LMFDB - Embedded newform 5054.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1528713.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3x^{4} + 7x^{3} + 3x^{2} - 3x - 1 $ x^6 - 3x^5 - 3x^4 + 7x^3 + 3x^2 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.19261$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.108781 q^{3} +1.00000 q^{4} -1.47989 q^{5} +0.108781 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.98817 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.108781 q^{3} +1.00000 q^{4} -1.47989 q^{5} +0.108781 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.98817 q^{9} +1.47989 q^{10} +3.35927 q^{11} -0.108781 q^{12} -1.08383 q^{13} +1.00000 q^{14} +0.160984 q^{15} +1.00000 q^{16} +0.00285624 q^{17} +2.98817 q^{18} -1.47989 q^{20} +0.108781 q^{21} -3.35927 q^{22} +1.10348 q^{23} +0.108781 q^{24} -2.80994 q^{25} +1.08383 q^{26} +0.651401 q^{27} -1.00000 q^{28} +3.77842 q^{29} -0.160984 q^{30} +0.689180 q^{31} -1.00000 q^{32} -0.365426 q^{33} -0.00285624 q^{34} +1.47989 q^{35} -2.98817 q^{36} +7.01708 q^{37} +0.117900 q^{39} +1.47989 q^{40} +3.11294 q^{41} -0.108781 q^{42} +9.33361 q^{43} +3.35927 q^{44} +4.42215 q^{45} -1.10348 q^{46} -12.2110 q^{47} -0.108781 q^{48} +1.00000 q^{49} +2.80994 q^{50} -0.000310706 q^{51} -1.08383 q^{52} +1.98931 q^{53} -0.651401 q^{54} -4.97134 q^{55} +1.00000 q^{56} -3.77842 q^{58} -9.37920 q^{59} +0.160984 q^{60} -3.29799 q^{61} -0.689180 q^{62} +2.98817 q^{63} +1.00000 q^{64} +1.60394 q^{65} +0.365426 q^{66} -1.13926 q^{67} +0.00285624 q^{68} -0.120038 q^{69} -1.47989 q^{70} +9.20003 q^{71} +2.98817 q^{72} -10.5877 q^{73} -7.01708 q^{74} +0.305669 q^{75} -3.35927 q^{77} -0.117900 q^{78} -1.03103 q^{79} -1.47989 q^{80} +8.89364 q^{81} -3.11294 q^{82} +8.24555 q^{83} +0.108781 q^{84} -0.00422691 q^{85} -9.33361 q^{86} -0.411022 q^{87} -3.35927 q^{88} -0.669280 q^{89} -4.42215 q^{90} +1.08383 q^{91} +1.10348 q^{92} -0.0749700 q^{93} +12.2110 q^{94} +0.108781 q^{96} +7.36563 q^{97} -1.00000 q^{98} -10.0381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 3 q^{31} - 6 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 3 q^{37} - 9 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} + 3 q^{48} + 6 q^{49} - 3 q^{50} - 27 q^{51} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 24 q^{55} + 6 q^{56} - 6 q^{58} + 15 q^{59} - 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} + 3 q^{65} - 6 q^{66} + 15 q^{67} - 9 q^{68} + 24 q^{69} - 3 q^{70} + 21 q^{71} + 3 q^{72} - 33 q^{73} + 3 q^{74} + 33 q^{75} - 3 q^{77} + 9 q^{78} - 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} - 3 q^{84} - 18 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 12 q^{89} + 12 q^{90} - 6 q^{91} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 18 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 3 * q^31 - 6 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 3 * q^37 - 9 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 + 3 * q^48 + 6 * q^49 - 3 * q^50 - 27 * q^51 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 24 * q^55 + 6 * q^56 - 6 * q^58 + 15 * q^59 - 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^65 - 6 * q^66 + 15 * q^67 - 9 * q^68 + 24 * q^69 - 3 * q^70 + 21 * q^71 + 3 * q^72 - 33 * q^73 + 3 * q^74 + 33 * q^75 - 3 * q^77 + 9 * q^78 - 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 - 3 * q^84 - 18 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 12 * q^89 + 12 * q^90 - 6 * q^91 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 18 * q^97 - 6 * q^98

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
$3$	−0.108781	−0.0628050	−0.0314025	−	0.999507i	$-0.509997\pi$
$3$	−0.108781	−0.0628050	−0.0314025	+	0.999507i	$0.509997\pi$
$4$	1.00000	0.500000
$5$	−1.47989	−0.661825	−0.330913	−	0.943661i	$-0.607357\pi$
$5$	−1.47989	−0.661825	−0.330913	+	0.943661i	$0.607357\pi$
$6$	0.108781	0.0444098
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.98817	−0.996056
$10$	1.47989	0.467981
$11$	3.35927	1.01286	0.506429	−	0.862282i	$-0.330965\pi$
$11$	3.35927	1.01286	0.506429	+	0.862282i	$0.330965\pi$
$12$	−0.108781	−0.0314025
$13$	−1.08383	−0.300600	−0.150300	−	0.988640i	$-0.548024\pi$
$13$	−1.08383	−0.300600	−0.150300	+	0.988640i	$0.548024\pi$
$14$	1.00000	0.267261
$15$	0.160984	0.0415659
$16$	1.00000	0.250000
$17$	0.00285624	0.000692740 0	0.000346370	−	1.00000i	$-0.499890\pi$
$17$	0.00285624	0.000692740 0	0.000346370		1.00000i	$0.499890\pi$
$18$	2.98817	0.704318
$19$	0	0
$19$	0	0
$20$	−1.47989	−0.330913
$21$	0.108781	0.0237380
$22$	−3.35927	−0.716199
$23$	1.10348	0.230091	0.115045	−	0.993360i	$-0.463299\pi$
$23$	1.10348	0.230091	0.115045	+	0.993360i	$0.463299\pi$
$24$	0.108781	0.0222049
$25$	−2.80994	−0.561987
$26$	1.08383	0.212556
$27$	0.651401	0.125362
$28$	−1.00000	−0.188982
$29$	3.77842	0.701635	0.350817	−	0.936444i	$-0.385904\pi$
$29$	3.77842	0.701635	0.350817	+	0.936444i	$0.385904\pi$
$30$	−0.160984	−0.0293915
$31$	0.689180	0.123780	0.0618902	−	0.998083i	$-0.480287\pi$
$31$	0.689180	0.123780	0.0618902	+	0.998083i	$0.480287\pi$
$32$	−1.00000	−0.176777
$33$	−0.365426	−0.0636125
$34$	−0.00285624	−0.000489841 0
$35$	1.47989	0.250146
$36$	−2.98817	−0.498028
$37$	7.01708	1.15360	0.576800	−	0.816885i	$-0.304301\pi$
$37$	7.01708	1.15360	0.576800	+	0.816885i	$0.304301\pi$
$38$	0	0
$39$	0.117900	0.0188791
$40$	1.47989	0.233991
$41$	3.11294	0.486160	0.243080	−	0.970006i	$-0.421842\pi$
$41$	3.11294	0.486160	0.243080	+	0.970006i	$0.421842\pi$
$42$	−0.108781	−0.0167853
$43$	9.33361	1.42336	0.711681	−	0.702503i	$-0.247934\pi$
$43$	9.33361	1.42336	0.711681	+	0.702503i	$0.247934\pi$
$44$	3.35927	0.506429
$45$	4.42215	0.659215
$46$	−1.10348	−0.162699
$47$	−12.2110	−1.78116	−0.890580	−	0.454826i	$-0.849701\pi$
$47$	−12.2110	−1.78116	−0.890580	+	0.454826i	$0.849701\pi$
$48$	−0.108781	−0.0157012
$49$	1.00000	0.142857
$50$	2.80994	0.397385
$51$	−0.000310706 0	−4.35075e−5 0
$52$	−1.08383	−0.150300
$53$	1.98931	0.273253	0.136627	−	0.990623i	$-0.456374\pi$
$53$	1.98931	0.273253	0.136627	+	0.990623i	$0.456374\pi$
$54$	−0.651401	−0.0886444
$55$	−4.97134	−0.670335
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.77842	−0.496131
$59$	−9.37920	−1.22107	−0.610534	−	0.791990i	$-0.709045\pi$
$59$	−9.37920	−1.22107	−0.610534	+	0.791990i	$0.709045\pi$
$60$	0.160984	0.0207830
$61$	−3.29799	−0.422265	−0.211132	−	0.977457i	$-0.567715\pi$
$61$	−3.29799	−0.422265	−0.211132	+	0.977457i	$0.567715\pi$
$62$	−0.689180	−0.0875260
$63$	2.98817	0.376474
$64$	1.00000	0.125000
$65$	1.60394	0.198944
$66$	0.365426	0.0449809
$67$	−1.13926	−0.139183	−0.0695914	−	0.997576i	$-0.522170\pi$
$67$	−1.13926	−0.139183	−0.0695914	+	0.997576i	$0.522170\pi$
$68$	0.00285624	0.000346370 0
$69$	−0.120038	−0.0144508
$70$	−1.47989	−0.176880
$71$	9.20003	1.09184	0.545921	−	0.837837i	$-0.316180\pi$
$71$	9.20003	1.09184	0.545921	+	0.837837i	$0.316180\pi$
$72$	2.98817	0.352159
$73$	−10.5877	−1.23920	−0.619599	−	0.784919i	$-0.712705\pi$
$73$	−10.5877	−1.23920	−0.619599	+	0.784919i	$0.712705\pi$
$74$	−7.01708	−0.815719
$75$	0.305669	0.0352956
$76$	0	0
$77$	−3.35927	−0.382825
$78$	−0.117900	−0.0133496
$79$	−1.03103	−0.116000	−0.0580000	−	0.998317i	$-0.518472\pi$
$79$	−1.03103	−0.116000	−0.0580000	+	0.998317i	$0.518472\pi$
$80$	−1.47989	−0.165456
$81$	8.89364	0.988182
$82$	−3.11294	−0.343767
$83$	8.24555	0.905066	0.452533	−	0.891748i	$-0.350520\pi$
$83$	8.24555	0.905066	0.452533	+	0.891748i	$0.350520\pi$
$84$	0.108781	0.0118690
$85$	−0.00422691	−0.000458473 0
$86$	−9.33361	−1.00647
$87$	−0.411022	−0.0440662
$88$	−3.35927	−0.358100
$89$	−0.669280	−0.0709435	−0.0354718	−	0.999371i	$-0.511293\pi$
$89$	−0.669280	−0.0709435	−0.0354718	+	0.999371i	$0.511293\pi$
$90$	−4.42215	−0.466135
$91$	1.08383	0.113616
$92$	1.10348	0.115045
$93$	−0.0749700	−0.00777403
$94$	12.2110	1.25947
$95$	0	0
$96$	0.108781	0.0111025
$97$	7.36563	0.747867	0.373933	−	0.927456i	$-0.378009\pi$
$97$	7.36563	0.747867	0.373933	+	0.927456i	$0.378009\pi$
$98$	−1.00000	−0.101015
$99$	−10.0381	−1.00886
$100$	−2.80994	−0.280994
$101$	−7.95223	−0.791276	−0.395638	−	0.918406i	$-0.629477\pi$
$101$	−7.95223	−0.791276	−0.395638	+	0.918406i	$0.629477\pi$
$102$	0.000310706 0	3.07644e−5 0
$103$	11.0692	1.09068	0.545341	−	0.838214i	$-0.316400\pi$
$103$	11.0692	1.09068	0.545341	+	0.838214i	$0.316400\pi$
$104$	1.08383	0.106278
$105$	−0.160984	−0.0157104
$106$	−1.98931	−0.193219
$107$	−9.93423	−0.960378	−0.480189	−	0.877165i	$-0.659432\pi$
$107$	−9.93423	−0.960378	−0.480189	+	0.877165i	$0.659432\pi$
$108$	0.651401	0.0626811
$109$	−1.32380	−0.126797	−0.0633985	−	0.997988i	$-0.520194\pi$
$109$	−1.32380	−0.126797	−0.0633985	+	0.997988i	$0.520194\pi$
$110$	4.97134	0.473999
$111$	−0.763327	−0.0724518
$112$	−1.00000	−0.0944911
$113$	18.8686	1.77501	0.887506	−	0.460796i	$-0.152436\pi$
$113$	18.8686	1.77501	0.887506	+	0.460796i	$0.152436\pi$
$114$	0	0
$115$	−1.63302	−0.152280
$116$	3.77842	0.350817
$117$	3.23866	0.299414
$118$	9.37920	0.863426
$119$	−0.00285624	−0.000261831 0
$120$	−0.160984	−0.0146958
$121$	0.284705	0.0258822
$122$	3.29799	0.298586
$123$	−0.338630	−0.0305332
$124$	0.689180	0.0618902
$125$	11.5578	1.03376
$126$	−2.98817	−0.266207
$127$	−13.5027	−1.19817	−0.599085	−	0.800685i	$-0.704469\pi$
$127$	−13.5027	−1.19817	−0.599085	+	0.800685i	$0.704469\pi$
$128$	−1.00000	−0.0883883
$129$	−1.01532	−0.0893942
$130$	−1.60394	−0.140675
$131$	−11.7452	−1.02618	−0.513091	−	0.858334i	$-0.671500\pi$
$131$	−11.7452	−1.02618	−0.513091	+	0.858334i	$0.671500\pi$
$132$	−0.365426	−0.0318063
$133$	0	0
$134$	1.13926	0.0984171
$135$	−0.963999	−0.0829679
$136$	−0.00285624	−0.000244920 0
$137$	−0.592734	−0.0506407	−0.0253203	−	0.999679i	$-0.508061\pi$
$137$	−0.592734	−0.0506407	−0.0253203	+	0.999679i	$0.508061\pi$
$138$	0.120038	0.0102183
$139$	−16.4918	−1.39881	−0.699406	−	0.714725i	$-0.746552\pi$
$139$	−16.4918	−1.39881	−0.699406	+	0.714725i	$0.746552\pi$
$140$	1.47989	0.125073
$141$	1.32833	0.111866
$142$	−9.20003	−0.772049
$143$	−3.64087	−0.304465
$144$	−2.98817	−0.249014
$145$	−5.59163	−0.464360
$146$	10.5877	0.876245
$147$	−0.108781	−0.00897214
$148$	7.01708	0.576800
$149$	−19.8299	−1.62453	−0.812265	−	0.583288i	$-0.801766\pi$
$149$	−19.8299	−1.62453	−0.812265	+	0.583288i	$0.801766\pi$
$150$	−0.305669	−0.0249578
$151$	−0.447072	−0.0363822	−0.0181911	−	0.999835i	$-0.505791\pi$
$151$	−0.447072	−0.0363822	−0.0181911	+	0.999835i	$0.505791\pi$
$152$	0	0
$153$	−0.00853492	−0.000690007 0
$154$	3.35927	0.270698
$155$	−1.01991	−0.0819210
$156$	0.117900	0.00943957
$157$	−4.32457	−0.345138	−0.172569	−	0.984997i	$-0.555207\pi$
$157$	−4.32457	−0.345138	−0.172569	+	0.984997i	$0.555207\pi$
$158$	1.03103	0.0820244
$159$	−0.216400	−0.0171616
$160$	1.47989	0.116995
$161$	−1.10348	−0.0869662
$162$	−8.89364	−0.698750
$163$	−11.6366	−0.911446	−0.455723	−	0.890122i	$-0.650619\pi$
$163$	−11.6366	−0.911446	−0.455723	+	0.890122i	$0.650619\pi$
$164$	3.11294	0.243080
$165$	0.540789	0.0421004
$166$	−8.24555	−0.639979
$167$	24.6233	1.90541	0.952704	−	0.303899i	$-0.0982886\pi$
$167$	24.6233	1.90541	0.952704	+	0.303899i	$0.0982886\pi$
$168$	−0.108781	−0.00839267
$169$	−11.8253	−0.909640
$170$	0.00422691	0.000324189 0
$171$	0	0
$172$	9.33361	0.711681
$173$	−16.0806	−1.22258	−0.611292	−	0.791405i	$-0.709350\pi$
$173$	−16.0806	−1.22258	−0.611292	+	0.791405i	$0.709350\pi$
$174$	0.411022	0.0311595
$175$	2.80994	0.212411
$176$	3.35927	0.253215
$177$	1.02028	0.0766891
$178$	0.669280	0.0501646
$179$	−13.1835	−0.985383	−0.492692	−	0.870204i	$-0.663987\pi$
$179$	−13.1835	−0.985383	−0.492692	+	0.870204i	$0.663987\pi$
$180$	4.42215	0.329607
$181$	17.8732	1.32850	0.664251	−	0.747510i	$-0.268751\pi$
$181$	17.8732	1.32850	0.664251	+	0.747510i	$0.268751\pi$
$182$	−1.08383	−0.0803386
$183$	0.358760	0.0265203
$184$	−1.10348	−0.0813494
$185$	−10.3845	−0.763482
$186$	0.0749700	0.00549707
$187$	0.00959488	0.000701647 0
$188$	−12.2110	−0.890580
$189$	−0.651401	−0.0473824
$190$	0	0
$191$	−8.60837	−0.622880	−0.311440	−	0.950266i	$-0.600811\pi$
$191$	−8.60837	−0.622880	−0.311440	+	0.950266i	$0.600811\pi$
$192$	−0.108781	−0.00785062
$193$	0.0199822	0.00143835	0.000719175	−	1.00000i	$-0.499771\pi$
$193$	0.0199822	0.00143835	0.000719175		1.00000i	$0.499771\pi$
$194$	−7.36563	−0.528822
$195$	−0.174479	−0.0124947
$196$	1.00000	0.0714286
$197$	−18.7427	−1.33536	−0.667681	−	0.744448i	$-0.732713\pi$
$197$	−18.7427	−1.33536	−0.667681	+	0.744448i	$0.732713\pi$
$198$	10.0381	0.713374
$199$	−17.8971	−1.26869	−0.634347	−	0.773048i	$-0.718731\pi$
$199$	−17.8971	−1.26869	−0.634347	+	0.773048i	$0.718731\pi$
$200$	2.80994	0.198693
$201$	0.123930	0.00874137
$202$	7.95223	0.559517
$203$	−3.77842	−0.265193
$204$	−0.000310706 0	−2.17537e−5 0
$205$	−4.60680	−0.321753
$206$	−11.0692	−0.771229
$207$	−3.29737	−0.229183
$208$	−1.08383	−0.0751499
$209$	0	0
$210$	0.160984	0.0111090
$211$	−25.3593	−1.74580	−0.872902	−	0.487896i	$-0.837764\pi$
$211$	−25.3593	−1.74580	−0.872902	+	0.487896i	$0.837764\pi$
$212$	1.98931	0.136627
$213$	−1.00079	−0.0685731
$214$	9.93423	0.679090
$215$	−13.8127	−0.942017
$216$	−0.651401	−0.0443222
$217$	−0.689180	−0.0467846
$218$	1.32380	0.0896590
$219$	1.15175	0.0778277
$220$	−4.97134	−0.335168
$221$	−0.00309567	−0.000208237 0
$222$	0.763327	0.0512312
$223$	−4.37342	−0.292866	−0.146433	−	0.989221i	$-0.546779\pi$
$223$	−4.37342	−0.292866	−0.146433	+	0.989221i	$0.546779\pi$
$224$	1.00000	0.0668153
$225$	8.39656	0.559771
$226$	−18.8686	−1.25512
$227$	−1.70261	−0.113006	−0.0565032	−	0.998402i	$-0.517995\pi$
$227$	−1.70261	−0.113006	−0.0565032	+	0.998402i	$0.517995\pi$
$228$	0	0
$229$	−8.60530	−0.568654	−0.284327	−	0.958727i	$-0.591770\pi$
$229$	−8.60530	−0.568654	−0.284327	+	0.958727i	$0.591770\pi$
$230$	1.63302	0.107678
$231$	0.365426	0.0240433
$232$	−3.77842	−0.248065
$233$	18.3851	1.20445	0.602225	−	0.798326i	$-0.294281\pi$
$233$	18.3851	1.20445	0.602225	+	0.798326i	$0.294281\pi$
$234$	−3.23866	−0.211718
$235$	18.0709	1.17882
$236$	−9.37920	−0.610534
$237$	0.112157	0.00728537
$238$	0.00285624	0.000185142 0
$239$	16.6973	1.08006	0.540030	−	0.841646i	$-0.318413\pi$
$239$	16.6973	1.08006	0.540030	+	0.841646i	$0.318413\pi$
$240$	0.160984	0.0103915
$241$	−0.180340	−0.0116167	−0.00580835	−	0.999983i	$-0.501849\pi$
$241$	−0.180340	−0.0116167	−0.00580835	+	0.999983i	$0.501849\pi$
$242$	−0.284705	−0.0183015
$243$	−2.92167	−0.187425
$244$	−3.29799	−0.211132
$245$	−1.47989	−0.0945465
$246$	0.338630	0.0215903
$247$	0	0
$248$	−0.689180	−0.0437630
$249$	−0.896962	−0.0568427
$250$	−11.5578	−0.730981
$251$	−1.76199	−0.111216	−0.0556078	−	0.998453i	$-0.517710\pi$
$251$	−1.76199	−0.111216	−0.0556078	+	0.998453i	$0.517710\pi$
$252$	2.98817	0.188237
$253$	3.70688	0.233049
$254$	13.5027	0.847235
$255$	0.000459809 0	2.87944e−5 0
$256$	1.00000	0.0625000
$257$	27.7639	1.73187	0.865933	−	0.500160i	$-0.166726\pi$
$257$	27.7639	1.73187	0.865933	+	0.500160i	$0.166726\pi$
$258$	1.01532	0.0632112
$259$	−7.01708	−0.436020
$260$	1.60394	0.0994722
$261$	−11.2905	−0.698867
$262$	11.7452	0.725621
$263$	−7.64376	−0.471334	−0.235667	−	0.971834i	$-0.575728\pi$
$263$	−7.64376	−0.471334	−0.235667	+	0.971834i	$0.575728\pi$
$264$	0.365426	0.0224904
$265$	−2.94396	−0.180846
$266$	0	0
$267$	0.0728052	0.00445560
$268$	−1.13926	−0.0695914
$269$	6.84128	0.417120	0.208560	−	0.978010i	$-0.433122\pi$
$269$	6.84128	0.417120	0.208560	+	0.978010i	$0.433122\pi$
$270$	0.963999	0.0586671
$271$	−1.90412	−0.115667	−0.0578335	−	0.998326i	$-0.518419\pi$
$271$	−1.90412	−0.115667	−0.0578335	+	0.998326i	$0.518419\pi$
$272$	0.00285624	0.000173185 0
$273$	−0.117900	−0.00713565
$274$	0.592734	0.0358084
$275$	−9.43934	−0.569214
$276$	−0.120038	−0.00722542
$277$	24.5531	1.47525	0.737626	−	0.675209i	$-0.235947\pi$
$277$	24.5531	1.47525	0.737626	+	0.675209i	$0.235947\pi$
$278$	16.4918	0.989110
$279$	−2.05939	−0.123292
$280$	−1.47989	−0.0884401
$281$	19.8835	1.18615	0.593077	−	0.805146i	$-0.297913\pi$
$281$	19.8835	1.18615	0.593077	+	0.805146i	$0.297913\pi$
$282$	−1.32833	−0.0791010
$283$	7.03113	0.417957	0.208979	−	0.977920i	$-0.432986\pi$
$283$	7.03113	0.417957	0.208979	+	0.977920i	$0.432986\pi$
$284$	9.20003	0.545921
$285$	0	0
$286$	3.64087	0.215289
$287$	−3.11294	−0.183751
$288$	2.98817	0.176079
$289$	−17.0000	−1.00000
$290$	5.59163	0.328352
$291$	−0.801243	−0.0469697
$292$	−10.5877	−0.619599
$293$	−24.6339	−1.43913	−0.719565	−	0.694425i	$-0.755659\pi$
$293$	−24.6339	−1.43913	−0.719565	+	0.694425i	$0.755659\pi$
$294$	0.108781	0.00634426
$295$	13.8802	0.808134
$296$	−7.01708	−0.407859
$297$	2.18823	0.126974
$298$	19.8299	1.14872
$299$	−1.19598	−0.0691652
$300$	0.305669	0.0176478
$301$	−9.33361	−0.537980
$302$	0.447072	0.0257261
$303$	0.865054	0.0496961
$304$	0	0
$305$	4.88066	0.279466
$306$	0.00853492	0.000487909 0
$307$	−11.2288	−0.640859	−0.320429	−	0.947272i	$-0.603827\pi$
$307$	−11.2288	−0.640859	−0.320429	+	0.947272i	$0.603827\pi$
$308$	−3.35927	−0.191412
$309$	−1.20413	−0.0685003
$310$	1.01991	0.0579269
$311$	−6.62413	−0.375620	−0.187810	−	0.982205i	$-0.560139\pi$
$311$	−6.62413	−0.375620	−0.187810	+	0.982205i	$0.560139\pi$
$312$	−0.117900	−0.00667479
$313$	−23.1672	−1.30949	−0.654743	−	0.755851i	$-0.727223\pi$
$313$	−23.1672	−1.30949	−0.654743	+	0.755851i	$0.727223\pi$
$314$	4.32457	0.244049
$315$	−4.42215	−0.249160
$316$	−1.03103	−0.0580000
$317$	−10.4993	−0.589701	−0.294850	−	0.955543i	$-0.595270\pi$
$317$	−10.4993	−0.589701	−0.294850	+	0.955543i	$0.595270\pi$
$318$	0.216400	0.0121351
$319$	12.6927	0.710657
$320$	−1.47989	−0.0827282
$321$	1.08066	0.0603165
$322$	1.10348	0.0614944
$323$	0	0
$324$	8.89364	0.494091
$325$	3.04549	0.168933
$326$	11.6366	0.644490
$327$	0.144005	0.00796347
$328$	−3.11294	−0.171883
$329$	12.2110	0.673215
$330$	−0.540789	−0.0297695
$331$	−15.8152	−0.869281	−0.434641	−	0.900604i	$-0.643125\pi$
$331$	−15.8152	−0.869281	−0.434641	+	0.900604i	$0.643125\pi$
$332$	8.24555	0.452533
$333$	−20.9682	−1.14905
$334$	−24.6233	−1.34733
$335$	1.68598	0.0921147
$336$	0.108781	0.00593451
$337$	−26.0310	−1.41800	−0.709000	−	0.705209i	$-0.750853\pi$
$337$	−26.0310	−1.41800	−0.709000	+	0.705209i	$0.750853\pi$
$338$	11.8253	0.643213
$339$	−2.05256	−0.111480
$340$	−0.00422691	−0.000229236 0
$341$	2.31514	0.125372
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−9.33361	−0.503234
$345$	0.177642	0.00956393
$346$	16.0806	0.864498
$347$	4.43153	0.237897	0.118948	−	0.992900i	$-0.462048\pi$
$347$	4.43153	0.237897	0.118948	+	0.992900i	$0.462048\pi$
$348$	−0.411022	−0.0220331
$349$	26.1315	1.39879	0.699394	−	0.714736i	$-0.253453\pi$
$349$	26.1315	1.39879	0.699394	+	0.714736i	$0.253453\pi$
$350$	−2.80994	−0.150197
$351$	−0.706006	−0.0376838
$352$	−3.35927	−0.179050
$353$	15.6799	0.834555	0.417278	−	0.908779i	$-0.362984\pi$
$353$	15.6799	0.834555	0.417278	+	0.908779i	$0.362984\pi$
$354$	−1.02028	−0.0542274
$355$	−13.6150	−0.722609
$356$	−0.669280	−0.0354718
$357$	0.000310706 0	1.64443e−5 0
$358$	13.1835	0.696771
$359$	28.0755	1.48177	0.740883	−	0.671634i	$-0.234407\pi$
$359$	28.0755	1.48177	0.740883	+	0.671634i	$0.234407\pi$
$360$	−4.42215	−0.233068
$361$	0	0
$362$	−17.8732	−0.939393
$363$	−0.0309706	−0.00162553
$364$	1.08383	0.0568080
$365$	15.6686	0.820132
$366$	−0.358760	−0.0187527
$367$	−14.2010	−0.741287	−0.370643	−	0.928775i	$-0.620863\pi$
$367$	−14.2010	−0.741287	−0.370643	+	0.928775i	$0.620863\pi$
$368$	1.10348	0.0575227
$369$	−9.30198	−0.484242
$370$	10.3845	0.539863
$371$	−1.98931	−0.103280
$372$	−0.0749700	−0.00388701
$373$	4.73281	0.245055	0.122528	−	0.992465i	$-0.460900\pi$
$373$	4.73281	0.245055	0.122528	+	0.992465i	$0.460900\pi$
$374$	−0.00959488	−0.000496140 0
$375$	−1.25728	−0.0649254
$376$	12.2110	0.629735
$377$	−4.09515	−0.210911
$378$	0.651401	0.0335045
$379$	−23.3580	−1.19982	−0.599910	−	0.800067i	$-0.704797\pi$
$379$	−23.3580	−1.19982	−0.599910	+	0.800067i	$0.704797\pi$
$380$	0	0
$381$	1.46884	0.0752511
$382$	8.60837	0.440443
$383$	−18.8327	−0.962308	−0.481154	−	0.876636i	$-0.659782\pi$
$383$	−18.8327	−0.962308	−0.481154	+	0.876636i	$0.659782\pi$
$384$	0.108781	0.00555123
$385$	4.97134	0.253363
$386$	−0.0199822	−0.00101707
$387$	−27.8904	−1.41775
$388$	7.36563	0.373933
$389$	9.78924	0.496334	0.248167	−	0.968717i	$-0.420172\pi$
$389$	9.78924	0.496334	0.248167	+	0.968717i	$0.420172\pi$
$390$	0.174479	0.00883508
$391$	0.00315179	0.000159393 0
$392$	−1.00000	−0.0505076
$393$	1.27766	0.0644494
$394$	18.7427	0.944243
$395$	1.52581	0.0767717
$396$	−10.0381	−0.504432
$397$	−31.0569	−1.55870	−0.779351	−	0.626587i	$-0.784451\pi$
$397$	−31.0569	−1.55870	−0.779351	+	0.626587i	$0.784451\pi$
$398$	17.8971	0.897103
$399$	0	0
$400$	−2.80994	−0.140497
$401$	3.52952	0.176256	0.0881280	−	0.996109i	$-0.471912\pi$
$401$	3.52952	0.176256	0.0881280	+	0.996109i	$0.471912\pi$
$402$	−0.123930	−0.00618108
$403$	−0.746953	−0.0372084
$404$	−7.95223	−0.395638
$405$	−13.1616	−0.654004
$406$	3.77842	0.187520
$407$	23.5723	1.16843
$408$	0.000310706 0	1.53822e−5 0
$409$	−39.0995	−1.93335	−0.966673	−	0.256013i	$-0.917591\pi$
$409$	−39.0995	−1.93335	−0.966673	+	0.256013i	$0.917591\pi$
$410$	4.60680	0.227514
$411$	0.0644784	0.00318049
$412$	11.0692	0.545341
$413$	9.37920	0.461520
$414$	3.29737	0.162057
$415$	−12.2025	−0.598996
$416$	1.08383	0.0531390
$417$	1.79400	0.0878523
$418$	0	0
$419$	−9.98187	−0.487646	−0.243823	−	0.969820i	$-0.578402\pi$
$419$	−9.98187	−0.487646	−0.243823	+	0.969820i	$0.578402\pi$
$420$	−0.160984	−0.00785522
$421$	−11.0666	−0.539352	−0.269676	−	0.962951i	$-0.586917\pi$
$421$	−11.0666	−0.539352	−0.269676	+	0.962951i	$0.586917\pi$
$422$	25.3593	1.23447
$423$	36.4886	1.77413
$424$	−1.98931	−0.0966095
$425$	−0.00802585	−0.000389311 0
$426$	1.00079	0.0484885
$427$	3.29799	0.159601
$428$	−9.93423	−0.480189
$429$	0.396059	0.0191219
$430$	13.8127	0.666107
$431$	−12.3449	−0.594635	−0.297317	−	0.954779i	$-0.596092\pi$
$431$	−12.3449	−0.594635	−0.297317	+	0.954779i	$0.596092\pi$
$432$	0.651401	0.0313405
$433$	−35.2843	−1.69566	−0.847829	−	0.530270i	$-0.822090\pi$
$433$	−35.2843	−1.69566	−0.847829	+	0.530270i	$0.822090\pi$
$434$	0.689180	0.0330817
$435$	0.608265	0.0291641
$436$	−1.32380	−0.0633985
$437$	0	0
$438$	−1.15175	−0.0550325
$439$	7.61854	0.363613	0.181806	−	0.983334i	$-0.441806\pi$
$439$	7.61854	0.363613	0.181806	+	0.983334i	$0.441806\pi$
$440$	4.97134	0.236999
$441$	−2.98817	−0.142294
$442$	0.00309567	0.000147246 0
$443$	9.31959	0.442787	0.221394	−	0.975185i	$-0.428939\pi$
$443$	9.31959	0.442787	0.221394	+	0.975185i	$0.428939\pi$
$444$	−0.763327	−0.0362259
$445$	0.990458	0.0469522
$446$	4.37342	0.207088
$447$	2.15713	0.102029
$448$	−1.00000	−0.0472456
$449$	−6.21354	−0.293235	−0.146618	−	0.989193i	$-0.546839\pi$
$449$	−6.21354	−0.293235	−0.146618	+	0.989193i	$0.546839\pi$
$450$	−8.39656	−0.395818
$451$	10.4572	0.492411
$452$	18.8686	0.887506
$453$	0.0486331	0.00228498
$454$	1.70261	0.0799075
$455$	−1.60394	−0.0751939
$456$	0	0
$457$	−19.7373	−0.923273	−0.461637	−	0.887069i	$-0.652738\pi$
$457$	−19.7373	−0.923273	−0.461637	+	0.887069i	$0.652738\pi$
$458$	8.60530	0.402099
$459$	0.00186056	8.68434e−5 0
$460$	−1.63302	−0.0761400
$461$	−30.0895	−1.40141	−0.700704	−	0.713452i	$-0.747131\pi$
$461$	−30.0895	−1.40141	−0.700704	+	0.713452i	$0.747131\pi$
$462$	−0.365426	−0.0170012
$463$	−0.987966	−0.0459147	−0.0229573	−	0.999736i	$-0.507308\pi$
$463$	−0.987966	−0.0459147	−0.0229573	+	0.999736i	$0.507308\pi$
$464$	3.77842	0.175409
$465$	0.110947	0.00514505
$466$	−18.3851	−0.851675
$467$	−5.51028	−0.254985	−0.127493	−	0.991840i	$-0.540693\pi$
$467$	−5.51028	−0.254985	−0.127493	+	0.991840i	$0.540693\pi$
$468$	3.23866	0.149707
$469$	1.13926	0.0526062
$470$	−18.0709	−0.833550
$471$	0.470432	0.0216764
$472$	9.37920	0.431713
$473$	31.3541	1.44166
$474$	−0.112157	−0.00515154
$475$	0	0
$476$	−0.00285624	−0.000130916 0
$477$	−5.94440	−0.272175
$478$	−16.6973	−0.763717
$479$	6.04291	0.276107	0.138054	−	0.990425i	$-0.455915\pi$
$479$	6.04291	0.276107	0.138054	+	0.990425i	$0.455915\pi$
$480$	−0.160984	−0.00734788
$481$	−7.60530	−0.346772
$482$	0.180340	0.00821424
$483$	0.120038	0.00546191
$484$	0.284705	0.0129411
$485$	−10.9003	−0.494957
$486$	2.92167	0.132529
$487$	−8.55200	−0.387528	−0.193764	−	0.981048i	$-0.562070\pi$
$487$	−8.55200	−0.387528	−0.193764	+	0.981048i	$0.562070\pi$
$488$	3.29799	0.149293
$489$	1.26584	0.0572433
$490$	1.47989	0.0668544
$491$	6.06026	0.273496	0.136748	−	0.990606i	$-0.456335\pi$
$491$	6.06026	0.273496	0.136748	+	0.990606i	$0.456335\pi$
$492$	−0.338630	−0.0152666
$493$	0.0107921	0.000486050 0
$494$	0	0
$495$	14.8552	0.667691
$496$	0.689180	0.0309451
$497$	−9.20003	−0.412678
$498$	0.896962	0.0401938
$499$	40.9454	1.83297	0.916484	−	0.400072i	$-0.131015\pi$
$499$	40.9454	1.83297	0.916484	+	0.400072i	$0.131015\pi$
$500$	11.5578	0.516881
$501$	−2.67856	−0.119669
$502$	1.76199	0.0786413
$503$	13.9145	0.620417	0.310209	−	0.950669i	$-0.399601\pi$
$503$	13.9145	0.620417	0.310209	+	0.950669i	$0.399601\pi$
$504$	−2.98817	−0.133104
$505$	11.7684	0.523687
$506$	−3.70688	−0.164791
$507$	1.28637	0.0571299
$508$	−13.5027	−0.599085
$509$	−20.2924	−0.899444	−0.449722	−	0.893169i	$-0.648477\pi$
$509$	−20.2924	−0.899444	−0.449722	+	0.893169i	$0.648477\pi$
$510$	−0.000459809 0	−2.03607e−5 0
$511$	10.5877	0.468373
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−27.7639	−1.22461
$515$	−16.3812	−0.721841
$516$	−1.01532	−0.0446971
$517$	−41.0201	−1.80406
$518$	7.01708	0.308313
$519$	1.74927	0.0767843
$520$	−1.60394	−0.0703375
$521$	−26.7636	−1.17253	−0.586266	−	0.810118i	$-0.699403\pi$
$521$	−26.7636	−1.17253	−0.586266	+	0.810118i	$0.699403\pi$
$522$	11.2905	0.494174
$523$	36.4267	1.59283	0.796414	−	0.604752i	$-0.206728\pi$
$523$	36.4267	1.59283	0.796414	+	0.604752i	$0.206728\pi$
$524$	−11.7452	−0.513091
$525$	−0.305669	−0.0133405
$526$	7.64376	0.333284
$527$	0.00196846	8.57476e−5 0
$528$	−0.365426	−0.0159031
$529$	−21.7823	−0.947058
$530$	2.94396	0.127877
$531$	28.0266	1.21625
$532$	0	0
$533$	−3.37389	−0.146139
$534$	−0.0728052	−0.00315059
$535$	14.7015	0.635602
$536$	1.13926	0.0492086
$537$	1.43412	0.0618870
$538$	−6.84128	−0.294949
$539$	3.35927	0.144694
$540$	−0.963999	−0.0414839
$541$	−0.203939	−0.00876802	−0.00438401	−	0.999990i	$-0.501395\pi$
$541$	−0.203939	−0.00876802	−0.00438401	+	0.999990i	$0.501395\pi$
$542$	1.90412	0.0817889
$543$	−1.94427	−0.0834365
$544$	−0.00285624	−0.000122460 0
$545$	1.95907	0.0839174
$546$	0.117900	0.00504566
$547$	−14.8597	−0.635357	−0.317678	−	0.948199i	$-0.602903\pi$
$547$	−14.8597	−0.635357	−0.317678	+	0.948199i	$0.602903\pi$
$548$	−0.592734	−0.0253203
$549$	9.85496	0.420599
$550$	9.43934	0.402495
$551$	0	0
$552$	0.120038	0.00510915
$553$	1.03103	0.0438439
$554$	−24.5531	−1.04316
$555$	1.12964	0.0479504
$556$	−16.4918	−0.699406
$557$	19.1359	0.810816	0.405408	−	0.914136i	$-0.367129\pi$
$557$	19.1359	0.810816	0.405408	+	0.914136i	$0.367129\pi$
$558$	2.05939	0.0871807
$559$	−10.1160	−0.427862
$560$	1.47989	0.0625366
$561$	−0.00104374	−4.40669e−5 0
$562$	−19.8835	−0.838737
$563$	23.2955	0.981790	0.490895	−	0.871219i	$-0.336670\pi$
$563$	23.2955	0.981790	0.490895	+	0.871219i	$0.336670\pi$
$564$	1.32833	0.0559329
$565$	−27.9234	−1.17475
$566$	−7.03113	−0.295540
$567$	−8.89364	−0.373498
$568$	−9.20003	−0.386025
$569$	−28.8823	−1.21081	−0.605404	−	0.795918i	$-0.706988\pi$
$569$	−28.8823	−1.21081	−0.605404	+	0.795918i	$0.706988\pi$
$570$	0	0
$571$	−26.5724	−1.11202	−0.556010	−	0.831176i	$-0.687668\pi$
$571$	−26.5724	−1.11202	−0.556010	+	0.831176i	$0.687668\pi$
$572$	−3.64087	−0.152232
$573$	0.936430	0.0391199
$574$	3.11294	0.129932
$575$	−3.10070	−0.129308
$576$	−2.98817	−0.124507
$577$	−5.56993	−0.231879	−0.115940	−	0.993256i	$-0.536988\pi$
$577$	−5.56993	−0.231879	−0.115940	+	0.993256i	$0.536988\pi$
$578$	17.0000	0.707106
$579$	−0.00217369	−9.03355e−5 0
$580$	−5.59163	−0.232180
$581$	−8.24555	−0.342083
$582$	0.801243	0.0332126
$583$	6.68264	0.276767
$584$	10.5877	0.438122
$585$	−4.79284	−0.198160
$586$	24.6339	1.01762
$587$	4.08489	0.168601	0.0843006	−	0.996440i	$-0.473134\pi$
$587$	4.08489	0.168601	0.0843006	+	0.996440i	$0.473134\pi$
$588$	−0.108781	−0.00448607
$589$	0	0
$590$	−13.8802	−0.571437
$591$	2.03886	0.0838673
$592$	7.01708	0.288400
$593$	−17.3725	−0.713402	−0.356701	−	0.934219i	$-0.616099\pi$
$593$	−17.3725	−0.713402	−0.356701	+	0.934219i	$0.616099\pi$
$594$	−2.18823	−0.0897843
$595$	0.00422691	0.000173286 0
$596$	−19.8299	−0.812265
$597$	1.94688	0.0796803
$598$	1.19598	0.0489072
$599$	−15.8235	−0.646530	−0.323265	−	0.946308i	$-0.604781\pi$
$599$	−15.8235	−0.646530	−0.323265	+	0.946308i	$0.604781\pi$
$600$	−0.305669	−0.0124789
$601$	18.0853	0.737714	0.368857	−	0.929486i	$-0.379749\pi$
$601$	18.0853	0.737714	0.368857	+	0.929486i	$0.379749\pi$
$602$	9.33361	0.380409
$603$	3.40430	0.138634
$604$	−0.447072	−0.0181911
$605$	−0.421331	−0.0171295
$606$	−0.865054	−0.0351404
$607$	−37.9504	−1.54036	−0.770179	−	0.637828i	$-0.779833\pi$
$607$	−37.9504	−1.54036	−0.770179	+	0.637828i	$0.779833\pi$
$608$	0	0
$609$	0.411022	0.0166554
$610$	−4.88066	−0.197612
$611$	13.2346	0.535416
$612$	−0.00853492	−0.000345004 0
$613$	−36.0335	−1.45538	−0.727689	−	0.685907i	$-0.759406\pi$
$613$	−36.0335	−1.45538	−0.727689	+	0.685907i	$0.759406\pi$
$614$	11.2288	0.453156
$615$	0.501134	0.0202077
$616$	3.35927	0.135349
$617$	−11.1185	−0.447615	−0.223808	−	0.974633i	$-0.571849\pi$
$617$	−11.1185	−0.447615	−0.223808	+	0.974633i	$0.571849\pi$
$618$	1.20413	0.0484370
$619$	−15.6979	−0.630953	−0.315477	−	0.948933i	$-0.602164\pi$
$619$	−15.6979	−0.630953	−0.315477	+	0.948933i	$0.602164\pi$
$620$	−1.01991	−0.0409605
$621$	0.718806	0.0288447
$622$	6.62413	0.265603
$623$	0.669280	0.0268141
$624$	0.117900	0.00471979
$625$	−3.05457	−0.122183
$626$	23.1672	0.925947
$627$	0	0
$628$	−4.32457	−0.172569
$629$	0.0200424	0.000799145 0
$630$	4.42215	0.176183
$631$	−46.7607	−1.86151	−0.930756	−	0.365641i	$-0.880850\pi$
$631$	−46.7607	−1.86151	−0.930756	+	0.365641i	$0.880850\pi$
$632$	1.03103	0.0410122
$633$	2.75861	0.109645
$634$	10.4993	0.416982
$635$	19.9825	0.792980
$636$	−0.216400	−0.00858082
$637$	−1.08383	−0.0429428
$638$	−12.6927	−0.502510
$639$	−27.4912	−1.08754
$640$	1.47989	0.0584976
$641$	39.5554	1.56234	0.781172	−	0.624316i	$-0.214622\pi$
$641$	39.5554	1.56234	0.781172	+	0.624316i	$0.214622\pi$
$642$	−1.08066	−0.0426502
$643$	16.0641	0.633508	0.316754	−	0.948508i	$-0.397407\pi$
$643$	16.0641	0.633508	0.316754	+	0.948508i	$0.397407\pi$
$644$	−1.10348	−0.0434831
$645$	1.50256	0.0591633
$646$	0	0
$647$	16.0754	0.631987	0.315994	−	0.948761i	$-0.397662\pi$
$647$	16.0754	0.631987	0.315994	+	0.948761i	$0.397662\pi$
$648$	−8.89364	−0.349375
$649$	−31.5073	−1.23677
$650$	−3.04549	−0.119454
$651$	0.0749700	0.00293831
$652$	−11.6366	−0.455723
$653$	19.6376	0.768478	0.384239	−	0.923234i	$-0.374464\pi$
$653$	19.6376	0.768478	0.384239	+	0.923234i	$0.374464\pi$
$654$	−0.144005	−0.00563103
$655$	17.3816	0.679154
$656$	3.11294	0.121540
$657$	31.6378	1.23431
$658$	−12.2110	−0.476035
$659$	2.56984	0.100107	0.0500535	−	0.998747i	$-0.484061\pi$
$659$	2.56984	0.100107	0.0500535	+	0.998747i	$0.484061\pi$
$660$	0.540789	0.0210502
$661$	−28.7805	−1.11943	−0.559715	−	0.828685i	$-0.689089\pi$
$661$	−28.7805	−1.11943	−0.559715	+	0.828685i	$0.689089\pi$
$662$	15.8152	0.614675
$663$	0.000336751 0	1.30783e−5 0
$664$	−8.24555	−0.319989
$665$	0	0
$666$	20.9682	0.812501
$667$	4.16940	0.161440
$668$	24.6233	0.952704
$669$	0.475747	0.0183934
$670$	−1.68598	−0.0651349
$671$	−11.0789	−0.427695
$672$	−0.108781	−0.00419633
$673$	8.50099	0.327689	0.163845	−	0.986486i	$-0.447610\pi$
$673$	8.50099	0.327689	0.163845	+	0.986486i	$0.447610\pi$
$674$	26.0310	1.00268
$675$	−1.83040	−0.0704520
$676$	−11.8253	−0.454820
$677$	47.0994	1.81018	0.905089	−	0.425223i	$-0.139804\pi$
$677$	47.0994	1.81018	0.905089	+	0.425223i	$0.139804\pi$
$678$	2.05256	0.0788280
$679$	−7.36563	−0.282667
$680$	0.00422691	0.000162095 0
$681$	0.185212	0.00709736
$682$	−2.31514	−0.0886514
$683$	17.9720	0.687679	0.343839	−	0.939028i	$-0.388272\pi$
$683$	17.9720	0.687679	0.343839	+	0.939028i	$0.388272\pi$
$684$	0	0
$685$	0.877179	0.0335153
$686$	1.00000	0.0381802
$687$	0.936097	0.0357143
$688$	9.33361	0.355841
$689$	−2.15607	−0.0821398
$690$	−0.177642	−0.00676272
$691$	−43.2223	−1.64425	−0.822126	−	0.569305i	$-0.807212\pi$
$691$	−43.2223	−1.64425	−0.822126	+	0.569305i	$0.807212\pi$
$692$	−16.0806	−0.611292
$693$	10.0381	0.381314
$694$	−4.43153	−0.168219
$695$	24.4059	0.925769
$696$	0.411022	0.0155797
$697$	0.00889130	0.000336782 0
$698$	−26.1315	−0.989093
$699$	−1.99996	−0.0756455
$700$	2.80994	0.106206
$701$	13.4801	0.509137	0.254569	−	0.967055i	$-0.418067\pi$
$701$	13.4801	0.509137	0.254569	+	0.967055i	$0.418067\pi$
$702$	0.706006	0.0266465
$703$	0	0
$704$	3.35927	0.126607
$705$	−1.96578	−0.0740355
$706$	−15.6799	−0.590120
$707$	7.95223	0.299074
$708$	1.02028	0.0383446
$709$	30.8203	1.15748	0.578740	−	0.815512i	$-0.303545\pi$
$709$	30.8203	1.15748	0.578740	+	0.815512i	$0.303545\pi$
$710$	13.6150	0.510962
$711$	3.08089	0.115542
$712$	0.669280	0.0250823
$713$	0.760495	0.0284807
$714$	−0.000310706 0	−1.16279e−5 0
$715$	5.38807	0.201503
$716$	−13.1835	−0.492692
$717$	−1.81636	−0.0678331
$718$	−28.0755	−1.04777
$719$	24.9881	0.931899	0.465950	−	0.884811i	$-0.345713\pi$
$719$	24.9881	0.931899	0.465950	+	0.884811i	$0.345713\pi$
$720$	4.42215	0.164804
$721$	−11.0692	−0.412239
$722$	0	0
$723$	0.0196176	0.000729586 0
$724$	17.8732	0.664251
$725$	−10.6171	−0.394310
$726$	0.0309706	0.00114943
$727$	−51.3613	−1.90489	−0.952443	−	0.304718i	$-0.901438\pi$
$727$	−51.3613	−1.90489	−0.952443	+	0.304718i	$0.901438\pi$
$728$	−1.08383	−0.0401693
$729$	−26.3631	−0.976411
$730$	−15.6686	−0.579921
$731$	0.0266590	0.000986019 0
$732$	0.358760	0.0132602
$733$	23.3035	0.860734	0.430367	−	0.902654i	$-0.358384\pi$
$733$	23.3035	0.860734	0.430367	+	0.902654i	$0.358384\pi$
$734$	14.2010	0.524169
$735$	0.160984	0.00593799
$736$	−1.10348	−0.0406747
$737$	−3.82709	−0.140972
$738$	9.30198	0.342411
$739$	49.2004	1.80986	0.904932	−	0.425556i	$-0.139921\pi$
$739$	49.2004	1.80986	0.904932	+	0.425556i	$0.139921\pi$
$740$	−10.3845	−0.381741
$741$	0	0
$742$	1.98931	0.0730299
$743$	−23.8284	−0.874179	−0.437089	−	0.899418i	$-0.643991\pi$
$743$	−23.8284	−0.874179	−0.437089	+	0.899418i	$0.643991\pi$
$744$	0.0749700	0.00274853
$745$	29.3460	1.07516
$746$	−4.73281	−0.173280
$747$	−24.6391	−0.901496
$748$	0.00959488	0.000350824 0
$749$	9.93423	0.362989
$750$	1.25728	0.0459092
$751$	9.95998	0.363445	0.181722	−	0.983350i	$-0.441833\pi$
$751$	9.95998	0.363445	0.181722	+	0.983350i	$0.441833\pi$
$752$	−12.2110	−0.445290
$753$	0.191671	0.00698489
$754$	4.09515	0.149137
$755$	0.661615	0.0240786
$756$	−0.651401	−0.0236912
$757$	−2.77981	−0.101034	−0.0505170	−	0.998723i	$-0.516087\pi$
$757$	−2.77981	−0.101034	−0.0505170	+	0.998723i	$0.516087\pi$
$758$	23.3580	0.848401
$759$	−0.403239	−0.0146367
$760$	0	0
$761$	24.5715	0.890718	0.445359	−	0.895352i	$-0.353076\pi$
$761$	24.5715	0.890718	0.445359	+	0.895352i	$0.353076\pi$
$762$	−1.46884	−0.0532105
$763$	1.32380	0.0479247
$764$	−8.60837	−0.311440
$765$	0.0126307	0.000456664 0
$766$	18.8327	0.680454
$767$	10.1654	0.367053
$768$	−0.108781	−0.00392531
$769$	−47.3694	−1.70818	−0.854092	−	0.520123i	$-0.825886\pi$
$769$	−47.3694	−1.70818	−0.854092	+	0.520123i	$0.825886\pi$
$770$	−4.97134	−0.179155
$771$	−3.02020	−0.108770
$772$	0.0199822	0.000719175 0
$773$	−48.0165	−1.72703	−0.863517	−	0.504319i	$-0.831743\pi$
$773$	−48.0165	−1.72703	−0.863517	+	0.504319i	$0.831743\pi$
$774$	27.8904	1.00250
$775$	−1.93655	−0.0695630
$776$	−7.36563	−0.264411
$777$	0.763327	0.0273842
$778$	−9.78924	−0.350961
$779$	0	0
$780$	−0.174479	−0.00624735
$781$	30.9054	1.10588
$782$	−0.00315179	−0.000112708 0
$783$	2.46127	0.0879585
$784$	1.00000	0.0357143
$785$	6.39986	0.228421
$786$	−1.27766	−0.0455726
$787$	−38.1497	−1.35989	−0.679944	−	0.733264i	$-0.737996\pi$
$787$	−38.1497	−1.35989	−0.679944	+	0.733264i	$0.737996\pi$
$788$	−18.7427	−0.667681
$789$	0.831499	0.0296021
$790$	−1.52581	−0.0542858
$791$	−18.8686	−0.670892
$792$	10.0381	0.356687
$793$	3.57446	0.126933
$794$	31.0569	1.10217
$795$	0.320248	0.0113580
$796$	−17.8971	−0.634347
$797$	3.53495	0.125214	0.0626072	−	0.998038i	$-0.480058\pi$
$797$	3.53495	0.125214	0.0626072	+	0.998038i	$0.480058\pi$
$798$	0	0
$799$	−0.0348776	−0.00123388
$800$	2.80994	0.0993463
$801$	1.99992	0.0706637
$802$	−3.52952	−0.124632
$803$	−35.5670	−1.25513
$804$	0.123930	0.00437069
$805$	1.63302	0.0575564
$806$	0.746953	0.0263103
$807$	−0.744204	−0.0261972
$808$	7.95223	0.279758
$809$	−27.0736	−0.951857	−0.475928	−	0.879484i	$-0.657888\pi$
$809$	−27.0736	−0.951857	−0.475928	+	0.879484i	$0.657888\pi$
$810$	13.1616	0.462451
$811$	25.5682	0.897821	0.448910	−	0.893577i	$-0.351812\pi$
$811$	25.5682	0.897821	0.448910	+	0.893577i	$0.351812\pi$
$812$	−3.77842	−0.132597
$813$	0.207133	0.00726446
$814$	−23.5723	−0.826207
$815$	17.2208	0.603218
$816$	−0.000310706 0	−1.08769e−5 0
$817$	0	0
$818$	39.0995	1.36708
$819$	−3.23866	−0.113168
$820$	−4.60680	−0.160876
$821$	39.6299	1.38309	0.691547	−	0.722332i	$-0.256930\pi$
$821$	39.6299	1.38309	0.691547	+	0.722332i	$0.256930\pi$
$822$	−0.0644784	−0.00224894
$823$	14.1441	0.493034	0.246517	−	0.969138i	$-0.420714\pi$
$823$	14.1441	0.493034	0.246517	+	0.969138i	$0.420714\pi$
$824$	−11.0692	−0.385615
$825$	1.02682	0.0357494
$826$	−9.37920	−0.326344
$827$	40.1029	1.39451	0.697257	−	0.716821i	$-0.254404\pi$
$827$	40.1029	1.39451	0.697257	+	0.716821i	$0.254404\pi$
$828$	−3.29737	−0.114592
$829$	−51.3546	−1.78362	−0.891810	−	0.452410i	$-0.850564\pi$
$829$	−51.3546	−1.78362	−0.891810	+	0.452410i	$0.850564\pi$
$830$	12.2025	0.423554
$831$	−2.67092	−0.0926532
$832$	−1.08383	−0.0375750
$833$	0.00285624	9.89628e−5 0
$834$	−1.79400	−0.0621210
$835$	−36.4397	−1.26105
$836$	0	0
$837$	0.448933	0.0155174
$838$	9.98187	0.344818
$839$	48.9883	1.69126	0.845631	−	0.533768i	$-0.179224\pi$
$839$	48.9883	1.69126	0.845631	+	0.533768i	$0.179224\pi$
$840$	0.160984	0.00555448
$841$	−14.7235	−0.507708
$842$	11.0666	0.381379
$843$	−2.16296	−0.0744963
$844$	−25.3593	−0.872902
$845$	17.5001	0.602023
$846$	−36.4886	−1.25450
$847$	−0.284705	−0.00978257
$848$	1.98931	0.0683133
$849$	−0.764856	−0.0262498
$850$	0.00802585	0.000275284 0
$851$	7.74318	0.265433
$852$	−1.00079	−0.0342866
$853$	25.8750	0.885945	0.442972	−	0.896535i	$-0.353924\pi$
$853$	25.8750	0.885945	0.442972	+	0.896535i	$0.353924\pi$
$854$	−3.29799	−0.112855
$855$	0	0
$856$	9.93423	0.339545
$857$	−8.62738	−0.294706	−0.147353	−	0.989084i	$-0.547075\pi$
$857$	−8.62738	−0.294706	−0.147353	+	0.989084i	$0.547075\pi$
$858$	−0.396059	−0.0135212
$859$	2.31255	0.0789032	0.0394516	−	0.999221i	$-0.487439\pi$
$859$	2.31255	0.0789032	0.0394516	+	0.999221i	$0.487439\pi$
$860$	−13.8127	−0.471008
$861$	0.338630	0.0115405
$862$	12.3449	0.420470
$863$	37.4174	1.27370	0.636851	−	0.770987i	$-0.280237\pi$
$863$	37.4174	1.27370	0.636851	+	0.770987i	$0.280237\pi$
$864$	−0.651401	−0.0221611
$865$	23.7974	0.809137
$866$	35.2843	1.19901
$867$	1.84928	0.0628049
$868$	−0.689180	−0.0233923
$869$	−3.46351	−0.117492
$870$	−0.608265	−0.0206221
$871$	1.23476	0.0418383
$872$	1.32380	0.0448295
$873$	−22.0097	−0.744917
$874$	0	0
$875$	−11.5578	−0.390726
$876$	1.15175	0.0389139
$877$	40.8795	1.38040	0.690201	−	0.723617i	$-0.257522\pi$
$877$	40.8795	1.38040	0.690201	+	0.723617i	$0.257522\pi$
$878$	−7.61854	−0.257113
$879$	2.67971	0.0903845
$880$	−4.97134	−0.167584
$881$	−49.5343	−1.66885	−0.834426	−	0.551120i	$-0.814201\pi$
$881$	−49.5343	−1.66885	−0.834426	+	0.551120i	$0.814201\pi$
$882$	2.98817	0.100617
$883$	24.3859	0.820652	0.410326	−	0.911939i	$-0.365415\pi$
$883$	24.3859	0.820652	0.410326	+	0.911939i	$0.365415\pi$
$884$	−0.00309567	−0.000104119 0
$885$	−1.50990	−0.0507548
$886$	−9.31959	−0.313098
$887$	−16.8006	−0.564110	−0.282055	−	0.959398i	$-0.591016\pi$
$887$	−16.8006	−0.564110	−0.282055	+	0.959398i	$0.591016\pi$
$888$	0.763327	0.0256156
$889$	13.5027	0.452866
$890$	−0.990458	−0.0332002
$891$	29.8761	1.00089
$892$	−4.37342	−0.146433
$893$	0	0
$894$	−2.15713	−0.0721451
$895$	19.5101	0.652152
$896$	1.00000	0.0334077
$897$	0.130100	0.00434392
$898$	6.21354	0.207349
$899$	2.60401	0.0868487
$900$	8.39656	0.279885
$901$	0.00568195	0.000189293 0
$902$	−10.4572	−0.348187
$903$	1.01532	0.0337878
$904$	−18.8686	−0.627562
$905$	−26.4503	−0.879236
$906$	−0.0486331	−0.00161573
$907$	36.0661	1.19755	0.598777	−	0.800916i	$-0.295654\pi$
$907$	36.0661	1.19755	0.598777	+	0.800916i	$0.295654\pi$
$908$	−1.70261	−0.0565032
$909$	23.7626	0.788155
$910$	1.60394	0.0531701
$911$	−32.1833	−1.06628	−0.533139	−	0.846027i	$-0.678988\pi$
$911$	−32.1833	−1.06628	−0.533139	+	0.846027i	$0.678988\pi$
$912$	0	0
$913$	27.6990	0.916704
$914$	19.7373	0.652853
$915$	−0.530924	−0.0175518
$916$	−8.60530	−0.284327
$917$	11.7452	0.387861
$918$	−0.00186056	−6.14075e−5 0
$919$	25.7067	0.847984	0.423992	−	0.905666i	$-0.360628\pi$
$919$	25.7067	0.847984	0.423992	+	0.905666i	$0.360628\pi$
$920$	1.63302	0.0538391
$921$	1.22148	0.0402491
$922$	30.0895	0.990945
$923$	−9.97124	−0.328207
$924$	0.365426	0.0120216
$925$	−19.7175	−0.648309
$926$	0.987966	0.0324666
$927$	−33.0767	−1.08638
$928$	−3.77842	−0.124033
$929$	−31.2937	−1.02671	−0.513356	−	0.858176i	$-0.671598\pi$
$929$	−31.2937	−1.02671	−0.513356	+	0.858176i	$0.671598\pi$
$930$	−0.110947	−0.00363810
$931$	0	0
$932$	18.3851	0.602225
$933$	0.720581	0.0235908
$934$	5.51028	0.180302
$935$	−0.0141993	−0.000464368 0
$936$	−3.23866	−0.105859
$937$	28.2271	0.922139	0.461069	−	0.887364i	$-0.347466\pi$
$937$	28.2271	0.922139	0.461069	+	0.887364i	$0.347466\pi$
$938$	−1.13926	−0.0371982
$939$	2.52016	0.0822423
$940$	18.0709	0.589409
$941$	−18.6422	−0.607719	−0.303859	−	0.952717i	$-0.598275\pi$
$941$	−18.6422	−0.607719	−0.303859	+	0.952717i	$0.598275\pi$
$942$	−0.470432	−0.0153275
$943$	3.43506	0.111861
$944$	−9.37920	−0.305267
$945$	0.963999	0.0313589
$946$	−31.3541	−1.01941
$947$	32.8436	1.06728	0.533638	−	0.845713i	$-0.320825\pi$
$947$	32.8436	1.06728	0.533638	+	0.845713i	$0.320825\pi$
$948$	0.112157	0.00364269
$949$	11.4752	0.372502
$950$	0	0
$951$	1.14213	0.0370361
$952$	0.00285624	9.25712e−5 0
$953$	−54.8374	−1.77636	−0.888179	−	0.459498i	$-0.848029\pi$
$953$	−54.8374	−1.77636	−0.888179	+	0.459498i	$0.848029\pi$
$954$	5.94440	0.192457
$955$	12.7394	0.412238
$956$	16.6973	0.540030
$957$	−1.38073	−0.0446328
$958$	−6.04291	−0.195237
$959$	0.592734	0.0191404
$960$	0.160984	0.00519574
$961$	−30.5250	−0.984678
$962$	7.60530	0.245205
$963$	29.6851	0.956590
$964$	−0.180340	−0.00580835
$965$	−0.0295714	−0.000951936 0
$966$	−0.120038	−0.00386215
$967$	−27.4526	−0.882816	−0.441408	−	0.897307i	$-0.645521\pi$
$967$	−27.4526	−0.882816	−0.441408	+	0.897307i	$0.645521\pi$
$968$	−0.284705	−0.00915075
$969$	0	0
$970$	10.9003	0.349987
$971$	−49.6930	−1.59472	−0.797362	−	0.603502i	$-0.793772\pi$
$971$	−49.6930	−1.59472	−0.797362	+	0.603502i	$0.793772\pi$
$972$	−2.92167	−0.0937125
$973$	16.4918	0.528701
$974$	8.55200	0.274024
$975$	−0.331292	−0.0106098
$976$	−3.29799	−0.105566
$977$	−32.6272	−1.04384	−0.521919	−	0.852995i	$-0.674783\pi$
$977$	−32.6272	−1.04384	−0.521919	+	0.852995i	$0.674783\pi$
$978$	−1.26584	−0.0404772
$979$	−2.24829	−0.0718557
$980$	−1.47989	−0.0472732
$981$	3.95573	0.126297
$982$	−6.06026	−0.193391
$983$	45.2473	1.44317	0.721583	−	0.692328i	$-0.243415\pi$
$983$	45.2473	1.44317	0.721583	+	0.692328i	$0.243415\pi$
$984$	0.338630	0.0107951
$985$	27.7371	0.883776
$986$	−0.0107921	−0.000343690 0
$987$	−1.32833	−0.0422813
$988$	0	0
$989$	10.2994	0.327503
$990$	−14.8552	−0.472129
$991$	56.9267	1.80834	0.904168	−	0.427177i	$-0.140492\pi$
$991$	56.9267	1.80834	0.904168	+	0.427177i	$0.140492\pi$
$992$	−0.689180	−0.0218815
$993$	1.72040	0.0545952
$994$	9.20003	0.291807
$995$	26.4857	0.839654
$996$	−0.896962	−0.0284213
$997$	31.4535	0.996143	0.498071	−	0.867136i	$-0.334042\pi$
$997$	31.4535	0.996143	0.498071	+	0.867136i	$0.334042\pi$
$998$	−40.9454	−1.29610
$999$	4.57093	0.144618

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bb.1.3		6
19.4	even	9		266.2.u.b.225.2	✓	12
19.5	even	9		266.2.u.b.253.2	yes	12
19.18	odd	2		5054.2.a.bc.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.b.225.2	✓	12	19.4	even	9
266.2.u.b.253.2	yes	12	19.5	even	9
5054.2.a.bb.1.3		6	1.1	even	1	trivial
5054.2.a.bc.1.4		6	19.18	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.108781 q^{3} +1.00000 q^{4} -1.47989 q^{5} +0.108781 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.98817 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.108781 q^{3} +1.00000 q^{4} -1.47989 q^{5} +0.108781 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.98817 q^{9} +1.47989 q^{10} +3.35927 q^{11} -0.108781 q^{12} -1.08383 q^{13} +1.00000 q^{14} +0.160984 q^{15} +1.00000 q^{16} +0.00285624 q^{17} +2.98817 q^{18} -1.47989 q^{20} +0.108781 q^{21} -3.35927 q^{22} +1.10348 q^{23} +0.108781 q^{24} -2.80994 q^{25} +1.08383 q^{26} +0.651401 q^{27} -1.00000 q^{28} +3.77842 q^{29} -0.160984 q^{30} +0.689180 q^{31} -1.00000 q^{32} -0.365426 q^{33} -0.00285624 q^{34} +1.47989 q^{35} -2.98817 q^{36} +7.01708 q^{37} +0.117900 q^{39} +1.47989 q^{40} +3.11294 q^{41} -0.108781 q^{42} +9.33361 q^{43} +3.35927 q^{44} +4.42215 q^{45} -1.10348 q^{46} -12.2110 q^{47} -0.108781 q^{48} +1.00000 q^{49} +2.80994 q^{50} -0.000310706 q^{51} -1.08383 q^{52} +1.98931 q^{53} -0.651401 q^{54} -4.97134 q^{55} +1.00000 q^{56} -3.77842 q^{58} -9.37920 q^{59} +0.160984 q^{60} -3.29799 q^{61} -0.689180 q^{62} +2.98817 q^{63} +1.00000 q^{64} +1.60394 q^{65} +0.365426 q^{66} -1.13926 q^{67} +0.00285624 q^{68} -0.120038 q^{69} -1.47989 q^{70} +9.20003 q^{71} +2.98817 q^{72} -10.5877 q^{73} -7.01708 q^{74} +0.305669 q^{75} -3.35927 q^{77} -0.117900 q^{78} -1.03103 q^{79} -1.47989 q^{80} +8.89364 q^{81} -3.11294 q^{82} +8.24555 q^{83} +0.108781 q^{84} -0.00422691 q^{85} -9.33361 q^{86} -0.411022 q^{87} -3.35927 q^{88} -0.669280 q^{89} -4.42215 q^{90} +1.08383 q^{91} +1.10348 q^{92} -0.0749700 q^{93} +12.2110 q^{94} +0.108781 q^{96} +7.36563 q^{97} -1.00000 q^{98} -10.0381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} + 6 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} - 3 q^{21} - 3 q^{22} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} + 6 q^{30} + 3 q^{31} - 6 q^{32} + 6 q^{33} + 9 q^{34} + 3 q^{35} - 3 q^{36} - 3 q^{37} - 9 q^{39} + 3 q^{40} + 9 q^{41} + 3 q^{42} - 6 q^{43} + 3 q^{44} - 12 q^{45} + 9 q^{47} + 3 q^{48} + 6 q^{49} - 3 q^{50} - 27 q^{51} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 24 q^{55} + 6 q^{56} - 6 q^{58} + 15 q^{59} - 6 q^{60} - 30 q^{61} - 3 q^{62} + 3 q^{63} + 6 q^{64} + 3 q^{65} - 6 q^{66} + 15 q^{67} - 9 q^{68} + 24 q^{69} - 3 q^{70} + 21 q^{71} + 3 q^{72} - 33 q^{73} + 3 q^{74} + 33 q^{75} - 3 q^{77} + 9 q^{78} - 30 q^{79} - 3 q^{80} - 18 q^{81} - 9 q^{82} - 33 q^{83} - 3 q^{84} - 18 q^{85} + 6 q^{86} + 15 q^{87} - 3 q^{88} - 12 q^{89} + 12 q^{90} - 6 q^{91} - 21 q^{93} - 9 q^{94} - 3 q^{96} - 18 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 + 6 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 - 3 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 6 * q^28 + 6 * q^29 + 6 * q^30 + 3 * q^31 - 6 * q^32 + 6 * q^33 + 9 * q^34 + 3 * q^35 - 3 * q^36 - 3 * q^37 - 9 * q^39 + 3 * q^40 + 9 * q^41 + 3 * q^42 - 6 * q^43 + 3 * q^44 - 12 * q^45 + 9 * q^47 + 3 * q^48 + 6 * q^49 - 3 * q^50 - 27 * q^51 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 24 * q^55 + 6 * q^56 - 6 * q^58 + 15 * q^59 - 6 * q^60 - 30 * q^61 - 3 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^65 - 6 * q^66 + 15 * q^67 - 9 * q^68 + 24 * q^69 - 3 * q^70 + 21 * q^71 + 3 * q^72 - 33 * q^73 + 3 * q^74 + 33 * q^75 - 3 * q^77 + 9 * q^78 - 30 * q^79 - 3 * q^80 - 18 * q^81 - 9 * q^82 - 33 * q^83 - 3 * q^84 - 18 * q^85 + 6 * q^86 + 15 * q^87 - 3 * q^88 - 12 * q^89 + 12 * q^90 - 6 * q^91 - 21 * q^93 - 9 * q^94 - 3 * q^96 - 18 * q^97 - 6 * q^98

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