LMFDB - Embedded newform 4021.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35347 q^{2} +0.704714 q^{3} +3.53883 q^{4} +3.49583 q^{5} -1.65853 q^{6} +1.05101 q^{7} -3.62159 q^{8} -2.50338 q^{9} +O(q^{10})$	\(q-2.35347 q^{2} +0.704714 q^{3} +3.53883 q^{4} +3.49583 q^{5} -1.65853 q^{6} +1.05101 q^{7} -3.62159 q^{8} -2.50338 q^{9} -8.22733 q^{10} -3.48445 q^{11} +2.49386 q^{12} +5.56850 q^{13} -2.47352 q^{14} +2.46356 q^{15} +1.44566 q^{16} +1.57082 q^{17} +5.89163 q^{18} +5.38439 q^{19} +12.3711 q^{20} +0.740661 q^{21} +8.20056 q^{22} +7.35867 q^{23} -2.55219 q^{24} +7.22081 q^{25} -13.1053 q^{26} -3.87831 q^{27} +3.71934 q^{28} +2.21192 q^{29} -5.79792 q^{30} -4.87773 q^{31} +3.84087 q^{32} -2.45554 q^{33} -3.69687 q^{34} +3.67414 q^{35} -8.85903 q^{36} -4.51020 q^{37} -12.6720 q^{38} +3.92420 q^{39} -12.6605 q^{40} +3.65600 q^{41} -1.74312 q^{42} +2.60372 q^{43} -12.3309 q^{44} -8.75138 q^{45} -17.3184 q^{46} +9.92507 q^{47} +1.01878 q^{48} -5.89538 q^{49} -16.9940 q^{50} +1.10698 q^{51} +19.7060 q^{52} -3.45867 q^{53} +9.12749 q^{54} -12.1810 q^{55} -3.80633 q^{56} +3.79445 q^{57} -5.20569 q^{58} +2.43101 q^{59} +8.71812 q^{60} -8.65176 q^{61} +11.4796 q^{62} -2.63107 q^{63} -11.9307 q^{64} +19.4665 q^{65} +5.77905 q^{66} +0.976185 q^{67} +5.55885 q^{68} +5.18576 q^{69} -8.64700 q^{70} -13.5107 q^{71} +9.06622 q^{72} +8.57710 q^{73} +10.6146 q^{74} +5.08861 q^{75} +19.0544 q^{76} -3.66219 q^{77} -9.23549 q^{78} -3.62742 q^{79} +5.05378 q^{80} +4.77703 q^{81} -8.60431 q^{82} +16.3546 q^{83} +2.62107 q^{84} +5.49130 q^{85} -6.12777 q^{86} +1.55877 q^{87} +12.6193 q^{88} +0.671884 q^{89} +20.5961 q^{90} +5.85254 q^{91} +26.0411 q^{92} -3.43740 q^{93} -23.3584 q^{94} +18.8229 q^{95} +2.70671 q^{96} +10.1893 q^{97} +13.8746 q^{98} +8.72290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.35347	−1.66416	−0.832078	−	0.554659i	$-0.812849\pi$
$2$	−2.35347	−1.66416	−0.832078	+	0.554659i	$0.812849\pi$
$3$	0.704714	0.406867	0.203434	−	0.979089i	$-0.434790\pi$
$3$	0.704714	0.406867	0.203434	+	0.979089i	$0.434790\pi$
$4$	3.53883	1.76942
$5$	3.49583	1.56338	0.781691	−	0.623666i	$-0.214358\pi$
$5$	3.49583	1.56338	0.781691	+	0.623666i	$0.214358\pi$
$6$	−1.65853	−0.677090
$7$	1.05101	0.397244	0.198622	−	0.980076i	$-0.436353\pi$
$7$	1.05101	0.397244	0.198622	+	0.980076i	$0.436353\pi$
$8$	−3.62159	−1.28043
$9$	−2.50338	−0.834459
$10$	−8.22733	−2.60171
$11$	−3.48445	−1.05060	−0.525301	−	0.850916i	$-0.676047\pi$
$11$	−3.48445	−1.05060	−0.525301	+	0.850916i	$0.676047\pi$
$12$	2.49386	0.719917
$13$	5.56850	1.54442	0.772211	−	0.635366i	$-0.219151\pi$
$13$	5.56850	1.54442	0.772211	+	0.635366i	$0.219151\pi$
$14$	−2.47352	−0.661076
$15$	2.46356	0.636088
$16$	1.44566	0.361415
$17$	1.57082	0.380979	0.190489	−	0.981689i	$-0.438993\pi$
$17$	1.57082	0.380979	0.190489	+	0.981689i	$0.438993\pi$
$18$	5.89163	1.38867
$19$	5.38439	1.23526	0.617631	−	0.786468i	$-0.288092\pi$
$19$	5.38439	1.23526	0.617631	+	0.786468i	$0.288092\pi$
$20$	12.3711	2.76627
$21$	0.740661	0.161625
$22$	8.20056	1.74837
$23$	7.35867	1.53439	0.767194	−	0.641415i	$-0.221652\pi$
$23$	7.35867	1.53439	0.767194	+	0.641415i	$0.221652\pi$
$24$	−2.55219	−0.520964
$25$	7.22081	1.44416
$26$	−13.1053	−2.57016
$27$	−3.87831	−0.746381
$28$	3.71934	0.702889
$29$	2.21192	0.410743	0.205372	−	0.978684i	$-0.434160\pi$
$29$	2.21192	0.410743	0.205372	+	0.978684i	$0.434160\pi$
$30$	−5.79792	−1.05855
$31$	−4.87773	−0.876066	−0.438033	−	0.898959i	$-0.644325\pi$
$31$	−4.87773	−0.876066	−0.438033	+	0.898959i	$0.644325\pi$
$32$	3.84087	0.678976
$33$	−2.45554	−0.427455
$34$	−3.69687	−0.634008
$35$	3.67414	0.621044
$36$	−8.85903	−1.47650
$37$	−4.51020	−0.741473	−0.370736	−	0.928738i	$-0.620895\pi$
$37$	−4.51020	−0.741473	−0.370736	+	0.928738i	$0.620895\pi$
$38$	−12.6720	−2.05567
$39$	3.92420	0.628375
$40$	−12.6605	−2.00180
$41$	3.65600	0.570972	0.285486	−	0.958383i	$-0.407845\pi$
$41$	3.65600	0.570972	0.285486	+	0.958383i	$0.407845\pi$
$42$	−1.74312	−0.268970
$43$	2.60372	0.397063	0.198532	−	0.980094i	$-0.436383\pi$
$43$	2.60372	0.397063	0.198532	+	0.980094i	$0.436383\pi$
$44$	−12.3309	−1.85895
$45$	−8.75138	−1.30458
$46$	−17.3184	−2.55346
$47$	9.92507	1.44772	0.723860	−	0.689947i	$-0.242366\pi$
$47$	9.92507	1.44772	0.723860	+	0.689947i	$0.242366\pi$
$48$	1.01878	0.147048
$49$	−5.89538	−0.842197
$50$	−16.9940	−2.40331
$51$	1.10698	0.155008
$52$	19.7060	2.73273
$53$	−3.45867	−0.475085	−0.237543	−	0.971377i	$-0.576342\pi$
$53$	−3.45867	−0.475085	−0.237543	+	0.971377i	$0.576342\pi$
$54$	9.12749	1.24209
$55$	−12.1810	−1.64249
$56$	−3.80633	−0.508642
$57$	3.79445	0.502588
$58$	−5.20569	−0.683540
$59$	2.43101	0.316490	0.158245	−	0.987400i	$-0.449416\pi$
$59$	2.43101	0.316490	0.158245	+	0.987400i	$0.449416\pi$
$60$	8.71812	1.12550
$61$	−8.65176	−1.10774	−0.553872	−	0.832602i	$-0.686850\pi$
$61$	−8.65176	−1.10774	−0.553872	+	0.832602i	$0.686850\pi$
$62$	11.4796	1.45791
$63$	−2.63107	−0.331484
$64$	−11.9307	−1.49134
$65$	19.4665	2.41452
$66$	5.77905	0.711352
$67$	0.976185	0.119260	0.0596300	−	0.998221i	$-0.481008\pi$
$67$	0.976185	0.119260	0.0596300	+	0.998221i	$0.481008\pi$
$68$	5.55885	0.674110
$69$	5.18576	0.624292
$70$	−8.64700	−1.03351
$71$	−13.5107	−1.60343	−0.801714	−	0.597708i	$-0.796078\pi$
$71$	−13.5107	−1.60343	−0.801714	+	0.597708i	$0.796078\pi$
$72$	9.06622	1.06846
$73$	8.57710	1.00387	0.501937	−	0.864904i	$-0.332621\pi$
$73$	8.57710	1.00387	0.501937	+	0.864904i	$0.332621\pi$
$74$	10.6146	1.23393
$75$	5.08861	0.587582
$76$	19.0544	2.18569
$77$	−3.66219	−0.417345
$78$	−9.23549	−1.04571
$79$	−3.62742	−0.408117	−0.204058	−	0.978959i	$-0.565413\pi$
$79$	−3.62742	−0.408117	−0.204058	+	0.978959i	$0.565413\pi$
$80$	5.05378	0.565030
$81$	4.77703	0.530781
$82$	−8.60431	−0.950187
$83$	16.3546	1.79515	0.897577	−	0.440858i	$-0.145326\pi$
$83$	16.3546	1.79515	0.897577	+	0.440858i	$0.145326\pi$
$84$	2.62107	0.285982
$85$	5.49130	0.595615
$86$	−6.12777	−0.660775
$87$	1.55877	0.167118
$88$	12.6193	1.34522
$89$	0.671884	0.0712195	0.0356098	−	0.999366i	$-0.488663\pi$
$89$	0.671884	0.0712195	0.0356098	+	0.999366i	$0.488663\pi$
$90$	20.5961	2.17102
$91$	5.85254	0.613512
$92$	26.0411	2.71497
$93$	−3.43740	−0.356442
$94$	−23.3584	−2.40923
$95$	18.8229	1.93119
$96$	2.70671	0.276253
$97$	10.1893	1.03456	0.517282	−	0.855815i	$-0.326944\pi$
$97$	10.1893	1.03456	0.517282	+	0.855815i	$0.326944\pi$
$98$	13.8746	1.40155
$99$	8.72290	0.876685
$100$	25.5532	2.55532
$101$	−11.2209	−1.11652	−0.558260	−	0.829666i	$-0.688531\pi$
$101$	−11.2209	−1.11652	−0.558260	+	0.829666i	$0.688531\pi$
$102$	−2.60524	−0.257957
$103$	−13.6652	−1.34648	−0.673238	−	0.739426i	$-0.735097\pi$
$103$	−13.6652	−1.34648	−0.673238	+	0.739426i	$0.735097\pi$
$104$	−20.1668	−1.97752
$105$	2.58922	0.252682
$106$	8.13989	0.790616
$107$	18.3710	1.77599	0.887995	−	0.459853i	$-0.152098\pi$
$107$	18.3710	1.77599	0.887995	+	0.459853i	$0.152098\pi$
$108$	−13.7247	−1.32066
$109$	8.52356	0.816409	0.408205	−	0.912890i	$-0.366155\pi$
$109$	8.52356	0.816409	0.408205	+	0.912890i	$0.366155\pi$
$110$	28.6678	2.73336
$111$	−3.17840	−0.301681
$112$	1.51940	0.143570
$113$	−2.10357	−0.197887	−0.0989434	−	0.995093i	$-0.531546\pi$
$113$	−2.10357	−0.197887	−0.0989434	+	0.995093i	$0.531546\pi$
$114$	−8.93014	−0.836384
$115$	25.7246	2.39883
$116$	7.82761	0.726775
$117$	−13.9400	−1.28876
$118$	−5.72131	−0.526689
$119$	1.65094	0.151342
$120$	−8.92201	−0.814465
$121$	1.14141	0.103765
$122$	20.3617	1.84346
$123$	2.57644	0.232310
$124$	−17.2614	−1.55012
$125$	7.76356	0.694394
$126$	6.19215	0.551641
$127$	11.0572	0.981169	0.490584	−	0.871394i	$-0.336783\pi$
$127$	11.0572	0.981169	0.490584	+	0.871394i	$0.336783\pi$
$128$	20.3968	1.80284
$129$	1.83488	0.161552
$130$	−45.8139	−4.01814
$131$	3.15170	0.275365	0.137683	−	0.990476i	$-0.456035\pi$
$131$	3.15170	0.275365	0.137683	+	0.990476i	$0.456035\pi$
$132$	−8.68975	−0.756346
$133$	5.65903	0.490701
$134$	−2.29742	−0.198467
$135$	−13.5579	−1.16688
$136$	−5.68886	−0.487816
$137$	13.6443	1.16571	0.582855	−	0.812576i	$-0.301936\pi$
$137$	13.6443	1.16571	0.582855	+	0.812576i	$0.301936\pi$
$138$	−12.2045	−1.03892
$139$	−12.7572	−1.08205	−0.541025	−	0.841007i	$-0.681963\pi$
$139$	−12.7572	−1.08205	−0.541025	+	0.841007i	$0.681963\pi$
$140$	13.0022	1.09888
$141$	6.99434	0.589030
$142$	31.7971	2.66835
$143$	−19.4032	−1.62257
$144$	−3.61903	−0.301586
$145$	7.73249	0.642148
$146$	−20.1860	−1.67060
$147$	−4.15456	−0.342662
$148$	−15.9608	−1.31197
$149$	−7.36261	−0.603169	−0.301584	−	0.953439i	$-0.597515\pi$
$149$	−7.36261	−0.603169	−0.301584	+	0.953439i	$0.597515\pi$
$150$	−11.9759	−0.977828
$151$	−14.1139	−1.14857	−0.574287	−	0.818654i	$-0.694721\pi$
$151$	−14.1139	−1.14857	−0.574287	+	0.818654i	$0.694721\pi$
$152$	−19.5001	−1.58166
$153$	−3.93235	−0.317911
$154$	8.61886	0.694528
$155$	−17.0517	−1.36962
$156$	13.8871	1.11186
$157$	−7.38444	−0.589342	−0.294671	−	0.955599i	$-0.595210\pi$
$157$	−7.38444	−0.589342	−0.294671	+	0.955599i	$0.595210\pi$
$158$	8.53703	0.679170
$159$	−2.43738	−0.193296
$160$	13.4270	1.06150
$161$	7.73402	0.609526
$162$	−11.2426	−0.883303
$163$	−5.95384	−0.466341	−0.233170	−	0.972436i	$-0.574910\pi$
$163$	−5.95384	−0.466341	−0.233170	+	0.972436i	$0.574910\pi$
$164$	12.9380	1.01029
$165$	−8.58416	−0.668276
$166$	−38.4902	−2.98742
$167$	−9.25145	−0.715899	−0.357949	−	0.933741i	$-0.616524\pi$
$167$	−9.25145	−0.715899	−0.357949	+	0.933741i	$0.616524\pi$
$168$	−2.68237	−0.206950
$169$	18.0081	1.38524
$170$	−12.9236	−0.991197
$171$	−13.4791	−1.03078
$172$	9.21411	0.702570
$173$	−14.8473	−1.12882	−0.564409	−	0.825495i	$-0.690896\pi$
$173$	−14.8473	−1.12882	−0.564409	+	0.825495i	$0.690896\pi$
$174$	−3.66852	−0.278110
$175$	7.58913	0.573684
$176$	−5.03734	−0.379703
$177$	1.71317	0.128770
$178$	−1.58126	−0.118520
$179$	5.50115	0.411175	0.205587	−	0.978639i	$-0.434089\pi$
$179$	5.50115	0.411175	0.205587	+	0.978639i	$0.434089\pi$
$180$	−30.9696	−2.30834
$181$	9.08666	0.675406	0.337703	−	0.941253i	$-0.390350\pi$
$181$	9.08666	0.675406	0.337703	+	0.941253i	$0.390350\pi$
$182$	−13.7738	−1.02098
$183$	−6.09702	−0.450705
$184$	−26.6501	−1.96467
$185$	−15.7669	−1.15920
$186$	8.08983	0.593175
$187$	−5.47344	−0.400257
$188$	35.1231	2.56162
$189$	−4.07614	−0.296495
$190$	−44.2991	−3.21380
$191$	19.1861	1.38826	0.694128	−	0.719852i	$-0.255790\pi$
$191$	19.1861	1.38826	0.694128	+	0.719852i	$0.255790\pi$
$192$	−8.40773	−0.606776
$193$	−4.19617	−0.302047	−0.151023	−	0.988530i	$-0.548257\pi$
$193$	−4.19617	−0.302047	−0.151023	+	0.988530i	$0.548257\pi$
$194$	−23.9802	−1.72168
$195$	13.7183	0.982389
$196$	−20.8628	−1.49020
$197$	11.6701	0.831462	0.415731	−	0.909488i	$-0.363526\pi$
$197$	11.6701	0.831462	0.415731	+	0.909488i	$0.363526\pi$
$198$	−20.5291	−1.45894
$199$	10.0438	0.711988	0.355994	−	0.934488i	$-0.384142\pi$
$199$	10.0438	0.711988	0.355994	+	0.934488i	$0.384142\pi$
$200$	−26.1508	−1.84914
$201$	0.687932	0.0485230
$202$	26.4081	1.85806
$203$	2.32475	0.163165
$204$	3.91740	0.274273
$205$	12.7808	0.892647
$206$	32.1608	2.24075
$207$	−18.4215	−1.28038
$208$	8.05015	0.558178
$209$	−18.7616	−1.29777
$210$	−6.09366	−0.420503
$211$	8.27593	0.569739	0.284869	−	0.958566i	$-0.408050\pi$
$211$	8.27593	0.569739	0.284869	+	0.958566i	$0.408050\pi$
$212$	−12.2397	−0.840623
$213$	−9.52120	−0.652382
$214$	−43.2356	−2.95552
$215$	9.10214	0.620761
$216$	14.0457	0.955686
$217$	−5.12653	−0.348012
$218$	−20.0600	−1.35863
$219$	6.04441	0.408443
$220$	−43.1067	−2.90625
$221$	8.74708	0.588392
$222$	7.48028	0.502044
$223$	22.4390	1.50263	0.751314	−	0.659944i	$-0.229420\pi$
$223$	22.4390	1.50263	0.751314	+	0.659944i	$0.229420\pi$
$224$	4.03678	0.269719
$225$	−18.0764	−1.20509
$226$	4.95068	0.329314
$227$	−11.6627	−0.774082	−0.387041	−	0.922062i	$-0.626503\pi$
$227$	−11.6627	−0.774082	−0.387041	+	0.922062i	$0.626503\pi$
$228$	13.4279	0.889286
$229$	4.18602	0.276620	0.138310	−	0.990389i	$-0.455833\pi$
$229$	4.18602	0.276620	0.138310	+	0.990389i	$0.455833\pi$
$230$	−60.5422	−3.99203
$231$	−2.58080	−0.169804
$232$	−8.01067	−0.525926
$233$	−16.2218	−1.06273	−0.531363	−	0.847144i	$-0.678320\pi$
$233$	−16.2218	−1.06273	−0.531363	+	0.847144i	$0.678320\pi$
$234$	32.8075	2.14469
$235$	34.6963	2.26334
$236$	8.60293	0.560003
$237$	−2.55630	−0.166049
$238$	−3.88544	−0.251856
$239$	−0.248580	−0.0160793	−0.00803967	−	0.999968i	$-0.502559\pi$
$239$	−0.248580	−0.0160793	−0.00803967	+	0.999968i	$0.502559\pi$
$240$	3.56147	0.229892
$241$	−6.94897	−0.447622	−0.223811	−	0.974633i	$-0.571850\pi$
$241$	−6.94897	−0.447622	−0.223811	+	0.974633i	$0.571850\pi$
$242$	−2.68628	−0.172681
$243$	15.0014	0.962338
$244$	−30.6171	−1.96006
$245$	−20.6092	−1.31668
$246$	−6.06358	−0.386600
$247$	29.9829	1.90777
$248$	17.6651	1.12174
$249$	11.5253	0.730389
$250$	−18.2713	−1.15558
$251$	29.5057	1.86239	0.931193	−	0.364527i	$-0.118769\pi$
$251$	29.5057	1.86239	0.931193	+	0.364527i	$0.118769\pi$
$252$	−9.31092	−0.586533
$253$	−25.6409	−1.61203
$254$	−26.0228	−1.63282
$255$	3.86980	0.242336
$256$	−24.1420	−1.50887
$257$	−4.81047	−0.300069	−0.150034	−	0.988681i	$-0.547938\pi$
$257$	−4.81047	−0.300069	−0.150034	+	0.988681i	$0.547938\pi$
$258$	−4.31833	−0.268848
$259$	−4.74026	−0.294545
$260$	68.8886	4.27229
$261$	−5.53727	−0.342748
$262$	−7.41744	−0.458251
$263$	20.4039	1.25816	0.629078	−	0.777342i	$-0.283432\pi$
$263$	20.4039	1.25816	0.629078	+	0.777342i	$0.283432\pi$
$264$	8.89298	0.547325
$265$	−12.0909	−0.742739
$266$	−13.3184	−0.816602
$267$	0.473486	0.0289769
$268$	3.45455	0.211020
$269$	−3.31240	−0.201961	−0.100980	−	0.994888i	$-0.532198\pi$
$269$	−3.31240	−0.201961	−0.100980	+	0.994888i	$0.532198\pi$
$270$	31.9081	1.94187
$271$	−31.3702	−1.90561	−0.952803	−	0.303588i	$-0.901815\pi$
$271$	−31.3702	−1.90561	−0.952803	+	0.303588i	$0.901815\pi$
$272$	2.27087	0.137692
$273$	4.12437	0.249618
$274$	−32.1114	−1.93992
$275$	−25.1606	−1.51724
$276$	18.3515	1.10463
$277$	−4.52853	−0.272093	−0.136047	−	0.990702i	$-0.543440\pi$
$277$	−4.52853	−0.272093	−0.136047	+	0.990702i	$0.543440\pi$
$278$	30.0236	1.80070
$279$	12.2108	0.731041
$280$	−13.3063	−0.795201
$281$	2.50191	0.149252	0.0746258	−	0.997212i	$-0.476224\pi$
$281$	2.50191	0.149252	0.0746258	+	0.997212i	$0.476224\pi$
$282$	−16.4610	−0.980237
$283$	18.1605	1.07953	0.539764	−	0.841817i	$-0.318514\pi$
$283$	18.1605	1.07953	0.539764	+	0.841817i	$0.318514\pi$
$284$	−47.8121	−2.83713
$285$	13.2648	0.785736
$286$	45.6648	2.70022
$287$	3.84249	0.226815
$288$	−9.61514	−0.566578
$289$	−14.5325	−0.854855
$290$	−18.1982	−1.06863
$291$	7.18053	0.420930
$292$	30.3529	1.77627
$293$	−11.5356	−0.673916	−0.336958	−	0.941520i	$-0.609398\pi$
$293$	−11.5356	−0.673916	−0.336958	+	0.941520i	$0.609398\pi$
$294$	9.77764	0.570244
$295$	8.49839	0.494795
$296$	16.3341	0.949402
$297$	13.5138	0.784149
$298$	17.3277	1.00377
$299$	40.9767	2.36974
$300$	18.0077	1.03968
$301$	2.73653	0.157731
$302$	33.2167	1.91141
$303$	−7.90752	−0.454275
$304$	7.78399	0.446443
$305$	−30.2451	−1.73183
$306$	9.25467	0.529054
$307$	−17.9984	−1.02722	−0.513612	−	0.858023i	$-0.671693\pi$
$307$	−17.9984	−1.02722	−0.513612	+	0.858023i	$0.671693\pi$
$308$	−12.9599	−0.738457
$309$	−9.63009	−0.547837
$310$	40.1307	2.27927
$311$	−7.33807	−0.416104	−0.208052	−	0.978118i	$-0.566712\pi$
$311$	−7.33807	−0.416104	−0.208052	+	0.978118i	$0.566712\pi$
$312$	−14.2119	−0.804588
$313$	−14.8835	−0.841265	−0.420633	−	0.907231i	$-0.638192\pi$
$313$	−14.8835	−0.841265	−0.420633	+	0.907231i	$0.638192\pi$
$314$	17.3791	0.980757
$315$	−9.19777	−0.518236
$316$	−12.8368	−0.722128
$317$	19.6609	1.10426	0.552132	−	0.833757i	$-0.313814\pi$
$317$	19.6609	1.10426	0.552132	+	0.833757i	$0.313814\pi$
$318$	5.73629	0.321675
$319$	−7.70733	−0.431527
$320$	−41.7077	−2.33153
$321$	12.9463	0.722592
$322$	−18.2018	−1.01435
$323$	8.45788	0.470609
$324$	16.9051	0.939173
$325$	40.2090	2.23040
$326$	14.0122	0.776064
$327$	6.00668	0.332170
$328$	−13.2406	−0.731088
$329$	10.4313	0.575098
$330$	20.2026	1.11212
$331$	10.9780	0.603406	0.301703	−	0.953402i	$-0.402445\pi$
$331$	10.9780	0.603406	0.301703	+	0.953402i	$0.402445\pi$
$332$	57.8763	3.17637
$333$	11.2907	0.618729
$334$	21.7730	1.19137
$335$	3.41258	0.186449
$336$	1.07074	0.0584139
$337$	8.64535	0.470942	0.235471	−	0.971881i	$-0.424337\pi$
$337$	8.64535	0.470942	0.235471	+	0.971881i	$0.424337\pi$
$338$	−42.3817	−2.30526
$339$	−1.48241	−0.0805136
$340$	19.4328	1.05389
$341$	16.9962	0.920396
$342$	31.7228	1.71537
$343$	−13.5532	−0.731802
$344$	−9.42961	−0.508410
$345$	18.1285	0.976007
$346$	34.9427	1.87853
$347$	6.62318	0.355551	0.177775	−	0.984071i	$-0.443110\pi$
$347$	6.62318	0.355551	0.177775	+	0.984071i	$0.443110\pi$
$348$	5.51623	0.295701
$349$	10.0278	0.536778	0.268389	−	0.963311i	$-0.413509\pi$
$349$	10.0278	0.536778	0.268389	+	0.963311i	$0.413509\pi$
$350$	−17.8608	−0.954700
$351$	−21.5963	−1.15273
$352$	−13.3833	−0.713334
$353$	21.3389	1.13575	0.567877	−	0.823113i	$-0.307765\pi$
$353$	21.3389	1.13575	0.567877	+	0.823113i	$0.307765\pi$
$354$	−4.03189	−0.214293
$355$	−47.2311	−2.50677
$356$	2.37768	0.126017
$357$	1.16344	0.0615759
$358$	−12.9468	−0.684259
$359$	18.1944	0.960266	0.480133	−	0.877196i	$-0.340588\pi$
$359$	18.1944	0.960266	0.480133	+	0.877196i	$0.340588\pi$
$360$	31.6939	1.67042
$361$	9.99160	0.525874
$362$	−21.3852	−1.12398
$363$	0.804370	0.0422185
$364$	20.7111	1.08556
$365$	29.9841	1.56944
$366$	14.3492	0.750043
$367$	−12.7563	−0.665871	−0.332936	−	0.942950i	$-0.608039\pi$
$367$	−12.7563	−0.665871	−0.332936	+	0.942950i	$0.608039\pi$
$368$	10.6381	0.554551
$369$	−9.15236	−0.476453
$370$	37.1069	1.92910
$371$	−3.63509	−0.188725
$372$	−12.1644	−0.630694
$373$	6.14711	0.318285	0.159143	−	0.987256i	$-0.449127\pi$
$373$	6.14711	0.318285	0.159143	+	0.987256i	$0.449127\pi$
$374$	12.8816	0.666090
$375$	5.47109	0.282526
$376$	−35.9446	−1.85370
$377$	12.3171	0.634361
$378$	9.59307	0.493414
$379$	21.7625	1.11786	0.558932	−	0.829213i	$-0.311211\pi$
$379$	21.7625	1.11786	0.558932	+	0.829213i	$0.311211\pi$
$380$	66.6110	3.41707
$381$	7.79217	0.399205
$382$	−45.1539	−2.31027
$383$	3.53478	0.180619	0.0903095	−	0.995914i	$-0.471214\pi$
$383$	3.53478	0.180619	0.0903095	+	0.995914i	$0.471214\pi$
$384$	14.3739	0.733517
$385$	−12.8024	−0.652470
$386$	9.87556	0.502653
$387$	−6.51809	−0.331333
$388$	36.0581	1.83057
$389$	−19.6041	−0.993965	−0.496982	−	0.867761i	$-0.665559\pi$
$389$	−19.6041	−0.993965	−0.496982	+	0.867761i	$0.665559\pi$
$390$	−32.2857	−1.63485
$391$	11.5591	0.584570
$392$	21.3507	1.07837
$393$	2.22105	0.112037
$394$	−27.4653	−1.38368
$395$	−12.6808	−0.638042
$396$	30.8689	1.55122
$397$	6.45079	0.323756	0.161878	−	0.986811i	$-0.448245\pi$
$397$	6.45079	0.323756	0.161878	+	0.986811i	$0.448245\pi$
$398$	−23.6379	−1.18486
$399$	3.98800	0.199650
$400$	10.4388	0.521942
$401$	−25.1461	−1.25574	−0.627868	−	0.778320i	$-0.716072\pi$
$401$	−25.1461	−1.25574	−0.627868	+	0.778320i	$0.716072\pi$
$402$	−1.61903	−0.0807498
$403$	−27.1616	−1.35302
$404$	−39.7088	−1.97559
$405$	16.6997	0.829814
$406$	−5.47122	−0.271532
$407$	15.7156	0.778993
$408$	−4.00902	−0.198476
$409$	−13.2231	−0.653840	−0.326920	−	0.945052i	$-0.606011\pi$
$409$	−13.2231	−0.653840	−0.326920	+	0.945052i	$0.606011\pi$
$410$	−30.0792	−1.48550
$411$	9.61532	0.474289
$412$	−48.3590	−2.38248
$413$	2.55501	0.125724
$414$	43.3545	2.13076
$415$	57.1730	2.80651
$416$	21.3879	1.04863
$417$	−8.99016	−0.440250
$418$	44.1550	2.15969
$419$	−14.9890	−0.732261	−0.366130	−	0.930564i	$-0.619318\pi$
$419$	−14.9890	−0.732261	−0.366130	+	0.930564i	$0.619318\pi$
$420$	9.16282	0.447100
$421$	−9.14429	−0.445666	−0.222833	−	0.974857i	$-0.571530\pi$
$421$	−9.14429	−0.445666	−0.222833	+	0.974857i	$0.571530\pi$
$422$	−19.4772	−0.948134
$423$	−24.8462	−1.20806
$424$	12.5259	0.608312
$425$	11.3426	0.550195
$426$	22.4079	1.08566
$427$	−9.09307	−0.440045
$428$	65.0118	3.14246
$429$	−13.6737	−0.660172
$430$	−21.4216	−1.03304
$431$	1.51677	0.0730604	0.0365302	−	0.999333i	$-0.488369\pi$
$431$	1.51677	0.0730604	0.0365302	+	0.999333i	$0.488369\pi$
$432$	−5.60672	−0.269753
$433$	11.8877	0.571286	0.285643	−	0.958336i	$-0.407793\pi$
$433$	11.8877	0.571286	0.285643	+	0.958336i	$0.407793\pi$
$434$	12.0652	0.579146
$435$	5.44919	0.261269
$436$	30.1634	1.44457
$437$	39.6219	1.89537
$438$	−14.2253	−0.679713
$439$	4.79845	0.229018	0.114509	−	0.993422i	$-0.463471\pi$
$439$	4.79845	0.229018	0.114509	+	0.993422i	$0.463471\pi$
$440$	44.1148	2.10309
$441$	14.7584	0.702779
$442$	−20.5860	−0.979177
$443$	−8.26743	−0.392798	−0.196399	−	0.980524i	$-0.562925\pi$
$443$	−8.26743	−0.392798	−0.196399	+	0.980524i	$0.562925\pi$
$444$	−11.2478	−0.533799
$445$	2.34879	0.111343
$446$	−52.8096	−2.50061
$447$	−5.18854	−0.245409
$448$	−12.5393	−0.592424
$449$	21.5603	1.01749	0.508746	−	0.860916i	$-0.330109\pi$
$449$	21.5603	1.01749	0.508746	+	0.860916i	$0.330109\pi$
$450$	42.5423	2.00546
$451$	−12.7392	−0.599864
$452$	−7.44416	−0.350144
$453$	−9.94628	−0.467317
$454$	27.4479	1.28819
$455$	20.4595	0.959154
$456$	−13.7420	−0.643527
$457$	7.09217	0.331758	0.165879	−	0.986146i	$-0.446954\pi$
$457$	7.09217	0.331758	0.165879	+	0.986146i	$0.446954\pi$
$458$	−9.85169	−0.460339
$459$	−6.09211	−0.284355
$460$	91.0351	4.24453
$461$	−24.3643	−1.13476	−0.567379	−	0.823457i	$-0.692042\pi$
$461$	−24.3643	−1.13476	−0.567379	+	0.823457i	$0.692042\pi$
$462$	6.07383	0.282580
$463$	−30.5490	−1.41973	−0.709866	−	0.704336i	$-0.751245\pi$
$463$	−30.5490	−1.41973	−0.709866	+	0.704336i	$0.751245\pi$
$464$	3.19768	0.148449
$465$	−12.0166	−0.557255
$466$	38.1776	1.76854
$467$	−8.46126	−0.391540	−0.195770	−	0.980650i	$-0.562721\pi$
$467$	−8.46126	−0.391540	−0.195770	+	0.980650i	$0.562721\pi$
$468$	−49.3315	−2.28035
$469$	1.02598	0.0473753
$470$	−81.6569	−3.76655
$471$	−5.20392	−0.239784
$472$	−8.80413	−0.405243
$473$	−9.07253	−0.417155
$474$	6.01617	0.276332
$475$	38.8796	1.78392
$476$	5.84240	0.267786
$477$	8.65836	0.396439
$478$	0.585027	0.0267585
$479$	15.4135	0.704259	0.352130	−	0.935951i	$-0.385458\pi$
$479$	15.4135	0.704259	0.352130	+	0.935951i	$0.385458\pi$
$480$	9.46221	0.431889
$481$	−25.1150	−1.14515
$482$	16.3542	0.744914
$483$	5.45028	0.247996
$484$	4.03927	0.183603
$485$	35.6200	1.61742
$486$	−35.3053	−1.60148
$487$	28.4692	1.29006	0.645031	−	0.764156i	$-0.276844\pi$
$487$	28.4692	1.29006	0.645031	+	0.764156i	$0.276844\pi$
$488$	31.3332	1.41839
$489$	−4.19576	−0.189739
$490$	48.5033	2.19115
$491$	43.7068	1.97246	0.986230	−	0.165379i	$-0.0528847\pi$
$491$	43.7068	1.97246	0.986230	+	0.165379i	$0.0528847\pi$
$492$	9.11758	0.411052
$493$	3.47452	0.156484
$494$	−70.5640	−3.17482
$495$	30.4938	1.37059
$496$	−7.05154	−0.316623
$497$	−14.1999	−0.636952
$498$	−27.1246	−1.21548
$499$	−17.5259	−0.784569	−0.392284	−	0.919844i	$-0.628315\pi$
$499$	−17.5259	−0.784569	−0.392284	+	0.919844i	$0.628315\pi$
$500$	27.4739	1.22867
$501$	−6.51963	−0.291276
$502$	−69.4409	−3.09930
$503$	39.1792	1.74691	0.873457	−	0.486902i	$-0.161873\pi$
$503$	39.1792	1.74691	0.873457	+	0.486902i	$0.161873\pi$
$504$	9.52867	0.424441
$505$	−39.2263	−1.74555
$506$	60.3452	2.68267
$507$	12.6906	0.563609
$508$	39.1296	1.73609
$509$	−30.8851	−1.36896	−0.684478	−	0.729033i	$-0.739970\pi$
$509$	−30.8851	−1.36896	−0.684478	+	0.729033i	$0.739970\pi$
$510$	−9.10746	−0.403285
$511$	9.01461	0.398783
$512$	16.0238	0.708158
$513$	−20.8823	−0.921977
$514$	11.3213	0.499361
$515$	−47.7713	−2.10506
$516$	6.49332	0.285852
$517$	−34.5834	−1.52098
$518$	11.1561	0.490170
$519$	−10.4631	−0.459279
$520$	−70.4998	−3.09162
$521$	−21.3878	−0.937018	−0.468509	−	0.883459i	$-0.655209\pi$
$521$	−21.3878	−0.937018	−0.468509	+	0.883459i	$0.655209\pi$
$522$	13.0318	0.570387
$523$	−12.6451	−0.552931	−0.276466	−	0.961024i	$-0.589163\pi$
$523$	−12.6451	−0.552931	−0.276466	+	0.961024i	$0.589163\pi$
$524$	11.1533	0.487235
$525$	5.34817	0.233413
$526$	−48.0200	−2.09377
$527$	−7.66201	−0.333762
$528$	−3.54988	−0.154489
$529$	31.1500	1.35435
$530$	28.4556	1.23603
$531$	−6.08573	−0.264098
$532$	20.0264	0.868253
$533$	20.3584	0.881822
$534$	−1.11434	−0.0482221
$535$	64.2218	2.77655
$536$	−3.53535	−0.152704
$537$	3.87674	0.167294
$538$	7.79564	0.336094
$539$	20.5422	0.884814
$540$	−47.9791	−2.06469
$541$	2.80201	0.120468	0.0602340	−	0.998184i	$-0.480815\pi$
$541$	2.80201	0.120468	0.0602340	+	0.998184i	$0.480815\pi$
$542$	73.8290	3.17123
$543$	6.40350	0.274800
$544$	6.03330	0.258675
$545$	29.7969	1.27636
$546$	−9.70658	−0.415403
$547$	−7.22615	−0.308968	−0.154484	−	0.987995i	$-0.549372\pi$
$547$	−7.22615	−0.308968	−0.154484	+	0.987995i	$0.549372\pi$
$548$	48.2848	2.06262
$549$	21.6586	0.924368
$550$	59.2147	2.52492
$551$	11.9098	0.507376
$552$	−18.7807	−0.799360
$553$	−3.81245	−0.162122
$554$	10.6578	0.452806
$555$	−11.1112	−0.471642
$556$	−45.1455	−1.91459
$557$	8.52188	0.361084	0.180542	−	0.983567i	$-0.442215\pi$
$557$	8.52188	0.361084	0.180542	+	0.983567i	$0.442215\pi$
$558$	−28.7378	−1.21657
$559$	14.4988	0.613233
$560$	5.31157	0.224455
$561$	−3.85721	−0.162851
$562$	−5.88818	−0.248378
$563$	6.09790	0.256996	0.128498	−	0.991710i	$-0.458984\pi$
$563$	6.09790	0.256996	0.128498	+	0.991710i	$0.458984\pi$
$564$	24.7518	1.04224
$565$	−7.35370	−0.309373
$566$	−42.7401	−1.79650
$567$	5.02070	0.210850
$568$	48.9304	2.05307
$569$	−13.6073	−0.570448	−0.285224	−	0.958461i	$-0.592068\pi$
$569$	−13.6073	−0.570448	−0.285224	+	0.958461i	$0.592068\pi$
$570$	−31.2182	−1.30759
$571$	−9.72167	−0.406839	−0.203420	−	0.979092i	$-0.565206\pi$
$571$	−9.72167	−0.406839	−0.203420	+	0.979092i	$0.565206\pi$
$572$	−68.6645	−2.87101
$573$	13.5207	0.564836
$574$	−9.04320	−0.377456
$575$	53.1355	2.21590
$576$	29.8670	1.24446
$577$	−0.00757051	−0.000315165 0	−0.000157582	−	1.00000i	$-0.500050\pi$
$577$	−0.00757051	−0.000315165 0	−0.000157582		1.00000i	$0.500050\pi$
$578$	34.2019	1.42261
$579$	−2.95710	−0.122893
$580$	27.3640	1.13623
$581$	17.1889	0.713114
$582$	−16.8992	−0.700494
$583$	12.0516	0.499125
$584$	−31.0628	−1.28539
$585$	−48.7320	−2.01482
$586$	27.1487	1.12150
$587$	35.3910	1.46074	0.730372	−	0.683049i	$-0.239347\pi$
$587$	35.3910	1.46074	0.730372	+	0.683049i	$0.239347\pi$
$588$	−14.7023	−0.606312
$589$	−26.2636	−1.08217
$590$	−20.0007	−0.823417
$591$	8.22411	0.338295
$592$	−6.52022	−0.267979
$593$	−20.3811	−0.836950	−0.418475	−	0.908228i	$-0.637435\pi$
$593$	−20.3811	−0.836950	−0.418475	+	0.908228i	$0.637435\pi$
$594$	−31.8043	−1.30495
$595$	5.77141	0.236605
$596$	−26.0550	−1.06726
$597$	7.07803	0.289685
$598$	−96.4375	−3.94362
$599$	46.8208	1.91305	0.956524	−	0.291654i	$-0.0942055\pi$
$599$	46.8208	1.91305	0.956524	+	0.291654i	$0.0942055\pi$
$600$	−18.4289	−0.752356
$601$	−26.6214	−1.08591	−0.542955	−	0.839762i	$-0.682694\pi$
$601$	−26.6214	−1.08591	−0.542955	+	0.839762i	$0.682694\pi$
$602$	−6.44034	−0.262489
$603$	−2.44376	−0.0995176
$604$	−49.9468	−2.03230
$605$	3.99018	0.162224
$606$	18.6101	0.755985
$607$	−42.1647	−1.71141	−0.855707	−	0.517461i	$-0.826877\pi$
$607$	−42.1647	−1.71141	−0.855707	+	0.517461i	$0.826877\pi$
$608$	20.6807	0.838714
$609$	1.63828	0.0663865
$610$	71.1809	2.88203
$611$	55.2677	2.23589
$612$	−13.9159	−0.562517
$613$	46.3634	1.87260	0.936299	−	0.351203i	$-0.114227\pi$
$613$	46.3634	1.87260	0.936299	+	0.351203i	$0.114227\pi$
$614$	42.3587	1.70946
$615$	9.00679	0.363189
$616$	13.2630	0.534380
$617$	36.2694	1.46015	0.730075	−	0.683367i	$-0.239485\pi$
$617$	36.2694	1.46015	0.730075	+	0.683367i	$0.239485\pi$
$618$	22.6642	0.911686
$619$	17.7029	0.711538	0.355769	−	0.934574i	$-0.384219\pi$
$619$	17.7029	0.711538	0.355769	+	0.934574i	$0.384219\pi$
$620$	−60.3430	−2.42343
$621$	−28.5392	−1.14524
$622$	17.2699	0.692461
$623$	0.706156	0.0282915
$624$	5.67306	0.227104
$625$	−8.96397	−0.358559
$626$	35.0279	1.40000
$627$	−13.2216	−0.528020
$628$	−26.1323	−1.04279
$629$	−7.08470	−0.282485
$630$	21.6467	0.862425
$631$	−14.1968	−0.565166	−0.282583	−	0.959243i	$-0.591191\pi$
$631$	−14.1968	−0.565166	−0.282583	+	0.959243i	$0.591191\pi$
$632$	13.1370	0.522564
$633$	5.83217	0.231808
$634$	−46.2713	−1.83767
$635$	38.6541	1.53394
$636$	−8.62546	−0.342022
$637$	−32.8284	−1.30071
$638$	18.1390	0.718129
$639$	33.8224	1.33799
$640$	71.3038	2.81853
$641$	26.4999	1.04668	0.523342	−	0.852123i	$-0.324685\pi$
$641$	26.4999	1.04668	0.523342	+	0.852123i	$0.324685\pi$
$642$	−30.4687	−1.20251
$643$	18.6661	0.736118	0.368059	−	0.929802i	$-0.380022\pi$
$643$	18.6661	0.736118	0.368059	+	0.929802i	$0.380022\pi$
$644$	27.3694	1.07851
$645$	6.41441	0.252567
$646$	−19.9054	−0.783167
$647$	−3.43589	−0.135079	−0.0675395	−	0.997717i	$-0.521515\pi$
$647$	−3.43589	−0.135079	−0.0675395	+	0.997717i	$0.521515\pi$
$648$	−17.3005	−0.679627
$649$	−8.47074	−0.332506
$650$	−94.6309	−3.71173
$651$	−3.61274	−0.141594
$652$	−21.0696	−0.825150
$653$	−13.2362	−0.517971	−0.258986	−	0.965881i	$-0.583388\pi$
$653$	−13.2362	−0.517971	−0.258986	+	0.965881i	$0.583388\pi$
$654$	−14.1365	−0.552783
$655$	11.0178	0.430501
$656$	5.28534	0.206358
$657$	−21.4717	−0.837692
$658$	−24.5499	−0.957053
$659$	−19.8924	−0.774896	−0.387448	−	0.921891i	$-0.626643\pi$
$659$	−19.8924	−0.774896	−0.387448	+	0.921891i	$0.626643\pi$
$660$	−30.3779	−1.18246
$661$	−5.77487	−0.224617	−0.112308	−	0.993673i	$-0.535824\pi$
$661$	−5.77487	−0.224617	−0.112308	+	0.993673i	$0.535824\pi$
$662$	−25.8364	−1.00416
$663$	6.16419	0.239397
$664$	−59.2299	−2.29856
$665$	19.7830	0.767152
$666$	−26.5724	−1.02966
$667$	16.2768	0.630239
$668$	−32.7393	−1.26672
$669$	15.8131	0.611370
$670$	−8.03140	−0.310280
$671$	30.1467	1.16380
$672$	2.84478	0.109740
$673$	−12.2651	−0.472785	−0.236393	−	0.971658i	$-0.575965\pi$
$673$	−12.2651	−0.472785	−0.236393	+	0.971658i	$0.575965\pi$
$674$	−20.3466	−0.783721
$675$	−28.0045	−1.07789
$676$	63.7278	2.45107
$677$	−41.8641	−1.60897	−0.804483	−	0.593975i	$-0.797558\pi$
$677$	−41.8641	−1.60897	−0.804483	+	0.593975i	$0.797558\pi$
$678$	3.48882	0.133987
$679$	10.7090	0.410975
$680$	−19.8873	−0.762642
$681$	−8.21889	−0.314949
$682$	−40.0001	−1.53168
$683$	2.49935	0.0956351	0.0478176	−	0.998856i	$-0.484773\pi$
$683$	2.49935	0.0956351	0.0478176	+	0.998856i	$0.484773\pi$
$684$	−47.7004	−1.82387
$685$	47.6981	1.82245
$686$	31.8970	1.21783
$687$	2.94995	0.112548
$688$	3.76409	0.143505
$689$	−19.2596	−0.733732
$690$	−42.6650	−1.62423
$691$	−16.0865	−0.611958	−0.305979	−	0.952038i	$-0.598984\pi$
$691$	−16.0865	−0.611958	−0.305979	+	0.952038i	$0.598984\pi$
$692$	−52.5420	−1.99735
$693$	9.16784	0.348258
$694$	−15.5875	−0.591692
$695$	−44.5969	−1.69166
$696$	−5.64524	−0.213982
$697$	5.74291	0.217528
$698$	−23.6002	−0.893282
$699$	−11.4317	−0.432388
$700$	26.8566	1.01509
$701$	−23.4962	−0.887441	−0.443721	−	0.896165i	$-0.646342\pi$
$701$	−23.4962	−0.887441	−0.443721	+	0.896165i	$0.646342\pi$
$702$	50.8264	1.91832
$703$	−24.2847	−0.915913
$704$	41.5719	1.56680
$705$	24.4510	0.920878
$706$	−50.2205	−1.89007
$707$	−11.7933	−0.443531
$708$	6.06261	0.227847
$709$	−12.9602	−0.486732	−0.243366	−	0.969935i	$-0.578252\pi$
$709$	−12.9602	−0.486732	−0.243366	+	0.969935i	$0.578252\pi$
$710$	111.157	4.17165
$711$	9.08081	0.340557
$712$	−2.43329	−0.0911914
$713$	−35.8936	−1.34422
$714$	−2.73813	−0.102472
$715$	−67.8301	−2.53670
$716$	19.4676	0.727539
$717$	−0.175178	−0.00654215
$718$	−42.8201	−1.59803
$719$	−25.8348	−0.963475	−0.481737	−	0.876316i	$-0.659994\pi$
$719$	−25.8348	−0.963475	−0.481737	+	0.876316i	$0.659994\pi$
$720$	−12.6515	−0.471494
$721$	−14.3623	−0.534880
$722$	−23.5150	−0.875136
$723$	−4.89704	−0.182123
$724$	32.1561	1.19507
$725$	15.9718	0.593179
$726$	−1.89306	−0.0702581
$727$	−39.1189	−1.45084	−0.725420	−	0.688306i	$-0.758355\pi$
$727$	−39.1189	−1.45084	−0.725420	+	0.688306i	$0.758355\pi$
$728$	−21.1955	−0.785558
$729$	−3.75942	−0.139238
$730$	−70.5667	−2.61179
$731$	4.08996	0.151273
$732$	−21.5763	−0.797484
$733$	42.4703	1.56868	0.784338	−	0.620334i	$-0.213003\pi$
$733$	42.4703	1.56868	0.784338	+	0.620334i	$0.213003\pi$
$734$	30.0215	1.10811
$735$	−14.5236	−0.535712
$736$	28.2637	1.04181
$737$	−3.40147	−0.125295
$738$	21.5398	0.792892
$739$	13.6898	0.503588	0.251794	−	0.967781i	$-0.418980\pi$
$739$	13.6898	0.503588	0.251794	+	0.967781i	$0.418980\pi$
$740$	−55.7963	−2.05111
$741$	21.1294	0.776208
$742$	8.55509	0.314067
$743$	−6.43701	−0.236151	−0.118075	−	0.993005i	$-0.537672\pi$
$743$	−6.43701	−0.236151	−0.118075	+	0.993005i	$0.537672\pi$
$744$	12.4489	0.456398
$745$	−25.7384	−0.942983
$746$	−14.4671	−0.529677
$747$	−40.9418	−1.49798
$748$	−19.3696	−0.708221
$749$	19.3081	0.705501
$750$	−12.8761	−0.470167
$751$	18.1930	0.663871	0.331935	−	0.943302i	$-0.392298\pi$
$751$	18.1930	0.663871	0.331935	+	0.943302i	$0.392298\pi$
$752$	14.3483	0.523228
$753$	20.7931	0.757743
$754$	−28.9879	−1.05568
$755$	−49.3398	−1.79566
$756$	−14.4248	−0.524623
$757$	7.55758	0.274685	0.137342	−	0.990524i	$-0.456144\pi$
$757$	7.55758	0.274685	0.137342	+	0.990524i	$0.456144\pi$
$758$	−51.2174	−1.86030
$759$	−18.0695	−0.655882
$760$	−68.1688	−2.47274
$761$	5.63773	0.204368	0.102184	−	0.994766i	$-0.467417\pi$
$761$	5.63773	0.204368	0.102184	+	0.994766i	$0.467417\pi$
$762$	−18.3387	−0.664340
$763$	8.95834	0.324314
$764$	67.8963	2.45640
$765$	−13.7468	−0.497017
$766$	−8.31901	−0.300578
$767$	13.5371	0.488795
$768$	−17.0132	−0.613910
$769$	5.39050	0.194386	0.0971932	−	0.995266i	$-0.469014\pi$
$769$	5.39050	0.194386	0.0971932	+	0.995266i	$0.469014\pi$
$770$	30.1300	1.08581
$771$	−3.39000	−0.122088
$772$	−14.8495	−0.534446
$773$	−6.57590	−0.236519	−0.118259	−	0.992983i	$-0.537731\pi$
$773$	−6.57590	−0.236519	−0.118259	+	0.992983i	$0.537731\pi$
$774$	15.3401	0.551390
$775$	−35.2211	−1.26518
$776$	−36.9014	−1.32468
$777$	−3.34053	−0.119841
$778$	46.1376	1.65411
$779$	19.6853	0.705300
$780$	48.5468	1.73825
$781$	47.0775	1.68456
$782$	−27.2041	−0.972815
$783$	−8.57851	−0.306571
$784$	−8.52272	−0.304383
$785$	−25.8147	−0.921367
$786$	−5.22717	−0.186447
$787$	−51.4395	−1.83362	−0.916810	−	0.399323i	$-0.869245\pi$
$787$	−51.4395	−1.83362	−0.916810	+	0.399323i	$0.869245\pi$
$788$	41.2986	1.47120
$789$	14.3789	0.511903
$790$	29.8440	1.06180
$791$	−2.21086	−0.0786093
$792$	−31.5908	−1.12253
$793$	−48.1773	−1.71083
$794$	−15.1817	−0.538780
$795$	−8.52064	−0.302196
$796$	35.5434	1.25980
$797$	12.6138	0.446805	0.223403	−	0.974726i	$-0.428284\pi$
$797$	12.6138	0.446805	0.223403	+	0.974726i	$0.428284\pi$
$798$	−9.38565	−0.332249
$799$	15.5905	0.551551
$800$	27.7342	0.980551
$801$	−1.68198	−0.0594298
$802$	59.1807	2.08974
$803$	−29.8865	−1.05467
$804$	2.43447	0.0858573
$805$	27.0368	0.952922
$806$	63.9241	2.25163
$807$	−2.33430	−0.0821711
$808$	40.6375	1.42962
$809$	−42.8489	−1.50649	−0.753243	−	0.657742i	$-0.771512\pi$
$809$	−42.8489	−1.50649	−0.753243	+	0.657742i	$0.771512\pi$
$810$	−39.3022	−1.38094
$811$	−13.5383	−0.475395	−0.237697	−	0.971339i	$-0.576393\pi$
$811$	−13.5383	−0.475395	−0.237697	+	0.971339i	$0.576393\pi$
$812$	8.22688	0.288707
$813$	−22.1071	−0.775329
$814$	−36.9862	−1.29637
$815$	−20.8136	−0.729068
$816$	1.60031	0.0560221
$817$	14.0194	0.490477
$818$	31.1202	1.08809
$819$	−14.6511	−0.511951
$820$	45.2289	1.57946
$821$	48.7381	1.70097	0.850486	−	0.525997i	$-0.176308\pi$
$821$	48.7381	1.70097	0.850486	+	0.525997i	$0.176308\pi$
$822$	−22.6294	−0.789291
$823$	−9.65254	−0.336466	−0.168233	−	0.985747i	$-0.553806\pi$
$823$	−9.65254	−0.336466	−0.168233	+	0.985747i	$0.553806\pi$
$824$	49.4900	1.72406
$825$	−17.7310	−0.617315
$826$	−6.01315	−0.209224
$827$	44.8840	1.56077	0.780384	−	0.625300i	$-0.215024\pi$
$827$	44.8840	1.56077	0.780384	+	0.625300i	$0.215024\pi$
$828$	−65.1907	−2.26553
$829$	−46.1980	−1.60452	−0.802262	−	0.596972i	$-0.796370\pi$
$829$	−46.1980	−1.60452	−0.802262	+	0.596972i	$0.796370\pi$
$830$	−134.555	−4.67047
$831$	−3.19132	−0.110706
$832$	−66.4360	−2.30325
$833$	−9.26056	−0.320859
$834$	21.1581	0.732645
$835$	−32.3415	−1.11922
$836$	−66.3943	−2.29629
$837$	18.9173	0.653879
$838$	35.2762	1.21860
$839$	40.1590	1.38644	0.693222	−	0.720724i	$-0.256191\pi$
$839$	40.1590	1.38644	0.693222	+	0.720724i	$0.256191\pi$
$840$	−9.37711	−0.323541
$841$	−24.1074	−0.831290
$842$	21.5208	0.741657
$843$	1.76313	0.0607256
$844$	29.2871	1.00810
$845$	62.9534	2.16566
$846$	58.4748	2.01041
$847$	1.19963	0.0412199
$848$	−5.00006	−0.171703
$849$	12.7979	0.439224
$850$	−26.6944	−0.915611
$851$	−33.1891	−1.13771
$852$	−33.6939	−1.15433
$853$	−39.8988	−1.36611	−0.683055	−	0.730367i	$-0.739349\pi$
$853$	−39.8988	−1.36611	−0.683055	+	0.730367i	$0.739349\pi$
$854$	21.4003	0.732303
$855$	−47.1208	−1.61150
$856$	−66.5323	−2.27403
$857$	16.2705	0.555790	0.277895	−	0.960611i	$-0.410363\pi$
$857$	16.2705	0.555790	0.277895	+	0.960611i	$0.410363\pi$
$858$	32.1806	1.09863
$859$	10.2253	0.348883	0.174442	−	0.984668i	$-0.444188\pi$
$859$	10.2253	0.348883	0.174442	+	0.984668i	$0.444188\pi$
$860$	32.2109	1.09838
$861$	2.70786	0.0922836
$862$	−3.56968	−0.121584
$863$	−26.8999	−0.915683	−0.457841	−	0.889034i	$-0.651377\pi$
$863$	−26.8999	−0.915683	−0.457841	+	0.889034i	$0.651377\pi$
$864$	−14.8961	−0.506775
$865$	−51.9036	−1.76477
$866$	−27.9774	−0.950710
$867$	−10.2413	−0.347812
$868$	−18.1419	−0.615777
$869$	12.6396	0.428768
$870$	−12.8245	−0.434792
$871$	5.43588	0.184188
$872$	−30.8689	−1.04535
$873$	−25.5076	−0.863302
$874$	−93.2490	−3.15420
$875$	8.15957	0.275844
$876$	21.3901	0.722705
$877$	41.2707	1.39361	0.696807	−	0.717259i	$-0.254603\pi$
$877$	41.2707	1.39361	0.696807	+	0.717259i	$0.254603\pi$
$878$	−11.2930	−0.381121
$879$	−8.12929	−0.274194
$880$	−17.6097	−0.593621
$881$	44.3718	1.49493	0.747463	−	0.664304i	$-0.231272\pi$
$881$	44.3718	1.49493	0.747463	+	0.664304i	$0.231272\pi$
$882$	−34.7334	−1.16953
$883$	−10.4451	−0.351507	−0.175754	−	0.984434i	$-0.556236\pi$
$883$	−10.4451	−0.351507	−0.175754	+	0.984434i	$0.556236\pi$
$884$	30.9544	1.04111
$885$	5.98894	0.201316
$886$	19.4572	0.653676
$887$	2.91892	0.0980078	0.0490039	−	0.998799i	$-0.484395\pi$
$887$	2.91892	0.0980078	0.0490039	+	0.998799i	$0.484395\pi$
$888$	11.5109	0.386280
$889$	11.6212	0.389763
$890$	−5.52781	−0.185293
$891$	−16.6453	−0.557640
$892$	79.4079	2.65877
$893$	53.4404	1.78832
$894$	12.2111	0.408400
$895$	19.2311	0.642823
$896$	21.4372	0.716168
$897$	28.8769	0.964171
$898$	−50.7415	−1.69327
$899$	−10.7891	−0.359838
$900$	−63.9694	−2.13231
$901$	−5.43294	−0.180997
$902$	29.9813	0.998268
$903$	1.92847	0.0641755
$904$	7.61826	0.253380
$905$	31.7654	1.05592
$906$	23.4083	0.777688
$907$	49.3899	1.63997	0.819983	−	0.572388i	$-0.193983\pi$
$907$	49.3899	1.63997	0.819983	+	0.572388i	$0.193983\pi$
$908$	−41.2724	−1.36967
$909$	28.0901	0.931691
$910$	−48.1508	−1.59618
$911$	33.7940	1.11964	0.559822	−	0.828613i	$-0.310869\pi$
$911$	33.7940	1.11964	0.559822	+	0.828613i	$0.310869\pi$
$912$	5.48549	0.181643
$913$	−56.9869	−1.88599
$914$	−16.6912	−0.552097
$915$	−21.3141	−0.704623
$916$	14.8136	0.489456
$917$	3.31246	0.109387
$918$	14.3376	0.473212
$919$	41.5755	1.37145	0.685724	−	0.727862i	$-0.259486\pi$
$919$	41.5755	1.37145	0.685724	+	0.727862i	$0.259486\pi$
$920$	−93.1642	−3.07153
$921$	−12.6837	−0.417943
$922$	57.3407	1.88841
$923$	−75.2344	−2.47637
$924$	−9.13301	−0.300454
$925$	−32.5673	−1.07081
$926$	71.8962	2.36266
$927$	34.2093	1.12358
$928$	8.49569	0.278885
$929$	52.2497	1.71426	0.857129	−	0.515102i	$-0.172246\pi$
$929$	52.2497	1.71426	0.857129	+	0.515102i	$0.172246\pi$
$930$	28.2807	0.927359
$931$	−31.7430	−1.04033
$932$	−57.4062	−1.88040
$933$	−5.17124	−0.169299
$934$	19.9133	0.651584
$935$	−19.1342	−0.625755
$936$	50.4852	1.65016
$937$	−1.34848	−0.0440531	−0.0220265	−	0.999757i	$-0.507012\pi$
$937$	−1.34848	−0.0440531	−0.0220265	+	0.999757i	$0.507012\pi$
$938$	−2.41461	−0.0788399
$939$	−10.4886	−0.342283
$940$	122.784	4.00479
$941$	−18.9885	−0.619007	−0.309504	−	0.950898i	$-0.600163\pi$
$941$	−18.9885	−0.619007	−0.309504	+	0.950898i	$0.600163\pi$
$942$	12.2473	0.399038
$943$	26.9033	0.876093
$944$	3.51441	0.114384
$945$	−14.2495	−0.463535
$946$	21.3519	0.694212
$947$	18.5861	0.603968	0.301984	−	0.953313i	$-0.402351\pi$
$947$	18.5861	0.603968	0.301984	+	0.953313i	$0.402351\pi$
$948$	−9.04630	−0.293810
$949$	47.7615	1.55041
$950$	−91.5021	−2.96872
$951$	13.8553	0.449289
$952$	−5.97904	−0.193782
$953$	11.9303	0.386461	0.193230	−	0.981153i	$-0.438103\pi$
$953$	11.9303	0.386461	0.193230	+	0.981153i	$0.438103\pi$
$954$	−20.3772	−0.659736
$955$	67.0712	2.17037
$956$	−0.879684	−0.0284510
$957$	−5.43146	−0.175574
$958$	−36.2752	−1.17200
$959$	14.3403	0.463071
$960$	−29.3920	−0.948622
$961$	−7.20778	−0.232509
$962$	59.1075	1.90570
$963$	−45.9895	−1.48199
$964$	−24.5912	−0.792030
$965$	−14.6691	−0.472214
$966$	−12.8271	−0.412704
$967$	−0.445464	−0.0143251	−0.00716257	−	0.999974i	$-0.502280\pi$
$967$	−0.445464	−0.0143251	−0.00716257	+	0.999974i	$0.502280\pi$
$968$	−4.13373	−0.132863
$969$	5.96039	0.191475
$970$	−83.8306	−2.69164
$971$	−5.24917	−0.168454	−0.0842270	−	0.996447i	$-0.526842\pi$
$971$	−5.24917	−0.168454	−0.0842270	+	0.996447i	$0.526842\pi$
$972$	53.0873	1.70278
$973$	−13.4079	−0.429837
$974$	−67.0015	−2.14686
$975$	28.3359	0.907475
$976$	−12.5075	−0.400356
$977$	30.8512	0.987018	0.493509	−	0.869741i	$-0.335714\pi$
$977$	30.8512	0.987018	0.493509	+	0.869741i	$0.335714\pi$
$978$	9.87459	0.315755
$979$	−2.34115	−0.0748234
$980$	−72.9326	−2.32975
$981$	−21.3377	−0.681260
$982$	−102.863	−3.28248
$983$	−36.0730	−1.15055	−0.575275	−	0.817960i	$-0.695105\pi$
$983$	−36.0730	−1.15055	−0.575275	+	0.817960i	$0.695105\pi$
$984$	−9.33082	−0.297456
$985$	40.7968	1.29989
$986$	−8.17718	−0.260414
$987$	7.35111	0.233988
$988$	106.104	3.37563
$989$	19.1599	0.609249
$990$	−71.7662	−2.28088
$991$	14.8307	0.471113	0.235556	−	0.971861i	$-0.424309\pi$
$991$	14.8307	0.471113	0.235556	+	0.971861i	$0.424309\pi$
$992$	−18.7347	−0.594827
$993$	7.73636	0.245506
$994$	33.4190	1.05999
$995$	35.1115	1.11311
$996$	40.7862	1.29236
$997$	30.7128	0.972683	0.486341	−	0.873769i	$-0.338331\pi$
$997$	30.7128	0.972683	0.486341	+	0.873769i	$0.338331\pi$
$998$	41.2468	1.30565
$999$	17.4920	0.553421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.19	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.19	✓	182	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35347 q^{2} +0.704714 q^{3} +3.53883 q^{4} +3.49583 q^{5} -1.65853 q^{6} +1.05101 q^{7} -3.62159 q^{8} -2.50338 q^{9} +O(q^{10})\)	\(q-2.35347 q^{2} +0.704714 q^{3} +3.53883 q^{4} +3.49583 q^{5} -1.65853 q^{6} +1.05101 q^{7} -3.62159 q^{8} -2.50338 q^{9} -8.22733 q^{10} -3.48445 q^{11} +2.49386 q^{12} +5.56850 q^{13} -2.47352 q^{14} +2.46356 q^{15} +1.44566 q^{16} +1.57082 q^{17} +5.89163 q^{18} +5.38439 q^{19} +12.3711 q^{20} +0.740661 q^{21} +8.20056 q^{22} +7.35867 q^{23} -2.55219 q^{24} +7.22081 q^{25} -13.1053 q^{26} -3.87831 q^{27} +3.71934 q^{28} +2.21192 q^{29} -5.79792 q^{30} -4.87773 q^{31} +3.84087 q^{32} -2.45554 q^{33} -3.69687 q^{34} +3.67414 q^{35} -8.85903 q^{36} -4.51020 q^{37} -12.6720 q^{38} +3.92420 q^{39} -12.6605 q^{40} +3.65600 q^{41} -1.74312 q^{42} +2.60372 q^{43} -12.3309 q^{44} -8.75138 q^{45} -17.3184 q^{46} +9.92507 q^{47} +1.01878 q^{48} -5.89538 q^{49} -16.9940 q^{50} +1.10698 q^{51} +19.7060 q^{52} -3.45867 q^{53} +9.12749 q^{54} -12.1810 q^{55} -3.80633 q^{56} +3.79445 q^{57} -5.20569 q^{58} +2.43101 q^{59} +8.71812 q^{60} -8.65176 q^{61} +11.4796 q^{62} -2.63107 q^{63} -11.9307 q^{64} +19.4665 q^{65} +5.77905 q^{66} +0.976185 q^{67} +5.55885 q^{68} +5.18576 q^{69} -8.64700 q^{70} -13.5107 q^{71} +9.06622 q^{72} +8.57710 q^{73} +10.6146 q^{74} +5.08861 q^{75} +19.0544 q^{76} -3.66219 q^{77} -9.23549 q^{78} -3.62742 q^{79} +5.05378 q^{80} +4.77703 q^{81} -8.60431 q^{82} +16.3546 q^{83} +2.62107 q^{84} +5.49130 q^{85} -6.12777 q^{86} +1.55877 q^{87} +12.6193 q^{88} +0.671884 q^{89} +20.5961 q^{90} +5.85254 q^{91} +26.0411 q^{92} -3.43740 q^{93} -23.3584 q^{94} +18.8229 q^{95} +2.70671 q^{96} +10.1893 q^{97} +13.8746 q^{98} +8.72290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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