LMFDB - Embedded newform 4029.2.a.j.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:	$0$
Dimension:	$25$
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)

$f(q)$	$=$	$q-2.01628 q^{2} +1.00000 q^{3} +2.06539 q^{4} +1.36022 q^{5} -2.01628 q^{6} -1.99574 q^{7} -0.131838 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.01628 q^{2} +1.00000 q^{3} +2.06539 q^{4} +1.36022 q^{5} -2.01628 q^{6} -1.99574 q^{7} -0.131838 q^{8} +1.00000 q^{9} -2.74259 q^{10} -2.11525 q^{11} +2.06539 q^{12} +4.89250 q^{13} +4.02397 q^{14} +1.36022 q^{15} -3.86495 q^{16} -1.00000 q^{17} -2.01628 q^{18} -2.67917 q^{19} +2.80939 q^{20} -1.99574 q^{21} +4.26494 q^{22} +5.13474 q^{23} -0.131838 q^{24} -3.14979 q^{25} -9.86466 q^{26} +1.00000 q^{27} -4.12197 q^{28} -9.06051 q^{29} -2.74259 q^{30} +4.22586 q^{31} +8.05650 q^{32} -2.11525 q^{33} +2.01628 q^{34} -2.71465 q^{35} +2.06539 q^{36} +1.64221 q^{37} +5.40196 q^{38} +4.89250 q^{39} -0.179330 q^{40} +11.0669 q^{41} +4.02397 q^{42} +7.04686 q^{43} -4.36882 q^{44} +1.36022 q^{45} -10.3531 q^{46} +4.15449 q^{47} -3.86495 q^{48} -3.01703 q^{49} +6.35086 q^{50} -1.00000 q^{51} +10.1049 q^{52} -2.69333 q^{53} -2.01628 q^{54} -2.87722 q^{55} +0.263115 q^{56} -2.67917 q^{57} +18.2685 q^{58} -0.0245970 q^{59} +2.80939 q^{60} -4.07834 q^{61} -8.52053 q^{62} -1.99574 q^{63} -8.51427 q^{64} +6.65490 q^{65} +4.26494 q^{66} -3.81295 q^{67} -2.06539 q^{68} +5.13474 q^{69} +5.47350 q^{70} +4.93890 q^{71} -0.131838 q^{72} -1.38793 q^{73} -3.31115 q^{74} -3.14979 q^{75} -5.53353 q^{76} +4.22149 q^{77} -9.86466 q^{78} -1.00000 q^{79} -5.25720 q^{80} +1.00000 q^{81} -22.3140 q^{82} +3.80623 q^{83} -4.12197 q^{84} -1.36022 q^{85} -14.2084 q^{86} -9.06051 q^{87} +0.278872 q^{88} -8.06558 q^{89} -2.74259 q^{90} -9.76416 q^{91} +10.6052 q^{92} +4.22586 q^{93} -8.37662 q^{94} -3.64428 q^{95} +8.05650 q^{96} +13.8326 q^{97} +6.08317 q^{98} -2.11525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.01628	−1.42573	−0.712863	−	0.701304i	$-0.752602\pi$
$2$	−2.01628	−1.42573	−0.712863	+	0.701304i	$0.752602\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.06539	1.03269
$5$	1.36022	0.608311	0.304155	−	0.952622i	$-0.401626\pi$
$5$	1.36022	0.608311	0.304155	+	0.952622i	$0.401626\pi$
$6$	−2.01628	−0.823143
$7$	−1.99574	−0.754318	−0.377159	−	0.926148i	$-0.623099\pi$
$7$	−1.99574	−0.754318	−0.377159	+	0.926148i	$0.623099\pi$
$8$	−0.131838	−0.0466119
$9$	1.00000	0.333333
$10$	−2.74259	−0.867284
$11$	−2.11525	−0.637773	−0.318886	−	0.947793i	$-0.603309\pi$
$11$	−2.11525	−0.637773	−0.318886	+	0.947793i	$0.603309\pi$
$12$	2.06539	0.596226
$13$	4.89250	1.35694	0.678468	−	0.734630i	$-0.262644\pi$
$13$	4.89250	1.35694	0.678468	+	0.734630i	$0.262644\pi$
$14$	4.02397	1.07545
$15$	1.36022	0.351208
$16$	−3.86495	−0.966238
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.01628	−0.475242
$19$	−2.67917	−0.614644	−0.307322	−	0.951606i	$-0.599433\pi$
$19$	−2.67917	−0.614644	−0.307322	+	0.951606i	$0.599433\pi$
$20$	2.80939	0.628199
$21$	−1.99574	−0.435506
$22$	4.26494	0.909289
$23$	5.13474	1.07067	0.535334	−	0.844641i	$-0.320186\pi$
$23$	5.13474	1.07067	0.535334	+	0.844641i	$0.320186\pi$
$24$	−0.131838	−0.0269114
$25$	−3.14979	−0.629958
$26$	−9.86466	−1.93462
$27$	1.00000	0.192450
$28$	−4.12197	−0.778980
$29$	−9.06051	−1.68249	−0.841247	−	0.540651i	$-0.818178\pi$
$29$	−9.06051	−1.68249	−0.841247	+	0.540651i	$0.818178\pi$
$30$	−2.74259	−0.500727
$31$	4.22586	0.758988	0.379494	−	0.925194i	$-0.376098\pi$
$31$	4.22586	0.758988	0.379494	+	0.925194i	$0.376098\pi$
$32$	8.05650	1.42420
$33$	−2.11525	−0.368218
$34$	2.01628	0.345789
$35$	−2.71465	−0.458860
$36$	2.06539	0.344231
$37$	1.64221	0.269977	0.134988	−	0.990847i	$-0.456900\pi$
$37$	1.64221	0.269977	0.134988	+	0.990847i	$0.456900\pi$
$38$	5.40196	0.876314
$39$	4.89250	0.783427
$40$	−0.179330	−0.0283545
$41$	11.0669	1.72836	0.864182	−	0.503179i	$-0.167836\pi$
$41$	11.0669	1.72836	0.864182	+	0.503179i	$0.167836\pi$
$42$	4.02397	0.620912
$43$	7.04686	1.07464	0.537318	−	0.843380i	$-0.319437\pi$
$43$	7.04686	1.07464	0.537318	+	0.843380i	$0.319437\pi$
$44$	−4.36882	−0.658624
$45$	1.36022	0.202770
$46$	−10.3531	−1.52648
$47$	4.15449	0.605995	0.302997	−	0.952991i	$-0.402013\pi$
$47$	4.15449	0.605995	0.302997	+	0.952991i	$0.402013\pi$
$48$	−3.86495	−0.557858
$49$	−3.01703	−0.431004
$50$	6.35086	0.898147
$51$	−1.00000	−0.140028
$52$	10.1049	1.40130
$53$	−2.69333	−0.369957	−0.184978	−	0.982743i	$-0.559221\pi$
$53$	−2.69333	−0.369957	−0.184978	+	0.982743i	$0.559221\pi$
$54$	−2.01628	−0.274381
$55$	−2.87722	−0.387964
$56$	0.263115	0.0351602
$57$	−2.67917	−0.354865
$58$	18.2685	2.39877
$59$	−0.0245970	−0.00320226	−0.00160113	−	0.999999i	$-0.500510\pi$
$59$	−0.0245970	−0.00320226	−0.00160113	+	0.999999i	$0.500510\pi$
$60$	2.80939	0.362691
$61$	−4.07834	−0.522178	−0.261089	−	0.965315i	$-0.584082\pi$
$61$	−4.07834	−0.522178	−0.261089	+	0.965315i	$0.584082\pi$
$62$	−8.52053	−1.08211
$63$	−1.99574	−0.251439
$64$	−8.51427	−1.06428
$65$	6.65490	0.825439
$66$	4.26494	0.524978
$67$	−3.81295	−0.465826	−0.232913	−	0.972498i	$-0.574826\pi$
$67$	−3.81295	−0.465826	−0.232913	+	0.972498i	$0.574826\pi$
$68$	−2.06539	−0.250465
$69$	5.13474	0.618150
$70$	5.47350	0.654209
$71$	4.93890	0.586139	0.293070	−	0.956091i	$-0.405323\pi$
$71$	4.93890	0.586139	0.293070	+	0.956091i	$0.405323\pi$
$72$	−0.131838	−0.0155373
$73$	−1.38793	−0.162444	−0.0812222	−	0.996696i	$-0.525882\pi$
$73$	−1.38793	−0.162444	−0.0812222	+	0.996696i	$0.525882\pi$
$74$	−3.31115	−0.384913
$75$	−3.14979	−0.363706
$76$	−5.53353	−0.634739
$77$	4.22149	0.481084
$78$	−9.86466	−1.11695
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−5.25720	−0.587773
$81$	1.00000	0.111111
$82$	−22.3140	−2.46417
$83$	3.80623	0.417788	0.208894	−	0.977938i	$-0.433014\pi$
$83$	3.80623	0.417788	0.208894	+	0.977938i	$0.433014\pi$
$84$	−4.12197	−0.449744
$85$	−1.36022	−0.147537
$86$	−14.2084	−1.53214
$87$	−9.06051	−0.971388
$88$	0.278872	0.0297278
$89$	−8.06558	−0.854950	−0.427475	−	0.904027i	$-0.640597\pi$
$89$	−8.06558	−0.854950	−0.427475	+	0.904027i	$0.640597\pi$
$90$	−2.74259	−0.289095
$91$	−9.76416	−1.02356
$92$	10.6052	1.10567
$93$	4.22586	0.438202
$94$	−8.37662	−0.863982
$95$	−3.64428	−0.373895
$96$	8.05650	0.822263
$97$	13.8326	1.40449	0.702244	−	0.711936i	$-0.252181\pi$
$97$	13.8326	1.40449	0.702244	+	0.711936i	$0.252181\pi$
$98$	6.08317	0.614493
$99$	−2.11525	−0.212591
$100$	−6.50553	−0.650553
$101$	19.8799	1.97812	0.989062	−	0.147501i	$-0.0471231\pi$
$101$	19.8799	1.97812	0.989062	+	0.147501i	$0.0471231\pi$
$102$	2.01628	0.199642
$103$	13.4164	1.32196	0.660978	−	0.750405i	$-0.270142\pi$
$103$	13.4164	1.32196	0.660978	+	0.750405i	$0.270142\pi$
$104$	−0.645020	−0.0632494
$105$	−2.71465	−0.264923
$106$	5.43050	0.527457
$107$	14.3040	1.38282	0.691409	−	0.722464i	$-0.256990\pi$
$107$	14.3040	1.38282	0.691409	+	0.722464i	$0.256990\pi$
$108$	2.06539	0.198742
$109$	10.2005	0.977032	0.488516	−	0.872555i	$-0.337538\pi$
$109$	10.2005	0.977032	0.488516	+	0.872555i	$0.337538\pi$
$110$	5.80128	0.553130
$111$	1.64221	0.155871
$112$	7.71343	0.728851
$113$	3.95752	0.372292	0.186146	−	0.982522i	$-0.440400\pi$
$113$	3.95752	0.372292	0.186146	+	0.982522i	$0.440400\pi$
$114$	5.40196	0.505940
$115$	6.98440	0.651299
$116$	−18.7135	−1.73750
$117$	4.89250	0.452312
$118$	0.0495945	0.00456554
$119$	1.99574	0.182949
$120$	−0.179330	−0.0163705
$121$	−6.52570	−0.593246
$122$	8.22308	0.744483
$123$	11.0669	0.997872
$124$	8.72805	0.783802
$125$	−11.0855	−0.991521
$126$	4.02397	0.358484
$127$	−11.5138	−1.02168	−0.510840	−	0.859676i	$-0.670666\pi$
$127$	−11.5138	−1.02168	−0.510840	+	0.859676i	$0.670666\pi$
$128$	1.05414	0.0931740
$129$	7.04686	0.620441
$130$	−13.4181	−1.17685
$131$	1.71127	0.149515	0.0747573	−	0.997202i	$-0.476182\pi$
$131$	1.71127	0.149515	0.0747573	+	0.997202i	$0.476182\pi$
$132$	−4.36882	−0.380257
$133$	5.34693	0.463638
$134$	7.68798	0.664140
$135$	1.36022	0.117069
$136$	0.131838	0.0113051
$137$	17.4954	1.49474	0.747368	−	0.664411i	$-0.231317\pi$
$137$	17.4954	1.49474	0.747368	+	0.664411i	$0.231317\pi$
$138$	−10.3531	−0.881312
$139$	−3.84925	−0.326489	−0.163245	−	0.986586i	$-0.552196\pi$
$139$	−3.84925	−0.326489	−0.163245	+	0.986586i	$0.552196\pi$
$140$	−5.60681	−0.473862
$141$	4.15449	0.349871
$142$	−9.95820	−0.835674
$143$	−10.3489	−0.865417
$144$	−3.86495	−0.322079
$145$	−12.3243	−1.02348
$146$	2.79845	0.231601
$147$	−3.01703	−0.248840
$148$	3.39179	0.278803
$149$	5.52040	0.452248	0.226124	−	0.974098i	$-0.427394\pi$
$149$	5.52040	0.452248	0.226124	+	0.974098i	$0.427394\pi$
$150$	6.35086	0.518545
$151$	−4.63236	−0.376976	−0.188488	−	0.982075i	$-0.560359\pi$
$151$	−4.63236	−0.376976	−0.188488	+	0.982075i	$0.560359\pi$
$152$	0.353218	0.0286498
$153$	−1.00000	−0.0808452
$154$	−8.51171	−0.685893
$155$	5.74812	0.461700
$156$	10.1049	0.809040
$157$	−19.7688	−1.57773	−0.788863	−	0.614569i	$-0.789330\pi$
$157$	−19.7688	−1.57773	−0.788863	+	0.614569i	$0.789330\pi$
$158$	2.01628	0.160407
$159$	−2.69333	−0.213595
$160$	10.9587	0.866357
$161$	−10.2476	−0.807624
$162$	−2.01628	−0.158414
$163$	−6.31801	−0.494865	−0.247432	−	0.968905i	$-0.579587\pi$
$163$	−6.31801	−0.494865	−0.247432	+	0.968905i	$0.579587\pi$
$164$	22.8575	1.78487
$165$	−2.87722	−0.223991
$166$	−7.67442	−0.595651
$167$	20.6299	1.59639	0.798195	−	0.602399i	$-0.205788\pi$
$167$	20.6299	1.59639	0.798195	+	0.602399i	$0.205788\pi$
$168$	0.263115	0.0202998
$169$	10.9366	0.841275
$170$	2.74259	0.210347
$171$	−2.67917	−0.204881
$172$	14.5545	1.10977
$173$	18.2480	1.38737	0.693685	−	0.720279i	$-0.255986\pi$
$173$	18.2480	1.38737	0.693685	+	0.720279i	$0.255986\pi$
$174$	18.2685	1.38493
$175$	6.28616	0.475189
$176$	8.17535	0.616240
$177$	−0.0245970	−0.00184882
$178$	16.2625	1.21892
$179$	−15.3799	−1.14955	−0.574775	−	0.818312i	$-0.694910\pi$
$179$	−15.3799	−1.14955	−0.574775	+	0.818312i	$0.694910\pi$
$180$	2.80939	0.209400
$181$	−6.54506	−0.486491	−0.243245	−	0.969965i	$-0.578212\pi$
$181$	−6.54506	−0.486491	−0.243245	+	0.969965i	$0.578212\pi$
$182$	19.6873	1.45932
$183$	−4.07834	−0.301480
$184$	−0.676956	−0.0499059
$185$	2.23377	0.164230
$186$	−8.52053	−0.624755
$187$	2.11525	0.154683
$188$	8.58063	0.625807
$189$	−1.99574	−0.145169
$190$	7.34788	0.533072
$191$	−1.42399	−0.103036	−0.0515181	−	0.998672i	$-0.516406\pi$
$191$	−1.42399	−0.103036	−0.0515181	+	0.998672i	$0.516406\pi$
$192$	−8.51427	−0.614464
$193$	−18.2474	−1.31348	−0.656740	−	0.754117i	$-0.728065\pi$
$193$	−18.2474	−1.31348	−0.656740	+	0.754117i	$0.728065\pi$
$194$	−27.8904	−2.00242
$195$	6.65490	0.476567
$196$	−6.23132	−0.445095
$197$	13.3833	0.953519	0.476759	−	0.879034i	$-0.341811\pi$
$197$	13.3833	0.953519	0.476759	+	0.879034i	$0.341811\pi$
$198$	4.26494	0.303096
$199$	5.32026	0.377143	0.188572	−	0.982059i	$-0.439614\pi$
$199$	5.32026	0.377143	0.188572	+	0.982059i	$0.439614\pi$
$200$	0.415263	0.0293635
$201$	−3.81295	−0.268945
$202$	−40.0834	−2.82026
$203$	18.0824	1.26914
$204$	−2.06539	−0.144606
$205$	15.0535	1.05138
$206$	−27.0512	−1.88475
$207$	5.13474	0.356889
$208$	−18.9093	−1.31112
$209$	5.66713	0.392004
$210$	5.47350	0.377708
$211$	10.6987	0.736528	0.368264	−	0.929721i	$-0.379952\pi$
$211$	10.6987	0.736528	0.368264	+	0.929721i	$0.379952\pi$
$212$	−5.56276	−0.382052
$213$	4.93890	0.338408
$214$	−28.8408	−1.97152
$215$	9.58531	0.653713
$216$	−0.131838	−0.00897047
$217$	−8.43372	−0.572518
$218$	−20.5671	−1.39298
$219$	−1.38793	−0.0937873
$220$	−5.94257	−0.400648
$221$	−4.89250	−0.329105
$222$	−3.31115	−0.222230
$223$	12.4447	0.833356	0.416678	−	0.909054i	$-0.363194\pi$
$223$	12.4447	0.833356	0.416678	+	0.909054i	$0.363194\pi$
$224$	−16.0787	−1.07430
$225$	−3.14979	−0.209986
$226$	−7.97946	−0.530786
$227$	−22.2353	−1.47581	−0.737903	−	0.674907i	$-0.764184\pi$
$227$	−22.2353	−1.47581	−0.737903	+	0.674907i	$0.764184\pi$
$228$	−5.53353	−0.366467
$229$	1.01424	0.0670228	0.0335114	−	0.999438i	$-0.489331\pi$
$229$	1.01424	0.0670228	0.0335114	+	0.999438i	$0.489331\pi$
$230$	−14.0825	−0.928573
$231$	4.22149	0.277754
$232$	1.19452	0.0784243
$233$	8.77029	0.574561	0.287280	−	0.957847i	$-0.407249\pi$
$233$	8.77029	0.574561	0.287280	+	0.957847i	$0.407249\pi$
$234$	−9.86466	−0.644873
$235$	5.65104	0.368633
$236$	−0.0508024	−0.00330695
$237$	−1.00000	−0.0649570
$238$	−4.02397	−0.260835
$239$	6.10950	0.395191	0.197595	−	0.980284i	$-0.436687\pi$
$239$	6.10950	0.395191	0.197595	+	0.980284i	$0.436687\pi$
$240$	−5.25720	−0.339351
$241$	−17.2854	−1.11345	−0.556725	−	0.830697i	$-0.687942\pi$
$241$	−17.2854	−1.11345	−0.556725	+	0.830697i	$0.687942\pi$
$242$	13.1577	0.845806
$243$	1.00000	0.0641500
$244$	−8.42335	−0.539250
$245$	−4.10383	−0.262184
$246$	−22.3140	−1.42269
$247$	−13.1079	−0.834033
$248$	−0.557131	−0.0353779
$249$	3.80623	0.241210
$250$	22.3516	1.41364
$251$	15.4736	0.976683	0.488341	−	0.872653i	$-0.337602\pi$
$251$	15.4736	0.976683	0.488341	+	0.872653i	$0.337602\pi$
$252$	−4.12197	−0.259660
$253$	−10.8613	−0.682843
$254$	23.2150	1.45664
$255$	−1.36022	−0.0851806
$256$	14.9031	0.931443
$257$	−27.7017	−1.72798	−0.863992	−	0.503506i	$-0.832043\pi$
$257$	−27.7017	−1.72798	−0.863992	+	0.503506i	$0.832043\pi$
$258$	−14.2084	−0.884579
$259$	−3.27741	−0.203649
$260$	13.7449	0.852425
$261$	−9.06051	−0.560831
$262$	−3.45040	−0.213167
$263$	15.4938	0.955391	0.477696	−	0.878525i	$-0.341472\pi$
$263$	15.4938	0.955391	0.477696	+	0.878525i	$0.341472\pi$
$264$	0.278872	0.0171634
$265$	−3.66353	−0.225049
$266$	−10.7809	−0.661020
$267$	−8.06558	−0.493606
$268$	−7.87522	−0.481056
$269$	30.9554	1.88738	0.943692	−	0.330826i	$-0.107327\pi$
$269$	30.9554	1.88738	0.943692	+	0.330826i	$0.107327\pi$
$270$	−2.74259	−0.166909
$271$	−11.8094	−0.717369	−0.358685	−	0.933459i	$-0.616775\pi$
$271$	−11.8094	−0.717369	−0.358685	+	0.933459i	$0.616775\pi$
$272$	3.86495	0.234347
$273$	−9.76416	−0.590954
$274$	−35.2757	−2.13108
$275$	6.66260	0.401770
$276$	10.6052	0.638360
$277$	1.21341	0.0729069	0.0364535	−	0.999335i	$-0.488394\pi$
$277$	1.21341	0.0729069	0.0364535	+	0.999335i	$0.488394\pi$
$278$	7.76117	0.465484
$279$	4.22586	0.252996
$280$	0.357896	0.0213884
$281$	9.00636	0.537275	0.268637	−	0.963241i	$-0.413427\pi$
$281$	9.00636	0.537275	0.268637	+	0.963241i	$0.413427\pi$
$282$	−8.37662	−0.498820
$283$	20.3954	1.21238	0.606190	−	0.795320i	$-0.292697\pi$
$283$	20.3954	1.21238	0.606190	+	0.795320i	$0.292697\pi$
$284$	10.2007	0.605302
$285$	−3.64428	−0.215868
$286$	20.8662	1.23385
$287$	−22.0867	−1.30374
$288$	8.05650	0.474734
$289$	1.00000	0.0588235
$290$	24.8493	1.45920
$291$	13.8326	0.810882
$292$	−2.86660	−0.167755
$293$	12.5842	0.735175	0.367588	−	0.929989i	$-0.380184\pi$
$293$	12.5842	0.735175	0.367588	+	0.929989i	$0.380184\pi$
$294$	6.08317	0.354778
$295$	−0.0334575	−0.00194797
$296$	−0.216506	−0.0125841
$297$	−2.11525	−0.122739
$298$	−11.1307	−0.644782
$299$	25.1217	1.45283
$300$	−6.50553	−0.375597
$301$	−14.0637	−0.810618
$302$	9.34014	0.537465
$303$	19.8799	1.14207
$304$	10.3549	0.593893
$305$	−5.54746	−0.317647
$306$	2.01628	0.115263
$307$	−13.2328	−0.755236	−0.377618	−	0.925961i	$-0.623257\pi$
$307$	−13.2328	−0.755236	−0.377618	+	0.925961i	$0.623257\pi$
$308$	8.71902	0.496812
$309$	13.4164	0.763232
$310$	−11.5898	−0.658258
$311$	−27.8528	−1.57939	−0.789693	−	0.613503i	$-0.789760\pi$
$311$	−27.8528	−1.57939	−0.789693	+	0.613503i	$0.789760\pi$
$312$	−0.645020	−0.0365171
$313$	0.750260	0.0424072	0.0212036	−	0.999775i	$-0.493250\pi$
$313$	0.750260	0.0424072	0.0212036	+	0.999775i	$0.493250\pi$
$314$	39.8595	2.24940
$315$	−2.71465	−0.152953
$316$	−2.06539	−0.116187
$317$	−9.32416	−0.523697	−0.261848	−	0.965109i	$-0.584332\pi$
$317$	−9.32416	−0.523697	−0.261848	+	0.965109i	$0.584332\pi$
$318$	5.43050	0.304527
$319$	19.1653	1.07305
$320$	−11.5813	−0.647415
$321$	14.3040	0.798370
$322$	20.6620	1.15145
$323$	2.67917	0.149073
$324$	2.06539	0.114744
$325$	−15.4104	−0.854813
$326$	12.7389	0.705541
$327$	10.2005	0.564090
$328$	−1.45905	−0.0805624
$329$	−8.29128	−0.457113
$330$	5.80128	0.319350
$331$	14.6227	0.803736	0.401868	−	0.915698i	$-0.368361\pi$
$331$	14.6227	0.803736	0.401868	+	0.915698i	$0.368361\pi$
$332$	7.86133	0.431447
$333$	1.64221	0.0899923
$334$	−41.5957	−2.27601
$335$	−5.18647	−0.283367
$336$	7.71343	0.420802
$337$	8.81748	0.480319	0.240159	−	0.970733i	$-0.422800\pi$
$337$	8.81748	0.480319	0.240159	+	0.970733i	$0.422800\pi$
$338$	−22.0512	−1.19943
$339$	3.95752	0.214943
$340$	−2.80939	−0.152361
$341$	−8.93877	−0.484062
$342$	5.40196	0.292105
$343$	19.9914	1.07943
$344$	−0.929047	−0.0500909
$345$	6.98440	0.376027
$346$	−36.7931	−1.97801
$347$	13.3534	0.716848	0.358424	−	0.933559i	$-0.383314\pi$
$347$	13.3534	0.716848	0.358424	+	0.933559i	$0.383314\pi$
$348$	−18.7135	−1.00315
$349$	−20.8798	−1.11767	−0.558836	−	0.829278i	$-0.688752\pi$
$349$	−20.8798	−1.11767	−0.558836	+	0.829278i	$0.688752\pi$
$350$	−12.6747	−0.677489
$351$	4.89250	0.261142
$352$	−17.0415	−0.908317
$353$	23.0255	1.22552	0.612762	−	0.790268i	$-0.290058\pi$
$353$	23.0255	1.22552	0.612762	+	0.790268i	$0.290058\pi$
$354$	0.0495945	0.00263592
$355$	6.71801	0.356555
$356$	−16.6585	−0.882901
$357$	1.99574	0.105626
$358$	31.0102	1.63894
$359$	11.4080	0.602091	0.301046	−	0.953610i	$-0.402664\pi$
$359$	11.4080	0.602091	0.301046	+	0.953610i	$0.402664\pi$
$360$	−0.179330	−0.00945151
$361$	−11.8220	−0.622212
$362$	13.1967	0.693602
$363$	−6.52570	−0.342511
$364$	−20.1668	−1.05703
$365$	−1.88789	−0.0988167
$366$	8.22308	0.429827
$367$	−3.34058	−0.174377	−0.0871885	−	0.996192i	$-0.527788\pi$
$367$	−3.34058	−0.174377	−0.0871885	+	0.996192i	$0.527788\pi$
$368$	−19.8455	−1.03452
$369$	11.0669	0.576122
$370$	−4.50390	−0.234147
$371$	5.37517	0.279065
$372$	8.72805	0.452528
$373$	−9.07862	−0.470073	−0.235037	−	0.971987i	$-0.575521\pi$
$373$	−9.07862	−0.470073	−0.235037	+	0.971987i	$0.575521\pi$
$374$	−4.26494	−0.220535
$375$	−11.0855	−0.572455
$376$	−0.547721	−0.0282466
$377$	−44.3286	−2.28304
$378$	4.02397	0.206971
$379$	18.9025	0.970956	0.485478	−	0.874249i	$-0.338646\pi$
$379$	18.9025	0.970956	0.485478	+	0.874249i	$0.338646\pi$
$380$	−7.52684	−0.386119
$381$	−11.5138	−0.589868
$382$	2.87116	0.146901
$383$	30.8283	1.57525	0.787627	−	0.616153i	$-0.211310\pi$
$383$	30.8283	1.57525	0.787627	+	0.616153i	$0.211310\pi$
$384$	1.05414	0.0537940
$385$	5.74218	0.292649
$386$	36.7919	1.87266
$387$	7.04686	0.358212
$388$	28.5697	1.45041
$389$	−8.91504	−0.452011	−0.226005	−	0.974126i	$-0.572567\pi$
$389$	−8.91504	−0.452011	−0.226005	+	0.974126i	$0.572567\pi$
$390$	−13.4181	−0.679454
$391$	−5.13474	−0.259675
$392$	0.397760	0.0200899
$393$	1.71127	0.0863223
$394$	−26.9844	−1.35946
$395$	−1.36022	−0.0684403
$396$	−4.36882	−0.219541
$397$	16.7321	0.839761	0.419881	−	0.907579i	$-0.362072\pi$
$397$	16.7321	0.839761	0.419881	+	0.907579i	$0.362072\pi$
$398$	−10.7271	−0.537703
$399$	5.34693	0.267681
$400$	12.1738	0.608689
$401$	−28.0724	−1.40187	−0.700934	−	0.713226i	$-0.747233\pi$
$401$	−28.0724	−1.40187	−0.700934	+	0.713226i	$0.747233\pi$
$402$	7.68798	0.383442
$403$	20.6751	1.02990
$404$	41.0597	2.04280
$405$	1.36022	0.0675901
$406$	−36.4592	−1.80944
$407$	−3.47368	−0.172184
$408$	0.131838	0.00652697
$409$	21.5595	1.06605	0.533024	−	0.846100i	$-0.321056\pi$
$409$	21.5595	1.06605	0.533024	+	0.846100i	$0.321056\pi$
$410$	−30.3521	−1.49898
$411$	17.4954	0.862986
$412$	27.7100	1.36518
$413$	0.0490892	0.00241552
$414$	−10.3531	−0.508826
$415$	5.17732	0.254145
$416$	39.4165	1.93255
$417$	−3.84925	−0.188499
$418$	−11.4265	−0.558889
$419$	27.7599	1.35616	0.678081	−	0.734987i	$-0.262812\pi$
$419$	27.7599	1.35616	0.678081	+	0.734987i	$0.262812\pi$
$420$	−5.60681	−0.273584
$421$	8.97690	0.437507	0.218754	−	0.975780i	$-0.429801\pi$
$421$	8.97690	0.437507	0.218754	+	0.975780i	$0.429801\pi$
$422$	−21.5715	−1.05009
$423$	4.15449	0.201998
$424$	0.355084	0.0172444
$425$	3.14979	0.152787
$426$	−9.95820	−0.482476
$427$	8.13930	0.393889
$428$	29.5432	1.42803
$429$	−10.3489	−0.499649
$430$	−19.3267	−0.932015
$431$	37.6004	1.81115	0.905574	−	0.424188i	$-0.139440\pi$
$431$	37.6004	1.81115	0.905574	+	0.424188i	$0.139440\pi$
$432$	−3.86495	−0.185953
$433$	29.9877	1.44112	0.720559	−	0.693394i	$-0.243885\pi$
$433$	29.9877	1.44112	0.720559	+	0.693394i	$0.243885\pi$
$434$	17.0048	0.816254
$435$	−12.3243	−0.590906
$436$	21.0680	1.00898
$437$	−13.7569	−0.658080
$438$	2.79845	0.133715
$439$	17.0882	0.815573	0.407786	−	0.913077i	$-0.366301\pi$
$439$	17.0882	0.815573	0.407786	+	0.913077i	$0.366301\pi$
$440$	0.379328	0.0180838
$441$	−3.01703	−0.143668
$442$	9.86466	0.469214
$443$	−8.26360	−0.392615	−0.196308	−	0.980542i	$-0.562895\pi$
$443$	−8.26360	−0.392615	−0.196308	+	0.980542i	$0.562895\pi$
$444$	3.39179	0.160967
$445$	−10.9710	−0.520075
$446$	−25.0919	−1.18814
$447$	5.52040	0.261106
$448$	16.9923	0.802808
$449$	−26.4498	−1.24824	−0.624121	−	0.781328i	$-0.714543\pi$
$449$	−26.4498	−1.24824	−0.624121	+	0.781328i	$0.714543\pi$
$450$	6.35086	0.299382
$451$	−23.4094	−1.10230
$452$	8.17380	0.384463
$453$	−4.63236	−0.217647
$454$	44.8325	2.10409
$455$	−13.2814	−0.622644
$456$	0.353218	0.0165409
$457$	−25.2777	−1.18244	−0.591222	−	0.806509i	$-0.701354\pi$
$457$	−25.2777	−1.18244	−0.591222	+	0.806509i	$0.701354\pi$
$458$	−2.04499	−0.0955561
$459$	−1.00000	−0.0466760
$460$	14.4255	0.672592
$461$	8.01861	0.373464	0.186732	−	0.982411i	$-0.440210\pi$
$461$	8.01861	0.373464	0.186732	+	0.982411i	$0.440210\pi$
$462$	−8.51171	−0.396001
$463$	−6.60040	−0.306747	−0.153373	−	0.988168i	$-0.549014\pi$
$463$	−6.60040	−0.306747	−0.153373	+	0.988168i	$0.549014\pi$
$464$	35.0184	1.62569
$465$	5.74812	0.266563
$466$	−17.6834	−0.819166
$467$	−10.4151	−0.481954	−0.240977	−	0.970531i	$-0.577468\pi$
$467$	−10.4151	−0.481954	−0.240977	+	0.970531i	$0.577468\pi$
$468$	10.1049	0.467100
$469$	7.60966	0.351381
$470$	−11.3941	−0.525570
$471$	−19.7688	−0.910900
$472$	0.00324283	0.000149263 0
$473$	−14.9059	−0.685374
$474$	2.01628	0.0926108
$475$	8.43883	0.387200
$476$	4.12197	0.188930
$477$	−2.69333	−0.123319
$478$	−12.3185	−0.563433
$479$	−24.9607	−1.14048	−0.570242	−	0.821477i	$-0.693151\pi$
$479$	−24.9607	−1.14048	−0.570242	+	0.821477i	$0.693151\pi$
$480$	10.9587	0.500192
$481$	8.03450	0.366341
$482$	34.8522	1.58747
$483$	−10.2476	−0.466282
$484$	−13.4781	−0.612641
$485$	18.8155	0.854366
$486$	−2.01628	−0.0914603
$487$	−7.31541	−0.331493	−0.165746	−	0.986168i	$-0.553003\pi$
$487$	−7.31541	−0.331493	−0.165746	+	0.986168i	$0.553003\pi$
$488$	0.537682	0.0243397
$489$	−6.31801	−0.285710
$490$	8.27448	0.373803
$491$	39.0202	1.76096	0.880478	−	0.474087i	$-0.157222\pi$
$491$	39.0202	1.76096	0.880478	+	0.474087i	$0.157222\pi$
$492$	22.8575	1.03050
$493$	9.06051	0.408065
$494$	26.4291	1.18910
$495$	−2.87722	−0.129321
$496$	−16.3328	−0.733362
$497$	−9.85675	−0.442136
$498$	−7.67442	−0.343899
$499$	13.1019	0.586520	0.293260	−	0.956033i	$-0.405260\pi$
$499$	13.1019	0.586520	0.293260	+	0.956033i	$0.405260\pi$
$500$	−22.8959	−1.02394
$501$	20.6299	0.921676
$502$	−31.1990	−1.39248
$503$	−1.20453	−0.0537071	−0.0268536	−	0.999639i	$-0.508549\pi$
$503$	−1.20453	−0.0537071	−0.0268536	+	0.999639i	$0.508549\pi$
$504$	0.263115	0.0117201
$505$	27.0411	1.20331
$506$	21.8994	0.973546
$507$	10.9366	0.485710
$508$	−23.7804	−1.05508
$509$	32.5123	1.44108	0.720542	−	0.693411i	$-0.243893\pi$
$509$	32.5123	1.44108	0.720542	+	0.693411i	$0.243893\pi$
$510$	2.74259	0.121444
$511$	2.76994	0.122535
$512$	−32.1571	−1.42116
$513$	−2.67917	−0.118288
$514$	55.8543	2.46363
$515$	18.2493	0.804161
$516$	14.5545	0.640726
$517$	−8.78780	−0.386487
$518$	6.60819	0.290347
$519$	18.2480	0.800998
$520$	−0.877372	−0.0384753
$521$	0.828095	0.0362795	0.0181397	−	0.999835i	$-0.494226\pi$
$521$	0.828095	0.0362795	0.0181397	+	0.999835i	$0.494226\pi$
$522$	18.2685	0.799592
$523$	17.4575	0.763363	0.381682	−	0.924294i	$-0.375345\pi$
$523$	17.4575	0.763363	0.381682	+	0.924294i	$0.375345\pi$
$524$	3.53444	0.154403
$525$	6.28616	0.274350
$526$	−31.2399	−1.36213
$527$	−4.22586	−0.184082
$528$	8.17535	0.355786
$529$	3.36556	0.146329
$530$	7.38670	0.320858
$531$	−0.0245970	−0.00106742
$532$	11.0435	0.478796
$533$	54.1450	2.34528
$534$	16.2625	0.703746
$535$	19.4566	0.841183
$536$	0.502694	0.0217131
$537$	−15.3799	−0.663693
$538$	−62.4148	−2.69089
$539$	6.38177	0.274882
$540$	2.80939	0.120897
$541$	1.98396	0.0852970	0.0426485	−	0.999090i	$-0.486420\pi$
$541$	1.98396	0.0852970	0.0426485	+	0.999090i	$0.486420\pi$
$542$	23.8110	1.02277
$543$	−6.54506	−0.280875
$544$	−8.05650	−0.345420
$545$	13.8750	0.594339
$546$	19.6873	0.842538
$547$	30.5531	1.30636	0.653179	−	0.757204i	$-0.273435\pi$
$547$	30.5531	1.30636	0.653179	+	0.757204i	$0.273435\pi$
$548$	36.1348	1.54360
$549$	−4.07834	−0.174059
$550$	−13.4337	−0.572814
$551$	24.2747	1.03414
$552$	−0.676956	−0.0288132
$553$	1.99574	0.0848675
$554$	−2.44658	−0.103945
$555$	2.23377	0.0948182
$556$	−7.95020	−0.337163
$557$	39.0049	1.65269	0.826346	−	0.563163i	$-0.190416\pi$
$557$	39.0049	1.65269	0.826346	+	0.563163i	$0.190416\pi$
$558$	−8.52053	−0.360703
$559$	34.4768	1.45821
$560$	10.4920	0.443368
$561$	2.11525	0.0893061
$562$	−18.1594	−0.766006
$563$	25.0677	1.05648	0.528239	−	0.849096i	$-0.322853\pi$
$563$	25.0677	1.05648	0.528239	+	0.849096i	$0.322853\pi$
$564$	8.58063	0.361310
$565$	5.38311	0.226469
$566$	−41.1228	−1.72852
$567$	−1.99574	−0.0838132
$568$	−0.651136	−0.0273211
$569$	14.5685	0.610743	0.305372	−	0.952233i	$-0.401219\pi$
$569$	14.5685	0.610743	0.305372	+	0.952233i	$0.401219\pi$
$570$	7.34788	0.307769
$571$	38.2299	1.59987	0.799935	−	0.600086i	$-0.204867\pi$
$571$	38.2299	1.59987	0.799935	+	0.600086i	$0.204867\pi$
$572$	−21.3744	−0.893710
$573$	−1.42399	−0.0594880
$574$	44.5330	1.85877
$575$	−16.1734	−0.674475
$576$	−8.51427	−0.354761
$577$	−3.24987	−0.135294	−0.0676469	−	0.997709i	$-0.521549\pi$
$577$	−3.24987	−0.135294	−0.0676469	+	0.997709i	$0.521549\pi$
$578$	−2.01628	−0.0838662
$579$	−18.2474	−0.758337
$580$	−25.4545	−1.05694
$581$	−7.59624	−0.315145
$582$	−27.8904	−1.15610
$583$	5.69706	0.235948
$584$	0.182982	0.00757184
$585$	6.65490	0.275146
$586$	−25.3732	−1.04816
$587$	−26.5268	−1.09488	−0.547440	−	0.836845i	$-0.684397\pi$
$587$	−26.5268	−1.09488	−0.547440	+	0.836845i	$0.684397\pi$
$588$	−6.23132	−0.256975
$589$	−11.3218	−0.466508
$590$	0.0674596	0.00277727
$591$	13.3833	0.550514
$592$	−6.34704	−0.260862
$593$	−15.9461	−0.654828	−0.327414	−	0.944881i	$-0.606177\pi$
$593$	−15.9461	−0.654828	−0.327414	+	0.944881i	$0.606177\pi$
$594$	4.26494	0.174993
$595$	2.71465	0.111290
$596$	11.4018	0.467034
$597$	5.32026	0.217744
$598$	−50.6525	−2.07133
$599$	36.8688	1.50642	0.753208	−	0.657782i	$-0.228505\pi$
$599$	36.8688	1.50642	0.753208	+	0.657782i	$0.228505\pi$
$600$	0.415263	0.0169531
$601$	−44.9790	−1.83473	−0.917365	−	0.398047i	$-0.869688\pi$
$601$	−44.9790	−1.83473	−0.917365	+	0.398047i	$0.869688\pi$
$602$	28.3564	1.15572
$603$	−3.81295	−0.155275
$604$	−9.56762	−0.389301
$605$	−8.87642	−0.360878
$606$	−40.0834	−1.62828
$607$	9.48728	0.385077	0.192539	−	0.981289i	$-0.438328\pi$
$607$	9.48728	0.385077	0.192539	+	0.981289i	$0.438328\pi$
$608$	−21.5848	−0.875378
$609$	18.0824	0.732736
$610$	11.1852	0.452877
$611$	20.3259	0.822296
$612$	−2.06539	−0.0834883
$613$	−3.69228	−0.149130	−0.0745649	−	0.997216i	$-0.523757\pi$
$613$	−3.69228	−0.149130	−0.0745649	+	0.997216i	$0.523757\pi$
$614$	26.6810	1.07676
$615$	15.0535	0.607016
$616$	−0.556555	−0.0224242
$617$	−12.7509	−0.513332	−0.256666	−	0.966500i	$-0.582624\pi$
$617$	−12.7509	−0.513332	−0.256666	+	0.966500i	$0.582624\pi$
$618$	−27.0512	−1.08816
$619$	−7.19886	−0.289347	−0.144673	−	0.989479i	$-0.546213\pi$
$619$	−7.19886	−0.289347	−0.144673	+	0.989479i	$0.546213\pi$
$620$	11.8721	0.476795
$621$	5.13474	0.206050
$622$	56.1590	2.25177
$623$	16.0968	0.644905
$624$	−18.9093	−0.756977
$625$	0.670121	0.0268048
$626$	−1.51273	−0.0604610
$627$	5.66713	0.226323
$628$	−40.8303	−1.62931
$629$	−1.64221	−0.0654790
$630$	5.47350	0.218070
$631$	28.0878	1.11816	0.559079	−	0.829115i	$-0.311155\pi$
$631$	28.0878	1.11816	0.559079	+	0.829115i	$0.311155\pi$
$632$	0.131838	0.00524425
$633$	10.6987	0.425234
$634$	18.8001	0.746648
$635$	−15.6613	−0.621500
$636$	−5.56276	−0.220578
$637$	−14.7608	−0.584844
$638$	−38.6426	−1.52987
$639$	4.93890	0.195380
$640$	1.43387	0.0566788
$641$	−27.4511	−1.08425	−0.542127	−	0.840296i	$-0.682381\pi$
$641$	−27.4511	−1.08425	−0.542127	+	0.840296i	$0.682381\pi$
$642$	−28.8408	−1.13826
$643$	−39.4003	−1.55379	−0.776897	−	0.629627i	$-0.783208\pi$
$643$	−39.4003	−1.55379	−0.776897	+	0.629627i	$0.783208\pi$
$644$	−21.1653	−0.834028
$645$	9.58531	0.377421
$646$	−5.40196	−0.212537
$647$	−13.7159	−0.539227	−0.269613	−	0.962969i	$-0.586896\pi$
$647$	−13.7159	−0.539227	−0.269613	+	0.962969i	$0.586896\pi$
$648$	−0.131838	−0.00517910
$649$	0.0520289	0.00204231
$650$	31.0716	1.21873
$651$	−8.43372	−0.330544
$652$	−13.0491	−0.511044
$653$	−6.32015	−0.247326	−0.123663	−	0.992324i	$-0.539464\pi$
$653$	−6.32015	−0.247326	−0.123663	+	0.992324i	$0.539464\pi$
$654$	−20.5671	−0.804237
$655$	2.32771	0.0909513
$656$	−42.7732	−1.67001
$657$	−1.38793	−0.0541481
$658$	16.7175	0.651718
$659$	12.2517	0.477257	0.238629	−	0.971111i	$-0.423302\pi$
$659$	12.2517	0.477257	0.238629	+	0.971111i	$0.423302\pi$
$660$	−5.94257	−0.231314
$661$	4.63490	0.180277	0.0901384	−	0.995929i	$-0.471269\pi$
$661$	4.63490	0.180277	0.0901384	+	0.995929i	$0.471269\pi$
$662$	−29.4835	−1.14591
$663$	−4.89250	−0.190009
$664$	−0.501807	−0.0194739
$665$	7.27303	0.282036
$666$	−3.31115	−0.128304
$667$	−46.5234	−1.80139
$668$	42.6087	1.64858
$669$	12.4447	0.481139
$670$	10.4574	0.404004
$671$	8.62672	0.333031
$672$	−16.0787	−0.620248
$673$	−34.8144	−1.34200	−0.670999	−	0.741458i	$-0.734134\pi$
$673$	−34.8144	−1.34200	−0.670999	+	0.741458i	$0.734134\pi$
$674$	−17.7785	−0.684803
$675$	−3.14979	−0.121235
$676$	22.5883	0.868779
$677$	−30.2698	−1.16336	−0.581681	−	0.813417i	$-0.697605\pi$
$677$	−30.2698	−1.16336	−0.581681	+	0.813417i	$0.697605\pi$
$678$	−7.97946	−0.306449
$679$	−27.6063	−1.05943
$680$	0.179330	0.00687699
$681$	−22.2353	−0.852057
$682$	18.0231	0.690139
$683$	−19.7157	−0.754401	−0.377200	−	0.926132i	$-0.623113\pi$
$683$	−19.7157	−0.754401	−0.377200	+	0.926132i	$0.623113\pi$
$684$	−5.53353	−0.211580
$685$	23.7977	0.909264
$686$	−40.3082	−1.53897
$687$	1.01424	0.0386956
$688$	−27.2358	−1.03835
$689$	−13.1771	−0.502007
$690$	−14.0825	−0.536112
$691$	−4.27336	−0.162566	−0.0812831	−	0.996691i	$-0.525902\pi$
$691$	−4.27336	−0.162566	−0.0812831	+	0.996691i	$0.525902\pi$
$692$	37.6892	1.43273
$693$	4.22149	0.160361
$694$	−26.9242	−1.02203
$695$	−5.23585	−0.198607
$696$	1.19452	0.0452783
$697$	−11.0669	−0.419190
$698$	42.0996	1.59349
$699$	8.77029	0.331723
$700$	12.9833	0.490724
$701$	−11.8522	−0.447653	−0.223827	−	0.974629i	$-0.571855\pi$
$701$	−11.8522	−0.447653	−0.223827	+	0.974629i	$0.571855\pi$
$702$	−9.86466	−0.372317
$703$	−4.39975	−0.165940
$704$	18.0098	0.678771
$705$	5.65104	0.212830
$706$	−46.4259	−1.74726
$707$	−39.6751	−1.49214
$708$	−0.0508024	−0.00190927
$709$	−39.3545	−1.47799	−0.738995	−	0.673711i	$-0.764699\pi$
$709$	−39.3545	−1.47799	−0.738995	+	0.673711i	$0.764699\pi$
$710$	−13.5454	−0.508349
$711$	−1.00000	−0.0375029
$712$	1.06335	0.0398509
$713$	21.6987	0.812623
$714$	−4.02397	−0.150593
$715$	−14.0768	−0.526442
$716$	−31.7655	−1.18713
$717$	6.10950	0.228163
$718$	−23.0017	−0.858417
$719$	11.7686	0.438896	0.219448	−	0.975624i	$-0.429574\pi$
$719$	11.7686	0.438896	0.219448	+	0.975624i	$0.429574\pi$
$720$	−5.25720	−0.195924
$721$	−26.7756	−0.997176
$722$	23.8365	0.887104
$723$	−17.2854	−0.642851
$724$	−13.5181	−0.502396
$725$	28.5387	1.05990
$726$	13.1577	0.488326
$727$	26.1826	0.971059	0.485530	−	0.874220i	$-0.338627\pi$
$727$	26.1826	0.971059	0.485530	+	0.874220i	$0.338627\pi$
$728$	1.28729	0.0477102
$729$	1.00000	0.0370370
$730$	3.80652	0.140885
$731$	−7.04686	−0.260638
$732$	−8.42335	−0.311336
$733$	−49.3757	−1.82373	−0.911866	−	0.410488i	$-0.865358\pi$
$733$	−49.3757	−1.82373	−0.911866	+	0.410488i	$0.865358\pi$
$734$	6.73555	0.248614
$735$	−4.10383	−0.151372
$736$	41.3680	1.52485
$737$	8.06536	0.297091
$738$	−22.3140	−0.821391
$739$	51.4167	1.89139	0.945697	−	0.325048i	$-0.105381\pi$
$739$	51.4167	1.89139	0.945697	+	0.325048i	$0.105381\pi$
$740$	4.61360	0.169599
$741$	−13.1079	−0.481529
$742$	−10.8379	−0.397870
$743$	−13.2884	−0.487504	−0.243752	−	0.969838i	$-0.578378\pi$
$743$	−13.2884	−0.487504	−0.243752	+	0.969838i	$0.578378\pi$
$744$	−0.557131	−0.0204254
$745$	7.50898	0.275108
$746$	18.3050	0.670195
$747$	3.80623	0.139263
$748$	4.36882	0.159740
$749$	−28.5470	−1.04308
$750$	22.3516	0.816164
$751$	17.5109	0.638982	0.319491	−	0.947589i	$-0.396488\pi$
$751$	17.5109	0.638982	0.319491	+	0.947589i	$0.396488\pi$
$752$	−16.0569	−0.585535
$753$	15.4736	0.563888
$754$	89.3788	3.25498
$755$	−6.30105	−0.229319
$756$	−4.12197	−0.149915
$757$	49.8302	1.81111	0.905555	−	0.424230i	$-0.139455\pi$
$757$	49.8302	1.81111	0.905555	+	0.424230i	$0.139455\pi$
$758$	−38.1127	−1.38432
$759$	−10.8613	−0.394239
$760$	0.480456	0.0174280
$761$	17.0638	0.618562	0.309281	−	0.950971i	$-0.399912\pi$
$761$	17.0638	0.618562	0.309281	+	0.950971i	$0.399912\pi$
$762$	23.2150	0.840989
$763$	−20.3576	−0.736994
$764$	−2.94109	−0.106405
$765$	−1.36022	−0.0491790
$766$	−62.1585	−2.24588
$767$	−0.120341	−0.00434526
$768$	14.9031	0.537769
$769$	11.6585	0.420415	0.210207	−	0.977657i	$-0.432586\pi$
$769$	11.6585	0.420415	0.210207	+	0.977657i	$0.432586\pi$
$770$	−11.5778	−0.417236
$771$	−27.7017	−0.997651
$772$	−37.6880	−1.35642
$773$	−5.80412	−0.208760	−0.104380	−	0.994538i	$-0.533286\pi$
$773$	−5.80412	−0.208760	−0.104380	+	0.994538i	$0.533286\pi$
$774$	−14.2084	−0.510712
$775$	−13.3106	−0.478130
$776$	−1.82367	−0.0654659
$777$	−3.27741	−0.117577
$778$	17.9752	0.644443
$779$	−29.6502	−1.06233
$780$	13.7449	0.492148
$781$	−10.4470	−0.373824
$782$	10.3531	0.370225
$783$	−9.06051	−0.323796
$784$	11.6607	0.416452
$785$	−26.8901	−0.959747
$786$	−3.45040	−0.123072
$787$	−1.19567	−0.0426212	−0.0213106	−	0.999773i	$-0.506784\pi$
$787$	−1.19567	−0.0426212	−0.0213106	+	0.999773i	$0.506784\pi$
$788$	27.6416	0.984693
$789$	15.4938	0.551596
$790$	2.74259	0.0975771
$791$	−7.89817	−0.280827
$792$	0.278872	0.00990927
$793$	−19.9533	−0.708562
$794$	−33.7367	−1.19727
$795$	−3.66353	−0.129932
$796$	10.9884	0.389473
$797$	−3.97010	−0.140628	−0.0703141	−	0.997525i	$-0.522400\pi$
$797$	−3.97010	−0.140628	−0.0703141	+	0.997525i	$0.522400\pi$
$798$	−10.7809	−0.381640
$799$	−4.15449	−0.146975
$800$	−25.3763	−0.897187
$801$	−8.06558	−0.284983
$802$	56.6018	1.99868
$803$	2.93581	0.103603
$804$	−7.87522	−0.277738
$805$	−13.9390	−0.491287
$806$	−41.6867	−1.46835
$807$	30.9554	1.08968
$808$	−2.62093	−0.0922041
$809$	39.8804	1.40212	0.701060	−	0.713103i	$-0.252711\pi$
$809$	39.8804	1.40212	0.701060	+	0.713103i	$0.252711\pi$
$810$	−2.74259	−0.0963649
$811$	27.8321	0.977316	0.488658	−	0.872475i	$-0.337487\pi$
$811$	27.8321	0.977316	0.488658	+	0.872475i	$0.337487\pi$
$812$	37.3472	1.31063
$813$	−11.8094	−0.414173
$814$	7.00391	0.245487
$815$	−8.59391	−0.301032
$816$	3.86495	0.135300
$817$	−18.8798	−0.660519
$818$	−43.4700	−1.51989
$819$	−9.76416	−0.341187
$820$	31.0913	1.08576
$821$	26.9408	0.940239	0.470120	−	0.882603i	$-0.344211\pi$
$821$	26.9408	0.940239	0.470120	+	0.882603i	$0.344211\pi$
$822$	−35.2757	−1.23038
$823$	10.9329	0.381098	0.190549	−	0.981678i	$-0.438973\pi$
$823$	10.9329	0.381098	0.190549	+	0.981678i	$0.438973\pi$
$824$	−1.76880	−0.0616189
$825$	6.66260	0.231962
$826$	−0.0989777	−0.00344387
$827$	−36.8524	−1.28148	−0.640742	−	0.767756i	$-0.721373\pi$
$827$	−36.8524	−1.28148	−0.640742	+	0.767756i	$0.721373\pi$
$828$	10.6052	0.368557
$829$	−16.3760	−0.568763	−0.284382	−	0.958711i	$-0.591788\pi$
$829$	−16.3760	−0.568763	−0.284382	+	0.958711i	$0.591788\pi$
$830$	−10.4389	−0.362341
$831$	1.21341	0.0420928
$832$	−41.6561	−1.44416
$833$	3.01703	0.104534
$834$	7.76117	0.268747
$835$	28.0613	0.971102
$836$	11.7048	0.404819
$837$	4.22586	0.146067
$838$	−55.9718	−1.93351
$839$	−46.8061	−1.61592	−0.807962	−	0.589234i	$-0.799429\pi$
$839$	−46.8061	−1.61592	−0.807962	+	0.589234i	$0.799429\pi$
$840$	0.357896	0.0123486
$841$	53.0928	1.83079
$842$	−18.0999	−0.623765
$843$	9.00636	0.310196
$844$	22.0969	0.760607
$845$	14.8762	0.511757
$846$	−8.37662	−0.287994
$847$	13.0236	0.447496
$848$	10.4096	0.357466
$849$	20.3954	0.699968
$850$	−6.35086	−0.217833
$851$	8.43230	0.289056
$852$	10.2007	0.349471
$853$	13.9246	0.476768	0.238384	−	0.971171i	$-0.423382\pi$
$853$	13.9246	0.476768	0.238384	+	0.971171i	$0.423382\pi$
$854$	−16.4111	−0.561577
$855$	−3.64428	−0.124632
$856$	−1.88581	−0.0644558
$857$	−22.5571	−0.770536	−0.385268	−	0.922805i	$-0.625891\pi$
$857$	−22.5571	−0.770536	−0.385268	+	0.922805i	$0.625891\pi$
$858$	20.8662	0.712362
$859$	−5.26831	−0.179752	−0.0898762	−	0.995953i	$-0.528647\pi$
$859$	−5.26831	−0.179752	−0.0898762	+	0.995953i	$0.528647\pi$
$860$	19.7974	0.675085
$861$	−22.0867	−0.752713
$862$	−75.8130	−2.58220
$863$	−9.54873	−0.325042	−0.162521	−	0.986705i	$-0.551963\pi$
$863$	−9.54873	−0.325042	−0.162521	+	0.986705i	$0.551963\pi$
$864$	8.05650	0.274088
$865$	24.8214	0.843952
$866$	−60.4636	−2.05464
$867$	1.00000	0.0339618
$868$	−17.4189	−0.591236
$869$	2.11525	0.0717550
$870$	24.8493	0.842470
$871$	−18.6549	−0.632096
$872$	−1.34482	−0.0455414
$873$	13.8326	0.468163
$874$	27.7377	0.938241
$875$	22.1239	0.747923
$876$	−2.86660	−0.0968535
$877$	8.04972	0.271820	0.135910	−	0.990721i	$-0.456604\pi$
$877$	8.04972	0.271820	0.135910	+	0.990721i	$0.456604\pi$
$878$	−34.4545	−1.16278
$879$	12.5842	0.424454
$880$	11.1203	0.374866
$881$	−23.0223	−0.775641	−0.387821	−	0.921735i	$-0.626772\pi$
$881$	−23.0223	−0.775641	−0.387821	+	0.921735i	$0.626772\pi$
$882$	6.08317	0.204831
$883$	5.88745	0.198129	0.0990643	−	0.995081i	$-0.468415\pi$
$883$	5.88745	0.198129	0.0990643	+	0.995081i	$0.468415\pi$
$884$	−10.1049	−0.339865
$885$	−0.0334575	−0.00112466
$886$	16.6617	0.559762
$887$	−53.0981	−1.78286	−0.891429	−	0.453160i	$-0.850297\pi$
$887$	−53.0981	−1.78286	−0.891429	+	0.453160i	$0.850297\pi$
$888$	−0.216506	−0.00726546
$889$	22.9785	0.770673
$890$	22.1206	0.741485
$891$	−2.11525	−0.0708636
$892$	25.7030	0.860602
$893$	−11.1306	−0.372471
$894$	−11.1307	−0.372265
$895$	−20.9202	−0.699284
$896$	−2.10380	−0.0702829
$897$	25.1217	0.838790
$898$	53.3301	1.77965
$899$	−38.2885	−1.27699
$900$	−6.50553	−0.216851
$901$	2.69333	0.0897277
$902$	47.1999	1.57158
$903$	−14.0637	−0.468010
$904$	−0.521753	−0.0173532
$905$	−8.90275	−0.295938
$906$	9.34014	0.310305
$907$	−55.6322	−1.84724	−0.923618	−	0.383313i	$-0.874783\pi$
$907$	−55.6322	−1.84724	−0.923618	+	0.383313i	$0.874783\pi$
$908$	−45.9244	−1.52405
$909$	19.8799	0.659375
$910$	26.7791	0.887719
$911$	−56.1717	−1.86105	−0.930526	−	0.366225i	$-0.880650\pi$
$911$	−56.1717	−1.86105	−0.930526	+	0.366225i	$0.880650\pi$
$912$	10.3549	0.342884
$913$	−8.05114	−0.266454
$914$	50.9670	1.68584
$915$	−5.54746	−0.183393
$916$	2.09480	0.0692140
$917$	−3.41525	−0.112782
$918$	2.01628	0.0665472
$919$	−16.9396	−0.558785	−0.279392	−	0.960177i	$-0.590133\pi$
$919$	−16.9396	−0.558785	−0.279392	+	0.960177i	$0.590133\pi$
$920$	−0.920812	−0.0303583
$921$	−13.2328	−0.436036
$922$	−16.1678	−0.532457
$923$	24.1636	0.795353
$924$	8.71902	0.286835
$925$	−5.17260	−0.170074
$926$	13.3083	0.437337
$927$	13.4164	0.440652
$928$	−72.9960	−2.39621
$929$	−7.05163	−0.231357	−0.115678	−	0.993287i	$-0.536904\pi$
$929$	−7.05163	−0.231357	−0.115678	+	0.993287i	$0.536904\pi$
$930$	−11.5898	−0.380046
$931$	8.08313	0.264914
$932$	18.1140	0.593345
$933$	−27.8528	−0.911858
$934$	20.9998	0.687134
$935$	2.87722	0.0940951
$936$	−0.645020	−0.0210831
$937$	−29.4355	−0.961616	−0.480808	−	0.876826i	$-0.659657\pi$
$937$	−29.4355	−0.961616	−0.480808	+	0.876826i	$0.659657\pi$
$938$	−15.3432	−0.500973
$939$	0.750260	0.0244838
$940$	11.6716	0.380685
$941$	−50.9922	−1.66230	−0.831149	−	0.556050i	$-0.812316\pi$
$941$	−50.9922	−1.66230	−0.831149	+	0.556050i	$0.812316\pi$
$942$	39.8595	1.29869
$943$	56.8258	1.85050
$944$	0.0950663	0.00309414
$945$	−2.71465	−0.0883077
$946$	30.0545	0.977155
$947$	−5.05899	−0.164395	−0.0821976	−	0.996616i	$-0.526194\pi$
$947$	−5.05899	−0.164395	−0.0821976	+	0.996616i	$0.526194\pi$
$948$	−2.06539	−0.0670806
$949$	−6.79043	−0.220427
$950$	−17.0151	−0.552041
$951$	−9.32416	−0.302357
$952$	−0.263115	−0.00852761
$953$	−1.63195	−0.0528641	−0.0264320	−	0.999651i	$-0.508415\pi$
$953$	−1.63195	−0.0528641	−0.0264320	+	0.999651i	$0.508415\pi$
$954$	5.43050	0.175819
$955$	−1.93694	−0.0626780
$956$	12.6185	0.408111
$957$	19.1653	0.619525
$958$	50.3278	1.62602
$959$	−34.9163	−1.12751
$960$	−11.5813	−0.373785
$961$	−13.1421	−0.423938
$962$	−16.1998	−0.522302
$963$	14.3040	0.460939
$964$	−35.7010	−1.14985
$965$	−24.8206	−0.799004
$966$	20.6620	0.664790
$967$	5.47878	0.176186	0.0880928	−	0.996112i	$-0.471923\pi$
$967$	5.47878	0.176186	0.0880928	+	0.996112i	$0.471923\pi$
$968$	0.860339	0.0276523
$969$	2.67917	0.0860674
$970$	−37.9372	−1.21809
$971$	55.4710	1.78015	0.890074	−	0.455815i	$-0.150652\pi$
$971$	55.4710	1.78015	0.890074	+	0.455815i	$0.150652\pi$
$972$	2.06539	0.0662473
$973$	7.68210	0.246277
$974$	14.7499	0.472618
$975$	−15.4104	−0.493526
$976$	15.7626	0.504548
$977$	−52.4774	−1.67890	−0.839450	−	0.543437i	$-0.817123\pi$
$977$	−52.4774	−1.67890	−0.839450	+	0.543437i	$0.817123\pi$
$978$	12.7389	0.407344
$979$	17.0607	0.545264
$980$	−8.47600	−0.270756
$981$	10.2005	0.325677
$982$	−78.6756	−2.51064
$983$	−15.1277	−0.482499	−0.241249	−	0.970463i	$-0.577557\pi$
$983$	−15.1277	−0.482499	−0.241249	+	0.970463i	$0.577557\pi$
$984$	−1.45905	−0.0465127
$985$	18.2043	0.580036
$986$	−18.2685	−0.581788
$987$	−8.29128	−0.263914
$988$	−27.0728	−0.861301
$989$	36.1838	1.15058
$990$	5.80128	0.184377
$991$	37.0518	1.17699	0.588494	−	0.808501i	$-0.299721\pi$
$991$	37.0518	1.17699	0.588494	+	0.808501i	$0.299721\pi$
$992$	34.0457	1.08095
$993$	14.6227	0.464037
$994$	19.8740	0.630364
$995$	7.23675	0.229420
$996$	7.86133	0.249096
$997$	−45.0133	−1.42559	−0.712793	−	0.701374i	$-0.752570\pi$
$997$	−45.0133	−1.42559	−0.712793	+	0.701374i	$0.752570\pi$
$998$	−26.4170	−0.836216
$999$	1.64221	0.0519571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.01628 q^{2} +1.00000 q^{3} +2.06539 q^{4} +1.36022 q^{5} -2.01628 q^{6} -1.99574 q^{7} -0.131838 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.01628 q^{2} +1.00000 q^{3} +2.06539 q^{4} +1.36022 q^{5} -2.01628 q^{6} -1.99574 q^{7} -0.131838 q^{8} +1.00000 q^{9} -2.74259 q^{10} -2.11525 q^{11} +2.06539 q^{12} +4.89250 q^{13} +4.02397 q^{14} +1.36022 q^{15} -3.86495 q^{16} -1.00000 q^{17} -2.01628 q^{18} -2.67917 q^{19} +2.80939 q^{20} -1.99574 q^{21} +4.26494 q^{22} +5.13474 q^{23} -0.131838 q^{24} -3.14979 q^{25} -9.86466 q^{26} +1.00000 q^{27} -4.12197 q^{28} -9.06051 q^{29} -2.74259 q^{30} +4.22586 q^{31} +8.05650 q^{32} -2.11525 q^{33} +2.01628 q^{34} -2.71465 q^{35} +2.06539 q^{36} +1.64221 q^{37} +5.40196 q^{38} +4.89250 q^{39} -0.179330 q^{40} +11.0669 q^{41} +4.02397 q^{42} +7.04686 q^{43} -4.36882 q^{44} +1.36022 q^{45} -10.3531 q^{46} +4.15449 q^{47} -3.86495 q^{48} -3.01703 q^{49} +6.35086 q^{50} -1.00000 q^{51} +10.1049 q^{52} -2.69333 q^{53} -2.01628 q^{54} -2.87722 q^{55} +0.263115 q^{56} -2.67917 q^{57} +18.2685 q^{58} -0.0245970 q^{59} +2.80939 q^{60} -4.07834 q^{61} -8.52053 q^{62} -1.99574 q^{63} -8.51427 q^{64} +6.65490 q^{65} +4.26494 q^{66} -3.81295 q^{67} -2.06539 q^{68} +5.13474 q^{69} +5.47350 q^{70} +4.93890 q^{71} -0.131838 q^{72} -1.38793 q^{73} -3.31115 q^{74} -3.14979 q^{75} -5.53353 q^{76} +4.22149 q^{77} -9.86466 q^{78} -1.00000 q^{79} -5.25720 q^{80} +1.00000 q^{81} -22.3140 q^{82} +3.80623 q^{83} -4.12197 q^{84} -1.36022 q^{85} -14.2084 q^{86} -9.06051 q^{87} +0.278872 q^{88} -8.06558 q^{89} -2.74259 q^{90} -9.76416 q^{91} +10.6052 q^{92} +4.22586 q^{93} -8.37662 q^{94} -3.64428 q^{95} +8.05650 q^{96} +13.8326 q^{97} +6.08317 q^{98} -2.11525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 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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