LMFDB - Embedded newform 2738.2.a.w.1.6

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			1.6
Root			$2.93806$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.844166 q^{3} +1.00000 q^{4} -2.97364 q^{5} +0.844166 q^{6} +4.24887 q^{7} -1.00000 q^{8} -2.28738 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.844166 q^{3} +1.00000 q^{4} -2.97364 q^{5} +0.844166 q^{6} +4.24887 q^{7} -1.00000 q^{8} -2.28738 q^{9} +2.97364 q^{10} +2.60565 q^{11} -0.844166 q^{12} -4.82103 q^{13} -4.24887 q^{14} +2.51025 q^{15} +1.00000 q^{16} +6.48622 q^{17} +2.28738 q^{18} -3.63746 q^{19} -2.97364 q^{20} -3.58675 q^{21} -2.60565 q^{22} -4.27541 q^{23} +0.844166 q^{24} +3.84253 q^{25} +4.82103 q^{26} +4.46343 q^{27} +4.24887 q^{28} -0.00416451 q^{29} -2.51025 q^{30} +5.72454 q^{31} -1.00000 q^{32} -2.19960 q^{33} -6.48622 q^{34} -12.6346 q^{35} -2.28738 q^{36} +3.63746 q^{38} +4.06975 q^{39} +2.97364 q^{40} -5.21988 q^{41} +3.58675 q^{42} +6.04556 q^{43} +2.60565 q^{44} +6.80186 q^{45} +4.27541 q^{46} -1.93422 q^{47} -0.844166 q^{48} +11.0529 q^{49} -3.84253 q^{50} -5.47545 q^{51} -4.82103 q^{52} -8.81490 q^{53} -4.46343 q^{54} -7.74826 q^{55} -4.24887 q^{56} +3.07062 q^{57} +0.00416451 q^{58} -6.32175 q^{59} +2.51025 q^{60} +6.62873 q^{61} -5.72454 q^{62} -9.71879 q^{63} +1.00000 q^{64} +14.3360 q^{65} +2.19960 q^{66} -7.37772 q^{67} +6.48622 q^{68} +3.60915 q^{69} +12.6346 q^{70} -1.17125 q^{71} +2.28738 q^{72} +15.4260 q^{73} -3.24374 q^{75} -3.63746 q^{76} +11.0710 q^{77} -4.06975 q^{78} -1.15625 q^{79} -2.97364 q^{80} +3.09428 q^{81} +5.21988 q^{82} -11.4527 q^{83} -3.58675 q^{84} -19.2877 q^{85} -6.04556 q^{86} +0.00351553 q^{87} -2.60565 q^{88} +12.6870 q^{89} -6.80186 q^{90} -20.4839 q^{91} -4.27541 q^{92} -4.83246 q^{93} +1.93422 q^{94} +10.8165 q^{95} +0.844166 q^{96} -7.48072 q^{97} -11.0529 q^{98} -5.96012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.844166	−0.487379	−0.243690	−	0.969853i	$-0.578358\pi$
$3$	−0.844166	−0.487379	−0.243690	+	0.969853i	$0.578358\pi$
$4$	1.00000	0.500000
$5$	−2.97364	−1.32985	−0.664926	−	0.746909i	$-0.731537\pi$
$5$	−2.97364	−1.32985	−0.664926	+	0.746909i	$0.731537\pi$
$6$	0.844166	0.344629
$7$	4.24887	1.60592	0.802960	−	0.596033i	$-0.203257\pi$
$7$	4.24887	1.60592	0.802960	+	0.596033i	$0.203257\pi$
$8$	−1.00000	−0.353553
$9$	−2.28738	−0.762461
$10$	2.97364	0.940347
$11$	2.60565	0.785632	0.392816	−	0.919617i	$-0.371501\pi$
$11$	2.60565	0.785632	0.392816	+	0.919617i	$0.371501\pi$
$12$	−0.844166	−0.243690
$13$	−4.82103	−1.33711	−0.668557	−	0.743661i	$-0.733088\pi$
$13$	−4.82103	−1.33711	−0.668557	+	0.743661i	$0.733088\pi$
$14$	−4.24887	−1.13556
$15$	2.51025	0.648142
$16$	1.00000	0.250000
$17$	6.48622	1.57314	0.786570	−	0.617501i	$-0.211855\pi$
$17$	6.48622	1.57314	0.786570	+	0.617501i	$0.211855\pi$
$18$	2.28738	0.539142
$19$	−3.63746	−0.834491	−0.417245	−	0.908794i	$-0.637004\pi$
$19$	−3.63746	−0.834491	−0.417245	+	0.908794i	$0.637004\pi$
$20$	−2.97364	−0.664926
$21$	−3.58675	−0.782692
$22$	−2.60565	−0.555526
$23$	−4.27541	−0.891484	−0.445742	−	0.895162i	$-0.647060\pi$
$23$	−4.27541	−0.891484	−0.445742	+	0.895162i	$0.647060\pi$
$24$	0.844166	0.172315
$25$	3.84253	0.768507
$26$	4.82103	0.945482
$27$	4.46343	0.858987
$28$	4.24887	0.802960
$29$	−0.00416451	−0.000773329 0	−0.000386665	−	1.00000i	$-0.500123\pi$
$29$	−0.00416451	−0.000773329 0	−0.000386665		1.00000i	$0.500123\pi$
$30$	−2.51025	−0.458306
$31$	5.72454	1.02816	0.514079	−	0.857743i	$-0.328134\pi$
$31$	5.72454	1.02816	0.514079	+	0.857743i	$0.328134\pi$
$32$	−1.00000	−0.176777
$33$	−2.19960	−0.382901
$34$	−6.48622	−1.11238
$35$	−12.6346	−2.13564
$36$	−2.28738	−0.381231
$37$	0	0
$37$	0	0
$38$	3.63746	0.590074
$39$	4.06975	0.651681
$40$	2.97364	0.470174
$41$	−5.21988	−0.815209	−0.407604	−	0.913159i	$-0.633636\pi$
$41$	−5.21988	−0.815209	−0.407604	+	0.913159i	$0.633636\pi$
$42$	3.58675	0.553447
$43$	6.04556	0.921939	0.460970	−	0.887416i	$-0.347502\pi$
$43$	6.04556	0.921939	0.460970	+	0.887416i	$0.347502\pi$
$44$	2.60565	0.392816
$45$	6.80186	1.01396
$46$	4.27541	0.630374
$47$	−1.93422	−0.282136	−0.141068	−	0.990000i	$-0.545054\pi$
$47$	−1.93422	−0.282136	−0.141068	+	0.990000i	$0.545054\pi$
$48$	−0.844166	−0.121845
$49$	11.0529	1.57898
$50$	−3.84253	−0.543416
$51$	−5.47545	−0.766716
$52$	−4.82103	−0.668557
$53$	−8.81490	−1.21082	−0.605410	−	0.795914i	$-0.706991\pi$
$53$	−8.81490	−1.21082	−0.605410	+	0.795914i	$0.706991\pi$
$54$	−4.46343	−0.607396
$55$	−7.74826	−1.04477
$56$	−4.24887	−0.567779
$57$	3.07062	0.406713
$58$	0.00416451	0.000546826 0
$59$	−6.32175	−0.823022	−0.411511	−	0.911405i	$-0.634999\pi$
$59$	−6.32175	−0.823022	−0.411511	+	0.911405i	$0.634999\pi$
$60$	2.51025	0.324071
$61$	6.62873	0.848722	0.424361	−	0.905493i	$-0.360499\pi$
$61$	6.62873	0.848722	0.424361	+	0.905493i	$0.360499\pi$
$62$	−5.72454	−0.727017
$63$	−9.71879	−1.22445
$64$	1.00000	0.125000
$65$	14.3360	1.77816
$66$	2.19960	0.270752
$67$	−7.37772	−0.901332	−0.450666	−	0.892693i	$-0.648813\pi$
$67$	−7.37772	−0.901332	−0.450666	+	0.892693i	$0.648813\pi$
$68$	6.48622	0.786570
$69$	3.60915	0.434491
$70$	12.6346	1.51012
$71$	−1.17125	−0.139002	−0.0695010	−	0.997582i	$-0.522141\pi$
$71$	−1.17125	−0.139002	−0.0695010	+	0.997582i	$0.522141\pi$
$72$	2.28738	0.269571
$73$	15.4260	1.80547	0.902737	−	0.430193i	$-0.141554\pi$
$73$	15.4260	1.80547	0.902737	+	0.430193i	$0.141554\pi$
$74$	0	0
$75$	−3.24374	−0.374554
$76$	−3.63746	−0.417245
$77$	11.0710	1.26166
$78$	−4.06975	−0.460808
$79$	−1.15625	−0.130089	−0.0650443	−	0.997882i	$-0.520719\pi$
$79$	−1.15625	−0.130089	−0.0650443	+	0.997882i	$0.520719\pi$
$80$	−2.97364	−0.332463
$81$	3.09428	0.343809
$82$	5.21988	0.576440
$83$	−11.4527	−1.25710	−0.628548	−	0.777771i	$-0.716350\pi$
$83$	−11.4527	−1.25710	−0.628548	+	0.777771i	$0.716350\pi$
$84$	−3.58675	−0.391346
$85$	−19.2877	−2.09204
$86$	−6.04556	−0.651910
$87$	0.00351553	0.000376905 0
$88$	−2.60565	−0.277763
$89$	12.6870	1.34482	0.672408	−	0.740180i	$-0.265260\pi$
$89$	12.6870	1.34482	0.672408	+	0.740180i	$0.265260\pi$
$90$	−6.80186	−0.716979
$91$	−20.4839	−2.14730
$92$	−4.27541	−0.445742
$93$	−4.83246	−0.501103
$94$	1.93422	0.199500
$95$	10.8165	1.10975
$96$	0.844166	0.0861573
$97$	−7.48072	−0.759552	−0.379776	−	0.925078i	$-0.623999\pi$
$97$	−7.48072	−0.759552	−0.379776	+	0.925078i	$0.623999\pi$
$98$	−11.0529	−1.11651
$99$	−5.96012	−0.599014
$100$	3.84253	0.384253
$101$	−0.389623	−0.0387689	−0.0193845	−	0.999812i	$-0.506171\pi$
$101$	−0.389623	−0.0387689	−0.0193845	+	0.999812i	$0.506171\pi$
$102$	5.47545	0.542150
$103$	9.59672	0.945593	0.472797	−	0.881172i	$-0.343245\pi$
$103$	9.59672	0.945593	0.472797	+	0.881172i	$0.343245\pi$
$104$	4.82103	0.472741
$105$	10.6657	1.04087
$106$	8.81490	0.856178
$107$	−11.6217	−1.12351	−0.561757	−	0.827302i	$-0.689875\pi$
$107$	−11.6217	−1.12351	−0.561757	+	0.827302i	$0.689875\pi$
$108$	4.46343	0.429494
$109$	10.4314	0.999149	0.499574	−	0.866271i	$-0.333490\pi$
$109$	10.4314	0.999149	0.499574	+	0.866271i	$0.333490\pi$
$110$	7.74826	0.738767
$111$	0	0
$112$	4.24887	0.401480
$113$	−1.44558	−0.135988	−0.0679941	−	0.997686i	$-0.521660\pi$
$113$	−1.44558	−0.135988	−0.0679941	+	0.997686i	$0.521660\pi$
$114$	−3.07062	−0.287590
$115$	12.7135	1.18554
$116$	−0.00416451	−0.000386665 0
$117$	11.0275	1.01950
$118$	6.32175	0.581964
$119$	27.5591	2.52634
$120$	−2.51025	−0.229153
$121$	−4.21060	−0.382782
$122$	−6.62873	−0.600137
$123$	4.40645	0.397316
$124$	5.72454	0.514079
$125$	3.44189	0.307852
$126$	9.71879	0.865818
$127$	14.5192	1.28837	0.644187	−	0.764868i	$-0.277196\pi$
$127$	14.5192	1.28837	0.644187	+	0.764868i	$0.277196\pi$
$128$	−1.00000	−0.0883883
$129$	−5.10346	−0.449334
$130$	−14.3360	−1.25735
$131$	−7.28479	−0.636475	−0.318237	−	0.948011i	$-0.603091\pi$
$131$	−7.28479	−0.636475	−0.318237	+	0.948011i	$0.603091\pi$
$132$	−2.19960	−0.191450
$133$	−15.4551	−1.34013
$134$	7.37772	0.637338
$135$	−13.2726	−1.14233
$136$	−6.48622	−0.556189
$137$	17.0539	1.45701	0.728507	−	0.685038i	$-0.240214\pi$
$137$	17.0539	1.45701	0.728507	+	0.685038i	$0.240214\pi$
$138$	−3.60915	−0.307231
$139$	0.673158	0.0570966	0.0285483	−	0.999592i	$-0.490912\pi$
$139$	0.673158	0.0570966	0.0285483	+	0.999592i	$0.490912\pi$
$140$	−12.6346	−1.06782
$141$	1.63281	0.137507
$142$	1.17125	0.0982893
$143$	−12.5619	−1.05048
$144$	−2.28738	−0.190615
$145$	0.0123837	0.00102841
$146$	−15.4260	−1.27666
$147$	−9.33045	−0.769562
$148$	0	0
$149$	8.68520	0.711519	0.355760	−	0.934577i	$-0.384222\pi$
$149$	8.68520	0.711519	0.355760	+	0.934577i	$0.384222\pi$
$150$	3.24374	0.264850
$151$	19.2083	1.56315	0.781573	−	0.623814i	$-0.214418\pi$
$151$	19.2083	1.56315	0.781573	+	0.623814i	$0.214418\pi$
$152$	3.63746	0.295037
$153$	−14.8365	−1.19946
$154$	−11.0710	−0.892130
$155$	−17.0227	−1.36730
$156$	4.06975	0.325841
$157$	13.7771	1.09954	0.549768	−	0.835317i	$-0.314716\pi$
$157$	13.7771	1.09954	0.549768	+	0.835317i	$0.314716\pi$
$158$	1.15625	0.0919865
$159$	7.44123	0.590128
$160$	2.97364	0.235087
$161$	−18.1656	−1.43165
$162$	−3.09428	−0.243109
$163$	16.8779	1.32198	0.660988	−	0.750397i	$-0.270138\pi$
$163$	16.8779	1.32198	0.660988	+	0.750397i	$0.270138\pi$
$164$	−5.21988	−0.407604
$165$	6.54081	0.509202
$166$	11.4527	0.888901
$167$	7.73567	0.598604	0.299302	−	0.954158i	$-0.403246\pi$
$167$	7.73567	0.598604	0.299302	+	0.954158i	$0.403246\pi$
$168$	3.58675	0.276724
$169$	10.2423	0.787872
$170$	19.2877	1.47930
$171$	8.32027	0.636267
$172$	6.04556	0.460970
$173$	8.60661	0.654348	0.327174	−	0.944964i	$-0.393904\pi$
$173$	8.60661	0.654348	0.327174	+	0.944964i	$0.393904\pi$
$174$	−0.00351553	−0.000266512 0
$175$	16.3264	1.23416
$176$	2.60565	0.196408
$177$	5.33660	0.401124
$178$	−12.6870	−0.950929
$179$	16.0095	1.19661	0.598303	−	0.801270i	$-0.295842\pi$
$179$	16.0095	1.19661	0.598303	+	0.801270i	$0.295842\pi$
$180$	6.80186	0.506980
$181$	2.45708	0.182634	0.0913168	−	0.995822i	$-0.470892\pi$
$181$	2.45708	0.182634	0.0913168	+	0.995822i	$0.470892\pi$
$182$	20.4839	1.51837
$183$	−5.59575	−0.413650
$184$	4.27541	0.315187
$185$	0	0
$186$	4.83246	0.354333
$187$	16.9008	1.23591
$188$	−1.93422	−0.141068
$189$	18.9645	1.37947
$190$	−10.8165	−0.784711
$191$	13.8365	1.00118	0.500588	−	0.865686i	$-0.333117\pi$
$191$	13.8365	1.00118	0.500588	+	0.865686i	$0.333117\pi$
$192$	−0.844166	−0.0609224
$193$	−23.8334	−1.71556	−0.857782	−	0.514013i	$-0.828158\pi$
$193$	−23.8334	−1.71556	−0.857782	+	0.514013i	$0.828158\pi$
$194$	7.48072	0.537084
$195$	−12.1020	−0.866640
$196$	11.0529	0.789490
$197$	13.6975	0.975907	0.487954	−	0.872870i	$-0.337743\pi$
$197$	13.6975	0.975907	0.487954	+	0.872870i	$0.337743\pi$
$198$	5.96012	0.423567
$199$	−14.9197	−1.05763	−0.528813	−	0.848738i	$-0.677363\pi$
$199$	−14.9197	−1.05763	−0.528813	+	0.848738i	$0.677363\pi$
$200$	−3.84253	−0.271708
$201$	6.22802	0.439291
$202$	0.389623	0.0274138
$203$	−0.0176944	−0.00124191
$204$	−5.47545	−0.383358
$205$	15.5221	1.08411
$206$	−9.59672	−0.668635
$207$	9.77949	0.679722
$208$	−4.82103	−0.334278
$209$	−9.47794	−0.655603
$210$	−10.6657	−0.736003
$211$	20.0203	1.37826	0.689128	−	0.724640i	$-0.257994\pi$
$211$	20.0203	1.37826	0.689128	+	0.724640i	$0.257994\pi$
$212$	−8.81490	−0.605410
$213$	0.988731	0.0677467
$214$	11.6217	0.794445
$215$	−17.9773	−1.22604
$216$	−4.46343	−0.303698
$217$	24.3228	1.65114
$218$	−10.4314	−0.706505
$219$	−13.0221	−0.879951
$220$	−7.74826	−0.522387
$221$	−31.2703	−2.10347
$222$	0	0
$223$	11.4789	0.768686	0.384343	−	0.923190i	$-0.374428\pi$
$223$	11.4789	0.768686	0.384343	+	0.923190i	$0.374428\pi$
$224$	−4.24887	−0.283889
$225$	−8.78935	−0.585957
$226$	1.44558	0.0961582
$227$	10.5204	0.698265	0.349132	−	0.937073i	$-0.386476\pi$
$227$	10.5204	0.698265	0.349132	+	0.937073i	$0.386476\pi$
$228$	3.07062	0.203357
$229$	14.2160	0.939419	0.469710	−	0.882821i	$-0.344359\pi$
$229$	14.2160	0.939419	0.469710	+	0.882821i	$0.344359\pi$
$230$	−12.7135	−0.838304
$231$	−9.34580	−0.614908
$232$	0.00416451	0.000273413 0
$233$	−5.94150	−0.389240	−0.194620	−	0.980879i	$-0.562347\pi$
$233$	−5.94150	−0.389240	−0.194620	+	0.980879i	$0.562347\pi$
$234$	−11.0275	−0.720893
$235$	5.75169	0.375199
$236$	−6.32175	−0.411511
$237$	0.976068	0.0634025
$238$	−27.5591	−1.78639
$239$	2.54774	0.164800	0.0823998	−	0.996599i	$-0.473742\pi$
$239$	2.54774	0.164800	0.0823998	+	0.996599i	$0.473742\pi$
$240$	2.51025	0.162036
$241$	11.9114	0.767282	0.383641	−	0.923482i	$-0.374670\pi$
$241$	11.9114	0.767282	0.383641	+	0.923482i	$0.374670\pi$
$242$	4.21060	0.270668
$243$	−16.0024	−1.02655
$244$	6.62873	0.424361
$245$	−32.8672	−2.09981
$246$	−4.40645	−0.280945
$247$	17.5363	1.11581
$248$	−5.72454	−0.363508
$249$	9.66797	0.612682
$250$	−3.44189	−0.217684
$251$	−13.2076	−0.833655	−0.416827	−	0.908986i	$-0.636858\pi$
$251$	−13.2076	−0.833655	−0.416827	+	0.908986i	$0.636858\pi$
$252$	−9.71879	−0.612226
$253$	−11.1402	−0.700378
$254$	−14.5192	−0.911017
$255$	16.2820	1.01962
$256$	1.00000	0.0625000
$257$	10.7130	0.668258	0.334129	−	0.942527i	$-0.391558\pi$
$257$	10.7130	0.668258	0.334129	+	0.942527i	$0.391558\pi$
$258$	5.10346	0.317727
$259$	0	0
$260$	14.3360	0.889081
$261$	0.00952582	0.000589634 0
$262$	7.28479	0.450056
$263$	−4.64467	−0.286403	−0.143201	−	0.989694i	$-0.545740\pi$
$263$	−4.64467	−0.286403	−0.143201	+	0.989694i	$0.545740\pi$
$264$	2.19960	0.135376
$265$	26.2123	1.61021
$266$	15.4551	0.947612
$267$	−10.7099	−0.655436
$268$	−7.37772	−0.450666
$269$	1.81950	0.110937	0.0554686	−	0.998460i	$-0.482335\pi$
$269$	1.81950	0.110937	0.0554686	+	0.998460i	$0.482335\pi$
$270$	13.2726	0.807747
$271$	−8.95467	−0.543957	−0.271979	−	0.962303i	$-0.587678\pi$
$271$	−8.95467	−0.543957	−0.271979	+	0.962303i	$0.587678\pi$
$272$	6.48622	0.393285
$273$	17.2918	1.04655
$274$	−17.0539	−1.03027
$275$	10.0123	0.603764
$276$	3.60915	0.217245
$277$	16.2243	0.974825	0.487413	−	0.873172i	$-0.337941\pi$
$277$	16.2243	0.974825	0.487413	+	0.873172i	$0.337941\pi$
$278$	−0.673158	−0.0403734
$279$	−13.0942	−0.783930
$280$	12.6346	0.755062
$281$	−18.0689	−1.07790	−0.538949	−	0.842338i	$-0.681178\pi$
$281$	−18.0689	−1.07790	−0.538949	+	0.842338i	$0.681178\pi$
$282$	−1.63281	−0.0972322
$283$	23.8536	1.41795	0.708976	−	0.705233i	$-0.249158\pi$
$283$	23.8536	1.41795	0.708976	+	0.705233i	$0.249158\pi$
$284$	−1.17125	−0.0695010
$285$	−9.13092	−0.540869
$286$	12.5619	0.742801
$287$	−22.1786	−1.30916
$288$	2.28738	0.134785
$289$	25.0711	1.47477
$290$	−0.0123837	−0.000727198 0
$291$	6.31497	0.370190
$292$	15.4260	0.902737
$293$	21.4472	1.25296	0.626478	−	0.779439i	$-0.284496\pi$
$293$	21.4472	1.25296	0.626478	+	0.779439i	$0.284496\pi$
$294$	9.33045	0.544163
$295$	18.7986	1.09450
$296$	0	0
$297$	11.6301	0.674848
$298$	−8.68520	−0.503120
$299$	20.6119	1.19201
$300$	−3.24374	−0.187277
$301$	25.6868	1.48056
$302$	−19.2083	−1.10531
$303$	0.328906	0.0188952
$304$	−3.63746	−0.208623
$305$	−19.7115	−1.12867
$306$	14.8365	0.848145
$307$	−28.4841	−1.62567	−0.812837	−	0.582491i	$-0.802078\pi$
$307$	−28.4841	−1.62567	−0.812837	+	0.582491i	$0.802078\pi$
$308$	11.0710	0.630831
$309$	−8.10123	−0.460863
$310$	17.0227	0.966825
$311$	−26.5499	−1.50551	−0.752753	−	0.658303i	$-0.771274\pi$
$311$	−26.5499	−1.50551	−0.752753	+	0.658303i	$0.771274\pi$
$312$	−4.06975	−0.230404
$313$	31.7094	1.79232	0.896160	−	0.443731i	$-0.146345\pi$
$313$	31.7094	1.79232	0.896160	+	0.443731i	$0.146345\pi$
$314$	−13.7771	−0.777489
$315$	28.9002	1.62834
$316$	−1.15625	−0.0650443
$317$	−0.752284	−0.0422525	−0.0211262	−	0.999777i	$-0.506725\pi$
$317$	−0.752284	−0.0422525	−0.0211262	+	0.999777i	$0.506725\pi$
$318$	−7.44123	−0.417284
$319$	−0.0108512	−0.000607553 0
$320$	−2.97364	−0.166232
$321$	9.81066	0.547578
$322$	18.1656	1.01233
$323$	−23.5934	−1.31277
$324$	3.09428	0.171904
$325$	−18.5250	−1.02758
$326$	−16.8779	−0.934778
$327$	−8.80585	−0.486964
$328$	5.21988	0.288220
$329$	−8.21826	−0.453087
$330$	−6.54081	−0.360060
$331$	−0.459790	−0.0252724	−0.0126362	−	0.999920i	$-0.504022\pi$
$331$	−0.459790	−0.0252724	−0.0126362	+	0.999920i	$0.504022\pi$
$332$	−11.4527	−0.628548
$333$	0	0
$334$	−7.73567	−0.423277
$335$	21.9387	1.19864
$336$	−3.58675	−0.195673
$337$	0.863055	0.0470136	0.0235068	−	0.999724i	$-0.492517\pi$
$337$	0.863055	0.0470136	0.0235068	+	0.999724i	$0.492517\pi$
$338$	−10.2423	−0.557109
$339$	1.22031	0.0662779
$340$	−19.2877	−1.04602
$341$	14.9161	0.807754
$342$	−8.32027	−0.449909
$343$	17.2201	0.929796
$344$	−6.04556	−0.325955
$345$	−10.7323	−0.577808
$346$	−8.60661	−0.462694
$347$	16.3171	0.875948	0.437974	−	0.898988i	$-0.355696\pi$
$347$	16.3171	0.875948	0.437974	+	0.898988i	$0.355696\pi$
$348$	0.00351553	0.000188452 0
$349$	−2.71625	−0.145397	−0.0726986	−	0.997354i	$-0.523161\pi$
$349$	−2.71625	−0.145397	−0.0726986	+	0.997354i	$0.523161\pi$
$350$	−16.3264	−0.872683
$351$	−21.5183	−1.14856
$352$	−2.60565	−0.138881
$353$	−6.01145	−0.319957	−0.159979	−	0.987120i	$-0.551143\pi$
$353$	−6.01145	−0.319957	−0.159979	+	0.987120i	$0.551143\pi$
$354$	−5.33660	−0.283637
$355$	3.48288	0.184852
$356$	12.6870	0.672408
$357$	−23.2644	−1.23128
$358$	−16.0095	−0.846129
$359$	−1.15424	−0.0609182	−0.0304591	−	0.999536i	$-0.509697\pi$
$359$	−1.15424	−0.0609182	−0.0304591	+	0.999536i	$0.509697\pi$
$360$	−6.80186	−0.358489
$361$	−5.76888	−0.303625
$362$	−2.45708	−0.129141
$363$	3.55444	0.186560
$364$	−20.4839	−1.07365
$365$	−45.8713	−2.40101
$366$	5.59575	0.292494
$367$	22.9469	1.19782	0.598909	−	0.800817i	$-0.295601\pi$
$367$	22.9469	1.19782	0.598909	+	0.800817i	$0.295601\pi$
$368$	−4.27541	−0.222871
$369$	11.9399	0.621565
$370$	0	0
$371$	−37.4533	−1.94448
$372$	−4.83246	−0.250551
$373$	−22.7669	−1.17883	−0.589414	−	0.807831i	$-0.700641\pi$
$373$	−22.7669	−1.17883	−0.589414	+	0.807831i	$0.700641\pi$
$374$	−16.9008	−0.873920
$375$	−2.90552	−0.150041
$376$	1.93422	0.0997500
$377$	0.0200772	0.00103403
$378$	−18.9645	−0.975429
$379$	13.7986	0.708787	0.354393	−	0.935096i	$-0.384687\pi$
$379$	13.7986	0.708787	0.354393	+	0.935096i	$0.384687\pi$
$380$	10.8165	0.554875
$381$	−12.2566	−0.627926
$382$	−13.8365	−0.707938
$383$	19.8710	1.01536	0.507680	−	0.861546i	$-0.330503\pi$
$383$	19.8710	1.01536	0.507680	+	0.861546i	$0.330503\pi$
$384$	0.844166	0.0430787
$385$	−32.9213	−1.67783
$386$	23.8334	1.21309
$387$	−13.8285	−0.702943
$388$	−7.48072	−0.379776
$389$	−5.99016	−0.303713	−0.151856	−	0.988403i	$-0.548525\pi$
$389$	−5.99016	−0.303713	−0.151856	+	0.988403i	$0.548525\pi$
$390$	12.1020	0.612807
$391$	−27.7312	−1.40243
$392$	−11.0529	−0.558254
$393$	6.14957	0.310205
$394$	−13.6975	−0.690071
$395$	3.43828	0.172998
$396$	−5.96012	−0.299507
$397$	13.5296	0.679032	0.339516	−	0.940600i	$-0.389737\pi$
$397$	13.5296	0.679032	0.339516	+	0.940600i	$0.389737\pi$
$398$	14.9197	0.747855
$399$	13.0466	0.653149
$400$	3.84253	0.192127
$401$	−12.7845	−0.638429	−0.319214	−	0.947682i	$-0.603419\pi$
$401$	−12.7845	−0.638429	−0.319214	+	0.947682i	$0.603419\pi$
$402$	−6.22802	−0.310625
$403$	−27.5982	−1.37476
$404$	−0.389623	−0.0193845
$405$	−9.20127	−0.457215
$406$	0.0176944	0.000878160 0
$407$	0	0
$408$	5.47545	0.271075
$409$	4.00498	0.198034	0.0990169	−	0.995086i	$-0.468430\pi$
$409$	4.00498	0.198034	0.0990169	+	0.995086i	$0.468430\pi$
$410$	−15.5221	−0.766580
$411$	−14.3963	−0.710119
$412$	9.59672	0.472797
$413$	−26.8603	−1.32171
$414$	−9.77949	−0.480636
$415$	34.0562	1.67175
$416$	4.82103	0.236370
$417$	−0.568257	−0.0278277
$418$	9.47794	0.463581
$419$	−0.214332	−0.0104708	−0.00523541	−	0.999986i	$-0.501666\pi$
$419$	−0.214332	−0.0104708	−0.00523541	+	0.999986i	$0.501666\pi$
$420$	10.6657	0.520433
$421$	6.58975	0.321165	0.160582	−	0.987022i	$-0.448663\pi$
$421$	6.58975	0.321165	0.160582	+	0.987022i	$0.448663\pi$
$422$	−20.0203	−0.974574
$423$	4.42431	0.215118
$424$	8.81490	0.428089
$425$	24.9235	1.20897
$426$	−0.988731	−0.0479042
$427$	28.1646	1.36298
$428$	−11.6217	−0.561757
$429$	10.6043	0.511982
$430$	17.9773	0.866943
$431$	23.5924	1.13641	0.568204	−	0.822888i	$-0.307638\pi$
$431$	23.5924	1.13641	0.568204	+	0.822888i	$0.307638\pi$
$432$	4.46343	0.214747
$433$	−39.5320	−1.89979	−0.949894	−	0.312571i	$-0.898810\pi$
$433$	−39.5320	−1.89979	−0.949894	+	0.312571i	$0.898810\pi$
$434$	−24.3228	−1.16753
$435$	−0.0104539	−0.000501228 0
$436$	10.4314	0.499574
$437$	15.5516	0.743935
$438$	13.0221	0.622219
$439$	19.2088	0.916787	0.458394	−	0.888749i	$-0.348425\pi$
$439$	19.2088	0.916787	0.458394	+	0.888749i	$0.348425\pi$
$440$	7.74826	0.369384
$441$	−25.2821	−1.20391
$442$	31.2703	1.48737
$443$	−20.7703	−0.986827	−0.493413	−	0.869795i	$-0.664251\pi$
$443$	−20.7703	−0.986827	−0.493413	+	0.869795i	$0.664251\pi$
$444$	0	0
$445$	−37.7265	−1.78841
$446$	−11.4789	−0.543543
$447$	−7.33175	−0.346780
$448$	4.24887	0.200740
$449$	−3.77753	−0.178273	−0.0891363	−	0.996019i	$-0.528411\pi$
$449$	−3.77753	−0.178273	−0.0891363	+	0.996019i	$0.528411\pi$
$450$	8.78935	0.414334
$451$	−13.6012	−0.640454
$452$	−1.44558	−0.0679941
$453$	−16.2149	−0.761845
$454$	−10.5204	−0.493748
$455$	60.9118	2.85559
$456$	−3.07062	−0.143795
$457$	20.9464	0.979832	0.489916	−	0.871770i	$-0.337028\pi$
$457$	20.9464	0.979832	0.489916	+	0.871770i	$0.337028\pi$
$458$	−14.2160	−0.664270
$459$	28.9508	1.35131
$460$	12.7135	0.592771
$461$	−8.27065	−0.385202	−0.192601	−	0.981277i	$-0.561692\pi$
$461$	−8.27065	−0.385202	−0.192601	+	0.981277i	$0.561692\pi$
$462$	9.34580	0.434806
$463$	12.9800	0.603232	0.301616	−	0.953429i	$-0.402474\pi$
$463$	12.9800	0.603232	0.301616	+	0.953429i	$0.402474\pi$
$464$	−0.00416451	−0.000193332 0
$465$	14.3700	0.666392
$466$	5.94150	0.275234
$467$	29.0797	1.34565	0.672825	−	0.739802i	$-0.265081\pi$
$467$	29.0797	1.34565	0.672825	+	0.739802i	$0.265081\pi$
$468$	11.0275	0.509749
$469$	−31.3469	−1.44747
$470$	−5.75169	−0.265306
$471$	−11.6302	−0.535891
$472$	6.32175	0.290982
$473$	15.7526	0.724305
$474$	−0.976068	−0.0448323
$475$	−13.9771	−0.641312
$476$	27.5591	1.26317
$477$	20.1631	0.923203
$478$	−2.54774	−0.116531
$479$	22.6214	1.03360	0.516799	−	0.856107i	$-0.327124\pi$
$479$	22.6214	1.03360	0.516799	+	0.856107i	$0.327124\pi$
$480$	−2.51025	−0.114576
$481$	0	0
$482$	−11.9114	−0.542550
$483$	15.3348	0.697757
$484$	−4.21060	−0.191391
$485$	22.2450	1.01009
$486$	16.0024	0.725882
$487$	−16.6885	−0.756228	−0.378114	−	0.925759i	$-0.623427\pi$
$487$	−16.6885	−0.756228	−0.378114	+	0.925759i	$0.623427\pi$
$488$	−6.62873	−0.300069
$489$	−14.2477	−0.644304
$490$	32.8672	1.48479
$491$	−4.17667	−0.188490	−0.0942452	−	0.995549i	$-0.530044\pi$
$491$	−4.17667	−0.188490	−0.0942452	+	0.995549i	$0.530044\pi$
$492$	4.40645	0.198658
$493$	−0.0270119	−0.00121656
$494$	−17.5363	−0.788996
$495$	17.7232	0.796600
$496$	5.72454	0.257039
$497$	−4.97649	−0.223226
$498$	−9.66797	−0.433232
$499$	6.05947	0.271259	0.135630	−	0.990760i	$-0.456694\pi$
$499$	6.05947	0.271259	0.135630	+	0.990760i	$0.456694\pi$
$500$	3.44189	0.153926
$501$	−6.53019	−0.291747
$502$	13.2076	0.589483
$503$	38.1524	1.70113	0.850567	−	0.525867i	$-0.176259\pi$
$503$	38.1524	1.70113	0.850567	+	0.525867i	$0.176259\pi$
$504$	9.71879	0.432909
$505$	1.15860	0.0515570
$506$	11.1402	0.495242
$507$	−8.64623	−0.383992
$508$	14.5192	0.644187
$509$	−27.5529	−1.22126	−0.610631	−	0.791915i	$-0.709084\pi$
$509$	−27.5529	−1.22126	−0.610631	+	0.791915i	$0.709084\pi$
$510$	−16.2820	−0.720979
$511$	65.5429	2.89945
$512$	−1.00000	−0.0441942
$513$	−16.2355	−0.716817
$514$	−10.7130	−0.472530
$515$	−28.5372	−1.25750
$516$	−5.10346	−0.224667
$517$	−5.03991	−0.221655
$518$	0	0
$519$	−7.26541	−0.318916
$520$	−14.3360	−0.628675
$521$	25.9296	1.13600	0.567998	−	0.823030i	$-0.307718\pi$
$521$	25.9296	1.13600	0.567998	+	0.823030i	$0.307718\pi$
$522$	−0.00952582	−0.000416934 0
$523$	−30.7006	−1.34244	−0.671221	−	0.741257i	$-0.734230\pi$
$523$	−30.7006	−1.34244	−0.671221	+	0.741257i	$0.734230\pi$
$524$	−7.28479	−0.318237
$525$	−13.7822	−0.601504
$526$	4.64467	0.202517
$527$	37.1306	1.61743
$528$	−2.19960	−0.0957252
$529$	−4.72091	−0.205257
$530$	−26.2123	−1.13859
$531$	14.4603	0.627522
$532$	−15.4551	−0.670063
$533$	25.1652	1.09003
$534$	10.7099	0.463463
$535$	34.5588	1.49411
$536$	7.37772	0.318669
$537$	−13.5147	−0.583201
$538$	−1.81950	−0.0784444
$539$	28.7999	1.24050
$540$	−13.2726	−0.571163
$541$	−33.6240	−1.44561	−0.722804	−	0.691053i	$-0.757147\pi$
$541$	−33.6240	−1.44561	−0.722804	+	0.691053i	$0.757147\pi$
$542$	8.95467	0.384636
$543$	−2.07419	−0.0890118
$544$	−6.48622	−0.278094
$545$	−31.0193	−1.32872
$546$	−17.2918	−0.740021
$547$	2.11075	0.0902490	0.0451245	−	0.998981i	$-0.485632\pi$
$547$	2.11075	0.0902490	0.0451245	+	0.998981i	$0.485632\pi$
$548$	17.0539	0.728507
$549$	−15.1625	−0.647118
$550$	−10.0123	−0.426925
$551$	0.0151482	0.000645336 0
$552$	−3.60915	−0.153616
$553$	−4.91276	−0.208912
$554$	−16.2243	−0.689305
$555$	0	0
$556$	0.673158	0.0285483
$557$	−43.9495	−1.86220	−0.931099	−	0.364766i	$-0.881149\pi$
$557$	−43.9495	−1.86220	−0.931099	+	0.364766i	$0.881149\pi$
$558$	13.0942	0.554322
$559$	−29.1458	−1.23274
$560$	−12.6346	−0.533909
$561$	−14.2671	−0.602357
$562$	18.0689	0.762189
$563$	−22.2050	−0.935829	−0.467914	−	0.883774i	$-0.654994\pi$
$563$	−22.2050	−0.935829	−0.467914	+	0.883774i	$0.654994\pi$
$564$	1.63281	0.0687536
$565$	4.29862	0.180844
$566$	−23.8536	−1.00264
$567$	13.1472	0.552129
$568$	1.17125	0.0491447
$569$	9.29682	0.389743	0.194872	−	0.980829i	$-0.437571\pi$
$569$	9.29682	0.389743	0.194872	+	0.980829i	$0.437571\pi$
$570$	9.13092	0.382452
$571$	26.0335	1.08947	0.544734	−	0.838609i	$-0.316631\pi$
$571$	26.0335	1.08947	0.544734	+	0.838609i	$0.316631\pi$
$572$	−12.5619	−0.525240
$573$	−11.6803	−0.487952
$574$	22.1786	0.925716
$575$	−16.4284	−0.685111
$576$	−2.28738	−0.0953077
$577$	−7.25977	−0.302228	−0.151114	−	0.988516i	$-0.548286\pi$
$577$	−7.25977	−0.302228	−0.151114	+	0.988516i	$0.548286\pi$
$578$	−25.0711	−1.04282
$579$	20.1193	0.836131
$580$	0.0123837	0.000514207 0
$581$	−48.6609	−2.01880
$582$	−6.31497	−0.261764
$583$	−22.9685	−0.951259
$584$	−15.4260	−0.638332
$585$	−32.7920	−1.35578
$586$	−21.4472	−0.885974
$587$	12.6919	0.523852	0.261926	−	0.965088i	$-0.415642\pi$
$587$	12.6919	0.523852	0.261926	+	0.965088i	$0.415642\pi$
$588$	−9.33045	−0.384781
$589$	−20.8228	−0.857988
$590$	−18.7986	−0.773926
$591$	−11.5630	−0.475637
$592$	0	0
$593$	13.5269	0.555485	0.277743	−	0.960656i	$-0.410414\pi$
$593$	13.5269	0.555485	0.277743	+	0.960656i	$0.410414\pi$
$594$	−11.6301	−0.477190
$595$	−81.9508	−3.35965
$596$	8.68520	0.355760
$597$	12.5947	0.515466
$598$	−20.6119	−0.842882
$599$	−10.0519	−0.410711	−0.205355	−	0.978687i	$-0.565835\pi$
$599$	−10.0519	−0.410711	−0.205355	+	0.978687i	$0.565835\pi$
$600$	3.24374	0.132425
$601$	3.71622	0.151588	0.0757940	−	0.997123i	$-0.475851\pi$
$601$	3.71622	0.151588	0.0757940	+	0.997123i	$0.475851\pi$
$602$	−25.6868	−1.04691
$603$	16.8757	0.687231
$604$	19.2083	0.781573
$605$	12.5208	0.509043
$606$	−0.328906	−0.0133609
$607$	21.8103	0.885251	0.442626	−	0.896707i	$-0.354047\pi$
$607$	21.8103	0.885251	0.442626	+	0.896707i	$0.354047\pi$
$608$	3.63746	0.147518
$609$	0.0149370	0.000605279 0
$610$	19.7115	0.798094
$611$	9.32496	0.377247
$612$	−14.8365	−0.599729
$613$	20.6795	0.835239	0.417619	−	0.908622i	$-0.362865\pi$
$613$	20.6795	0.835239	0.417619	+	0.908622i	$0.362865\pi$
$614$	28.4841	1.14953
$615$	−13.1032	−0.528372
$616$	−11.0710	−0.446065
$617$	32.3777	1.30348	0.651739	−	0.758443i	$-0.274040\pi$
$617$	32.3777	1.30348	0.651739	+	0.758443i	$0.274040\pi$
$618$	8.10123	0.325879
$619$	16.2258	0.652170	0.326085	−	0.945341i	$-0.394270\pi$
$619$	16.2258	0.652170	0.326085	+	0.945341i	$0.394270\pi$
$620$	−17.0227	−0.683649
$621$	−19.0830	−0.765773
$622$	26.5499	1.06455
$623$	53.9053	2.15967
$624$	4.06975	0.162920
$625$	−29.4476	−1.17790
$626$	−31.7094	−1.26736
$627$	8.00095	0.319527
$628$	13.7771	0.549768
$629$	0	0
$630$	−28.9002	−1.15141
$631$	−46.4818	−1.85041	−0.925206	−	0.379465i	$-0.876108\pi$
$631$	−46.4818	−1.85041	−0.925206	+	0.379465i	$0.876108\pi$
$632$	1.15625	0.0459932
$633$	−16.9005	−0.671733
$634$	0.752284	0.0298770
$635$	−43.1750	−1.71335
$636$	7.44123	0.295064
$637$	−53.2862	−2.11127
$638$	0.0108512	0.000429605 0
$639$	2.67910	0.105984
$640$	2.97364	0.117543
$641$	−42.8908	−1.69409	−0.847043	−	0.531525i	$-0.821619\pi$
$641$	−42.8908	−1.69409	−0.847043	+	0.531525i	$0.821619\pi$
$642$	−9.81066	−0.387196
$643$	−10.9395	−0.431410	−0.215705	−	0.976459i	$-0.569205\pi$
$643$	−10.9395	−0.431410	−0.215705	+	0.976459i	$0.569205\pi$
$644$	−18.1656	−0.715826
$645$	15.1758	0.597548
$646$	23.5934	0.928269
$647$	−32.2390	−1.26745	−0.633723	−	0.773560i	$-0.718474\pi$
$647$	−32.2390	−1.26745	−0.633723	+	0.773560i	$0.718474\pi$
$648$	−3.09428	−0.121555
$649$	−16.4723	−0.646592
$650$	18.5250	0.726609
$651$	−20.5325	−0.804731
$652$	16.8779	0.660988
$653$	35.0809	1.37282	0.686411	−	0.727214i	$-0.259185\pi$
$653$	35.0809	1.37282	0.686411	+	0.727214i	$0.259185\pi$
$654$	8.80585	0.344336
$655$	21.6623	0.846417
$656$	−5.21988	−0.203802
$657$	−35.2851	−1.37660
$658$	8.21826	0.320381
$659$	−37.4507	−1.45887	−0.729437	−	0.684048i	$-0.760218\pi$
$659$	−37.4507	−1.45887	−0.729437	+	0.684048i	$0.760218\pi$
$660$	6.54081	0.254601
$661$	−40.0165	−1.55646	−0.778232	−	0.627977i	$-0.783883\pi$
$661$	−40.0165	−1.55646	−0.778232	+	0.627977i	$0.783883\pi$
$662$	0.459790	0.0178703
$663$	26.3973	1.02519
$664$	11.4527	0.444450
$665$	45.9578	1.78217
$666$	0	0
$667$	0.0178050	0.000689410 0
$668$	7.73567	0.299302
$669$	−9.69012	−0.374642
$670$	−21.9387	−0.847565
$671$	17.2721	0.666783
$672$	3.58675	0.138362
$673$	−38.5553	−1.48620	−0.743098	−	0.669182i	$-0.766644\pi$
$673$	−38.5553	−1.48620	−0.743098	+	0.669182i	$0.766644\pi$
$674$	−0.863055	−0.0332436
$675$	17.1509	0.660138
$676$	10.2423	0.393936
$677$	34.6376	1.33123	0.665615	−	0.746295i	$-0.268169\pi$
$677$	34.6376	1.33123	0.665615	+	0.746295i	$0.268169\pi$
$678$	−1.22031	−0.0468655
$679$	−31.7846	−1.21978
$680$	19.2877	0.739649
$681$	−8.88098	−0.340320
$682$	−14.9161	−0.571168
$683$	7.99015	0.305735	0.152867	−	0.988247i	$-0.451149\pi$
$683$	7.99015	0.305735	0.152867	+	0.988247i	$0.451149\pi$
$684$	8.32027	0.318133
$685$	−50.7122	−1.93761
$686$	−17.2201	−0.657465
$687$	−12.0007	−0.457853
$688$	6.04556	0.230485
$689$	42.4969	1.61900
$690$	10.7323	0.408572
$691$	−29.9403	−1.13898	−0.569491	−	0.821997i	$-0.692860\pi$
$691$	−29.9403	−1.13898	−0.569491	+	0.821997i	$0.692860\pi$
$692$	8.60661	0.327174
$693$	−25.3237	−0.961969
$694$	−16.3171	−0.619389
$695$	−2.00173	−0.0759300
$696$	−0.00351553	−0.000133256 0
$697$	−33.8573	−1.28244
$698$	2.71625	0.102811
$699$	5.01561	0.189708
$700$	16.3264	0.617080
$701$	21.0605	0.795443	0.397722	−	0.917506i	$-0.369801\pi$
$701$	21.0605	0.795443	0.397722	+	0.917506i	$0.369801\pi$
$702$	21.5183	0.812157
$703$	0	0
$704$	2.60565	0.0982040
$705$	−4.85538	−0.182864
$706$	6.01145	0.226244
$707$	−1.65546	−0.0622598
$708$	5.33660	0.200562
$709$	4.40490	0.165429	0.0827147	−	0.996573i	$-0.473641\pi$
$709$	4.40490	0.165429	0.0827147	+	0.996573i	$0.473641\pi$
$710$	−3.48288	−0.130710
$711$	2.64479	0.0991875
$712$	−12.6870	−0.475465
$713$	−24.4747	−0.916585
$714$	23.2644	0.870650
$715$	37.3546	1.39698
$716$	16.0095	0.598303
$717$	−2.15071	−0.0803199
$718$	1.15424	0.0430757
$719$	−36.9834	−1.37925	−0.689623	−	0.724168i	$-0.742224\pi$
$719$	−36.9834	−1.37925	−0.689623	+	0.724168i	$0.742224\pi$
$720$	6.80186	0.253490
$721$	40.7752	1.51855
$722$	5.76888	0.214696
$723$	−10.0552	−0.373957
$724$	2.45708	0.0913168
$725$	−0.0160023	−0.000594309 0
$726$	−3.55444	−0.131918
$727$	13.8883	0.515088	0.257544	−	0.966267i	$-0.417087\pi$
$727$	13.8883	0.515088	0.257544	+	0.966267i	$0.417087\pi$
$728$	20.4839	0.759184
$729$	4.22582	0.156512
$730$	45.8713	1.69777
$731$	39.2128	1.45034
$732$	−5.59575	−0.206825
$733$	17.6695	0.652639	0.326320	−	0.945259i	$-0.394191\pi$
$733$	17.6695	0.652639	0.326320	+	0.945259i	$0.394191\pi$
$734$	−22.9469	−0.846986
$735$	27.7454	1.02340
$736$	4.27541	0.157594
$737$	−19.2237	−0.708116
$738$	−11.9399	−0.439513
$739$	−40.5432	−1.49140	−0.745702	−	0.666279i	$-0.767886\pi$
$739$	−40.5432	−1.49140	−0.745702	+	0.666279i	$0.767886\pi$
$740$	0	0
$741$	−14.8035	−0.543822
$742$	37.4533	1.37495
$743$	−47.3389	−1.73669	−0.868347	−	0.495956i	$-0.834818\pi$
$743$	−47.3389	−1.73669	−0.868347	+	0.495956i	$0.834818\pi$
$744$	4.83246	0.177167
$745$	−25.8267	−0.946216
$746$	22.7669	0.833557
$747$	26.1967	0.958487
$748$	16.9008	0.617955
$749$	−49.3791	−1.80427
$750$	2.90552	0.106095
$751$	−16.9082	−0.616989	−0.308494	−	0.951226i	$-0.599825\pi$
$751$	−16.9082	−0.616989	−0.308494	+	0.951226i	$0.599825\pi$
$752$	−1.93422	−0.0705339
$753$	11.1494	0.406306
$754$	−0.0200772	−0.000731169 0
$755$	−57.1184	−2.07875
$756$	18.9645	0.689733
$757$	−42.3132	−1.53790	−0.768950	−	0.639309i	$-0.779220\pi$
$757$	−42.3132	−1.53790	−0.768950	+	0.639309i	$0.779220\pi$
$758$	−13.7986	−0.501188
$759$	9.40418	0.341350
$760$	−10.8165	−0.392356
$761$	−26.9374	−0.976480	−0.488240	−	0.872709i	$-0.662361\pi$
$761$	−26.9374	−0.976480	−0.488240	+	0.872709i	$0.662361\pi$
$762$	12.2566	0.444011
$763$	44.3217	1.60455
$764$	13.8365	0.500588
$765$	44.1183	1.59510
$766$	−19.8710	−0.717968
$767$	30.4773	1.10047
$768$	−0.844166	−0.0304612
$769$	5.98222	0.215724	0.107862	−	0.994166i	$-0.465599\pi$
$769$	5.98222	0.215724	0.107862	+	0.994166i	$0.465599\pi$
$770$	32.9213	1.18640
$771$	−9.04354	−0.325695
$772$	−23.8334	−0.857782
$773$	25.9471	0.933254	0.466627	−	0.884454i	$-0.345469\pi$
$773$	25.9471	0.933254	0.466627	+	0.884454i	$0.345469\pi$
$774$	13.8285	0.497056
$775$	21.9967	0.790146
$776$	7.48072	0.268542
$777$	0	0
$778$	5.99016	0.214758
$779$	18.9871	0.680284
$780$	−12.1020	−0.433320
$781$	−3.05187	−0.109205
$782$	27.7312	0.991666
$783$	−0.0185880	−0.000664280 0
$784$	11.0529	0.394745
$785$	−40.9683	−1.46222
$786$	−6.14957	−0.219348
$787$	31.4132	1.11976	0.559881	−	0.828573i	$-0.310847\pi$
$787$	31.4132	1.11976	0.559881	+	0.828573i	$0.310847\pi$
$788$	13.6975	0.487954
$789$	3.92087	0.139587
$790$	−3.43828	−0.122328
$791$	−6.14206	−0.218386
$792$	5.96012	0.211784
$793$	−31.9573	−1.13484
$794$	−13.5296	−0.480148
$795$	−22.1276	−0.784783
$796$	−14.9197	−0.528813
$797$	−33.3671	−1.18192	−0.590961	−	0.806700i	$-0.701251\pi$
$797$	−33.3671	−1.18192	−0.590961	+	0.806700i	$0.701251\pi$
$798$	−13.0466	−0.461846
$799$	−12.5458	−0.443839
$800$	−3.84253	−0.135854
$801$	−29.0200	−1.02537
$802$	12.7845	0.451437
$803$	40.1947	1.41844
$804$	6.22802	0.219645
$805$	54.0180	1.90388
$806$	27.5982	0.972104
$807$	−1.53596	−0.0540685
$808$	0.389623	0.0137069
$809$	−34.4506	−1.21122	−0.605609	−	0.795762i	$-0.707070\pi$
$809$	−34.4506	−1.21122	−0.605609	+	0.795762i	$0.707070\pi$
$810$	9.20127	0.323300
$811$	6.59421	0.231554	0.115777	−	0.993275i	$-0.463064\pi$
$811$	6.59421	0.231554	0.115777	+	0.993275i	$0.463064\pi$
$812$	−0.0176944	−0.000620953 0
$813$	7.55922	0.265114
$814$	0	0
$815$	−50.1887	−1.75803
$816$	−5.47545	−0.191679
$817$	−21.9905	−0.769350
$818$	−4.00498	−0.140031
$819$	46.8546	1.63723
$820$	15.5221	0.542054
$821$	53.6254	1.87154	0.935770	−	0.352611i	$-0.114706\pi$
$821$	53.6254	1.87154	0.935770	+	0.352611i	$0.114706\pi$
$822$	14.3963	0.502130
$823$	50.6719	1.76631	0.883156	−	0.469080i	$-0.155414\pi$
$823$	50.6719	1.76631	0.883156	+	0.469080i	$0.155414\pi$
$824$	−9.59672	−0.334318
$825$	−8.45203	−0.294262
$826$	26.8603	0.934588
$827$	−24.0982	−0.837977	−0.418988	−	0.907992i	$-0.637615\pi$
$827$	−24.0982	−0.837977	−0.418988	+	0.907992i	$0.637615\pi$
$828$	9.77949	0.339861
$829$	−22.9240	−0.796184	−0.398092	−	0.917346i	$-0.630328\pi$
$829$	−22.9240	−0.796184	−0.398092	+	0.917346i	$0.630328\pi$
$830$	−34.0562	−1.18211
$831$	−13.6960	−0.475110
$832$	−4.82103	−0.167139
$833$	71.6913	2.48396
$834$	0.568257	0.0196771
$835$	−23.0031	−0.796055
$836$	−9.47794	−0.327801
$837$	25.5511	0.883174
$838$	0.214332	0.00740398
$839$	8.56505	0.295698	0.147849	−	0.989010i	$-0.452765\pi$
$839$	8.56505	0.295698	0.147849	+	0.989010i	$0.452765\pi$
$840$	−10.6657	−0.368001
$841$	−29.0000	−0.999999
$842$	−6.58975	−0.227098
$843$	15.2531	0.525345
$844$	20.0203	0.689128
$845$	−30.4570	−1.04775
$846$	−4.42431	−0.152111
$847$	−17.8903	−0.614717
$848$	−8.81490	−0.302705
$849$	−20.1364	−0.691080
$850$	−24.9235	−0.854870
$851$	0	0
$852$	0.988731	0.0338734
$853$	19.7948	0.677760	0.338880	−	0.940830i	$-0.389952\pi$
$853$	19.7948	0.677760	0.338880	+	0.940830i	$0.389952\pi$
$854$	−28.1646	−0.963772
$855$	−24.7415	−0.846141
$856$	11.6217	0.397222
$857$	27.3087	0.932848	0.466424	−	0.884561i	$-0.345542\pi$
$857$	27.3087	0.932848	0.466424	+	0.884561i	$0.345542\pi$
$858$	−10.6043	−0.362026
$859$	−1.84587	−0.0629803	−0.0314902	−	0.999504i	$-0.510025\pi$
$859$	−1.84587	−0.0629803	−0.0314902	+	0.999504i	$0.510025\pi$
$860$	−17.9773	−0.613022
$861$	18.7224	0.638058
$862$	−23.5924	−0.803562
$863$	−23.9388	−0.814886	−0.407443	−	0.913231i	$-0.633579\pi$
$863$	−23.9388	−0.814886	−0.407443	+	0.913231i	$0.633579\pi$
$864$	−4.46343	−0.151849
$865$	−25.5930	−0.870187
$866$	39.5320	1.34335
$867$	−21.1641	−0.718772
$868$	24.3228	0.825569
$869$	−3.01279	−0.102202
$870$	0.0104539	0.000354421 0
$871$	35.5682	1.20518
$872$	−10.4314	−0.353252
$873$	17.1113	0.579129
$874$	−15.5516	−0.526041
$875$	14.6241	0.494386
$876$	−13.0221	−0.439975
$877$	−21.6840	−0.732217	−0.366109	−	0.930572i	$-0.619310\pi$
$877$	−21.6840	−0.732217	−0.366109	+	0.930572i	$0.619310\pi$
$878$	−19.2088	−0.648267
$879$	−18.1050	−0.610665
$880$	−7.74826	−0.261194
$881$	28.1195	0.947371	0.473685	−	0.880694i	$-0.342923\pi$
$881$	28.1195	0.947371	0.473685	+	0.880694i	$0.342923\pi$
$882$	25.2821	0.851294
$883$	−21.8797	−0.736312	−0.368156	−	0.929764i	$-0.620011\pi$
$883$	−21.8797	−0.736312	−0.368156	+	0.929764i	$0.620011\pi$
$884$	−31.2703	−1.05173
$885$	−15.8691	−0.533435
$886$	20.7703	0.697792
$887$	39.9963	1.34295	0.671473	−	0.741029i	$-0.265662\pi$
$887$	39.9963	1.34295	0.671473	+	0.741029i	$0.265662\pi$
$888$	0	0
$889$	61.6903	2.06902
$890$	37.7265	1.26460
$891$	8.06260	0.270107
$892$	11.4789	0.384343
$893$	7.03567	0.235440
$894$	7.33175	0.245210
$895$	−47.6065	−1.59131
$896$	−4.24887	−0.141945
$897$	−17.3998	−0.580963
$898$	3.77753	0.126058
$899$	−0.0238399	−0.000795104 0
$900$	−8.78935	−0.292978
$901$	−57.1754	−1.90479
$902$	13.6012	0.452870
$903$	−21.6839	−0.721595
$904$	1.44558	0.0480791
$905$	−7.30648	−0.242876
$906$	16.2149	0.538706
$907$	−5.40981	−0.179630	−0.0898148	−	0.995958i	$-0.528628\pi$
$907$	−5.40981	−0.179630	−0.0898148	+	0.995958i	$0.528628\pi$
$908$	10.5204	0.349132
$909$	0.891217	0.0295598
$910$	−60.9118	−2.01921
$911$	−0.154456	−0.00511737	−0.00255869	−	0.999997i	$-0.500814\pi$
$911$	−0.154456	−0.00511737	−0.00255869	+	0.999997i	$0.500814\pi$
$912$	3.07062	0.101678
$913$	−29.8417	−0.987615
$914$	−20.9464	−0.692846
$915$	16.6397	0.550093
$916$	14.2160	0.469710
$917$	−30.9521	−1.02213
$918$	−28.9508	−0.955518
$919$	−50.7690	−1.67471	−0.837357	−	0.546657i	$-0.815900\pi$
$919$	−50.7690	−1.67471	−0.837357	+	0.546657i	$0.815900\pi$
$920$	−12.7135	−0.419152
$921$	24.0453	0.792320
$922$	8.27065	0.272379
$923$	5.64664	0.185862
$924$	−9.34580	−0.307454
$925$	0	0
$926$	−12.9800	−0.426549
$927$	−21.9514	−0.720978
$928$	0.00416451	0.000136707 0
$929$	9.52603	0.312539	0.156269	−	0.987714i	$-0.450053\pi$
$929$	9.52603	0.312539	0.156269	+	0.987714i	$0.450053\pi$
$930$	−14.3700	−0.471211
$931$	−40.2043	−1.31764
$932$	−5.94150	−0.194620
$933$	22.4125	0.733752
$934$	−29.0797	−0.951518
$935$	−50.2569	−1.64358
$936$	−11.0275	−0.360447
$937$	24.2931	0.793622	0.396811	−	0.917900i	$-0.370117\pi$
$937$	24.2931	0.793622	0.396811	+	0.917900i	$0.370117\pi$
$938$	31.3469	1.02351
$939$	−26.7680	−0.873540
$940$	5.75169	0.187599
$941$	9.47935	0.309018	0.154509	−	0.987991i	$-0.450620\pi$
$941$	9.47935	0.309018	0.154509	+	0.987991i	$0.450620\pi$
$942$	11.6302	0.378932
$943$	22.3171	0.726745
$944$	−6.32175	−0.205755
$945$	−56.3936	−1.83448
$946$	−15.7526	−0.512161
$947$	−26.1204	−0.848798	−0.424399	−	0.905475i	$-0.639515\pi$
$947$	−26.1204	−0.848798	−0.424399	+	0.905475i	$0.639515\pi$
$948$	0.976068	0.0317012
$949$	−74.3691	−2.41412
$950$	13.9771	0.453476
$951$	0.635053	0.0205930
$952$	−27.5591	−0.893195
$953$	14.9201	0.483310	0.241655	−	0.970362i	$-0.422310\pi$
$953$	14.9201	0.483310	0.241655	+	0.970362i	$0.422310\pi$
$954$	−20.1631	−0.652803
$955$	−41.1448	−1.33142
$956$	2.54774	0.0823998
$957$	0.00916024	0.000296109 0
$958$	−22.6214	−0.730864
$959$	72.4598	2.33985
$960$	2.51025	0.0810178
$961$	1.77033	0.0571073
$962$	0	0
$963$	26.5833	0.856636
$964$	11.9114	0.383641
$965$	70.8719	2.28145
$966$	−15.3348	−0.493389
$967$	8.78152	0.282395	0.141197	−	0.989981i	$-0.454905\pi$
$967$	8.78152	0.282395	0.141197	+	0.989981i	$0.454905\pi$
$968$	4.21060	0.135334
$969$	19.9167	0.639817
$970$	−22.2450	−0.714243
$971$	−1.72427	−0.0553344	−0.0276672	−	0.999617i	$-0.508808\pi$
$971$	−1.72427	−0.0553344	−0.0276672	+	0.999617i	$0.508808\pi$
$972$	−16.0024	−0.513276
$973$	2.86016	0.0916925
$974$	16.6885	0.534734
$975$	15.6381	0.500822
$976$	6.62873	0.212180
$977$	49.8530	1.59494	0.797469	−	0.603359i	$-0.206172\pi$
$977$	49.8530	1.59494	0.797469	+	0.603359i	$0.206172\pi$
$978$	14.2477	0.455591
$979$	33.0578	1.05653
$980$	−32.8672	−1.04990
$981$	−23.8607	−0.761812
$982$	4.17667	0.133283
$983$	3.49278	0.111402	0.0557012	−	0.998447i	$-0.482261\pi$
$983$	3.49278	0.111402	0.0557012	+	0.998447i	$0.482261\pi$
$984$	−4.40645	−0.140472
$985$	−40.7315	−1.29781
$986$	0.0270119	0.000860234 0
$987$	6.93758	0.220825
$988$	17.5363	0.557904
$989$	−25.8472	−0.821894
$990$	−17.7232	−0.563282
$991$	−0.501171	−0.0159202	−0.00796011	−	0.999968i	$-0.502534\pi$
$991$	−0.501171	−0.0159202	−0.00796011	+	0.999968i	$0.502534\pi$
$992$	−5.72454	−0.181754
$993$	0.388139	0.0123172
$994$	4.97649	0.157845
$995$	44.3657	1.40649
$996$	9.66797	0.306341
$997$	21.0769	0.667512	0.333756	−	0.942659i	$-0.391684\pi$
$997$	21.0769	0.667512	0.333756	+	0.942659i	$0.391684\pi$
$998$	−6.05947	−0.191809
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.w.1.6	✓	18
37.36	even	2		2738.2.a.x.1.6	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.6	✓	18	1.1	even	1	trivial
2738.2.a.x.1.6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.844166 q^{3} +1.00000 q^{4} -2.97364 q^{5} +0.844166 q^{6} +4.24887 q^{7} -1.00000 q^{8} -2.28738 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.844166 q^{3} +1.00000 q^{4} -2.97364 q^{5} +0.844166 q^{6} +4.24887 q^{7} -1.00000 q^{8} -2.28738 q^{9} +2.97364 q^{10} +2.60565 q^{11} -0.844166 q^{12} -4.82103 q^{13} -4.24887 q^{14} +2.51025 q^{15} +1.00000 q^{16} +6.48622 q^{17} +2.28738 q^{18} -3.63746 q^{19} -2.97364 q^{20} -3.58675 q^{21} -2.60565 q^{22} -4.27541 q^{23} +0.844166 q^{24} +3.84253 q^{25} +4.82103 q^{26} +4.46343 q^{27} +4.24887 q^{28} -0.00416451 q^{29} -2.51025 q^{30} +5.72454 q^{31} -1.00000 q^{32} -2.19960 q^{33} -6.48622 q^{34} -12.6346 q^{35} -2.28738 q^{36} +3.63746 q^{38} +4.06975 q^{39} +2.97364 q^{40} -5.21988 q^{41} +3.58675 q^{42} +6.04556 q^{43} +2.60565 q^{44} +6.80186 q^{45} +4.27541 q^{46} -1.93422 q^{47} -0.844166 q^{48} +11.0529 q^{49} -3.84253 q^{50} -5.47545 q^{51} -4.82103 q^{52} -8.81490 q^{53} -4.46343 q^{54} -7.74826 q^{55} -4.24887 q^{56} +3.07062 q^{57} +0.00416451 q^{58} -6.32175 q^{59} +2.51025 q^{60} +6.62873 q^{61} -5.72454 q^{62} -9.71879 q^{63} +1.00000 q^{64} +14.3360 q^{65} +2.19960 q^{66} -7.37772 q^{67} +6.48622 q^{68} +3.60915 q^{69} +12.6346 q^{70} -1.17125 q^{71} +2.28738 q^{72} +15.4260 q^{73} -3.24374 q^{75} -3.63746 q^{76} +11.0710 q^{77} -4.06975 q^{78} -1.15625 q^{79} -2.97364 q^{80} +3.09428 q^{81} +5.21988 q^{82} -11.4527 q^{83} -3.58675 q^{84} -19.2877 q^{85} -6.04556 q^{86} +0.00351553 q^{87} -2.60565 q^{88} +12.6870 q^{89} -6.80186 q^{90} -20.4839 q^{91} -4.27541 q^{92} -4.83246 q^{93} +1.93422 q^{94} +10.8165 q^{95} +0.844166 q^{96} -7.48072 q^{97} -11.0529 q^{98} -5.96012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 8 q^{3} + 18 q^{4} - 9 q^{5} - 8 q^{6} + 18 q^{7} - 18 q^{8} + 26 q^{9}+O(q^{10}) \) 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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