LMFDB - Embedded newform 8043.2.a.t.1.12

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:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.77779 q^{2} -1.00000 q^{3} +1.16053 q^{4} +3.56820 q^{5} +1.77779 q^{6} +1.00000 q^{7} +1.49240 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.77779 q^{2} -1.00000 q^{3} +1.16053 q^{4} +3.56820 q^{5} +1.77779 q^{6} +1.00000 q^{7} +1.49240 q^{8} +1.00000 q^{9} -6.34350 q^{10} +5.16426 q^{11} -1.16053 q^{12} +2.64380 q^{13} -1.77779 q^{14} -3.56820 q^{15} -4.97423 q^{16} +5.04956 q^{17} -1.77779 q^{18} -5.59180 q^{19} +4.14100 q^{20} -1.00000 q^{21} -9.18096 q^{22} -3.54738 q^{23} -1.49240 q^{24} +7.73206 q^{25} -4.70011 q^{26} -1.00000 q^{27} +1.16053 q^{28} +9.81363 q^{29} +6.34350 q^{30} -2.67330 q^{31} +5.85833 q^{32} -5.16426 q^{33} -8.97704 q^{34} +3.56820 q^{35} +1.16053 q^{36} -5.45641 q^{37} +9.94104 q^{38} -2.64380 q^{39} +5.32518 q^{40} -11.2201 q^{41} +1.77779 q^{42} -3.36590 q^{43} +5.99327 q^{44} +3.56820 q^{45} +6.30648 q^{46} +9.80452 q^{47} +4.97423 q^{48} +1.00000 q^{49} -13.7460 q^{50} -5.04956 q^{51} +3.06820 q^{52} -6.98261 q^{53} +1.77779 q^{54} +18.4271 q^{55} +1.49240 q^{56} +5.59180 q^{57} -17.4466 q^{58} +2.82993 q^{59} -4.14100 q^{60} -3.17822 q^{61} +4.75256 q^{62} +1.00000 q^{63} -0.466399 q^{64} +9.43360 q^{65} +9.18096 q^{66} -5.16188 q^{67} +5.86016 q^{68} +3.54738 q^{69} -6.34350 q^{70} +15.3563 q^{71} +1.49240 q^{72} -12.2590 q^{73} +9.70034 q^{74} -7.73206 q^{75} -6.48945 q^{76} +5.16426 q^{77} +4.70011 q^{78} -4.35170 q^{79} -17.7491 q^{80} +1.00000 q^{81} +19.9470 q^{82} +10.3624 q^{83} -1.16053 q^{84} +18.0178 q^{85} +5.98386 q^{86} -9.81363 q^{87} +7.70714 q^{88} +10.7515 q^{89} -6.34350 q^{90} +2.64380 q^{91} -4.11683 q^{92} +2.67330 q^{93} -17.4303 q^{94} -19.9527 q^{95} -5.85833 q^{96} +2.13548 q^{97} -1.77779 q^{98} +5.16426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	−1.77779	−1.25709	−0.628543	−	0.777775i	$-0.716348\pi$
$2$	−1.77779	−1.25709	−0.628543	+	0.777775i	$0.716348\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.16053	0.580265
$5$	3.56820	1.59575	0.797874	−	0.602824i	$-0.205958\pi$
$5$	3.56820	1.59575	0.797874	+	0.602824i	$0.205958\pi$
$6$	1.77779	0.725779
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.49240	0.527643
$9$	1.00000	0.333333
$10$	−6.34350	−2.00599
$11$	5.16426	1.55708	0.778541	−	0.627593i	$-0.215960\pi$
$11$	5.16426	1.55708	0.778541	+	0.627593i	$0.215960\pi$
$12$	−1.16053	−0.335016
$13$	2.64380	0.733257	0.366629	−	0.930367i	$-0.380512\pi$
$13$	2.64380	0.733257	0.366629	+	0.930367i	$0.380512\pi$
$14$	−1.77779	−0.475134
$15$	−3.56820	−0.921306
$16$	−4.97423	−1.24356
$17$	5.04956	1.22470	0.612349	−	0.790588i	$-0.290225\pi$
$17$	5.04956	1.22470	0.612349	+	0.790588i	$0.290225\pi$
$18$	−1.77779	−0.419029
$19$	−5.59180	−1.28285	−0.641424	−	0.767187i	$-0.721656\pi$
$19$	−5.59180	−1.28285	−0.641424	+	0.767187i	$0.721656\pi$
$20$	4.14100	0.925956
$21$	−1.00000	−0.218218
$22$	−9.18096	−1.95739
$23$	−3.54738	−0.739679	−0.369839	−	0.929096i	$-0.620587\pi$
$23$	−3.54738	−0.739679	−0.369839	+	0.929096i	$0.620587\pi$
$24$	−1.49240	−0.304635
$25$	7.73206	1.54641
$26$	−4.70011	−0.921768
$27$	−1.00000	−0.192450
$28$	1.16053	0.219319
$29$	9.81363	1.82235	0.911173	−	0.412025i	$-0.135178\pi$
$29$	9.81363	1.82235	0.911173	+	0.412025i	$0.135178\pi$
$30$	6.34350	1.15816
$31$	−2.67330	−0.480139	−0.240069	−	0.970756i	$-0.577170\pi$
$31$	−2.67330	−0.480139	−0.240069	+	0.970756i	$0.577170\pi$
$32$	5.85833	1.03562
$33$	−5.16426	−0.898982
$34$	−8.97704	−1.53955
$35$	3.56820	0.603136
$36$	1.16053	0.193422
$37$	−5.45641	−0.897028	−0.448514	−	0.893776i	$-0.648047\pi$
$37$	−5.45641	−0.897028	−0.448514	+	0.893776i	$0.648047\pi$
$38$	9.94104	1.61265
$39$	−2.64380	−0.423346
$40$	5.32518	0.841986
$41$	−11.2201	−1.75229	−0.876143	−	0.482052i	$-0.839892\pi$
$41$	−11.2201	−1.75229	−0.876143	+	0.482052i	$0.839892\pi$
$42$	1.77779	0.274319
$43$	−3.36590	−0.513296	−0.256648	−	0.966505i	$-0.582618\pi$
$43$	−3.36590	−0.513296	−0.256648	+	0.966505i	$0.582618\pi$
$44$	5.99327	0.903520
$45$	3.56820	0.531916
$46$	6.30648	0.929840
$47$	9.80452	1.43014	0.715068	−	0.699055i	$-0.246396\pi$
$47$	9.80452	1.43014	0.715068	+	0.699055i	$0.246396\pi$
$48$	4.97423	0.717968
$49$	1.00000	0.142857
$50$	−13.7460	−1.94397
$51$	−5.04956	−0.707079
$52$	3.06820	0.425483
$53$	−6.98261	−0.959135	−0.479567	−	0.877505i	$-0.659206\pi$
$53$	−6.98261	−0.959135	−0.479567	+	0.877505i	$0.659206\pi$
$54$	1.77779	0.241926
$55$	18.4271	2.48471
$56$	1.49240	0.199430
$57$	5.59180	0.740652
$58$	−17.4466	−2.29084
$59$	2.82993	0.368426	0.184213	−	0.982886i	$-0.441026\pi$
$59$	2.82993	0.368426	0.184213	+	0.982886i	$0.441026\pi$
$60$	−4.14100	−0.534601
$61$	−3.17822	−0.406930	−0.203465	−	0.979082i	$-0.565220\pi$
$61$	−3.17822	−0.406930	−0.203465	+	0.979082i	$0.565220\pi$
$62$	4.75256	0.603575
$63$	1.00000	0.125988
$64$	−0.466399	−0.0582998
$65$	9.43360	1.17009
$66$	9.18096	1.13010
$67$	−5.16188	−0.630624	−0.315312	−	0.948988i	$-0.602109\pi$
$67$	−5.16188	−0.630624	−0.315312	+	0.948988i	$0.602109\pi$
$68$	5.86016	0.710649
$69$	3.54738	0.427054
$70$	−6.34350	−0.758194
$71$	15.3563	1.82246	0.911229	−	0.411900i	$-0.135135\pi$
$71$	15.3563	1.82246	0.911229	+	0.411900i	$0.135135\pi$
$72$	1.49240	0.175881
$73$	−12.2590	−1.43481	−0.717406	−	0.696656i	$-0.754671\pi$
$73$	−12.2590	−1.43481	−0.717406	+	0.696656i	$0.754671\pi$
$74$	9.70034	1.12764
$75$	−7.73206	−0.892821
$76$	−6.48945	−0.744391
$77$	5.16426	0.588522
$78$	4.70011	0.532183
$79$	−4.35170	−0.489605	−0.244802	−	0.969573i	$-0.578723\pi$
$79$	−4.35170	−0.489605	−0.244802	+	0.969573i	$0.578723\pi$
$80$	−17.7491	−1.98440
$81$	1.00000	0.111111
$82$	19.9470	2.20277
$83$	10.3624	1.13742	0.568709	−	0.822539i	$-0.307443\pi$
$83$	10.3624	1.13742	0.568709	+	0.822539i	$0.307443\pi$
$84$	−1.16053	−0.126624
$85$	18.0178	1.95431
$86$	5.98386	0.645257
$87$	−9.81363	−1.05213
$88$	7.70714	0.821584
$89$	10.7515	1.13965	0.569827	−	0.821765i	$-0.307010\pi$
$89$	10.7515	1.13965	0.569827	+	0.821765i	$0.307010\pi$
$90$	−6.34350	−0.668664
$91$	2.64380	0.277145
$92$	−4.11683	−0.429210
$93$	2.67330	0.277208
$94$	−17.4303	−1.79780
$95$	−19.9527	−2.04710
$96$	−5.85833	−0.597913
$97$	2.13548	0.216825	0.108412	−	0.994106i	$-0.465423\pi$
$97$	2.13548	0.216825	0.108412	+	0.994106i	$0.465423\pi$
$98$	−1.77779	−0.179584
$99$	5.16426	0.519028
$100$	8.97328	0.897328
$101$	12.6656	1.26027	0.630137	−	0.776484i	$-0.282999\pi$
$101$	12.6656	1.26027	0.630137	+	0.776484i	$0.282999\pi$
$102$	8.97704	0.888859
$103$	11.6109	1.14405	0.572026	−	0.820236i	$-0.306158\pi$
$103$	11.6109	1.14405	0.572026	+	0.820236i	$0.306158\pi$
$104$	3.94560	0.386898
$105$	−3.56820	−0.348221
$106$	12.4136	1.20571
$107$	4.66636	0.451114	0.225557	−	0.974230i	$-0.427580\pi$
$107$	4.66636	0.451114	0.225557	+	0.974230i	$0.427580\pi$
$108$	−1.16053	−0.111672
$109$	12.1226	1.16114	0.580569	−	0.814211i	$-0.302830\pi$
$109$	12.1226	1.16114	0.580569	+	0.814211i	$0.302830\pi$
$110$	−32.7595	−3.12350
$111$	5.45641	0.517899
$112$	−4.97423	−0.470021
$113$	1.28147	0.120551	0.0602754	−	0.998182i	$-0.480802\pi$
$113$	1.28147	0.120551	0.0602754	+	0.998182i	$0.480802\pi$
$114$	−9.94104	−0.931064
$115$	−12.6577	−1.18034
$116$	11.3890	1.05744
$117$	2.64380	0.244419
$118$	−5.03102	−0.463143
$119$	5.04956	0.462892
$120$	−5.32518	−0.486121
$121$	15.6696	1.42451
$122$	5.65021	0.511546
$123$	11.2201	1.01168
$124$	−3.10244	−0.278608
$125$	9.74853	0.871935
$126$	−1.77779	−0.158378
$127$	3.66781	0.325465	0.162733	−	0.986670i	$-0.447969\pi$
$127$	3.66781	0.325465	0.162733	+	0.986670i	$0.447969\pi$
$128$	−10.8875	−0.962327
$129$	3.36590	0.296351
$130$	−16.7709	−1.47091
$131$	−17.1864	−1.50159	−0.750793	−	0.660537i	$-0.770329\pi$
$131$	−17.1864	−1.50159	−0.750793	+	0.660537i	$0.770329\pi$
$132$	−5.99327	−0.521648
$133$	−5.59180	−0.484871
$134$	9.17673	0.792749
$135$	−3.56820	−0.307102
$136$	7.53596	0.646203
$137$	16.7456	1.43067	0.715337	−	0.698779i	$-0.246273\pi$
$137$	16.7456	1.43067	0.715337	+	0.698779i	$0.246273\pi$
$138$	−6.30648	−0.536843
$139$	−12.6400	−1.07211	−0.536056	−	0.844183i	$-0.680086\pi$
$139$	−12.6400	−1.07211	−0.536056	+	0.844183i	$0.680086\pi$
$140$	4.14100	0.349979
$141$	−9.80452	−0.825689
$142$	−27.3002	−2.29099
$143$	13.6533	1.14174
$144$	−4.97423	−0.414519
$145$	35.0170	2.90800
$146$	21.7940	1.80368
$147$	−1.00000	−0.0824786
$148$	−6.33232	−0.520514
$149$	8.12880	0.665937	0.332969	−	0.942938i	$-0.391950\pi$
$149$	8.12880	0.665937	0.332969	+	0.942938i	$0.391950\pi$
$150$	13.7460	1.12235
$151$	−4.23418	−0.344573	−0.172286	−	0.985047i	$-0.555115\pi$
$151$	−4.23418	−0.344573	−0.172286	+	0.985047i	$0.555115\pi$
$152$	−8.34521	−0.676886
$153$	5.04956	0.408232
$154$	−9.18096	−0.739823
$155$	−9.53887	−0.766180
$156$	−3.06820	−0.245653
$157$	13.2965	1.06117	0.530587	−	0.847631i	$-0.321972\pi$
$157$	13.2965	1.06117	0.530587	+	0.847631i	$0.321972\pi$
$158$	7.73640	0.615475
$159$	6.98261	0.553757
$160$	20.9037	1.65258
$161$	−3.54738	−0.279572
$162$	−1.77779	−0.139676
$163$	1.02659	0.0804084	0.0402042	−	0.999191i	$-0.487199\pi$
$163$	1.02659	0.0804084	0.0402042	+	0.999191i	$0.487199\pi$
$164$	−13.0213	−1.01679
$165$	−18.4271	−1.43455
$166$	−18.4221	−1.42983
$167$	−0.549046	−0.0424865	−0.0212432	−	0.999774i	$-0.506762\pi$
$167$	−0.549046	−0.0424865	−0.0212432	+	0.999774i	$0.506762\pi$
$168$	−1.49240	−0.115141
$169$	−6.01034	−0.462334
$170$	−32.0319	−2.45673
$171$	−5.59180	−0.427616
$172$	−3.90623	−0.297847
$173$	5.50542	0.418569	0.209285	−	0.977855i	$-0.432886\pi$
$173$	5.50542	0.418569	0.209285	+	0.977855i	$0.432886\pi$
$174$	17.4466	1.32262
$175$	7.73206	0.584489
$176$	−25.6882	−1.93632
$177$	−2.82993	−0.212711
$178$	−19.1138	−1.43264
$179$	16.4288	1.22795	0.613974	−	0.789326i	$-0.289570\pi$
$179$	16.4288	1.22795	0.613974	+	0.789326i	$0.289570\pi$
$180$	4.14100	0.308652
$181$	8.02365	0.596393	0.298197	−	0.954504i	$-0.403615\pi$
$181$	8.02365	0.596393	0.298197	+	0.954504i	$0.403615\pi$
$182$	−4.70011	−0.348395
$183$	3.17822	0.234941
$184$	−5.29411	−0.390287
$185$	−19.4696	−1.43143
$186$	−4.75256	−0.348474
$187$	26.0772	1.90695
$188$	11.3784	0.829857
$189$	−1.00000	−0.0727393
$190$	35.4716	2.57338
$191$	−25.7675	−1.86447	−0.932234	−	0.361856i	$-0.882143\pi$
$191$	−25.7675	−1.86447	−0.932234	+	0.361856i	$0.882143\pi$
$192$	0.466399	0.0336594
$193$	21.8665	1.57398	0.786991	−	0.616964i	$-0.211638\pi$
$193$	21.8665	1.57398	0.786991	+	0.616964i	$0.211638\pi$
$194$	−3.79642	−0.272567
$195$	−9.43360	−0.675554
$196$	1.16053	0.0828950
$197$	11.0476	0.787107	0.393553	−	0.919302i	$-0.371246\pi$
$197$	11.0476	0.787107	0.393553	+	0.919302i	$0.371246\pi$
$198$	−9.18096	−0.652462
$199$	−2.43275	−0.172453	−0.0862264	−	0.996276i	$-0.527481\pi$
$199$	−2.43275	−0.172453	−0.0862264	+	0.996276i	$0.527481\pi$
$200$	11.5393	0.815954
$201$	5.16188	0.364091
$202$	−22.5167	−1.58427
$203$	9.81363	0.688782
$204$	−5.86016	−0.410293
$205$	−40.0356	−2.79621
$206$	−20.6416	−1.43817
$207$	−3.54738	−0.246560
$208$	−13.1509	−0.911848
$209$	−28.8775	−1.99750
$210$	6.34350	0.437743
$211$	14.1449	0.973778	0.486889	−	0.873464i	$-0.338132\pi$
$211$	14.1449	0.973778	0.486889	+	0.873464i	$0.338132\pi$
$212$	−8.10352	−0.556552
$213$	−15.3563	−1.05220
$214$	−8.29579	−0.567089
$215$	−12.0102	−0.819091
$216$	−1.49240	−0.101545
$217$	−2.67330	−0.181475
$218$	−21.5515	−1.45965
$219$	12.2590	0.828389
$220$	21.3852	1.44179
$221$	13.3500	0.898018
$222$	−9.70034	−0.651044
$223$	−22.0031	−1.47344	−0.736718	−	0.676200i	$-0.763625\pi$
$223$	−22.0031	−1.47344	−0.736718	+	0.676200i	$0.763625\pi$
$224$	5.85833	0.391426
$225$	7.73206	0.515471
$226$	−2.27819	−0.151543
$227$	−5.19944	−0.345099	−0.172549	−	0.985001i	$-0.555200\pi$
$227$	−5.19944	−0.345099	−0.172549	+	0.985001i	$0.555200\pi$
$228$	6.48945	0.429774
$229$	4.65236	0.307437	0.153718	−	0.988115i	$-0.450875\pi$
$229$	4.65236	0.307437	0.153718	+	0.988115i	$0.450875\pi$
$230$	22.5028	1.48379
$231$	−5.16426	−0.339783
$232$	14.6459	0.961548
$233$	−1.65730	−0.108573	−0.0542867	−	0.998525i	$-0.517289\pi$
$233$	−1.65730	−0.108573	−0.0542867	+	0.998525i	$0.517289\pi$
$234$	−4.70011	−0.307256
$235$	34.9845	2.28214
$236$	3.28422	0.213785
$237$	4.35170	0.282673
$238$	−8.97704	−0.581895
$239$	−19.8635	−1.28486	−0.642431	−	0.766344i	$-0.722074\pi$
$239$	−19.8635	−1.28486	−0.642431	+	0.766344i	$0.722074\pi$
$240$	17.7491	1.14570
$241$	1.30808	0.0842606	0.0421303	−	0.999112i	$-0.486586\pi$
$241$	1.30808	0.0842606	0.0421303	+	0.999112i	$0.486586\pi$
$242$	−27.8572	−1.79073
$243$	−1.00000	−0.0641500
$244$	−3.68842	−0.236127
$245$	3.56820	0.227964
$246$	−19.9470	−1.27177
$247$	−14.7836	−0.940657
$248$	−3.98963	−0.253342
$249$	−10.3624	−0.656688
$250$	−17.3308	−1.09610
$251$	2.76424	0.174477	0.0872387	−	0.996187i	$-0.472196\pi$
$251$	2.76424	0.174477	0.0872387	+	0.996187i	$0.472196\pi$
$252$	1.16053	0.0731065
$253$	−18.3196	−1.15174
$254$	−6.52058	−0.409138
$255$	−18.0178	−1.12832
$256$	20.2884	1.26803
$257$	−11.5308	−0.719270	−0.359635	−	0.933093i	$-0.617099\pi$
$257$	−11.5308	−0.719270	−0.359635	+	0.933093i	$0.617099\pi$
$258$	−5.98386	−0.372539
$259$	−5.45641	−0.339045
$260$	10.9480	0.678964
$261$	9.81363	0.607449
$262$	30.5538	1.88762
$263$	18.6024	1.14708	0.573538	−	0.819179i	$-0.305571\pi$
$263$	18.6024	1.14708	0.573538	+	0.819179i	$0.305571\pi$
$264$	−7.70714	−0.474342
$265$	−24.9153	−1.53054
$266$	9.94104	0.609524
$267$	−10.7515	−0.657979
$268$	−5.99052	−0.365929
$269$	4.15629	0.253414	0.126707	−	0.991940i	$-0.459559\pi$
$269$	4.15629	0.253414	0.126707	+	0.991940i	$0.459559\pi$
$270$	6.34350	0.386053
$271$	23.7689	1.44386	0.721930	−	0.691966i	$-0.243255\pi$
$271$	23.7689	1.44386	0.721930	+	0.691966i	$0.243255\pi$
$272$	−25.1177	−1.52298
$273$	−2.64380	−0.160010
$274$	−29.7702	−1.79848
$275$	39.9303	2.40789
$276$	4.11683	0.247804
$277$	−17.1397	−1.02982	−0.514912	−	0.857243i	$-0.672175\pi$
$277$	−17.1397	−1.02982	−0.514912	+	0.857243i	$0.672175\pi$
$278$	22.4713	1.34774
$279$	−2.67330	−0.160046
$280$	5.32518	0.318241
$281$	7.18469	0.428603	0.214301	−	0.976768i	$-0.431253\pi$
$281$	7.18469	0.428603	0.214301	+	0.976768i	$0.431253\pi$
$282$	17.4303	1.03796
$283$	−1.70929	−0.101607	−0.0508035	−	0.998709i	$-0.516178\pi$
$283$	−1.70929	−0.101607	−0.0508035	+	0.998709i	$0.516178\pi$
$284$	17.8214	1.05751
$285$	19.9527	1.18189
$286$	−24.2726	−1.43527
$287$	−11.2201	−0.662302
$288$	5.85833	0.345205
$289$	8.49801	0.499883
$290$	−62.2528	−3.65561
$291$	−2.13548	−0.125184
$292$	−14.2270	−0.832570
$293$	2.03527	0.118902	0.0594509	−	0.998231i	$-0.481065\pi$
$293$	2.03527	0.118902	0.0594509	+	0.998231i	$0.481065\pi$
$294$	1.77779	0.103683
$295$	10.0978	0.587915
$296$	−8.14315	−0.473311
$297$	−5.16426	−0.299661
$298$	−14.4513	−0.837140
$299$	−9.37854	−0.542375
$300$	−8.97328	−0.518073
$301$	−3.36590	−0.194008
$302$	7.52748	0.433158
$303$	−12.6656	−0.727620
$304$	27.8149	1.59529
$305$	−11.3405	−0.649357
$306$	−8.97704	−0.513183
$307$	−4.42991	−0.252828	−0.126414	−	0.991978i	$-0.540347\pi$
$307$	−4.42991	−0.252828	−0.126414	+	0.991978i	$0.540347\pi$
$308$	5.99327	0.341499
$309$	−11.6109	−0.660519
$310$	16.9581	0.963154
$311$	−18.8365	−1.06812	−0.534059	−	0.845447i	$-0.679334\pi$
$311$	−18.8365	−1.06812	−0.534059	+	0.845447i	$0.679334\pi$
$312$	−3.94560	−0.223376
$313$	−12.1668	−0.687711	−0.343855	−	0.939023i	$-0.611733\pi$
$313$	−12.1668	−0.687711	−0.343855	+	0.939023i	$0.611733\pi$
$314$	−23.6383	−1.33399
$315$	3.56820	0.201045
$316$	−5.05028	−0.284100
$317$	5.28744	0.296972	0.148486	−	0.988914i	$-0.452560\pi$
$317$	5.28744	0.296972	0.148486	+	0.988914i	$0.452560\pi$
$318$	−12.4136	−0.696120
$319$	50.6801	2.83754
$320$	−1.66420	−0.0930318
$321$	−4.66636	−0.260451
$322$	6.30648	0.351446
$323$	−28.2361	−1.57110
$324$	1.16053	0.0644739
$325$	20.4420	1.13392
$326$	−1.82505	−0.101080
$327$	−12.1226	−0.670384
$328$	−16.7449	−0.924581
$329$	9.80452	0.540540
$330$	32.7595	1.80335
$331$	28.6932	1.57712	0.788560	−	0.614958i	$-0.210827\pi$
$331$	28.6932	1.57712	0.788560	+	0.614958i	$0.210827\pi$
$332$	12.0258	0.660003
$333$	−5.45641	−0.299009
$334$	0.976087	0.0534091
$335$	−18.4186	−1.00632
$336$	4.97423	0.271367
$337$	30.3775	1.65477	0.827384	−	0.561637i	$-0.189828\pi$
$337$	30.3775	1.65477	0.827384	+	0.561637i	$0.189828\pi$
$338$	10.6851	0.581193
$339$	−1.28147	−0.0696001
$340$	20.9102	1.13402
$341$	−13.8056	−0.747616
$342$	9.94104	0.537550
$343$	1.00000	0.0539949
$344$	−5.02328	−0.270837
$345$	12.6577	0.681470
$346$	−9.78746	−0.526177
$347$	−19.7778	−1.06173	−0.530863	−	0.847458i	$-0.678132\pi$
$347$	−19.7778	−1.06173	−0.530863	+	0.847458i	$0.678132\pi$
$348$	−11.3890	−0.610515
$349$	6.77139	0.362464	0.181232	−	0.983440i	$-0.441991\pi$
$349$	6.77139	0.362464	0.181232	+	0.983440i	$0.441991\pi$
$350$	−13.7460	−0.734752
$351$	−2.64380	−0.141115
$352$	30.2539	1.61254
$353$	8.51251	0.453075	0.226538	−	0.974002i	$-0.427259\pi$
$353$	8.51251	0.453075	0.226538	+	0.974002i	$0.427259\pi$
$354$	5.03102	0.267396
$355$	54.7944	2.90818
$356$	12.4774	0.661301
$357$	−5.04956	−0.267251
$358$	−29.2070	−1.54364
$359$	−32.2581	−1.70251	−0.851257	−	0.524748i	$-0.824159\pi$
$359$	−32.2581	−1.70251	−0.851257	+	0.524748i	$0.824159\pi$
$360$	5.32518	0.280662
$361$	12.2683	0.645698
$362$	−14.2643	−0.749717
$363$	−15.6696	−0.822439
$364$	3.06820	0.160818
$365$	−43.7427	−2.28960
$366$	−5.65021	−0.295341
$367$	0.942900	0.0492190	0.0246095	−	0.999697i	$-0.492166\pi$
$367$	0.942900	0.0492190	0.0246095	+	0.999697i	$0.492166\pi$
$368$	17.6455	0.919833
$369$	−11.2201	−0.584095
$370$	34.6128	1.79943
$371$	−6.98261	−0.362519
$372$	3.10244	0.160854
$373$	−5.26452	−0.272586	−0.136293	−	0.990669i	$-0.543519\pi$
$373$	−5.26452	−0.272586	−0.136293	+	0.990669i	$0.543519\pi$
$374$	−46.3597	−2.39721
$375$	−9.74853	−0.503412
$376$	14.6323	0.754601
$377$	25.9453	1.33625
$378$	1.77779	0.0914395
$379$	−24.6145	−1.26436	−0.632182	−	0.774820i	$-0.717840\pi$
$379$	−24.6145	−1.26436	−0.632182	+	0.774820i	$0.717840\pi$
$380$	−23.1557	−1.18786
$381$	−3.66781	−0.187907
$382$	45.8091	2.34380
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	10.8875	0.555600
$385$	18.4271	0.939133
$386$	−38.8739	−1.97863
$387$	−3.36590	−0.171099
$388$	2.47828	0.125816
$389$	22.9733	1.16479	0.582397	−	0.812905i	$-0.302115\pi$
$389$	22.9733	1.16479	0.582397	+	0.812905i	$0.302115\pi$
$390$	16.7709	0.849230
$391$	−17.9127	−0.905883
$392$	1.49240	0.0753776
$393$	17.1864	0.866941
$394$	−19.6402	−0.989460
$395$	−15.5277	−0.781286
$396$	5.99327	0.301173
$397$	−15.0916	−0.757428	−0.378714	−	0.925514i	$-0.623634\pi$
$397$	−15.0916	−0.757428	−0.378714	+	0.925514i	$0.623634\pi$
$398$	4.32491	0.216788
$399$	5.59180	0.279940
$400$	−38.4610	−1.92305
$401$	3.73872	0.186703	0.0933514	−	0.995633i	$-0.470242\pi$
$401$	3.73872	0.186703	0.0933514	+	0.995633i	$0.470242\pi$
$402$	−9.17673	−0.457694
$403$	−7.06766	−0.352065
$404$	14.6988	0.731293
$405$	3.56820	0.177305
$406$	−17.4466	−0.865858
$407$	−28.1783	−1.39675
$408$	−7.53596	−0.373086
$409$	−1.09450	−0.0541194	−0.0270597	−	0.999634i	$-0.508614\pi$
$409$	−1.09450	−0.0541194	−0.0270597	+	0.999634i	$0.508614\pi$
$410$	71.1748	3.51507
$411$	−16.7456	−0.826001
$412$	13.4747	0.663853
$413$	2.82993	0.139252
$414$	6.30648	0.309947
$415$	36.9750	1.81503
$416$	15.4882	0.759373
$417$	12.6400	0.618984
$418$	51.3381	2.51103
$419$	−17.0939	−0.835093	−0.417547	−	0.908656i	$-0.637110\pi$
$419$	−17.0939	−0.835093	−0.417547	+	0.908656i	$0.637110\pi$
$420$	−4.14100	−0.202060
$421$	−24.3624	−1.18735	−0.593676	−	0.804704i	$-0.702324\pi$
$421$	−24.3624	−1.18735	−0.593676	+	0.804704i	$0.702324\pi$
$422$	−25.1467	−1.22412
$423$	9.80452	0.476712
$424$	−10.4208	−0.506081
$425$	39.0435	1.89389
$426$	27.3002	1.32270
$427$	−3.17822	−0.153805
$428$	5.41544	0.261765
$429$	−13.6533	−0.659185
$430$	21.3516	1.02967
$431$	37.8944	1.82531	0.912654	−	0.408734i	$-0.134030\pi$
$431$	37.8944	1.82531	0.912654	+	0.408734i	$0.134030\pi$
$432$	4.97423	0.239323
$433$	32.8122	1.57685	0.788426	−	0.615130i	$-0.210896\pi$
$433$	32.8122	1.57685	0.788426	+	0.615130i	$0.210896\pi$
$434$	4.75256	0.228130
$435$	−35.0170	−1.67894
$436$	14.0687	0.673768
$437$	19.8362	0.948895
$438$	−21.7940	−1.04136
$439$	10.5354	0.502825	0.251413	−	0.967880i	$-0.419105\pi$
$439$	10.5354	0.502825	0.251413	+	0.967880i	$0.419105\pi$
$440$	27.5006	1.31104
$441$	1.00000	0.0476190
$442$	−23.7335	−1.12889
$443$	21.9001	1.04050	0.520252	−	0.854013i	$-0.325838\pi$
$443$	21.9001	1.04050	0.520252	+	0.854013i	$0.325838\pi$
$444$	6.33232	0.300519
$445$	38.3634	1.81860
$446$	39.1168	1.85224
$447$	−8.12880	−0.384479
$448$	−0.466399	−0.0220353
$449$	19.9363	0.940852	0.470426	−	0.882440i	$-0.344100\pi$
$449$	19.9363	0.940852	0.470426	+	0.882440i	$0.344100\pi$
$450$	−13.7460	−0.647991
$451$	−57.9435	−2.72845
$452$	1.48719	0.0699514
$453$	4.23418	0.198939
$454$	9.24349	0.433819
$455$	9.43360	0.442254
$456$	8.34521	0.390800
$457$	−9.61335	−0.449694	−0.224847	−	0.974394i	$-0.572188\pi$
$457$	−9.61335	−0.449694	−0.224847	+	0.974394i	$0.572188\pi$
$458$	−8.27091	−0.386474
$459$	−5.04956	−0.235693
$460$	−14.6897	−0.684910
$461$	−14.5863	−0.679350	−0.339675	−	0.940543i	$-0.610317\pi$
$461$	−14.5863	−0.679350	−0.339675	+	0.940543i	$0.610317\pi$
$462$	9.18096	0.427137
$463$	−42.3415	−1.96778	−0.983888	−	0.178786i	$-0.942783\pi$
$463$	−42.3415	−1.96778	−0.983888	+	0.178786i	$0.942783\pi$
$464$	−48.8153	−2.26619
$465$	9.53887	0.442354
$466$	2.94633	0.136486
$467$	−32.6293	−1.50990	−0.754952	−	0.655780i	$-0.772340\pi$
$467$	−32.6293	−1.50990	−0.754952	+	0.655780i	$0.772340\pi$
$468$	3.06820	0.141828
$469$	−5.16188	−0.238354
$470$	−62.1950	−2.86884
$471$	−13.2965	−0.612669
$472$	4.22339	0.194397
$473$	−17.3824	−0.799244
$474$	−7.73640	−0.355345
$475$	−43.2361	−1.98381
$476$	5.86016	0.268600
$477$	−6.98261	−0.319712
$478$	35.3131	1.61518
$479$	25.8706	1.18206	0.591028	−	0.806651i	$-0.298722\pi$
$479$	25.8706	1.18206	0.591028	+	0.806651i	$0.298722\pi$
$480$	−20.9037	−0.954118
$481$	−14.4256	−0.657753
$482$	−2.32548	−0.105923
$483$	3.54738	0.161411
$484$	18.1850	0.826591
$485$	7.61981	0.345998
$486$	1.77779	0.0806421
$487$	−19.8336	−0.898746	−0.449373	−	0.893344i	$-0.648353\pi$
$487$	−19.8336	−0.898746	−0.449373	+	0.893344i	$0.648353\pi$
$488$	−4.74318	−0.214714
$489$	−1.02659	−0.0464238
$490$	−6.34350	−0.286570
$491$	−13.2526	−0.598082	−0.299041	−	0.954240i	$-0.596667\pi$
$491$	−13.2526	−0.598082	−0.299041	+	0.954240i	$0.596667\pi$
$492$	13.0213	0.587044
$493$	49.5545	2.23182
$494$	26.2821	1.18249
$495$	18.4271	0.828237
$496$	13.2976	0.597080
$497$	15.3563	0.688824
$498$	18.4221	0.825513
$499$	−37.2234	−1.66635	−0.833175	−	0.553010i	$-0.813479\pi$
$499$	−37.2234	−1.66635	−0.833175	+	0.553010i	$0.813479\pi$
$500$	11.3135	0.505953
$501$	0.549046	0.0245296
$502$	−4.91424	−0.219333
$503$	−37.1974	−1.65855	−0.829274	−	0.558842i	$-0.811246\pi$
$503$	−37.1974	−1.65855	−0.829274	+	0.558842i	$0.811246\pi$
$504$	1.49240	0.0664768
$505$	45.1934	2.01108
$506$	32.5683	1.44784
$507$	6.01034	0.266928
$508$	4.25660	0.188856
$509$	7.35668	0.326079	0.163039	−	0.986620i	$-0.447870\pi$
$509$	7.35668	0.326079	0.163039	+	0.986620i	$0.447870\pi$
$510$	32.0319	1.41840
$511$	−12.2590	−0.542308
$512$	−14.2936	−0.631693
$513$	5.59180	0.246884
$514$	20.4993	0.904184
$515$	41.4299	1.82562
$516$	3.90623	0.171962
$517$	50.6331	2.22684
$518$	9.70034	0.426208
$519$	−5.50542	−0.241661
$520$	14.0787	0.617392
$521$	21.2458	0.930794	0.465397	−	0.885102i	$-0.345912\pi$
$521$	21.2458	0.930794	0.465397	+	0.885102i	$0.345912\pi$
$522$	−17.4466	−0.763615
$523$	20.3002	0.887666	0.443833	−	0.896109i	$-0.353618\pi$
$523$	20.3002	0.887666	0.443833	+	0.896109i	$0.353618\pi$
$524$	−19.9454	−0.871318
$525$	−7.73206	−0.337455
$526$	−33.0712	−1.44197
$527$	−13.4990	−0.588024
$528$	25.6882	1.11794
$529$	−10.4161	−0.452875
$530$	44.2942	1.92402
$531$	2.82993	0.122809
$532$	−6.48945	−0.281353
$533$	−29.6637	−1.28488
$534$	19.1138	0.827136
$535$	16.6505	0.719864
$536$	−7.70360	−0.332745
$537$	−16.4288	−0.708956
$538$	−7.38901	−0.318563
$539$	5.16426	0.222440
$540$	−4.14100	−0.178200
$541$	−10.4628	−0.449830	−0.224915	−	0.974378i	$-0.572210\pi$
$541$	−10.4628	−0.449830	−0.224915	+	0.974378i	$0.572210\pi$
$542$	−42.2561	−1.81506
$543$	−8.02365	−0.344328
$544$	29.5819	1.26832
$545$	43.2560	1.85289
$546$	4.70011	0.201146
$547$	4.64212	0.198483	0.0992414	−	0.995063i	$-0.468358\pi$
$547$	4.64212	0.198483	0.0992414	+	0.995063i	$0.468358\pi$
$548$	19.4338	0.830170
$549$	−3.17822	−0.135643
$550$	−70.9877	−3.02693
$551$	−54.8759	−2.33779
$552$	5.29411	0.225332
$553$	−4.35170	−0.185053
$554$	30.4707	1.29458
$555$	19.4696	0.826437
$556$	−14.6691	−0.622109
$557$	−9.39100	−0.397909	−0.198955	−	0.980009i	$-0.563755\pi$
$557$	−9.39100	−0.397909	−0.198955	+	0.980009i	$0.563755\pi$
$558$	4.75256	0.201192
$559$	−8.89877	−0.376378
$560$	−17.7491	−0.750034
$561$	−26.0772	−1.10098
$562$	−12.7729	−0.538791
$563$	40.5858	1.71049	0.855244	−	0.518225i	$-0.173407\pi$
$563$	40.5858	1.71049	0.855244	+	0.518225i	$0.173407\pi$
$564$	−11.3784	−0.479118
$565$	4.57255	0.192369
$566$	3.03876	0.127729
$567$	1.00000	0.0419961
$568$	22.9178	0.961608
$569$	30.7513	1.28916	0.644580	−	0.764537i	$-0.277032\pi$
$569$	30.7513	1.28916	0.644580	+	0.764537i	$0.277032\pi$
$570$	−35.4716	−1.48574
$571$	−7.72106	−0.323116	−0.161558	−	0.986863i	$-0.551652\pi$
$571$	−7.72106	−0.323116	−0.161558	+	0.986863i	$0.551652\pi$
$572$	15.8450	0.662513
$573$	25.7675	1.07645
$574$	19.9470	0.832570
$575$	−27.4285	−1.14385
$576$	−0.466399	−0.0194333
$577$	−1.62087	−0.0674777	−0.0337389	−	0.999431i	$-0.510741\pi$
$577$	−1.62087	−0.0674777	−0.0337389	+	0.999431i	$0.510741\pi$
$578$	−15.1077	−0.628396
$579$	−21.8665	−0.908739
$580$	40.6383	1.68741
$581$	10.3624	0.429903
$582$	3.79642	0.157367
$583$	−36.0600	−1.49345
$584$	−18.2954	−0.757069
$585$	9.43360	0.390031
$586$	−3.61828	−0.149470
$587$	−4.34958	−0.179526	−0.0897632	−	0.995963i	$-0.528611\pi$
$587$	−4.34958	−0.179526	−0.0897632	+	0.995963i	$0.528611\pi$
$588$	−1.16053	−0.0478594
$589$	14.9486	0.615945
$590$	−17.9517	−0.739060
$591$	−11.0476	−0.454436
$592$	27.1414	1.11551
$593$	−3.98308	−0.163565	−0.0817827	−	0.996650i	$-0.526061\pi$
$593$	−3.98308	−0.163565	−0.0817827	+	0.996650i	$0.526061\pi$
$594$	9.18096	0.376699
$595$	18.0178	0.738659
$596$	9.43371	0.386420
$597$	2.43275	0.0995657
$598$	16.6731	0.681812
$599$	5.98169	0.244405	0.122203	−	0.992505i	$-0.461004\pi$
$599$	5.98169	0.244405	0.122203	+	0.992505i	$0.461004\pi$
$600$	−11.5393	−0.471091
$601$	23.9260	0.975963	0.487982	−	0.872854i	$-0.337733\pi$
$601$	23.9260	0.975963	0.487982	+	0.872854i	$0.337733\pi$
$602$	5.98386	0.243884
$603$	−5.16188	−0.210208
$604$	−4.91389	−0.199944
$605$	55.9122	2.27315
$606$	22.5167	0.914680
$607$	−28.8160	−1.16961	−0.584803	−	0.811176i	$-0.698828\pi$
$607$	−28.8160	−1.16961	−0.584803	+	0.811176i	$0.698828\pi$
$608$	−32.7586	−1.32854
$609$	−9.81363	−0.397668
$610$	20.1611	0.816298
$611$	25.9212	1.04866
$612$	5.86016	0.236883
$613$	−29.8068	−1.20388	−0.601942	−	0.798540i	$-0.705606\pi$
$613$	−29.8068	−1.20388	−0.601942	+	0.798540i	$0.705606\pi$
$614$	7.87544	0.317827
$615$	40.0356	1.61439
$616$	7.70714	0.310530
$617$	−31.0774	−1.25113	−0.625564	−	0.780173i	$-0.715131\pi$
$617$	−31.0774	−1.25113	−0.625564	+	0.780173i	$0.715131\pi$
$618$	20.6416	0.830329
$619$	20.5262	0.825017	0.412508	−	0.910954i	$-0.364653\pi$
$619$	20.5262	0.825017	0.412508	+	0.910954i	$0.364653\pi$
$620$	−11.0701	−0.444587
$621$	3.54738	0.142351
$622$	33.4873	1.34272
$623$	10.7515	0.430748
$624$	13.1509	0.526456
$625$	−3.87556	−0.155023
$626$	21.6301	0.864512
$627$	28.8775	1.15326
$628$	15.4309	0.615762
$629$	−27.5524	−1.09859
$630$	−6.34350	−0.252731
$631$	16.5800	0.660040	0.330020	−	0.943974i	$-0.392944\pi$
$631$	16.5800	0.660040	0.330020	+	0.943974i	$0.392944\pi$
$632$	−6.49448	−0.258337
$633$	−14.1449	−0.562211
$634$	−9.39995	−0.373320
$635$	13.0875	0.519360
$636$	8.10352	0.321326
$637$	2.64380	0.104751
$638$	−90.0985	−3.56703
$639$	15.3563	0.607486
$640$	−38.8488	−1.53563
$641$	−36.5145	−1.44224	−0.721118	−	0.692812i	$-0.756372\pi$
$641$	−36.5145	−1.44224	−0.721118	+	0.692812i	$0.756372\pi$
$642$	8.29579	0.327409
$643$	25.1649	0.992408	0.496204	−	0.868206i	$-0.334727\pi$
$643$	25.1649	0.992408	0.496204	+	0.868206i	$0.334727\pi$
$644$	−4.11683	−0.162226
$645$	12.0102	0.472902
$646$	50.1978	1.97501
$647$	−20.5297	−0.807107	−0.403553	−	0.914956i	$-0.632225\pi$
$647$	−20.5297	−0.807107	−0.403553	+	0.914956i	$0.632225\pi$
$648$	1.49240	0.0586270
$649$	14.6145	0.573670
$650$	−36.3415	−1.42543
$651$	2.67330	0.104775
$652$	1.19138	0.0466582
$653$	31.8731	1.24729	0.623646	−	0.781707i	$-0.285651\pi$
$653$	31.8731	1.24729	0.623646	+	0.781707i	$0.285651\pi$
$654$	21.5515	0.842730
$655$	−61.3247	−2.39615
$656$	55.8114	2.17907
$657$	−12.2590	−0.478270
$658$	−17.4303	−0.679506
$659$	22.5572	0.878704	0.439352	−	0.898315i	$-0.355208\pi$
$659$	22.5572	0.878704	0.439352	+	0.898315i	$0.355208\pi$
$660$	−21.3852	−0.832418
$661$	−33.1690	−1.29012	−0.645062	−	0.764131i	$-0.723168\pi$
$661$	−33.1690	−1.29012	−0.645062	+	0.764131i	$0.723168\pi$
$662$	−51.0104	−1.98257
$663$	−13.3500	−0.518471
$664$	15.4648	0.600151
$665$	−19.9527	−0.773732
$666$	9.70034	0.375880
$667$	−34.8126	−1.34795
$668$	−0.637184	−0.0246534
$669$	22.0031	0.850689
$670$	32.7444	1.26503
$671$	−16.4132	−0.633623
$672$	−5.85833	−0.225990
$673$	32.8484	1.26621	0.633107	−	0.774064i	$-0.281779\pi$
$673$	32.8484	1.26621	0.633107	+	0.774064i	$0.281779\pi$
$674$	−54.0048	−2.08019
$675$	−7.73206	−0.297607
$676$	−6.97517	−0.268276
$677$	−28.2666	−1.08637	−0.543186	−	0.839612i	$-0.682782\pi$
$677$	−28.2666	−1.08637	−0.543186	+	0.839612i	$0.682782\pi$
$678$	2.27819	0.0874933
$679$	2.13548	0.0819520
$680$	26.8898	1.03118
$681$	5.19944	0.199243
$682$	24.5434	0.939817
$683$	36.2892	1.38857	0.694283	−	0.719702i	$-0.255722\pi$
$683$	36.2892	1.38857	0.694283	+	0.719702i	$0.255722\pi$
$684$	−6.48945	−0.248130
$685$	59.7517	2.28300
$686$	−1.77779	−0.0678763
$687$	−4.65236	−0.177499
$688$	16.7428	0.638313
$689$	−18.4606	−0.703293
$690$	−22.5028	−0.856667
$691$	−25.4549	−0.968348	−0.484174	−	0.874972i	$-0.660880\pi$
$691$	−25.4549	−0.968348	−0.484174	+	0.874972i	$0.660880\pi$
$692$	6.38920	0.242881
$693$	5.16426	0.196174
$694$	35.1607	1.33468
$695$	−45.1021	−1.71082
$696$	−14.6459	−0.555150
$697$	−56.6565	−2.14602
$698$	−12.0381	−0.455649
$699$	1.65730	0.0626849
$700$	8.97328	0.339158
$701$	6.77285	0.255807	0.127904	−	0.991787i	$-0.459175\pi$
$701$	6.77285	0.255807	0.127904	+	0.991787i	$0.459175\pi$
$702$	4.70011	0.177394
$703$	30.5112	1.15075
$704$	−2.40860	−0.0907776
$705$	−34.9845	−1.31759
$706$	−15.1334	−0.569555
$707$	12.6656	0.476339
$708$	−3.28422	−0.123429
$709$	0.0602769	0.00226375	0.00113187	−	0.999999i	$-0.499640\pi$
$709$	0.0602769	0.00226375	0.00113187	+	0.999999i	$0.499640\pi$
$710$	−97.4128	−3.65584
$711$	−4.35170	−0.163202
$712$	16.0455	0.601330
$713$	9.48320	0.355148
$714$	8.97704	0.335957
$715$	48.7176	1.82193
$716$	19.0661	0.712535
$717$	19.8635	0.741815
$718$	57.3480	2.14021
$719$	−24.0018	−0.895117	−0.447558	−	0.894255i	$-0.647706\pi$
$719$	−24.0018	−0.895117	−0.447558	+	0.894255i	$0.647706\pi$
$720$	−17.7491	−0.661468
$721$	11.6109	0.432411
$722$	−21.8104	−0.811697
$723$	−1.30808	−0.0486479
$724$	9.31168	0.346066
$725$	75.8796	2.81810
$726$	27.8572	1.03388
$727$	49.9055	1.85089	0.925446	−	0.378879i	$-0.123690\pi$
$727$	49.9055	1.85089	0.925446	+	0.378879i	$0.123690\pi$
$728$	3.94560	0.146234
$729$	1.00000	0.0370370
$730$	77.7652	2.87822
$731$	−16.9963	−0.628632
$732$	3.68842	0.136328
$733$	25.7436	0.950861	0.475430	−	0.879753i	$-0.342292\pi$
$733$	25.7436	0.950861	0.475430	+	0.879753i	$0.342292\pi$
$734$	−1.67628	−0.0618725
$735$	−3.56820	−0.131615
$736$	−20.7817	−0.766023
$737$	−26.6573	−0.981934
$738$	19.9470	0.734258
$739$	33.6369	1.23735	0.618676	−	0.785646i	$-0.287669\pi$
$739$	33.6369	1.23735	0.618676	+	0.785646i	$0.287669\pi$
$740$	−22.5950	−0.830609
$741$	14.7836	0.543089
$742$	12.4136	0.455717
$743$	−13.6689	−0.501464	−0.250732	−	0.968057i	$-0.580671\pi$
$743$	−13.6689	−0.501464	−0.250732	+	0.968057i	$0.580671\pi$
$744$	3.98963	0.146267
$745$	29.0052	1.06267
$746$	9.35919	0.342664
$747$	10.3624	0.379139
$748$	30.2634	1.10654
$749$	4.66636	0.170505
$750$	17.3308	0.632832
$751$	−4.88749	−0.178347	−0.0891735	−	0.996016i	$-0.528423\pi$
$751$	−4.88749	−0.178347	−0.0891735	+	0.996016i	$0.528423\pi$
$752$	−48.7699	−1.77846
$753$	−2.76424	−0.100735
$754$	−46.1252	−1.67978
$755$	−15.1084	−0.549852
$756$	−1.16053	−0.0422081
$757$	33.4597	1.21611	0.608057	−	0.793893i	$-0.291949\pi$
$757$	33.4597	1.21611	0.608057	+	0.793893i	$0.291949\pi$
$758$	43.7594	1.58941
$759$	18.3196	0.664958
$760$	−29.7774	−1.08014
$761$	−11.2136	−0.406492	−0.203246	−	0.979128i	$-0.565149\pi$
$761$	−11.2136	−0.406492	−0.203246	+	0.979128i	$0.565149\pi$
$762$	6.52058	0.236216
$763$	12.1226	0.438869
$764$	−29.9039	−1.08189
$765$	18.0178	0.651436
$766$	1.77779	0.0642341
$767$	7.48177	0.270151
$768$	−20.2884	−0.732096
$769$	34.2687	1.23576	0.617880	−	0.786272i	$-0.287992\pi$
$769$	34.2687	1.23576	0.617880	+	0.786272i	$0.287992\pi$
$770$	−32.7595	−1.18057
$771$	11.5308	0.415271
$772$	25.3767	0.913327
$773$	26.5659	0.955510	0.477755	−	0.878493i	$-0.341451\pi$
$773$	26.5659	0.955510	0.477755	+	0.878493i	$0.341451\pi$
$774$	5.98386	0.215086
$775$	−20.6701	−0.742492
$776$	3.18698	0.114406
$777$	5.45641	0.195748
$778$	−40.8417	−1.46424
$779$	62.7406	2.24791
$780$	−10.9480	−0.392000
$781$	79.3039	2.83772
$782$	31.8449	1.13877
$783$	−9.81363	−0.350711
$784$	−4.97423	−0.177651
$785$	47.4445	1.69337
$786$	−30.5538	−1.08982
$787$	−3.72281	−0.132704	−0.0663519	−	0.997796i	$-0.521136\pi$
$787$	−3.72281	−0.132704	−0.0663519	+	0.997796i	$0.521136\pi$
$788$	12.8210	0.456730
$789$	−18.6024	−0.662265
$790$	27.6050	0.982143
$791$	1.28147	0.0455639
$792$	7.70714	0.273861
$793$	−8.40258	−0.298384
$794$	26.8297	0.952152
$795$	24.9153	0.883656
$796$	−2.82327	−0.100068
$797$	29.1112	1.03117	0.515587	−	0.856838i	$-0.327574\pi$
$797$	29.1112	1.03117	0.515587	+	0.856838i	$0.327574\pi$
$798$	−9.94104	−0.351909
$799$	49.5084	1.75148
$800$	45.2969	1.60149
$801$	10.7515	0.379884
$802$	−6.64665	−0.234702
$803$	−63.3088	−2.23412
$804$	5.99052	0.211269
$805$	−12.6577	−0.446127
$806$	12.5648	0.442576
$807$	−4.15629	−0.146308
$808$	18.9021	0.664975
$809$	42.0568	1.47864	0.739319	−	0.673355i	$-0.235148\pi$
$809$	42.0568	1.47864	0.739319	+	0.673355i	$0.235148\pi$
$810$	−6.34350	−0.222888
$811$	−38.5695	−1.35436	−0.677180	−	0.735817i	$-0.736798\pi$
$811$	−38.5695	−1.35436	−0.677180	+	0.735817i	$0.736798\pi$
$812$	11.3890	0.399676
$813$	−23.7689	−0.833613
$814$	50.0951	1.75583
$815$	3.66307	0.128312
$816$	25.1177	0.879294
$817$	18.8215	0.658480
$818$	1.94579	0.0680328
$819$	2.64380	0.0923818
$820$	−46.4625	−1.62254
$821$	−22.3203	−0.778983	−0.389491	−	0.921030i	$-0.627349\pi$
$821$	−22.3203	−0.778983	−0.389491	+	0.921030i	$0.627349\pi$
$822$	29.7702	1.03835
$823$	1.82260	0.0635319	0.0317660	−	0.999495i	$-0.489887\pi$
$823$	1.82260	0.0635319	0.0317660	+	0.999495i	$0.489887\pi$
$824$	17.3280	0.603651
$825$	−39.9303	−1.39020
$826$	−5.03102	−0.175052
$827$	40.9423	1.42370	0.711852	−	0.702329i	$-0.247857\pi$
$827$	40.9423	1.42370	0.711852	+	0.702329i	$0.247857\pi$
$828$	−4.11683	−0.143070
$829$	−17.8541	−0.620098	−0.310049	−	0.950721i	$-0.600345\pi$
$829$	−17.8541	−0.620098	−0.310049	+	0.950721i	$0.600345\pi$
$830$	−65.7337	−2.28165
$831$	17.1397	0.594569
$832$	−1.23306	−0.0427488
$833$	5.04956	0.174957
$834$	−22.4713	−0.778116
$835$	−1.95911	−0.0677977
$836$	−33.5132	−1.15908
$837$	2.67330	0.0924027
$838$	30.3894	1.04978
$839$	9.12909	0.315171	0.157586	−	0.987505i	$-0.449629\pi$
$839$	9.12909	0.315171	0.157586	+	0.987505i	$0.449629\pi$
$840$	−5.32518	−0.183736
$841$	67.3074	2.32094
$842$	43.3112	1.49260
$843$	−7.18469	−0.247454
$844$	16.4156	0.565049
$845$	−21.4461	−0.737768
$846$	−17.4303	−0.599268
$847$	15.6696	0.538413
$848$	34.7331	1.19274
$849$	1.70929	0.0586628
$850$	−69.4110	−2.38078
$851$	19.3559	0.663513
$852$	−17.8214	−0.610553
$853$	−26.0818	−0.893022	−0.446511	−	0.894778i	$-0.647334\pi$
$853$	−26.0818	−0.893022	−0.446511	+	0.894778i	$0.647334\pi$
$854$	5.65021	0.193346
$855$	−19.9527	−0.682367
$856$	6.96407	0.238027
$857$	45.0053	1.53735	0.768676	−	0.639639i	$-0.220916\pi$
$857$	45.0053	1.53735	0.768676	+	0.639639i	$0.220916\pi$
$858$	24.2726	0.828652
$859$	9.13913	0.311823	0.155912	−	0.987771i	$-0.450169\pi$
$859$	9.13913	0.311823	0.155912	+	0.987771i	$0.450169\pi$
$860$	−13.9382	−0.475289
$861$	11.2201	0.382380
$862$	−67.3681	−2.29457
$863$	48.3617	1.64625	0.823126	−	0.567859i	$-0.192228\pi$
$863$	48.3617	1.64625	0.823126	+	0.567859i	$0.192228\pi$
$864$	−5.85833	−0.199304
$865$	19.6444	0.667931
$866$	−58.3331	−1.98224
$867$	−8.49801	−0.288608
$868$	−3.10244	−0.105304
$869$	−22.4733	−0.762355
$870$	62.2528	2.11057
$871$	−13.6470	−0.462410
$872$	18.0918	0.612667
$873$	2.13548	0.0722749
$874$	−35.2646	−1.19284
$875$	9.74853	0.329561
$876$	14.2270	0.480685
$877$	47.4991	1.60393	0.801965	−	0.597371i	$-0.203788\pi$
$877$	47.4991	1.60393	0.801965	+	0.597371i	$0.203788\pi$
$878$	−18.7296	−0.632095
$879$	−2.03527	−0.0686480
$880$	−91.6607	−3.08988
$881$	−51.9485	−1.75019	−0.875095	−	0.483950i	$-0.839202\pi$
$881$	−51.9485	−1.75019	−0.875095	+	0.483950i	$0.839202\pi$
$882$	−1.77779	−0.0598612
$883$	−8.06942	−0.271558	−0.135779	−	0.990739i	$-0.543354\pi$
$883$	−8.06942	−0.271558	−0.135779	+	0.990739i	$0.543354\pi$
$884$	15.4931	0.521088
$885$	−10.0978	−0.339433
$886$	−38.9337	−1.30800
$887$	−39.1341	−1.31399	−0.656997	−	0.753893i	$-0.728173\pi$
$887$	−39.1341	−1.31399	−0.656997	+	0.753893i	$0.728173\pi$
$888$	8.14315	0.273266
$889$	3.66781	0.123014
$890$	−68.2020	−2.28614
$891$	5.16426	0.173009
$892$	−25.5352	−0.854983
$893$	−54.8249	−1.83465
$894$	14.4513	0.483323
$895$	58.6213	1.95949
$896$	−10.8875	−0.363726
$897$	9.37854	0.313140
$898$	−35.4425	−1.18273
$899$	−26.2348	−0.874979
$900$	8.97328	0.299109
$901$	−35.2591	−1.17465
$902$	103.011	3.42990
$903$	3.36590	0.112010
$904$	1.91247	0.0636079
$905$	28.6300	0.951693
$906$	−7.52748	−0.250084
$907$	46.8084	1.55425	0.777123	−	0.629348i	$-0.216678\pi$
$907$	46.8084	1.55425	0.777123	+	0.629348i	$0.216678\pi$
$908$	−6.03410	−0.200249
$909$	12.6656	0.420091
$910$	−16.7709	−0.555951
$911$	−35.1859	−1.16576	−0.582881	−	0.812557i	$-0.698075\pi$
$911$	−35.1859	−1.16576	−0.582881	+	0.812557i	$0.698075\pi$
$912$	−27.8149	−0.921044
$913$	53.5139	1.77105
$914$	17.0905	0.565304
$915$	11.3405	0.374907
$916$	5.39920	0.178395
$917$	−17.1864	−0.567546
$918$	8.97704	0.296286
$919$	36.1632	1.19291	0.596457	−	0.802645i	$-0.296575\pi$
$919$	36.1632	1.19291	0.596457	+	0.802645i	$0.296575\pi$
$920$	−18.8904	−0.622799
$921$	4.42991	0.145971
$922$	25.9313	0.854001
$923$	40.5990	1.33633
$924$	−5.99327	−0.197164
$925$	−42.1893	−1.38717
$926$	75.2742	2.47366
$927$	11.6109	0.381351
$928$	57.4914	1.88725
$929$	0.489260	0.0160521	0.00802606	−	0.999968i	$-0.497445\pi$
$929$	0.489260	0.0160521	0.00802606	+	0.999968i	$0.497445\pi$
$930$	−16.9581	−0.556077
$931$	−5.59180	−0.183264
$932$	−1.92335	−0.0630013
$933$	18.8365	0.616679
$934$	58.0080	1.89808
$935$	93.0487	3.04302
$936$	3.94560	0.128966
$937$	1.33237	0.0435267	0.0217633	−	0.999763i	$-0.493072\pi$
$937$	1.33237	0.0435267	0.0217633	+	0.999763i	$0.493072\pi$
$938$	9.17673	0.299631
$939$	12.1668	0.397050
$940$	40.6005	1.32424
$941$	29.0206	0.946046	0.473023	−	0.881050i	$-0.343163\pi$
$941$	29.0206	0.946046	0.473023	+	0.881050i	$0.343163\pi$
$942$	23.6383	0.770177
$943$	39.8019	1.29613
$944$	−14.0767	−0.458159
$945$	−3.56820	−0.116074
$946$	30.9022	1.00472
$947$	12.0354	0.391098	0.195549	−	0.980694i	$-0.437351\pi$
$947$	12.0354	0.391098	0.195549	+	0.980694i	$0.437351\pi$
$948$	5.05028	0.164025
$949$	−32.4104	−1.05209
$950$	76.8647	2.49382
$951$	−5.28744	−0.171457
$952$	7.53596	0.244242
$953$	36.9603	1.19726	0.598631	−	0.801025i	$-0.295712\pi$
$953$	36.9603	1.19726	0.598631	+	0.801025i	$0.295712\pi$
$954$	12.4136	0.401905
$955$	−91.9435	−2.97522
$956$	−23.0522	−0.745560
$957$	−50.6801	−1.63826
$958$	−45.9924	−1.48595
$959$	16.7456	0.540744
$960$	1.66420	0.0537119
$961$	−23.8535	−0.769467
$962$	25.6457	0.826851
$963$	4.66636	0.150371
$964$	1.51806	0.0488935
$965$	78.0239	2.51168
$966$	−6.30648	−0.202908
$967$	−34.0293	−1.09431	−0.547154	−	0.837032i	$-0.684289\pi$
$967$	−34.0293	−1.09431	−0.547154	+	0.837032i	$0.684289\pi$
$968$	23.3853	0.751631
$969$	28.2361	0.907075
$970$	−13.5464	−0.434949
$971$	−7.01562	−0.225142	−0.112571	−	0.993644i	$-0.535909\pi$
$971$	−7.01562	−0.225142	−0.112571	+	0.993644i	$0.535909\pi$
$972$	−1.16053	−0.0372240
$973$	−12.6400	−0.405220
$974$	35.2599	1.12980
$975$	−20.4420	−0.654668
$976$	15.8092	0.506041
$977$	26.3046	0.841557	0.420779	−	0.907163i	$-0.361757\pi$
$977$	26.3046	0.841557	0.420779	+	0.907163i	$0.361757\pi$
$978$	1.82505	0.0583587
$979$	55.5234	1.77453
$980$	4.14100	0.132279
$981$	12.1226	0.387046
$982$	23.5603	0.751841
$983$	21.3138	0.679805	0.339902	−	0.940461i	$-0.389606\pi$
$983$	21.3138	0.679805	0.339902	+	0.940461i	$0.389606\pi$
$984$	16.7449	0.533807
$985$	39.4199	1.25602
$986$	−88.0973	−2.80559
$987$	−9.80452	−0.312081
$988$	−17.1568	−0.545830
$989$	11.9401	0.379674
$990$	−32.7595	−1.04117
$991$	4.29404	0.136405	0.0682023	−	0.997672i	$-0.478274\pi$
$991$	4.29404	0.136405	0.0682023	+	0.997672i	$0.478274\pi$
$992$	−15.6611	−0.497239
$993$	−28.6932	−0.910550
$994$	−27.3002	−0.865911
$995$	−8.68053	−0.275191
$996$	−12.0258	−0.381053
$997$	−9.54370	−0.302252	−0.151126	−	0.988515i	$-0.548290\pi$
$997$	−9.54370	−0.302252	−0.151126	+	0.988515i	$0.548290\pi$
$998$	66.1753	2.09474
$999$	5.45641	0.172633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.12	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.12	✓	52	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)

\(f(q)\)	\(=\)	\(q-1.77779 q^{2} -1.00000 q^{3} +1.16053 q^{4} +3.56820 q^{5} +1.77779 q^{6} +1.00000 q^{7} +1.49240 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.77779 q^{2} -1.00000 q^{3} +1.16053 q^{4} +3.56820 q^{5} +1.77779 q^{6} +1.00000 q^{7} +1.49240 q^{8} +1.00000 q^{9} -6.34350 q^{10} +5.16426 q^{11} -1.16053 q^{12} +2.64380 q^{13} -1.77779 q^{14} -3.56820 q^{15} -4.97423 q^{16} +5.04956 q^{17} -1.77779 q^{18} -5.59180 q^{19} +4.14100 q^{20} -1.00000 q^{21} -9.18096 q^{22} -3.54738 q^{23} -1.49240 q^{24} +7.73206 q^{25} -4.70011 q^{26} -1.00000 q^{27} +1.16053 q^{28} +9.81363 q^{29} +6.34350 q^{30} -2.67330 q^{31} +5.85833 q^{32} -5.16426 q^{33} -8.97704 q^{34} +3.56820 q^{35} +1.16053 q^{36} -5.45641 q^{37} +9.94104 q^{38} -2.64380 q^{39} +5.32518 q^{40} -11.2201 q^{41} +1.77779 q^{42} -3.36590 q^{43} +5.99327 q^{44} +3.56820 q^{45} +6.30648 q^{46} +9.80452 q^{47} +4.97423 q^{48} +1.00000 q^{49} -13.7460 q^{50} -5.04956 q^{51} +3.06820 q^{52} -6.98261 q^{53} +1.77779 q^{54} +18.4271 q^{55} +1.49240 q^{56} +5.59180 q^{57} -17.4466 q^{58} +2.82993 q^{59} -4.14100 q^{60} -3.17822 q^{61} +4.75256 q^{62} +1.00000 q^{63} -0.466399 q^{64} +9.43360 q^{65} +9.18096 q^{66} -5.16188 q^{67} +5.86016 q^{68} +3.54738 q^{69} -6.34350 q^{70} +15.3563 q^{71} +1.49240 q^{72} -12.2590 q^{73} +9.70034 q^{74} -7.73206 q^{75} -6.48945 q^{76} +5.16426 q^{77} +4.70011 q^{78} -4.35170 q^{79} -17.7491 q^{80} +1.00000 q^{81} +19.9470 q^{82} +10.3624 q^{83} -1.16053 q^{84} +18.0178 q^{85} +5.98386 q^{86} -9.81363 q^{87} +7.70714 q^{88} +10.7515 q^{89} -6.34350 q^{90} +2.64380 q^{91} -4.11683 q^{92} +2.67330 q^{93} -17.4303 q^{94} -19.9527 q^{95} -5.85833 q^{96} +2.13548 q^{97} -1.77779 q^{98} +5.16426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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