LMFDB - Embedded newform 507.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(1,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, 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("507.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	507.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04892 q^{2} -1.00000 q^{3} +2.19806 q^{4} +3.35690 q^{5} +2.04892 q^{6} +2.24698 q^{7} -0.405813 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.04892 q^{2} -1.00000 q^{3} +2.19806 q^{4} +3.35690 q^{5} +2.04892 q^{6} +2.24698 q^{7} -0.405813 q^{8} +1.00000 q^{9} -6.87800 q^{10} +4.93900 q^{11} -2.19806 q^{12} -4.60388 q^{14} -3.35690 q^{15} -3.56465 q^{16} +0.911854 q^{17} -2.04892 q^{18} -3.80194 q^{19} +7.37867 q^{20} -2.24698 q^{21} -10.1196 q^{22} +2.02715 q^{23} +0.405813 q^{24} +6.26875 q^{25} -1.00000 q^{27} +4.93900 q^{28} -3.93900 q^{29} +6.87800 q^{30} -8.82908 q^{31} +8.11529 q^{32} -4.93900 q^{33} -1.86831 q^{34} +7.54288 q^{35} +2.19806 q^{36} +8.80194 q^{37} +7.78986 q^{38} -1.36227 q^{40} +6.93900 q^{41} +4.60388 q^{42} -2.28621 q^{43} +10.8562 q^{44} +3.35690 q^{45} -4.15346 q^{46} +3.80194 q^{47} +3.56465 q^{48} -1.95108 q^{49} -12.8442 q^{50} -0.911854 q^{51} +0.542877 q^{53} +2.04892 q^{54} +16.5797 q^{55} -0.911854 q^{56} +3.80194 q^{57} +8.07069 q^{58} -4.71379 q^{59} -7.37867 q^{60} +3.67994 q^{61} +18.0901 q^{62} +2.24698 q^{63} -9.49827 q^{64} +10.1196 q^{66} -1.52111 q^{67} +2.00431 q^{68} -2.02715 q^{69} -15.4547 q^{70} +2.37867 q^{71} -0.405813 q^{72} +7.41119 q^{73} -18.0344 q^{74} -6.26875 q^{75} -8.35690 q^{76} +11.0978 q^{77} -3.74094 q^{79} -11.9661 q^{80} +1.00000 q^{81} -14.2174 q^{82} +2.30798 q^{83} -4.93900 q^{84} +3.06100 q^{85} +4.68425 q^{86} +3.93900 q^{87} -2.00431 q^{88} -10.0586 q^{89} -6.87800 q^{90} +4.45580 q^{92} +8.82908 q^{93} -7.78986 q^{94} -12.7627 q^{95} -8.11529 q^{96} -16.1293 q^{97} +3.99761 q^{98} +4.93900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 11 q^{4} + 6 q^{5} - 3 q^{6} + 2 q^{7} + 12 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 11 * q^4 + 6 * q^5 - 3 * q^6 + 2 * q^7 + 12 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 11 q^{4} + 6 q^{5} - 3 q^{6} + 2 q^{7} + 12 q^{8} + 3 q^{9} - q^{10} + 5 q^{11} - 11 q^{12} - 5 q^{14} - 6 q^{15} + 11 q^{16} - q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} - 2 q^{21} - 9 q^{22} - 12 q^{24} + 11 q^{25} - 3 q^{27} + 5 q^{28} - 2 q^{29} + q^{30} - 16 q^{31} + 22 q^{32} - 5 q^{33} - 8 q^{34} + 4 q^{35} + 11 q^{36} + 22 q^{37} + 3 q^{40} + 11 q^{41} + 5 q^{42} - 15 q^{43} + 16 q^{44} + 6 q^{45} - 7 q^{46} + 7 q^{47} - 11 q^{48} - 15 q^{49} - 3 q^{50} + q^{51} - 17 q^{53} - 3 q^{54} + 3 q^{55} + q^{56} + 7 q^{57} + 12 q^{58} - 6 q^{59} - 15 q^{60} - 13 q^{61} - 2 q^{62} + 2 q^{63} + 9 q^{66} + 11 q^{67} - 13 q^{68} - 24 q^{70} + 12 q^{72} + 6 q^{73} + 15 q^{74} - 11 q^{75} - 21 q^{76} + 15 q^{77} + 3 q^{79} - 20 q^{80} + 3 q^{81} - 3 q^{82} + 12 q^{83} - 5 q^{84} + 19 q^{85} - 29 q^{86} + 2 q^{87} + 13 q^{88} + q^{89} - q^{90} + 7 q^{92} + 16 q^{93} - 21 q^{95} - 22 q^{96} - 5 q^{97} - 29 q^{98} + 5 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 11 * q^4 + 6 * q^5 - 3 * q^6 + 2 * q^7 + 12 * q^8 + 3 * q^9 - q^10 + 5 * q^11 - 11 * q^12 - 5 * q^14 - 6 * q^15 + 11 * q^16 - q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 - 2 * q^21 - 9 * q^22 - 12 * q^24 + 11 * q^25 - 3 * q^27 + 5 * q^28 - 2 * q^29 + q^30 - 16 * q^31 + 22 * q^32 - 5 * q^33 - 8 * q^34 + 4 * q^35 + 11 * q^36 + 22 * q^37 + 3 * q^40 + 11 * q^41 + 5 * q^42 - 15 * q^43 + 16 * q^44 + 6 * q^45 - 7 * q^46 + 7 * q^47 - 11 * q^48 - 15 * q^49 - 3 * q^50 + q^51 - 17 * q^53 - 3 * q^54 + 3 * q^55 + q^56 + 7 * q^57 + 12 * q^58 - 6 * q^59 - 15 * q^60 - 13 * q^61 - 2 * q^62 + 2 * q^63 + 9 * q^66 + 11 * q^67 - 13 * q^68 - 24 * q^70 + 12 * q^72 + 6 * q^73 + 15 * q^74 - 11 * q^75 - 21 * q^76 + 15 * q^77 + 3 * q^79 - 20 * q^80 + 3 * q^81 - 3 * q^82 + 12 * q^83 - 5 * q^84 + 19 * q^85 - 29 * q^86 + 2 * q^87 + 13 * q^88 + q^89 - q^90 + 7 * q^92 + 16 * q^93 - 21 * q^95 - 22 * q^96 - 5 * q^97 - 29 * q^98 + 5 * 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 $

$2$	−2.04892	−1.44880	−0.724402	−	0.689378i	$-0.757884\pi$
$2$	−2.04892	−1.44880	−0.724402	+	0.689378i	$0.757884\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.19806	1.09903
$5$	3.35690	1.50125	0.750625	−	0.660729i	$-0.229753\pi$
$5$	3.35690	1.50125	0.750625	+	0.660729i	$0.229753\pi$
$6$	2.04892	0.836467
$7$	2.24698	0.849278	0.424639	−	0.905363i	$-0.360401\pi$
$7$	2.24698	0.849278	0.424639	+	0.905363i	$0.360401\pi$
$8$	−0.405813	−0.143477
$9$	1.00000	0.333333
$10$	−6.87800	−2.17502
$11$	4.93900	1.48916	0.744582	−	0.667531i	$-0.232649\pi$
$11$	4.93900	1.48916	0.744582	+	0.667531i	$0.232649\pi$
$12$	−2.19806	−0.634526
$13$	0	0
$13$	0	0
$14$	−4.60388	−1.23044
$15$	−3.35690	−0.866747
$16$	−3.56465	−0.891162
$17$	0.911854	0.221157	0.110579	−	0.993867i	$-0.464730\pi$
$17$	0.911854	0.221157	0.110579	+	0.993867i	$0.464730\pi$
$18$	−2.04892	−0.482934
$19$	−3.80194	−0.872224	−0.436112	−	0.899892i	$-0.643645\pi$
$19$	−3.80194	−0.872224	−0.436112	+	0.899892i	$0.643645\pi$
$20$	7.37867	1.64992
$21$	−2.24698	−0.490331
$22$	−10.1196	−2.15751
$23$	2.02715	0.422689	0.211345	−	0.977412i	$-0.432216\pi$
$23$	2.02715	0.422689	0.211345	+	0.977412i	$0.432216\pi$
$24$	0.405813	0.0828363
$25$	6.26875	1.25375
$26$	0	0
$27$	−1.00000	−0.192450
$28$	4.93900	0.933383
$29$	−3.93900	−0.731454	−0.365727	−	0.930722i	$-0.619180\pi$
$29$	−3.93900	−0.731454	−0.365727	+	0.930722i	$0.619180\pi$
$30$	6.87800	1.25575
$31$	−8.82908	−1.58575	−0.792875	−	0.609384i	$-0.791417\pi$
$31$	−8.82908	−1.58575	−0.792875	+	0.609384i	$0.791417\pi$
$32$	8.11529	1.43459
$33$	−4.93900	−0.859770
$34$	−1.86831	−0.320413
$35$	7.54288	1.27498
$36$	2.19806	0.366344
$37$	8.80194	1.44703	0.723515	−	0.690309i	$-0.242525\pi$
$37$	8.80194	1.44703	0.723515	+	0.690309i	$0.242525\pi$
$38$	7.78986	1.26368
$39$	0	0
$40$	−1.36227	−0.215394
$41$	6.93900	1.08369	0.541845	−	0.840478i	$-0.317726\pi$
$41$	6.93900	1.08369	0.541845	+	0.840478i	$0.317726\pi$
$42$	4.60388	0.710393
$43$	−2.28621	−0.348643	−0.174322	−	0.984689i	$-0.555773\pi$
$43$	−2.28621	−0.348643	−0.174322	+	0.984689i	$0.555773\pi$
$44$	10.8562	1.63664
$45$	3.35690	0.500416
$46$	−4.15346	−0.612394
$47$	3.80194	0.554570	0.277285	−	0.960788i	$-0.410565\pi$
$47$	3.80194	0.554570	0.277285	+	0.960788i	$0.410565\pi$
$48$	3.56465	0.514512
$49$	−1.95108	−0.278726
$50$	−12.8442	−1.81644
$51$	−0.911854	−0.127685
$52$	0	0
$53$	0.542877	0.0745698	0.0372849	−	0.999305i	$-0.488129\pi$
$53$	0.542877	0.0745698	0.0372849	+	0.999305i	$0.488129\pi$
$54$	2.04892	0.278822
$55$	16.5797	2.23561
$56$	−0.911854	−0.121852
$57$	3.80194	0.503579
$58$	8.07069	1.05973
$59$	−4.71379	−0.613683	−0.306842	−	0.951761i	$-0.599272\pi$
$59$	−4.71379	−0.613683	−0.306842	+	0.951761i	$0.599272\pi$
$60$	−7.37867	−0.952582
$61$	3.67994	0.471168	0.235584	−	0.971854i	$-0.424300\pi$
$61$	3.67994	0.471168	0.235584	+	0.971854i	$0.424300\pi$
$62$	18.0901	2.29744
$63$	2.24698	0.283093
$64$	−9.49827	−1.18728
$65$	0	0
$66$	10.1196	1.24564
$67$	−1.52111	−0.185833	−0.0929164	−	0.995674i	$-0.529619\pi$
$67$	−1.52111	−0.185833	−0.0929164	+	0.995674i	$0.529619\pi$
$68$	2.00431	0.243059
$69$	−2.02715	−0.244040
$70$	−15.4547	−1.84719
$71$	2.37867	0.282296	0.141148	−	0.989989i	$-0.454921\pi$
$71$	2.37867	0.282296	0.141148	+	0.989989i	$0.454921\pi$
$72$	−0.405813	−0.0478255
$73$	7.41119	0.867414	0.433707	−	0.901054i	$-0.357205\pi$
$73$	7.41119	0.867414	0.433707	+	0.901054i	$0.357205\pi$
$74$	−18.0344	−2.09646
$75$	−6.26875	−0.723853
$76$	−8.35690	−0.958602
$77$	11.0978	1.26472
$78$	0	0
$79$	−3.74094	−0.420888	−0.210444	−	0.977606i	$-0.567491\pi$
$79$	−3.74094	−0.420888	−0.210444	+	0.977606i	$0.567491\pi$
$80$	−11.9661	−1.33786
$81$	1.00000	0.111111
$82$	−14.2174	−1.57005
$83$	2.30798	0.253334	0.126667	−	0.991945i	$-0.459572\pi$
$83$	2.30798	0.253334	0.126667	+	0.991945i	$0.459572\pi$
$84$	−4.93900	−0.538889
$85$	3.06100	0.332012
$86$	4.68425	0.505116
$87$	3.93900	0.422305
$88$	−2.00431	−0.213660
$89$	−10.0586	−1.06621	−0.533105	−	0.846049i	$-0.678975\pi$
$89$	−10.0586	−1.06621	−0.533105	+	0.846049i	$0.678975\pi$
$90$	−6.87800	−0.725005
$91$	0	0
$92$	4.45580	0.464549
$93$	8.82908	0.915533
$94$	−7.78986	−0.803462
$95$	−12.7627	−1.30943
$96$	−8.11529	−0.828264
$97$	−16.1293	−1.63768	−0.818841	−	0.574021i	$-0.805383\pi$
$97$	−16.1293	−1.63768	−0.818841	+	0.574021i	$0.805383\pi$
$98$	3.99761	0.403819
$99$	4.93900	0.496388
$100$	13.7791	1.37791
$101$	−9.94869	−0.989932	−0.494966	−	0.868912i	$-0.664819\pi$
$101$	−9.94869	−0.989932	−0.494966	+	0.868912i	$0.664819\pi$
$102$	1.86831	0.184991
$103$	−10.9879	−1.08267	−0.541336	−	0.840806i	$-0.682081\pi$
$103$	−10.9879	−1.08267	−0.541336	+	0.840806i	$0.682081\pi$
$104$	0	0
$105$	−7.54288	−0.736109
$106$	−1.11231	−0.108037
$107$	−9.87263	−0.954423	−0.477211	−	0.878789i	$-0.658352\pi$
$107$	−9.87263	−0.954423	−0.477211	+	0.878789i	$0.658352\pi$
$108$	−2.19806	−0.211509
$109$	20.2446	1.93908	0.969540	−	0.244934i	$-0.0787662\pi$
$109$	20.2446	1.93908	0.969540	+	0.244934i	$0.0787662\pi$
$110$	−33.9705	−3.23896
$111$	−8.80194	−0.835443
$112$	−8.00969	−0.756844
$113$	9.69202	0.911749	0.455874	−	0.890044i	$-0.349327\pi$
$113$	9.69202	0.911749	0.455874	+	0.890044i	$0.349327\pi$
$114$	−7.78986	−0.729587
$115$	6.80492	0.634562
$116$	−8.65817	−0.803891
$117$	0	0
$118$	9.65817	0.889107
$119$	2.04892	0.187824
$120$	1.36227	0.124358
$121$	13.3937	1.21761
$122$	−7.53989	−0.682630
$123$	−6.93900	−0.625669
$124$	−19.4069	−1.74279
$125$	4.25906	0.380942
$126$	−4.60388	−0.410146
$127$	13.8116	1.22558	0.612792	−	0.790244i	$-0.290046\pi$
$127$	13.8116	1.22558	0.612792	+	0.790244i	$0.290046\pi$
$128$	3.23059	0.285546
$129$	2.28621	0.201289
$130$	0	0
$131$	2.99462	0.261641	0.130821	−	0.991406i	$-0.458239\pi$
$131$	2.99462	0.261641	0.130821	+	0.991406i	$0.458239\pi$
$132$	−10.8562	−0.944914
$133$	−8.54288	−0.740761
$134$	3.11662	0.269235
$135$	−3.35690	−0.288916
$136$	−0.370042	−0.0317309
$137$	23.0194	1.96668	0.983339	−	0.181781i	$-0.0581862\pi$
$137$	23.0194	1.96668	0.983339	+	0.181781i	$0.0581862\pi$
$138$	4.15346	0.353566
$139$	0.982542	0.0833381	0.0416690	−	0.999131i	$-0.486732\pi$
$139$	0.982542	0.0833381	0.0416690	+	0.999131i	$0.486732\pi$
$140$	16.5797	1.40124
$141$	−3.80194	−0.320181
$142$	−4.87369	−0.408991
$143$	0	0
$144$	−3.56465	−0.297054
$145$	−13.2228	−1.09810
$146$	−15.1849	−1.25671
$147$	1.95108	0.160923
$148$	19.3472	1.59033
$149$	10.2591	0.840455	0.420228	−	0.907419i	$-0.361950\pi$
$149$	10.2591	0.840455	0.420228	+	0.907419i	$0.361950\pi$
$150$	12.8442	1.04872
$151$	−20.1685	−1.64129	−0.820646	−	0.571438i	$-0.806386\pi$
$151$	−20.1685	−1.64129	−0.820646	+	0.571438i	$0.806386\pi$
$152$	1.54288	0.125144
$153$	0.911854	0.0737190
$154$	−22.7385	−1.83232
$155$	−29.6383	−2.38061
$156$	0	0
$157$	10.4383	0.833070	0.416535	−	0.909120i	$-0.363244\pi$
$157$	10.4383	0.833070	0.416535	+	0.909120i	$0.363244\pi$
$158$	7.66487	0.609785
$159$	−0.542877	−0.0430529
$160$	27.2422	2.15368
$161$	4.55496	0.358981
$162$	−2.04892	−0.160978
$163$	−11.0465	−0.865231	−0.432615	−	0.901579i	$-0.642409\pi$
$163$	−11.0465	−0.865231	−0.432615	+	0.901579i	$0.642409\pi$
$164$	15.2524	1.19101
$165$	−16.5797	−1.29073
$166$	−4.72886	−0.367031
$167$	8.10992	0.627564	0.313782	−	0.949495i	$-0.398404\pi$
$167$	8.10992	0.627564	0.313782	+	0.949495i	$0.398404\pi$
$168$	0.911854	0.0703511
$169$	0	0
$170$	−6.27173	−0.481020
$171$	−3.80194	−0.290741
$172$	−5.02523	−0.383170
$173$	−18.0562	−1.37279	−0.686394	−	0.727230i	$-0.740808\pi$
$173$	−18.0562	−1.37279	−0.686394	+	0.727230i	$0.740808\pi$
$174$	−8.07069	−0.611837
$175$	14.0858	1.06478
$176$	−17.6058	−1.32709
$177$	4.71379	0.354310
$178$	20.6093	1.54473
$179$	−19.8702	−1.48517	−0.742585	−	0.669751i	$-0.766401\pi$
$179$	−19.8702	−1.48517	−0.742585	+	0.669751i	$0.766401\pi$
$180$	7.37867	0.549973
$181$	−10.0828	−0.749446	−0.374723	−	0.927137i	$-0.622262\pi$
$181$	−10.0828	−0.749446	−0.374723	+	0.927137i	$0.622262\pi$
$182$	0	0
$183$	−3.67994	−0.272029
$184$	−0.822643	−0.0606461
$185$	29.5472	2.17235
$186$	−18.0901	−1.32643
$187$	4.50365	0.329339
$188$	8.35690	0.609489
$189$	−2.24698	−0.163444
$190$	26.1497	1.89710
$191$	−6.58748	−0.476653	−0.238327	−	0.971185i	$-0.576599\pi$
$191$	−6.58748	−0.476653	−0.238327	+	0.971185i	$0.576599\pi$
$192$	9.49827	0.685479
$193$	10.8672	0.782242	0.391121	−	0.920339i	$-0.372087\pi$
$193$	10.8672	0.782242	0.391121	+	0.920339i	$0.372087\pi$
$194$	33.0476	2.37268
$195$	0	0
$196$	−4.28860	−0.306329
$197$	9.24160	0.658437	0.329218	−	0.944254i	$-0.393215\pi$
$197$	9.24160	0.658437	0.329218	+	0.944254i	$0.393215\pi$
$198$	−10.1196	−0.719169
$199$	−1.56465	−0.110915	−0.0554574	−	0.998461i	$-0.517662\pi$
$199$	−1.56465	−0.110915	−0.0554574	+	0.998461i	$0.517662\pi$
$200$	−2.54394	−0.179884
$201$	1.52111	0.107291
$202$	20.3840	1.43422
$203$	−8.85086	−0.621208
$204$	−2.00431	−0.140330
$205$	23.2935	1.62689
$206$	22.5133	1.56858
$207$	2.02715	0.140896
$208$	0	0
$209$	−18.7778	−1.29889
$210$	15.4547	1.06648
$211$	23.2446	1.60022	0.800112	−	0.599851i	$-0.204774\pi$
$211$	23.2446	1.60022	0.800112	+	0.599851i	$0.204774\pi$
$212$	1.19328	0.0819546
$213$	−2.37867	−0.162984
$214$	20.2282	1.38277
$215$	−7.67456	−0.523401
$216$	0.405813	0.0276121
$217$	−19.8388	−1.34674
$218$	−41.4795	−2.80935
$219$	−7.41119	−0.500802
$220$	36.4432	2.45700
$221$	0	0
$222$	18.0344	1.21039
$223$	10.7385	0.719106	0.359553	−	0.933125i	$-0.382929\pi$
$223$	10.7385	0.719106	0.359553	+	0.933125i	$0.382929\pi$
$224$	18.2349	1.21837
$225$	6.26875	0.417917
$226$	−19.8582	−1.32094
$227$	−6.97584	−0.463003	−0.231501	−	0.972835i	$-0.574364\pi$
$227$	−6.97584	−0.463003	−0.231501	+	0.972835i	$0.574364\pi$
$228$	8.35690	0.553449
$229$	−16.8049	−1.11050	−0.555250	−	0.831683i	$-0.687378\pi$
$229$	−16.8049	−1.11050	−0.555250	+	0.831683i	$0.687378\pi$
$230$	−13.9427	−0.919356
$231$	−11.0978	−0.730184
$232$	1.59850	0.104947
$233$	8.69202	0.569433	0.284717	−	0.958612i	$-0.408100\pi$
$233$	8.69202	0.569433	0.284717	+	0.958612i	$0.408100\pi$
$234$	0	0
$235$	12.7627	0.832547
$236$	−10.3612	−0.674457
$237$	3.74094	0.243000
$238$	−4.19806	−0.272120
$239$	−22.9191	−1.48252	−0.741258	−	0.671220i	$-0.765771\pi$
$239$	−22.9191	−1.48252	−0.741258	+	0.671220i	$0.765771\pi$
$240$	11.9661	0.772412
$241$	21.9801	1.41587	0.707933	−	0.706280i	$-0.249628\pi$
$241$	21.9801	1.41587	0.707933	+	0.706280i	$0.249628\pi$
$242$	−27.4426	−1.76408
$243$	−1.00000	−0.0641500
$244$	8.08874	0.517828
$245$	−6.54958	−0.418437
$246$	14.2174	0.906471
$247$	0	0
$248$	3.58296	0.227518
$249$	−2.30798	−0.146262
$250$	−8.72646	−0.551910
$251$	26.6437	1.68174	0.840868	−	0.541241i	$-0.182045\pi$
$251$	26.6437	1.68174	0.840868	+	0.541241i	$0.182045\pi$
$252$	4.93900	0.311128
$253$	10.0121	0.629454
$254$	−28.2989	−1.77563
$255$	−3.06100	−0.191687
$256$	12.3773	0.773584
$257$	23.1444	1.44371	0.721853	−	0.692047i	$-0.243291\pi$
$257$	23.1444	1.44371	0.721853	+	0.692047i	$0.243291\pi$
$258$	−4.68425	−0.291629
$259$	19.7778	1.22893
$260$	0	0
$261$	−3.93900	−0.243818
$262$	−6.13574	−0.379067
$263$	−18.5284	−1.14251	−0.571255	−	0.820773i	$-0.693543\pi$
$263$	−18.5284	−1.14251	−0.571255	+	0.820773i	$0.693543\pi$
$264$	2.00431	0.123357
$265$	1.82238	0.111948
$266$	17.5036	1.07322
$267$	10.0586	0.615577
$268$	−3.34349	−0.204236
$269$	9.75840	0.594980	0.297490	−	0.954725i	$-0.403851\pi$
$269$	9.75840	0.594980	0.297490	+	0.954725i	$0.403851\pi$
$270$	6.87800	0.418582
$271$	−22.8019	−1.38512	−0.692560	−	0.721361i	$-0.743517\pi$
$271$	−22.8019	−1.38512	−0.692560	+	0.721361i	$0.743517\pi$
$272$	−3.25044	−0.197087
$273$	0	0
$274$	−47.1648	−2.84933
$275$	30.9614	1.86704
$276$	−4.45580	−0.268207
$277$	−23.9705	−1.44025	−0.720123	−	0.693847i	$-0.755914\pi$
$277$	−23.9705	−1.44025	−0.720123	+	0.693847i	$0.755914\pi$
$278$	−2.01315	−0.120741
$279$	−8.82908	−0.528583
$280$	−3.06100	−0.182930
$281$	−4.12498	−0.246076	−0.123038	−	0.992402i	$-0.539264\pi$
$281$	−4.12498	−0.246076	−0.123038	+	0.992402i	$0.539264\pi$
$282$	7.78986	0.463879
$283$	−15.6558	−0.930639	−0.465320	−	0.885143i	$-0.654061\pi$
$283$	−15.6558	−0.930639	−0.465320	+	0.885143i	$0.654061\pi$
$284$	5.22846	0.310252
$285$	12.7627	0.755998
$286$	0	0
$287$	15.5918	0.920354
$288$	8.11529	0.478198
$289$	−16.1685	−0.951090
$290$	27.0925	1.59092
$291$	16.1293	0.945516
$292$	16.2903	0.953315
$293$	22.5948	1.32000	0.660001	−	0.751265i	$-0.270556\pi$
$293$	22.5948	1.32000	0.660001	+	0.751265i	$0.270556\pi$
$294$	−3.99761	−0.233145
$295$	−15.8237	−0.921292
$296$	−3.57194	−0.207615
$297$	−4.93900	−0.286590
$298$	−21.0200	−1.21765
$299$	0	0
$300$	−13.7791	−0.795537
$301$	−5.13706	−0.296095
$302$	41.3236	2.37791
$303$	9.94869	0.571537
$304$	13.5526	0.777293
$305$	12.3532	0.707341
$306$	−1.86831	−0.106804
$307$	−6.55496	−0.374111	−0.187056	−	0.982349i	$-0.559894\pi$
$307$	−6.55496	−0.374111	−0.187056	+	0.982349i	$0.559894\pi$
$308$	24.3937	1.38996
$309$	10.9879	0.625081
$310$	60.7265	3.44903
$311$	−12.0392	−0.682682	−0.341341	−	0.939940i	$-0.610881\pi$
$311$	−12.0392	−0.682682	−0.341341	+	0.939940i	$0.610881\pi$
$312$	0	0
$313$	−33.8950	−1.91586	−0.957929	−	0.287005i	$-0.907340\pi$
$313$	−33.8950	−1.91586	−0.957929	+	0.287005i	$0.907340\pi$
$314$	−21.3873	−1.20695
$315$	7.54288	0.424993
$316$	−8.22282	−0.462570
$317$	−4.49827	−0.252648	−0.126324	−	0.991989i	$-0.540318\pi$
$317$	−4.49827	−0.252648	−0.126324	+	0.991989i	$0.540318\pi$
$318$	1.11231	0.0623752
$319$	−19.4547	−1.08926
$320$	−31.8847	−1.78241
$321$	9.87263	0.551036
$322$	−9.33273	−0.520093
$323$	−3.46681	−0.192899
$324$	2.19806	0.122115
$325$	0	0
$326$	22.6334	1.25355
$327$	−20.2446	−1.11953
$328$	−2.81594	−0.155484
$329$	8.54288	0.470984
$330$	33.9705	1.87001
$331$	−11.2131	−0.616329	−0.308165	−	0.951333i	$-0.599715\pi$
$331$	−11.2131	−0.616329	−0.308165	+	0.951333i	$0.599715\pi$
$332$	5.07308	0.278421
$333$	8.80194	0.482343
$334$	−16.6165	−0.909217
$335$	−5.10620	−0.278981
$336$	8.00969	0.436964
$337$	7.04892	0.383979	0.191989	−	0.981397i	$-0.438506\pi$
$337$	7.04892	0.383979	0.191989	+	0.981397i	$0.438506\pi$
$338$	0	0
$339$	−9.69202	−0.526398
$340$	6.72827	0.364891
$341$	−43.6069	−2.36144
$342$	7.78986	0.421227
$343$	−20.1129	−1.08599
$344$	0.927774	0.0500222
$345$	−6.80492	−0.366365
$346$	36.9957	1.98890
$347$	−2.70410	−0.145164	−0.0725819	−	0.997362i	$-0.523124\pi$
$347$	−2.70410	−0.145164	−0.0725819	+	0.997362i	$0.523124\pi$
$348$	8.65817	0.464127
$349$	−0.415502	−0.0222413	−0.0111207	−	0.999938i	$-0.503540\pi$
$349$	−0.415502	−0.0222413	−0.0111207	+	0.999938i	$0.503540\pi$
$350$	−28.8605	−1.54266
$351$	0	0
$352$	40.0814	2.13635
$353$	−32.1672	−1.71209	−0.856044	−	0.516904i	$-0.827084\pi$
$353$	−32.1672	−1.71209	−0.856044	+	0.516904i	$0.827084\pi$
$354$	−9.65817	−0.513326
$355$	7.98493	0.423796
$356$	−22.1094	−1.17180
$357$	−2.04892	−0.108440
$358$	40.7125	2.15172
$359$	22.3521	1.17970	0.589850	−	0.807513i	$-0.299187\pi$
$359$	22.3521	1.17970	0.589850	+	0.807513i	$0.299187\pi$
$360$	−1.36227	−0.0717981
$361$	−4.54527	−0.239225
$362$	20.6588	1.08580
$363$	−13.3937	−0.702989
$364$	0	0
$365$	24.8786	1.30221
$366$	7.53989	0.394117
$367$	−2.30260	−0.120195	−0.0600974	−	0.998193i	$-0.519141\pi$
$367$	−2.30260	−0.120195	−0.0600974	+	0.998193i	$0.519141\pi$
$368$	−7.22606	−0.376685
$369$	6.93900	0.361230
$370$	−60.5397	−3.14731
$371$	1.21983	0.0633305
$372$	19.4069	1.00620
$373$	−19.2760	−0.998076	−0.499038	−	0.866580i	$-0.666313\pi$
$373$	−19.2760	−0.998076	−0.499038	+	0.866580i	$0.666313\pi$
$374$	−9.22760	−0.477148
$375$	−4.25906	−0.219937
$376$	−1.54288	−0.0795678
$377$	0	0
$378$	4.60388	0.236798
$379$	−7.33944	−0.377002	−0.188501	−	0.982073i	$-0.560363\pi$
$379$	−7.33944	−0.377002	−0.188501	+	0.982073i	$0.560363\pi$
$380$	−28.0532	−1.43910
$381$	−13.8116	−0.707591
$382$	13.4972	0.690577
$383$	19.0901	0.975457	0.487728	−	0.872995i	$-0.337826\pi$
$383$	19.0901	0.975457	0.487728	+	0.872995i	$0.337826\pi$
$384$	−3.23059	−0.164860
$385$	37.2543	1.89865
$386$	−22.2661	−1.13331
$387$	−2.28621	−0.116214
$388$	−35.4532	−1.79986
$389$	−23.9879	−1.21624	−0.608118	−	0.793847i	$-0.708075\pi$
$389$	−23.9879	−1.21624	−0.608118	+	0.793847i	$0.708075\pi$
$390$	0	0
$391$	1.84846	0.0934807
$392$	0.791775	0.0399907
$393$	−2.99462	−0.151059
$394$	−18.9353	−0.953946
$395$	−12.5579	−0.631859
$396$	10.8562	0.545546
$397$	−4.41789	−0.221728	−0.110864	−	0.993836i	$-0.535362\pi$
$397$	−4.41789	−0.221728	−0.110864	+	0.993836i	$0.535362\pi$
$398$	3.20583	0.160694
$399$	8.54288	0.427679
$400$	−22.3459	−1.11729
$401$	−20.4088	−1.01917	−0.509583	−	0.860421i	$-0.670200\pi$
$401$	−20.4088	−1.01917	−0.509583	+	0.860421i	$0.670200\pi$
$402$	−3.11662	−0.155443
$403$	0	0
$404$	−21.8678	−1.08797
$405$	3.35690	0.166805
$406$	18.1347	0.900009
$407$	43.4728	2.15487
$408$	0.370042	0.0183198
$409$	−22.1491	−1.09520	−0.547602	−	0.836739i	$-0.684459\pi$
$409$	−22.1491	−1.09520	−0.547602	+	0.836739i	$0.684459\pi$
$410$	−47.7265	−2.35704
$411$	−23.0194	−1.13546
$412$	−24.1521	−1.18989
$413$	−10.5918	−0.521188
$414$	−4.15346	−0.204131
$415$	7.74764	0.380317
$416$	0	0
$417$	−0.982542	−0.0481153
$418$	38.4741	1.88183
$419$	14.7560	0.720878	0.360439	−	0.932783i	$-0.382627\pi$
$419$	14.7560	0.720878	0.360439	+	0.932783i	$0.382627\pi$
$420$	−16.5797	−0.809007
$421$	8.47219	0.412909	0.206455	−	0.978456i	$-0.433807\pi$
$421$	8.47219	0.412909	0.206455	+	0.978456i	$0.433807\pi$
$422$	−47.6262	−2.31841
$423$	3.80194	0.184857
$424$	−0.220306	−0.0106990
$425$	5.71618	0.277276
$426$	4.87369	0.236131
$427$	8.26875	0.400153
$428$	−21.7006	−1.04894
$429$	0	0
$430$	15.7245	0.758305
$431$	2.39181	0.115210	0.0576048	−	0.998339i	$-0.481654\pi$
$431$	2.39181	0.115210	0.0576048	+	0.998339i	$0.481654\pi$
$432$	3.56465	0.171504
$433$	−10.4286	−0.501169	−0.250584	−	0.968095i	$-0.580623\pi$
$433$	−10.4286	−0.501169	−0.250584	+	0.968095i	$0.580623\pi$
$434$	40.6480	1.95117
$435$	13.2228	0.633986
$436$	44.4989	2.13111
$437$	−7.70709	−0.368680
$438$	15.1849	0.725563
$439$	−32.5502	−1.55353	−0.776767	−	0.629787i	$-0.783142\pi$
$439$	−32.5502	−1.55353	−0.776767	+	0.629787i	$0.783142\pi$
$440$	−6.72827	−0.320758
$441$	−1.95108	−0.0929087
$442$	0	0
$443$	9.58211	0.455260	0.227630	−	0.973748i	$-0.426902\pi$
$443$	9.58211	0.455260	0.227630	+	0.973748i	$0.426902\pi$
$444$	−19.3472	−0.918178
$445$	−33.7657	−1.60065
$446$	−22.0024	−1.04184
$447$	−10.2591	−0.485237
$448$	−21.3424	−1.00833
$449$	−28.3937	−1.33998	−0.669992	−	0.742369i	$-0.733702\pi$
$449$	−28.3937	−1.33998	−0.669992	+	0.742369i	$0.733702\pi$
$450$	−12.8442	−0.605479
$451$	34.2717	1.61379
$452$	21.3037	1.00204
$453$	20.1685	0.947600
$454$	14.2929	0.670800
$455$	0	0
$456$	−1.54288	−0.0722518
$457$	4.99569	0.233688	0.116844	−	0.993150i	$-0.462722\pi$
$457$	4.99569	0.233688	0.116844	+	0.993150i	$0.462722\pi$
$458$	34.4319	1.60890
$459$	−0.911854	−0.0425617
$460$	14.9576	0.697404
$461$	1.35258	0.0629961	0.0314981	−	0.999504i	$-0.489972\pi$
$461$	1.35258	0.0629961	0.0314981	+	0.999504i	$0.489972\pi$
$462$	22.7385	1.05789
$463$	−3.36467	−0.156369	−0.0781846	−	0.996939i	$-0.524912\pi$
$463$	−3.36467	−0.156369	−0.0781846	+	0.996939i	$0.524912\pi$
$464$	14.0411	0.651844
$465$	29.6383	1.37444
$466$	−17.8092	−0.824997
$467$	6.91079	0.319793	0.159897	−	0.987134i	$-0.448884\pi$
$467$	6.91079	0.319793	0.159897	+	0.987134i	$0.448884\pi$
$468$	0	0
$469$	−3.41789	−0.157824
$470$	−26.1497	−1.20620
$471$	−10.4383	−0.480973
$472$	1.91292	0.0880492
$473$	−11.2916	−0.519188
$474$	−7.66487	−0.352059
$475$	−23.8334	−1.09355
$476$	4.50365	0.206424
$477$	0.542877	0.0248566
$478$	46.9594	2.14787
$479$	3.51573	0.160638	0.0803189	−	0.996769i	$-0.474406\pi$
$479$	3.51573	0.160638	0.0803189	+	0.996769i	$0.474406\pi$
$480$	−27.2422	−1.24343
$481$	0	0
$482$	−45.0355	−2.05131
$483$	−4.55496	−0.207258
$484$	29.4403	1.33819
$485$	−54.1444	−2.45857
$486$	2.04892	0.0929408
$487$	−12.8479	−0.582193	−0.291096	−	0.956694i	$-0.594020\pi$
$487$	−12.8479	−0.582193	−0.291096	+	0.956694i	$0.594020\pi$
$488$	−1.49337	−0.0676016
$489$	11.0465	0.499541
$490$	13.4196	0.606234
$491$	28.6708	1.29390	0.646948	−	0.762534i	$-0.276045\pi$
$491$	28.6708	1.29390	0.646948	+	0.762534i	$0.276045\pi$
$492$	−15.2524	−0.687629
$493$	−3.59179	−0.161766
$494$	0	0
$495$	16.5797	0.745203
$496$	31.4726	1.41316
$497$	5.34481	0.239748
$498$	4.72886	0.211905
$499$	−33.5555	−1.50215	−0.751076	−	0.660215i	$-0.770465\pi$
$499$	−33.5555	−1.50215	−0.751076	+	0.660215i	$0.770465\pi$
$500$	9.36168	0.418667
$501$	−8.10992	−0.362324
$502$	−54.5907	−2.43650
$503$	21.5633	0.961461	0.480730	−	0.876868i	$-0.340372\pi$
$503$	21.5633	0.961461	0.480730	+	0.876868i	$0.340372\pi$
$504$	−0.911854	−0.0406172
$505$	−33.3967	−1.48613
$506$	−20.5139	−0.911955
$507$	0	0
$508$	30.3588	1.34695
$509$	−8.89008	−0.394046	−0.197023	−	0.980399i	$-0.563127\pi$
$509$	−8.89008	−0.394046	−0.197023	+	0.980399i	$0.563127\pi$
$510$	6.27173	0.277717
$511$	16.6528	0.736676
$512$	−31.8213	−1.40632
$513$	3.80194	0.167860
$514$	−47.4209	−2.09165
$515$	−36.8853	−1.62536
$516$	5.02523	0.221223
$517$	18.7778	0.825846
$518$	−40.5230	−1.78048
$519$	18.0562	0.792580
$520$	0	0
$521$	19.3478	0.847642	0.423821	−	0.905746i	$-0.360688\pi$
$521$	19.3478	0.847642	0.423821	+	0.905746i	$0.360688\pi$
$522$	8.07069	0.353244
$523$	−12.5948	−0.550731	−0.275366	−	0.961340i	$-0.588799\pi$
$523$	−12.5948	−0.550731	−0.275366	+	0.961340i	$0.588799\pi$
$524$	6.58237	0.287552
$525$	−14.0858	−0.614753
$526$	37.9632	1.65527
$527$	−8.05084	−0.350700
$528$	17.6058	0.766194
$529$	−18.8907	−0.821334
$530$	−3.73391	−0.162191
$531$	−4.71379	−0.204561
$532$	−18.7778	−0.814120
$533$	0	0
$534$	−20.6093	−0.891850
$535$	−33.1414	−1.43283
$536$	0.617285	0.0266627
$537$	19.8702	0.857464
$538$	−19.9941	−0.862009
$539$	−9.63640	−0.415069
$540$	−7.37867	−0.317527
$541$	29.0019	1.24689	0.623445	−	0.781867i	$-0.285733\pi$
$541$	29.0019	1.24689	0.623445	+	0.781867i	$0.285733\pi$
$542$	46.7193	2.00677
$543$	10.0828	0.432693
$544$	7.39996	0.317271
$545$	67.9590	2.91104
$546$	0	0
$547$	27.7006	1.18439	0.592197	−	0.805793i	$-0.298261\pi$
$547$	27.7006	1.18439	0.592197	+	0.805793i	$0.298261\pi$
$548$	50.5980	2.16144
$549$	3.67994	0.157056
$550$	−63.4373	−2.70497
$551$	14.9758	0.637992
$552$	0.822643	0.0350140
$553$	−8.40581	−0.357452
$554$	49.1135	2.08663
$555$	−29.5472	−1.25421
$556$	2.15969	0.0915912
$557$	6.80971	0.288537	0.144268	−	0.989539i	$-0.453917\pi$
$557$	6.80971	0.288537	0.144268	+	0.989539i	$0.453917\pi$
$558$	18.0901	0.765814
$559$	0	0
$560$	−26.8877	−1.13621
$561$	−4.50365	−0.190144
$562$	8.45175	0.356515
$563$	−19.2524	−0.811390	−0.405695	−	0.914008i	$-0.632970\pi$
$563$	−19.2524	−0.811390	−0.405695	+	0.914008i	$0.632970\pi$
$564$	−8.35690	−0.351889
$565$	32.5351	1.36876
$566$	32.0774	1.34831
$567$	2.24698	0.0943643
$568$	−0.965294	−0.0405028
$569$	7.84846	0.329025	0.164512	−	0.986375i	$-0.447395\pi$
$569$	7.84846	0.329025	0.164512	+	0.986375i	$0.447395\pi$
$570$	−26.1497	−1.09529
$571$	29.8568	1.24947	0.624735	−	0.780837i	$-0.285207\pi$
$571$	29.8568	1.24947	0.624735	+	0.780837i	$0.285207\pi$
$572$	0	0
$573$	6.58748	0.275196
$574$	−31.9463	−1.33341
$575$	12.7077	0.529947
$576$	−9.49827	−0.395761
$577$	8.97823	0.373769	0.186884	−	0.982382i	$-0.440161\pi$
$577$	8.97823	0.373769	0.186884	+	0.982382i	$0.440161\pi$
$578$	33.1280	1.37794
$579$	−10.8672	−0.451627
$580$	−29.0646	−1.20684
$581$	5.18598	0.215151
$582$	−33.0476	−1.36987
$583$	2.68127	0.111047
$584$	−3.00756	−0.124454
$585$	0	0
$586$	−46.2948	−1.91242
$587$	23.8538	0.984553	0.492277	−	0.870439i	$-0.336165\pi$
$587$	23.8538	0.984553	0.492277	+	0.870439i	$0.336165\pi$
$588$	4.28860	0.176859
$589$	33.5676	1.38313
$590$	32.4215	1.33477
$591$	−9.24160	−0.380149
$592$	−31.3758	−1.28954
$593$	11.9866	0.492230	0.246115	−	0.969241i	$-0.420846\pi$
$593$	11.9866	0.492230	0.246115	+	0.969241i	$0.420846\pi$
$594$	10.1196	0.415212
$595$	6.87800	0.281971
$596$	22.5501	0.923686
$597$	1.56465	0.0640367
$598$	0	0
$599$	29.1142	1.18958	0.594788	−	0.803883i	$-0.297236\pi$
$599$	29.1142	1.18958	0.594788	+	0.803883i	$0.297236\pi$
$600$	2.54394	0.103856
$601$	37.1366	1.51483	0.757417	−	0.652932i	$-0.226461\pi$
$601$	37.1366	1.51483	0.757417	+	0.652932i	$0.226461\pi$
$602$	10.5254	0.428984
$603$	−1.52111	−0.0619442
$604$	−44.3317	−1.80383
$605$	44.9614	1.82794
$606$	−20.3840	−0.828045
$607$	−14.2325	−0.577680	−0.288840	−	0.957377i	$-0.593269\pi$
$607$	−14.2325	−0.577680	−0.288840	+	0.957377i	$0.593269\pi$
$608$	−30.8538	−1.25129
$609$	8.85086	0.358655
$610$	−25.3106	−1.02480
$611$	0	0
$612$	2.00431	0.0810195
$613$	30.3139	1.22437	0.612184	−	0.790715i	$-0.290291\pi$
$613$	30.3139	1.22437	0.612184	+	0.790715i	$0.290291\pi$
$614$	13.4306	0.542014
$615$	−23.2935	−0.939285
$616$	−4.50365	−0.181457
$617$	−24.9638	−1.00500	−0.502501	−	0.864576i	$-0.667587\pi$
$617$	−24.9638	−1.00500	−0.502501	+	0.864576i	$0.667587\pi$
$618$	−22.5133	−0.905619
$619$	35.6122	1.43138	0.715688	−	0.698420i	$-0.246113\pi$
$619$	35.6122	1.43138	0.715688	+	0.698420i	$0.246113\pi$
$620$	−65.1469	−2.61636
$621$	−2.02715	−0.0813466
$622$	24.6674	0.989072
$623$	−22.6015	−0.905509
$624$	0	0
$625$	−17.0465	−0.681861
$626$	69.4480	2.77570
$627$	18.7778	0.749912
$628$	22.9441	0.915570
$629$	8.02608	0.320021
$630$	−15.4547	−0.615731
$631$	23.8829	0.950763	0.475382	−	0.879780i	$-0.342310\pi$
$631$	23.8829	0.950763	0.475382	+	0.879780i	$0.342310\pi$
$632$	1.51812	0.0603877
$633$	−23.2446	−0.923889
$634$	9.21659	0.366037
$635$	46.3642	1.83991
$636$	−1.19328	−0.0473165
$637$	0	0
$638$	39.8611	1.57812
$639$	2.37867	0.0940986
$640$	10.8447	0.428676
$641$	−24.6577	−0.973920	−0.486960	−	0.873424i	$-0.661894\pi$
$641$	−24.6577	−0.973920	−0.486960	+	0.873424i	$0.661894\pi$
$642$	−20.2282	−0.798343
$643$	47.8165	1.88570	0.942850	−	0.333218i	$-0.108134\pi$
$643$	47.8165	1.88570	0.942850	+	0.333218i	$0.108134\pi$
$644$	10.0121	0.394531
$645$	7.67456	0.302186
$646$	7.10321	0.279472
$647$	−5.38942	−0.211880	−0.105940	−	0.994373i	$-0.533785\pi$
$647$	−5.38942	−0.211880	−0.105940	+	0.994373i	$0.533785\pi$
$648$	−0.405813	−0.0159418
$649$	−23.2814	−0.913876
$650$	0	0
$651$	19.8388	0.777543
$652$	−24.2809	−0.950915
$653$	−5.03790	−0.197148	−0.0985741	−	0.995130i	$-0.531428\pi$
$653$	−5.03790	−0.197148	−0.0985741	+	0.995130i	$0.531428\pi$
$654$	41.4795	1.62198
$655$	10.0526	0.392789
$656$	−24.7351	−0.965743
$657$	7.41119	0.289138
$658$	−17.5036	−0.682363
$659$	−43.9812	−1.71326	−0.856632	−	0.515927i	$-0.827447\pi$
$659$	−43.9812	−1.71326	−0.856632	+	0.515927i	$0.827447\pi$
$660$	−36.4432	−1.41855
$661$	−38.2194	−1.48656	−0.743280	−	0.668980i	$-0.766731\pi$
$661$	−38.2194	−1.48656	−0.743280	+	0.668980i	$0.766731\pi$
$662$	22.9748	0.892940
$663$	0	0
$664$	−0.936608	−0.0363474
$665$	−28.6775	−1.11207
$666$	−18.0344	−0.698820
$667$	−7.98493	−0.309178
$668$	17.8261	0.689713
$669$	−10.7385	−0.415176
$670$	10.4622	0.404189
$671$	18.1752	0.701647
$672$	−18.2349	−0.703426
$673$	−6.66487	−0.256912	−0.128456	−	0.991715i	$-0.541002\pi$
$673$	−6.66487	−0.256912	−0.128456	+	0.991715i	$0.541002\pi$
$674$	−14.4426	−0.556310
$675$	−6.26875	−0.241284
$676$	0	0
$677$	4.80194	0.184553	0.0922767	−	0.995733i	$-0.470586\pi$
$677$	4.80194	0.184553	0.0922767	+	0.995733i	$0.470586\pi$
$678$	19.8582	0.762648
$679$	−36.2422	−1.39085
$680$	−1.24219	−0.0476360
$681$	6.97584	0.267315
$682$	89.3469	3.42127
$683$	11.2591	0.430816	0.215408	−	0.976524i	$-0.430892\pi$
$683$	11.2591	0.430816	0.215408	+	0.976524i	$0.430892\pi$
$684$	−8.35690	−0.319534
$685$	77.2737	2.95247
$686$	41.2097	1.57339
$687$	16.8049	0.641148
$688$	8.14952	0.310698
$689$	0	0
$690$	13.9427	0.530790
$691$	−24.7144	−0.940179	−0.470090	−	0.882619i	$-0.655778\pi$
$691$	−24.7144	−0.940179	−0.470090	+	0.882619i	$0.655778\pi$
$692$	−39.6887	−1.50874
$693$	11.0978	0.421572
$694$	5.54048	0.210314
$695$	3.29829	0.125111
$696$	−1.59850	−0.0605909
$697$	6.32736	0.239666
$698$	0.851329	0.0322233
$699$	−8.69202	−0.328762
$700$	30.9614	1.17023
$701$	25.8920	0.977927	0.488964	−	0.872304i	$-0.337375\pi$
$701$	25.8920	0.977927	0.488964	+	0.872304i	$0.337375\pi$
$702$	0	0
$703$	−33.4644	−1.26213
$704$	−46.9120	−1.76806
$705$	−12.7627	−0.480671
$706$	65.9079	2.48048
$707$	−22.3545	−0.840728
$708$	10.3612	0.389398
$709$	0.0851621	0.00319833	0.00159916	−	0.999999i	$-0.499491\pi$
$709$	0.0851621	0.00319833	0.00159916	+	0.999999i	$0.499491\pi$
$710$	−16.3605	−0.613998
$711$	−3.74094	−0.140296
$712$	4.08192	0.152976
$713$	−17.8979	−0.670280
$714$	4.19806	0.157109
$715$	0	0
$716$	−43.6760	−1.63225
$717$	22.9191	0.855931
$718$	−45.7976	−1.70915
$719$	27.0508	1.00883	0.504413	−	0.863463i	$-0.331709\pi$
$719$	27.0508	1.00883	0.504413	+	0.863463i	$0.331709\pi$
$720$	−11.9661	−0.445952
$721$	−24.6896	−0.919490
$722$	9.31288	0.346590
$723$	−21.9801	−0.817451
$724$	−22.1626	−0.823665
$725$	−24.6926	−0.917061
$726$	27.4426	1.01849
$727$	−47.1584	−1.74901	−0.874503	−	0.485019i	$-0.838813\pi$
$727$	−47.1584	−1.74901	−0.874503	+	0.485019i	$0.838813\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−50.9742	−1.88664
$731$	−2.08469	−0.0771050
$732$	−8.08874	−0.298968
$733$	−9.68186	−0.357608	−0.178804	−	0.983885i	$-0.557223\pi$
$733$	−9.68186	−0.357608	−0.178804	+	0.983885i	$0.557223\pi$
$734$	4.71784	0.174139
$735$	6.54958	0.241585
$736$	16.4509	0.606388
$737$	−7.51275	−0.276736
$738$	−14.2174	−0.523351
$739$	36.3139	1.33583	0.667915	−	0.744238i	$-0.267187\pi$
$739$	36.3139	1.33583	0.667915	+	0.744238i	$0.267187\pi$
$740$	64.9466	2.38748
$741$	0	0
$742$	−2.49934	−0.0917535
$743$	−41.7536	−1.53179	−0.765896	−	0.642965i	$-0.777704\pi$
$743$	−41.7536	−1.53179	−0.765896	+	0.642965i	$0.777704\pi$
$744$	−3.58296	−0.131358
$745$	34.4386	1.26173
$746$	39.4950	1.44602
$747$	2.30798	0.0844445
$748$	9.89930	0.361954
$749$	−22.1836	−0.810571
$750$	8.72646	0.318645
$751$	−22.1927	−0.809823	−0.404911	−	0.914356i	$-0.632698\pi$
$751$	−22.1927	−0.809823	−0.404911	+	0.914356i	$0.632698\pi$
$752$	−13.5526	−0.494211
$753$	−26.6437	−0.970950
$754$	0	0
$755$	−67.7036	−2.46399
$756$	−4.93900	−0.179630
$757$	9.23729	0.335735	0.167868	−	0.985810i	$-0.446312\pi$
$757$	9.23729	0.335735	0.167868	+	0.985810i	$0.446312\pi$
$758$	15.0379	0.546201
$759$	−10.0121	−0.363416
$760$	5.17928	0.187872
$761$	−7.50173	−0.271937	−0.135969	−	0.990713i	$-0.543415\pi$
$761$	−7.50173	−0.271937	−0.135969	+	0.990713i	$0.543415\pi$
$762$	28.2989	1.02516
$763$	45.4892	1.64682
$764$	−14.4797	−0.523857
$765$	3.06100	0.110671
$766$	−39.1140	−1.41325
$767$	0	0
$768$	−12.3773	−0.446629
$769$	5.14005	0.185355	0.0926774	−	0.995696i	$-0.470457\pi$
$769$	5.14005	0.185355	0.0926774	+	0.995696i	$0.470457\pi$
$770$	−76.3309	−2.75078
$771$	−23.1444	−0.833524
$772$	23.8869	0.859708
$773$	−8.50173	−0.305786	−0.152893	−	0.988243i	$-0.548859\pi$
$773$	−8.50173	−0.305786	−0.152893	+	0.988243i	$0.548859\pi$
$774$	4.68425	0.168372
$775$	−55.3473	−1.98813
$776$	6.54548	0.234969
$777$	−19.7778	−0.709524
$778$	49.1493	1.76209
$779$	−26.3817	−0.945221
$780$	0	0
$781$	11.7482	0.420385
$782$	−3.78735	−0.135435
$783$	3.93900	0.140768
$784$	6.95492	0.248390
$785$	35.0404	1.25065
$786$	6.13574	0.218854
$787$	−7.78554	−0.277525	−0.138762	−	0.990326i	$-0.544312\pi$
$787$	−7.78554	−0.277525	−0.138762	+	0.990326i	$0.544312\pi$
$788$	20.3136	0.723643
$789$	18.5284	0.659629
$790$	25.7302	0.915439
$791$	21.7778	0.774329
$792$	−2.00431	−0.0712201
$793$	0	0
$794$	9.05190	0.321240
$795$	−1.82238	−0.0646332
$796$	−3.43919	−0.121899
$797$	21.3840	0.757462	0.378731	−	0.925507i	$-0.376361\pi$
$797$	21.3840	0.757462	0.378731	+	0.925507i	$0.376361\pi$
$798$	−17.5036	−0.619622
$799$	3.46681	0.122647
$800$	50.8727	1.79862
$801$	−10.0586	−0.355403
$802$	41.8159	1.47657
$803$	36.6039	1.29172
$804$	3.34349	0.117916
$805$	15.2905	0.538920
$806$	0	0
$807$	−9.75840	−0.343512
$808$	4.03731	0.142032
$809$	2.28621	0.0803788	0.0401894	−	0.999192i	$-0.487204\pi$
$809$	2.28621	0.0803788	0.0401894	+	0.999192i	$0.487204\pi$
$810$	−6.87800	−0.241668
$811$	17.8079	0.625320	0.312660	−	0.949865i	$-0.398780\pi$
$811$	17.8079	0.625320	0.312660	+	0.949865i	$0.398780\pi$
$812$	−19.4547	−0.682727
$813$	22.8019	0.799699
$814$	−89.0721	−3.12198
$815$	−37.0820	−1.29893
$816$	3.25044	0.113788
$817$	8.69202	0.304095
$818$	45.3818	1.58674
$819$	0	0
$820$	51.2006	1.78800
$821$	13.9054	0.485302	0.242651	−	0.970114i	$-0.421983\pi$
$821$	13.9054	0.485302	0.242651	+	0.970114i	$0.421983\pi$
$822$	47.1648	1.64506
$823$	−7.24831	−0.252660	−0.126330	−	0.991988i	$-0.540320\pi$
$823$	−7.24831	−0.252660	−0.126330	+	0.991988i	$0.540320\pi$
$824$	4.45904	0.155338
$825$	−30.9614	−1.07794
$826$	21.7017	0.755099
$827$	54.1191	1.88191	0.940953	−	0.338536i	$-0.109932\pi$
$827$	54.1191	1.88191	0.940953	+	0.338536i	$0.109932\pi$
$828$	4.45580	0.154850
$829$	−5.79178	−0.201157	−0.100578	−	0.994929i	$-0.532069\pi$
$829$	−5.79178	−0.201157	−0.100578	+	0.994929i	$0.532069\pi$
$830$	−15.8743	−0.551004
$831$	23.9705	0.831526
$832$	0	0
$833$	−1.77910	−0.0616422
$834$	2.01315	0.0697096
$835$	27.2241	0.942130
$836$	−41.2747	−1.42752
$837$	8.82908	0.305178
$838$	−30.2338	−1.04441
$839$	−5.29350	−0.182752	−0.0913760	−	0.995816i	$-0.529127\pi$
$839$	−5.29350	−0.182752	−0.0913760	+	0.995816i	$0.529127\pi$
$840$	3.06100	0.105614
$841$	−13.4843	−0.464975
$842$	−17.3588	−0.598224
$843$	4.12498	0.142072
$844$	51.0930	1.75870
$845$	0	0
$846$	−7.78986	−0.267821
$847$	30.0954	1.03409
$848$	−1.93516	−0.0664538
$849$	15.6558	0.537305
$850$	−11.7120	−0.401718
$851$	17.8428	0.611644
$852$	−5.22846	−0.179124
$853$	−13.5961	−0.465522	−0.232761	−	0.972534i	$-0.574776\pi$
$853$	−13.5961	−0.465522	−0.232761	+	0.972534i	$0.574776\pi$
$854$	−16.9420	−0.579743
$855$	−12.7627	−0.436475
$856$	4.00644	0.136937
$857$	−23.8323	−0.814097	−0.407048	−	0.913407i	$-0.633442\pi$
$857$	−23.8323	−0.814097	−0.407048	+	0.913407i	$0.633442\pi$
$858$	0	0
$859$	−26.9861	−0.920754	−0.460377	−	0.887723i	$-0.652286\pi$
$859$	−26.9861	−0.920754	−0.460377	+	0.887723i	$0.652286\pi$
$860$	−16.8692	−0.575234
$861$	−15.5918	−0.531367
$862$	−4.90063	−0.166916
$863$	−27.0291	−0.920080	−0.460040	−	0.887898i	$-0.652165\pi$
$863$	−27.0291	−0.920080	−0.460040	+	0.887898i	$0.652165\pi$
$864$	−8.11529	−0.276088
$865$	−60.6128	−2.06090
$866$	21.3674	0.726095
$867$	16.1685	0.549112
$868$	−43.6069	−1.48011
$869$	−18.4765	−0.626772
$870$	−27.0925	−0.918520
$871$	0	0
$872$	−8.21552	−0.278213
$873$	−16.1293	−0.545894
$874$	15.7912	0.534145
$875$	9.57002	0.323526
$876$	−16.2903	−0.550397
$877$	40.8780	1.38035	0.690176	−	0.723642i	$-0.257533\pi$
$877$	40.8780	1.38035	0.690176	+	0.723642i	$0.257533\pi$
$878$	66.6926	2.25077
$879$	−22.5948	−0.762103
$880$	−59.1008	−1.99229
$881$	−22.4964	−0.757921	−0.378961	−	0.925413i	$-0.623718\pi$
$881$	−22.4964	−0.757921	−0.378961	+	0.925413i	$0.623718\pi$
$882$	3.99761	0.134606
$883$	−4.16315	−0.140101	−0.0700505	−	0.997543i	$-0.522316\pi$
$883$	−4.16315	−0.140101	−0.0700505	+	0.997543i	$0.522316\pi$
$884$	0	0
$885$	15.8237	0.531908
$886$	−19.6329	−0.659582
$887$	−26.3002	−0.883075	−0.441537	−	0.897243i	$-0.645567\pi$
$887$	−26.3002	−0.883075	−0.441537	+	0.897243i	$0.645567\pi$
$888$	3.57194	0.119867
$889$	31.0344	1.04086
$890$	69.1831	2.31902
$891$	4.93900	0.165463
$892$	23.6040	0.790320
$893$	−14.4547	−0.483709
$894$	21.0200	0.703013
$895$	−66.7023	−2.22961
$896$	7.25906	0.242508
$897$	0	0
$898$	58.1764	1.94137
$899$	34.7778	1.15990
$900$	13.7791	0.459303
$901$	0.495024	0.0164916
$902$	−70.2199	−2.33807
$903$	5.13706	0.170951
$904$	−3.93315	−0.130815
$905$	−33.8468	−1.12511
$906$	−41.3236	−1.37289
$907$	−57.9114	−1.92292	−0.961458	−	0.274952i	$-0.911338\pi$
$907$	−57.9114	−1.92292	−0.961458	+	0.274952i	$0.911338\pi$
$908$	−15.3333	−0.508854
$909$	−9.94869	−0.329977
$910$	0	0
$911$	−0.286799	−0.00950208	−0.00475104	−	0.999989i	$-0.501512\pi$
$911$	−0.286799	−0.00950208	−0.00475104	+	0.999989i	$0.501512\pi$
$912$	−13.5526	−0.448770
$913$	11.3991	0.377255
$914$	−10.2358	−0.338569
$915$	−12.3532	−0.408383
$916$	−36.9383	−1.22047
$917$	6.72886	0.222206
$918$	1.86831	0.0616635
$919$	−31.1239	−1.02668	−0.513342	−	0.858184i	$-0.671593\pi$
$919$	−31.1239	−1.02668	−0.513342	+	0.858184i	$0.671593\pi$
$920$	−2.76153	−0.0910449
$921$	6.55496	0.215993
$922$	−2.77133	−0.0912690
$923$	0	0
$924$	−24.3937	−0.802495
$925$	55.1771	1.81421
$926$	6.89392	0.226548
$927$	−10.9879	−0.360891
$928$	−31.9661	−1.04934
$929$	7.62671	0.250224	0.125112	−	0.992143i	$-0.460071\pi$
$929$	7.62671	0.250224	0.125112	+	0.992143i	$0.460071\pi$
$930$	−60.7265	−1.99130
$931$	7.41789	0.243112
$932$	19.1056	0.625825
$933$	12.0392	0.394147
$934$	−14.1596	−0.463317
$935$	15.1183	0.494421
$936$	0	0
$937$	−5.67324	−0.185337	−0.0926683	−	0.995697i	$-0.529540\pi$
$937$	−5.67324	−0.185337	−0.0926683	+	0.995697i	$0.529540\pi$
$938$	7.00298	0.228656
$939$	33.8950	1.10612
$940$	28.0532	0.914995
$941$	41.5394	1.35415	0.677073	−	0.735916i	$-0.263248\pi$
$941$	41.5394	1.35415	0.677073	+	0.735916i	$0.263248\pi$
$942$	21.3873	0.696836
$943$	14.0664	0.458064
$944$	16.8030	0.546891
$945$	−7.54288	−0.245370
$946$	23.1355	0.752201
$947$	−47.3110	−1.53740	−0.768700	−	0.639610i	$-0.779096\pi$
$947$	−47.3110	−1.53740	−0.768700	+	0.639610i	$0.779096\pi$
$948$	8.22282	0.267065
$949$	0	0
$950$	48.8327	1.58434
$951$	4.49827	0.145866
$952$	−0.831478	−0.0269483
$953$	−34.3435	−1.11249	−0.556247	−	0.831017i	$-0.687759\pi$
$953$	−34.3435	−1.11249	−0.556247	+	0.831017i	$0.687759\pi$
$954$	−1.11231	−0.0360123
$955$	−22.1135	−0.715576
$956$	−50.3777	−1.62933
$957$	19.4547	0.628882
$958$	−7.20344	−0.232733
$959$	51.7241	1.67026
$960$	31.8847	1.02907
$961$	46.9527	1.51460
$962$	0	0
$963$	−9.87263	−0.318141
$964$	48.3137	1.55608
$965$	36.4802	1.17434
$966$	9.33273	0.300276
$967$	48.5096	1.55996	0.779982	−	0.625802i	$-0.215228\pi$
$967$	48.5096	1.55996	0.779982	+	0.625802i	$0.215228\pi$
$968$	−5.43535	−0.174699
$969$	3.46681	0.111370
$970$	110.937	3.56198
$971$	41.4650	1.33068	0.665338	−	0.746542i	$-0.268288\pi$
$971$	41.4650	1.33068	0.665338	+	0.746542i	$0.268288\pi$
$972$	−2.19806	−0.0705029
$973$	2.20775	0.0707772
$974$	26.3242	0.843483
$975$	0	0
$976$	−13.1177	−0.419887
$977$	−2.09677	−0.0670816	−0.0335408	−	0.999437i	$-0.510678\pi$
$977$	−2.09677	−0.0670816	−0.0335408	+	0.999437i	$0.510678\pi$
$978$	−22.6334	−0.723737
$979$	−49.6795	−1.58776
$980$	−14.3964	−0.459876
$981$	20.2446	0.646360
$982$	−58.7442	−1.87460
$983$	25.2336	0.804826	0.402413	−	0.915458i	$-0.368172\pi$
$983$	25.2336	0.804826	0.402413	+	0.915458i	$0.368172\pi$
$984$	2.81594	0.0897688
$985$	31.0231	0.988478
$986$	7.35929	0.234367
$987$	−8.54288	−0.271923
$988$	0	0
$989$	−4.63448	−0.147368
$990$	−33.9705	−1.07965
$991$	12.0489	0.382746	0.191373	−	0.981517i	$-0.438706\pi$
$991$	12.0489	0.382746	0.191373	+	0.981517i	$0.438706\pi$
$992$	−71.6506	−2.27491
$993$	11.2131	0.355838
$994$	−10.9511	−0.347347
$995$	−5.25236	−0.166511
$996$	−5.07308	−0.160747
$997$	−1.43403	−0.0454160	−0.0227080	−	0.999742i	$-0.507229\pi$
$997$	−1.43403	−0.0454160	−0.0227080	+	0.999742i	$0.507229\pi$
$998$	68.7525	2.17632
$999$	−8.80194	−0.278481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.a.l.1.1	yes	3
3.2	odd	2		1521.2.a.n.1.3		3
4.3	odd	2		8112.2.a.cp.1.2		3
13.2	odd	12		507.2.j.i.316.3		12
13.3	even	3		507.2.e.i.22.3		6
13.4	even	6		507.2.e.l.484.1		6
13.5	odd	4		507.2.b.f.337.4		6
13.6	odd	12		507.2.j.i.361.4		12
13.7	odd	12		507.2.j.i.361.3		12
13.8	odd	4		507.2.b.f.337.3		6
13.9	even	3		507.2.e.i.484.3		6
13.10	even	6		507.2.e.l.22.1		6
13.11	odd	12		507.2.j.i.316.4		12
13.12	even	2		507.2.a.i.1.3	✓	3
39.5	even	4		1521.2.b.k.1351.3		6
39.8	even	4		1521.2.b.k.1351.4		6
39.38	odd	2		1521.2.a.s.1.1		3
52.51	odd	2		8112.2.a.cg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.i.1.3	✓	3	13.12	even	2
507.2.a.l.1.1	yes	3	1.1	even	1	trivial
507.2.b.f.337.3		6	13.8	odd	4
507.2.b.f.337.4		6	13.5	odd	4
507.2.e.i.22.3		6	13.3	even	3
507.2.e.i.484.3		6	13.9	even	3
507.2.e.l.22.1		6	13.10	even	6
507.2.e.l.484.1		6	13.4	even	6
507.2.j.i.316.3		12	13.2	odd	12
507.2.j.i.316.4		12	13.11	odd	12
507.2.j.i.361.3		12	13.7	odd	12
507.2.j.i.361.4		12	13.6	odd	12
1521.2.a.n.1.3		3	3.2	odd	2
1521.2.a.s.1.1		3	39.38	odd	2
1521.2.b.k.1351.3		6	39.5	even	4
1521.2.b.k.1351.4		6	39.8	even	4
8112.2.a.cg.1.2		3	52.51	odd	2
8112.2.a.cp.1.2		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.a (trivial)

\(f(q)\)	\(=\)	\(q-2.04892 q^{2} -1.00000 q^{3} +2.19806 q^{4} +3.35690 q^{5} +2.04892 q^{6} +2.24698 q^{7} -0.405813 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.04892 q^{2} -1.00000 q^{3} +2.19806 q^{4} +3.35690 q^{5} +2.04892 q^{6} +2.24698 q^{7} -0.405813 q^{8} +1.00000 q^{9} -6.87800 q^{10} +4.93900 q^{11} -2.19806 q^{12} -4.60388 q^{14} -3.35690 q^{15} -3.56465 q^{16} +0.911854 q^{17} -2.04892 q^{18} -3.80194 q^{19} +7.37867 q^{20} -2.24698 q^{21} -10.1196 q^{22} +2.02715 q^{23} +0.405813 q^{24} +6.26875 q^{25} -1.00000 q^{27} +4.93900 q^{28} -3.93900 q^{29} +6.87800 q^{30} -8.82908 q^{31} +8.11529 q^{32} -4.93900 q^{33} -1.86831 q^{34} +7.54288 q^{35} +2.19806 q^{36} +8.80194 q^{37} +7.78986 q^{38} -1.36227 q^{40} +6.93900 q^{41} +4.60388 q^{42} -2.28621 q^{43} +10.8562 q^{44} +3.35690 q^{45} -4.15346 q^{46} +3.80194 q^{47} +3.56465 q^{48} -1.95108 q^{49} -12.8442 q^{50} -0.911854 q^{51} +0.542877 q^{53} +2.04892 q^{54} +16.5797 q^{55} -0.911854 q^{56} +3.80194 q^{57} +8.07069 q^{58} -4.71379 q^{59} -7.37867 q^{60} +3.67994 q^{61} +18.0901 q^{62} +2.24698 q^{63} -9.49827 q^{64} +10.1196 q^{66} -1.52111 q^{67} +2.00431 q^{68} -2.02715 q^{69} -15.4547 q^{70} +2.37867 q^{71} -0.405813 q^{72} +7.41119 q^{73} -18.0344 q^{74} -6.26875 q^{75} -8.35690 q^{76} +11.0978 q^{77} -3.74094 q^{79} -11.9661 q^{80} +1.00000 q^{81} -14.2174 q^{82} +2.30798 q^{83} -4.93900 q^{84} +3.06100 q^{85} +4.68425 q^{86} +3.93900 q^{87} -2.00431 q^{88} -10.0586 q^{89} -6.87800 q^{90} +4.45580 q^{92} +8.82908 q^{93} -7.78986 q^{94} -12.7627 q^{95} -8.11529 q^{96} -16.1293 q^{97} +3.99761 q^{98} +4.93900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 11 q^{4} + 6 q^{5} - 3 q^{6} + 2 q^{7} + 12 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 11 * q^4 + 6 * q^5 - 3 * q^6 + 2 * q^7 + 12 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 11 q^{4} + 6 q^{5} - 3 q^{6} + 2 q^{7} + 12 q^{8} + 3 q^{9} - q^{10} + 5 q^{11} - 11 q^{12} - 5 q^{14} - 6 q^{15} + 11 q^{16} - q^{17} + 3 q^{18} - 7 q^{19} + 15 q^{20} - 2 q^{21} - 9 q^{22} - 12 q^{24} + 11 q^{25} - 3 q^{27} + 5 q^{28} - 2 q^{29} + q^{30} - 16 q^{31} + 22 q^{32} - 5 q^{33} - 8 q^{34} + 4 q^{35} + 11 q^{36} + 22 q^{37} + 3 q^{40} + 11 q^{41} + 5 q^{42} - 15 q^{43} + 16 q^{44} + 6 q^{45} - 7 q^{46} + 7 q^{47} - 11 q^{48} - 15 q^{49} - 3 q^{50} + q^{51} - 17 q^{53} - 3 q^{54} + 3 q^{55} + q^{56} + 7 q^{57} + 12 q^{58} - 6 q^{59} - 15 q^{60} - 13 q^{61} - 2 q^{62} + 2 q^{63} + 9 q^{66} + 11 q^{67} - 13 q^{68} - 24 q^{70} + 12 q^{72} + 6 q^{73} + 15 q^{74} - 11 q^{75} - 21 q^{76} + 15 q^{77} + 3 q^{79} - 20 q^{80} + 3 q^{81} - 3 q^{82} + 12 q^{83} - 5 q^{84} + 19 q^{85} - 29 q^{86} + 2 q^{87} + 13 q^{88} + q^{89} - q^{90} + 7 q^{92} + 16 q^{93} - 21 q^{95} - 22 q^{96} - 5 q^{97} - 29 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 11 * q^4 + 6 * q^5 - 3 * q^6 + 2 * q^7 + 12 * q^8 + 3 * q^9 - q^10 + 5 * q^11 - 11 * q^12 - 5 * q^14 - 6 * q^15 + 11 * q^16 - q^17 + 3 * q^18 - 7 * q^19 + 15 * q^20 - 2 * q^21 - 9 * q^22 - 12 * q^24 + 11 * q^25 - 3 * q^27 + 5 * q^28 - 2 * q^29 + q^30 - 16 * q^31 + 22 * q^32 - 5 * q^33 - 8 * q^34 + 4 * q^35 + 11 * q^36 + 22 * q^37 + 3 * q^40 + 11 * q^41 + 5 * q^42 - 15 * q^43 + 16 * q^44 + 6 * q^45 - 7 * q^46 + 7 * q^47 - 11 * q^48 - 15 * q^49 - 3 * q^50 + q^51 - 17 * q^53 - 3 * q^54 + 3 * q^55 + q^56 + 7 * q^57 + 12 * q^58 - 6 * q^59 - 15 * q^60 - 13 * q^61 - 2 * q^62 + 2 * q^63 + 9 * q^66 + 11 * q^67 - 13 * q^68 - 24 * q^70 + 12 * q^72 + 6 * q^73 + 15 * q^74 - 11 * q^75 - 21 * q^76 + 15 * q^77 + 3 * q^79 - 20 * q^80 + 3 * q^81 - 3 * q^82 + 12 * q^83 - 5 * q^84 + 19 * q^85 - 29 * q^86 + 2 * q^87 + 13 * q^88 + q^89 - q^90 + 7 * q^92 + 16 * q^93 - 21 * q^95 - 22 * q^96 - 5 * q^97 - 29 * q^98 + 5 * q^99

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