LMFDB - Embedded newform 8003.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.45028 q^{2} -2.96227 q^{3} +4.00387 q^{4} -1.96635 q^{5} +7.25838 q^{6} -3.26353 q^{7} -4.91003 q^{8} +5.77502 q^{9} +O(q^{10})$	\(q-2.45028 q^{2} -2.96227 q^{3} +4.00387 q^{4} -1.96635 q^{5} +7.25838 q^{6} -3.26353 q^{7} -4.91003 q^{8} +5.77502 q^{9} +4.81810 q^{10} +3.56216 q^{11} -11.8605 q^{12} +1.09024 q^{13} +7.99655 q^{14} +5.82484 q^{15} +4.02322 q^{16} -5.29205 q^{17} -14.1504 q^{18} -3.97632 q^{19} -7.87299 q^{20} +9.66744 q^{21} -8.72828 q^{22} +0.162150 q^{23} +14.5448 q^{24} -1.13348 q^{25} -2.67140 q^{26} -8.22034 q^{27} -13.0667 q^{28} +6.56483 q^{29} -14.2725 q^{30} +3.12887 q^{31} -0.0379352 q^{32} -10.5521 q^{33} +12.9670 q^{34} +6.41723 q^{35} +23.1224 q^{36} +5.80524 q^{37} +9.74308 q^{38} -3.22959 q^{39} +9.65483 q^{40} -6.58031 q^{41} -23.6879 q^{42} +2.90103 q^{43} +14.2624 q^{44} -11.3557 q^{45} -0.397313 q^{46} -6.26327 q^{47} -11.9178 q^{48} +3.65061 q^{49} +2.77734 q^{50} +15.6765 q^{51} +4.36518 q^{52} -1.00000 q^{53} +20.1421 q^{54} -7.00444 q^{55} +16.0240 q^{56} +11.7789 q^{57} -16.0857 q^{58} +10.7020 q^{59} +23.3219 q^{60} +1.30768 q^{61} -7.66661 q^{62} -18.8469 q^{63} -7.95348 q^{64} -2.14379 q^{65} +25.8555 q^{66} -1.23584 q^{67} -21.1887 q^{68} -0.480332 q^{69} -15.7240 q^{70} -12.4187 q^{71} -28.3555 q^{72} -12.5572 q^{73} -14.2245 q^{74} +3.35767 q^{75} -15.9206 q^{76} -11.6252 q^{77} +7.91339 q^{78} -2.70892 q^{79} -7.91104 q^{80} +7.02579 q^{81} +16.1236 q^{82} -14.0500 q^{83} +38.7071 q^{84} +10.4060 q^{85} -7.10834 q^{86} -19.4468 q^{87} -17.4903 q^{88} +3.16585 q^{89} +27.8246 q^{90} -3.55803 q^{91} +0.649227 q^{92} -9.26855 q^{93} +15.3468 q^{94} +7.81881 q^{95} +0.112374 q^{96} -14.7322 q^{97} -8.94502 q^{98} +20.5715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.45028	−1.73261	−0.866304	−	0.499516i	$-0.833511\pi$
$2$	−2.45028	−1.73261	−0.866304	+	0.499516i	$0.833511\pi$
$3$	−2.96227	−1.71026	−0.855132	−	0.518410i	$-0.826524\pi$
$3$	−2.96227	−1.71026	−0.855132	+	0.518410i	$0.826524\pi$
$4$	4.00387	2.00193
$5$	−1.96635	−0.879377	−0.439688	−	0.898150i	$-0.644911\pi$
$5$	−1.96635	−0.879377	−0.439688	+	0.898150i	$0.644911\pi$
$6$	7.25838	2.96322
$7$	−3.26353	−1.23350	−0.616749	−	0.787160i	$-0.711551\pi$
$7$	−3.26353	−1.23350	−0.616749	+	0.787160i	$0.711551\pi$
$8$	−4.91003	−1.73596
$9$	5.77502	1.92501
$10$	4.81810	1.52362
$11$	3.56216	1.07403	0.537015	−	0.843572i	$-0.319552\pi$
$11$	3.56216	1.07403	0.537015	+	0.843572i	$0.319552\pi$
$12$	−11.8605	−3.42384
$13$	1.09024	0.302379	0.151189	−	0.988505i	$-0.451690\pi$
$13$	1.09024	0.302379	0.151189	+	0.988505i	$0.451690\pi$
$14$	7.99655	2.13717
$15$	5.82484	1.50397
$16$	4.02322	1.00580
$17$	−5.29205	−1.28351	−0.641755	−	0.766910i	$-0.721793\pi$
$17$	−5.29205	−1.28351	−0.641755	+	0.766910i	$0.721793\pi$
$18$	−14.1504	−3.33528
$19$	−3.97632	−0.912229	−0.456115	−	0.889921i	$-0.650759\pi$
$19$	−3.97632	−0.912229	−0.456115	+	0.889921i	$0.650759\pi$
$20$	−7.87299	−1.76045
$21$	9.66744	2.10961
$22$	−8.72828	−1.86088
$23$	0.162150	0.0338106	0.0169053	−	0.999857i	$-0.494619\pi$
$23$	0.162150	0.0338106	0.0169053	+	0.999857i	$0.494619\pi$
$24$	14.5448	2.96895
$25$	−1.13348	−0.226696
$26$	−2.67140	−0.523904
$27$	−8.22034	−1.58201
$28$	−13.0667	−2.46938
$29$	6.56483	1.21906	0.609529	−	0.792764i	$-0.291359\pi$
$29$	6.56483	1.21906	0.609529	+	0.792764i	$0.291359\pi$
$30$	−14.2725	−2.60579
$31$	3.12887	0.561962	0.280981	−	0.959713i	$-0.409340\pi$
$31$	3.12887	0.561962	0.280981	+	0.959713i	$0.409340\pi$
$32$	−0.0379352	−0.00670606
$33$	−10.5521	−1.83688
$34$	12.9670	2.22382
$35$	6.41723	1.08471
$36$	23.1224	3.85373
$37$	5.80524	0.954375	0.477188	−	0.878801i	$-0.341656\pi$
$37$	5.80524	0.954375	0.477188	+	0.878801i	$0.341656\pi$
$38$	9.74308	1.58054
$39$	−3.22959	−0.517148
$40$	9.65483	1.52656
$41$	−6.58031	−1.02767	−0.513836	−	0.857889i	$-0.671776\pi$
$41$	−6.58031	−1.02767	−0.513836	+	0.857889i	$0.671776\pi$
$42$	−23.6879	−3.65512
$43$	2.90103	0.442404	0.221202	−	0.975228i	$-0.429002\pi$
$43$	2.90103	0.442404	0.221202	+	0.975228i	$0.429002\pi$
$44$	14.2624	2.15014
$45$	−11.3557	−1.69281
$46$	−0.397313	−0.0585806
$47$	−6.26327	−0.913592	−0.456796	−	0.889572i	$-0.651003\pi$
$47$	−6.26327	−0.913592	−0.456796	+	0.889572i	$0.651003\pi$
$48$	−11.9178	−1.72019
$49$	3.65061	0.521516
$50$	2.77734	0.392776
$51$	15.6765	2.19514
$52$	4.36518	0.605342
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	20.1421	2.74100
$55$	−7.00444	−0.944478
$56$	16.0240	2.14130
$57$	11.7789	1.56015
$58$	−16.0857	−2.11215
$59$	10.7020	1.39328	0.696639	−	0.717422i	$-0.254678\pi$
$59$	10.7020	1.39328	0.696639	+	0.717422i	$0.254678\pi$
$60$	23.3219	3.01084
$61$	1.30768	0.167432	0.0837159	−	0.996490i	$-0.473321\pi$
$61$	1.30768	0.167432	0.0837159	+	0.996490i	$0.473321\pi$
$62$	−7.66661	−0.973660
$63$	−18.8469	−2.37449
$64$	−7.95348	−0.994185
$65$	−2.14379	−0.265905
$66$	25.8555	3.18259
$67$	−1.23584	−0.150981	−0.0754907	−	0.997147i	$-0.524052\pi$
$67$	−1.23584	−0.150981	−0.0754907	+	0.997147i	$0.524052\pi$
$68$	−21.1887	−2.56950
$69$	−0.480332	−0.0578251
$70$	−15.7240	−1.87938
$71$	−12.4187	−1.47383	−0.736914	−	0.675986i	$-0.763718\pi$
$71$	−12.4187	−1.47383	−0.736914	+	0.675986i	$0.763718\pi$
$72$	−28.3555	−3.34173
$73$	−12.5572	−1.46970	−0.734852	−	0.678227i	$-0.762748\pi$
$73$	−12.5572	−1.46970	−0.734852	+	0.678227i	$0.762748\pi$
$74$	−14.2245	−1.65356
$75$	3.35767	0.387711
$76$	−15.9206	−1.82622
$77$	−11.6252	−1.32481
$78$	7.91339	0.896015
$79$	−2.70892	−0.304777	−0.152388	−	0.988321i	$-0.548696\pi$
$79$	−2.70892	−0.304777	−0.152388	+	0.988321i	$0.548696\pi$
$80$	−7.91104	−0.884481
$81$	7.02579	0.780643
$82$	16.1236	1.78055
$83$	−14.0500	−1.54219	−0.771093	−	0.636723i	$-0.780290\pi$
$83$	−14.0500	−1.54219	−0.771093	+	0.636723i	$0.780290\pi$
$84$	38.7071	4.22329
$85$	10.4060	1.12869
$86$	−7.10834	−0.766512
$87$	−19.4468	−2.08491
$88$	−17.4903	−1.86447
$89$	3.16585	0.335579	0.167789	−	0.985823i	$-0.446337\pi$
$89$	3.16585	0.335579	0.167789	+	0.985823i	$0.446337\pi$
$90$	27.8246	2.93297
$91$	−3.55803	−0.372983
$92$	0.649227	0.0676866
$93$	−9.26855	−0.961104
$94$	15.3468	1.58290
$95$	7.81881	0.802193
$96$	0.112374	0.0114691
$97$	−14.7322	−1.49583	−0.747914	−	0.663795i	$-0.768945\pi$
$97$	−14.7322	−1.49583	−0.747914	+	0.663795i	$0.768945\pi$
$98$	−8.94502	−0.903584
$99$	20.5715	2.06752
$100$	−4.53831	−0.453831
$101$	−8.49672	−0.845456	−0.422728	−	0.906257i	$-0.638927\pi$
$101$	−8.49672	−0.845456	−0.422728	+	0.906257i	$0.638927\pi$
$102$	−38.4117	−3.80332
$103$	17.2789	1.70254	0.851272	−	0.524725i	$-0.175832\pi$
$103$	17.2789	1.70254	0.851272	+	0.524725i	$0.175832\pi$
$104$	−5.35312	−0.524917
$105$	−19.0095	−1.85514
$106$	2.45028	0.237992
$107$	2.26294	0.218766	0.109383	−	0.994000i	$-0.465112\pi$
$107$	2.26294	0.218766	0.109383	+	0.994000i	$0.465112\pi$
$108$	−32.9132	−3.16707
$109$	0.443095	0.0424408	0.0212204	−	0.999775i	$-0.493245\pi$
$109$	0.443095	0.0424408	0.0212204	+	0.999775i	$0.493245\pi$
$110$	17.1628	1.63641
$111$	−17.1967	−1.63223
$112$	−13.1299	−1.24066
$113$	6.68196	0.628586	0.314293	−	0.949326i	$-0.398233\pi$
$113$	6.68196	0.628586	0.314293	+	0.949326i	$0.398233\pi$
$114$	−28.8616	−2.70314
$115$	−0.318843	−0.0297323
$116$	26.2847	2.44047
$117$	6.29617	0.582081
$118$	−26.2228	−2.41401
$119$	17.2707	1.58321
$120$	−28.6002	−2.61083
$121$	1.68897	0.153542
$122$	−3.20419	−0.290094
$123$	19.4926	1.75759
$124$	12.5276	1.12501
$125$	12.0605	1.07873
$126$	46.1802	4.11406
$127$	−1.65972	−0.147277	−0.0736383	−	0.997285i	$-0.523461\pi$
$127$	−1.65972	−0.147277	−0.0736383	+	0.997285i	$0.523461\pi$
$128$	19.5641	1.72924
$129$	−8.59363	−0.756627
$130$	5.25289	0.460709
$131$	12.4205	1.08518	0.542590	−	0.839998i	$-0.317444\pi$
$131$	12.4205	1.08518	0.542590	+	0.839998i	$0.317444\pi$
$132$	−42.2490	−3.67731
$133$	12.9768	1.12523
$134$	3.02814	0.261592
$135$	16.1640	1.39118
$136$	25.9841	2.22812
$137$	−1.71680	−0.146676	−0.0733382	−	0.997307i	$-0.523365\pi$
$137$	−1.71680	−0.146676	−0.0733382	+	0.997307i	$0.523365\pi$
$138$	1.17695	0.100188
$139$	10.4177	0.883617	0.441808	−	0.897109i	$-0.354337\pi$
$139$	10.4177	0.883617	0.441808	+	0.897109i	$0.354337\pi$
$140$	25.6937	2.17152
$141$	18.5535	1.56248
$142$	30.4293	2.55357
$143$	3.88361	0.324764
$144$	23.2341	1.93618
$145$	−12.9087	−1.07201
$146$	30.7685	2.54642
$147$	−10.8141	−0.891931
$148$	23.2434	1.91060
$149$	16.6667	1.36539	0.682697	−	0.730702i	$-0.260807\pi$
$149$	16.6667	1.36539	0.682697	+	0.730702i	$0.260807\pi$
$150$	−8.22723	−0.671751
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	19.5238	1.58359
$153$	−30.5617	−2.47077
$154$	28.4850	2.29539
$155$	−6.15245	−0.494177
$156$	−12.9308	−1.03530
$157$	4.32729	0.345355	0.172678	−	0.984978i	$-0.444758\pi$
$157$	4.32729	0.345355	0.172678	+	0.984978i	$0.444758\pi$
$158$	6.63760	0.528059
$159$	2.96227	0.234923
$160$	0.0745938	0.00589716
$161$	−0.529181	−0.0417053
$162$	−17.2151	−1.35255
$163$	−19.2665	−1.50907	−0.754534	−	0.656261i	$-0.772137\pi$
$163$	−19.2665	−1.50907	−0.754534	+	0.656261i	$0.772137\pi$
$164$	−26.3467	−2.05733
$165$	20.7490	1.61531
$166$	34.4264	2.67200
$167$	5.22062	0.403984	0.201992	−	0.979387i	$-0.435259\pi$
$167$	5.22062	0.403984	0.201992	+	0.979387i	$0.435259\pi$
$168$	−47.4674	−3.66219
$169$	−11.8114	−0.908567
$170$	−25.4976	−1.95558
$171$	−22.9633	−1.75605
$172$	11.6154	0.885662
$173$	−3.55070	−0.269955	−0.134978	−	0.990849i	$-0.543096\pi$
$173$	−3.55070	−0.269955	−0.134978	+	0.990849i	$0.543096\pi$
$174$	47.6500	3.61234
$175$	3.69915	0.279629
$176$	14.3313	1.08026
$177$	−31.7021	−2.38287
$178$	−7.75720	−0.581427
$179$	4.39686	0.328637	0.164318	−	0.986407i	$-0.447458\pi$
$179$	4.39686	0.328637	0.164318	+	0.986407i	$0.447458\pi$
$180$	−45.4667	−3.38889
$181$	4.21653	0.313412	0.156706	−	0.987645i	$-0.449912\pi$
$181$	4.21653	0.313412	0.156706	+	0.987645i	$0.449912\pi$
$182$	8.71818	0.646234
$183$	−3.87371	−0.286353
$184$	−0.796162	−0.0586939
$185$	−11.4151	−0.839255
$186$	22.7105	1.66522
$187$	−18.8511	−1.37853
$188$	−25.0773	−1.82895
$189$	26.8273	1.95140
$190$	−19.1583	−1.38989
$191$	8.23548	0.595898	0.297949	−	0.954582i	$-0.403697\pi$
$191$	8.23548	0.595898	0.297949	+	0.954582i	$0.403697\pi$
$192$	23.5603	1.70032
$193$	−1.42050	−0.102250	−0.0511250	−	0.998692i	$-0.516281\pi$
$193$	−1.42050	−0.102250	−0.0511250	+	0.998692i	$0.516281\pi$
$194$	36.0980	2.59169
$195$	6.35049	0.454768
$196$	14.6166	1.04404
$197$	5.98355	0.426310	0.213155	−	0.977018i	$-0.431626\pi$
$197$	5.98355	0.426310	0.213155	+	0.977018i	$0.431626\pi$
$198$	−50.4060	−3.58220
$199$	1.19685	0.0848427	0.0424214	−	0.999100i	$-0.486493\pi$
$199$	1.19685	0.0848427	0.0424214	+	0.999100i	$0.486493\pi$
$200$	5.56543	0.393535
$201$	3.66088	0.258218
$202$	20.8193	1.46484
$203$	−21.4245	−1.50370
$204$	62.7664	4.39453
$205$	12.9392	0.903711
$206$	−42.3382	−2.94984
$207$	0.936420	0.0650857
$208$	4.38628	0.304134
$209$	−14.1643	−0.979763
$210$	46.5787	3.21423
$211$	17.7688	1.22326	0.611628	−	0.791145i	$-0.290515\pi$
$211$	17.7688	1.22326	0.611628	+	0.791145i	$0.290515\pi$
$212$	−4.00387	−0.274987
$213$	36.7875	2.52064
$214$	−5.54482	−0.379036
$215$	−5.70444	−0.389039
$216$	40.3622	2.74630
$217$	−10.2112	−0.693179
$218$	−1.08571	−0.0735333
$219$	37.1976	2.51358
$220$	−28.0448	−1.89078
$221$	−5.76961	−0.388106
$222$	42.1366	2.82802
$223$	13.6375	0.913232	0.456616	−	0.889664i	$-0.349061\pi$
$223$	13.6375	0.913232	0.456616	+	0.889664i	$0.349061\pi$
$224$	0.123803	0.00827191
$225$	−6.54587	−0.436392
$226$	−16.3727	−1.08909
$227$	14.6922	0.975153	0.487576	−	0.873080i	$-0.337881\pi$
$227$	14.6922	0.975153	0.487576	+	0.873080i	$0.337881\pi$
$228$	47.1612	3.12332
$229$	−7.23368	−0.478015	−0.239008	−	0.971018i	$-0.576822\pi$
$229$	−7.23368	−0.478015	−0.239008	+	0.971018i	$0.576822\pi$
$230$	0.781255	0.0515144
$231$	34.4369	2.26578
$232$	−32.2335	−2.11623
$233$	26.8164	1.75680	0.878401	−	0.477924i	$-0.158611\pi$
$233$	26.8164	1.75680	0.878401	+	0.477924i	$0.158611\pi$
$234$	−15.4274	−1.00852
$235$	12.3158	0.803392
$236$	42.8493	2.78925
$237$	8.02453	0.521249
$238$	−42.3182	−2.74308
$239$	−2.46332	−0.159339	−0.0796695	−	0.996821i	$-0.525387\pi$
$239$	−2.46332	−0.159339	−0.0796695	+	0.996821i	$0.525387\pi$
$240$	23.4346	1.51270
$241$	−22.1624	−1.42760	−0.713802	−	0.700348i	$-0.753028\pi$
$241$	−22.1624	−1.42760	−0.713802	+	0.700348i	$0.753028\pi$
$242$	−4.13844	−0.266029
$243$	3.84879	0.246900
$244$	5.23579	0.335187
$245$	−7.17837	−0.458609
$246$	−47.7624	−3.04522
$247$	−4.33515	−0.275839
$248$	−15.3629	−0.975543
$249$	41.6198	2.63755
$250$	−29.5517	−1.86901
$251$	1.19272	0.0752840	0.0376420	−	0.999291i	$-0.488015\pi$
$251$	1.19272	0.0752840	0.0376420	+	0.999291i	$0.488015\pi$
$252$	−75.4606	−4.75357
$253$	0.577604	0.0363137
$254$	4.06678	0.255173
$255$	−30.8253	−1.93036
$256$	−32.0306	−2.00191
$257$	17.6728	1.10240	0.551198	−	0.834374i	$-0.314171\pi$
$257$	17.6728	1.10240	0.551198	+	0.834374i	$0.314171\pi$
$258$	21.0568	1.31094
$259$	−18.9456	−1.17722
$260$	−8.58346	−0.532324
$261$	37.9120	2.34669
$262$	−30.4336	−1.88019
$263$	24.1349	1.48822	0.744112	−	0.668055i	$-0.232873\pi$
$263$	24.1349	1.48822	0.744112	+	0.668055i	$0.232873\pi$
$264$	51.8109	3.18874
$265$	1.96635	0.120792
$266$	−31.7968	−1.94959
$267$	−9.37808	−0.573929
$268$	−4.94812	−0.302255
$269$	1.07322	0.0654355	0.0327178	−	0.999465i	$-0.489584\pi$
$269$	1.07322	0.0654355	0.0327178	+	0.999465i	$0.489584\pi$
$270$	−39.6064	−2.41037
$271$	2.30668	0.140121	0.0700604	−	0.997543i	$-0.477681\pi$
$271$	2.30668	0.140121	0.0700604	+	0.997543i	$0.477681\pi$
$272$	−21.2911	−1.29096
$273$	10.5398	0.637900
$274$	4.20665	0.254133
$275$	−4.03764	−0.243479
$276$	−1.92318	−0.115762
$277$	−16.4807	−0.990228	−0.495114	−	0.868828i	$-0.664874\pi$
$277$	−16.4807	−0.990228	−0.495114	+	0.868828i	$0.664874\pi$
$278$	−25.5262	−1.53096
$279$	18.0693	1.08178
$280$	−31.5088	−1.88301
$281$	16.6634	0.994056	0.497028	−	0.867735i	$-0.334425\pi$
$281$	16.6634	0.994056	0.497028	+	0.867735i	$0.334425\pi$
$282$	−45.4612	−2.70717
$283$	−13.2183	−0.785745	−0.392872	−	0.919593i	$-0.628519\pi$
$283$	−13.2183	−0.785745	−0.392872	+	0.919593i	$0.628519\pi$
$284$	−49.7228	−2.95051
$285$	−23.1614	−1.37196
$286$	−9.51594	−0.562689
$287$	21.4750	1.26763
$288$	−0.219077	−0.0129092
$289$	11.0058	0.647399
$290$	31.6300	1.85738
$291$	43.6407	2.55826
$292$	−50.2772	−2.94225
$293$	23.9230	1.39760	0.698798	−	0.715319i	$-0.253719\pi$
$293$	23.9230	1.39760	0.698798	+	0.715319i	$0.253719\pi$
$294$	26.4975	1.54537
$295$	−21.0438	−1.22522
$296$	−28.5039	−1.65676
$297$	−29.2822	−1.69912
$298$	−40.8382	−2.36569
$299$	0.176783	0.0102236
$300$	13.4437	0.776171
$301$	−9.46760	−0.545704
$302$	2.45028	0.140998
$303$	25.1696	1.44595
$304$	−15.9976	−0.917524
$305$	−2.57136	−0.147236
$306$	74.8846	4.28087
$307$	25.1651	1.43625	0.718125	−	0.695914i	$-0.245001\pi$
$307$	25.1651	1.43625	0.718125	+	0.695914i	$0.245001\pi$
$308$	−46.5458	−2.65219
$309$	−51.1848	−2.91180
$310$	15.0752	0.856215
$311$	17.9741	1.01922	0.509608	−	0.860407i	$-0.329790\pi$
$311$	17.9741	1.01922	0.509608	+	0.860407i	$0.329790\pi$
$312$	15.8574	0.897747
$313$	−4.05388	−0.229139	−0.114570	−	0.993415i	$-0.536549\pi$
$313$	−4.05388	−0.229139	−0.114570	+	0.993415i	$0.536549\pi$
$314$	−10.6031	−0.598366
$315$	37.0596	2.08807
$316$	−10.8461	−0.610143
$317$	17.6752	0.992740	0.496370	−	0.868111i	$-0.334666\pi$
$317$	17.6752	0.992740	0.496370	+	0.868111i	$0.334666\pi$
$318$	−7.25838	−0.407030
$319$	23.3849	1.30931
$320$	15.6393	0.874263
$321$	−6.70342	−0.374148
$322$	1.29664	0.0722590
$323$	21.0429	1.17086
$324$	28.1303	1.56279
$325$	−1.23577	−0.0685481
$326$	47.2083	2.61463
$327$	−1.31256	−0.0725850
$328$	32.3095	1.78400
$329$	20.4404	1.12691
$330$	−50.8408	−2.79870
$331$	−18.9977	−1.04421	−0.522105	−	0.852881i	$-0.674853\pi$
$331$	−18.9977	−1.04421	−0.522105	+	0.852881i	$0.674853\pi$
$332$	−56.2542	−3.08735
$333$	33.5254	1.83718
$334$	−12.7920	−0.699945
$335$	2.43008	0.132770
$336$	38.8942	2.12185
$337$	15.8202	0.861783	0.430891	−	0.902404i	$-0.358199\pi$
$337$	15.8202	0.861783	0.430891	+	0.902404i	$0.358199\pi$
$338$	28.9412	1.57419
$339$	−19.7938	−1.07505
$340$	41.6642	2.25956
$341$	11.1455	0.603565
$342$	56.2665	3.04254
$343$	10.9308	0.590209
$344$	−14.2442	−0.767994
$345$	0.944499	0.0508501
$346$	8.70022	0.467727
$347$	−8.06703	−0.433061	−0.216530	−	0.976276i	$-0.569474\pi$
$347$	−8.06703	−0.433061	−0.216530	+	0.976276i	$0.569474\pi$
$348$	−77.8622	−4.17385
$349$	−16.5903	−0.888057	−0.444028	−	0.896013i	$-0.646451\pi$
$349$	−16.5903	−0.888057	−0.444028	+	0.896013i	$0.646451\pi$
$350$	−9.06394	−0.484488
$351$	−8.96216	−0.478365
$352$	−0.135131	−0.00720252
$353$	−32.6584	−1.73823	−0.869115	−	0.494611i	$-0.835311\pi$
$353$	−32.6584	−1.73823	−0.869115	+	0.494611i	$0.835311\pi$
$354$	77.6789	4.12859
$355$	24.4195	1.29605
$356$	12.6756	0.671807
$357$	−51.1605	−2.70770
$358$	−10.7735	−0.569399
$359$	15.2901	0.806980	0.403490	−	0.914984i	$-0.367797\pi$
$359$	15.2901	0.806980	0.403490	+	0.914984i	$0.367797\pi$
$360$	55.7568	2.93864
$361$	−3.18891	−0.167838
$362$	−10.3317	−0.543021
$363$	−5.00317	−0.262598
$364$	−14.2459	−0.746688
$365$	24.6917	1.29242
$366$	9.49166	0.496137
$367$	18.1862	0.949312	0.474656	−	0.880171i	$-0.342572\pi$
$367$	18.1862	0.949312	0.474656	+	0.880171i	$0.342572\pi$
$368$	0.652365	0.0340069
$369$	−38.0014	−1.97827
$370$	27.9702	1.45410
$371$	3.26353	0.169434
$372$	−37.1100	−1.92407
$373$	−9.10499	−0.471438	−0.235719	−	0.971821i	$-0.575745\pi$
$373$	−9.10499	−0.471438	−0.235719	+	0.971821i	$0.575745\pi$
$374$	46.1905	2.38845
$375$	−35.7266	−1.84491
$376$	30.7529	1.58596
$377$	7.15725	0.368617
$378$	−65.7344	−3.38101
$379$	9.51955	0.488987	0.244493	−	0.969651i	$-0.421378\pi$
$379$	9.51955	0.488987	0.244493	+	0.969651i	$0.421378\pi$
$380$	31.3055	1.60594
$381$	4.91654	0.251882
$382$	−20.1792	−1.03246
$383$	−22.8947	−1.16986	−0.584932	−	0.811083i	$-0.698879\pi$
$383$	−22.8947	−1.16986	−0.584932	+	0.811083i	$0.698879\pi$
$384$	−57.9541	−2.95746
$385$	22.8592	1.16501
$386$	3.48063	0.177159
$387$	16.7535	0.851630
$388$	−58.9858	−2.99455
$389$	4.86002	0.246413	0.123206	−	0.992381i	$-0.460682\pi$
$389$	4.86002	0.246413	0.123206	+	0.992381i	$0.460682\pi$
$390$	−15.5605	−0.787935
$391$	−0.858106	−0.0433963
$392$	−17.9246	−0.905331
$393$	−36.7927	−1.85594
$394$	−14.6614	−0.738629
$395$	5.32667	0.268014
$396$	82.3657	4.13903
$397$	25.6001	1.28483	0.642417	−	0.766355i	$-0.277932\pi$
$397$	25.6001	1.28483	0.642417	+	0.766355i	$0.277932\pi$
$398$	−2.93263	−0.146999
$399$	−38.4408	−1.92445
$400$	−4.56024	−0.228012
$401$	−26.1927	−1.30800	−0.654000	−	0.756495i	$-0.726910\pi$
$401$	−26.1927	−1.30800	−0.654000	+	0.756495i	$0.726910\pi$
$402$	−8.97017	−0.447391
$403$	3.41123	0.169925
$404$	−34.0198	−1.69255
$405$	−13.8151	−0.686479
$406$	52.4960	2.60533
$407$	20.6792	1.02503
$408$	−76.9719	−3.81068
$409$	−8.40417	−0.415560	−0.207780	−	0.978176i	$-0.566624\pi$
$409$	−8.40417	−0.415560	−0.207780	+	0.978176i	$0.566624\pi$
$410$	−31.7046	−1.56578
$411$	5.08563	0.250855
$412$	69.1825	3.40838
$413$	−34.9262	−1.71860
$414$	−2.29449	−0.112768
$415$	27.6271	1.35616
$416$	−0.0413586	−0.00202777
$417$	−30.8600	−1.51122
$418$	34.7064	1.69755
$419$	−7.78340	−0.380244	−0.190122	−	0.981760i	$-0.560888\pi$
$419$	−7.78340	−0.380244	−0.190122	+	0.981760i	$0.560888\pi$
$420$	−76.1116	−3.71387
$421$	5.51175	0.268626	0.134313	−	0.990939i	$-0.457117\pi$
$421$	5.51175	0.268626	0.134313	+	0.990939i	$0.457117\pi$
$422$	−43.5386	−2.11942
$423$	−36.1705	−1.75867
$424$	4.91003	0.238452
$425$	5.99844	0.290967
$426$	−90.1396	−4.36728
$427$	−4.26766	−0.206527
$428$	9.06049	0.437955
$429$	−11.5043	−0.555433
$430$	13.9775	0.674053
$431$	32.0908	1.54576	0.772879	−	0.634553i	$-0.218816\pi$
$431$	32.0908	1.54576	0.772879	+	0.634553i	$0.218816\pi$
$432$	−33.0722	−1.59119
$433$	−8.75824	−0.420894	−0.210447	−	0.977605i	$-0.567492\pi$
$433$	−8.75824	−0.420894	−0.210447	+	0.977605i	$0.567492\pi$
$434$	25.0202	1.20101
$435$	38.2391	1.83342
$436$	1.77409	0.0849636
$437$	−0.644760	−0.0308431
$438$	−91.1446	−4.35506
$439$	−37.3328	−1.78180	−0.890898	−	0.454203i	$-0.849924\pi$
$439$	−37.3328	−1.78180	−0.890898	+	0.454203i	$0.849924\pi$
$440$	34.3920	1.63957
$441$	21.0824	1.00392
$442$	14.1372	0.672436
$443$	7.55558	0.358976	0.179488	−	0.983760i	$-0.442556\pi$
$443$	7.55558	0.358976	0.179488	+	0.983760i	$0.442556\pi$
$444$	−68.8531	−3.26762
$445$	−6.22515	−0.295100
$446$	−33.4156	−1.58227
$447$	−49.3713	−2.33518
$448$	25.9564	1.22632
$449$	28.7793	1.35818	0.679089	−	0.734056i	$-0.262375\pi$
$449$	28.7793	1.35818	0.679089	+	0.734056i	$0.262375\pi$
$450$	16.0392	0.756096
$451$	−23.4401	−1.10375
$452$	26.7537	1.25839
$453$	2.96227	0.139179
$454$	−35.9999	−1.68956
$455$	6.99633	0.327993
$456$	−57.8348	−2.70836
$457$	16.0985	0.753058	0.376529	−	0.926405i	$-0.377118\pi$
$457$	16.0985	0.753058	0.376529	+	0.926405i	$0.377118\pi$
$458$	17.7245	0.828213
$459$	43.5025	2.03052
$460$	−1.27661	−0.0595221
$461$	10.9706	0.510950	0.255475	−	0.966816i	$-0.417768\pi$
$461$	10.9706	0.510950	0.255475	+	0.966816i	$0.417768\pi$
$462$	−84.3801	−3.92572
$463$	−9.21276	−0.428153	−0.214077	−	0.976817i	$-0.568674\pi$
$463$	−9.21276	−0.428153	−0.214077	+	0.976817i	$0.568674\pi$
$464$	26.4117	1.22613
$465$	18.2252	0.845173
$466$	−65.7077	−3.04385
$467$	39.4780	1.82682	0.913411	−	0.407038i	$-0.133438\pi$
$467$	39.4780	1.82682	0.913411	+	0.407038i	$0.133438\pi$
$468$	25.2090	1.16529
$469$	4.03319	0.186235
$470$	−30.1770	−1.39196
$471$	−12.8186	−0.590649
$472$	−52.5470	−2.41867
$473$	10.3339	0.475155
$474$	−19.6623	−0.903121
$475$	4.50708	0.206799
$476$	69.1498	3.16947
$477$	−5.77502	−0.264420
$478$	6.03583	0.276072
$479$	6.77108	0.309379	0.154689	−	0.987963i	$-0.450562\pi$
$479$	6.77108	0.309379	0.154689	+	0.987963i	$0.450562\pi$
$480$	−0.220967	−0.0100857
$481$	6.32911	0.288583
$482$	54.3040	2.47348
$483$	1.56758	0.0713272
$484$	6.76240	0.307382
$485$	28.9686	1.31540
$486$	−9.43060	−0.427781
$487$	−25.4186	−1.15182	−0.575912	−	0.817511i	$-0.695353\pi$
$487$	−25.4186	−1.15182	−0.575912	+	0.817511i	$0.695353\pi$
$488$	−6.42077	−0.290655
$489$	57.0725	2.58091
$490$	17.5890	0.794591
$491$	−24.3051	−1.09687	−0.548437	−	0.836192i	$-0.684777\pi$
$491$	−24.3051	−1.09687	−0.548437	+	0.836192i	$0.684777\pi$
$492$	78.0459	3.51858
$493$	−34.7414	−1.56467
$494$	10.6223	0.477921
$495$	−40.4508	−1.81813
$496$	12.5881	0.565224
$497$	40.5288	1.81796
$498$	−101.980	−4.56984
$499$	24.7739	1.10903	0.554516	−	0.832173i	$-0.312903\pi$
$499$	24.7739	1.10903	0.554516	+	0.832173i	$0.312903\pi$
$500$	48.2888	2.15954
$501$	−15.4649	−0.690919
$502$	−2.92250	−0.130438
$503$	−18.0043	−0.802771	−0.401385	−	0.915909i	$-0.631471\pi$
$503$	−18.0043	−0.802771	−0.401385	+	0.915909i	$0.631471\pi$
$504$	92.5391	4.12202
$505$	16.7075	0.743474
$506$	−1.41529	−0.0629174
$507$	34.9884	1.55389
$508$	−6.64531	−0.294838
$509$	24.5310	1.08732	0.543659	−	0.839306i	$-0.317039\pi$
$509$	24.5310	1.08732	0.543659	+	0.839306i	$0.317039\pi$
$510$	75.5307	3.34456
$511$	40.9806	1.81288
$512$	39.3556	1.73929
$513$	32.6867	1.44315
$514$	−43.3032	−1.91002
$515$	−33.9764	−1.49718
$516$	−34.4078	−1.51472
$517$	−22.3108	−0.981226
$518$	46.4219	2.03966
$519$	10.5181	0.461695
$520$	10.5261	0.461600
$521$	−27.9598	−1.22494	−0.612471	−	0.790493i	$-0.709824\pi$
$521$	−27.9598	−1.22494	−0.612471	+	0.790493i	$0.709824\pi$
$522$	−92.8949	−4.06590
$523$	30.0613	1.31449	0.657244	−	0.753678i	$-0.271722\pi$
$523$	30.0613	1.31449	0.657244	+	0.753678i	$0.271722\pi$
$524$	49.7298	2.17246
$525$	−10.9579	−0.478240
$526$	−59.1373	−2.57851
$527$	−16.5581	−0.721284
$528$	−42.4532	−1.84754
$529$	−22.9737	−0.998857
$530$	−4.81810	−0.209285
$531$	61.8041	2.68207
$532$	51.9574	2.25264
$533$	−7.17413	−0.310746
$534$	22.9789	0.994394
$535$	−4.44972	−0.192378
$536$	6.06800	0.262098
$537$	−13.0247	−0.562056
$538$	−2.62969	−0.113374
$539$	13.0041	0.560125
$540$	64.7187	2.78505
$541$	−10.9625	−0.471314	−0.235657	−	0.971836i	$-0.575724\pi$
$541$	−10.9625	−0.471314	−0.235657	+	0.971836i	$0.575724\pi$
$542$	−5.65201	−0.242775
$543$	−12.4905	−0.536018
$544$	0.200755	0.00860730
$545$	−0.871278	−0.0373214
$546$	−25.8256	−1.10523
$547$	43.4615	1.85828	0.929140	−	0.369728i	$-0.120549\pi$
$547$	43.4615	1.85828	0.929140	+	0.369728i	$0.120549\pi$
$548$	−6.87385	−0.293636
$549$	7.55190	0.322307
$550$	9.89334	0.421853
$551$	−26.1038	−1.11206
$552$	2.35844	0.100382
$553$	8.84062	0.375942
$554$	40.3822	1.71568
$555$	33.8146	1.43535
$556$	41.7110	1.76894
$557$	−11.3213	−0.479699	−0.239850	−	0.970810i	$-0.577098\pi$
$557$	−11.3213	−0.479699	−0.239850	+	0.970810i	$0.577098\pi$
$558$	−44.2748	−1.87430
$559$	3.16283	0.133773
$560$	25.8179	1.09100
$561$	55.8420	2.35765
$562$	−40.8300	−1.72231
$563$	−23.7475	−1.00084	−0.500418	−	0.865784i	$-0.666820\pi$
$563$	−23.7475	−1.00084	−0.500418	+	0.865784i	$0.666820\pi$
$564$	74.2856	3.12799
$565$	−13.1391	−0.552764
$566$	32.3884	1.36139
$567$	−22.9288	−0.962921
$568$	60.9762	2.55850
$569$	21.5985	0.905454	0.452727	−	0.891649i	$-0.350451\pi$
$569$	21.5985	0.905454	0.452727	+	0.891649i	$0.350451\pi$
$570$	56.7519	2.37708
$571$	5.94116	0.248630	0.124315	−	0.992243i	$-0.460327\pi$
$571$	5.94116	0.248630	0.124315	+	0.992243i	$0.460327\pi$
$572$	15.5495	0.650156
$573$	−24.3957	−1.01914
$574$	−52.6198	−2.19631
$575$	−0.183794	−0.00766474
$576$	−45.9315	−1.91381
$577$	−18.8625	−0.785255	−0.392628	−	0.919698i	$-0.628434\pi$
$577$	−18.8625	−0.785255	−0.392628	+	0.919698i	$0.628434\pi$
$578$	−26.9672	−1.12169
$579$	4.20791	0.174875
$580$	−51.6848	−2.14609
$581$	45.8525	1.90228
$582$	−106.932	−4.43247
$583$	−3.56216	−0.147529
$584$	61.6561	2.55135
$585$	−12.3804	−0.511869
$586$	−58.6180	−2.42149
$587$	−17.4219	−0.719077	−0.359538	−	0.933130i	$-0.617066\pi$
$587$	−17.4219	−0.719077	−0.359538	+	0.933130i	$0.617066\pi$
$588$	−43.2982	−1.78559
$589$	−12.4414	−0.512638
$590$	51.5631	2.12282
$591$	−17.7249	−0.729103
$592$	23.3557	0.959914
$593$	43.8395	1.80027	0.900136	−	0.435609i	$-0.143467\pi$
$593$	43.8395	1.80027	0.900136	+	0.435609i	$0.143467\pi$
$594$	71.7495	2.94392
$595$	−33.9603	−1.39224
$596$	66.7314	2.73343
$597$	−3.54540	−0.145104
$598$	−0.433167	−0.0177135
$599$	35.0789	1.43328	0.716642	−	0.697441i	$-0.245678\pi$
$599$	35.0789	1.43328	0.716642	+	0.697441i	$0.245678\pi$
$600$	−16.4863	−0.673049
$601$	24.3495	0.993238	0.496619	−	0.867969i	$-0.334575\pi$
$601$	24.3495	0.993238	0.496619	+	0.867969i	$0.334575\pi$
$602$	23.1983	0.945491
$603$	−7.13698	−0.290640
$604$	−4.00387	−0.162915
$605$	−3.32109	−0.135022
$606$	−61.6724	−2.50527
$607$	−11.5199	−0.467579	−0.233790	−	0.972287i	$-0.575113\pi$
$607$	−11.5199	−0.467579	−0.233790	+	0.972287i	$0.575113\pi$
$608$	0.150842	0.00611747
$609$	63.4650	2.57173
$610$	6.30055	0.255102
$611$	−6.82848	−0.276251
$612$	−122.365	−4.94631
$613$	−25.8075	−1.04235	−0.521177	−	0.853449i	$-0.674507\pi$
$613$	−25.8075	−1.04235	−0.521177	+	0.853449i	$0.674507\pi$
$614$	−61.6616	−2.48846
$615$	−38.3293	−1.54558
$616$	57.0801	2.29982
$617$	0.852748	0.0343303	0.0171652	−	0.999853i	$-0.494536\pi$
$617$	0.852748	0.0343303	0.0171652	+	0.999853i	$0.494536\pi$
$618$	125.417	5.04501
$619$	−34.9995	−1.40675	−0.703375	−	0.710819i	$-0.748324\pi$
$619$	−34.9995	−1.40675	−0.703375	+	0.710819i	$0.748324\pi$
$620$	−24.6336	−0.989308
$621$	−1.33293	−0.0534886
$622$	−44.0415	−1.76590
$623$	−10.3318	−0.413936
$624$	−12.9933	−0.520149
$625$	−18.0478	−0.721913
$626$	9.93314	0.397008
$627$	41.9583	1.67565
$628$	17.3259	0.691378
$629$	−30.7216	−1.22495
$630$	−90.8064	−3.61781
$631$	−6.30963	−0.251183	−0.125591	−	0.992082i	$-0.540083\pi$
$631$	−6.30963	−0.251183	−0.125591	+	0.992082i	$0.540083\pi$
$632$	13.3009	0.529080
$633$	−52.6360	−2.09209
$634$	−43.3093	−1.72003
$635$	3.26359	0.129512
$636$	11.8605	0.470300
$637$	3.98005	0.157695
$638$	−57.2996	−2.26851
$639$	−71.7182	−2.83713
$640$	−38.4698	−1.52065
$641$	18.8798	0.745705	0.372853	−	0.927891i	$-0.378380\pi$
$641$	18.8798	0.745705	0.372853	+	0.927891i	$0.378380\pi$
$642$	16.4252	0.648253
$643$	3.98211	0.157039	0.0785196	−	0.996913i	$-0.474981\pi$
$643$	3.98211	0.157039	0.0785196	+	0.996913i	$0.474981\pi$
$644$	−2.11877	−0.0834913
$645$	16.8981	0.665361
$646$	−51.5609	−2.02864
$647$	−11.7687	−0.462676	−0.231338	−	0.972873i	$-0.574310\pi$
$647$	−11.7687	−0.462676	−0.231338	+	0.972873i	$0.574310\pi$
$648$	−34.4968	−1.35516
$649$	38.1221	1.49642
$650$	3.02798	0.118767
$651$	30.2482	1.18552
$652$	−77.1405	−3.02105
$653$	−11.8183	−0.462485	−0.231242	−	0.972896i	$-0.574279\pi$
$653$	−11.8183	−0.462485	−0.231242	+	0.972896i	$0.574279\pi$
$654$	3.21615	0.125761
$655$	−24.4229	−0.954282
$656$	−26.4740	−1.03364
$657$	−72.5178	−2.82919
$658$	−50.0846	−1.95250
$659$	−0.414096	−0.0161309	−0.00806545	−	0.999967i	$-0.502567\pi$
$659$	−0.414096	−0.0161309	−0.00806545	+	0.999967i	$0.502567\pi$
$660$	83.0762	3.23374
$661$	5.01480	0.195053	0.0975266	−	0.995233i	$-0.468907\pi$
$661$	5.01480	0.195053	0.0975266	+	0.995233i	$0.468907\pi$
$662$	46.5498	1.80921
$663$	17.0911	0.663764
$664$	68.9859	2.67717
$665$	−25.5169	−0.989504
$666$	−82.1465	−3.18311
$667$	1.06449	0.0412171
$668$	20.9027	0.808748
$669$	−40.3978	−1.56187
$670$	−5.95438	−0.230038
$671$	4.65818	0.179827
$672$	−0.366736	−0.0141472
$673$	−36.5076	−1.40727	−0.703633	−	0.710563i	$-0.748440\pi$
$673$	−36.5076	−1.40727	−0.703633	+	0.710563i	$0.748440\pi$
$674$	−38.7640	−1.49313
$675$	9.31760	0.358635
$676$	−47.2912	−1.81889
$677$	−21.3313	−0.819829	−0.409915	−	0.912124i	$-0.634441\pi$
$677$	−21.3313	−0.819829	−0.409915	+	0.912124i	$0.634441\pi$
$678$	48.5002	1.86264
$679$	48.0790	1.84510
$680$	−51.0938	−1.95936
$681$	−43.5221	−1.66777
$682$	−27.3097	−1.04574
$683$	14.6046	0.558831	0.279415	−	0.960170i	$-0.409859\pi$
$683$	14.6046	0.558831	0.279415	+	0.960170i	$0.409859\pi$
$684$	−91.9420	−3.51549
$685$	3.37583	0.128984
$686$	−26.7835	−1.02260
$687$	21.4281	0.817533
$688$	11.6715	0.444971
$689$	−1.09024	−0.0415349
$690$	−2.31429	−0.0881033
$691$	−24.8921	−0.946942	−0.473471	−	0.880810i	$-0.656999\pi$
$691$	−24.8921	−0.946942	−0.473471	+	0.880810i	$0.656999\pi$
$692$	−14.2165	−0.540432
$693$	−67.1357	−2.55028
$694$	19.7665	0.750325
$695$	−20.4848	−0.777032
$696$	95.4842	3.61932
$697$	34.8233	1.31903
$698$	40.6508	1.53865
$699$	−79.4374	−3.00460
$700$	14.8109	0.559799
$701$	31.2330	1.17965	0.589827	−	0.807529i	$-0.299196\pi$
$701$	31.2330	1.17965	0.589827	+	0.807529i	$0.299196\pi$
$702$	21.9598	0.828819
$703$	−23.0835	−0.870609
$704$	−28.3315	−1.06779
$705$	−36.4826	−1.37401
$706$	80.0221	3.01167
$707$	27.7293	1.04287
$708$	−126.931	−4.77035
$709$	−33.5776	−1.26103	−0.630517	−	0.776176i	$-0.717157\pi$
$709$	−33.5776	−1.26103	−0.630517	+	0.776176i	$0.717157\pi$
$710$	−59.8345	−2.24555
$711$	−15.6440	−0.586697
$712$	−15.5444	−0.582551
$713$	0.507347	0.0190003
$714$	125.358	4.69139
$715$	−7.63653	−0.285590
$716$	17.6044	0.657909
$717$	7.29701	0.272512
$718$	−37.4650	−1.39818
$719$	−29.8743	−1.11412	−0.557062	−	0.830471i	$-0.688071\pi$
$719$	−29.8743	−1.11412	−0.557062	+	0.830471i	$0.688071\pi$
$720$	−45.6864	−1.70263
$721$	−56.3903	−2.10008
$722$	7.81373	0.290797
$723$	65.6508	2.44158
$724$	16.8824	0.627431
$725$	−7.44110	−0.276356
$726$	12.2592	0.454980
$727$	−5.35827	−0.198727	−0.0993636	−	0.995051i	$-0.531681\pi$
$727$	−5.35827	−0.198727	−0.0993636	+	0.995051i	$0.531681\pi$
$728$	17.4701	0.647484
$729$	−32.4785	−1.20291
$730$	−60.5016	−2.23927
$731$	−15.3524	−0.567830
$732$	−15.5098	−0.573259
$733$	−17.5986	−0.650020	−0.325010	−	0.945711i	$-0.605368\pi$
$733$	−17.5986	−0.650020	−0.325010	+	0.945711i	$0.605368\pi$
$734$	−44.5613	−1.64479
$735$	21.2642	0.784343
$736$	−0.00615120	−0.000226736 0
$737$	−4.40224	−0.162159
$738$	93.1140	3.42758
$739$	0.486686	0.0179030	0.00895152	−	0.999960i	$-0.497151\pi$
$739$	0.486686	0.0179030	0.00895152	+	0.999960i	$0.497151\pi$
$740$	−45.7046	−1.68013
$741$	12.8419	0.471757
$742$	−7.99655	−0.293563
$743$	0.801487	0.0294037	0.0147019	−	0.999892i	$-0.495320\pi$
$743$	0.801487	0.0294037	0.0147019	+	0.999892i	$0.495320\pi$
$744$	45.5089	1.66844
$745$	−32.7726	−1.20070
$746$	22.3098	0.816818
$747$	−81.1389	−2.96872
$748$	−75.4773	−2.75972
$749$	−7.38515	−0.269848
$750$	87.5400	3.19651
$751$	46.2840	1.68893	0.844464	−	0.535613i	$-0.179919\pi$
$751$	46.2840	1.68893	0.844464	+	0.535613i	$0.179919\pi$
$752$	−25.1985	−0.918894
$753$	−3.53316	−0.128756
$754$	−17.5373	−0.638669
$755$	1.96635	0.0715627
$756$	107.413	3.90657
$757$	−28.4996	−1.03583	−0.517917	−	0.855431i	$-0.673292\pi$
$757$	−28.4996	−1.03583	−0.517917	+	0.855431i	$0.673292\pi$
$758$	−23.3256	−0.847223
$759$	−1.71102	−0.0621060
$760$	−38.3906	−1.39257
$761$	17.7227	0.642446	0.321223	−	0.947004i	$-0.395906\pi$
$761$	17.7227	0.642446	0.321223	+	0.947004i	$0.395906\pi$
$762$	−12.0469	−0.436413
$763$	−1.44605	−0.0523506
$764$	32.9737	1.19295
$765$	60.0949	2.17273
$766$	56.0983	2.02692
$767$	11.6677	0.421297
$768$	94.8831	3.42380
$769$	−11.2835	−0.406893	−0.203446	−	0.979086i	$-0.565214\pi$
$769$	−11.2835	−0.406893	−0.203446	+	0.979086i	$0.565214\pi$
$770$	−56.0114	−2.01851
$771$	−52.3514	−1.88539
$772$	−5.68750	−0.204698
$773$	1.62369	0.0584002	0.0292001	−	0.999574i	$-0.490704\pi$
$773$	1.62369	0.0584002	0.0292001	+	0.999574i	$0.490704\pi$
$774$	−41.0508	−1.47554
$775$	−3.54652	−0.127395
$776$	72.3356	2.59670
$777$	56.1218	2.01336
$778$	−11.9084	−0.426937
$779$	26.1654	0.937472
$780$	25.4265	0.910415
$781$	−44.2374	−1.58294
$782$	2.10260	0.0751888
$783$	−53.9651	−1.92856
$784$	14.6872	0.524543
$785$	−8.50895	−0.303697
$786$	90.1523	3.21563
$787$	31.0802	1.10789	0.553944	−	0.832554i	$-0.313122\pi$
$787$	31.0802	1.10789	0.553944	+	0.832554i	$0.313122\pi$
$788$	23.9573	0.853444
$789$	−71.4941	−2.54526
$790$	−13.0518	−0.464363
$791$	−21.8068	−0.775360
$792$	−101.007	−3.58912
$793$	1.42569	0.0506278
$794$	−62.7275	−2.22611
$795$	−5.82484	−0.206586
$796$	4.79204	0.169849
$797$	−36.5664	−1.29525	−0.647624	−	0.761960i	$-0.724237\pi$
$797$	−36.5664	−1.29525	−0.647624	+	0.761960i	$0.724237\pi$
$798$	94.1906	3.33431
$799$	33.1455	1.17260
$800$	0.0429988	0.00152024
$801$	18.2828	0.645992
$802$	64.1794	2.26625
$803$	−44.7306	−1.57851
$804$	14.6577	0.516936
$805$	1.04055	0.0366747
$806$	−8.35846	−0.294414
$807$	−3.17917	−0.111912
$808$	41.7192	1.46768
$809$	−24.4929	−0.861126	−0.430563	−	0.902561i	$-0.641685\pi$
$809$	−24.4929	−0.861126	−0.430563	+	0.902561i	$0.641685\pi$
$810$	33.8509	1.18940
$811$	43.8376	1.53935	0.769673	−	0.638438i	$-0.220419\pi$
$811$	43.8376	1.53935	0.769673	+	0.638438i	$0.220419\pi$
$812$	−85.7808	−3.01032
$813$	−6.83300	−0.239644
$814$	−50.6697	−1.77597
$815$	37.8846	1.32704
$816$	63.0698	2.20788
$817$	−11.5354	−0.403573
$818$	20.5926	0.720002
$819$	−20.5477	−0.717995
$820$	51.8067	1.80917
$821$	2.06908	0.0722113	0.0361056	−	0.999348i	$-0.488505\pi$
$821$	2.06908	0.0722113	0.0361056	+	0.999348i	$0.488505\pi$
$822$	−12.4612	−0.434634
$823$	−33.1957	−1.15713	−0.578565	−	0.815637i	$-0.696387\pi$
$823$	−33.1957	−1.15713	−0.578565	+	0.815637i	$0.696387\pi$
$824$	−84.8401	−2.95554
$825$	11.9606	0.416413
$826$	85.5789	2.97767
$827$	−37.6137	−1.30796	−0.653979	−	0.756513i	$-0.726901\pi$
$827$	−37.6137	−1.30796	−0.653979	+	0.756513i	$0.726901\pi$
$828$	3.74930	0.130297
$829$	13.8814	0.482119	0.241060	−	0.970510i	$-0.422505\pi$
$829$	13.8814	0.482119	0.241060	+	0.970510i	$0.422505\pi$
$830$	−67.6942	−2.34970
$831$	48.8201	1.69355
$832$	−8.67122	−0.300620
$833$	−19.3192	−0.669371
$834$	75.6155	2.61835
$835$	−10.2655	−0.355254
$836$	−56.7118	−1.96142
$837$	−25.7204	−0.889027
$838$	19.0715	0.658814
$839$	33.9640	1.17257	0.586283	−	0.810106i	$-0.300591\pi$
$839$	33.9640	1.17257	0.586283	+	0.810106i	$0.300591\pi$
$840$	93.3374	3.22045
$841$	14.0969	0.486101
$842$	−13.5053	−0.465425
$843$	−49.3615	−1.70010
$844$	71.1440	2.44888
$845$	23.2253	0.798973
$846$	88.6278	3.04709
$847$	−5.51199	−0.189394
$848$	−4.02322	−0.138158
$849$	39.1560	1.34383
$850$	−14.6978	−0.504132
$851$	0.941320	0.0322680
$852$	147.292	5.04615
$853$	−29.8424	−1.02178	−0.510892	−	0.859645i	$-0.670685\pi$
$853$	−29.8424	−1.02178	−0.510892	+	0.859645i	$0.670685\pi$
$854$	10.4570	0.357830
$855$	45.1538	1.54423
$856$	−11.1111	−0.379769
$857$	−36.7877	−1.25665	−0.628323	−	0.777953i	$-0.716258\pi$
$857$	−36.7877	−1.25665	−0.628323	+	0.777953i	$0.716258\pi$
$858$	28.1887	0.962348
$859$	50.3098	1.71655	0.858275	−	0.513190i	$-0.171536\pi$
$859$	50.3098	1.71655	0.858275	+	0.513190i	$0.171536\pi$
$860$	−22.8398	−0.778831
$861$	−63.6147	−2.16798
$862$	−78.6314	−2.67819
$863$	33.9217	1.15471	0.577355	−	0.816493i	$-0.304085\pi$
$863$	33.9217	1.15471	0.577355	+	0.816493i	$0.304085\pi$
$864$	0.311840	0.0106090
$865$	6.98192	0.237392
$866$	21.4601	0.729245
$867$	−32.6021	−1.10722
$868$	−40.8841	−1.38770
$869$	−9.64959	−0.327340
$870$	−93.6964	−3.17660
$871$	−1.34736	−0.0456536
$872$	−2.17561	−0.0736754
$873$	−85.0788	−2.87948
$874$	1.57984	0.0534390
$875$	−39.3599	−1.33061
$876$	148.934	5.03203
$877$	50.8266	1.71629	0.858147	−	0.513404i	$-0.171616\pi$
$877$	50.8266	1.71629	0.858147	+	0.513404i	$0.171616\pi$
$878$	91.4758	3.08716
$879$	−70.8662	−2.39026
$880$	−28.1804	−0.949960
$881$	−4.30083	−0.144899	−0.0724493	−	0.997372i	$-0.523082\pi$
$881$	−4.30083	−0.144899	−0.0724493	+	0.997372i	$0.523082\pi$
$882$	−51.6577	−1.73940
$883$	−42.9355	−1.44489	−0.722447	−	0.691426i	$-0.756983\pi$
$883$	−42.9355	−1.44489	−0.722447	+	0.691426i	$0.756983\pi$
$884$	−23.1008	−0.776963
$885$	62.3373	2.09544
$886$	−18.5133	−0.621966
$887$	−12.4257	−0.417214	−0.208607	−	0.978000i	$-0.566893\pi$
$887$	−12.4257	−0.417214	−0.208607	+	0.978000i	$0.566893\pi$
$888$	84.4361	2.83349
$889$	5.41655	0.181665
$890$	15.2534	0.511294
$891$	25.0270	0.838434
$892$	54.6026	1.82823
$893$	24.9047	0.833405
$894$	120.974	4.04596
$895$	−8.64575	−0.288996
$896$	−63.8480	−2.13301
$897$	−0.523678	−0.0174851
$898$	−70.5173	−2.35319
$899$	20.5405	0.685064
$900$	−26.2088	−0.873627
$901$	5.29205	0.176304
$902$	57.4348	1.91237
$903$	28.0456	0.933298
$904$	−32.8087	−1.09120
$905$	−8.29117	−0.275608
$906$	−7.25838	−0.241143
$907$	−52.3413	−1.73796	−0.868982	−	0.494843i	$-0.835225\pi$
$907$	−52.3413	−1.73796	−0.868982	+	0.494843i	$0.835225\pi$
$908$	58.8255	1.95219
$909$	−49.0687	−1.62751
$910$	−17.1430	−0.568284
$911$	50.2606	1.66521	0.832604	−	0.553869i	$-0.186849\pi$
$911$	50.2606	1.66521	0.832604	+	0.553869i	$0.186849\pi$
$912$	47.3891	1.56921
$913$	−50.0482	−1.65636
$914$	−39.4459	−1.30475
$915$	7.61705	0.251812
$916$	−28.9627	−0.956955
$917$	−40.5345	−1.33857
$918$	−106.593	−3.51810
$919$	31.1967	1.02908	0.514542	−	0.857465i	$-0.327962\pi$
$919$	31.1967	1.02908	0.514542	+	0.857465i	$0.327962\pi$
$920$	1.56553	0.0516140
$921$	−74.5458	−2.45637
$922$	−26.8810	−0.885277
$923$	−13.5394	−0.445654
$924$	137.881	4.53595
$925$	−6.58013	−0.216353
$926$	22.5738	0.741822
$927$	99.7861	3.27741
$928$	−0.249038	−0.00817507
$929$	−5.95097	−0.195245	−0.0976225	−	0.995224i	$-0.531124\pi$
$929$	−5.95097	−0.195245	−0.0976225	+	0.995224i	$0.531124\pi$
$930$	−44.6568	−1.46435
$931$	−14.5160	−0.475742
$932$	107.369	3.51700
$933$	−53.2440	−1.74313
$934$	−96.7320	−3.16517
$935$	37.0678	1.21225
$936$	−30.9144	−1.01047
$937$	33.5806	1.09703	0.548515	−	0.836141i	$-0.315193\pi$
$937$	33.5806	1.09703	0.548515	+	0.836141i	$0.315193\pi$
$938$	−9.88243	−0.322673
$939$	12.0087	0.391888
$940$	49.3107	1.60834
$941$	−18.0817	−0.589448	−0.294724	−	0.955582i	$-0.595228\pi$
$941$	−18.0817	−0.589448	−0.294724	+	0.955582i	$0.595228\pi$
$942$	31.4091	1.02336
$943$	−1.06700	−0.0347462
$944$	43.0563	1.40136
$945$	−52.7518	−1.71602
$946$	−25.3210	−0.823258
$947$	10.7948	0.350783	0.175391	−	0.984499i	$-0.443881\pi$
$947$	10.7948	0.350783	0.175391	+	0.984499i	$0.443881\pi$
$948$	32.1291	1.04351
$949$	−13.6903	−0.444407
$950$	−11.0436	−0.358302
$951$	−52.3588	−1.69785
$952$	−84.7999	−2.74838
$953$	−33.1558	−1.07402	−0.537010	−	0.843576i	$-0.680446\pi$
$953$	−33.1558	−1.07402	−0.537010	+	0.843576i	$0.680446\pi$
$954$	14.1504	0.458136
$955$	−16.1938	−0.524019
$956$	−9.86281	−0.318986
$957$	−69.2724	−2.23926
$958$	−16.5910	−0.536032
$959$	5.60283	0.180925
$960$	−46.3278	−1.49522
$961$	−21.2102	−0.684199
$962$	−15.5081	−0.500001
$963$	13.0685	0.421126
$964$	−88.7352	−2.85797
$965$	2.79320	0.0899163
$966$	−3.84100	−0.123582
$967$	−8.92640	−0.287054	−0.143527	−	0.989646i	$-0.545844\pi$
$967$	−8.92640	−0.287054	−0.143527	+	0.989646i	$0.545844\pi$
$968$	−8.29288	−0.266543
$969$	−62.3345	−2.00247
$970$	−70.9812	−2.27907
$971$	−56.0548	−1.79889	−0.899443	−	0.437039i	$-0.856027\pi$
$971$	−56.0548	−1.79889	−0.899443	+	0.437039i	$0.856027\pi$
$972$	15.4100	0.494277
$973$	−33.9984	−1.08994
$974$	62.2826	1.99566
$975$	3.66067	0.117235
$976$	5.26109	0.168404
$977$	19.0003	0.607875	0.303937	−	0.952692i	$-0.401699\pi$
$977$	19.0003	0.607875	0.303937	+	0.952692i	$0.401699\pi$
$978$	−139.843	−4.47170
$979$	11.2772	0.360422
$980$	−28.7412	−0.918105
$981$	2.55888	0.0816987
$982$	59.5542	1.90045
$983$	−46.5060	−1.48331	−0.741655	−	0.670781i	$-0.765959\pi$
$983$	−46.5060	−1.48331	−0.741655	+	0.670781i	$0.765959\pi$
$984$	−95.7094	−3.05110
$985$	−11.7657	−0.374887
$986$	85.1261	2.71097
$987$	−60.5498	−1.92732
$988$	−17.3573	−0.552211
$989$	0.470403	0.0149579
$990$	99.1156	3.15010
$991$	27.8489	0.884650	0.442325	−	0.896855i	$-0.354154\pi$
$991$	27.8489	0.884650	0.442325	+	0.896855i	$0.354154\pi$
$992$	−0.118694	−0.00376855
$993$	56.2763	1.78588
$994$	−99.3068	−3.14982
$995$	−2.35343	−0.0746087
$996$	166.640	5.28019
$997$	35.2711	1.11705	0.558523	−	0.829489i	$-0.311368\pi$
$997$	35.2711	1.11705	0.558523	+	0.829489i	$0.311368\pi$
$998$	−60.7030	−1.92152
$999$	−47.7210	−1.50983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.13	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.45028 q^{2} -2.96227 q^{3} +4.00387 q^{4} -1.96635 q^{5} +7.25838 q^{6} -3.26353 q^{7} -4.91003 q^{8} +5.77502 q^{9} +O(q^{10})\)	\(q-2.45028 q^{2} -2.96227 q^{3} +4.00387 q^{4} -1.96635 q^{5} +7.25838 q^{6} -3.26353 q^{7} -4.91003 q^{8} +5.77502 q^{9} +4.81810 q^{10} +3.56216 q^{11} -11.8605 q^{12} +1.09024 q^{13} +7.99655 q^{14} +5.82484 q^{15} +4.02322 q^{16} -5.29205 q^{17} -14.1504 q^{18} -3.97632 q^{19} -7.87299 q^{20} +9.66744 q^{21} -8.72828 q^{22} +0.162150 q^{23} +14.5448 q^{24} -1.13348 q^{25} -2.67140 q^{26} -8.22034 q^{27} -13.0667 q^{28} +6.56483 q^{29} -14.2725 q^{30} +3.12887 q^{31} -0.0379352 q^{32} -10.5521 q^{33} +12.9670 q^{34} +6.41723 q^{35} +23.1224 q^{36} +5.80524 q^{37} +9.74308 q^{38} -3.22959 q^{39} +9.65483 q^{40} -6.58031 q^{41} -23.6879 q^{42} +2.90103 q^{43} +14.2624 q^{44} -11.3557 q^{45} -0.397313 q^{46} -6.26327 q^{47} -11.9178 q^{48} +3.65061 q^{49} +2.77734 q^{50} +15.6765 q^{51} +4.36518 q^{52} -1.00000 q^{53} +20.1421 q^{54} -7.00444 q^{55} +16.0240 q^{56} +11.7789 q^{57} -16.0857 q^{58} +10.7020 q^{59} +23.3219 q^{60} +1.30768 q^{61} -7.66661 q^{62} -18.8469 q^{63} -7.95348 q^{64} -2.14379 q^{65} +25.8555 q^{66} -1.23584 q^{67} -21.1887 q^{68} -0.480332 q^{69} -15.7240 q^{70} -12.4187 q^{71} -28.3555 q^{72} -12.5572 q^{73} -14.2245 q^{74} +3.35767 q^{75} -15.9206 q^{76} -11.6252 q^{77} +7.91339 q^{78} -2.70892 q^{79} -7.91104 q^{80} +7.02579 q^{81} +16.1236 q^{82} -14.0500 q^{83} +38.7071 q^{84} +10.4060 q^{85} -7.10834 q^{86} -19.4468 q^{87} -17.4903 q^{88} +3.16585 q^{89} +27.8246 q^{90} -3.55803 q^{91} +0.649227 q^{92} -9.26855 q^{93} +15.3468 q^{94} +7.81881 q^{95} +0.112374 q^{96} -14.7322 q^{97} -8.94502 q^{98} +20.5715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 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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