LMFDB - Embedded newform 6034.2.a.p.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.302933 q^{3} +1.00000 q^{4} +3.48262 q^{5} +0.302933 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.90823 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.302933 q^{3} +1.00000 q^{4} +3.48262 q^{5} +0.302933 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.90823 q^{9} -3.48262 q^{10} -1.91437 q^{11} -0.302933 q^{12} -1.92516 q^{13} -1.00000 q^{14} -1.05500 q^{15} +1.00000 q^{16} +1.82639 q^{17} +2.90823 q^{18} +1.01716 q^{19} +3.48262 q^{20} -0.302933 q^{21} +1.91437 q^{22} +6.54224 q^{23} +0.302933 q^{24} +7.12864 q^{25} +1.92516 q^{26} +1.78980 q^{27} +1.00000 q^{28} -3.90924 q^{29} +1.05500 q^{30} +0.512000 q^{31} -1.00000 q^{32} +0.579926 q^{33} -1.82639 q^{34} +3.48262 q^{35} -2.90823 q^{36} +7.40250 q^{37} -1.01716 q^{38} +0.583195 q^{39} -3.48262 q^{40} -0.862951 q^{41} +0.302933 q^{42} -9.48027 q^{43} -1.91437 q^{44} -10.1283 q^{45} -6.54224 q^{46} +10.0569 q^{47} -0.302933 q^{48} +1.00000 q^{49} -7.12864 q^{50} -0.553274 q^{51} -1.92516 q^{52} -8.58123 q^{53} -1.78980 q^{54} -6.66702 q^{55} -1.00000 q^{56} -0.308130 q^{57} +3.90924 q^{58} -8.32439 q^{59} -1.05500 q^{60} +7.64798 q^{61} -0.512000 q^{62} -2.90823 q^{63} +1.00000 q^{64} -6.70461 q^{65} -0.579926 q^{66} +4.94053 q^{67} +1.82639 q^{68} -1.98186 q^{69} -3.48262 q^{70} +15.2352 q^{71} +2.90823 q^{72} +1.56068 q^{73} -7.40250 q^{74} -2.15950 q^{75} +1.01716 q^{76} -1.91437 q^{77} -0.583195 q^{78} -13.3175 q^{79} +3.48262 q^{80} +8.18250 q^{81} +0.862951 q^{82} -7.95719 q^{83} -0.302933 q^{84} +6.36062 q^{85} +9.48027 q^{86} +1.18424 q^{87} +1.91437 q^{88} +10.4230 q^{89} +10.1283 q^{90} -1.92516 q^{91} +6.54224 q^{92} -0.155102 q^{93} -10.0569 q^{94} +3.54237 q^{95} +0.302933 q^{96} +14.5403 q^{97} -1.00000 q^{98} +5.56743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.302933	−0.174899	−0.0874493	−	0.996169i	$-0.527872\pi$
$3$	−0.302933	−0.174899	−0.0874493	+	0.996169i	$0.527872\pi$
$4$	1.00000	0.500000
$5$	3.48262	1.55747	0.778737	−	0.627350i	$-0.215860\pi$
$5$	3.48262	1.55747	0.778737	+	0.627350i	$0.215860\pi$
$6$	0.302933	0.123672
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.90823	−0.969410
$10$	−3.48262	−1.10130
$11$	−1.91437	−0.577204	−0.288602	−	0.957449i	$-0.593190\pi$
$11$	−1.91437	−0.577204	−0.288602	+	0.957449i	$0.593190\pi$
$12$	−0.302933	−0.0874493
$13$	−1.92516	−0.533944	−0.266972	−	0.963704i	$-0.586023\pi$
$13$	−1.92516	−0.533944	−0.266972	+	0.963704i	$0.586023\pi$
$14$	−1.00000	−0.267261
$15$	−1.05500	−0.272400
$16$	1.00000	0.250000
$17$	1.82639	0.442965	0.221482	−	0.975164i	$-0.428910\pi$
$17$	1.82639	0.442965	0.221482	+	0.975164i	$0.428910\pi$
$18$	2.90823	0.685477
$19$	1.01716	0.233352	0.116676	−	0.993170i	$-0.462776\pi$
$19$	1.01716	0.233352	0.116676	+	0.993170i	$0.462776\pi$
$20$	3.48262	0.778737
$21$	−0.302933	−0.0661055
$22$	1.91437	0.408145
$23$	6.54224	1.36415	0.682076	−	0.731281i	$-0.261077\pi$
$23$	6.54224	1.36415	0.682076	+	0.731281i	$0.261077\pi$
$24$	0.302933	0.0618360
$25$	7.12864	1.42573
$26$	1.92516	0.377555
$27$	1.78980	0.344447
$28$	1.00000	0.188982
$29$	−3.90924	−0.725927	−0.362964	−	0.931803i	$-0.618235\pi$
$29$	−3.90924	−0.725927	−0.362964	+	0.931803i	$0.618235\pi$
$30$	1.05500	0.192616
$31$	0.512000	0.0919579	0.0459789	−	0.998942i	$-0.485359\pi$
$31$	0.512000	0.0919579	0.0459789	+	0.998942i	$0.485359\pi$
$32$	−1.00000	−0.176777
$33$	0.579926	0.100952
$34$	−1.82639	−0.313223
$35$	3.48262	0.588670
$36$	−2.90823	−0.484705
$37$	7.40250	1.21696	0.608481	−	0.793568i	$-0.291779\pi$
$37$	7.40250	1.21696	0.608481	+	0.793568i	$0.291779\pi$
$38$	−1.01716	−0.165005
$39$	0.583195	0.0933860
$40$	−3.48262	−0.550651
$41$	−0.862951	−0.134770	−0.0673852	−	0.997727i	$-0.521466\pi$
$41$	−0.862951	−0.134770	−0.0673852	+	0.997727i	$0.521466\pi$
$42$	0.302933	0.0467436
$43$	−9.48027	−1.44573	−0.722864	−	0.690991i	$-0.757175\pi$
$43$	−9.48027	−1.44573	−0.722864	+	0.690991i	$0.757175\pi$
$44$	−1.91437	−0.288602
$45$	−10.1283	−1.50983
$46$	−6.54224	−0.964601
$47$	10.0569	1.46694	0.733472	−	0.679719i	$-0.237898\pi$
$47$	10.0569	1.46694	0.733472	+	0.679719i	$0.237898\pi$
$48$	−0.302933	−0.0437246
$49$	1.00000	0.142857
$50$	−7.12864	−1.00814
$51$	−0.553274	−0.0774739
$52$	−1.92516	−0.266972
$53$	−8.58123	−1.17872	−0.589361	−	0.807870i	$-0.700621\pi$
$53$	−8.58123	−1.17872	−0.589361	+	0.807870i	$0.700621\pi$
$54$	−1.78980	−0.243561
$55$	−6.66702	−0.898980
$56$	−1.00000	−0.133631
$57$	−0.308130	−0.0408129
$58$	3.90924	0.513308
$59$	−8.32439	−1.08374	−0.541872	−	0.840461i	$-0.682284\pi$
$59$	−8.32439	−1.08374	−0.541872	+	0.840461i	$0.682284\pi$
$60$	−1.05500	−0.136200
$61$	7.64798	0.979224	0.489612	−	0.871941i	$-0.337138\pi$
$61$	7.64798	0.979224	0.489612	+	0.871941i	$0.337138\pi$
$62$	−0.512000	−0.0650241
$63$	−2.90823	−0.366403
$64$	1.00000	0.125000
$65$	−6.70461	−0.831604
$66$	−0.579926	−0.0713839
$67$	4.94053	0.603581	0.301791	−	0.953374i	$-0.402416\pi$
$67$	4.94053	0.603581	0.301791	+	0.953374i	$0.402416\pi$
$68$	1.82639	0.221482
$69$	−1.98186	−0.238588
$70$	−3.48262	−0.416253
$71$	15.2352	1.80809	0.904046	−	0.427436i	$-0.140583\pi$
$71$	15.2352	1.80809	0.904046	+	0.427436i	$0.140583\pi$
$72$	2.90823	0.342738
$73$	1.56068	0.182664	0.0913319	−	0.995821i	$-0.470888\pi$
$73$	1.56068	0.182664	0.0913319	+	0.995821i	$0.470888\pi$
$74$	−7.40250	−0.860523
$75$	−2.15950	−0.249358
$76$	1.01716	0.116676
$77$	−1.91437	−0.218163
$78$	−0.583195	−0.0660339
$79$	−13.3175	−1.49834	−0.749168	−	0.662380i	$-0.769547\pi$
$79$	−13.3175	−1.49834	−0.749168	+	0.662380i	$0.769547\pi$
$80$	3.48262	0.389369
$81$	8.18250	0.909167
$82$	0.862951	0.0952970
$83$	−7.95719	−0.873415	−0.436707	−	0.899604i	$-0.643855\pi$
$83$	−7.95719	−0.873415	−0.436707	+	0.899604i	$0.643855\pi$
$84$	−0.302933	−0.0330527
$85$	6.36062	0.689906
$86$	9.48027	1.02228
$87$	1.18424	0.126964
$88$	1.91437	0.204072
$89$	10.4230	1.10483	0.552416	−	0.833568i	$-0.313706\pi$
$89$	10.4230	1.10483	0.552416	+	0.833568i	$0.313706\pi$
$90$	10.1283	1.06761
$91$	−1.92516	−0.201812
$92$	6.54224	0.682076
$93$	−0.155102	−0.0160833
$94$	−10.0569	−1.03729
$95$	3.54237	0.363439
$96$	0.302933	0.0309180
$97$	14.5403	1.47634	0.738169	−	0.674615i	$-0.235690\pi$
$97$	14.5403	1.47634	0.738169	+	0.674615i	$0.235690\pi$
$98$	−1.00000	−0.101015
$99$	5.56743	0.559547
$100$	7.12864	0.712864
$101$	−3.27506	−0.325880	−0.162940	−	0.986636i	$-0.552098\pi$
$101$	−3.27506	−0.325880	−0.162940	+	0.986636i	$0.552098\pi$
$102$	0.553274	0.0547823
$103$	13.8964	1.36926	0.684628	−	0.728893i	$-0.259965\pi$
$103$	13.8964	1.36926	0.684628	+	0.728893i	$0.259965\pi$
$104$	1.92516	0.188778
$105$	−1.05500	−0.102958
$106$	8.58123	0.833483
$107$	9.35436	0.904320	0.452160	−	0.891937i	$-0.350654\pi$
$107$	9.35436	0.904320	0.452160	+	0.891937i	$0.350654\pi$
$108$	1.78980	0.172224
$109$	−2.66608	−0.255364	−0.127682	−	0.991815i	$-0.540754\pi$
$109$	−2.66608	−0.255364	−0.127682	+	0.991815i	$0.540754\pi$
$110$	6.66702	0.635675
$111$	−2.24246	−0.212845
$112$	1.00000	0.0944911
$113$	5.46792	0.514379	0.257189	−	0.966361i	$-0.417204\pi$
$113$	5.46792	0.514379	0.257189	+	0.966361i	$0.417204\pi$
$114$	0.308130	0.0288591
$115$	22.7842	2.12463
$116$	−3.90924	−0.362964
$117$	5.59882	0.517611
$118$	8.32439	0.766322
$119$	1.82639	0.167425
$120$	1.05500	0.0963080
$121$	−7.33519	−0.666836
$122$	−7.64798	−0.692416
$123$	0.261417	0.0235711
$124$	0.512000	0.0459789
$125$	7.41324	0.663060
$126$	2.90823	0.259086
$127$	0.571720	0.0507319	0.0253660	−	0.999678i	$-0.491925\pi$
$127$	0.571720	0.0507319	0.0253660	+	0.999678i	$0.491925\pi$
$128$	−1.00000	−0.0883883
$129$	2.87189	0.252856
$130$	6.70461	0.588033
$131$	−10.9741	−0.958815	−0.479408	−	0.877592i	$-0.659148\pi$
$131$	−10.9741	−0.958815	−0.479408	+	0.877592i	$0.659148\pi$
$132$	0.579926	0.0504761
$133$	1.01716	0.0881987
$134$	−4.94053	−0.426797
$135$	6.23319	0.536468
$136$	−1.82639	−0.156612
$137$	22.2644	1.90218	0.951088	−	0.308921i	$-0.0999677\pi$
$137$	22.2644	1.90218	0.951088	+	0.308921i	$0.0999677\pi$
$138$	1.98186	0.168707
$139$	8.58524	0.728191	0.364095	−	0.931362i	$-0.381378\pi$
$139$	8.58524	0.728191	0.364095	+	0.931362i	$0.381378\pi$
$140$	3.48262	0.294335
$141$	−3.04656	−0.256566
$142$	−15.2352	−1.27851
$143$	3.68547	0.308194
$144$	−2.90823	−0.242353
$145$	−13.6144	−1.13061
$146$	−1.56068	−0.129163
$147$	−0.302933	−0.0249855
$148$	7.40250	0.608481
$149$	−15.8274	−1.29663	−0.648316	−	0.761371i	$-0.724526\pi$
$149$	−15.8274	−1.29663	−0.648316	+	0.761371i	$0.724526\pi$
$150$	2.15950	0.176323
$151$	20.5923	1.67578	0.837888	−	0.545841i	$-0.183790\pi$
$151$	20.5923	1.67578	0.837888	+	0.545841i	$0.183790\pi$
$152$	−1.01716	−0.0825023
$153$	−5.31157	−0.429415
$154$	1.91437	0.154264
$155$	1.78310	0.143222
$156$	0.583195	0.0466930
$157$	−0.115956	−0.00925432	−0.00462716	−	0.999989i	$-0.501473\pi$
$157$	−0.115956	−0.00925432	−0.00462716	+	0.999989i	$0.501473\pi$
$158$	13.3175	1.05948
$159$	2.59954	0.206157
$160$	−3.48262	−0.275325
$161$	6.54224	0.515601
$162$	−8.18250	−0.642878
$163$	1.34615	0.105439	0.0527195	−	0.998609i	$-0.483211\pi$
$163$	1.34615	0.105439	0.0527195	+	0.998609i	$0.483211\pi$
$164$	−0.862951	−0.0673852
$165$	2.01966	0.157230
$166$	7.95719	0.617597
$167$	4.88861	0.378292	0.189146	−	0.981949i	$-0.439428\pi$
$167$	4.88861	0.378292	0.189146	+	0.981949i	$0.439428\pi$
$168$	0.302933	0.0233718
$169$	−9.29375	−0.714904
$170$	−6.36062	−0.487837
$171$	−2.95813	−0.226214
$172$	−9.48027	−0.722864
$173$	15.1827	1.15432	0.577159	−	0.816632i	$-0.304161\pi$
$173$	15.1827	1.15432	0.577159	+	0.816632i	$0.304161\pi$
$174$	−1.18424	−0.0897769
$175$	7.12864	0.538874
$176$	−1.91437	−0.144301
$177$	2.52173	0.189545
$178$	−10.4230	−0.781235
$179$	0.169747	0.0126875	0.00634376	−	0.999980i	$-0.497981\pi$
$179$	0.169747	0.0126875	0.00634376	+	0.999980i	$0.497981\pi$
$180$	−10.1283	−0.754916
$181$	21.4257	1.59256	0.796278	−	0.604930i	$-0.206799\pi$
$181$	21.4257	1.59256	0.796278	+	0.604930i	$0.206799\pi$
$182$	1.92516	0.142702
$183$	−2.31683	−0.171265
$184$	−6.54224	−0.482301
$185$	25.7801	1.89539
$186$	0.155102	0.0113726
$187$	−3.49638	−0.255681
$188$	10.0569	0.733472
$189$	1.78980	0.130189
$190$	−3.54237	−0.256990
$191$	18.0481	1.30591	0.652957	−	0.757395i	$-0.273528\pi$
$191$	18.0481	1.30591	0.652957	+	0.757395i	$0.273528\pi$
$192$	−0.302933	−0.0218623
$193$	4.28509	0.308447	0.154224	−	0.988036i	$-0.450712\pi$
$193$	4.28509	0.308447	0.154224	+	0.988036i	$0.450712\pi$
$194$	−14.5403	−1.04393
$195$	2.03105	0.145446
$196$	1.00000	0.0714286
$197$	−22.1478	−1.57797	−0.788983	−	0.614414i	$-0.789392\pi$
$197$	−22.1478	−1.57797	−0.788983	+	0.614414i	$0.789392\pi$
$198$	−5.56743	−0.395660
$199$	−0.693164	−0.0491371	−0.0245686	−	0.999698i	$-0.507821\pi$
$199$	−0.693164	−0.0491371	−0.0245686	+	0.999698i	$0.507821\pi$
$200$	−7.12864	−0.504071
$201$	−1.49665	−0.105566
$202$	3.27506	0.230432
$203$	−3.90924	−0.274375
$204$	−0.553274	−0.0387369
$205$	−3.00533	−0.209901
$206$	−13.8964	−0.968210
$207$	−19.0264	−1.32242
$208$	−1.92516	−0.133486
$209$	−1.94721	−0.134691
$210$	1.05500	0.0728020
$211$	−23.5216	−1.61929	−0.809646	−	0.586918i	$-0.800341\pi$
$211$	−23.5216	−1.61929	−0.809646	+	0.586918i	$0.800341\pi$
$212$	−8.58123	−0.589361
$213$	−4.61526	−0.316233
$214$	−9.35436	−0.639451
$215$	−33.0162	−2.25168
$216$	−1.78980	−0.121780
$217$	0.512000	0.0347568
$218$	2.66608	0.180569
$219$	−0.472782	−0.0319476
$220$	−6.66702	−0.449490
$221$	−3.51610	−0.236518
$222$	2.24246	0.150504
$223$	4.79823	0.321313	0.160657	−	0.987010i	$-0.448639\pi$
$223$	4.79823	0.321313	0.160657	+	0.987010i	$0.448639\pi$
$224$	−1.00000	−0.0668153
$225$	−20.7317	−1.38212
$226$	−5.46792	−0.363721
$227$	−22.3634	−1.48431	−0.742154	−	0.670229i	$-0.766196\pi$
$227$	−22.3634	−1.48431	−0.742154	+	0.670229i	$0.766196\pi$
$228$	−0.308130	−0.0204064
$229$	−18.5439	−1.22542	−0.612709	−	0.790309i	$-0.709920\pi$
$229$	−18.5439	−1.22542	−0.612709	+	0.790309i	$0.709920\pi$
$230$	−22.7842	−1.50234
$231$	0.579926	0.0381563
$232$	3.90924	0.256654
$233$	26.7539	1.75271	0.876354	−	0.481668i	$-0.159969\pi$
$233$	26.7539	1.75271	0.876354	+	0.481668i	$0.159969\pi$
$234$	−5.59882	−0.366006
$235$	35.0242	2.28473
$236$	−8.32439	−0.541872
$237$	4.03432	0.262057
$238$	−1.82639	−0.118387
$239$	25.9927	1.68133	0.840664	−	0.541557i	$-0.182165\pi$
$239$	25.9927	1.68133	0.840664	+	0.541557i	$0.182165\pi$
$240$	−1.05500	−0.0681000
$241$	7.96288	0.512935	0.256467	−	0.966553i	$-0.417441\pi$
$241$	7.96288	0.512935	0.256467	+	0.966553i	$0.417441\pi$
$242$	7.33519	0.471524
$243$	−7.84815	−0.503459
$244$	7.64798	0.489612
$245$	3.48262	0.222496
$246$	−0.261417	−0.0166673
$247$	−1.95819	−0.124597
$248$	−0.512000	−0.0325120
$249$	2.41050	0.152759
$250$	−7.41324	−0.468854
$251$	19.9403	1.25862	0.629310	−	0.777154i	$-0.283338\pi$
$251$	19.9403	1.25862	0.629310	+	0.777154i	$0.283338\pi$
$252$	−2.90823	−0.183201
$253$	−12.5243	−0.787394
$254$	−0.571720	−0.0358729
$255$	−1.92684	−0.120664
$256$	1.00000	0.0625000
$257$	19.1718	1.19590	0.597951	−	0.801533i	$-0.295982\pi$
$257$	19.1718	1.19590	0.597951	+	0.801533i	$0.295982\pi$
$258$	−2.87189	−0.178796
$259$	7.40250	0.459969
$260$	−6.70461	−0.415802
$261$	11.3690	0.703722
$262$	10.9741	0.677985
$263$	−25.0637	−1.54549	−0.772747	−	0.634715i	$-0.781118\pi$
$263$	−25.0637	−1.54549	−0.772747	+	0.634715i	$0.781118\pi$
$264$	−0.579926	−0.0356920
$265$	−29.8852	−1.83583
$266$	−1.01716	−0.0623659
$267$	−3.15746	−0.193234
$268$	4.94053	0.301791
$269$	−15.4170	−0.939994	−0.469997	−	0.882668i	$-0.655745\pi$
$269$	−15.4170	−0.939994	−0.469997	+	0.882668i	$0.655745\pi$
$270$	−6.23319	−0.379340
$271$	13.3381	0.810232	0.405116	−	0.914265i	$-0.367231\pi$
$271$	13.3381	0.810232	0.405116	+	0.914265i	$0.367231\pi$
$272$	1.82639	0.110741
$273$	0.583195	0.0352966
$274$	−22.2644	−1.34504
$275$	−13.6468	−0.822935
$276$	−1.98186	−0.119294
$277$	6.92924	0.416337	0.208169	−	0.978093i	$-0.433250\pi$
$277$	6.92924	0.416337	0.208169	+	0.978093i	$0.433250\pi$
$278$	−8.58524	−0.514909
$279$	−1.48901	−0.0891449
$280$	−3.48262	−0.208126
$281$	−25.6536	−1.53037	−0.765183	−	0.643813i	$-0.777352\pi$
$281$	−25.6536	−1.53037	−0.765183	+	0.643813i	$0.777352\pi$
$282$	3.04656	0.181420
$283$	23.0644	1.37104	0.685518	−	0.728056i	$-0.259576\pi$
$283$	23.0644	1.37104	0.685518	+	0.728056i	$0.259576\pi$
$284$	15.2352	0.904046
$285$	−1.07310	−0.0635650
$286$	−3.68547	−0.217926
$287$	−0.862951	−0.0509384
$288$	2.90823	0.171369
$289$	−13.6643	−0.803782
$290$	13.6144	0.799465
$291$	−4.40473	−0.258210
$292$	1.56068	0.0913319
$293$	−9.00057	−0.525819	−0.262909	−	0.964821i	$-0.584682\pi$
$293$	−9.00057	−0.525819	−0.262909	+	0.964821i	$0.584682\pi$
$294$	0.302933	0.0176674
$295$	−28.9907	−1.68790
$296$	−7.40250	−0.430261
$297$	−3.42634	−0.198816
$298$	15.8274	0.916857
$299$	−12.5949	−0.728381
$300$	−2.15950	−0.124679
$301$	−9.48027	−0.546434
$302$	−20.5923	−1.18495
$303$	0.992124	0.0569960
$304$	1.01716	0.0583379
$305$	26.6350	1.52512
$306$	5.31157	0.303642
$307$	12.1794	0.695118	0.347559	−	0.937658i	$-0.387011\pi$
$307$	12.1794	0.695118	0.347559	+	0.937658i	$0.387011\pi$
$308$	−1.91437	−0.109081
$309$	−4.20969	−0.239481
$310$	−1.78310	−0.101273
$311$	27.3388	1.55024	0.775120	−	0.631815i	$-0.217690\pi$
$311$	27.3388	1.55024	0.775120	+	0.631815i	$0.217690\pi$
$312$	−0.583195	−0.0330169
$313$	−28.4950	−1.61063	−0.805315	−	0.592847i	$-0.798004\pi$
$313$	−28.4950	−1.61063	−0.805315	+	0.592847i	$0.798004\pi$
$314$	0.115956	0.00654379
$315$	−10.1283	−0.570663
$316$	−13.3175	−0.749168
$317$	3.10398	0.174337	0.0871685	−	0.996194i	$-0.472218\pi$
$317$	3.10398	0.174337	0.0871685	+	0.996194i	$0.472218\pi$
$318$	−2.59954	−0.145775
$319$	7.48372	0.419008
$320$	3.48262	0.194684
$321$	−2.83375	−0.158164
$322$	−6.54224	−0.364585
$323$	1.85772	0.103367
$324$	8.18250	0.454584
$325$	−13.7238	−0.761258
$326$	−1.34615	−0.0745566
$327$	0.807643	0.0446628
$328$	0.862951	0.0476485
$329$	10.0569	0.554453
$330$	−2.01966	−0.111179
$331$	21.7628	1.19619	0.598096	−	0.801424i	$-0.295924\pi$
$331$	21.7628	1.19619	0.598096	+	0.801424i	$0.295924\pi$
$332$	−7.95719	−0.436707
$333$	−21.5282	−1.17974
$334$	−4.88861	−0.267493
$335$	17.2060	0.940063
$336$	−0.302933	−0.0165264
$337$	−11.4965	−0.626254	−0.313127	−	0.949711i	$-0.601376\pi$
$337$	−11.4965	−0.626254	−0.313127	+	0.949711i	$0.601376\pi$
$338$	9.29375	0.505514
$339$	−1.65641	−0.0899641
$340$	6.36062	0.344953
$341$	−0.980156	−0.0530784
$342$	2.95813	0.159957
$343$	1.00000	0.0539949
$344$	9.48027	0.511142
$345$	−6.90208	−0.371595
$346$	−15.1827	−0.816226
$347$	13.2049	0.708876	0.354438	−	0.935080i	$-0.384672\pi$
$347$	13.2049	0.708876	0.354438	+	0.935080i	$0.384672\pi$
$348$	1.18424	0.0634818
$349$	14.9290	0.799129	0.399564	−	0.916705i	$-0.369161\pi$
$349$	14.9290	0.799129	0.399564	+	0.916705i	$0.369161\pi$
$350$	−7.12864	−0.381042
$351$	−3.44565	−0.183915
$352$	1.91437	0.102036
$353$	−10.0961	−0.537362	−0.268681	−	0.963229i	$-0.586588\pi$
$353$	−10.0961	−0.537362	−0.268681	+	0.963229i	$0.586588\pi$
$354$	−2.52173	−0.134029
$355$	53.0586	2.81606
$356$	10.4230	0.552416
$357$	−0.553274	−0.0292824
$358$	−0.169747	−0.00897143
$359$	8.88249	0.468800	0.234400	−	0.972140i	$-0.424687\pi$
$359$	8.88249	0.468800	0.234400	+	0.972140i	$0.424687\pi$
$360$	10.1283	0.533806
$361$	−17.9654	−0.945547
$362$	−21.4257	−1.12611
$363$	2.22207	0.116629
$364$	−1.92516	−0.100906
$365$	5.43526	0.284494
$366$	2.31683	0.121103
$367$	16.2208	0.846721	0.423361	−	0.905961i	$-0.360850\pi$
$367$	16.2208	0.846721	0.423361	+	0.905961i	$0.360850\pi$
$368$	6.54224	0.341038
$369$	2.50966	0.130648
$370$	−25.7801	−1.34024
$371$	−8.58123	−0.445515
$372$	−0.155102	−0.00804165
$373$	−36.6280	−1.89652	−0.948262	−	0.317488i	$-0.897161\pi$
$373$	−36.6280	−1.89652	−0.948262	+	0.317488i	$0.897161\pi$
$374$	3.49638	0.180794
$375$	−2.24572	−0.115968
$376$	−10.0569	−0.518643
$377$	7.52592	0.387604
$378$	−1.78980	−0.0920574
$379$	−23.9027	−1.22780	−0.613900	−	0.789384i	$-0.710400\pi$
$379$	−23.9027	−1.22780	−0.613900	+	0.789384i	$0.710400\pi$
$380$	3.54237	0.181720
$381$	−0.173193	−0.00887294
$382$	−18.0481	−0.923421
$383$	23.7631	1.21424	0.607119	−	0.794611i	$-0.292325\pi$
$383$	23.7631	1.21424	0.607119	+	0.794611i	$0.292325\pi$
$384$	0.302933	0.0154590
$385$	−6.66702	−0.339783
$386$	−4.28509	−0.218105
$387$	27.5708	1.40150
$388$	14.5403	0.738169
$389$	16.0455	0.813539	0.406770	−	0.913531i	$-0.366655\pi$
$389$	16.0455	0.813539	0.406770	+	0.913531i	$0.366655\pi$
$390$	−2.03105	−0.102846
$391$	11.9487	0.604271
$392$	−1.00000	−0.0505076
$393$	3.32443	0.167695
$394$	22.1478	1.11579
$395$	−46.3798	−2.33362
$396$	5.56743	0.279774
$397$	−14.3095	−0.718172	−0.359086	−	0.933304i	$-0.616912\pi$
$397$	−14.3095	−0.718172	−0.359086	+	0.933304i	$0.616912\pi$
$398$	0.693164	0.0347452
$399$	−0.308130	−0.0154258
$400$	7.12864	0.356432
$401$	−21.7196	−1.08463	−0.542313	−	0.840176i	$-0.682451\pi$
$401$	−21.7196	−1.08463	−0.542313	+	0.840176i	$0.682451\pi$
$402$	1.49665	0.0746461
$403$	−0.985682	−0.0491003
$404$	−3.27506	−0.162940
$405$	28.4966	1.41600
$406$	3.90924	0.194012
$407$	−14.1711	−0.702435
$408$	0.553274	0.0273912
$409$	−3.32431	−0.164376	−0.0821882	−	0.996617i	$-0.526191\pi$
$409$	−3.32431	−0.164376	−0.0821882	+	0.996617i	$0.526191\pi$
$410$	3.00533	0.148423
$411$	−6.74463	−0.332688
$412$	13.8964	0.684628
$413$	−8.32439	−0.409616
$414$	19.0264	0.935095
$415$	−27.7119	−1.36032
$416$	1.92516	0.0943888
$417$	−2.60076	−0.127360
$418$	1.94721	0.0952413
$419$	14.8310	0.724541	0.362270	−	0.932073i	$-0.382002\pi$
$419$	14.8310	0.724541	0.362270	+	0.932073i	$0.382002\pi$
$420$	−1.05500	−0.0514788
$421$	−9.59142	−0.467457	−0.233729	−	0.972302i	$-0.575093\pi$
$421$	−9.59142	−0.467457	−0.233729	+	0.972302i	$0.575093\pi$
$422$	23.5216	1.14501
$423$	−29.2477	−1.42207
$424$	8.58123	0.416741
$425$	13.0197	0.631547
$426$	4.61526	0.223610
$427$	7.64798	0.370112
$428$	9.35436	0.452160
$429$	−1.11645	−0.0539028
$430$	33.0162	1.59218
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.78980	0.0861118
$433$	32.8822	1.58022	0.790108	−	0.612968i	$-0.210024\pi$
$433$	32.8822	1.58022	0.790108	+	0.612968i	$0.210024\pi$
$434$	−0.512000	−0.0245768
$435$	4.12425	0.197743
$436$	−2.66608	−0.127682
$437$	6.65449	0.318327
$438$	0.472782	0.0225904
$439$	34.9620	1.66864	0.834322	−	0.551277i	$-0.185859\pi$
$439$	34.9620	1.66864	0.834322	+	0.551277i	$0.185859\pi$
$440$	6.66702	0.317838
$441$	−2.90823	−0.138487
$442$	3.51610	0.167244
$443$	−18.9694	−0.901264	−0.450632	−	0.892710i	$-0.648801\pi$
$443$	−18.9694	−0.901264	−0.450632	+	0.892710i	$0.648801\pi$
$444$	−2.24246	−0.106423
$445$	36.2992	1.72075
$446$	−4.79823	−0.227203
$447$	4.79465	0.226779
$448$	1.00000	0.0472456
$449$	22.8591	1.07879	0.539394	−	0.842054i	$-0.318654\pi$
$449$	22.8591	1.07879	0.539394	+	0.842054i	$0.318654\pi$
$450$	20.7317	0.977303
$451$	1.65201	0.0777900
$452$	5.46792	0.257189
$453$	−6.23809	−0.293091
$454$	22.3634	1.04956
$455$	−6.70461	−0.314317
$456$	0.308130	0.0144295
$457$	21.8786	1.02344	0.511719	−	0.859153i	$-0.329009\pi$
$457$	21.8786	1.02344	0.511719	+	0.859153i	$0.329009\pi$
$458$	18.5439	0.866501
$459$	3.26887	0.152578
$460$	22.7842	1.06232
$461$	10.8196	0.503917	0.251959	−	0.967738i	$-0.418925\pi$
$461$	10.8196	0.503917	0.251959	+	0.967738i	$0.418925\pi$
$462$	−0.579926	−0.0269806
$463$	14.8770	0.691394	0.345697	−	0.938346i	$-0.387642\pi$
$463$	14.8770	0.691394	0.345697	+	0.938346i	$0.387642\pi$
$464$	−3.90924	−0.181482
$465$	−0.540161	−0.0250493
$466$	−26.7539	−1.23935
$467$	31.2927	1.44805	0.724027	−	0.689771i	$-0.242289\pi$
$467$	31.2927	1.44805	0.724027	+	0.689771i	$0.242289\pi$
$468$	5.59882	0.258805
$469$	4.94053	0.228132
$470$	−35.0242	−1.61555
$471$	0.0351270	0.00161857
$472$	8.32439	0.383161
$473$	18.1487	0.834479
$474$	−4.03432	−0.185302
$475$	7.25094	0.332696
$476$	1.82639	0.0837125
$477$	24.9562	1.14267
$478$	−25.9927	−1.18888
$479$	−13.2879	−0.607139	−0.303569	−	0.952809i	$-0.598178\pi$
$479$	−13.2879	−0.607139	−0.303569	+	0.952809i	$0.598178\pi$
$480$	1.05500	0.0481540
$481$	−14.2510	−0.649790
$482$	−7.96288	−0.362699
$483$	−1.98186	−0.0901779
$484$	−7.33519	−0.333418
$485$	50.6382	2.29936
$486$	7.84815	0.355999
$487$	−5.51871	−0.250077	−0.125038	−	0.992152i	$-0.539905\pi$
$487$	−5.51871	−0.250077	−0.125038	+	0.992152i	$0.539905\pi$
$488$	−7.64798	−0.346208
$489$	−0.407795	−0.0184411
$490$	−3.48262	−0.157329
$491$	−36.8120	−1.66130	−0.830650	−	0.556795i	$-0.812031\pi$
$491$	−36.8120	−1.66130	−0.830650	+	0.556795i	$0.812031\pi$
$492$	0.261417	0.0117856
$493$	−7.13980	−0.321560
$494$	1.95819	0.0881032
$495$	19.3892	0.871481
$496$	0.512000	0.0229895
$497$	15.2352	0.683394
$498$	−2.41050	−0.108017
$499$	−4.65066	−0.208192	−0.104096	−	0.994567i	$-0.533195\pi$
$499$	−4.65066	−0.208192	−0.104096	+	0.994567i	$0.533195\pi$
$500$	7.41324	0.331530
$501$	−1.48092	−0.0661628
$502$	−19.9403	−0.889979
$503$	−9.96403	−0.444274	−0.222137	−	0.975015i	$-0.571303\pi$
$503$	−9.96403	−0.444274	−0.222137	+	0.975015i	$0.571303\pi$
$504$	2.90823	0.129543
$505$	−11.4058	−0.507551
$506$	12.5243	0.556772
$507$	2.81539	0.125036
$508$	0.571720	0.0253660
$509$	−25.8537	−1.14595	−0.572974	−	0.819574i	$-0.694210\pi$
$509$	−25.8537	−1.14595	−0.572974	+	0.819574i	$0.694210\pi$
$510$	1.92684	0.0853221
$511$	1.56068	0.0690404
$512$	−1.00000	−0.0441942
$513$	1.82051	0.0803773
$514$	−19.1718	−0.845631
$515$	48.3960	2.13258
$516$	2.87189	0.126428
$517$	−19.2525	−0.846726
$518$	−7.40250	−0.325247
$519$	−4.59934	−0.201888
$520$	6.70461	0.294016
$521$	22.7595	0.997112	0.498556	−	0.866858i	$-0.333864\pi$
$521$	22.7595	0.997112	0.498556	+	0.866858i	$0.333864\pi$
$522$	−11.3690	−0.497606
$523$	27.2108	1.18984	0.594922	−	0.803784i	$-0.297183\pi$
$523$	27.2108	1.18984	0.594922	+	0.803784i	$0.297183\pi$
$524$	−10.9741	−0.479408
$525$	−2.15950	−0.0942484
$526$	25.0637	1.09283
$527$	0.935112	0.0407341
$528$	0.579926	0.0252380
$529$	19.8010	0.860912
$530$	29.8852	1.29813
$531$	24.2093	1.05059
$532$	1.01716	0.0440993
$533$	1.66132	0.0719598
$534$	3.15746	0.136637
$535$	32.5777	1.40846
$536$	−4.94053	−0.213398
$537$	−0.0514221	−0.00221903
$538$	15.4170	0.664676
$539$	−1.91437	−0.0824577
$540$	6.23319	0.268234
$541$	−33.8480	−1.45524	−0.727619	−	0.685981i	$-0.759373\pi$
$541$	−33.8480	−1.45524	−0.727619	+	0.685981i	$0.759373\pi$
$542$	−13.3381	−0.572920
$543$	−6.49054	−0.278536
$544$	−1.82639	−0.0783058
$545$	−9.28493	−0.397723
$546$	−0.583195	−0.0249585
$547$	20.3965	0.872089	0.436045	−	0.899925i	$-0.356379\pi$
$547$	20.3965	0.872089	0.436045	+	0.899925i	$0.356379\pi$
$548$	22.2644	0.951088
$549$	−22.2421	−0.949270
$550$	13.6468	0.581903
$551$	−3.97631	−0.169396
$552$	1.98186	0.0843537
$553$	−13.3175	−0.566318
$554$	−6.92924	−0.294395
$555$	−7.80964	−0.331501
$556$	8.58524	0.364095
$557$	−26.1282	−1.10709	−0.553543	−	0.832821i	$-0.686725\pi$
$557$	−26.1282	−1.10709	−0.553543	+	0.832821i	$0.686725\pi$
$558$	1.48901	0.0630350
$559$	18.2510	0.771937
$560$	3.48262	0.147168
$561$	1.05917	0.0447182
$562$	25.6536	1.08213
$563$	25.1695	1.06077	0.530385	−	0.847757i	$-0.322048\pi$
$563$	25.1695	1.06077	0.530385	+	0.847757i	$0.322048\pi$
$564$	−3.04656	−0.128283
$565$	19.0427	0.801132
$566$	−23.0644	−0.969468
$567$	8.18250	0.343633
$568$	−15.2352	−0.639257
$569$	9.49145	0.397902	0.198951	−	0.980009i	$-0.436247\pi$
$569$	9.49145	0.397902	0.198951	+	0.980009i	$0.436247\pi$
$570$	1.07310	0.0449473
$571$	−24.2199	−1.01357	−0.506786	−	0.862072i	$-0.669167\pi$
$571$	−24.2199	−1.01357	−0.506786	+	0.862072i	$0.669167\pi$
$572$	3.68547	0.154097
$573$	−5.46737	−0.228402
$574$	0.862951	0.0360189
$575$	46.6373	1.94491
$576$	−2.90823	−0.121176
$577$	−10.0433	−0.418108	−0.209054	−	0.977904i	$-0.567038\pi$
$577$	−10.0433	−0.418108	−0.209054	+	0.977904i	$0.567038\pi$
$578$	13.6643	0.568360
$579$	−1.29810	−0.0539470
$580$	−13.6144	−0.565307
$581$	−7.95719	−0.330120
$582$	4.40473	0.182582
$583$	16.4276	0.680363
$584$	−1.56068	−0.0645814
$585$	19.4985	0.806166
$586$	9.00057	0.371810
$587$	−38.7854	−1.60084	−0.800422	−	0.599436i	$-0.795391\pi$
$587$	−38.7854	−1.60084	−0.800422	+	0.599436i	$0.795391\pi$
$588$	−0.302933	−0.0124928
$589$	0.520784	0.0214585
$590$	28.9907	1.19353
$591$	6.70931	0.275984
$592$	7.40250	0.304241
$593$	34.7154	1.42559	0.712795	−	0.701373i	$-0.247429\pi$
$593$	34.7154	1.42559	0.712795	+	0.701373i	$0.247429\pi$
$594$	3.42634	0.140584
$595$	6.36062	0.260760
$596$	−15.8274	−0.648316
$597$	0.209983	0.00859401
$598$	12.5949	0.515043
$599$	30.9846	1.26600	0.632998	−	0.774154i	$-0.281824\pi$
$599$	30.9846	1.26600	0.632998	+	0.774154i	$0.281824\pi$
$600$	2.15950	0.0881613
$601$	−10.1282	−0.413139	−0.206569	−	0.978432i	$-0.566230\pi$
$601$	−10.1282	−0.413139	−0.206569	+	0.978432i	$0.566230\pi$
$602$	9.48027	0.386387
$603$	−14.3682	−0.585118
$604$	20.5923	0.837888
$605$	−25.5457	−1.03858
$606$	−0.992124	−0.0403023
$607$	−35.9899	−1.46078	−0.730392	−	0.683029i	$-0.760662\pi$
$607$	−35.9899	−1.46078	−0.730392	+	0.683029i	$0.760662\pi$
$608$	−1.01716	−0.0412511
$609$	1.18424	0.0479878
$610$	−26.6350	−1.07842
$611$	−19.3611	−0.783266
$612$	−5.31157	−0.214707
$613$	−4.26780	−0.172375	−0.0861874	−	0.996279i	$-0.527468\pi$
$613$	−4.26780	−0.172375	−0.0861874	+	0.996279i	$0.527468\pi$
$614$	−12.1794	−0.491523
$615$	0.910415	0.0367115
$616$	1.91437	0.0771321
$617$	−22.2743	−0.896731	−0.448365	−	0.893850i	$-0.647994\pi$
$617$	−22.2743	−0.896731	−0.448365	+	0.893850i	$0.647994\pi$
$618$	4.20969	0.169338
$619$	8.29204	0.333285	0.166643	−	0.986017i	$-0.446707\pi$
$619$	8.29204	0.333285	0.166643	+	0.986017i	$0.446707\pi$
$620$	1.78310	0.0716111
$621$	11.7093	0.469878
$622$	−27.3388	−1.09618
$623$	10.4230	0.417588
$624$	0.583195	0.0233465
$625$	−9.82570	−0.393028
$626$	28.4950	1.13889
$627$	0.589875	0.0235573
$628$	−0.115956	−0.00462716
$629$	13.5198	0.539072
$630$	10.1283	0.403520
$631$	−17.9364	−0.714036	−0.357018	−	0.934097i	$-0.616207\pi$
$631$	−17.9364	−0.714036	−0.357018	+	0.934097i	$0.616207\pi$
$632$	13.3175	0.529742
$633$	7.12547	0.283212
$634$	−3.10398	−0.123275
$635$	1.99108	0.0790137
$636$	2.59954	0.103078
$637$	−1.92516	−0.0762777
$638$	−7.48372	−0.296283
$639$	−44.3076	−1.75278
$640$	−3.48262	−0.137663
$641$	14.5639	0.575240	0.287620	−	0.957745i	$-0.407136\pi$
$641$	14.5639	0.575240	0.287620	+	0.957745i	$0.407136\pi$
$642$	2.83375	0.111839
$643$	−21.5888	−0.851379	−0.425689	−	0.904869i	$-0.639968\pi$
$643$	−21.5888	−0.851379	−0.425689	+	0.904869i	$0.639968\pi$
$644$	6.54224	0.257801
$645$	10.0017	0.393816
$646$	−1.85772	−0.0730912
$647$	13.6456	0.536465	0.268233	−	0.963354i	$-0.413560\pi$
$647$	13.6456	0.536465	0.268233	+	0.963354i	$0.413560\pi$
$648$	−8.18250	−0.321439
$649$	15.9359	0.625541
$650$	13.7238	0.538291
$651$	−0.155102	−0.00607892
$652$	1.34615	0.0527195
$653$	−15.8211	−0.619128	−0.309564	−	0.950879i	$-0.600183\pi$
$653$	−15.8211	−0.619128	−0.309564	+	0.950879i	$0.600183\pi$
$654$	−0.807643	−0.0315813
$655$	−38.2188	−1.49333
$656$	−0.862951	−0.0336926
$657$	−4.53882	−0.177076
$658$	−10.0569	−0.392057
$659$	39.6128	1.54310	0.771548	−	0.636171i	$-0.219483\pi$
$659$	39.6128	1.54310	0.771548	+	0.636171i	$0.219483\pi$
$660$	2.01966	0.0786152
$661$	12.5026	0.486294	0.243147	−	0.969989i	$-0.421820\pi$
$661$	12.5026	0.486294	0.243147	+	0.969989i	$0.421820\pi$
$662$	−21.7628	−0.845836
$663$	1.06514	0.0413667
$664$	7.95719	0.308799
$665$	3.54237	0.137367
$666$	21.5282	0.834200
$667$	−25.5752	−0.990276
$668$	4.88861	0.189146
$669$	−1.45354	−0.0561972
$670$	−17.2060	−0.664725
$671$	−14.6411	−0.565212
$672$	0.302933	0.0116859
$673$	0.131949	0.00508625	0.00254312	−	0.999997i	$-0.499190\pi$
$673$	0.131949	0.00508625	0.00254312	+	0.999997i	$0.499190\pi$
$674$	11.4965	0.442828
$675$	12.7588	0.491088
$676$	−9.29375	−0.357452
$677$	49.5905	1.90592	0.952958	−	0.303102i	$-0.0980221\pi$
$677$	49.5905	1.90592	0.952958	+	0.303102i	$0.0980221\pi$
$678$	1.65641	0.0636142
$679$	14.5403	0.558004
$680$	−6.36062	−0.243919
$681$	6.77460	0.259603
$682$	0.980156	0.0375321
$683$	11.7692	0.450337	0.225169	−	0.974320i	$-0.427707\pi$
$683$	11.7692	0.450337	0.225169	+	0.974320i	$0.427707\pi$
$684$	−2.95813	−0.113107
$685$	77.5384	2.96259
$686$	−1.00000	−0.0381802
$687$	5.61758	0.214324
$688$	−9.48027	−0.361432
$689$	16.5203	0.629372
$690$	6.90208	0.262758
$691$	31.9012	1.21358	0.606789	−	0.794863i	$-0.292457\pi$
$691$	31.9012	1.21358	0.606789	+	0.794863i	$0.292457\pi$
$692$	15.1827	0.577159
$693$	5.56743	0.211489
$694$	−13.2049	−0.501251
$695$	29.8991	1.13414
$696$	−1.18424	−0.0448884
$697$	−1.57609	−0.0596985
$698$	−14.9290	−0.565069
$699$	−8.10465	−0.306546
$700$	7.12864	0.269437
$701$	29.7539	1.12379	0.561895	−	0.827209i	$-0.310073\pi$
$701$	29.7539	1.12379	0.561895	+	0.827209i	$0.310073\pi$
$702$	3.44565	0.130048
$703$	7.52950	0.283980
$704$	−1.91437	−0.0721505
$705$	−10.6100	−0.399596
$706$	10.0961	0.379972
$707$	−3.27506	−0.123171
$708$	2.52173	0.0947726
$709$	−11.8607	−0.445437	−0.222719	−	0.974883i	$-0.571493\pi$
$709$	−11.8607	−0.445437	−0.222719	+	0.974883i	$0.571493\pi$
$710$	−53.0586	−1.99125
$711$	38.7304	1.45250
$712$	−10.4230	−0.390617
$713$	3.34963	0.125445
$714$	0.553274	0.0207058
$715$	12.8351	0.480005
$716$	0.169747	0.00634376
$717$	−7.87405	−0.294062
$718$	−8.88249	−0.331491
$719$	−39.6319	−1.47802	−0.739011	−	0.673694i	$-0.764707\pi$
$719$	−39.6319	−1.47802	−0.739011	+	0.673694i	$0.764707\pi$
$720$	−10.1283	−0.377458
$721$	13.8964	0.517530
$722$	17.9654	0.668603
$723$	−2.41222	−0.0897115
$724$	21.4257	0.796278
$725$	−27.8676	−1.03498
$726$	−2.22207	−0.0824689
$727$	−10.0250	−0.371805	−0.185903	−	0.982568i	$-0.559521\pi$
$727$	−10.0250	−0.371805	−0.185903	+	0.982568i	$0.559521\pi$
$728$	1.92516	0.0713512
$729$	−22.1700	−0.821113
$730$	−5.43526	−0.201168
$731$	−17.3147	−0.640406
$732$	−2.31683	−0.0856324
$733$	−39.9629	−1.47606	−0.738032	−	0.674766i	$-0.764245\pi$
$733$	−39.9629	−1.47606	−0.738032	+	0.674766i	$0.764245\pi$
$734$	−16.2208	−0.598722
$735$	−1.05500	−0.0389143
$736$	−6.54224	−0.241150
$737$	−9.45799	−0.348389
$738$	−2.50966	−0.0923820
$739$	48.6988	1.79141	0.895707	−	0.444645i	$-0.146670\pi$
$739$	48.6988	1.79141	0.895707	+	0.444645i	$0.146670\pi$
$740$	25.7801	0.947694
$741$	0.593201	0.0217918
$742$	8.58123	0.315027
$743$	3.03146	0.111213	0.0556067	−	0.998453i	$-0.482291\pi$
$743$	3.03146	0.111213	0.0556067	+	0.998453i	$0.482291\pi$
$744$	0.155102	0.00568631
$745$	−55.1209	−2.01947
$746$	36.6280	1.34105
$747$	23.1413	0.846697
$748$	−3.49638	−0.127840
$749$	9.35436	0.341801
$750$	2.24572	0.0820020
$751$	−12.1665	−0.443962	−0.221981	−	0.975051i	$-0.571252\pi$
$751$	−12.1665	−0.443962	−0.221981	+	0.975051i	$0.571252\pi$
$752$	10.0569	0.366736
$753$	−6.04058	−0.220131
$754$	−7.52592	−0.274078
$755$	71.7151	2.60998
$756$	1.78980	0.0650944
$757$	−25.0250	−0.909549	−0.454775	−	0.890607i	$-0.650280\pi$
$757$	−25.0250	−0.909549	−0.454775	+	0.890607i	$0.650280\pi$
$758$	23.9027	0.868186
$759$	3.79402	0.137714
$760$	−3.54237	−0.128495
$761$	−53.5845	−1.94243	−0.971217	−	0.238195i	$-0.923444\pi$
$761$	−53.5845	−1.94243	−0.971217	+	0.238195i	$0.923444\pi$
$762$	0.173193	0.00627412
$763$	−2.66608	−0.0965184
$764$	18.0481	0.652957
$765$	−18.4982	−0.668802
$766$	−23.7631	−0.858596
$767$	16.0258	0.578658
$768$	−0.302933	−0.0109312
$769$	12.5340	0.451986	0.225993	−	0.974129i	$-0.427437\pi$
$769$	12.5340	0.451986	0.225993	+	0.974129i	$0.427437\pi$
$770$	6.66702	0.240263
$771$	−5.80777	−0.209162
$772$	4.28509	0.154224
$773$	−11.4383	−0.411406	−0.205703	−	0.978614i	$-0.565948\pi$
$773$	−11.4383	−0.411406	−0.205703	+	0.978614i	$0.565948\pi$
$774$	−27.5708	−0.991012
$775$	3.64986	0.131107
$776$	−14.5403	−0.521965
$777$	−2.24246	−0.0804479
$778$	−16.0455	−0.575259
$779$	−0.877757	−0.0314489
$780$	2.03105	0.0727232
$781$	−29.1659	−1.04364
$782$	−11.9487	−0.427284
$783$	−6.99676	−0.250044
$784$	1.00000	0.0357143
$785$	−0.403832	−0.0144134
$786$	−3.32443	−0.118579
$787$	53.6837	1.91362	0.956808	−	0.290720i	$-0.0938947\pi$
$787$	53.6837	1.91362	0.956808	+	0.290720i	$0.0938947\pi$
$788$	−22.1478	−0.788983
$789$	7.59263	0.270305
$790$	46.3798	1.65012
$791$	5.46792	0.194417
$792$	−5.56743	−0.197830
$793$	−14.7236	−0.522850
$794$	14.3095	0.507824
$795$	9.05321	0.321084
$796$	−0.693164	−0.0245686
$797$	−33.3613	−1.18172	−0.590858	−	0.806775i	$-0.701211\pi$
$797$	−33.3613	−1.18172	−0.590858	+	0.806775i	$0.701211\pi$
$798$	0.308130	0.0109077
$799$	18.3678	0.649805
$800$	−7.12864	−0.252035
$801$	−30.3124	−1.07104
$802$	21.7196	0.766947
$803$	−2.98772	−0.105434
$804$	−1.49665	−0.0527828
$805$	22.7842	0.803036
$806$	0.985682	0.0347192
$807$	4.67033	0.164404
$808$	3.27506	0.115216
$809$	7.16277	0.251830	0.125915	−	0.992041i	$-0.459813\pi$
$809$	7.16277	0.251830	0.125915	+	0.992041i	$0.459813\pi$
$810$	−28.4966	−1.00127
$811$	−4.89382	−0.171845	−0.0859226	−	0.996302i	$-0.527384\pi$
$811$	−4.89382	−0.171845	−0.0859226	+	0.996302i	$0.527384\pi$
$812$	−3.90924	−0.137187
$813$	−4.04055	−0.141708
$814$	14.1711	0.496697
$815$	4.68814	0.164219
$816$	−0.553274	−0.0193685
$817$	−9.64292	−0.337363
$818$	3.32431	0.116232
$819$	5.59882	0.195638
$820$	−3.00533	−0.104951
$821$	11.7816	0.411182	0.205591	−	0.978638i	$-0.434088\pi$
$821$	11.7816	0.411182	0.205591	+	0.978638i	$0.434088\pi$
$822$	6.74463	0.235246
$823$	17.5592	0.612074	0.306037	−	0.952020i	$-0.400997\pi$
$823$	17.5592	0.612074	0.306037	+	0.952020i	$0.400997\pi$
$824$	−13.8964	−0.484105
$825$	4.13408	0.143930
$826$	8.32439	0.289643
$827$	4.94668	0.172013	0.0860064	−	0.996295i	$-0.472589\pi$
$827$	4.94668	0.172013	0.0860064	+	0.996295i	$0.472589\pi$
$828$	−19.0264	−0.661212
$829$	−36.8482	−1.27979	−0.639896	−	0.768462i	$-0.721023\pi$
$829$	−36.8482	−1.27979	−0.639896	+	0.768462i	$0.721023\pi$
$830$	27.7119	0.961892
$831$	−2.09910	−0.0728168
$832$	−1.92516	−0.0667430
$833$	1.82639	0.0632807
$834$	2.60076	0.0900568
$835$	17.0252	0.589181
$836$	−1.94721	−0.0673457
$837$	0.916377	0.0316746
$838$	−14.8310	−0.512328
$839$	−49.8656	−1.72155	−0.860776	−	0.508984i	$-0.830021\pi$
$839$	−49.8656	−1.72155	−0.860776	+	0.508984i	$0.830021\pi$
$840$	1.05500	0.0364010
$841$	−13.7178	−0.473029
$842$	9.59142	0.330542
$843$	7.77133	0.267659
$844$	−23.5216	−0.809646
$845$	−32.3666	−1.11345
$846$	29.2477	1.00556
$847$	−7.33519	−0.252040
$848$	−8.58123	−0.294681
$849$	−6.98697	−0.239792
$850$	−13.0197	−0.446571
$851$	48.4289	1.66012
$852$	−4.61526	−0.158116
$853$	36.7154	1.25711	0.628556	−	0.777765i	$-0.283646\pi$
$853$	36.7154	1.25711	0.628556	+	0.777765i	$0.283646\pi$
$854$	−7.64798	−0.261709
$855$	−10.3020	−0.352322
$856$	−9.35436	−0.319725
$857$	17.4971	0.597689	0.298844	−	0.954302i	$-0.403399\pi$
$857$	17.4971	0.597689	0.298844	+	0.954302i	$0.403399\pi$
$858$	1.11645	0.0381150
$859$	−48.7728	−1.66411	−0.832053	−	0.554696i	$-0.812835\pi$
$859$	−48.7728	−1.66411	−0.832053	+	0.554696i	$0.812835\pi$
$860$	−33.0162	−1.12584
$861$	0.261417	0.00890906
$862$	1.00000	0.0340601
$863$	16.8647	0.574080	0.287040	−	0.957919i	$-0.407329\pi$
$863$	16.8647	0.574080	0.287040	+	0.957919i	$0.407329\pi$
$864$	−1.78980	−0.0608902
$865$	52.8755	1.79782
$866$	−32.8822	−1.11738
$867$	4.13937	0.140580
$868$	0.512000	0.0173784
$869$	25.4946	0.864846
$870$	−4.12425	−0.139825
$871$	−9.51131	−0.322279
$872$	2.66608	0.0902847
$873$	−42.2864	−1.43118
$874$	−6.65449	−0.225091
$875$	7.41324	0.250613
$876$	−0.472782	−0.0159738
$877$	−4.09448	−0.138261	−0.0691304	−	0.997608i	$-0.522022\pi$
$877$	−4.09448	−0.138261	−0.0691304	+	0.997608i	$0.522022\pi$
$878$	−34.9620	−1.17991
$879$	2.72657	0.0919650
$880$	−6.66702	−0.224745
$881$	27.2124	0.916810	0.458405	−	0.888744i	$-0.348421\pi$
$881$	27.2124	0.916810	0.458405	+	0.888744i	$0.348421\pi$
$882$	2.90823	0.0979252
$883$	18.6097	0.626268	0.313134	−	0.949709i	$-0.398621\pi$
$883$	18.6097	0.626268	0.313134	+	0.949709i	$0.398621\pi$
$884$	−3.51610	−0.118259
$885$	8.78224	0.295212
$886$	18.9694	0.637290
$887$	−4.40692	−0.147970	−0.0739849	−	0.997259i	$-0.523572\pi$
$887$	−4.40692	−0.147970	−0.0739849	+	0.997259i	$0.523572\pi$
$888$	2.24246	0.0752521
$889$	0.571720	0.0191749
$890$	−36.2992	−1.21675
$891$	−15.6643	−0.524775
$892$	4.79823	0.160657
$893$	10.2294	0.342314
$894$	−4.79465	−0.160357
$895$	0.591166	0.0197605
$896$	−1.00000	−0.0334077
$897$	3.81541	0.127393
$898$	−22.8591	−0.762818
$899$	−2.00153	−0.0667548
$900$	−20.7317	−0.691058
$901$	−15.6727	−0.522133
$902$	−1.65201	−0.0550058
$903$	2.87189	0.0955704
$904$	−5.46792	−0.181860
$905$	74.6174	2.48037
$906$	6.23809	0.207247
$907$	4.78175	0.158775	0.0793877	−	0.996844i	$-0.474703\pi$
$907$	4.78175	0.158775	0.0793877	+	0.996844i	$0.474703\pi$
$908$	−22.3634	−0.742154
$909$	9.52463	0.315912
$910$	6.70461	0.222255
$911$	38.5724	1.27796	0.638979	−	0.769224i	$-0.279357\pi$
$911$	38.5724	1.27796	0.638979	+	0.769224i	$0.279357\pi$
$912$	−0.308130	−0.0102032
$913$	15.2330	0.504138
$914$	−21.8786	−0.723681
$915$	−8.06863	−0.266741
$916$	−18.5439	−0.612709
$917$	−10.9741	−0.362398
$918$	−3.26887	−0.107889
$919$	−46.4614	−1.53262	−0.766310	−	0.642472i	$-0.777909\pi$
$919$	−46.4614	−1.53262	−0.766310	+	0.642472i	$0.777909\pi$
$920$	−22.7842	−0.751171
$921$	−3.68956	−0.121575
$922$	−10.8196	−0.356323
$923$	−29.3303	−0.965419
$924$	0.579926	0.0190782
$925$	52.7697	1.73506
$926$	−14.8770	−0.488890
$927$	−40.4140	−1.32737
$928$	3.90924	0.128327
$929$	25.2526	0.828512	0.414256	−	0.910160i	$-0.364042\pi$
$929$	25.2526	0.828512	0.414256	+	0.910160i	$0.364042\pi$
$930$	0.540161	0.0177126
$931$	1.01716	0.0333360
$932$	26.7539	0.876354
$933$	−8.28182	−0.271135
$934$	−31.2927	−1.02393
$935$	−12.1766	−0.398217
$936$	−5.59882	−0.183003
$937$	−31.6735	−1.03473	−0.517364	−	0.855765i	$-0.673087\pi$
$937$	−31.6735	−1.03473	−0.517364	+	0.855765i	$0.673087\pi$
$938$	−4.94053	−0.161314
$939$	8.63207	0.281697
$940$	35.0242	1.14236
$941$	−13.4369	−0.438030	−0.219015	−	0.975721i	$-0.570284\pi$
$941$	−13.4369	−0.438030	−0.219015	+	0.975721i	$0.570284\pi$
$942$	−0.0351270	−0.00114450
$943$	−5.64564	−0.183847
$944$	−8.32439	−0.270936
$945$	6.23319	0.202766
$946$	−18.1487	−0.590066
$947$	−30.6121	−0.994758	−0.497379	−	0.867533i	$-0.665704\pi$
$947$	−30.6121	−0.994758	−0.497379	+	0.867533i	$0.665704\pi$
$948$	4.03432	0.131028
$949$	−3.00456	−0.0975322
$950$	−7.25094	−0.235252
$951$	−0.940299	−0.0304913
$952$	−1.82639	−0.0591936
$953$	−23.9520	−0.775880	−0.387940	−	0.921685i	$-0.626813\pi$
$953$	−23.9520	−0.775880	−0.387940	+	0.921685i	$0.626813\pi$
$954$	−24.9562	−0.807987
$955$	62.8546	2.03393
$956$	25.9927	0.840664
$957$	−2.26707	−0.0732839
$958$	13.2879	0.429312
$959$	22.2644	0.718955
$960$	−1.05500	−0.0340500
$961$	−30.7379	−0.991544
$962$	14.2510	0.459471
$963$	−27.2046	−0.876657
$964$	7.96288	0.256467
$965$	14.9233	0.480399
$966$	1.98186	0.0637654
$967$	−1.89730	−0.0610130	−0.0305065	−	0.999535i	$-0.509712\pi$
$967$	−1.89730	−0.0610130	−0.0305065	+	0.999535i	$0.509712\pi$
$968$	7.33519	0.235762
$969$	−0.562767	−0.0180787
$970$	−50.6382	−1.62589
$971$	−14.6254	−0.469351	−0.234676	−	0.972074i	$-0.575403\pi$
$971$	−14.6254	−0.469351	−0.234676	+	0.972074i	$0.575403\pi$
$972$	−7.84815	−0.251730
$973$	8.58524	0.275230
$974$	5.51871	0.176831
$975$	4.15739	0.133143
$976$	7.64798	0.244806
$977$	−27.5758	−0.882228	−0.441114	−	0.897451i	$-0.645417\pi$
$977$	−27.5758	−0.882228	−0.441114	+	0.897451i	$0.645417\pi$
$978$	0.407795	0.0130398
$979$	−19.9534	−0.637714
$980$	3.48262	0.111248
$981$	7.75357	0.247552
$982$	36.8120	1.17472
$983$	43.1401	1.37596	0.687978	−	0.725732i	$-0.258499\pi$
$983$	43.1401	1.37596	0.687978	+	0.725732i	$0.258499\pi$
$984$	−0.261417	−0.00833366
$985$	−77.1324	−2.45764
$986$	7.13980	0.227377
$987$	−3.04656	−0.0969730
$988$	−1.95819	−0.0622983
$989$	−62.0222	−1.97219
$990$	−19.3892	−0.616230
$991$	31.2498	0.992683	0.496341	−	0.868127i	$-0.334676\pi$
$991$	31.2498	0.992683	0.496341	+	0.868127i	$0.334676\pi$
$992$	−0.512000	−0.0162560
$993$	−6.59268	−0.209212
$994$	−15.2352	−0.483233
$995$	−2.41403	−0.0765298
$996$	2.41050	0.0763795
$997$	−51.8527	−1.64219	−0.821096	−	0.570790i	$-0.806637\pi$
$997$	−51.8527	−1.64219	−0.821096	+	0.570790i	$0.806637\pi$
$998$	4.65066	0.147214
$999$	13.2490	0.419179

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.12	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.12	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.302933 q^{3} +1.00000 q^{4} +3.48262 q^{5} +0.302933 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.90823 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.302933 q^{3} +1.00000 q^{4} +3.48262 q^{5} +0.302933 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.90823 q^{9} -3.48262 q^{10} -1.91437 q^{11} -0.302933 q^{12} -1.92516 q^{13} -1.00000 q^{14} -1.05500 q^{15} +1.00000 q^{16} +1.82639 q^{17} +2.90823 q^{18} +1.01716 q^{19} +3.48262 q^{20} -0.302933 q^{21} +1.91437 q^{22} +6.54224 q^{23} +0.302933 q^{24} +7.12864 q^{25} +1.92516 q^{26} +1.78980 q^{27} +1.00000 q^{28} -3.90924 q^{29} +1.05500 q^{30} +0.512000 q^{31} -1.00000 q^{32} +0.579926 q^{33} -1.82639 q^{34} +3.48262 q^{35} -2.90823 q^{36} +7.40250 q^{37} -1.01716 q^{38} +0.583195 q^{39} -3.48262 q^{40} -0.862951 q^{41} +0.302933 q^{42} -9.48027 q^{43} -1.91437 q^{44} -10.1283 q^{45} -6.54224 q^{46} +10.0569 q^{47} -0.302933 q^{48} +1.00000 q^{49} -7.12864 q^{50} -0.553274 q^{51} -1.92516 q^{52} -8.58123 q^{53} -1.78980 q^{54} -6.66702 q^{55} -1.00000 q^{56} -0.308130 q^{57} +3.90924 q^{58} -8.32439 q^{59} -1.05500 q^{60} +7.64798 q^{61} -0.512000 q^{62} -2.90823 q^{63} +1.00000 q^{64} -6.70461 q^{65} -0.579926 q^{66} +4.94053 q^{67} +1.82639 q^{68} -1.98186 q^{69} -3.48262 q^{70} +15.2352 q^{71} +2.90823 q^{72} +1.56068 q^{73} -7.40250 q^{74} -2.15950 q^{75} +1.01716 q^{76} -1.91437 q^{77} -0.583195 q^{78} -13.3175 q^{79} +3.48262 q^{80} +8.18250 q^{81} +0.862951 q^{82} -7.95719 q^{83} -0.302933 q^{84} +6.36062 q^{85} +9.48027 q^{86} +1.18424 q^{87} +1.91437 q^{88} +10.4230 q^{89} +10.1283 q^{90} -1.92516 q^{91} +6.54224 q^{92} -0.155102 q^{93} -10.0569 q^{94} +3.54237 q^{95} +0.302933 q^{96} +14.5403 q^{97} -1.00000 q^{98} +5.56743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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