LMFDB - Embedded newform 4033.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.58089 q^{2} +0.557711 q^{3} +0.499209 q^{4} +2.89052 q^{5} -0.881678 q^{6} +1.64472 q^{7} +2.37258 q^{8} -2.68896 q^{9} +O(q^{10})$	\(q-1.58089 q^{2} +0.557711 q^{3} +0.499209 q^{4} +2.89052 q^{5} -0.881678 q^{6} +1.64472 q^{7} +2.37258 q^{8} -2.68896 q^{9} -4.56959 q^{10} -3.25353 q^{11} +0.278414 q^{12} +5.06130 q^{13} -2.60012 q^{14} +1.61207 q^{15} -4.74921 q^{16} +3.13459 q^{17} +4.25094 q^{18} +0.363981 q^{19} +1.44297 q^{20} +0.917280 q^{21} +5.14347 q^{22} +5.35614 q^{23} +1.32321 q^{24} +3.35512 q^{25} -8.00135 q^{26} -3.17279 q^{27} +0.821060 q^{28} -6.20526 q^{29} -2.54851 q^{30} +0.0463776 q^{31} +2.76280 q^{32} -1.81453 q^{33} -4.95543 q^{34} +4.75411 q^{35} -1.34235 q^{36} -1.00000 q^{37} -0.575413 q^{38} +2.82274 q^{39} +6.85801 q^{40} +8.35718 q^{41} -1.45012 q^{42} +7.90126 q^{43} -1.62419 q^{44} -7.77250 q^{45} -8.46747 q^{46} -2.86590 q^{47} -2.64868 q^{48} -4.29488 q^{49} -5.30407 q^{50} +1.74819 q^{51} +2.52664 q^{52} +5.16161 q^{53} +5.01583 q^{54} -9.40439 q^{55} +3.90224 q^{56} +0.202996 q^{57} +9.80982 q^{58} -3.15597 q^{59} +0.804762 q^{60} +5.85226 q^{61} -0.0733179 q^{62} -4.42259 q^{63} +5.13073 q^{64} +14.6298 q^{65} +2.86856 q^{66} -12.1705 q^{67} +1.56481 q^{68} +2.98718 q^{69} -7.51572 q^{70} +10.5305 q^{71} -6.37978 q^{72} +2.40197 q^{73} +1.58089 q^{74} +1.87118 q^{75} +0.181702 q^{76} -5.35115 q^{77} -4.46244 q^{78} +13.2876 q^{79} -13.7277 q^{80} +6.29738 q^{81} -13.2118 q^{82} +2.27158 q^{83} +0.457914 q^{84} +9.06059 q^{85} -12.4910 q^{86} -3.46074 q^{87} -7.71927 q^{88} +0.764911 q^{89} +12.2874 q^{90} +8.32444 q^{91} +2.67383 q^{92} +0.0258653 q^{93} +4.53067 q^{94} +1.05209 q^{95} +1.54084 q^{96} -13.5380 q^{97} +6.78973 q^{98} +8.74860 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * 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 $

$2$	−1.58089	−1.11786	−0.558929	−	0.829216i	$-0.688787\pi$
$2$	−1.58089	−1.11786	−0.558929	+	0.829216i	$0.688787\pi$
$3$	0.557711	0.321994	0.160997	−	0.986955i	$-0.448529\pi$
$3$	0.557711	0.321994	0.160997	+	0.986955i	$0.448529\pi$
$4$	0.499209	0.249604
$5$	2.89052	1.29268	0.646340	−	0.763049i	$-0.276299\pi$
$5$	2.89052	1.29268	0.646340	+	0.763049i	$0.276299\pi$
$6$	−0.881678	−0.359944
$7$	1.64472	0.621647	0.310824	−	0.950468i	$-0.399395\pi$
$7$	1.64472	0.621647	0.310824	+	0.950468i	$0.399395\pi$
$8$	2.37258	0.838835
$9$	−2.68896	−0.896320
$10$	−4.56959	−1.44503
$11$	−3.25353	−0.980976	−0.490488	−	0.871448i	$-0.663181\pi$
$11$	−3.25353	−0.980976	−0.490488	+	0.871448i	$0.663181\pi$
$12$	0.278414	0.0803712
$13$	5.06130	1.40375	0.701876	−	0.712299i	$-0.252346\pi$
$13$	5.06130	1.40375	0.701876	+	0.712299i	$0.252346\pi$
$14$	−2.60012	−0.694913
$15$	1.61207	0.416236
$16$	−4.74921	−1.18730
$17$	3.13459	0.760249	0.380124	−	0.924935i	$-0.375881\pi$
$17$	3.13459	0.760249	0.380124	+	0.924935i	$0.375881\pi$
$18$	4.25094	1.00196
$19$	0.363981	0.0835029	0.0417514	−	0.999128i	$-0.486706\pi$
$19$	0.363981	0.0835029	0.0417514	+	0.999128i	$0.486706\pi$
$20$	1.44297	0.322659
$21$	0.917280	0.200167
$22$	5.14347	1.09659
$23$	5.35614	1.11683	0.558417	−	0.829561i	$-0.311409\pi$
$23$	5.35614	1.11683	0.558417	+	0.829561i	$0.311409\pi$
$24$	1.32321	0.270100
$25$	3.35512	0.671024
$26$	−8.00135	−1.56919
$27$	−3.17279	−0.610604
$28$	0.821060	0.155166
$29$	−6.20526	−1.15229	−0.576144	−	0.817349i	$-0.695443\pi$
$29$	−6.20526	−1.15229	−0.576144	+	0.817349i	$0.695443\pi$
$30$	−2.54851	−0.465292
$31$	0.0463776	0.00832967	0.00416483	−	0.999991i	$-0.498674\pi$
$31$	0.0463776	0.00832967	0.00416483	+	0.999991i	$0.498674\pi$
$32$	2.76280	0.488399
$33$	−1.81453	−0.315869
$34$	−4.95543	−0.849850
$35$	4.75411	0.803591
$36$	−1.34235	−0.223725
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−0.575413	−0.0933443
$39$	2.82274	0.452000
$40$	6.85801	1.08435
$41$	8.35718	1.30517	0.652586	−	0.757714i	$-0.273684\pi$
$41$	8.35718	1.30517	0.652586	+	0.757714i	$0.273684\pi$
$42$	−1.45012	−0.223758
$43$	7.90126	1.20493	0.602465	−	0.798145i	$-0.294185\pi$
$43$	7.90126	1.20493	0.602465	+	0.798145i	$0.294185\pi$
$44$	−1.62419	−0.244856
$45$	−7.77250	−1.15866
$46$	−8.46747	−1.24846
$47$	−2.86590	−0.418034	−0.209017	−	0.977912i	$-0.567026\pi$
$47$	−2.86590	−0.418034	−0.209017	+	0.977912i	$0.567026\pi$
$48$	−2.64868	−0.382305
$49$	−4.29488	−0.613555
$50$	−5.30407	−0.750108
$51$	1.74819	0.244796
$52$	2.52664	0.350383
$53$	5.16161	0.709002	0.354501	−	0.935056i	$-0.384651\pi$
$53$	5.16161	0.709002	0.354501	+	0.935056i	$0.384651\pi$
$54$	5.01583	0.682568
$55$	−9.40439	−1.26809
$56$	3.90224	0.521459
$57$	0.202996	0.0268875
$58$	9.80982	1.28809
$59$	−3.15597	−0.410872	−0.205436	−	0.978671i	$-0.565861\pi$
$59$	−3.15597	−0.410872	−0.205436	+	0.978671i	$0.565861\pi$
$60$	0.804762	0.103894
$61$	5.85226	0.749305	0.374652	−	0.927165i	$-0.377762\pi$
$61$	5.85226	0.749305	0.374652	+	0.927165i	$0.377762\pi$
$62$	−0.0733179	−0.00931138
$63$	−4.42259	−0.557195
$64$	5.13073	0.641342
$65$	14.6298	1.81460
$66$	2.86856	0.353096
$67$	−12.1705	−1.48687	−0.743433	−	0.668810i	$-0.766804\pi$
$67$	−12.1705	−1.48687	−0.743433	+	0.668810i	$0.766804\pi$
$68$	1.56481	0.189761
$69$	2.98718	0.359614
$70$	−7.51572	−0.898300
$71$	10.5305	1.24974	0.624871	−	0.780728i	$-0.285151\pi$
$71$	10.5305	1.24974	0.624871	+	0.780728i	$0.285151\pi$
$72$	−6.37978	−0.751864
$73$	2.40197	0.281129	0.140565	−	0.990071i	$-0.455108\pi$
$73$	2.40197	0.281129	0.140565	+	0.990071i	$0.455108\pi$
$74$	1.58089	0.183775
$75$	1.87118	0.216066
$76$	0.181702	0.0208427
$77$	−5.35115	−0.609821
$78$	−4.46244	−0.505271
$79$	13.2876	1.49497	0.747483	−	0.664281i	$-0.231262\pi$
$79$	13.2876	1.49497	0.747483	+	0.664281i	$0.231262\pi$
$80$	−13.7277	−1.53480
$81$	6.29738	0.699709
$82$	−13.2118	−1.45900
$83$	2.27158	0.249338	0.124669	−	0.992198i	$-0.460213\pi$
$83$	2.27158	0.249338	0.124669	+	0.992198i	$0.460213\pi$
$84$	0.457914	0.0499625
$85$	9.06059	0.982759
$86$	−12.4910	−1.34694
$87$	−3.46074	−0.371030
$88$	−7.71927	−0.822877
$89$	0.764911	0.0810804	0.0405402	−	0.999178i	$-0.487092\pi$
$89$	0.764911	0.0810804	0.0405402	+	0.999178i	$0.487092\pi$
$90$	12.2874	1.29521
$91$	8.32444	0.872638
$92$	2.67383	0.278766
$93$	0.0258653	0.00268211
$94$	4.53067	0.467303
$95$	1.05209	0.107943
$96$	1.54084	0.157262
$97$	−13.5380	−1.37458	−0.687290	−	0.726383i	$-0.741200\pi$
$97$	−13.5380	−1.37458	−0.687290	+	0.726383i	$0.741200\pi$
$98$	6.78973	0.685867
$99$	8.74860	0.879268
$100$	1.67490	0.167490
$101$	5.30792	0.528158	0.264079	−	0.964501i	$-0.414932\pi$
$101$	5.30792	0.528158	0.264079	+	0.964501i	$0.414932\pi$
$102$	−2.76370	−0.273647
$103$	14.1401	1.39327	0.696633	−	0.717428i	$-0.254681\pi$
$103$	14.1401	1.39327	0.696633	+	0.717428i	$0.254681\pi$
$104$	12.0084	1.17752
$105$	2.65142	0.258752
$106$	−8.15994	−0.792563
$107$	11.4709	1.10894	0.554468	−	0.832205i	$-0.312922\pi$
$107$	11.4709	1.10894	0.554468	+	0.832205i	$0.312922\pi$
$108$	−1.58389	−0.152409
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	14.8673	1.41754
$111$	−0.557711	−0.0529355
$112$	−7.81113	−0.738083
$113$	−10.8880	−1.02425	−0.512126	−	0.858910i	$-0.671142\pi$
$113$	−10.8880	−1.02425	−0.512126	+	0.858910i	$0.671142\pi$
$114$	−0.320914	−0.0300563
$115$	15.4820	1.44371
$116$	−3.09772	−0.287616
$117$	−13.6096	−1.25821
$118$	4.98924	0.459297
$119$	5.15553	0.472606
$120$	3.82478	0.349153
$121$	−0.414556	−0.0376869
$122$	−9.25177	−0.837616
$123$	4.66089	0.420258
$124$	0.0231521	0.00207912
$125$	−4.75457	−0.425262
$126$	6.99163	0.622864
$127$	7.10666	0.630614	0.315307	−	0.948990i	$-0.397892\pi$
$127$	7.10666	0.630614	0.315307	+	0.948990i	$0.397892\pi$
$128$	−13.6367	−1.20533
$129$	4.40662	0.387981
$130$	−23.1281	−2.02847
$131$	10.8371	0.946845	0.473422	−	0.880836i	$-0.343018\pi$
$131$	10.8371	0.946845	0.473422	+	0.880836i	$0.343018\pi$
$132$	−0.905828	−0.0788422
$133$	0.598648	0.0519093
$134$	19.2402	1.66210
$135$	−9.17103	−0.789316
$136$	7.43707	0.637723
$137$	1.65701	0.141568	0.0707841	−	0.997492i	$-0.477450\pi$
$137$	1.65701	0.141568	0.0707841	+	0.997492i	$0.477450\pi$
$138$	−4.72239	−0.401997
$139$	4.24241	0.359837	0.179918	−	0.983682i	$-0.442417\pi$
$139$	4.24241	0.359837	0.179918	+	0.983682i	$0.442417\pi$
$140$	2.37329	0.200580
$141$	−1.59834	−0.134605
$142$	−16.6476	−1.39703
$143$	−16.4671	−1.37705
$144$	12.7704	1.06420
$145$	−17.9364	−1.48954
$146$	−3.79725	−0.314262
$147$	−2.39530	−0.197561
$148$	−0.499209	−0.0410347
$149$	−5.10461	−0.418186	−0.209093	−	0.977896i	$-0.567051\pi$
$149$	−5.10461	−0.418186	−0.209093	+	0.977896i	$0.567051\pi$
$150$	−2.95813	−0.241531
$151$	−3.63078	−0.295469	−0.147734	−	0.989027i	$-0.547198\pi$
$151$	−3.63078	−0.295469	−0.147734	+	0.989027i	$0.547198\pi$
$152$	0.863575	0.0700451
$153$	−8.42877	−0.681426
$154$	8.45958	0.681692
$155$	0.134056	0.0107676
$156$	1.40914	0.112821
$157$	−7.83438	−0.625251	−0.312626	−	0.949876i	$-0.601209\pi$
$157$	−7.83438	−0.625251	−0.312626	+	0.949876i	$0.601209\pi$
$158$	−21.0061	−1.67116
$159$	2.87869	0.228295
$160$	7.98594	0.631344
$161$	8.80938	0.694276
$162$	−9.95545	−0.782174
$163$	−18.9264	−1.48243	−0.741216	−	0.671267i	$-0.765751\pi$
$163$	−18.9264	−1.48243	−0.741216	+	0.671267i	$0.765751\pi$
$164$	4.17198	0.325777
$165$	−5.24493	−0.408317
$166$	−3.59111	−0.278724
$167$	17.4397	1.34952	0.674762	−	0.738035i	$-0.264246\pi$
$167$	17.4397	1.34952	0.674762	+	0.738035i	$0.264246\pi$
$168$	2.17632	0.167907
$169$	12.6167	0.970518
$170$	−14.3238	−1.09858
$171$	−0.978729	−0.0748453
$172$	3.94438	0.300756
$173$	3.42409	0.260329	0.130164	−	0.991492i	$-0.458450\pi$
$173$	3.42409	0.260329	0.130164	+	0.991492i	$0.458450\pi$
$174$	5.47104	0.414758
$175$	5.51824	0.417140
$176$	15.4517	1.16471
$177$	−1.76012	−0.132299
$178$	−1.20924	−0.0906363
$179$	−15.7836	−1.17972	−0.589860	−	0.807506i	$-0.700817\pi$
$179$	−15.7836	−1.17972	−0.589860	+	0.807506i	$0.700817\pi$
$180$	−3.88010	−0.289205
$181$	15.9288	1.18398	0.591990	−	0.805945i	$-0.298342\pi$
$181$	15.9288	1.18398	0.591990	+	0.805945i	$0.298342\pi$
$182$	−13.1600	−0.975485
$183$	3.26387	0.241272
$184$	12.7079	0.936839
$185$	−2.89052	−0.212515
$186$	−0.0408901	−0.00299821
$187$	−10.1985	−0.745786
$188$	−1.43068	−0.104343
$189$	−5.21837	−0.379580
$190$	−1.66324	−0.120664
$191$	−18.7203	−1.35456	−0.677278	−	0.735727i	$-0.736841\pi$
$191$	−18.7203	−1.35456	−0.677278	+	0.735727i	$0.736841\pi$
$192$	2.86146	0.206508
$193$	−14.1773	−1.02050	−0.510251	−	0.860026i	$-0.670447\pi$
$193$	−14.1773	−1.02050	−0.510251	+	0.860026i	$0.670447\pi$
$194$	21.4021	1.53658
$195$	8.15919	0.584292
$196$	−2.14404	−0.153146
$197$	−13.3734	−0.952818	−0.476409	−	0.879224i	$-0.658062\pi$
$197$	−13.3734	−0.952818	−0.476409	+	0.879224i	$0.658062\pi$
$198$	−13.8306	−0.982896
$199$	20.7083	1.46797	0.733985	−	0.679166i	$-0.237658\pi$
$199$	20.7083	1.46797	0.733985	+	0.679166i	$0.237658\pi$
$200$	7.96030	0.562878
$201$	−6.78763	−0.478762
$202$	−8.39123	−0.590405
$203$	−10.2059	−0.716316
$204$	0.872713	0.0611021
$205$	24.1566	1.68717
$206$	−22.3539	−1.55747
$207$	−14.4024	−1.00104
$208$	−24.0372	−1.66668
$209$	−1.18422	−0.0819143
$210$	−4.19159	−0.289248
$211$	−4.69841	−0.323452	−0.161726	−	0.986836i	$-0.551706\pi$
$211$	−4.69841	−0.323452	−0.161726	+	0.986836i	$0.551706\pi$
$212$	2.57672	0.176970
$213$	5.87298	0.402410
$214$	−18.1343	−1.23963
$215$	22.8388	1.55759
$216$	−7.52772	−0.512196
$217$	0.0762784	0.00517811
$218$	−1.58089	−0.107071
$219$	1.33960	0.0905221
$220$	−4.69476	−0.316520
$221$	15.8651	1.06720
$222$	0.881678	0.0591744
$223$	−10.2185	−0.684282	−0.342141	−	0.939649i	$-0.611152\pi$
$223$	−10.2185	−0.684282	−0.342141	+	0.939649i	$0.611152\pi$
$224$	4.54405	0.303612
$225$	−9.02177	−0.601452
$226$	17.2126	1.14497
$227$	−8.30602	−0.551290	−0.275645	−	0.961260i	$-0.588891\pi$
$227$	−8.30602	−0.551290	−0.275645	+	0.961260i	$0.588891\pi$
$228$	0.101337	0.00671123
$229$	−0.0344947	−0.00227947	−0.00113974	−	0.999999i	$-0.500363\pi$
$229$	−0.0344947	−0.00227947	−0.00113974	+	0.999999i	$0.500363\pi$
$230$	−24.4754	−1.61386
$231$	−2.98439	−0.196359
$232$	−14.7225	−0.966579
$233$	21.7167	1.42271	0.711356	−	0.702832i	$-0.248082\pi$
$233$	21.7167	1.42271	0.711356	+	0.702832i	$0.248082\pi$
$234$	21.5153	1.40650
$235$	−8.28394	−0.540385
$236$	−1.57549	−0.102556
$237$	7.41061	0.481371
$238$	−8.15032	−0.528306
$239$	−19.4993	−1.26130	−0.630652	−	0.776066i	$-0.717212\pi$
$239$	−19.4993	−1.26130	−0.630652	+	0.776066i	$0.717212\pi$
$240$	−7.65608	−0.494198
$241$	3.66535	0.236106	0.118053	−	0.993007i	$-0.462335\pi$
$241$	3.66535	0.236106	0.118053	+	0.993007i	$0.462335\pi$
$242$	0.655368	0.0421286
$243$	13.0305	0.835906
$244$	2.92150	0.187030
$245$	−12.4145	−0.793131
$246$	−7.36835	−0.469789
$247$	1.84221	0.117217
$248$	0.110035	0.00698722
$249$	1.26688	0.0802854
$250$	7.51644	0.475382
$251$	0.136362	0.00860709	0.00430354	−	0.999991i	$-0.498630\pi$
$251$	0.136362	0.00860709	0.00430354	+	0.999991i	$0.498630\pi$
$252$	−2.20780	−0.139078
$253$	−17.4264	−1.09559
$254$	−11.2348	−0.704937
$255$	5.05319	0.316443
$256$	11.2967	0.706042
$257$	8.70595	0.543062	0.271531	−	0.962430i	$-0.412470\pi$
$257$	8.70595	0.543062	0.271531	+	0.962430i	$0.412470\pi$
$258$	−6.96637	−0.433707
$259$	−1.64472	−0.102198
$260$	7.30332	0.452933
$261$	16.6857	1.03282
$262$	−17.1323	−1.05844
$263$	17.6519	1.08846	0.544230	−	0.838936i	$-0.316822\pi$
$263$	17.6519	1.08846	0.544230	+	0.838936i	$0.316822\pi$
$264$	−4.30512	−0.264962
$265$	14.9198	0.916514
$266$	−0.946395	−0.0580272
$267$	0.426599	0.0261074
$268$	−6.07563	−0.371128
$269$	−10.5030	−0.640378	−0.320189	−	0.947354i	$-0.603746\pi$
$269$	−10.5030	−0.640378	−0.320189	+	0.947354i	$0.603746\pi$
$270$	14.4984	0.882343
$271$	30.3910	1.84612	0.923060	−	0.384656i	$-0.125680\pi$
$271$	30.3910	1.84612	0.923060	+	0.384656i	$0.125680\pi$
$272$	−14.8868	−0.902645
$273$	4.64263	0.280984
$274$	−2.61956	−0.158253
$275$	−10.9160	−0.658258
$276$	1.49123	0.0897612
$277$	−21.3246	−1.28127	−0.640636	−	0.767845i	$-0.721329\pi$
$277$	−21.3246	−1.28127	−0.640636	+	0.767845i	$0.721329\pi$
$278$	−6.70678	−0.402246
$279$	−0.124708	−0.00746604
$280$	11.2795	0.674080
$281$	9.10807	0.543342	0.271671	−	0.962390i	$-0.412424\pi$
$281$	9.10807	0.543342	0.271671	+	0.962390i	$0.412424\pi$
$282$	2.52680	0.150469
$283$	20.4702	1.21682	0.608412	−	0.793621i	$-0.291807\pi$
$283$	20.4702	1.21682	0.608412	+	0.793621i	$0.291807\pi$
$284$	5.25693	0.311941
$285$	0.586764	0.0347569
$286$	26.0326	1.53934
$287$	13.7453	0.811357
$288$	−7.42906	−0.437762
$289$	−7.17437	−0.422022
$290$	28.3555	1.66509
$291$	−7.55030	−0.442607
$292$	1.19908	0.0701711
$293$	4.76810	0.278555	0.139278	−	0.990253i	$-0.455522\pi$
$293$	4.76810	0.278555	0.139278	+	0.990253i	$0.455522\pi$
$294$	3.78671	0.220845
$295$	−9.12240	−0.531127
$296$	−2.37258	−0.137904
$297$	10.3228	0.598988
$298$	8.06982	0.467472
$299$	27.1090	1.56776
$300$	0.934112	0.0539310
$301$	12.9954	0.749042
$302$	5.73986	0.330292
$303$	2.96028	0.170064
$304$	−1.72862	−0.0991431
$305$	16.9161	0.968612
$306$	13.3250	0.761737
$307$	−0.872961	−0.0498225	−0.0249113	−	0.999690i	$-0.507930\pi$
$307$	−0.872961	−0.0498225	−0.0249113	+	0.999690i	$0.507930\pi$
$308$	−2.67134	−0.152214
$309$	7.88608	0.448623
$310$	−0.211927	−0.0120366
$311$	28.1702	1.59739	0.798694	−	0.601738i	$-0.205525\pi$
$311$	28.1702	1.59739	0.798694	+	0.601738i	$0.205525\pi$
$312$	6.69718	0.379153
$313$	4.74671	0.268300	0.134150	−	0.990961i	$-0.457170\pi$
$313$	4.74671	0.268300	0.134150	+	0.990961i	$0.457170\pi$
$314$	12.3853	0.698942
$315$	−12.7836	−0.720275
$316$	6.63326	0.373150
$317$	20.5608	1.15481	0.577406	−	0.816457i	$-0.304065\pi$
$317$	20.5608	1.15481	0.577406	+	0.816457i	$0.304065\pi$
$318$	−4.55088	−0.255201
$319$	20.1890	1.13037
$320$	14.8305	0.829050
$321$	6.39746	0.357071
$322$	−13.9266	−0.776101
$323$	1.14093	0.0634830
$324$	3.14371	0.174650
$325$	16.9812	0.941950
$326$	29.9206	1.65715
$327$	0.557711	0.0308415
$328$	19.8281	1.09482
$329$	−4.71361	−0.259870
$330$	8.29165	0.456440
$331$	17.4388	0.958524	0.479262	−	0.877672i	$-0.340904\pi$
$331$	17.4388	0.958524	0.479262	+	0.877672i	$0.340904\pi$
$332$	1.13399	0.0622358
$333$	2.68896	0.147354
$334$	−27.5702	−1.50858
$335$	−35.1792	−1.92204
$336$	−4.35635	−0.237658
$337$	28.6313	1.55965	0.779823	−	0.625999i	$-0.215309\pi$
$337$	28.6313	1.55965	0.779823	+	0.625999i	$0.215309\pi$
$338$	−19.9457	−1.08490
$339$	−6.07232	−0.329803
$340$	4.52313	0.245301
$341$	−0.150891	−0.00817120
$342$	1.54726	0.0836663
$343$	−18.5770	−1.00306
$344$	18.7464	1.01074
$345$	8.63450	0.464866
$346$	−5.41310	−0.291010
$347$	20.2373	1.08639	0.543197	−	0.839605i	$-0.317214\pi$
$347$	20.2373	1.08639	0.543197	+	0.839605i	$0.317214\pi$
$348$	−1.72763	−0.0926107
$349$	1.14769	0.0614343	0.0307172	−	0.999528i	$-0.490221\pi$
$349$	1.14769	0.0614343	0.0307172	+	0.999528i	$0.490221\pi$
$350$	−8.72372	−0.466303
$351$	−16.0584	−0.857136
$352$	−8.98885	−0.479107
$353$	25.7048	1.36813	0.684065	−	0.729421i	$-0.260210\pi$
$353$	25.7048	1.36813	0.684065	+	0.729421i	$0.260210\pi$
$354$	2.78255	0.147891
$355$	30.4387	1.61552
$356$	0.381850	0.0202380
$357$	2.87529	0.152177
$358$	24.9521	1.31876
$359$	6.66544	0.351789	0.175894	−	0.984409i	$-0.443718\pi$
$359$	6.66544	0.351789	0.175894	+	0.984409i	$0.443718\pi$
$360$	−18.4409	−0.971921
$361$	−18.8675	−0.993027
$362$	−25.1817	−1.32352
$363$	−0.231202	−0.0121350
$364$	4.15563	0.217814
$365$	6.94295	0.363411
$366$	−5.15981	−0.269708
$367$	8.91166	0.465185	0.232592	−	0.972574i	$-0.425279\pi$
$367$	8.91166	0.465185	0.232592	+	0.972574i	$0.425279\pi$
$368$	−25.4374	−1.32602
$369$	−22.4721	−1.16985
$370$	4.56959	0.237562
$371$	8.48943	0.440749
$372$	0.0129122	0.000669465 0
$373$	9.67189	0.500791	0.250396	−	0.968144i	$-0.419439\pi$
$373$	9.67189	0.500791	0.250396	+	0.968144i	$0.419439\pi$
$374$	16.1226	0.833682
$375$	−2.65167	−0.136932
$376$	−6.79959	−0.350662
$377$	−31.4067	−1.61752
$378$	8.24966	0.424317
$379$	−24.2138	−1.24378	−0.621889	−	0.783105i	$-0.713634\pi$
$379$	−24.2138	−1.24378	−0.621889	+	0.783105i	$0.713634\pi$
$380$	0.525215	0.0269429
$381$	3.96346	0.203054
$382$	29.5948	1.51420
$383$	−10.2129	−0.521856	−0.260928	−	0.965358i	$-0.584029\pi$
$383$	−10.2129	−0.521856	−0.260928	+	0.965358i	$0.584029\pi$
$384$	−7.60534	−0.388109
$385$	−15.4676	−0.788303
$386$	22.4127	1.14078
$387$	−21.2462	−1.08000
$388$	−6.75831	−0.343101
$389$	−28.2547	−1.43257	−0.716286	−	0.697807i	$-0.754159\pi$
$389$	−28.2547	−1.43257	−0.716286	+	0.697807i	$0.754159\pi$
$390$	−12.8988	−0.653155
$391$	16.7893	0.849071
$392$	−10.1900	−0.514671
$393$	6.04398	0.304879
$394$	21.1419	1.06511
$395$	38.4080	1.93251
$396$	4.36738	0.219469
$397$	−21.1537	−1.06167	−0.530837	−	0.847474i	$-0.678123\pi$
$397$	−21.1537	−1.06167	−0.530837	+	0.847474i	$0.678123\pi$
$398$	−32.7374	−1.64098
$399$	0.333872	0.0167145
$400$	−15.9342	−0.796708
$401$	7.36206	0.367644	0.183822	−	0.982960i	$-0.441153\pi$
$401$	7.36206	0.367644	0.183822	+	0.982960i	$0.441153\pi$
$402$	10.7305	0.535188
$403$	0.234731	0.0116928
$404$	2.64976	0.131830
$405$	18.2027	0.904500
$406$	16.1344	0.800739
$407$	3.25353	0.161271
$408$	4.14773	0.205343
$409$	12.5369	0.619909	0.309955	−	0.950751i	$-0.399686\pi$
$409$	12.5369	0.619909	0.309955	+	0.950751i	$0.399686\pi$
$410$	−38.1889	−1.88602
$411$	0.924134	0.0455842
$412$	7.05886	0.347765
$413$	−5.19070	−0.255418
$414$	22.7687	1.11902
$415$	6.56604	0.322314
$416$	13.9834	0.685591
$417$	2.36604	0.115865
$418$	1.87212	0.0915685
$419$	−19.4845	−0.951882	−0.475941	−	0.879477i	$-0.657892\pi$
$419$	−19.4845	−0.951882	−0.475941	+	0.879477i	$0.657892\pi$
$420$	1.32361	0.0645856
$421$	−16.1078	−0.785044	−0.392522	−	0.919743i	$-0.628397\pi$
$421$	−16.1078	−0.785044	−0.392522	+	0.919743i	$0.628397\pi$
$422$	7.42767	0.361573
$423$	7.70629	0.374692
$424$	12.2464	0.594736
$425$	10.5169	0.510145
$426$	−9.28453	−0.449837
$427$	9.62535	0.465803
$428$	5.72639	0.276795
$429$	−9.18386	−0.443401
$430$	−36.1055	−1.74116
$431$	−1.68159	−0.0809995	−0.0404997	−	0.999180i	$-0.512895\pi$
$431$	−1.68159	−0.0809995	−0.0404997	+	0.999180i	$0.512895\pi$
$432$	15.0683	0.724972
$433$	−10.7530	−0.516755	−0.258377	−	0.966044i	$-0.583188\pi$
$433$	−10.7530	−0.516755	−0.258377	+	0.966044i	$0.583188\pi$
$434$	−0.120588	−0.00578839
$435$	−10.0033	−0.479623
$436$	0.499209	0.0239078
$437$	1.94953	0.0932588
$438$	−2.11777	−0.101191
$439$	8.70649	0.415538	0.207769	−	0.978178i	$-0.433380\pi$
$439$	8.70649	0.415538	0.207769	+	0.978178i	$0.433380\pi$
$440$	−22.3127	−1.06372
$441$	11.5488	0.549941
$442$	−25.0809	−1.19298
$443$	24.1903	1.14932	0.574658	−	0.818394i	$-0.305135\pi$
$443$	24.1903	1.14932	0.574658	+	0.818394i	$0.305135\pi$
$444$	−0.278414	−0.0132129
$445$	2.21099	0.104811
$446$	16.1543	0.764929
$447$	−2.84690	−0.134654
$448$	8.43864	0.398688
$449$	−17.3525	−0.818913	−0.409456	−	0.912330i	$-0.634282\pi$
$449$	−17.3525	−0.818913	−0.409456	+	0.912330i	$0.634282\pi$
$450$	14.2624	0.672337
$451$	−27.1903	−1.28034
$452$	−5.43536	−0.255658
$453$	−2.02492	−0.0951392
$454$	13.1309	0.616263
$455$	24.0620	1.12804
$456$	0.481625	0.0225541
$457$	0.0326682	0.00152816	0.000764078	−	1.00000i	$-0.499757\pi$
$457$	0.0326682	0.00152816	0.000764078		1.00000i	$0.499757\pi$
$458$	0.0545323	0.00254813
$459$	−9.94539	−0.464211
$460$	7.72878	0.360356
$461$	−12.4596	−0.580302	−0.290151	−	0.956981i	$-0.593706\pi$
$461$	−12.4596	−0.580302	−0.290151	+	0.956981i	$0.593706\pi$
$462$	4.71800	0.219501
$463$	15.0490	0.699386	0.349693	−	0.936864i	$-0.386286\pi$
$463$	15.0490	0.699386	0.349693	+	0.936864i	$0.386286\pi$
$464$	29.4701	1.36811
$465$	0.0747642	0.00346711
$466$	−34.3318	−1.59039
$467$	40.5271	1.87537	0.937685	−	0.347488i	$-0.112965\pi$
$467$	40.5271	1.87537	0.937685	+	0.347488i	$0.112965\pi$
$468$	−6.79404	−0.314055
$469$	−20.0171	−0.924306
$470$	13.0960	0.604073
$471$	−4.36931	−0.201327
$472$	−7.48780	−0.344654
$473$	−25.7070	−1.18201
$474$	−11.7153	−0.538104
$475$	1.22120	0.0560324
$476$	2.57368	0.117965
$477$	−13.8794	−0.635493
$478$	30.8262	1.40996
$479$	18.0017	0.822520	0.411260	−	0.911518i	$-0.365089\pi$
$479$	18.0017	0.822520	0.411260	+	0.911518i	$0.365089\pi$
$480$	4.45384	0.203289
$481$	−5.06130	−0.230775
$482$	−5.79450	−0.263932
$483$	4.91308	0.223553
$484$	−0.206950	−0.00940683
$485$	−39.1320	−1.77689
$486$	−20.5998	−0.934424
$487$	−19.6799	−0.891782	−0.445891	−	0.895087i	$-0.647113\pi$
$487$	−19.6799	−0.891782	−0.445891	+	0.895087i	$0.647113\pi$
$488$	13.8850	0.628543
$489$	−10.5555	−0.477335
$490$	19.6259	0.886607
$491$	15.8791	0.716613	0.358306	−	0.933604i	$-0.383354\pi$
$491$	15.8791	0.716613	0.358306	+	0.933604i	$0.383354\pi$
$492$	2.32676	0.104898
$493$	−19.4509	−0.876025
$494$	−2.91234	−0.131032
$495$	25.2880	1.13661
$496$	−0.220257	−0.00988983
$497$	17.3198	0.776899
$498$	−2.00280	−0.0897476
$499$	30.8242	1.37988	0.689940	−	0.723866i	$-0.257637\pi$
$499$	30.8242	1.37988	0.689940	+	0.723866i	$0.257637\pi$
$500$	−2.37352	−0.106147
$501$	9.72631	0.434539
$502$	−0.215573	−0.00962149
$503$	10.4507	0.465975	0.232988	−	0.972480i	$-0.425150\pi$
$503$	10.4507	0.465975	0.232988	+	0.972480i	$0.425150\pi$
$504$	−10.4930	−0.467394
$505$	15.3427	0.682739
$506$	27.5491	1.22471
$507$	7.03649	0.312501
$508$	3.54771	0.157404
$509$	14.9588	0.663036	0.331518	−	0.943449i	$-0.392439\pi$
$509$	14.9588	0.663036	0.331518	+	0.943449i	$0.392439\pi$
$510$	−7.98852	−0.353738
$511$	3.95058	0.174763
$512$	9.41467	0.416073
$513$	−1.15483	−0.0509872
$514$	−13.7631	−0.607066
$515$	40.8723	1.80105
$516$	2.19982	0.0968417
$517$	9.32428	0.410081
$518$	2.60012	0.114243
$519$	1.90965	0.0838243
$520$	34.7104	1.52215
$521$	14.2744	0.625374	0.312687	−	0.949856i	$-0.398771\pi$
$521$	14.2744	0.625374	0.312687	+	0.949856i	$0.398771\pi$
$522$	−26.3782	−1.15454
$523$	−33.3425	−1.45797	−0.728984	−	0.684531i	$-0.760007\pi$
$523$	−33.3425	−1.45797	−0.728984	+	0.684531i	$0.760007\pi$
$524$	5.40999	0.236337
$525$	3.07758	0.134317
$526$	−27.9056	−1.21674
$527$	0.145375	0.00633262
$528$	8.61756	0.375031
$529$	5.68827	0.247316
$530$	−23.5865	−1.02453
$531$	8.48627	0.368273
$532$	0.298850	0.0129568
$533$	42.2982	1.83214
$534$	−0.674406	−0.0291844
$535$	33.1570	1.43350
$536$	−28.8756	−1.24724
$537$	−8.80267	−0.379863
$538$	16.6040	0.715851
$539$	13.9735	0.601882
$540$	−4.57826	−0.197017
$541$	−1.63856	−0.0704473	−0.0352236	−	0.999379i	$-0.511214\pi$
$541$	−1.63856	−0.0704473	−0.0352236	+	0.999379i	$0.511214\pi$
$542$	−48.0447	−2.06370
$543$	8.88367	0.381235
$544$	8.66024	0.371305
$545$	2.89052	0.123816
$546$	−7.33947	−0.314100
$547$	−19.8264	−0.847715	−0.423858	−	0.905729i	$-0.639324\pi$
$547$	−19.8264	−0.847715	−0.423858	+	0.905729i	$0.639324\pi$
$548$	0.827196	0.0353361
$549$	−15.7365	−0.671617
$550$	17.2569	0.735838
$551$	−2.25859	−0.0962193
$552$	7.08733	0.301657
$553$	21.8544	0.929342
$554$	33.7118	1.43228
$555$	−1.61207	−0.0684288
$556$	2.11785	0.0898168
$557$	−25.0527	−1.06152	−0.530759	−	0.847523i	$-0.678093\pi$
$557$	−25.0527	−1.06152	−0.530759	+	0.847523i	$0.678093\pi$
$558$	0.197149	0.00834597
$559$	39.9906	1.69142
$560$	−22.5783	−0.954106
$561$	−5.68779	−0.240139
$562$	−14.3988	−0.607378
$563$	5.80998	0.244861	0.122431	−	0.992477i	$-0.460931\pi$
$563$	5.80998	0.244861	0.122431	+	0.992477i	$0.460931\pi$
$564$	−0.797906	−0.0335979
$565$	−31.4719	−1.32403
$566$	−32.3610	−1.36024
$567$	10.3574	0.434972
$568$	24.9845	1.04833
$569$	25.2142	1.05703	0.528517	−	0.848923i	$-0.322748\pi$
$569$	25.2142	1.05703	0.528517	+	0.848923i	$0.322748\pi$
$570$	−0.927608	−0.0388532
$571$	32.8148	1.37326	0.686628	−	0.727009i	$-0.259090\pi$
$571$	32.8148	1.37326	0.686628	+	0.727009i	$0.259090\pi$
$572$	−8.22051	−0.343717
$573$	−10.4405	−0.436159
$574$	−21.7297	−0.906981
$575$	17.9705	0.749421
$576$	−13.7963	−0.574847
$577$	−45.3392	−1.88750	−0.943748	−	0.330666i	$-0.892727\pi$
$577$	−45.3392	−1.88750	−0.943748	+	0.330666i	$0.892727\pi$
$578$	11.3419	0.471760
$579$	−7.90681	−0.328596
$580$	−8.95402	−0.371796
$581$	3.73612	0.155000
$582$	11.9362	0.494771
$583$	−16.7935	−0.695514
$584$	5.69888	0.235821
$585$	−39.3389	−1.62646
$586$	−7.53783	−0.311385
$587$	−2.99578	−0.123649	−0.0618245	−	0.998087i	$-0.519692\pi$
$587$	−2.99578	−0.123649	−0.0618245	+	0.998087i	$0.519692\pi$
$588$	−1.19576	−0.0493121
$589$	0.0168806	0.000695551 0
$590$	14.4215	0.593724
$591$	−7.45851	−0.306802
$592$	4.74921	0.195191
$593$	25.4469	1.04498	0.522490	−	0.852645i	$-0.325003\pi$
$593$	25.4469	1.04498	0.522490	+	0.852645i	$0.325003\pi$
$594$	−16.3191	−0.669583
$595$	14.9022	0.610929
$596$	−2.54827	−0.104381
$597$	11.5492	0.472678
$598$	−42.8564	−1.75253
$599$	−22.7900	−0.931174	−0.465587	−	0.885002i	$-0.654157\pi$
$599$	−22.7900	−0.931174	−0.465587	+	0.885002i	$0.654157\pi$
$600$	4.43954	0.181244
$601$	27.5179	1.12248	0.561240	−	0.827653i	$-0.310325\pi$
$601$	27.5179	1.12248	0.561240	+	0.827653i	$0.310325\pi$
$602$	−20.5443	−0.837322
$603$	32.7260	1.33271
$604$	−1.81252	−0.0737503
$605$	−1.19828	−0.0487172
$606$	−4.67988	−0.190107
$607$	8.57233	0.347940	0.173970	−	0.984751i	$-0.444340\pi$
$607$	8.57233	0.347940	0.173970	+	0.984751i	$0.444340\pi$
$608$	1.00561	0.0407827
$609$	−5.69196	−0.230650
$610$	−26.7424	−1.08277
$611$	−14.5052	−0.586816
$612$	−4.20772	−0.170087
$613$	−19.8650	−0.802340	−0.401170	−	0.916004i	$-0.631396\pi$
$613$	−19.8650	−0.802340	−0.401170	+	0.916004i	$0.631396\pi$
$614$	1.38005	0.0556945
$615$	13.4724	0.543260
$616$	−12.6961	−0.511539
$617$	35.9891	1.44887	0.724433	−	0.689345i	$-0.242102\pi$
$617$	35.9891	1.44887	0.724433	+	0.689345i	$0.242102\pi$
$618$	−12.4670	−0.501497
$619$	−12.2054	−0.490576	−0.245288	−	0.969450i	$-0.578883\pi$
$619$	−12.2054	−0.490576	−0.245288	+	0.969450i	$0.578883\pi$
$620$	0.0669217	0.00268764
$621$	−16.9939	−0.681943
$622$	−44.5340	−1.78565
$623$	1.25807	0.0504034
$624$	−13.4058	−0.536661
$625$	−30.5188	−1.22075
$626$	−7.50402	−0.299921
$627$	−0.660453	−0.0263759
$628$	−3.91099	−0.156065
$629$	−3.13459	−0.124984
$630$	20.2095	0.805164
$631$	−16.1701	−0.643722	−0.321861	−	0.946787i	$-0.604308\pi$
$631$	−16.1701	−0.643722	−0.321861	+	0.946787i	$0.604308\pi$
$632$	31.5258	1.25403
$633$	−2.62035	−0.104150
$634$	−32.5044	−1.29091
$635$	20.5420	0.815183
$636$	1.43707	0.0569834
$637$	−21.7377	−0.861279
$638$	−31.9165	−1.26359
$639$	−28.3161	−1.12017
$640$	−39.4172	−1.55810
$641$	−16.3823	−0.647064	−0.323532	−	0.946217i	$-0.604870\pi$
$641$	−16.3823	−0.647064	−0.323532	+	0.946217i	$0.604870\pi$
$642$	−10.1137	−0.399155
$643$	−3.56572	−0.140618	−0.0703091	−	0.997525i	$-0.522399\pi$
$643$	−3.56572	−0.140618	−0.0703091	+	0.997525i	$0.522399\pi$
$644$	4.39772	0.173294
$645$	12.7374	0.501535
$646$	−1.80368	−0.0709649
$647$	2.67325	0.105096	0.0525482	−	0.998618i	$-0.483266\pi$
$647$	2.67325	0.105096	0.0525482	+	0.998618i	$0.483266\pi$
$648$	14.9411	0.586940
$649$	10.2680	0.403056
$650$	−26.8455	−1.05297
$651$	0.0425413	0.00166732
$652$	−9.44824	−0.370022
$653$	−5.22178	−0.204344	−0.102172	−	0.994767i	$-0.532579\pi$
$653$	−5.22178	−0.204344	−0.102172	+	0.994767i	$0.532579\pi$
$654$	−0.881678	−0.0344763
$655$	31.3250	1.22397
$656$	−39.6900	−1.54963
$657$	−6.45880	−0.251982
$658$	7.45170	0.290497
$659$	35.5012	1.38293	0.691464	−	0.722411i	$-0.256966\pi$
$659$	35.5012	1.38293	0.691464	+	0.722411i	$0.256966\pi$
$660$	−2.61831	−0.101918
$661$	−10.2650	−0.399262	−0.199631	−	0.979871i	$-0.563974\pi$
$661$	−10.2650	−0.399262	−0.199631	+	0.979871i	$0.563974\pi$
$662$	−27.5688	−1.07149
$663$	8.84812	0.343632
$664$	5.38951	0.209153
$665$	1.73040	0.0671022
$666$	−4.25094	−0.164721
$667$	−33.2362	−1.28691
$668$	8.70605	0.336847
$669$	−5.69897	−0.220335
$670$	55.6143	2.14857
$671$	−19.0405	−0.735050
$672$	2.53426	0.0977613
$673$	29.2718	1.12835	0.564173	−	0.825657i	$-0.309195\pi$
$673$	29.2718	1.12835	0.564173	+	0.825657i	$0.309195\pi$
$674$	−45.2629	−1.74346
$675$	−10.6451	−0.409730
$676$	6.29839	0.242246
$677$	0.593234	0.0227998	0.0113999	−	0.999935i	$-0.496371\pi$
$677$	0.593234	0.0227998	0.0113999	+	0.999935i	$0.496371\pi$
$678$	9.59967	0.368673
$679$	−22.2663	−0.854503
$680$	21.4970	0.824373
$681$	−4.63235	−0.177512
$682$	0.238542	0.00913423
$683$	3.96598	0.151754	0.0758770	−	0.997117i	$-0.475824\pi$
$683$	3.96598	0.151754	0.0758770	+	0.997117i	$0.475824\pi$
$684$	−0.488590	−0.0186817
$685$	4.78964	0.183003
$686$	29.3681	1.12128
$687$	−0.0192380	−0.000733977 0
$688$	−37.5247	−1.43062
$689$	26.1245	0.995263
$690$	−13.6502	−0.519654
$691$	−32.8289	−1.24887	−0.624434	−	0.781077i	$-0.714670\pi$
$691$	−32.8289	−1.24887	−0.624434	+	0.781077i	$0.714670\pi$
$692$	1.70934	0.0649792
$693$	14.3890	0.546594
$694$	−31.9929	−1.21443
$695$	12.2628	0.465154
$696$	−8.21089	−0.311233
$697$	26.1963	0.992256
$698$	−1.81437	−0.0686748
$699$	12.1117	0.458105
$700$	2.75475	0.104120
$701$	31.8299	1.20220	0.601099	−	0.799175i	$-0.294730\pi$
$701$	31.8299	1.20220	0.601099	+	0.799175i	$0.294730\pi$
$702$	25.3866	0.958156
$703$	−0.363981	−0.0137278
$704$	−16.6930	−0.629141
$705$	−4.62004	−0.174001
$706$	−40.6365	−1.52937
$707$	8.73006	0.328328
$708$	−0.878666	−0.0330223
$709$	−17.9164	−0.672865	−0.336433	−	0.941708i	$-0.609220\pi$
$709$	−17.9164	−0.672865	−0.336433	+	0.941708i	$0.609220\pi$
$710$	−48.1202	−1.80592
$711$	−35.7297	−1.33997
$712$	1.81482	0.0680131
$713$	0.248405	0.00930285
$714$	−4.54552	−0.170112
$715$	−47.5984	−1.78008
$716$	−7.87930	−0.294463
$717$	−10.8750	−0.406133
$718$	−10.5373	−0.393249
$719$	0.301858	0.0112574	0.00562870	−	0.999984i	$-0.498208\pi$
$719$	0.301858	0.0112574	0.00562870	+	0.999984i	$0.498208\pi$
$720$	36.9132	1.37567
$721$	23.2566	0.866119
$722$	29.8274	1.11006
$723$	2.04420	0.0760247
$724$	7.95181	0.295527
$725$	−20.8194	−0.773212
$726$	0.365505	0.0135652
$727$	−29.1609	−1.08152	−0.540759	−	0.841178i	$-0.681863\pi$
$727$	−29.1609	−1.08152	−0.540759	+	0.841178i	$0.681863\pi$
$728$	19.7504	0.731999
$729$	−11.6249	−0.430552
$730$	−10.9760	−0.406241
$731$	24.7672	0.916047
$732$	1.62935	0.0602225
$733$	−27.2366	−1.00601	−0.503004	−	0.864284i	$-0.667772\pi$
$733$	−27.2366	−1.00601	−0.503004	+	0.864284i	$0.667772\pi$
$734$	−14.0883	−0.520010
$735$	−6.92367	−0.255384
$736$	14.7980	0.545460
$737$	39.5971	1.45858
$738$	35.5259	1.30773
$739$	−7.33084	−0.269669	−0.134835	−	0.990868i	$-0.543050\pi$
$739$	−7.33084	−0.269669	−0.134835	+	0.990868i	$0.543050\pi$
$740$	−1.44297	−0.0530448
$741$	1.02742	0.0377433
$742$	−13.4208	−0.492695
$743$	−37.3965	−1.37194	−0.685972	−	0.727628i	$-0.740623\pi$
$743$	−37.3965	−1.37194	−0.685972	+	0.727628i	$0.740623\pi$
$744$	0.0613676	0.00224984
$745$	−14.7550	−0.540581
$746$	−15.2902	−0.559813
$747$	−6.10818	−0.223486
$748$	−5.09116	−0.186151
$749$	18.8665	0.689367
$750$	4.19200	0.153070
$751$	14.3024	0.521902	0.260951	−	0.965352i	$-0.415964\pi$
$751$	14.3024	0.521902	0.260951	+	0.965352i	$0.415964\pi$
$752$	13.6108	0.496333
$753$	0.0760505	0.00277143
$754$	49.6504	1.80816
$755$	−10.4948	−0.381947
$756$	−2.60505	−0.0947449
$757$	−29.9828	−1.08974	−0.544872	−	0.838519i	$-0.683422\pi$
$757$	−29.9828	−1.08974	−0.544872	+	0.838519i	$0.683422\pi$
$758$	38.2793	1.39037
$759$	−9.71886	−0.352772
$760$	2.49618	0.0905460
$761$	44.2151	1.60280	0.801399	−	0.598131i	$-0.204090\pi$
$761$	44.2151	1.60280	0.801399	+	0.598131i	$0.204090\pi$
$762$	−6.26579	−0.226986
$763$	1.64472	0.0595430
$764$	−9.34536	−0.338103
$765$	−24.3636	−0.880866
$766$	16.1455	0.583360
$767$	−15.9733	−0.576763
$768$	6.30027	0.227341
$769$	−12.7259	−0.458909	−0.229455	−	0.973319i	$-0.573694\pi$
$769$	−12.7259	−0.458909	−0.229455	+	0.973319i	$0.573694\pi$
$770$	24.4526	0.881210
$771$	4.85540	0.174863
$772$	−7.07741	−0.254722
$773$	−38.5682	−1.38720	−0.693600	−	0.720360i	$-0.743976\pi$
$773$	−38.5682	−1.38720	−0.693600	+	0.720360i	$0.743976\pi$
$774$	33.5878	1.20729
$775$	0.155602	0.00558940
$776$	−32.1201	−1.15305
$777$	−0.917280	−0.0329072
$778$	44.6676	1.60141
$779$	3.04185	0.108986
$780$	4.07314	0.145842
$781$	−34.2613	−1.22597
$782$	−26.5420	−0.949140
$783$	19.6880	0.703591
$784$	20.3973	0.728475
$785$	−22.6454	−0.808250
$786$	−9.55487	−0.340811
$787$	−19.8384	−0.707163	−0.353582	−	0.935404i	$-0.615036\pi$
$787$	−19.8384	−0.707163	−0.353582	+	0.935404i	$0.615036\pi$
$788$	−6.67614	−0.237828
$789$	9.84463	0.350478
$790$	−60.7187	−2.16027
$791$	−17.9077	−0.636723
$792$	20.7568	0.737561
$793$	29.6200	1.05184
$794$	33.4417	1.18680
$795$	8.32091	0.295112
$796$	10.3377	0.366412
$797$	23.0806	0.817556	0.408778	−	0.912634i	$-0.365955\pi$
$797$	23.0806	0.817556	0.408778	+	0.912634i	$0.365955\pi$
$798$	−0.527814	−0.0186844
$799$	−8.98341	−0.317810
$800$	9.26952	0.327727
$801$	−2.05682	−0.0726740
$802$	−11.6386	−0.410973
$803$	−7.81488	−0.275781
$804$	−3.38844	−0.119501
$805$	25.4637	0.897477
$806$	−0.371084	−0.0130709
$807$	−5.85762	−0.206198
$808$	12.5935	0.443037
$809$	−10.6114	−0.373079	−0.186539	−	0.982448i	$-0.559727\pi$
$809$	−10.6114	−0.373079	−0.186539	+	0.982448i	$0.559727\pi$
$810$	−28.7765	−1.01110
$811$	−31.5872	−1.10918	−0.554588	−	0.832125i	$-0.687124\pi$
$811$	−31.5872	−1.10918	−0.554588	+	0.832125i	$0.687124\pi$
$812$	−5.09489	−0.178796
$813$	16.9494	0.594440
$814$	−5.14347	−0.180278
$815$	−54.7073	−1.91631
$816$	−8.30253	−0.290647
$817$	2.87591	0.100615
$818$	−19.8194	−0.692970
$819$	−22.3841	−0.782163
$820$	12.0592	0.421125
$821$	18.1597	0.633779	0.316890	−	0.948462i	$-0.397361\pi$
$821$	18.1597	0.633779	0.316890	+	0.948462i	$0.397361\pi$
$822$	−1.46095	−0.0509566
$823$	−3.52731	−0.122954	−0.0614771	−	0.998108i	$-0.519581\pi$
$823$	−3.52731	−0.122954	−0.0614771	+	0.998108i	$0.519581\pi$
$824$	33.5486	1.16872
$825$	−6.08795	−0.211955
$826$	8.20592	0.285520
$827$	44.8566	1.55982	0.779909	−	0.625893i	$-0.215265\pi$
$827$	44.8566	1.55982	0.779909	+	0.625893i	$0.215265\pi$
$828$	−7.18983	−0.249864
$829$	−2.87164	−0.0997362	−0.0498681	−	0.998756i	$-0.515880\pi$
$829$	−2.87164	−0.0997362	−0.0498681	+	0.998756i	$0.515880\pi$
$830$	−10.3802	−0.360301
$831$	−11.8930	−0.412562
$832$	25.9682	0.900285
$833$	−13.4627	−0.466454
$834$	−3.74044	−0.129521
$835$	50.4098	1.74450
$836$	−0.591174	−0.0204462
$837$	−0.147147	−0.00508613
$838$	30.8029	1.06407
$839$	−1.10301	−0.0380802	−0.0190401	−	0.999819i	$-0.506061\pi$
$839$	−1.10301	−0.0380802	−0.0190401	+	0.999819i	$0.506061\pi$
$840$	6.29071	0.217050
$841$	9.50521	0.327766
$842$	25.4646	0.877568
$843$	5.07966	0.174953
$844$	−2.34549	−0.0807351
$845$	36.4690	1.25457
$846$	−12.1828	−0.418853
$847$	−0.681831	−0.0234280
$848$	−24.5136	−0.841800
$849$	11.4164	0.391810
$850$	−16.6261	−0.570269
$851$	−5.35614	−0.183606
$852$	2.93184	0.100443
$853$	−54.9636	−1.88192	−0.940959	−	0.338521i	$-0.890073\pi$
$853$	−54.9636	−1.88192	−0.940959	+	0.338521i	$0.890073\pi$
$854$	−15.2166	−0.520701
$855$	−2.82904	−0.0967510
$856$	27.2157	0.930215
$857$	−37.2354	−1.27194	−0.635968	−	0.771715i	$-0.719399\pi$
$857$	−37.2354	−1.27194	−0.635968	+	0.771715i	$0.719399\pi$
$858$	14.5187	0.495659
$859$	−13.5797	−0.463334	−0.231667	−	0.972795i	$-0.574418\pi$
$859$	−13.5797	−0.463334	−0.231667	+	0.972795i	$0.574418\pi$
$860$	11.4013	0.388782
$861$	7.66587	0.261252
$862$	2.65841	0.0905458
$863$	−32.9317	−1.12101	−0.560505	−	0.828151i	$-0.689393\pi$
$863$	−32.9317	−1.12101	−0.560505	+	0.828151i	$0.689393\pi$
$864$	−8.76580	−0.298218
$865$	9.89740	0.336522
$866$	16.9993	0.577658
$867$	−4.00122	−0.135889
$868$	0.0380788	0.00129248
$869$	−43.2314	−1.46653
$870$	15.8142	0.536150
$871$	−61.5987	−2.08719
$872$	2.37258	0.0803458
$873$	36.4032	1.23206
$874$	−3.08199	−0.104250
$875$	−7.81995	−0.264363
$876$	0.668742	0.0225947
$877$	40.6638	1.37312	0.686559	−	0.727074i	$-0.259120\pi$
$877$	40.6638	1.37312	0.686559	+	0.727074i	$0.259120\pi$
$878$	−13.7640	−0.464512
$879$	2.65922	0.0896932
$880$	44.6634	1.50560
$881$	−55.4783	−1.86911	−0.934555	−	0.355819i	$-0.884202\pi$
$881$	−55.4783	−1.86911	−0.934555	+	0.355819i	$0.884202\pi$
$882$	−18.2573	−0.614756
$883$	−30.0077	−1.00984	−0.504920	−	0.863166i	$-0.668478\pi$
$883$	−30.0077	−1.00984	−0.504920	+	0.863166i	$0.668478\pi$
$884$	7.91998	0.266378
$885$	−5.08766	−0.171020
$886$	−38.2422	−1.28477
$887$	−6.20304	−0.208278	−0.104139	−	0.994563i	$-0.533209\pi$
$887$	−6.20304	−0.208278	−0.104139	+	0.994563i	$0.533209\pi$
$888$	−1.32321	−0.0444042
$889$	11.6885	0.392020
$890$	−3.49533	−0.117164
$891$	−20.4887	−0.686397
$892$	−5.10117	−0.170800
$893$	−1.04313	−0.0349071
$894$	4.50063	0.150523
$895$	−45.6228	−1.52500
$896$	−22.4286	−0.749288
$897$	15.1190	0.504809
$898$	27.4323	0.915428
$899$	−0.287785	−0.00959817
$900$	−4.50375	−0.150125
$901$	16.1795	0.539018
$902$	42.9849	1.43124
$903$	7.24766	0.241187
$904$	−25.8326	−0.859179
$905$	46.0426	1.53051
$906$	3.20118	0.106352
$907$	33.2208	1.10308	0.551539	−	0.834149i	$-0.314041\pi$
$907$	33.2208	1.10308	0.551539	+	0.834149i	$0.314041\pi$
$908$	−4.14644	−0.137604
$909$	−14.2728	−0.473398
$910$	−38.0393	−1.26099
$911$	36.7503	1.21759	0.608795	−	0.793327i	$-0.291653\pi$
$911$	36.7503	1.21759	0.608795	+	0.793327i	$0.291653\pi$
$912$	−0.964069	−0.0319235
$913$	−7.39064	−0.244594
$914$	−0.0516449	−0.00170826
$915$	9.43428	0.311888
$916$	−0.0172201	−0.000568967 0
$917$	17.8241	0.588603
$918$	15.7226	0.518922
$919$	−56.6323	−1.86813	−0.934064	−	0.357106i	$-0.883763\pi$
$919$	−56.6323	−1.86813	−0.934064	+	0.357106i	$0.883763\pi$
$920$	36.7325	1.21103
$921$	−0.486860	−0.0160426
$922$	19.6973	0.648695
$923$	53.2981	1.75433
$924$	−1.48984	−0.0490120
$925$	−3.35512	−0.110316
$926$	−23.7908	−0.781813
$927$	−38.0221	−1.24881
$928$	−17.1439	−0.562776
$929$	−18.4543	−0.605466	−0.302733	−	0.953075i	$-0.597899\pi$
$929$	−18.4543	−0.605466	−0.302733	+	0.953075i	$0.597899\pi$
$930$	−0.118194	−0.00387573
$931$	−1.56325	−0.0512336
$932$	10.8412	0.355115
$933$	15.7108	0.514350
$934$	−64.0688	−2.09639
$935$	−29.4789	−0.964063
$936$	−32.2900	−1.05543
$937$	−11.4997	−0.375679	−0.187840	−	0.982200i	$-0.560148\pi$
$937$	−11.4997	−0.375679	−0.187840	+	0.982200i	$0.560148\pi$
$938$	31.6449	1.03324
$939$	2.64729	0.0863911
$940$	−4.13542	−0.134882
$941$	24.5941	0.801746	0.400873	−	0.916134i	$-0.368707\pi$
$941$	24.5941	0.801746	0.400873	+	0.916134i	$0.368707\pi$
$942$	6.90740	0.225055
$943$	44.7623	1.45766
$944$	14.9884	0.487830
$945$	−15.0838	−0.490676
$946$	40.6399	1.32132
$947$	10.4555	0.339759	0.169879	−	0.985465i	$-0.445662\pi$
$947$	10.4555	0.339759	0.169879	+	0.985465i	$0.445662\pi$
$948$	3.69944	0.120152
$949$	12.1571	0.394636
$950$	−1.93058	−0.0626362
$951$	11.4670	0.371843
$952$	12.2319	0.396439
$953$	13.7319	0.444820	0.222410	−	0.974953i	$-0.428608\pi$
$953$	13.7319	0.444820	0.222410	+	0.974953i	$0.428608\pi$
$954$	21.9417	0.710390
$955$	−54.1116	−1.75101
$956$	−9.73421	−0.314827
$957$	11.2596	0.363971
$958$	−28.4587	−0.919460
$959$	2.72533	0.0880055
$960$	8.27113	0.266949
$961$	−30.9978	−0.999931
$962$	8.00135	0.257974
$963$	−30.8449	−0.993962
$964$	1.82977	0.0589330
$965$	−40.9797	−1.31918
$966$	−7.76703	−0.249900
$967$	24.6160	0.791598	0.395799	−	0.918337i	$-0.370468\pi$
$967$	24.6160	0.791598	0.395799	+	0.918337i	$0.370468\pi$
$968$	−0.983570	−0.0316131
$969$	0.636308	0.0204412
$970$	61.8633	1.98631
$971$	−41.1162	−1.31948	−0.659740	−	0.751494i	$-0.729334\pi$
$971$	−41.1162	−1.31948	−0.659740	+	0.751494i	$0.729334\pi$
$972$	6.50494	0.208646
$973$	6.97759	0.223691
$974$	31.1118	0.996885
$975$	9.47062	0.303303
$976$	−27.7936	−0.889651
$977$	−40.7518	−1.30376	−0.651882	−	0.758320i	$-0.726020\pi$
$977$	−40.7518	−1.30376	−0.651882	+	0.758320i	$0.726020\pi$
$978$	16.6870	0.533592
$979$	−2.48866	−0.0795379
$980$	−6.19741	−0.197969
$981$	−2.68896	−0.0858519
$982$	−25.1031	−0.801071
$983$	55.3302	1.76476	0.882379	−	0.470538i	$-0.155940\pi$
$983$	55.3302	1.76476	0.882379	+	0.470538i	$0.155940\pi$
$984$	11.0583	0.352527
$985$	−38.6562	−1.23169
$986$	30.7497	0.979271
$987$	−2.62883	−0.0836766
$988$	0.919650	0.0292580
$989$	42.3203	1.34571
$990$	−39.9776	−1.27057
$991$	−6.67602	−0.212071	−0.106035	−	0.994362i	$-0.533816\pi$
$991$	−6.67602	−0.212071	−0.106035	+	0.994362i	$0.533816\pi$
$992$	0.128132	0.00406820
$993$	9.72581	0.308639
$994$	−27.3807	−0.868462
$995$	59.8577	1.89762
$996$	0.632439	0.0200396
$997$	19.7144	0.624362	0.312181	−	0.950023i	$-0.398940\pi$
$997$	19.7144	0.624362	0.312181	+	0.950023i	$0.398940\pi$
$998$	−48.7296	−1.54251
$999$	3.17279	0.100383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.19	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.19	✓	82	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.58089 q^{2} +0.557711 q^{3} +0.499209 q^{4} +2.89052 q^{5} -0.881678 q^{6} +1.64472 q^{7} +2.37258 q^{8} -2.68896 q^{9} +O(q^{10})\)	\(q-1.58089 q^{2} +0.557711 q^{3} +0.499209 q^{4} +2.89052 q^{5} -0.881678 q^{6} +1.64472 q^{7} +2.37258 q^{8} -2.68896 q^{9} -4.56959 q^{10} -3.25353 q^{11} +0.278414 q^{12} +5.06130 q^{13} -2.60012 q^{14} +1.61207 q^{15} -4.74921 q^{16} +3.13459 q^{17} +4.25094 q^{18} +0.363981 q^{19} +1.44297 q^{20} +0.917280 q^{21} +5.14347 q^{22} +5.35614 q^{23} +1.32321 q^{24} +3.35512 q^{25} -8.00135 q^{26} -3.17279 q^{27} +0.821060 q^{28} -6.20526 q^{29} -2.54851 q^{30} +0.0463776 q^{31} +2.76280 q^{32} -1.81453 q^{33} -4.95543 q^{34} +4.75411 q^{35} -1.34235 q^{36} -1.00000 q^{37} -0.575413 q^{38} +2.82274 q^{39} +6.85801 q^{40} +8.35718 q^{41} -1.45012 q^{42} +7.90126 q^{43} -1.62419 q^{44} -7.77250 q^{45} -8.46747 q^{46} -2.86590 q^{47} -2.64868 q^{48} -4.29488 q^{49} -5.30407 q^{50} +1.74819 q^{51} +2.52664 q^{52} +5.16161 q^{53} +5.01583 q^{54} -9.40439 q^{55} +3.90224 q^{56} +0.202996 q^{57} +9.80982 q^{58} -3.15597 q^{59} +0.804762 q^{60} +5.85226 q^{61} -0.0733179 q^{62} -4.42259 q^{63} +5.13073 q^{64} +14.6298 q^{65} +2.86856 q^{66} -12.1705 q^{67} +1.56481 q^{68} +2.98718 q^{69} -7.51572 q^{70} +10.5305 q^{71} -6.37978 q^{72} +2.40197 q^{73} +1.58089 q^{74} +1.87118 q^{75} +0.181702 q^{76} -5.35115 q^{77} -4.46244 q^{78} +13.2876 q^{79} -13.7277 q^{80} +6.29738 q^{81} -13.2118 q^{82} +2.27158 q^{83} +0.457914 q^{84} +9.06059 q^{85} -12.4910 q^{86} -3.46074 q^{87} -7.71927 q^{88} +0.764911 q^{89} +12.2874 q^{90} +8.32444 q^{91} +2.67383 q^{92} +0.0258653 q^{93} +4.53067 q^{94} +1.05209 q^{95} +1.54084 q^{96} -13.5380 q^{97} +6.78973 q^{98} +8.74860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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