LMFDB - Embedded newform 8003.2.a.d.1.10

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:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.59548 q^{2} -2.23952 q^{3} +4.73650 q^{4} -0.915423 q^{5} +5.81261 q^{6} -1.92878 q^{7} -7.10252 q^{8} +2.01543 q^{9} +O(q^{10})$	\(q-2.59548 q^{2} -2.23952 q^{3} +4.73650 q^{4} -0.915423 q^{5} +5.81261 q^{6} -1.92878 q^{7} -7.10252 q^{8} +2.01543 q^{9} +2.37596 q^{10} -1.40497 q^{11} -10.6075 q^{12} -4.73029 q^{13} +5.00609 q^{14} +2.05010 q^{15} +8.96142 q^{16} +6.19564 q^{17} -5.23101 q^{18} -5.43193 q^{19} -4.33590 q^{20} +4.31952 q^{21} +3.64657 q^{22} -1.13085 q^{23} +15.9062 q^{24} -4.16200 q^{25} +12.2774 q^{26} +2.20495 q^{27} -9.13564 q^{28} -0.475004 q^{29} -5.32100 q^{30} +0.173094 q^{31} -9.05412 q^{32} +3.14646 q^{33} -16.0806 q^{34} +1.76564 q^{35} +9.54610 q^{36} +5.39098 q^{37} +14.0984 q^{38} +10.5936 q^{39} +6.50181 q^{40} +1.13606 q^{41} -11.2112 q^{42} +0.281797 q^{43} -6.65464 q^{44} -1.84497 q^{45} +2.93508 q^{46} -8.99914 q^{47} -20.0693 q^{48} -3.27983 q^{49} +10.8024 q^{50} -13.8752 q^{51} -22.4050 q^{52} +1.00000 q^{53} -5.72290 q^{54} +1.28614 q^{55} +13.6992 q^{56} +12.1649 q^{57} +1.23286 q^{58} -11.2777 q^{59} +9.71032 q^{60} -0.0211009 q^{61} -0.449262 q^{62} -3.88732 q^{63} +5.57692 q^{64} +4.33022 q^{65} -8.16655 q^{66} +10.0137 q^{67} +29.3456 q^{68} +2.53255 q^{69} -4.58269 q^{70} -12.2715 q^{71} -14.3147 q^{72} +10.5694 q^{73} -13.9922 q^{74} +9.32087 q^{75} -25.7283 q^{76} +2.70987 q^{77} -27.4954 q^{78} -13.2834 q^{79} -8.20349 q^{80} -10.9843 q^{81} -2.94861 q^{82} -10.1607 q^{83} +20.4594 q^{84} -5.67163 q^{85} -0.731398 q^{86} +1.06378 q^{87} +9.97883 q^{88} +0.0261827 q^{89} +4.78859 q^{90} +9.12368 q^{91} -5.35625 q^{92} -0.387647 q^{93} +23.3571 q^{94} +4.97251 q^{95} +20.2769 q^{96} +9.24864 q^{97} +8.51271 q^{98} -2.83163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.59548	−1.83528	−0.917640	−	0.397414i	$-0.869908\pi$
$2$	−2.59548	−1.83528	−0.917640	+	0.397414i	$0.869908\pi$
$3$	−2.23952	−1.29299	−0.646493	−	0.762920i	$-0.723765\pi$
$3$	−2.23952	−1.29299	−0.646493	+	0.762920i	$0.723765\pi$
$4$	4.73650	2.36825
$5$	−0.915423	−0.409389	−0.204695	−	0.978826i	$-0.565620\pi$
$5$	−0.915423	−0.409389	−0.204695	+	0.978826i	$0.565620\pi$
$6$	5.81261	2.37299
$7$	−1.92878	−0.729009	−0.364504	−	0.931202i	$-0.618762\pi$
$7$	−1.92878	−0.729009	−0.364504	+	0.931202i	$0.618762\pi$
$8$	−7.10252	−2.51112
$9$	2.01543	0.671811
$10$	2.37596	0.751344
$11$	−1.40497	−0.423615	−0.211807	−	0.977311i	$-0.567935\pi$
$11$	−1.40497	−0.423615	−0.211807	+	0.977311i	$0.567935\pi$
$12$	−10.6075	−3.06211
$13$	−4.73029	−1.31195	−0.655974	−	0.754784i	$-0.727742\pi$
$13$	−4.73029	−1.31195	−0.655974	+	0.754784i	$0.727742\pi$
$14$	5.00609	1.33793
$15$	2.05010	0.529335
$16$	8.96142	2.24036
$17$	6.19564	1.50266	0.751332	−	0.659925i	$-0.229412\pi$
$17$	6.19564	1.50266	0.751332	+	0.659925i	$0.229412\pi$
$18$	−5.23101	−1.23296
$19$	−5.43193	−1.24617	−0.623085	−	0.782154i	$-0.714121\pi$
$19$	−5.43193	−1.24617	−0.623085	+	0.782154i	$0.714121\pi$
$20$	−4.33590	−0.969536
$21$	4.31952	0.942597
$22$	3.64657	0.777451
$23$	−1.13085	−0.235798	−0.117899	−	0.993026i	$-0.537616\pi$
$23$	−1.13085	−0.235798	−0.117899	+	0.993026i	$0.537616\pi$
$24$	15.9062	3.24684
$25$	−4.16200	−0.832400
$26$	12.2774	2.40779
$27$	2.20495	0.424343
$28$	−9.13564	−1.72647
$29$	−0.475004	−0.0882060	−0.0441030	−	0.999027i	$-0.514043\pi$
$29$	−0.475004	−0.0882060	−0.0441030	+	0.999027i	$0.514043\pi$
$30$	−5.32100	−0.971477
$31$	0.173094	0.0310886	0.0155443	−	0.999879i	$-0.495052\pi$
$31$	0.173094	0.0310886	0.0155443	+	0.999879i	$0.495052\pi$
$32$	−9.05412	−1.60056
$33$	3.14646	0.547728
$34$	−16.0806	−2.75781
$35$	1.76564	0.298448
$36$	9.54610	1.59102
$37$	5.39098	0.886272	0.443136	−	0.896454i	$-0.353866\pi$
$37$	5.39098	0.886272	0.443136	+	0.896454i	$0.353866\pi$
$38$	14.0984	2.28707
$39$	10.5936	1.69633
$40$	6.50181	1.02803
$41$	1.13606	0.177422	0.0887112	−	0.996057i	$-0.471725\pi$
$41$	1.13606	0.177422	0.0887112	+	0.996057i	$0.471725\pi$
$42$	−11.2112	−1.72993
$43$	0.281797	0.0429737	0.0214868	−	0.999769i	$-0.493160\pi$
$43$	0.281797	0.0429737	0.0214868	+	0.999769i	$0.493160\pi$
$44$	−6.65464	−1.00323
$45$	−1.84497	−0.275032
$46$	2.93508	0.432754
$47$	−8.99914	−1.31266	−0.656330	−	0.754474i	$-0.727892\pi$
$47$	−8.99914	−1.31266	−0.656330	+	0.754474i	$0.727892\pi$
$48$	−20.0693	−2.89675
$49$	−3.27983	−0.468546
$50$	10.8024	1.52769
$51$	−13.8752	−1.94292
$52$	−22.4050	−3.10702
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−5.72290	−0.778788
$55$	1.28614	0.173423
$56$	13.6992	1.83063
$57$	12.1649	1.61128
$58$	1.23286	0.161883
$59$	−11.2777	−1.46823	−0.734114	−	0.679026i	$-0.762402\pi$
$59$	−11.2777	−1.46823	−0.734114	+	0.679026i	$0.762402\pi$
$60$	9.71032	1.25360
$61$	−0.0211009	−0.00270169	−0.00135084	−	0.999999i	$-0.500430\pi$
$61$	−0.0211009	−0.00270169	−0.00135084	+	0.999999i	$0.500430\pi$
$62$	−0.449262	−0.0570563
$63$	−3.88732	−0.489756
$64$	5.57692	0.697116
$65$	4.33022	0.537098
$66$	−8.16655	−1.00523
$67$	10.0137	1.22336	0.611681	−	0.791104i	$-0.290493\pi$
$67$	10.0137	1.22336	0.611681	+	0.791104i	$0.290493\pi$
$68$	29.3456	3.55868
$69$	2.53255	0.304883
$70$	−4.58269	−0.547736
$71$	−12.2715	−1.45636	−0.728179	−	0.685387i	$-0.759633\pi$
$71$	−12.2715	−1.45636	−0.728179	+	0.685387i	$0.759633\pi$
$72$	−14.3147	−1.68700
$73$	10.5694	1.23706	0.618529	−	0.785762i	$-0.287729\pi$
$73$	10.5694	1.23706	0.618529	+	0.785762i	$0.287729\pi$
$74$	−13.9922	−1.62656
$75$	9.32087	1.07628
$76$	−25.7283	−2.95124
$77$	2.70987	0.308819
$78$	−27.4954	−3.11324
$79$	−13.2834	−1.49450	−0.747252	−	0.664541i	$-0.768627\pi$
$79$	−13.2834	−1.49450	−0.747252	+	0.664541i	$0.768627\pi$
$80$	−8.20349	−0.917178
$81$	−10.9843	−1.22048
$82$	−2.94861	−0.325619
$83$	−10.1607	−1.11528	−0.557642	−	0.830081i	$-0.688294\pi$
$83$	−10.1607	−1.11528	−0.557642	+	0.830081i	$0.688294\pi$
$84$	20.4594	2.23231
$85$	−5.67163	−0.615174
$86$	−0.731398	−0.0788687
$87$	1.06378	0.114049
$88$	9.97883	1.06375
$89$	0.0261827	0.00277537	0.00138768	−	0.999999i	$-0.499558\pi$
$89$	0.0261827	0.00277537	0.00138768	+	0.999999i	$0.499558\pi$
$90$	4.78859	0.504761
$91$	9.12368	0.956421
$92$	−5.35625	−0.558428
$93$	−0.387647	−0.0401972
$94$	23.3571	2.40910
$95$	4.97251	0.510169
$96$	20.2769	2.06950
$97$	9.24864	0.939057	0.469529	−	0.882917i	$-0.344424\pi$
$97$	9.24864	0.939057	0.469529	+	0.882917i	$0.344424\pi$
$98$	8.51271	0.859914
$99$	−2.83163	−0.284589
$100$	−19.7133	−1.97133
$101$	−9.86776	−0.981879	−0.490939	−	0.871194i	$-0.663346\pi$
$101$	−9.86776	−0.981879	−0.490939	+	0.871194i	$0.663346\pi$
$102$	36.0128	3.56580
$103$	−13.0108	−1.28199	−0.640996	−	0.767544i	$-0.721478\pi$
$103$	−13.0108	−1.28199	−0.640996	+	0.767544i	$0.721478\pi$
$104$	33.5970	3.29446
$105$	−3.95419	−0.385889
$106$	−2.59548	−0.252095
$107$	4.49778	0.434817	0.217409	−	0.976081i	$-0.430240\pi$
$107$	4.49778	0.434817	0.217409	+	0.976081i	$0.430240\pi$
$108$	10.4438	1.00495
$109$	−15.7049	−1.50426	−0.752128	−	0.659016i	$-0.770973\pi$
$109$	−15.7049	−1.50426	−0.752128	+	0.659016i	$0.770973\pi$
$110$	−3.33815	−0.318280
$111$	−12.0732	−1.14594
$112$	−17.2846	−1.63324
$113$	2.90124	0.272926	0.136463	−	0.990645i	$-0.456427\pi$
$113$	2.90124	0.272926	0.136463	+	0.990645i	$0.456427\pi$
$114$	−31.5737	−2.95715
$115$	1.03520	0.0965331
$116$	−2.24985	−0.208894
$117$	−9.53360	−0.881381
$118$	29.2709	2.69461
$119$	−11.9500	−1.09545
$120$	−14.5609	−1.32922
$121$	−9.02606	−0.820551
$122$	0.0547668	0.00495835
$123$	−2.54422	−0.229404
$124$	0.819860	0.0736256
$125$	8.38710	0.750165
$126$	10.0894	0.898839
$127$	7.81813	0.693747	0.346873	−	0.937912i	$-0.387243\pi$
$127$	7.81813	0.693747	0.346873	+	0.937912i	$0.387243\pi$
$128$	3.63347	0.321157
$129$	−0.631090	−0.0555644
$130$	−11.2390	−0.985724
$131$	−20.2337	−1.76782	−0.883912	−	0.467653i	$-0.845100\pi$
$131$	−20.2337	−1.76782	−0.883912	+	0.467653i	$0.845100\pi$
$132$	14.9032	1.29716
$133$	10.4770	0.908469
$134$	−25.9902	−2.24521
$135$	−2.01846	−0.173722
$136$	−44.0046	−3.77337
$137$	−14.0223	−1.19801	−0.599005	−	0.800746i	$-0.704437\pi$
$137$	−14.0223	−1.19801	−0.599005	+	0.800746i	$0.704437\pi$
$138$	−6.57317	−0.559545
$139$	22.1859	1.88178	0.940890	−	0.338712i	$-0.109991\pi$
$139$	22.1859	1.88178	0.940890	+	0.338712i	$0.109991\pi$
$140$	8.36297	0.706800
$141$	20.1537	1.69725
$142$	31.8504	2.67282
$143$	6.64593	0.555760
$144$	18.0612	1.50510
$145$	0.434829	0.0361106
$146$	−27.4327	−2.27035
$147$	7.34522	0.605824
$148$	25.5344	2.09891
$149$	8.32775	0.682236	0.341118	−	0.940021i	$-0.389194\pi$
$149$	8.32775	0.682236	0.341118	+	0.940021i	$0.389194\pi$
$150$	−24.1921	−1.97528
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	38.5804	3.12928
$153$	12.4869	1.00951
$154$	−7.03341	−0.566769
$155$	−0.158454	−0.0127274
$156$	50.1764	4.01733
$157$	−6.00646	−0.479368	−0.239684	−	0.970851i	$-0.577044\pi$
$157$	−6.00646	−0.479368	−0.239684	+	0.970851i	$0.577044\pi$
$158$	34.4769	2.74283
$159$	−2.23952	−0.177605
$160$	8.28835	0.655252
$161$	2.18115	0.171899
$162$	28.5096	2.23992
$163$	12.7717	1.00036	0.500180	−	0.865921i	$-0.333267\pi$
$163$	12.7717	1.00036	0.500180	+	0.865921i	$0.333267\pi$
$164$	5.38093	0.420180
$165$	−2.88034	−0.224234
$166$	26.3719	2.04686
$167$	−9.42386	−0.729240	−0.364620	−	0.931156i	$-0.618801\pi$
$167$	−9.42386	−0.729240	−0.364620	+	0.931156i	$0.618801\pi$
$168$	−30.6795	−2.36697
$169$	9.37569	0.721207
$170$	14.7206	1.12902
$171$	−10.9477	−0.837191
$172$	1.33473	0.101772
$173$	−24.0964	−1.83201	−0.916007	−	0.401163i	$-0.868606\pi$
$173$	−24.0964	−1.83201	−0.916007	+	0.401163i	$0.868606\pi$
$174$	−2.76101	−0.209312
$175$	8.02757	0.606827
$176$	−12.5905	−0.949047
$177$	25.2565	1.89840
$178$	−0.0679567	−0.00509357
$179$	−4.83894	−0.361680	−0.180840	−	0.983513i	$-0.557882\pi$
$179$	−4.83894	−0.361680	−0.180840	+	0.983513i	$0.557882\pi$
$180$	−8.73872	−0.651345
$181$	8.82661	0.656077	0.328039	−	0.944664i	$-0.393612\pi$
$181$	8.82661	0.656077	0.328039	+	0.944664i	$0.393612\pi$
$182$	−23.6803	−1.75530
$183$	0.0472557	0.00349325
$184$	8.03185	0.592116
$185$	−4.93503	−0.362830
$186$	1.00613	0.0737730
$187$	−8.70469	−0.636550
$188$	−42.6244	−3.10870
$189$	−4.25286	−0.309350
$190$	−12.9060	−0.936302
$191$	−24.5905	−1.77930	−0.889652	−	0.456639i	$-0.849053\pi$
$191$	−24.5905	−1.77930	−0.889652	+	0.456639i	$0.849053\pi$
$192$	−12.4896	−0.901360
$193$	−15.2749	−1.09951	−0.549755	−	0.835326i	$-0.685279\pi$
$193$	−15.2749	−1.09951	−0.549755	+	0.835326i	$0.685279\pi$
$194$	−24.0046	−1.72343
$195$	−9.69760	−0.694459
$196$	−15.5349	−1.10963
$197$	12.5708	0.895630	0.447815	−	0.894126i	$-0.352202\pi$
$197$	12.5708	0.895630	0.447815	+	0.894126i	$0.352202\pi$
$198$	7.34942	0.522300
$199$	2.69173	0.190812	0.0954058	−	0.995438i	$-0.469585\pi$
$199$	2.69173	0.190812	0.0954058	+	0.995438i	$0.469585\pi$
$200$	29.5607	2.09026
$201$	−22.4257	−1.58179
$202$	25.6115	1.80202
$203$	0.916175	0.0643029
$204$	−65.7200	−4.60132
$205$	−1.03997	−0.0726348
$206$	33.7692	2.35281
$207$	−2.27914	−0.158412
$208$	−42.3902	−2.93923
$209$	7.63170	0.527896
$210$	10.2630	0.708215
$211$	−14.9066	−1.02621	−0.513105	−	0.858326i	$-0.671505\pi$
$211$	−14.9066	−1.02621	−0.513105	+	0.858326i	$0.671505\pi$
$212$	4.73650	0.325304
$213$	27.4822	1.88305
$214$	−11.6739	−0.798011
$215$	−0.257964	−0.0175930
$216$	−15.6607	−1.06558
$217$	−0.333860	−0.0226639
$218$	40.7617	2.76073
$219$	−23.6704	−1.59950
$220$	6.09181	0.410710
$221$	−29.3072	−1.97142
$222$	31.3357	2.10311
$223$	26.9242	1.80298	0.901488	−	0.432804i	$-0.142476\pi$
$223$	26.9242	1.80298	0.901488	+	0.432804i	$0.142476\pi$
$224$	17.4634	1.16682
$225$	−8.38824	−0.559216
$226$	−7.53011	−0.500895
$227$	−11.7941	−0.782803	−0.391401	−	0.920220i	$-0.628010\pi$
$227$	−11.7941	−0.782803	−0.391401	+	0.920220i	$0.628010\pi$
$228$	57.6190	3.81591
$229$	15.5279	1.02611	0.513057	−	0.858355i	$-0.328513\pi$
$229$	15.5279	1.02611	0.513057	+	0.858355i	$0.328513\pi$
$230$	−2.68684	−0.177165
$231$	−6.06881	−0.399298
$232$	3.37372	0.221496
$233$	−2.45302	−0.160703	−0.0803515	−	0.996767i	$-0.525604\pi$
$233$	−2.45302	−0.160703	−0.0803515	+	0.996767i	$0.525604\pi$
$234$	24.7442	1.61758
$235$	8.23802	0.537389
$236$	−53.4167	−3.47713
$237$	29.7485	1.93237
$238$	31.0159	2.01046
$239$	−29.4889	−1.90748	−0.953738	−	0.300640i	$-0.902800\pi$
$239$	−29.4889	−1.90748	−0.953738	+	0.300640i	$0.902800\pi$
$240$	18.3718	1.18590
$241$	−11.6183	−0.748403	−0.374201	−	0.927347i	$-0.622083\pi$
$241$	−11.6183	−0.748403	−0.374201	+	0.927347i	$0.622083\pi$
$242$	23.4269	1.50594
$243$	17.9847	1.15372
$244$	−0.0999443	−0.00639828
$245$	3.00243	0.191818
$246$	6.60346	0.421021
$247$	25.6946	1.63491
$248$	−1.22940	−0.0780673
$249$	22.7551	1.44205
$250$	−21.7685	−1.37676
$251$	8.14918	0.514372	0.257186	−	0.966362i	$-0.417205\pi$
$251$	8.14918	0.514372	0.257186	+	0.966362i	$0.417205\pi$
$252$	−18.4123	−1.15986
$253$	1.58881	0.0998873
$254$	−20.2918	−1.27322
$255$	12.7017	0.795412
$256$	−20.5844	−1.28653
$257$	−23.9653	−1.49491	−0.747456	−	0.664311i	$-0.768725\pi$
$257$	−23.9653	−1.49491	−0.747456	+	0.664311i	$0.768725\pi$
$258$	1.63798	0.101976
$259$	−10.3980	−0.646100
$260$	20.5101	1.27198
$261$	−0.957338	−0.0592578
$262$	52.5160	3.24445
$263$	3.98244	0.245568	0.122784	−	0.992433i	$-0.460818\pi$
$263$	3.98244	0.245568	0.122784	+	0.992433i	$0.460818\pi$
$264$	−22.3478	−1.37541
$265$	−0.915423	−0.0562340
$266$	−27.1927	−1.66729
$267$	−0.0586367	−0.00358851
$268$	47.4297	2.89723
$269$	10.1580	0.619345	0.309672	−	0.950843i	$-0.399781\pi$
$269$	10.1580	0.619345	0.309672	+	0.950843i	$0.399781\pi$
$270$	5.23887	0.318828
$271$	2.39275	0.145349	0.0726746	−	0.997356i	$-0.476847\pi$
$271$	2.39275	0.145349	0.0726746	+	0.997356i	$0.476847\pi$
$272$	55.5217	3.36650
$273$	−20.4326	−1.23664
$274$	36.3947	2.19868
$275$	5.84749	0.352617
$276$	11.9954	0.722039
$277$	−25.3491	−1.52308	−0.761539	−	0.648119i	$-0.775556\pi$
$277$	−25.3491	−1.52308	−0.761539	+	0.648119i	$0.775556\pi$
$278$	−57.5829	−3.45359
$279$	0.348860	0.0208857
$280$	−12.5405	−0.749440
$281$	−13.5331	−0.807314	−0.403657	−	0.914910i	$-0.632261\pi$
$281$	−13.5331	−0.807314	−0.403657	+	0.914910i	$0.632261\pi$
$282$	−52.3085	−3.11493
$283$	−22.5588	−1.34098	−0.670490	−	0.741919i	$-0.733916\pi$
$283$	−22.5588	−1.34098	−0.670490	+	0.741919i	$0.733916\pi$
$284$	−58.1239	−3.44902
$285$	−11.1360	−0.659641
$286$	−17.2493	−1.01998
$287$	−2.19120	−0.129342
$288$	−18.2480	−1.07527
$289$	21.3859	1.25800
$290$	−1.12859	−0.0662730
$291$	−20.7125	−1.21419
$292$	50.0621	2.92966
$293$	23.1877	1.35464	0.677320	−	0.735688i	$-0.263141\pi$
$293$	23.1877	1.35464	0.677320	+	0.735688i	$0.263141\pi$
$294$	−19.0644	−1.11186
$295$	10.3238	0.601077
$296$	−38.2895	−2.22553
$297$	−3.09789	−0.179758
$298$	−21.6145	−1.25209
$299$	5.34923	0.309354
$300$	44.1483	2.54890
$301$	−0.543524	−0.0313282
$302$	2.59548	0.149353
$303$	22.0990	1.26956
$304$	−48.6778	−2.79186
$305$	0.0193162	0.00110604
$306$	−32.4095	−1.85273
$307$	−24.2096	−1.38172	−0.690858	−	0.722991i	$-0.742767\pi$
$307$	−24.2096	−1.38172	−0.690858	+	0.722991i	$0.742767\pi$
$308$	12.8353	0.731360
$309$	29.1379	1.65760
$310$	0.411265	0.0233583
$311$	−11.5510	−0.654998	−0.327499	−	0.944851i	$-0.606206\pi$
$311$	−11.5510	−0.654998	−0.327499	+	0.944851i	$0.606206\pi$
$312$	−75.2410	−4.25969
$313$	−28.5031	−1.61109	−0.805545	−	0.592535i	$-0.798127\pi$
$313$	−28.5031	−1.61109	−0.805545	+	0.592535i	$0.798127\pi$
$314$	15.5896	0.879774
$315$	3.55854	0.200501
$316$	−62.9170	−3.53936
$317$	0.750276	0.0421397	0.0210699	−	0.999778i	$-0.493293\pi$
$317$	0.750276	0.0421397	0.0210699	+	0.999778i	$0.493293\pi$
$318$	5.81261	0.325955
$319$	0.667366	0.0373653
$320$	−5.10524	−0.285392
$321$	−10.0729	−0.562212
$322$	−5.66112	−0.315482
$323$	−33.6543	−1.87257
$324$	−52.0273	−2.89040
$325$	19.6875	1.09207
$326$	−33.1488	−1.83594
$327$	35.1714	1.94498
$328$	−8.06887	−0.445529
$329$	17.3573	0.956940
$330$	7.47585	0.411532
$331$	−20.6983	−1.13768	−0.568842	−	0.822447i	$-0.692608\pi$
$331$	−20.6983	−1.13768	−0.568842	+	0.822447i	$0.692608\pi$
$332$	−48.1263	−2.64127
$333$	10.8652	0.595407
$334$	24.4594	1.33836
$335$	−9.16673	−0.500832
$336$	38.7091	2.11175
$337$	−10.5763	−0.576128	−0.288064	−	0.957611i	$-0.593012\pi$
$337$	−10.5763	−0.576128	−0.288064	+	0.957611i	$0.593012\pi$
$338$	−24.3344	−1.32362
$339$	−6.49738	−0.352889
$340$	−26.8637	−1.45689
$341$	−0.243192	−0.0131696
$342$	28.4145	1.53648
$343$	19.8275	1.07058
$344$	−2.00147	−0.107912
$345$	−2.31835	−0.124816
$346$	62.5416	3.36226
$347$	−3.64359	−0.195598	−0.0977991	−	0.995206i	$-0.531180\pi$
$347$	−3.64359	−0.195598	−0.0977991	+	0.995206i	$0.531180\pi$
$348$	5.03859	0.270097
$349$	15.2532	0.816488	0.408244	−	0.912873i	$-0.366141\pi$
$349$	15.2532	0.816488	0.408244	+	0.912873i	$0.366141\pi$
$350$	−20.8354	−1.11370
$351$	−10.4301	−0.556716
$352$	12.7208	0.678020
$353$	−6.88166	−0.366274	−0.183137	−	0.983087i	$-0.558625\pi$
$353$	−6.88166	−0.366274	−0.183137	+	0.983087i	$0.558625\pi$
$354$	−65.5527	−3.48409
$355$	11.2336	0.596218
$356$	0.124015	0.00657276
$357$	26.7622	1.41641
$358$	12.5594	0.663783
$359$	−1.96041	−0.103466	−0.0517332	−	0.998661i	$-0.516475\pi$
$359$	−1.96041	−0.103466	−0.0517332	+	0.998661i	$0.516475\pi$
$360$	13.1040	0.690639
$361$	10.5059	0.552940
$362$	−22.9093	−1.20408
$363$	20.2140	1.06096
$364$	43.2143	2.26504
$365$	−9.67550	−0.506439
$366$	−0.122651	−0.00641108
$367$	−12.6874	−0.662279	−0.331139	−	0.943582i	$-0.607433\pi$
$367$	−12.6874	−0.662279	−0.331139	+	0.943582i	$0.607433\pi$
$368$	−10.1340	−0.528271
$369$	2.28965	0.119194
$370$	12.8087	0.665895
$371$	−1.92878	−0.100137
$372$	−1.83609	−0.0951969
$373$	−8.42879	−0.436426	−0.218213	−	0.975901i	$-0.570023\pi$
$373$	−8.42879	−0.436426	−0.218213	+	0.975901i	$0.570023\pi$
$374$	22.5928	1.16825
$375$	−18.7831	−0.969953
$376$	63.9166	3.29624
$377$	2.24691	0.115722
$378$	11.0382	0.567743
$379$	15.0186	0.771453	0.385726	−	0.922613i	$-0.373951\pi$
$379$	15.0186	0.771453	0.385726	+	0.922613i	$0.373951\pi$
$380$	23.5523	1.20821
$381$	−17.5088	−0.897004
$382$	63.8240	3.26552
$383$	−15.9739	−0.816229	−0.408114	−	0.912931i	$-0.633814\pi$
$383$	−15.9739	−0.816229	−0.408114	+	0.912931i	$0.633814\pi$
$384$	−8.13722	−0.415251
$385$	−2.48068	−0.126427
$386$	39.6456	2.01791
$387$	0.567944	0.0288702
$388$	43.8062	2.22392
$389$	−1.69938	−0.0861621	−0.0430810	−	0.999072i	$-0.513717\pi$
$389$	−1.69938	−0.0861621	−0.0430810	+	0.999072i	$0.513717\pi$
$390$	25.1699	1.27453
$391$	−7.00631	−0.354324
$392$	23.2950	1.17658
$393$	45.3136	2.28577
$394$	−32.6271	−1.64373
$395$	12.1600	0.611834
$396$	−13.4120	−0.673978
$397$	−14.3248	−0.718943	−0.359471	−	0.933156i	$-0.617043\pi$
$397$	−14.3248	−0.718943	−0.359471	+	0.933156i	$0.617043\pi$
$398$	−6.98632	−0.350193
$399$	−23.4634	−1.17464
$400$	−37.2974	−1.86487
$401$	−35.2531	−1.76045	−0.880227	−	0.474553i	$-0.842610\pi$
$401$	−35.2531	−1.76045	−0.880227	+	0.474553i	$0.842610\pi$
$402$	58.2055	2.90303
$403$	−0.818787	−0.0407867
$404$	−46.7386	−2.32533
$405$	10.0553	0.499652
$406$	−2.37791	−0.118014
$407$	−7.57417	−0.375438
$408$	98.5491	4.87891
$409$	−17.4175	−0.861240	−0.430620	−	0.902533i	$-0.641705\pi$
$409$	−17.4175	−0.861240	−0.430620	+	0.902533i	$0.641705\pi$
$410$	2.69922	0.133305
$411$	31.4033	1.54901
$412$	−61.6256	−3.03608
$413$	21.7521	1.07035
$414$	5.91547	0.290729
$415$	9.30136	0.456586
$416$	42.8287	2.09985
$417$	−49.6856	−2.43311
$418$	−19.8079	−0.968836
$419$	−32.1615	−1.57119	−0.785597	−	0.618739i	$-0.787644\pi$
$419$	−32.1615	−1.57119	−0.785597	+	0.618739i	$0.787644\pi$
$420$	−18.7290	−0.913883
$421$	1.73999	0.0848019	0.0424009	−	0.999101i	$-0.486499\pi$
$421$	1.73999	0.0848019	0.0424009	+	0.999101i	$0.486499\pi$
$422$	38.6897	1.88338
$423$	−18.1372	−0.881859
$424$	−7.10252	−0.344929
$425$	−25.7863	−1.25082
$426$	−71.3294	−3.45592
$427$	0.0406988	0.00196956
$428$	21.3037	1.02976
$429$	−14.8837	−0.718590
$430$	0.669539	0.0322880
$431$	13.9656	0.672700	0.336350	−	0.941737i	$-0.390807\pi$
$431$	13.9656	0.672700	0.336350	+	0.941737i	$0.390807\pi$
$432$	19.7595	0.950680
$433$	−30.8270	−1.48145	−0.740727	−	0.671807i	$-0.765519\pi$
$433$	−30.8270	−1.48145	−0.740727	+	0.671807i	$0.765519\pi$
$434$	0.866525	0.0415946
$435$	−0.973807	−0.0466905
$436$	−74.3863	−3.56246
$437$	6.14267	0.293844
$438$	61.4360	2.93553
$439$	8.84366	0.422085	0.211042	−	0.977477i	$-0.432314\pi$
$439$	8.84366	0.422085	0.211042	+	0.977477i	$0.432314\pi$
$440$	−9.13485	−0.435487
$441$	−6.61027	−0.314775
$442$	76.0661	3.61810
$443$	−29.9752	−1.42416	−0.712082	−	0.702097i	$-0.752247\pi$
$443$	−29.9752	−1.42416	−0.712082	+	0.702097i	$0.752247\pi$
$444$	−57.1846	−2.71386
$445$	−0.0239683	−0.00113621
$446$	−69.8811	−3.30897
$447$	−18.6501	−0.882121
$448$	−10.7566	−0.508203
$449$	16.6323	0.784929	0.392464	−	0.919767i	$-0.371623\pi$
$449$	16.6323	0.784929	0.392464	+	0.919767i	$0.371623\pi$
$450$	21.7715	1.02632
$451$	−1.59613	−0.0751587
$452$	13.7417	0.646357
$453$	2.23952	0.105222
$454$	30.6113	1.43666
$455$	−8.35202	−0.391549
$456$	−86.4014	−4.04612
$457$	−2.95227	−0.138101	−0.0690506	−	0.997613i	$-0.521997\pi$
$457$	−2.95227	−0.138101	−0.0690506	+	0.997613i	$0.521997\pi$
$458$	−40.3023	−1.88320
$459$	13.6611	0.637645
$460$	4.90323	0.228614
$461$	7.26264	0.338255	0.169127	−	0.985594i	$-0.445905\pi$
$461$	7.26264	0.338255	0.169127	+	0.985594i	$0.445905\pi$
$462$	15.7514	0.732823
$463$	−28.5288	−1.32585	−0.662923	−	0.748687i	$-0.730685\pi$
$463$	−28.5288	−1.32585	−0.662923	+	0.748687i	$0.730685\pi$
$464$	−4.25671	−0.197613
$465$	0.354861	0.0164563
$466$	6.36677	0.294935
$467$	−29.1857	−1.35055	−0.675277	−	0.737564i	$-0.735976\pi$
$467$	−29.1857	−1.35055	−0.675277	+	0.737564i	$0.735976\pi$
$468$	−45.1559	−2.08733
$469$	−19.3141	−0.891842
$470$	−21.3816	−0.986259
$471$	13.4516	0.619816
$472$	80.0999	3.68689
$473$	−0.395917	−0.0182043
$474$	−77.2115	−3.54644
$475$	22.6077	1.03731
$476$	−56.6011	−2.59431
$477$	2.01543	0.0922804
$478$	76.5376	3.50075
$479$	38.9292	1.77872	0.889361	−	0.457205i	$-0.151149\pi$
$479$	38.9292	1.77872	0.889361	+	0.457205i	$0.151149\pi$
$480$	−18.5619	−0.847231
$481$	−25.5009	−1.16274
$482$	30.1551	1.37353
$483$	−4.88472	−0.222262
$484$	−42.7519	−1.94327
$485$	−8.46642	−0.384440
$486$	−46.6789	−2.11740
$487$	27.0210	1.22444	0.612218	−	0.790689i	$-0.290277\pi$
$487$	27.0210	1.22444	0.612218	+	0.790689i	$0.290277\pi$
$488$	0.149869	0.00678427
$489$	−28.6025	−1.29345
$490$	−7.79273	−0.352040
$491$	7.35559	0.331953	0.165977	−	0.986130i	$-0.446922\pi$
$491$	7.35559	0.331953	0.165977	+	0.986130i	$0.446922\pi$
$492$	−12.0507	−0.543287
$493$	−2.94295	−0.132544
$494$	−66.6898	−3.00052
$495$	2.59213	0.116508
$496$	1.55117	0.0696496
$497$	23.6689	1.06170
$498$	−59.0604	−2.64656
$499$	27.1308	1.21454	0.607271	−	0.794495i	$-0.292264\pi$
$499$	27.1308	1.21454	0.607271	+	0.794495i	$0.292264\pi$
$500$	39.7255	1.77658
$501$	21.1049	0.942897
$502$	−21.1510	−0.944015
$503$	0.324456	0.0144668	0.00723338	−	0.999974i	$-0.497698\pi$
$503$	0.324456	0.0144668	0.00723338	+	0.999974i	$0.497698\pi$
$504$	27.6098	1.22984
$505$	9.03317	0.401971
$506$	−4.12371	−0.183321
$507$	−20.9970	−0.932510
$508$	37.0306	1.64297
$509$	−12.4878	−0.553510	−0.276755	−	0.960941i	$-0.589259\pi$
$509$	−12.4878	−0.553510	−0.276755	+	0.960941i	$0.589259\pi$
$510$	−32.9670	−1.45980
$511$	−20.3861	−0.901826
$512$	46.1595	2.03998
$513$	−11.9771	−0.528804
$514$	62.2013	2.74358
$515$	11.9104	0.524834
$516$	−2.98916	−0.131590
$517$	12.6435	0.556062
$518$	26.9877	1.18577
$519$	53.9642	2.36877
$520$	−30.7555	−1.34872
$521$	14.6288	0.640899	0.320449	−	0.947266i	$-0.396166\pi$
$521$	14.6288	0.640899	0.320449	+	0.947266i	$0.396166\pi$
$522$	2.48475	0.108755
$523$	−10.3413	−0.452192	−0.226096	−	0.974105i	$-0.572596\pi$
$523$	−10.3413	−0.452192	−0.226096	+	0.974105i	$0.572596\pi$
$524$	−95.8368	−4.18665
$525$	−17.9779	−0.784618
$526$	−10.3363	−0.450685
$527$	1.07243	0.0467157
$528$	28.1967	1.22710
$529$	−21.7212	−0.944399
$530$	2.37596	0.103205
$531$	−22.7294	−0.986372
$532$	49.6242	2.15148
$533$	−5.37389	−0.232769
$534$	0.152190	0.00658591
$535$	−4.11737	−0.178010
$536$	−71.1222	−3.07201
$537$	10.8369	0.467646
$538$	−26.3649	−1.13667
$539$	4.60806	0.198483
$540$	−9.56045	−0.411416
$541$	39.4200	1.69480	0.847400	−	0.530955i	$-0.178167\pi$
$541$	39.4200	1.69480	0.847400	+	0.530955i	$0.178167\pi$
$542$	−6.21032	−0.266756
$543$	−19.7673	−0.848298
$544$	−56.0961	−2.40510
$545$	14.3766	0.615827
$546$	53.0324	2.26958
$547$	−12.7784	−0.546363	−0.273182	−	0.961962i	$-0.588076\pi$
$547$	−12.7784	−0.546363	−0.273182	+	0.961962i	$0.588076\pi$
$548$	−66.4168	−2.83718
$549$	−0.0425274	−0.00181503
$550$	−15.1770	−0.647150
$551$	2.58019	0.109920
$552$	−17.9875	−0.765597
$553$	25.6208	1.08951
$554$	65.7930	2.79527
$555$	11.0521	0.469134
$556$	105.083	4.45652
$557$	−20.9673	−0.888413	−0.444206	−	0.895925i	$-0.646514\pi$
$557$	−20.9673	−0.888413	−0.444206	+	0.895925i	$0.646514\pi$
$558$	−0.905458	−0.0383311
$559$	−1.33298	−0.0563792
$560$	15.8227	0.668631
$561$	19.4943	0.823050
$562$	35.1247	1.48165
$563$	−22.2170	−0.936334	−0.468167	−	0.883640i	$-0.655085\pi$
$563$	−22.2170	−0.936334	−0.468167	+	0.883640i	$0.655085\pi$
$564$	95.4581	4.01951
$565$	−2.65586	−0.111733
$566$	58.5507	2.46107
$567$	21.1863	0.889741
$568$	87.1585	3.65709
$569$	−5.35056	−0.224307	−0.112153	−	0.993691i	$-0.535775\pi$
$569$	−5.35056	−0.224307	−0.112153	+	0.993691i	$0.535775\pi$
$570$	28.9033	1.21063
$571$	−25.6917	−1.07517	−0.537583	−	0.843211i	$-0.680662\pi$
$571$	−25.6917	−1.07517	−0.537583	+	0.843211i	$0.680662\pi$
$572$	31.4784	1.31618
$573$	55.0708	2.30061
$574$	5.68721	0.237379
$575$	4.70658	0.196278
$576$	11.2399	0.468330
$577$	−9.69911	−0.403779	−0.201890	−	0.979408i	$-0.564708\pi$
$577$	−9.69911	−0.403779	−0.201890	+	0.979408i	$0.564708\pi$
$578$	−55.5067	−2.30877
$579$	34.2084	1.42165
$580$	2.05957	0.0855189
$581$	19.5978	0.813052
$582$	53.7588	2.22837
$583$	−1.40497	−0.0581879
$584$	−75.0696	−3.10640
$585$	8.72727	0.360828
$586$	−60.1831	−2.48614
$587$	−0.447424	−0.0184672	−0.00923358	−	0.999957i	$-0.502939\pi$
$587$	−0.447424	−0.0184672	−0.00923358	+	0.999957i	$0.502939\pi$
$588$	34.7906	1.43474
$589$	−0.940236	−0.0387417
$590$	−26.7953	−1.10314
$591$	−28.1524	−1.15804
$592$	48.3109	1.98556
$593$	−13.4924	−0.554067	−0.277034	−	0.960860i	$-0.589351\pi$
$593$	−13.4924	−0.554067	−0.277034	+	0.960860i	$0.589351\pi$
$594$	8.04051	0.329906
$595$	10.9393	0.448467
$596$	39.4444	1.61570
$597$	−6.02817	−0.246717
$598$	−13.8838	−0.567751
$599$	−45.8820	−1.87469	−0.937343	−	0.348408i	$-0.886722\pi$
$599$	−45.8820	−1.87469	−0.937343	+	0.348408i	$0.886722\pi$
$600$	−66.2016	−2.70267
$601$	5.85474	0.238820	0.119410	−	0.992845i	$-0.461900\pi$
$601$	5.85474	0.238820	0.119410	+	0.992845i	$0.461900\pi$
$602$	1.41070	0.0574960
$603$	20.1819	0.821869
$604$	−4.73650	−0.192725
$605$	8.26266	0.335925
$606$	−57.3575	−2.32999
$607$	44.4328	1.80347	0.901735	−	0.432289i	$-0.142294\pi$
$607$	44.4328	1.80347	0.901735	+	0.432289i	$0.142294\pi$
$608$	49.1814	1.99457
$609$	−2.05179	−0.0831427
$610$	−0.0501348	−0.00202990
$611$	42.5686	1.72214
$612$	59.1442	2.39076
$613$	16.6245	0.671459	0.335729	−	0.941959i	$-0.391017\pi$
$613$	16.6245	0.671459	0.335729	+	0.941959i	$0.391017\pi$
$614$	62.8355	2.53583
$615$	2.32904	0.0939158
$616$	−19.2469	−0.775481
$617$	11.0852	0.446273	0.223136	−	0.974787i	$-0.428371\pi$
$617$	11.0852	0.446273	0.223136	+	0.974787i	$0.428371\pi$
$618$	−75.6267	−3.04215
$619$	48.2928	1.94105	0.970526	−	0.240997i	$-0.0774743\pi$
$619$	48.2928	1.94105	0.970526	+	0.240997i	$0.0774743\pi$
$620$	−0.750519	−0.0301416
$621$	−2.49346	−0.100059
$622$	29.9804	1.20210
$623$	−0.0505006	−0.00202327
$624$	94.9335	3.80038
$625$	13.1323	0.525290
$626$	73.9791	2.95680
$627$	−17.0913	−0.682562
$628$	−28.4496	−1.13526
$629$	33.4006	1.33177
$630$	−9.23611	−0.367975
$631$	4.18873	0.166751	0.0833754	−	0.996518i	$-0.473430\pi$
$631$	4.18873	0.166751	0.0833754	+	0.996518i	$0.473430\pi$
$632$	94.3459	3.75288
$633$	33.3835	1.32688
$634$	−1.94732	−0.0773381
$635$	−7.15689	−0.284013
$636$	−10.6075	−0.420613
$637$	15.5145	0.614708
$638$	−1.73213	−0.0685758
$639$	−24.7324	−0.978398
$640$	−3.32616	−0.131478
$641$	49.1571	1.94159	0.970794	−	0.239915i	$-0.0771195\pi$
$641$	49.1571	1.94159	0.970794	+	0.239915i	$0.0771195\pi$
$642$	26.1439	1.03182
$643$	4.24484	0.167400	0.0837001	−	0.996491i	$-0.473326\pi$
$643$	4.24484	0.167400	0.0837001	+	0.996491i	$0.473326\pi$
$644$	10.3310	0.407099
$645$	0.577714	0.0227475
$646$	87.3489	3.43670
$647$	−4.44464	−0.174737	−0.0873683	−	0.996176i	$-0.527846\pi$
$647$	−4.44464	−0.174737	−0.0873683	+	0.996176i	$0.527846\pi$
$648$	78.0164	3.06477
$649$	15.8448	0.621963
$650$	−51.0984	−2.00425
$651$	0.747685	0.0293041
$652$	60.4934	2.36910
$653$	−14.5703	−0.570179	−0.285089	−	0.958501i	$-0.592023\pi$
$653$	−14.5703	−0.570179	−0.285089	+	0.958501i	$0.592023\pi$
$654$	−91.2865	−3.56959
$655$	18.5224	0.723729
$656$	10.1807	0.397489
$657$	21.3020	0.831070
$658$	−45.0505	−1.75625
$659$	33.8578	1.31891	0.659456	−	0.751743i	$-0.270787\pi$
$659$	33.8578	1.31891	0.659456	+	0.751743i	$0.270787\pi$
$660$	−13.6427	−0.531042
$661$	−4.68338	−0.182162	−0.0910812	−	0.995843i	$-0.529032\pi$
$661$	−4.68338	−0.182162	−0.0910812	+	0.995843i	$0.529032\pi$
$662$	53.7221	2.08797
$663$	65.6339	2.54901
$664$	72.1668	2.80061
$665$	−9.59086	−0.371918
$666$	−28.2003	−1.09274
$667$	0.537156	0.0207988
$668$	−44.6361	−1.72702
$669$	−60.2971	−2.33122
$670$	23.7920	0.919166
$671$	0.0296461	0.00114448
$672$	−39.1095	−1.50868
$673$	49.7267	1.91682	0.958412	−	0.285388i	$-0.0921225\pi$
$673$	49.7267	1.91682	0.958412	+	0.285388i	$0.0921225\pi$
$674$	27.4506	1.05736
$675$	−9.17701	−0.353223
$676$	44.4079	1.70800
$677$	35.6773	1.37119	0.685596	−	0.727982i	$-0.259542\pi$
$677$	35.6773	1.37119	0.685596	+	0.727982i	$0.259542\pi$
$678$	16.8638	0.647650
$679$	−17.8386	−0.684581
$680$	40.2828	1.54478
$681$	26.4131	1.01215
$682$	0.631200	0.0241699
$683$	−3.57858	−0.136930	−0.0684652	−	0.997654i	$-0.521810\pi$
$683$	−3.57858	−0.136930	−0.0684652	+	0.997654i	$0.521810\pi$
$684$	−51.8537	−1.98268
$685$	12.8364	0.490452
$686$	−51.4617	−1.96482
$687$	−34.7750	−1.32675
$688$	2.52531	0.0962764
$689$	−4.73029	−0.180210
$690$	6.01723	0.229072
$691$	50.4774	1.92025	0.960125	−	0.279570i	$-0.0901919\pi$
$691$	50.4774	1.92025	0.960125	+	0.279570i	$0.0901919\pi$
$692$	−114.132	−4.33867
$693$	5.46157	0.207468
$694$	9.45685	0.358977
$695$	−20.3094	−0.770381
$696$	−7.55551	−0.286391
$697$	7.03860	0.266606
$698$	−39.5894	−1.49848
$699$	5.49359	0.207787
$700$	38.0226	1.43712
$701$	−25.8321	−0.975666	−0.487833	−	0.872937i	$-0.662213\pi$
$701$	−25.8321	−0.975666	−0.487833	+	0.872937i	$0.662213\pi$
$702$	27.0710	1.02173
$703$	−29.2834	−1.10445
$704$	−7.83542	−0.295308
$705$	−18.4492	−0.694836
$706$	17.8612	0.672215
$707$	19.0327	0.715798
$708$	119.628	4.49588
$709$	37.7668	1.41836	0.709181	−	0.705026i	$-0.249065\pi$
$709$	37.7668	1.41836	0.709181	+	0.705026i	$0.249065\pi$
$710$	−29.1565	−1.09423
$711$	−26.7719	−1.00402
$712$	−0.185963	−0.00696927
$713$	−0.195743	−0.00733063
$714$	−69.4607	−2.59950
$715$	−6.08383	−0.227522
$716$	−22.9196	−0.856548
$717$	66.0408	2.46634
$718$	5.08820	0.189890
$719$	13.5118	0.503904	0.251952	−	0.967740i	$-0.418928\pi$
$719$	13.5118	0.503904	0.251952	+	0.967740i	$0.418928\pi$
$720$	−16.5336	−0.616170
$721$	25.0949	0.934583
$722$	−27.2677	−1.01480
$723$	26.0195	0.967674
$724$	41.8072	1.55375
$725$	1.97697	0.0734227
$726$	−52.4650	−1.94716
$727$	−0.909933	−0.0337476	−0.0168738	−	0.999858i	$-0.505371\pi$
$727$	−0.909933	−0.0337476	−0.0168738	+	0.999858i	$0.505371\pi$
$728$	−64.8011	−2.40169
$729$	−7.32410	−0.271263
$730$	25.1125	0.929456
$731$	1.74591	0.0645750
$732$	0.223827	0.00827288
$733$	−11.1235	−0.410857	−0.205429	−	0.978672i	$-0.565859\pi$
$733$	−11.1235	−0.410857	−0.205429	+	0.978672i	$0.565859\pi$
$734$	32.9299	1.21547
$735$	−6.72398	−0.248018
$736$	10.2388	0.377408
$737$	−14.0689	−0.518234
$738$	−5.94273	−0.218755
$739$	38.7261	1.42456	0.712282	−	0.701894i	$-0.247662\pi$
$739$	38.7261	1.42456	0.712282	+	0.701894i	$0.247662\pi$
$740$	−23.3747	−0.859273
$741$	−57.5435	−2.11391
$742$	5.00609	0.183779
$743$	8.16600	0.299582	0.149791	−	0.988718i	$-0.452140\pi$
$743$	8.16600	0.299582	0.149791	+	0.988718i	$0.452140\pi$
$744$	2.75327	0.100940
$745$	−7.62341	−0.279300
$746$	21.8767	0.800964
$747$	−20.4783	−0.749261
$748$	−41.2298	−1.50751
$749$	−8.67521	−0.316985
$750$	48.7510	1.78013
$751$	−5.06604	−0.184863	−0.0924313	−	0.995719i	$-0.529464\pi$
$751$	−5.06604	−0.184863	−0.0924313	+	0.995719i	$0.529464\pi$
$752$	−80.6451	−2.94082
$753$	−18.2502	−0.665075
$754$	−5.83180	−0.212381
$755$	0.915423	0.0333156
$756$	−20.1437	−0.732618
$757$	−22.9193	−0.833016	−0.416508	−	0.909132i	$-0.636746\pi$
$757$	−22.9193	−0.833016	−0.416508	+	0.909132i	$0.636746\pi$
$758$	−38.9804	−1.41583
$759$	−3.55816	−0.129153
$760$	−35.3174	−1.28110
$761$	−14.6692	−0.531758	−0.265879	−	0.964006i	$-0.585662\pi$
$761$	−14.6692	−0.531758	−0.265879	+	0.964006i	$0.585662\pi$
$762$	45.4437	1.64625
$763$	30.2912	1.09662
$764$	−116.473	−4.21383
$765$	−11.4308	−0.413281
$766$	41.4599	1.49801
$767$	53.3467	1.92624
$768$	46.0992	1.66346
$769$	−30.3536	−1.09458	−0.547289	−	0.836944i	$-0.684340\pi$
$769$	−30.3536	−1.09458	−0.547289	+	0.836944i	$0.684340\pi$
$770$	6.43855	0.232029
$771$	53.6706	1.93290
$772$	−72.3495	−2.60391
$773$	7.24859	0.260714	0.130357	−	0.991467i	$-0.458388\pi$
$773$	7.24859	0.260714	0.130357	+	0.991467i	$0.458388\pi$
$774$	−1.47409	−0.0529849
$775$	−0.720418	−0.0258782
$776$	−65.6887	−2.35809
$777$	23.2865	0.835398
$778$	4.41071	0.158131
$779$	−6.17098	−0.221098
$780$	−45.9327	−1.64465
$781$	17.2411	0.616935
$782$	18.1847	0.650284
$783$	−1.04736	−0.0374296
$784$	−29.3919	−1.04971
$785$	5.49845	0.196248
$786$	−117.610	−4.19503
$787$	−44.9306	−1.60160	−0.800802	−	0.598929i	$-0.795593\pi$
$787$	−44.9306	−1.60160	−0.800802	+	0.598929i	$0.795593\pi$
$788$	59.5414	2.12108
$789$	−8.91873	−0.317515
$790$	−31.5609	−1.12289
$791$	−5.59585	−0.198965
$792$	20.1117	0.714637
$793$	0.0998133	0.00354448
$794$	37.1798	1.31946
$795$	2.05010	0.0727097
$796$	12.7494	0.451890
$797$	19.7845	0.700803	0.350402	−	0.936600i	$-0.386045\pi$
$797$	19.7845	0.700803	0.350402	+	0.936600i	$0.386045\pi$
$798$	60.8986	2.15579
$799$	−55.7554	−1.97248
$800$	37.6833	1.33231
$801$	0.0527696	0.00186452
$802$	91.4985	3.23092
$803$	−14.8497	−0.524036
$804$	−106.220	−3.74607
$805$	−1.99667	−0.0703734
$806$	2.12514	0.0748549
$807$	−22.7490	−0.800804
$808$	70.0859	2.46561
$809$	−15.8874	−0.558570	−0.279285	−	0.960208i	$-0.590097\pi$
$809$	−15.8874	−0.558570	−0.279285	+	0.960208i	$0.590097\pi$
$810$	−26.0983	−0.917001
$811$	−31.5445	−1.10768	−0.553838	−	0.832625i	$-0.686837\pi$
$811$	−31.5445	−1.10768	−0.553838	+	0.832625i	$0.686837\pi$
$812$	4.33946	0.152285
$813$	−5.35860	−0.187934
$814$	19.6586	0.689033
$815$	−11.6915	−0.409537
$816$	−124.342	−4.35283
$817$	−1.53070	−0.0535525
$818$	45.2067	1.58062
$819$	18.3882	0.642534
$820$	−4.92583	−0.172017
$821$	−40.0120	−1.39643	−0.698214	−	0.715889i	$-0.746022\pi$
$821$	−40.0120	−1.39643	−0.698214	+	0.715889i	$0.746022\pi$
$822$	−81.5064	−2.84286
$823$	−4.38506	−0.152854	−0.0764268	−	0.997075i	$-0.524351\pi$
$823$	−4.38506	−0.152854	−0.0764268	+	0.997075i	$0.524351\pi$
$824$	92.4094	3.21923
$825$	−13.0956	−0.455929
$826$	−56.4570	−1.96439
$827$	−21.3622	−0.742836	−0.371418	−	0.928466i	$-0.621128\pi$
$827$	−21.3622	−0.742836	−0.371418	+	0.928466i	$0.621128\pi$
$828$	−10.7952	−0.375158
$829$	8.39222	0.291474	0.145737	−	0.989323i	$-0.453445\pi$
$829$	8.39222	0.291474	0.145737	+	0.989323i	$0.453445\pi$
$830$	−24.1415	−0.837962
$831$	56.7697	1.96932
$832$	−26.3805	−0.914579
$833$	−20.3206	−0.704068
$834$	128.958	4.46544
$835$	8.62682	0.298543
$836$	36.1475	1.25019
$837$	0.381665	0.0131923
$838$	83.4745	2.88358
$839$	23.0943	0.797304	0.398652	−	0.917102i	$-0.369478\pi$
$839$	23.0943	0.797304	0.398652	+	0.917102i	$0.369478\pi$
$840$	28.0847	0.969015
$841$	−28.7744	−0.992220
$842$	−4.51610	−0.155635
$843$	30.3075	1.04385
$844$	−70.6050	−2.43032
$845$	−8.58272	−0.295255
$846$	47.0746	1.61846
$847$	17.4092	0.598188
$848$	8.96142	0.307736
$849$	50.5207	1.73387
$850$	66.9276	2.29560
$851$	−6.09637	−0.208981
$852$	130.169	4.45953
$853$	41.6724	1.42684	0.713418	−	0.700739i	$-0.247146\pi$
$853$	41.6724	1.42684	0.713418	+	0.700739i	$0.247146\pi$
$854$	−0.105633	−0.00361468
$855$	10.0218	0.342737
$856$	−31.9456	−1.09188
$857$	14.4831	0.494732	0.247366	−	0.968922i	$-0.420435\pi$
$857$	14.4831	0.494732	0.247366	+	0.968922i	$0.420435\pi$
$858$	38.6302	1.31881
$859$	25.6595	0.875490	0.437745	−	0.899099i	$-0.355777\pi$
$859$	25.6595	0.875490	0.437745	+	0.899099i	$0.355777\pi$
$860$	−1.22184	−0.0416646
$861$	4.90723	0.167238
$862$	−36.2474	−1.23459
$863$	−12.2604	−0.417347	−0.208674	−	0.977985i	$-0.566915\pi$
$863$	−12.2604	−0.417347	−0.208674	+	0.977985i	$0.566915\pi$
$864$	−19.9639	−0.679186
$865$	22.0584	0.750007
$866$	80.0109	2.71888
$867$	−47.8942	−1.62657
$868$	−1.58133	−0.0536737
$869$	18.6629	0.633094
$870$	2.52749	0.0856900
$871$	−47.3675	−1.60499
$872$	111.544	3.77737
$873$	18.6400	0.630869
$874$	−15.9432	−0.539286
$875$	−16.1768	−0.546877
$876$	−112.115	−3.78801
$877$	18.7815	0.634208	0.317104	−	0.948391i	$-0.397290\pi$
$877$	18.7815	0.634208	0.317104	+	0.948391i	$0.397290\pi$
$878$	−22.9535	−0.774644
$879$	−51.9292	−1.75153
$880$	11.5257	0.388530
$881$	22.5324	0.759136	0.379568	−	0.925164i	$-0.376073\pi$
$881$	22.5324	0.759136	0.379568	+	0.925164i	$0.376073\pi$
$882$	17.1568	0.577700
$883$	−38.6033	−1.29911	−0.649553	−	0.760317i	$-0.725044\pi$
$883$	−38.6033	−1.29911	−0.649553	+	0.760317i	$0.725044\pi$
$884$	−138.813	−4.66880
$885$	−23.1204	−0.777184
$886$	77.7999	2.61374
$887$	−12.7037	−0.426549	−0.213275	−	0.976992i	$-0.568413\pi$
$887$	−12.7037	−0.426549	−0.213275	+	0.976992i	$0.568413\pi$
$888$	85.7501	2.87758
$889$	−15.0794	−0.505747
$890$	0.0622091	0.00208525
$891$	15.4327	0.517014
$892$	127.526	4.26990
$893$	48.8827	1.63580
$894$	48.4060	1.61894
$895$	4.42968	0.148068
$896$	−7.00815	−0.234126
$897$	−11.9797	−0.399990
$898$	−43.1689	−1.44056
$899$	−0.0822204	−0.00274220
$900$	−39.7309	−1.32436
$901$	6.19564	0.206407
$902$	4.14271	0.137937
$903$	1.21723	0.0405069
$904$	−20.6061	−0.685350
$905$	−8.08008	−0.268591
$906$	−5.81261	−0.193111
$907$	45.1381	1.49879	0.749393	−	0.662126i	$-0.230346\pi$
$907$	45.1381	1.49879	0.749393	+	0.662126i	$0.230346\pi$
$908$	−55.8628	−1.85387
$909$	−19.8878	−0.659637
$910$	21.6775	0.718601
$911$	13.1106	0.434373	0.217187	−	0.976130i	$-0.430312\pi$
$911$	13.1106	0.434373	0.217187	+	0.976130i	$0.430312\pi$
$912$	109.015	3.60984
$913$	14.2755	0.472451
$914$	7.66254	0.253454
$915$	−0.0432590	−0.00143010
$916$	73.5479	2.43009
$917$	39.0262	1.28876
$918$	−35.4570	−1.17026
$919$	−12.4633	−0.411127	−0.205563	−	0.978644i	$-0.565903\pi$
$919$	−12.4633	−0.411127	−0.205563	+	0.978644i	$0.565903\pi$
$920$	−7.35254	−0.242406
$921$	54.2178	1.78654
$922$	−18.8500	−0.620792
$923$	58.0478	1.91067
$924$	−28.7449	−0.945637
$925$	−22.4373	−0.737733
$926$	74.0459	2.43330
$927$	−26.2224	−0.861256
$928$	4.30074	0.141179
$929$	−22.9564	−0.753174	−0.376587	−	0.926381i	$-0.622902\pi$
$929$	−22.9564	−0.753174	−0.376587	+	0.926381i	$0.622902\pi$
$930$	−0.921034	−0.0302019
$931$	17.8158	0.583889
$932$	−11.6187	−0.380585
$933$	25.8687	0.846903
$934$	75.7508	2.47864
$935$	7.96847	0.260597
$936$	67.7125	2.21325
$937$	39.3761	1.28636	0.643181	−	0.765714i	$-0.277614\pi$
$937$	39.3761	1.28636	0.643181	+	0.765714i	$0.277614\pi$
$938$	50.1293	1.63678
$939$	63.8331	2.08311
$940$	39.0194	1.27267
$941$	48.8973	1.59401	0.797004	−	0.603974i	$-0.206417\pi$
$941$	48.8973	1.59401	0.797004	+	0.603974i	$0.206417\pi$
$942$	−34.9132	−1.13753
$943$	−1.28471	−0.0418358
$944$	−101.064	−3.28935
$945$	3.89316	0.126645
$946$	1.02759	0.0334099
$947$	−11.7124	−0.380603	−0.190302	−	0.981726i	$-0.560947\pi$
$947$	−11.7124	−0.380603	−0.190302	+	0.981726i	$0.560947\pi$
$948$	140.904	4.57634
$949$	−49.9965	−1.62296
$950$	−58.6777	−1.90376
$951$	−1.68026	−0.0544860
$952$	84.8751	2.75082
$953$	5.80969	0.188194	0.0940972	−	0.995563i	$-0.470004\pi$
$953$	5.80969	0.188194	0.0940972	+	0.995563i	$0.470004\pi$
$954$	−5.23101	−0.169360
$955$	22.5107	0.728428
$956$	−139.674	−4.51738
$957$	−1.49458	−0.0483128
$958$	−101.040	−3.26445
$959$	27.0459	0.873359
$960$	11.4333	0.369007
$961$	−30.9700	−0.999033
$962$	66.1871	2.13396
$963$	9.06498	0.292115
$964$	−55.0302	−1.77240
$965$	13.9830	0.450128
$966$	12.6782	0.407913
$967$	25.3804	0.816179	0.408089	−	0.912942i	$-0.366195\pi$
$967$	25.3804	0.816179	0.408089	+	0.912942i	$0.366195\pi$
$968$	64.1077	2.06050
$969$	75.3693	2.42121
$970$	21.9744	0.705555
$971$	49.4845	1.58803	0.794016	−	0.607896i	$-0.207986\pi$
$971$	49.4845	1.58803	0.794016	+	0.607896i	$0.207986\pi$
$972$	85.1846	2.73230
$973$	−42.7915	−1.37183
$974$	−70.1323	−2.24718
$975$	−44.0905	−1.41202
$976$	−0.189094	−0.00605275
$977$	52.9016	1.69247	0.846237	−	0.532807i	$-0.178863\pi$
$977$	52.9016	1.69247	0.846237	+	0.532807i	$0.178863\pi$
$978$	74.2372	2.37384
$979$	−0.0367860	−0.00117569
$980$	14.2210	0.454273
$981$	−31.6522	−1.01058
$982$	−19.0913	−0.609227
$983$	−24.5416	−0.782757	−0.391378	−	0.920230i	$-0.628002\pi$
$983$	−24.5416	−0.782757	−0.391378	+	0.920230i	$0.628002\pi$
$984$	18.0704	0.576062
$985$	−11.5076	−0.366662
$986$	7.63836	0.243255
$987$	−38.8720	−1.23731
$988$	121.703	3.87187
$989$	−0.318669	−0.0101331
$990$	−6.72782	−0.213824
$991$	−46.9471	−1.49132	−0.745661	−	0.666325i	$-0.767866\pi$
$991$	−46.9471	−1.49132	−0.745661	+	0.666325i	$0.767866\pi$
$992$	−1.56722	−0.0497592
$993$	46.3543	1.47101
$994$	−61.4322	−1.94851
$995$	−2.46407	−0.0781163
$996$	107.780	3.41513
$997$	25.9911	0.823146	0.411573	−	0.911377i	$-0.364979\pi$
$997$	25.9911	0.823146	0.411573	+	0.911377i	$0.364979\pi$
$998$	−70.4174	−2.22902
$999$	11.8869	0.376083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.10	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.10	✓	179	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)

\(f(q)\)	\(=\)	\(q-2.59548 q^{2} -2.23952 q^{3} +4.73650 q^{4} -0.915423 q^{5} +5.81261 q^{6} -1.92878 q^{7} -7.10252 q^{8} +2.01543 q^{9} +O(q^{10})\)	\(q-2.59548 q^{2} -2.23952 q^{3} +4.73650 q^{4} -0.915423 q^{5} +5.81261 q^{6} -1.92878 q^{7} -7.10252 q^{8} +2.01543 q^{9} +2.37596 q^{10} -1.40497 q^{11} -10.6075 q^{12} -4.73029 q^{13} +5.00609 q^{14} +2.05010 q^{15} +8.96142 q^{16} +6.19564 q^{17} -5.23101 q^{18} -5.43193 q^{19} -4.33590 q^{20} +4.31952 q^{21} +3.64657 q^{22} -1.13085 q^{23} +15.9062 q^{24} -4.16200 q^{25} +12.2774 q^{26} +2.20495 q^{27} -9.13564 q^{28} -0.475004 q^{29} -5.32100 q^{30} +0.173094 q^{31} -9.05412 q^{32} +3.14646 q^{33} -16.0806 q^{34} +1.76564 q^{35} +9.54610 q^{36} +5.39098 q^{37} +14.0984 q^{38} +10.5936 q^{39} +6.50181 q^{40} +1.13606 q^{41} -11.2112 q^{42} +0.281797 q^{43} -6.65464 q^{44} -1.84497 q^{45} +2.93508 q^{46} -8.99914 q^{47} -20.0693 q^{48} -3.27983 q^{49} +10.8024 q^{50} -13.8752 q^{51} -22.4050 q^{52} +1.00000 q^{53} -5.72290 q^{54} +1.28614 q^{55} +13.6992 q^{56} +12.1649 q^{57} +1.23286 q^{58} -11.2777 q^{59} +9.71032 q^{60} -0.0211009 q^{61} -0.449262 q^{62} -3.88732 q^{63} +5.57692 q^{64} +4.33022 q^{65} -8.16655 q^{66} +10.0137 q^{67} +29.3456 q^{68} +2.53255 q^{69} -4.58269 q^{70} -12.2715 q^{71} -14.3147 q^{72} +10.5694 q^{73} -13.9922 q^{74} +9.32087 q^{75} -25.7283 q^{76} +2.70987 q^{77} -27.4954 q^{78} -13.2834 q^{79} -8.20349 q^{80} -10.9843 q^{81} -2.94861 q^{82} -10.1607 q^{83} +20.4594 q^{84} -5.67163 q^{85} -0.731398 q^{86} +1.06378 q^{87} +9.97883 q^{88} +0.0261827 q^{89} +4.78859 q^{90} +9.12368 q^{91} -5.35625 q^{92} -0.387647 q^{93} +23.3571 q^{94} +4.97251 q^{95} +20.2769 q^{96} +9.24864 q^{97} +8.51271 q^{98} -2.83163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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