LMFDB - Embedded newform 2738.2.a.w.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} + \cdots + 113 $ x^18 - 8x^17 - 8x^16 + 209x^15 - 253x^14 - 1996x^13 + 4196x^12 + 8667x^11 - 24522x^10 - 18284x^9 + 68697x^8 + 20865x^7 - 97011x^6 - 20844x^5 + 64568x^4 + 17499x^3 - 13387x^2 - 3713*x + 113
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.01728$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.561002 q^{3} +1.00000 q^{4} -3.29795 q^{5} -0.561002 q^{6} -3.86349 q^{7} -1.00000 q^{8} -2.68528 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.561002 q^{3} +1.00000 q^{4} -3.29795 q^{5} -0.561002 q^{6} -3.86349 q^{7} -1.00000 q^{8} -2.68528 q^{9} +3.29795 q^{10} +0.120988 q^{11} +0.561002 q^{12} -1.45272 q^{13} +3.86349 q^{14} -1.85016 q^{15} +1.00000 q^{16} -5.48151 q^{17} +2.68528 q^{18} -7.85428 q^{19} -3.29795 q^{20} -2.16742 q^{21} -0.120988 q^{22} +2.95207 q^{23} -0.561002 q^{24} +5.87646 q^{25} +1.45272 q^{26} -3.18945 q^{27} -3.86349 q^{28} -8.23703 q^{29} +1.85016 q^{30} +4.80383 q^{31} -1.00000 q^{32} +0.0678744 q^{33} +5.48151 q^{34} +12.7416 q^{35} -2.68528 q^{36} +7.85428 q^{38} -0.814982 q^{39} +3.29795 q^{40} +4.89424 q^{41} +2.16742 q^{42} -6.23549 q^{43} +0.120988 q^{44} +8.85590 q^{45} -2.95207 q^{46} -5.41297 q^{47} +0.561002 q^{48} +7.92652 q^{49} -5.87646 q^{50} -3.07514 q^{51} -1.45272 q^{52} +1.80979 q^{53} +3.18945 q^{54} -0.399011 q^{55} +3.86349 q^{56} -4.40627 q^{57} +8.23703 q^{58} -8.11719 q^{59} -1.85016 q^{60} -11.5758 q^{61} -4.80383 q^{62} +10.3745 q^{63} +1.00000 q^{64} +4.79101 q^{65} -0.0678744 q^{66} -3.84265 q^{67} -5.48151 q^{68} +1.65612 q^{69} -12.7416 q^{70} -8.79384 q^{71} +2.68528 q^{72} +10.1464 q^{73} +3.29671 q^{75} -7.85428 q^{76} -0.467434 q^{77} +0.814982 q^{78} +5.19713 q^{79} -3.29795 q^{80} +6.26654 q^{81} -4.89424 q^{82} +7.48901 q^{83} -2.16742 q^{84} +18.0777 q^{85} +6.23549 q^{86} -4.62099 q^{87} -0.120988 q^{88} +7.01242 q^{89} -8.85590 q^{90} +5.61258 q^{91} +2.95207 q^{92} +2.69496 q^{93} +5.41297 q^{94} +25.9030 q^{95} -0.561002 q^{96} +15.1511 q^{97} -7.92652 q^{98} -0.324885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} - 9 q^{13} - 18 q^{14} + 4 q^{15} + 18 q^{16} - 13 q^{17} - 26 q^{18} - 2 q^{19} - 9 q^{20} + 24 q^{21} - 10 q^{22} + 11 q^{23} - 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} - 30 q^{29} - 4 q^{30} + 8 q^{31} - 18 q^{32} + 42 q^{33} + 13 q^{34} - 25 q^{35} + 26 q^{36} + 2 q^{38} + 45 q^{39} + 9 q^{40} + 5 q^{41} - 24 q^{42} + 3 q^{43} + 10 q^{44} + 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} - 49 q^{50} - 10 q^{51} - 9 q^{52} + 25 q^{53} - 29 q^{54} + 44 q^{55} - 18 q^{56} - 22 q^{57} + 30 q^{58} - 26 q^{59} + 4 q^{60} - 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} - 42 q^{66} + 23 q^{67} - 13 q^{68} + 2 q^{69} + 25 q^{70} - 25 q^{71} - 26 q^{72} + 77 q^{73} - q^{75} - 2 q^{76} - 6 q^{77} - 45 q^{78} + 13 q^{79} - 9 q^{80} + 38 q^{81} - 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} + 55 q^{87} - 10 q^{88} - 55 q^{89} - 30 q^{90} - 12 q^{91} + 11 q^{92} + 58 q^{93} - 37 q^{94} - 18 q^{95} - 8 q^{96} + 59 q^{97} - 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 - 9 * q^13 - 18 * q^14 + 4 * q^15 + 18 * q^16 - 13 * q^17 - 26 * q^18 - 2 * q^19 - 9 * q^20 + 24 * q^21 - 10 * q^22 + 11 * q^23 - 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 - 30 * q^29 - 4 * q^30 + 8 * q^31 - 18 * q^32 + 42 * q^33 + 13 * q^34 - 25 * q^35 + 26 * q^36 + 2 * q^38 + 45 * q^39 + 9 * q^40 + 5 * q^41 - 24 * q^42 + 3 * q^43 + 10 * q^44 + 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 - 49 * q^50 - 10 * q^51 - 9 * q^52 + 25 * q^53 - 29 * q^54 + 44 * q^55 - 18 * q^56 - 22 * q^57 + 30 * q^58 - 26 * q^59 + 4 * q^60 - 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 - 42 * q^66 + 23 * q^67 - 13 * q^68 + 2 * q^69 + 25 * q^70 - 25 * q^71 - 26 * q^72 + 77 * q^73 - q^75 - 2 * q^76 - 6 * q^77 - 45 * q^78 + 13 * q^79 - 9 * q^80 + 38 * q^81 - 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 + 55 * q^87 - 10 * q^88 - 55 * q^89 - 30 * q^90 - 12 * q^91 + 11 * q^92 + 58 * q^93 - 37 * q^94 - 18 * q^95 - 8 * q^96 + 59 * q^97 - 50 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.561002	0.323895	0.161947	−	0.986799i	$-0.448223\pi$
$3$	0.561002	0.323895	0.161947	+	0.986799i	$0.448223\pi$
$4$	1.00000	0.500000
$5$	−3.29795	−1.47489	−0.737444	−	0.675409i	$-0.763967\pi$
$5$	−3.29795	−1.47489	−0.737444	+	0.675409i	$0.763967\pi$
$6$	−0.561002	−0.229028
$7$	−3.86349	−1.46026	−0.730130	−	0.683308i	$-0.760541\pi$
$7$	−3.86349	−1.46026	−0.730130	+	0.683308i	$0.760541\pi$
$8$	−1.00000	−0.353553
$9$	−2.68528	−0.895092
$10$	3.29795	1.04290
$11$	0.120988	0.0364792	0.0182396	−	0.999834i	$-0.494194\pi$
$11$	0.120988	0.0364792	0.0182396	+	0.999834i	$0.494194\pi$
$12$	0.561002	0.161947
$13$	−1.45272	−0.402913	−0.201457	−	0.979497i	$-0.564568\pi$
$13$	−1.45272	−0.402913	−0.201457	+	0.979497i	$0.564568\pi$
$14$	3.86349	1.03256
$15$	−1.85016	−0.477708
$16$	1.00000	0.250000
$17$	−5.48151	−1.32946	−0.664731	−	0.747083i	$-0.731454\pi$
$17$	−5.48151	−1.32946	−0.664731	+	0.747083i	$0.731454\pi$
$18$	2.68528	0.632926
$19$	−7.85428	−1.80190	−0.900948	−	0.433928i	$-0.857127\pi$
$19$	−7.85428	−1.80190	−0.900948	+	0.433928i	$0.857127\pi$
$20$	−3.29795	−0.737444
$21$	−2.16742	−0.472971
$22$	−0.120988	−0.0257947
$23$	2.95207	0.615549	0.307774	−	0.951459i	$-0.400416\pi$
$23$	2.95207	0.615549	0.307774	+	0.951459i	$0.400416\pi$
$24$	−0.561002	−0.114514
$25$	5.87646	1.17529
$26$	1.45272	0.284903
$27$	−3.18945	−0.613810
$28$	−3.86349	−0.730130
$29$	−8.23703	−1.52958	−0.764789	−	0.644280i	$-0.777157\pi$
$29$	−8.23703	−1.52958	−0.764789	+	0.644280i	$0.777157\pi$
$30$	1.85016	0.337791
$31$	4.80383	0.862793	0.431396	−	0.902163i	$-0.358021\pi$
$31$	4.80383	0.862793	0.431396	+	0.902163i	$0.358021\pi$
$32$	−1.00000	−0.176777
$33$	0.0678744	0.0118154
$34$	5.48151	0.940072
$35$	12.7416	2.15372
$36$	−2.68528	−0.447546
$37$	0	0
$37$	0	0
$38$	7.85428	1.27413
$39$	−0.814982	−0.130502
$40$	3.29795	0.521451
$41$	4.89424	0.764352	0.382176	−	0.924090i	$-0.375175\pi$
$41$	4.89424	0.764352	0.382176	+	0.924090i	$0.375175\pi$
$42$	2.16742	0.334441
$43$	−6.23549	−0.950903	−0.475452	−	0.879742i	$-0.657715\pi$
$43$	−6.23549	−0.950903	−0.475452	+	0.879742i	$0.657715\pi$
$44$	0.120988	0.0182396
$45$	8.85590	1.32016
$46$	−2.95207	−0.435259
$47$	−5.41297	−0.789563	−0.394782	−	0.918775i	$-0.629180\pi$
$47$	−5.41297	−0.789563	−0.394782	+	0.918775i	$0.629180\pi$
$48$	0.561002	0.0809737
$49$	7.92652	1.13236
$50$	−5.87646	−0.831057
$51$	−3.07514	−0.430606
$52$	−1.45272	−0.201457
$53$	1.80979	0.248594	0.124297	−	0.992245i	$-0.460333\pi$
$53$	1.80979	0.248594	0.124297	+	0.992245i	$0.460333\pi$
$54$	3.18945	0.434030
$55$	−0.399011	−0.0538026
$56$	3.86349	0.516280
$57$	−4.40627	−0.583624
$58$	8.23703	1.08158
$59$	−8.11719	−1.05677	−0.528384	−	0.849005i	$-0.677202\pi$
$59$	−8.11719	−1.05677	−0.528384	+	0.849005i	$0.677202\pi$
$60$	−1.85016	−0.238854
$61$	−11.5758	−1.48213	−0.741067	−	0.671431i	$-0.765680\pi$
$61$	−11.5758	−1.48213	−0.741067	+	0.671431i	$0.765680\pi$
$62$	−4.80383	−0.610086
$63$	10.3745	1.30707
$64$	1.00000	0.125000
$65$	4.79101	0.594252
$66$	−0.0678744	−0.00835476
$67$	−3.84265	−0.469455	−0.234727	−	0.972061i	$-0.575420\pi$
$67$	−3.84265	−0.469455	−0.234727	+	0.972061i	$0.575420\pi$
$68$	−5.48151	−0.664731
$69$	1.65612	0.199373
$70$	−12.7416	−1.52291
$71$	−8.79384	−1.04364	−0.521818	−	0.853057i	$-0.674746\pi$
$71$	−8.79384	−1.04364	−0.521818	+	0.853057i	$0.674746\pi$
$72$	2.68528	0.316463
$73$	10.1464	1.18755	0.593773	−	0.804632i	$-0.297638\pi$
$73$	10.1464	1.18755	0.593773	+	0.804632i	$0.297638\pi$
$74$	0	0
$75$	3.29671	0.380671
$76$	−7.85428	−0.900948
$77$	−0.467434	−0.0532691
$78$	0.814982	0.0922785
$79$	5.19713	0.584722	0.292361	−	0.956308i	$-0.405559\pi$
$79$	5.19713	0.584722	0.292361	+	0.956308i	$0.405559\pi$
$80$	−3.29795	−0.368722
$81$	6.26654	0.696282
$82$	−4.89424	−0.540479
$83$	7.48901	0.822025	0.411013	−	0.911630i	$-0.365175\pi$
$83$	7.48901	0.822025	0.411013	+	0.911630i	$0.365175\pi$
$84$	−2.16742	−0.236485
$85$	18.0777	1.96081
$86$	6.23549	0.672390
$87$	−4.62099	−0.495423
$88$	−0.120988	−0.0128973
$89$	7.01242	0.743315	0.371658	−	0.928370i	$-0.378789\pi$
$89$	7.01242	0.743315	0.371658	+	0.928370i	$0.378789\pi$
$90$	−8.85590	−0.933494
$91$	5.61258	0.588358
$92$	2.95207	0.307774
$93$	2.69496	0.279454
$94$	5.41297	0.558306
$95$	25.9030	2.65759
$96$	−0.561002	−0.0572570
$97$	15.1511	1.53836	0.769179	−	0.639034i	$-0.220666\pi$
$97$	15.1511	1.53836	0.769179	+	0.639034i	$0.220666\pi$
$98$	−7.92652	−0.800699
$99$	−0.324885	−0.0326522
$100$	5.87646	0.587646
$101$	−10.3189	−1.02677	−0.513383	−	0.858159i	$-0.671608\pi$
$101$	−10.3189	−1.02677	−0.513383	+	0.858159i	$0.671608\pi$
$102$	3.07514	0.304484
$103$	8.09728	0.797849	0.398924	−	0.916984i	$-0.369384\pi$
$103$	8.09728	0.797849	0.398924	+	0.916984i	$0.369384\pi$
$104$	1.45272	0.142451
$105$	7.14805	0.697578
$106$	−1.80979	−0.175782
$107$	3.35122	0.323975	0.161988	−	0.986793i	$-0.448210\pi$
$107$	3.35122	0.323975	0.161988	+	0.986793i	$0.448210\pi$
$108$	−3.18945	−0.306905
$109$	18.0589	1.72973	0.864867	−	0.502001i	$-0.167403\pi$
$109$	18.0589	1.72973	0.864867	+	0.502001i	$0.167403\pi$
$110$	0.399011	0.0380442
$111$	0	0
$112$	−3.86349	−0.365065
$113$	−19.8570	−1.86799	−0.933996	−	0.357284i	$-0.883703\pi$
$113$	−19.8570	−1.86799	−0.933996	+	0.357284i	$0.883703\pi$
$114$	4.40627	0.412685
$115$	−9.73577	−0.907865
$116$	−8.23703	−0.764789
$117$	3.90097	0.360645
$118$	8.11719	0.747248
$119$	21.1777	1.94136
$120$	1.85016	0.168895
$121$	−10.9854	−0.998669
$122$	11.5758	1.04803
$123$	2.74568	0.247570
$124$	4.80383	0.431396
$125$	−2.89052	−0.258536
$126$	−10.3745	−0.924236
$127$	4.79541	0.425524	0.212762	−	0.977104i	$-0.431754\pi$
$127$	4.79541	0.425524	0.212762	+	0.977104i	$0.431754\pi$
$128$	−1.00000	−0.0883883
$129$	−3.49812	−0.307993
$130$	−4.79101	−0.420199
$131$	−11.7688	−1.02825	−0.514123	−	0.857716i	$-0.671883\pi$
$131$	−11.7688	−1.02825	−0.514123	+	0.857716i	$0.671883\pi$
$132$	0.0678744	0.00590771
$133$	30.3449	2.63124
$134$	3.84265	0.331955
$135$	10.5186	0.905301
$136$	5.48151	0.470036
$137$	−11.3568	−0.970273	−0.485136	−	0.874438i	$-0.661230\pi$
$137$	−11.3568	−0.970273	−0.485136	+	0.874438i	$0.661230\pi$
$138$	−1.65612	−0.140978
$139$	−10.1558	−0.861405	−0.430703	−	0.902494i	$-0.641734\pi$
$139$	−10.1558	−0.861405	−0.430703	+	0.902494i	$0.641734\pi$
$140$	12.7416	1.07686
$141$	−3.03669	−0.255735
$142$	8.79384	0.737963
$143$	−0.175762	−0.0146979
$144$	−2.68528	−0.223773
$145$	27.1653	2.25596
$146$	−10.1464	−0.839723
$147$	4.44679	0.366765
$148$	0	0
$149$	−8.82258	−0.722774	−0.361387	−	0.932416i	$-0.617697\pi$
$149$	−8.82258	−0.722774	−0.361387	+	0.932416i	$0.617697\pi$
$150$	−3.29671	−0.269175
$151$	−0.646318	−0.0525966	−0.0262983	−	0.999654i	$-0.508372\pi$
$151$	−0.646318	−0.0525966	−0.0262983	+	0.999654i	$0.508372\pi$
$152$	7.85428	0.637066
$153$	14.7194	1.18999
$154$	0.467434	0.0376669
$155$	−15.8428	−1.27252
$156$	−0.814982	−0.0652508
$157$	7.39208	0.589952	0.294976	−	0.955505i	$-0.404688\pi$
$157$	7.39208	0.589952	0.294976	+	0.955505i	$0.404688\pi$
$158$	−5.19713	−0.413461
$159$	1.01530	0.0805182
$160$	3.29795	0.260726
$161$	−11.4053	−0.898862
$162$	−6.26654	−0.492346
$163$	−10.5364	−0.825273	−0.412637	−	0.910896i	$-0.635392\pi$
$163$	−10.5364	−0.825273	−0.412637	+	0.910896i	$0.635392\pi$
$164$	4.89424	0.382176
$165$	−0.223846	−0.0174264
$166$	−7.48901	−0.581260
$167$	4.35466	0.336974	0.168487	−	0.985704i	$-0.446112\pi$
$167$	4.35466	0.336974	0.168487	+	0.985704i	$0.446112\pi$
$168$	2.16742	0.167220
$169$	−10.8896	−0.837661
$170$	−18.0777	−1.38650
$171$	21.0909	1.61286
$172$	−6.23549	−0.475452
$173$	0.404323	0.0307401	0.0153701	−	0.999882i	$-0.495107\pi$
$173$	0.404323	0.0307401	0.0153701	+	0.999882i	$0.495107\pi$
$174$	4.62099	0.350317
$175$	−22.7036	−1.71623
$176$	0.120988	0.00911979
$177$	−4.55376	−0.342282
$178$	−7.01242	−0.525603
$179$	10.2329	0.764844	0.382422	−	0.923988i	$-0.375090\pi$
$179$	10.2329	0.764844	0.382422	+	0.923988i	$0.375090\pi$
$180$	8.85590	0.660080
$181$	−9.74821	−0.724578	−0.362289	−	0.932066i	$-0.618005\pi$
$181$	−9.74821	−0.724578	−0.362289	+	0.932066i	$0.618005\pi$
$182$	−5.61258	−0.416032
$183$	−6.49407	−0.480055
$184$	−2.95207	−0.217629
$185$	0	0
$186$	−2.69496	−0.197604
$187$	−0.663196	−0.0484977
$188$	−5.41297	−0.394782
$189$	12.3224	0.896323
$190$	−25.9030	−1.87920
$191$	4.88402	0.353395	0.176698	−	0.984265i	$-0.443459\pi$
$191$	4.88402	0.353395	0.176698	+	0.984265i	$0.443459\pi$
$192$	0.561002	0.0404868
$193$	−8.49231	−0.611290	−0.305645	−	0.952146i	$-0.598872\pi$
$193$	−8.49231	−0.611290	−0.305645	+	0.952146i	$0.598872\pi$
$194$	−15.1511	−1.08778
$195$	2.68777	0.192475
$196$	7.92652	0.566180
$197$	6.29762	0.448687	0.224344	−	0.974510i	$-0.427976\pi$
$197$	6.29762	0.448687	0.224344	+	0.974510i	$0.427976\pi$
$198$	0.324885	0.0230886
$199$	24.6364	1.74643	0.873215	−	0.487335i	$-0.162031\pi$
$199$	24.6364	1.74643	0.873215	+	0.487335i	$0.162031\pi$
$200$	−5.87646	−0.415529
$201$	−2.15574	−0.152054
$202$	10.3189	0.726034
$203$	31.8237	2.23358
$204$	−3.07514	−0.215303
$205$	−16.1410	−1.12733
$206$	−8.09728	−0.564164
$207$	−7.92712	−0.550973
$208$	−1.45272	−0.100728
$209$	−0.950271	−0.0657316
$210$	−7.14805	−0.493262
$211$	−15.7937	−1.08728	−0.543641	−	0.839318i	$-0.682955\pi$
$211$	−15.7937	−1.08728	−0.543641	+	0.839318i	$0.682955\pi$
$212$	1.80979	0.124297
$213$	−4.93336	−0.338029
$214$	−3.35122	−0.229085
$215$	20.5643	1.40247
$216$	3.18945	0.217015
$217$	−18.5595	−1.25990
$218$	−18.0589	−1.22311
$219$	5.69216	0.384640
$220$	−0.399011	−0.0269013
$221$	7.96313	0.535658
$222$	0	0
$223$	11.4565	0.767183	0.383591	−	0.923503i	$-0.374687\pi$
$223$	11.4565	0.767183	0.383591	+	0.923503i	$0.374687\pi$
$224$	3.86349	0.258140
$225$	−15.7799	−1.05199
$226$	19.8570	1.32087
$227$	−22.1402	−1.46950	−0.734748	−	0.678340i	$-0.762700\pi$
$227$	−22.1402	−1.46950	−0.734748	+	0.678340i	$0.762700\pi$
$228$	−4.40627	−0.291812
$229$	7.70162	0.508938	0.254469	−	0.967081i	$-0.418099\pi$
$229$	7.70162	0.508938	0.254469	+	0.967081i	$0.418099\pi$
$230$	9.73577	0.641958
$231$	−0.262232	−0.0172536
$232$	8.23703	0.540788
$233$	−3.98679	−0.261183	−0.130592	−	0.991436i	$-0.541688\pi$
$233$	−3.98679	−0.261183	−0.130592	+	0.991436i	$0.541688\pi$
$234$	−3.90097	−0.255014
$235$	17.8517	1.16452
$236$	−8.11719	−0.528384
$237$	2.91560	0.189389
$238$	−21.1777	−1.37275
$239$	−27.7921	−1.79772	−0.898860	−	0.438237i	$-0.855603\pi$
$239$	−27.7921	−1.79772	−0.898860	+	0.438237i	$0.855603\pi$
$240$	−1.85016	−0.119427
$241$	8.63923	0.556501	0.278251	−	0.960508i	$-0.410245\pi$
$241$	8.63923	0.556501	0.278251	+	0.960508i	$0.410245\pi$
$242$	10.9854	0.706166
$243$	13.0839	0.839333
$244$	−11.5758	−0.741067
$245$	−26.1412	−1.67010
$246$	−2.74568	−0.175058
$247$	11.4101	0.726007
$248$	−4.80383	−0.305043
$249$	4.20135	0.266250
$250$	2.89052	0.182813
$251$	−8.64129	−0.545433	−0.272717	−	0.962094i	$-0.587922\pi$
$251$	−8.64129	−0.545433	−0.272717	+	0.962094i	$0.587922\pi$
$252$	10.3745	0.653534
$253$	0.357164	0.0224547
$254$	−4.79541	−0.300891
$255$	10.1417	0.635095
$256$	1.00000	0.0625000
$257$	6.78630	0.423318	0.211659	−	0.977344i	$-0.432113\pi$
$257$	6.78630	0.423318	0.211659	+	0.977344i	$0.432113\pi$
$258$	3.49812	0.217784
$259$	0	0
$260$	4.79101	0.297126
$261$	22.1187	1.36911
$262$	11.7688	0.727080
$263$	−12.4311	−0.766536	−0.383268	−	0.923637i	$-0.625201\pi$
$263$	−12.4311	−0.766536	−0.383268	+	0.923637i	$0.625201\pi$
$264$	−0.0678744	−0.00417738
$265$	−5.96859	−0.366647
$266$	−30.3449	−1.86056
$267$	3.93399	0.240756
$268$	−3.84265	−0.234727
$269$	−9.23562	−0.563106	−0.281553	−	0.959546i	$-0.590849\pi$
$269$	−9.23562	−0.563106	−0.281553	+	0.959546i	$0.590849\pi$
$270$	−10.5186	−0.640145
$271$	−27.5920	−1.67610	−0.838048	−	0.545596i	$-0.816303\pi$
$271$	−27.5920	−1.67610	−0.838048	+	0.545596i	$0.816303\pi$
$272$	−5.48151	−0.332366
$273$	3.14867	0.190566
$274$	11.3568	0.686086
$275$	0.710979	0.0428737
$276$	1.65612	0.0996865
$277$	6.34936	0.381496	0.190748	−	0.981639i	$-0.438909\pi$
$277$	6.34936	0.381496	0.190748	+	0.981639i	$0.438909\pi$
$278$	10.1558	0.609106
$279$	−12.8996	−0.772279
$280$	−12.7416	−0.761455
$281$	−15.3300	−0.914510	−0.457255	−	0.889336i	$-0.651167\pi$
$281$	−15.3300	−0.914510	−0.457255	+	0.889336i	$0.651167\pi$
$282$	3.03669	0.180832
$283$	24.3850	1.44954	0.724770	−	0.688991i	$-0.241946\pi$
$283$	24.3850	1.44954	0.724770	+	0.688991i	$0.241946\pi$
$284$	−8.79384	−0.521818
$285$	14.5316	0.860780
$286$	0.175762	0.0103930
$287$	−18.9088	−1.11615
$288$	2.68528	0.158231
$289$	13.0470	0.767470
$290$	−27.1653	−1.59520
$291$	8.49978	0.498266
$292$	10.1464	0.593773
$293$	5.87846	0.343423	0.171712	−	0.985147i	$-0.445070\pi$
$293$	5.87846	0.343423	0.171712	+	0.985147i	$0.445070\pi$
$294$	−4.44679	−0.259342
$295$	26.7701	1.55861
$296$	0	0
$297$	−0.385885	−0.0223913
$298$	8.82258	0.511078
$299$	−4.28854	−0.248013
$300$	3.29671	0.190335
$301$	24.0907	1.38857
$302$	0.646318	0.0371914
$303$	−5.78891	−0.332564
$304$	−7.85428	−0.450474
$305$	38.1765	2.18598
$306$	−14.7194	−0.841451
$307$	−25.6672	−1.46490	−0.732452	−	0.680819i	$-0.761624\pi$
$307$	−25.6672	−1.46490	−0.732452	+	0.680819i	$0.761624\pi$
$308$	−0.467434	−0.0266345
$309$	4.54259	0.258419
$310$	15.8428	0.899809
$311$	9.93891	0.563584	0.281792	−	0.959476i	$-0.409071\pi$
$311$	9.93891	0.563584	0.281792	+	0.959476i	$0.409071\pi$
$312$	0.814982	0.0461392
$313$	−5.41564	−0.306110	−0.153055	−	0.988218i	$-0.548911\pi$
$313$	−5.41564	−0.306110	−0.153055	+	0.988218i	$0.548911\pi$
$314$	−7.39208	−0.417159
$315$	−34.2146	−1.92778
$316$	5.19713	0.292361
$317$	−13.5919	−0.763396	−0.381698	−	0.924287i	$-0.624661\pi$
$317$	−13.5919	−0.763396	−0.381698	+	0.924287i	$0.624661\pi$
$318$	−1.01530	−0.0569349
$319$	−0.996580	−0.0557977
$320$	−3.29795	−0.184361
$321$	1.88004	0.104934
$322$	11.4053	0.635591
$323$	43.0533	2.39555
$324$	6.26654	0.348141
$325$	−8.53688	−0.473541
$326$	10.5364	0.583556
$327$	10.1311	0.560252
$328$	−4.89424	−0.270239
$329$	20.9129	1.15297
$330$	0.223846	0.0123223
$331$	13.8105	0.759091	0.379546	−	0.925173i	$-0.376080\pi$
$331$	13.8105	0.759091	0.379546	+	0.925173i	$0.376080\pi$
$332$	7.48901	0.411013
$333$	0	0
$334$	−4.35466	−0.238276
$335$	12.6729	0.692393
$336$	−2.16742	−0.118243
$337$	9.25241	0.504011	0.252005	−	0.967726i	$-0.418910\pi$
$337$	9.25241	0.504011	0.252005	+	0.967726i	$0.418910\pi$
$338$	10.8896	0.592316
$339$	−11.1398	−0.605033
$340$	18.0777	0.980403
$341$	0.581204	0.0314740
$342$	−21.0909	−1.14047
$343$	−3.57959	−0.193280
$344$	6.23549	0.336195
$345$	−5.46179	−0.294053
$346$	−0.404323	−0.0217365
$347$	−22.8417	−1.22621	−0.613104	−	0.790002i	$-0.710079\pi$
$347$	−22.8417	−1.22621	−0.613104	+	0.790002i	$0.710079\pi$
$348$	−4.62099	−0.247711
$349$	0.974846	0.0521823	0.0260911	−	0.999660i	$-0.491694\pi$
$349$	0.974846	0.0521823	0.0260911	+	0.999660i	$0.491694\pi$
$350$	22.7036	1.21356
$351$	4.63340	0.247312
$352$	−0.120988	−0.00644867
$353$	3.20706	0.170695	0.0853474	−	0.996351i	$-0.472800\pi$
$353$	3.20706	0.170695	0.0853474	+	0.996351i	$0.472800\pi$
$354$	4.55376	0.242030
$355$	29.0016	1.53925
$356$	7.01242	0.371658
$357$	11.8808	0.628797
$358$	−10.2329	−0.540826
$359$	14.9610	0.789610	0.394805	−	0.918765i	$-0.370812\pi$
$359$	14.9610	0.789610	0.394805	+	0.918765i	$0.370812\pi$
$360$	−8.85590	−0.466747
$361$	42.6897	2.24683
$362$	9.74821	0.512354
$363$	−6.16281	−0.323464
$364$	5.61258	0.294179
$365$	−33.4623	−1.75150
$366$	6.49407	0.339450
$367$	−2.76360	−0.144259	−0.0721294	−	0.997395i	$-0.522979\pi$
$367$	−2.76360	−0.144259	−0.0721294	+	0.997395i	$0.522979\pi$
$368$	2.95207	0.153887
$369$	−13.1424	−0.684166
$370$	0	0
$371$	−6.99209	−0.363011
$372$	2.69496	0.139727
$373$	20.5705	1.06510	0.532551	−	0.846398i	$-0.321234\pi$
$373$	20.5705	1.06510	0.532551	+	0.846398i	$0.321234\pi$
$374$	0.663196	0.0342930
$375$	−1.62159	−0.0837385
$376$	5.41297	0.279153
$377$	11.9661	0.616288
$378$	−12.3224	−0.633796
$379$	0.584666	0.0300323	0.0150161	−	0.999887i	$-0.495220\pi$
$379$	0.584666	0.0300323	0.0150161	+	0.999887i	$0.495220\pi$
$380$	25.9030	1.32880
$381$	2.69024	0.137825
$382$	−4.88402	−0.249888
$383$	15.6344	0.798882	0.399441	−	0.916759i	$-0.369204\pi$
$383$	15.6344	0.798882	0.399441	+	0.916759i	$0.369204\pi$
$384$	−0.561002	−0.0286285
$385$	1.54157	0.0785659
$386$	8.49231	0.432247
$387$	16.7440	0.851146
$388$	15.1511	0.769179
$389$	2.14121	0.108564	0.0542819	−	0.998526i	$-0.482713\pi$
$389$	2.14121	0.108564	0.0542819	+	0.998526i	$0.482713\pi$
$390$	−2.68777	−0.136100
$391$	−16.1818	−0.818349
$392$	−7.92652	−0.400350
$393$	−6.60234	−0.333044
$394$	−6.29762	−0.317270
$395$	−17.1399	−0.862399
$396$	−0.324885	−0.0163261
$397$	3.71738	0.186570	0.0932849	−	0.995639i	$-0.470263\pi$
$397$	3.71738	0.186570	0.0932849	+	0.995639i	$0.470263\pi$
$398$	−24.6364	−1.23491
$399$	17.0236	0.852244
$400$	5.87646	0.293823
$401$	0.791673	0.0395342	0.0197671	−	0.999805i	$-0.493708\pi$
$401$	0.791673	0.0395342	0.0197671	+	0.999805i	$0.493708\pi$
$402$	2.15574	0.107518
$403$	−6.97863	−0.347631
$404$	−10.3189	−0.513383
$405$	−20.6667	−1.02694
$406$	−31.8237	−1.57938
$407$	0	0
$408$	3.07514	0.152242
$409$	12.8555	0.635666	0.317833	−	0.948147i	$-0.397045\pi$
$409$	12.8555	0.635666	0.317833	+	0.948147i	$0.397045\pi$
$410$	16.1410	0.797145
$411$	−6.37116	−0.314266
$412$	8.09728	0.398924
$413$	31.3607	1.54316
$414$	7.92712	0.389597
$415$	−24.6984	−1.21239
$416$	1.45272	0.0712257
$417$	−5.69744	−0.279005
$418$	0.950271	0.0464793
$419$	−7.38854	−0.360954	−0.180477	−	0.983579i	$-0.557764\pi$
$419$	−7.38854	−0.360954	−0.180477	+	0.983579i	$0.557764\pi$
$420$	7.14805	0.348789
$421$	−24.4734	−1.19276	−0.596379	−	0.802703i	$-0.703395\pi$
$421$	−24.4734	−1.19276	−0.596379	+	0.802703i	$0.703395\pi$
$422$	15.7937	0.768824
$423$	14.5353	0.706732
$424$	−1.80979	−0.0878911
$425$	−32.2119	−1.56251
$426$	4.93336	0.239022
$427$	44.7231	2.16430
$428$	3.35122	0.161988
$429$	−0.0986027	−0.00476059
$430$	−20.5643	−0.991699
$431$	−20.0000	−0.963367	−0.481683	−	0.876345i	$-0.659974\pi$
$431$	−20.0000	−0.963367	−0.481683	+	0.876345i	$0.659974\pi$
$432$	−3.18945	−0.153453
$433$	−27.0437	−1.29964	−0.649819	−	0.760089i	$-0.725155\pi$
$433$	−27.0437	−1.29964	−0.649819	+	0.760089i	$0.725155\pi$
$434$	18.5595	0.890885
$435$	15.2398	0.730692
$436$	18.0589	0.864867
$437$	−23.1864	−1.10915
$438$	−5.69216	−0.271982
$439$	5.46988	0.261063	0.130531	−	0.991444i	$-0.458332\pi$
$439$	5.46988	0.261063	0.130531	+	0.991444i	$0.458332\pi$
$440$	0.399011	0.0190221
$441$	−21.2849	−1.01357
$442$	−7.96313	−0.378767
$443$	−14.4882	−0.688354	−0.344177	−	0.938905i	$-0.611842\pi$
$443$	−14.4882	−0.688354	−0.344177	+	0.938905i	$0.611842\pi$
$444$	0	0
$445$	−23.1266	−1.09631
$446$	−11.4565	−0.542480
$447$	−4.94949	−0.234103
$448$	−3.86349	−0.182533
$449$	−25.3813	−1.19782	−0.598909	−	0.800817i	$-0.704399\pi$
$449$	−25.3813	−1.19782	−0.598909	+	0.800817i	$0.704399\pi$
$450$	15.7799	0.743873
$451$	0.592143	0.0278829
$452$	−19.8570	−0.933996
$453$	−0.362586	−0.0170358
$454$	22.1402	1.03909
$455$	−18.5100	−0.867762
$456$	4.40627	0.206342
$457$	−29.8308	−1.39543	−0.697713	−	0.716377i	$-0.745799\pi$
$457$	−29.8308	−1.39543	−0.697713	+	0.716377i	$0.745799\pi$
$458$	−7.70162	−0.359873
$459$	17.4830	0.816038
$460$	−9.73577	−0.453933
$461$	14.7184	0.685505	0.342753	−	0.939426i	$-0.388641\pi$
$461$	14.7184	0.685505	0.342753	+	0.939426i	$0.388641\pi$
$462$	0.262232	0.0122001
$463$	17.0140	0.790707	0.395354	−	0.918529i	$-0.370622\pi$
$463$	17.0140	0.790707	0.395354	+	0.918529i	$0.370622\pi$
$464$	−8.23703	−0.382395
$465$	−8.88783	−0.412163
$466$	3.98679	0.184684
$467$	−2.25257	−0.104236	−0.0521182	−	0.998641i	$-0.516597\pi$
$467$	−2.25257	−0.104236	−0.0521182	+	0.998641i	$0.516597\pi$
$468$	3.90097	0.180322
$469$	14.8460	0.685526
$470$	−17.8517	−0.823438
$471$	4.14697	0.191082
$472$	8.11719	0.373624
$473$	−0.754417	−0.0346882
$474$	−2.91560	−0.133918
$475$	−46.1554	−2.11775
$476$	21.1777	0.970680
$477$	−4.85978	−0.222514
$478$	27.7921	1.27118
$479$	−33.2447	−1.51899	−0.759494	−	0.650515i	$-0.774553\pi$
$479$	−33.2447	−1.51899	−0.759494	+	0.650515i	$0.774553\pi$
$480$	1.85016	0.0844477
$481$	0	0
$482$	−8.63923	−0.393506
$483$	−6.39838	−0.291137
$484$	−10.9854	−0.499335
$485$	−49.9674	−2.26890
$486$	−13.0839	−0.593498
$487$	1.53826	0.0697052	0.0348526	−	0.999392i	$-0.488904\pi$
$487$	1.53826	0.0697052	0.0348526	+	0.999392i	$0.488904\pi$
$488$	11.5758	0.524013
$489$	−5.91093	−0.267302
$490$	26.1412	1.18094
$491$	−19.0143	−0.858103	−0.429051	−	0.903280i	$-0.641152\pi$
$491$	−19.0143	−0.858103	−0.429051	+	0.903280i	$0.641152\pi$
$492$	2.74568	0.123785
$493$	45.1514	2.03352
$494$	−11.4101	−0.513365
$495$	1.07146	0.0481583
$496$	4.80383	0.215698
$497$	33.9749	1.52398
$498$	−4.20135	−0.188267
$499$	−15.3083	−0.685296	−0.342648	−	0.939464i	$-0.611324\pi$
$499$	−15.3083	−0.685296	−0.342648	+	0.939464i	$0.611324\pi$
$500$	−2.89052	−0.129268
$501$	2.44297	0.109144
$502$	8.64129	0.385680
$503$	29.0078	1.29340	0.646698	−	0.762747i	$-0.276150\pi$
$503$	29.0078	1.29340	0.646698	+	0.762747i	$0.276150\pi$
$504$	−10.3745	−0.462118
$505$	34.0311	1.51437
$506$	−0.357164	−0.0158779
$507$	−6.10908	−0.271314
$508$	4.79541	0.212762
$509$	−18.1054	−0.802507	−0.401253	−	0.915967i	$-0.631425\pi$
$509$	−18.1054	−0.802507	−0.401253	+	0.915967i	$0.631425\pi$
$510$	−10.1417	−0.449080
$511$	−39.2005	−1.73413
$512$	−1.00000	−0.0441942
$513$	25.0509	1.10602
$514$	−6.78630	−0.299331
$515$	−26.7044	−1.17674
$516$	−3.49812	−0.153996
$517$	−0.654903	−0.0288026
$518$	0	0
$519$	0.226826	0.00995656
$520$	−4.79101	−0.210100
$521$	−8.95808	−0.392461	−0.196230	−	0.980558i	$-0.562870\pi$
$521$	−8.95808	−0.392461	−0.196230	+	0.980558i	$0.562870\pi$
$522$	−22.1187	−0.968110
$523$	27.7220	1.21220	0.606100	−	0.795388i	$-0.292733\pi$
$523$	27.7220	1.21220	0.606100	+	0.795388i	$0.292733\pi$
$524$	−11.7688	−0.514123
$525$	−12.7368	−0.555879
$526$	12.4311	0.542023
$527$	−26.3322	−1.14705
$528$	0.0678744	0.00295385
$529$	−14.2853	−0.621100
$530$	5.96859	0.259259
$531$	21.7969	0.945905
$532$	30.3449	1.31562
$533$	−7.10998	−0.307968
$534$	−3.93399	−0.170240
$535$	−11.0522	−0.477827
$536$	3.84265	0.165977
$537$	5.74069	0.247729
$538$	9.23562	0.398176
$539$	0.959011	0.0413075
$540$	10.5186	0.452651
$541$	9.69530	0.416833	0.208417	−	0.978040i	$-0.433169\pi$
$541$	9.69530	0.416833	0.208417	+	0.978040i	$0.433169\pi$
$542$	27.5920	1.18518
$543$	−5.46876	−0.234687
$544$	5.48151	0.235018
$545$	−59.5575	−2.55116
$546$	−3.14867	−0.134751
$547$	−16.6498	−0.711895	−0.355948	−	0.934506i	$-0.615842\pi$
$547$	−16.6498	−0.711895	−0.355948	+	0.934506i	$0.615842\pi$
$548$	−11.3568	−0.485136
$549$	31.0843	1.32665
$550$	−0.710979	−0.0303163
$551$	64.6960	2.75614
$552$	−1.65612	−0.0704890
$553$	−20.0790	−0.853847
$554$	−6.34936	−0.269759
$555$	0	0
$556$	−10.1558	−0.430703
$557$	−5.23887	−0.221978	−0.110989	−	0.993822i	$-0.535402\pi$
$557$	−5.23887	−0.221978	−0.110989	+	0.993822i	$0.535402\pi$
$558$	12.8996	0.546084
$559$	9.05845	0.383132
$560$	12.7416	0.538430
$561$	−0.372054	−0.0157081
$562$	15.3300	0.646656
$563$	28.7717	1.21258	0.606291	−	0.795243i	$-0.292657\pi$
$563$	28.7717	1.21258	0.606291	+	0.795243i	$0.292657\pi$
$564$	−3.03669	−0.127868
$565$	65.4874	2.75508
$566$	−24.3850	−1.02498
$567$	−24.2107	−1.01675
$568$	8.79384	0.368981
$569$	−29.9357	−1.25497	−0.627485	−	0.778629i	$-0.715916\pi$
$569$	−29.9357	−1.25497	−0.627485	+	0.778629i	$0.715916\pi$
$570$	−14.5316	−0.608663
$571$	−42.6677	−1.78559	−0.892794	−	0.450465i	$-0.851258\pi$
$571$	−42.6677	−1.78559	−0.892794	+	0.450465i	$0.851258\pi$
$572$	−0.175762	−0.00734897
$573$	2.73995	0.114463
$574$	18.9088	0.789239
$575$	17.3477	0.723450
$576$	−2.68528	−0.111887
$577$	−5.87125	−0.244423	−0.122212	−	0.992504i	$-0.538999\pi$
$577$	−5.87125	−0.244423	−0.122212	+	0.992504i	$0.538999\pi$
$578$	−13.0470	−0.542683
$579$	−4.76420	−0.197993
$580$	27.1653	1.12798
$581$	−28.9337	−1.20037
$582$	−8.49978	−0.352327
$583$	0.218962	0.00906849
$584$	−10.1464	−0.419861
$585$	−12.8652	−0.531910
$586$	−5.87846	−0.242837
$587$	42.3476	1.74787	0.873937	−	0.486040i	$-0.161559\pi$
$587$	42.3476	1.74787	0.873937	+	0.486040i	$0.161559\pi$
$588$	4.44679	0.183383
$589$	−37.7306	−1.55466
$590$	−26.7701	−1.10211
$591$	3.53298	0.145327
$592$	0	0
$593$	11.4764	0.471278	0.235639	−	0.971841i	$-0.424282\pi$
$593$	11.4764	0.471278	0.235639	+	0.971841i	$0.424282\pi$
$594$	0.385885	0.0158330
$595$	−69.8431	−2.86329
$596$	−8.82258	−0.361387
$597$	13.8211	0.565660
$598$	4.28854	0.175372
$599$	30.9762	1.26565	0.632826	−	0.774294i	$-0.281895\pi$
$599$	30.9762	1.26565	0.632826	+	0.774294i	$0.281895\pi$
$600$	−3.29671	−0.134588
$601$	−19.1431	−0.780864	−0.390432	−	0.920632i	$-0.627674\pi$
$601$	−19.1431	−0.780864	−0.390432	+	0.920632i	$0.627674\pi$
$602$	−24.0907	−0.981864
$603$	10.3186	0.420205
$604$	−0.646318	−0.0262983
$605$	36.2292	1.47292
$606$	5.78891	0.235159
$607$	10.8490	0.440346	0.220173	−	0.975461i	$-0.429338\pi$
$607$	10.8490	0.440346	0.220173	+	0.975461i	$0.429338\pi$
$608$	7.85428	0.318533
$609$	17.8531	0.723446
$610$	−38.1765	−1.54572
$611$	7.86356	0.318126
$612$	14.7194	0.594996
$613$	−31.1505	−1.25816	−0.629078	−	0.777342i	$-0.716567\pi$
$613$	−31.1505	−1.25816	−0.629078	+	0.777342i	$0.716567\pi$
$614$	25.6672	1.03584
$615$	−9.05511	−0.365137
$616$	0.467434	0.0188335
$617$	27.6409	1.11278	0.556390	−	0.830921i	$-0.312186\pi$
$617$	27.6409	1.11278	0.556390	+	0.830921i	$0.312186\pi$
$618$	−4.54259	−0.182730
$619$	43.6974	1.75635	0.878174	−	0.478341i	$-0.158762\pi$
$619$	43.6974	1.75635	0.878174	+	0.478341i	$0.158762\pi$
$620$	−15.8428	−0.636261
$621$	−9.41548	−0.377830
$622$	−9.93891	−0.398514
$623$	−27.0924	−1.08543
$624$	−0.814982	−0.0326254
$625$	−19.8495	−0.793981
$626$	5.41564	0.216453
$627$	−0.533104	−0.0212901
$628$	7.39208	0.294976
$629$	0	0
$630$	34.2146	1.36314
$631$	23.1648	0.922176	0.461088	−	0.887354i	$-0.347459\pi$
$631$	23.1648	0.922176	0.461088	+	0.887354i	$0.347459\pi$
$632$	−5.19713	−0.206731
$633$	−8.86028	−0.352165
$634$	13.5919	0.539802
$635$	−15.8150	−0.627600
$636$	1.01530	0.0402591
$637$	−11.5150	−0.456243
$638$	0.996580	0.0394550
$639$	23.6139	0.934151
$640$	3.29795	0.130363
$641$	−43.8498	−1.73196	−0.865981	−	0.500077i	$-0.833305\pi$
$641$	−43.8498	−1.73196	−0.865981	+	0.500077i	$0.833305\pi$
$642$	−1.88004	−0.0741994
$643$	29.8734	1.17809	0.589046	−	0.808100i	$-0.299504\pi$
$643$	29.8734	1.17809	0.589046	+	0.808100i	$0.299504\pi$
$644$	−11.4053	−0.449431
$645$	11.5366	0.454254
$646$	−43.0533	−1.69391
$647$	−30.9739	−1.21771	−0.608856	−	0.793281i	$-0.708371\pi$
$647$	−30.9739	−1.21771	−0.608856	+	0.793281i	$0.708371\pi$
$648$	−6.26654	−0.246173
$649$	−0.982081	−0.0385500
$650$	8.53688	0.334844
$651$	−10.4119	−0.408076
$652$	−10.5364	−0.412637
$653$	−5.64864	−0.221048	−0.110524	−	0.993873i	$-0.535253\pi$
$653$	−5.64864	−0.221048	−0.110524	+	0.993873i	$0.535253\pi$
$654$	−10.1311	−0.396158
$655$	38.8130	1.51655
$656$	4.89424	0.191088
$657$	−27.2459	−1.06296
$658$	−20.9129	−0.815272
$659$	−12.9440	−0.504228	−0.252114	−	0.967698i	$-0.581126\pi$
$659$	−12.9440	−0.504228	−0.252114	+	0.967698i	$0.581126\pi$
$660$	−0.223846	−0.00871320
$661$	16.9374	0.658790	0.329395	−	0.944192i	$-0.393155\pi$
$661$	16.9374	0.658790	0.329395	+	0.944192i	$0.393155\pi$
$662$	−13.8105	−0.536759
$663$	4.46733	0.173497
$664$	−7.48901	−0.290630
$665$	−100.076	−3.88078
$666$	0	0
$667$	−24.3163	−0.941530
$668$	4.35466	0.168487
$669$	6.42711	0.248487
$670$	−12.6729	−0.489596
$671$	−1.40053	−0.0540670
$672$	2.16742	0.0836102
$673$	−5.66509	−0.218373	−0.109187	−	0.994021i	$-0.534825\pi$
$673$	−5.66509	−0.218373	−0.109187	+	0.994021i	$0.534825\pi$
$674$	−9.25241	−0.356390
$675$	−18.7427	−0.721407
$676$	−10.8896	−0.418830
$677$	−46.5084	−1.78746	−0.893732	−	0.448602i	$-0.851922\pi$
$677$	−46.5084	−1.78746	−0.893732	+	0.448602i	$0.851922\pi$
$678$	11.1398	0.427823
$679$	−58.5359	−2.24640
$680$	−18.0777	−0.693250
$681$	−12.4207	−0.475962
$682$	−0.581204	−0.0222554
$683$	−26.9646	−1.03177	−0.515886	−	0.856657i	$-0.672537\pi$
$683$	−26.9646	−1.03177	−0.515886	+	0.856657i	$0.672537\pi$
$684$	21.0909	0.806431
$685$	37.4540	1.43104
$686$	3.57959	0.136669
$687$	4.32063	0.164842
$688$	−6.23549	−0.237726
$689$	−2.62912	−0.100162
$690$	5.46179	0.207927
$691$	4.84832	0.184439	0.0922194	−	0.995739i	$-0.470604\pi$
$691$	4.84832	0.184439	0.0922194	+	0.995739i	$0.470604\pi$
$692$	0.404323	0.0153701
$693$	1.25519	0.0476807
$694$	22.8417	0.867060
$695$	33.4934	1.27048
$696$	4.62099	0.175158
$697$	−26.8279	−1.01618
$698$	−0.974846	−0.0368985
$699$	−2.23660	−0.0845958
$700$	−22.7036	−0.858116
$701$	−17.9449	−0.677770	−0.338885	−	0.940828i	$-0.610050\pi$
$701$	−17.9449	−0.677770	−0.338885	+	0.940828i	$0.610050\pi$
$702$	−4.63340	−0.174876
$703$	0	0
$704$	0.120988	0.00455990
$705$	10.0148	0.377181
$706$	−3.20706	−0.120699
$707$	39.8668	1.49935
$708$	−4.55376	−0.171141
$709$	16.4553	0.617992	0.308996	−	0.951063i	$-0.400007\pi$
$709$	16.4553	0.617992	0.308996	+	0.951063i	$0.400007\pi$
$710$	−29.0016	−1.08841
$711$	−13.9557	−0.523380
$712$	−7.01242	−0.262802
$713$	14.1812	0.531091
$714$	−11.8808	−0.444626
$715$	0.579653	0.0216778
$716$	10.2329	0.382422
$717$	−15.5914	−0.582272
$718$	−14.9610	−0.558339
$719$	4.08487	0.152340	0.0761700	−	0.997095i	$-0.475731\pi$
$719$	4.08487	0.152340	0.0761700	+	0.997095i	$0.475731\pi$
$720$	8.85590	0.330040
$721$	−31.2837	−1.16507
$722$	−42.6897	−1.58875
$723$	4.84662	0.180248
$724$	−9.74821	−0.362289
$725$	−48.4046	−1.79770
$726$	6.16281	0.228723
$727$	−46.8000	−1.73572	−0.867859	−	0.496811i	$-0.834504\pi$
$727$	−46.8000	−1.73572	−0.867859	+	0.496811i	$0.834504\pi$
$728$	−5.61258	−0.208016
$729$	−11.4595	−0.424427
$730$	33.4623	1.23850
$731$	34.1799	1.26419
$732$	−6.49407	−0.240028
$733$	44.6042	1.64749	0.823747	−	0.566958i	$-0.191880\pi$
$733$	44.6042	1.64749	0.823747	+	0.566958i	$0.191880\pi$
$734$	2.76360	0.102006
$735$	−14.6653	−0.540938
$736$	−2.95207	−0.108815
$737$	−0.464914	−0.0171253
$738$	13.1424	0.483778
$739$	30.6832	1.12870	0.564350	−	0.825536i	$-0.309127\pi$
$739$	30.6832	1.12870	0.564350	+	0.825536i	$0.309127\pi$
$740$	0	0
$741$	6.40109	0.235150
$742$	6.99209	0.256688
$743$	53.6916	1.96976	0.984878	−	0.173250i	$-0.0554270\pi$
$743$	53.6916	1.96976	0.984878	+	0.173250i	$0.0554270\pi$
$744$	−2.69496	−0.0988019
$745$	29.0964	1.06601
$746$	−20.5705	−0.753141
$747$	−20.1101	−0.735788
$748$	−0.663196	−0.0242488
$749$	−12.9474	−0.473088
$750$	1.62159	0.0592120
$751$	26.3602	0.961897	0.480948	−	0.876749i	$-0.340292\pi$
$751$	26.3602	0.961897	0.480948	+	0.876749i	$0.340292\pi$
$752$	−5.41297	−0.197391
$753$	−4.84778	−0.176663
$754$	−11.9661	−0.435781
$755$	2.13152	0.0775741
$756$	12.3224	0.448161
$757$	−13.0288	−0.473541	−0.236770	−	0.971566i	$-0.576089\pi$
$757$	−13.0288	−0.473541	−0.236770	+	0.971566i	$0.576089\pi$
$758$	−0.584666	−0.0212360
$759$	0.200370	0.00727296
$760$	−25.9030	−0.939601
$761$	10.7042	0.388026	0.194013	−	0.980999i	$-0.437850\pi$
$761$	10.7042	0.388026	0.194013	+	0.980999i	$0.437850\pi$
$762$	−2.69024	−0.0974570
$763$	−69.7705	−2.52586
$764$	4.88402	0.176698
$765$	−48.5437	−1.75510
$766$	−15.6344	−0.564895
$767$	11.7920	0.425786
$768$	0.561002	0.0202434
$769$	−47.8572	−1.72578	−0.862888	−	0.505395i	$-0.831347\pi$
$769$	−47.8572	−1.72578	−0.862888	+	0.505395i	$0.831347\pi$
$770$	−1.54157	−0.0555545
$771$	3.80713	0.137110
$772$	−8.49231	−0.305645
$773$	−11.5120	−0.414056	−0.207028	−	0.978335i	$-0.566379\pi$
$773$	−11.5120	−0.414056	−0.207028	+	0.978335i	$0.566379\pi$
$774$	−16.7440	−0.601851
$775$	28.2295	1.01403
$776$	−15.1511	−0.543892
$777$	0	0
$778$	−2.14121	−0.0767662
$779$	−38.4407	−1.37728
$780$	2.68777	0.0962375
$781$	−1.06395	−0.0380710
$782$	16.1818	0.578660
$783$	26.2716	0.938871
$784$	7.92652	0.283090
$785$	−24.3787	−0.870113
$786$	6.60234	0.235498
$787$	17.8786	0.637305	0.318652	−	0.947872i	$-0.396770\pi$
$787$	17.8786	0.637305	0.318652	+	0.947872i	$0.396770\pi$
$788$	6.29762	0.224344
$789$	−6.97389	−0.248277
$790$	17.1399	0.609809
$791$	76.7173	2.72775
$792$	0.324885	0.0115443
$793$	16.8165	0.597171
$794$	−3.71738	−0.131925
$795$	−3.34839	−0.118755
$796$	24.6364	0.873215
$797$	−10.8731	−0.385146	−0.192573	−	0.981283i	$-0.561683\pi$
$797$	−10.8731	−0.385146	−0.192573	+	0.981283i	$0.561683\pi$
$798$	−17.0236	−0.602627
$799$	29.6713	1.04969
$800$	−5.87646	−0.207764
$801$	−18.8303	−0.665336
$802$	−0.791673	−0.0279549
$803$	1.22759	0.0433207
$804$	−2.15574	−0.0760270
$805$	37.6140	1.32572
$806$	6.97863	0.245812
$807$	−5.18120	−0.182387
$808$	10.3189	0.363017
$809$	−10.7839	−0.379143	−0.189572	−	0.981867i	$-0.560710\pi$
$809$	−10.7839	−0.379143	−0.189572	+	0.981867i	$0.560710\pi$
$810$	20.6667	0.726155
$811$	3.27059	0.114846	0.0574230	−	0.998350i	$-0.481712\pi$
$811$	3.27059	0.114846	0.0574230	+	0.998350i	$0.481712\pi$
$812$	31.8237	1.11679
$813$	−15.4792	−0.542879
$814$	0	0
$815$	34.7484	1.21718
$816$	−3.07514	−0.107651
$817$	48.9753	1.71343
$818$	−12.8555	−0.449484
$819$	−15.0713	−0.526635
$820$	−16.1410	−0.563667
$821$	−14.0395	−0.489982	−0.244991	−	0.969525i	$-0.578785\pi$
$821$	−14.0395	−0.489982	−0.244991	+	0.969525i	$0.578785\pi$
$822$	6.37116	0.222220
$823$	−4.95050	−0.172563	−0.0862817	−	0.996271i	$-0.527499\pi$
$823$	−4.95050	−0.172563	−0.0862817	+	0.996271i	$0.527499\pi$
$824$	−8.09728	−0.282082
$825$	0.398861	0.0138866
$826$	−31.3607	−1.09118
$827$	43.9864	1.52956	0.764778	−	0.644294i	$-0.222849\pi$
$827$	43.9864	1.52956	0.764778	+	0.644294i	$0.222849\pi$
$828$	−7.92712	−0.275487
$829$	−14.5295	−0.504630	−0.252315	−	0.967645i	$-0.581192\pi$
$829$	−14.5295	−0.504630	−0.252315	+	0.967645i	$0.581192\pi$
$830$	24.6984	0.857292
$831$	3.56201	0.123565
$832$	−1.45272	−0.0503642
$833$	−43.4493	−1.50543
$834$	5.69744	0.197286
$835$	−14.3614	−0.496998
$836$	−0.950271	−0.0328658
$837$	−15.3216	−0.529591
$838$	7.38854	0.255233
$839$	−21.5173	−0.742859	−0.371430	−	0.928461i	$-0.621132\pi$
$839$	−21.5173	−0.742859	−0.371430	+	0.928461i	$0.621132\pi$
$840$	−7.14805	−0.246631
$841$	38.8487	1.33961
$842$	24.4734	0.843408
$843$	−8.60015	−0.296205
$844$	−15.7937	−0.543641
$845$	35.9133	1.23546
$846$	−14.5353	−0.499735
$847$	42.4418	1.45832
$848$	1.80979	0.0621484
$849$	13.6801	0.469499
$850$	32.2119	1.10486
$851$	0	0
$852$	−4.93336	−0.169014
$853$	40.4387	1.38459	0.692297	−	0.721612i	$-0.256599\pi$
$853$	40.4387	1.38459	0.692297	+	0.721612i	$0.256599\pi$
$854$	−44.7231	−1.53039
$855$	−69.5567	−2.37879
$856$	−3.35122	−0.114543
$857$	−12.8602	−0.439297	−0.219649	−	0.975579i	$-0.570491\pi$
$857$	−12.8602	−0.439297	−0.219649	+	0.975579i	$0.570491\pi$
$858$	0.0986027	0.00336624
$859$	−19.9296	−0.679991	−0.339995	−	0.940427i	$-0.610425\pi$
$859$	−19.9296	−0.679991	−0.339995	+	0.940427i	$0.610425\pi$
$860$	20.5643	0.701237
$861$	−10.6079	−0.361516
$862$	20.0000	0.681203
$863$	−19.0058	−0.646964	−0.323482	−	0.946234i	$-0.604854\pi$
$863$	−19.0058	−0.646964	−0.323482	+	0.946234i	$0.604854\pi$
$864$	3.18945	0.108507
$865$	−1.33344	−0.0453382
$866$	27.0437	0.918983
$867$	7.31939	0.248580
$868$	−18.5595	−0.629951
$869$	0.628788	0.0213302
$870$	−15.2398	−0.516677
$871$	5.58231	0.189150
$872$	−18.0589	−0.611553
$873$	−40.6848	−1.37697
$874$	23.1864	0.784291
$875$	11.1675	0.377530
$876$	5.69216	0.192320
$877$	11.8181	0.399071	0.199535	−	0.979891i	$-0.436057\pi$
$877$	11.8181	0.399071	0.199535	+	0.979891i	$0.436057\pi$
$878$	−5.46988	−0.184599
$879$	3.29783	0.111233
$880$	−0.399011	−0.0134507
$881$	35.5505	1.19773	0.598863	−	0.800851i	$-0.295619\pi$
$881$	35.5505	1.19773	0.598863	+	0.800851i	$0.295619\pi$
$882$	21.2849	0.716700
$883$	−18.7915	−0.632383	−0.316192	−	0.948695i	$-0.602404\pi$
$883$	−18.7915	−0.632383	−0.316192	+	0.948695i	$0.602404\pi$
$884$	7.96313	0.267829
$885$	15.0181	0.504827
$886$	14.4882	0.486740
$887$	2.16205	0.0725946	0.0362973	−	0.999341i	$-0.488444\pi$
$887$	2.16205	0.0725946	0.0362973	+	0.999341i	$0.488444\pi$
$888$	0	0
$889$	−18.5270	−0.621376
$890$	23.1266	0.775206
$891$	0.758174	0.0253998
$892$	11.4565	0.383591
$893$	42.5150	1.42271
$894$	4.94949	0.165536
$895$	−33.7476	−1.12806
$896$	3.86349	0.129070
$897$	−2.40588	−0.0803301
$898$	25.3813	0.846985
$899$	−39.5693	−1.31971
$900$	−15.7799	−0.525997
$901$	−9.92038	−0.330496
$902$	−0.592143	−0.0197162
$903$	13.5149	0.449749
$904$	19.8570	0.660435
$905$	32.1491	1.06867
$906$	0.362586	0.0120461
$907$	−13.5657	−0.450441	−0.225220	−	0.974308i	$-0.572310\pi$
$907$	−13.5657	−0.450441	−0.225220	+	0.974308i	$0.572310\pi$
$908$	−22.1402	−0.734748
$909$	27.7090	0.919051
$910$	18.5100	0.613600
$911$	32.5969	1.07998	0.539992	−	0.841670i	$-0.318427\pi$
$911$	32.5969	1.07998	0.539992	+	0.841670i	$0.318427\pi$
$912$	−4.40627	−0.145906
$913$	0.906078	0.0299868
$914$	29.8308	0.986716
$915$	21.4171	0.708027
$916$	7.70162	0.254469
$917$	45.4687	1.50151
$918$	−17.4830	−0.577026
$919$	−59.8290	−1.97358	−0.986789	−	0.162013i	$-0.948201\pi$
$919$	−59.8290	−1.97358	−0.986789	+	0.162013i	$0.948201\pi$
$920$	9.73577	0.320979
$921$	−14.3993	−0.474475
$922$	−14.7184	−0.484725
$923$	12.7750	0.420495
$924$	−0.262232	−0.00862679
$925$	0	0
$926$	−17.0140	−0.559115
$927$	−21.7434	−0.714148
$928$	8.23703	0.270394
$929$	−3.45076	−0.113216	−0.0566078	−	0.998396i	$-0.518028\pi$
$929$	−3.45076	−0.113216	−0.0566078	+	0.998396i	$0.518028\pi$
$930$	8.88783	0.291443
$931$	−62.2571	−2.04039
$932$	−3.98679	−0.130592
$933$	5.57575	0.182542
$934$	2.25257	0.0737063
$935$	2.18718	0.0715286
$936$	−3.90097	−0.127507
$937$	11.2127	0.366302	0.183151	−	0.983085i	$-0.441370\pi$
$937$	11.2127	0.366302	0.183151	+	0.983085i	$0.441370\pi$
$938$	−14.8460	−0.484740
$939$	−3.03819	−0.0991475
$940$	17.8517	0.582259
$941$	−25.3113	−0.825124	−0.412562	−	0.910929i	$-0.635366\pi$
$941$	−25.3113	−0.825124	−0.412562	+	0.910929i	$0.635366\pi$
$942$	−4.14697	−0.135116
$943$	14.4481	0.470496
$944$	−8.11719	−0.264192
$945$	−40.6386	−1.32198
$946$	0.754417	0.0245282
$947$	39.1566	1.27242	0.636209	−	0.771517i	$-0.280502\pi$
$947$	39.1566	1.27242	0.636209	+	0.771517i	$0.280502\pi$
$948$	2.91560	0.0946943
$949$	−14.7399	−0.478478
$950$	46.1554	1.49748
$951$	−7.62507	−0.247260
$952$	−21.1777	−0.686375
$953$	−53.4418	−1.73115	−0.865575	−	0.500779i	$-0.833047\pi$
$953$	−53.4418	−1.73115	−0.865575	+	0.500779i	$0.833047\pi$
$954$	4.85978	0.157341
$955$	−16.1072	−0.521218
$956$	−27.7921	−0.898860
$957$	−0.559083	−0.0180726
$958$	33.2447	1.07409
$959$	43.8766	1.41685
$960$	−1.85016	−0.0597135
$961$	−7.92326	−0.255589
$962$	0	0
$963$	−8.99897	−0.289988
$964$	8.63923	0.278251
$965$	28.0072	0.901583
$966$	6.39838	0.205865
$967$	−53.5527	−1.72214	−0.861069	−	0.508488i	$-0.830205\pi$
$967$	−53.5527	−1.72214	−0.861069	+	0.508488i	$0.830205\pi$
$968$	10.9854	0.353083
$969$	24.1530	0.775907
$970$	49.9674	1.60436
$971$	1.62778	0.0522381	0.0261190	−	0.999659i	$-0.491685\pi$
$971$	1.62778	0.0522381	0.0261190	+	0.999659i	$0.491685\pi$
$972$	13.0839	0.419666
$973$	39.2369	1.25788
$974$	−1.53826	−0.0492890
$975$	−4.78921	−0.153377
$976$	−11.5758	−0.370533
$977$	−12.4828	−0.399360	−0.199680	−	0.979861i	$-0.563990\pi$
$977$	−12.4828	−0.399360	−0.199680	+	0.979861i	$0.563990\pi$
$978$	5.91093	0.189011
$979$	0.848417	0.0271155
$980$	−26.1412	−0.835052
$981$	−48.4933	−1.54827
$982$	19.0143	0.606770
$983$	−11.5455	−0.368245	−0.184123	−	0.982903i	$-0.558944\pi$
$983$	−11.5455	−0.368245	−0.184123	+	0.982903i	$0.558944\pi$
$984$	−2.74568	−0.0875291
$985$	−20.7692	−0.661763
$986$	−45.1514	−1.43791
$987$	11.7322	0.373440
$988$	11.4101	0.363004
$989$	−18.4076	−0.585327
$990$	−1.07146	−0.0340531
$991$	12.1054	0.384540	0.192270	−	0.981342i	$-0.438415\pi$
$991$	12.1054	0.384540	0.192270	+	0.981342i	$0.438415\pi$
$992$	−4.80383	−0.152522
$993$	7.74770	0.245866
$994$	−33.9749	−1.07762
$995$	−81.2497	−2.57579
$996$	4.20135	0.133125
$997$	−12.8633	−0.407384	−0.203692	−	0.979035i	$-0.565294\pi$
$997$	−12.8633	−0.407384	−0.203692	+	0.979035i	$0.565294\pi$
$998$	15.3083	0.484577
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.w.1.10	✓	18
37.36	even	2		2738.2.a.x.1.10	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.10	✓	18	1.1	even	1	trivial
2738.2.a.x.1.10	yes	18	37.36	even	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.561002 q^{3} +1.00000 q^{4} -3.29795 q^{5} -0.561002 q^{6} -3.86349 q^{7} -1.00000 q^{8} -2.68528 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.561002 q^{3} +1.00000 q^{4} -3.29795 q^{5} -0.561002 q^{6} -3.86349 q^{7} -1.00000 q^{8} -2.68528 q^{9} +3.29795 q^{10} +0.120988 q^{11} +0.561002 q^{12} -1.45272 q^{13} +3.86349 q^{14} -1.85016 q^{15} +1.00000 q^{16} -5.48151 q^{17} +2.68528 q^{18} -7.85428 q^{19} -3.29795 q^{20} -2.16742 q^{21} -0.120988 q^{22} +2.95207 q^{23} -0.561002 q^{24} +5.87646 q^{25} +1.45272 q^{26} -3.18945 q^{27} -3.86349 q^{28} -8.23703 q^{29} +1.85016 q^{30} +4.80383 q^{31} -1.00000 q^{32} +0.0678744 q^{33} +5.48151 q^{34} +12.7416 q^{35} -2.68528 q^{36} +7.85428 q^{38} -0.814982 q^{39} +3.29795 q^{40} +4.89424 q^{41} +2.16742 q^{42} -6.23549 q^{43} +0.120988 q^{44} +8.85590 q^{45} -2.95207 q^{46} -5.41297 q^{47} +0.561002 q^{48} +7.92652 q^{49} -5.87646 q^{50} -3.07514 q^{51} -1.45272 q^{52} +1.80979 q^{53} +3.18945 q^{54} -0.399011 q^{55} +3.86349 q^{56} -4.40627 q^{57} +8.23703 q^{58} -8.11719 q^{59} -1.85016 q^{60} -11.5758 q^{61} -4.80383 q^{62} +10.3745 q^{63} +1.00000 q^{64} +4.79101 q^{65} -0.0678744 q^{66} -3.84265 q^{67} -5.48151 q^{68} +1.65612 q^{69} -12.7416 q^{70} -8.79384 q^{71} +2.68528 q^{72} +10.1464 q^{73} +3.29671 q^{75} -7.85428 q^{76} -0.467434 q^{77} +0.814982 q^{78} +5.19713 q^{79} -3.29795 q^{80} +6.26654 q^{81} -4.89424 q^{82} +7.48901 q^{83} -2.16742 q^{84} +18.0777 q^{85} +6.23549 q^{86} -4.62099 q^{87} -0.120988 q^{88} +7.01242 q^{89} -8.85590 q^{90} +5.61258 q^{91} +2.95207 q^{92} +2.69496 q^{93} +5.41297 q^{94} +25.9030 q^{95} -0.561002 q^{96} +15.1511 q^{97} -7.92652 q^{98} -0.324885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9} + 9 q^{10} + 10 q^{11} + 8 q^{12} - 9 q^{13} - 18 q^{14} + 4 q^{15} + 18 q^{16} - 13 q^{17} - 26 q^{18} - 2 q^{19} - 9 q^{20} + 24 q^{21} - 10 q^{22} + 11 q^{23} - 8 q^{24} + 49 q^{25} + 9 q^{26} + 29 q^{27} + 18 q^{28} - 30 q^{29} - 4 q^{30} + 8 q^{31} - 18 q^{32} + 42 q^{33} + 13 q^{34} - 25 q^{35} + 26 q^{36} + 2 q^{38} + 45 q^{39} + 9 q^{40} + 5 q^{41} - 24 q^{42} + 3 q^{43} + 10 q^{44} + 30 q^{45} - 11 q^{46} + 37 q^{47} + 8 q^{48} + 50 q^{49} - 49 q^{50} - 10 q^{51} - 9 q^{52} + 25 q^{53} - 29 q^{54} + 44 q^{55} - 18 q^{56} - 22 q^{57} + 30 q^{58} - 26 q^{59} + 4 q^{60} - 27 q^{61} - 8 q^{62} + 74 q^{63} + 18 q^{64} - 16 q^{65} - 42 q^{66} + 23 q^{67} - 13 q^{68} + 2 q^{69} + 25 q^{70} - 25 q^{71} - 26 q^{72} + 77 q^{73} - q^{75} - 2 q^{76} - 6 q^{77} - 45 q^{78} + 13 q^{79} - 9 q^{80} + 38 q^{81} - 5 q^{82} - 10 q^{83} + 24 q^{84} + 16 q^{85} - 3 q^{86} + 55 q^{87} - 10 q^{88} - 55 q^{89} - 30 q^{90} - 12 q^{91} + 11 q^{92} + 58 q^{93} - 37 q^{94} - 18 q^{95} - 8 q^{96} + 59 q^{97} - 50 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 8 * q^3 + 18 * q^4 - 9 * q^5 - 8 * q^6 + 18 * q^7 - 18 * q^8 + 26 * q^9 + 9 * q^10 + 10 * q^11 + 8 * q^12 - 9 * q^13 - 18 * q^14 + 4 * q^15 + 18 * q^16 - 13 * q^17 - 26 * q^18 - 2 * q^19 - 9 * q^20 + 24 * q^21 - 10 * q^22 + 11 * q^23 - 8 * q^24 + 49 * q^25 + 9 * q^26 + 29 * q^27 + 18 * q^28 - 30 * q^29 - 4 * q^30 + 8 * q^31 - 18 * q^32 + 42 * q^33 + 13 * q^34 - 25 * q^35 + 26 * q^36 + 2 * q^38 + 45 * q^39 + 9 * q^40 + 5 * q^41 - 24 * q^42 + 3 * q^43 + 10 * q^44 + 30 * q^45 - 11 * q^46 + 37 * q^47 + 8 * q^48 + 50 * q^49 - 49 * q^50 - 10 * q^51 - 9 * q^52 + 25 * q^53 - 29 * q^54 + 44 * q^55 - 18 * q^56 - 22 * q^57 + 30 * q^58 - 26 * q^59 + 4 * q^60 - 27 * q^61 - 8 * q^62 + 74 * q^63 + 18 * q^64 - 16 * q^65 - 42 * q^66 + 23 * q^67 - 13 * q^68 + 2 * q^69 + 25 * q^70 - 25 * q^71 - 26 * q^72 + 77 * q^73 - q^75 - 2 * q^76 - 6 * q^77 - 45 * q^78 + 13 * q^79 - 9 * q^80 + 38 * q^81 - 5 * q^82 - 10 * q^83 + 24 * q^84 + 16 * q^85 - 3 * q^86 + 55 * q^87 - 10 * q^88 - 55 * q^89 - 30 * q^90 - 12 * q^91 + 11 * q^92 + 58 * q^93 - 37 * q^94 - 18 * q^95 - 8 * q^96 + 59 * q^97 - 50 * q^98 + 11 * q^99

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