LMFDB - Embedded newform 8003.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.49383 q^{2} -0.270355 q^{3} +4.21918 q^{4} -2.99495 q^{5} +0.674220 q^{6} -3.80387 q^{7} -5.53426 q^{8} -2.92691 q^{9} +O(q^{10})$	\(q-2.49383 q^{2} -0.270355 q^{3} +4.21918 q^{4} -2.99495 q^{5} +0.674220 q^{6} -3.80387 q^{7} -5.53426 q^{8} -2.92691 q^{9} +7.46890 q^{10} -5.91933 q^{11} -1.14068 q^{12} -0.710532 q^{13} +9.48621 q^{14} +0.809702 q^{15} +5.36314 q^{16} -1.35009 q^{17} +7.29921 q^{18} -5.05928 q^{19} -12.6363 q^{20} +1.02840 q^{21} +14.7618 q^{22} +6.13130 q^{23} +1.49622 q^{24} +3.96974 q^{25} +1.77195 q^{26} +1.60237 q^{27} -16.0492 q^{28} -0.793559 q^{29} -2.01926 q^{30} +1.55429 q^{31} -2.30622 q^{32} +1.60032 q^{33} +3.36690 q^{34} +11.3924 q^{35} -12.3492 q^{36} -11.1363 q^{37} +12.6170 q^{38} +0.192096 q^{39} +16.5748 q^{40} +7.91233 q^{41} -2.56465 q^{42} -11.5314 q^{43} -24.9747 q^{44} +8.76595 q^{45} -15.2904 q^{46} -3.68696 q^{47} -1.44995 q^{48} +7.46946 q^{49} -9.89985 q^{50} +0.365005 q^{51} -2.99786 q^{52} -1.00000 q^{53} -3.99604 q^{54} +17.7281 q^{55} +21.0516 q^{56} +1.36780 q^{57} +1.97900 q^{58} +1.22514 q^{59} +3.41628 q^{60} +1.94993 q^{61} -3.87613 q^{62} +11.1336 q^{63} -4.97495 q^{64} +2.12801 q^{65} -3.99093 q^{66} +6.11454 q^{67} -5.69629 q^{68} -1.65763 q^{69} -28.4108 q^{70} -13.2576 q^{71} +16.1983 q^{72} +5.38563 q^{73} +27.7720 q^{74} -1.07324 q^{75} -21.3460 q^{76} +22.5164 q^{77} -0.479055 q^{78} +10.0480 q^{79} -16.0623 q^{80} +8.34751 q^{81} -19.7320 q^{82} +13.3540 q^{83} +4.33900 q^{84} +4.04346 q^{85} +28.7574 q^{86} +0.214543 q^{87} +32.7591 q^{88} +7.27485 q^{89} -21.8608 q^{90} +2.70278 q^{91} +25.8691 q^{92} -0.420210 q^{93} +9.19464 q^{94} +15.1523 q^{95} +0.623500 q^{96} -12.8467 q^{97} -18.6276 q^{98} +17.3253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.49383	−1.76340	−0.881702	−	0.471807i	$-0.843602\pi$
$2$	−2.49383	−1.76340	−0.881702	+	0.471807i	$0.843602\pi$
$3$	−0.270355	−0.156090	−0.0780449	−	0.996950i	$-0.524868\pi$
$3$	−0.270355	−0.156090	−0.0780449	+	0.996950i	$0.524868\pi$
$4$	4.21918	2.10959
$5$	−2.99495	−1.33938	−0.669692	−	0.742639i	$-0.733574\pi$
$5$	−2.99495	−1.33938	−0.669692	+	0.742639i	$0.733574\pi$
$6$	0.674220	0.275249
$7$	−3.80387	−1.43773	−0.718865	−	0.695150i	$-0.755338\pi$
$7$	−3.80387	−1.43773	−0.718865	+	0.695150i	$0.755338\pi$
$8$	−5.53426	−1.95666
$9$	−2.92691	−0.975636
$10$	7.46890	2.36187
$11$	−5.91933	−1.78475	−0.892373	−	0.451299i	$-0.850961\pi$
$11$	−5.91933	−1.78475	−0.892373	+	0.451299i	$0.850961\pi$
$12$	−1.14068	−0.329286
$13$	−0.710532	−0.197066	−0.0985331	−	0.995134i	$-0.531415\pi$
$13$	−0.710532	−0.197066	−0.0985331	+	0.995134i	$0.531415\pi$
$14$	9.48621	2.53530
$15$	0.809702	0.209064
$16$	5.36314	1.34078
$17$	−1.35009	−0.327446	−0.163723	−	0.986506i	$-0.552350\pi$
$17$	−1.35009	−0.327446	−0.163723	+	0.986506i	$0.552350\pi$
$18$	7.29921	1.72044
$19$	−5.05928	−1.16068	−0.580339	−	0.814375i	$-0.697080\pi$
$19$	−5.05928	−1.16068	−0.580339	+	0.814375i	$0.697080\pi$
$20$	−12.6363	−2.82555
$21$	1.02840	0.224415
$22$	14.7618	3.14723
$23$	6.13130	1.27847	0.639233	−	0.769013i	$-0.279252\pi$
$23$	6.13130	1.27847	0.639233	+	0.769013i	$0.279252\pi$
$24$	1.49622	0.305414
$25$	3.96974	0.793948
$26$	1.77195	0.347507
$27$	1.60237	0.308377
$28$	−16.0492	−3.03302
$29$	−0.793559	−0.147360	−0.0736801	−	0.997282i	$-0.523474\pi$
$29$	−0.793559	−0.147360	−0.0736801	+	0.997282i	$0.523474\pi$
$30$	−2.01926	−0.368664
$31$	1.55429	0.279158	0.139579	−	0.990211i	$-0.455425\pi$
$31$	1.55429	0.279158	0.139579	+	0.990211i	$0.455425\pi$
$32$	−2.30622	−0.407686
$33$	1.60032	0.278581
$34$	3.36690	0.577419
$35$	11.3924	1.92567
$36$	−12.3492	−2.05819
$37$	−11.1363	−1.83080	−0.915399	−	0.402548i	$-0.868125\pi$
$37$	−11.1363	−1.83080	−0.915399	+	0.402548i	$0.868125\pi$
$38$	12.6170	2.04674
$39$	0.192096	0.0307600
$40$	16.5748	2.62071
$41$	7.91233	1.23570	0.617849	−	0.786297i	$-0.288004\pi$
$41$	7.91233	1.23570	0.617849	+	0.786297i	$0.288004\pi$
$42$	−2.56465	−0.395734
$43$	−11.5314	−1.75852	−0.879262	−	0.476339i	$-0.841963\pi$
$43$	−11.5314	−1.75852	−0.879262	+	0.476339i	$0.841963\pi$
$44$	−24.9747	−3.76508
$45$	8.76595	1.30675
$46$	−15.2904	−2.25445
$47$	−3.68696	−0.537798	−0.268899	−	0.963168i	$-0.586660\pi$
$47$	−3.68696	−0.537798	−0.268899	+	0.963168i	$0.586660\pi$
$48$	−1.44995	−0.209283
$49$	7.46946	1.06707
$50$	−9.89985	−1.40005
$51$	0.365005	0.0511109
$52$	−2.99786	−0.415729
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−3.99604	−0.543792
$55$	17.7281	2.39046
$56$	21.0516	2.81314
$57$	1.36780	0.181170
$58$	1.97900	0.259855
$59$	1.22514	0.159499	0.0797496	−	0.996815i	$-0.474588\pi$
$59$	1.22514	0.159499	0.0797496	+	0.996815i	$0.474588\pi$
$60$	3.41628	0.441040
$61$	1.94993	0.249663	0.124831	−	0.992178i	$-0.460161\pi$
$61$	1.94993	0.249663	0.124831	+	0.992178i	$0.460161\pi$
$62$	−3.87613	−0.492269
$63$	11.1336	1.40270
$64$	−4.97495	−0.621869
$65$	2.12801	0.263947
$66$	−3.99093	−0.491250
$67$	6.11454	0.747009	0.373505	−	0.927628i	$-0.378156\pi$
$67$	6.11454	0.747009	0.373505	+	0.927628i	$0.378156\pi$
$68$	−5.69629	−0.690776
$69$	−1.65763	−0.199555
$70$	−28.4108	−3.39573
$71$	−13.2576	−1.57339	−0.786694	−	0.617343i	$-0.788209\pi$
$71$	−13.2576	−1.57339	−0.786694	+	0.617343i	$0.788209\pi$
$72$	16.1983	1.90898
$73$	5.38563	0.630340	0.315170	−	0.949035i	$-0.397938\pi$
$73$	5.38563	0.630340	0.315170	+	0.949035i	$0.397938\pi$
$74$	27.7720	3.22843
$75$	−1.07324	−0.123927
$76$	−21.3460	−2.44856
$77$	22.5164	2.56598
$78$	−0.479055	−0.0542423
$79$	10.0480	1.13049	0.565247	−	0.824922i	$-0.308781\pi$
$79$	10.0480	1.13049	0.565247	+	0.824922i	$0.308781\pi$
$80$	−16.0623	−1.79582
$81$	8.34751	0.927502
$82$	−19.7320	−2.17903
$83$	13.3540	1.46579	0.732895	−	0.680342i	$-0.238169\pi$
$83$	13.3540	1.46579	0.732895	+	0.680342i	$0.238169\pi$
$84$	4.33900	0.473424
$85$	4.04346	0.438575
$86$	28.7574	3.10099
$87$	0.214543	0.0230014
$88$	32.7591	3.49213
$89$	7.27485	0.771132	0.385566	−	0.922680i	$-0.374006\pi$
$89$	7.27485	0.771132	0.385566	+	0.922680i	$0.374006\pi$
$90$	−21.8608	−2.30433
$91$	2.70278	0.283328
$92$	25.8691	2.69704
$93$	−0.420210	−0.0435738
$94$	9.19464	0.948355
$95$	15.1523	1.55459
$96$	0.623500	0.0636357
$97$	−12.8467	−1.30438	−0.652190	−	0.758056i	$-0.726150\pi$
$97$	−12.8467	−1.30438	−0.652190	+	0.758056i	$0.726150\pi$
$98$	−18.6276	−1.88167
$99$	17.3253	1.74126
$100$	16.7491	1.67491
$101$	−12.7204	−1.26573	−0.632863	−	0.774264i	$-0.718120\pi$
$101$	−12.7204	−1.26573	−0.632863	+	0.774264i	$0.718120\pi$
$102$	−0.910260	−0.0901292
$103$	6.80892	0.670903	0.335451	−	0.942058i	$-0.391111\pi$
$103$	6.80892	0.670903	0.335451	+	0.942058i	$0.391111\pi$
$104$	3.93227	0.385591
$105$	−3.08000	−0.300578
$106$	2.49383	0.242222
$107$	7.22091	0.698071	0.349036	−	0.937109i	$-0.386509\pi$
$107$	7.22091	0.698071	0.349036	+	0.937109i	$0.386509\pi$
$108$	6.76070	0.650549
$109$	−17.5619	−1.68212	−0.841061	−	0.540941i	$-0.818068\pi$
$109$	−17.5619	−1.68212	−0.841061	+	0.540941i	$0.818068\pi$
$110$	−44.2109	−4.21534
$111$	3.01076	0.285769
$112$	−20.4007	−1.92768
$113$	−0.715990	−0.0673547	−0.0336773	−	0.999433i	$-0.510722\pi$
$113$	−0.715990	−0.0673547	−0.0336773	+	0.999433i	$0.510722\pi$
$114$	−3.41107	−0.319476
$115$	−18.3630	−1.71236
$116$	−3.34817	−0.310870
$117$	2.07966	0.192265
$118$	−3.05528	−0.281261
$119$	5.13558	0.470778
$120$	−4.48110	−0.409067
$121$	24.0385	2.18532
$122$	−4.86279	−0.440256
$123$	−2.13914	−0.192880
$124$	6.55782	0.588910
$125$	3.08558	0.275983
$126$	−27.7653	−2.47353
$127$	5.75524	0.510695	0.255348	−	0.966849i	$-0.417810\pi$
$127$	5.75524	0.510695	0.255348	+	0.966849i	$0.417810\pi$
$128$	17.0191	1.50429
$129$	3.11758	0.274488
$130$	−5.30689	−0.465445
$131$	4.95580	0.432991	0.216495	−	0.976284i	$-0.430537\pi$
$131$	4.95580	0.432991	0.216495	+	0.976284i	$0.430537\pi$
$132$	6.75206	0.587691
$133$	19.2449	1.66874
$134$	−15.2486	−1.31728
$135$	−4.79903	−0.413035
$136$	7.47177	0.640699
$137$	21.0949	1.80226	0.901128	−	0.433553i	$-0.142740\pi$
$137$	21.0949	1.80226	0.901128	+	0.433553i	$0.142740\pi$
$138$	4.13385	0.351897
$139$	−12.6542	−1.07331	−0.536657	−	0.843801i	$-0.680313\pi$
$139$	−12.6542	−1.07331	−0.536657	+	0.843801i	$0.680313\pi$
$140$	48.0667	4.06238
$141$	0.996790	0.0839448
$142$	33.0622	2.77452
$143$	4.20587	0.351713
$144$	−15.6974	−1.30812
$145$	2.37667	0.197372
$146$	−13.4308	−1.11154
$147$	−2.01941	−0.166558
$148$	−46.9861	−3.86224
$149$	20.6126	1.68865	0.844326	−	0.535831i	$-0.180001\pi$
$149$	20.6126	1.68865	0.844326	+	0.535831i	$0.180001\pi$
$150$	2.67648	0.218534
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	27.9994	2.27105
$153$	3.95160	0.319468
$154$	−56.1520	−4.52486
$155$	−4.65502	−0.373900
$156$	0.810489	0.0648911
$157$	3.26944	0.260929	0.130465	−	0.991453i	$-0.458353\pi$
$157$	3.26944	0.260929	0.130465	+	0.991453i	$0.458353\pi$
$158$	−25.0581	−1.99352
$159$	0.270355	0.0214406
$160$	6.90702	0.546048
$161$	−23.3227	−1.83809
$162$	−20.8173	−1.63556
$163$	−4.61933	−0.361813	−0.180907	−	0.983500i	$-0.557903\pi$
$163$	−4.61933	−0.361813	−0.180907	+	0.983500i	$0.557903\pi$
$164$	33.3836	2.60682
$165$	−4.79289	−0.373126
$166$	−33.3025	−2.58478
$167$	13.8528	1.07196	0.535981	−	0.844230i	$-0.319942\pi$
$167$	13.8528	1.07196	0.535981	+	0.844230i	$0.319942\pi$
$168$	−5.69143	−0.439103
$169$	−12.4951	−0.961165
$170$	−10.0837	−0.773385
$171$	14.8081	1.13240
$172$	−48.6531	−3.70977
$173$	−7.01099	−0.533036	−0.266518	−	0.963830i	$-0.585873\pi$
$173$	−7.01099	−0.533036	−0.266518	+	0.963830i	$0.585873\pi$
$174$	−0.535033	−0.0405608
$175$	−15.1004	−1.14148
$176$	−31.7462	−2.39296
$177$	−0.331222	−0.0248962
$178$	−18.1422	−1.35982
$179$	18.7287	1.39985	0.699923	−	0.714218i	$-0.253218\pi$
$179$	18.7287	1.39985	0.699923	+	0.714218i	$0.253218\pi$
$180$	36.9851	2.75671
$181$	23.8184	1.77041	0.885205	−	0.465201i	$-0.154018\pi$
$181$	23.8184	1.77041	0.885205	+	0.465201i	$0.154018\pi$
$182$	−6.74026	−0.499621
$183$	−0.527174	−0.0389698
$184$	−33.9322	−2.50152
$185$	33.3527	2.45214
$186$	1.04793	0.0768381
$187$	7.99164	0.584407
$188$	−15.5560	−1.13453
$189$	−6.09522	−0.443362
$190$	−37.7873	−2.74138
$191$	−2.16339	−0.156537	−0.0782687	−	0.996932i	$-0.524939\pi$
$191$	−2.16339	−0.156537	−0.0782687	+	0.996932i	$0.524939\pi$
$192$	1.34501	0.0970674
$193$	−9.37160	−0.674582	−0.337291	−	0.941400i	$-0.609511\pi$
$193$	−9.37160	−0.674582	−0.337291	+	0.941400i	$0.609511\pi$
$194$	32.0373	2.30015
$195$	−0.575319	−0.0411995
$196$	31.5150	2.25107
$197$	−16.5235	−1.17725	−0.588627	−	0.808405i	$-0.700331\pi$
$197$	−16.5235	−1.17725	−0.588627	+	0.808405i	$0.700331\pi$
$198$	−43.2064	−3.07055
$199$	−0.932005	−0.0660681	−0.0330341	−	0.999454i	$-0.510517\pi$
$199$	−0.932005	−0.0660681	−0.0330341	+	0.999454i	$0.510517\pi$
$200$	−21.9696	−1.55348
$201$	−1.65310	−0.116601
$202$	31.7225	2.23198
$203$	3.01860	0.211864
$204$	1.54002	0.107823
$205$	−23.6970	−1.65507
$206$	−16.9803	−1.18307
$207$	−17.9458	−1.24732
$208$	−3.81068	−0.264223
$209$	29.9476	2.07152
$210$	7.68100	0.530040
$211$	12.3506	0.850250	0.425125	−	0.905135i	$-0.360230\pi$
$211$	12.3506	0.850250	0.425125	+	0.905135i	$0.360230\pi$
$212$	−4.21918	−0.289775
$213$	3.58427	0.245590
$214$	−18.0077	−1.23098
$215$	34.5360	2.35534
$216$	−8.86795	−0.603387
$217$	−5.91232	−0.401354
$218$	43.7963	2.96626
$219$	−1.45603	−0.0983897
$220$	74.7981	5.04289
$221$	0.959284	0.0645284
$222$	−7.50833	−0.503926
$223$	−26.4463	−1.77097	−0.885487	−	0.464665i	$-0.846175\pi$
$223$	−26.4463	−1.77097	−0.885487	+	0.464665i	$0.846175\pi$
$224$	8.77258	0.586142
$225$	−11.6191	−0.774604
$226$	1.78556	0.118773
$227$	−27.5481	−1.82843	−0.914217	−	0.405225i	$-0.867193\pi$
$227$	−27.5481	−1.82843	−0.914217	+	0.405225i	$0.867193\pi$
$228$	5.77102	0.382195
$229$	17.4888	1.15570	0.577848	−	0.816145i	$-0.303893\pi$
$229$	17.4888	1.15570	0.577848	+	0.816145i	$0.303893\pi$
$230$	45.7941	3.01957
$231$	−6.08743	−0.400524
$232$	4.39176	0.288333
$233$	15.6435	1.02484	0.512421	−	0.858734i	$-0.328749\pi$
$233$	15.6435	1.02484	0.512421	+	0.858734i	$0.328749\pi$
$234$	−5.18632	−0.339040
$235$	11.0423	0.720318
$236$	5.16908	0.336478
$237$	−2.71654	−0.176458
$238$	−12.8073	−0.830172
$239$	3.08331	0.199443	0.0997213	−	0.995015i	$-0.468205\pi$
$239$	3.08331	0.199443	0.0997213	+	0.995015i	$0.468205\pi$
$240$	4.34254	0.280310
$241$	−13.8297	−0.890847	−0.445423	−	0.895320i	$-0.646947\pi$
$241$	−13.8297	−0.890847	−0.445423	+	0.895320i	$0.646947\pi$
$242$	−59.9478	−3.85359
$243$	−7.06391	−0.453150
$244$	8.22711	0.526687
$245$	−22.3707	−1.42921
$246$	5.33465	0.340125
$247$	3.59478	0.228731
$248$	−8.60184	−0.546217
$249$	−3.61032	−0.228795
$250$	−7.69491	−0.486669
$251$	−12.5883	−0.794567	−0.397283	−	0.917696i	$-0.630047\pi$
$251$	−12.5883	−0.794567	−0.397283	+	0.917696i	$0.630047\pi$
$252$	46.9747	2.95913
$253$	−36.2932	−2.28173
$254$	−14.3526	−0.900562
$255$	−1.09317	−0.0684571
$256$	−32.4929	−2.03080
$257$	−9.11094	−0.568325	−0.284162	−	0.958776i	$-0.591715\pi$
$257$	−9.11094	−0.568325	−0.284162	+	0.958776i	$0.591715\pi$
$258$	−7.77471	−0.484032
$259$	42.3611	2.63219
$260$	8.97846	0.556821
$261$	2.32267	0.143770
$262$	−12.3589	−0.763537
$263$	−17.4088	−1.07347	−0.536737	−	0.843750i	$-0.680343\pi$
$263$	−17.4088	−1.07347	−0.536737	+	0.843750i	$0.680343\pi$
$264$	−8.85661	−0.545087
$265$	2.99495	0.183978
$266$	−47.9934	−2.94267
$267$	−1.96679	−0.120366
$268$	25.7983	1.57588
$269$	−12.0663	−0.735695	−0.367848	−	0.929886i	$-0.619905\pi$
$269$	−12.0663	−0.735695	−0.367848	+	0.929886i	$0.619905\pi$
$270$	11.9680	0.728347
$271$	17.1722	1.04314	0.521569	−	0.853209i	$-0.325347\pi$
$271$	17.1722	1.04314	0.521569	+	0.853209i	$0.325347\pi$
$272$	−7.24073	−0.439034
$273$	−0.730710	−0.0442246
$274$	−52.6070	−3.17810
$275$	−23.4982	−1.41699
$276$	−6.99385	−0.420980
$277$	26.6336	1.60026	0.800129	−	0.599828i	$-0.204765\pi$
$277$	26.6336	1.60026	0.800129	+	0.599828i	$0.204765\pi$
$278$	31.5574	1.89268
$279$	−4.54926	−0.272357
$280$	−63.0487	−3.76788
$281$	1.20934	0.0721429	0.0360714	−	0.999349i	$-0.488516\pi$
$281$	1.20934	0.0721429	0.0360714	+	0.999349i	$0.488516\pi$
$282$	−2.48582	−0.148029
$283$	−9.16240	−0.544648	−0.272324	−	0.962206i	$-0.587792\pi$
$283$	−9.16240	−0.544648	−0.272324	+	0.962206i	$0.587792\pi$
$284$	−55.9363	−3.31921
$285$	−4.09651	−0.242656
$286$	−10.4887	−0.620212
$287$	−30.0975	−1.77660
$288$	6.75010	0.397753
$289$	−15.1772	−0.892779
$290$	−5.92701	−0.348046
$291$	3.47316	0.203600
$292$	22.7229	1.32976
$293$	−13.2386	−0.773408	−0.386704	−	0.922204i	$-0.626387\pi$
$293$	−13.2386	−0.773408	−0.386704	+	0.922204i	$0.626387\pi$
$294$	5.03606	0.293709
$295$	−3.66923	−0.213631
$296$	61.6312	3.58224
$297$	−9.48497	−0.550374
$298$	−51.4043	−2.97777
$299$	−4.35649	−0.251942
$300$	−4.52820	−0.261436
$301$	43.8640	2.52828
$302$	2.49383	0.143504
$303$	3.43903	0.197567
$304$	−27.1336	−1.55622
$305$	−5.83995	−0.334394
$306$	−9.85461	−0.563350
$307$	−12.3148	−0.702843	−0.351421	−	0.936217i	$-0.614302\pi$
$307$	−12.3148	−0.702843	−0.351421	+	0.936217i	$0.614302\pi$
$308$	95.0008	5.41317
$309$	−1.84083	−0.104721
$310$	11.6088	0.659337
$311$	17.8033	1.00953	0.504765	−	0.863257i	$-0.331579\pi$
$311$	17.8033	1.00953	0.504765	+	0.863257i	$0.331579\pi$
$312$	−1.06311	−0.0601868
$313$	4.60176	0.260107	0.130054	−	0.991507i	$-0.458485\pi$
$313$	4.60176	0.260107	0.130054	+	0.991507i	$0.458485\pi$
$314$	−8.15342	−0.460124
$315$	−33.3446	−1.87875
$316$	42.3945	2.38488
$317$	−26.0244	−1.46168	−0.730839	−	0.682550i	$-0.760871\pi$
$317$	−26.0244	−1.46168	−0.730839	+	0.682550i	$0.760871\pi$
$318$	−0.674220	−0.0378084
$319$	4.69734	0.263000
$320$	14.8997	0.832921
$321$	−1.95221	−0.108962
$322$	58.1629	3.24129
$323$	6.83050	0.380059
$324$	35.2197	1.95665
$325$	−2.82063	−0.156460
$326$	11.5198	0.638023
$327$	4.74795	0.262562
$328$	−43.7889	−2.41784
$329$	14.0247	0.773208
$330$	11.9527	0.657972
$331$	−34.8481	−1.91542	−0.957712	−	0.287727i	$-0.907100\pi$
$331$	−34.8481	−1.91542	−0.957712	+	0.287727i	$0.907100\pi$
$332$	56.3429	3.09222
$333$	32.5949	1.78619
$334$	−34.5465	−1.89030
$335$	−18.3127	−1.00053
$336$	5.51544	0.300892
$337$	−19.4476	−1.05938	−0.529688	−	0.848193i	$-0.677691\pi$
$337$	−19.4476	−1.05938	−0.529688	+	0.848193i	$0.677691\pi$
$338$	31.1608	1.69492
$339$	0.193572	0.0105134
$340$	17.0601	0.925214
$341$	−9.20034	−0.498227
$342$	−36.9287	−1.99688
$343$	−1.78578	−0.0964231
$344$	63.8178	3.44083
$345$	4.96453	0.267281
$346$	17.4842	0.939957
$347$	−1.99030	−0.106845	−0.0534224	−	0.998572i	$-0.517013\pi$
$347$	−1.99030	−0.106845	−0.0534224	+	0.998572i	$0.517013\pi$
$348$	0.905196	0.0485236
$349$	−28.4979	−1.52546	−0.762728	−	0.646719i	$-0.776141\pi$
$349$	−28.4979	−1.52546	−0.762728	+	0.646719i	$0.776141\pi$
$350$	37.6578	2.01289
$351$	−1.13854	−0.0607706
$352$	13.6513	0.727616
$353$	−12.3755	−0.658681	−0.329340	−	0.944211i	$-0.606826\pi$
$353$	−12.3755	−0.658681	−0.329340	+	0.944211i	$0.606826\pi$
$354$	0.826012	0.0439021
$355$	39.7059	2.10737
$356$	30.6939	1.62677
$357$	−1.38843	−0.0734837
$358$	−46.7061	−2.46849
$359$	18.6661	0.985160	0.492580	−	0.870267i	$-0.336054\pi$
$359$	18.6661	0.985160	0.492580	+	0.870267i	$0.336054\pi$
$360$	−48.5131	−2.55686
$361$	6.59633	0.347175
$362$	−59.3991	−3.12195
$363$	−6.49893	−0.341106
$364$	11.4035	0.597706
$365$	−16.1297	−0.844267
$366$	1.31468	0.0687195
$367$	20.6907	1.08004	0.540022	−	0.841651i	$-0.318416\pi$
$367$	20.6907	1.08004	0.540022	+	0.841651i	$0.318416\pi$
$368$	32.8830	1.71415
$369$	−23.1587	−1.20559
$370$	−83.1760	−4.32411
$371$	3.80387	0.197487
$372$	−1.77294	−0.0919229
$373$	31.1248	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$373$	31.1248	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$374$	−19.9298	−1.03055
$375$	−0.834204	−0.0430781
$376$	20.4046	1.05229
$377$	0.563849	0.0290397
$378$	15.2004	0.781826
$379$	25.2642	1.29774	0.648868	−	0.760901i	$-0.275243\pi$
$379$	25.2642	1.29774	0.648868	+	0.760901i	$0.275243\pi$
$380$	63.9303	3.27956
$381$	−1.55596	−0.0797143
$382$	5.39512	0.276039
$383$	33.1576	1.69427	0.847136	−	0.531376i	$-0.178325\pi$
$383$	33.1576	1.69427	0.847136	+	0.531376i	$0.178325\pi$
$384$	−4.60121	−0.234805
$385$	−67.4355	−3.43683
$386$	23.3712	1.18956
$387$	33.7514	1.71568
$388$	−54.2024	−2.75171
$389$	−2.79210	−0.141565	−0.0707827	−	0.997492i	$-0.522550\pi$
$389$	−2.79210	−0.141565	−0.0707827	+	0.997492i	$0.522550\pi$
$390$	1.43475	0.0726513
$391$	−8.27783	−0.418628
$392$	−41.3380	−2.08788
$393$	−1.33983	−0.0675854
$394$	41.2069	2.07597
$395$	−30.0934	−1.51416
$396$	73.0988	3.67335
$397$	−25.0948	−1.25947	−0.629735	−	0.776810i	$-0.716837\pi$
$397$	−25.0948	−1.25947	−0.629735	+	0.776810i	$0.716837\pi$
$398$	2.32426	0.116505
$399$	−5.20296	−0.260474
$400$	21.2903	1.06451
$401$	18.6521	0.931442	0.465721	−	0.884932i	$-0.345795\pi$
$401$	18.6521	0.931442	0.465721	+	0.884932i	$0.345795\pi$
$402$	4.12254	0.205614
$403$	−1.10437	−0.0550127
$404$	−53.6696	−2.67016
$405$	−25.0004	−1.24228
$406$	−7.52787	−0.373602
$407$	65.9195	3.26751
$408$	−2.02003	−0.100007
$409$	16.0222	0.792248	0.396124	−	0.918197i	$-0.370355\pi$
$409$	16.0222	0.792248	0.396124	+	0.918197i	$0.370355\pi$
$410$	59.0964	2.91856
$411$	−5.70311	−0.281314
$412$	28.7281	1.41533
$413$	−4.66027	−0.229317
$414$	44.7537	2.19952
$415$	−39.9945	−1.96325
$416$	1.63864	0.0803411
$417$	3.42113	0.167533
$418$	−74.6841	−3.65292
$419$	32.2329	1.57468	0.787340	−	0.616520i	$-0.211458\pi$
$419$	32.2329	1.57468	0.787340	+	0.616520i	$0.211458\pi$
$420$	−12.9951	−0.634096
$421$	−3.91209	−0.190663	−0.0953317	−	0.995446i	$-0.530391\pi$
$421$	−3.91209	−0.190663	−0.0953317	+	0.995446i	$0.530391\pi$
$422$	−30.8003	−1.49933
$423$	10.7914	0.524695
$424$	5.53426	0.268767
$425$	−5.35952	−0.259975
$426$	−8.93855	−0.433074
$427$	−7.41729	−0.358948
$428$	30.4663	1.47265
$429$	−1.13708	−0.0548988
$430$	−86.1269	−4.15341
$431$	18.8524	0.908090	0.454045	−	0.890979i	$-0.349981\pi$
$431$	18.8524	0.908090	0.454045	+	0.890979i	$0.349981\pi$
$432$	8.59374	0.413467
$433$	−27.0571	−1.30028	−0.650140	−	0.759815i	$-0.725290\pi$
$433$	−27.0571	−1.30028	−0.650140	+	0.759815i	$0.725290\pi$
$434$	14.7443	0.707749
$435$	−0.642546	−0.0308077
$436$	−74.0967	−3.54859
$437$	−31.0200	−1.48389
$438$	3.63110	0.173501
$439$	18.9505	0.904458	0.452229	−	0.891902i	$-0.350629\pi$
$439$	18.9505	0.904458	0.452229	+	0.891902i	$0.350629\pi$
$440$	−98.1120	−4.67731
$441$	−21.8624	−1.04107
$442$	−2.39229	−0.113790
$443$	−34.4655	−1.63750	−0.818752	−	0.574148i	$-0.805333\pi$
$443$	−34.4655	−1.63750	−0.818752	+	0.574148i	$0.805333\pi$
$444$	12.7030	0.602856
$445$	−21.7878	−1.03284
$446$	65.9525	3.12294
$447$	−5.57273	−0.263581
$448$	18.9241	0.894079
$449$	5.47937	0.258588	0.129294	−	0.991606i	$-0.458729\pi$
$449$	5.47937	0.258588	0.129294	+	0.991606i	$0.458729\pi$
$450$	28.9759	1.36594
$451$	−46.8357	−2.20541
$452$	−3.02089	−0.142091
$453$	0.270355	0.0127024
$454$	68.7003	3.22427
$455$	−8.09468	−0.379485
$456$	−7.56979	−0.354488
$457$	3.31085	0.154875	0.0774374	−	0.996997i	$-0.475326\pi$
$457$	3.31085	0.154875	0.0774374	+	0.996997i	$0.475326\pi$
$458$	−43.6142	−2.03796
$459$	−2.16335	−0.100977
$460$	−77.4767	−3.61237
$461$	3.79258	0.176638	0.0883189	−	0.996092i	$-0.471851\pi$
$461$	3.79258	0.176638	0.0883189	+	0.996092i	$0.471851\pi$
$462$	15.1810	0.706285
$463$	−20.1484	−0.936376	−0.468188	−	0.883629i	$-0.655093\pi$
$463$	−20.1484	−0.936376	−0.468188	+	0.883629i	$0.655093\pi$
$464$	−4.25596	−0.197578
$465$	1.25851	0.0583620
$466$	−39.0123	−1.80721
$467$	27.3475	1.26549	0.632746	−	0.774359i	$-0.281928\pi$
$467$	27.3475	1.26549	0.632746	+	0.774359i	$0.281928\pi$
$468$	8.77447	0.405600
$469$	−23.2589	−1.07400
$470$	−27.5375	−1.27021
$471$	−0.883910	−0.0407284
$472$	−6.78023	−0.312085
$473$	68.2582	3.13852
$474$	6.77459	0.311167
$475$	−20.0840	−0.921518
$476$	21.6680	0.993149
$477$	2.92691	0.134014
$478$	−7.68924	−0.351698
$479$	30.7768	1.40623	0.703114	−	0.711078i	$-0.251793\pi$
$479$	30.7768	1.40623	0.703114	+	0.711078i	$0.251793\pi$
$480$	−1.86735	−0.0852325
$481$	7.91271	0.360788
$482$	34.4888	1.57092
$483$	6.30542	0.286907
$484$	101.423	4.61012
$485$	38.4751	1.74706
$486$	17.6162	0.799087
$487$	−3.29348	−0.149242	−0.0746209	−	0.997212i	$-0.523775\pi$
$487$	−3.29348	−0.149242	−0.0746209	+	0.997212i	$0.523775\pi$
$488$	−10.7914	−0.488505
$489$	1.24886	0.0564754
$490$	55.7887	2.52028
$491$	−7.82130	−0.352970	−0.176485	−	0.984303i	$-0.556473\pi$
$491$	−7.82130	−0.352970	−0.176485	+	0.984303i	$0.556473\pi$
$492$	−9.02543	−0.406898
$493$	1.07138	0.0482524
$494$	−8.96477	−0.403344
$495$	−51.8886	−2.33222
$496$	8.33586	0.374291
$497$	50.4303	2.26211
$498$	9.00353	0.403458
$499$	26.3426	1.17926	0.589629	−	0.807674i	$-0.299274\pi$
$499$	26.3426	1.17926	0.589629	+	0.807674i	$0.299274\pi$
$500$	13.0186	0.582211
$501$	−3.74518	−0.167322
$502$	31.3931	1.40114
$503$	39.4518	1.75907	0.879534	−	0.475836i	$-0.157854\pi$
$503$	39.4518	1.75907	0.879534	+	0.475836i	$0.157854\pi$
$504$	−61.6162	−2.74460
$505$	38.0969	1.69529
$506$	90.5091	4.02362
$507$	3.37813	0.150028
$508$	24.2824	1.07736
$509$	−13.5318	−0.599788	−0.299894	−	0.953973i	$-0.596951\pi$
$509$	−13.5318	−0.599788	−0.299894	+	0.953973i	$0.596951\pi$
$510$	2.72619	0.120718
$511$	−20.4863	−0.906258
$512$	46.9934	2.07684
$513$	−8.10685	−0.357926
$514$	22.7211	1.00219
$515$	−20.3924	−0.898596
$516$	13.1536	0.579057
$517$	21.8243	0.959833
$518$	−105.641	−4.64162
$519$	1.89546	0.0832014
$520$	−11.7770	−0.516454
$521$	30.1322	1.32012	0.660058	−	0.751215i	$-0.270532\pi$
$521$	30.1322	1.32012	0.660058	+	0.751215i	$0.270532\pi$
$522$	−5.79235	−0.253524
$523$	20.9590	0.916472	0.458236	−	0.888831i	$-0.348482\pi$
$523$	20.9590	0.916472	0.458236	+	0.888831i	$0.348482\pi$
$524$	20.9094	0.913433
$525$	4.08247	0.178174
$526$	43.4146	1.89297
$527$	−2.09843	−0.0914092
$528$	8.58275	0.373516
$529$	14.5929	0.634473
$530$	−7.46890	−0.324428
$531$	−3.58586	−0.155613
$532$	81.1976	3.52036
$533$	−5.62196	−0.243514
$534$	4.90485	0.212254
$535$	−21.6263	−0.934985
$536$	−33.8394	−1.46164
$537$	−5.06340	−0.218502
$538$	30.0913	1.29733
$539$	−44.2142	−1.90444
$540$	−20.2480	−0.871334
$541$	11.7712	0.506082	0.253041	−	0.967456i	$-0.418569\pi$
$541$	11.7712	0.506082	0.253041	+	0.967456i	$0.418569\pi$
$542$	−42.8245	−1.83947
$543$	−6.43944	−0.276343
$544$	3.11361	0.133495
$545$	52.5969	2.25301
$546$	1.82227	0.0779858
$547$	−38.8657	−1.66178	−0.830888	−	0.556440i	$-0.812167\pi$
$547$	−38.8657	−1.66178	−0.830888	+	0.556440i	$0.812167\pi$
$548$	89.0031	3.80202
$549$	−5.70726	−0.243580
$550$	58.6005	2.49873
$551$	4.01484	0.171038
$552$	9.17377	0.390461
$553$	−38.2215	−1.62534
$554$	−66.4196	−2.82190
$555$	−9.01709	−0.382754
$556$	−53.3903	−2.26425
$557$	−9.30813	−0.394398	−0.197199	−	0.980363i	$-0.563185\pi$
$557$	−9.30813	−0.394398	−0.197199	+	0.980363i	$0.563185\pi$
$558$	11.3451	0.480275
$559$	8.19344	0.346545
$560$	61.0991	2.58191
$561$	−2.16059	−0.0912200
$562$	−3.01587	−0.127217
$563$	−46.8765	−1.97561	−0.987804	−	0.155705i	$-0.950235\pi$
$563$	−46.8765	−1.97561	−0.987804	+	0.155705i	$0.950235\pi$
$564$	4.20564	0.177089
$565$	2.14436	0.0902137
$566$	22.8495	0.960435
$567$	−31.7529	−1.33350
$568$	73.3711	3.07858
$569$	4.50586	0.188895	0.0944477	−	0.995530i	$-0.469891\pi$
$569$	4.50586	0.188895	0.0944477	+	0.995530i	$0.469891\pi$
$570$	10.2160	0.427901
$571$	19.3350	0.809144	0.404572	−	0.914506i	$-0.367421\pi$
$571$	19.3350	0.809144	0.404572	+	0.914506i	$0.367421\pi$
$572$	17.7454	0.741971
$573$	0.584884	0.0244339
$574$	75.0580	3.13286
$575$	24.3397	1.01503
$576$	14.5612	0.606718
$577$	11.9494	0.497461	0.248731	−	0.968573i	$-0.419987\pi$
$577$	11.9494	0.497461	0.248731	+	0.968573i	$0.419987\pi$
$578$	37.8495	1.57433
$579$	2.53366	0.105295
$580$	10.0276	0.416374
$581$	−50.7969	−2.10741
$582$	−8.66147	−0.359030
$583$	5.91933	0.245154
$584$	−29.8055	−1.23336
$585$	−6.22849	−0.257516
$586$	33.0148	1.36383
$587$	−44.6268	−1.84195	−0.920973	−	0.389626i	$-0.872604\pi$
$587$	−44.6268	−1.84195	−0.920973	+	0.389626i	$0.872604\pi$
$588$	−8.52026	−0.351370
$589$	−7.86358	−0.324013
$590$	9.15042	0.376717
$591$	4.46723	0.183757
$592$	−59.7255	−2.45470
$593$	33.5780	1.37888	0.689442	−	0.724341i	$-0.257856\pi$
$593$	33.5780	1.37888	0.689442	+	0.724341i	$0.257856\pi$
$594$	23.6539	0.970531
$595$	−15.3808	−0.630552
$596$	86.9684	3.56236
$597$	0.251973	0.0103126
$598$	10.8643	0.444276
$599$	−7.11680	−0.290784	−0.145392	−	0.989374i	$-0.546444\pi$
$599$	−7.11680	−0.290784	−0.145392	+	0.989374i	$0.546444\pi$
$600$	5.93960	0.242483
$601$	−8.78356	−0.358289	−0.179144	−	0.983823i	$-0.557333\pi$
$601$	−8.78356	−0.358289	−0.179144	+	0.983823i	$0.557333\pi$
$602$	−109.389	−4.45838
$603$	−17.8967	−0.728809
$604$	−4.21918	−0.171676
$605$	−71.9941	−2.92698
$606$	−8.57634	−0.348390
$607$	19.7804	0.802862	0.401431	−	0.915889i	$-0.368513\pi$
$607$	19.7804	0.802862	0.401431	+	0.915889i	$0.368513\pi$
$608$	11.6678	0.473193
$609$	−0.816094	−0.0330698
$610$	14.5638	0.589672
$611$	2.61970	0.105982
$612$	16.6725	0.673946
$613$	−37.0598	−1.49683	−0.748415	−	0.663231i	$-0.769185\pi$
$613$	−37.0598	−1.49683	−0.748415	+	0.663231i	$0.769185\pi$
$614$	30.7110	1.23940
$615$	6.40663	0.258340
$616$	−124.612	−5.02074
$617$	0.629611	0.0253472	0.0126736	−	0.999920i	$-0.495966\pi$
$617$	0.629611	0.0253472	0.0126736	+	0.999920i	$0.495966\pi$
$618$	4.59071	0.184666
$619$	−13.4695	−0.541385	−0.270692	−	0.962666i	$-0.587253\pi$
$619$	−13.4695	−0.541385	−0.270692	+	0.962666i	$0.587253\pi$
$620$	−19.6404	−0.788776
$621$	9.82463	0.394249
$622$	−44.3983	−1.78021
$623$	−27.6726	−1.10868
$624$	1.03024	0.0412425
$625$	−29.0899	−1.16359
$626$	−11.4760	−0.458674
$627$	−8.09649	−0.323343
$628$	13.7944	0.550455
$629$	15.0350	0.599487
$630$	83.1557	3.31300
$631$	−17.0508	−0.678781	−0.339390	−	0.940646i	$-0.610221\pi$
$631$	−17.0508	−0.678781	−0.339390	+	0.940646i	$0.610221\pi$
$632$	−55.6085	−2.21199
$633$	−3.33905	−0.132715
$634$	64.9005	2.57753
$635$	−17.2367	−0.684017
$636$	1.14068	0.0452309
$637$	−5.30729	−0.210283
$638$	−11.7144	−0.463776
$639$	38.8038	1.53505
$640$	−50.9715	−2.01482
$641$	−25.8251	−1.02003	−0.510015	−	0.860165i	$-0.670360\pi$
$641$	−25.8251	−1.02003	−0.510015	+	0.860165i	$0.670360\pi$
$642$	4.86848	0.192144
$643$	−9.98445	−0.393748	−0.196874	−	0.980429i	$-0.563079\pi$
$643$	−9.98445	−0.393748	−0.196874	+	0.980429i	$0.563079\pi$
$644$	−98.4028	−3.87761
$645$	−9.33700	−0.367644
$646$	−17.0341	−0.670197
$647$	−28.3035	−1.11273	−0.556363	−	0.830939i	$-0.687804\pi$
$647$	−28.3035	−1.11273	−0.556363	+	0.830939i	$0.687804\pi$
$648$	−46.1973	−1.81480
$649$	−7.25199	−0.284666
$650$	7.03416	0.275903
$651$	1.59843	0.0626473
$652$	−19.4898	−0.763279
$653$	6.16685	0.241327	0.120664	−	0.992693i	$-0.461498\pi$
$653$	6.16685	0.241327	0.120664	+	0.992693i	$0.461498\pi$
$654$	−11.8406	−0.463003
$655$	−14.8424	−0.579940
$656$	42.4349	1.65680
$657$	−15.7632	−0.614982
$658$	−34.9753	−1.36348
$659$	7.71567	0.300560	0.150280	−	0.988643i	$-0.451983\pi$
$659$	7.71567	0.300560	0.150280	+	0.988643i	$0.451983\pi$
$660$	−20.2221	−0.787144
$661$	6.20728	0.241435	0.120718	−	0.992687i	$-0.461480\pi$
$661$	6.20728	0.241435	0.120718	+	0.992687i	$0.461480\pi$
$662$	86.9052	3.37767
$663$	−0.259348	−0.0100722
$664$	−73.9044	−2.86805
$665$	−57.6375	−2.23509
$666$	−81.2862	−3.14978
$667$	−4.86555	−0.188395
$668$	58.4475	2.26140
$669$	7.14989	0.276431
$670$	45.6688	1.76434
$671$	−11.5423	−0.445585
$672$	−2.37171	−0.0914909
$673$	1.45038	0.0559082	0.0279541	−	0.999609i	$-0.491101\pi$
$673$	1.45038	0.0559082	0.0279541	+	0.999609i	$0.491101\pi$
$674$	48.4989	1.86811
$675$	6.36100	0.244835
$676$	−52.7193	−2.02767
$677$	7.96736	0.306210	0.153105	−	0.988210i	$-0.451073\pi$
$677$	7.96736	0.306210	0.153105	+	0.988210i	$0.451073\pi$
$678$	−0.482735	−0.0185393
$679$	48.8671	1.87535
$680$	−22.3776	−0.858141
$681$	7.44779	0.285400
$682$	22.9441	0.878574
$683$	−12.7448	−0.487667	−0.243833	−	0.969817i	$-0.578405\pi$
$683$	−12.7448	−0.487667	−0.243833	+	0.969817i	$0.578405\pi$
$684$	62.4779	2.38890
$685$	−63.1781	−2.41391
$686$	4.45343	0.170033
$687$	−4.72821	−0.180392
$688$	−61.8445	−2.35780
$689$	0.710532	0.0270691
$690$	−12.3807	−0.471325
$691$	10.4885	0.399002	0.199501	−	0.979898i	$-0.436068\pi$
$691$	10.4885	0.399002	0.199501	+	0.979898i	$0.436068\pi$
$692$	−29.5806	−1.12449
$693$	−65.9034	−2.50346
$694$	4.96346	0.188411
$695$	37.8987	1.43758
$696$	−1.18734	−0.0450059
$697$	−10.6824	−0.404624
$698$	71.0689	2.69000
$699$	−4.22932	−0.159967
$700$	−63.7113	−2.40806
$701$	−8.51378	−0.321561	−0.160781	−	0.986990i	$-0.551401\pi$
$701$	−8.51378	−0.321561	−0.160781	+	0.986990i	$0.551401\pi$
$702$	2.83932	0.107163
$703$	56.3417	2.12497
$704$	29.4484	1.10988
$705$	−2.98534	−0.112434
$706$	30.8624	1.16152
$707$	48.3867	1.81977
$708$	−1.39749	−0.0525208
$709$	12.5248	0.470378	0.235189	−	0.971950i	$-0.424429\pi$
$709$	12.5248	0.470378	0.235189	+	0.971950i	$0.424429\pi$
$710$	−99.0197	−3.71614
$711$	−29.4097	−1.10295
$712$	−40.2609	−1.50884
$713$	9.52981	0.356894
$714$	3.46251	0.129581
$715$	−12.5964	−0.471078
$716$	79.0197	2.95310
$717$	−0.833589	−0.0311310
$718$	−46.5501	−1.73723
$719$	15.4011	0.574366	0.287183	−	0.957876i	$-0.407281\pi$
$719$	15.4011	0.574366	0.287183	+	0.957876i	$0.407281\pi$
$720$	47.0130	1.75207
$721$	−25.9003	−0.964577
$722$	−16.4501	−0.612210
$723$	3.73892	0.139052
$724$	100.494	3.73484
$725$	−3.15022	−0.116996
$726$	16.2072	0.601507
$727$	28.9939	1.07532	0.537662	−	0.843161i	$-0.319308\pi$
$727$	28.9939	1.07532	0.537662	+	0.843161i	$0.319308\pi$
$728$	−14.9579	−0.554375
$729$	−23.1328	−0.856769
$730$	40.2247	1.48878
$731$	15.5685	0.575821
$732$	−2.22424	−0.0822104
$733$	12.5287	0.462758	0.231379	−	0.972864i	$-0.425676\pi$
$733$	12.5287	0.462758	0.231379	+	0.972864i	$0.425676\pi$
$734$	−51.5990	−1.90455
$735$	6.04804	0.223085
$736$	−14.1401	−0.521213
$737$	−36.1940	−1.33322
$738$	57.7537	2.12594
$739$	34.7636	1.27880	0.639400	−	0.768874i	$-0.279183\pi$
$739$	34.7636	1.27880	0.639400	+	0.768874i	$0.279183\pi$
$740$	140.721	5.17301
$741$	−0.971869	−0.0357025
$742$	−9.48621	−0.348250
$743$	−17.8328	−0.654223	−0.327112	−	0.944986i	$-0.606075\pi$
$743$	−17.8328	−0.654223	−0.327112	+	0.944986i	$0.606075\pi$
$744$	2.32555	0.0852589
$745$	−61.7338	−2.26175
$746$	−77.6199	−2.84187
$747$	−39.0859	−1.43008
$748$	33.7182	1.23286
$749$	−27.4674	−1.00364
$750$	2.08036	0.0759641
$751$	−32.8177	−1.19753	−0.598767	−	0.800923i	$-0.704343\pi$
$751$	−32.8177	−1.19753	−0.598767	+	0.800923i	$0.704343\pi$
$752$	−19.7737	−0.721071
$753$	3.40332	0.124024
$754$	−1.40614	−0.0512087
$755$	2.99495	0.108997
$756$	−25.7169	−0.935313
$757$	19.2850	0.700925	0.350463	−	0.936577i	$-0.386024\pi$
$757$	19.2850	0.700925	0.350463	+	0.936577i	$0.386024\pi$
$758$	−63.0047	−2.28843
$759$	9.81207	0.356156
$760$	−83.8568	−3.04181
$761$	−9.65993	−0.350172	−0.175086	−	0.984553i	$-0.556020\pi$
$761$	−9.65993	−0.350172	−0.175086	+	0.984553i	$0.556020\pi$
$762$	3.88030	0.140569
$763$	66.8031	2.41844
$764$	−9.12774	−0.330230
$765$	−11.8348	−0.427890
$766$	−82.6893	−2.98769
$767$	−0.870499	−0.0314319
$768$	8.78463	0.316988
$769$	5.82885	0.210194	0.105097	−	0.994462i	$-0.466485\pi$
$769$	5.82885	0.210194	0.105097	+	0.994462i	$0.466485\pi$
$770$	168.173	6.06052
$771$	2.46319	0.0887097
$772$	−39.5405	−1.42309
$773$	8.60045	0.309337	0.154668	−	0.987966i	$-0.450569\pi$
$773$	8.60045	0.309337	0.154668	+	0.987966i	$0.450569\pi$
$774$	−84.1701	−3.02543
$775$	6.17012	0.221637
$776$	71.0967	2.55222
$777$	−11.4526	−0.410858
$778$	6.96303	0.249637
$779$	−40.0307	−1.43425
$780$	−2.42738	−0.0869140
$781$	78.4761	2.80810
$782$	20.6435	0.738210
$783$	−1.27158	−0.0454424
$784$	40.0598	1.43071
$785$	−9.79181	−0.349485
$786$	3.34130	0.119180
$787$	21.7986	0.777037	0.388518	−	0.921441i	$-0.372987\pi$
$787$	21.7986	0.777037	0.388518	+	0.921441i	$0.372987\pi$
$788$	−69.7159	−2.48352
$789$	4.70657	0.167558
$790$	75.0478	2.67008
$791$	2.72354	0.0968378
$792$	−95.8829	−3.40705
$793$	−1.38549	−0.0492001
$794$	62.5821	2.22095
$795$	−0.809702	−0.0287172
$796$	−3.93230	−0.139377
$797$	−45.0899	−1.59717	−0.798584	−	0.601883i	$-0.794417\pi$
$797$	−45.0899	−1.59717	−0.798584	+	0.601883i	$0.794417\pi$
$798$	12.9753	0.459320
$799$	4.97774	0.176100
$800$	−9.15510	−0.323682
$801$	−21.2928	−0.752344
$802$	−46.5152	−1.64251
$803$	−31.8793	−1.12500
$804$	−6.97472	−0.245980
$805$	69.8504	2.46190
$806$	2.75411	0.0970095
$807$	3.26219	0.114835
$808$	70.3979	2.47659
$809$	10.5838	0.372107	0.186054	−	0.982540i	$-0.440430\pi$
$809$	10.5838	0.372107	0.186054	+	0.982540i	$0.440430\pi$
$810$	62.3467	2.19064
$811$	49.0823	1.72351	0.861756	−	0.507323i	$-0.169365\pi$
$811$	49.0823	1.72351	0.861756	+	0.507323i	$0.169365\pi$
$812$	12.7360	0.446946
$813$	−4.64260	−0.162823
$814$	−164.392	−5.76193
$815$	13.8347	0.484607
$816$	1.95757	0.0685287
$817$	58.3406	2.04108
$818$	−39.9567	−1.39705
$819$	−7.91077	−0.276425
$820$	−99.9821	−3.49153
$821$	−45.1254	−1.57489	−0.787443	−	0.616387i	$-0.788596\pi$
$821$	−45.1254	−1.57489	−0.787443	+	0.616387i	$0.788596\pi$
$822$	14.2226	0.496070
$823$	−24.2784	−0.846291	−0.423146	−	0.906062i	$-0.639074\pi$
$823$	−24.2784	−0.846291	−0.423146	+	0.906062i	$0.639074\pi$
$824$	−37.6823	−1.31273
$825$	6.35287	0.221178
$826$	11.6219	0.404378
$827$	−40.3463	−1.40298	−0.701489	−	0.712680i	$-0.747481\pi$
$827$	−40.3463	−1.40298	−0.701489	+	0.712680i	$0.747481\pi$
$828$	−75.7164	−2.63133
$829$	55.2221	1.91794	0.958971	−	0.283504i	$-0.0914969\pi$
$829$	55.2221	1.91794	0.958971	+	0.283504i	$0.0914969\pi$
$830$	99.7395	3.46201
$831$	−7.20054	−0.249784
$832$	3.53486	0.122549
$833$	−10.0845	−0.349406
$834$	−8.53171	−0.295429
$835$	−41.4885	−1.43577
$836$	126.354	4.37005
$837$	2.49055	0.0860859
$838$	−80.3833	−2.77679
$839$	−18.1392	−0.626233	−0.313117	−	0.949715i	$-0.601373\pi$
$839$	−18.1392	−0.626233	−0.313117	+	0.949715i	$0.601373\pi$
$840$	17.0455	0.588127
$841$	−28.3703	−0.978285
$842$	9.75607	0.336217
$843$	−0.326950	−0.0112608
$844$	52.1094	1.79368
$845$	37.4224	1.28737
$846$	−26.9119	−0.925249
$847$	−91.4394	−3.14189
$848$	−5.36314	−0.184171
$849$	2.47711	0.0850140
$850$	13.3657	0.458440
$851$	−68.2801	−2.34061
$852$	15.1227	0.518094
$853$	−1.67034	−0.0571914	−0.0285957	−	0.999591i	$-0.509104\pi$
$853$	−1.67034	−0.0571914	−0.0285957	+	0.999591i	$0.509104\pi$
$854$	18.4974	0.632970
$855$	−44.3494	−1.51672
$856$	−39.9624	−1.36589
$857$	9.03369	0.308585	0.154292	−	0.988025i	$-0.450690\pi$
$857$	9.03369	0.308585	0.154292	+	0.988025i	$0.450690\pi$
$858$	2.83569	0.0968087
$859$	−36.1729	−1.23420	−0.617101	−	0.786884i	$-0.711693\pi$
$859$	−36.1729	−1.23420	−0.617101	+	0.786884i	$0.711693\pi$
$860$	145.714	4.96880
$861$	8.13703	0.277309
$862$	−47.0147	−1.60133
$863$	−40.4673	−1.37752	−0.688761	−	0.724989i	$-0.741845\pi$
$863$	−40.4673	−1.37752	−0.688761	+	0.724989i	$0.741845\pi$
$864$	−3.69542	−0.125721
$865$	20.9976	0.713939
$866$	67.4757	2.29292
$867$	4.10325	0.139354
$868$	−24.9451	−0.846693
$869$	−59.4777	−2.01764
$870$	1.60240	0.0543264
$871$	−4.34457	−0.147210
$872$	97.1919	3.29133
$873$	37.6010	1.27260
$874$	77.3585	2.61669
$875$	−11.7372	−0.396789
$876$	−6.14327	−0.207562
$877$	−38.4110	−1.29705	−0.648524	−	0.761194i	$-0.724614\pi$
$877$	−38.4110	−1.29705	−0.648524	+	0.761194i	$0.724614\pi$
$878$	−47.2593	−1.59492
$879$	3.57913	0.120721
$880$	95.0783	3.20509
$881$	−7.06338	−0.237971	−0.118986	−	0.992896i	$-0.537964\pi$
$881$	−7.06338	−0.237971	−0.118986	+	0.992896i	$0.537964\pi$
$882$	54.5212	1.83582
$883$	7.98840	0.268831	0.134416	−	0.990925i	$-0.457084\pi$
$883$	7.98840	0.268831	0.134416	+	0.990925i	$0.457084\pi$
$884$	4.04740	0.136129
$885$	0.991995	0.0333456
$886$	85.9509	2.88758
$887$	29.8603	1.00261	0.501305	−	0.865270i	$-0.332853\pi$
$887$	29.8603	1.00261	0.501305	+	0.865270i	$0.332853\pi$
$888$	−16.6623	−0.559152
$889$	−21.8922	−0.734242
$890$	54.3351	1.82132
$891$	−49.4117	−1.65535
$892$	−111.582	−3.73603
$893$	18.6534	0.624211
$894$	13.8974	0.464800
$895$	−56.0915	−1.87493
$896$	−64.7386	−2.16277
$897$	1.17780	0.0393256
$898$	−13.6646	−0.455994
$899$	−1.23342	−0.0411368
$900$	−49.0229	−1.63410
$901$	1.35009	0.0449781
$902$	116.800	3.88902
$903$	−11.8589	−0.394639
$904$	3.96248	0.131790
$905$	−71.3351	−2.37126
$906$	−0.674220	−0.0223995
$907$	30.3325	1.00717	0.503587	−	0.863944i	$-0.332013\pi$
$907$	30.3325	1.00717	0.503587	+	0.863944i	$0.332013\pi$
$908$	−116.231	−3.85725
$909$	37.2314	1.23489
$910$	20.1868	0.669184
$911$	−20.5698	−0.681507	−0.340753	−	0.940153i	$-0.610682\pi$
$911$	−20.5698	−0.681507	−0.340753	+	0.940153i	$0.610682\pi$
$912$	7.33572	0.242910
$913$	−79.0466	−2.61606
$914$	−8.25669	−0.273107
$915$	1.57886	0.0521956
$916$	73.7886	2.43804
$917$	−18.8513	−0.622523
$918$	5.39503	0.178062
$919$	−10.0515	−0.331569	−0.165784	−	0.986162i	$-0.553016\pi$
$919$	−10.0515	−0.331569	−0.165784	+	0.986162i	$0.553016\pi$
$920$	101.625	3.35049
$921$	3.32937	0.109707
$922$	−9.45804	−0.311484
$923$	9.41995	0.310062
$924$	−25.6840	−0.844941
$925$	−44.2082	−1.45356
$926$	50.2467	1.65121
$927$	−19.9291	−0.654557
$928$	1.83012	0.0600767
$929$	38.7601	1.27168	0.635839	−	0.771822i	$-0.280654\pi$
$929$	38.7601	1.27168	0.635839	+	0.771822i	$0.280654\pi$
$930$	−3.13851	−0.102916
$931$	−37.7901	−1.23852
$932$	66.0029	2.16200
$933$	−4.81321	−0.157577
$934$	−68.2000	−2.23157
$935$	−23.9346	−0.782745
$936$	−11.5094	−0.376196
$937$	28.0589	0.916645	0.458323	−	0.888786i	$-0.348450\pi$
$937$	28.0589	0.916645	0.458323	+	0.888786i	$0.348450\pi$
$938$	58.0038	1.89389
$939$	−1.24411	−0.0406001
$940$	46.5893	1.51958
$941$	−0.0441714	−0.00143995	−0.000719974	−	1.00000i	$-0.500229\pi$
$941$	−0.0441714	−0.00143995	−0.000719974		1.00000i	$0.500229\pi$
$942$	2.20432	0.0718207
$943$	48.5129	1.57980
$944$	6.57058	0.213854
$945$	18.2549	0.593832
$946$	−170.224	−5.53447
$947$	28.2800	0.918975	0.459488	−	0.888184i	$-0.348033\pi$
$947$	28.2800	0.918975	0.459488	+	0.888184i	$0.348033\pi$
$948$	−11.4616	−0.372255
$949$	−3.82666	−0.124219
$950$	50.0861	1.62501
$951$	7.03585	0.228153
$952$	−28.4217	−0.921151
$953$	−26.8106	−0.868481	−0.434240	−	0.900797i	$-0.642983\pi$
$953$	−26.8106	−0.868481	−0.434240	+	0.900797i	$0.642983\pi$
$954$	−7.29921	−0.236321
$955$	6.47925	0.209664
$956$	13.0090	0.420742
$957$	−1.26995	−0.0410517
$958$	−76.7520	−2.47975
$959$	−80.2422	−2.59116
$960$	−4.02823	−0.130010
$961$	−28.5842	−0.922071
$962$	−19.7329	−0.636215
$963$	−21.1349	−0.681064
$964$	−58.3498	−1.87932
$965$	28.0675	0.903525
$966$	−15.7246	−0.505932
$967$	−28.5787	−0.919028	−0.459514	−	0.888171i	$-0.651976\pi$
$967$	−28.5787	−0.919028	−0.459514	+	0.888171i	$0.651976\pi$
$968$	−133.035	−4.27591
$969$	−1.84666	−0.0593234
$970$	−95.9503	−3.08078
$971$	−6.40099	−0.205417	−0.102709	−	0.994711i	$-0.532751\pi$
$971$	−6.40099	−0.205417	−0.102709	+	0.994711i	$0.532751\pi$
$972$	−29.8039	−0.955962
$973$	48.1349	1.54313
$974$	8.21337	0.263173
$975$	0.762572	0.0244219
$976$	10.4577	0.334744
$977$	15.9966	0.511775	0.255887	−	0.966707i	$-0.417632\pi$
$977$	15.9966	0.511775	0.255887	+	0.966707i	$0.417632\pi$
$978$	−3.11444	−0.0995889
$979$	−43.0622	−1.37627
$980$	−94.3860	−3.01505
$981$	51.4020	1.64114
$982$	19.5050	0.622429
$983$	46.7269	1.49036	0.745178	−	0.666866i	$-0.232364\pi$
$983$	46.7269	1.49036	0.745178	+	0.666866i	$0.232364\pi$
$984$	11.8386	0.377400
$985$	49.4872	1.57679
$986$	−2.67183	−0.0850885
$987$	−3.79166	−0.120690
$988$	15.1670	0.482528
$989$	−70.7026	−2.24821
$990$	129.401	4.11264
$991$	−11.5653	−0.367383	−0.183691	−	0.982984i	$-0.558805\pi$
$991$	−11.5653	−0.367383	−0.183691	+	0.982984i	$0.558805\pi$
$992$	−3.58453	−0.113809
$993$	9.42138	0.298978
$994$	−125.764	−3.98901
$995$	2.79131	0.0884905
$996$	−15.2326	−0.482664
$997$	8.85376	0.280401	0.140201	−	0.990123i	$-0.455225\pi$
$997$	8.85376	0.280401	0.140201	+	0.990123i	$0.455225\pi$
$998$	−65.6940	−2.07951
$999$	−17.8445	−0.564575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.11	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.49383 q^{2} -0.270355 q^{3} +4.21918 q^{4} -2.99495 q^{5} +0.674220 q^{6} -3.80387 q^{7} -5.53426 q^{8} -2.92691 q^{9} +O(q^{10})\)	\(q-2.49383 q^{2} -0.270355 q^{3} +4.21918 q^{4} -2.99495 q^{5} +0.674220 q^{6} -3.80387 q^{7} -5.53426 q^{8} -2.92691 q^{9} +7.46890 q^{10} -5.91933 q^{11} -1.14068 q^{12} -0.710532 q^{13} +9.48621 q^{14} +0.809702 q^{15} +5.36314 q^{16} -1.35009 q^{17} +7.29921 q^{18} -5.05928 q^{19} -12.6363 q^{20} +1.02840 q^{21} +14.7618 q^{22} +6.13130 q^{23} +1.49622 q^{24} +3.96974 q^{25} +1.77195 q^{26} +1.60237 q^{27} -16.0492 q^{28} -0.793559 q^{29} -2.01926 q^{30} +1.55429 q^{31} -2.30622 q^{32} +1.60032 q^{33} +3.36690 q^{34} +11.3924 q^{35} -12.3492 q^{36} -11.1363 q^{37} +12.6170 q^{38} +0.192096 q^{39} +16.5748 q^{40} +7.91233 q^{41} -2.56465 q^{42} -11.5314 q^{43} -24.9747 q^{44} +8.76595 q^{45} -15.2904 q^{46} -3.68696 q^{47} -1.44995 q^{48} +7.46946 q^{49} -9.89985 q^{50} +0.365005 q^{51} -2.99786 q^{52} -1.00000 q^{53} -3.99604 q^{54} +17.7281 q^{55} +21.0516 q^{56} +1.36780 q^{57} +1.97900 q^{58} +1.22514 q^{59} +3.41628 q^{60} +1.94993 q^{61} -3.87613 q^{62} +11.1336 q^{63} -4.97495 q^{64} +2.12801 q^{65} -3.99093 q^{66} +6.11454 q^{67} -5.69629 q^{68} -1.65763 q^{69} -28.4108 q^{70} -13.2576 q^{71} +16.1983 q^{72} +5.38563 q^{73} +27.7720 q^{74} -1.07324 q^{75} -21.3460 q^{76} +22.5164 q^{77} -0.479055 q^{78} +10.0480 q^{79} -16.0623 q^{80} +8.34751 q^{81} -19.7320 q^{82} +13.3540 q^{83} +4.33900 q^{84} +4.04346 q^{85} +28.7574 q^{86} +0.214543 q^{87} +32.7591 q^{88} +7.27485 q^{89} -21.8608 q^{90} +2.70278 q^{91} +25.8691 q^{92} -0.420210 q^{93} +9.19464 q^{94} +15.1523 q^{95} +0.623500 q^{96} -12.8467 q^{97} -18.6276 q^{98} +17.3253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 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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