LMFDB - Embedded newform 4029.2.a.j.1.19

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:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+1.88836 q^{2} +1.00000 q^{3} +1.56590 q^{4} -1.95166 q^{5} +1.88836 q^{6} -1.51083 q^{7} -0.819741 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.88836 q^{2} +1.00000 q^{3} +1.56590 q^{4} -1.95166 q^{5} +1.88836 q^{6} -1.51083 q^{7} -0.819741 q^{8} +1.00000 q^{9} -3.68543 q^{10} +1.07251 q^{11} +1.56590 q^{12} +4.52580 q^{13} -2.85299 q^{14} -1.95166 q^{15} -4.67976 q^{16} -1.00000 q^{17} +1.88836 q^{18} +5.39886 q^{19} -3.05609 q^{20} -1.51083 q^{21} +2.02529 q^{22} +4.97123 q^{23} -0.819741 q^{24} -1.19104 q^{25} +8.54634 q^{26} +1.00000 q^{27} -2.36581 q^{28} -2.95308 q^{29} -3.68543 q^{30} -1.89548 q^{31} -7.19758 q^{32} +1.07251 q^{33} -1.88836 q^{34} +2.94863 q^{35} +1.56590 q^{36} +10.4146 q^{37} +10.1950 q^{38} +4.52580 q^{39} +1.59985 q^{40} +12.5327 q^{41} -2.85299 q^{42} +2.97048 q^{43} +1.67944 q^{44} -1.95166 q^{45} +9.38747 q^{46} -2.85747 q^{47} -4.67976 q^{48} -4.71738 q^{49} -2.24911 q^{50} -1.00000 q^{51} +7.08694 q^{52} +7.75147 q^{53} +1.88836 q^{54} -2.09317 q^{55} +1.23849 q^{56} +5.39886 q^{57} -5.57648 q^{58} +9.78104 q^{59} -3.05609 q^{60} -12.5428 q^{61} -3.57935 q^{62} -1.51083 q^{63} -4.23209 q^{64} -8.83281 q^{65} +2.02529 q^{66} +10.4348 q^{67} -1.56590 q^{68} +4.97123 q^{69} +5.56807 q^{70} +11.0022 q^{71} -0.819741 q^{72} +5.29045 q^{73} +19.6666 q^{74} -1.19104 q^{75} +8.45406 q^{76} -1.62039 q^{77} +8.54634 q^{78} -1.00000 q^{79} +9.13328 q^{80} +1.00000 q^{81} +23.6662 q^{82} -6.35570 q^{83} -2.36581 q^{84} +1.95166 q^{85} +5.60933 q^{86} -2.95308 q^{87} -0.879182 q^{88} +12.9757 q^{89} -3.68543 q^{90} -6.83773 q^{91} +7.78444 q^{92} -1.89548 q^{93} -5.39593 q^{94} -10.5367 q^{95} -7.19758 q^{96} +1.47249 q^{97} -8.90811 q^{98} +1.07251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.88836	1.33527	0.667635	−	0.744488i	$-0.267306\pi$
$2$	1.88836	1.33527	0.667635	+	0.744488i	$0.267306\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.56590	0.782949
$5$	−1.95166	−0.872807	−0.436404	−	0.899751i	$-0.643748\pi$
$5$	−1.95166	−0.872807	−0.436404	+	0.899751i	$0.643748\pi$
$6$	1.88836	0.770919
$7$	−1.51083	−0.571041	−0.285521	−	0.958373i	$-0.592167\pi$
$7$	−1.51083	−0.571041	−0.285521	+	0.958373i	$0.592167\pi$
$8$	−0.819741	−0.289822
$9$	1.00000	0.333333
$10$	−3.68543	−1.16543
$11$	1.07251	0.323374	0.161687	−	0.986842i	$-0.448306\pi$
$11$	1.07251	0.323374	0.161687	+	0.986842i	$0.448306\pi$
$12$	1.56590	0.452036
$13$	4.52580	1.25523	0.627616	−	0.778523i	$-0.284031\pi$
$13$	4.52580	1.25523	0.627616	+	0.778523i	$0.284031\pi$
$14$	−2.85299	−0.762495
$15$	−1.95166	−0.503915
$16$	−4.67976	−1.16994
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.88836	0.445090
$19$	5.39886	1.23858	0.619291	−	0.785161i	$-0.287420\pi$
$19$	5.39886	1.23858	0.619291	+	0.785161i	$0.287420\pi$
$20$	−3.05609	−0.683363
$21$	−1.51083	−0.329691
$22$	2.02529	0.431793
$23$	4.97123	1.03657	0.518287	−	0.855207i	$-0.326570\pi$
$23$	4.97123	1.03657	0.518287	+	0.855207i	$0.326570\pi$
$24$	−0.819741	−0.167329
$25$	−1.19104	−0.238208
$26$	8.54634	1.67607
$27$	1.00000	0.192450
$28$	−2.36581	−0.447096
$29$	−2.95308	−0.548374	−0.274187	−	0.961676i	$-0.588409\pi$
$29$	−2.95308	−0.548374	−0.274187	+	0.961676i	$0.588409\pi$
$30$	−3.68543	−0.672864
$31$	−1.89548	−0.340438	−0.170219	−	0.985406i	$-0.554448\pi$
$31$	−1.89548	−0.340438	−0.170219	+	0.985406i	$0.554448\pi$
$32$	−7.19758	−1.27236
$33$	1.07251	0.186700
$34$	−1.88836	−0.323851
$35$	2.94863	0.498409
$36$	1.56590	0.260983
$37$	10.4146	1.71216	0.856078	−	0.516847i	$-0.172894\pi$
$37$	10.4146	1.71216	0.856078	+	0.516847i	$0.172894\pi$
$38$	10.1950	1.65384
$39$	4.52580	0.724708
$40$	1.59985	0.252959
$41$	12.5327	1.95727	0.978637	−	0.205596i	$-0.0659132\pi$
$41$	12.5327	1.95727	0.978637	+	0.205596i	$0.0659132\pi$
$42$	−2.85299	−0.440227
$43$	2.97048	0.452994	0.226497	−	0.974012i	$-0.427273\pi$
$43$	2.97048	0.452994	0.226497	+	0.974012i	$0.427273\pi$
$44$	1.67944	0.253186
$45$	−1.95166	−0.290936
$46$	9.38747	1.38411
$47$	−2.85747	−0.416805	−0.208402	−	0.978043i	$-0.566826\pi$
$47$	−2.85747	−0.416805	−0.208402	+	0.978043i	$0.566826\pi$
$48$	−4.67976	−0.675465
$49$	−4.71738	−0.673912
$50$	−2.24911	−0.318072
$51$	−1.00000	−0.140028
$52$	7.08694	0.982782
$53$	7.75147	1.06475	0.532373	−	0.846510i	$-0.321300\pi$
$53$	7.75147	1.06475	0.532373	+	0.846510i	$0.321300\pi$
$54$	1.88836	0.256973
$55$	−2.09317	−0.282244
$56$	1.23849	0.165501
$57$	5.39886	0.715096
$58$	−5.57648	−0.732228
$59$	9.78104	1.27338	0.636691	−	0.771119i	$-0.280303\pi$
$59$	9.78104	1.27338	0.636691	+	0.771119i	$0.280303\pi$
$60$	−3.05609	−0.394540
$61$	−12.5428	−1.60594	−0.802970	−	0.596019i	$-0.796748\pi$
$61$	−12.5428	−1.60594	−0.802970	+	0.596019i	$0.796748\pi$
$62$	−3.57935	−0.454578
$63$	−1.51083	−0.190347
$64$	−4.23209	−0.529012
$65$	−8.83281	−1.09558
$66$	2.02529	0.249296
$67$	10.4348	1.27482	0.637409	−	0.770526i	$-0.280006\pi$
$67$	10.4348	1.27482	0.637409	+	0.770526i	$0.280006\pi$
$68$	−1.56590	−0.189893
$69$	4.97123	0.598466
$70$	5.56807	0.665511
$71$	11.0022	1.30572	0.652862	−	0.757476i	$-0.273568\pi$
$71$	11.0022	1.30572	0.652862	+	0.757476i	$0.273568\pi$
$72$	−0.819741	−0.0966075
$73$	5.29045	0.619200	0.309600	−	0.950867i	$-0.399805\pi$
$73$	5.29045	0.619200	0.309600	+	0.950867i	$0.399805\pi$
$74$	19.6666	2.28619
$75$	−1.19104	−0.137529
$76$	8.45406	0.969747
$77$	−1.62039	−0.184660
$78$	8.54634	0.967682
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	9.13328	1.02113
$81$	1.00000	0.111111
$82$	23.6662	2.61349
$83$	−6.35570	−0.697629	−0.348815	−	0.937192i	$-0.613416\pi$
$83$	−6.35570	−0.697629	−0.348815	+	0.937192i	$0.613416\pi$
$84$	−2.36581	−0.258131
$85$	1.95166	0.211687
$86$	5.60933	0.604869
$87$	−2.95308	−0.316604
$88$	−0.879182	−0.0937212
$89$	12.9757	1.37542	0.687710	−	0.725986i	$-0.258616\pi$
$89$	12.9757	1.37542	0.687710	+	0.725986i	$0.258616\pi$
$90$	−3.68543	−0.388478
$91$	−6.83773	−0.716789
$92$	7.78444	0.811584
$93$	−1.89548	−0.196552
$94$	−5.39593	−0.556547
$95$	−10.5367	−1.08104
$96$	−7.19758	−0.734600
$97$	1.47249	0.149509	0.0747544	−	0.997202i	$-0.476183\pi$
$97$	1.47249	0.149509	0.0747544	+	0.997202i	$0.476183\pi$
$98$	−8.90811	−0.899855
$99$	1.07251	0.107791
$100$	−1.86504	−0.186504
$101$	7.36162	0.732509	0.366254	−	0.930515i	$-0.380640\pi$
$101$	7.36162	0.732509	0.366254	+	0.930515i	$0.380640\pi$
$102$	−1.88836	−0.186975
$103$	−15.2728	−1.50487	−0.752437	−	0.658664i	$-0.771122\pi$
$103$	−15.2728	−1.50487	−0.752437	+	0.658664i	$0.771122\pi$
$104$	−3.70999	−0.363794
$105$	2.94863	0.287757
$106$	14.6376	1.42173
$107$	−11.0079	−1.06418	−0.532089	−	0.846689i	$-0.678593\pi$
$107$	−11.0079	−1.06418	−0.532089	+	0.846689i	$0.678593\pi$
$108$	1.56590	0.150679
$109$	−5.86425	−0.561693	−0.280846	−	0.959753i	$-0.590615\pi$
$109$	−5.86425	−0.561693	−0.280846	+	0.959753i	$0.590615\pi$
$110$	−3.95266	−0.376872
$111$	10.4146	0.988514
$112$	7.07034	0.668084
$113$	−9.58210	−0.901409	−0.450704	−	0.892673i	$-0.648827\pi$
$113$	−9.58210	−0.901409	−0.450704	+	0.892673i	$0.648827\pi$
$114$	10.1950	0.954847
$115$	−9.70214	−0.904729
$116$	−4.62423	−0.429349
$117$	4.52580	0.418411
$118$	18.4701	1.70031
$119$	1.51083	0.138498
$120$	1.59985	0.146046
$121$	−9.84972	−0.895429
$122$	−23.6853	−2.14437
$123$	12.5327	1.13003
$124$	−2.96813	−0.266546
$125$	12.0828	1.08072
$126$	−2.85299	−0.254165
$127$	11.1583	0.990140	0.495070	−	0.868853i	$-0.335142\pi$
$127$	11.1583	0.990140	0.495070	+	0.868853i	$0.335142\pi$
$128$	6.40346	0.565991
$129$	2.97048	0.261536
$130$	−16.6795	−1.46289
$131$	0.818267	0.0714923	0.0357462	−	0.999361i	$-0.488619\pi$
$131$	0.818267	0.0714923	0.0357462	+	0.999361i	$0.488619\pi$
$132$	1.67944	0.146177
$133$	−8.15677	−0.707282
$134$	19.7047	1.70223
$135$	−1.95166	−0.167972
$136$	0.819741	0.0702923
$137$	18.9672	1.62048	0.810238	−	0.586101i	$-0.199338\pi$
$137$	18.9672	1.62048	0.810238	+	0.586101i	$0.199338\pi$
$138$	9.38747	0.799115
$139$	5.44662	0.461976	0.230988	−	0.972957i	$-0.425804\pi$
$139$	5.44662	0.461976	0.230988	+	0.972957i	$0.425804\pi$
$140$	4.61725	0.390229
$141$	−2.85747	−0.240642
$142$	20.7762	1.74350
$143$	4.85398	0.405910
$144$	−4.67976	−0.389980
$145$	5.76341	0.478625
$146$	9.99026	0.826800
$147$	−4.71738	−0.389083
$148$	16.3083	1.34053
$149$	0.968805	0.0793676	0.0396838	−	0.999212i	$-0.487365\pi$
$149$	0.968805	0.0793676	0.0396838	+	0.999212i	$0.487365\pi$
$150$	−2.24911	−0.183639
$151$	4.34450	0.353550	0.176775	−	0.984251i	$-0.443433\pi$
$151$	4.34450	0.353550	0.176775	+	0.984251i	$0.443433\pi$
$152$	−4.42567	−0.358969
$153$	−1.00000	−0.0808452
$154$	−3.05987	−0.246571
$155$	3.69933	0.297137
$156$	7.08694	0.567409
$157$	−4.19604	−0.334880	−0.167440	−	0.985882i	$-0.553550\pi$
$157$	−4.19604	−0.334880	−0.167440	+	0.985882i	$0.553550\pi$
$158$	−1.88836	−0.150230
$159$	7.75147	0.614732
$160$	14.0472	1.11053
$161$	−7.51071	−0.591927
$162$	1.88836	0.148363
$163$	−13.7882	−1.07997	−0.539987	−	0.841673i	$-0.681571\pi$
$163$	−13.7882	−1.07997	−0.539987	+	0.841673i	$0.681571\pi$
$164$	19.6249	1.53244
$165$	−2.09317	−0.162953
$166$	−12.0018	−0.931524
$167$	2.31499	0.179139	0.0895697	−	0.995981i	$-0.471451\pi$
$167$	2.31499	0.179139	0.0895697	+	0.995981i	$0.471451\pi$
$168$	1.23849	0.0955518
$169$	7.48288	0.575606
$170$	3.68543	0.282659
$171$	5.39886	0.412861
$172$	4.65146	0.354671
$173$	−15.6510	−1.18993	−0.594963	−	0.803753i	$-0.702833\pi$
$173$	−15.6510	−1.18993	−0.594963	+	0.803753i	$0.702833\pi$
$174$	−5.57648	−0.422752
$175$	1.79946	0.136026
$176$	−5.01910	−0.378329
$177$	9.78104	0.735188
$178$	24.5027	1.83656
$179$	5.57963	0.417041	0.208520	−	0.978018i	$-0.433135\pi$
$179$	5.57963	0.417041	0.208520	+	0.978018i	$0.433135\pi$
$180$	−3.05609	−0.227788
$181$	7.32439	0.544417	0.272209	−	0.962238i	$-0.412246\pi$
$181$	7.32439	0.544417	0.272209	+	0.962238i	$0.412246\pi$
$182$	−12.9121	−0.957108
$183$	−12.5428	−0.927190
$184$	−4.07513	−0.300422
$185$	−20.3258	−1.49438
$186$	−3.57935	−0.262451
$187$	−1.07251	−0.0784298
$188$	−4.47450	−0.326337
$189$	−1.51083	−0.109897
$190$	−19.8971	−1.44349
$191$	−6.53762	−0.473045	−0.236523	−	0.971626i	$-0.576008\pi$
$191$	−6.53762	−0.473045	−0.236523	+	0.971626i	$0.576008\pi$
$192$	−4.23209	−0.305425
$193$	−0.946454	−0.0681273	−0.0340636	−	0.999420i	$-0.510845\pi$
$193$	−0.946454	−0.0681273	−0.0340636	+	0.999420i	$0.510845\pi$
$194$	2.78059	0.199635
$195$	−8.83281	−0.632531
$196$	−7.38694	−0.527638
$197$	7.02011	0.500162	0.250081	−	0.968225i	$-0.419543\pi$
$197$	7.02011	0.500162	0.250081	+	0.968225i	$0.419543\pi$
$198$	2.02529	0.143931
$199$	−15.6580	−1.10996	−0.554982	−	0.831863i	$-0.687275\pi$
$199$	−15.6580	−1.10996	−0.554982	+	0.831863i	$0.687275\pi$
$200$	0.976343	0.0690379
$201$	10.4348	0.736016
$202$	13.9014	0.978098
$203$	4.46162	0.313144
$204$	−1.56590	−0.109635
$205$	−24.4595	−1.70832
$206$	−28.8405	−2.00942
$207$	4.97123	0.345525
$208$	−21.1797	−1.46855
$209$	5.79034	0.400526
$210$	5.56807	0.384233
$211$	−11.8240	−0.813998	−0.406999	−	0.913429i	$-0.633425\pi$
$211$	−11.8240	−0.813998	−0.406999	+	0.913429i	$0.633425\pi$
$212$	12.1380	0.833642
$213$	11.0022	0.753861
$214$	−20.7869	−1.42096
$215$	−5.79735	−0.395376
$216$	−0.819741	−0.0557763
$217$	2.86376	0.194404
$218$	−11.0738	−0.750012
$219$	5.29045	0.357495
$220$	−3.27770	−0.220982
$221$	−4.52580	−0.304438
$222$	19.6666	1.31993
$223$	−8.90987	−0.596649	−0.298325	−	0.954464i	$-0.596428\pi$
$223$	−8.90987	−0.596649	−0.298325	+	0.954464i	$0.596428\pi$
$224$	10.8743	0.726573
$225$	−1.19104	−0.0794025
$226$	−18.0944	−1.20362
$227$	8.30745	0.551385	0.275692	−	0.961246i	$-0.411093\pi$
$227$	8.30745	0.551385	0.275692	+	0.961246i	$0.411093\pi$
$228$	8.45406	0.559884
$229$	−0.295677	−0.0195389	−0.00976944	−	0.999952i	$-0.503110\pi$
$229$	−0.295677	−0.0195389	−0.00976944	+	0.999952i	$0.503110\pi$
$230$	−18.3211	−1.20806
$231$	−1.62039	−0.106614
$232$	2.42077	0.158931
$233$	−0.0123872	−0.000811511 0	−0.000405756	−	1.00000i	$-0.500129\pi$
$233$	−0.0123872	−0.000811511 0	−0.000405756		1.00000i	$0.500129\pi$
$234$	8.54634	0.558691
$235$	5.57680	0.363790
$236$	15.3161	0.996993
$237$	−1.00000	−0.0649570
$238$	2.85299	0.184932
$239$	−17.4337	−1.12769	−0.563846	−	0.825880i	$-0.690679\pi$
$239$	−17.4337	−1.12769	−0.563846	+	0.825880i	$0.690679\pi$
$240$	9.13328	0.589551
$241$	2.67127	0.172071	0.0860357	−	0.996292i	$-0.472580\pi$
$241$	2.67127	0.172071	0.0860357	+	0.996292i	$0.472580\pi$
$242$	−18.5998	−1.19564
$243$	1.00000	0.0641500
$244$	−19.6407	−1.25737
$245$	9.20671	0.588195
$246$	23.6662	1.50890
$247$	24.4342	1.55471
$248$	1.55380	0.0986667
$249$	−6.35570	−0.402776
$250$	22.8166	1.44305
$251$	−18.6030	−1.17421	−0.587106	−	0.809510i	$-0.699733\pi$
$251$	−18.6030	−1.17421	−0.587106	+	0.809510i	$0.699733\pi$
$252$	−2.36581	−0.149032
$253$	5.33171	0.335202
$254$	21.0709	1.32210
$255$	1.95166	0.122217
$256$	20.5562	1.28476
$257$	16.7273	1.04342	0.521711	−	0.853122i	$-0.325294\pi$
$257$	16.7273	1.04342	0.521711	+	0.853122i	$0.325294\pi$
$258$	5.60933	0.349221
$259$	−15.7348	−0.977712
$260$	−13.8313	−0.857779
$261$	−2.95308	−0.182791
$262$	1.54518	0.0954616
$263$	9.85976	0.607979	0.303990	−	0.952675i	$-0.401681\pi$
$263$	9.85976	0.607979	0.303990	+	0.952675i	$0.401681\pi$
$264$	−0.879182	−0.0541099
$265$	−15.1282	−0.929319
$266$	−15.4029	−0.944413
$267$	12.9757	0.794099
$268$	16.3399	0.998117
$269$	−27.4181	−1.67171	−0.835856	−	0.548949i	$-0.815028\pi$
$269$	−27.4181	−1.67171	−0.835856	+	0.548949i	$0.815028\pi$
$270$	−3.68543	−0.224288
$271$	20.7431	1.26005	0.630027	−	0.776573i	$-0.283044\pi$
$271$	20.7431	1.26005	0.630027	+	0.776573i	$0.283044\pi$
$272$	4.67976	0.283752
$273$	−6.83773	−0.413838
$274$	35.8168	2.16377
$275$	−1.27740	−0.0770302
$276$	7.78444	0.468568
$277$	−13.9262	−0.836744	−0.418372	−	0.908276i	$-0.637399\pi$
$277$	−13.9262	−0.836744	−0.418372	+	0.908276i	$0.637399\pi$
$278$	10.2852	0.616863
$279$	−1.89548	−0.113479
$280$	−2.41711	−0.144450
$281$	9.90914	0.591130	0.295565	−	0.955323i	$-0.404492\pi$
$281$	9.90914	0.591130	0.295565	+	0.955323i	$0.404492\pi$
$282$	−5.39593	−0.321323
$283$	−10.3306	−0.614093	−0.307047	−	0.951694i	$-0.599341\pi$
$283$	−10.3306	−0.614093	−0.307047	+	0.951694i	$0.599341\pi$
$284$	17.2284	1.02232
$285$	−10.5367	−0.624141
$286$	9.16605	0.542000
$287$	−18.9348	−1.11768
$288$	−7.19758	−0.424122
$289$	1.00000	0.0588235
$290$	10.8834	0.639094
$291$	1.47249	0.0863189
$292$	8.28430	0.484802
$293$	−2.34651	−0.137085	−0.0685424	−	0.997648i	$-0.521835\pi$
$293$	−2.34651	−0.137085	−0.0685424	+	0.997648i	$0.521835\pi$
$294$	−8.90811	−0.519531
$295$	−19.0892	−1.11142
$296$	−8.53731	−0.496221
$297$	1.07251	0.0622334
$298$	1.82945	0.105977
$299$	22.4988	1.30114
$300$	−1.86504	−0.107678
$301$	−4.48790	−0.258678
$302$	8.20397	0.472085
$303$	7.36162	0.422914
$304$	−25.2654	−1.44907
$305$	24.4792	1.40168
$306$	−1.88836	−0.107950
$307$	22.2342	1.26897	0.634486	−	0.772934i	$-0.281212\pi$
$307$	22.2342	1.26897	0.634486	+	0.772934i	$0.281212\pi$
$308$	−2.53736	−0.144579
$309$	−15.2728	−0.868840
$310$	6.98566	0.396759
$311$	−7.09232	−0.402169	−0.201084	−	0.979574i	$-0.564447\pi$
$311$	−7.09232	−0.402169	−0.201084	+	0.979574i	$0.564447\pi$
$312$	−3.70999	−0.210037
$313$	−18.5004	−1.04570	−0.522852	−	0.852423i	$-0.675132\pi$
$313$	−18.5004	−1.04570	−0.522852	+	0.852423i	$0.675132\pi$
$314$	−7.92362	−0.447156
$315$	2.94863	0.166136
$316$	−1.56590	−0.0880886
$317$	−8.59214	−0.482583	−0.241291	−	0.970453i	$-0.577571\pi$
$317$	−8.59214	−0.482583	−0.241291	+	0.970453i	$0.577571\pi$
$318$	14.6376	0.820834
$319$	−3.16722	−0.177330
$320$	8.25959	0.461725
$321$	−11.0079	−0.614403
$322$	−14.1829	−0.790382
$323$	−5.39886	−0.300400
$324$	1.56590	0.0869943
$325$	−5.39040	−0.299006
$326$	−26.0370	−1.44206
$327$	−5.86425	−0.324294
$328$	−10.2735	−0.567262
$329$	4.31716	0.238013
$330$	−3.95266	−0.217587
$331$	−5.28351	−0.290408	−0.145204	−	0.989402i	$-0.546384\pi$
$331$	−5.28351	−0.290408	−0.145204	+	0.989402i	$0.546384\pi$
$332$	−9.95238	−0.546208
$333$	10.4146	0.570719
$334$	4.37154	0.239200
$335$	−20.3652	−1.11267
$336$	7.07034	0.385719
$337$	−25.7447	−1.40241	−0.701203	−	0.712962i	$-0.747353\pi$
$337$	−25.7447	−1.40241	−0.701203	+	0.712962i	$0.747353\pi$
$338$	14.1304	0.768591
$339$	−9.58210	−0.520428
$340$	3.05609	0.165740
$341$	−2.03293	−0.110089
$342$	10.1950	0.551281
$343$	17.7030	0.955873
$344$	−2.43502	−0.131288
$345$	−9.70214	−0.522346
$346$	−29.5548	−1.58887
$347$	−26.3439	−1.41422	−0.707108	−	0.707105i	$-0.750001\pi$
$347$	−26.3439	−1.41422	−0.707108	+	0.707105i	$0.750001\pi$
$348$	−4.62423	−0.247885
$349$	−5.88639	−0.315091	−0.157546	−	0.987512i	$-0.550358\pi$
$349$	−5.88639	−0.315091	−0.157546	+	0.987512i	$0.550358\pi$
$350$	3.39802	0.181632
$351$	4.52580	0.241569
$352$	−7.71949	−0.411450
$353$	14.8119	0.788359	0.394179	−	0.919033i	$-0.371029\pi$
$353$	14.8119	0.788359	0.394179	+	0.919033i	$0.371029\pi$
$354$	18.4701	0.981675
$355$	−21.4726	−1.13965
$356$	20.3186	1.07688
$357$	1.51083	0.0799618
$358$	10.5363	0.556863
$359$	25.4710	1.34431	0.672155	−	0.740411i	$-0.265369\pi$
$359$	25.4710	1.34431	0.672155	+	0.740411i	$0.265369\pi$
$360$	1.59985	0.0843197
$361$	10.1477	0.534088
$362$	13.8311	0.726945
$363$	−9.84972	−0.516976
$364$	−10.7072	−0.561209
$365$	−10.3251	−0.540442
$366$	−23.6853	−1.23805
$367$	−14.1368	−0.737936	−0.368968	−	0.929442i	$-0.620289\pi$
$367$	−14.1368	−0.737936	−0.368968	+	0.929442i	$0.620289\pi$
$368$	−23.2642	−1.21273
$369$	12.5327	0.652425
$370$	−38.3824	−1.99541
$371$	−11.7112	−0.608014
$372$	−2.96813	−0.153890
$373$	−3.88382	−0.201097	−0.100548	−	0.994932i	$-0.532060\pi$
$373$	−3.88382	−0.201097	−0.100548	+	0.994932i	$0.532060\pi$
$374$	−2.02529	−0.104725
$375$	12.0828	0.623952
$376$	2.34239	0.120799
$377$	−13.3651	−0.688336
$378$	−2.85299	−0.146742
$379$	−1.38921	−0.0713590	−0.0356795	−	0.999363i	$-0.511360\pi$
$379$	−1.38921	−0.0713590	−0.0356795	+	0.999363i	$0.511360\pi$
$380$	−16.4994	−0.846402
$381$	11.1583	0.571657
$382$	−12.3454	−0.631644
$383$	21.6836	1.10798	0.553989	−	0.832524i	$-0.313105\pi$
$383$	21.6836	1.10798	0.553989	+	0.832524i	$0.313105\pi$
$384$	6.40346	0.326775
$385$	3.16244	0.161173
$386$	−1.78724	−0.0909684
$387$	2.97048	0.150998
$388$	2.30577	0.117058
$389$	33.5606	1.70159	0.850796	−	0.525497i	$-0.176120\pi$
$389$	33.5606	1.70159	0.850796	+	0.525497i	$0.176120\pi$
$390$	−16.6795	−0.844600
$391$	−4.97123	−0.251406
$392$	3.86703	0.195315
$393$	0.818267	0.0412761
$394$	13.2565	0.667852
$395$	1.95166	0.0981985
$396$	1.67944	0.0843952
$397$	−10.6202	−0.533011	−0.266506	−	0.963833i	$-0.585869\pi$
$397$	−10.6202	−0.533011	−0.266506	+	0.963833i	$0.585869\pi$
$398$	−29.5678	−1.48210
$399$	−8.15677	−0.408349
$400$	5.57377	0.278689
$401$	−18.2130	−0.909514	−0.454757	−	0.890616i	$-0.650274\pi$
$401$	−18.2130	−0.909514	−0.454757	+	0.890616i	$0.650274\pi$
$402$	19.7047	0.982781
$403$	−8.57857	−0.427329
$404$	11.5275	0.573517
$405$	−1.95166	−0.0969786
$406$	8.42514	0.418132
$407$	11.1698	0.553668
$408$	0.819741	0.0405833
$409$	17.2278	0.851858	0.425929	−	0.904757i	$-0.359947\pi$
$409$	17.2278	0.851858	0.425929	+	0.904757i	$0.359947\pi$
$410$	−46.1882	−2.28107
$411$	18.9672	0.935582
$412$	−23.9157	−1.17824
$413$	−14.7775	−0.727154
$414$	9.38747	0.461369
$415$	12.4041	0.608896
$416$	−32.5748	−1.59711
$417$	5.44662	0.266722
$418$	10.9342	0.534811
$419$	−23.1063	−1.12882	−0.564408	−	0.825496i	$-0.690895\pi$
$419$	−23.1063	−1.12882	−0.564408	+	0.825496i	$0.690895\pi$
$420$	4.61725	0.225299
$421$	−30.5178	−1.48735	−0.743673	−	0.668544i	$-0.766918\pi$
$421$	−30.5178	−1.48735	−0.743673	+	0.668544i	$0.766918\pi$
$422$	−22.3280	−1.08691
$423$	−2.85747	−0.138935
$424$	−6.35420	−0.308587
$425$	1.19104	0.0577738
$426$	20.7762	1.00661
$427$	18.9501	0.917058
$428$	−17.2373	−0.833196
$429$	4.85398	0.234352
$430$	−10.9475	−0.527934
$431$	−11.8681	−0.571667	−0.285834	−	0.958279i	$-0.592270\pi$
$431$	−11.8681	−0.571667	−0.285834	+	0.958279i	$0.592270\pi$
$432$	−4.67976	−0.225155
$433$	−1.46188	−0.0702534	−0.0351267	−	0.999383i	$-0.511183\pi$
$433$	−1.46188	−0.0702534	−0.0351267	+	0.999383i	$0.511183\pi$
$434$	5.40780	0.259583
$435$	5.76341	0.276334
$436$	−9.18281	−0.439777
$437$	26.8390	1.28388
$438$	9.99026	0.477353
$439$	−14.5187	−0.692938	−0.346469	−	0.938062i	$-0.612619\pi$
$439$	−14.5187	−0.692938	−0.346469	+	0.938062i	$0.612619\pi$
$440$	1.71586	0.0818005
$441$	−4.71738	−0.224637
$442$	−8.54634	−0.406508
$443$	13.2027	0.627281	0.313641	−	0.949542i	$-0.398451\pi$
$443$	13.2027	0.627281	0.313641	+	0.949542i	$0.398451\pi$
$444$	16.3083	0.773955
$445$	−25.3241	−1.20048
$446$	−16.8250	−0.796688
$447$	0.968805	0.0458229
$448$	6.39399	0.302087
$449$	−15.1693	−0.715882	−0.357941	−	0.933744i	$-0.616521\pi$
$449$	−15.1693	−0.715882	−0.357941	+	0.933744i	$0.616521\pi$
$450$	−2.24911	−0.106024
$451$	13.4414	0.632932
$452$	−15.0046	−0.705757
$453$	4.34450	0.204122
$454$	15.6874	0.736248
$455$	13.3449	0.625619
$456$	−4.42567	−0.207251
$457$	−4.55222	−0.212944	−0.106472	−	0.994316i	$-0.533955\pi$
$457$	−4.55222	−0.212944	−0.106472	+	0.994316i	$0.533955\pi$
$458$	−0.558344	−0.0260897
$459$	−1.00000	−0.0466760
$460$	−15.1926	−0.708357
$461$	−28.1320	−1.31024	−0.655119	−	0.755526i	$-0.727381\pi$
$461$	−28.1320	−1.31024	−0.655119	+	0.755526i	$0.727381\pi$
$462$	−3.05987	−0.142358
$463$	−20.6342	−0.958954	−0.479477	−	0.877554i	$-0.659174\pi$
$463$	−20.6342	−0.958954	−0.479477	+	0.877554i	$0.659174\pi$
$464$	13.8197	0.641565
$465$	3.69933	0.171552
$466$	−0.0233914	−0.00108359
$467$	13.6019	0.629422	0.314711	−	0.949187i	$-0.398092\pi$
$467$	13.6019	0.629422	0.314711	+	0.949187i	$0.398092\pi$
$468$	7.08694	0.327594
$469$	−15.7653	−0.727973
$470$	10.5310	0.485759
$471$	−4.19604	−0.193343
$472$	−8.01792	−0.369055
$473$	3.18587	0.146487
$474$	−1.88836	−0.0867352
$475$	−6.43024	−0.295040
$476$	2.36581	0.108437
$477$	7.75147	0.354916
$478$	−32.9210	−1.50577
$479$	−34.0703	−1.55671	−0.778355	−	0.627824i	$-0.783946\pi$
$479$	−34.0703	−1.55671	−0.778355	+	0.627824i	$0.783946\pi$
$480$	14.0472	0.641164
$481$	47.1346	2.14915
$482$	5.04431	0.229762
$483$	−7.51071	−0.341749
$484$	−15.4236	−0.701075
$485$	−2.87380	−0.130492
$486$	1.88836	0.0856577
$487$	31.5645	1.43032	0.715162	−	0.698959i	$-0.246353\pi$
$487$	31.5645	1.43032	0.715162	+	0.698959i	$0.246353\pi$
$488$	10.2818	0.465437
$489$	−13.7882	−0.623524
$490$	17.3856	0.785400
$491$	13.7320	0.619718	0.309859	−	0.950783i	$-0.399718\pi$
$491$	13.7320	0.619718	0.309859	+	0.950783i	$0.399718\pi$
$492$	19.6249	0.884758
$493$	2.95308	0.133000
$494$	46.1405	2.07596
$495$	−2.09317	−0.0940812
$496$	8.87040	0.398293
$497$	−16.6225	−0.745623
$498$	−12.0018	−0.537816
$499$	5.01308	0.224416	0.112208	−	0.993685i	$-0.464208\pi$
$499$	5.01308	0.224416	0.112208	+	0.993685i	$0.464208\pi$
$500$	18.9204	0.846146
$501$	2.31499	0.103426
$502$	−35.1292	−1.56789
$503$	26.1584	1.16635	0.583173	−	0.812348i	$-0.301811\pi$
$503$	26.1584	1.16635	0.583173	+	0.812348i	$0.301811\pi$
$504$	1.23849	0.0551669
$505$	−14.3674	−0.639339
$506$	10.0682	0.447585
$507$	7.48288	0.332327
$508$	17.4728	0.775228
$509$	7.16425	0.317550	0.158775	−	0.987315i	$-0.449246\pi$
$509$	7.16425	0.317550	0.158775	+	0.987315i	$0.449246\pi$
$510$	3.68543	0.163193
$511$	−7.99299	−0.353589
$512$	26.0106	1.14952
$513$	5.39886	0.238365
$514$	31.5872	1.39325
$515$	29.8073	1.31347
$516$	4.65146	0.204769
$517$	−3.06467	−0.134784
$518$	−29.7129	−1.30551
$519$	−15.6510	−0.687004
$520$	7.24062	0.317522
$521$	44.4653	1.94806	0.974031	−	0.226417i	$-0.0727011\pi$
$521$	44.4653	1.94806	0.974031	+	0.226417i	$0.0727011\pi$
$522$	−5.57648	−0.244076
$523$	11.0477	0.483081	0.241541	−	0.970391i	$-0.422347\pi$
$523$	11.0477	0.483081	0.241541	+	0.970391i	$0.422347\pi$
$524$	1.28132	0.0559748
$525$	1.79946	0.0785348
$526$	18.6188	0.811817
$527$	1.89548	0.0825685
$528$	−5.01910	−0.218428
$529$	1.71317	0.0744858
$530$	−28.5675	−1.24089
$531$	9.78104	0.424461
$532$	−12.7727	−0.553766
$533$	56.7204	2.45683
$534$	24.5027	1.06034
$535$	21.4837	0.928821
$536$	−8.55386	−0.369471
$537$	5.57963	0.240779
$538$	−51.7752	−2.23219
$539$	−5.05945	−0.217926
$540$	−3.05609	−0.131513
$541$	22.2369	0.956041	0.478021	−	0.878349i	$-0.341354\pi$
$541$	22.2369	0.956041	0.478021	+	0.878349i	$0.341354\pi$
$542$	39.1704	1.68251
$543$	7.32439	0.314320
$544$	7.19758	0.308594
$545$	11.4450	0.490250
$546$	−12.9121	−0.552586
$547$	33.4054	1.42831	0.714157	−	0.699986i	$-0.246810\pi$
$547$	33.4054	1.42831	0.714157	+	0.699986i	$0.246810\pi$
$548$	29.7007	1.26875
$549$	−12.5428	−0.535313
$550$	−2.41219	−0.102856
$551$	−15.9433	−0.679207
$552$	−4.07513	−0.173449
$553$	1.51083	0.0642472
$554$	−26.2977	−1.11728
$555$	−20.3258	−0.862782
$556$	8.52884	0.361703
$557$	−33.4381	−1.41682	−0.708408	−	0.705803i	$-0.750586\pi$
$557$	−33.4381	−1.41682	−0.708408	+	0.705803i	$0.750586\pi$
$558$	−3.57935	−0.151526
$559$	13.4438	0.568612
$560$	−13.7989	−0.583109
$561$	−1.07251	−0.0452815
$562$	18.7120	0.789318
$563$	8.74285	0.368467	0.184234	−	0.982882i	$-0.441020\pi$
$563$	8.74285	0.368467	0.184234	+	0.982882i	$0.441020\pi$
$564$	−4.47450	−0.188411
$565$	18.7010	0.786756
$566$	−19.5080	−0.819981
$567$	−1.51083	−0.0634490
$568$	−9.01899	−0.378428
$569$	10.6819	0.447809	0.223905	−	0.974611i	$-0.428120\pi$
$569$	10.6819	0.447809	0.223905	+	0.974611i	$0.428120\pi$
$570$	−19.8971	−0.833398
$571$	30.6136	1.28114	0.640571	−	0.767899i	$-0.278698\pi$
$571$	30.6136	1.28114	0.640571	+	0.767899i	$0.278698\pi$
$572$	7.60083	0.317807
$573$	−6.53762	−0.273113
$574$	−35.7556	−1.49241
$575$	−5.92093	−0.246920
$576$	−4.23209	−0.176337
$577$	−5.67513	−0.236259	−0.118129	−	0.992998i	$-0.537690\pi$
$577$	−5.67513	−0.236259	−0.118129	+	0.992998i	$0.537690\pi$
$578$	1.88836	0.0785454
$579$	−0.946454	−0.0393333
$580$	9.02490	0.374739
$581$	9.60241	0.398375
$582$	2.78059	0.115259
$583$	8.31355	0.344312
$584$	−4.33680	−0.179458
$585$	−8.83281	−0.365192
$586$	−4.43106	−0.183045
$587$	−38.2209	−1.57755	−0.788773	−	0.614685i	$-0.789283\pi$
$587$	−38.2209	−1.57755	−0.788773	+	0.614685i	$0.789283\pi$
$588$	−7.38694	−0.304632
$589$	−10.2334	−0.421661
$590$	−36.0473	−1.48404
$591$	7.02011	0.288769
$592$	−48.7380	−2.00312
$593$	−26.1955	−1.07572	−0.537861	−	0.843034i	$-0.680767\pi$
$593$	−26.1955	−1.07572	−0.537861	+	0.843034i	$0.680767\pi$
$594$	2.02529	0.0830985
$595$	−2.94863	−0.120882
$596$	1.51705	0.0621408
$597$	−15.6580	−0.640838
$598$	42.4858	1.73738
$599$	−44.5079	−1.81854	−0.909272	−	0.416202i	$-0.863361\pi$
$599$	−44.5079	−1.81854	−0.909272	+	0.416202i	$0.863361\pi$
$600$	0.976343	0.0398590
$601$	22.0656	0.900074	0.450037	−	0.893010i	$-0.351411\pi$
$601$	22.0656	0.900074	0.450037	+	0.893010i	$0.351411\pi$
$602$	−8.47476	−0.345405
$603$	10.4348	0.424939
$604$	6.80303	0.276812
$605$	19.2233	0.781537
$606$	13.9014	0.564705
$607$	36.8452	1.49550	0.747751	−	0.663979i	$-0.231134\pi$
$607$	36.8452	1.49550	0.747751	+	0.663979i	$0.231134\pi$
$608$	−38.8587	−1.57593
$609$	4.46162	0.180794
$610$	46.2255	1.87162
$611$	−12.9323	−0.523187
$612$	−1.56590	−0.0632976
$613$	21.6718	0.875315	0.437657	−	0.899142i	$-0.355808\pi$
$613$	21.6718	0.875315	0.437657	+	0.899142i	$0.355808\pi$
$614$	41.9861	1.69442
$615$	−24.4595	−0.986301
$616$	1.32830	0.0535187
$617$	29.8079	1.20002	0.600011	−	0.799992i	$-0.295163\pi$
$617$	29.8079	1.20002	0.600011	+	0.799992i	$0.295163\pi$
$618$	−28.8405	−1.16014
$619$	−43.3182	−1.74111	−0.870553	−	0.492074i	$-0.836239\pi$
$619$	−43.3182	−1.74111	−0.870553	+	0.492074i	$0.836239\pi$
$620$	5.79277	0.232643
$621$	4.97123	0.199489
$622$	−13.3928	−0.537004
$623$	−19.6041	−0.785421
$624$	−21.1797	−0.847865
$625$	−17.6262	−0.705050
$626$	−34.9354	−1.39630
$627$	5.79034	0.231244
$628$	−6.57056	−0.262194
$629$	−10.4146	−0.415259
$630$	5.56807	0.221837
$631$	6.95584	0.276908	0.138454	−	0.990369i	$-0.455787\pi$
$631$	6.95584	0.276908	0.138454	+	0.990369i	$0.455787\pi$
$632$	0.819741	0.0326076
$633$	−11.8240	−0.469962
$634$	−16.2250	−0.644379
$635$	−21.7772	−0.864201
$636$	12.1380	0.481303
$637$	−21.3499	−0.845915
$638$	−5.98084	−0.236784
$639$	11.0022	0.435242
$640$	−12.4973	−0.494001
$641$	19.9951	0.789757	0.394879	−	0.918733i	$-0.370787\pi$
$641$	19.9951	0.789757	0.394879	+	0.918733i	$0.370787\pi$
$642$	−20.7869	−0.820394
$643$	21.4610	0.846338	0.423169	−	0.906051i	$-0.360918\pi$
$643$	21.4610	0.846338	0.423169	+	0.906051i	$0.360918\pi$
$644$	−11.7610	−0.463448
$645$	−5.79735	−0.228270
$646$	−10.1950	−0.401116
$647$	−4.36022	−0.171418	−0.0857089	−	0.996320i	$-0.527316\pi$
$647$	−4.36022	−0.171418	−0.0857089	+	0.996320i	$0.527316\pi$
$648$	−0.819741	−0.0322025
$649$	10.4903	0.411779
$650$	−10.1790	−0.399254
$651$	2.86376	0.112239
$652$	−21.5909	−0.845565
$653$	−17.5077	−0.685128	−0.342564	−	0.939495i	$-0.611295\pi$
$653$	−17.5077	−0.685128	−0.342564	+	0.939495i	$0.611295\pi$
$654$	−11.0738	−0.433020
$655$	−1.59698	−0.0623990
$656$	−58.6499	−2.28989
$657$	5.29045	0.206400
$658$	8.15235	0.317812
$659$	11.5531	0.450045	0.225023	−	0.974354i	$-0.427754\pi$
$659$	11.5531	0.450045	0.225023	+	0.974354i	$0.427754\pi$
$660$	−3.27770	−0.127584
$661$	−10.3827	−0.403841	−0.201921	−	0.979402i	$-0.564718\pi$
$661$	−10.3827	−0.403841	−0.201921	+	0.979402i	$0.564718\pi$
$662$	−9.97715	−0.387773
$663$	−4.52580	−0.175768
$664$	5.21003	0.202189
$665$	15.9192	0.617321
$666$	19.6666	0.762064
$667$	−14.6805	−0.568430
$668$	3.62504	0.140257
$669$	−8.90987	−0.344475
$670$	−38.4568	−1.48572
$671$	−13.4523	−0.519320
$672$	10.8743	0.419487
$673$	10.4099	0.401270	0.200635	−	0.979666i	$-0.435699\pi$
$673$	10.4099	0.401270	0.200635	+	0.979666i	$0.435699\pi$
$674$	−48.6153	−1.87259
$675$	−1.19104	−0.0458431
$676$	11.7174	0.450670
$677$	40.6998	1.56422	0.782110	−	0.623141i	$-0.214144\pi$
$677$	40.6998	1.56422	0.782110	+	0.623141i	$0.214144\pi$
$678$	−18.0944	−0.694913
$679$	−2.22469	−0.0853757
$680$	−1.59985	−0.0613516
$681$	8.30745	0.318342
$682$	−3.83889	−0.146999
$683$	2.48006	0.0948968	0.0474484	−	0.998874i	$-0.484891\pi$
$683$	2.48006	0.0948968	0.0474484	+	0.998874i	$0.484891\pi$
$684$	8.45406	0.323249
$685$	−37.0174	−1.41436
$686$	33.4296	1.27635
$687$	−0.295677	−0.0112808
$688$	−13.9011	−0.529975
$689$	35.0816	1.33650
$690$	−18.3211	−0.697473
$691$	−2.32762	−0.0885468	−0.0442734	−	0.999019i	$-0.514097\pi$
$691$	−2.32762	−0.0885468	−0.0442734	+	0.999019i	$0.514097\pi$
$692$	−24.5079	−0.931651
$693$	−1.62039	−0.0615534
$694$	−49.7468	−1.88836
$695$	−10.6299	−0.403216
$696$	2.42077	0.0917589
$697$	−12.5327	−0.474709
$698$	−11.1156	−0.420732
$699$	−0.0123872	−0.000468526 0
$700$	2.81777	0.106502
$701$	−14.2315	−0.537516	−0.268758	−	0.963208i	$-0.586613\pi$
$701$	−14.2315	−0.537516	−0.268758	+	0.963208i	$0.586613\pi$
$702$	8.54634	0.322561
$703$	56.2271	2.12065
$704$	−4.53897	−0.171069
$705$	5.57680	0.210034
$706$	27.9702	1.05267
$707$	−11.1222	−0.418293
$708$	15.3161	0.575614
$709$	7.64252	0.287021	0.143511	−	0.989649i	$-0.454161\pi$
$709$	7.64252	0.287021	0.143511	+	0.989649i	$0.454161\pi$
$710$	−40.5479	−1.52174
$711$	−1.00000	−0.0375029
$712$	−10.6367	−0.398627
$713$	−9.42288	−0.352890
$714$	2.85299	0.106771
$715$	−9.47329	−0.354281
$716$	8.73712	0.326522
$717$	−17.4337	−0.651073
$718$	48.0984	1.79502
$719$	−44.7537	−1.66903	−0.834515	−	0.550985i	$-0.814252\pi$
$719$	−44.7537	−1.66903	−0.834515	+	0.550985i	$0.814252\pi$
$720$	9.13328	0.340377
$721$	23.0747	0.859346
$722$	19.1624	0.713152
$723$	2.67127	0.0993455
$724$	11.4692	0.426251
$725$	3.51724	0.130627
$726$	−18.5998	−0.690303
$727$	−0.622986	−0.0231053	−0.0115526	−	0.999933i	$-0.503677\pi$
$727$	−0.622986	−0.0231053	−0.0115526	+	0.999933i	$0.503677\pi$
$728$	5.60517	0.207742
$729$	1.00000	0.0370370
$730$	−19.4976	−0.721637
$731$	−2.97048	−0.109867
$732$	−19.6407	−0.725942
$733$	5.38166	0.198776	0.0993882	−	0.995049i	$-0.468311\pi$
$733$	5.38166	0.198776	0.0993882	+	0.995049i	$0.468311\pi$
$734$	−26.6954	−0.985344
$735$	9.20671	0.339595
$736$	−35.7809	−1.31890
$737$	11.1915	0.412243
$738$	23.6662	0.871164
$739$	5.18703	0.190808	0.0954041	−	0.995439i	$-0.469586\pi$
$739$	5.18703	0.190808	0.0954041	+	0.995439i	$0.469586\pi$
$740$	−31.8281	−1.17002
$741$	24.4342	0.897611
$742$	−22.1149	−0.811864
$743$	32.5664	1.19475	0.597373	−	0.801963i	$-0.296211\pi$
$743$	32.5664	1.19475	0.597373	+	0.801963i	$0.296211\pi$
$744$	1.55380	0.0569652
$745$	−1.89077	−0.0692726
$746$	−7.33405	−0.268519
$747$	−6.35570	−0.232543
$748$	−1.67944	−0.0614065
$749$	16.6312	0.607689
$750$	22.8166	0.833145
$751$	3.72407	0.135893	0.0679467	−	0.997689i	$-0.478355\pi$
$751$	3.72407	0.135893	0.0679467	+	0.997689i	$0.478355\pi$
$752$	13.3723	0.487637
$753$	−18.6030	−0.677932
$754$	−25.2381	−0.919116
$755$	−8.47896	−0.308581
$756$	−2.36581	−0.0860437
$757$	−22.7720	−0.827663	−0.413831	−	0.910354i	$-0.635810\pi$
$757$	−22.7720	−0.827663	−0.413831	+	0.910354i	$0.635810\pi$
$758$	−2.62333	−0.0952836
$759$	5.33171	0.193529
$760$	8.63738	0.313311
$761$	44.8881	1.62719	0.813596	−	0.581430i	$-0.197507\pi$
$761$	44.8881	1.62719	0.813596	+	0.581430i	$0.197507\pi$
$762$	21.0709	0.763318
$763$	8.85990	0.320750
$764$	−10.2372	−0.370370
$765$	1.95166	0.0705623
$766$	40.9463	1.47945
$767$	44.2670	1.59839
$768$	20.5562	0.741758
$769$	31.4877	1.13547	0.567737	−	0.823210i	$-0.307819\pi$
$769$	31.4877	1.13547	0.567737	+	0.823210i	$0.307819\pi$
$770$	5.97182	0.215209
$771$	16.7273	0.602420
$772$	−1.48205	−0.0533401
$773$	35.5992	1.28041	0.640207	−	0.768203i	$-0.278849\pi$
$773$	35.5992	1.28041	0.640207	+	0.768203i	$0.278849\pi$
$774$	5.60933	0.201623
$775$	2.25759	0.0810950
$776$	−1.20706	−0.0433310
$777$	−15.7348	−0.564482
$778$	63.3745	2.27209
$779$	67.6621	2.42425
$780$	−13.8313	−0.495239
$781$	11.8000	0.422238
$782$	−9.38747	−0.335695
$783$	−2.95308	−0.105535
$784$	22.0762	0.788436
$785$	8.18922	0.292286
$786$	1.54518	0.0551148
$787$	27.2120	0.970003	0.485002	−	0.874513i	$-0.338819\pi$
$787$	27.2120	0.970003	0.485002	+	0.874513i	$0.338819\pi$
$788$	10.9928	0.391601
$789$	9.85976	0.351017
$790$	3.68543	0.131122
$791$	14.4770	0.514742
$792$	−0.879182	−0.0312404
$793$	−56.7662	−2.01583
$794$	−20.0547	−0.711715
$795$	−15.1282	−0.536542
$796$	−24.5188	−0.869044
$797$	−34.2806	−1.21428	−0.607140	−	0.794595i	$-0.707683\pi$
$797$	−34.2806	−1.21428	−0.607140	+	0.794595i	$0.707683\pi$
$798$	−15.4029	−0.545257
$799$	2.85747	0.101090
$800$	8.57259	0.303087
$801$	12.9757	0.458473
$802$	−34.3927	−1.21445
$803$	5.67407	0.200234
$804$	16.3399	0.576263
$805$	14.6583	0.516638
$806$	−16.1994	−0.570600
$807$	−27.4181	−0.965163
$808$	−6.03463	−0.212297
$809$	−18.2319	−0.640998	−0.320499	−	0.947249i	$-0.603851\pi$
$809$	−18.2319	−0.640998	−0.320499	+	0.947249i	$0.603851\pi$
$810$	−3.68543	−0.129493
$811$	−13.7870	−0.484127	−0.242063	−	0.970260i	$-0.577824\pi$
$811$	−13.7870	−0.484127	−0.242063	+	0.970260i	$0.577824\pi$
$812$	6.98644	0.245176
$813$	20.7431	0.727492
$814$	21.0926	0.739296
$815$	26.9098	0.942610
$816$	4.67976	0.163824
$817$	16.0372	0.561070
$818$	32.5322	1.13746
$819$	−6.83773	−0.238930
$820$	−38.3010	−1.33753
$821$	6.36199	0.222035	0.111018	−	0.993818i	$-0.464589\pi$
$821$	6.36199	0.222035	0.111018	+	0.993818i	$0.464589\pi$
$822$	35.8168	1.24926
$823$	−5.20720	−0.181512	−0.0907558	−	0.995873i	$-0.528928\pi$
$823$	−5.20720	−0.181512	−0.0907558	+	0.995873i	$0.528928\pi$
$824$	12.5198	0.436146
$825$	−1.27740	−0.0444734
$826$	−27.9052	−0.970948
$827$	31.7411	1.10375	0.551874	−	0.833928i	$-0.313913\pi$
$827$	31.7411	1.10375	0.551874	+	0.833928i	$0.313913\pi$
$828$	7.78444	0.270528
$829$	4.41354	0.153289	0.0766443	−	0.997059i	$-0.475579\pi$
$829$	4.41354	0.153289	0.0766443	+	0.997059i	$0.475579\pi$
$830$	23.4235	0.813041
$831$	−13.9262	−0.483095
$832$	−19.1536	−0.664032
$833$	4.71738	0.163448
$834$	10.2852	0.356146
$835$	−4.51807	−0.156354
$836$	9.06708	0.313591
$837$	−1.89548	−0.0655174
$838$	−43.6329	−1.50727
$839$	−25.9067	−0.894399	−0.447199	−	0.894434i	$-0.647579\pi$
$839$	−25.9067	−0.894399	−0.447199	+	0.894434i	$0.647579\pi$
$840$	−2.41711	−0.0833983
$841$	−20.2793	−0.699286
$842$	−57.6285	−1.98601
$843$	9.90914	0.341289
$844$	−18.5152	−0.637318
$845$	−14.6040	−0.502393
$846$	−5.39593	−0.185516
$847$	14.8813	0.511327
$848$	−36.2750	−1.24569
$849$	−10.3306	−0.354547
$850$	2.24911	0.0771437
$851$	51.7736	1.77478
$852$	17.2284	0.590234
$853$	−34.0954	−1.16740	−0.583702	−	0.811968i	$-0.698396\pi$
$853$	−34.0954	−1.16740	−0.583702	+	0.811968i	$0.698396\pi$
$854$	35.7845	1.22452
$855$	−10.5367	−0.360348
$856$	9.02366	0.308422
$857$	−16.1996	−0.553368	−0.276684	−	0.960961i	$-0.589236\pi$
$857$	−16.1996	−0.553368	−0.276684	+	0.960961i	$0.589236\pi$
$858$	9.16605	0.312924
$859$	−0.452070	−0.0154244	−0.00771221	−	0.999970i	$-0.502455\pi$
$859$	−0.452070	−0.0154244	−0.00771221	+	0.999970i	$0.502455\pi$
$860$	−9.07806	−0.309559
$861$	−18.9348	−0.645295
$862$	−22.4113	−0.763331
$863$	27.3979	0.932636	0.466318	−	0.884617i	$-0.345580\pi$
$863$	27.3979	0.932636	0.466318	+	0.884617i	$0.345580\pi$
$864$	−7.19758	−0.244867
$865$	30.5454	1.03858
$866$	−2.76055	−0.0938073
$867$	1.00000	0.0339618
$868$	4.48435	0.152209
$869$	−1.07251	−0.0363825
$870$	10.8834	0.368981
$871$	47.2260	1.60019
$872$	4.80717	0.162791
$873$	1.47249	0.0498363
$874$	50.6816	1.71433
$875$	−18.2551	−0.617134
$876$	8.28430	0.279901
$877$	−38.7737	−1.30929	−0.654647	−	0.755934i	$-0.727183\pi$
$877$	−38.7737	−1.30929	−0.654647	+	0.755934i	$0.727183\pi$
$878$	−27.4164	−0.925259
$879$	−2.34651	−0.0791460
$880$	9.79555	0.330208
$881$	−56.9516	−1.91875	−0.959374	−	0.282139i	$-0.908956\pi$
$881$	−56.9516	−1.91875	−0.959374	+	0.282139i	$0.908956\pi$
$882$	−8.90811	−0.299952
$883$	−29.7794	−1.00215	−0.501077	−	0.865402i	$-0.667063\pi$
$883$	−29.7794	−1.00215	−0.501077	+	0.865402i	$0.667063\pi$
$884$	−7.08694	−0.238360
$885$	−19.0892	−0.641677
$886$	24.9315	0.837590
$887$	24.0843	0.808672	0.404336	−	0.914611i	$-0.367503\pi$
$887$	24.0843	0.808672	0.404336	+	0.914611i	$0.367503\pi$
$888$	−8.53731	−0.286493
$889$	−16.8583	−0.565411
$890$	−47.8209	−1.60296
$891$	1.07251	0.0359305
$892$	−13.9519	−0.467146
$893$	−15.4271	−0.516247
$894$	1.82945	0.0611860
$895$	−10.8895	−0.363996
$896$	−9.67455	−0.323204
$897$	22.4988	0.751214
$898$	−28.6450	−0.955897
$899$	5.59752	0.186688
$900$	−1.86504	−0.0621681
$901$	−7.75147	−0.258239
$902$	25.3822	0.845136
$903$	−4.48790	−0.149348
$904$	7.85485	0.261248
$905$	−14.2947	−0.475171
$906$	8.20397	0.272559
$907$	−45.3458	−1.50568	−0.752841	−	0.658203i	$-0.771317\pi$
$907$	−45.3458	−1.50568	−0.752841	+	0.658203i	$0.771317\pi$
$908$	13.0086	0.431706
$909$	7.36162	0.244170
$910$	25.2000	0.835371
$911$	32.5863	1.07963	0.539817	−	0.841783i	$-0.318493\pi$
$911$	32.5863	1.07963	0.539817	+	0.841783i	$0.318493\pi$
$912$	−25.2654	−0.836620
$913$	−6.81657	−0.225595
$914$	−8.59622	−0.284338
$915$	24.4792	0.809258
$916$	−0.462999	−0.0152979
$917$	−1.23626	−0.0408251
$918$	−1.88836	−0.0623251
$919$	−40.3233	−1.33014	−0.665072	−	0.746780i	$-0.731599\pi$
$919$	−40.3233	−1.33014	−0.665072	+	0.746780i	$0.731599\pi$
$920$	7.95325	0.262211
$921$	22.2342	0.732641
$922$	−53.1233	−1.74952
$923$	49.7939	1.63899
$924$	−2.53736	−0.0834730
$925$	−12.4042	−0.407848
$926$	−38.9648	−1.28046
$927$	−15.2728	−0.501625
$928$	21.2551	0.697732
$929$	−1.88348	−0.0617948	−0.0308974	−	0.999523i	$-0.509837\pi$
$929$	−1.88348	−0.0617948	−0.0308974	+	0.999523i	$0.509837\pi$
$930$	6.98566	0.229069
$931$	−25.4685	−0.834696
$932$	−0.0193971	−0.000635372 0
$933$	−7.09232	−0.232192
$934$	25.6853	0.840450
$935$	2.09317	0.0684541
$936$	−3.70999	−0.121265
$937$	35.1465	1.14819	0.574093	−	0.818790i	$-0.305355\pi$
$937$	35.1465	1.14819	0.574093	+	0.818790i	$0.305355\pi$
$938$	−29.7705	−0.972042
$939$	−18.5004	−0.603738
$940$	8.73270	0.284829
$941$	28.5307	0.930073	0.465037	−	0.885291i	$-0.346041\pi$
$941$	28.5307	0.930073	0.465037	+	0.885291i	$0.346041\pi$
$942$	−7.92362	−0.258166
$943$	62.3028	2.02886
$944$	−45.7729	−1.48978
$945$	2.94863	0.0959189
$946$	6.01607	0.195599
$947$	−25.0335	−0.813479	−0.406740	−	0.913544i	$-0.633334\pi$
$947$	−25.0335	−0.813479	−0.406740	+	0.913544i	$0.633334\pi$
$948$	−1.56590	−0.0508580
$949$	23.9435	0.777240
$950$	−12.1426	−0.393958
$951$	−8.59214	−0.278619
$952$	−1.23849	−0.0401398
$953$	−32.0482	−1.03814	−0.519072	−	0.854730i	$-0.673722\pi$
$953$	−32.0482	−1.03814	−0.519072	+	0.854730i	$0.673722\pi$
$954$	14.6376	0.473908
$955$	12.7592	0.412877
$956$	−27.2994	−0.882924
$957$	−3.16722	−0.102382
$958$	−64.3369	−2.07863
$959$	−28.6563	−0.925359
$960$	8.25959	0.266577
$961$	−27.4072	−0.884102
$962$	89.0070	2.86970
$963$	−11.0079	−0.354726
$964$	4.18293	0.134723
$965$	1.84715	0.0594620
$966$	−14.1829	−0.456328
$967$	1.33206	0.0428363	0.0214182	−	0.999771i	$-0.493182\pi$
$967$	1.33206	0.0428363	0.0214182	+	0.999771i	$0.493182\pi$
$968$	8.07422	0.259515
$969$	−5.39886	−0.173436
$970$	−5.42676	−0.174243
$971$	39.3572	1.26303	0.631517	−	0.775362i	$-0.282433\pi$
$971$	39.3572	1.26303	0.631517	+	0.775362i	$0.282433\pi$
$972$	1.56590	0.0502262
$973$	−8.22893	−0.263807
$974$	59.6051	1.90987
$975$	−5.39040	−0.172631
$976$	58.6973	1.87885
$977$	39.2816	1.25673	0.628365	−	0.777919i	$-0.283724\pi$
$977$	39.2816	1.25673	0.628365	+	0.777919i	$0.283724\pi$
$978$	−26.0370	−0.832573
$979$	13.9166	0.444776
$980$	14.4168	0.460527
$981$	−5.86425	−0.187231
$982$	25.9310	0.827492
$983$	−10.8515	−0.346109	−0.173054	−	0.984912i	$-0.555364\pi$
$983$	−10.8515	−0.346109	−0.173054	+	0.984912i	$0.555364\pi$
$984$	−10.2735	−0.327509
$985$	−13.7008	−0.436545
$986$	5.57648	0.177591
$987$	4.31716	0.137417
$988$	38.2614	1.21726
$989$	14.7669	0.469561
$990$	−3.95266	−0.125624
$991$	31.3184	0.994861	0.497431	−	0.867504i	$-0.334277\pi$
$991$	31.3184	0.994861	0.497431	+	0.867504i	$0.334277\pi$
$992$	13.6429	0.433162
$993$	−5.28351	−0.167667
$994$	−31.3893	−0.995609
$995$	30.5590	0.968784
$996$	−9.95238	−0.315353
$997$	−30.0857	−0.952824	−0.476412	−	0.879222i	$-0.658063\pi$
$997$	−30.0857	−0.952824	−0.476412	+	0.879222i	$0.658063\pi$
$998$	9.46649	0.299657
$999$	10.4146	0.329505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.19	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.19	✓	25	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)

\(f(q)\)	\(=\)	\(q+1.88836 q^{2} +1.00000 q^{3} +1.56590 q^{4} -1.95166 q^{5} +1.88836 q^{6} -1.51083 q^{7} -0.819741 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.88836 q^{2} +1.00000 q^{3} +1.56590 q^{4} -1.95166 q^{5} +1.88836 q^{6} -1.51083 q^{7} -0.819741 q^{8} +1.00000 q^{9} -3.68543 q^{10} +1.07251 q^{11} +1.56590 q^{12} +4.52580 q^{13} -2.85299 q^{14} -1.95166 q^{15} -4.67976 q^{16} -1.00000 q^{17} +1.88836 q^{18} +5.39886 q^{19} -3.05609 q^{20} -1.51083 q^{21} +2.02529 q^{22} +4.97123 q^{23} -0.819741 q^{24} -1.19104 q^{25} +8.54634 q^{26} +1.00000 q^{27} -2.36581 q^{28} -2.95308 q^{29} -3.68543 q^{30} -1.89548 q^{31} -7.19758 q^{32} +1.07251 q^{33} -1.88836 q^{34} +2.94863 q^{35} +1.56590 q^{36} +10.4146 q^{37} +10.1950 q^{38} +4.52580 q^{39} +1.59985 q^{40} +12.5327 q^{41} -2.85299 q^{42} +2.97048 q^{43} +1.67944 q^{44} -1.95166 q^{45} +9.38747 q^{46} -2.85747 q^{47} -4.67976 q^{48} -4.71738 q^{49} -2.24911 q^{50} -1.00000 q^{51} +7.08694 q^{52} +7.75147 q^{53} +1.88836 q^{54} -2.09317 q^{55} +1.23849 q^{56} +5.39886 q^{57} -5.57648 q^{58} +9.78104 q^{59} -3.05609 q^{60} -12.5428 q^{61} -3.57935 q^{62} -1.51083 q^{63} -4.23209 q^{64} -8.83281 q^{65} +2.02529 q^{66} +10.4348 q^{67} -1.56590 q^{68} +4.97123 q^{69} +5.56807 q^{70} +11.0022 q^{71} -0.819741 q^{72} +5.29045 q^{73} +19.6666 q^{74} -1.19104 q^{75} +8.45406 q^{76} -1.62039 q^{77} +8.54634 q^{78} -1.00000 q^{79} +9.13328 q^{80} +1.00000 q^{81} +23.6662 q^{82} -6.35570 q^{83} -2.36581 q^{84} +1.95166 q^{85} +5.60933 q^{86} -2.95308 q^{87} -0.879182 q^{88} +12.9757 q^{89} -3.68543 q^{90} -6.83773 q^{91} +7.78444 q^{92} -1.89548 q^{93} -5.39593 q^{94} -10.5367 q^{95} -7.19758 q^{96} +1.47249 q^{97} -8.90811 q^{98} +1.07251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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