LMFDB - Embedded newform 3721.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3721,2,Mod(1,3721)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3721, 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("3721.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3721 = 61^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3721.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:	$29.7123345921$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 11 x^{14} + 86 x^{13} + 5 x^{12} - 562 x^{11} + 362 x^{10} + 1761 x^{9} - 1799 x^{8} + \cdots - 9 $ x^16 - 5x^15 - 11x^14 + 86x^13 + 5x^12 - 562x^11 + 362x^10 + 1761x^9 - 1799x^8 - 2672x^7 + 3614x^6 + 1572x^5 - 3212x^4 + 144x^3 + 1005x^2 - 279*x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 61)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.12973$ of defining polynomial
Character	$\chi$	$=$	3721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12973 q^{2} -2.31072 q^{3} +2.53577 q^{4} +1.23124 q^{5} +4.92121 q^{6} -3.86982 q^{7} -1.14104 q^{8} +2.33940 q^{9} +O(q^{10})$	\(q-2.12973 q^{2} -2.31072 q^{3} +2.53577 q^{4} +1.23124 q^{5} +4.92121 q^{6} -3.86982 q^{7} -1.14104 q^{8} +2.33940 q^{9} -2.62222 q^{10} -1.98434 q^{11} -5.85943 q^{12} -5.45874 q^{13} +8.24168 q^{14} -2.84505 q^{15} -2.64143 q^{16} +5.38110 q^{17} -4.98231 q^{18} -4.52421 q^{19} +3.12214 q^{20} +8.94205 q^{21} +4.22612 q^{22} +7.26650 q^{23} +2.63661 q^{24} -3.48404 q^{25} +11.6257 q^{26} +1.52645 q^{27} -9.81295 q^{28} +0.414565 q^{29} +6.05920 q^{30} -2.48075 q^{31} +7.90761 q^{32} +4.58525 q^{33} -11.4603 q^{34} -4.76468 q^{35} +5.93218 q^{36} +7.37383 q^{37} +9.63537 q^{38} +12.6136 q^{39} -1.40489 q^{40} +3.86159 q^{41} -19.0442 q^{42} -2.53536 q^{43} -5.03182 q^{44} +2.88037 q^{45} -15.4757 q^{46} -3.95154 q^{47} +6.10358 q^{48} +7.97549 q^{49} +7.42009 q^{50} -12.4342 q^{51} -13.8421 q^{52} +3.00295 q^{53} -3.25093 q^{54} -2.44320 q^{55} +4.41561 q^{56} +10.4542 q^{57} -0.882913 q^{58} -1.46693 q^{59} -7.21437 q^{60} +5.28333 q^{62} -9.05307 q^{63} -11.5582 q^{64} -6.72103 q^{65} -9.76535 q^{66} -6.06334 q^{67} +13.6452 q^{68} -16.7908 q^{69} +10.1475 q^{70} +8.72796 q^{71} -2.66935 q^{72} +6.14472 q^{73} -15.7043 q^{74} +8.05063 q^{75} -11.4723 q^{76} +7.67904 q^{77} -26.8636 q^{78} -9.04686 q^{79} -3.25223 q^{80} -10.5454 q^{81} -8.22416 q^{82} +5.10163 q^{83} +22.6749 q^{84} +6.62543 q^{85} +5.39965 q^{86} -0.957942 q^{87} +2.26421 q^{88} +7.97724 q^{89} -6.13442 q^{90} +21.1243 q^{91} +18.4261 q^{92} +5.73230 q^{93} +8.41572 q^{94} -5.57040 q^{95} -18.2722 q^{96} +4.47521 q^{97} -16.9857 q^{98} -4.64217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9} + 20 q^{10} - 9 q^{11} - 17 q^{12} - 11 q^{14} - 12 q^{15} + 9 q^{16} + 4 q^{17} - 35 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} - 11 q^{22} + 4 q^{23} + 15 q^{24} - 8 q^{25} + 19 q^{26} - 5 q^{27} + 22 q^{28} + 4 q^{29} - 24 q^{30} - 9 q^{31} - 34 q^{32} + 10 q^{33} - 6 q^{34} - 37 q^{35} + 20 q^{36} + 38 q^{37} + 18 q^{38} - 12 q^{39} + 60 q^{40} - 37 q^{41} + 17 q^{42} + 15 q^{43} - 34 q^{44} - 32 q^{45} - 41 q^{46} - 40 q^{47} - 43 q^{48} + 24 q^{49} - 28 q^{50} + 19 q^{51} - 56 q^{52} - 19 q^{53} + 6 q^{54} - 30 q^{55} - 58 q^{56} + 8 q^{57} - 21 q^{58} + q^{59} - 10 q^{60} - 37 q^{62} - 17 q^{63} + 28 q^{64} - 34 q^{65} - 59 q^{66} + 3 q^{67} - 2 q^{68} - 31 q^{69} + 17 q^{70} - 8 q^{71} + 9 q^{72} + 6 q^{73} + 10 q^{74} - q^{75} - 65 q^{76} - 39 q^{77} + 68 q^{78} - 56 q^{79} - 14 q^{80} - 56 q^{81} - 39 q^{82} + 6 q^{83} + 65 q^{84} + 53 q^{85} - 54 q^{86} + 83 q^{87} - 5 q^{88} + 66 q^{89} + 60 q^{90} + 5 q^{91} - 37 q^{92} - 67 q^{93} + 43 q^{94} - 39 q^{95} - 14 q^{96} + 13 q^{97} + 16 q^{98} + 47 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9 + 20 * q^10 - 9 * q^11 - 17 * q^12 - 11 * q^14 - 12 * q^15 + 9 * q^16 + 4 * q^17 - 35 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 - 11 * q^22 + 4 * q^23 + 15 * q^24 - 8 * q^25 + 19 * q^26 - 5 * q^27 + 22 * q^28 + 4 * q^29 - 24 * q^30 - 9 * q^31 - 34 * q^32 + 10 * q^33 - 6 * q^34 - 37 * q^35 + 20 * q^36 + 38 * q^37 + 18 * q^38 - 12 * q^39 + 60 * q^40 - 37 * q^41 + 17 * q^42 + 15 * q^43 - 34 * q^44 - 32 * q^45 - 41 * q^46 - 40 * q^47 - 43 * q^48 + 24 * q^49 - 28 * q^50 + 19 * q^51 - 56 * q^52 - 19 * q^53 + 6 * q^54 - 30 * q^55 - 58 * q^56 + 8 * q^57 - 21 * q^58 + q^59 - 10 * q^60 - 37 * q^62 - 17 * q^63 + 28 * q^64 - 34 * q^65 - 59 * q^66 + 3 * q^67 - 2 * q^68 - 31 * q^69 + 17 * q^70 - 8 * q^71 + 9 * q^72 + 6 * q^73 + 10 * q^74 - q^75 - 65 * q^76 - 39 * q^77 + 68 * q^78 - 56 * q^79 - 14 * q^80 - 56 * q^81 - 39 * q^82 + 6 * q^83 + 65 * q^84 + 53 * q^85 - 54 * q^86 + 83 * q^87 - 5 * q^88 + 66 * q^89 + 60 * q^90 + 5 * q^91 - 37 * q^92 - 67 * q^93 + 43 * q^94 - 39 * q^95 - 14 * q^96 + 13 * q^97 + 16 * q^98 + 47 * 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 $

$2$	−2.12973	−1.50595	−0.752975	−	0.658050i	$-0.771382\pi$
$2$	−2.12973	−1.50595	−0.752975	+	0.658050i	$0.771382\pi$
$3$	−2.31072	−1.33409	−0.667046	−	0.745017i	$-0.732442\pi$
$3$	−2.31072	−1.33409	−0.667046	+	0.745017i	$0.732442\pi$
$4$	2.53577	1.26788
$5$	1.23124	0.550628	0.275314	−	0.961354i	$-0.411218\pi$
$5$	1.23124	0.550628	0.275314	+	0.961354i	$0.411218\pi$
$6$	4.92121	2.00907
$7$	−3.86982	−1.46265	−0.731327	−	0.682027i	$-0.761099\pi$
$7$	−3.86982	−1.46265	−0.731327	+	0.682027i	$0.761099\pi$
$8$	−1.14104	−0.403418
$9$	2.33940	0.779801
$10$	−2.62222	−0.829218
$11$	−1.98434	−0.598301	−0.299151	−	0.954206i	$-0.596703\pi$
$11$	−1.98434	−0.598301	−0.299151	+	0.954206i	$0.596703\pi$
$12$	−5.85943	−1.69147
$13$	−5.45874	−1.51398	−0.756991	−	0.653425i	$-0.773332\pi$
$13$	−5.45874	−1.51398	−0.756991	+	0.653425i	$0.773332\pi$
$14$	8.24168	2.20268
$15$	−2.84505	−0.734588
$16$	−2.64143	−0.660356
$17$	5.38110	1.30511	0.652554	−	0.757742i	$-0.273697\pi$
$17$	5.38110	1.30511	0.652554	+	0.757742i	$0.273697\pi$
$18$	−4.98231	−1.17434
$19$	−4.52421	−1.03793	−0.518963	−	0.854797i	$-0.673682\pi$
$19$	−4.52421	−1.03793	−0.518963	+	0.854797i	$0.673682\pi$
$20$	3.12214	0.698132
$21$	8.94205	1.95131
$22$	4.22612	0.901011
$23$	7.26650	1.51517	0.757585	−	0.652736i	$-0.226379\pi$
$23$	7.26650	1.51517	0.757585	+	0.652736i	$0.226379\pi$
$24$	2.63661	0.538196
$25$	−3.48404	−0.696809
$26$	11.6257	2.27998
$27$	1.52645	0.293765
$28$	−9.81295	−1.85447
$29$	0.414565	0.0769828	0.0384914	−	0.999259i	$-0.487745\pi$
$29$	0.414565	0.0769828	0.0384914	+	0.999259i	$0.487745\pi$
$30$	6.05920	1.10625
$31$	−2.48075	−0.445555	−0.222778	−	0.974869i	$-0.571512\pi$
$31$	−2.48075	−0.445555	−0.222778	+	0.974869i	$0.571512\pi$
$32$	7.90761	1.39788
$33$	4.58525	0.798189
$34$	−11.4603	−1.96543
$35$	−4.76468	−0.805378
$36$	5.93218	0.988697
$37$	7.37383	1.21225	0.606125	−	0.795370i	$-0.292723\pi$
$37$	7.37383	1.21225	0.606125	+	0.795370i	$0.292723\pi$
$38$	9.63537	1.56306
$39$	12.6136	2.01979
$40$	−1.40489	−0.222133
$41$	3.86159	0.603079	0.301540	−	0.953454i	$-0.402499\pi$
$41$	3.86159	0.603079	0.301540	+	0.953454i	$0.402499\pi$
$42$	−19.0442	−2.93858
$43$	−2.53536	−0.386639	−0.193320	−	0.981136i	$-0.561925\pi$
$43$	−2.53536	−0.386639	−0.193320	+	0.981136i	$0.561925\pi$
$44$	−5.03182	−0.758576
$45$	2.88037	0.429380
$46$	−15.4757	−2.28177
$47$	−3.95154	−0.576391	−0.288195	−	0.957572i	$-0.593055\pi$
$47$	−3.95154	−0.576391	−0.288195	+	0.957572i	$0.593055\pi$
$48$	6.10358	0.880976
$49$	7.97549	1.13936
$50$	7.42009	1.04936
$51$	−12.4342	−1.74113
$52$	−13.8421	−1.91955
$53$	3.00295	0.412486	0.206243	−	0.978501i	$-0.433876\pi$
$53$	3.00295	0.412486	0.206243	+	0.978501i	$0.433876\pi$
$54$	−3.25093	−0.442396
$55$	−2.44320	−0.329441
$56$	4.41561	0.590060
$57$	10.4542	1.38469
$58$	−0.882913	−0.115932
$59$	−1.46693	−0.190978	−0.0954888	−	0.995431i	$-0.530441\pi$
$59$	−1.46693	−0.190978	−0.0954888	+	0.995431i	$0.530441\pi$
$60$	−7.21437	−0.931372
$61$	0	0
$61$	0	0
$62$	5.28333	0.670983
$63$	−9.05307	−1.14058
$64$	−11.5582	−1.44478
$65$	−6.72103	−0.833641
$66$	−9.76535	−1.20203
$67$	−6.06334	−0.740755	−0.370377	−	0.928881i	$-0.620772\pi$
$67$	−6.06334	−0.740755	−0.370377	+	0.928881i	$0.620772\pi$
$68$	13.6452	1.65472
$69$	−16.7908	−2.02138
$70$	10.1475	1.21286
$71$	8.72796	1.03582	0.517909	−	0.855436i	$-0.326710\pi$
$71$	8.72796	1.03582	0.517909	+	0.855436i	$0.326710\pi$
$72$	−2.66935	−0.314586
$73$	6.14472	0.719185	0.359593	−	0.933109i	$-0.382916\pi$
$73$	6.14472	0.719185	0.359593	+	0.933109i	$0.382916\pi$
$74$	−15.7043	−1.82559
$75$	8.05063	0.929607
$76$	−11.4723	−1.31597
$77$	7.67904	0.875108
$78$	−26.8636	−3.04170
$79$	−9.04686	−1.01785	−0.508925	−	0.860811i	$-0.669957\pi$
$79$	−9.04686	−1.01785	−0.508925	+	0.860811i	$0.669957\pi$
$80$	−3.25223	−0.363611
$81$	−10.5454	−1.17171
$82$	−8.22416	−0.908207
$83$	5.10163	0.559977	0.279989	−	0.960003i	$-0.409669\pi$
$83$	5.10163	0.559977	0.279989	+	0.960003i	$0.409669\pi$
$84$	22.6749	2.47404
$85$	6.62543	0.718629
$86$	5.39965	0.582259
$87$	−0.957942	−0.102702
$88$	2.26421	0.241365
$89$	7.97724	0.845586	0.422793	−	0.906226i	$-0.361050\pi$
$89$	7.97724	0.845586	0.422793	+	0.906226i	$0.361050\pi$
$90$	−6.13442	−0.646625
$91$	21.1243	2.21443
$92$	18.4261	1.92106
$93$	5.73230	0.594412
$94$	8.41572	0.868015
$95$	−5.57040	−0.571511
$96$	−18.2722	−1.86490
$97$	4.47521	0.454389	0.227195	−	0.973849i	$-0.427045\pi$
$97$	4.47521	0.454389	0.227195	+	0.973849i	$0.427045\pi$
$98$	−16.9857	−1.71581
$99$	−4.64217	−0.466556
$100$	−8.83472	−0.883472
$101$	4.64223	0.461919	0.230960	−	0.972963i	$-0.425813\pi$
$101$	4.64223	0.461919	0.230960	+	0.972963i	$0.425813\pi$
$102$	26.4815	2.62206
$103$	−0.940677	−0.0926877	−0.0463438	−	0.998926i	$-0.514757\pi$
$103$	−0.940677	−0.0926877	−0.0463438	+	0.998926i	$0.514757\pi$
$104$	6.22863	0.610767
$105$	11.0098	1.07445
$106$	−6.39547	−0.621183
$107$	14.5077	1.40251	0.701255	−	0.712911i	$-0.252623\pi$
$107$	14.5077	1.40251	0.701255	+	0.712911i	$0.252623\pi$
$108$	3.87072	0.372460
$109$	0.397574	0.0380807	0.0190404	−	0.999819i	$-0.493939\pi$
$109$	0.397574	0.0380807	0.0190404	+	0.999819i	$0.493939\pi$
$110$	5.20337	0.496122
$111$	−17.0388	−1.61725
$112$	10.2218	0.965873
$113$	−5.98087	−0.562633	−0.281316	−	0.959615i	$-0.590771\pi$
$113$	−5.98087	−0.562633	−0.281316	+	0.959615i	$0.590771\pi$
$114$	−22.2646	−2.08527
$115$	8.94682	0.834295
$116$	1.05124	0.0976051
$117$	−12.7702	−1.18061
$118$	3.12416	0.287602
$119$	−20.8239	−1.90892
$120$	3.24631	0.296346
$121$	−7.06239	−0.642036
$122$	0	0
$123$	−8.92304	−0.804563
$124$	−6.29059	−0.564912
$125$	−10.4459	−0.934310
$126$	19.2806	1.71765
$127$	2.56637	0.227729	0.113864	−	0.993496i	$-0.463677\pi$
$127$	2.56637	0.227729	0.113864	+	0.993496i	$0.463677\pi$
$128$	8.80077	0.777886
$129$	5.85850	0.515812
$130$	14.3140	1.25542
$131$	−13.4348	−1.17381	−0.586903	−	0.809657i	$-0.699653\pi$
$131$	−13.4348	−1.17381	−0.586903	+	0.809657i	$0.699653\pi$
$132$	11.6271	1.01201
$133$	17.5079	1.51813
$134$	12.9133	1.11554
$135$	1.87943	0.161755
$136$	−6.14004	−0.526504
$137$	14.0334	1.19895	0.599475	−	0.800393i	$-0.295376\pi$
$137$	14.0334	1.19895	0.599475	+	0.800393i	$0.295376\pi$
$138$	35.7600	3.04409
$139$	5.77781	0.490067	0.245034	−	0.969515i	$-0.421201\pi$
$139$	5.77781	0.490067	0.245034	+	0.969515i	$0.421201\pi$
$140$	−12.0821	−1.02112
$141$	9.13087	0.768958
$142$	−18.5882	−1.55989
$143$	10.8320	0.905818
$144$	−6.17936	−0.514947
$145$	0.510430	0.0423889
$146$	−13.0866	−1.08306
$147$	−18.4291	−1.52001
$148$	18.6983	1.53699
$149$	22.8073	1.86845	0.934225	−	0.356685i	$-0.116093\pi$
$149$	22.8073	1.86845	0.934225	+	0.356685i	$0.116093\pi$
$150$	−17.1457	−1.39994
$151$	11.1029	0.903544	0.451772	−	0.892133i	$-0.350792\pi$
$151$	11.1029	0.903544	0.451772	+	0.892133i	$0.350792\pi$
$152$	5.16230	0.418717
$153$	12.5886	1.01773
$154$	−16.3543	−1.31787
$155$	−3.05440	−0.245335
$156$	31.9851	2.56086
$157$	8.65906	0.691068	0.345534	−	0.938406i	$-0.387698\pi$
$157$	8.65906	0.691068	0.345534	+	0.938406i	$0.387698\pi$
$158$	19.2674	1.53283
$159$	−6.93895	−0.550295
$160$	9.73617	0.769712
$161$	−28.1200	−2.21617
$162$	22.4589	1.76454
$163$	19.8928	1.55812	0.779062	−	0.626947i	$-0.215696\pi$
$163$	19.8928	1.55812	0.779062	+	0.626947i	$0.215696\pi$
$164$	9.79209	0.764634
$165$	5.64555	0.439505
$166$	−10.8651	−0.843297
$167$	−11.2956	−0.874078	−0.437039	−	0.899443i	$-0.643973\pi$
$167$	−11.2956	−0.874078	−0.437039	+	0.899443i	$0.643973\pi$
$168$	−10.2032	−0.787195
$169$	16.7979	1.29214
$170$	−14.1104	−1.08222
$171$	−10.5840	−0.809376
$172$	−6.42908	−0.490213
$173$	9.45795	0.719075	0.359537	−	0.933131i	$-0.382935\pi$
$173$	9.45795	0.719075	0.359537	+	0.933131i	$0.382935\pi$
$174$	2.04016	0.154664
$175$	13.4826	1.01919
$176$	5.24149	0.395092
$177$	3.38965	0.254782
$178$	−16.9894	−1.27341
$179$	1.74509	0.130435	0.0652173	−	0.997871i	$-0.479226\pi$
$179$	1.74509	0.130435	0.0652173	+	0.997871i	$0.479226\pi$
$180$	7.30395	0.544404
$181$	22.1092	1.64337	0.821683	−	0.569945i	$-0.193036\pi$
$181$	22.1092	1.64337	0.821683	+	0.569945i	$0.193036\pi$
$182$	−44.9892	−3.33482
$183$	0	0
$184$	−8.29135	−0.611246
$185$	9.07896	0.667498
$186$	−12.2083	−0.895154
$187$	−10.6779	−0.780848
$188$	−10.0202	−0.730796
$189$	−5.90708	−0.429677
$190$	11.8635	0.860666
$191$	−4.09008	−0.295948	−0.147974	−	0.988991i	$-0.547275\pi$
$191$	−4.09008	−0.295948	−0.147974	+	0.988991i	$0.547275\pi$
$192$	26.7078	1.92747
$193$	−21.2840	−1.53206	−0.766028	−	0.642807i	$-0.777770\pi$
$193$	−21.2840	−1.53206	−0.766028	+	0.642807i	$0.777770\pi$
$194$	−9.53101	−0.684287
$195$	15.5304	1.11215
$196$	20.2240	1.44457
$197$	−0.926910	−0.0660396	−0.0330198	−	0.999455i	$-0.510512\pi$
$197$	−0.926910	−0.0660396	−0.0330198	+	0.999455i	$0.510512\pi$
$198$	9.88660	0.702610
$199$	−27.7484	−1.96703	−0.983516	−	0.180820i	$-0.942125\pi$
$199$	−27.7484	−1.96703	−0.983516	+	0.180820i	$0.942125\pi$
$200$	3.97542	0.281105
$201$	14.0107	0.988235
$202$	−9.88672	−0.695627
$203$	−1.60429	−0.112599
$204$	−31.5302	−2.20755
$205$	4.75455	0.332072
$206$	2.00339	0.139583
$207$	16.9993	1.18153
$208$	14.4189	0.999768
$209$	8.97758	0.620992
$210$	−23.4480	−1.61806
$211$	−1.72054	−0.118447	−0.0592234	−	0.998245i	$-0.518862\pi$
$211$	−1.72054	−0.118447	−0.0592234	+	0.998245i	$0.518862\pi$
$212$	7.61476	0.522984
$213$	−20.1678	−1.38188
$214$	−30.8975	−2.11211
$215$	−3.12164	−0.212894
$216$	−1.74174	−0.118510
$217$	9.60004	0.651693
$218$	−0.846727	−0.0573476
$219$	−14.1987	−0.959459
$220$	−6.19539	−0.417693
$221$	−29.3740	−1.97591
$222$	36.2881	2.43550
$223$	−14.7460	−0.987468	−0.493734	−	0.869613i	$-0.664368\pi$
$223$	−14.7460	−0.987468	−0.493734	+	0.869613i	$0.664368\pi$
$224$	−30.6010	−2.04462
$225$	−8.15059	−0.543372
$226$	12.7377	0.847296
$227$	−6.27832	−0.416707	−0.208353	−	0.978054i	$-0.566810\pi$
$227$	−6.27832	−0.416707	−0.208353	+	0.978054i	$0.566810\pi$
$228$	26.5093	1.75562
$229$	−1.82525	−0.120616	−0.0603079	−	0.998180i	$-0.519208\pi$
$229$	−1.82525	−0.120616	−0.0603079	+	0.998180i	$0.519208\pi$
$230$	−19.0543	−1.25641
$231$	−17.7441	−1.16747
$232$	−0.473034	−0.0310562
$233$	−11.4021	−0.746974	−0.373487	−	0.927635i	$-0.621838\pi$
$233$	−11.4021	−0.746974	−0.373487	+	0.927635i	$0.621838\pi$
$234$	27.1971	1.77793
$235$	−4.86530	−0.317377
$236$	−3.71978	−0.242137
$237$	20.9047	1.35791
$238$	44.3493	2.87474
$239$	−5.82492	−0.376783	−0.188392	−	0.982094i	$-0.560327\pi$
$239$	−5.82492	−0.376783	−0.188392	+	0.982094i	$0.560327\pi$
$240$	7.51498	0.485090
$241$	−17.3490	−1.11754	−0.558772	−	0.829321i	$-0.688727\pi$
$241$	−17.3490	−1.11754	−0.558772	+	0.829321i	$0.688727\pi$
$242$	15.0410	0.966873
$243$	19.7881	1.26941
$244$	0	0
$245$	9.81975	0.627361
$246$	19.0037	1.21163
$247$	24.6965	1.57140
$248$	2.83062	0.179745
$249$	−11.7884	−0.747061
$250$	22.2470	1.40702
$251$	5.07225	0.320157	0.160079	−	0.987104i	$-0.448825\pi$
$251$	5.07225	0.320157	0.160079	+	0.987104i	$0.448825\pi$
$252$	−22.9565	−1.44612
$253$	−14.4192	−0.906528
$254$	−5.46569	−0.342948
$255$	−15.3095	−0.958717
$256$	4.37319	0.273325
$257$	21.6969	1.35341	0.676707	−	0.736252i	$-0.263406\pi$
$257$	21.6969	1.35341	0.676707	+	0.736252i	$0.263406\pi$
$258$	−12.4770	−0.776787
$259$	−28.5354	−1.77310
$260$	−17.0430	−1.05696
$261$	0.969835	0.0600313
$262$	28.6126	1.76769
$263$	−0.366402	−0.0225933	−0.0112967	−	0.999936i	$-0.503596\pi$
$263$	−0.366402	−0.0225933	−0.0112967	+	0.999936i	$0.503596\pi$
$264$	−5.23194	−0.322003
$265$	3.69735	0.227126
$266$	−37.2871	−2.28622
$267$	−18.4331	−1.12809
$268$	−15.3752	−0.939190
$269$	−20.5834	−1.25499	−0.627495	−	0.778621i	$-0.715920\pi$
$269$	−20.5834	−1.25499	−0.627495	+	0.778621i	$0.715920\pi$
$270$	−4.00268	−0.243595
$271$	−32.4011	−1.96822	−0.984112	−	0.177549i	$-0.943183\pi$
$271$	−32.4011	−1.96822	−0.984112	+	0.177549i	$0.943183\pi$
$272$	−14.2138	−0.861837
$273$	−48.8123	−2.95426
$274$	−29.8873	−1.80556
$275$	6.91353	0.416902
$276$	−42.5776	−2.56287
$277$	4.21433	0.253215	0.126607	−	0.991953i	$-0.459591\pi$
$277$	4.21433	0.253215	0.126607	+	0.991953i	$0.459591\pi$
$278$	−12.3052	−0.738016
$279$	−5.80347	−0.347445
$280$	5.43668	0.324904
$281$	3.68009	0.219536	0.109768	−	0.993957i	$-0.464989\pi$
$281$	3.68009	0.219536	0.109768	+	0.993957i	$0.464989\pi$
$282$	−19.4463	−1.15801
$283$	19.7452	1.17373	0.586866	−	0.809684i	$-0.300361\pi$
$283$	19.7452	1.17373	0.586866	+	0.809684i	$0.300361\pi$
$284$	22.1321	1.31330
$285$	12.8716	0.762448
$286$	−23.0693	−1.36412
$287$	−14.9437	−0.882096
$288$	18.4991	1.09007
$289$	11.9562	0.703308
$290$	−1.08708	−0.0638355
$291$	−10.3409	−0.606197
$292$	15.5816	0.911843
$293$	1.71009	0.0999044	0.0499522	−	0.998752i	$-0.484093\pi$
$293$	1.71009	0.0999044	0.0499522	+	0.998752i	$0.484093\pi$
$294$	39.2490	2.28905
$295$	−1.80614	−0.105158
$296$	−8.41381	−0.489043
$297$	−3.02900	−0.175760
$298$	−48.5735	−2.81379
$299$	−39.6660	−2.29394
$300$	20.4145	1.17863
$301$	9.81139	0.565519
$302$	−23.6463	−1.36069
$303$	−10.7269	−0.616243
$304$	11.9504	0.685401
$305$	0	0
$306$	−26.8103	−1.53264
$307$	17.5002	0.998789	0.499395	−	0.866375i	$-0.333556\pi$
$307$	17.5002	0.998789	0.499395	+	0.866375i	$0.333556\pi$
$308$	19.4722	1.10953
$309$	2.17364	0.123654
$310$	6.50505	0.369462
$311$	14.7425	0.835972	0.417986	−	0.908453i	$-0.362736\pi$
$311$	14.7425	0.835972	0.417986	+	0.908453i	$0.362736\pi$
$312$	−14.3926	−0.814820
$313$	−12.9067	−0.729530	−0.364765	−	0.931100i	$-0.618851\pi$
$313$	−12.9067	−0.729530	−0.364765	+	0.931100i	$0.618851\pi$
$314$	−18.4415	−1.04071
$315$	−11.1465	−0.628035
$316$	−22.9407	−1.29052
$317$	−14.6724	−0.824087	−0.412043	−	0.911164i	$-0.635185\pi$
$317$	−14.6724	−0.824087	−0.412043	+	0.911164i	$0.635185\pi$
$318$	14.7781	0.828716
$319$	−0.822638	−0.0460589
$320$	−14.2310	−0.795537
$321$	−33.5231	−1.87108
$322$	59.8882	3.33744
$323$	−24.3452	−1.35461
$324$	−26.7407	−1.48559
$325$	19.0185	1.05496
$326$	−42.3664	−2.34646
$327$	−0.918681	−0.0508032
$328$	−4.40622	−0.243293
$329$	15.2917	0.843060
$330$	−12.0235	−0.661872
$331$	1.12072	0.0616006	0.0308003	−	0.999526i	$-0.490194\pi$
$331$	1.12072	0.0616006	0.0308003	+	0.999526i	$0.490194\pi$
$332$	12.9365	0.709985
$333$	17.2504	0.945314
$334$	24.0566	1.31632
$335$	−7.46544	−0.407880
$336$	−23.6197	−1.28856
$337$	−19.4241	−1.05810	−0.529050	−	0.848591i	$-0.677452\pi$
$337$	−19.4241	−1.05810	−0.529050	+	0.848591i	$0.677452\pi$
$338$	−35.7750	−1.94590
$339$	13.8201	0.750604
$340$	16.8005	0.911137
$341$	4.92265	0.266576
$342$	22.5410	1.21888
$343$	−3.77497	−0.203829
$344$	2.89294	0.155977
$345$	−20.6735	−1.11303
$346$	−20.1429	−1.08289
$347$	28.0921	1.50806	0.754031	−	0.656839i	$-0.228107\pi$
$347$	28.0921	1.50806	0.754031	+	0.656839i	$0.228107\pi$
$348$	−2.42912	−0.130214
$349$	−11.0699	−0.592558	−0.296279	−	0.955101i	$-0.595746\pi$
$349$	−11.0699	−0.592558	−0.296279	+	0.955101i	$0.595746\pi$
$350$	−28.7144	−1.53485
$351$	−8.33249	−0.444756
$352$	−15.6914	−0.836354
$353$	−10.5167	−0.559748	−0.279874	−	0.960037i	$-0.590293\pi$
$353$	−10.5167	−0.559748	−0.279874	+	0.960037i	$0.590293\pi$
$354$	−7.21905	−0.383688
$355$	10.7462	0.570351
$356$	20.2284	1.07210
$357$	48.1180	2.54668
$358$	−3.71659	−0.196428
$359$	−11.8546	−0.625664	−0.312832	−	0.949809i	$-0.601278\pi$
$359$	−11.8546	−0.625664	−0.312832	+	0.949809i	$0.601278\pi$
$360$	−3.28661	−0.173220
$361$	1.46850	0.0772896
$362$	−47.0867	−2.47482
$363$	16.3192	0.856535
$364$	53.5664	2.80764
$365$	7.56564	0.396004
$366$	0	0
$367$	−8.31934	−0.434266	−0.217133	−	0.976142i	$-0.569671\pi$
$367$	−8.31934	−0.434266	−0.217133	+	0.976142i	$0.569671\pi$
$368$	−19.1939	−1.00055
$369$	9.03383	0.470282
$370$	−19.3358	−1.00522
$371$	−11.6209	−0.603325
$372$	14.5358	0.753644
$373$	−7.56523	−0.391713	−0.195856	−	0.980633i	$-0.562749\pi$
$373$	−7.56523	−0.391713	−0.195856	+	0.980633i	$0.562749\pi$
$374$	22.7412	1.17592
$375$	24.1375	1.24646
$376$	4.50885	0.232526
$377$	−2.26300	−0.116551
$378$	12.5805	0.647071
$379$	−21.8560	−1.12267	−0.561333	−	0.827590i	$-0.689711\pi$
$379$	−21.8560	−1.12267	−0.561333	+	0.827590i	$0.689711\pi$
$380$	−14.1252	−0.724609
$381$	−5.93016	−0.303811
$382$	8.71077	0.445682
$383$	31.1638	1.59240	0.796198	−	0.605036i	$-0.206841\pi$
$383$	31.1638	1.59240	0.796198	+	0.605036i	$0.206841\pi$
$384$	−20.3361	−1.03777
$385$	9.45475	0.481859
$386$	45.3292	2.30720
$387$	−5.93124	−0.301502
$388$	11.3481	0.576112
$389$	−24.0279	−1.21826	−0.609132	−	0.793069i	$-0.708482\pi$
$389$	−24.0279	−1.21826	−0.609132	+	0.793069i	$0.708482\pi$
$390$	−33.0756	−1.67485
$391$	39.1018	1.97746
$392$	−9.10033	−0.459636
$393$	31.0441	1.56597
$394$	1.97407	0.0994522
$395$	−11.1389	−0.560457
$396$	−11.7715	−0.591538
$397$	−1.30564	−0.0655280	−0.0327640	−	0.999463i	$-0.510431\pi$
$397$	−1.30564	−0.0655280	−0.0327640	+	0.999463i	$0.510431\pi$
$398$	59.0967	2.96225
$399$	−40.4557	−2.02532
$400$	9.20284	0.460142
$401$	−19.9221	−0.994860	−0.497430	−	0.867504i	$-0.665723\pi$
$401$	−19.9221	−0.994860	−0.497430	+	0.867504i	$0.665723\pi$
$402$	−29.8390	−1.48823
$403$	13.5418	0.674563
$404$	11.7716	0.585659
$405$	−12.9839	−0.645177
$406$	3.41671	0.169569
$407$	−14.6322	−0.725290
$408$	14.1879	0.702404
$409$	−10.8695	−0.537461	−0.268730	−	0.963215i	$-0.586604\pi$
$409$	−10.8695	−0.537461	−0.268730	+	0.963215i	$0.586604\pi$
$410$	−10.1259	−0.500084
$411$	−32.4271	−1.59951
$412$	−2.38534	−0.117517
$413$	5.67674	0.279334
$414$	−36.2039	−1.77933
$415$	6.28134	0.308339
$416$	−43.1656	−2.11637
$417$	−13.3509	−0.653794
$418$	−19.1199	−0.935183
$419$	−37.3008	−1.82226	−0.911132	−	0.412114i	$-0.864791\pi$
$419$	−37.3008	−1.82226	−0.911132	+	0.412114i	$0.864791\pi$
$420$	27.9183	1.36227
$421$	−10.4098	−0.507341	−0.253671	−	0.967291i	$-0.581638\pi$
$421$	−10.4098	−0.507341	−0.253671	+	0.967291i	$0.581638\pi$
$422$	3.66429	0.178375
$423$	−9.24424	−0.449470
$424$	−3.42647	−0.166404
$425$	−18.7480	−0.909411
$426$	42.9521	2.08104
$427$	0	0
$428$	36.7881	1.77822
$429$	−25.0297	−1.20844
$430$	6.64827	0.320608
$431$	−19.2578	−0.927614	−0.463807	−	0.885936i	$-0.653517\pi$
$431$	−19.2578	−0.927614	−0.463807	+	0.885936i	$0.653517\pi$
$432$	−4.03200	−0.193990
$433$	15.7253	0.755709	0.377855	−	0.925865i	$-0.376662\pi$
$433$	15.7253	0.755709	0.377855	+	0.925865i	$0.376662\pi$
$434$	−20.4455	−0.981416
$435$	−1.17946	−0.0565507
$436$	1.00815	0.0482819
$437$	−32.8752	−1.57263
$438$	30.2395	1.44490
$439$	−23.3265	−1.11331	−0.556657	−	0.830742i	$-0.687916\pi$
$439$	−23.3265	−1.11331	−0.556657	+	0.830742i	$0.687916\pi$
$440$	2.78779	0.132902
$441$	18.6579	0.888471
$442$	62.5589	2.97562
$443$	14.3088	0.679830	0.339915	−	0.940456i	$-0.389602\pi$
$443$	14.3088	0.679830	0.339915	+	0.940456i	$0.389602\pi$
$444$	−43.2064	−2.05049
$445$	9.82191	0.465603
$446$	31.4051	1.48708
$447$	−52.7013	−2.49268
$448$	44.7283	2.11321
$449$	7.95243	0.375298	0.187649	−	0.982236i	$-0.439913\pi$
$449$	7.95243	0.375298	0.187649	+	0.982236i	$0.439913\pi$
$450$	17.3586	0.818291
$451$	−7.66272	−0.360823
$452$	−15.1661	−0.713352
$453$	−25.6557	−1.20541
$454$	13.3711	0.627539
$455$	26.0092	1.21933
$456$	−11.9286	−0.558608
$457$	−32.1972	−1.50612	−0.753061	−	0.657951i	$-0.771424\pi$
$457$	−32.1972	−1.50612	−0.753061	+	0.657951i	$0.771424\pi$
$458$	3.88729	0.181641
$459$	8.21398	0.383396
$460$	22.6870	1.05779
$461$	31.4884	1.46656	0.733281	−	0.679926i	$-0.237988\pi$
$461$	31.4884	1.46656	0.733281	+	0.679926i	$0.237988\pi$
$462$	37.7901	1.75816
$463$	15.4042	0.715896	0.357948	−	0.933742i	$-0.383477\pi$
$463$	15.4042	0.715896	0.357948	+	0.933742i	$0.383477\pi$
$464$	−1.09504	−0.0508361
$465$	7.05784	0.327300
$466$	24.2834	1.12490
$467$	−24.6225	−1.13939	−0.569696	−	0.821855i	$-0.692939\pi$
$467$	−24.6225	−1.13939	−0.569696	+	0.821855i	$0.692939\pi$
$468$	−32.3822	−1.49687
$469$	23.4640	1.08347
$470$	10.3618	0.477953
$471$	−20.0086	−0.921948
$472$	1.67382	0.0770437
$473$	5.03102	0.231327
$474$	−44.5215	−2.04494
$475$	15.7626	0.723236
$476$	−52.8045	−2.42029
$477$	7.02510	0.321657
$478$	12.4055	0.567416
$479$	−8.83870	−0.403851	−0.201925	−	0.979401i	$-0.564720\pi$
$479$	−8.83870	−0.403851	−0.201925	+	0.979401i	$0.564720\pi$
$480$	−22.4975	−1.02687
$481$	−40.2518	−1.83532
$482$	36.9487	1.68297
$483$	64.9774	2.95657
$484$	−17.9086	−0.814026
$485$	5.51007	0.250199
$486$	−42.1433	−1.91166
$487$	−14.6614	−0.664373	−0.332187	−	0.943214i	$-0.607786\pi$
$487$	−14.6614	−0.664373	−0.332187	+	0.943214i	$0.607786\pi$
$488$	0	0
$489$	−45.9666	−2.07868
$490$	−20.9135	−0.944774
$491$	−26.5279	−1.19719	−0.598594	−	0.801053i	$-0.704274\pi$
$491$	−26.5279	−1.19719	−0.598594	+	0.801053i	$0.704274\pi$
$492$	−22.6267	−1.02009
$493$	2.23082	0.100471
$494$	−52.5970	−2.36645
$495$	−5.71564	−0.256899
$496$	6.55271	0.294225
$497$	−33.7756	−1.51504
$498$	25.1062	1.12504
$499$	15.8024	0.707412	0.353706	−	0.935357i	$-0.384921\pi$
$499$	15.8024	0.707412	0.353706	+	0.935357i	$0.384921\pi$
$500$	−26.4884	−1.18460
$501$	26.1009	1.16610
$502$	−10.8025	−0.482141
$503$	−34.7443	−1.54917	−0.774587	−	0.632468i	$-0.782042\pi$
$503$	−34.7443	−1.54917	−0.774587	+	0.632468i	$0.782042\pi$
$504$	10.3299	0.460130
$505$	5.71571	0.254346
$506$	30.7091	1.36519
$507$	−38.8151	−1.72384
$508$	6.50772	0.288733
$509$	27.2992	1.21002	0.605009	−	0.796219i	$-0.293170\pi$
$509$	27.2992	1.21002	0.605009	+	0.796219i	$0.293170\pi$
$510$	32.6051	1.44378
$511$	−23.7790	−1.05192
$512$	−26.9153	−1.18950
$513$	−6.90598	−0.304907
$514$	−46.2086	−2.03817
$515$	−1.15820	−0.0510364
$516$	14.8558	0.653989
$517$	7.84119	0.344855
$518$	60.7727	2.67020
$519$	−21.8546	−0.959312
$520$	7.66895	0.336306
$521$	−13.9517	−0.611234	−0.305617	−	0.952155i	$-0.598863\pi$
$521$	−13.9517	−0.611234	−0.305617	+	0.952155i	$0.598863\pi$
$522$	−2.06549	−0.0904041
$523$	−17.4020	−0.760936	−0.380468	−	0.924794i	$-0.624237\pi$
$523$	−17.4020	−0.760936	−0.380468	+	0.924794i	$0.624237\pi$
$524$	−34.0676	−1.48825
$525$	−31.1545	−1.35969
$526$	0.780339	0.0340244
$527$	−13.3491	−0.581498
$528$	−12.1116	−0.527089
$529$	29.8020	1.29574
$530$	−7.87437	−0.342041
$531$	−3.43173	−0.148925
$532$	44.3959	1.92481
$533$	−21.0794	−0.913052
$534$	39.2577	1.69885
$535$	17.8625	0.772261
$536$	6.91850	0.298834
$537$	−4.03242	−0.174012
$538$	43.8371	1.88995
$539$	−15.8261	−0.681678
$540$	4.76579	0.205087
$541$	33.2230	1.42837	0.714185	−	0.699957i	$-0.246798\pi$
$541$	33.2230	1.42837	0.714185	+	0.699957i	$0.246798\pi$
$542$	69.0056	2.96404
$543$	−51.0881	−2.19240
$544$	42.5516	1.82439
$545$	0.489510	0.0209683
$546$	103.957	4.44896
$547$	−44.0766	−1.88458	−0.942289	−	0.334802i	$-0.891331\pi$
$547$	−44.0766	−1.88458	−0.942289	+	0.334802i	$0.891331\pi$
$548$	35.5853	1.52013
$549$	0	0
$550$	−14.7240	−0.627833
$551$	−1.87558	−0.0799024
$552$	19.1589	0.815459
$553$	35.0097	1.48876
$554$	−8.97540	−0.381328
$555$	−20.9789	−0.890504
$556$	14.6512	0.621347
$557$	39.8522	1.68859	0.844295	−	0.535878i	$-0.180019\pi$
$557$	39.8522	1.68859	0.844295	+	0.535878i	$0.180019\pi$
$558$	12.3598	0.523234
$559$	13.8399	0.585365
$560$	12.5855	0.531836
$561$	24.6737	1.04172
$562$	−7.83761	−0.330610
$563$	−25.4157	−1.07115	−0.535573	−	0.844489i	$-0.679904\pi$
$563$	−25.4157	−1.07115	−0.535573	+	0.844489i	$0.679904\pi$
$564$	23.1538	0.974949
$565$	−7.36389	−0.309801
$566$	−42.0521	−1.76758
$567$	40.8088	1.71381
$568$	−9.95893	−0.417867
$569$	−13.9601	−0.585237	−0.292618	−	0.956229i	$-0.594527\pi$
$569$	−13.9601	−0.585237	−0.292618	+	0.956229i	$0.594527\pi$
$570$	−27.4131	−1.14821
$571$	−21.9867	−0.920114	−0.460057	−	0.887889i	$-0.652171\pi$
$571$	−21.9867	−0.920114	−0.460057	+	0.887889i	$0.652171\pi$
$572$	27.4674	1.14847
$573$	9.45100	0.394821
$574$	31.8260	1.32839
$575$	−25.3168	−1.05578
$576$	−27.0394	−1.12664
$577$	−32.9099	−1.37006	−0.685030	−	0.728515i	$-0.740211\pi$
$577$	−32.9099	−1.37006	−0.685030	+	0.728515i	$0.740211\pi$
$578$	−25.4636	−1.05915
$579$	49.1813	2.04390
$580$	1.29433	0.0537441
$581$	−19.7424	−0.819053
$582$	22.0235	0.912902
$583$	−5.95887	−0.246791
$584$	−7.01136	−0.290132
$585$	−15.7232	−0.650075
$586$	−3.64203	−0.150451
$587$	25.4227	1.04931	0.524653	−	0.851316i	$-0.324195\pi$
$587$	25.4227	1.04931	0.524653	+	0.851316i	$0.324195\pi$
$588$	−46.7318	−1.92719
$589$	11.2234	0.462453
$590$	3.84660	0.158362
$591$	2.14182	0.0881029
$592$	−19.4774	−0.800516
$593$	20.4821	0.841098	0.420549	−	0.907270i	$-0.361838\pi$
$593$	20.4821	0.841098	0.420549	+	0.907270i	$0.361838\pi$
$594$	6.45095	0.264686
$595$	−25.6392	−1.05111
$596$	57.8340	2.36897
$597$	64.1187	2.62420
$598$	84.4779	3.45456
$599$	24.3177	0.993593	0.496797	−	0.867867i	$-0.334510\pi$
$599$	24.3177	0.993593	0.496797	+	0.867867i	$0.334510\pi$
$600$	−9.18607	−0.375020
$601$	−20.0769	−0.818953	−0.409476	−	0.912321i	$-0.634289\pi$
$601$	−20.0769	−0.818953	−0.409476	+	0.912321i	$0.634289\pi$
$602$	−20.8956	−0.851643
$603$	−14.1846	−0.577642
$604$	28.1544	1.14559
$605$	−8.69551	−0.353523
$606$	22.8454	0.928030
$607$	0.0230638	0.000936129 0	0.000468065	−	1.00000i	$-0.499851\pi$
$607$	0.0230638	0.000936129 0	0.000468065		1.00000i	$0.499851\pi$
$608$	−35.7757	−1.45090
$609$	3.70706	0.150218
$610$	0	0
$611$	21.5704	0.872646
$612$	31.9217	1.29036
$613$	41.7034	1.68438	0.842192	−	0.539178i	$-0.181265\pi$
$613$	41.7034	1.68438	0.842192	+	0.539178i	$0.181265\pi$
$614$	−37.2708	−1.50413
$615$	−10.9864	−0.443015
$616$	−8.76207	−0.353034
$617$	42.4297	1.70815	0.854077	−	0.520146i	$-0.174123\pi$
$617$	42.4297	1.70815	0.854077	+	0.520146i	$0.174123\pi$
$618$	−4.62927	−0.186216
$619$	2.48351	0.0998207	0.0499103	−	0.998754i	$-0.484106\pi$
$619$	2.48351	0.0998207	0.0499103	+	0.998754i	$0.484106\pi$
$620$	−7.74524	−0.311056
$621$	11.0919	0.445104
$622$	−31.3977	−1.25893
$623$	−30.8705	−1.23680
$624$	−33.3179	−1.33378
$625$	4.55879	0.182351
$626$	27.4879	1.09864
$627$	−20.7446	−0.828461
$628$	21.9573	0.876193
$629$	39.6793	1.58212
$630$	23.7391	0.945788
$631$	17.4798	0.695861	0.347930	−	0.937520i	$-0.386885\pi$
$631$	17.4798	0.695861	0.347930	+	0.937520i	$0.386885\pi$
$632$	10.3228	0.410619
$633$	3.97568	0.158019
$634$	31.2484	1.24103
$635$	3.15983	0.125394
$636$	−17.5956	−0.697709
$637$	−43.5362	−1.72497
$638$	1.75200	0.0693624
$639$	20.4182	0.807733
$640$	10.8359	0.428326
$641$	38.8995	1.53644	0.768218	−	0.640188i	$-0.221143\pi$
$641$	38.8995	1.53644	0.768218	+	0.640188i	$0.221143\pi$
$642$	71.3953	2.81775
$643$	9.81189	0.386943	0.193472	−	0.981106i	$-0.438025\pi$
$643$	9.81189	0.386943	0.193472	+	0.981106i	$0.438025\pi$
$644$	−71.3058	−2.80984
$645$	7.21323	0.284021
$646$	51.8489	2.03997
$647$	36.8539	1.44888	0.724439	−	0.689339i	$-0.242099\pi$
$647$	36.8539	1.44888	0.724439	+	0.689339i	$0.242099\pi$
$648$	12.0327	0.472689
$649$	2.91088	0.114262
$650$	−40.5043	−1.58871
$651$	−22.1829	−0.869418
$652$	50.4435	1.97552
$653$	21.9441	0.858737	0.429369	−	0.903129i	$-0.358736\pi$
$653$	21.9441	0.858737	0.429369	+	0.903129i	$0.358736\pi$
$654$	1.95655	0.0765070
$655$	−16.5415	−0.646331
$656$	−10.2001	−0.398247
$657$	14.3750	0.560822
$658$	−32.5673	−1.26961
$659$	−2.02351	−0.0788248	−0.0394124	−	0.999223i	$-0.512549\pi$
$659$	−2.02351	−0.0788248	−0.0394124	+	0.999223i	$0.512549\pi$
$660$	14.3158	0.557241
$661$	−38.9282	−1.51413	−0.757065	−	0.653339i	$-0.773367\pi$
$661$	−38.9282	−1.51413	−0.757065	+	0.653339i	$0.773367\pi$
$662$	−2.38684	−0.0927673
$663$	67.8750	2.63605
$664$	−5.82115	−0.225905
$665$	21.5564	0.835922
$666$	−36.7387	−1.42359
$667$	3.01244	0.116642
$668$	−28.6429	−1.10823
$669$	34.0739	1.31737
$670$	15.8994	0.614247
$671$	0	0
$672$	70.7102	2.72770
$673$	−33.3724	−1.28641	−0.643205	−	0.765694i	$-0.722396\pi$
$673$	−33.3724	−1.28641	−0.643205	+	0.765694i	$0.722396\pi$
$674$	41.3682	1.59345
$675$	−5.31822	−0.204698
$676$	42.5955	1.63829
$677$	24.3898	0.937376	0.468688	−	0.883364i	$-0.344727\pi$
$677$	24.3898	0.937376	0.468688	+	0.883364i	$0.344727\pi$
$678$	−29.4331	−1.13037
$679$	−17.3183	−0.664614
$680$	−7.55987	−0.289908
$681$	14.5074	0.555925
$682$	−10.4839	−0.401450
$683$	13.2609	0.507415	0.253707	−	0.967281i	$-0.418350\pi$
$683$	13.2609	0.507415	0.253707	+	0.967281i	$0.418350\pi$
$684$	−26.8384	−1.02619
$685$	17.2785	0.660176
$686$	8.03968	0.306956
$687$	4.21763	0.160913
$688$	6.69697	0.255320
$689$	−16.3923	−0.624497
$690$	44.0291	1.67616
$691$	−7.94811	−0.302361	−0.151180	−	0.988506i	$-0.548307\pi$
$691$	−7.94811	−0.302361	−0.151180	+	0.988506i	$0.548307\pi$
$692$	23.9831	0.911702
$693$	17.9644	0.682410
$694$	−59.8286	−2.27106
$695$	7.11387	0.269845
$696$	1.09305	0.0414318
$697$	20.7796	0.787084
$698$	23.5759	0.892362
$699$	26.3469	0.996532
$700$	34.1888	1.29221
$701$	−22.8812	−0.864210	−0.432105	−	0.901823i	$-0.642229\pi$
$701$	−22.8812	−0.864210	−0.432105	+	0.901823i	$0.642229\pi$
$702$	17.7460	0.669779
$703$	−33.3608	−1.25822
$704$	22.9355	0.864414
$705$	11.2423	0.423410
$706$	22.3978	0.842953
$707$	−17.9646	−0.675628
$708$	8.59535	0.323033
$709$	40.4308	1.51841	0.759205	−	0.650852i	$-0.225588\pi$
$709$	40.4308	1.51841	0.759205	+	0.650852i	$0.225588\pi$
$710$	−22.8866	−0.858919
$711$	−21.1643	−0.793721
$712$	−9.10233	−0.341124
$713$	−18.0263	−0.675092
$714$	−102.479	−3.83517
$715$	13.3368	0.498769
$716$	4.42515	0.165376
$717$	13.4597	0.502663
$718$	25.2472	0.942218
$719$	−10.8035	−0.402904	−0.201452	−	0.979498i	$-0.564566\pi$
$719$	−10.8035	−0.402904	−0.201452	+	0.979498i	$0.564566\pi$
$720$	−7.60829	−0.283544
$721$	3.64025	0.135570
$722$	−3.12752	−0.116394
$723$	40.0885	1.49091
$724$	56.0638	2.08359
$725$	−1.44436	−0.0536423
$726$	−34.7555	−1.28990
$727$	−37.6655	−1.39694	−0.698469	−	0.715641i	$-0.746135\pi$
$727$	−37.6655	−1.39694	−0.698469	+	0.715641i	$0.746135\pi$
$728$	−24.1037	−0.893341
$729$	−14.0884	−0.521792
$730$	−16.1128	−0.596361
$731$	−13.6430	−0.504606
$732$	0	0
$733$	2.42808	0.0896831	0.0448416	−	0.998994i	$-0.485722\pi$
$733$	2.42808	0.0896831	0.0448416	+	0.998994i	$0.485722\pi$
$734$	17.7180	0.653982
$735$	−22.6907	−0.836957
$736$	57.4606	2.11803
$737$	12.0317	0.443195
$738$	−19.2396	−0.708221
$739$	1.38081	0.0507940	0.0253970	−	0.999677i	$-0.491915\pi$
$739$	1.38081	0.0507940	0.0253970	+	0.999677i	$0.491915\pi$
$740$	23.0221	0.846310
$741$	−57.0666	−2.09639
$742$	24.7493	0.908576
$743$	−33.5407	−1.23049	−0.615245	−	0.788336i	$-0.710943\pi$
$743$	−33.5407	−1.23049	−0.615245	+	0.788336i	$0.710943\pi$
$744$	−6.54077	−0.239796
$745$	28.0813	1.02882
$746$	16.1119	0.589899
$747$	11.9348	0.436671
$748$	−27.0767	−0.990024
$749$	−56.1421	−2.05139
$750$	−51.4065	−1.87710
$751$	−27.1319	−0.990057	−0.495028	−	0.868877i	$-0.664842\pi$
$751$	−27.1319	−0.990057	−0.495028	+	0.868877i	$0.664842\pi$
$752$	10.4377	0.380623
$753$	−11.7205	−0.427119
$754$	4.81960	0.175519
$755$	13.6704	0.497517
$756$	−14.9790	−0.544780
$757$	3.44351	0.125156	0.0625782	−	0.998040i	$-0.480068\pi$
$757$	3.44351	0.125156	0.0625782	+	0.998040i	$0.480068\pi$
$758$	46.5474	1.69068
$759$	33.3187	1.20939
$760$	6.35603	0.230558
$761$	−26.5679	−0.963086	−0.481543	−	0.876422i	$-0.659924\pi$
$761$	−26.5679	−0.963086	−0.481543	+	0.876422i	$0.659924\pi$
$762$	12.6297	0.457524
$763$	−1.53854	−0.0556989
$764$	−10.3715	−0.375227
$765$	15.4996	0.560388
$766$	−66.3706	−2.39807
$767$	8.00757	0.289137
$768$	−10.1052	−0.364640
$769$	−13.8092	−0.497973	−0.248986	−	0.968507i	$-0.580097\pi$
$769$	−13.8092	−0.497973	−0.248986	+	0.968507i	$0.580097\pi$
$770$	−20.1361	−0.725655
$771$	−50.1353	−1.80558
$772$	−53.9712	−1.94247
$773$	−13.2271	−0.475745	−0.237872	−	0.971296i	$-0.576450\pi$
$773$	−13.2271	−0.475745	−0.237872	+	0.971296i	$0.576450\pi$
$774$	12.6320	0.454046
$775$	8.64303	0.310467
$776$	−5.10639	−0.183309
$777$	65.9371	2.36548
$778$	51.1731	1.83464
$779$	−17.4707	−0.625952
$780$	39.3814	1.41008
$781$	−17.3193	−0.619731
$782$	−83.2763	−2.97796
$783$	0.632812	0.0226149
$784$	−21.0667	−0.752381
$785$	10.6614	0.380521
$786$	−66.1156	−2.35826
$787$	−14.0151	−0.499583	−0.249792	−	0.968300i	$-0.580362\pi$
$787$	−14.0151	−0.499583	−0.249792	+	0.968300i	$0.580362\pi$
$788$	−2.35042	−0.0837304
$789$	0.846651	0.0301416
$790$	23.7228	0.844020
$791$	23.1449	0.822937
$792$	5.29689	0.188217
$793$	0	0
$794$	2.78066	0.0986819
$795$	−8.54352	−0.303008
$796$	−70.3634	−2.49397
$797$	−9.74134	−0.345056	−0.172528	−	0.985005i	$-0.555194\pi$
$797$	−9.74134	−0.345056	−0.172528	+	0.985005i	$0.555194\pi$
$798$	86.1599	3.05003
$799$	−21.2636	−0.752252
$800$	−27.5505	−0.974056
$801$	18.6620	0.659389
$802$	42.4287	1.49821
$803$	−12.1932	−0.430289
$804$	35.5277	1.25297
$805$	−34.6226	−1.22028
$806$	−28.8403	−1.01586
$807$	47.5623	1.67427
$808$	−5.29696	−0.186346
$809$	35.0291	1.23156	0.615778	−	0.787919i	$-0.288842\pi$
$809$	35.0291	1.23156	0.615778	+	0.787919i	$0.288842\pi$
$810$	27.6523	0.971604
$811$	−17.5223	−0.615293	−0.307646	−	0.951501i	$-0.599541\pi$
$811$	−17.5223	−0.615293	−0.307646	+	0.951501i	$0.599541\pi$
$812$	−4.06811	−0.142763
$813$	74.8696	2.62579
$814$	31.1627	1.09225
$815$	24.4928	0.857947
$816$	32.8440	1.14977
$817$	11.4705	0.401303
$818$	23.1491	0.809388
$819$	49.4184	1.72682
$820$	12.0564	0.421029
$821$	−12.6151	−0.440269	−0.220135	−	0.975469i	$-0.570650\pi$
$821$	−12.6151	−0.440269	−0.220135	+	0.975469i	$0.570650\pi$
$822$	69.0611	2.40878
$823$	−40.8927	−1.42543	−0.712714	−	0.701455i	$-0.752534\pi$
$823$	−40.8927	−1.42543	−0.712714	+	0.701455i	$0.752534\pi$
$824$	1.07335	0.0373918
$825$	−15.9752	−0.556185
$826$	−12.0899	−0.420663
$827$	−11.7912	−0.410020	−0.205010	−	0.978760i	$-0.565723\pi$
$827$	−11.7912	−0.410020	−0.205010	+	0.978760i	$0.565723\pi$
$828$	43.1062	1.49804
$829$	13.8059	0.479500	0.239750	−	0.970835i	$-0.422935\pi$
$829$	13.8059	0.479500	0.239750	+	0.970835i	$0.422935\pi$
$830$	−13.3776	−0.464343
$831$	−9.73812	−0.337812
$832$	63.0935	2.18737
$833$	42.9169	1.48698
$834$	28.4338	0.984581
$835$	−13.9076	−0.481292
$836$	22.7650	0.787345
$837$	−3.78673	−0.130889
$838$	79.4408	2.74424
$839$	11.6503	0.402214	0.201107	−	0.979569i	$-0.435546\pi$
$839$	11.6503	0.402214	0.201107	+	0.979569i	$0.435546\pi$
$840$	−12.5626	−0.433451
$841$	−28.8281	−0.994074
$842$	22.1700	0.764030
$843$	−8.50364	−0.292881
$844$	−4.36288	−0.150177
$845$	20.6822	0.711491
$846$	19.6878	0.676879
$847$	27.3302	0.939076
$848$	−7.93206	−0.272388
$849$	−45.6256	−1.56587
$850$	39.9282	1.36953
$851$	53.5819	1.83676
$852$	−51.1409	−1.75206
$853$	−18.2376	−0.624444	−0.312222	−	0.950009i	$-0.601073\pi$
$853$	−18.2376	−0.624444	−0.312222	+	0.950009i	$0.601073\pi$
$854$	0	0
$855$	−13.0314	−0.445665
$856$	−16.5538	−0.565797
$857$	−50.3463	−1.71980	−0.859898	−	0.510465i	$-0.829473\pi$
$857$	−50.3463	−1.71980	−0.859898	+	0.510465i	$0.829473\pi$
$858$	53.3066	1.81986
$859$	51.0133	1.74055	0.870276	−	0.492565i	$-0.163940\pi$
$859$	51.0133	1.74055	0.870276	+	0.492565i	$0.163940\pi$
$860$	−7.91576	−0.269925
$861$	34.5305	1.17680
$862$	41.0139	1.39694
$863$	29.5619	1.00630	0.503149	−	0.864200i	$-0.332175\pi$
$863$	29.5619	1.00630	0.503149	+	0.864200i	$0.332175\pi$
$864$	12.0706	0.410649
$865$	11.6450	0.395943
$866$	−33.4907	−1.13806
$867$	−27.6275	−0.938278
$868$	24.3434	0.826270
$869$	17.9520	0.608981
$870$	2.51193	0.0851624
$871$	33.0982	1.12149
$872$	−0.453647	−0.0153624
$873$	10.4693	0.354333
$874$	70.0154	2.36831
$875$	40.4238	1.36657
$876$	−36.0046	−1.21648
$877$	−5.74437	−0.193973	−0.0969867	−	0.995286i	$-0.530920\pi$
$877$	−5.74437	−0.193973	−0.0969867	+	0.995286i	$0.530920\pi$
$878$	49.6793	1.67659
$879$	−3.95153	−0.133282
$880$	6.45354	0.217549
$881$	−35.2701	−1.18828	−0.594141	−	0.804361i	$-0.702508\pi$
$881$	−35.2701	−1.18828	−0.594141	+	0.804361i	$0.702508\pi$
$882$	−39.7363	−1.33799
$883$	−40.4178	−1.36017	−0.680083	−	0.733135i	$-0.738056\pi$
$883$	−40.4178	−1.36017	−0.680083	+	0.733135i	$0.738056\pi$
$884$	−74.4857	−2.50522
$885$	4.17348	0.140290
$886$	−30.4739	−1.02379
$887$	23.3404	0.783695	0.391848	−	0.920030i	$-0.371836\pi$
$887$	23.3404	0.783695	0.391848	+	0.920030i	$0.371836\pi$
$888$	19.4419	0.652428
$889$	−9.93140	−0.333088
$890$	−20.9181	−0.701175
$891$	20.9257	0.701036
$892$	−37.3925	−1.25199
$893$	17.8776	0.598251
$894$	112.240	3.75385
$895$	2.14863	0.0718209
$896$	−34.0574	−1.13778
$897$	91.6567	3.06033
$898$	−16.9366	−0.565180
$899$	−1.02843	−0.0343001
$900$	−20.6680	−0.688933
$901$	16.1591	0.538339
$902$	16.3195	0.543381
$903$	−22.6713	−0.754455
$904$	6.82439	0.226976
$905$	27.2218	0.904883
$906$	54.6399	1.81529
$907$	1.61768	0.0537142	0.0268571	−	0.999639i	$-0.491450\pi$
$907$	1.61768	0.0537142	0.0268571	+	0.999639i	$0.491450\pi$
$908$	−15.9203	−0.528335
$909$	10.8601	0.360205
$910$	−55.3926	−1.83625
$911$	−36.3708	−1.20502	−0.602509	−	0.798112i	$-0.705832\pi$
$911$	−36.3708	−1.20502	−0.602509	+	0.798112i	$0.705832\pi$
$912$	−27.6139	−0.914388
$913$	−10.1234	−0.335035
$914$	68.5715	2.26814
$915$	0	0
$916$	−4.62840	−0.152927
$917$	51.9903	1.71687
$918$	−17.4936	−0.577374
$919$	17.1832	0.566820	0.283410	−	0.958999i	$-0.408534\pi$
$919$	17.1832	0.566820	0.283410	+	0.958999i	$0.408534\pi$
$920$	−10.2087	−0.336569
$921$	−40.4380	−1.33248
$922$	−67.0619	−2.20857
$923$	−47.6437	−1.56821
$924$	−44.9948	−1.48022
$925$	−25.6907	−0.844706
$926$	−32.8069	−1.07810
$927$	−2.20062	−0.0722780
$928$	3.27822	0.107613
$929$	23.1638	0.759980	0.379990	−	0.924991i	$-0.375927\pi$
$929$	23.1638	0.759980	0.379990	+	0.924991i	$0.375927\pi$
$930$	−15.0313	−0.492897
$931$	−36.0828	−1.18257
$932$	−28.9130	−0.947075
$933$	−34.0658	−1.11526
$934$	52.4393	1.71587
$935$	−13.1471	−0.429957
$936$	14.5713	0.476277
$937$	2.67762	0.0874741	0.0437370	−	0.999043i	$-0.486074\pi$
$937$	2.67762	0.0874741	0.0437370	+	0.999043i	$0.486074\pi$
$938$	−49.9721	−1.63165
$939$	29.8237	0.973261
$940$	−12.3372	−0.402397
$941$	−48.6027	−1.58440	−0.792202	−	0.610259i	$-0.791065\pi$
$941$	−48.6027	−1.58440	−0.792202	+	0.610259i	$0.791065\pi$
$942$	42.6130	1.38841
$943$	28.0603	0.913768
$944$	3.87478	0.126113
$945$	−7.27304	−0.236592
$946$	−10.7147	−0.348366
$947$	55.7385	1.81126	0.905630	−	0.424070i	$-0.139399\pi$
$947$	55.7385	1.81126	0.905630	+	0.424070i	$0.139399\pi$
$948$	53.0094	1.72167
$949$	−33.5425	−1.08883
$950$	−33.5701	−1.08916
$951$	33.9038	1.09941
$952$	23.7608	0.770093
$953$	−27.0431	−0.876012	−0.438006	−	0.898972i	$-0.644315\pi$
$953$	−27.0431	−0.876012	−0.438006	+	0.898972i	$0.644315\pi$
$954$	−14.9616	−0.484400
$955$	−5.03587	−0.162957
$956$	−14.7706	−0.477717
$957$	1.90088	0.0614468
$958$	18.8241	0.608179
$959$	−54.3065	−1.75365
$960$	32.8838	1.06132
$961$	−24.8459	−0.801481
$962$	85.7257	2.76391
$963$	33.9393	1.09368
$964$	−43.9929	−1.41692
$965$	−26.2057	−0.843593
$966$	−138.385	−4.45245
$967$	−20.0900	−0.646050	−0.323025	−	0.946390i	$-0.604700\pi$
$967$	−20.0900	−0.646050	−0.323025	+	0.946390i	$0.604700\pi$
$968$	8.05845	0.259008
$969$	56.2549	1.80717
$970$	−11.7350	−0.376788
$971$	20.9208	0.671381	0.335690	−	0.941972i	$-0.391030\pi$
$971$	20.9208	0.671381	0.335690	+	0.941972i	$0.391030\pi$
$972$	50.1779	1.60946
$973$	−22.3591	−0.716798
$974$	31.2250	1.00051
$975$	−43.9463	−1.40741
$976$	0	0
$977$	60.1275	1.92365	0.961824	−	0.273669i	$-0.0882372\pi$
$977$	60.1275	1.92365	0.961824	+	0.273669i	$0.0882372\pi$
$978$	97.8966	3.13039
$979$	−15.8296	−0.505915
$980$	24.9006	0.795420
$981$	0.930087	0.0296954
$982$	56.4974	1.80290
$983$	−33.3865	−1.06486	−0.532432	−	0.846473i	$-0.678722\pi$
$983$	−33.3865	−1.06486	−0.532432	+	0.846473i	$0.678722\pi$
$984$	10.1815	0.324575
$985$	−1.14125	−0.0363632
$986$	−4.75104	−0.151304
$987$	−35.3348	−1.12472
$988$	62.6246	1.99235
$989$	−18.4232	−0.585824
$990$	12.1728	0.386877
$991$	−30.1575	−0.957986	−0.478993	−	0.877819i	$-0.658998\pi$
$991$	−30.1575	−0.957986	−0.478993	+	0.877819i	$0.658998\pi$
$992$	−19.6168	−0.622833
$993$	−2.58967	−0.0821808
$994$	71.9331	2.28158
$995$	−34.1650	−1.08310
$996$	−29.8927	−0.947186
$997$	−36.4997	−1.15596	−0.577979	−	0.816052i	$-0.696158\pi$
$997$	−36.4997	−1.15596	−0.577979	+	0.816052i	$0.696158\pi$
$998$	−33.6549	−1.06533
$999$	11.2558	0.356117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3721.2.a.j.1.4		16
61.16	even	15		61.2.i.a.12.2	✓	32
61.42	even	15		61.2.i.a.56.2	yes	32
61.60	even	2		3721.2.a.l.1.13		16
183.77	odd	30		549.2.bl.b.73.3		32
183.164	odd	30		549.2.bl.b.361.3		32
244.103	odd	30		976.2.bw.c.849.1		32
244.199	odd	30		976.2.bw.c.561.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.12.2	✓	32	61.16	even	15
61.2.i.a.56.2	yes	32	61.42	even	15
549.2.bl.b.73.3		32	183.77	odd	30
549.2.bl.b.361.3		32	183.164	odd	30
976.2.bw.c.561.1		32	244.199	odd	30
976.2.bw.c.849.1		32	244.103	odd	30
3721.2.a.j.1.4		16	1.1	even	1	trivial
3721.2.a.l.1.13		16	61.60	even	2

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:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12973 q^{2} -2.31072 q^{3} +2.53577 q^{4} +1.23124 q^{5} +4.92121 q^{6} -3.86982 q^{7} -1.14104 q^{8} +2.33940 q^{9} +O(q^{10})\)	\(q-2.12973 q^{2} -2.31072 q^{3} +2.53577 q^{4} +1.23124 q^{5} +4.92121 q^{6} -3.86982 q^{7} -1.14104 q^{8} +2.33940 q^{9} -2.62222 q^{10} -1.98434 q^{11} -5.85943 q^{12} -5.45874 q^{13} +8.24168 q^{14} -2.84505 q^{15} -2.64143 q^{16} +5.38110 q^{17} -4.98231 q^{18} -4.52421 q^{19} +3.12214 q^{20} +8.94205 q^{21} +4.22612 q^{22} +7.26650 q^{23} +2.63661 q^{24} -3.48404 q^{25} +11.6257 q^{26} +1.52645 q^{27} -9.81295 q^{28} +0.414565 q^{29} +6.05920 q^{30} -2.48075 q^{31} +7.90761 q^{32} +4.58525 q^{33} -11.4603 q^{34} -4.76468 q^{35} +5.93218 q^{36} +7.37383 q^{37} +9.63537 q^{38} +12.6136 q^{39} -1.40489 q^{40} +3.86159 q^{41} -19.0442 q^{42} -2.53536 q^{43} -5.03182 q^{44} +2.88037 q^{45} -15.4757 q^{46} -3.95154 q^{47} +6.10358 q^{48} +7.97549 q^{49} +7.42009 q^{50} -12.4342 q^{51} -13.8421 q^{52} +3.00295 q^{53} -3.25093 q^{54} -2.44320 q^{55} +4.41561 q^{56} +10.4542 q^{57} -0.882913 q^{58} -1.46693 q^{59} -7.21437 q^{60} +5.28333 q^{62} -9.05307 q^{63} -11.5582 q^{64} -6.72103 q^{65} -9.76535 q^{66} -6.06334 q^{67} +13.6452 q^{68} -16.7908 q^{69} +10.1475 q^{70} +8.72796 q^{71} -2.66935 q^{72} +6.14472 q^{73} -15.7043 q^{74} +8.05063 q^{75} -11.4723 q^{76} +7.67904 q^{77} -26.8636 q^{78} -9.04686 q^{79} -3.25223 q^{80} -10.5454 q^{81} -8.22416 q^{82} +5.10163 q^{83} +22.6749 q^{84} +6.62543 q^{85} +5.39965 q^{86} -0.957942 q^{87} +2.26421 q^{88} +7.97724 q^{89} -6.13442 q^{90} +21.1243 q^{91} +18.4261 q^{92} +5.73230 q^{93} +8.41572 q^{94} -5.57040 q^{95} -18.2722 q^{96} +4.47521 q^{97} -16.9857 q^{98} -4.64217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q - 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} + 9 q^{6} + 4 q^{7} - 12 q^{8} + 4 q^{9} + 20 q^{10} - 9 q^{11} - 17 q^{12} - 11 q^{14} - 12 q^{15} + 9 q^{16} + 4 q^{17} - 35 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} - 11 q^{22} + 4 q^{23} + 15 q^{24} - 8 q^{25} + 19 q^{26} - 5 q^{27} + 22 q^{28} + 4 q^{29} - 24 q^{30} - 9 q^{31} - 34 q^{32} + 10 q^{33} - 6 q^{34} - 37 q^{35} + 20 q^{36} + 38 q^{37} + 18 q^{38} - 12 q^{39} + 60 q^{40} - 37 q^{41} + 17 q^{42} + 15 q^{43} - 34 q^{44} - 32 q^{45} - 41 q^{46} - 40 q^{47} - 43 q^{48} + 24 q^{49} - 28 q^{50} + 19 q^{51} - 56 q^{52} - 19 q^{53} + 6 q^{54} - 30 q^{55} - 58 q^{56} + 8 q^{57} - 21 q^{58} + q^{59} - 10 q^{60} - 37 q^{62} - 17 q^{63} + 28 q^{64} - 34 q^{65} - 59 q^{66} + 3 q^{67} - 2 q^{68} - 31 q^{69} + 17 q^{70} - 8 q^{71} + 9 q^{72} + 6 q^{73} + 10 q^{74} - q^{75} - 65 q^{76} - 39 q^{77} + 68 q^{78} - 56 q^{79} - 14 q^{80} - 56 q^{81} - 39 q^{82} + 6 q^{83} + 65 q^{84} + 53 q^{85} - 54 q^{86} + 83 q^{87} - 5 q^{88} + 66 q^{89} + 60 q^{90} + 5 q^{91} - 37 q^{92} - 67 q^{93} + 43 q^{94} - 39 q^{95} - 14 q^{96} + 13 q^{97} + 16 q^{98} + 47 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 + 9 * q^6 + 4 * q^7 - 12 * q^8 + 4 * q^9 + 20 * q^10 - 9 * q^11 - 17 * q^12 - 11 * q^14 - 12 * q^15 + 9 * q^16 + 4 * q^17 - 35 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 - 11 * q^22 + 4 * q^23 + 15 * q^24 - 8 * q^25 + 19 * q^26 - 5 * q^27 + 22 * q^28 + 4 * q^29 - 24 * q^30 - 9 * q^31 - 34 * q^32 + 10 * q^33 - 6 * q^34 - 37 * q^35 + 20 * q^36 + 38 * q^37 + 18 * q^38 - 12 * q^39 + 60 * q^40 - 37 * q^41 + 17 * q^42 + 15 * q^43 - 34 * q^44 - 32 * q^45 - 41 * q^46 - 40 * q^47 - 43 * q^48 + 24 * q^49 - 28 * q^50 + 19 * q^51 - 56 * q^52 - 19 * q^53 + 6 * q^54 - 30 * q^55 - 58 * q^56 + 8 * q^57 - 21 * q^58 + q^59 - 10 * q^60 - 37 * q^62 - 17 * q^63 + 28 * q^64 - 34 * q^65 - 59 * q^66 + 3 * q^67 - 2 * q^68 - 31 * q^69 + 17 * q^70 - 8 * q^71 + 9 * q^72 + 6 * q^73 + 10 * q^74 - q^75 - 65 * q^76 - 39 * q^77 + 68 * q^78 - 56 * q^79 - 14 * q^80 - 56 * q^81 - 39 * q^82 + 6 * q^83 + 65 * q^84 + 53 * q^85 - 54 * q^86 + 83 * q^87 - 5 * q^88 + 66 * q^89 + 60 * q^90 + 5 * q^91 - 37 * q^92 - 67 * q^93 + 43 * q^94 - 39 * q^95 - 14 * q^96 + 13 * q^97 + 16 * q^98 + 47 * q^99

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