LMFDB - Embedded newform 8003.2.a.b.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.40368 q^{2} +2.42213 q^{3} +3.77770 q^{4} +1.57847 q^{5} -5.82205 q^{6} -3.75128 q^{7} -4.27303 q^{8} +2.86673 q^{9} +O(q^{10})$	\(q-2.40368 q^{2} +2.42213 q^{3} +3.77770 q^{4} +1.57847 q^{5} -5.82205 q^{6} -3.75128 q^{7} -4.27303 q^{8} +2.86673 q^{9} -3.79414 q^{10} +2.83952 q^{11} +9.15010 q^{12} +2.38822 q^{13} +9.01688 q^{14} +3.82326 q^{15} +2.71562 q^{16} -1.20694 q^{17} -6.89073 q^{18} -2.50380 q^{19} +5.96298 q^{20} -9.08609 q^{21} -6.82532 q^{22} -6.40600 q^{23} -10.3499 q^{24} -2.50844 q^{25} -5.74053 q^{26} -0.322786 q^{27} -14.1712 q^{28} +5.21159 q^{29} -9.18992 q^{30} +6.95630 q^{31} +2.01856 q^{32} +6.87771 q^{33} +2.90109 q^{34} -5.92127 q^{35} +10.8297 q^{36} -2.27675 q^{37} +6.01834 q^{38} +5.78460 q^{39} -6.74485 q^{40} -3.13902 q^{41} +21.8401 q^{42} -1.85137 q^{43} +10.7269 q^{44} +4.52505 q^{45} +15.3980 q^{46} -5.28542 q^{47} +6.57760 q^{48} +7.07207 q^{49} +6.02950 q^{50} -2.92336 q^{51} +9.02199 q^{52} -1.00000 q^{53} +0.775876 q^{54} +4.48210 q^{55} +16.0293 q^{56} -6.06454 q^{57} -12.5270 q^{58} -10.9540 q^{59} +14.4431 q^{60} -4.26030 q^{61} -16.7207 q^{62} -10.7539 q^{63} -10.2832 q^{64} +3.76973 q^{65} -16.5318 q^{66} +7.32529 q^{67} -4.55944 q^{68} -15.5162 q^{69} +14.2329 q^{70} +2.39880 q^{71} -12.2497 q^{72} +12.3298 q^{73} +5.47260 q^{74} -6.07578 q^{75} -9.45860 q^{76} -10.6518 q^{77} -13.9043 q^{78} -14.0130 q^{79} +4.28652 q^{80} -9.38204 q^{81} +7.54523 q^{82} -6.98219 q^{83} -34.3245 q^{84} -1.90511 q^{85} +4.45010 q^{86} +12.6232 q^{87} -12.1334 q^{88} -16.4636 q^{89} -10.8768 q^{90} -8.95888 q^{91} -24.1999 q^{92} +16.8491 q^{93} +12.7045 q^{94} -3.95217 q^{95} +4.88923 q^{96} -8.99278 q^{97} -16.9990 q^{98} +8.14016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40368	−1.69966	−0.849831	−	0.527055i	$-0.823296\pi$
$2$	−2.40368	−1.69966	−0.849831	+	0.527055i	$0.823296\pi$
$3$	2.42213	1.39842	0.699210	−	0.714916i	$-0.253535\pi$
$3$	2.42213	1.39842	0.699210	+	0.714916i	$0.253535\pi$
$4$	3.77770	1.88885
$5$	1.57847	0.705912	0.352956	−	0.935640i	$-0.385176\pi$
$5$	1.57847	0.705912	0.352956	+	0.935640i	$0.385176\pi$
$6$	−5.82205	−2.37684
$7$	−3.75128	−1.41785	−0.708924	−	0.705284i	$-0.750819\pi$
$7$	−3.75128	−1.41785	−0.708924	+	0.705284i	$0.750819\pi$
$8$	−4.27303	−1.51075
$9$	2.86673	0.955578
$10$	−3.79414	−1.19981
$11$	2.83952	0.856148	0.428074	−	0.903744i	$-0.359192\pi$
$11$	2.83952	0.856148	0.428074	+	0.903744i	$0.359192\pi$
$12$	9.15010	2.64141
$13$	2.38822	0.662374	0.331187	−	0.943565i	$-0.392551\pi$
$13$	2.38822	0.662374	0.331187	+	0.943565i	$0.392551\pi$
$14$	9.01688	2.40986
$15$	3.82326	0.987162
$16$	2.71562	0.678906
$17$	−1.20694	−0.292725	−0.146363	−	0.989231i	$-0.546757\pi$
$17$	−1.20694	−0.292725	−0.146363	+	0.989231i	$0.546757\pi$
$18$	−6.89073	−1.62416
$19$	−2.50380	−0.574411	−0.287205	−	0.957869i	$-0.592726\pi$
$19$	−2.50380	−0.574411	−0.287205	+	0.957869i	$0.592726\pi$
$20$	5.96298	1.33336
$21$	−9.08609	−1.98275
$22$	−6.82532	−1.45516
$23$	−6.40600	−1.33574	−0.667872	−	0.744277i	$-0.732794\pi$
$23$	−6.40600	−1.33574	−0.667872	+	0.744277i	$0.732794\pi$
$24$	−10.3499	−2.11266
$25$	−2.50844	−0.501688
$26$	−5.74053	−1.12581
$27$	−0.322786	−0.0621202
$28$	−14.1712	−2.67810
$29$	5.21159	0.967767	0.483884	−	0.875132i	$-0.339226\pi$
$29$	5.21159	0.967767	0.483884	+	0.875132i	$0.339226\pi$
$30$	−9.18992	−1.67784
$31$	6.95630	1.24939	0.624694	−	0.780870i	$-0.285224\pi$
$31$	6.95630	1.24939	0.624694	+	0.780870i	$0.285224\pi$
$32$	2.01856	0.356835
$33$	6.87771	1.19726
$34$	2.90109	0.497534
$35$	−5.92127	−1.00088
$36$	10.8297	1.80494
$37$	−2.27675	−0.374296	−0.187148	−	0.982332i	$-0.559924\pi$
$37$	−2.27675	−0.374296	−0.187148	+	0.982332i	$0.559924\pi$
$38$	6.01834	0.976304
$39$	5.78460	0.926277
$40$	−6.74485	−1.06645
$41$	−3.13902	−0.490233	−0.245117	−	0.969494i	$-0.578826\pi$
$41$	−3.13902	−0.490233	−0.245117	+	0.969494i	$0.578826\pi$
$42$	21.8401	3.37000
$43$	−1.85137	−0.282331	−0.141165	−	0.989986i	$-0.545085\pi$
$43$	−1.85137	−0.282331	−0.141165	+	0.989986i	$0.545085\pi$
$44$	10.7269	1.61714
$45$	4.52505	0.674554
$46$	15.3980	2.27031
$47$	−5.28542	−0.770958	−0.385479	−	0.922717i	$-0.625964\pi$
$47$	−5.28542	−0.770958	−0.385479	+	0.922717i	$0.625964\pi$
$48$	6.57760	0.949395
$49$	7.07207	1.01030
$50$	6.02950	0.852700
$51$	−2.92336	−0.409353
$52$	9.02199	1.25113
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	0.775876	0.105583
$55$	4.48210	0.604366
$56$	16.0293	2.14201
$57$	−6.06454	−0.803267
$58$	−12.5270	−1.64488
$59$	−10.9540	−1.42609	−0.713043	−	0.701121i	$-0.752683\pi$
$59$	−10.9540	−1.42609	−0.713043	+	0.701121i	$0.752683\pi$
$60$	14.4431	1.86460
$61$	−4.26030	−0.545475	−0.272738	−	0.962088i	$-0.587929\pi$
$61$	−4.26030	−0.545475	−0.272738	+	0.962088i	$0.587929\pi$
$62$	−16.7207	−2.12354
$63$	−10.7539	−1.35487
$64$	−10.2832	−1.28540
$65$	3.76973	0.467578
$66$	−16.5318	−2.03493
$67$	7.32529	0.894927	0.447464	−	0.894302i	$-0.352327\pi$
$67$	7.32529	0.894927	0.447464	+	0.894302i	$0.352327\pi$
$68$	−4.55944	−0.552914
$69$	−15.5162	−1.86793
$70$	14.2329	1.70115
$71$	2.39880	0.284685	0.142342	−	0.989817i	$-0.454537\pi$
$71$	2.39880	0.284685	0.142342	+	0.989817i	$0.454537\pi$
$72$	−12.2497	−1.44364
$73$	12.3298	1.44310	0.721549	−	0.692363i	$-0.243430\pi$
$73$	12.3298	1.44310	0.721549	+	0.692363i	$0.243430\pi$
$74$	5.47260	0.636176
$75$	−6.07578	−0.701570
$76$	−9.45860	−1.08498
$77$	−10.6518	−1.21389
$78$	−13.9043	−1.57436
$79$	−14.0130	−1.57658	−0.788290	−	0.615304i	$-0.789033\pi$
$79$	−14.0130	−1.57658	−0.788290	+	0.615304i	$0.789033\pi$
$80$	4.28652	0.479248
$81$	−9.38204	−1.04245
$82$	7.54523	0.833231
$83$	−6.98219	−0.766395	−0.383197	−	0.923666i	$-0.625177\pi$
$83$	−6.98219	−0.766395	−0.383197	+	0.923666i	$0.625177\pi$
$84$	−34.3245	−3.74511
$85$	−1.90511	−0.206638
$86$	4.45010	0.479867
$87$	12.6232	1.35334
$88$	−12.1334	−1.29342
$89$	−16.4636	−1.74514	−0.872568	−	0.488492i	$-0.837547\pi$
$89$	−16.4636	−1.74514	−0.872568	+	0.488492i	$0.837547\pi$
$90$	−10.8768	−1.14651
$91$	−8.95888	−0.939146
$92$	−24.1999	−2.52302
$93$	16.8491	1.74717
$94$	12.7045	1.31037
$95$	−3.95217	−0.405484
$96$	4.88923	0.499005
$97$	−8.99278	−0.913079	−0.456539	−	0.889703i	$-0.650911\pi$
$97$	−8.99278	−0.913079	−0.456539	+	0.889703i	$0.650911\pi$
$98$	−16.9990	−1.71716
$99$	8.14016	0.818117
$100$	−9.47613	−0.947613
$101$	6.90734	0.687306	0.343653	−	0.939097i	$-0.388336\pi$
$101$	6.90734	0.687306	0.343653	+	0.939097i	$0.388336\pi$
$102$	7.02684	0.695761
$103$	5.39416	0.531502	0.265751	−	0.964042i	$-0.414380\pi$
$103$	5.39416	0.531502	0.265751	+	0.964042i	$0.414380\pi$
$104$	−10.2050	−1.00068
$105$	−14.3421	−1.39965
$106$	2.40368	0.233467
$107$	4.17172	0.403296	0.201648	−	0.979458i	$-0.435370\pi$
$107$	4.17172	0.403296	0.201648	+	0.979458i	$0.435370\pi$
$108$	−1.21939	−0.117336
$109$	4.86152	0.465650	0.232825	−	0.972519i	$-0.425203\pi$
$109$	4.86152	0.465650	0.232825	+	0.972519i	$0.425203\pi$
$110$	−10.7735	−1.02722
$111$	−5.51460	−0.523423
$112$	−10.1871	−0.962586
$113$	3.21602	0.302538	0.151269	−	0.988493i	$-0.451664\pi$
$113$	3.21602	0.302538	0.151269	+	0.988493i	$0.451664\pi$
$114$	14.5772	1.36528
$115$	−10.1117	−0.942918
$116$	19.6878	1.82797
$117$	6.84640	0.632950
$118$	26.3299	2.42386
$119$	4.52755	0.415040
$120$	−16.3369	−1.49135
$121$	−2.93711	−0.267010
$122$	10.2404	0.927123
$123$	−7.60314	−0.685552
$124$	26.2788	2.35991
$125$	−11.8518	−1.06006
$126$	25.8490	2.30281
$127$	2.30053	0.204139	0.102069	−	0.994777i	$-0.467454\pi$
$127$	2.30053	0.204139	0.102069	+	0.994777i	$0.467454\pi$
$128$	20.6805	1.82792
$129$	−4.48426	−0.394817
$130$	−9.06125	−0.794724
$131$	0.986426	0.0861844	0.0430922	−	0.999071i	$-0.486279\pi$
$131$	0.986426	0.0861844	0.0430922	+	0.999071i	$0.486279\pi$
$132$	25.9819	2.26144
$133$	9.39244	0.814428
$134$	−17.6077	−1.52107
$135$	−0.509508	−0.0438514
$136$	5.15728	0.442233
$137$	−10.9831	−0.938353	−0.469177	−	0.883104i	$-0.655449\pi$
$137$	−10.9831	−0.938353	−0.469177	+	0.883104i	$0.655449\pi$
$138$	37.2960	3.17485
$139$	20.2952	1.72142	0.860710	−	0.509096i	$-0.170020\pi$
$139$	20.2952	1.72142	0.860710	+	0.509096i	$0.170020\pi$
$140$	−22.3688	−1.89051
$141$	−12.8020	−1.07812
$142$	−5.76595	−0.483868
$143$	6.78141	0.567090
$144$	7.78497	0.648748
$145$	8.22632	0.683159
$146$	−29.6370	−2.45278
$147$	17.1295	1.41282
$148$	−8.60089	−0.706989
$149$	−3.46818	−0.284124	−0.142062	−	0.989858i	$-0.545373\pi$
$149$	−3.46818	−0.284124	−0.142062	+	0.989858i	$0.545373\pi$
$150$	14.6043	1.19243
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	10.6988	0.867788
$153$	−3.45997	−0.279722
$154$	25.6037	2.06320
$155$	10.9803	0.881958
$156$	21.8525	1.74960
$157$	−18.5966	−1.48417	−0.742085	−	0.670306i	$-0.766163\pi$
$157$	−18.5966	−1.48417	−0.742085	+	0.670306i	$0.766163\pi$
$158$	33.6827	2.67965
$159$	−2.42213	−0.192088
$160$	3.18624	0.251894
$161$	24.0307	1.89388
$162$	22.5515	1.77181
$163$	9.32753	0.730589	0.365294	−	0.930892i	$-0.380968\pi$
$163$	9.32753	0.730589	0.365294	+	0.930892i	$0.380968\pi$
$164$	−11.8583	−0.925977
$165$	10.8562	0.845157
$166$	16.7830	1.30261
$167$	−12.8931	−0.997697	−0.498849	−	0.866689i	$-0.666244\pi$
$167$	−12.8931	−0.997697	−0.498849	+	0.866689i	$0.666244\pi$
$168$	38.8252	2.99543
$169$	−7.29639	−0.561261
$170$	4.57928	0.351215
$171$	−7.17773	−0.548894
$172$	−6.99391	−0.533281
$173$	−5.87716	−0.446832	−0.223416	−	0.974723i	$-0.571721\pi$
$173$	−5.87716	−0.446832	−0.223416	+	0.974723i	$0.571721\pi$
$174$	−30.3421	−2.30023
$175$	9.40985	0.711317
$176$	7.71108	0.581244
$177$	−26.5320	−1.99427
$178$	39.5733	2.96614
$179$	20.8473	1.55820	0.779099	−	0.626901i	$-0.215677\pi$
$179$	20.8473	1.55820	0.779099	+	0.626901i	$0.215677\pi$
$180$	17.0943	1.27413
$181$	−10.4849	−0.779333	−0.389667	−	0.920956i	$-0.627410\pi$
$181$	−10.4849	−0.779333	−0.389667	+	0.920956i	$0.627410\pi$
$182$	21.5343	1.59623
$183$	−10.3190	−0.762803
$184$	27.3730	2.01797
$185$	−3.59378	−0.264220
$186$	−40.4999	−2.96960
$187$	−3.42712	−0.250616
$188$	−19.9668	−1.45623
$189$	1.21086	0.0880771
$190$	9.49976	0.689185
$191$	10.1470	0.734213	0.367106	−	0.930179i	$-0.380348\pi$
$191$	10.1470	0.734213	0.367106	+	0.930179i	$0.380348\pi$
$192$	−24.9074	−1.79754
$193$	−6.77082	−0.487375	−0.243687	−	0.969854i	$-0.578357\pi$
$193$	−6.77082	−0.487375	−0.243687	+	0.969854i	$0.578357\pi$
$194$	21.6158	1.55193
$195$	9.13080	0.653870
$196$	26.7162	1.90830
$197$	7.38688	0.526293	0.263147	−	0.964756i	$-0.415240\pi$
$197$	7.38688	0.526293	0.263147	+	0.964756i	$0.415240\pi$
$198$	−19.5664	−1.39052
$199$	−14.8010	−1.04921	−0.524606	−	0.851345i	$-0.675787\pi$
$199$	−14.8010	−1.04921	−0.524606	+	0.851345i	$0.675787\pi$
$200$	10.7186	0.757923
$201$	17.7428	1.25148
$202$	−16.6031	−1.16819
$203$	−19.5501	−1.37215
$204$	−11.0436	−0.773206
$205$	−4.95485	−0.346062
$206$	−12.9659	−0.903374
$207$	−18.3643	−1.27641
$208$	6.48551	0.449689
$209$	−7.10959	−0.491781
$210$	34.4739	2.37893
$211$	−7.94259	−0.546791	−0.273395	−	0.961902i	$-0.588147\pi$
$211$	−7.94259	−0.546791	−0.273395	+	0.961902i	$0.588147\pi$
$212$	−3.77770	−0.259454
$213$	5.81021	0.398109
$214$	−10.0275	−0.685467
$215$	−2.92232	−0.199301
$216$	1.37928	0.0938478
$217$	−26.0950	−1.77144
$218$	−11.6856	−0.791447
$219$	29.8645	2.01806
$220$	16.9320	1.14156
$221$	−2.88243	−0.193893
$222$	13.2554	0.889642
$223$	−25.9156	−1.73544	−0.867718	−	0.497056i	$-0.834414\pi$
$223$	−25.9156	−1.73544	−0.867718	+	0.497056i	$0.834414\pi$
$224$	−7.57219	−0.505938
$225$	−7.19103	−0.479402
$226$	−7.73030	−0.514212
$227$	−7.83570	−0.520073	−0.260037	−	0.965599i	$-0.583735\pi$
$227$	−7.83570	−0.520073	−0.260037	+	0.965599i	$0.583735\pi$
$228$	−22.9100	−1.51725
$229$	12.4189	0.820661	0.410330	−	0.911937i	$-0.365413\pi$
$229$	12.4189	0.820661	0.410330	+	0.911937i	$0.365413\pi$
$230$	24.3053	1.60264
$231$	−25.8002	−1.69753
$232$	−22.2693	−1.46205
$233$	8.64607	0.566423	0.283211	−	0.959057i	$-0.408600\pi$
$233$	8.64607	0.566423	0.283211	+	0.959057i	$0.408600\pi$
$234$	−16.4566	−1.07580
$235$	−8.34287	−0.544229
$236$	−41.3808	−2.69366
$237$	−33.9413	−2.20472
$238$	−10.8828	−0.705427
$239$	30.0760	1.94545	0.972726	−	0.231956i	$-0.0745124\pi$
$239$	30.0760	1.94545	0.972726	+	0.231956i	$0.0745124\pi$
$240$	10.3825	0.670190
$241$	19.5405	1.25871	0.629357	−	0.777117i	$-0.283319\pi$
$241$	19.5405	1.25871	0.629357	+	0.777117i	$0.283319\pi$
$242$	7.05988	0.453826
$243$	−21.7562	−1.39566
$244$	−16.0941	−1.03032
$245$	11.1630	0.713180
$246$	18.2756	1.16521
$247$	−5.97963	−0.380475
$248$	−29.7245	−1.88751
$249$	−16.9118	−1.07174
$250$	28.4881	1.80174
$251$	2.74701	0.173390	0.0866948	−	0.996235i	$-0.472370\pi$
$251$	2.74701	0.173390	0.0866948	+	0.996235i	$0.472370\pi$
$252$	−40.6251	−2.55914
$253$	−18.1900	−1.14359
$254$	−5.52974	−0.346967
$255$	−4.61443	−0.288967
$256$	−29.1430	−1.82144
$257$	−29.2490	−1.82450	−0.912250	−	0.409634i	$-0.865656\pi$
$257$	−29.2490	−1.82450	−0.912250	+	0.409634i	$0.865656\pi$
$258$	10.7787	0.671056
$259$	8.54072	0.530695
$260$	14.2409	0.883185
$261$	14.9402	0.924777
$262$	−2.37106	−0.146484
$263$	−10.6878	−0.659040	−0.329520	−	0.944149i	$-0.606887\pi$
$263$	−10.6878	−0.659040	−0.329520	+	0.944149i	$0.606887\pi$
$264$	−29.3887	−1.80875
$265$	−1.57847	−0.0969645
$266$	−22.5765	−1.38425
$267$	−39.8770	−2.44043
$268$	27.6728	1.69038
$269$	3.93504	0.239924	0.119962	−	0.992778i	$-0.461723\pi$
$269$	3.93504	0.239924	0.119962	+	0.992778i	$0.461723\pi$
$270$	1.22470	0.0745326
$271$	−12.4841	−0.758353	−0.379176	−	0.925324i	$-0.623793\pi$
$271$	−12.4841	−0.758353	−0.379176	+	0.925324i	$0.623793\pi$
$272$	−3.27758	−0.198733
$273$	−21.6996	−1.31332
$274$	26.4000	1.59488
$275$	−7.12277	−0.429519
$276$	−58.6155	−3.52824
$277$	−2.10637	−0.126560	−0.0632799	−	0.997996i	$-0.520156\pi$
$277$	−2.10637	−0.126560	−0.0632799	+	0.997996i	$0.520156\pi$
$278$	−48.7834	−2.92583
$279$	19.9419	1.19389
$280$	25.3018	1.51207
$281$	6.64271	0.396271	0.198135	−	0.980175i	$-0.436511\pi$
$281$	6.64271	0.396271	0.198135	+	0.980175i	$0.436511\pi$
$282$	30.7720	1.83245
$283$	−11.9042	−0.707629	−0.353814	−	0.935316i	$-0.615116\pi$
$283$	−11.9042	−0.707629	−0.353814	+	0.935316i	$0.615116\pi$
$284$	9.06193	0.537727
$285$	−9.57267	−0.567036
$286$	−16.3004	−0.963862
$287$	11.7753	0.695077
$288$	5.78669	0.340984
$289$	−15.5433	−0.914312
$290$	−19.7735	−1.16114
$291$	−21.7817	−1.27687
$292$	46.5784	2.72580
$293$	−14.2875	−0.834687	−0.417343	−	0.908749i	$-0.637039\pi$
$293$	−14.2875	−0.834687	−0.417343	+	0.908749i	$0.637039\pi$
$294$	−41.1739	−2.40131
$295$	−17.2905	−1.00669
$296$	9.72864	0.565466
$297$	−0.916559	−0.0531841
$298$	8.33641	0.482915
$299$	−15.2990	−0.884761
$300$	−22.9525	−1.32516
$301$	6.94499	0.400303
$302$	2.40368	0.138317
$303$	16.7305	0.961142
$304$	−6.79937	−0.389971
$305$	−6.72474	−0.385058
$306$	8.31667	0.475432
$307$	−12.9623	−0.739797	−0.369898	−	0.929072i	$-0.620608\pi$
$307$	−12.9623	−0.739797	−0.369898	+	0.929072i	$0.620608\pi$
$308$	−40.2394	−2.29286
$309$	13.0654	0.743263
$310$	−26.3932	−1.49903
$311$	31.9300	1.81059	0.905293	−	0.424788i	$-0.139651\pi$
$311$	31.9300	1.81059	0.905293	+	0.424788i	$0.139651\pi$
$312$	−24.7178	−1.39937
$313$	−4.03535	−0.228091	−0.114046	−	0.993475i	$-0.536381\pi$
$313$	−4.03535	−0.228091	−0.114046	+	0.993475i	$0.536381\pi$
$314$	44.7003	2.52259
$315$	−16.9747	−0.956416
$316$	−52.9368	−2.97792
$317$	−20.2195	−1.13564	−0.567820	−	0.823153i	$-0.692213\pi$
$317$	−20.2195	−1.13564	−0.567820	+	0.823153i	$0.692213\pi$
$318$	5.82205	0.326484
$319$	14.7984	0.828552
$320$	−16.2318	−0.907383
$321$	10.1045	0.563977
$322$	−57.7622	−3.21896
$323$	3.02193	0.168144
$324$	−35.4425	−1.96903
$325$	−5.99071	−0.332305
$326$	−22.4205	−1.24175
$327$	11.7753	0.651174
$328$	13.4132	0.740618
$329$	19.8271	1.09310
$330$	−26.0950	−1.43648
$331$	−11.4199	−0.627696	−0.313848	−	0.949473i	$-0.601618\pi$
$331$	−11.4199	−0.627696	−0.313848	+	0.949473i	$0.601618\pi$
$332$	−26.3766	−1.44761
$333$	−6.52685	−0.357669
$334$	30.9909	1.69575
$335$	11.5627	0.631740
$336$	−24.6744	−1.34610
$337$	−15.8766	−0.864854	−0.432427	−	0.901669i	$-0.642343\pi$
$337$	−15.8766	−0.864854	−0.432427	+	0.901669i	$0.642343\pi$
$338$	17.5382	0.953954
$339$	7.78963	0.423075
$340$	−7.19694	−0.390309
$341$	19.7526	1.06966
$342$	17.2530	0.932935
$343$	−0.270344	−0.0145972
$344$	7.91095	0.426530
$345$	−24.4918	−1.31859
$346$	14.1268	0.759464
$347$	0.826373	0.0443620	0.0221810	−	0.999754i	$-0.492939\pi$
$347$	0.826373	0.0443620	0.0221810	+	0.999754i	$0.492939\pi$
$348$	47.6865	2.55627
$349$	−23.3241	−1.24851	−0.624256	−	0.781220i	$-0.714598\pi$
$349$	−23.3241	−1.24851	−0.624256	+	0.781220i	$0.714598\pi$
$350$	−22.6183	−1.20900
$351$	−0.770885	−0.0411468
$352$	5.73176	0.305504
$353$	−11.3747	−0.605412	−0.302706	−	0.953084i	$-0.597890\pi$
$353$	−11.3747	−0.605412	−0.302706	+	0.953084i	$0.597890\pi$
$354$	63.7745	3.38958
$355$	3.78642	0.200962
$356$	−62.1945	−3.29630
$357$	10.9663	0.580400
$358$	−50.1102	−2.64841
$359$	14.1037	0.744367	0.372184	−	0.928159i	$-0.378609\pi$
$359$	14.1037	0.744367	0.372184	+	0.928159i	$0.378609\pi$
$360$	−19.3357	−1.01908
$361$	−12.7310	−0.670052
$362$	25.2023	1.32460
$363$	−7.11407	−0.373392
$364$	−33.8440	−1.77391
$365$	19.4622	1.01870
$366$	24.8037	1.29651
$367$	0.449979	0.0234887	0.0117443	−	0.999931i	$-0.496262\pi$
$367$	0.449979	0.0234887	0.0117443	+	0.999931i	$0.496262\pi$
$368$	−17.3963	−0.906844
$369$	−8.99875	−0.468456
$370$	8.63832	0.449085
$371$	3.75128	0.194757
$372$	63.6508	3.30014
$373$	7.96094	0.412202	0.206101	−	0.978531i	$-0.433922\pi$
$373$	7.96094	0.412202	0.206101	+	0.978531i	$0.433922\pi$
$374$	8.23773	0.425963
$375$	−28.7067	−1.48241
$376$	22.5848	1.16472
$377$	12.4464	0.641024
$378$	−2.91053	−0.149701
$379$	15.7089	0.806914	0.403457	−	0.914999i	$-0.367808\pi$
$379$	15.7089	0.806914	0.403457	+	0.914999i	$0.367808\pi$
$380$	−14.9301	−0.765898
$381$	5.57219	0.285472
$382$	−24.3903	−1.24791
$383$	30.5471	1.56088	0.780441	−	0.625229i	$-0.214994\pi$
$383$	30.5471	1.56088	0.780441	+	0.625229i	$0.214994\pi$
$384$	50.0910	2.55620
$385$	−16.8136	−0.856899
$386$	16.2749	0.828372
$387$	−5.30738	−0.269789
$388$	−33.9720	−1.72467
$389$	−13.3576	−0.677257	−0.338628	−	0.940920i	$-0.609963\pi$
$389$	−13.3576	−0.677257	−0.338628	+	0.940920i	$0.609963\pi$
$390$	−21.9476	−1.11136
$391$	7.73163	0.391005
$392$	−30.2192	−1.52630
$393$	2.38926	0.120522
$394$	−17.7557	−0.894521
$395$	−22.1190	−1.11293
$396$	30.7511	1.54530
$397$	−35.2040	−1.76684	−0.883419	−	0.468585i	$-0.844764\pi$
$397$	−35.2040	−1.76684	−0.883419	+	0.468585i	$0.844764\pi$
$398$	35.5769	1.78331
$399$	22.7497	1.13891
$400$	−6.81198	−0.340599
$401$	−17.5374	−0.875775	−0.437887	−	0.899030i	$-0.644273\pi$
$401$	−17.5374	−0.875775	−0.437887	+	0.899030i	$0.644273\pi$
$402$	−42.6482	−2.12710
$403$	16.6132	0.827562
$404$	26.0938	1.29822
$405$	−14.8092	−0.735877
$406$	46.9923	2.33219
$407$	−6.46489	−0.320453
$408$	12.4916	0.618428
$409$	20.6312	1.02015	0.510073	−	0.860131i	$-0.329618\pi$
$409$	20.6312	1.02015	0.510073	+	0.860131i	$0.329618\pi$
$410$	11.9099	0.588188
$411$	−26.6027	−1.31221
$412$	20.3775	1.00393
$413$	41.0914	2.02197
$414$	44.1420	2.16946
$415$	−11.0212	−0.541008
$416$	4.82078	0.236358
$417$	49.1578	2.40727
$418$	17.0892	0.835861
$419$	22.2186	1.08545	0.542726	−	0.839910i	$-0.317392\pi$
$419$	22.2186	1.08545	0.542726	+	0.839910i	$0.317392\pi$
$420$	−54.1802	−2.64372
$421$	−3.81156	−0.185764	−0.0928821	−	0.995677i	$-0.529608\pi$
$421$	−3.81156	−0.185764	−0.0928821	+	0.995677i	$0.529608\pi$
$422$	19.0915	0.929359
$423$	−15.1519	−0.736711
$424$	4.27303	0.207517
$425$	3.02753	0.146857
$426$	−13.9659	−0.676650
$427$	15.9815	0.773401
$428$	15.7595	0.761766
$429$	16.4255	0.793030
$430$	7.02435	0.338744
$431$	−6.84137	−0.329537	−0.164769	−	0.986332i	$-0.552688\pi$
$431$	−6.84137	−0.329537	−0.164769	+	0.986332i	$0.552688\pi$
$432$	−0.876566	−0.0421738
$433$	16.3119	0.783900	0.391950	−	0.919987i	$-0.371801\pi$
$433$	16.3119	0.783900	0.391950	+	0.919987i	$0.371801\pi$
$434$	62.7241	3.01085
$435$	19.9253	0.955343
$436$	18.3654	0.879542
$437$	16.0393	0.767265
$438$	−71.7849	−3.43001
$439$	5.83894	0.278678	0.139339	−	0.990245i	$-0.455502\pi$
$439$	5.83894	0.278678	0.139339	+	0.990245i	$0.455502\pi$
$440$	−19.1521	−0.913043
$441$	20.2737	0.965416
$442$	6.92846	0.329553
$443$	35.0640	1.66594	0.832972	−	0.553316i	$-0.186638\pi$
$443$	35.0640	1.66594	0.832972	+	0.553316i	$0.186638\pi$
$444$	−20.8325	−0.988667
$445$	−25.9872	−1.23191
$446$	62.2929	2.94966
$447$	−8.40040	−0.397325
$448$	38.5753	1.82251
$449$	18.1293	0.855574	0.427787	−	0.903880i	$-0.359293\pi$
$449$	18.1293	0.855574	0.427787	+	0.903880i	$0.359293\pi$
$450$	17.2850	0.814821
$451$	−8.91333	−0.419712
$452$	12.1492	0.571449
$453$	−2.42213	−0.113802
$454$	18.8345	0.883949
$455$	−14.1413	−0.662955
$456$	25.9140	1.21353
$457$	20.3238	0.950708	0.475354	−	0.879795i	$-0.342320\pi$
$457$	20.3238	0.950708	0.475354	+	0.879795i	$0.342320\pi$
$458$	−29.8510	−1.39485
$459$	0.389582	0.0181841
$460$	−38.1988	−1.78103
$461$	4.90690	0.228537	0.114268	−	0.993450i	$-0.463548\pi$
$461$	4.90690	0.228537	0.114268	+	0.993450i	$0.463548\pi$
$462$	62.0155	2.88522
$463$	4.83514	0.224708	0.112354	−	0.993668i	$-0.464161\pi$
$463$	4.83514	0.224708	0.112354	+	0.993668i	$0.464161\pi$
$464$	14.1527	0.657023
$465$	26.5957	1.23335
$466$	−20.7824	−0.962727
$467$	−15.4888	−0.716735	−0.358367	−	0.933581i	$-0.616666\pi$
$467$	−15.4888	−0.716735	−0.358367	+	0.933581i	$0.616666\pi$
$468$	25.8637	1.19555
$469$	−27.4792	−1.26887
$470$	20.0536	0.925005
$471$	−45.0434	−2.07549
$472$	46.8067	2.15445
$473$	−5.25700	−0.241717
$474$	81.5841	3.74728
$475$	6.28063	0.288175
$476$	17.1037	0.783948
$477$	−2.86673	−0.131259
$478$	−72.2932	−3.30661
$479$	−32.1674	−1.46976	−0.734882	−	0.678195i	$-0.762763\pi$
$479$	−32.1674	−1.46976	−0.734882	+	0.678195i	$0.762763\pi$
$480$	7.71750	0.352254
$481$	−5.43739	−0.247924
$482$	−46.9692	−2.13939
$483$	58.2055	2.64844
$484$	−11.0955	−0.504342
$485$	−14.1948	−0.644554
$486$	52.2950	2.37215
$487$	−0.814366	−0.0369025	−0.0184512	−	0.999830i	$-0.505874\pi$
$487$	−0.814366	−0.0369025	−0.0184512	+	0.999830i	$0.505874\pi$
$488$	18.2044	0.824074
$489$	22.5925	1.02167
$490$	−26.8324	−1.21216
$491$	26.0192	1.17423	0.587116	−	0.809503i	$-0.300263\pi$
$491$	26.0192	1.17423	0.587116	+	0.809503i	$0.300263\pi$
$492$	−28.7224	−1.29491
$493$	−6.29005	−0.283290
$494$	14.3731	0.646678
$495$	12.8490	0.577519
$496$	18.8907	0.848217
$497$	−8.99854	−0.403640
$498$	40.6506	1.82160
$499$	−15.5272	−0.695095	−0.347548	−	0.937662i	$-0.612985\pi$
$499$	−15.5272	−0.695095	−0.347548	+	0.937662i	$0.612985\pi$
$500$	−44.7727	−2.00229
$501$	−31.2288	−1.39520
$502$	−6.60294	−0.294704
$503$	−37.5124	−1.67259	−0.836297	−	0.548277i	$-0.815284\pi$
$503$	−37.5124	−1.67259	−0.836297	+	0.548277i	$0.815284\pi$
$504$	45.9518	2.04686
$505$	10.9030	0.485177
$506$	43.7230	1.94372
$507$	−17.6728	−0.784879
$508$	8.69071	0.385588
$509$	−34.1133	−1.51204	−0.756022	−	0.654546i	$-0.772860\pi$
$509$	−34.1133	−1.51204	−0.756022	+	0.654546i	$0.772860\pi$
$510$	11.0916	0.491146
$511$	−46.2526	−2.04609
$512$	28.6896	1.26791
$513$	0.808191	0.0356825
$514$	70.3053	3.10103
$515$	8.51451	0.375194
$516$	−16.9402	−0.745751
$517$	−15.0081	−0.660055
$518$	−20.5292	−0.902002
$519$	−14.2353	−0.624859
$520$	−16.1082	−0.706391
$521$	14.6023	0.639736	0.319868	−	0.947462i	$-0.396361\pi$
$521$	14.6023	0.639736	0.319868	+	0.947462i	$0.396361\pi$
$522$	−35.9116	−1.57181
$523$	3.72926	0.163069	0.0815347	−	0.996671i	$-0.474018\pi$
$523$	3.72926	0.163069	0.0815347	+	0.996671i	$0.474018\pi$
$524$	3.72642	0.162790
$525$	22.7919	0.994721
$526$	25.6902	1.12015
$527$	−8.39581	−0.365727
$528$	18.6773	0.812823
$529$	18.0368	0.784210
$530$	3.79414	0.164807
$531$	−31.4021	−1.36274
$532$	35.4818	1.53833
$533$	−7.49669	−0.324718
$534$	95.8518	4.14791
$535$	6.58493	0.284691
$536$	−31.3012	−1.35201
$537$	50.4949	2.17901
$538$	−9.45860	−0.407789
$539$	20.0813	0.864963
$540$	−1.92477	−0.0828288
$541$	−26.2522	−1.12867	−0.564335	−	0.825546i	$-0.690867\pi$
$541$	−26.2522	−1.12867	−0.564335	+	0.825546i	$0.690867\pi$
$542$	30.0077	1.28894
$543$	−25.3957	−1.08983
$544$	−2.43628	−0.104455
$545$	7.67376	0.328708
$546$	52.1590	2.23220
$547$	−13.2251	−0.565463	−0.282731	−	0.959199i	$-0.591240\pi$
$547$	−13.2251	−0.565463	−0.282731	+	0.959199i	$0.591240\pi$
$548$	−41.4910	−1.77241
$549$	−12.2131	−0.521244
$550$	17.1209	0.730037
$551$	−13.0488	−0.555896
$552$	66.3012	2.82197
$553$	52.5664	2.23535
$554$	5.06306	0.215109
$555$	−8.70462	−0.369490
$556$	76.6693	3.25150
$557$	41.0420	1.73900	0.869502	−	0.493930i	$-0.164440\pi$
$557$	41.0420	1.73900	0.869502	+	0.493930i	$0.164440\pi$
$558$	−47.9339	−2.02921
$559$	−4.42148	−0.187009
$560$	−16.0799	−0.679501
$561$	−8.30095	−0.350467
$562$	−15.9670	−0.673526
$563$	−38.6381	−1.62840	−0.814200	−	0.580584i	$-0.802824\pi$
$563$	−38.6381	−1.62840	−0.814200	+	0.580584i	$0.802824\pi$
$564$	−48.3622	−2.03641
$565$	5.07639	0.213565
$566$	28.6139	1.20273
$567$	35.1946	1.47803
$568$	−10.2501	−0.430086
$569$	16.5901	0.695493	0.347746	−	0.937589i	$-0.386947\pi$
$569$	16.5901	0.695493	0.347746	+	0.937589i	$0.386947\pi$
$570$	23.0097	0.963770
$571$	31.7119	1.32710	0.663550	−	0.748132i	$-0.269049\pi$
$571$	31.7119	1.32710	0.663550	+	0.748132i	$0.269049\pi$
$572$	25.6182	1.07115
$573$	24.5775	1.02674
$574$	−28.3042	−1.18140
$575$	16.0691	0.670126
$576$	−29.4793	−1.22830
$577$	−8.67383	−0.361096	−0.180548	−	0.983566i	$-0.557787\pi$
$577$	−8.67383	−0.361096	−0.180548	+	0.983566i	$0.557787\pi$
$578$	37.3612	1.55402
$579$	−16.3998	−0.681554
$580$	31.0766	1.29038
$581$	26.1921	1.08663
$582$	52.3564	2.17024
$583$	−2.83952	−0.117601
$584$	−52.6858	−2.18015
$585$	10.8068	0.446807
$586$	34.3427	1.41869
$587$	−35.9896	−1.48545	−0.742726	−	0.669596i	$-0.766467\pi$
$587$	−35.9896	−1.48545	−0.742726	+	0.669596i	$0.766467\pi$
$588$	64.7101	2.66860
$589$	−17.4172	−0.717662
$590$	41.5609	1.71103
$591$	17.8920	0.735979
$592$	−6.18280	−0.254112
$593$	1.41898	0.0582704	0.0291352	−	0.999575i	$-0.490725\pi$
$593$	1.41898	0.0582704	0.0291352	+	0.999575i	$0.490725\pi$
$594$	2.20312	0.0903950
$595$	7.14659	0.292982
$596$	−13.1017	−0.536668
$597$	−35.8499	−1.46724
$598$	36.7739	1.50379
$599$	38.5688	1.57588	0.787940	−	0.615752i	$-0.211148\pi$
$599$	38.5688	1.57588	0.787940	+	0.615752i	$0.211148\pi$
$600$	25.9620	1.05989
$601$	−11.0190	−0.449475	−0.224738	−	0.974419i	$-0.572152\pi$
$601$	−11.0190	−0.449475	−0.224738	+	0.974419i	$0.572152\pi$
$602$	−16.6936	−0.680379
$603$	20.9997	0.855173
$604$	−3.77770	−0.153712
$605$	−4.63613	−0.188486
$606$	−40.2148	−1.63362
$607$	−8.78187	−0.356445	−0.178223	−	0.983990i	$-0.557035\pi$
$607$	−8.78187	−0.356445	−0.178223	+	0.983990i	$0.557035\pi$
$608$	−5.05408	−0.204970
$609$	−47.3530	−1.91884
$610$	16.1642	0.654468
$611$	−12.6228	−0.510663
$612$	−13.0707	−0.528353
$613$	−35.1540	−1.41986	−0.709929	−	0.704273i	$-0.751273\pi$
$613$	−35.1540	−1.41986	−0.709929	+	0.704273i	$0.751273\pi$
$614$	31.1573	1.25740
$615$	−12.0013	−0.483940
$616$	45.5156	1.83388
$617$	39.7995	1.60227	0.801135	−	0.598484i	$-0.204230\pi$
$617$	39.7995	1.60227	0.801135	+	0.598484i	$0.204230\pi$
$618$	−31.4050	−1.26330
$619$	18.0851	0.726901	0.363450	−	0.931614i	$-0.381599\pi$
$619$	18.0851	0.726901	0.363450	+	0.931614i	$0.381599\pi$
$620$	41.4803	1.66589
$621$	2.06777	0.0829767
$622$	−76.7497	−3.07738
$623$	61.7594	2.47434
$624$	15.7088	0.628855
$625$	−6.16554	−0.246622
$626$	9.69971	0.387678
$627$	−17.2204	−0.687716
$628$	−70.2524	−2.80337
$629$	2.74790	0.109566
$630$	40.8018	1.62558
$631$	−0.895242	−0.0356390	−0.0178195	−	0.999841i	$-0.505672\pi$
$631$	−0.895242	−0.0356390	−0.0178195	+	0.999841i	$0.505672\pi$
$632$	59.8778	2.38181
$633$	−19.2380	−0.764643
$634$	48.6013	1.93020
$635$	3.63131	0.144104
$636$	−9.15010	−0.362825
$637$	16.8897	0.669193
$638$	−35.5707	−1.40826
$639$	6.87671	0.272039
$640$	32.6436	1.29035
$641$	−8.58602	−0.339127	−0.169564	−	0.985519i	$-0.554236\pi$
$641$	−8.58602	−0.339127	−0.169564	+	0.985519i	$0.554236\pi$
$642$	−24.2880	−0.958570
$643$	9.72406	0.383479	0.191740	−	0.981446i	$-0.438587\pi$
$643$	9.72406	0.383479	0.191740	+	0.981446i	$0.438587\pi$
$644$	90.7807	3.57726
$645$	−7.07826	−0.278706
$646$	−7.26376	−0.285789
$647$	−13.9584	−0.548763	−0.274381	−	0.961621i	$-0.588473\pi$
$647$	−13.9584	−0.548763	−0.274381	+	0.961621i	$0.588473\pi$
$648$	40.0898	1.57487
$649$	−31.1041	−1.22094
$650$	14.3998	0.564806
$651$	−63.2056	−2.47722
$652$	35.2366	1.37997
$653$	−36.2427	−1.41829	−0.709143	−	0.705065i	$-0.750918\pi$
$653$	−36.2427	−1.41829	−0.709143	+	0.705065i	$0.750918\pi$
$654$	−28.3040	−1.10677
$655$	1.55704	0.0608387
$656$	−8.52441	−0.332822
$657$	35.3464	1.37899
$658$	−47.6581	−1.85790
$659$	16.1040	0.627324	0.313662	−	0.949535i	$-0.398444\pi$
$659$	16.1040	0.627324	0.313662	+	0.949535i	$0.398444\pi$
$660$	41.0116	1.59638
$661$	−3.65684	−0.142234	−0.0711172	−	0.997468i	$-0.522656\pi$
$661$	−3.65684	−0.142234	−0.0711172	+	0.997468i	$0.522656\pi$
$662$	27.4499	1.06687
$663$	−6.98164	−0.271144
$664$	29.8351	1.15783
$665$	14.8257	0.574914
$666$	15.6885	0.607916
$667$	−33.3854	−1.29269
$668$	−48.7062	−1.88450
$669$	−62.7711	−2.42687
$670$	−27.7932	−1.07374
$671$	−12.0972	−0.467008
$672$	−18.3409	−0.707514
$673$	11.8992	0.458679	0.229339	−	0.973347i	$-0.426343\pi$
$673$	11.8992	0.458679	0.229339	+	0.973347i	$0.426343\pi$
$674$	38.1624	1.46996
$675$	0.809689	0.0311650
$676$	−27.5636	−1.06014
$677$	32.4936	1.24883	0.624415	−	0.781093i	$-0.285338\pi$
$677$	32.4936	1.24883	0.624415	+	0.781093i	$0.285338\pi$
$678$	−18.7238	−0.719084
$679$	33.7344	1.29461
$680$	8.14060	0.312178
$681$	−18.9791	−0.727281
$682$	−47.4789	−1.81806
$683$	3.62747	0.138801	0.0694005	−	0.997589i	$-0.477891\pi$
$683$	3.62747	0.138801	0.0694005	+	0.997589i	$0.477891\pi$
$684$	−27.1153	−1.03678
$685$	−17.3365	−0.662395
$686$	0.649822	0.0248103
$687$	30.0801	1.14763
$688$	−5.02762	−0.191676
$689$	−2.38822	−0.0909840
$690$	58.8706	2.24117
$691$	−36.0676	−1.37207	−0.686037	−	0.727566i	$-0.740651\pi$
$691$	−36.0676	−1.37207	−0.686037	+	0.727566i	$0.740651\pi$
$692$	−22.2022	−0.844000
$693$	−30.5360	−1.15997
$694$	−1.98634	−0.0754004
$695$	32.0354	1.21517
$696$	−53.9392	−2.04456
$697$	3.78860	0.143504
$698$	56.0639	2.12205
$699$	20.9419	0.792097
$700$	35.5476	1.34357
$701$	15.2388	0.575561	0.287780	−	0.957696i	$-0.407083\pi$
$701$	15.2388	0.575561	0.287780	+	0.957696i	$0.407083\pi$
$702$	1.85296	0.0699357
$703$	5.70053	0.214999
$704$	−29.1995	−1.10050
$705$	−20.2076	−0.761061
$706$	27.3411	1.02899
$707$	−25.9113	−0.974495
$708$	−100.230	−3.76687
$709$	4.20490	0.157918	0.0789592	−	0.996878i	$-0.474840\pi$
$709$	4.20490	0.157918	0.0789592	+	0.996878i	$0.474840\pi$
$710$	−9.10137	−0.341568
$711$	−40.1714	−1.50655
$712$	70.3494	2.63646
$713$	−44.5620	−1.66886
$714$	−26.3596	−0.986484
$715$	10.7042	0.400316
$716$	78.7547	2.94320
$717$	72.8480	2.72056
$718$	−33.9010	−1.26517
$719$	7.06419	0.263450	0.131725	−	0.991286i	$-0.457948\pi$
$719$	7.06419	0.263450	0.131725	+	0.991286i	$0.457948\pi$
$720$	12.2883	0.457959
$721$	−20.2350	−0.753590
$722$	30.6013	1.13886
$723$	47.3297	1.76021
$724$	−39.6086	−1.47204
$725$	−13.0729	−0.485517
$726$	17.1000	0.634640
$727$	−42.0260	−1.55866	−0.779329	−	0.626615i	$-0.784440\pi$
$727$	−42.0260	−1.55866	−0.779329	+	0.626615i	$0.784440\pi$
$728$	38.2816	1.41881
$729$	−24.5503	−0.909271
$730$	−46.7811	−1.73145
$731$	2.23448	0.0826453
$732$	−38.9821	−1.44082
$733$	−12.6726	−0.468072	−0.234036	−	0.972228i	$-0.575193\pi$
$733$	−12.6726	−0.468072	−0.234036	+	0.972228i	$0.575193\pi$
$734$	−1.08161	−0.0399228
$735$	27.0384	0.997325
$736$	−12.9309	−0.476640
$737$	20.8003	0.766191
$738$	21.6302	0.796217
$739$	−38.9112	−1.43137	−0.715685	−	0.698423i	$-0.753886\pi$
$739$	−38.9112	−1.43137	−0.715685	+	0.698423i	$0.753886\pi$
$740$	−13.5762	−0.499072
$741$	−14.4835	−0.532063
$742$	−9.01688	−0.331020
$743$	15.8388	0.581071	0.290535	−	0.956864i	$-0.406167\pi$
$743$	15.8388	0.581071	0.290535	+	0.956864i	$0.406167\pi$
$744$	−71.9967	−2.63953
$745$	−5.47441	−0.200567
$746$	−19.1356	−0.700604
$747$	−20.0161	−0.732350
$748$	−12.9466	−0.473376
$749$	−15.6493	−0.571813
$750$	69.0019	2.51959
$751$	44.2746	1.61560	0.807802	−	0.589454i	$-0.200657\pi$
$751$	44.2746	1.61560	0.807802	+	0.589454i	$0.200657\pi$
$752$	−14.3532	−0.523408
$753$	6.65362	0.242471
$754$	−29.9173	−1.08952
$755$	−1.57847	−0.0574463
$756$	4.57427	0.166364
$757$	−15.0084	−0.545490	−0.272745	−	0.962086i	$-0.587932\pi$
$757$	−15.0084	−0.545490	−0.272745	+	0.962086i	$0.587932\pi$
$758$	−37.7593	−1.37148
$759$	−44.0586	−1.59923
$760$	16.8877	0.612582
$761$	−50.5056	−1.83083	−0.915413	−	0.402517i	$-0.868135\pi$
$761$	−50.5056	−1.83083	−0.915413	+	0.402517i	$0.868135\pi$
$762$	−13.3938	−0.485206
$763$	−18.2369	−0.660221
$764$	38.3324	1.38682
$765$	−5.46145	−0.197459
$766$	−73.4256	−2.65297
$767$	−26.1605	−0.944602
$768$	−70.5883	−2.54714
$769$	−4.11073	−0.148237	−0.0741183	−	0.997249i	$-0.523614\pi$
$769$	−4.11073	−0.148237	−0.0741183	+	0.997249i	$0.523614\pi$
$770$	40.4145	1.45644
$771$	−70.8449	−2.55142
$772$	−25.5781	−0.920578
$773$	8.21353	0.295420	0.147710	−	0.989031i	$-0.452810\pi$
$773$	8.21353	0.295420	0.147710	+	0.989031i	$0.452810\pi$
$774$	12.7573	0.458551
$775$	−17.4494	−0.626803
$776$	38.4265	1.37943
$777$	20.6868	0.742134
$778$	32.1074	1.15111
$779$	7.85948	0.281595
$780$	34.4934	1.23506
$781$	6.81144	0.243732
$782$	−18.5844	−0.664577
$783$	−1.68223	−0.0601179
$784$	19.2051	0.685895
$785$	−29.3541	−1.04769
$786$	−5.74302	−0.204847
$787$	40.4303	1.44119	0.720593	−	0.693359i	$-0.243870\pi$
$787$	40.4303	1.44119	0.720593	+	0.693359i	$0.243870\pi$
$788$	27.9054	0.994089
$789$	−25.8874	−0.921615
$790$	53.1671	1.89160
$791$	−12.0642	−0.428953
$792$	−34.7832	−1.23597
$793$	−10.1745	−0.361308
$794$	84.6193	3.00303
$795$	−3.82326	−0.135597
$796$	−55.9136	−1.98181
$797$	−18.7392	−0.663775	−0.331888	−	0.943319i	$-0.607686\pi$
$797$	−18.7392	−0.663775	−0.331888	+	0.943319i	$0.607686\pi$
$798$	−54.6832	−1.93576
$799$	6.37917	0.225679
$800$	−5.06344	−0.179020
$801$	−47.1967	−1.66761
$802$	42.1543	1.48852
$803$	35.0109	1.23551
$804$	67.0272	2.36387
$805$	37.9316	1.33691
$806$	−39.9329	−1.40657
$807$	9.53120	0.335514
$808$	−29.5153	−1.03834
$809$	16.3720	0.575610	0.287805	−	0.957689i	$-0.407074\pi$
$809$	16.3720	0.575610	0.287805	+	0.957689i	$0.407074\pi$
$810$	35.5968	1.25074
$811$	18.7958	0.660008	0.330004	−	0.943979i	$-0.392950\pi$
$811$	18.7958	0.660008	0.330004	+	0.943979i	$0.392950\pi$
$812$	−73.8544	−2.59178
$813$	−30.2381	−1.06050
$814$	15.5396	0.544661
$815$	14.7232	0.515732
$816$	−7.93875	−0.277912
$817$	4.63545	0.162174
$818$	−49.5909	−1.73390
$819$	−25.6827	−0.897427
$820$	−18.7179	−0.653659
$821$	−20.6437	−0.720468	−0.360234	−	0.932862i	$-0.617303\pi$
$821$	−20.6437	−0.720468	−0.360234	+	0.932862i	$0.617303\pi$
$822$	63.9444	2.23032
$823$	5.59875	0.195160	0.0975801	−	0.995228i	$-0.468890\pi$
$823$	5.59875	0.195160	0.0975801	+	0.995228i	$0.468890\pi$
$824$	−23.0494	−0.802965
$825$	−17.2523	−0.600648
$826$	−98.7707	−3.43667
$827$	−36.5470	−1.27086	−0.635431	−	0.772157i	$-0.719178\pi$
$827$	−36.5470	−1.27086	−0.635431	+	0.772157i	$0.719178\pi$
$828$	−69.3748	−2.41094
$829$	35.0523	1.21742	0.608708	−	0.793394i	$-0.291688\pi$
$829$	35.0523	1.21742	0.608708	+	0.793394i	$0.291688\pi$
$830$	26.4914	0.919530
$831$	−5.10192	−0.176984
$832$	−24.5587	−0.851418
$833$	−8.53554	−0.295739
$834$	−118.160	−4.09154
$835$	−20.3513	−0.704287
$836$	−26.8579	−0.928900
$837$	−2.24540	−0.0776122
$838$	−53.4066	−1.84490
$839$	24.8153	0.856719	0.428360	−	0.903608i	$-0.359092\pi$
$839$	24.8153	0.856719	0.428360	+	0.903608i	$0.359092\pi$
$840$	61.2843	2.11451
$841$	−1.83938	−0.0634268
$842$	9.16179	0.315736
$843$	16.0895	0.554153
$844$	−30.0047	−1.03281
$845$	−11.5171	−0.396201
$846$	36.4204	1.25216
$847$	11.0179	0.378580
$848$	−2.71562	−0.0932549
$849$	−28.8335	−0.989562
$850$	−7.27722	−0.249607
$851$	14.5849	0.499963
$852$	21.9492	0.751968
$853$	−21.5019	−0.736212	−0.368106	−	0.929784i	$-0.619994\pi$
$853$	−21.5019	−0.736212	−0.368106	+	0.929784i	$0.619994\pi$
$854$	−38.4146	−1.31452
$855$	−11.3298	−0.387471
$856$	−17.8259	−0.609277
$857$	46.8424	1.60010	0.800052	−	0.599930i	$-0.204805\pi$
$857$	46.8424	1.60010	0.800052	+	0.599930i	$0.204805\pi$
$858$	−39.4817	−1.34788
$859$	−12.4843	−0.425959	−0.212980	−	0.977057i	$-0.568317\pi$
$859$	−12.4843	−0.425959	−0.212980	+	0.977057i	$0.568317\pi$
$860$	−11.0397	−0.376450
$861$	28.5215	0.972009
$862$	16.4445	0.560102
$863$	38.6416	1.31538	0.657688	−	0.753291i	$-0.271535\pi$
$863$	38.6416	1.31538	0.657688	+	0.753291i	$0.271535\pi$
$864$	−0.651564	−0.0221667
$865$	−9.27691	−0.315425
$866$	−39.2087	−1.33236
$867$	−37.6480	−1.27859
$868$	−98.5790	−3.34599
$869$	−39.7901	−1.34979
$870$	−47.8940	−1.62376
$871$	17.4944	0.592776
$872$	−20.7735	−0.703478
$873$	−25.7799	−0.872518
$874$	−38.5535	−1.30409
$875$	44.4595	1.50300
$876$	112.819	3.81181
$877$	3.62945	0.122558	0.0612789	−	0.998121i	$-0.480482\pi$
$877$	3.62945	0.122558	0.0612789	+	0.998121i	$0.480482\pi$
$878$	−14.0350	−0.473658
$879$	−34.6063	−1.16724
$880$	12.1717	0.410307
$881$	9.54126	0.321453	0.160727	−	0.986999i	$-0.448616\pi$
$881$	9.54126	0.321453	0.160727	+	0.986999i	$0.448616\pi$
$882$	−48.7317	−1.64088
$883$	26.1741	0.880828	0.440414	−	0.897795i	$-0.354832\pi$
$883$	26.1741	0.880828	0.440414	+	0.897795i	$0.354832\pi$
$884$	−10.8890	−0.366236
$885$	−41.8799	−1.40778
$886$	−84.2829	−2.83154
$887$	7.84727	0.263486	0.131743	−	0.991284i	$-0.457943\pi$
$887$	7.84727	0.263486	0.131743	+	0.991284i	$0.457943\pi$
$888$	23.5641	0.790758
$889$	−8.62991	−0.289438
$890$	62.4651	2.09384
$891$	−26.6405	−0.892491
$892$	−97.9014	−3.27798
$893$	13.2336	0.442847
$894$	20.1919	0.675318
$895$	32.9067	1.09995
$896$	−77.5784	−2.59171
$897$	−37.0561	−1.23727
$898$	−43.5771	−1.45419
$899$	36.2533	1.20912
$900$	−27.1656	−0.905519
$901$	1.20694	0.0402089
$902$	21.4248	0.713369
$903$	16.8217	0.559791
$904$	−13.7422	−0.457058
$905$	−16.5500	−0.550141
$906$	5.82205	0.193425
$907$	29.1445	0.967729	0.483864	−	0.875143i	$-0.339233\pi$
$907$	29.1445	0.967729	0.483864	+	0.875143i	$0.339233\pi$
$908$	−29.6009	−0.982341
$909$	19.8015	0.656774
$910$	33.9912	1.12680
$911$	−10.1576	−0.336535	−0.168267	−	0.985741i	$-0.553817\pi$
$911$	−10.1576	−0.336535	−0.168267	+	0.985741i	$0.553817\pi$
$912$	−16.4690	−0.545343
$913$	−19.8261	−0.656148
$914$	−48.8521	−1.61588
$915$	−16.2882	−0.538472
$916$	46.9147	1.55011
$917$	−3.70036	−0.122197
$918$	−0.936433	−0.0309069
$919$	20.8141	0.686593	0.343296	−	0.939227i	$-0.388457\pi$
$919$	20.8141	0.686593	0.343296	+	0.939227i	$0.388457\pi$
$920$	43.2075	1.42451
$921$	−31.3964	−1.03455
$922$	−11.7946	−0.388436
$923$	5.72886	0.188568
$924$	−97.4653	−3.20637
$925$	5.71109	0.187780
$926$	−11.6222	−0.381928
$927$	15.4636	0.507892
$928$	10.5199	0.345333
$929$	−33.8827	−1.11166	−0.555828	−	0.831297i	$-0.687599\pi$
$929$	−33.8827	−1.11166	−0.555828	+	0.831297i	$0.687599\pi$
$930$	−63.9278	−2.09627
$931$	−17.7070	−0.580324
$932$	32.6623	1.06989
$933$	77.3388	2.53196
$934$	37.2301	1.21821
$935$	−5.40960	−0.176913
$936$	−29.2549	−0.956226
$937$	−33.6988	−1.10089	−0.550446	−	0.834871i	$-0.685542\pi$
$937$	−33.6988	−1.10089	−0.550446	+	0.834871i	$0.685542\pi$
$938$	66.0513	2.15665
$939$	−9.77416	−0.318968
$940$	−31.5169	−1.02797
$941$	−11.6528	−0.379869	−0.189935	−	0.981797i	$-0.560828\pi$
$941$	−11.6528	−0.379869	−0.189935	+	0.981797i	$0.560828\pi$
$942$	108.270	3.52764
$943$	20.1086	0.654826
$944$	−29.7469	−0.968178
$945$	1.91130	0.0621747
$946$	12.6362	0.410837
$947$	−13.7648	−0.447296	−0.223648	−	0.974670i	$-0.571797\pi$
$947$	−13.7648	−0.447296	−0.223648	+	0.974670i	$0.571797\pi$
$948$	−128.220	−4.16439
$949$	29.4464	0.955870
$950$	−15.0966	−0.489800
$951$	−48.9743	−1.58810
$952$	−19.3464	−0.627020
$953$	29.2856	0.948654	0.474327	−	0.880349i	$-0.342691\pi$
$953$	29.2856	0.948654	0.474327	+	0.880349i	$0.342691\pi$
$954$	6.89073	0.223096
$955$	16.0168	0.518290
$956$	113.618	3.67467
$957$	35.8438	1.15866
$958$	77.3202	2.49810
$959$	41.2008	1.33044
$960$	−39.3155	−1.26890
$961$	17.3901	0.560970
$962$	13.0698	0.421386
$963$	11.9592	0.385381
$964$	73.8181	2.37752
$965$	−10.6875	−0.344044
$966$	−139.908	−4.50146
$967$	6.37922	0.205142	0.102571	−	0.994726i	$-0.467293\pi$
$967$	6.37922	0.205142	0.102571	+	0.994726i	$0.467293\pi$
$968$	12.5504	0.403384
$969$	7.31951	0.235136
$970$	34.1199	1.09552
$971$	26.2942	0.843821	0.421911	−	0.906637i	$-0.361360\pi$
$971$	26.2942	0.843821	0.421911	+	0.906637i	$0.361360\pi$
$972$	−82.1884	−2.63619
$973$	−76.1330	−2.44071
$974$	1.95748	0.0627217
$975$	−14.5103	−0.464702
$976$	−11.5694	−0.370326
$977$	13.2902	0.425192	0.212596	−	0.977140i	$-0.431808\pi$
$977$	13.2902	0.425192	0.212596	+	0.977140i	$0.431808\pi$
$978$	−54.3053	−1.73649
$979$	−46.7487	−1.49410
$980$	42.1706	1.34709
$981$	13.9367	0.444965
$982$	−62.5420	−1.99580
$983$	−31.3255	−0.999129	−0.499565	−	0.866277i	$-0.666507\pi$
$983$	−31.3255	−0.999129	−0.499565	+	0.866277i	$0.666507\pi$
$984$	32.4885	1.03569
$985$	11.6600	0.371517
$986$	15.1193	0.481497
$987$	48.0239	1.52862
$988$	−22.5892	−0.718660
$989$	11.8599	0.377122
$990$	−30.8849	−0.981587
$991$	−61.0554	−1.93949	−0.969744	−	0.244125i	$-0.921499\pi$
$991$	−61.0554	−1.93949	−0.969744	+	0.244125i	$0.921499\pi$
$992$	14.0417	0.445825
$993$	−27.6606	−0.877782
$994$	21.6297	0.686051
$995$	−23.3628	−0.740652
$996$	−63.8877	−2.02436
$997$	29.2574	0.926591	0.463295	−	0.886204i	$-0.346667\pi$
$997$	29.2574	0.926591	0.463295	+	0.886204i	$0.346667\pi$
$998$	37.3226	1.18143
$999$	0.734904	0.0232513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.15	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.40368 q^{2} +2.42213 q^{3} +3.77770 q^{4} +1.57847 q^{5} -5.82205 q^{6} -3.75128 q^{7} -4.27303 q^{8} +2.86673 q^{9} +O(q^{10})\)	\(q-2.40368 q^{2} +2.42213 q^{3} +3.77770 q^{4} +1.57847 q^{5} -5.82205 q^{6} -3.75128 q^{7} -4.27303 q^{8} +2.86673 q^{9} -3.79414 q^{10} +2.83952 q^{11} +9.15010 q^{12} +2.38822 q^{13} +9.01688 q^{14} +3.82326 q^{15} +2.71562 q^{16} -1.20694 q^{17} -6.89073 q^{18} -2.50380 q^{19} +5.96298 q^{20} -9.08609 q^{21} -6.82532 q^{22} -6.40600 q^{23} -10.3499 q^{24} -2.50844 q^{25} -5.74053 q^{26} -0.322786 q^{27} -14.1712 q^{28} +5.21159 q^{29} -9.18992 q^{30} +6.95630 q^{31} +2.01856 q^{32} +6.87771 q^{33} +2.90109 q^{34} -5.92127 q^{35} +10.8297 q^{36} -2.27675 q^{37} +6.01834 q^{38} +5.78460 q^{39} -6.74485 q^{40} -3.13902 q^{41} +21.8401 q^{42} -1.85137 q^{43} +10.7269 q^{44} +4.52505 q^{45} +15.3980 q^{46} -5.28542 q^{47} +6.57760 q^{48} +7.07207 q^{49} +6.02950 q^{50} -2.92336 q^{51} +9.02199 q^{52} -1.00000 q^{53} +0.775876 q^{54} +4.48210 q^{55} +16.0293 q^{56} -6.06454 q^{57} -12.5270 q^{58} -10.9540 q^{59} +14.4431 q^{60} -4.26030 q^{61} -16.7207 q^{62} -10.7539 q^{63} -10.2832 q^{64} +3.76973 q^{65} -16.5318 q^{66} +7.32529 q^{67} -4.55944 q^{68} -15.5162 q^{69} +14.2329 q^{70} +2.39880 q^{71} -12.2497 q^{72} +12.3298 q^{73} +5.47260 q^{74} -6.07578 q^{75} -9.45860 q^{76} -10.6518 q^{77} -13.9043 q^{78} -14.0130 q^{79} +4.28652 q^{80} -9.38204 q^{81} +7.54523 q^{82} -6.98219 q^{83} -34.3245 q^{84} -1.90511 q^{85} +4.45010 q^{86} +12.6232 q^{87} -12.1334 q^{88} -16.4636 q^{89} -10.8768 q^{90} -8.95888 q^{91} -24.1999 q^{92} +16.8491 q^{93} +12.7045 q^{94} -3.95217 q^{95} +4.88923 q^{96} -8.99278 q^{97} -16.9990 q^{98} +8.14016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 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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