LMFDB - Embedded newform 8043.2.a.q.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.54621 q^{2} +1.00000 q^{3} +4.48317 q^{4} +3.86614 q^{5} -2.54621 q^{6} -1.00000 q^{7} -6.32268 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.54621 q^{2} +1.00000 q^{3} +4.48317 q^{4} +3.86614 q^{5} -2.54621 q^{6} -1.00000 q^{7} -6.32268 q^{8} +1.00000 q^{9} -9.84400 q^{10} +0.530571 q^{11} +4.48317 q^{12} -3.89037 q^{13} +2.54621 q^{14} +3.86614 q^{15} +7.13250 q^{16} -0.207504 q^{17} -2.54621 q^{18} -1.98286 q^{19} +17.3326 q^{20} -1.00000 q^{21} -1.35094 q^{22} -6.59413 q^{23} -6.32268 q^{24} +9.94704 q^{25} +9.90568 q^{26} +1.00000 q^{27} -4.48317 q^{28} +7.18099 q^{29} -9.84400 q^{30} -7.37153 q^{31} -5.51547 q^{32} +0.530571 q^{33} +0.528348 q^{34} -3.86614 q^{35} +4.48317 q^{36} -9.83192 q^{37} +5.04877 q^{38} -3.89037 q^{39} -24.4444 q^{40} -6.61082 q^{41} +2.54621 q^{42} +7.11092 q^{43} +2.37864 q^{44} +3.86614 q^{45} +16.7900 q^{46} -4.71323 q^{47} +7.13250 q^{48} +1.00000 q^{49} -25.3272 q^{50} -0.207504 q^{51} -17.4412 q^{52} -9.30059 q^{53} -2.54621 q^{54} +2.05126 q^{55} +6.32268 q^{56} -1.98286 q^{57} -18.2843 q^{58} +9.81150 q^{59} +17.3326 q^{60} +4.17280 q^{61} +18.7694 q^{62} -1.00000 q^{63} -0.221460 q^{64} -15.0407 q^{65} -1.35094 q^{66} -12.2594 q^{67} -0.930276 q^{68} -6.59413 q^{69} +9.84400 q^{70} -4.15436 q^{71} -6.32268 q^{72} +8.57276 q^{73} +25.0341 q^{74} +9.94704 q^{75} -8.88949 q^{76} -0.530571 q^{77} +9.90568 q^{78} +13.3823 q^{79} +27.5752 q^{80} +1.00000 q^{81} +16.8325 q^{82} +13.1883 q^{83} -4.48317 q^{84} -0.802239 q^{85} -18.1059 q^{86} +7.18099 q^{87} -3.35463 q^{88} +4.45224 q^{89} -9.84400 q^{90} +3.89037 q^{91} -29.5626 q^{92} -7.37153 q^{93} +12.0009 q^{94} -7.66600 q^{95} -5.51547 q^{96} -1.62148 q^{97} -2.54621 q^{98} +0.530571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.54621	−1.80044	−0.900220	−	0.435435i	$-0.856595\pi$
$2$	−2.54621	−1.80044	−0.900220	+	0.435435i	$0.856595\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.48317	2.24159
$5$	3.86614	1.72899	0.864495	−	0.502641i	$-0.167638\pi$
$5$	3.86614	1.72899	0.864495	+	0.502641i	$0.167638\pi$
$6$	−2.54621	−1.03948
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.32268	−2.23540
$9$	1.00000	0.333333
$10$	−9.84400	−3.11295
$11$	0.530571	0.159973	0.0799866	−	0.996796i	$-0.474512\pi$
$11$	0.530571	0.159973	0.0799866	+	0.996796i	$0.474512\pi$
$12$	4.48317	1.29418
$13$	−3.89037	−1.07899	−0.539497	−	0.841988i	$-0.681385\pi$
$13$	−3.89037	−1.07899	−0.539497	+	0.841988i	$0.681385\pi$
$14$	2.54621	0.680503
$15$	3.86614	0.998233
$16$	7.13250	1.78312
$17$	−0.207504	−0.0503271	−0.0251635	−	0.999683i	$-0.508011\pi$
$17$	−0.207504	−0.0503271	−0.0251635	+	0.999683i	$0.508011\pi$
$18$	−2.54621	−0.600147
$19$	−1.98286	−0.454899	−0.227449	−	0.973790i	$-0.573039\pi$
$19$	−1.98286	−0.454899	−0.227449	+	0.973790i	$0.573039\pi$
$20$	17.3326	3.87568
$21$	−1.00000	−0.218218
$22$	−1.35094	−0.288022
$23$	−6.59413	−1.37497	−0.687485	−	0.726198i	$-0.741285\pi$
$23$	−6.59413	−1.37497	−0.687485	+	0.726198i	$0.741285\pi$
$24$	−6.32268	−1.29061
$25$	9.94704	1.98941
$26$	9.90568	1.94266
$27$	1.00000	0.192450
$28$	−4.48317	−0.847240
$29$	7.18099	1.33348	0.666738	−	0.745292i	$-0.267690\pi$
$29$	7.18099	1.33348	0.666738	+	0.745292i	$0.267690\pi$
$30$	−9.84400	−1.79726
$31$	−7.37153	−1.32397	−0.661983	−	0.749519i	$-0.730285\pi$
$31$	−7.37153	−1.32397	−0.661983	+	0.749519i	$0.730285\pi$
$32$	−5.51547	−0.975007
$33$	0.530571	0.0923605
$34$	0.528348	0.0906109
$35$	−3.86614	−0.653497
$36$	4.48317	0.747196
$37$	−9.83192	−1.61636	−0.808179	−	0.588937i	$-0.799546\pi$
$37$	−9.83192	−1.61636	−0.808179	+	0.588937i	$0.799546\pi$
$38$	5.04877	0.819018
$39$	−3.89037	−0.622957
$40$	−24.4444	−3.86499
$41$	−6.61082	−1.03244	−0.516218	−	0.856457i	$-0.672661\pi$
$41$	−6.61082	−1.03244	−0.516218	+	0.856457i	$0.672661\pi$
$42$	2.54621	0.392888
$43$	7.11092	1.08440	0.542202	−	0.840248i	$-0.317591\pi$
$43$	7.11092	1.08440	0.542202	+	0.840248i	$0.317591\pi$
$44$	2.37864	0.358594
$45$	3.86614	0.576330
$46$	16.7900	2.47555
$47$	−4.71323	−0.687495	−0.343748	−	0.939062i	$-0.611696\pi$
$47$	−4.71323	−0.687495	−0.343748	+	0.939062i	$0.611696\pi$
$48$	7.13250	1.02949
$49$	1.00000	0.142857
$50$	−25.3272	−3.58181
$51$	−0.207504	−0.0290563
$52$	−17.4412	−2.41866
$53$	−9.30059	−1.27753	−0.638767	−	0.769400i	$-0.720555\pi$
$53$	−9.30059	−1.27753	−0.638767	+	0.769400i	$0.720555\pi$
$54$	−2.54621	−0.346495
$55$	2.05126	0.276592
$56$	6.32268	0.844903
$57$	−1.98286	−0.262636
$58$	−18.2843	−2.40084
$59$	9.81150	1.27735	0.638674	−	0.769477i	$-0.279483\pi$
$59$	9.81150	1.27735	0.638674	+	0.769477i	$0.279483\pi$
$60$	17.3326	2.23763
$61$	4.17280	0.534272	0.267136	−	0.963659i	$-0.413923\pi$
$61$	4.17280	0.534272	0.267136	+	0.963659i	$0.413923\pi$
$62$	18.7694	2.38372
$63$	−1.00000	−0.125988
$64$	−0.221460	−0.0276825
$65$	−15.0407	−1.86557
$66$	−1.35094	−0.166290
$67$	−12.2594	−1.49773	−0.748864	−	0.662724i	$-0.769400\pi$
$67$	−12.2594	−1.49773	−0.748864	+	0.662724i	$0.769400\pi$
$68$	−0.930276	−0.112813
$69$	−6.59413	−0.793840
$70$	9.84400	1.17658
$71$	−4.15436	−0.493032	−0.246516	−	0.969139i	$-0.579286\pi$
$71$	−4.15436	−0.493032	−0.246516	+	0.969139i	$0.579286\pi$
$72$	−6.32268	−0.745135
$73$	8.57276	1.00337	0.501683	−	0.865052i	$-0.332715\pi$
$73$	8.57276	1.00337	0.501683	+	0.865052i	$0.332715\pi$
$74$	25.0341	2.91016
$75$	9.94704	1.14859
$76$	−8.88949	−1.01969
$77$	−0.530571	−0.0604642
$78$	9.90568	1.12160
$79$	13.3823	1.50563	0.752813	−	0.658234i	$-0.228696\pi$
$79$	13.3823	1.50563	0.752813	+	0.658234i	$0.228696\pi$
$80$	27.5752	3.08301
$81$	1.00000	0.111111
$82$	16.8325	1.85884
$83$	13.1883	1.44761	0.723805	−	0.690005i	$-0.242392\pi$
$83$	13.1883	1.44761	0.723805	+	0.690005i	$0.242392\pi$
$84$	−4.48317	−0.489154
$85$	−0.802239	−0.0870150
$86$	−18.1059	−1.95241
$87$	7.18099	0.769883
$88$	−3.35463	−0.357605
$89$	4.45224	0.471936	0.235968	−	0.971761i	$-0.424174\pi$
$89$	4.45224	0.471936	0.235968	+	0.971761i	$0.424174\pi$
$90$	−9.84400	−1.03765
$91$	3.89037	0.407821
$92$	−29.5626	−3.08212
$93$	−7.37153	−0.764392
$94$	12.0009	1.23779
$95$	−7.66600	−0.786515
$96$	−5.51547	−0.562921
$97$	−1.62148	−0.164636	−0.0823180	−	0.996606i	$-0.526232\pi$
$97$	−1.62148	−0.164636	−0.0823180	+	0.996606i	$0.526232\pi$
$98$	−2.54621	−0.257206
$99$	0.530571	0.0533244
$100$	44.5943	4.45943
$101$	−14.9060	−1.48320	−0.741601	−	0.670841i	$-0.765933\pi$
$101$	−14.9060	−1.48320	−0.741601	+	0.670841i	$0.765933\pi$
$102$	0.528348	0.0523142
$103$	16.6491	1.64049	0.820244	−	0.572013i	$-0.193837\pi$
$103$	16.6491	1.64049	0.820244	+	0.572013i	$0.193837\pi$
$104$	24.5975	2.41199
$105$	−3.86614	−0.377297
$106$	23.6812	2.30012
$107$	−11.5538	−1.11695	−0.558474	−	0.829522i	$-0.688613\pi$
$107$	−11.5538	−1.11695	−0.558474	+	0.829522i	$0.688613\pi$
$108$	4.48317	0.431394
$109$	−7.48819	−0.717239	−0.358619	−	0.933484i	$-0.616752\pi$
$109$	−7.48819	−0.717239	−0.358619	+	0.933484i	$0.616752\pi$
$110$	−5.22294	−0.497988
$111$	−9.83192	−0.933204
$112$	−7.13250	−0.673958
$113$	−17.2842	−1.62596	−0.812981	−	0.582291i	$-0.802156\pi$
$113$	−17.2842	−1.62596	−0.812981	+	0.582291i	$0.802156\pi$
$114$	5.04877	0.472860
$115$	−25.4938	−2.37731
$116$	32.1936	2.98910
$117$	−3.89037	−0.359665
$118$	−24.9821	−2.29979
$119$	0.207504	0.0190218
$120$	−24.4444	−2.23145
$121$	−10.7185	−0.974409
$122$	−10.6248	−0.961925
$123$	−6.61082	−0.596078
$124$	−33.0479	−2.96779
$125$	19.1260	1.71068
$126$	2.54621	0.226834
$127$	0.221692	0.0196719	0.00983597	−	0.999952i	$-0.496869\pi$
$127$	0.221692	0.0196719	0.00983597	+	0.999952i	$0.496869\pi$
$128$	11.5948	1.02485
$129$	7.11092	0.626081
$130$	38.2968	3.35885
$131$	17.3228	1.51350	0.756749	−	0.653706i	$-0.226787\pi$
$131$	17.3228	1.51350	0.756749	+	0.653706i	$0.226787\pi$
$132$	2.37864	0.207034
$133$	1.98286	0.171936
$134$	31.2151	2.69657
$135$	3.86614	0.332744
$136$	1.31198	0.112501
$137$	12.0514	1.02962	0.514810	−	0.857304i	$-0.327863\pi$
$137$	12.0514	1.02962	0.514810	+	0.857304i	$0.327863\pi$
$138$	16.7900	1.42926
$139$	−22.2446	−1.88676	−0.943382	−	0.331709i	$-0.892375\pi$
$139$	−22.2446	−1.88676	−0.943382	+	0.331709i	$0.892375\pi$
$140$	−17.3326	−1.46487
$141$	−4.71323	−0.396925
$142$	10.5779	0.887675
$143$	−2.06412	−0.172610
$144$	7.13250	0.594375
$145$	27.7627	2.30557
$146$	−21.8280	−1.80650
$147$	1.00000	0.0824786
$148$	−44.0782	−3.62321
$149$	4.82638	0.395392	0.197696	−	0.980263i	$-0.436654\pi$
$149$	4.82638	0.395392	0.197696	+	0.980263i	$0.436654\pi$
$150$	−25.3272	−2.06796
$151$	17.5069	1.42469	0.712345	−	0.701829i	$-0.247633\pi$
$151$	17.5069	1.42469	0.712345	+	0.701829i	$0.247633\pi$
$152$	12.5370	1.01688
$153$	−0.207504	−0.0167757
$154$	1.35094	0.108862
$155$	−28.4994	−2.28912
$156$	−17.4412	−1.39641
$157$	−8.08838	−0.645523	−0.322761	−	0.946480i	$-0.604611\pi$
$157$	−8.08838	−0.645523	−0.322761	+	0.946480i	$0.604611\pi$
$158$	−34.0741	−2.71079
$159$	−9.30059	−0.737585
$160$	−21.3236	−1.68578
$161$	6.59413	0.519690
$162$	−2.54621	−0.200049
$163$	4.38554	0.343502	0.171751	−	0.985140i	$-0.445058\pi$
$163$	4.38554	0.343502	0.171751	+	0.985140i	$0.445058\pi$
$164$	−29.6375	−2.31430
$165$	2.05126	0.159690
$166$	−33.5803	−2.60634
$167$	−16.5761	−1.28270	−0.641348	−	0.767250i	$-0.721625\pi$
$167$	−16.5761	−1.28270	−0.641348	+	0.767250i	$0.721625\pi$
$168$	6.32268	0.487805
$169$	2.13495	0.164227
$170$	2.04267	0.156665
$171$	−1.98286	−0.151633
$172$	31.8795	2.43079
$173$	−21.2797	−1.61786	−0.808932	−	0.587902i	$-0.799954\pi$
$173$	−21.2797	−1.61786	−0.808932	+	0.587902i	$0.799954\pi$
$174$	−18.2843	−1.38613
$175$	−9.94704	−0.751926
$176$	3.78430	0.285252
$177$	9.81150	0.737477
$178$	−11.3363	−0.849693
$179$	−21.3760	−1.59772	−0.798859	−	0.601518i	$-0.794563\pi$
$179$	−21.3760	−1.59772	−0.798859	+	0.601518i	$0.794563\pi$
$180$	17.3326	1.29189
$181$	7.95361	0.591187	0.295594	−	0.955314i	$-0.404483\pi$
$181$	7.95361	0.591187	0.295594	+	0.955314i	$0.404483\pi$
$182$	−9.90568	−0.734258
$183$	4.17280	0.308462
$184$	41.6925	3.07361
$185$	−38.0116	−2.79467
$186$	18.7694	1.37624
$187$	−0.110095	−0.00805098
$188$	−21.1302	−1.54108
$189$	−1.00000	−0.0727393
$190$	19.5192	1.41607
$191$	−13.8035	−0.998786	−0.499393	−	0.866376i	$-0.666444\pi$
$191$	−13.8035	−0.998786	−0.499393	+	0.866376i	$0.666444\pi$
$192$	−0.221460	−0.0159825
$193$	9.09777	0.654872	0.327436	−	0.944873i	$-0.393815\pi$
$193$	9.09777	0.654872	0.327436	+	0.944873i	$0.393815\pi$
$194$	4.12862	0.296418
$195$	−15.0407	−1.07709
$196$	4.48317	0.320227
$197$	−18.4983	−1.31795	−0.658975	−	0.752164i	$-0.729010\pi$
$197$	−18.4983	−1.31795	−0.658975	+	0.752164i	$0.729010\pi$
$198$	−1.35094	−0.0960074
$199$	−15.7429	−1.11599	−0.557993	−	0.829846i	$-0.688428\pi$
$199$	−15.7429	−1.11599	−0.557993	+	0.829846i	$0.688428\pi$
$200$	−62.8919	−4.44713
$201$	−12.2594	−0.864714
$202$	37.9538	2.67042
$203$	−7.18099	−0.504006
$204$	−0.930276	−0.0651323
$205$	−25.5584	−1.78507
$206$	−42.3922	−2.95360
$207$	−6.59413	−0.458324
$208$	−27.7480	−1.92398
$209$	−1.05205	−0.0727716
$210$	9.84400	0.679300
$211$	25.5458	1.75864	0.879322	−	0.476228i	$-0.157996\pi$
$211$	25.5458	1.75864	0.879322	+	0.476228i	$0.157996\pi$
$212$	−41.6961	−2.86370
$213$	−4.15436	−0.284652
$214$	29.4184	2.01100
$215$	27.4918	1.87493
$216$	−6.32268	−0.430204
$217$	7.37153	0.500412
$218$	19.0665	1.29135
$219$	8.57276	0.579293
$220$	9.19616	0.620005
$221$	0.807266	0.0543026
$222$	25.0341	1.68018
$223$	−4.74847	−0.317981	−0.158990	−	0.987280i	$-0.550824\pi$
$223$	−4.74847	−0.317981	−0.158990	+	0.987280i	$0.550824\pi$
$224$	5.51547	0.368518
$225$	9.94704	0.663136
$226$	44.0092	2.92745
$227$	−27.1708	−1.80339	−0.901696	−	0.432371i	$-0.857677\pi$
$227$	−27.1708	−1.80339	−0.901696	+	0.432371i	$0.857677\pi$
$228$	−8.88949	−0.588721
$229$	−17.0656	−1.12773	−0.563863	−	0.825869i	$-0.690685\pi$
$229$	−17.0656	−1.12773	−0.563863	+	0.825869i	$0.690685\pi$
$230$	64.9126	4.28021
$231$	−0.530571	−0.0349090
$232$	−45.4031	−2.98086
$233$	−5.79694	−0.379770	−0.189885	−	0.981806i	$-0.560811\pi$
$233$	−5.79694	−0.379770	−0.189885	+	0.981806i	$0.560811\pi$
$234$	9.90568	0.647555
$235$	−18.2220	−1.18867
$236$	43.9867	2.86329
$237$	13.3823	0.869274
$238$	−0.528348	−0.0342477
$239$	17.9995	1.16429	0.582144	−	0.813085i	$-0.302214\pi$
$239$	17.9995	1.16429	0.582144	+	0.813085i	$0.302214\pi$
$240$	27.5752	1.77997
$241$	2.40238	0.154751	0.0773753	−	0.997002i	$-0.475346\pi$
$241$	2.40238	0.154751	0.0773753	+	0.997002i	$0.475346\pi$
$242$	27.2915	1.75436
$243$	1.00000	0.0641500
$244$	18.7074	1.19762
$245$	3.86614	0.246999
$246$	16.8325	1.07320
$247$	7.71404	0.490833
$248$	46.6078	2.95960
$249$	13.1883	0.835778
$250$	−48.6987	−3.07997
$251$	−15.7241	−0.992498	−0.496249	−	0.868180i	$-0.665290\pi$
$251$	−15.7241	−0.992498	−0.496249	+	0.868180i	$0.665290\pi$
$252$	−4.48317	−0.282413
$253$	−3.49865	−0.219958
$254$	−0.564473	−0.0354182
$255$	−0.802239	−0.0502382
$256$	−29.0799	−1.81750
$257$	−12.4562	−0.776998	−0.388499	−	0.921449i	$-0.627006\pi$
$257$	−12.4562	−0.776998	−0.388499	+	0.921449i	$0.627006\pi$
$258$	−18.1059	−1.12722
$259$	9.83192	0.610926
$260$	−67.4301	−4.18184
$261$	7.18099	0.444492
$262$	−44.1074	−2.72496
$263$	−27.5673	−1.69987	−0.849937	−	0.526884i	$-0.823360\pi$
$263$	−27.5673	−1.69987	−0.849937	+	0.526884i	$0.823360\pi$
$264$	−3.35463	−0.206463
$265$	−35.9574	−2.20884
$266$	−5.04877	−0.309560
$267$	4.45224	0.272473
$268$	−54.9612	−3.35729
$269$	−20.8195	−1.26939	−0.634695	−	0.772763i	$-0.718874\pi$
$269$	−20.8195	−1.26939	−0.634695	+	0.772763i	$0.718874\pi$
$270$	−9.84400	−0.599087
$271$	21.4307	1.30183	0.650913	−	0.759153i	$-0.274386\pi$
$271$	21.4307	1.30183	0.650913	+	0.759153i	$0.274386\pi$
$272$	−1.48002	−0.0897395
$273$	3.89037	0.235456
$274$	−30.6853	−1.85377
$275$	5.27761	0.318252
$276$	−29.5626	−1.77946
$277$	−9.12868	−0.548489	−0.274245	−	0.961660i	$-0.588428\pi$
$277$	−9.12868	−0.548489	−0.274245	+	0.961660i	$0.588428\pi$
$278$	56.6394	3.39701
$279$	−7.37153	−0.441322
$280$	24.4444	1.46083
$281$	−10.6097	−0.632920	−0.316460	−	0.948606i	$-0.602494\pi$
$281$	−10.6097	−0.632920	−0.316460	+	0.948606i	$0.602494\pi$
$282$	12.0009	0.714641
$283$	4.35519	0.258889	0.129445	−	0.991587i	$-0.458681\pi$
$283$	4.35519	0.258889	0.129445	+	0.991587i	$0.458681\pi$
$284$	−18.6247	−1.10517
$285$	−7.66600	−0.454095
$286$	5.25567	0.310774
$287$	6.61082	0.390224
$288$	−5.51547	−0.325002
$289$	−16.9569	−0.997467
$290$	−70.6896	−4.15104
$291$	−1.62148	−0.0950527
$292$	38.4332	2.24913
$293$	−13.6203	−0.795705	−0.397853	−	0.917449i	$-0.630244\pi$
$293$	−13.6203	−0.795705	−0.397853	+	0.917449i	$0.630244\pi$
$294$	−2.54621	−0.148498
$295$	37.9326	2.20852
$296$	62.1640	3.61321
$297$	0.530571	0.0307868
$298$	−12.2890	−0.711880
$299$	25.6536	1.48358
$300$	44.5943	2.57465
$301$	−7.11092	−0.409866
$302$	−44.5762	−2.56507
$303$	−14.9060	−0.856327
$304$	−14.1427	−0.811141
$305$	16.1326	0.923751
$306$	0.528348	0.0302036
$307$	30.2545	1.72671	0.863357	−	0.504594i	$-0.168358\pi$
$307$	30.2545	1.72671	0.863357	+	0.504594i	$0.168358\pi$
$308$	−2.37864	−0.135536
$309$	16.6491	0.947136
$310$	72.5653	4.12143
$311$	16.2092	0.919137	0.459568	−	0.888142i	$-0.348004\pi$
$311$	16.2092	0.919137	0.459568	+	0.888142i	$0.348004\pi$
$312$	24.5975	1.39256
$313$	−13.0217	−0.736029	−0.368015	−	0.929820i	$-0.619962\pi$
$313$	−13.0217	−0.736029	−0.368015	+	0.929820i	$0.619962\pi$
$314$	20.5947	1.16223
$315$	−3.86614	−0.217832
$316$	59.9952	3.37499
$317$	−15.8276	−0.888968	−0.444484	−	0.895787i	$-0.646613\pi$
$317$	−15.8276	−0.888968	−0.444484	+	0.895787i	$0.646613\pi$
$318$	23.6812	1.32798
$319$	3.81002	0.213320
$320$	−0.856194	−0.0478627
$321$	−11.5538	−0.644870
$322$	−16.7900	−0.935671
$323$	0.411450	0.0228937
$324$	4.48317	0.249065
$325$	−38.6976	−2.14656
$326$	−11.1665	−0.618455
$327$	−7.48819	−0.414098
$328$	41.7981	2.30791
$329$	4.71323	0.259849
$330$	−5.22294	−0.287513
$331$	3.68194	0.202378	0.101189	−	0.994867i	$-0.467735\pi$
$331$	3.68194	0.202378	0.101189	+	0.994867i	$0.467735\pi$
$332$	59.1257	3.24494
$333$	−9.83192	−0.538786
$334$	42.2062	2.30942
$335$	−47.3967	−2.58956
$336$	−7.13250	−0.389110
$337$	−27.3792	−1.49144	−0.745720	−	0.666260i	$-0.767894\pi$
$337$	−27.3792	−1.49144	−0.745720	+	0.666260i	$0.767894\pi$
$338$	−5.43603	−0.295681
$339$	−17.2842	−0.938749
$340$	−3.59658	−0.195052
$341$	−3.91112	−0.211799
$342$	5.04877	0.273006
$343$	−1.00000	−0.0539949
$344$	−44.9600	−2.42408
$345$	−25.4938	−1.37254
$346$	54.1825	2.91287
$347$	−23.2231	−1.24668	−0.623341	−	0.781950i	$-0.714225\pi$
$347$	−23.2231	−1.24668	−0.623341	+	0.781950i	$0.714225\pi$
$348$	32.1936	1.72576
$349$	−29.4702	−1.57750	−0.788751	−	0.614713i	$-0.789272\pi$
$349$	−29.4702	−1.57750	−0.788751	+	0.614713i	$0.789272\pi$
$350$	25.3272	1.35380
$351$	−3.89037	−0.207652
$352$	−2.92635	−0.155975
$353$	22.4833	1.19666	0.598332	−	0.801248i	$-0.295830\pi$
$353$	22.4833	1.19666	0.598332	+	0.801248i	$0.295830\pi$
$354$	−24.9821	−1.32778
$355$	−16.0613	−0.852448
$356$	19.9602	1.05789
$357$	0.207504	0.0109823
$358$	54.4278	2.87660
$359$	−14.3140	−0.755465	−0.377732	−	0.925915i	$-0.623296\pi$
$359$	−14.3140	−0.755465	−0.377732	+	0.925915i	$0.623296\pi$
$360$	−24.4444	−1.28833
$361$	−15.0683	−0.793067
$362$	−20.2515	−1.06440
$363$	−10.7185	−0.562575
$364$	17.4412	0.914167
$365$	33.1435	1.73481
$366$	−10.6248	−0.555368
$367$	−13.2554	−0.691925	−0.345962	−	0.938248i	$-0.612448\pi$
$367$	−13.2554	−0.691925	−0.345962	+	0.938248i	$0.612448\pi$
$368$	−47.0326	−2.45174
$369$	−6.61082	−0.344146
$370$	96.7854	5.03163
$371$	9.30059	0.482862
$372$	−33.0479	−1.71345
$373$	17.7758	0.920394	0.460197	−	0.887817i	$-0.347779\pi$
$373$	17.7758	0.920394	0.460197	+	0.887817i	$0.347779\pi$
$374$	0.280326	0.0144953
$375$	19.1260	0.987660
$376$	29.8002	1.53683
$377$	−27.9367	−1.43881
$378$	2.54621	0.130963
$379$	11.3211	0.581524	0.290762	−	0.956795i	$-0.406091\pi$
$379$	11.3211	0.581524	0.290762	+	0.956795i	$0.406091\pi$
$380$	−34.3680	−1.76304
$381$	0.221692	0.0113576
$382$	35.1466	1.79825
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	11.5948	0.591696
$385$	−2.05126	−0.104542
$386$	−23.1648	−1.17906
$387$	7.11092	0.361468
$388$	−7.26937	−0.369046
$389$	28.3837	1.43911	0.719554	−	0.694436i	$-0.244346\pi$
$389$	28.3837	1.43911	0.719554	+	0.694436i	$0.244346\pi$
$390$	38.2968	1.93923
$391$	1.36831	0.0691982
$392$	−6.32268	−0.319343
$393$	17.3228	0.873818
$394$	47.1006	2.37289
$395$	51.7378	2.60321
$396$	2.37864	0.119531
$397$	3.38347	0.169811	0.0849057	−	0.996389i	$-0.472941\pi$
$397$	3.38347	0.169811	0.0849057	+	0.996389i	$0.472941\pi$
$398$	40.0847	2.00927
$399$	1.98286	0.0992670
$400$	70.9473	3.54736
$401$	−13.7868	−0.688478	−0.344239	−	0.938882i	$-0.611863\pi$
$401$	−13.7868	−0.688478	−0.344239	+	0.938882i	$0.611863\pi$
$402$	31.2151	1.55687
$403$	28.6780	1.42855
$404$	−66.8262	−3.32473
$405$	3.86614	0.192110
$406$	18.2843	0.907434
$407$	−5.21653	−0.258574
$408$	1.31198	0.0649527
$409$	12.4703	0.616615	0.308308	−	0.951287i	$-0.400237\pi$
$409$	12.4703	0.616615	0.308308	+	0.951287i	$0.400237\pi$
$410$	65.0769	3.21392
$411$	12.0514	0.594451
$412$	74.6410	3.67730
$413$	−9.81150	−0.482792
$414$	16.7900	0.825184
$415$	50.9880	2.50290
$416$	21.4572	1.05203
$417$	−22.2446	−1.08932
$418$	2.67873	0.131021
$419$	33.7875	1.65063	0.825314	−	0.564674i	$-0.190998\pi$
$419$	33.7875	1.65063	0.825314	+	0.564674i	$0.190998\pi$
$420$	−17.3326	−0.845743
$421$	−34.3345	−1.67336	−0.836681	−	0.547690i	$-0.815507\pi$
$421$	−34.3345	−1.67336	−0.836681	+	0.547690i	$0.815507\pi$
$422$	−65.0449	−3.16633
$423$	−4.71323	−0.229165
$424$	58.8046	2.85580
$425$	−2.06405	−0.100121
$426$	10.5779	0.512499
$427$	−4.17280	−0.201936
$428$	−51.7977	−2.50373
$429$	−2.06412	−0.0996564
$430$	−69.9998	−3.37569
$431$	4.92654	0.237303	0.118652	−	0.992936i	$-0.462143\pi$
$431$	4.92654	0.237303	0.118652	+	0.992936i	$0.462143\pi$
$432$	7.13250	0.343163
$433$	24.6260	1.18345	0.591725	−	0.806140i	$-0.298447\pi$
$433$	24.6260	1.18345	0.591725	+	0.806140i	$0.298447\pi$
$434$	−18.7694	−0.900962
$435$	27.7627	1.33112
$436$	−33.5709	−1.60775
$437$	13.0752	0.625472
$438$	−21.8280	−1.04298
$439$	3.11093	0.148476	0.0742382	−	0.997241i	$-0.476347\pi$
$439$	3.11093	0.148476	0.0742382	+	0.997241i	$0.476347\pi$
$440$	−12.9695	−0.618295
$441$	1.00000	0.0476190
$442$	−2.05547	−0.0977686
$443$	23.3544	1.10960	0.554800	−	0.831984i	$-0.312795\pi$
$443$	23.3544	1.10960	0.554800	+	0.831984i	$0.312795\pi$
$444$	−44.0782	−2.09186
$445$	17.2130	0.815973
$446$	12.0906	0.572506
$447$	4.82638	0.228280
$448$	0.221460	0.0104630
$449$	17.4094	0.821601	0.410800	−	0.911725i	$-0.365249\pi$
$449$	17.4094	0.821601	0.410800	+	0.911725i	$0.365249\pi$
$450$	−25.3272	−1.19394
$451$	−3.50751	−0.165162
$452$	−77.4881	−3.64473
$453$	17.5069	0.822545
$454$	69.1826	3.24690
$455$	15.0407	0.705119
$456$	12.5370	0.587097
$457$	38.5439	1.80301	0.901503	−	0.432773i	$-0.142465\pi$
$457$	38.5439	1.80301	0.901503	+	0.432773i	$0.142465\pi$
$458$	43.4525	2.03040
$459$	−0.207504	−0.00968545
$460$	−114.293	−5.32895
$461$	−23.8182	−1.10932	−0.554661	−	0.832076i	$-0.687152\pi$
$461$	−23.8182	−1.10932	−0.554661	+	0.832076i	$0.687152\pi$
$462$	1.35094	0.0628516
$463$	14.1367	0.656988	0.328494	−	0.944506i	$-0.393459\pi$
$463$	14.1367	0.656988	0.328494	+	0.944506i	$0.393459\pi$
$464$	51.2184	2.37775
$465$	−28.4994	−1.32163
$466$	14.7602	0.683753
$467$	8.88362	0.411085	0.205542	−	0.978648i	$-0.434104\pi$
$467$	8.88362	0.411085	0.205542	+	0.978648i	$0.434104\pi$
$468$	−17.4412	−0.806219
$469$	12.2594	0.566088
$470$	46.3970	2.14013
$471$	−8.08838	−0.372693
$472$	−62.0349	−2.85539
$473$	3.77285	0.173476
$474$	−34.0741	−1.56508
$475$	−19.7236	−0.904979
$476$	0.930276	0.0426391
$477$	−9.30059	−0.425845
$478$	−45.8304	−2.09623
$479$	19.1248	0.873837	0.436918	−	0.899501i	$-0.356070\pi$
$479$	19.1248	0.873837	0.436918	+	0.899501i	$0.356070\pi$
$480$	−21.3236	−0.973284
$481$	38.2498	1.74404
$482$	−6.11695	−0.278619
$483$	6.59413	0.300043
$484$	−48.0529	−2.18422
$485$	−6.26886	−0.284654
$486$	−2.54621	−0.115498
$487$	−14.9076	−0.675528	−0.337764	−	0.941231i	$-0.609671\pi$
$487$	−14.9076	−0.675528	−0.337764	+	0.941231i	$0.609671\pi$
$488$	−26.3833	−1.19431
$489$	4.38554	0.198321
$490$	−9.84400	−0.444706
$491$	32.7394	1.47751	0.738754	−	0.673975i	$-0.235415\pi$
$491$	32.7394	1.47751	0.738754	+	0.673975i	$0.235415\pi$
$492$	−29.6375	−1.33616
$493$	−1.49008	−0.0671099
$494$	−19.6416	−0.883715
$495$	2.05126	0.0921973
$496$	−52.5774	−2.36080
$497$	4.15436	0.186349
$498$	−33.5803	−1.50477
$499$	10.0860	0.451510	0.225755	−	0.974184i	$-0.427515\pi$
$499$	10.0860	0.451510	0.225755	+	0.974184i	$0.427515\pi$
$500$	85.7450	3.83463
$501$	−16.5761	−0.740565
$502$	40.0369	1.78693
$503$	12.0283	0.536317	0.268158	−	0.963375i	$-0.413585\pi$
$503$	12.0283	0.536317	0.268158	+	0.963375i	$0.413585\pi$
$504$	6.32268	0.281634
$505$	−57.6287	−2.56444
$506$	8.90829	0.396022
$507$	2.13495	0.0948165
$508$	0.993882	0.0440964
$509$	−2.04621	−0.0906967	−0.0453484	−	0.998971i	$-0.514440\pi$
$509$	−2.04621	−0.0906967	−0.0453484	+	0.998971i	$0.514440\pi$
$510$	2.04267	0.0904508
$511$	−8.57276	−0.379236
$512$	50.8539	2.24744
$513$	−1.98286	−0.0875453
$514$	31.7162	1.39894
$515$	64.3679	2.83639
$516$	31.8795	1.40342
$517$	−2.50070	−0.109981
$518$	−25.0341	−1.09994
$519$	−21.2797	−0.934075
$520$	95.0975	4.17030
$521$	−7.28518	−0.319169	−0.159585	−	0.987184i	$-0.551016\pi$
$521$	−7.28518	−0.319169	−0.159585	+	0.987184i	$0.551016\pi$
$522$	−18.2843	−0.800281
$523$	4.33267	0.189454	0.0947272	−	0.995503i	$-0.469802\pi$
$523$	4.33267	0.189454	0.0947272	+	0.995503i	$0.469802\pi$
$524$	77.6610	3.39264
$525$	−9.94704	−0.434124
$526$	70.1921	3.06052
$527$	1.52962	0.0666313
$528$	3.78430	0.164690
$529$	20.4825	0.890544
$530$	91.5549	3.97689
$531$	9.81150	0.425783
$532$	8.88949	0.385408
$533$	25.7185	1.11399
$534$	−11.3363	−0.490571
$535$	−44.6686	−1.93119
$536$	77.5124	3.34803
$537$	−21.3760	−0.922443
$538$	53.0109	2.28546
$539$	0.530571	0.0228533
$540$	17.3326	0.745875
$541$	1.05142	0.0452042	0.0226021	−	0.999745i	$-0.492805\pi$
$541$	1.05142	0.0452042	0.0226021	+	0.999745i	$0.492805\pi$
$542$	−54.5671	−2.34386
$543$	7.95361	0.341322
$544$	1.14448	0.0490692
$545$	−28.9504	−1.24010
$546$	−9.90568	−0.423924
$547$	20.0204	0.856012	0.428006	−	0.903776i	$-0.359216\pi$
$547$	20.0204	0.856012	0.428006	+	0.903776i	$0.359216\pi$
$548$	54.0285	2.30798
$549$	4.17280	0.178091
$550$	−13.4379	−0.572994
$551$	−14.2389	−0.606596
$552$	41.6925	1.77455
$553$	−13.3823	−0.569073
$554$	23.2435	0.987523
$555$	−38.0116	−1.61350
$556$	−99.7265	−4.22934
$557$	−30.2298	−1.28088	−0.640439	−	0.768009i	$-0.721247\pi$
$557$	−30.2298	−1.28088	−0.640439	+	0.768009i	$0.721247\pi$
$558$	18.7694	0.794574
$559$	−27.6641	−1.17007
$560$	−27.5752	−1.16527
$561$	−0.110095	−0.00464823
$562$	27.0144	1.13954
$563$	−32.9165	−1.38726	−0.693632	−	0.720329i	$-0.743991\pi$
$563$	−32.9165	−1.38726	−0.693632	+	0.720329i	$0.743991\pi$
$564$	−21.1302	−0.889743
$565$	−66.8232	−2.81127
$566$	−11.0892	−0.466115
$567$	−1.00000	−0.0419961
$568$	26.2667	1.10213
$569$	−5.41626	−0.227061	−0.113531	−	0.993534i	$-0.536216\pi$
$569$	−5.41626	−0.227061	−0.113531	+	0.993534i	$0.536216\pi$
$570$	19.5192	0.817571
$571$	−15.2263	−0.637203	−0.318601	−	0.947889i	$-0.603213\pi$
$571$	−15.2263	−0.637203	−0.318601	+	0.947889i	$0.603213\pi$
$572$	−9.25379	−0.386920
$573$	−13.8035	−0.576649
$574$	−16.8325	−0.702576
$575$	−65.5921	−2.73538
$576$	−0.221460	−0.00922749
$577$	12.6524	0.526727	0.263364	−	0.964697i	$-0.415168\pi$
$577$	12.6524	0.526727	0.263364	+	0.964697i	$0.415168\pi$
$578$	43.1759	1.79588
$579$	9.09777	0.378090
$580$	124.465	5.16813
$581$	−13.1883	−0.547145
$582$	4.12862	0.171137
$583$	−4.93462	−0.204371
$584$	−54.2028	−2.24293
$585$	−15.0407	−0.621857
$586$	34.6801	1.43262
$587$	21.9448	0.905757	0.452878	−	0.891572i	$-0.350397\pi$
$587$	21.9448	0.905757	0.452878	+	0.891572i	$0.350397\pi$
$588$	4.48317	0.184883
$589$	14.6167	0.602270
$590$	−96.5844	−3.97632
$591$	−18.4983	−0.760919
$592$	−70.1261	−2.88217
$593$	15.3536	0.630497	0.315249	−	0.949009i	$-0.397912\pi$
$593$	15.3536	0.630497	0.315249	+	0.949009i	$0.397912\pi$
$594$	−1.35094	−0.0554299
$595$	0.802239	0.0328886
$596$	21.6375	0.886306
$597$	−15.7429	−0.644314
$598$	−65.3193	−2.67111
$599$	20.2517	0.827463	0.413732	−	0.910399i	$-0.364225\pi$
$599$	20.2517	0.827463	0.413732	+	0.910399i	$0.364225\pi$
$600$	−62.8919	−2.56755
$601$	10.1752	0.415054	0.207527	−	0.978229i	$-0.433458\pi$
$601$	10.1752	0.415054	0.207527	+	0.978229i	$0.433458\pi$
$602$	18.1059	0.737940
$603$	−12.2594	−0.499243
$604$	78.4864	3.19357
$605$	−41.4392	−1.68474
$606$	37.9538	1.54177
$607$	−47.3217	−1.92073	−0.960364	−	0.278750i	$-0.910080\pi$
$607$	−47.3217	−1.92073	−0.960364	+	0.278750i	$0.910080\pi$
$608$	10.9364	0.443529
$609$	−7.18099	−0.290988
$610$	−41.0770	−1.66316
$611$	18.3362	0.741803
$612$	−0.930276	−0.0376042
$613$	48.4271	1.95595	0.977976	−	0.208719i	$-0.0669293\pi$
$613$	48.4271	1.95595	0.977976	+	0.208719i	$0.0669293\pi$
$614$	−77.0342	−3.10885
$615$	−25.5584	−1.03061
$616$	3.35463	0.135162
$617$	4.78303	0.192557	0.0962787	−	0.995354i	$-0.469306\pi$
$617$	4.78303	0.192557	0.0962787	+	0.995354i	$0.469306\pi$
$618$	−42.3922	−1.70526
$619$	−20.0189	−0.804626	−0.402313	−	0.915502i	$-0.631794\pi$
$619$	−20.0189	−0.804626	−0.402313	+	0.915502i	$0.631794\pi$
$620$	−127.768	−5.13127
$621$	−6.59413	−0.264613
$622$	−41.2719	−1.65485
$623$	−4.45224	−0.178375
$624$	−27.7480	−1.11081
$625$	24.2084	0.968337
$626$	33.1559	1.32518
$627$	−1.05205	−0.0420147
$628$	−36.2616	−1.44700
$629$	2.04016	0.0813465
$630$	9.84400	0.392194
$631$	30.4039	1.21036	0.605181	−	0.796088i	$-0.293101\pi$
$631$	30.4039	1.21036	0.605181	+	0.796088i	$0.293101\pi$
$632$	−84.6119	−3.36568
$633$	25.5458	1.01535
$634$	40.3004	1.60053
$635$	0.857090	0.0340126
$636$	−41.6961	−1.65336
$637$	−3.89037	−0.154142
$638$	−9.70111	−0.384071
$639$	−4.15436	−0.164344
$640$	44.8272	1.77195
$641$	−29.3538	−1.15941	−0.579703	−	0.814828i	$-0.696832\pi$
$641$	−29.3538	−1.15941	−0.579703	+	0.814828i	$0.696832\pi$
$642$	29.4184	1.16105
$643$	18.7638	0.739970	0.369985	−	0.929038i	$-0.379363\pi$
$643$	18.7638	0.739970	0.369985	+	0.929038i	$0.379363\pi$
$644$	29.5626	1.16493
$645$	27.4918	1.08249
$646$	−1.04764	−0.0412188
$647$	−7.83544	−0.308043	−0.154022	−	0.988067i	$-0.549223\pi$
$647$	−7.83544	−0.308043	−0.154022	+	0.988067i	$0.549223\pi$
$648$	−6.32268	−0.248378
$649$	5.20570	0.204341
$650$	98.5322	3.86475
$651$	7.37153	0.288913
$652$	19.6611	0.769990
$653$	4.24137	0.165977	0.0829887	−	0.996550i	$-0.473553\pi$
$653$	4.24137	0.165977	0.0829887	+	0.996550i	$0.473553\pi$
$654$	19.0665	0.745559
$655$	66.9722	2.61682
$656$	−47.1517	−1.84096
$657$	8.57276	0.334455
$658$	−12.0009	−0.467842
$659$	−8.49231	−0.330813	−0.165407	−	0.986225i	$-0.552894\pi$
$659$	−8.49231	−0.330813	−0.165407	+	0.986225i	$0.552894\pi$
$660$	9.19616	0.357960
$661$	14.8616	0.578049	0.289024	−	0.957322i	$-0.406669\pi$
$661$	14.8616	0.578049	0.289024	+	0.957322i	$0.406669\pi$
$662$	−9.37498	−0.364369
$663$	0.807266	0.0313516
$664$	−83.3857	−3.23599
$665$	7.66600	0.297275
$666$	25.0341	0.970052
$667$	−47.3523	−1.83349
$668$	−74.3135	−2.87528
$669$	−4.74847	−0.183586
$670$	120.682	4.66234
$671$	2.21397	0.0854692
$672$	5.51547	0.212764
$673$	26.6968	1.02909	0.514543	−	0.857465i	$-0.327962\pi$
$673$	26.6968	1.02909	0.514543	+	0.857465i	$0.327962\pi$
$674$	69.7131	2.68525
$675$	9.94704	0.382862
$676$	9.57136	0.368129
$677$	−30.7455	−1.18164	−0.590822	−	0.806802i	$-0.701197\pi$
$677$	−30.7455	−1.18164	−0.590822	+	0.806802i	$0.701197\pi$
$678$	44.0092	1.69016
$679$	1.62148	0.0622266
$680$	5.07230	0.194514
$681$	−27.1708	−1.04119
$682$	9.95852	0.381332
$683$	22.0934	0.845380	0.422690	−	0.906274i	$-0.361086\pi$
$683$	22.0934	0.845380	0.422690	+	0.906274i	$0.361086\pi$
$684$	−8.88949	−0.339898
$685$	46.5924	1.78020
$686$	2.54621	0.0972147
$687$	−17.0656	−0.651093
$688$	50.7186	1.93363
$689$	36.1827	1.37845
$690$	64.9126	2.47118
$691$	−14.8878	−0.566359	−0.283179	−	0.959067i	$-0.591389\pi$
$691$	−14.8878	−0.566359	−0.283179	+	0.959067i	$0.591389\pi$
$692$	−95.4005	−3.62658
$693$	−0.530571	−0.0201547
$694$	59.1309	2.24458
$695$	−86.0008	−3.26220
$696$	−45.4031	−1.72100
$697$	1.37177	0.0519595
$698$	75.0372	2.84020
$699$	−5.79694	−0.219260
$700$	−44.5943	−1.68551
$701$	−5.04069	−0.190384	−0.0951921	−	0.995459i	$-0.530347\pi$
$701$	−5.04069	−0.190384	−0.0951921	+	0.995459i	$0.530347\pi$
$702$	9.90568	0.373866
$703$	19.4953	0.735279
$704$	−0.117500	−0.00442845
$705$	−18.2220	−0.686280
$706$	−57.2471	−2.15452
$707$	14.9060	0.560598
$708$	43.9867	1.65312
$709$	−2.08466	−0.0782912	−0.0391456	−	0.999234i	$-0.512464\pi$
$709$	−2.08466	−0.0782912	−0.0391456	+	0.999234i	$0.512464\pi$
$710$	40.8955	1.53478
$711$	13.3823	0.501875
$712$	−28.1501	−1.05497
$713$	48.6088	1.82041
$714$	−0.528348	−0.0197729
$715$	−7.98016	−0.298441
$716$	−95.8324	−3.58143
$717$	17.9995	0.672202
$718$	36.4464	1.36017
$719$	−3.05474	−0.113922	−0.0569612	−	0.998376i	$-0.518141\pi$
$719$	−3.05474	−0.113922	−0.0569612	+	0.998376i	$0.518141\pi$
$720$	27.5752	1.02767
$721$	−16.6491	−0.620046
$722$	38.3670	1.42787
$723$	2.40238	0.0893453
$724$	35.6574	1.32520
$725$	71.4296	2.65283
$726$	27.2915	1.01288
$727$	−15.1664	−0.562490	−0.281245	−	0.959636i	$-0.590747\pi$
$727$	−15.1664	−0.562490	−0.281245	+	0.959636i	$0.590747\pi$
$728$	−24.5975	−0.911645
$729$	1.00000	0.0370370
$730$	−84.3902	−3.12342
$731$	−1.47554	−0.0545749
$732$	18.7074	0.691445
$733$	−36.0586	−1.33185	−0.665927	−	0.746017i	$-0.731964\pi$
$733$	−36.0586	−1.33185	−0.665927	+	0.746017i	$0.731964\pi$
$734$	33.7509	1.24577
$735$	3.86614	0.142605
$736$	36.3697	1.34061
$737$	−6.50450	−0.239596
$738$	16.8325	0.619614
$739$	−48.9632	−1.80114	−0.900571	−	0.434710i	$-0.856851\pi$
$739$	−48.9632	−1.80114	−0.900571	+	0.434710i	$0.856851\pi$
$740$	−170.412	−6.26449
$741$	7.71404	0.283382
$742$	−23.6812	−0.869365
$743$	−17.4418	−0.639879	−0.319939	−	0.947438i	$-0.603663\pi$
$743$	−17.4418	−0.639879	−0.319939	+	0.947438i	$0.603663\pi$
$744$	46.6078	1.70873
$745$	18.6594	0.683629
$746$	−45.2608	−1.65711
$747$	13.1883	0.482536
$748$	−0.493577	−0.0180470
$749$	11.5538	0.422166
$750$	−48.6987	−1.77822
$751$	−19.7497	−0.720677	−0.360339	−	0.932822i	$-0.617339\pi$
$751$	−19.7497	−0.720677	−0.360339	+	0.932822i	$0.617339\pi$
$752$	−33.6171	−1.22589
$753$	−15.7241	−0.573019
$754$	71.1326	2.59050
$755$	67.6841	2.46328
$756$	−4.48317	−0.163051
$757$	2.96897	0.107909	0.0539545	−	0.998543i	$-0.482817\pi$
$757$	2.96897	0.107909	0.0539545	+	0.998543i	$0.482817\pi$
$758$	−28.8258	−1.04700
$759$	−3.49865	−0.126993
$760$	48.4697	1.75818
$761$	−7.91764	−0.287014	−0.143507	−	0.989649i	$-0.545838\pi$
$761$	−7.91764	−0.287014	−0.143507	+	0.989649i	$0.545838\pi$
$762$	−0.564473	−0.0204487
$763$	7.48819	0.271091
$764$	−61.8835	−2.23886
$765$	−0.802239	−0.0290050
$766$	−2.54621	−0.0919982
$767$	−38.1703	−1.37825
$768$	−29.0799	−1.04933
$769$	4.71245	0.169935	0.0849677	−	0.996384i	$-0.472921\pi$
$769$	4.71245	0.169935	0.0849677	+	0.996384i	$0.472921\pi$
$770$	5.22294	0.188222
$771$	−12.4562	−0.448600
$772$	40.7869	1.46795
$773$	−44.8271	−1.61232	−0.806159	−	0.591698i	$-0.798458\pi$
$773$	−44.8271	−1.61232	−0.806159	+	0.591698i	$0.798458\pi$
$774$	−18.1059	−0.650802
$775$	−73.3249	−2.63391
$776$	10.2521	0.368028
$777$	9.83192	0.352718
$778$	−72.2707	−2.59103
$779$	13.1083	0.469654
$780$	−67.4301	−2.41438
$781$	−2.20418	−0.0788719
$782$	−3.48399	−0.124587
$783$	7.18099	0.256628
$784$	7.13250	0.254732
$785$	−31.2708	−1.11610
$786$	−44.1074	−1.57326
$787$	12.5148	0.446106	0.223053	−	0.974806i	$-0.428398\pi$
$787$	12.5148	0.446106	0.223053	+	0.974806i	$0.428398\pi$
$788$	−82.9312	−2.95430
$789$	−27.5673	−0.981423
$790$	−131.735	−4.68693
$791$	17.2842	0.614555
$792$	−3.35463	−0.119202
$793$	−16.2337	−0.576476
$794$	−8.61501	−0.305735
$795$	−35.9574	−1.27528
$796$	−70.5782	−2.50158
$797$	−13.3354	−0.472362	−0.236181	−	0.971709i	$-0.575896\pi$
$797$	−13.3354	−0.472362	−0.236181	+	0.971709i	$0.575896\pi$
$798$	−5.04877	−0.178724
$799$	0.978013	0.0345996
$800$	−54.8626	−1.93969
$801$	4.45224	0.157312
$802$	35.1040	1.23956
$803$	4.54845	0.160511
$804$	−54.9612	−1.93833
$805$	25.4938	0.898539
$806$	−73.0200	−2.57202
$807$	−20.8195	−0.732882
$808$	94.2458	3.31555
$809$	−7.73065	−0.271795	−0.135898	−	0.990723i	$-0.543392\pi$
$809$	−7.73065	−0.271795	−0.135898	+	0.990723i	$0.543392\pi$
$810$	−9.84400	−0.345883
$811$	−0.883498	−0.0310238	−0.0155119	−	0.999880i	$-0.504938\pi$
$811$	−0.883498	−0.0310238	−0.0155119	+	0.999880i	$0.504938\pi$
$812$	−32.1936	−1.12977
$813$	21.4307	0.751609
$814$	13.2824	0.465547
$815$	16.9551	0.593912
$816$	−1.48002	−0.0518111
$817$	−14.0999	−0.493294
$818$	−31.7519	−1.11018
$819$	3.89037	0.135940
$820$	−114.583	−4.00140
$821$	48.9405	1.70804	0.854018	−	0.520244i	$-0.174159\pi$
$821$	48.9405	1.70804	0.854018	+	0.520244i	$0.174159\pi$
$822$	−30.6853	−1.07027
$823$	−11.3875	−0.396943	−0.198471	−	0.980107i	$-0.563598\pi$
$823$	−11.3875	−0.396943	−0.198471	+	0.980107i	$0.563598\pi$
$824$	−105.267	−3.66715
$825$	5.27761	0.183743
$826$	24.9821	0.869239
$827$	−12.5583	−0.436695	−0.218347	−	0.975871i	$-0.570067\pi$
$827$	−12.5583	−0.436695	−0.218347	+	0.975871i	$0.570067\pi$
$828$	−29.5626	−1.02737
$829$	13.2967	0.461812	0.230906	−	0.972976i	$-0.425831\pi$
$829$	13.2967	0.461812	0.230906	+	0.972976i	$0.425831\pi$
$830$	−129.826	−4.50633
$831$	−9.12868	−0.316671
$832$	0.861559	0.0298692
$833$	−0.207504	−0.00718958
$834$	56.6394	1.96126
$835$	−64.0855	−2.21777
$836$	−4.71651	−0.163124
$837$	−7.37153	−0.254797
$838$	−86.0300	−2.97186
$839$	−33.2390	−1.14754	−0.573768	−	0.819018i	$-0.694519\pi$
$839$	−33.2390	−1.14754	−0.573768	+	0.819018i	$0.694519\pi$
$840$	24.4444	0.843410
$841$	22.5666	0.778157
$842$	87.4229	3.01279
$843$	−10.6097	−0.365417
$844$	114.526	3.94215
$845$	8.25402	0.283947
$846$	12.0009	0.412598
$847$	10.7185	0.368292
$848$	−66.3364	−2.27800
$849$	4.35519	0.149470
$850$	5.25550	0.180262
$851$	64.8329	2.22244
$852$	−18.6247	−0.638073
$853$	54.2162	1.85633	0.928163	−	0.372173i	$-0.121387\pi$
$853$	54.2162	1.85633	0.928163	+	0.372173i	$0.121387\pi$
$854$	10.6248	0.363574
$855$	−7.66600	−0.262172
$856$	73.0509	2.49683
$857$	−43.3041	−1.47924	−0.739621	−	0.673024i	$-0.764995\pi$
$857$	−43.3041	−1.47924	−0.739621	+	0.673024i	$0.764995\pi$
$858$	5.25567	0.179425
$859$	1.84928	0.0630968	0.0315484	−	0.999502i	$-0.489956\pi$
$859$	1.84928	0.0630968	0.0315484	+	0.999502i	$0.489956\pi$
$860$	123.251	4.20281
$861$	6.61082	0.225296
$862$	−12.5440	−0.427250
$863$	33.2628	1.13228	0.566139	−	0.824310i	$-0.308436\pi$
$863$	33.2628	1.13228	0.566139	+	0.824310i	$0.308436\pi$
$864$	−5.51547	−0.187640
$865$	−82.2703	−2.79727
$866$	−62.7029	−2.13073
$867$	−16.9569	−0.575888
$868$	33.0479	1.12172
$869$	7.10026	0.240860
$870$	−70.6896	−2.39660
$871$	47.6937	1.61604
$872$	47.3454	1.60332
$873$	−1.62148	−0.0548787
$874$	−33.2922	−1.12613
$875$	−19.1260	−0.646575
$876$	38.4332	1.29854
$877$	28.9848	0.978746	0.489373	−	0.872075i	$-0.337226\pi$
$877$	28.9848	0.978746	0.489373	+	0.872075i	$0.337226\pi$
$878$	−7.92106	−0.267323
$879$	−13.6203	−0.459401
$880$	14.6306	0.493198
$881$	11.9268	0.401825	0.200913	−	0.979609i	$-0.435609\pi$
$881$	11.9268	0.401825	0.200913	+	0.979609i	$0.435609\pi$
$882$	−2.54621	−0.0857353
$883$	−34.2818	−1.15367	−0.576837	−	0.816859i	$-0.695713\pi$
$883$	−34.2818	−1.15367	−0.576837	+	0.816859i	$0.695713\pi$
$884$	3.61911	0.121724
$885$	37.9326	1.27509
$886$	−59.4651	−1.99777
$887$	21.4144	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$887$	21.4144	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$888$	62.1640	2.08609
$889$	−0.221692	−0.00743529
$890$	−43.8278	−1.46911
$891$	0.530571	0.0177748
$892$	−21.2882	−0.712782
$893$	9.34566	0.312741
$894$	−12.2890	−0.411004
$895$	−82.6427	−2.76244
$896$	−11.5948	−0.387356
$897$	25.6536	0.856548
$898$	−44.3280	−1.47924
$899$	−52.9349	−1.76548
$900$	44.5943	1.48648
$901$	1.92991	0.0642945
$902$	8.93085	0.297365
$903$	−7.11092	−0.236637
$904$	109.282	3.63468
$905$	30.7498	1.02216
$906$	−44.5762	−1.48094
$907$	27.4987	0.913080	0.456540	−	0.889703i	$-0.349088\pi$
$907$	27.4987	0.913080	0.456540	+	0.889703i	$0.349088\pi$
$908$	−121.812	−4.04246
$909$	−14.9060	−0.494401
$910$	−38.2968	−1.26953
$911$	−47.6455	−1.57857	−0.789283	−	0.614029i	$-0.789548\pi$
$911$	−47.6455	−1.57857	−0.789283	+	0.614029i	$0.789548\pi$
$912$	−14.1427	−0.468313
$913$	6.99735	0.231579
$914$	−98.1407	−3.24621
$915$	16.1326	0.533328
$916$	−76.5080	−2.52789
$917$	−17.3228	−0.572048
$918$	0.528348	0.0174381
$919$	−14.9797	−0.494135	−0.247068	−	0.968998i	$-0.579467\pi$
$919$	−14.9797	−0.494135	−0.247068	+	0.968998i	$0.579467\pi$
$920$	161.189	5.31425
$921$	30.2545	0.996919
$922$	60.6460	1.99727
$923$	16.1620	0.531978
$924$	−2.37864	−0.0782516
$925$	−97.7985	−3.21559
$926$	−35.9950	−1.18287
$927$	16.6491	0.546829
$928$	−39.6065	−1.30015
$929$	−55.3773	−1.81687	−0.908436	−	0.418025i	$-0.862723\pi$
$929$	−55.3773	−1.81687	−0.908436	+	0.418025i	$0.862723\pi$
$930$	72.5653	2.37951
$931$	−1.98286	−0.0649855
$932$	−25.9887	−0.851287
$933$	16.2092	0.530664
$934$	−22.6195	−0.740134
$935$	−0.425645	−0.0139201
$936$	24.5975	0.803995
$937$	27.1223	0.886048	0.443024	−	0.896510i	$-0.353906\pi$
$937$	27.1223	0.886048	0.443024	+	0.896510i	$0.353906\pi$
$938$	−31.2151	−1.01921
$939$	−13.0217	−0.424947
$940$	−81.6924	−2.66451
$941$	41.0032	1.33666	0.668332	−	0.743863i	$-0.267008\pi$
$941$	41.0032	1.33666	0.668332	+	0.743863i	$0.267008\pi$
$942$	20.5947	0.671011
$943$	43.5926	1.41957
$944$	69.9805	2.27767
$945$	−3.86614	−0.125766
$946$	−9.60645	−0.312333
$947$	35.0776	1.13987	0.569935	−	0.821690i	$-0.306968\pi$
$947$	35.0776	1.13987	0.569935	+	0.821690i	$0.306968\pi$
$948$	59.9952	1.94855
$949$	−33.3512	−1.08262
$950$	50.2203	1.62936
$951$	−15.8276	−0.513246
$952$	−1.31198	−0.0425215
$953$	15.8363	0.512988	0.256494	−	0.966546i	$-0.417433\pi$
$953$	15.8363	0.512988	0.256494	+	0.966546i	$0.417433\pi$
$954$	23.6812	0.766708
$955$	−53.3662	−1.72689
$956$	80.6947	2.60985
$957$	3.81002	0.123161
$958$	−48.6958	−1.57329
$959$	−12.0514	−0.389160
$960$	−0.856194	−0.0276336
$961$	23.3395	0.752886
$962$	−97.3918	−3.14004
$963$	−11.5538	−0.372316
$964$	10.7703	0.346887
$965$	35.1732	1.13227
$966$	−16.7900	−0.540210
$967$	−24.0687	−0.773996	−0.386998	−	0.922081i	$-0.626488\pi$
$967$	−24.0687	−0.773996	−0.386998	+	0.922081i	$0.626488\pi$
$968$	67.7696	2.17820
$969$	0.411450	0.0132177
$970$	15.9618	0.512503
$971$	−34.1518	−1.09598	−0.547992	−	0.836484i	$-0.684608\pi$
$971$	−34.1518	−1.09598	−0.547992	+	0.836484i	$0.684608\pi$
$972$	4.48317	0.143798
$973$	22.2446	0.713130
$974$	37.9579	1.21625
$975$	−38.6976	−1.23932
$976$	29.7625	0.952674
$977$	−15.0901	−0.482776	−0.241388	−	0.970429i	$-0.577603\pi$
$977$	−15.0901	−0.482776	−0.241388	+	0.970429i	$0.577603\pi$
$978$	−11.1665	−0.357065
$979$	2.36223	0.0754971
$980$	17.3326	0.553669
$981$	−7.48819	−0.239080
$982$	−83.3613	−2.66017
$983$	51.9527	1.65703	0.828516	−	0.559965i	$-0.189185\pi$
$983$	51.9527	1.65703	0.828516	+	0.559965i	$0.189185\pi$
$984$	41.7981	1.33247
$985$	−71.5171	−2.27872
$986$	3.79406	0.120827
$987$	4.71323	0.150024
$988$	34.5834	1.10024
$989$	−46.8903	−1.49102
$990$	−5.22294	−0.165996
$991$	59.2812	1.88313	0.941565	−	0.336832i	$-0.109355\pi$
$991$	59.2812	1.88313	0.941565	+	0.336832i	$0.109355\pi$
$992$	40.6575	1.29088
$993$	3.68194	0.116843
$994$	−10.5779	−0.335510
$995$	−60.8643	−1.92953
$996$	59.1257	1.87347
$997$	20.0124	0.633798	0.316899	−	0.948459i	$-0.397358\pi$
$997$	20.0124	0.633798	0.316899	+	0.948459i	$0.397358\pi$
$998$	−25.6810	−0.812917
$999$	−9.83192	−0.311068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.4	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.54621 q^{2} +1.00000 q^{3} +4.48317 q^{4} +3.86614 q^{5} -2.54621 q^{6} -1.00000 q^{7} -6.32268 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.54621 q^{2} +1.00000 q^{3} +4.48317 q^{4} +3.86614 q^{5} -2.54621 q^{6} -1.00000 q^{7} -6.32268 q^{8} +1.00000 q^{9} -9.84400 q^{10} +0.530571 q^{11} +4.48317 q^{12} -3.89037 q^{13} +2.54621 q^{14} +3.86614 q^{15} +7.13250 q^{16} -0.207504 q^{17} -2.54621 q^{18} -1.98286 q^{19} +17.3326 q^{20} -1.00000 q^{21} -1.35094 q^{22} -6.59413 q^{23} -6.32268 q^{24} +9.94704 q^{25} +9.90568 q^{26} +1.00000 q^{27} -4.48317 q^{28} +7.18099 q^{29} -9.84400 q^{30} -7.37153 q^{31} -5.51547 q^{32} +0.530571 q^{33} +0.528348 q^{34} -3.86614 q^{35} +4.48317 q^{36} -9.83192 q^{37} +5.04877 q^{38} -3.89037 q^{39} -24.4444 q^{40} -6.61082 q^{41} +2.54621 q^{42} +7.11092 q^{43} +2.37864 q^{44} +3.86614 q^{45} +16.7900 q^{46} -4.71323 q^{47} +7.13250 q^{48} +1.00000 q^{49} -25.3272 q^{50} -0.207504 q^{51} -17.4412 q^{52} -9.30059 q^{53} -2.54621 q^{54} +2.05126 q^{55} +6.32268 q^{56} -1.98286 q^{57} -18.2843 q^{58} +9.81150 q^{59} +17.3326 q^{60} +4.17280 q^{61} +18.7694 q^{62} -1.00000 q^{63} -0.221460 q^{64} -15.0407 q^{65} -1.35094 q^{66} -12.2594 q^{67} -0.930276 q^{68} -6.59413 q^{69} +9.84400 q^{70} -4.15436 q^{71} -6.32268 q^{72} +8.57276 q^{73} +25.0341 q^{74} +9.94704 q^{75} -8.88949 q^{76} -0.530571 q^{77} +9.90568 q^{78} +13.3823 q^{79} +27.5752 q^{80} +1.00000 q^{81} +16.8325 q^{82} +13.1883 q^{83} -4.48317 q^{84} -0.802239 q^{85} -18.1059 q^{86} +7.18099 q^{87} -3.35463 q^{88} +4.45224 q^{89} -9.84400 q^{90} +3.89037 q^{91} -29.5626 q^{92} -7.37153 q^{93} +12.0009 q^{94} -7.66600 q^{95} -5.51547 q^{96} -1.62148 q^{97} -2.54621 q^{98} +0.530571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 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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