467$	−6.27833	−0.290526	−0.145263	−	0.989393i	$-0.546403\pi$
$467$	−6.27833	−0.290526	−0.145263	+	0.989393i	$0.546403\pi$
$468$	−123.444	−5.70622
$469$	−3.86463	−0.178452
$470$	0.993084	0.0458075
$471$	58.8668	2.71244
$472$	−94.6032	−4.35446
$473$	3.24301	0.149114
$474$	68.2133	3.13314
$475$	−6.15194	−0.282270
$476$	52.1362	2.38966
$477$	−4.57441	−0.209448
$478$	−68.8574	−3.14946
$479$	−36.6003	−1.67231	−0.836155	−	0.548494i	$-0.815202\pi$
$479$	−36.6003	−1.67231	−0.836155	+	0.548494i	$0.815202\pi$
$480$	−1.22172	−0.0557635
$481$	−18.0125	−0.821301
$482$	30.1468	1.37315
$483$	−60.8296	−2.76784
$484$	34.8902	1.58592
$485$	−0.666881	−0.0302815
$486$	−45.6672	−2.07151
$487$	−20.9091	−0.947481	−0.473741	−	0.880664i	$-0.657097\pi$
$487$	−20.9091	−0.947481	−0.473741	+	0.880664i	$0.657097\pi$
$488$	50.7765	2.29854
$489$	16.7270	0.756420
$490$	−0.142571	−0.00644069
$491$	30.6214	1.38192	0.690962	−	0.722891i	$-0.257187\pi$
$491$	30.6214	1.38192	0.690962	+	0.722891i	$0.257187\pi$
$492$	−135.652	−6.11567
$493$	16.7473	0.754259
$494$	18.9073	0.850679
$495$	1.63000	0.0732632
$496$	−44.7775	−2.01057
$497$	−26.6860	−1.19703
$498$	55.5826	2.49072
$499$	−30.7377	−1.37601	−0.688003	−	0.725707i	$-0.741513\pi$
$499$	−30.7377	−1.37601	−0.688003	+	0.725707i	$0.741513\pi$
$500$	3.67489	0.164346
$501$	−14.9587	−0.668305
$502$	39.3459	1.75609
$503$	39.7702	1.77327	0.886634	−	0.462473i	$-0.153038\pi$
$503$	39.7702	1.77327	0.886634	+	0.462473i	$0.153038\pi$
$504$	72.3946	3.22471
$505$	0.227401	0.0101192
$506$	−97.0052	−4.31241
$507$	−64.3310	−2.85704
$508$	−81.1724	−3.60144
$509$	−15.1723	−0.672502	−0.336251	−	0.941772i	$-0.609159\pi$
$509$	−15.1723	−0.672502	−0.336251	+	0.941772i	$0.609159\pi$
$510$	2.66797	0.118140
$511$	−0.353307	−0.0156294
$512$	50.8514	2.24734
$513$	−5.33853	−0.235702
$514$	50.1371	2.21145
$515$	−1.02391	−0.0451191
$516$	9.21101	0.405492
$517$	−20.5891	−0.905507
$518$	19.1018	0.839283
$519$	33.2982	1.46163
$520$	−3.12086	−0.136859
$521$	39.8510	1.74590	0.872952	−	0.487807i	$-0.162203\pi$
$521$	39.8510	1.74590	0.872952	+	0.487807i	$0.162203\pi$
$522$	42.0508	1.84051
$523$	−33.0569	−1.44548	−0.722738	−	0.691122i	$-0.757117\pi$
$523$	−33.0569	−1.44548	−0.722738	+	0.691122i	$0.757117\pi$
$524$	46.9342	2.05033
$525$	−34.5426	−1.50756
$526$	4.61816	0.201361
$527$	29.3528	1.27863
$528$	84.3805	3.67219
$529$	54.3188	2.36169
$530$	−0.209123	−0.00908371
$531$	68.7334	2.98278
$532$	−13.8568	−0.600770
$533$	−66.4378	−2.87774
$534$	−7.41428	−0.320847
$535$	0.740848	0.0320296
$536$	−9.68016	−0.418119
$537$	35.7062	1.54084
$538$	26.4905	1.14209
$539$	2.95584	0.127317
$540$	1.59342	0.0685698
$541$	−7.65697	−0.329199	−0.164600	−	0.986360i	$-0.552633\pi$
$541$	−7.65697	−0.329199	−0.164600	+	0.986360i	$0.552633\pi$
$542$	1.15650	0.0496757
$543$	−4.22448	−0.181290
$544$	25.0380	1.07350
$545$	−0.00469952	−0.000201305 0
$546$	106.163	4.54335
$547$	6.11122	0.261297	0.130648	−	0.991429i	$-0.458294\pi$
$547$	6.11122	0.261297	0.130648	+	0.991429i	$0.458294\pi$
$548$	44.8362	1.91531
$549$	−36.8914	−1.57448
$550$	−55.0853	−2.34884
$551$	−4.45111	−0.189624
$552$	−152.367	−6.48515
$553$	−24.4846	−1.04119
$554$	−23.2528	−0.987919
$555$	0.675539	0.0286750
$556$	−8.07900	−0.342626
$557$	−19.9654	−0.845960	−0.422980	−	0.906139i	$-0.639016\pi$
$557$	−19.9654	−0.845960	−0.422980	+	0.906139i	$0.639016\pi$
$558$	73.7021	3.12006
$559$	4.51124	0.190805
$560$	1.46088	0.0617334
$561$	−55.3135	−2.33534
$562$	−58.4478	−2.46547
$563$	13.7152	0.578028	0.289014	−	0.957325i	$-0.406673\pi$
$563$	13.7152	0.578028	0.289014	+	0.957325i	$0.406673\pi$
$564$	−58.4784	−2.46238
$565$	0.310345	0.0130563
$566$	−19.9457	−0.838382
$567$	4.51949	0.189801
$568$	−66.8433	−2.80468
$569$	17.1926	0.720751	0.360376	−	0.932807i	$-0.382649\pi$
$569$	17.1926	0.720751	0.360376	+	0.932807i	$0.382649\pi$
$570$	−0.709096	−0.0297008
$571$	−39.7594	−1.66388	−0.831939	−	0.554867i	$-0.812769\pi$
$571$	−39.7594	−1.66388	−0.831939	+	0.554867i	$0.812769\pi$
$572$	117.001	4.89205
$573$	27.6960	1.15702
$574$	70.4554	2.94075
$575$	43.9062	1.83101
$576$	−1.82830	−0.0761790
$577$	6.22280	0.259059	0.129529	−	0.991576i	$-0.458653\pi$
$577$	6.22280	0.259059	0.129529	+	0.991576i	$0.458653\pi$
$578$	−11.4213	−0.475065
$579$	−4.23737	−0.176099
$580$	1.32855	0.0551649
$581$	−19.9509	−0.827702
$582$	56.8227	2.35538
$583$	4.33563	0.179564
$584$	−0.884966	−0.0366202
$585$	2.26744	0.0937471
$586$	−13.8670	−0.572840
$587$	−4.57601	−0.188872	−0.0944361	−	0.995531i	$-0.530105\pi$
$587$	−4.57601	−0.188872	−0.0944361	+	0.995531i	$0.530105\pi$
$588$	8.39537	0.346219
$589$	−7.80142	−0.321452
$590$	3.14220	0.129362
$591$	−59.4274	−2.44452
$592$	21.1198	0.868020
$593$	−27.8178	−1.14234	−0.571171	−	0.820831i	$-0.693511\pi$
$593$	−27.8178	−1.14234	−0.571171	+	0.820831i	$0.693511\pi$
$594$	−47.8019	−1.96133
$595$	−0.957643	−0.0392595
$596$	−51.7495	−2.11974
$597$	−27.3650	−1.11998
$598$	−134.941	−5.51813
$599$	−35.2287	−1.43940	−0.719702	−	0.694283i	$-0.755722\pi$
$599$	−35.2287	−1.43940	−0.719702	+	0.694283i	$0.755722\pi$
$600$	−86.5227	−3.53228
$601$	−29.1471	−1.18894	−0.594468	−	0.804119i	$-0.702637\pi$
$601$	−29.1471	−1.18894	−0.594468	+	0.804119i	$0.702637\pi$
$602$	−4.78404	−0.194983
$603$	7.03307	0.286409
$604$	−4.47442	−0.182061
$605$	−0.640867	−0.0260549
$606$	−19.3761	−0.787099
$607$	20.3246	0.824948	0.412474	−	0.910969i	$-0.364665\pi$
$607$	20.3246	0.824948	0.412474	+	0.910969i	$0.364665\pi$
$608$	−6.65464	−0.269881
$609$	−24.9926	−1.01275
$610$	−1.68652	−0.0682851
$611$	−28.6408	−1.15868
$612$	−94.8803	−3.83531
$613$	−18.1015	−0.731112	−0.365556	−	0.930789i	$-0.619121\pi$
$613$	−18.1015	−0.731112	−0.365556	+	0.930789i	$0.619121\pi$
$614$	25.8184	1.04195
$615$	2.49167	0.100474
$616$	−68.6157	−2.76461
$617$	−43.0603	−1.73354	−0.866771	−	0.498707i	$-0.833808\pi$
$617$	−43.0603	−1.73354	−0.866771	+	0.498707i	$0.833808\pi$
$618$	87.2444	3.50948
$619$	−37.2095	−1.49557	−0.747787	−	0.663938i	$-0.768884\pi$
$619$	−37.2095	−1.49557	−0.747787	+	0.663938i	$0.768884\pi$
$620$	2.32853	0.0935160
$621$	38.1008	1.52893
$622$	−41.5920	−1.66769
$623$	2.66129	0.106622
$624$	117.379	4.69891
$625$	24.8987	0.995949
$626$	64.9578	2.59624
$627$	14.7013	0.587114
$628$	−95.7045	−3.81903
$629$	−13.8446	−0.552019
$630$	−2.40455	−0.0957997
$631$	−27.0966	−1.07870	−0.539349	−	0.842082i	$-0.681330\pi$
$631$	−27.0966	−1.07870	−0.539349	+	0.842082i	$0.681330\pi$
$632$	−61.3292	−2.43954
$633$	−34.5168	−1.37192
$634$	−1.02861	−0.0408514
$635$	1.49099	0.0591679
$636$	12.3143	0.488295
$637$	4.11177	0.162914
$638$	−39.8558	−1.57791
$639$	48.5646	1.92119
$640$	−0.971405	−0.0383981
$641$	−25.8139	−1.01959	−0.509795	−	0.860296i	$-0.670279\pi$
$641$	−25.8139	−1.01959	−0.509795	+	0.860296i	$0.670279\pi$
$642$	−63.1252	−2.49135
$643$	36.8107	1.45167	0.725836	−	0.687868i	$-0.241453\pi$
$643$	36.8107	1.45167	0.725836	+	0.687868i	$0.241453\pi$
$644$	98.8956	3.89703
$645$	−0.169189	−0.00666180
$646$	14.5323	0.571765
$647$	−21.3255	−0.838393	−0.419196	−	0.907896i	$-0.637688\pi$
$647$	−21.3255	−0.838393	−0.419196	+	0.907896i	$0.637688\pi$
$648$	11.3205	0.444709
$649$	−65.1456	−2.55719
$650$	−76.6272	−3.00557
$651$	−43.8043	−1.71683
$652$	−27.1944	−1.06502
$653$	27.6488	1.08198	0.540991	−	0.841028i	$-0.318049\pi$
$653$	27.6488	1.08198	0.540991	+	0.841028i	$0.318049\pi$
$654$	0.400431	0.0156581
$655$	−0.862094	−0.0336848
$656$	77.8989	3.04144
$657$	0.642967	0.0250845
$658$	30.3727	1.18405
$659$	−1.84756	−0.0719707	−0.0359853	−	0.999352i	$-0.511457\pi$
$659$	−1.84756	−0.0719707	−0.0359853	+	0.999352i	$0.511457\pi$
$660$	−4.38797	−0.170802
$661$	3.21923	0.125213	0.0626067	−	0.998038i	$-0.480059\pi$
$661$	3.21923	0.125213	0.0626067	+	0.998038i	$0.480059\pi$
$662$	−60.1949	−2.33954
$663$	−76.9447	−2.98829
$664$	−49.9732	−1.93934
$665$	0.254524	0.00987001
$666$	−34.7625	−1.34702
$667$	31.7674	1.23004
$668$	24.3196	0.940952
$669$	0.342496	0.0132417
$670$	0.321522	0.0124215
$671$	34.9657	1.34984
$672$	−37.3653	−1.44140
$673$	21.8528	0.842362	0.421181	−	0.906977i	$-0.361616\pi$
$673$	21.8528	0.842362	0.421181	+	0.906977i	$0.361616\pi$
$674$	−2.99946	−0.115535
$675$	21.6359	0.832766
$676$	104.588	4.02262
$677$	−35.8799	−1.37898	−0.689488	−	0.724297i	$-0.742165\pi$
$677$	−35.8799	−1.37898	−0.689488	+	0.724297i	$0.742165\pi$
$678$	−26.4435	−1.01556
$679$	−20.3960	−0.782727
$680$	−2.39871	−0.0919865
$681$	−35.5313	−1.36156
$682$	−69.8549	−2.67488
$683$	−24.3429	−0.931457	−0.465728	−	0.884928i	$-0.654208\pi$
$683$	−24.3429	−0.931457	−0.465728	+	0.884928i	$0.654208\pi$
$684$	25.2174	0.964212
$685$	−0.823557	−0.0314665
$686$	−49.1314	−1.87584
$687$	70.9418	2.70660
$688$	−5.28946	−0.201659
$689$	6.03114	0.229768
$690$	5.06079	0.192661
$691$	−0.695643	−0.0264635	−0.0132318	−	0.999912i	$-0.504212\pi$
$691$	−0.695643	−0.0264635	−0.0132318	+	0.999912i	$0.504212\pi$
$692$	−54.1356	−2.05793
$693$	49.8524	1.89373
$694$	−13.0048	−0.493655
$695$	0.148396	0.00562898
$696$	−62.6018	−2.37291
$697$	−51.0646	−1.93421
$698$	−57.4133	−2.17313
$699$	9.44197	0.357128
$700$	56.1587	2.12260
$701$	−18.4070	−0.695224	−0.347612	−	0.937638i	$-0.613007\pi$
$701$	−18.4070	−0.695224	−0.347612	+	0.937638i	$0.613007\pi$
$702$	−66.4955	−2.50971
$703$	3.67963	0.138780
$704$	1.73286	0.0653097
$705$	1.07414	0.0404544
$706$	−80.9183	−3.04540
$707$	6.95487	0.261565
$708$	−185.031	−6.95388
$709$	33.5958	1.26172	0.630859	−	0.775897i	$-0.282703\pi$
$709$	33.5958	1.26172	0.630859	+	0.775897i	$0.282703\pi$
$710$	2.22017	0.0833215
$711$	44.5584	1.67107
$712$	6.66603	0.249820
$713$	55.6784	2.08517
$714$	81.5976	3.05371
$715$	−2.14908	−0.0803711
$716$	−58.0505	−2.16945
$717$	−74.4774	−2.78141
$718$	82.4237	3.07603
$719$	−19.6546	−0.732992	−0.366496	−	0.930420i	$-0.619443\pi$
$719$	−19.6546	−0.732992	−0.366496	+	0.930420i	$0.619443\pi$
$720$	−2.65859	−0.0990798
$721$	−31.3156	−1.16625
$722$	44.4828	1.65548
$723$	32.6073	1.21268
$724$	6.86808	0.255250
$725$	18.0394	0.669967
$726$	54.6061	2.02662
$727$	−2.90746	−0.107832	−0.0539158	−	0.998545i	$-0.517170\pi$
$727$	−2.90746	−0.107832	−0.0539158	+	0.998545i	$0.517170\pi$
$728$	−95.4489	−3.53757
$729$	−44.0005	−1.62965
$730$	0.0293937	0.00108791
$731$	3.46738	0.128246
$732$	99.3117	3.67066
$733$	15.5628	0.574823	0.287412	−	0.957807i	$-0.407205\pi$
$733$	15.5628	0.574823	0.287412	+	0.957807i	$0.407205\pi$
$734$	−7.14429	−0.263700
$735$	−0.154207	−0.00568802
$736$	47.4939	1.75065
$737$	−6.66595	−0.245543
$738$	−128.219	−4.71979
$739$	37.7847	1.38993	0.694966	−	0.719043i	$-0.255419\pi$
$739$	37.7847	1.38993	0.694966	+	0.719043i	$0.255419\pi$
$740$	−1.09828	−0.0403735
$741$	20.4505	0.751267
$742$	−6.39585	−0.234799
$743$	3.52976	0.129494	0.0647472	−	0.997902i	$-0.479376\pi$
$743$	3.52976	0.129494	0.0647472	+	0.997902i	$0.479376\pi$
$744$	−109.721	−4.02259
$745$	0.950540	0.0348251
$746$	−70.6424	−2.58640
$747$	36.3077	1.32843
$748$	89.9277	3.28808
$749$	22.6582	0.827914
$750$	5.75151	0.210016
$751$	−37.5878	−1.37160	−0.685800	−	0.727790i	$-0.740548\pi$
$751$	−37.5878	−1.37160	−0.685800	+	0.727790i	$0.740548\pi$
$752$	33.5815	1.22459
$753$	42.5572	1.55087
$754$	−55.4421	−2.01908
$755$	0.0821866	0.00299108
$756$	48.7334	1.77242
$757$	−40.2226	−1.46191	−0.730957	−	0.682423i	$-0.760926\pi$
$757$	−40.2226	−1.46191	−0.730957	+	0.682423i	$0.760926\pi$
$758$	−38.9474	−1.41463
$759$	−104.923	−3.80845
$760$	0.637534	0.0231258
$761$	35.9693	1.30389	0.651943	−	0.758268i	$-0.273954\pi$
$761$	35.9693	1.30389	0.651943	+	0.758268i	$0.273954\pi$
$762$	−127.042	−4.60224
$763$	−0.143731	−0.00520342
$764$	−45.0276	−1.62904
$765$	1.74277	0.0630101
$766$	−19.9737	−0.721678
$767$	−90.6218	−3.27216
$768$	80.5702	2.90733
$769$	42.6516	1.53806	0.769028	−	0.639215i	$-0.220741\pi$
$769$	42.6516	1.53806	0.769028	+	0.639215i	$0.220741\pi$
$770$	2.27904	0.0821309
$771$	54.2293	1.95302
$772$	6.88904	0.247942
$773$	−11.2535	−0.404761	−0.202381	−	0.979307i	$-0.564868\pi$
$773$	−11.2535	−0.404761	−0.202381	+	0.979307i	$0.564868\pi$
$774$	8.70626	0.312940
$775$	31.6175	1.13573
$776$	−51.0881	−1.83396
$777$	20.6608	0.741203
$778$	6.99748	0.250872
$779$	13.5720	0.486269
$780$	−6.10396	−0.218557
$781$	−46.0296	−1.64707
$782$	−103.716	−3.70889
$783$	15.6542	0.559436
$784$	−4.82108	−0.172181
$785$	1.75791	0.0627426
$786$	73.4561	2.62009
$787$	11.1517	0.397515	0.198757	−	0.980049i	$-0.436309\pi$
$787$	11.1517	0.397515	0.198757	+	0.980049i	$0.436309\pi$
$788$	96.6158	3.44180
$789$	4.99509	0.177830
$790$	2.03702	0.0724740
$791$	9.49166	0.337485
$792$	124.871	4.43709
$793$	48.6395	1.72724
$794$	51.4747	1.82677
$795$	−0.226191	−0.00802217
$796$	44.4895	1.57689
$797$	23.0908	0.817920	0.408960	−	0.912552i	$-0.365892\pi$
$797$	23.0908	0.817920	0.408960	+	0.912552i	$0.365892\pi$
$798$	−21.6871	−0.767716
$799$	−22.0135	−0.778782
$800$	26.9698	0.953528
$801$	−4.84317	−0.171125
$802$	41.7662	1.47482
$803$	−0.609405	−0.0215054
$804$	−18.9330	−0.667717
$805$	−1.81653	−0.0640241
$806$	−97.1727	−3.42276
$807$	28.6527	1.00862
$808$	17.4206	0.612855
$809$	41.9200	1.47383	0.736914	−	0.675986i	$-0.236282\pi$
$809$	41.9200	1.47383	0.736914	+	0.675986i	$0.236282\pi$
$810$	−0.376004	−0.0132114
$811$	31.9734	1.12274	0.561369	−	0.827566i	$-0.310275\pi$
$811$	31.9734	1.12274	0.561369	+	0.827566i	$0.310275\pi$
$812$	40.6325	1.42592
$813$	1.25089	0.0438705
$814$	32.9479	1.15482
$815$	0.499510	0.0174971
$816$	90.2182	3.15827
$817$	−0.921564	−0.0322415
$818$	54.2826	1.89795
$819$	69.3479	2.42321
$820$	−4.05091	−0.141464
$821$	9.34786	0.326243	0.163121	−	0.986606i	$-0.447844\pi$
$821$	9.34786	0.326243	0.163121	+	0.986606i	$0.447844\pi$
$822$	70.1726	2.44755
$823$	25.9014	0.902865	0.451433	−	0.892305i	$-0.350913\pi$
$823$	25.9014	0.902865	0.451433	+	0.892305i	$0.350913\pi$
$824$	−78.4397	−2.73258
$825$	−59.5813	−2.07435
$826$	96.1018	3.34381
$827$	−28.0019	−0.973722	−0.486861	−	0.873479i	$-0.661858\pi$
$827$	−28.0019	−0.973722	−0.486861	+	0.873479i	$0.661858\pi$
$828$	−179.976	−6.25459
$829$	38.4111	1.33407	0.667036	−	0.745025i	$-0.267563\pi$
$829$	38.4111	1.33407	0.667036	+	0.745025i	$0.267563\pi$
$830$	1.65984	0.0576138
$831$	−25.1507	−0.872468
$832$	2.41052	0.0835698
$833$	3.16034	0.109499
$834$	−12.6443	−0.437838
$835$	−0.446705	−0.0154588
$836$	−23.9011	−0.826637
$837$	27.4370	0.948361
$838$	−52.0307	−1.79737
$839$	29.9158	1.03281	0.516405	−	0.856345i	$-0.327270\pi$
$839$	29.9158	1.03281	0.516405	+	0.856345i	$0.327270\pi$
$840$	3.57970	0.123511
$841$	−15.9480	−0.549930
$842$	42.6184	1.46873
$843$	−63.2182	−2.17735
$844$	56.1167	1.93162
$845$	−1.92109	−0.0660874
$846$	−55.2739	−1.90036
$847$	−19.6004	−0.673478
$848$	−7.07156	−0.242838
$849$	−21.5737	−0.740407
$850$	−58.8963	−2.02013
$851$	−26.2614	−0.900228
$852$	−130.736	−4.47895
$853$	−51.3535	−1.75831	−0.879155	−	0.476537i	$-0.841892\pi$
$853$	−51.3535	−1.75831	−0.879155	+	0.476537i	$0.841892\pi$
$854$	−51.5808	−1.76506
$855$	−0.463197	−0.0158410
$856$	56.7546	1.93983
$857$	12.4954	0.426833	0.213417	−	0.976961i	$-0.431541\pi$
$857$	12.4954	0.426833	0.213417	+	0.976961i	$0.431541\pi$
$858$	183.116	6.25149
$859$	0.742927	0.0253483	0.0126742	−	0.999920i	$-0.495966\pi$
$859$	0.742927	0.0253483	0.0126742	+	0.999920i	$0.495966\pi$
$860$	0.275064	0.00937960
$861$	76.2059	2.59709
$862$	−57.5176	−1.95906
$863$	12.4872	0.425069	0.212534	−	0.977154i	$-0.431828\pi$
$863$	12.4872	0.425069	0.212534	+	0.977154i	$0.431828\pi$
$864$	23.4039	0.796216
$865$	0.994370	0.0338096
$866$	−44.1338	−1.49973
$867$	−12.3535	−0.419547
$868$	71.2162	2.41724
$869$	−42.2325	−1.43264
$870$	2.07929	0.0704945
$871$	−9.27277	−0.314196
$872$	−0.360019	−0.0121918
$873$	37.1178	1.25625
$874$	27.5659	0.932430
$875$	−2.06446	−0.0697914
$876$	−1.73087	−0.0584807
$877$	13.8040	0.466127	0.233064	−	0.972461i	$-0.425125\pi$
$877$	13.8040	0.466127	0.233064	+	0.972461i	$0.425125\pi$
$878$	−37.4461	−1.26374
$879$	−14.9988	−0.505897
$880$	2.51982	0.0849430
$881$	−6.26251	−0.210989	−0.105495	−	0.994420i	$-0.533643\pi$
$881$	−6.26251	−0.210989	−0.105495	+	0.994420i	$0.533643\pi$
$882$	7.93532	0.267196
$883$	37.9742	1.27793	0.638966	−	0.769235i	$-0.279362\pi$
$883$	37.9742	1.27793	0.638966	+	0.769235i	$0.279362\pi$
$884$	125.095	4.20741
$885$	3.39866	0.114245
$886$	−52.5686	−1.76608
$887$	−6.05758	−0.203394	−0.101697	−	0.994815i	$-0.532427\pi$
$887$	−6.05758	−0.203394	−0.101697	+	0.994815i	$0.532427\pi$
$888$	51.7514	1.73666
$889$	45.6006	1.52939
$890$	−0.221409	−0.00742165
$891$	7.79549	0.261159
$892$	−0.556824	−0.0186438
$893$	5.85078	0.195789
$894$	−80.9924	−2.70879
$895$	1.06628	0.0356418
$896$	−29.7096	−0.992530
$897$	−145.954	−4.87327
$898$	−6.28073	−0.209591
$899$	22.8762	0.762964
$900$	−102.201	−3.40669
$901$	4.63559	0.154434
$902$	121.526	4.04637
$903$	−5.17451	−0.172197
$904$	23.7748	0.790738
$905$	−0.126154	−0.00419349
$906$	−7.00285	−0.232654
$907$	16.4302	0.545557	0.272778	−	0.962077i	$-0.412057\pi$
$907$	16.4302	0.545557	0.272778	+	0.962077i	$0.412057\pi$
$908$	57.7662	1.91704
$909$	−12.6569	−0.419801
$910$	3.17029	0.105094
$911$	6.22670	0.206300	0.103150	−	0.994666i	$-0.467108\pi$
$911$	6.22670	0.206300	0.103150	+	0.994666i	$0.467108\pi$
$912$	−23.9783	−0.794002
$913$	−34.4125	−1.13889
$914$	−9.17371	−0.303439
$915$	−1.82417	−0.0603051
$916$	−115.336	−3.81080
$917$	−26.3664	−0.870697
$918$	−51.1090	−1.68685
$919$	−25.8843	−0.853843	−0.426922	−	0.904289i	$-0.640402\pi$
$919$	−25.8843	−0.853843	−0.426922	+	0.904289i	$0.640402\pi$
$920$	−4.55005	−0.150011
$921$	27.9257	0.920182
$922$	−65.5003	−2.15714
$923$	−64.0302	−2.10758
$924$	−134.203	−4.41495
$925$	−14.9128	−0.490328
$926$	50.3200	1.65362
$927$	56.9899	1.87179
$928$	19.5135	0.640561
$929$	−10.9990	−0.360864	−0.180432	−	0.983587i	$-0.557750\pi$
$929$	−10.9990	−0.360864	−0.180432	+	0.983587i	$0.557750\pi$
$930$	3.64435	0.119503
$931$	−0.839959	−0.0275286
$932$	−15.3506	−0.502825
$933$	−44.9867	−1.47280
$934$	15.9751	0.522722
$935$	−1.65180	−0.0540197
$936$	173.703	5.67767
$937$	8.73378	0.285320	0.142660	−	0.989772i	$-0.454434\pi$
$937$	8.73378	0.285320	0.142660	+	0.989772i	$0.454434\pi$
$938$	9.83350	0.321075
$939$	70.2595	2.29283
$940$	−1.74631	−0.0569584
$941$	17.3878	0.566825	0.283412	−	0.958998i	$-0.408533\pi$
$941$	17.3878	0.566825	0.283412	+	0.958998i	$0.408533\pi$
$942$	−149.786	−4.88029
$943$	−96.8631	−3.15430
$944$	106.255	3.45830
$945$	−0.895141	−0.0291189
$946$	−8.25181	−0.268289
$947$	42.6828	1.38700	0.693502	−	0.720455i	$-0.256067\pi$
$947$	42.6828	1.38700	0.693502	+	0.720455i	$0.256067\pi$
$948$	−119.951	−3.89584
$949$	−0.847722	−0.0275182
$950$	15.6535	0.507868
$951$	−1.11257	−0.0360774
$952$	−73.3628	−2.37770
$953$	−15.6047	−0.505484	−0.252742	−	0.967534i	$-0.581332\pi$
$953$	−15.6047	−0.505484	−0.252742	+	0.967534i	$0.581332\pi$
$954$	11.6395	0.376844
$955$	0.827073	0.0267634
$956$	121.084	3.91613
$957$	−43.1088	−1.39351
$958$	93.1289	3.00886
$959$	−25.1878	−0.813358
$960$	−0.0904038	−0.00291777
$961$	9.09487	0.293383
$962$	45.8327	1.47770
$963$	−41.2347	−1.32877
$964$	−53.0123	−1.70741
$965$	−0.126539	−0.00407343
$966$	154.780	4.97997
$967$	44.5276	1.43191	0.715955	−	0.698146i	$-0.245992\pi$
$967$	44.5276	1.43191	0.715955	+	0.698146i	$0.245992\pi$
$968$	−49.0953	−1.57798
$969$	15.7184	0.504948
$970$	1.69687	0.0544832
$971$	9.85220	0.316172	0.158086	−	0.987425i	$-0.449468\pi$
$971$	9.85220	0.316172	0.158086	+	0.987425i	$0.449468\pi$
$972$	80.3046	2.57577
$973$	4.53858	0.145500
$974$	53.2029	1.70473
$975$	−82.8814	−2.65433
$976$	−57.0302	−1.82549
$977$	19.0304	0.608837	0.304418	−	0.952538i	$-0.401538\pi$
$977$	19.0304	0.608837	0.304418	+	0.952538i	$0.401538\pi$
$978$	−42.5616	−1.36097
$979$	4.59036	0.146709
$980$	0.250707	0.00800854
$981$	0.261570	0.00835129
$982$	−77.9158	−2.48639
$983$	−19.9750	−0.637104	−0.318552	−	0.947905i	$-0.603196\pi$
$983$	−19.9750	−0.637104	−0.318552	+	0.947905i	$0.603196\pi$
$984$	190.881	6.08507
$985$	−1.77465	−0.0565451
$986$	−42.6132	−1.35708
$987$	32.8517	1.04568
$988$	−33.2480	−1.05776
$989$	6.57717	0.209142
$990$	−4.14752	−0.131817
$991$	−19.6606	−0.624539	−0.312270	−	0.949994i	$-0.601089\pi$
$991$	−19.6606	−0.624539	−0.312270	+	0.949994i	$0.601089\pi$
$992$	34.2011	1.08589
$993$	−65.1079	−2.06614
$994$	67.9021	2.15372
$995$	−0.817189	−0.0259066
$996$	−97.7405	−3.09703
$997$	16.2073	0.513291	0.256646	−	0.966506i	$-0.417383\pi$
$997$	16.2073	0.513291	0.256646	+	0.966506i	$0.417383\pi$
$998$	78.2116	2.47574
$999$	−12.9410	−0.409435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.9	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.54449 q^{2} -2.75216 q^{3} +4.47442 q^{4} -0.0821866 q^{5} +7.00285 q^{6} -2.51361 q^{7} -6.29612 q^{8} +4.57441 q^{9} +O(q^{10})\)	\(q-2.54449 q^{2} -2.75216 q^{3} +4.47442 q^{4} -0.0821866 q^{5} +7.00285 q^{6} -2.51361 q^{7} -6.29612 q^{8} +4.57441 q^{9} +0.209123 q^{10} -4.33563 q^{11} -12.3143 q^{12} -6.03114 q^{13} +6.39585 q^{14} +0.226191 q^{15} +7.07156 q^{16} -4.63559 q^{17} -11.6395 q^{18} +1.23205 q^{19} -0.367737 q^{20} +6.91787 q^{21} +11.0320 q^{22} -8.79311 q^{23} +17.3280 q^{24} -4.99325 q^{25} +15.3462 q^{26} -4.33303 q^{27} -11.2469 q^{28} -3.61276 q^{29} -0.575540 q^{30} -6.33205 q^{31} -5.40126 q^{32} +11.9324 q^{33} +11.7952 q^{34} +0.206585 q^{35} +20.4678 q^{36} +2.98659 q^{37} -3.13494 q^{38} +16.5987 q^{39} +0.517457 q^{40} +11.0158 q^{41} -17.6024 q^{42} -0.747991 q^{43} -19.3994 q^{44} -0.375955 q^{45} +22.3740 q^{46} +4.74881 q^{47} -19.4621 q^{48} -0.681756 q^{49} +12.7052 q^{50} +12.7579 q^{51} -26.9858 q^{52} -1.00000 q^{53} +11.0254 q^{54} +0.356331 q^{55} +15.8260 q^{56} -3.39081 q^{57} +9.19262 q^{58} +15.0256 q^{59} +1.01207 q^{60} -8.06472 q^{61} +16.1118 q^{62} -11.4983 q^{63} -0.399679 q^{64} +0.495679 q^{65} -30.3618 q^{66} +1.53748 q^{67} -20.7415 q^{68} +24.2001 q^{69} -0.525653 q^{70} +10.6166 q^{71} -28.8010 q^{72} +0.140557 q^{73} -7.59933 q^{74} +13.7422 q^{75} +5.51272 q^{76} +10.8981 q^{77} -42.2352 q^{78} +9.74079 q^{79} -0.581188 q^{80} -1.79800 q^{81} -28.0295 q^{82} +7.93714 q^{83} +30.9534 q^{84} +0.380983 q^{85} +1.90325 q^{86} +9.94291 q^{87} +27.2977 q^{88} -1.05875 q^{89} +0.956613 q^{90} +15.1600 q^{91} -39.3440 q^{92} +17.4268 q^{93} -12.0833 q^{94} -0.101258 q^{95} +14.8652 q^{96} +8.11423 q^{97} +1.73472 q^{98} -19.8330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 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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