LMFDB - Embedded newform 4029.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12762 q^{2} -1.00000 q^{3} +2.52678 q^{4} -3.72932 q^{5} +2.12762 q^{6} -2.25712 q^{7} -1.12080 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.12762 q^{2} -1.00000 q^{3} +2.52678 q^{4} -3.72932 q^{5} +2.12762 q^{6} -2.25712 q^{7} -1.12080 q^{8} +1.00000 q^{9} +7.93460 q^{10} -0.182142 q^{11} -2.52678 q^{12} -4.75632 q^{13} +4.80230 q^{14} +3.72932 q^{15} -2.66893 q^{16} -1.00000 q^{17} -2.12762 q^{18} -4.54286 q^{19} -9.42320 q^{20} +2.25712 q^{21} +0.387530 q^{22} +1.66498 q^{23} +1.12080 q^{24} +8.90786 q^{25} +10.1197 q^{26} -1.00000 q^{27} -5.70325 q^{28} +6.17388 q^{29} -7.93460 q^{30} -1.79786 q^{31} +7.92008 q^{32} +0.182142 q^{33} +2.12762 q^{34} +8.41753 q^{35} +2.52678 q^{36} +2.70096 q^{37} +9.66550 q^{38} +4.75632 q^{39} +4.17983 q^{40} +1.99136 q^{41} -4.80230 q^{42} -1.55845 q^{43} -0.460234 q^{44} -3.72932 q^{45} -3.54245 q^{46} +0.626105 q^{47} +2.66893 q^{48} -1.90541 q^{49} -18.9526 q^{50} +1.00000 q^{51} -12.0182 q^{52} +6.60092 q^{53} +2.12762 q^{54} +0.679267 q^{55} +2.52978 q^{56} +4.54286 q^{57} -13.1357 q^{58} -14.4808 q^{59} +9.42320 q^{60} -7.62701 q^{61} +3.82518 q^{62} -2.25712 q^{63} -11.5131 q^{64} +17.7379 q^{65} -0.387530 q^{66} +9.89492 q^{67} -2.52678 q^{68} -1.66498 q^{69} -17.9093 q^{70} +0.689145 q^{71} -1.12080 q^{72} +3.09573 q^{73} -5.74664 q^{74} -8.90786 q^{75} -11.4788 q^{76} +0.411116 q^{77} -10.1197 q^{78} -1.00000 q^{79} +9.95330 q^{80} +1.00000 q^{81} -4.23687 q^{82} +16.9237 q^{83} +5.70325 q^{84} +3.72932 q^{85} +3.31580 q^{86} -6.17388 q^{87} +0.204145 q^{88} +16.5519 q^{89} +7.93460 q^{90} +10.7356 q^{91} +4.20704 q^{92} +1.79786 q^{93} -1.33212 q^{94} +16.9418 q^{95} -7.92008 q^{96} +6.97050 q^{97} +4.05401 q^{98} -0.182142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * 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 $

$2$	−2.12762	−1.50446	−0.752229	−	0.658902i	$-0.771021\pi$
$2$	−2.12762	−1.50446	−0.752229	+	0.658902i	$0.771021\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.52678	1.26339
$5$	−3.72932	−1.66780	−0.833902	−	0.551912i	$-0.813898\pi$
$5$	−3.72932	−1.66780	−0.833902	+	0.551912i	$0.813898\pi$
$6$	2.12762	0.868599
$7$	−2.25712	−0.853111	−0.426555	−	0.904461i	$-0.640273\pi$
$7$	−2.25712	−0.853111	−0.426555	+	0.904461i	$0.640273\pi$
$8$	−1.12080	−0.396263
$9$	1.00000	0.333333
$10$	7.93460	2.50914
$11$	−0.182142	−0.0549179	−0.0274589	−	0.999623i	$-0.508742\pi$
$11$	−0.182142	−0.0549179	−0.0274589	+	0.999623i	$0.508742\pi$
$12$	−2.52678	−0.729420
$13$	−4.75632	−1.31917	−0.659583	−	0.751632i	$-0.729267\pi$
$13$	−4.75632	−1.31917	−0.659583	+	0.751632i	$0.729267\pi$
$14$	4.80230	1.28347
$15$	3.72932	0.962908
$16$	−2.66893	−0.667232
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.12762	−0.501486
$19$	−4.54286	−1.04220	−0.521102	−	0.853495i	$-0.674479\pi$
$19$	−4.54286	−1.04220	−0.521102	+	0.853495i	$0.674479\pi$
$20$	−9.42320	−2.10709
$21$	2.25712	0.492544
$22$	0.387530	0.0826216
$23$	1.66498	0.347172	0.173586	−	0.984819i	$-0.444465\pi$
$23$	1.66498	0.347172	0.173586	+	0.984819i	$0.444465\pi$
$24$	1.12080	0.228782
$25$	8.90786	1.78157
$26$	10.1197	1.98463
$27$	−1.00000	−0.192450
$28$	−5.70325	−1.07781
$29$	6.17388	1.14646	0.573230	−	0.819394i	$-0.305690\pi$
$29$	6.17388	1.14646	0.573230	+	0.819394i	$0.305690\pi$
$30$	−7.93460	−1.44865
$31$	−1.79786	−0.322906	−0.161453	−	0.986880i	$-0.551618\pi$
$31$	−1.79786	−0.322906	−0.161453	+	0.986880i	$0.551618\pi$
$32$	7.92008	1.40008
$33$	0.182142	0.0317069
$34$	2.12762	0.364885
$35$	8.41753	1.42282
$36$	2.52678	0.421131
$37$	2.70096	0.444036	0.222018	−	0.975043i	$-0.428736\pi$
$37$	2.70096	0.444036	0.222018	+	0.975043i	$0.428736\pi$
$38$	9.66550	1.56795
$39$	4.75632	0.761621
$40$	4.17983	0.660889
$41$	1.99136	0.310999	0.155499	−	0.987836i	$-0.450301\pi$
$41$	1.99136	0.310999	0.155499	+	0.987836i	$0.450301\pi$
$42$	−4.80230	−0.741011
$43$	−1.55845	−0.237662	−0.118831	−	0.992915i	$-0.537915\pi$
$43$	−1.55845	−0.237662	−0.118831	+	0.992915i	$0.537915\pi$
$44$	−0.460234	−0.0693828
$45$	−3.72932	−0.555935
$46$	−3.54245	−0.522306
$47$	0.626105	0.0913268	0.0456634	−	0.998957i	$-0.485460\pi$
$47$	0.626105	0.0913268	0.0456634	+	0.998957i	$0.485460\pi$
$48$	2.66893	0.385227
$49$	−1.90541	−0.272202
$50$	−18.9526	−2.68030
$51$	1.00000	0.140028
$52$	−12.0182	−1.66662
$53$	6.60092	0.906706	0.453353	−	0.891331i	$-0.350228\pi$
$53$	6.60092	0.906706	0.453353	+	0.891331i	$0.350228\pi$
$54$	2.12762	0.289533
$55$	0.679267	0.0915923
$56$	2.52978	0.338056
$57$	4.54286	0.601716
$58$	−13.1357	−1.72480
$59$	−14.4808	−1.88525	−0.942623	−	0.333860i	$-0.891649\pi$
$59$	−14.4808	−1.88525	−0.942623	+	0.333860i	$0.891649\pi$
$60$	9.42320	1.21653
$61$	−7.62701	−0.976538	−0.488269	−	0.872693i	$-0.662372\pi$
$61$	−7.62701	−0.976538	−0.488269	+	0.872693i	$0.662372\pi$
$62$	3.82518	0.485798
$63$	−2.25712	−0.284370
$64$	−11.5131	−1.43914
$65$	17.7379	2.20011
$66$	−0.387530	−0.0477016
$67$	9.89492	1.20886	0.604429	−	0.796659i	$-0.293401\pi$
$67$	9.89492	1.20886	0.604429	+	0.796659i	$0.293401\pi$
$68$	−2.52678	−0.306418
$69$	−1.66498	−0.200440
$70$	−17.9093	−2.14058
$71$	0.689145	0.0817864	0.0408932	−	0.999164i	$-0.486980\pi$
$71$	0.689145	0.0817864	0.0408932	+	0.999164i	$0.486980\pi$
$72$	−1.12080	−0.132088
$73$	3.09573	0.362327	0.181164	−	0.983453i	$-0.442014\pi$
$73$	3.09573	0.362327	0.181164	+	0.983453i	$0.442014\pi$
$74$	−5.74664	−0.668033
$75$	−8.90786	−1.02859
$76$	−11.4788	−1.31671
$77$	0.411116	0.0468510
$78$	−10.1197	−1.14583
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	9.95330	1.11281
$81$	1.00000	0.111111
$82$	−4.23687	−0.467884
$83$	16.9237	1.85762	0.928811	−	0.370555i	$-0.120832\pi$
$83$	16.9237	1.85762	0.928811	+	0.370555i	$0.120832\pi$
$84$	5.70325	0.622276
$85$	3.72932	0.404502
$86$	3.31580	0.357552
$87$	−6.17388	−0.661910
$88$	0.204145	0.0217619
$89$	16.5519	1.75450	0.877248	−	0.480038i	$-0.159377\pi$
$89$	16.5519	1.75450	0.877248	+	0.480038i	$0.159377\pi$
$90$	7.93460	0.836380
$91$	10.7356	1.12539
$92$	4.20704	0.438614
$93$	1.79786	0.186430
$94$	−1.33212	−0.137397
$95$	16.9418	1.73819
$96$	−7.92008	−0.808339
$97$	6.97050	0.707747	0.353873	−	0.935293i	$-0.384864\pi$
$97$	6.97050	0.707747	0.353873	+	0.935293i	$0.384864\pi$
$98$	4.05401	0.409516
$99$	−0.182142	−0.0183060
$100$	22.5083	2.25083
$101$	−2.01299	−0.200300	−0.100150	−	0.994972i	$-0.531932\pi$
$101$	−2.01299	−0.200300	−0.100150	+	0.994972i	$0.531932\pi$
$102$	−2.12762	−0.210666
$103$	12.1529	1.19747	0.598733	−	0.800949i	$-0.295671\pi$
$103$	12.1529	1.19747	0.598733	+	0.800949i	$0.295671\pi$
$104$	5.33089	0.522737
$105$	−8.41753	−0.821467
$106$	−14.0443	−1.36410
$107$	11.9012	1.15053	0.575267	−	0.817966i	$-0.304898\pi$
$107$	11.9012	1.15053	0.575267	+	0.817966i	$0.304898\pi$
$108$	−2.52678	−0.243140
$109$	−2.03940	−0.195339	−0.0976697	−	0.995219i	$-0.531139\pi$
$109$	−2.03940	−0.195339	−0.0976697	+	0.995219i	$0.531139\pi$
$110$	−1.44522	−0.137797
$111$	−2.70096	−0.256364
$112$	6.02409	0.569223
$113$	6.33896	0.596319	0.298160	−	0.954516i	$-0.403627\pi$
$113$	6.33896	0.596319	0.298160	+	0.954516i	$0.403627\pi$
$114$	−9.66550	−0.905257
$115$	−6.20925	−0.579015
$116$	15.6001	1.44843
$117$	−4.75632	−0.439722
$118$	30.8098	2.83627
$119$	2.25712	0.206910
$120$	−4.17983	−0.381564
$121$	−10.9668	−0.996984
$122$	16.2274	1.46916
$123$	−1.99136	−0.179555
$124$	−4.54281	−0.407957
$125$	−14.5737	−1.30351
$126$	4.80230	0.427823
$127$	−5.72668	−0.508161	−0.254080	−	0.967183i	$-0.581773\pi$
$127$	−5.72668	−0.508161	−0.254080	+	0.967183i	$0.581773\pi$
$128$	8.65538	0.765035
$129$	1.55845	0.137214
$130$	−37.7395	−3.30997
$131$	−19.6202	−1.71422	−0.857112	−	0.515130i	$-0.827743\pi$
$131$	−19.6202	−1.71422	−0.857112	+	0.515130i	$0.827743\pi$
$132$	0.460234	0.0400582
$133$	10.2538	0.889115
$134$	−21.0527	−1.81867
$135$	3.72932	0.320969
$136$	1.12080	0.0961078
$137$	5.31788	0.454337	0.227169	−	0.973855i	$-0.427053\pi$
$137$	5.31788	0.454337	0.227169	+	0.973855i	$0.427053\pi$
$138$	3.54245	0.301553
$139$	−18.2682	−1.54949	−0.774746	−	0.632273i	$-0.782122\pi$
$139$	−18.2682	−1.54949	−0.774746	+	0.632273i	$0.782122\pi$
$140$	21.2693	1.79758
$141$	−0.626105	−0.0527276
$142$	−1.46624	−0.123044
$143$	0.866326	0.0724458
$144$	−2.66893	−0.222411
$145$	−23.0244	−1.91207
$146$	−6.58654	−0.545106
$147$	1.90541	0.157156
$148$	6.82476	0.560991
$149$	10.8744	0.890865	0.445432	−	0.895316i	$-0.353050\pi$
$149$	10.8744	0.890865	0.445432	+	0.895316i	$0.353050\pi$
$150$	18.9526	1.54747
$151$	23.7251	1.93072	0.965361	−	0.260919i	$-0.0840256\pi$
$151$	23.7251	1.93072	0.965361	+	0.260919i	$0.0840256\pi$
$152$	5.09164	0.412986
$153$	−1.00000	−0.0808452
$154$	−0.874701	−0.0704854
$155$	6.70481	0.538544
$156$	12.0182	0.962226
$157$	−0.748926	−0.0597708	−0.0298854	−	0.999553i	$-0.509514\pi$
$157$	−0.748926	−0.0597708	−0.0298854	+	0.999553i	$0.509514\pi$
$158$	2.12762	0.169265
$159$	−6.60092	−0.523487
$160$	−29.5365	−2.33507
$161$	−3.75805	−0.296176
$162$	−2.12762	−0.167162
$163$	−3.02035	−0.236572	−0.118286	−	0.992980i	$-0.537740\pi$
$163$	−3.02035	−0.236572	−0.118286	+	0.992980i	$0.537740\pi$
$164$	5.03175	0.392913
$165$	−0.679267	−0.0528808
$166$	−36.0074	−2.79471
$167$	20.8973	1.61708	0.808542	−	0.588439i	$-0.200257\pi$
$167$	20.8973	1.61708	0.808542	+	0.588439i	$0.200257\pi$
$168$	−2.52978	−0.195177
$169$	9.62260	0.740200
$170$	−7.93460	−0.608556
$171$	−4.54286	−0.347401
$172$	−3.93787	−0.300260
$173$	14.4564	1.09910	0.549548	−	0.835462i	$-0.314800\pi$
$173$	14.4564	1.09910	0.549548	+	0.835462i	$0.314800\pi$
$174$	13.1357	0.995815
$175$	−20.1061	−1.51988
$176$	0.486124	0.0366430
$177$	14.4808	1.08845
$178$	−35.2162	−2.63956
$179$	−9.26490	−0.692491	−0.346246	−	0.938144i	$-0.612544\pi$
$179$	−9.26490	−0.692491	−0.346246	+	0.938144i	$0.612544\pi$
$180$	−9.42320	−0.702364
$181$	18.0183	1.33929	0.669644	−	0.742682i	$-0.266446\pi$
$181$	18.0183	1.33929	0.669644	+	0.742682i	$0.266446\pi$
$182$	−22.8413	−1.69311
$183$	7.62701	0.563805
$184$	−1.86611	−0.137571
$185$	−10.0728	−0.740565
$186$	−3.82518	−0.280476
$187$	0.182142	0.0133195
$188$	1.58203	0.115382
$189$	2.25712	0.164181
$190$	−36.0458	−2.61504
$191$	−19.2021	−1.38941	−0.694706	−	0.719293i	$-0.744466\pi$
$191$	−19.2021	−1.38941	−0.694706	+	0.719293i	$0.744466\pi$
$192$	11.5131	0.830886
$193$	8.99343	0.647361	0.323681	−	0.946166i	$-0.395080\pi$
$193$	8.99343	0.647361	0.323681	+	0.946166i	$0.395080\pi$
$194$	−14.8306	−1.06478
$195$	−17.7379	−1.27024
$196$	−4.81457	−0.343898
$197$	−10.6425	−0.758247	−0.379124	−	0.925346i	$-0.623774\pi$
$197$	−10.6425	−0.758247	−0.379124	+	0.925346i	$0.623774\pi$
$198$	0.387530	0.0275405
$199$	5.99330	0.424854	0.212427	−	0.977177i	$-0.431863\pi$
$199$	5.99330	0.424854	0.212427	+	0.977177i	$0.431863\pi$
$200$	−9.98394	−0.705971
$201$	−9.89492	−0.697934
$202$	4.28288	0.301342
$203$	−13.9352	−0.978058
$204$	2.52678	0.176910
$205$	−7.42644	−0.518685
$206$	−25.8569	−1.80154
$207$	1.66498	0.115724
$208$	12.6943	0.880190
$209$	0.827446	0.0572356
$210$	17.9093	1.23586
$211$	1.08688	0.0748236	0.0374118	−	0.999300i	$-0.488089\pi$
$211$	1.08688	0.0748236	0.0374118	+	0.999300i	$0.488089\pi$
$212$	16.6791	1.14553
$213$	−0.689145	−0.0472194
$214$	−25.3213	−1.73093
$215$	5.81198	0.396373
$216$	1.12080	0.0762608
$217$	4.05799	0.275474
$218$	4.33908	0.293880
$219$	−3.09573	−0.209190
$220$	1.71636	0.115717
$221$	4.75632	0.319945
$222$	5.74664	0.385689
$223$	−21.9806	−1.47193	−0.735966	−	0.677019i	$-0.763272\pi$
$223$	−21.9806	−1.47193	−0.735966	+	0.677019i	$0.763272\pi$
$224$	−17.8766	−1.19443
$225$	8.90786	0.593858
$226$	−13.4869	−0.897137
$227$	27.7205	1.83987	0.919937	−	0.392067i	$-0.128240\pi$
$227$	27.7205	1.83987	0.919937	+	0.392067i	$0.128240\pi$
$228$	11.4788	0.760204
$229$	−4.91796	−0.324988	−0.162494	−	0.986710i	$-0.551954\pi$
$229$	−4.91796	−0.324988	−0.162494	+	0.986710i	$0.551954\pi$
$230$	13.2109	0.871104
$231$	−0.411116	−0.0270495
$232$	−6.91969	−0.454300
$233$	−23.2705	−1.52450	−0.762250	−	0.647283i	$-0.775905\pi$
$233$	−23.2705	−1.52450	−0.762250	+	0.647283i	$0.775905\pi$
$234$	10.1197	0.661543
$235$	−2.33495	−0.152315
$236$	−36.5900	−2.38181
$237$	1.00000	0.0649570
$238$	−4.80230	−0.311287
$239$	13.6271	0.881466	0.440733	−	0.897638i	$-0.354719\pi$
$239$	13.6271	0.881466	0.440733	+	0.897638i	$0.354719\pi$
$240$	−9.95330	−0.642483
$241$	17.2249	1.10955	0.554775	−	0.832000i	$-0.312804\pi$
$241$	17.2249	1.10955	0.554775	+	0.832000i	$0.312804\pi$
$242$	23.3333	1.49992
$243$	−1.00000	−0.0641500
$244$	−19.2718	−1.23375
$245$	7.10591	0.453980
$246$	4.23687	0.270133
$247$	21.6073	1.37484
$248$	2.01505	0.127955
$249$	−16.9237	−1.07250
$250$	31.0073	1.96108
$251$	−18.7482	−1.18337	−0.591687	−	0.806167i	$-0.701538\pi$
$251$	−18.7482	−1.18337	−0.591687	+	0.806167i	$0.701538\pi$
$252$	−5.70325	−0.359271
$253$	−0.303263	−0.0190660
$254$	12.1842	0.764506
$255$	−3.72932	−0.233539
$256$	4.61079	0.288174
$257$	−23.0030	−1.43489	−0.717443	−	0.696617i	$-0.754688\pi$
$257$	−23.0030	−1.43489	−0.717443	+	0.696617i	$0.754688\pi$
$258$	−3.31580	−0.206433
$259$	−6.09640	−0.378812
$260$	44.8198	2.77960
$261$	6.17388	0.382154
$262$	41.7444	2.57898
$263$	−0.522362	−0.0322102	−0.0161051	−	0.999870i	$-0.505127\pi$
$263$	−0.522362	−0.0322102	−0.0161051	+	0.999870i	$0.505127\pi$
$264$	−0.204145	−0.0125642
$265$	−24.6170	−1.51221
$266$	−21.8162	−1.33764
$267$	−16.5519	−1.01296
$268$	25.0023	1.52726
$269$	−5.01416	−0.305719	−0.152859	−	0.988248i	$-0.548848\pi$
$269$	−5.01416	−0.305719	−0.152859	+	0.988248i	$0.548848\pi$
$270$	−7.93460	−0.482884
$271$	−12.9034	−0.783829	−0.391914	−	0.920002i	$-0.628187\pi$
$271$	−12.9034	−0.783829	−0.391914	+	0.920002i	$0.628187\pi$
$272$	2.66893	0.161828
$273$	−10.7356	−0.649747
$274$	−11.3144	−0.683531
$275$	−1.62250	−0.0978402
$276$	−4.20704	−0.253234
$277$	−12.1096	−0.727595	−0.363797	−	0.931478i	$-0.618520\pi$
$277$	−12.1096	−0.727595	−0.363797	+	0.931478i	$0.618520\pi$
$278$	38.8680	2.33115
$279$	−1.79786	−0.107635
$280$	−9.43437	−0.563811
$281$	−14.1905	−0.846536	−0.423268	−	0.906004i	$-0.639117\pi$
$281$	−14.1905	−0.846536	−0.423268	+	0.906004i	$0.639117\pi$
$282$	1.33212	0.0793264
$283$	−0.819726	−0.0487276	−0.0243638	−	0.999703i	$-0.507756\pi$
$283$	−0.819726	−0.0487276	−0.0243638	+	0.999703i	$0.507756\pi$
$284$	1.74132	0.103328
$285$	−16.9418	−1.00355
$286$	−1.84322	−0.108992
$287$	−4.49474	−0.265316
$288$	7.92008	0.466695
$289$	1.00000	0.0588235
$290$	48.9873	2.87663
$291$	−6.97050	−0.408618
$292$	7.82223	0.457762
$293$	−25.7375	−1.50360	−0.751800	−	0.659392i	$-0.770814\pi$
$293$	−25.7375	−1.50360	−0.751800	+	0.659392i	$0.770814\pi$
$294$	−4.05401	−0.236434
$295$	54.0038	3.14422
$296$	−3.02724	−0.175955
$297$	0.182142	0.0105690
$298$	−23.1366	−1.34027
$299$	−7.91917	−0.457978
$300$	−22.5083	−1.29951
$301$	3.51761	0.202752
$302$	−50.4781	−2.90469
$303$	2.01299	0.115643
$304$	12.1246	0.695391
$305$	28.4436	1.62868
$306$	2.12762	0.121628
$307$	−18.3837	−1.04921	−0.524606	−	0.851345i	$-0.675788\pi$
$307$	−18.3837	−1.04921	−0.524606	+	0.851345i	$0.675788\pi$
$308$	1.03880	0.0591913
$309$	−12.1529	−0.691357
$310$	−14.2653	−0.810216
$311$	26.6624	1.51189	0.755944	−	0.654636i	$-0.227178\pi$
$311$	26.6624	1.51189	0.755944	+	0.654636i	$0.227178\pi$
$312$	−5.33089	−0.301802
$313$	−12.3763	−0.699553	−0.349776	−	0.936833i	$-0.613742\pi$
$313$	−12.3763	−0.699553	−0.349776	+	0.936833i	$0.613742\pi$
$314$	1.59343	0.0899226
$315$	8.41753	0.474274
$316$	−2.52678	−0.142143
$317$	21.3954	1.20168	0.600842	−	0.799368i	$-0.294832\pi$
$317$	21.3954	1.20168	0.600842	+	0.799368i	$0.294832\pi$
$318$	14.0443	0.787564
$319$	−1.12452	−0.0629612
$320$	42.9361	2.40020
$321$	−11.9012	−0.664261
$322$	7.99573	0.445584
$323$	4.54286	0.252771
$324$	2.52678	0.140377
$325$	−42.3687	−2.35019
$326$	6.42617	0.355913
$327$	2.03940	0.112779
$328$	−2.23192	−0.123237
$329$	−1.41319	−0.0779119
$330$	1.44522	0.0795570
$331$	0.231979	0.0127507	0.00637536	−	0.999980i	$-0.497971\pi$
$331$	0.231979	0.0127507	0.00637536	+	0.999980i	$0.497971\pi$
$332$	42.7626	2.34690
$333$	2.70096	0.148012
$334$	−44.4616	−2.43283
$335$	−36.9014	−2.01614
$336$	−6.02409	−0.328641
$337$	−32.5227	−1.77163	−0.885813	−	0.464042i	$-0.846399\pi$
$337$	−32.5227	−1.77163	−0.885813	+	0.464042i	$0.846399\pi$
$338$	−20.4733	−1.11360
$339$	−6.33896	−0.344285
$340$	9.42320	0.511045
$341$	0.327466	0.0177333
$342$	9.66550	0.522650
$343$	20.1006	1.08533
$344$	1.74671	0.0941765
$345$	6.20925	0.334295
$346$	−30.7577	−1.65354
$347$	−17.1022	−0.918095	−0.459047	−	0.888412i	$-0.651809\pi$
$347$	−17.1022	−0.918095	−0.459047	+	0.888412i	$0.651809\pi$
$348$	−15.6001	−0.836252
$349$	−0.250699	−0.0134196	−0.00670981	−	0.999977i	$-0.502136\pi$
$349$	−0.250699	−0.0134196	−0.00670981	+	0.999977i	$0.502136\pi$
$350$	42.7782	2.28659
$351$	4.75632	0.253874
$352$	−1.44258	−0.0768897
$353$	−9.18244	−0.488732	−0.244366	−	0.969683i	$-0.578580\pi$
$353$	−9.18244	−0.488732	−0.244366	+	0.969683i	$0.578580\pi$
$354$	−30.8098	−1.63752
$355$	−2.57004	−0.136404
$356$	41.8230	2.21662
$357$	−2.25712	−0.119459
$358$	19.7122	1.04182
$359$	−2.88798	−0.152422	−0.0762110	−	0.997092i	$-0.524282\pi$
$359$	−2.88798	−0.152422	−0.0762110	+	0.997092i	$0.524282\pi$
$360$	4.17983	0.220296
$361$	1.63757	0.0861879
$362$	−38.3362	−2.01490
$363$	10.9668	0.575609
$364$	27.1265	1.42182
$365$	−11.5450	−0.604291
$366$	−16.2274	−0.848220
$367$	21.6166	1.12838	0.564188	−	0.825647i	$-0.309189\pi$
$367$	21.6166	1.12838	0.564188	+	0.825647i	$0.309189\pi$
$368$	−4.44371	−0.231644
$369$	1.99136	0.103666
$370$	21.4311	1.11415
$371$	−14.8991	−0.773521
$372$	4.54281	0.235534
$373$	−8.51664	−0.440975	−0.220487	−	0.975390i	$-0.570765\pi$
$373$	−8.51664	−0.440975	−0.220487	+	0.975390i	$0.570765\pi$
$374$	−0.387530	−0.0200387
$375$	14.5737	0.752582
$376$	−0.701739	−0.0361894
$377$	−29.3650	−1.51237
$378$	−4.80230	−0.247004
$379$	−35.3729	−1.81698	−0.908491	−	0.417903i	$-0.862765\pi$
$379$	−35.3729	−1.81698	−0.908491	+	0.417903i	$0.862765\pi$
$380$	42.8083	2.19602
$381$	5.72668	0.293387
$382$	40.8548	2.09031
$383$	7.62286	0.389510	0.194755	−	0.980852i	$-0.437609\pi$
$383$	7.62286	0.389510	0.194755	+	0.980852i	$0.437609\pi$
$384$	−8.65538	−0.441693
$385$	−1.53319	−0.0781384
$386$	−19.1346	−0.973928
$387$	−1.55845	−0.0792206
$388$	17.6130	0.894162
$389$	27.1633	1.37723	0.688617	−	0.725125i	$-0.258218\pi$
$389$	27.1633	1.37723	0.688617	+	0.725125i	$0.258218\pi$
$390$	37.7395	1.91101
$391$	−1.66498	−0.0842016
$392$	2.13559	0.107864
$393$	19.6202	0.989707
$394$	22.6433	1.14075
$395$	3.72932	0.187643
$396$	−0.460234	−0.0231276
$397$	−8.09989	−0.406522	−0.203261	−	0.979125i	$-0.565154\pi$
$397$	−8.09989	−0.406522	−0.203261	+	0.979125i	$0.565154\pi$
$398$	−12.7515	−0.639175
$399$	−10.2538	−0.513331
$400$	−23.7744	−1.18872
$401$	−3.17292	−0.158448	−0.0792240	−	0.996857i	$-0.525244\pi$
$401$	−3.17292	−0.158448	−0.0792240	+	0.996857i	$0.525244\pi$
$402$	21.0527	1.05001
$403$	8.55121	0.425966
$404$	−5.08639	−0.253057
$405$	−3.72932	−0.185312
$406$	29.6488	1.47145
$407$	−0.491959	−0.0243855
$408$	−1.12080	−0.0554879
$409$	6.80410	0.336441	0.168221	−	0.985749i	$-0.446198\pi$
$409$	6.80410	0.336441	0.168221	+	0.985749i	$0.446198\pi$
$410$	15.8007	0.780340
$411$	−5.31788	−0.262312
$412$	30.7079	1.51287
$413$	32.6850	1.60832
$414$	−3.54245	−0.174102
$415$	−63.1141	−3.09815
$416$	−37.6704	−1.84694
$417$	18.2682	0.894600
$418$	−1.76049	−0.0861085
$419$	−5.89967	−0.288218	−0.144109	−	0.989562i	$-0.546032\pi$
$419$	−5.89967	−0.288218	−0.144109	+	0.989562i	$0.546032\pi$
$420$	−21.2693	−1.03783
$421$	23.0223	1.12204	0.561020	−	0.827802i	$-0.310409\pi$
$421$	23.0223	1.12204	0.561020	+	0.827802i	$0.310409\pi$
$422$	−2.31246	−0.112569
$423$	0.626105	0.0304423
$424$	−7.39832	−0.359294
$425$	−8.90786	−0.432095
$426$	1.46624	0.0710396
$427$	17.2151	0.833095
$428$	30.0718	1.45358
$429$	−0.866326	−0.0418266
$430$	−12.3657	−0.596327
$431$	3.78225	0.182185	0.0910923	−	0.995842i	$-0.470964\pi$
$431$	3.78225	0.182185	0.0910923	+	0.995842i	$0.470964\pi$
$432$	2.66893	0.128409
$433$	−7.39834	−0.355542	−0.177771	−	0.984072i	$-0.556889\pi$
$433$	−7.39834	−0.355542	−0.177771	+	0.984072i	$0.556889\pi$
$434$	−8.63388	−0.414439
$435$	23.0244	1.10394
$436$	−5.15313	−0.246790
$437$	−7.56376	−0.361824
$438$	6.58654	0.314717
$439$	2.29646	0.109604	0.0548020	−	0.998497i	$-0.482547\pi$
$439$	2.29646	0.109604	0.0548020	+	0.998497i	$0.482547\pi$
$440$	−0.761323	−0.0362946
$441$	−1.90541	−0.0907340
$442$	−10.1197	−0.481343
$443$	−13.9423	−0.662418	−0.331209	−	0.943557i	$-0.607456\pi$
$443$	−13.9423	−0.662418	−0.331209	+	0.943557i	$0.607456\pi$
$444$	−6.82476	−0.323889
$445$	−61.7273	−2.92616
$446$	46.7665	2.21446
$447$	−10.8744	−0.514341
$448$	25.9864	1.22774
$449$	28.9350	1.36553	0.682765	−	0.730638i	$-0.260777\pi$
$449$	28.9350	1.36553	0.682765	+	0.730638i	$0.260777\pi$
$450$	−18.9526	−0.893433
$451$	−0.362711	−0.0170794
$452$	16.0172	0.753385
$453$	−23.7251	−1.11470
$454$	−58.9788	−2.76801
$455$	−40.0365	−1.87694
$456$	−5.09164	−0.238438
$457$	−20.2621	−0.947822	−0.473911	−	0.880573i	$-0.657158\pi$
$457$	−20.2621	−0.947822	−0.473911	+	0.880573i	$0.657158\pi$
$458$	10.4636	0.488931
$459$	1.00000	0.0466760
$460$	−15.6894	−0.731523
$461$	−28.3988	−1.32266	−0.661331	−	0.750094i	$-0.730008\pi$
$461$	−28.3988	−1.32266	−0.661331	+	0.750094i	$0.730008\pi$
$462$	0.874701	0.0406948
$463$	35.2258	1.63708	0.818541	−	0.574449i	$-0.194783\pi$
$463$	35.2258	1.63708	0.818541	+	0.574449i	$0.194783\pi$
$464$	−16.4776	−0.764955
$465$	−6.70481	−0.310928
$466$	49.5108	2.29355
$467$	−16.8396	−0.779245	−0.389622	−	0.920975i	$-0.627394\pi$
$467$	−16.8396	−0.779245	−0.389622	+	0.920975i	$0.627394\pi$
$468$	−12.0182	−0.555542
$469$	−22.3340	−1.03129
$470$	4.96790	0.229152
$471$	0.748926	0.0345087
$472$	16.2301	0.747053
$473$	0.283860	0.0130519
$474$	−2.12762	−0.0977250
$475$	−40.4672	−1.85676
$476$	5.70325	0.261408
$477$	6.60092	0.302235
$478$	−28.9934	−1.32613
$479$	−6.12111	−0.279681	−0.139840	−	0.990174i	$-0.544659\pi$
$479$	−6.12111	−0.279681	−0.139840	+	0.990174i	$0.544659\pi$
$480$	29.5365	1.34815
$481$	−12.8467	−0.585757
$482$	−36.6480	−1.66927
$483$	3.75805	0.170997
$484$	−27.7108	−1.25958
$485$	−25.9953	−1.18038
$486$	2.12762	0.0965110
$487$	−8.41162	−0.381167	−0.190583	−	0.981671i	$-0.561038\pi$
$487$	−8.41162	−0.381167	−0.190583	+	0.981671i	$0.561038\pi$
$488$	8.54835	0.386966
$489$	3.02035	0.136585
$490$	−15.1187	−0.682993
$491$	−26.4626	−1.19424	−0.597120	−	0.802152i	$-0.703688\pi$
$491$	−26.4626	−1.19424	−0.597120	+	0.802152i	$0.703688\pi$
$492$	−5.03175	−0.226849
$493$	−6.17388	−0.278058
$494$	−45.9722	−2.06839
$495$	0.679267	0.0305308
$496$	4.79837	0.215453
$497$	−1.55548	−0.0697729
$498$	36.0074	1.61353
$499$	23.2127	1.03914	0.519572	−	0.854427i	$-0.326092\pi$
$499$	23.2127	1.03914	0.519572	+	0.854427i	$0.326092\pi$
$500$	−36.8246	−1.64685
$501$	−20.8973	−0.933623
$502$	39.8891	1.78034
$503$	−38.8218	−1.73098	−0.865489	−	0.500927i	$-0.832992\pi$
$503$	−38.8218	−1.73098	−0.865489	+	0.500927i	$0.832992\pi$
$504$	2.52978	0.112685
$505$	7.50708	0.334061
$506$	0.645229	0.0286839
$507$	−9.62260	−0.427354
$508$	−14.4701	−0.642006
$509$	−34.6638	−1.53645	−0.768224	−	0.640181i	$-0.778859\pi$
$509$	−34.6638	−1.53645	−0.768224	+	0.640181i	$0.778859\pi$
$510$	7.93460	0.351350
$511$	−6.98742	−0.309105
$512$	−27.1208	−1.19858
$513$	4.54286	0.200572
$514$	48.9417	2.15873
$515$	−45.3223	−1.99714
$516$	3.93787	0.173355
$517$	−0.114040	−0.00501548
$518$	12.9708	0.569906
$519$	−14.4564	−0.634564
$520$	−19.8806	−0.871822
$521$	29.9613	1.31263	0.656315	−	0.754487i	$-0.272114\pi$
$521$	29.9613	1.31263	0.656315	+	0.754487i	$0.272114\pi$
$522$	−13.1357	−0.574934
$523$	9.53351	0.416871	0.208436	−	0.978036i	$-0.433163\pi$
$523$	9.53351	0.416871	0.208436	+	0.978036i	$0.433163\pi$
$524$	−49.5760	−2.16574
$525$	20.1061	0.877502
$526$	1.11139	0.0484589
$527$	1.79786	0.0783161
$528$	−0.486124	−0.0211558
$529$	−20.2278	−0.879472
$530$	52.3757	2.27505
$531$	−14.4808	−0.628415
$532$	25.9091	1.12330
$533$	−9.47157	−0.410259
$534$	35.2162	1.52395
$535$	−44.3835	−1.91887
$536$	−11.0902	−0.479025
$537$	9.26490	0.399810
$538$	10.6682	0.459941
$539$	0.347056	0.0149488
$540$	9.42320	0.405510
$541$	26.6029	1.14375	0.571875	−	0.820341i	$-0.306216\pi$
$541$	26.6029	1.14375	0.571875	+	0.820341i	$0.306216\pi$
$542$	27.4537	1.17924
$543$	−18.0183	−0.773239
$544$	−7.92008	−0.339570
$545$	7.60560	0.325788
$546$	22.8413	0.977517
$547$	30.8411	1.31867	0.659336	−	0.751849i	$-0.270838\pi$
$547$	30.8411	1.31867	0.659336	+	0.751849i	$0.270838\pi$
$548$	13.4371	0.574006
$549$	−7.62701	−0.325513
$550$	3.45206	0.147196
$551$	−28.0471	−1.19485
$552$	1.86611	0.0794269
$553$	2.25712	0.0959825
$554$	25.7647	1.09464
$555$	10.0728	0.427565
$556$	−46.1599	−1.95762
$557$	32.8329	1.39117	0.695587	−	0.718442i	$-0.255145\pi$
$557$	32.8329	1.39117	0.695587	+	0.718442i	$0.255145\pi$
$558$	3.82518	0.161933
$559$	7.41250	0.313515
$560$	−22.4658	−0.949352
$561$	−0.182142	−0.00769004
$562$	30.1921	1.27358
$563$	−13.9980	−0.589944	−0.294972	−	0.955506i	$-0.595310\pi$
$563$	−13.9980	−0.589944	−0.294972	+	0.955506i	$0.595310\pi$
$564$	−1.58203	−0.0666156
$565$	−23.6400	−0.994544
$566$	1.74407	0.0733087
$567$	−2.25712	−0.0947901
$568$	−0.772393	−0.0324089
$569$	13.0472	0.546967	0.273483	−	0.961877i	$-0.411824\pi$
$569$	13.0472	0.546967	0.273483	+	0.961877i	$0.411824\pi$
$570$	36.0458	1.50979
$571$	1.26230	0.0528258	0.0264129	−	0.999651i	$-0.491592\pi$
$571$	1.26230	0.0528258	0.0264129	+	0.999651i	$0.491592\pi$
$572$	2.18902	0.0915275
$573$	19.2021	0.802178
$574$	9.56313	0.399157
$575$	14.8314	0.618512
$576$	−11.5131	−0.479712
$577$	15.6296	0.650667	0.325333	−	0.945599i	$-0.394523\pi$
$577$	15.6296	0.650667	0.325333	+	0.945599i	$0.394523\pi$
$578$	−2.12762	−0.0884975
$579$	−8.99343	−0.373754
$580$	−58.1777	−2.41570
$581$	−38.1989	−1.58476
$582$	14.8306	0.614748
$583$	−1.20231	−0.0497944
$584$	−3.46969	−0.143577
$585$	17.7379	0.733371
$586$	54.7597	2.26210
$587$	−2.02711	−0.0836677	−0.0418338	−	0.999125i	$-0.513320\pi$
$587$	−2.02711	−0.0836677	−0.0418338	+	0.999125i	$0.513320\pi$
$588$	4.81457	0.198550
$589$	8.16744	0.336533
$590$	−114.900	−4.73035
$591$	10.6425	0.437774
$592$	−7.20868	−0.296275
$593$	21.1716	0.869414	0.434707	−	0.900572i	$-0.356852\pi$
$593$	21.1716	0.869414	0.434707	+	0.900572i	$0.356852\pi$
$594$	−0.387530	−0.0159005
$595$	−8.41753	−0.345085
$596$	27.4772	1.12551
$597$	−5.99330	−0.245290
$598$	16.8490	0.689008
$599$	−28.2538	−1.15442	−0.577210	−	0.816596i	$-0.695859\pi$
$599$	−28.2538	−1.15442	−0.577210	+	0.816596i	$0.695859\pi$
$600$	9.98394	0.407593
$601$	−10.6462	−0.434266	−0.217133	−	0.976142i	$-0.569670\pi$
$601$	−10.6462	−0.434266	−0.217133	+	0.976142i	$0.569670\pi$
$602$	−7.48416	−0.305032
$603$	9.89492	0.402952
$604$	59.9482	2.43926
$605$	40.8988	1.66277
$606$	−4.28288	−0.173980
$607$	7.31608	0.296951	0.148475	−	0.988916i	$-0.452563\pi$
$607$	7.31608	0.296951	0.148475	+	0.988916i	$0.452563\pi$
$608$	−35.9798	−1.45917
$609$	13.9352	0.564682
$610$	−60.5173	−2.45027
$611$	−2.97796	−0.120475
$612$	−2.52678	−0.102139
$613$	−6.59292	−0.266285	−0.133143	−	0.991097i	$-0.542507\pi$
$613$	−6.59292	−0.266285	−0.133143	+	0.991097i	$0.542507\pi$
$614$	39.1136	1.57850
$615$	7.42644	0.299463
$616$	−0.460779	−0.0185653
$617$	−25.5166	−1.02726	−0.513629	−	0.858012i	$-0.671699\pi$
$617$	−25.5166	−1.02726	−0.513629	+	0.858012i	$0.671699\pi$
$618$	25.8569	1.04012
$619$	11.5906	0.465867	0.232933	−	0.972493i	$-0.425168\pi$
$619$	11.5906	0.465867	0.232933	+	0.972493i	$0.425168\pi$
$620$	16.9416	0.680392
$621$	−1.66498	−0.0668133
$622$	−56.7276	−2.27457
$623$	−37.3596	−1.49678
$624$	−12.6943	−0.508178
$625$	9.81071	0.392428
$626$	26.3322	1.05245
$627$	−0.827446	−0.0330450
$628$	−1.89237	−0.0755140
$629$	−2.70096	−0.107694
$630$	−17.9093	−0.713525
$631$	21.5417	0.857562	0.428781	−	0.903408i	$-0.358943\pi$
$631$	21.5417	0.857562	0.428781	+	0.903408i	$0.358943\pi$
$632$	1.12080	0.0445830
$633$	−1.08688	−0.0431994
$634$	−45.5213	−1.80788
$635$	21.3567	0.847513
$636$	−16.6791	−0.661370
$637$	9.06276	0.359080
$638$	2.39256	0.0947225
$639$	0.689145	0.0272621
$640$	−32.2787	−1.27593
$641$	12.0931	0.477648	0.238824	−	0.971063i	$-0.423238\pi$
$641$	12.0931	0.477648	0.238824	+	0.971063i	$0.423238\pi$
$642$	25.3213	0.999353
$643$	−14.2591	−0.562325	−0.281162	−	0.959660i	$-0.590720\pi$
$643$	−14.2591	−0.562325	−0.281162	+	0.959660i	$0.590720\pi$
$644$	−9.49580	−0.374187
$645$	−5.81198	−0.228846
$646$	−9.66550	−0.380284
$647$	10.9017	0.428590	0.214295	−	0.976769i	$-0.431255\pi$
$647$	10.9017	0.428590	0.214295	+	0.976769i	$0.431255\pi$
$648$	−1.12080	−0.0440292
$649$	2.63757	0.103534
$650$	90.1446	3.53576
$651$	−4.05799	−0.159045
$652$	−7.63178	−0.298884
$653$	17.8820	0.699777	0.349889	−	0.936791i	$-0.386219\pi$
$653$	17.8820	0.699777	0.349889	+	0.936791i	$0.386219\pi$
$654$	−4.33908	−0.169672
$655$	73.1700	2.85899
$656$	−5.31481	−0.207508
$657$	3.09573	0.120776
$658$	3.00675	0.117215
$659$	9.80753	0.382047	0.191024	−	0.981585i	$-0.438819\pi$
$659$	9.80753	0.382047	0.191024	+	0.981585i	$0.438819\pi$
$660$	−1.71636	−0.0668093
$661$	25.0154	0.972985	0.486492	−	0.873685i	$-0.338276\pi$
$661$	25.0154	0.972985	0.486492	+	0.873685i	$0.338276\pi$
$662$	−0.493565	−0.0191829
$663$	−4.75632	−0.184720
$664$	−18.9681	−0.736106
$665$	−38.2397	−1.48287
$666$	−5.74664	−0.222678
$667$	10.2794	0.398019
$668$	52.8030	2.04301
$669$	21.9806	0.849820
$670$	78.5123	3.03319
$671$	1.38920	0.0536294
$672$	17.8766	0.689603
$673$	−13.5473	−0.522211	−0.261106	−	0.965310i	$-0.584087\pi$
$673$	−13.5473	−0.522211	−0.261106	+	0.965310i	$0.584087\pi$
$674$	69.1962	2.66534
$675$	−8.90786	−0.342864
$676$	24.3142	0.935163
$677$	−24.1996	−0.930067	−0.465034	−	0.885293i	$-0.653958\pi$
$677$	−24.1996	−0.930067	−0.465034	+	0.885293i	$0.653958\pi$
$678$	13.4869	0.517962
$679$	−15.7332	−0.603787
$680$	−4.17983	−0.160289
$681$	−27.7205	−1.06225
$682$	−0.696725	−0.0266790
$683$	27.0438	1.03480	0.517400	−	0.855744i	$-0.326900\pi$
$683$	27.0438	1.03480	0.517400	+	0.855744i	$0.326900\pi$
$684$	−11.4788	−0.438904
$685$	−19.8321	−0.757746
$686$	−42.7665	−1.63283
$687$	4.91796	0.187632
$688$	4.15940	0.158576
$689$	−31.3961	−1.19610
$690$	−13.2109	−0.502932
$691$	14.4303	0.548956	0.274478	−	0.961593i	$-0.411495\pi$
$691$	14.4303	0.548956	0.274478	+	0.961593i	$0.411495\pi$
$692$	36.5281	1.38859
$693$	0.411116	0.0156170
$694$	36.3871	1.38123
$695$	68.1282	2.58425
$696$	6.91969	0.262290
$697$	−1.99136	−0.0754283
$698$	0.533393	0.0201892
$699$	23.2705	0.880170
$700$	−50.8038	−1.92020
$701$	7.38879	0.279071	0.139535	−	0.990217i	$-0.455439\pi$
$701$	7.38879	0.279071	0.139535	+	0.990217i	$0.455439\pi$
$702$	−10.1197	−0.381942
$703$	−12.2701	−0.462776
$704$	2.09702	0.0790343
$705$	2.33495	0.0879393
$706$	19.5368	0.735277
$707$	4.54355	0.170878
$708$	36.5900	1.37514
$709$	−11.5939	−0.435418	−0.217709	−	0.976014i	$-0.569858\pi$
$709$	−11.5939	−0.435418	−0.217709	+	0.976014i	$0.569858\pi$
$710$	5.46809	0.205214
$711$	−1.00000	−0.0375029
$712$	−18.5514	−0.695241
$713$	−2.99340	−0.112104
$714$	4.80230	0.179722
$715$	−3.23081	−0.120825
$716$	−23.4104	−0.874888
$717$	−13.6271	−0.508915
$718$	6.14454	0.229312
$719$	−38.9174	−1.45137	−0.725687	−	0.688025i	$-0.758478\pi$
$719$	−38.9174	−1.45137	−0.725687	+	0.688025i	$0.758478\pi$
$720$	9.95330	0.370938
$721$	−27.4307	−1.02157
$722$	−3.48413	−0.129666
$723$	−17.2249	−0.640599
$724$	45.5283	1.69205
$725$	54.9961	2.04250
$726$	−23.3333	−0.865979
$727$	33.6087	1.24648	0.623238	−	0.782032i	$-0.285817\pi$
$727$	33.6087	1.24648	0.623238	+	0.782032i	$0.285817\pi$
$728$	−12.0324	−0.445952
$729$	1.00000	0.0370370
$730$	24.5634	0.909130
$731$	1.55845	0.0576414
$732$	19.2718	0.712307
$733$	−39.8624	−1.47235	−0.736176	−	0.676790i	$-0.763371\pi$
$733$	−39.8624	−1.47235	−0.736176	+	0.676790i	$0.763371\pi$
$734$	−45.9919	−1.69759
$735$	−7.10591	−0.262105
$736$	13.1868	0.486070
$737$	−1.80228	−0.0663879
$738$	−4.23687	−0.155961
$739$	−30.4187	−1.11897	−0.559484	−	0.828841i	$-0.689001\pi$
$739$	−30.4187	−1.11897	−0.559484	+	0.828841i	$0.689001\pi$
$740$	−25.4517	−0.935624
$741$	−21.6073	−0.793764
$742$	31.6996	1.16373
$743$	−37.4856	−1.37521	−0.687606	−	0.726084i	$-0.741338\pi$
$743$	−37.4856	−1.37521	−0.687606	+	0.726084i	$0.741338\pi$
$744$	−2.01505	−0.0738751
$745$	−40.5541	−1.48579
$746$	18.1202	0.663428
$747$	16.9237	0.619207
$748$	0.460234	0.0168278
$749$	−26.8625	−0.981533
$750$	−31.0073	−1.13223
$751$	−3.02995	−0.110564	−0.0552822	−	0.998471i	$-0.517606\pi$
$751$	−3.02995	−0.110564	−0.0552822	+	0.998471i	$0.517606\pi$
$752$	−1.67103	−0.0609362
$753$	18.7482	0.683222
$754$	62.4776	2.27530
$755$	−88.4786	−3.22007
$756$	5.70325	0.207425
$757$	−31.2631	−1.13628	−0.568139	−	0.822932i	$-0.692337\pi$
$757$	−31.2631	−1.13628	−0.568139	+	0.822932i	$0.692337\pi$
$758$	75.2602	2.73357
$759$	0.303263	0.0110077
$760$	−18.9884	−0.688781
$761$	32.8544	1.19097	0.595486	−	0.803366i	$-0.296959\pi$
$761$	32.8544	1.19097	0.595486	+	0.803366i	$0.296959\pi$
$762$	−12.1842	−0.441388
$763$	4.60318	0.166646
$764$	−48.5195	−1.75537
$765$	3.72932	0.134834
$766$	−16.2186	−0.586001
$767$	68.8756	2.48695
$768$	−4.61079	−0.166377
$769$	−27.0566	−0.975687	−0.487844	−	0.872931i	$-0.662216\pi$
$769$	−27.0566	−0.975687	−0.487844	+	0.872931i	$0.662216\pi$
$770$	3.26204	0.117556
$771$	23.0030	0.828432
$772$	22.7245	0.817871
$773$	33.0909	1.19020	0.595099	−	0.803653i	$-0.297113\pi$
$773$	33.0909	1.19020	0.595099	+	0.803653i	$0.297113\pi$
$774$	3.31580	0.119184
$775$	−16.0151	−0.575280
$776$	−7.81254	−0.280454
$777$	6.09640	0.218707
$778$	−57.7933	−2.07199
$779$	−9.04648	−0.324124
$780$	−44.8198	−1.60481
$781$	−0.125522	−0.00449154
$782$	3.54245	0.126678
$783$	−6.17388	−0.220637
$784$	5.08541	0.181622
$785$	2.79299	0.0996860
$786$	−41.7444	−1.48897
$787$	−36.8791	−1.31460	−0.657299	−	0.753630i	$-0.728301\pi$
$787$	−36.8791	−1.31460	−0.657299	+	0.753630i	$0.728301\pi$
$788$	−26.8913	−0.957964
$789$	0.522362	0.0185966
$790$	−7.93460	−0.282300
$791$	−14.3078	−0.508726
$792$	0.204145	0.00725397
$793$	36.2765	1.28822
$794$	17.2335	0.611595
$795$	24.6170	0.873074
$796$	15.1438	0.536757
$797$	21.6518	0.766946	0.383473	−	0.923552i	$-0.374728\pi$
$797$	21.6518	0.766946	0.383473	+	0.923552i	$0.374728\pi$
$798$	21.8162	0.772284
$799$	−0.626105	−0.0221500
$800$	70.5510	2.49435
$801$	16.5519	0.584832
$802$	6.75078	0.238378
$803$	−0.563862	−0.0198983
$804$	−25.0023	−0.881765
$805$	14.0150	0.493964
$806$	−18.1938	−0.640848
$807$	5.01416	0.176507
$808$	2.25616	0.0793713
$809$	15.3399	0.539322	0.269661	−	0.962955i	$-0.413088\pi$
$809$	15.3399	0.539322	0.269661	+	0.962955i	$0.413088\pi$
$810$	7.93460	0.278793
$811$	12.0698	0.423827	0.211914	−	0.977288i	$-0.432030\pi$
$811$	12.0698	0.423827	0.211914	+	0.977288i	$0.432030\pi$
$812$	−35.2112	−1.23567
$813$	12.9034	0.452544
$814$	1.04670	0.0366870
$815$	11.2639	0.394556
$816$	−2.66893	−0.0934312
$817$	7.07983	0.247692
$818$	−14.4766	−0.506161
$819$	10.7356	0.375132
$820$	−18.7650	−0.655303
$821$	6.93533	0.242045	0.121022	−	0.992650i	$-0.461383\pi$
$821$	6.93533	0.242045	0.121022	+	0.992650i	$0.461383\pi$
$822$	11.3144	0.394637
$823$	−16.3347	−0.569392	−0.284696	−	0.958618i	$-0.591893\pi$
$823$	−16.3347	−0.569392	−0.284696	+	0.958618i	$0.591893\pi$
$824$	−13.6210	−0.474511
$825$	1.62250	0.0564881
$826$	−69.5414	−2.41965
$827$	14.0195	0.487507	0.243753	−	0.969837i	$-0.421621\pi$
$827$	14.0195	0.487507	0.243753	+	0.969837i	$0.421621\pi$
$828$	4.20704	0.146205
$829$	−16.7859	−0.582998	−0.291499	−	0.956571i	$-0.594154\pi$
$829$	−16.7859	−0.582998	−0.291499	+	0.956571i	$0.594154\pi$
$830$	134.283	4.66103
$831$	12.1096	0.420077
$832$	54.7600	1.89846
$833$	1.90541	0.0660187
$834$	−38.8680	−1.34589
$835$	−77.9329	−2.69698
$836$	2.09078	0.0723110
$837$	1.79786	0.0621432
$838$	12.5523	0.433611
$839$	−37.4165	−1.29176	−0.645881	−	0.763438i	$-0.723510\pi$
$839$	−37.4165	−1.29176	−0.645881	+	0.763438i	$0.723510\pi$
$840$	9.43437	0.325517
$841$	9.11681	0.314373
$842$	−48.9829	−1.68806
$843$	14.1905	0.488748
$844$	2.74630	0.0945316
$845$	−35.8858	−1.23451
$846$	−1.33212	−0.0457991
$847$	24.7534	0.850538
$848$	−17.6174	−0.604983
$849$	0.819726	0.0281329
$850$	18.9526	0.650068
$851$	4.49705	0.154157
$852$	−1.74132	−0.0596566
$853$	25.2376	0.864118	0.432059	−	0.901845i	$-0.357787\pi$
$853$	25.2376	0.864118	0.432059	+	0.901845i	$0.357787\pi$
$854$	−36.6272	−1.25336
$855$	16.9418	0.579397
$856$	−13.3389	−0.455914
$857$	28.9914	0.990327	0.495164	−	0.868800i	$-0.335108\pi$
$857$	28.9914	0.990327	0.495164	+	0.868800i	$0.335108\pi$
$858$	1.84322	0.0629264
$859$	−31.6500	−1.07988	−0.539942	−	0.841702i	$-0.681554\pi$
$859$	−31.6500	−1.07988	−0.539942	+	0.841702i	$0.681554\pi$
$860$	14.6856	0.500775
$861$	4.49474	0.153180
$862$	−8.04721	−0.274089
$863$	20.1947	0.687435	0.343717	−	0.939073i	$-0.388314\pi$
$863$	20.1947	0.687435	0.343717	+	0.939073i	$0.388314\pi$
$864$	−7.92008	−0.269446
$865$	−53.9124	−1.83308
$866$	15.7409	0.534897
$867$	−1.00000	−0.0339618
$868$	10.2537	0.348032
$869$	0.182142	0.00617875
$870$	−48.9873	−1.66082
$871$	−47.0634	−1.59468
$872$	2.28576	0.0774057
$873$	6.97050	0.235916
$874$	16.0928	0.544349
$875$	32.8946	1.11204
$876$	−7.82223	−0.264289
$877$	41.9456	1.41640	0.708201	−	0.706011i	$-0.249507\pi$
$877$	41.9456	1.41640	0.708201	+	0.706011i	$0.249507\pi$
$878$	−4.88600	−0.164895
$879$	25.7375	0.868103
$880$	−1.81291	−0.0611133
$881$	45.5012	1.53297	0.766487	−	0.642260i	$-0.222003\pi$
$881$	45.5012	1.53297	0.766487	+	0.642260i	$0.222003\pi$
$882$	4.05401	0.136505
$883$	36.2899	1.22125	0.610626	−	0.791919i	$-0.290918\pi$
$883$	36.2899	1.22125	0.610626	+	0.791919i	$0.290918\pi$
$884$	12.0182	0.404216
$885$	−54.0038	−1.81532
$886$	29.6639	0.996579
$887$	7.82597	0.262770	0.131385	−	0.991331i	$-0.458058\pi$
$887$	7.82597	0.262770	0.131385	+	0.991331i	$0.458058\pi$
$888$	3.02724	0.101588
$889$	12.9258	0.433517
$890$	131.333	4.40228
$891$	−0.182142	−0.00610199
$892$	−55.5403	−1.85963
$893$	−2.84431	−0.0951812
$894$	23.1366	0.773804
$895$	34.5518	1.15494
$896$	−19.5362	−0.652659
$897$	7.91917	0.264413
$898$	−61.5629	−2.05438
$899$	−11.0998	−0.370199
$900$	22.5083	0.750275
$901$	−6.60092	−0.219909
$902$	0.771713	0.0256952
$903$	−3.51761	−0.117059
$904$	−7.10471	−0.236299
$905$	−67.1961	−2.23367
$906$	50.4781	1.67702
$907$	−42.8354	−1.42233	−0.711163	−	0.703027i	$-0.751831\pi$
$907$	−42.8354	−1.42233	−0.711163	+	0.703027i	$0.751831\pi$
$908$	70.0437	2.32448
$909$	−2.01299	−0.0667666
$910$	85.1826	2.82378
$911$	40.6123	1.34555	0.672773	−	0.739849i	$-0.265103\pi$
$911$	40.6123	1.34555	0.672773	+	0.739849i	$0.265103\pi$
$912$	−12.1246	−0.401484
$913$	−3.08252	−0.102017
$914$	43.1102	1.42596
$915$	−28.4436	−0.940316
$916$	−12.4266	−0.410587
$917$	44.2851	1.46242
$918$	−2.12762	−0.0702221
$919$	−21.0212	−0.693426	−0.346713	−	0.937971i	$-0.612702\pi$
$919$	−21.0212	−0.693426	−0.346713	+	0.937971i	$0.612702\pi$
$920$	6.95932	0.229442
$921$	18.3837	0.605763
$922$	60.4219	1.98989
$923$	−3.27779	−0.107890
$924$	−1.03880	−0.0341741
$925$	24.0598	0.791082
$926$	−74.9473	−2.46292
$927$	12.1529	0.399155
$928$	48.8976	1.60514
$929$	42.4314	1.39213	0.696064	−	0.717980i	$-0.254933\pi$
$929$	42.4314	1.39213	0.696064	+	0.717980i	$0.254933\pi$
$930$	14.2653	0.467778
$931$	8.65603	0.283690
$932$	−58.7995	−1.92604
$933$	−26.6624	−0.872889
$934$	35.8284	1.17234
$935$	−0.679267	−0.0222144
$936$	5.33089	0.174246
$937$	37.4699	1.22409	0.612043	−	0.790824i	$-0.290348\pi$
$937$	37.4699	1.22409	0.612043	+	0.790824i	$0.290348\pi$
$938$	47.5184	1.55153
$939$	12.3763	0.403887
$940$	−5.89992	−0.192434
$941$	−0.826615	−0.0269469	−0.0134734	−	0.999909i	$-0.504289\pi$
$941$	−0.826615	−0.0269469	−0.0134734	+	0.999909i	$0.504289\pi$
$942$	−1.59343	−0.0519169
$943$	3.31558	0.107970
$944$	38.6483	1.25790
$945$	−8.41753	−0.273822
$946$	−0.603947	−0.0196360
$947$	13.2980	0.432126	0.216063	−	0.976379i	$-0.430678\pi$
$947$	13.2980	0.432126	0.216063	+	0.976379i	$0.430678\pi$
$948$	2.52678	0.0820662
$949$	−14.7243	−0.477970
$950$	86.0989	2.79342
$951$	−21.3954	−0.693792
$952$	−2.52978	−0.0819906
$953$	16.9821	0.550103	0.275051	−	0.961430i	$-0.411305\pi$
$953$	16.9821	0.550103	0.275051	+	0.961430i	$0.411305\pi$
$954$	−14.0443	−0.454700
$955$	71.6107	2.31727
$956$	34.4328	1.11364
$957$	1.12452	0.0363507
$958$	13.0234	0.420768
$959$	−12.0031	−0.387600
$960$	−42.9361	−1.38576
$961$	−27.7677	−0.895732
$962$	27.3329	0.881247
$963$	11.9012	0.383511
$964$	43.5235	1.40180
$965$	−33.5394	−1.07967
$966$	−7.99573	−0.257258
$967$	−22.7985	−0.733151	−0.366575	−	0.930388i	$-0.619470\pi$
$967$	−22.7985	−0.733151	−0.366575	+	0.930388i	$0.619470\pi$
$968$	12.2916	0.395068
$969$	−4.54286	−0.145938
$970$	55.3081	1.77584
$971$	−23.9106	−0.767327	−0.383664	−	0.923473i	$-0.625338\pi$
$971$	−23.9106	−0.767327	−0.383664	+	0.923473i	$0.625338\pi$
$972$	−2.52678	−0.0810467
$973$	41.2336	1.32189
$974$	17.8968	0.573449
$975$	42.3687	1.35688
$976$	20.3559	0.651578
$977$	−18.5686	−0.594062	−0.297031	−	0.954868i	$-0.595996\pi$
$977$	−18.5686	−0.594062	−0.297031	+	0.954868i	$0.595996\pi$
$978$	−6.42617	−0.205486
$979$	−3.01479	−0.0963532
$980$	17.9551	0.573555
$981$	−2.03940	−0.0651131
$982$	56.3025	1.79668
$983$	26.8111	0.855141	0.427570	−	0.903982i	$-0.359370\pi$
$983$	26.8111	0.855141	0.427570	+	0.903982i	$0.359370\pi$
$984$	2.23192	0.0711510
$985$	39.6894	1.26461
$986$	13.1357	0.418326
$987$	1.41319	0.0449825
$988$	54.5970	1.73696
$989$	−2.59479	−0.0825095
$990$	−1.44522	−0.0459323
$991$	40.5352	1.28764	0.643822	−	0.765175i	$-0.277348\pi$
$991$	40.5352	1.28764	0.643822	+	0.765175i	$0.277348\pi$
$992$	−14.2392	−0.452095
$993$	−0.231979	−0.00736164
$994$	3.30948	0.104970
$995$	−22.3510	−0.708573
$996$	−42.7626	−1.35499
$997$	−36.0671	−1.14226	−0.571128	−	0.820861i	$-0.693494\pi$
$997$	−36.0671	−1.14226	−0.571128	+	0.820861i	$0.693494\pi$
$998$	−49.3879	−1.56335
$999$	−2.70096	−0.0854547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.3	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12762 q^{2} -1.00000 q^{3} +2.52678 q^{4} -3.72932 q^{5} +2.12762 q^{6} -2.25712 q^{7} -1.12080 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.12762 q^{2} -1.00000 q^{3} +2.52678 q^{4} -3.72932 q^{5} +2.12762 q^{6} -2.25712 q^{7} -1.12080 q^{8} +1.00000 q^{9} +7.93460 q^{10} -0.182142 q^{11} -2.52678 q^{12} -4.75632 q^{13} +4.80230 q^{14} +3.72932 q^{15} -2.66893 q^{16} -1.00000 q^{17} -2.12762 q^{18} -4.54286 q^{19} -9.42320 q^{20} +2.25712 q^{21} +0.387530 q^{22} +1.66498 q^{23} +1.12080 q^{24} +8.90786 q^{25} +10.1197 q^{26} -1.00000 q^{27} -5.70325 q^{28} +6.17388 q^{29} -7.93460 q^{30} -1.79786 q^{31} +7.92008 q^{32} +0.182142 q^{33} +2.12762 q^{34} +8.41753 q^{35} +2.52678 q^{36} +2.70096 q^{37} +9.66550 q^{38} +4.75632 q^{39} +4.17983 q^{40} +1.99136 q^{41} -4.80230 q^{42} -1.55845 q^{43} -0.460234 q^{44} -3.72932 q^{45} -3.54245 q^{46} +0.626105 q^{47} +2.66893 q^{48} -1.90541 q^{49} -18.9526 q^{50} +1.00000 q^{51} -12.0182 q^{52} +6.60092 q^{53} +2.12762 q^{54} +0.679267 q^{55} +2.52978 q^{56} +4.54286 q^{57} -13.1357 q^{58} -14.4808 q^{59} +9.42320 q^{60} -7.62701 q^{61} +3.82518 q^{62} -2.25712 q^{63} -11.5131 q^{64} +17.7379 q^{65} -0.387530 q^{66} +9.89492 q^{67} -2.52678 q^{68} -1.66498 q^{69} -17.9093 q^{70} +0.689145 q^{71} -1.12080 q^{72} +3.09573 q^{73} -5.74664 q^{74} -8.90786 q^{75} -11.4788 q^{76} +0.411116 q^{77} -10.1197 q^{78} -1.00000 q^{79} +9.95330 q^{80} +1.00000 q^{81} -4.23687 q^{82} +16.9237 q^{83} +5.70325 q^{84} +3.72932 q^{85} +3.31580 q^{86} -6.17388 q^{87} +0.204145 q^{88} +16.5519 q^{89} +7.93460 q^{90} +10.7356 q^{91} +4.20704 q^{92} +1.79786 q^{93} -1.33212 q^{94} +16.9418 q^{95} -7.92008 q^{96} +6.97050 q^{97} +4.05401 q^{98} -0.182142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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