LMFDB - Embedded newform 8003.2.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.34552 q^{2} +3.15214 q^{3} +3.50145 q^{4} -3.97132 q^{5} -7.39341 q^{6} -1.04283 q^{7} -3.52168 q^{8} +6.93601 q^{9} +O(q^{10})$	\(q-2.34552 q^{2} +3.15214 q^{3} +3.50145 q^{4} -3.97132 q^{5} -7.39341 q^{6} -1.04283 q^{7} -3.52168 q^{8} +6.93601 q^{9} +9.31479 q^{10} -5.50344 q^{11} +11.0371 q^{12} -4.82534 q^{13} +2.44599 q^{14} -12.5182 q^{15} +1.25726 q^{16} +6.98013 q^{17} -16.2685 q^{18} +2.80545 q^{19} -13.9054 q^{20} -3.28716 q^{21} +12.9084 q^{22} +5.55558 q^{23} -11.1008 q^{24} +10.7713 q^{25} +11.3179 q^{26} +12.4069 q^{27} -3.65143 q^{28} +2.52356 q^{29} +29.3616 q^{30} -4.92733 q^{31} +4.09443 q^{32} -17.3476 q^{33} -16.3720 q^{34} +4.14142 q^{35} +24.2861 q^{36} -4.19053 q^{37} -6.58023 q^{38} -15.2102 q^{39} +13.9857 q^{40} -2.26840 q^{41} +7.71010 q^{42} +0.103309 q^{43} -19.2700 q^{44} -27.5451 q^{45} -13.0307 q^{46} +13.3859 q^{47} +3.96307 q^{48} -5.91250 q^{49} -25.2644 q^{50} +22.0024 q^{51} -16.8957 q^{52} -1.00000 q^{53} -29.1005 q^{54} +21.8559 q^{55} +3.67253 q^{56} +8.84318 q^{57} -5.91906 q^{58} -11.5829 q^{59} -43.8317 q^{60} -5.00345 q^{61} +11.5571 q^{62} -7.23311 q^{63} -12.1181 q^{64} +19.1629 q^{65} +40.6892 q^{66} +9.25657 q^{67} +24.4406 q^{68} +17.5120 q^{69} -9.71378 q^{70} -4.37839 q^{71} -24.4264 q^{72} -5.17646 q^{73} +9.82897 q^{74} +33.9528 q^{75} +9.82314 q^{76} +5.73917 q^{77} +35.6757 q^{78} -3.52255 q^{79} -4.99299 q^{80} +18.3002 q^{81} +5.32057 q^{82} +12.2718 q^{83} -11.5098 q^{84} -27.7203 q^{85} -0.242314 q^{86} +7.95463 q^{87} +19.3814 q^{88} -8.95032 q^{89} +64.6075 q^{90} +5.03202 q^{91} +19.4526 q^{92} -15.5317 q^{93} -31.3968 q^{94} -11.1413 q^{95} +12.9062 q^{96} +12.3696 q^{97} +13.8679 q^{98} -38.1719 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.34552	−1.65853	−0.829266	−	0.558855i	$-0.811241\pi$
$2$	−2.34552	−1.65853	−0.829266	+	0.558855i	$0.811241\pi$
$3$	3.15214	1.81989	0.909945	−	0.414728i	$-0.136123\pi$
$3$	3.15214	1.81989	0.909945	+	0.414728i	$0.136123\pi$
$4$	3.50145	1.75073
$5$	−3.97132	−1.77603	−0.888013	−	0.459818i	$-0.847915\pi$
$5$	−3.97132	−1.77603	−0.888013	+	0.459818i	$0.847915\pi$
$6$	−7.39341	−3.01835
$7$	−1.04283	−0.394154	−0.197077	−	0.980388i	$-0.563145\pi$
$7$	−1.04283	−0.394154	−0.197077	+	0.980388i	$0.563145\pi$
$8$	−3.52168	−1.24510
$9$	6.93601	2.31200
$10$	9.31479	2.94560
$11$	−5.50344	−1.65935	−0.829674	−	0.558248i	$-0.811474\pi$
$11$	−5.50344	−1.65935	−0.829674	+	0.558248i	$0.811474\pi$
$12$	11.0371	3.18613
$13$	−4.82534	−1.33831	−0.669154	−	0.743124i	$-0.733343\pi$
$13$	−4.82534	−1.33831	−0.669154	+	0.743124i	$0.733343\pi$
$14$	2.44599	0.653717
$15$	−12.5182	−3.23217
$16$	1.25726	0.314316
$17$	6.98013	1.69293	0.846465	−	0.532445i	$-0.178727\pi$
$17$	6.98013	1.69293	0.846465	+	0.532445i	$0.178727\pi$
$18$	−16.2685	−3.83453
$19$	2.80545	0.643614	0.321807	−	0.946805i	$-0.395710\pi$
$19$	2.80545	0.643614	0.321807	+	0.946805i	$0.395710\pi$
$20$	−13.9054	−3.10934
$21$	−3.28716	−0.717318
$22$	12.9084	2.75208
$23$	5.55558	1.15842	0.579210	−	0.815179i	$-0.303361\pi$
$23$	5.55558	1.15842	0.579210	+	0.815179i	$0.303361\pi$
$24$	−11.1008	−2.26595
$25$	10.7713	2.15427
$26$	11.3179	2.21962
$27$	12.4069	2.38770
$28$	−3.65143	−0.690056
$29$	2.52356	0.468614	0.234307	−	0.972163i	$-0.424718\pi$
$29$	2.52356	0.468614	0.234307	+	0.972163i	$0.424718\pi$
$30$	29.3616	5.36066
$31$	−4.92733	−0.884975	−0.442488	−	0.896775i	$-0.645904\pi$
$31$	−4.92733	−0.884975	−0.442488	+	0.896775i	$0.645904\pi$
$32$	4.09443	0.723800
$33$	−17.3476	−3.01983
$34$	−16.3720	−2.80778
$35$	4.14142	0.700028
$36$	24.2861	4.04768
$37$	−4.19053	−0.688919	−0.344460	−	0.938801i	$-0.611938\pi$
$37$	−4.19053	−0.688919	−0.344460	+	0.938801i	$0.611938\pi$
$38$	−6.58023	−1.06745
$39$	−15.2102	−2.43557
$40$	13.9857	2.21134
$41$	−2.26840	−0.354264	−0.177132	−	0.984187i	$-0.556682\pi$
$41$	−2.26840	−0.354264	−0.177132	+	0.984187i	$0.556682\pi$
$42$	7.71010	1.18969
$43$	0.103309	0.0157545	0.00787726	−	0.999969i	$-0.497493\pi$
$43$	0.103309	0.0157545	0.00787726	+	0.999969i	$0.497493\pi$
$44$	−19.2700	−2.90506
$45$	−27.5451	−4.10618
$46$	−13.0307	−1.92127
$47$	13.3859	1.95253	0.976267	−	0.216572i	$-0.0694876\pi$
$47$	13.3859	1.95253	0.976267	+	0.216572i	$0.0694876\pi$
$48$	3.96307	0.572021
$49$	−5.91250	−0.844642
$50$	−25.2644	−3.57292
$51$	22.0024	3.08095
$52$	−16.8957	−2.34301
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−29.1005	−3.96008
$55$	21.8559	2.94705
$56$	3.67253	0.490762
$57$	8.84318	1.17131
$58$	−5.91906	−0.777211
$59$	−11.5829	−1.50797	−0.753983	−	0.656894i	$-0.771870\pi$
$59$	−11.5829	−1.50797	−0.753983	+	0.656894i	$0.771870\pi$
$60$	−43.8317	−5.65865
$61$	−5.00345	−0.640626	−0.320313	−	0.947312i	$-0.603788\pi$
$61$	−5.00345	−0.640626	−0.320313	+	0.947312i	$0.603788\pi$
$62$	11.5571	1.46776
$63$	−7.23311	−0.911286
$64$	−12.1181	−1.51476
$65$	19.1629	2.37687
$66$	40.6892	5.00849
$67$	9.25657	1.13087	0.565435	−	0.824793i	$-0.308708\pi$
$67$	9.25657	1.13087	0.565435	+	0.824793i	$0.308708\pi$
$68$	24.4406	2.96386
$69$	17.5120	2.10820
$70$	−9.71378	−1.16102
$71$	−4.37839	−0.519619	−0.259809	−	0.965660i	$-0.583660\pi$
$71$	−4.37839	−0.519619	−0.259809	+	0.965660i	$0.583660\pi$
$72$	−24.4264	−2.87868
$73$	−5.17646	−0.605859	−0.302930	−	0.953013i	$-0.597965\pi$
$73$	−5.17646	−0.605859	−0.302930	+	0.953013i	$0.597965\pi$
$74$	9.82897	1.14259
$75$	33.9528	3.92054
$76$	9.82314	1.12679
$77$	5.73917	0.654039
$78$	35.6757	4.03948
$79$	−3.52255	−0.396318	−0.198159	−	0.980170i	$-0.563496\pi$
$79$	−3.52255	−0.396318	−0.198159	+	0.980170i	$0.563496\pi$
$80$	−4.99299	−0.558233
$81$	18.3002	2.03335
$82$	5.32057	0.587558
$83$	12.2718	1.34700	0.673501	−	0.739186i	$-0.264790\pi$
$83$	12.2718	1.34700	0.673501	+	0.739186i	$0.264790\pi$
$84$	−11.5098	−1.25583
$85$	−27.7203	−3.00669
$86$	−0.242314	−0.0261294
$87$	7.95463	0.852826
$88$	19.3814	2.06606
$89$	−8.95032	−0.948732	−0.474366	−	0.880328i	$-0.657323\pi$
$89$	−8.95032	−0.948732	−0.474366	+	0.880328i	$0.657323\pi$
$90$	64.6075	6.81023
$91$	5.03202	0.527500
$92$	19.4526	2.02807
$93$	−15.5317	−1.61056
$94$	−31.3968	−3.23834
$95$	−11.1413	−1.14308
$96$	12.9062	1.31724
$97$	12.3696	1.25595	0.627973	−	0.778235i	$-0.283885\pi$
$97$	12.3696	1.25595	0.627973	+	0.778235i	$0.283885\pi$
$98$	13.8679	1.40087
$99$	−38.1719	−3.83642
$100$	37.7154	3.77154
$101$	10.1738	1.01233	0.506167	−	0.862436i	$-0.331062\pi$
$101$	10.1738	1.01233	0.506167	+	0.862436i	$0.331062\pi$
$102$	−51.6069	−5.10985
$103$	−14.1633	−1.39555	−0.697776	−	0.716316i	$-0.745827\pi$
$103$	−14.1633	−1.39555	−0.697776	+	0.716316i	$0.745827\pi$
$104$	16.9933	1.66633
$105$	13.0544	1.27398
$106$	2.34552	0.227817
$107$	−12.2679	−1.18599	−0.592993	−	0.805207i	$-0.702054\pi$
$107$	−12.2679	−1.18599	−0.592993	+	0.805207i	$0.702054\pi$
$108$	43.4420	4.18021
$109$	6.13508	0.587634	0.293817	−	0.955862i	$-0.405074\pi$
$109$	6.13508	0.587634	0.293817	+	0.955862i	$0.405074\pi$
$110$	−51.2634	−4.88777
$111$	−13.2092	−1.25376
$112$	−1.31112	−0.123889
$113$	15.4606	1.45441	0.727205	−	0.686420i	$-0.240819\pi$
$113$	15.4606	1.45441	0.727205	+	0.686420i	$0.240819\pi$
$114$	−20.7418	−1.94265
$115$	−22.0630	−2.05738
$116$	8.83614	0.820415
$117$	−33.4686	−3.09417
$118$	27.1679	2.50101
$119$	−7.27911	−0.667275
$120$	44.0850	4.02439
$121$	19.2878	1.75344
$122$	11.7357	1.06250
$123$	−7.15031	−0.644722
$124$	−17.2528	−1.54935
$125$	−22.9199	−2.05001
$126$	16.9654	1.51140
$127$	−9.88057	−0.876759	−0.438379	−	0.898790i	$-0.644447\pi$
$127$	−9.88057	−0.876759	−0.438379	+	0.898790i	$0.644447\pi$
$128$	20.2343	1.78848
$129$	0.325646	0.0286715
$130$	−44.9470	−3.94211
$131$	−12.4196	−1.08511	−0.542553	−	0.840021i	$-0.682542\pi$
$131$	−12.4196	−1.08511	−0.542553	+	0.840021i	$0.682542\pi$
$132$	−60.7419	−5.28690
$133$	−2.92562	−0.253683
$134$	−21.7114	−1.87558
$135$	−49.2716	−4.24062
$136$	−24.5818	−2.10787
$137$	14.5989	1.24727	0.623633	−	0.781717i	$-0.285656\pi$
$137$	14.5989	1.24727	0.623633	+	0.781717i	$0.285656\pi$
$138$	−41.0747	−3.49651
$139$	10.2468	0.869125	0.434563	−	0.900642i	$-0.356903\pi$
$139$	10.2468	0.869125	0.434563	+	0.900642i	$0.356903\pi$
$140$	14.5010	1.22556
$141$	42.1943	3.55340
$142$	10.2696	0.861804
$143$	26.5559	2.22072
$144$	8.72039	0.726699
$145$	−10.0219	−0.832271
$146$	12.1415	1.00484
$147$	−18.6370	−1.53716
$148$	−14.6730	−1.20611
$149$	−6.64792	−0.544619	−0.272310	−	0.962210i	$-0.587787\pi$
$149$	−6.64792	−0.544619	−0.272310	+	0.962210i	$0.587787\pi$
$150$	−79.6370	−6.50233
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−9.87990	−0.801366
$153$	48.4142	3.91406
$154$	−13.4613	−1.08474
$155$	19.5680	1.57174
$156$	−53.2576	−4.26402
$157$	−6.63538	−0.529561	−0.264780	−	0.964309i	$-0.585299\pi$
$157$	−6.63538	−0.529561	−0.264780	+	0.964309i	$0.585299\pi$
$158$	8.26221	0.657306
$159$	−3.15214	−0.249981
$160$	−16.2603	−1.28549
$161$	−5.79355	−0.456596
$162$	−42.9234	−3.37238
$163$	24.6232	1.92864	0.964319	−	0.264742i	$-0.0852868\pi$
$163$	24.6232	1.92864	0.964319	+	0.264742i	$0.0852868\pi$
$164$	−7.94269	−0.620220
$165$	68.8929	5.36330
$166$	−28.7837	−2.23404
$167$	−3.06144	−0.236901	−0.118451	−	0.992960i	$-0.537793\pi$
$167$	−3.06144	−0.236901	−0.118451	+	0.992960i	$0.537793\pi$
$168$	11.5763	0.893134
$169$	10.2839	0.791067
$170$	65.0184	4.98669
$171$	19.4586	1.48804
$172$	0.361733	0.0275819
$173$	−8.88290	−0.675355	−0.337677	−	0.941262i	$-0.609641\pi$
$173$	−8.88290	−0.675355	−0.337677	+	0.941262i	$0.609641\pi$
$174$	−18.6577	−1.41444
$175$	−11.2327	−0.849115
$176$	−6.91927	−0.521560
$177$	−36.5110	−2.74433
$178$	20.9931	1.57350
$179$	−1.87234	−0.139945	−0.0699726	−	0.997549i	$-0.522291\pi$
$179$	−1.87234	−0.139945	−0.0699726	+	0.997549i	$0.522291\pi$
$180$	−96.4478	−7.18879
$181$	−20.2306	−1.50373	−0.751865	−	0.659317i	$-0.770845\pi$
$181$	−20.2306	−1.50373	−0.751865	+	0.659317i	$0.770845\pi$
$182$	−11.8027	−0.874874
$183$	−15.7716	−1.16587
$184$	−19.5650	−1.44235
$185$	16.6419	1.22354
$186$	36.4298	2.67116
$187$	−38.4147	−2.80916
$188$	46.8701	3.41835
$189$	−12.9383	−0.941123
$190$	26.1322	1.89583
$191$	13.1056	0.948286	0.474143	−	0.880448i	$-0.342758\pi$
$191$	13.1056	0.948286	0.474143	+	0.880448i	$0.342758\pi$
$192$	−38.1980	−2.75670
$193$	19.1966	1.38180	0.690902	−	0.722948i	$-0.257214\pi$
$193$	19.1966	1.38180	0.690902	+	0.722948i	$0.257214\pi$
$194$	−29.0132	−2.08303
$195$	60.4043	4.32564
$196$	−20.7023	−1.47874
$197$	24.5624	1.75000	0.875001	−	0.484121i	$-0.160861\pi$
$197$	24.5624	1.75000	0.875001	+	0.484121i	$0.160861\pi$
$198$	89.5328	6.36282
$199$	−19.2496	−1.36457	−0.682285	−	0.731086i	$-0.739014\pi$
$199$	−19.2496	−1.36457	−0.682285	+	0.731086i	$0.739014\pi$
$200$	−37.9333	−2.68229
$201$	29.1780	2.05806
$202$	−23.8629	−1.67899
$203$	−2.63166	−0.184706
$204$	77.0402	5.39390
$205$	9.00852	0.629183
$206$	33.2203	2.31457
$207$	38.5336	2.67827
$208$	−6.06672	−0.420651
$209$	−15.4396	−1.06798
$210$	−30.6192	−2.11293
$211$	−16.5678	−1.14057	−0.570287	−	0.821446i	$-0.693168\pi$
$211$	−16.5678	−1.14057	−0.570287	+	0.821446i	$0.693168\pi$
$212$	−3.50145	−0.240481
$213$	−13.8013	−0.945650
$214$	28.7747	1.96700
$215$	−0.410274	−0.0279805
$216$	−43.6930	−2.97293
$217$	5.13839	0.348817
$218$	−14.3899	−0.974609
$219$	−16.3170	−1.10260
$220$	76.5273	5.15947
$221$	−33.6815	−2.26566
$222$	30.9823	2.07940
$223$	−5.81768	−0.389581	−0.194790	−	0.980845i	$-0.562403\pi$
$223$	−5.81768	−0.389581	−0.194790	+	0.980845i	$0.562403\pi$
$224$	−4.26981	−0.285289
$225$	74.7102	4.98068
$226$	−36.2631	−2.41219
$227$	8.09810	0.537490	0.268745	−	0.963211i	$-0.413391\pi$
$227$	8.09810	0.537490	0.268745	+	0.963211i	$0.413391\pi$
$228$	30.9640	2.05064
$229$	−15.9430	−1.05354	−0.526772	−	0.850007i	$-0.676598\pi$
$229$	−15.9430	−1.05354	−0.526772	+	0.850007i	$0.676598\pi$
$230$	51.7491	3.41223
$231$	18.0907	1.19028
$232$	−8.88719	−0.583473
$233$	−15.8721	−1.03982	−0.519909	−	0.854222i	$-0.674034\pi$
$233$	−15.8721	−1.03982	−0.519909	+	0.854222i	$0.674034\pi$
$234$	78.5011	5.13178
$235$	−53.1596	−3.46775
$236$	−40.5570	−2.64004
$237$	−11.1036	−0.721256
$238$	17.0733	1.10670
$239$	14.1564	0.915703	0.457852	−	0.889029i	$-0.348619\pi$
$239$	14.1564	0.915703	0.457852	+	0.889029i	$0.348619\pi$
$240$	−15.7386	−1.01592
$241$	−12.9146	−0.831904	−0.415952	−	0.909387i	$-0.636552\pi$
$241$	−12.9146	−0.831904	−0.415952	+	0.909387i	$0.636552\pi$
$242$	−45.2399	−2.90813
$243$	20.4642	1.31278
$244$	−17.5193	−1.12156
$245$	23.4804	1.50011
$246$	16.7712	1.06929
$247$	−13.5372	−0.861354
$248$	17.3525	1.10189
$249$	38.6824	2.45140
$250$	53.7589	3.40001
$251$	13.0071	0.821000	0.410500	−	0.911861i	$-0.365354\pi$
$251$	13.0071	0.821000	0.410500	+	0.911861i	$0.365354\pi$
$252$	−25.3264	−1.59541
$253$	−30.5748	−1.92222
$254$	23.1751	1.45413
$255$	−87.3783	−5.47184
$256$	−23.2238	−1.45149
$257$	6.84507	0.426984	0.213492	−	0.976945i	$-0.431516\pi$
$257$	6.84507	0.426984	0.213492	+	0.976945i	$0.431516\pi$
$258$	−0.763808	−0.0475526
$259$	4.37003	0.271541
$260$	67.0981	4.16125
$261$	17.5035	1.08344
$262$	29.1304	1.79968
$263$	−10.3701	−0.639448	−0.319724	−	0.947511i	$-0.603590\pi$
$263$	−10.3701	−0.639448	−0.319724	+	0.947511i	$0.603590\pi$
$264$	61.0928	3.76000
$265$	3.97132	0.243956
$266$	6.86209	0.420741
$267$	−28.2127	−1.72659
$268$	32.4114	1.97984
$269$	−20.4535	−1.24707	−0.623535	−	0.781795i	$-0.714304\pi$
$269$	−20.4535	−1.24707	−0.623535	+	0.781795i	$0.714304\pi$
$270$	115.567	7.03320
$271$	0.574480	0.0348972	0.0174486	−	0.999848i	$-0.494446\pi$
$271$	0.574480	0.0348972	0.0174486	+	0.999848i	$0.494446\pi$
$272$	8.77586	0.532115
$273$	15.8617	0.959992
$274$	−34.2419	−2.06863
$275$	−59.2794	−3.57468
$276$	61.3174	3.69087
$277$	7.36175	0.442325	0.221162	−	0.975237i	$-0.429015\pi$
$277$	7.36175	0.442325	0.221162	+	0.975237i	$0.429015\pi$
$278$	−24.0341	−1.44147
$279$	−34.1760	−2.04607
$280$	−14.5848	−0.871607
$281$	−29.8642	−1.78155	−0.890774	−	0.454446i	$-0.849837\pi$
$281$	−29.8642	−1.78155	−0.890774	+	0.454446i	$0.849837\pi$
$282$	−98.9674	−5.89342
$283$	−27.3521	−1.62591	−0.812956	−	0.582324i	$-0.802143\pi$
$283$	−27.3521	−1.62591	−0.812956	+	0.582324i	$0.802143\pi$
$284$	−15.3307	−0.909710
$285$	−35.1190	−2.08027
$286$	−62.2874	−3.68313
$287$	2.36556	0.139635
$288$	28.3990	1.67343
$289$	31.7222	1.86601
$290$	23.5065	1.38035
$291$	38.9908	2.28568
$292$	−18.1251	−1.06069
$293$	−13.1653	−0.769124	−0.384562	−	0.923099i	$-0.625648\pi$
$293$	−13.1653	−0.769124	−0.384562	+	0.923099i	$0.625648\pi$
$294$	43.7135	2.54942
$295$	45.9994	2.67819
$296$	14.7577	0.857776
$297$	−68.2804	−3.96203
$298$	15.5928	0.903268
$299$	−26.8076	−1.55032
$300$	118.884	6.86379
$301$	−0.107734	−0.00620971
$302$	2.34552	0.134969
$303$	32.0694	1.84234
$304$	3.52719	0.202298
$305$	19.8703	1.13777
$306$	−113.556	−6.49159
$307$	−26.6418	−1.52053	−0.760265	−	0.649613i	$-0.774931\pi$
$307$	−26.6418	−1.52053	−0.760265	+	0.649613i	$0.774931\pi$
$308$	20.0954	1.14504
$309$	−44.6448	−2.53975
$310$	−45.8971	−2.60678
$311$	−13.8513	−0.785438	−0.392719	−	0.919659i	$-0.628465\pi$
$311$	−13.8513	−0.785438	−0.392719	+	0.919659i	$0.628465\pi$
$312$	53.5653	3.03254
$313$	−29.9143	−1.69086	−0.845429	−	0.534088i	$-0.820655\pi$
$313$	−29.9143	−1.69086	−0.845429	+	0.534088i	$0.820655\pi$
$314$	15.5634	0.878293
$315$	28.7249	1.61847
$316$	−12.3341	−0.693845
$317$	−35.5414	−1.99620	−0.998101	−	0.0615969i	$-0.980381\pi$
$317$	−35.5414	−1.99620	−0.998101	+	0.0615969i	$0.980381\pi$
$318$	7.39341	0.414602
$319$	−13.8883	−0.777594
$320$	48.1248	2.69026
$321$	−38.6703	−2.15837
$322$	13.5889	0.757278
$323$	19.5824	1.08959
$324$	64.0772	3.55985
$325$	−51.9754	−2.88308
$326$	−57.7542	−3.19871
$327$	19.3386	1.06943
$328$	7.98858	0.441095
$329$	−13.9593	−0.769599
$330$	−161.589	−8.89521
$331$	−23.7422	−1.30499	−0.652494	−	0.757794i	$-0.726277\pi$
$331$	−23.7422	−1.30499	−0.652494	+	0.757794i	$0.726277\pi$
$332$	42.9690	2.35823
$333$	−29.0656	−1.59278
$334$	7.18066	0.392908
$335$	−36.7608	−2.00845
$336$	−4.13283	−0.225464
$337$	14.5673	0.793530	0.396765	−	0.917920i	$-0.370133\pi$
$337$	14.5673	0.793530	0.396765	+	0.917920i	$0.370133\pi$
$338$	−24.1210	−1.31201
$339$	48.7340	2.64687
$340$	−97.0613	−5.26389
$341$	27.1173	1.46848
$342$	−45.6405	−2.46796
$343$	13.4656	0.727074
$344$	−0.363823	−0.0196160
$345$	−69.5457	−3.74421
$346$	20.8350	1.12010
$347$	8.79001	0.471873	0.235936	−	0.971769i	$-0.424184\pi$
$347$	8.79001	0.471873	0.235936	+	0.971769i	$0.424184\pi$
$348$	27.8528	1.49307
$349$	−4.51073	−0.241454	−0.120727	−	0.992686i	$-0.538523\pi$
$349$	−4.51073	−0.241454	−0.120727	+	0.992686i	$0.538523\pi$
$350$	26.3466	1.40828
$351$	−59.8673	−3.19548
$352$	−22.5334	−1.20104
$353$	−26.9852	−1.43628	−0.718140	−	0.695899i	$-0.755006\pi$
$353$	−26.9852	−1.43628	−0.718140	+	0.695899i	$0.755006\pi$
$354$	85.6371	4.55156
$355$	17.3880	0.922857
$356$	−31.3391	−1.66097
$357$	−22.9448	−1.21437
$358$	4.39160	0.232103
$359$	−1.42982	−0.0754631	−0.0377315	−	0.999288i	$-0.512013\pi$
$359$	−1.42982	−0.0754631	−0.0377315	+	0.999288i	$0.512013\pi$
$360$	97.0050	5.11261
$361$	−11.1295	−0.585761
$362$	47.4513	2.49398
$363$	60.7980	3.19107
$364$	17.6194	0.923507
$365$	20.5574	1.07602
$366$	36.9925	1.93363
$367$	10.4541	0.545700	0.272850	−	0.962057i	$-0.412034\pi$
$367$	10.4541	0.545700	0.272850	+	0.962057i	$0.412034\pi$
$368$	6.98483	0.364109
$369$	−15.7336	−0.819060
$370$	−39.0339	−2.02928
$371$	1.04283	0.0541412
$372$	−54.3834	−2.81965
$373$	−8.75035	−0.453076	−0.226538	−	0.974002i	$-0.572741\pi$
$373$	−8.75035	−0.453076	−0.226538	+	0.974002i	$0.572741\pi$
$374$	90.1023	4.65908
$375$	−72.2467	−3.73080
$376$	−47.1409	−2.43110
$377$	−12.1770	−0.627150
$378$	30.3470	1.56088
$379$	−22.0649	−1.13340	−0.566699	−	0.823925i	$-0.691780\pi$
$379$	−22.0649	−1.13340	−0.566699	+	0.823925i	$0.691780\pi$
$380$	−39.0108	−2.00121
$381$	−31.1450	−1.59561
$382$	−30.7393	−1.57276
$383$	−8.02210	−0.409910	−0.204955	−	0.978771i	$-0.565705\pi$
$383$	−8.02210	−0.409910	−0.204955	+	0.978771i	$0.565705\pi$
$384$	63.7815	3.25484
$385$	−22.7921	−1.16159
$386$	−45.0260	−2.29177
$387$	0.716554	0.0364245
$388$	43.3117	2.19882
$389$	−0.885811	−0.0449124	−0.0224562	−	0.999748i	$-0.507149\pi$
$389$	−0.885811	−0.0449124	−0.0224562	+	0.999748i	$0.507149\pi$
$390$	−141.679	−7.17421
$391$	38.7787	1.96112
$392$	20.8219	1.05167
$393$	−39.1484	−1.97478
$394$	−57.6117	−2.90243
$395$	13.9892	0.703872
$396$	−133.657	−6.71652
$397$	−35.9632	−1.80494	−0.902470	−	0.430754i	$-0.858248\pi$
$397$	−35.9632	−1.80494	−0.902470	+	0.430754i	$0.858248\pi$
$398$	45.1504	2.26318
$399$	−9.22196	−0.461676
$400$	13.5424	0.677121
$401$	−2.38362	−0.119032	−0.0595160	−	0.998227i	$-0.518956\pi$
$401$	−2.38362	−0.119032	−0.0595160	+	0.998227i	$0.518956\pi$
$402$	−68.4376	−3.41336
$403$	23.7760	1.18437
$404$	35.6232	1.77232
$405$	−72.6758	−3.61129
$406$	6.17260	0.306341
$407$	23.0623	1.14316
$408$	−77.4853	−3.83610
$409$	0.0752741	0.00372206	0.00186103	−	0.999998i	$-0.499408\pi$
$409$	0.0752741	0.00372206	0.00186103	+	0.999998i	$0.499408\pi$
$410$	−21.1296	−1.04352
$411$	46.0178	2.26989
$412$	−49.5921	−2.44323
$413$	12.0790	0.594371
$414$	−90.3812	−4.44199
$415$	−48.7351	−2.39231
$416$	−19.7570	−0.968667
$417$	32.2995	1.58171
$418$	36.2139	1.77128
$419$	7.32288	0.357746	0.178873	−	0.983872i	$-0.442755\pi$
$419$	7.32288	0.357746	0.178873	+	0.983872i	$0.442755\pi$
$420$	45.7092	2.23038
$421$	15.1602	0.738862	0.369431	−	0.929258i	$-0.379553\pi$
$421$	15.1602	0.738862	0.369431	+	0.929258i	$0.379553\pi$
$422$	38.8600	1.89168
$423$	92.8447	4.51426
$424$	3.52168	0.171028
$425$	75.1854	3.64703
$426$	32.3712	1.56839
$427$	5.21776	0.252505
$428$	−42.9556	−2.07634
$429$	83.7081	4.04147
$430$	0.962305	0.0464065
$431$	33.1437	1.59648	0.798238	−	0.602342i	$-0.205766\pi$
$431$	33.1437	1.59648	0.798238	+	0.602342i	$0.205766\pi$
$432$	15.5987	0.750493
$433$	6.80192	0.326879	0.163440	−	0.986553i	$-0.447741\pi$
$433$	6.80192	0.326879	0.163440	+	0.986553i	$0.447741\pi$
$434$	−12.0522	−0.578523
$435$	−31.5904	−1.51464
$436$	21.4817	1.02879
$437$	15.5859	0.745575
$438$	38.2717	1.82869
$439$	−2.27086	−0.108382	−0.0541912	−	0.998531i	$-0.517258\pi$
$439$	−2.27086	−0.108382	−0.0541912	+	0.998531i	$0.517258\pi$
$440$	−76.9695	−3.66938
$441$	−41.0091	−1.95282
$442$	79.0005	3.75767
$443$	17.9739	0.853966	0.426983	−	0.904260i	$-0.359576\pi$
$443$	17.9739	0.853966	0.426983	+	0.904260i	$0.359576\pi$
$444$	−46.2513	−2.19499
$445$	35.5445	1.68497
$446$	13.6455	0.646132
$447$	−20.9552	−0.991147
$448$	12.6372	0.597049
$449$	−11.7656	−0.555255	−0.277628	−	0.960689i	$-0.589548\pi$
$449$	−11.7656	−0.555255	−0.277628	+	0.960689i	$0.589548\pi$
$450$	−175.234	−8.26061
$451$	12.4840	0.587848
$452$	54.1345	2.54627
$453$	−3.15214	−0.148101
$454$	−18.9942	−0.891444
$455$	−19.9838	−0.936853
$456$	−31.1429	−1.45840
$457$	−30.7963	−1.44059	−0.720295	−	0.693668i	$-0.755994\pi$
$457$	−30.7963	−1.44059	−0.720295	+	0.693668i	$0.755994\pi$
$458$	37.3946	1.74733
$459$	86.6015	4.04221
$460$	−77.2525	−3.60191
$461$	6.98632	0.325385	0.162693	−	0.986677i	$-0.447982\pi$
$461$	6.98632	0.325385	0.162693	+	0.986677i	$0.447982\pi$
$462$	−42.4320	−1.97412
$463$	−30.6727	−1.42548	−0.712741	−	0.701427i	$-0.752546\pi$
$463$	−30.6727	−1.42548	−0.712741	+	0.701427i	$0.752546\pi$
$464$	3.17278	0.147293
$465$	61.6811	2.86039
$466$	37.2283	1.72457
$467$	−7.67184	−0.355010	−0.177505	−	0.984120i	$-0.556803\pi$
$467$	−7.67184	−0.355010	−0.177505	+	0.984120i	$0.556803\pi$
$468$	−117.189	−5.41705
$469$	−9.65306	−0.445737
$470$	124.687	5.75137
$471$	−20.9157	−0.963743
$472$	40.7913	1.87757
$473$	−0.568556	−0.0261423
$474$	26.0437	1.19623
$475$	30.2185	1.38652
$476$	−25.4875	−1.16822
$477$	−6.93601	−0.317578
$478$	−33.2041	−1.51872
$479$	−24.3706	−1.11352	−0.556761	−	0.830673i	$-0.687956\pi$
$479$	−24.3706	−1.11352	−0.556761	+	0.830673i	$0.687956\pi$
$480$	−51.2547	−2.33945
$481$	20.2207	0.921986
$482$	30.2915	1.37974
$483$	−18.2621	−0.830955
$484$	67.5354	3.06979
$485$	−49.1237	−2.23059
$486$	−47.9992	−2.17729
$487$	−25.0511	−1.13517	−0.567586	−	0.823314i	$-0.692123\pi$
$487$	−25.0511	−1.13517	−0.567586	+	0.823314i	$0.692123\pi$
$488$	17.6205	0.797645
$489$	77.6159	3.50991
$490$	−55.0737	−2.48798
$491$	−43.4091	−1.95902	−0.979512	−	0.201384i	$-0.935456\pi$
$491$	−43.4091	−1.95902	−0.979512	+	0.201384i	$0.935456\pi$
$492$	−25.0365	−1.12873
$493$	17.6148	0.793331
$494$	31.7518	1.42858
$495$	151.593	6.81358
$496$	−6.19496	−0.278162
$497$	4.56593	0.204810
$498$	−90.7302	−4.06572
$499$	−18.1571	−0.812823	−0.406411	−	0.913690i	$-0.633220\pi$
$499$	−18.1571	−0.812823	−0.406411	+	0.913690i	$0.633220\pi$
$500$	−80.2528	−3.58901
$501$	−9.65010	−0.431134
$502$	−30.5083	−1.36165
$503$	−3.95074	−0.176155	−0.0880773	−	0.996114i	$-0.528072\pi$
$503$	−3.95074	−0.176155	−0.0880773	+	0.996114i	$0.528072\pi$
$504$	25.4727	1.13464
$505$	−40.4035	−1.79793
$506$	71.7137	3.18806
$507$	32.4162	1.43966
$508$	−34.5963	−1.53496
$509$	−17.0282	−0.754759	−0.377380	−	0.926059i	$-0.623175\pi$
$509$	−17.0282	−0.754759	−0.377380	+	0.926059i	$0.623175\pi$
$510$	204.947	9.07522
$511$	5.39819	0.238802
$512$	14.0031	0.618857
$513$	34.8068	1.53676
$514$	−16.0552	−0.708166
$515$	56.2469	2.47854
$516$	1.14023	0.0501960
$517$	−73.6684	−3.23993
$518$	−10.2500	−0.450358
$519$	−28.0002	−1.22907
$520$	−67.4858	−2.95945
$521$	16.9285	0.741652	0.370826	−	0.928702i	$-0.379075\pi$
$521$	16.9285	0.741652	0.370826	+	0.928702i	$0.379075\pi$
$522$	−41.0547	−1.79691
$523$	−37.9676	−1.66021	−0.830103	−	0.557610i	$-0.811718\pi$
$523$	−37.9676	−1.66021	−0.830103	+	0.557610i	$0.811718\pi$
$524$	−43.4867	−1.89973
$525$	−35.4072	−1.54530
$526$	24.3233	1.06054
$527$	−34.3934	−1.49820
$528$	−21.8105	−0.949181
$529$	7.86451	0.341935
$530$	−9.31479	−0.404609
$531$	−80.3391	−3.48642
$532$	−10.2439	−0.444130
$533$	10.9458	0.474114
$534$	66.1733	2.86360
$535$	48.7199	2.10634
$536$	−32.5987	−1.40805
$537$	−5.90188	−0.254685
$538$	47.9740	2.06831
$539$	32.5391	1.40156
$540$	−172.522	−7.42417
$541$	−0.869907	−0.0374002	−0.0187001	−	0.999825i	$-0.505953\pi$
$541$	−0.869907	−0.0374002	−0.0187001	+	0.999825i	$0.505953\pi$
$542$	−1.34745	−0.0578780
$543$	−63.7698	−2.73662
$544$	28.5797	1.22534
$545$	−24.3643	−1.04365
$546$	−37.2038	−1.59218
$547$	41.6084	1.77905	0.889523	−	0.456890i	$-0.151037\pi$
$547$	41.6084	1.77905	0.889523	+	0.456890i	$0.151037\pi$
$548$	51.1173	2.18362
$549$	−34.7039	−1.48113
$550$	139.041	5.92873
$551$	7.07973	0.301607
$552$	−61.6717	−2.62492
$553$	3.67344	0.156210
$554$	−17.2671	−0.733610
$555$	52.4578	2.22671
$556$	35.8788	1.52160
$557$	20.4343	0.865829	0.432914	−	0.901435i	$-0.357485\pi$
$557$	20.4343	0.865829	0.432914	+	0.901435i	$0.357485\pi$
$558$	80.1605	3.39346
$559$	−0.498502	−0.0210844
$560$	5.20686	0.220030
$561$	−121.089	−5.11237
$562$	70.0470	2.95475
$563$	30.5117	1.28591	0.642957	−	0.765903i	$-0.277708\pi$
$563$	30.5117	1.28591	0.642957	+	0.765903i	$0.277708\pi$
$564$	147.741	6.22103
$565$	−61.3989	−2.58307
$566$	64.1548	2.69663
$567$	−19.0841	−0.801455
$568$	15.4193	0.646979
$569$	27.8902	1.16922	0.584610	−	0.811314i	$-0.301248\pi$
$569$	27.8902	1.16922	0.584610	+	0.811314i	$0.301248\pi$
$570$	82.3723	3.45020
$571$	−8.26252	−0.345776	−0.172888	−	0.984942i	$-0.555310\pi$
$571$	−8.26252	−0.345776	−0.172888	+	0.984942i	$0.555310\pi$
$572$	92.9843	3.88787
$573$	41.3106	1.72578
$574$	−5.54847	−0.231589
$575$	59.8411	2.49555
$576$	−84.0512	−3.50213
$577$	−4.44259	−0.184948	−0.0924738	−	0.995715i	$-0.529477\pi$
$577$	−4.44259	−0.184948	−0.0924738	+	0.995715i	$0.529477\pi$
$578$	−74.4050	−3.09484
$579$	60.5105	2.51473
$580$	−35.0911	−1.45708
$581$	−12.7974	−0.530926
$582$	−91.4537	−3.79088
$583$	5.50344	0.227929
$584$	18.2299	0.754357
$585$	132.914	5.49533
$586$	30.8794	1.27562
$587$	−4.97345	−0.205276	−0.102638	−	0.994719i	$-0.532728\pi$
$587$	−4.97345	−0.205276	−0.102638	+	0.994719i	$0.532728\pi$
$588$	−65.2567	−2.69114
$589$	−13.8234	−0.569582
$590$	−107.892	−4.44186
$591$	77.4244	3.18481
$592$	−5.26860	−0.216538
$593$	−5.21919	−0.214326	−0.107163	−	0.994241i	$-0.534177\pi$
$593$	−5.21919	−0.214326	−0.107163	+	0.994241i	$0.534177\pi$
$594$	160.153	6.57115
$595$	28.9077	1.18510
$596$	−23.2774	−0.953479
$597$	−60.6776	−2.48337
$598$	62.8776	2.57126
$599$	3.68277	0.150474	0.0752370	−	0.997166i	$-0.476029\pi$
$599$	3.68277	0.150474	0.0752370	+	0.997166i	$0.476029\pi$
$600$	−119.571	−4.88147
$601$	−15.9179	−0.649305	−0.324653	−	0.945833i	$-0.605247\pi$
$601$	−15.9179	−0.649305	−0.324653	+	0.945833i	$0.605247\pi$
$602$	0.252693	0.0102990
$603$	64.2036	2.61457
$604$	−3.50145	−0.142472
$605$	−76.5980	−3.11415
$606$	−75.2193	−3.05557
$607$	−31.5212	−1.27941	−0.639704	−	0.768622i	$-0.720943\pi$
$607$	−31.5212	−1.27941	−0.639704	+	0.768622i	$0.720943\pi$
$608$	11.4867	0.465848
$609$	−8.29536	−0.336145
$610$	−46.6061	−1.88702
$611$	−64.5914	−2.61309
$612$	169.520	6.85244
$613$	15.4872	0.625523	0.312761	−	0.949832i	$-0.398746\pi$
$613$	15.4872	0.625523	0.312761	+	0.949832i	$0.398746\pi$
$614$	62.4889	2.52185
$615$	28.3962	1.14504
$616$	−20.2115	−0.814346
$617$	−12.3772	−0.498285	−0.249143	−	0.968467i	$-0.580149\pi$
$617$	−12.3772	−0.498285	−0.249143	+	0.968467i	$0.580149\pi$
$618$	104.715	4.21226
$619$	−25.5839	−1.02830	−0.514151	−	0.857700i	$-0.671893\pi$
$619$	−25.5839	−1.02830	−0.514151	+	0.857700i	$0.671893\pi$
$620$	68.5164	2.75169
$621$	68.9274	2.76596
$622$	32.4886	1.30267
$623$	9.33370	0.373947
$624$	−19.1232	−0.765539
$625$	37.1652	1.48661
$626$	70.1646	2.80434
$627$	−48.6679	−1.94361
$628$	−23.2335	−0.927116
$629$	−29.2505	−1.16629
$630$	−67.3749	−2.68428
$631$	43.4395	1.72930	0.864650	−	0.502374i	$-0.167540\pi$
$631$	43.4395	1.72930	0.864650	+	0.502374i	$0.167540\pi$
$632$	12.4053	0.493457
$633$	−52.2241	−2.07572
$634$	83.3629	3.31076
$635$	39.2389	1.55715
$636$	−11.0371	−0.437649
$637$	28.5298	1.13039
$638$	32.5752	1.28966
$639$	−30.3685	−1.20136
$640$	−80.3569	−3.17639
$641$	34.6308	1.36784	0.683918	−	0.729559i	$-0.260275\pi$
$641$	34.6308	1.36784	0.683918	+	0.729559i	$0.260275\pi$
$642$	90.7019	3.57972
$643$	3.66932	0.144704	0.0723519	−	0.997379i	$-0.476950\pi$
$643$	3.66932	0.144704	0.0723519	+	0.997379i	$0.476950\pi$
$644$	−20.2858	−0.799374
$645$	−1.29324	−0.0509214
$646$	−45.9308	−1.80712
$647$	−31.2028	−1.22671	−0.613354	−	0.789808i	$-0.710180\pi$
$647$	−31.2028	−1.22671	−0.613354	+	0.789808i	$0.710180\pi$
$648$	−64.4475	−2.53174
$649$	63.7458	2.50224
$650$	121.909	4.78167
$651$	16.1969	0.634808
$652$	86.2170	3.37652
$653$	−10.4249	−0.407959	−0.203980	−	0.978975i	$-0.565388\pi$
$653$	−10.4249	−0.407959	−0.203980	+	0.978975i	$0.565388\pi$
$654$	−45.3591	−1.77368
$655$	49.3222	1.92718
$656$	−2.85197	−0.111351
$657$	−35.9040	−1.40075
$658$	32.7417	1.27640
$659$	−47.1818	−1.83794	−0.918971	−	0.394326i	$-0.870978\pi$
$659$	−47.1818	−1.83794	−0.918971	+	0.394326i	$0.870978\pi$
$660$	241.225	9.38968
$661$	8.45099	0.328705	0.164353	−	0.986402i	$-0.447446\pi$
$661$	8.45099	0.328705	0.164353	+	0.986402i	$0.447446\pi$
$662$	55.6877	2.16436
$663$	−106.169	−4.12326
$664$	−43.2173	−1.67716
$665$	11.6185	0.450548
$666$	68.1738	2.64168
$667$	14.0199	0.542851
$668$	−10.7195	−0.414749
$669$	−18.3382	−0.708995
$670$	86.2230	3.33108
$671$	27.5362	1.06302
$672$	−13.4591	−0.519195
$673$	33.6766	1.29814	0.649069	−	0.760729i	$-0.275158\pi$
$673$	33.6766	1.29814	0.649069	+	0.760729i	$0.275158\pi$
$674$	−34.1678	−1.31609
$675$	133.639	5.14375
$676$	36.0085	1.38494
$677$	18.7060	0.718929	0.359465	−	0.933159i	$-0.382959\pi$
$677$	18.7060	0.718929	0.359465	+	0.933159i	$0.382959\pi$
$678$	−114.307	−4.38992
$679$	−12.8995	−0.495036
$680$	97.6221	3.74364
$681$	25.5264	0.978173
$682$	−63.6040	−2.43552
$683$	40.0938	1.53415	0.767073	−	0.641560i	$-0.221713\pi$
$683$	40.0938	1.53415	0.767073	+	0.641560i	$0.221713\pi$
$684$	68.1334	2.60515
$685$	−57.9768	−2.21518
$686$	−31.5838	−1.20587
$687$	−50.2546	−1.91733
$688$	0.129887	0.00495190
$689$	4.82534	0.183831
$690$	163.121	6.20989
$691$	0.481014	0.0182987	0.00914933	−	0.999958i	$-0.497088\pi$
$691$	0.481014	0.0182987	0.00914933	+	0.999958i	$0.497088\pi$
$692$	−31.1031	−1.18236
$693$	39.8069	1.51214
$694$	−20.6171	−0.782616
$695$	−40.6934	−1.54359
$696$	−28.0137	−1.06186
$697$	−15.8337	−0.599744
$698$	10.5800	0.400459
$699$	−50.0312	−1.89235
$700$	−39.3309	−1.48657
$701$	−14.8744	−0.561800	−0.280900	−	0.959737i	$-0.590633\pi$
$701$	−14.8744	−0.561800	−0.280900	+	0.959737i	$0.590633\pi$
$702$	140.420	5.29980
$703$	−11.7563	−0.443398
$704$	66.6911	2.51352
$705$	−167.567	−6.31093
$706$	63.2944	2.38211
$707$	−10.6096	−0.399016
$708$	−127.841	−4.80458
$709$	−19.6190	−0.736808	−0.368404	−	0.929666i	$-0.620096\pi$
$709$	−19.6190	−0.736808	−0.368404	+	0.929666i	$0.620096\pi$
$710$	−40.7838	−1.53059
$711$	−24.4325	−0.916289
$712$	31.5202	1.18127
$713$	−27.3742	−1.02517
$714$	53.8175	2.01407
$715$	−105.462	−3.94406
$716$	−6.55590	−0.245006
$717$	44.6231	1.66648
$718$	3.35367	0.125158
$719$	8.32799	0.310582	0.155291	−	0.987869i	$-0.450369\pi$
$719$	8.32799	0.310582	0.155291	+	0.987869i	$0.450369\pi$
$720$	−34.6314	−1.29064
$721$	14.7700	0.550062
$722$	26.1043	0.971503
$723$	−40.7087	−1.51397
$724$	−70.8365	−2.63262
$725$	27.1822	1.00952
$726$	−142.603	−5.29248
$727$	37.2688	1.38222	0.691112	−	0.722747i	$-0.257121\pi$
$727$	37.2688	1.38222	0.691112	+	0.722747i	$0.257121\pi$
$728$	−17.7212	−0.656791
$729$	9.60563	0.355764
$730$	−48.2177	−1.78462
$731$	0.721112	0.0266713
$732$	−55.2234	−2.04112
$733$	28.2789	1.04451	0.522253	−	0.852791i	$-0.325092\pi$
$733$	28.2789	1.04451	0.522253	+	0.852791i	$0.325092\pi$
$734$	−24.5203	−0.905060
$735$	74.0136	2.73003
$736$	22.7470	0.838464
$737$	−50.9429	−1.87651
$738$	36.9035	1.35844
$739$	17.1794	0.631955	0.315977	−	0.948767i	$-0.397668\pi$
$739$	17.1794	0.631955	0.315977	+	0.948767i	$0.397668\pi$
$740$	58.2709	2.14208
$741$	−42.6713	−1.56757
$742$	−2.44599	−0.0897949
$743$	−40.0252	−1.46838	−0.734191	−	0.678943i	$-0.762438\pi$
$743$	−40.0252	−1.46838	−0.734191	+	0.678943i	$0.762438\pi$
$744$	54.6976	2.00531
$745$	26.4010	0.967258
$746$	20.5241	0.751441
$747$	85.1171	3.11427
$748$	−134.507	−4.91807
$749$	12.7934	0.467462
$750$	169.456	6.18765
$751$	39.3096	1.43443	0.717213	−	0.696854i	$-0.245417\pi$
$751$	39.3096	1.43443	0.717213	+	0.696854i	$0.245417\pi$
$752$	16.8296	0.613712
$753$	41.0002	1.49413
$754$	28.5615	1.04015
$755$	3.97132	0.144531
$756$	−45.3028	−1.64765
$757$	6.63238	0.241058	0.120529	−	0.992710i	$-0.461541\pi$
$757$	6.63238	0.241058	0.120529	+	0.992710i	$0.461541\pi$
$758$	51.7536	1.87978
$759$	−96.3762	−3.49823
$760$	39.2362	1.42325
$761$	−18.3538	−0.665325	−0.332663	−	0.943046i	$-0.607947\pi$
$761$	−18.3538	−0.665325	−0.332663	+	0.943046i	$0.607947\pi$
$762$	73.0511	2.64636
$763$	−6.39787	−0.231618
$764$	45.8885	1.66019
$765$	−192.268	−6.95147
$766$	18.8160	0.679849
$767$	55.8914	2.01812
$768$	−73.2047	−2.64155
$769$	21.4488	0.773463	0.386732	−	0.922192i	$-0.373604\pi$
$769$	21.4488	0.773463	0.386732	+	0.922192i	$0.373604\pi$
$770$	53.4592	1.92653
$771$	21.5766	0.777064
$772$	67.2161	2.41916
$773$	−36.9424	−1.32872	−0.664362	−	0.747411i	$-0.731297\pi$
$773$	−36.9424	−1.32872	−0.664362	+	0.747411i	$0.731297\pi$
$774$	−1.68069	−0.0604112
$775$	−53.0740	−1.90648
$776$	−43.5619	−1.56378
$777$	13.7750	0.494174
$778$	2.07769	0.0744887
$779$	−6.36387	−0.228009
$780$	211.503	7.57302
$781$	24.0962	0.862229
$782$	−90.9561	−3.25258
$783$	31.3095	1.11891
$784$	−7.43357	−0.265484
$785$	26.3512	0.940514
$786$	91.8233	3.27523
$787$	22.1028	0.787878	0.393939	−	0.919137i	$-0.371112\pi$
$787$	22.1028	0.787878	0.393939	+	0.919137i	$0.371112\pi$
$788$	86.0042	3.06377
$789$	−32.6881	−1.16373
$790$	−32.8118	−1.16739
$791$	−16.1228	−0.573262
$792$	134.429	4.77674
$793$	24.1433	0.857354
$794$	84.3522	2.99355
$795$	12.5182	0.443973
$796$	−67.4017	−2.38899
$797$	−10.8488	−0.384285	−0.192142	−	0.981367i	$-0.561544\pi$
$797$	−10.8488	−0.384285	−0.192142	+	0.981367i	$0.561544\pi$
$798$	21.6303	0.765704
$799$	93.4353	3.30550
$800$	44.1026	1.55926
$801$	−62.0795	−2.19347
$802$	5.59081	0.197418
$803$	28.4883	1.00533
$804$	102.165	3.60310
$805$	23.0080	0.810926
$806$	−55.7671	−1.96431
$807$	−64.4723	−2.26953
$808$	−35.8290	−1.26046
$809$	−5.86806	−0.206310	−0.103155	−	0.994665i	$-0.532894\pi$
$809$	−5.86806	−0.206310	−0.103155	+	0.994665i	$0.532894\pi$
$810$	170.462	5.98944
$811$	−10.4415	−0.366651	−0.183325	−	0.983052i	$-0.558686\pi$
$811$	−10.4415	−0.366651	−0.183325	+	0.983052i	$0.558686\pi$
$812$	−9.21462	−0.323370
$813$	1.81084	0.0635090
$814$	−54.0931	−1.89596
$815$	−97.7865	−3.42531
$816$	27.6628	0.968391
$817$	0.289829	0.0101398
$818$	−0.176557	−0.00617316
$819$	34.9022	1.21958
$820$	31.5429	1.10153
$821$	51.5650	1.79963	0.899815	−	0.436271i	$-0.143701\pi$
$821$	51.5650	1.79963	0.899815	+	0.436271i	$0.143701\pi$
$822$	−107.935	−3.76468
$823$	52.6092	1.83384	0.916920	−	0.399071i	$-0.130667\pi$
$823$	52.6092	1.83384	0.916920	+	0.399071i	$0.130667\pi$
$824$	49.8786	1.73761
$825$	−186.857	−6.50554
$826$	−28.3316	−0.985783
$827$	2.56059	0.0890405	0.0445203	−	0.999008i	$-0.485824\pi$
$827$	2.56059	0.0890405	0.0445203	+	0.999008i	$0.485824\pi$
$828$	134.923	4.68891
$829$	−26.3995	−0.916894	−0.458447	−	0.888722i	$-0.651594\pi$
$829$	−26.3995	−0.916894	−0.458447	+	0.888722i	$0.651594\pi$
$830$	114.309	3.96772
$831$	23.2053	0.804983
$832$	58.4739	2.02722
$833$	−41.2700	−1.42992
$834$	−75.7591	−2.62332
$835$	12.1579	0.420743
$836$	−54.0611	−1.86974
$837$	−61.1328	−2.11306
$838$	−17.1760	−0.593333
$839$	29.7082	1.02564	0.512821	−	0.858496i	$-0.328601\pi$
$839$	29.7082	1.02564	0.512821	+	0.858496i	$0.328601\pi$
$840$	−45.9733	−1.58623
$841$	−22.6316	−0.780401
$842$	−35.5585	−1.22543
$843$	−94.1362	−3.24222
$844$	−58.0113	−1.99683
$845$	−40.8405	−1.40496
$846$	−217.769	−7.48705
$847$	−20.1140	−0.691125
$848$	−1.25726	−0.0431746
$849$	−86.2177	−2.95898
$850$	−176.349	−6.04871
$851$	−23.2809	−0.798058
$852$	−48.3246	−1.65557
$853$	−2.99792	−0.102647	−0.0513234	−	0.998682i	$-0.516344\pi$
$853$	−2.99792	−0.102647	−0.0513234	+	0.998682i	$0.516344\pi$
$854$	−12.2384	−0.418788
$855$	−77.2763	−2.64279
$856$	43.2038	1.47667
$857$	−30.2001	−1.03162	−0.515808	−	0.856704i	$-0.672508\pi$
$857$	−30.2001	−1.03162	−0.515808	+	0.856704i	$0.672508\pi$
$858$	−196.339	−6.70290
$859$	8.94004	0.305030	0.152515	−	0.988301i	$-0.451263\pi$
$859$	8.94004	0.305030	0.152515	+	0.988301i	$0.451263\pi$
$860$	−1.43655	−0.0489861
$861$	7.45659	0.254120
$862$	−77.7391	−2.64780
$863$	−4.85757	−0.165353	−0.0826767	−	0.996576i	$-0.526347\pi$
$863$	−4.85757	−0.165353	−0.0826767	+	0.996576i	$0.526347\pi$
$864$	50.7991	1.72822
$865$	35.2768	1.19945
$866$	−15.9540	−0.542140
$867$	99.9929	3.39594
$868$	17.9918	0.610682
$869$	19.3861	0.657630
$870$	74.0958	2.51208
$871$	−44.6660	−1.51345
$872$	−21.6058	−0.731664
$873$	85.7959	2.90375
$874$	−36.5570	−1.23656
$875$	23.9016	0.808022
$876$	−57.1331	−1.93035
$877$	−17.8263	−0.601950	−0.300975	−	0.953632i	$-0.597312\pi$
$877$	−17.8263	−0.601950	−0.300975	+	0.953632i	$0.597312\pi$
$878$	5.32635	0.179755
$879$	−41.4989	−1.39972
$880$	27.4786	0.926304
$881$	18.4207	0.620608	0.310304	−	0.950637i	$-0.399569\pi$
$881$	18.4207	0.620608	0.310304	+	0.950637i	$0.399569\pi$
$882$	96.1876	3.23881
$883$	−23.6326	−0.795301	−0.397650	−	0.917537i	$-0.630174\pi$
$883$	−23.6326	−0.795301	−0.397650	+	0.917537i	$0.630174\pi$
$884$	−117.934	−3.96655
$885$	144.997	4.87401
$886$	−42.1581	−1.41633
$887$	53.5529	1.79813	0.899065	−	0.437815i	$-0.144248\pi$
$887$	53.5529	1.79813	0.899065	+	0.437815i	$0.144248\pi$
$888$	46.5185	1.56106
$889$	10.3038	0.345578
$890$	−83.3703	−2.79458
$891$	−100.714	−3.37404
$892$	−20.3703	−0.682050
$893$	37.5534	1.25668
$894$	49.1508	1.64385
$895$	7.43565	0.248546
$896$	−21.1010	−0.704936
$897$	−84.5013	−2.82142
$898$	27.5965	0.920908
$899$	−12.4344	−0.414712
$900$	261.594	8.71980
$901$	−6.98013	−0.232542
$902$	−29.2814	−0.974964
$903$	−0.339595	−0.0113010
$904$	−54.4473	−1.81089
$905$	80.3422	2.67066
$906$	7.39341	0.245630
$907$	27.9646	0.928548	0.464274	−	0.885692i	$-0.346315\pi$
$907$	27.9646	0.928548	0.464274	+	0.885692i	$0.346315\pi$
$908$	28.3551	0.940998
$909$	70.5658	2.34052
$910$	46.8723	1.55380
$911$	−37.5412	−1.24380	−0.621898	−	0.783098i	$-0.713638\pi$
$911$	−37.5412	−1.24380	−0.621898	+	0.783098i	$0.713638\pi$
$912$	11.1182	0.368160
$913$	−67.5369	−2.23515
$914$	72.2333	2.38926
$915$	62.6339	2.07061
$916$	−55.8237	−1.84447
$917$	12.9516	0.427699
$918$	−203.125	−6.70414
$919$	−20.0748	−0.662205	−0.331102	−	0.943595i	$-0.607421\pi$
$919$	−20.0748	−0.662205	−0.331102	+	0.943595i	$0.607421\pi$
$920$	77.6988	2.56165
$921$	−83.9789	−2.76720
$922$	−16.3865	−0.539662
$923$	21.1272	0.695410
$924$	63.3437	2.08385
$925$	−45.1377	−1.48412
$926$	71.9434	2.36421
$927$	−98.2368	−3.22652
$928$	10.3326	0.339183
$929$	−13.9540	−0.457815	−0.228907	−	0.973448i	$-0.573515\pi$
$929$	−13.9540	−0.457815	−0.228907	+	0.973448i	$0.573515\pi$
$930$	−144.674	−4.74405
$931$	−16.5872	−0.543624
$932$	−55.5755	−1.82044
$933$	−43.6614	−1.42941
$934$	17.9944	0.588796
$935$	152.557	4.98914
$936$	117.866	3.85256
$937$	23.9229	0.781528	0.390764	−	0.920491i	$-0.372211\pi$
$937$	23.9229	0.781528	0.390764	+	0.920491i	$0.372211\pi$
$938$	22.6414	0.739269
$939$	−94.2942	−3.07718
$940$	−186.136	−6.07108
$941$	−4.86204	−0.158498	−0.0792490	−	0.996855i	$-0.525252\pi$
$941$	−4.86204	−0.158498	−0.0792490	+	0.996855i	$0.525252\pi$
$942$	49.0581	1.59840
$943$	−12.6023	−0.410386
$944$	−14.5628	−0.473978
$945$	51.3821	1.67146
$946$	1.33356	0.0433577
$947$	15.1351	0.491825	0.245913	−	0.969292i	$-0.420912\pi$
$947$	15.1351	0.491825	0.245913	+	0.969292i	$0.420912\pi$
$948$	−38.8787	−1.26272
$949$	24.9782	0.810826
$950$	−70.8779	−2.29958
$951$	−112.031	−3.63287
$952$	25.6347	0.830826
$953$	26.6970	0.864801	0.432400	−	0.901682i	$-0.357667\pi$
$953$	26.6970	0.864801	0.432400	+	0.901682i	$0.357667\pi$
$954$	16.2685	0.526713
$955$	−52.0463	−1.68418
$956$	49.5680	1.60315
$957$	−43.7778	−1.41514
$958$	57.1617	1.84681
$959$	−15.2242	−0.491615
$960$	151.696	4.89597
$961$	−6.72138	−0.216819
$962$	−47.4281	−1.52914
$963$	−85.0905	−2.74200
$964$	−45.2199	−1.45644
$965$	−76.2359	−2.45412
$966$	42.8341	1.37816
$967$	−12.7153	−0.408896	−0.204448	−	0.978877i	$-0.565540\pi$
$967$	−12.7153	−0.408896	−0.204448	+	0.978877i	$0.565540\pi$
$968$	−67.9256	−2.18321
$969$	61.7265	1.98294
$970$	115.221	3.69951
$971$	−17.7984	−0.571179	−0.285590	−	0.958352i	$-0.592189\pi$
$971$	−17.7984	−0.571179	−0.285590	+	0.958352i	$0.592189\pi$
$972$	71.6545	2.29832
$973$	−10.6858	−0.342569
$974$	58.7577	1.88272
$975$	−163.834	−5.24688
$976$	−6.29065	−0.201359
$977$	−46.3300	−1.48223	−0.741113	−	0.671380i	$-0.765702\pi$
$977$	−46.3300	−1.48223	−0.741113	+	0.671380i	$0.765702\pi$
$978$	−182.049	−5.82130
$979$	49.2575	1.57428
$980$	82.2155	2.62628
$981$	42.5529	1.35861
$982$	101.817	3.24910
$983$	7.82079	0.249445	0.124722	−	0.992192i	$-0.460196\pi$
$983$	7.82079	0.249445	0.124722	+	0.992192i	$0.460196\pi$
$984$	25.1811	0.802745
$985$	−97.5452	−3.10805
$986$	−41.3158	−1.31576
$987$	−44.0016	−1.40059
$988$	−47.4000	−1.50799
$989$	0.573944	0.0182503
$990$	−355.563	−11.3005
$991$	−7.67415	−0.243777	−0.121889	−	0.992544i	$-0.538895\pi$
$991$	−7.67415	−0.243777	−0.121889	+	0.992544i	$0.538895\pi$
$992$	−20.1746	−0.640545
$993$	−74.8388	−2.37494
$994$	−10.7095	−0.339684
$995$	76.4464	2.42351
$996$	135.445	4.29172
$997$	41.8751	1.32620	0.663099	−	0.748532i	$-0.269241\pi$
$997$	41.8751	1.32620	0.663099	+	0.748532i	$0.269241\pi$
$998$	42.5878	1.34809
$999$	−51.9914	−1.64493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.19	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.34552 q^{2} +3.15214 q^{3} +3.50145 q^{4} -3.97132 q^{5} -7.39341 q^{6} -1.04283 q^{7} -3.52168 q^{8} +6.93601 q^{9} +O(q^{10})\)	\(q-2.34552 q^{2} +3.15214 q^{3} +3.50145 q^{4} -3.97132 q^{5} -7.39341 q^{6} -1.04283 q^{7} -3.52168 q^{8} +6.93601 q^{9} +9.31479 q^{10} -5.50344 q^{11} +11.0371 q^{12} -4.82534 q^{13} +2.44599 q^{14} -12.5182 q^{15} +1.25726 q^{16} +6.98013 q^{17} -16.2685 q^{18} +2.80545 q^{19} -13.9054 q^{20} -3.28716 q^{21} +12.9084 q^{22} +5.55558 q^{23} -11.1008 q^{24} +10.7713 q^{25} +11.3179 q^{26} +12.4069 q^{27} -3.65143 q^{28} +2.52356 q^{29} +29.3616 q^{30} -4.92733 q^{31} +4.09443 q^{32} -17.3476 q^{33} -16.3720 q^{34} +4.14142 q^{35} +24.2861 q^{36} -4.19053 q^{37} -6.58023 q^{38} -15.2102 q^{39} +13.9857 q^{40} -2.26840 q^{41} +7.71010 q^{42} +0.103309 q^{43} -19.2700 q^{44} -27.5451 q^{45} -13.0307 q^{46} +13.3859 q^{47} +3.96307 q^{48} -5.91250 q^{49} -25.2644 q^{50} +22.0024 q^{51} -16.8957 q^{52} -1.00000 q^{53} -29.1005 q^{54} +21.8559 q^{55} +3.67253 q^{56} +8.84318 q^{57} -5.91906 q^{58} -11.5829 q^{59} -43.8317 q^{60} -5.00345 q^{61} +11.5571 q^{62} -7.23311 q^{63} -12.1181 q^{64} +19.1629 q^{65} +40.6892 q^{66} +9.25657 q^{67} +24.4406 q^{68} +17.5120 q^{69} -9.71378 q^{70} -4.37839 q^{71} -24.4264 q^{72} -5.17646 q^{73} +9.82897 q^{74} +33.9528 q^{75} +9.82314 q^{76} +5.73917 q^{77} +35.6757 q^{78} -3.52255 q^{79} -4.99299 q^{80} +18.3002 q^{81} +5.32057 q^{82} +12.2718 q^{83} -11.5098 q^{84} -27.7203 q^{85} -0.242314 q^{86} +7.95463 q^{87} +19.3814 q^{88} -8.95032 q^{89} +64.6075 q^{90} +5.03202 q^{91} +19.4526 q^{92} -15.5317 q^{93} -31.3968 q^{94} -11.1413 q^{95} +12.9062 q^{96} +12.3696 q^{97} +13.8679 q^{98} -38.1719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 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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