LMFDB - Embedded newform 8043.2.a.q.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.20214 q^{2} +1.00000 q^{3} -0.554856 q^{4} -0.710682 q^{5} -1.20214 q^{6} -1.00000 q^{7} +3.07130 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.20214 q^{2} +1.00000 q^{3} -0.554856 q^{4} -0.710682 q^{5} -1.20214 q^{6} -1.00000 q^{7} +3.07130 q^{8} +1.00000 q^{9} +0.854341 q^{10} +4.29139 q^{11} -0.554856 q^{12} -0.453742 q^{13} +1.20214 q^{14} -0.710682 q^{15} -2.58242 q^{16} +2.81690 q^{17} -1.20214 q^{18} -4.03447 q^{19} +0.394326 q^{20} -1.00000 q^{21} -5.15886 q^{22} +0.134035 q^{23} +3.07130 q^{24} -4.49493 q^{25} +0.545462 q^{26} +1.00000 q^{27} +0.554856 q^{28} +10.5955 q^{29} +0.854341 q^{30} -8.49499 q^{31} -3.03816 q^{32} +4.29139 q^{33} -3.38631 q^{34} +0.710682 q^{35} -0.554856 q^{36} +3.22345 q^{37} +4.85001 q^{38} -0.453742 q^{39} -2.18272 q^{40} -8.16684 q^{41} +1.20214 q^{42} -11.3731 q^{43} -2.38110 q^{44} -0.710682 q^{45} -0.161129 q^{46} -0.247867 q^{47} -2.58242 q^{48} +1.00000 q^{49} +5.40354 q^{50} +2.81690 q^{51} +0.251761 q^{52} +9.46209 q^{53} -1.20214 q^{54} -3.04981 q^{55} -3.07130 q^{56} -4.03447 q^{57} -12.7373 q^{58} -10.6577 q^{59} +0.394326 q^{60} -4.10013 q^{61} +10.2122 q^{62} -1.00000 q^{63} +8.81714 q^{64} +0.322466 q^{65} -5.15886 q^{66} +0.630549 q^{67} -1.56297 q^{68} +0.134035 q^{69} -0.854341 q^{70} +0.205700 q^{71} +3.07130 q^{72} -2.56439 q^{73} -3.87504 q^{74} -4.49493 q^{75} +2.23855 q^{76} -4.29139 q^{77} +0.545462 q^{78} +7.76979 q^{79} +1.83528 q^{80} +1.00000 q^{81} +9.81769 q^{82} +13.6719 q^{83} +0.554856 q^{84} -2.00192 q^{85} +13.6721 q^{86} +10.5955 q^{87} +13.1801 q^{88} -16.0109 q^{89} +0.854341 q^{90} +0.453742 q^{91} -0.0743701 q^{92} -8.49499 q^{93} +0.297971 q^{94} +2.86723 q^{95} -3.03816 q^{96} -11.0979 q^{97} -1.20214 q^{98} +4.29139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.20214	−0.850042	−0.425021	−	0.905183i	$-0.639733\pi$
$2$	−1.20214	−0.850042	−0.425021	+	0.905183i	$0.639733\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.554856	−0.277428
$5$	−0.710682	−0.317827	−0.158913	−	0.987293i	$-0.550799\pi$
$5$	−0.710682	−0.317827	−0.158913	+	0.987293i	$0.550799\pi$
$6$	−1.20214	−0.490772
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.07130	1.08587
$9$	1.00000	0.333333
$10$	0.854341	0.270166
$11$	4.29139	1.29390	0.646951	−	0.762531i	$-0.276044\pi$
$11$	4.29139	1.29390	0.646951	+	0.762531i	$0.276044\pi$
$12$	−0.554856	−0.160173
$13$	−0.453742	−0.125845	−0.0629227	−	0.998018i	$-0.520042\pi$
$13$	−0.453742	−0.125845	−0.0629227	+	0.998018i	$0.520042\pi$
$14$	1.20214	0.321286
$15$	−0.710682	−0.183497
$16$	−2.58242	−0.645606
$17$	2.81690	0.683198	0.341599	−	0.939846i	$-0.389031\pi$
$17$	2.81690	0.683198	0.341599	+	0.939846i	$0.389031\pi$
$18$	−1.20214	−0.283347
$19$	−4.03447	−0.925572	−0.462786	−	0.886470i	$-0.653150\pi$
$19$	−4.03447	−0.925572	−0.462786	+	0.886470i	$0.653150\pi$
$20$	0.394326	0.0881741
$21$	−1.00000	−0.218218
$22$	−5.15886	−1.09987
$23$	0.134035	0.0279482	0.0139741	−	0.999902i	$-0.495552\pi$
$23$	0.134035	0.0279482	0.0139741	+	0.999902i	$0.495552\pi$
$24$	3.07130	0.626926
$25$	−4.49493	−0.898986
$26$	0.545462	0.106974
$27$	1.00000	0.192450
$28$	0.554856	0.104858
$29$	10.5955	1.96753	0.983767	−	0.179448i	$-0.0574311\pi$
$29$	10.5955	1.96753	0.983767	+	0.179448i	$0.0574311\pi$
$30$	0.854341	0.155981
$31$	−8.49499	−1.52575	−0.762873	−	0.646549i	$-0.776212\pi$
$31$	−8.49499	−1.52575	−0.762873	+	0.646549i	$0.776212\pi$
$32$	−3.03816	−0.537076
$33$	4.29139	0.747035
$34$	−3.38631	−0.580748
$35$	0.710682	0.120127
$36$	−0.554856	−0.0924760
$37$	3.22345	0.529932	0.264966	−	0.964258i	$-0.414639\pi$
$37$	3.22345	0.529932	0.264966	+	0.964258i	$0.414639\pi$
$38$	4.85001	0.786775
$39$	−0.453742	−0.0726568
$40$	−2.18272	−0.345118
$41$	−8.16684	−1.27545	−0.637723	−	0.770266i	$-0.720123\pi$
$41$	−8.16684	−1.27545	−0.637723	+	0.770266i	$0.720123\pi$
$42$	1.20214	0.185494
$43$	−11.3731	−1.73439	−0.867193	−	0.497972i	$-0.834078\pi$
$43$	−11.3731	−1.73439	−0.867193	+	0.497972i	$0.834078\pi$
$44$	−2.38110	−0.358965
$45$	−0.710682	−0.105942
$46$	−0.161129	−0.0237572
$47$	−0.247867	−0.0361551	−0.0180775	−	0.999837i	$-0.505755\pi$
$47$	−0.247867	−0.0361551	−0.0180775	+	0.999837i	$0.505755\pi$
$48$	−2.58242	−0.372741
$49$	1.00000	0.142857
$50$	5.40354	0.764176
$51$	2.81690	0.394445
$52$	0.251761	0.0349130
$53$	9.46209	1.29972	0.649859	−	0.760055i	$-0.274828\pi$
$53$	9.46209	1.29972	0.649859	+	0.760055i	$0.274828\pi$
$54$	−1.20214	−0.163591
$55$	−3.04981	−0.411237
$56$	−3.07130	−0.410419
$57$	−4.03447	−0.534379
$58$	−12.7373	−1.67249
$59$	−10.6577	−1.38751	−0.693756	−	0.720210i	$-0.744046\pi$
$59$	−10.6577	−1.38751	−0.693756	+	0.720210i	$0.744046\pi$
$60$	0.394326	0.0509073
$61$	−4.10013	−0.524968	−0.262484	−	0.964936i	$-0.584542\pi$
$61$	−4.10013	−0.524968	−0.262484	+	0.964936i	$0.584542\pi$
$62$	10.2122	1.29695
$63$	−1.00000	−0.125988
$64$	8.81714	1.10214
$65$	0.322466	0.0399970
$66$	−5.15886	−0.635011
$67$	0.630549	0.0770338	0.0385169	−	0.999258i	$-0.487737\pi$
$67$	0.630549	0.0770338	0.0385169	+	0.999258i	$0.487737\pi$
$68$	−1.56297	−0.189538
$69$	0.134035	0.0161359
$70$	−0.854341	−0.102113
$71$	0.205700	0.0244121	0.0122061	−	0.999926i	$-0.496115\pi$
$71$	0.205700	0.0244121	0.0122061	+	0.999926i	$0.496115\pi$
$72$	3.07130	0.361956
$73$	−2.56439	−0.300140	−0.150070	−	0.988675i	$-0.547950\pi$
$73$	−2.56439	−0.300140	−0.150070	+	0.988675i	$0.547950\pi$
$74$	−3.87504	−0.450464
$75$	−4.49493	−0.519030
$76$	2.23855	0.256779
$77$	−4.29139	−0.489049
$78$	0.545462	0.0617614
$79$	7.76979	0.874169	0.437085	−	0.899420i	$-0.356011\pi$
$79$	7.76979	0.874169	0.437085	+	0.899420i	$0.356011\pi$
$80$	1.83528	0.205191
$81$	1.00000	0.111111
$82$	9.81769	1.08418
$83$	13.6719	1.50068	0.750342	−	0.661049i	$-0.229889\pi$
$83$	13.6719	1.50068	0.750342	+	0.661049i	$0.229889\pi$
$84$	0.554856	0.0605398
$85$	−2.00192	−0.217139
$86$	13.6721	1.47430
$87$	10.5955	1.13596
$88$	13.1801	1.40501
$89$	−16.0109	−1.69715	−0.848576	−	0.529073i	$-0.822540\pi$
$89$	−16.0109	−1.69715	−0.848576	+	0.529073i	$0.822540\pi$
$90$	0.854341	0.0900554
$91$	0.453742	0.0475651
$92$	−0.0743701	−0.00775362
$93$	−8.49499	−0.880890
$94$	0.297971	0.0307334
$95$	2.86723	0.294171
$96$	−3.03816	−0.310081
$97$	−11.0979	−1.12682	−0.563408	−	0.826179i	$-0.690510\pi$
$97$	−11.0979	−1.12682	−0.563408	+	0.826179i	$0.690510\pi$
$98$	−1.20214	−0.121435
$99$	4.29139	0.431301
$100$	2.49404	0.249404
$101$	1.94214	0.193250	0.0966252	−	0.995321i	$-0.469195\pi$
$101$	1.94214	0.193250	0.0966252	+	0.995321i	$0.469195\pi$
$102$	−3.38631	−0.335295
$103$	−5.45138	−0.537140	−0.268570	−	0.963260i	$-0.586551\pi$
$103$	−5.45138	−0.537140	−0.268570	+	0.963260i	$0.586551\pi$
$104$	−1.39358	−0.136651
$105$	0.710682	0.0693555
$106$	−11.3748	−1.10482
$107$	5.40198	0.522229	0.261115	−	0.965308i	$-0.415910\pi$
$107$	5.40198	0.522229	0.261115	+	0.965308i	$0.415910\pi$
$108$	−0.554856	−0.0533910
$109$	−12.8868	−1.23433	−0.617164	−	0.786835i	$-0.711719\pi$
$109$	−12.8868	−1.23433	−0.617164	+	0.786835i	$0.711719\pi$
$110$	3.66631	0.349569
$111$	3.22345	0.305956
$112$	2.58242	0.244016
$113$	4.55364	0.428371	0.214185	−	0.976793i	$-0.431290\pi$
$113$	4.55364	0.428371	0.214185	+	0.976793i	$0.431290\pi$
$114$	4.85001	0.454245
$115$	−0.0952563	−0.00888269
$116$	−5.87898	−0.545849
$117$	−0.453742	−0.0419485
$118$	12.8120	1.17944
$119$	−2.81690	−0.258225
$120$	−2.18272	−0.199254
$121$	7.41602	0.674183
$122$	4.92894	0.446245
$123$	−8.16684	−0.736379
$124$	4.71350	0.423285
$125$	6.74788	0.603549
$126$	1.20214	0.107095
$127$	−3.07844	−0.273167	−0.136583	−	0.990629i	$-0.543612\pi$
$127$	−3.07844	−0.273167	−0.136583	+	0.990629i	$0.543612\pi$
$128$	−4.52313	−0.399792
$129$	−11.3731	−1.00135
$130$	−0.387650	−0.0339992
$131$	−20.4511	−1.78682	−0.893411	−	0.449240i	$-0.851695\pi$
$131$	−20.4511	−1.78682	−0.893411	+	0.449240i	$0.851695\pi$
$132$	−2.38110	−0.207248
$133$	4.03447	0.349833
$134$	−0.758009	−0.0654820
$135$	−0.710682	−0.0611658
$136$	8.65154	0.741863
$137$	5.94409	0.507838	0.253919	−	0.967225i	$-0.418280\pi$
$137$	5.94409	0.507838	0.253919	+	0.967225i	$0.418280\pi$
$138$	−0.161129	−0.0137162
$139$	8.78879	0.745456	0.372728	−	0.927941i	$-0.378423\pi$
$139$	8.78879	0.745456	0.372728	+	0.927941i	$0.378423\pi$
$140$	−0.394326	−0.0333267
$141$	−0.247867	−0.0208741
$142$	−0.247281	−0.0207514
$143$	−1.94718	−0.162832
$144$	−2.58242	−0.215202
$145$	−7.53004	−0.625335
$146$	3.08276	0.255131
$147$	1.00000	0.0824786
$148$	−1.78855	−0.147018
$149$	−9.01777	−0.738765	−0.369382	−	0.929278i	$-0.620431\pi$
$149$	−9.01777	−0.738765	−0.369382	+	0.929278i	$0.620431\pi$
$150$	5.40354	0.441197
$151$	−0.529859	−0.0431193	−0.0215596	−	0.999768i	$-0.506863\pi$
$151$	−0.529859	−0.0431193	−0.0215596	+	0.999768i	$0.506863\pi$
$152$	−12.3911	−1.00505
$153$	2.81690	0.227733
$154$	5.15886	0.415712
$155$	6.03724	0.484923
$156$	0.251761	0.0201570
$157$	−6.14923	−0.490762	−0.245381	−	0.969427i	$-0.578913\pi$
$157$	−6.14923	−0.490762	−0.245381	+	0.969427i	$0.578913\pi$
$158$	−9.34038	−0.743081
$159$	9.46209	0.750393
$160$	2.15917	0.170697
$161$	−0.134035	−0.0105634
$162$	−1.20214	−0.0944491
$163$	23.0149	1.80267	0.901335	−	0.433123i	$-0.142589\pi$
$163$	23.0149	1.80267	0.901335	+	0.433123i	$0.142589\pi$
$164$	4.53142	0.353844
$165$	−3.04981	−0.237428
$166$	−16.4355	−1.27565
$167$	4.42086	0.342096	0.171048	−	0.985263i	$-0.445285\pi$
$167$	4.42086	0.342096	0.171048	+	0.985263i	$0.445285\pi$
$168$	−3.07130	−0.236956
$169$	−12.7941	−0.984163
$170$	2.40659	0.184577
$171$	−4.03447	−0.308524
$172$	6.31045	0.481167
$173$	−7.18175	−0.546018	−0.273009	−	0.962011i	$-0.588019\pi$
$173$	−7.18175	−0.546018	−0.273009	+	0.962011i	$0.588019\pi$
$174$	−12.7373	−0.965611
$175$	4.49493	0.339785
$176$	−11.0822	−0.835351
$177$	−10.6577	−0.801081
$178$	19.2474	1.44265
$179$	21.6029	1.61468	0.807338	−	0.590089i	$-0.200907\pi$
$179$	21.6029	1.61468	0.807338	+	0.590089i	$0.200907\pi$
$180$	0.394326	0.0293914
$181$	19.6392	1.45977	0.729887	−	0.683568i	$-0.239573\pi$
$181$	19.6392	1.45977	0.729887	+	0.683568i	$0.239573\pi$
$182$	−0.545462	−0.0404323
$183$	−4.10013	−0.303091
$184$	0.411661	0.0303481
$185$	−2.29085	−0.168427
$186$	10.2122	0.748794
$187$	12.0884	0.883992
$188$	0.137530	0.0100304
$189$	−1.00000	−0.0727393
$190$	−3.44681	−0.250058
$191$	−12.6020	−0.911848	−0.455924	−	0.890019i	$-0.650691\pi$
$191$	−12.6020	−0.911848	−0.455924	+	0.890019i	$0.650691\pi$
$192$	8.81714	0.636322
$193$	−1.67886	−0.120847	−0.0604234	−	0.998173i	$-0.519245\pi$
$193$	−1.67886	−0.120847	−0.0604234	+	0.998173i	$0.519245\pi$
$194$	13.3412	0.957842
$195$	0.322466	0.0230923
$196$	−0.554856	−0.0396326
$197$	5.79154	0.412630	0.206315	−	0.978486i	$-0.433853\pi$
$197$	5.79154	0.412630	0.206315	+	0.978486i	$0.433853\pi$
$198$	−5.15886	−0.366624
$199$	−6.41777	−0.454944	−0.227472	−	0.973785i	$-0.573046\pi$
$199$	−6.41777	−0.454944	−0.227472	+	0.973785i	$0.573046\pi$
$200$	−13.8053	−0.976180
$201$	0.630549	0.0444755
$202$	−2.33473	−0.164271
$203$	−10.5955	−0.743658
$204$	−1.56297	−0.109430
$205$	5.80403	0.405371
$206$	6.55333	0.456592
$207$	0.134035	0.00931607
$208$	1.17175	0.0812465
$209$	−17.3135	−1.19760
$210$	−0.854341	−0.0589551
$211$	20.3189	1.39881	0.699407	−	0.714724i	$-0.253448\pi$
$211$	20.3189	1.39881	0.699407	+	0.714724i	$0.253448\pi$
$212$	−5.25010	−0.360578
$213$	0.205700	0.0140944
$214$	−6.49395	−0.443917
$215$	8.08268	0.551234
$216$	3.07130	0.208975
$217$	8.49499	0.576678
$218$	15.4917	1.04923
$219$	−2.56439	−0.173286
$220$	1.69221	0.114089
$221$	−1.27815	−0.0859774
$222$	−3.87504	−0.260076
$223$	5.00604	0.335230	0.167615	−	0.985853i	$-0.446394\pi$
$223$	5.00604	0.335230	0.167615	+	0.985853i	$0.446394\pi$
$224$	3.03816	0.202996
$225$	−4.49493	−0.299662
$226$	−5.47412	−0.364133
$227$	29.1553	1.93511	0.967553	−	0.252666i	$-0.0813075\pi$
$227$	29.1553	1.93511	0.967553	+	0.252666i	$0.0813075\pi$
$228$	2.23855	0.148252
$229$	4.18822	0.276766	0.138383	−	0.990379i	$-0.455810\pi$
$229$	4.18822	0.276766	0.138383	+	0.990379i	$0.455810\pi$
$230$	0.114511	0.00755066
$231$	−4.29139	−0.282353
$232$	32.5419	2.13648
$233$	−20.2806	−1.32863	−0.664314	−	0.747454i	$-0.731276\pi$
$233$	−20.2806	−1.32863	−0.664314	+	0.747454i	$0.731276\pi$
$234$	0.545462	0.0356580
$235$	0.176155	0.0114911
$236$	5.91348	0.384935
$237$	7.76979	0.504702
$238$	3.38631	0.219502
$239$	14.9996	0.970245	0.485122	−	0.874446i	$-0.338775\pi$
$239$	14.9996	0.970245	0.485122	+	0.874446i	$0.338775\pi$
$240$	1.83528	0.118467
$241$	1.22071	0.0786327	0.0393163	−	0.999227i	$-0.487482\pi$
$241$	1.22071	0.0786327	0.0393163	+	0.999227i	$0.487482\pi$
$242$	−8.91510	−0.573084
$243$	1.00000	0.0641500
$244$	2.27498	0.145641
$245$	−0.710682	−0.0454038
$246$	9.81769	0.625953
$247$	1.83061	0.116479
$248$	−26.0907	−1.65676
$249$	13.6719	0.866421
$250$	−8.11191	−0.513042
$251$	−24.1511	−1.52440	−0.762202	−	0.647340i	$-0.775882\pi$
$251$	−24.1511	−1.52440	−0.762202	+	0.647340i	$0.775882\pi$
$252$	0.554856	0.0349526
$253$	0.575196	0.0361623
$254$	3.70071	0.232203
$255$	−2.00192	−0.125365
$256$	−12.1968	−0.762302
$257$	−24.9165	−1.55425	−0.777124	−	0.629347i	$-0.783322\pi$
$257$	−24.9165	−1.55425	−0.777124	+	0.629347i	$0.783322\pi$
$258$	13.6721	0.851188
$259$	−3.22345	−0.200295
$260$	−0.178922	−0.0110963
$261$	10.5955	0.655845
$262$	24.5851	1.51887
$263$	−3.03785	−0.187322	−0.0936608	−	0.995604i	$-0.529857\pi$
$263$	−3.03785	−0.187322	−0.0936608	+	0.995604i	$0.529857\pi$
$264$	13.1801	0.811181
$265$	−6.72454	−0.413085
$266$	−4.85001	−0.297373
$267$	−16.0109	−0.979852
$268$	−0.349864	−0.0213713
$269$	−6.06539	−0.369813	−0.184907	−	0.982756i	$-0.559198\pi$
$269$	−6.06539	−0.369813	−0.184907	+	0.982756i	$0.559198\pi$
$270$	0.854341	0.0519935
$271$	−13.2556	−0.805218	−0.402609	−	0.915372i	$-0.631897\pi$
$271$	−13.2556	−0.805218	−0.402609	+	0.915372i	$0.631897\pi$
$272$	−7.27443	−0.441077
$273$	0.453742	0.0274617
$274$	−7.14564	−0.431684
$275$	−19.2895	−1.16320
$276$	−0.0743701	−0.00447655
$277$	−31.2421	−1.87716	−0.938579	−	0.345064i	$-0.887857\pi$
$277$	−31.2421	−1.87716	−0.938579	+	0.345064i	$0.887857\pi$
$278$	−10.5654	−0.633669
$279$	−8.49499	−0.508582
$280$	2.18272	0.130442
$281$	13.1593	0.785018	0.392509	−	0.919748i	$-0.371607\pi$
$281$	13.1593	0.785018	0.392509	+	0.919748i	$0.371607\pi$
$282$	0.297971	0.0177439
$283$	−9.07992	−0.539745	−0.269873	−	0.962896i	$-0.586982\pi$
$283$	−9.07992	−0.539745	−0.269873	+	0.962896i	$0.586982\pi$
$284$	−0.114134	−0.00677261
$285$	2.86723	0.169840
$286$	2.34079	0.138414
$287$	8.16684	0.482073
$288$	−3.03816	−0.179025
$289$	−9.06508	−0.533240
$290$	9.05217	0.531562
$291$	−11.0979	−0.650568
$292$	1.42287	0.0832671
$293$	−33.7848	−1.97373	−0.986865	−	0.161545i	$-0.948352\pi$
$293$	−33.7848	−1.97373	−0.986865	+	0.161545i	$0.948352\pi$
$294$	−1.20214	−0.0701103
$295$	7.57423	0.440989
$296$	9.90017	0.575436
$297$	4.29139	0.249012
$298$	10.8406	0.627981
$299$	−0.0608173	−0.00351715
$300$	2.49404	0.143993
$301$	11.3731	0.655536
$302$	0.636965	0.0366532
$303$	1.94214	0.111573
$304$	10.4187	0.597554
$305$	2.91389	0.166849
$306$	−3.38631	−0.193583
$307$	4.73442	0.270208	0.135104	−	0.990831i	$-0.456863\pi$
$307$	4.73442	0.270208	0.135104	+	0.990831i	$0.456863\pi$
$308$	2.38110	0.135676
$309$	−5.45138	−0.310118
$310$	−7.25762	−0.412205
$311$	−4.20686	−0.238549	−0.119275	−	0.992861i	$-0.538057\pi$
$311$	−4.20686	−0.238549	−0.119275	+	0.992861i	$0.538057\pi$
$312$	−1.39358	−0.0788957
$313$	−17.1565	−0.969744	−0.484872	−	0.874585i	$-0.661134\pi$
$313$	−17.1565	−0.969744	−0.484872	+	0.874585i	$0.661134\pi$
$314$	7.39224	0.417168
$315$	0.710682	0.0400424
$316$	−4.31111	−0.242519
$317$	29.7745	1.67231	0.836153	−	0.548497i	$-0.184800\pi$
$317$	29.7745	1.67231	0.836153	+	0.548497i	$0.184800\pi$
$318$	−11.3748	−0.637866
$319$	45.4694	2.54580
$320$	−6.26619	−0.350291
$321$	5.40198	0.301509
$322$	0.161129	0.00897936
$323$	−11.3647	−0.632349
$324$	−0.554856	−0.0308253
$325$	2.03954	0.113133
$326$	−27.6672	−1.53235
$327$	−12.8868	−0.712640
$328$	−25.0828	−1.38497
$329$	0.247867	0.0136653
$330$	3.66631	0.201824
$331$	−10.2010	−0.560699	−0.280349	−	0.959898i	$-0.590450\pi$
$331$	−10.2010	−0.560699	−0.280349	+	0.959898i	$0.590450\pi$
$332$	−7.58593	−0.416332
$333$	3.22345	0.176644
$334$	−5.31450	−0.290796
$335$	−0.448120	−0.0244834
$336$	2.58242	0.140883
$337$	−27.2354	−1.48361	−0.741804	−	0.670617i	$-0.766029\pi$
$337$	−27.2354	−1.48361	−0.741804	+	0.670617i	$0.766029\pi$
$338$	15.3803	0.836580
$339$	4.55364	0.247320
$340$	1.11078	0.0602404
$341$	−36.4553	−1.97417
$342$	4.85001	0.262258
$343$	−1.00000	−0.0539949
$344$	−34.9303	−1.88331
$345$	−0.0952563	−0.00512842
$346$	8.63347	0.464138
$347$	−2.45417	−0.131747	−0.0658734	−	0.997828i	$-0.520983\pi$
$347$	−2.45417	−0.131747	−0.0658734	+	0.997828i	$0.520983\pi$
$348$	−5.87898	−0.315146
$349$	19.1616	1.02570	0.512848	−	0.858479i	$-0.328590\pi$
$349$	19.1616	1.02570	0.512848	+	0.858479i	$0.328590\pi$
$350$	−5.40354	−0.288831
$351$	−0.453742	−0.0242189
$352$	−13.0379	−0.694924
$353$	14.4330	0.768191	0.384096	−	0.923293i	$-0.374513\pi$
$353$	14.4330	0.768191	0.384096	+	0.923293i	$0.374513\pi$
$354$	12.8120	0.680953
$355$	−0.146188	−0.00775883
$356$	8.88375	0.470838
$357$	−2.81690	−0.149086
$358$	−25.9697	−1.37254
$359$	−3.83391	−0.202346	−0.101173	−	0.994869i	$-0.532260\pi$
$359$	−3.83391	−0.202346	−0.101173	+	0.994869i	$0.532260\pi$
$360$	−2.18272	−0.115039
$361$	−2.72303	−0.143317
$362$	−23.6091	−1.24087
$363$	7.41602	0.389240
$364$	−0.251761	−0.0131959
$365$	1.82247	0.0953924
$366$	4.92894	0.257640
$367$	−19.6731	−1.02693	−0.513463	−	0.858112i	$-0.671638\pi$
$367$	−19.6731	−1.02693	−0.513463	+	0.858112i	$0.671638\pi$
$368$	−0.346135	−0.0180435
$369$	−8.16684	−0.425149
$370$	2.75392	0.143170
$371$	−9.46209	−0.491247
$372$	4.71350	0.244383
$373$	−23.2255	−1.20257	−0.601286	−	0.799034i	$-0.705345\pi$
$373$	−23.2255	−1.20257	−0.601286	+	0.799034i	$0.705345\pi$
$374$	−14.5320	−0.751431
$375$	6.74788	0.348459
$376$	−0.761273	−0.0392596
$377$	−4.80762	−0.247605
$378$	1.20214	0.0618315
$379$	29.8428	1.53292	0.766462	−	0.642290i	$-0.222015\pi$
$379$	29.8428	1.53292	0.766462	+	0.642290i	$0.222015\pi$
$380$	−1.59090	−0.0816114
$381$	−3.07844	−0.157713
$382$	15.1494	0.775109
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−4.52313	−0.230820
$385$	3.04981	0.155433
$386$	2.01822	0.102725
$387$	−11.3731	−0.578129
$388$	6.15771	0.312611
$389$	−10.3697	−0.525766	−0.262883	−	0.964828i	$-0.584673\pi$
$389$	−10.3697	−0.525766	−0.262883	+	0.964828i	$0.584673\pi$
$390$	−0.387650	−0.0196294
$391$	0.377563	0.0190942
$392$	3.07130	0.155124
$393$	−20.4511	−1.03162
$394$	−6.96225	−0.350753
$395$	−5.52185	−0.277834
$396$	−2.38110	−0.119655
$397$	−18.1294	−0.909890	−0.454945	−	0.890520i	$-0.650341\pi$
$397$	−18.1294	−0.909890	−0.454945	+	0.890520i	$0.650341\pi$
$398$	7.71507	0.386721
$399$	4.03447	0.201976
$400$	11.6078	0.580391
$401$	13.5194	0.675128	0.337564	−	0.941303i	$-0.390397\pi$
$401$	13.5194	0.675128	0.337564	+	0.941303i	$0.390397\pi$
$402$	−0.758009	−0.0378060
$403$	3.85453	0.192008
$404$	−1.07761	−0.0536131
$405$	−0.710682	−0.0353141
$406$	12.7373	0.632141
$407$	13.8331	0.685680
$408$	8.65154	0.428315
$409$	−14.0821	−0.696316	−0.348158	−	0.937436i	$-0.613193\pi$
$409$	−14.0821	−0.696316	−0.348158	+	0.937436i	$0.613193\pi$
$410$	−6.97726	−0.344582
$411$	5.94409	0.293201
$412$	3.02473	0.149018
$413$	10.6577	0.524430
$414$	−0.161129	−0.00791905
$415$	−9.71637	−0.476958
$416$	1.37854	0.0675885
$417$	8.78879	0.430389
$418$	20.8133	1.01801
$419$	20.3288	0.993128	0.496564	−	0.868000i	$-0.334595\pi$
$419$	20.3288	0.993128	0.496564	+	0.868000i	$0.334595\pi$
$420$	−0.394326	−0.0192412
$421$	−15.7728	−0.768720	−0.384360	−	0.923183i	$-0.625578\pi$
$421$	−15.7728	−0.768720	−0.384360	+	0.923183i	$0.625578\pi$
$422$	−24.4262	−1.18905
$423$	−0.247867	−0.0120517
$424$	29.0609	1.41132
$425$	−12.6618	−0.614186
$426$	−0.247281	−0.0119808
$427$	4.10013	0.198419
$428$	−2.99732	−0.144881
$429$	−1.94718	−0.0940109
$430$	−9.71653	−0.468573
$431$	−34.9403	−1.68301	−0.841507	−	0.540246i	$-0.818331\pi$
$431$	−34.9403	−1.68301	−0.841507	+	0.540246i	$0.818331\pi$
$432$	−2.58242	−0.124247
$433$	14.6308	0.703111	0.351555	−	0.936167i	$-0.385653\pi$
$433$	14.6308	0.703111	0.351555	+	0.936167i	$0.385653\pi$
$434$	−10.2122	−0.490200
$435$	−7.53004	−0.361038
$436$	7.15030	0.342437
$437$	−0.540760	−0.0258681
$438$	3.08276	0.147300
$439$	−14.1175	−0.673791	−0.336895	−	0.941542i	$-0.609377\pi$
$439$	−14.1175	−0.673791	−0.336895	+	0.941542i	$0.609377\pi$
$440$	−9.36689	−0.446549
$441$	1.00000	0.0476190
$442$	1.53651	0.0730844
$443$	−12.1487	−0.577201	−0.288600	−	0.957450i	$-0.593190\pi$
$443$	−12.1487	−0.577201	−0.288600	+	0.957450i	$0.593190\pi$
$444$	−1.78855	−0.0848808
$445$	11.3787	0.539401
$446$	−6.01797	−0.284959
$447$	−9.01777	−0.426526
$448$	−8.81714	−0.416571
$449$	10.9996	0.519104	0.259552	−	0.965729i	$-0.416425\pi$
$449$	10.9996	0.519104	0.259552	+	0.965729i	$0.416425\pi$
$450$	5.40354	0.254725
$451$	−35.0471	−1.65030
$452$	−2.52662	−0.118842
$453$	−0.529859	−0.0248949
$454$	−35.0488	−1.64492
$455$	−0.322466	−0.0151175
$456$	−12.3911	−0.580265
$457$	−8.29354	−0.387956	−0.193978	−	0.981006i	$-0.562139\pi$
$457$	−8.29354	−0.387956	−0.193978	+	0.981006i	$0.562139\pi$
$458$	−5.03484	−0.235262
$459$	2.81690	0.131482
$460$	0.0528535	0.00246431
$461$	−24.2509	−1.12948	−0.564739	−	0.825270i	$-0.691023\pi$
$461$	−24.2509	−1.12948	−0.564739	+	0.825270i	$0.691023\pi$
$462$	5.15886	0.240012
$463$	−34.3454	−1.59616	−0.798082	−	0.602548i	$-0.794152\pi$
$463$	−34.3454	−1.59616	−0.798082	+	0.602548i	$0.794152\pi$
$464$	−27.3621	−1.27025
$465$	6.03724	0.279970
$466$	24.3802	1.12939
$467$	−4.20707	−0.194680	−0.0973399	−	0.995251i	$-0.531033\pi$
$467$	−4.20707	−0.194680	−0.0973399	+	0.995251i	$0.531033\pi$
$468$	0.251761	0.0116377
$469$	−0.630549	−0.0291160
$470$	−0.211763	−0.00976789
$471$	−6.14923	−0.283342
$472$	−32.7329	−1.50666
$473$	−48.8065	−2.24413
$474$	−9.34038	−0.429018
$475$	18.1347	0.832076
$476$	1.56297	0.0716388
$477$	9.46209	0.433239
$478$	−18.0317	−0.824749
$479$	−13.5776	−0.620377	−0.310188	−	0.950675i	$-0.600392\pi$
$479$	−13.5776	−0.620377	−0.310188	+	0.950675i	$0.600392\pi$
$480$	2.15917	0.0985520
$481$	−1.46261	−0.0666895
$482$	−1.46746	−0.0668411
$483$	−0.134035	−0.00609880
$484$	−4.11482	−0.187037
$485$	7.88705	0.358133
$486$	−1.20214	−0.0545302
$487$	30.4987	1.38203	0.691015	−	0.722841i	$-0.257164\pi$
$487$	30.4987	1.38203	0.691015	+	0.722841i	$0.257164\pi$
$488$	−12.5927	−0.570046
$489$	23.0149	1.04077
$490$	0.854341	0.0385952
$491$	11.9282	0.538312	0.269156	−	0.963097i	$-0.413255\pi$
$491$	11.9282	0.538312	0.269156	+	0.963097i	$0.413255\pi$
$492$	4.53142	0.204292
$493$	29.8465	1.34422
$494$	−2.20065	−0.0990120
$495$	−3.04981	−0.137079
$496$	21.9377	0.985030
$497$	−0.205700	−0.00922692
$498$	−16.4355	−0.736494
$499$	−10.6688	−0.477603	−0.238801	−	0.971068i	$-0.576754\pi$
$499$	−10.6688	−0.477603	−0.238801	+	0.971068i	$0.576754\pi$
$500$	−3.74410	−0.167441
$501$	4.42086	0.197509
$502$	29.0330	1.29581
$503$	−36.6856	−1.63573	−0.817866	−	0.575409i	$-0.804843\pi$
$503$	−36.6856	−1.63573	−0.817866	+	0.575409i	$0.804843\pi$
$504$	−3.07130	−0.136806
$505$	−1.38025	−0.0614201
$506$	−0.691467	−0.0307394
$507$	−12.7941	−0.568207
$508$	1.70809	0.0757842
$509$	−36.7926	−1.63080	−0.815402	−	0.578895i	$-0.803484\pi$
$509$	−36.7926	−1.63080	−0.815402	+	0.578895i	$0.803484\pi$
$510$	2.40659	0.106566
$511$	2.56439	0.113442
$512$	23.7086	1.04778
$513$	−4.03447	−0.178126
$514$	29.9532	1.32118
$515$	3.87420	0.170718
$516$	6.31045	0.277802
$517$	−1.06369	−0.0467812
$518$	3.87504	0.170260
$519$	−7.18175	−0.315244
$520$	0.990390	0.0434315
$521$	−4.66471	−0.204364	−0.102182	−	0.994766i	$-0.532582\pi$
$521$	−4.66471	−0.204364	−0.102182	+	0.994766i	$0.532582\pi$
$522$	−12.7373	−0.557496
$523$	−26.6862	−1.16691	−0.583454	−	0.812146i	$-0.698299\pi$
$523$	−26.6862	−1.16691	−0.583454	+	0.812146i	$0.698299\pi$
$524$	11.3474	0.495715
$525$	4.49493	0.196175
$526$	3.65192	0.159231
$527$	−23.9295	−1.04239
$528$	−11.0822	−0.482290
$529$	−22.9820	−0.999219
$530$	8.08385	0.351140
$531$	−10.6577	−0.462504
$532$	−2.23855	−0.0970535
$533$	3.70564	0.160509
$534$	19.2474	0.832915
$535$	−3.83909	−0.165979
$536$	1.93660	0.0836485
$537$	21.6029	0.932234
$538$	7.29146	0.314357
$539$	4.29139	0.184843
$540$	0.394326	0.0169691
$541$	30.7340	1.32136	0.660679	−	0.750669i	$-0.270269\pi$
$541$	30.7340	1.32136	0.660679	+	0.750669i	$0.270269\pi$
$542$	15.9351	0.684469
$543$	19.6392	0.842800
$544$	−8.55819	−0.366929
$545$	9.15840	0.392303
$546$	−0.545462	−0.0233436
$547$	−10.7655	−0.460300	−0.230150	−	0.973155i	$-0.573922\pi$
$547$	−10.7655	−0.460300	−0.230150	+	0.973155i	$0.573922\pi$
$548$	−3.29812	−0.140889
$549$	−4.10013	−0.174989
$550$	23.1887	0.988769
$551$	−42.7473	−1.82109
$552$	0.411661	0.0175215
$553$	−7.76979	−0.330405
$554$	37.5575	1.59566
$555$	−2.29085	−0.0972411
$556$	−4.87651	−0.206810
$557$	42.0144	1.78021	0.890103	−	0.455759i	$-0.150632\pi$
$557$	42.0144	1.78021	0.890103	+	0.455759i	$0.150632\pi$
$558$	10.2122	0.432316
$559$	5.16046	0.218264
$560$	−1.83528	−0.0775548
$561$	12.0884	0.510373
$562$	−15.8193	−0.667298
$563$	−14.2376	−0.600042	−0.300021	−	0.953933i	$-0.596994\pi$
$563$	−14.2376	−0.600042	−0.300021	+	0.953933i	$0.596994\pi$
$564$	0.137530	0.00579107
$565$	−3.23619	−0.136148
$566$	10.9153	0.458806
$567$	−1.00000	−0.0419961
$568$	0.631767	0.0265084
$569$	−5.77095	−0.241931	−0.120965	−	0.992657i	$-0.538599\pi$
$569$	−5.77095	−0.241931	−0.120965	+	0.992657i	$0.538599\pi$
$570$	−3.44681	−0.144371
$571$	8.71963	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$571$	8.71963	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$572$	1.08041	0.0451740
$573$	−12.6020	−0.526456
$574$	−9.81769	−0.409783
$575$	−0.602478	−0.0251251
$576$	8.81714	0.367381
$577$	21.0548	0.876523	0.438262	−	0.898847i	$-0.355594\pi$
$577$	21.0548	0.876523	0.438262	+	0.898847i	$0.355594\pi$
$578$	10.8975	0.453276
$579$	−1.67886	−0.0697709
$580$	4.17809	0.173486
$581$	−13.6719	−0.567205
$582$	13.3412	0.553010
$583$	40.6055	1.68171
$584$	−7.87602	−0.325912
$585$	0.322466	0.0133323
$586$	40.6141	1.67775
$587$	36.2230	1.49508	0.747541	−	0.664216i	$-0.231234\pi$
$587$	36.2230	1.49508	0.747541	+	0.664216i	$0.231234\pi$
$588$	−0.554856	−0.0228819
$589$	34.2728	1.41219
$590$	−9.10530	−0.374859
$591$	5.79154	0.238232
$592$	−8.32431	−0.342127
$593$	41.8226	1.71745	0.858725	−	0.512437i	$-0.171257\pi$
$593$	41.8226	1.71745	0.858725	+	0.512437i	$0.171257\pi$
$594$	−5.15886	−0.211670
$595$	2.00192	0.0820708
$596$	5.00356	0.204954
$597$	−6.41777	−0.262662
$598$	0.0731109	0.00298973
$599$	−34.2552	−1.39963	−0.699816	−	0.714323i	$-0.746735\pi$
$599$	−34.2552	−1.39963	−0.699816	+	0.714323i	$0.746735\pi$
$600$	−13.8053	−0.563598
$601$	−15.4531	−0.630344	−0.315172	−	0.949035i	$-0.602062\pi$
$601$	−15.4531	−0.630344	−0.315172	+	0.949035i	$0.602062\pi$
$602$	−13.6721	−0.557234
$603$	0.630549	0.0256779
$604$	0.293995	0.0119625
$605$	−5.27043	−0.214274
$606$	−2.33473	−0.0948419
$607$	6.39041	0.259379	0.129689	−	0.991555i	$-0.458602\pi$
$607$	6.39041	0.259379	0.129689	+	0.991555i	$0.458602\pi$
$608$	12.2574	0.497102
$609$	−10.5955	−0.429351
$610$	−3.50291	−0.141829
$611$	0.112468	0.00454995
$612$	−1.56297	−0.0631795
$613$	22.0303	0.889795	0.444897	−	0.895582i	$-0.353240\pi$
$613$	22.0303	0.889795	0.444897	+	0.895582i	$0.353240\pi$
$614$	−5.69145	−0.229688
$615$	5.80403	0.234041
$616$	−13.1801	−0.531043
$617$	−9.65346	−0.388634	−0.194317	−	0.980939i	$-0.562249\pi$
$617$	−9.65346	−0.388634	−0.194317	+	0.980939i	$0.562249\pi$
$618$	6.55333	0.263614
$619$	−27.1721	−1.09214	−0.546070	−	0.837740i	$-0.683877\pi$
$619$	−27.1721	−1.09214	−0.546070	+	0.837740i	$0.683877\pi$
$620$	−3.34980	−0.134531
$621$	0.134035	0.00537864
$622$	5.05724	0.202777
$623$	16.0109	0.641463
$624$	1.17175	0.0469077
$625$	17.6791	0.707162
$626$	20.6246	0.824323
$627$	−17.3135	−0.691434
$628$	3.41194	0.136151
$629$	9.08013	0.362049
$630$	−0.854341	−0.0340378
$631$	−7.45068	−0.296607	−0.148303	−	0.988942i	$-0.547381\pi$
$631$	−7.45068	−0.296607	−0.148303	+	0.988942i	$0.547381\pi$
$632$	23.8633	0.949232
$633$	20.3189	0.807605
$634$	−35.7932	−1.42153
$635$	2.18779	0.0868198
$636$	−5.25010	−0.208180
$637$	−0.453742	−0.0179779
$638$	−54.6607	−2.16404
$639$	0.205700	0.00813738
$640$	3.21451	0.127065
$641$	34.4189	1.35947	0.679733	−	0.733460i	$-0.262096\pi$
$641$	34.4189	1.35947	0.679733	+	0.733460i	$0.262096\pi$
$642$	−6.49395	−0.256296
$643$	−2.85451	−0.112571	−0.0562855	−	0.998415i	$-0.517926\pi$
$643$	−2.85451	−0.112571	−0.0562855	+	0.998415i	$0.517926\pi$
$644$	0.0743701	0.00293059
$645$	8.08268	0.318255
$646$	13.6620	0.537523
$647$	10.6816	0.419937	0.209969	−	0.977708i	$-0.432664\pi$
$647$	10.6816	0.419937	0.209969	+	0.977708i	$0.432664\pi$
$648$	3.07130	0.120652
$649$	−45.7363	−1.79531
$650$	−2.45181	−0.0961680
$651$	8.49499	0.332945
$652$	−12.7700	−0.500111
$653$	27.4184	1.07297	0.536483	−	0.843911i	$-0.319753\pi$
$653$	27.4184	1.07297	0.536483	+	0.843911i	$0.319753\pi$
$654$	15.4917	0.605774
$655$	14.5342	0.567900
$656$	21.0902	0.823435
$657$	−2.56439	−0.100047
$658$	−0.297971	−0.0116161
$659$	−19.5706	−0.762364	−0.381182	−	0.924500i	$-0.624483\pi$
$659$	−19.5706	−0.762364	−0.381182	+	0.924500i	$0.624483\pi$
$660$	1.69221	0.0658691
$661$	14.5180	0.564686	0.282343	−	0.959314i	$-0.408888\pi$
$661$	14.5180	0.564686	0.282343	+	0.959314i	$0.408888\pi$
$662$	12.2631	0.476618
$663$	−1.27815	−0.0496390
$664$	41.9904	1.62955
$665$	−2.86723	−0.111186
$666$	−3.87504	−0.150155
$667$	1.42017	0.0549891
$668$	−2.45294	−0.0949071
$669$	5.00604	0.193545
$670$	0.538703	0.0208119
$671$	−17.5953	−0.679258
$672$	3.03816	0.117200
$673$	−33.9008	−1.30678	−0.653390	−	0.757022i	$-0.726654\pi$
$673$	−33.9008	−1.30678	−0.653390	+	0.757022i	$0.726654\pi$
$674$	32.7408	1.26113
$675$	−4.49493	−0.173010
$676$	7.09889	0.273034
$677$	−16.2167	−0.623257	−0.311629	−	0.950204i	$-0.600874\pi$
$677$	−16.2167	−0.623257	−0.311629	+	0.950204i	$0.600874\pi$
$678$	−5.47412	−0.210232
$679$	11.0979	0.425897
$680$	−6.14850	−0.235784
$681$	29.1553	1.11723
$682$	43.8244	1.67812
$683$	−11.2502	−0.430477	−0.215238	−	0.976562i	$-0.569053\pi$
$683$	−11.2502	−0.430477	−0.215238	+	0.976562i	$0.569053\pi$
$684$	2.23855	0.0855932
$685$	−4.22436	−0.161405
$686$	1.20214	0.0458980
$687$	4.18822	0.159791
$688$	29.3702	1.11973
$689$	−4.29335	−0.163563
$690$	0.114511	0.00435938
$691$	10.8422	0.412458	0.206229	−	0.978504i	$-0.433881\pi$
$691$	10.8422	0.412458	0.206229	+	0.978504i	$0.433881\pi$
$692$	3.98484	0.151481
$693$	−4.29139	−0.163016
$694$	2.95026	0.111990
$695$	−6.24604	−0.236926
$696$	32.5419	1.23350
$697$	−23.0052	−0.871383
$698$	−23.0349	−0.871885
$699$	−20.2806	−0.767084
$700$	−2.49404	−0.0942658
$701$	−33.5046	−1.26545	−0.632726	−	0.774376i	$-0.718064\pi$
$701$	−33.5046	−1.26545	−0.632726	+	0.774376i	$0.718064\pi$
$702$	0.545462	0.0205871
$703$	−13.0049	−0.490490
$704$	37.8378	1.42607
$705$	0.176155	0.00663436
$706$	−17.3505	−0.652995
$707$	−1.94214	−0.0730418
$708$	5.91348	0.222242
$709$	−15.7885	−0.592951	−0.296475	−	0.955040i	$-0.595811\pi$
$709$	−15.7885	−0.592951	−0.296475	+	0.955040i	$0.595811\pi$
$710$	0.175738	0.00659534
$711$	7.76979	0.291390
$712$	−49.1743	−1.84288
$713$	−1.13863	−0.0426419
$714$	3.38631	0.126730
$715$	1.38383	0.0517523
$716$	−11.9865	−0.447956
$717$	14.9996	0.560171
$718$	4.60890	0.172002
$719$	−14.2114	−0.529996	−0.264998	−	0.964249i	$-0.585371\pi$
$719$	−14.2114	−0.529996	−0.264998	+	0.964249i	$0.585371\pi$
$720$	1.83528	0.0683969
$721$	5.45138	0.203020
$722$	3.27347	0.121826
$723$	1.22071	0.0453986
$724$	−10.8970	−0.404982
$725$	−47.6260	−1.76879
$726$	−8.91510	−0.330870
$727$	0.536797	0.0199087	0.00995435	−	0.999950i	$-0.496831\pi$
$727$	0.536797	0.0199087	0.00995435	+	0.999950i	$0.496831\pi$
$728$	1.39358	0.0516494
$729$	1.00000	0.0370370
$730$	−2.19087	−0.0810876
$731$	−32.0370	−1.18493
$732$	2.27498	0.0840858
$733$	−24.8777	−0.918877	−0.459439	−	0.888210i	$-0.651949\pi$
$733$	−24.8777	−0.918877	−0.459439	+	0.888210i	$0.651949\pi$
$734$	23.6498	0.872931
$735$	−0.710682	−0.0262139
$736$	−0.407219	−0.0150103
$737$	2.70593	0.0996742
$738$	9.81769	0.361394
$739$	0.460343	0.0169340	0.00846699	−	0.999964i	$-0.497305\pi$
$739$	0.460343	0.0169340	0.00846699	+	0.999964i	$0.497305\pi$
$740$	1.27109	0.0467262
$741$	1.83061	0.0672491
$742$	11.3748	0.417581
$743$	−29.3468	−1.07663	−0.538315	−	0.842744i	$-0.680939\pi$
$743$	−29.3468	−1.07663	−0.538315	+	0.842744i	$0.680939\pi$
$744$	−26.0907	−0.956530
$745$	6.40877	0.234799
$746$	27.9204	1.02224
$747$	13.6719	0.500228
$748$	−6.70733	−0.245244
$749$	−5.40198	−0.197384
$750$	−8.11191	−0.296205
$751$	11.4043	0.416147	0.208074	−	0.978113i	$-0.433281\pi$
$751$	11.4043	0.416147	0.208074	+	0.978113i	$0.433281\pi$
$752$	0.640097	0.0233419
$753$	−24.1511	−0.880115
$754$	5.77944	0.210475
$755$	0.376561	0.0137045
$756$	0.554856	0.0201799
$757$	−52.2820	−1.90022	−0.950110	−	0.311914i	$-0.899030\pi$
$757$	−52.2820	−1.90022	−0.950110	+	0.311914i	$0.899030\pi$
$758$	−35.8753	−1.30305
$759$	0.575196	0.0208783
$760$	8.80612	0.319431
$761$	−3.62861	−0.131537	−0.0657686	−	0.997835i	$-0.520950\pi$
$761$	−3.62861	−0.131537	−0.0657686	+	0.997835i	$0.520950\pi$
$762$	3.70071	0.134063
$763$	12.8868	0.466532
$764$	6.99229	0.252972
$765$	−2.00192	−0.0723796
$766$	−1.20214	−0.0434351
$767$	4.83584	0.174612
$768$	−12.1968	−0.440116
$769$	17.7755	0.641000	0.320500	−	0.947248i	$-0.396149\pi$
$769$	17.7755	0.641000	0.320500	+	0.947248i	$0.396149\pi$
$770$	−3.66631	−0.132125
$771$	−24.9165	−0.897346
$772$	0.931524	0.0335263
$773$	−35.1912	−1.26574	−0.632870	−	0.774258i	$-0.718123\pi$
$773$	−35.1912	−1.26574	−0.632870	+	0.774258i	$0.718123\pi$
$774$	13.6721	0.491434
$775$	38.1844	1.37162
$776$	−34.0848	−1.22357
$777$	−3.22345	−0.115641
$778$	12.4659	0.446923
$779$	32.9489	1.18052
$780$	−0.178922	−0.00640645
$781$	0.882740	0.0315869
$782$	−0.453884	−0.0162309
$783$	10.5955	0.378652
$784$	−2.58242	−0.0922294
$785$	4.37015	0.155977
$786$	24.5851	0.876923
$787$	15.1709	0.540786	0.270393	−	0.962750i	$-0.412846\pi$
$787$	15.1709	0.540786	0.270393	+	0.962750i	$0.412846\pi$
$788$	−3.21347	−0.114475
$789$	−3.03785	−0.108150
$790$	6.63804	0.236171
$791$	−4.55364	−0.161909
$792$	13.1801	0.468336
$793$	1.86040	0.0660648
$794$	21.7941	0.773445
$795$	−6.72454	−0.238495
$796$	3.56094	0.126214
$797$	51.3063	1.81736	0.908682	−	0.417490i	$-0.137090\pi$
$797$	51.3063	1.81736	0.908682	+	0.417490i	$0.137090\pi$
$798$	−4.85001	−0.171688
$799$	−0.698216	−0.0247011
$800$	13.6563	0.482824
$801$	−16.0109	−0.565718
$802$	−16.2523	−0.573887
$803$	−11.0048	−0.388351
$804$	−0.349864	−0.0123387
$805$	0.0952563	0.00335734
$806$	−4.63369	−0.163215
$807$	−6.06539	−0.213512
$808$	5.96490	0.209844
$809$	−19.5320	−0.686708	−0.343354	−	0.939206i	$-0.611563\pi$
$809$	−19.5320	−0.686708	−0.343354	+	0.939206i	$0.611563\pi$
$810$	0.854341	0.0300185
$811$	9.06440	0.318294	0.159147	−	0.987255i	$-0.449126\pi$
$811$	9.06440	0.318294	0.159147	+	0.987255i	$0.449126\pi$
$812$	5.87898	0.206312
$813$	−13.2556	−0.464893
$814$	−16.6293	−0.582857
$815$	−16.3563	−0.572937
$816$	−7.27443	−0.254656
$817$	45.8846	1.60530
$818$	16.9287	0.591898
$819$	0.453742	0.0158550
$820$	−3.22040	−0.112461
$821$	49.3514	1.72237	0.861187	−	0.508288i	$-0.169721\pi$
$821$	49.3514	1.72237	0.861187	+	0.508288i	$0.169721\pi$
$822$	−7.14564	−0.249233
$823$	−20.6705	−0.720527	−0.360264	−	0.932851i	$-0.617313\pi$
$823$	−20.6705	−0.720527	−0.360264	+	0.932851i	$0.617313\pi$
$824$	−16.7428	−0.583263
$825$	−19.2895	−0.671574
$826$	−12.8120	−0.445788
$827$	5.48559	0.190753	0.0953764	−	0.995441i	$-0.469595\pi$
$827$	5.48559	0.190753	0.0953764	+	0.995441i	$0.469595\pi$
$828$	−0.0743701	−0.00258454
$829$	17.9416	0.623139	0.311570	−	0.950223i	$-0.399145\pi$
$829$	17.9416	0.623139	0.311570	+	0.950223i	$0.399145\pi$
$830$	11.6805	0.405434
$831$	−31.2421	−1.08378
$832$	−4.00071	−0.138700
$833$	2.81690	0.0975998
$834$	−10.5654	−0.365849
$835$	−3.14183	−0.108727
$836$	9.60650	0.332248
$837$	−8.49499	−0.293630
$838$	−24.4381	−0.844201
$839$	−23.2644	−0.803176	−0.401588	−	0.915821i	$-0.631542\pi$
$839$	−23.2644	−0.803176	−0.401588	+	0.915821i	$0.631542\pi$
$840$	2.18272	0.0753109
$841$	83.2646	2.87119
$842$	18.9611	0.653444
$843$	13.1593	0.453230
$844$	−11.2741	−0.388070
$845$	9.09255	0.312793
$846$	0.297971	0.0102445
$847$	−7.41602	−0.254817
$848$	−24.4351	−0.839105
$849$	−9.07992	−0.311622
$850$	15.2212	0.522084
$851$	0.432055	0.0148106
$852$	−0.114134	−0.00391017
$853$	31.2465	1.06986	0.534930	−	0.844897i	$-0.320338\pi$
$853$	31.2465	1.06986	0.534930	+	0.844897i	$0.320338\pi$
$854$	−4.92894	−0.168665
$855$	2.86723	0.0980572
$856$	16.5911	0.567072
$857$	20.0220	0.683937	0.341969	−	0.939711i	$-0.388906\pi$
$857$	20.0220	0.683937	0.341969	+	0.939711i	$0.388906\pi$
$858$	2.34079	0.0799132
$859$	14.9395	0.509727	0.254864	−	0.966977i	$-0.417969\pi$
$859$	14.9395	0.509727	0.254864	+	0.966977i	$0.417969\pi$
$860$	−4.48472	−0.152928
$861$	8.16684	0.278325
$862$	42.0032	1.43063
$863$	−47.3901	−1.61318	−0.806589	−	0.591113i	$-0.798689\pi$
$863$	−47.3901	−1.61318	−0.806589	+	0.591113i	$0.798689\pi$
$864$	−3.03816	−0.103360
$865$	5.10394	0.173539
$866$	−17.5883	−0.597674
$867$	−9.06508	−0.307866
$868$	−4.71350	−0.159987
$869$	33.3432	1.13109
$870$	9.05217	0.306897
$871$	−0.286106	−0.00969434
$872$	−39.5791	−1.34032
$873$	−11.0979	−0.375606
$874$	0.650070	0.0219890
$875$	−6.74788	−0.228120
$876$	1.42287	0.0480743
$877$	31.6483	1.06869	0.534344	−	0.845267i	$-0.320559\pi$
$877$	31.6483	1.06869	0.534344	+	0.845267i	$0.320559\pi$
$878$	16.9712	0.572751
$879$	−33.7848	−1.13953
$880$	7.87591	0.265497
$881$	−3.13222	−0.105527	−0.0527636	−	0.998607i	$-0.516803\pi$
$881$	−3.13222	−0.105527	−0.0527636	+	0.998607i	$0.516803\pi$
$882$	−1.20214	−0.0404782
$883$	−31.1434	−1.04806	−0.524029	−	0.851700i	$-0.675572\pi$
$883$	−31.1434	−1.04806	−0.524029	+	0.851700i	$0.675572\pi$
$884$	0.709187	0.0238525
$885$	7.57423	0.254605
$886$	14.6044	0.490645
$887$	31.5691	1.05999	0.529993	−	0.848002i	$-0.322195\pi$
$887$	31.5691	1.05999	0.529993	+	0.848002i	$0.322195\pi$
$888$	9.90017	0.332228
$889$	3.07844	0.103247
$890$	−13.6788	−0.458513
$891$	4.29139	0.143767
$892$	−2.77763	−0.0930021
$893$	1.00001	0.0334641
$894$	10.8406	0.362565
$895$	−15.3528	−0.513188
$896$	4.52313	0.151107
$897$	−0.0608173	−0.00203063
$898$	−13.2231	−0.441260
$899$	−90.0087	−3.00196
$900$	2.49404	0.0831346
$901$	26.6538	0.887965
$902$	42.1315	1.40283
$903$	11.3731	0.378474
$904$	13.9856	0.465154
$905$	−13.9573	−0.463955
$906$	0.636965	0.0211617
$907$	−12.6199	−0.419038	−0.209519	−	0.977805i	$-0.567190\pi$
$907$	−12.6199	−0.419038	−0.209519	+	0.977805i	$0.567190\pi$
$908$	−16.1770	−0.536853
$909$	1.94214	0.0644168
$910$	0.387650	0.0128505
$911$	−27.4135	−0.908251	−0.454125	−	0.890938i	$-0.650048\pi$
$911$	−27.4135	−0.908251	−0.454125	+	0.890938i	$0.650048\pi$
$912$	10.4187	0.344998
$913$	58.6714	1.94174
$914$	9.97001	0.329779
$915$	2.91389	0.0963303
$916$	−2.32386	−0.0767825
$917$	20.4511	0.675355
$918$	−3.38631	−0.111765
$919$	30.1088	0.993196	0.496598	−	0.867981i	$-0.334582\pi$
$919$	30.1088	0.993196	0.496598	+	0.867981i	$0.334582\pi$
$920$	−0.292560	−0.00964543
$921$	4.73442	0.156005
$922$	29.1530	0.960104
$923$	−0.0933349	−0.00307215
$924$	2.38110	0.0783325
$925$	−14.4892	−0.476401
$926$	41.2880	1.35681
$927$	−5.45138	−0.179047
$928$	−32.1908	−1.05672
$929$	−55.8693	−1.83301	−0.916506	−	0.400022i	$-0.869003\pi$
$929$	−55.8693	−1.83301	−0.916506	+	0.400022i	$0.869003\pi$
$930$	−7.25762	−0.237987
$931$	−4.03447	−0.132225
$932$	11.2528	0.368599
$933$	−4.20686	−0.137726
$934$	5.05749	0.165486
$935$	−8.59102	−0.280956
$936$	−1.39358	−0.0455505
$937$	−32.2019	−1.05199	−0.525995	−	0.850488i	$-0.676307\pi$
$937$	−32.2019	−1.05199	−0.525995	+	0.850488i	$0.676307\pi$
$938$	0.758009	0.0247499
$939$	−17.1565	−0.559882
$940$	−0.0977404	−0.00318794
$941$	−9.33694	−0.304375	−0.152188	−	0.988352i	$-0.548632\pi$
$941$	−9.33694	−0.304375	−0.152188	+	0.988352i	$0.548632\pi$
$942$	7.39224	0.240852
$943$	−1.09464	−0.0356464
$944$	27.5227	0.895786
$945$	0.710682	0.0231185
$946$	58.6723	1.90760
$947$	−30.6971	−0.997522	−0.498761	−	0.866739i	$-0.666212\pi$
$947$	−30.6971	−0.997522	−0.498761	+	0.866739i	$0.666212\pi$
$948$	−4.31111	−0.140018
$949$	1.16357	0.0377712
$950$	−21.8004	−0.707300
$951$	29.7745	0.965506
$952$	−8.65154	−0.280398
$953$	−27.3893	−0.887227	−0.443613	−	0.896218i	$-0.646304\pi$
$953$	−27.3893	−0.887227	−0.443613	+	0.896218i	$0.646304\pi$
$954$	−11.3748	−0.368272
$955$	8.95601	0.289810
$956$	−8.32263	−0.269173
$957$	45.4694	1.46982
$958$	16.3222	0.527347
$959$	−5.94409	−0.191945
$960$	−6.26619	−0.202240
$961$	41.1649	1.32790
$962$	1.75827	0.0566889
$963$	5.40198	0.174076
$964$	−0.677317	−0.0218149
$965$	1.19313	0.0384084
$966$	0.161129	0.00518424
$967$	−28.0691	−0.902640	−0.451320	−	0.892362i	$-0.649047\pi$
$967$	−28.0691	−0.902640	−0.451320	+	0.892362i	$0.649047\pi$
$968$	22.7768	0.732074
$969$	−11.3647	−0.365087
$970$	−9.48135	−0.304428
$971$	10.5341	0.338056	0.169028	−	0.985611i	$-0.445937\pi$
$971$	10.5341	0.338056	0.169028	+	0.985611i	$0.445937\pi$
$972$	−0.554856	−0.0177970
$973$	−8.78879	−0.281756
$974$	−36.6638	−1.17478
$975$	2.03954	0.0653175
$976$	10.5883	0.338923
$977$	−32.1867	−1.02974	−0.514872	−	0.857267i	$-0.672160\pi$
$977$	−32.1867	−1.02974	−0.514872	+	0.857267i	$0.672160\pi$
$978$	−27.6672	−0.884700
$979$	−68.7090	−2.19595
$980$	0.394326	0.0125963
$981$	−12.8868	−0.411443
$982$	−14.3394	−0.457588
$983$	−3.33692	−0.106431	−0.0532155	−	0.998583i	$-0.516947\pi$
$983$	−3.33692	−0.106431	−0.0532155	+	0.998583i	$0.516947\pi$
$984$	−25.0828	−0.799610
$985$	−4.11595	−0.131145
$986$	−35.8797	−1.14264
$987$	0.247867	0.00788969
$988$	−1.01572	−0.0323145
$989$	−1.52440	−0.0484730
$990$	3.66631	0.116523
$991$	−14.5188	−0.461204	−0.230602	−	0.973048i	$-0.574070\pi$
$991$	−14.5188	−0.461204	−0.230602	+	0.973048i	$0.574070\pi$
$992$	25.8091	0.819441
$993$	−10.2010	−0.323720
$994$	0.247281	0.00784328
$995$	4.56100	0.144593
$996$	−7.58593	−0.240369
$997$	−37.0192	−1.17241	−0.586205	−	0.810163i	$-0.699379\pi$
$997$	−37.0192	−1.17241	−0.586205	+	0.810163i	$0.699379\pi$
$998$	12.8254	0.405982
$999$	3.22345	0.101985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.16	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.16	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.20214 q^{2} +1.00000 q^{3} -0.554856 q^{4} -0.710682 q^{5} -1.20214 q^{6} -1.00000 q^{7} +3.07130 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.20214 q^{2} +1.00000 q^{3} -0.554856 q^{4} -0.710682 q^{5} -1.20214 q^{6} -1.00000 q^{7} +3.07130 q^{8} +1.00000 q^{9} +0.854341 q^{10} +4.29139 q^{11} -0.554856 q^{12} -0.453742 q^{13} +1.20214 q^{14} -0.710682 q^{15} -2.58242 q^{16} +2.81690 q^{17} -1.20214 q^{18} -4.03447 q^{19} +0.394326 q^{20} -1.00000 q^{21} -5.15886 q^{22} +0.134035 q^{23} +3.07130 q^{24} -4.49493 q^{25} +0.545462 q^{26} +1.00000 q^{27} +0.554856 q^{28} +10.5955 q^{29} +0.854341 q^{30} -8.49499 q^{31} -3.03816 q^{32} +4.29139 q^{33} -3.38631 q^{34} +0.710682 q^{35} -0.554856 q^{36} +3.22345 q^{37} +4.85001 q^{38} -0.453742 q^{39} -2.18272 q^{40} -8.16684 q^{41} +1.20214 q^{42} -11.3731 q^{43} -2.38110 q^{44} -0.710682 q^{45} -0.161129 q^{46} -0.247867 q^{47} -2.58242 q^{48} +1.00000 q^{49} +5.40354 q^{50} +2.81690 q^{51} +0.251761 q^{52} +9.46209 q^{53} -1.20214 q^{54} -3.04981 q^{55} -3.07130 q^{56} -4.03447 q^{57} -12.7373 q^{58} -10.6577 q^{59} +0.394326 q^{60} -4.10013 q^{61} +10.2122 q^{62} -1.00000 q^{63} +8.81714 q^{64} +0.322466 q^{65} -5.15886 q^{66} +0.630549 q^{67} -1.56297 q^{68} +0.134035 q^{69} -0.854341 q^{70} +0.205700 q^{71} +3.07130 q^{72} -2.56439 q^{73} -3.87504 q^{74} -4.49493 q^{75} +2.23855 q^{76} -4.29139 q^{77} +0.545462 q^{78} +7.76979 q^{79} +1.83528 q^{80} +1.00000 q^{81} +9.81769 q^{82} +13.6719 q^{83} +0.554856 q^{84} -2.00192 q^{85} +13.6721 q^{86} +10.5955 q^{87} +13.1801 q^{88} -16.0109 q^{89} +0.854341 q^{90} +0.453742 q^{91} -0.0743701 q^{92} -8.49499 q^{93} +0.297971 q^{94} +2.86723 q^{95} -3.03816 q^{96} -11.0979 q^{97} -1.20214 q^{98} +4.29139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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