LMFDB - Embedded newform 2738.2.a.x.1.5

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			1.5
Root			$0.0277653$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00049 q^{3} +1.00000 q^{4} +2.36317 q^{5} -1.00049 q^{6} +3.55615 q^{7} +1.00000 q^{8} -1.99902 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00049 q^{3} +1.00000 q^{4} +2.36317 q^{5} -1.00049 q^{6} +3.55615 q^{7} +1.00000 q^{8} -1.99902 q^{9} +2.36317 q^{10} -6.50402 q^{11} -1.00049 q^{12} +3.51172 q^{13} +3.55615 q^{14} -2.36433 q^{15} +1.00000 q^{16} +4.49162 q^{17} -1.99902 q^{18} -0.0970235 q^{19} +2.36317 q^{20} -3.55788 q^{21} -6.50402 q^{22} -0.893227 q^{23} -1.00049 q^{24} +0.584595 q^{25} +3.51172 q^{26} +5.00146 q^{27} +3.55615 q^{28} +3.31710 q^{29} -2.36433 q^{30} +2.91276 q^{31} +1.00000 q^{32} +6.50719 q^{33} +4.49162 q^{34} +8.40379 q^{35} -1.99902 q^{36} -0.0970235 q^{38} -3.51343 q^{39} +2.36317 q^{40} +10.4281 q^{41} -3.55788 q^{42} +9.93127 q^{43} -6.50402 q^{44} -4.72404 q^{45} -0.893227 q^{46} -5.67060 q^{47} -1.00049 q^{48} +5.64617 q^{49} +0.584595 q^{50} -4.49381 q^{51} +3.51172 q^{52} +11.3483 q^{53} +5.00146 q^{54} -15.3701 q^{55} +3.55615 q^{56} +0.0970708 q^{57} +3.31710 q^{58} +3.35492 q^{59} -2.36433 q^{60} -6.52412 q^{61} +2.91276 q^{62} -7.10882 q^{63} +1.00000 q^{64} +8.29880 q^{65} +6.50719 q^{66} +2.64576 q^{67} +4.49162 q^{68} +0.893663 q^{69} +8.40379 q^{70} +1.05301 q^{71} -1.99902 q^{72} -1.36406 q^{73} -0.584881 q^{75} -0.0970235 q^{76} -23.1292 q^{77} -3.51343 q^{78} -14.3610 q^{79} +2.36317 q^{80} +0.993169 q^{81} +10.4281 q^{82} -11.7131 q^{83} -3.55788 q^{84} +10.6145 q^{85} +9.93127 q^{86} -3.31871 q^{87} -6.50402 q^{88} +1.41659 q^{89} -4.72404 q^{90} +12.4882 q^{91} -0.893227 q^{92} -2.91418 q^{93} -5.67060 q^{94} -0.229283 q^{95} -1.00049 q^{96} -9.89517 q^{97} +5.64617 q^{98} +13.0017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.00049	−0.577632	−0.288816	−	0.957385i	$-0.593262\pi$
$3$	−1.00049	−0.577632	−0.288816	+	0.957385i	$0.593262\pi$
$4$	1.00000	0.500000
$5$	2.36317	1.05684	0.528422	−	0.848982i	$-0.322784\pi$
$5$	2.36317	1.05684	0.528422	+	0.848982i	$0.322784\pi$
$6$	−1.00049	−0.408447
$7$	3.55615	1.34410	0.672048	−	0.740507i	$-0.265415\pi$
$7$	3.55615	1.34410	0.672048	+	0.740507i	$0.265415\pi$
$8$	1.00000	0.353553
$9$	−1.99902	−0.666341
$10$	2.36317	0.747302
$11$	−6.50402	−1.96104	−0.980518	−	0.196431i	$-0.937065\pi$
$11$	−6.50402	−1.96104	−0.980518	+	0.196431i	$0.937065\pi$
$12$	−1.00049	−0.288816
$13$	3.51172	0.973975	0.486988	−	0.873409i	$-0.338096\pi$
$13$	3.51172	0.973975	0.486988	+	0.873409i	$0.338096\pi$
$14$	3.55615	0.950420
$15$	−2.36433	−0.610467
$16$	1.00000	0.250000
$17$	4.49162	1.08938	0.544689	−	0.838638i	$-0.316648\pi$
$17$	4.49162	1.08938	0.544689	+	0.838638i	$0.316648\pi$
$18$	−1.99902	−0.471174
$19$	−0.0970235	−0.0222587	−0.0111294	−	0.999938i	$-0.503543\pi$
$19$	−0.0970235	−0.0222587	−0.0111294	+	0.999938i	$0.503543\pi$
$20$	2.36317	0.528422
$21$	−3.55788	−0.776393
$22$	−6.50402	−1.38666
$23$	−0.893227	−0.186251	−0.0931254	−	0.995654i	$-0.529686\pi$
$23$	−0.893227	−0.186251	−0.0931254	+	0.995654i	$0.529686\pi$
$24$	−1.00049	−0.204224
$25$	0.584595	0.116919
$26$	3.51172	0.688705
$27$	5.00146	0.962532
$28$	3.55615	0.672048
$29$	3.31710	0.615969	0.307985	−	0.951391i	$-0.400345\pi$
$29$	3.31710	0.615969	0.307985	+	0.951391i	$0.400345\pi$
$30$	−2.36433	−0.431665
$31$	2.91276	0.523147	0.261574	−	0.965183i	$-0.415759\pi$
$31$	2.91276	0.523147	0.261574	+	0.965183i	$0.415759\pi$
$32$	1.00000	0.176777
$33$	6.50719	1.13276
$34$	4.49162	0.770306
$35$	8.40379	1.42050
$36$	−1.99902	−0.333171
$37$	0	0
$37$	0	0
$38$	−0.0970235	−0.0157393
$39$	−3.51343	−0.562599
$40$	2.36317	0.373651
$41$	10.4281	1.62860	0.814300	−	0.580444i	$-0.197121\pi$
$41$	10.4281	1.62860	0.814300	+	0.580444i	$0.197121\pi$
$42$	−3.55788	−0.548993
$43$	9.93127	1.51450	0.757252	−	0.653123i	$-0.226541\pi$
$43$	9.93127	1.51450	0.757252	+	0.653123i	$0.226541\pi$
$44$	−6.50402	−0.980518
$45$	−4.72404	−0.704219
$46$	−0.893227	−0.131699
$47$	−5.67060	−0.827142	−0.413571	−	0.910472i	$-0.635719\pi$
$47$	−5.67060	−0.827142	−0.413571	+	0.910472i	$0.635719\pi$
$48$	−1.00049	−0.144408
$49$	5.64617	0.806595
$50$	0.584595	0.0826743
$51$	−4.49381	−0.629259
$52$	3.51172	0.486988
$53$	11.3483	1.55881	0.779407	−	0.626517i	$-0.215520\pi$
$53$	11.3483	1.55881	0.779407	+	0.626517i	$0.215520\pi$
$54$	5.00146	0.680613
$55$	−15.3701	−2.07251
$56$	3.55615	0.475210
$57$	0.0970708	0.0128573
$58$	3.31710	0.435556
$59$	3.35492	0.436774	0.218387	−	0.975862i	$-0.429921\pi$
$59$	3.35492	0.436774	0.218387	+	0.975862i	$0.429921\pi$
$60$	−2.36433	−0.305233
$61$	−6.52412	−0.835329	−0.417664	−	0.908601i	$-0.637151\pi$
$61$	−6.52412	−0.835329	−0.417664	+	0.908601i	$0.637151\pi$
$62$	2.91276	0.369921
$63$	−7.10882	−0.895627
$64$	1.00000	0.125000
$65$	8.29880	1.02934
$66$	6.50719	0.800980
$67$	2.64576	0.323231	0.161615	−	0.986854i	$-0.448330\pi$
$67$	2.64576	0.323231	0.161615	+	0.986854i	$0.448330\pi$
$68$	4.49162	0.544689
$69$	0.893663	0.107584
$70$	8.40379	1.00445
$71$	1.05301	0.124969	0.0624846	−	0.998046i	$-0.480098\pi$
$71$	1.05301	0.124969	0.0624846	+	0.998046i	$0.480098\pi$
$72$	−1.99902	−0.235587
$73$	−1.36406	−0.159652	−0.0798258	−	0.996809i	$-0.525436\pi$
$73$	−1.36406	−0.159652	−0.0798258	+	0.996809i	$0.525436\pi$
$74$	0	0
$75$	−0.584881	−0.0675362
$76$	−0.0970235	−0.0111294
$77$	−23.1292	−2.63582
$78$	−3.51343	−0.397818
$79$	−14.3610	−1.61573	−0.807867	−	0.589365i	$-0.799378\pi$
$79$	−14.3610	−1.61573	−0.807867	+	0.589365i	$0.799378\pi$
$80$	2.36317	0.264211
$81$	0.993169	0.110352
$82$	10.4281	1.15159
$83$	−11.7131	−1.28568	−0.642840	−	0.766000i	$-0.722244\pi$
$83$	−11.7131	−1.28568	−0.642840	+	0.766000i	$0.722244\pi$
$84$	−3.55788	−0.388197
$85$	10.6145	1.15130
$86$	9.93127	1.07092
$87$	−3.31871	−0.355803
$88$	−6.50402	−0.693331
$89$	1.41659	0.150158	0.0750792	−	0.997178i	$-0.476079\pi$
$89$	1.41659	0.150158	0.0750792	+	0.997178i	$0.476079\pi$
$90$	−4.72404	−0.497958
$91$	12.4882	1.30912
$92$	−0.893227	−0.0931254
$93$	−2.91418	−0.302187
$94$	−5.67060	−0.584878
$95$	−0.229283	−0.0235240
$96$	−1.00049	−0.102112
$97$	−9.89517	−1.00470	−0.502351	−	0.864664i	$-0.667532\pi$
$97$	−9.89517	−1.00470	−0.502351	+	0.864664i	$0.667532\pi$
$98$	5.64617	0.570349
$99$	13.0017	1.30672
$100$	0.584595	0.0584595
$101$	−17.7542	−1.76660	−0.883302	−	0.468804i	$-0.844685\pi$
$101$	−17.7542	−1.76660	−0.883302	+	0.468804i	$0.844685\pi$
$102$	−4.49381	−0.444953
$103$	9.78820	0.964460	0.482230	−	0.876045i	$-0.339827\pi$
$103$	9.78820	0.964460	0.482230	+	0.876045i	$0.339827\pi$
$104$	3.51172	0.344352
$105$	−8.40789	−0.820526
$106$	11.3483	1.10225
$107$	−5.00740	−0.484084	−0.242042	−	0.970266i	$-0.577817\pi$
$107$	−5.00740	−0.484084	−0.242042	+	0.970266i	$0.577817\pi$
$108$	5.00146	0.481266
$109$	18.9059	1.81085	0.905427	−	0.424503i	$-0.139551\pi$
$109$	18.9059	1.81085	0.905427	+	0.424503i	$0.139551\pi$
$110$	−15.3701	−1.46548
$111$	0	0
$112$	3.55615	0.336024
$113$	8.16977	0.768548	0.384274	−	0.923219i	$-0.374452\pi$
$113$	8.16977	0.768548	0.384274	+	0.923219i	$0.374452\pi$
$114$	0.0970708	0.00909151
$115$	−2.11085	−0.196838
$116$	3.31710	0.307985
$117$	−7.02001	−0.649000
$118$	3.35492	0.308846
$119$	15.9728	1.46423
$120$	−2.36433	−0.215833
$121$	31.3022	2.84566
$122$	−6.52412	−0.590666
$123$	−10.4332	−0.940732
$124$	2.91276	0.261574
$125$	−10.4344	−0.933279
$126$	−7.10882	−0.633304
$127$	0.494102	0.0438445	0.0219222	−	0.999760i	$-0.493021\pi$
$127$	0.494102	0.0438445	0.0219222	+	0.999760i	$0.493021\pi$
$128$	1.00000	0.0883883
$129$	−9.93611	−0.874826
$130$	8.29880	0.727853
$131$	0.159827	0.0139641	0.00698206	−	0.999976i	$-0.497778\pi$
$131$	0.159827	0.0139641	0.00698206	+	0.999976i	$0.497778\pi$
$132$	6.50719	0.566378
$133$	−0.345029	−0.0299179
$134$	2.64576	0.228559
$135$	11.8193	1.01725
$136$	4.49162	0.385153
$137$	9.12625	0.779708	0.389854	−	0.920877i	$-0.372525\pi$
$137$	9.12625	0.779708	0.389854	+	0.920877i	$0.372525\pi$
$138$	0.893663	0.0760736
$139$	8.19560	0.695142	0.347571	−	0.937654i	$-0.387007\pi$
$139$	8.19560	0.695142	0.347571	+	0.937654i	$0.387007\pi$
$140$	8.40379	0.710250
$141$	5.67337	0.477784
$142$	1.05301	0.0883666
$143$	−22.8403	−1.91000
$144$	−1.99902	−0.166585
$145$	7.83888	0.650983
$146$	−1.36406	−0.112891
$147$	−5.64892	−0.465915
$148$	0	0
$149$	0.0392104	0.00321224	0.00160612	−	0.999999i	$-0.499489\pi$
$149$	0.0392104	0.00321224	0.00160612	+	0.999999i	$0.499489\pi$
$150$	−0.584881	−0.0477553
$151$	0.647093	0.0526597	0.0263299	−	0.999653i	$-0.491618\pi$
$151$	0.647093	0.0526597	0.0263299	+	0.999653i	$0.491618\pi$
$152$	−0.0970235	−0.00786964
$153$	−8.97885	−0.725897
$154$	−23.1292	−1.86381
$155$	6.88337	0.552885
$156$	−3.51343	−0.281300
$157$	12.8536	1.02583	0.512913	−	0.858440i	$-0.328566\pi$
$157$	12.8536	1.02583	0.512913	+	0.858440i	$0.328566\pi$
$158$	−14.3610	−1.14250
$159$	−11.3539	−0.900421
$160$	2.36317	0.186825
$161$	−3.17645	−0.250339
$162$	0.993169	0.0780307
$163$	−14.2212	−1.11389	−0.556944	−	0.830550i	$-0.688026\pi$
$163$	−14.2212	−1.11389	−0.556944	+	0.830550i	$0.688026\pi$
$164$	10.4281	0.814300
$165$	15.3776	1.19715
$166$	−11.7131	−0.909114
$167$	−4.22151	−0.326671	−0.163335	−	0.986571i	$-0.552225\pi$
$167$	−4.22151	−0.326671	−0.163335	+	0.986571i	$0.552225\pi$
$168$	−3.55788	−0.274496
$169$	−0.667833	−0.0513718
$170$	10.6145	0.814093
$171$	0.193952	0.0148319
$172$	9.93127	0.757252
$173$	1.55366	0.118123	0.0590615	−	0.998254i	$-0.481189\pi$
$173$	1.55366	0.118123	0.0590615	+	0.998254i	$0.481189\pi$
$174$	−3.31871	−0.251591
$175$	2.07891	0.157151
$176$	−6.50402	−0.490259
$177$	−3.35656	−0.252295
$178$	1.41659	0.106178
$179$	−6.21134	−0.464257	−0.232129	−	0.972685i	$-0.574569\pi$
$179$	−6.21134	−0.464257	−0.232129	+	0.972685i	$0.574569\pi$
$180$	−4.72404	−0.352109
$181$	2.17418	0.161605	0.0808027	−	0.996730i	$-0.474252\pi$
$181$	2.17418	0.161605	0.0808027	+	0.996730i	$0.474252\pi$
$182$	12.4882	0.925686
$183$	6.52731	0.482512
$184$	−0.893227	−0.0658496
$185$	0	0
$186$	−2.91418	−0.213678
$187$	−29.2136	−2.13631
$188$	−5.67060	−0.413571
$189$	17.7859	1.29374
$190$	−0.229283	−0.0166340
$191$	3.85269	0.278771	0.139385	−	0.990238i	$-0.455487\pi$
$191$	3.85269	0.278771	0.139385	+	0.990238i	$0.455487\pi$
$192$	−1.00049	−0.0722040
$193$	−15.9928	−1.15119	−0.575594	−	0.817736i	$-0.695229\pi$
$193$	−15.9928	−1.15119	−0.575594	+	0.817736i	$0.695229\pi$
$194$	−9.89517	−0.710432
$195$	−8.30285	−0.594580
$196$	5.64617	0.403298
$197$	−9.80398	−0.698505	−0.349252	−	0.937029i	$-0.613564\pi$
$197$	−9.80398	−0.698505	−0.349252	+	0.937029i	$0.613564\pi$
$198$	13.0017	0.923990
$199$	−13.8114	−0.979066	−0.489533	−	0.871985i	$-0.662833\pi$
$199$	−13.8114	−0.979066	−0.489533	+	0.871985i	$0.662833\pi$
$200$	0.584595	0.0413371
$201$	−2.64705	−0.186708
$202$	−17.7542	−1.24918
$203$	11.7961	0.827922
$204$	−4.49381	−0.314630
$205$	24.6435	1.72118
$206$	9.78820	0.681976
$207$	1.78558	0.124107
$208$	3.51172	0.243494
$209$	0.631042	0.0436501
$210$	−8.40789	−0.580200
$211$	23.8026	1.63864	0.819321	−	0.573336i	$-0.194351\pi$
$211$	23.8026	1.63864	0.819321	+	0.573336i	$0.194351\pi$
$212$	11.3483	0.779407
$213$	−1.05352	−0.0721862
$214$	−5.00740	−0.342299
$215$	23.4693	1.60059
$216$	5.00146	0.340306
$217$	10.3582	0.703161
$218$	18.9059	1.28047
$219$	1.36473	0.0922199
$220$	−15.3701	−1.03625
$221$	15.7733	1.06103
$222$	0	0
$223$	1.79531	0.120223	0.0601113	−	0.998192i	$-0.480854\pi$
$223$	1.79531	0.120223	0.0601113	+	0.998192i	$0.480854\pi$
$224$	3.55615	0.237605
$225$	−1.16862	−0.0779080
$226$	8.16977	0.543445
$227$	−25.8385	−1.71496	−0.857482	−	0.514513i	$-0.827973\pi$
$227$	−25.8385	−1.71496	−0.857482	+	0.514513i	$0.827973\pi$
$228$	0.0970708	0.00642867
$229$	9.04832	0.597930	0.298965	−	0.954264i	$-0.403359\pi$
$229$	9.04832	0.597930	0.298965	+	0.954264i	$0.403359\pi$
$230$	−2.11085	−0.139185
$231$	23.1405	1.52253
$232$	3.31710	0.217778
$233$	−22.4890	−1.47330	−0.736652	−	0.676272i	$-0.763595\pi$
$233$	−22.4890	−1.47330	−0.736652	+	0.676272i	$0.763595\pi$
$234$	−7.02001	−0.458912
$235$	−13.4006	−0.874160
$236$	3.35492	0.218387
$237$	14.3680	0.933300
$238$	15.9728	1.03537
$239$	−8.26614	−0.534692	−0.267346	−	0.963601i	$-0.586147\pi$
$239$	−8.26614	−0.534692	−0.267346	+	0.963601i	$0.586147\pi$
$240$	−2.36433	−0.152617
$241$	21.5829	1.39027	0.695137	−	0.718877i	$-0.255344\pi$
$241$	21.5829	1.39027	0.695137	+	0.718877i	$0.255344\pi$
$242$	31.3022	2.01218
$243$	−15.9980	−1.02627
$244$	−6.52412	−0.417664
$245$	13.3429	0.852446
$246$	−10.4332	−0.665198
$247$	−0.340719	−0.0216794
$248$	2.91276	0.184961
$249$	11.7188	0.742650
$250$	−10.4344	−0.659928
$251$	−1.14656	−0.0723705	−0.0361852	−	0.999345i	$-0.511521\pi$
$251$	−1.14656	−0.0723705	−0.0361852	+	0.999345i	$0.511521\pi$
$252$	−7.10882	−0.447814
$253$	5.80956	0.365244
$254$	0.494102	0.0310027
$255$	−10.6197	−0.665029
$256$	1.00000	0.0625000
$257$	−14.7551	−0.920397	−0.460198	−	0.887816i	$-0.652222\pi$
$257$	−14.7551	−0.920397	−0.460198	+	0.887816i	$0.652222\pi$
$258$	−9.93611	−0.618595
$259$	0	0
$260$	8.29880	0.514670
$261$	−6.63095	−0.410446
$262$	0.159827	0.00987413
$263$	−3.51258	−0.216595	−0.108297	−	0.994119i	$-0.534540\pi$
$263$	−3.51258	−0.216595	−0.108297	+	0.994119i	$0.534540\pi$
$264$	6.50719	0.400490
$265$	26.8181	1.64742
$266$	−0.345029	−0.0211551
$267$	−1.41728	−0.0867363
$268$	2.64576	0.161615
$269$	5.32084	0.324417	0.162209	−	0.986757i	$-0.448138\pi$
$269$	5.32084	0.324417	0.162209	+	0.986757i	$0.448138\pi$
$270$	11.8193	0.719302
$271$	22.9576	1.39457	0.697287	−	0.716792i	$-0.254390\pi$
$271$	22.9576	1.39457	0.697287	+	0.716792i	$0.254390\pi$
$272$	4.49162	0.272344
$273$	−12.4943	−0.756188
$274$	9.12625	0.551337
$275$	−3.80222	−0.229282
$276$	0.893663	0.0537922
$277$	18.8329	1.13156	0.565781	−	0.824556i	$-0.308575\pi$
$277$	18.8329	1.13156	0.565781	+	0.824556i	$0.308575\pi$
$278$	8.19560	0.491540
$279$	−5.82268	−0.348595
$280$	8.40379	0.502223
$281$	−27.6609	−1.65011	−0.825055	−	0.565053i	$-0.808856\pi$
$281$	−27.6609	−1.65011	−0.825055	+	0.565053i	$0.808856\pi$
$282$	5.67337	0.337844
$283$	8.31192	0.494093	0.247046	−	0.969004i	$-0.420540\pi$
$283$	8.31192	0.494093	0.247046	+	0.969004i	$0.420540\pi$
$284$	1.05301	0.0624846
$285$	0.229395	0.0135882
$286$	−22.8403	−1.35057
$287$	37.0840	2.18900
$288$	−1.99902	−0.117794
$289$	3.17463	0.186743
$290$	7.83888	0.460315
$291$	9.90000	0.580348
$292$	−1.36406	−0.0798258
$293$	−13.1535	−0.768437	−0.384219	−	0.923242i	$-0.625529\pi$
$293$	−13.1535	−0.768437	−0.384219	+	0.923242i	$0.625529\pi$
$294$	−5.64892	−0.329452
$295$	7.92827	0.461602
$296$	0	0
$297$	−32.5296	−1.88756
$298$	0.0392104	0.00227140
$299$	−3.13676	−0.181404
$300$	−0.584881	−0.0337681
$301$	35.3170	2.03564
$302$	0.647093	0.0372360
$303$	17.7628	1.02045
$304$	−0.0970235	−0.00556468
$305$	−15.4176	−0.882812
$306$	−8.97885	−0.513287
$307$	16.4204	0.937160	0.468580	−	0.883421i	$-0.344766\pi$
$307$	16.4204	0.937160	0.468580	+	0.883421i	$0.344766\pi$
$308$	−23.1292	−1.31791
$309$	−9.79297	−0.557103
$310$	6.88337	0.390949
$311$	−4.13825	−0.234659	−0.117329	−	0.993093i	$-0.537433\pi$
$311$	−4.13825	−0.234659	−0.117329	+	0.993093i	$0.537433\pi$
$312$	−3.51343	−0.198909
$313$	−24.8294	−1.40344	−0.701721	−	0.712451i	$-0.747585\pi$
$313$	−24.8294	−1.40344	−0.701721	+	0.712451i	$0.747585\pi$
$314$	12.8536	0.725369
$315$	−16.7994	−0.946538
$316$	−14.3610	−0.807867
$317$	28.9692	1.62707	0.813535	−	0.581515i	$-0.197540\pi$
$317$	28.9692	1.62707	0.813535	+	0.581515i	$0.197540\pi$
$318$	−11.3539	−0.636694
$319$	−21.5744	−1.20794
$320$	2.36317	0.132105
$321$	5.00985	0.279622
$322$	−3.17645	−0.177016
$323$	−0.435792	−0.0242481
$324$	0.993169	0.0551761
$325$	2.05293	0.113876
$326$	−14.2212	−0.787638
$327$	−18.9151	−1.04601
$328$	10.4281	0.575797
$329$	−20.1655	−1.11176
$330$	15.3776	0.846511
$331$	17.0383	0.936510	0.468255	−	0.883593i	$-0.344883\pi$
$331$	17.0383	0.936510	0.468255	+	0.883593i	$0.344883\pi$
$332$	−11.7131	−0.642840
$333$	0	0
$334$	−4.22151	−0.230991
$335$	6.25239	0.341604
$336$	−3.55788	−0.194098
$337$	0.708862	0.0386142	0.0193071	−	0.999814i	$-0.493854\pi$
$337$	0.708862	0.0386142	0.0193071	+	0.999814i	$0.493854\pi$
$338$	−0.667833	−0.0363254
$339$	−8.17376	−0.443938
$340$	10.6145	0.575651
$341$	−18.9447	−1.02591
$342$	0.193952	0.0104877
$343$	−4.81442	−0.259954
$344$	9.93127	0.535458
$345$	2.11188	0.113700
$346$	1.55366	0.0835255
$347$	14.3348	0.769533	0.384766	−	0.923014i	$-0.374282\pi$
$347$	14.3348	0.769533	0.384766	+	0.923014i	$0.374282\pi$
$348$	−3.31871	−0.177902
$349$	−28.0820	−1.50319	−0.751597	−	0.659622i	$-0.770716\pi$
$349$	−28.0820	−1.50319	−0.751597	+	0.659622i	$0.770716\pi$
$350$	2.07891	0.111122
$351$	17.5637	0.937483
$352$	−6.50402	−0.346665
$353$	−5.38537	−0.286634	−0.143317	−	0.989677i	$-0.545777\pi$
$353$	−5.38537	−0.286634	−0.143317	+	0.989677i	$0.545777\pi$
$354$	−3.35656	−0.178399
$355$	2.48845	0.132073
$356$	1.41659	0.0750792
$357$	−15.9806	−0.845785
$358$	−6.21134	−0.328279
$359$	−33.2322	−1.75393	−0.876965	−	0.480555i	$-0.840435\pi$
$359$	−33.2322	−1.75393	−0.876965	+	0.480555i	$0.840435\pi$
$360$	−4.72404	−0.248979
$361$	−18.9906	−0.999505
$362$	2.17418	0.114272
$363$	−31.3175	−1.64374
$364$	12.4882	0.654559
$365$	−3.22352	−0.168727
$366$	6.52731	0.341188
$367$	−27.7993	−1.45111	−0.725555	−	0.688164i	$-0.758417\pi$
$367$	−27.7993	−1.45111	−0.725555	+	0.688164i	$0.758417\pi$
$368$	−0.893227	−0.0465627
$369$	−20.8461	−1.08520
$370$	0	0
$371$	40.3564	2.09520
$372$	−2.91418	−0.151093
$373$	−3.23460	−0.167481	−0.0837406	−	0.996488i	$-0.526687\pi$
$373$	−3.23460	−0.167481	−0.0837406	+	0.996488i	$0.526687\pi$
$374$	−29.2136	−1.51060
$375$	10.4395	0.539092
$376$	−5.67060	−0.292439
$377$	11.6487	0.599939
$378$	17.7859	0.914809
$379$	3.98720	0.204809	0.102404	−	0.994743i	$-0.467346\pi$
$379$	3.98720	0.204809	0.102404	+	0.994743i	$0.467346\pi$
$380$	−0.229283	−0.0117620
$381$	−0.494343	−0.0253260
$382$	3.85269	0.197121
$383$	1.59572	0.0815374	0.0407687	−	0.999169i	$-0.487019\pi$
$383$	1.59572	0.0815374	0.0407687	+	0.999169i	$0.487019\pi$
$384$	−1.00049	−0.0510559
$385$	−54.6584	−2.78565
$386$	−15.9928	−0.814012
$387$	−19.8528	−1.00918
$388$	−9.89517	−0.502351
$389$	−7.42233	−0.376327	−0.188164	−	0.982138i	$-0.560254\pi$
$389$	−7.42233	−0.376327	−0.188164	+	0.982138i	$0.560254\pi$
$390$	−8.30285	−0.420431
$391$	−4.01203	−0.202897
$392$	5.64617	0.285175
$393$	−0.159905	−0.00806612
$394$	−9.80398	−0.493917
$395$	−33.9375	−1.70758
$396$	13.0017	0.653359
$397$	−14.8046	−0.743020	−0.371510	−	0.928429i	$-0.621160\pi$
$397$	−14.8046	−0.743020	−0.371510	+	0.928429i	$0.621160\pi$
$398$	−13.8114	−0.692304
$399$	0.345198	0.0172815
$400$	0.584595	0.0292298
$401$	−27.9814	−1.39733	−0.698663	−	0.715451i	$-0.746221\pi$
$401$	−27.9814	−1.39733	−0.698663	+	0.715451i	$0.746221\pi$
$402$	−2.64705	−0.132023
$403$	10.2288	0.509533
$404$	−17.7542	−0.883302
$405$	2.34703	0.116625
$406$	11.7961	0.585429
$407$	0	0
$408$	−4.49381	−0.222477
$409$	32.0567	1.58510	0.792551	−	0.609806i	$-0.208753\pi$
$409$	32.0567	1.58510	0.792551	+	0.609806i	$0.208753\pi$
$410$	24.6435	1.21706
$411$	−9.13070	−0.450384
$412$	9.78820	0.482230
$413$	11.9306	0.587066
$414$	1.78558	0.0877566
$415$	−27.6801	−1.35876
$416$	3.51172	0.172176
$417$	−8.19960	−0.401536
$418$	0.631042	0.0308653
$419$	−17.9414	−0.876495	−0.438247	−	0.898854i	$-0.644401\pi$
$419$	−17.9414	−0.876495	−0.438247	+	0.898854i	$0.644401\pi$
$420$	−8.40789	−0.410263
$421$	7.77982	0.379165	0.189583	−	0.981865i	$-0.439287\pi$
$421$	7.77982	0.379165	0.189583	+	0.981865i	$0.439287\pi$
$422$	23.8026	1.15869
$423$	11.3357	0.551159
$424$	11.3483	0.551124
$425$	2.62578	0.127369
$426$	−1.05352	−0.0510434
$427$	−23.2007	−1.12276
$428$	−5.00740	−0.242042
$429$	22.8514	1.10328
$430$	23.4693	1.13179
$431$	15.9195	0.766816	0.383408	−	0.923579i	$-0.374750\pi$
$431$	15.9195	0.766816	0.383408	+	0.923579i	$0.374750\pi$
$432$	5.00146	0.240633
$433$	4.27498	0.205443	0.102721	−	0.994710i	$-0.467245\pi$
$433$	4.27498	0.205443	0.102721	+	0.994710i	$0.467245\pi$
$434$	10.3582	0.497210
$435$	−7.84270	−0.376029
$436$	18.9059	0.905427
$437$	0.0866640	0.00414570
$438$	1.36473	0.0652093
$439$	−8.24455	−0.393491	−0.196745	−	0.980455i	$-0.563037\pi$
$439$	−8.24455	−0.393491	−0.196745	+	0.980455i	$0.563037\pi$
$440$	−15.3701	−0.732742
$441$	−11.2868	−0.537468
$442$	15.7733	0.750259
$443$	7.74272	0.367868	0.183934	−	0.982939i	$-0.441117\pi$
$443$	7.74272	0.367868	0.183934	+	0.982939i	$0.441117\pi$
$444$	0	0
$445$	3.34765	0.158694
$446$	1.79531	0.0850102
$447$	−0.0392295	−0.00185549
$448$	3.55615	0.168012
$449$	−3.70290	−0.174751	−0.0873754	−	0.996175i	$-0.527848\pi$
$449$	−3.70290	−0.174751	−0.0873754	+	0.996175i	$0.527848\pi$
$450$	−1.16862	−0.0550893
$451$	−67.8248	−3.19374
$452$	8.16977	0.384274
$453$	−0.647409	−0.0304179
$454$	−25.8385	−1.21266
$455$	29.5118	1.38353
$456$	0.0970708	0.00454576
$457$	−10.2275	−0.478424	−0.239212	−	0.970967i	$-0.576889\pi$
$457$	−10.2275	−0.478424	−0.239212	+	0.970967i	$0.576889\pi$
$458$	9.04832	0.422800
$459$	22.4647	1.04856
$460$	−2.11085	−0.0984190
$461$	22.9629	1.06949	0.534744	−	0.845014i	$-0.320408\pi$
$461$	22.9629	1.06949	0.534744	+	0.845014i	$0.320408\pi$
$462$	23.1405	1.07659
$463$	−28.7681	−1.33697	−0.668483	−	0.743727i	$-0.733056\pi$
$463$	−28.7681	−1.33697	−0.668483	+	0.743727i	$0.733056\pi$
$464$	3.31710	0.153992
$465$	−6.88672	−0.319364
$466$	−22.4890	−1.04178
$467$	−18.8665	−0.873038	−0.436519	−	0.899695i	$-0.643789\pi$
$467$	−18.8665	−0.873038	−0.436519	+	0.899695i	$0.643789\pi$
$468$	−7.02001	−0.324500
$469$	9.40870	0.434453
$470$	−13.4006	−0.618125
$471$	−12.8598	−0.592550
$472$	3.35492	0.154423
$473$	−64.5931	−2.97000
$474$	14.3680	0.659943
$475$	−0.0567195	−0.00260247
$476$	15.9728	0.732114
$477$	−22.6856	−1.03870
$478$	−8.26614	−0.378084
$479$	−25.2986	−1.15592	−0.577960	−	0.816065i	$-0.696151\pi$
$479$	−25.2986	−1.15592	−0.577960	+	0.816065i	$0.696151\pi$
$480$	−2.36433	−0.107916
$481$	0	0
$482$	21.5829	0.983073
$483$	3.17799	0.144604
$484$	31.3022	1.42283
$485$	−23.3840	−1.06181
$486$	−15.9980	−0.725686
$487$	−25.6291	−1.16136	−0.580682	−	0.814130i	$-0.697214\pi$
$487$	−25.6291	−1.16136	−0.580682	+	0.814130i	$0.697214\pi$
$488$	−6.52412	−0.295333
$489$	14.2281	0.643417
$490$	13.3429	0.602770
$491$	−9.79999	−0.442267	−0.221134	−	0.975244i	$-0.570976\pi$
$491$	−9.79999	−0.442267	−0.221134	+	0.975244i	$0.570976\pi$
$492$	−10.4332	−0.470366
$493$	14.8991	0.671023
$494$	−0.340719	−0.0153297
$495$	30.7253	1.38100
$496$	2.91276	0.130787
$497$	3.74466	0.167971
$498$	11.7188	0.525133
$499$	−3.61306	−0.161743	−0.0808713	−	0.996725i	$-0.525770\pi$
$499$	−3.61306	−0.161743	−0.0808713	+	0.996725i	$0.525770\pi$
$500$	−10.4344	−0.466639
$501$	4.22357	0.188695
$502$	−1.14656	−0.0511737
$503$	25.9407	1.15664	0.578318	−	0.815811i	$-0.303709\pi$
$503$	25.9407	1.15664	0.578318	+	0.815811i	$0.303709\pi$
$504$	−7.10882	−0.316652
$505$	−41.9562	−1.86703
$506$	5.80956	0.258267
$507$	0.668159	0.0296740
$508$	0.494102	0.0219222
$509$	6.10851	0.270755	0.135378	−	0.990794i	$-0.456775\pi$
$509$	6.10851	0.270755	0.135378	+	0.990794i	$0.456775\pi$
$510$	−10.6197	−0.470246
$511$	−4.85081	−0.214587
$512$	1.00000	0.0441942
$513$	−0.485259	−0.0214247
$514$	−14.7551	−0.650819
$515$	23.1312	1.01928
$516$	−9.93611	−0.437413
$517$	36.8817	1.62205
$518$	0	0
$519$	−1.55442	−0.0682316
$520$	8.29880	0.363927
$521$	28.0931	1.23078	0.615391	−	0.788222i	$-0.288998\pi$
$521$	28.0931	1.23078	0.615391	+	0.788222i	$0.288998\pi$
$522$	−6.63095	−0.290229
$523$	−3.37283	−0.147484	−0.0737418	−	0.997277i	$-0.523494\pi$
$523$	−3.37283	−0.147484	−0.0737418	+	0.997277i	$0.523494\pi$
$524$	0.159827	0.00698206
$525$	−2.07992	−0.0907752
$526$	−3.51258	−0.153156
$527$	13.0830	0.569905
$528$	6.50719	0.283189
$529$	−22.2021	−0.965311
$530$	26.8181	1.16490
$531$	−6.70657	−0.291041
$532$	−0.345029	−0.0149589
$533$	36.6207	1.58622
$534$	−1.41728	−0.0613318
$535$	−11.8334	−0.511601
$536$	2.64576	0.114279
$537$	6.21437	0.268170
$538$	5.32084	0.229398
$539$	−36.7228	−1.58176
$540$	11.8193	0.508623
$541$	23.1280	0.994352	0.497176	−	0.867650i	$-0.334370\pi$
$541$	23.1280	0.994352	0.497176	+	0.867650i	$0.334370\pi$
$542$	22.9576	0.986113
$543$	−2.17524	−0.0933484
$544$	4.49162	0.192577
$545$	44.6779	1.91379
$546$	−12.4943	−0.534706
$547$	−28.2956	−1.20983	−0.604917	−	0.796288i	$-0.706794\pi$
$547$	−28.2956	−1.20983	−0.604917	+	0.796288i	$0.706794\pi$
$548$	9.12625	0.389854
$549$	13.0419	0.556614
$550$	−3.80222	−0.162127
$551$	−0.321836	−0.0137107
$552$	0.893663	0.0380368
$553$	−51.0697	−2.17170
$554$	18.8329	0.800135
$555$	0	0
$556$	8.19560	0.347571
$557$	−13.3156	−0.564198	−0.282099	−	0.959385i	$-0.591031\pi$
$557$	−13.3156	−0.564198	−0.282099	+	0.959385i	$0.591031\pi$
$558$	−5.82268	−0.246494
$559$	34.8758	1.47509
$560$	8.40379	0.355125
$561$	29.2278	1.23400
$562$	−27.6609	−1.16680
$563$	−2.40108	−0.101193	−0.0505966	−	0.998719i	$-0.516112\pi$
$563$	−2.40108	−0.101193	−0.0505966	+	0.998719i	$0.516112\pi$
$564$	5.67337	0.238892
$565$	19.3066	0.812235
$566$	8.31192	0.349376
$567$	3.53185	0.148324
$568$	1.05301	0.0441833
$569$	−1.45035	−0.0608017	−0.0304008	−	0.999538i	$-0.509678\pi$
$569$	−1.45035	−0.0608017	−0.0304008	+	0.999538i	$0.509678\pi$
$570$	0.229395	0.00960831
$571$	4.19207	0.175432	0.0877162	−	0.996146i	$-0.472043\pi$
$571$	4.19207	0.175432	0.0877162	+	0.996146i	$0.472043\pi$
$572$	−22.8403	−0.955000
$573$	−3.85456	−0.161027
$574$	37.0840	1.54785
$575$	−0.522176	−0.0217763
$576$	−1.99902	−0.0832927
$577$	20.1326	0.838130	0.419065	−	0.907956i	$-0.362358\pi$
$577$	20.1326	0.838130	0.419065	+	0.907956i	$0.362358\pi$
$578$	3.17463	0.132047
$579$	16.0006	0.664962
$580$	7.83888	0.325492
$581$	−41.6535	−1.72808
$582$	9.90000	0.410368
$583$	−73.8098	−3.05689
$584$	−1.36406	−0.0564454
$585$	−16.5895	−0.685892
$586$	−13.1535	−0.543367
$587$	−21.4456	−0.885153	−0.442576	−	0.896731i	$-0.645935\pi$
$587$	−21.4456	−0.885153	−0.442576	+	0.896731i	$0.645935\pi$
$588$	−5.64892	−0.232958
$589$	−0.282606	−0.0116446
$590$	7.92827	0.326402
$591$	9.80876	0.403479
$592$	0	0
$593$	−29.0308	−1.19215	−0.596077	−	0.802928i	$-0.703275\pi$
$593$	−29.0308	−1.19215	−0.596077	+	0.802928i	$0.703275\pi$
$594$	−32.5296	−1.33471
$595$	37.7466	1.54746
$596$	0.0392104	0.00160612
$597$	13.8182	0.565540
$598$	−3.13676	−0.128272
$599$	−24.3888	−0.996497	−0.498249	−	0.867034i	$-0.666023\pi$
$599$	−24.3888	−0.996497	−0.498249	+	0.867034i	$0.666023\pi$
$600$	−0.584881	−0.0238776
$601$	−4.40481	−0.179676	−0.0898380	−	0.995956i	$-0.528635\pi$
$601$	−4.40481	−0.179676	−0.0898380	+	0.995956i	$0.528635\pi$
$602$	35.3170	1.43941
$603$	−5.28893	−0.215382
$604$	0.647093	0.0263299
$605$	73.9727	3.00742
$606$	17.7628	0.721565
$607$	−6.47822	−0.262943	−0.131471	−	0.991320i	$-0.541970\pi$
$607$	−6.47822	−0.262943	−0.131471	+	0.991320i	$0.541970\pi$
$608$	−0.0970235	−0.00393482
$609$	−11.8018	−0.478234
$610$	−15.4176	−0.624242
$611$	−19.9136	−0.805616
$612$	−8.97885	−0.362949
$613$	−32.9632	−1.33137	−0.665685	−	0.746233i	$-0.731860\pi$
$613$	−32.9632	−1.33137	−0.665685	+	0.746233i	$0.731860\pi$
$614$	16.4204	0.662672
$615$	−24.6555	−0.994207
$616$	−23.1292	−0.931903
$617$	−7.48900	−0.301496	−0.150748	−	0.988572i	$-0.548168\pi$
$617$	−7.48900	−0.301496	−0.150748	+	0.988572i	$0.548168\pi$
$618$	−9.79297	−0.393931
$619$	−36.7349	−1.47650	−0.738251	−	0.674526i	$-0.764348\pi$
$619$	−36.7349	−1.47650	−0.738251	+	0.674526i	$0.764348\pi$
$620$	6.88337	0.276443
$621$	−4.46744	−0.179272
$622$	−4.13825	−0.165929
$623$	5.03761	0.201827
$624$	−3.51343	−0.140650
$625$	−27.5812	−1.10325
$626$	−24.8294	−0.992384
$627$	−0.631350	−0.0252137
$628$	12.8536	0.512913
$629$	0	0
$630$	−16.7994	−0.669303
$631$	26.5109	1.05538	0.527691	−	0.849436i	$-0.323058\pi$
$631$	26.5109	1.05538	0.527691	+	0.849436i	$0.323058\pi$
$632$	−14.3610	−0.571248
$633$	−23.8142	−0.946531
$634$	28.9692	1.15051
$635$	1.16765	0.0463368
$636$	−11.3539	−0.450211
$637$	19.8278	0.785604
$638$	−21.5744	−0.854140
$639$	−2.10499	−0.0832722
$640$	2.36317	0.0934127
$641$	19.2411	0.759978	0.379989	−	0.924991i	$-0.375928\pi$
$641$	19.2411	0.759978	0.379989	+	0.924991i	$0.375928\pi$
$642$	5.00985	0.197723
$643$	−6.80308	−0.268287	−0.134144	−	0.990962i	$-0.542828\pi$
$643$	−6.80308	−0.268287	−0.134144	+	0.990962i	$0.542828\pi$
$644$	−3.17645	−0.125169
$645$	−23.4808	−0.924554
$646$	−0.435792	−0.0171460
$647$	−19.9875	−0.785789	−0.392895	−	0.919584i	$-0.628526\pi$
$647$	−19.9875	−0.785789	−0.392895	+	0.919584i	$0.628526\pi$
$648$	0.993169	0.0390154
$649$	−21.8205	−0.856529
$650$	2.05293	0.0805227
$651$	−10.3633	−0.406168
$652$	−14.2212	−0.556944
$653$	−1.62437	−0.0635666	−0.0317833	−	0.999495i	$-0.510119\pi$
$653$	−1.62437	−0.0635666	−0.0317833	+	0.999495i	$0.510119\pi$
$654$	−18.9151	−0.739638
$655$	0.377698	0.0147579
$656$	10.4281	0.407150
$657$	2.72680	0.106382
$658$	−20.1655	−0.786132
$659$	−5.27482	−0.205478	−0.102739	−	0.994708i	$-0.532761\pi$
$659$	−5.27482	−0.205478	−0.102739	+	0.994708i	$0.532761\pi$
$660$	15.3776	0.598573
$661$	11.7598	0.457404	0.228702	−	0.973497i	$-0.426552\pi$
$661$	11.7598	0.457404	0.228702	+	0.973497i	$0.426552\pi$
$662$	17.0383	0.662213
$663$	−15.7810	−0.612883
$664$	−11.7131	−0.454557
$665$	−0.815365	−0.0316185
$666$	0	0
$667$	−2.96292	−0.114725
$668$	−4.22151	−0.163335
$669$	−1.79618	−0.0694444
$670$	6.25239	0.241551
$671$	42.4330	1.63811
$672$	−3.55788	−0.137248
$673$	36.5318	1.40820	0.704099	−	0.710102i	$-0.251351\pi$
$673$	36.5318	1.40820	0.704099	+	0.710102i	$0.251351\pi$
$674$	0.708862	0.0273043
$675$	2.92383	0.112538
$676$	−0.667833	−0.0256859
$677$	21.0301	0.808251	0.404125	−	0.914704i	$-0.367576\pi$
$677$	21.0301	0.808251	0.404125	+	0.914704i	$0.367576\pi$
$678$	−8.17376	−0.313911
$679$	−35.1887	−1.35042
$680$	10.6145	0.407047
$681$	25.8512	0.990618
$682$	−18.9447	−0.725428
$683$	−8.64924	−0.330954	−0.165477	−	0.986214i	$-0.552916\pi$
$683$	−8.64924	−0.330954	−0.165477	+	0.986214i	$0.552916\pi$
$684$	0.193952	0.00741595
$685$	21.5669	0.824030
$686$	−4.81442	−0.183815
$687$	−9.05274	−0.345384
$688$	9.93127	0.378626
$689$	39.8522	1.51825
$690$	2.11188	0.0803980
$691$	−39.5205	−1.50343	−0.751715	−	0.659488i	$-0.770773\pi$
$691$	−39.5205	−1.50343	−0.751715	+	0.659488i	$0.770773\pi$
$692$	1.55366	0.0590615
$693$	46.2359	1.75636
$694$	14.3348	0.544142
$695$	19.3676	0.734656
$696$	−3.31871	−0.125796
$697$	46.8392	1.77416
$698$	−28.0820	−1.06292
$699$	22.5000	0.851028
$700$	2.07891	0.0785753
$701$	28.3522	1.07085	0.535424	−	0.844583i	$-0.320152\pi$
$701$	28.3522	1.07085	0.535424	+	0.844583i	$0.320152\pi$
$702$	17.5637	0.662900
$703$	0	0
$704$	−6.50402	−0.245129
$705$	13.4072	0.504943
$706$	−5.38537	−0.202681
$707$	−63.1364	−2.37449
$708$	−3.35656	−0.126147
$709$	−25.3436	−0.951800	−0.475900	−	0.879499i	$-0.657878\pi$
$709$	−25.3436	−0.951800	−0.475900	+	0.879499i	$0.657878\pi$
$710$	2.48845	0.0933897
$711$	28.7079	1.07663
$712$	1.41659	0.0530890
$713$	−2.60176	−0.0974366
$714$	−15.9806	−0.598060
$715$	−53.9756	−2.01857
$716$	−6.21134	−0.232129
$717$	8.27017	0.308855
$718$	−33.2322	−1.24022
$719$	2.70069	0.100719	0.0503594	−	0.998731i	$-0.483963\pi$
$719$	2.70069	0.100719	0.0503594	+	0.998731i	$0.483963\pi$
$720$	−4.72404	−0.176055
$721$	34.8082	1.29633
$722$	−18.9906	−0.706756
$723$	−21.5934	−0.803067
$724$	2.17418	0.0808027
$725$	1.93916	0.0720185
$726$	−31.3175	−1.16230
$727$	11.6346	0.431505	0.215752	−	0.976448i	$-0.430780\pi$
$727$	11.6346	0.431505	0.215752	+	0.976448i	$0.430780\pi$
$728$	12.4882	0.462843
$729$	13.0263	0.482457
$730$	−3.22352	−0.119308
$731$	44.6075	1.64987
$732$	6.52731	0.241256
$733$	12.8566	0.474870	0.237435	−	0.971403i	$-0.423693\pi$
$733$	12.8566	0.474870	0.237435	+	0.971403i	$0.423693\pi$
$734$	−27.7993	−1.02609
$735$	−13.3494	−0.492400
$736$	−0.893227	−0.0329248
$737$	−17.2081	−0.633867
$738$	−20.8461	−0.767355
$739$	19.7490	0.726477	0.363238	−	0.931696i	$-0.381671\pi$
$739$	19.7490	0.726477	0.363238	+	0.931696i	$0.381671\pi$
$740$	0	0
$741$	0.340885	0.0125227
$742$	40.3564	1.48153
$743$	38.8927	1.42683	0.713417	−	0.700740i	$-0.247146\pi$
$743$	38.8927	1.42683	0.713417	+	0.700740i	$0.247146\pi$
$744$	−2.91418	−0.106839
$745$	0.0926610	0.00339483
$746$	−3.23460	−0.118427
$747$	23.4148	0.856702
$748$	−29.2136	−1.06815
$749$	−17.8071	−0.650656
$750$	10.4395	0.381195
$751$	−14.7512	−0.538280	−0.269140	−	0.963101i	$-0.586739\pi$
$751$	−14.7512	−0.538280	−0.269140	+	0.963101i	$0.586739\pi$
$752$	−5.67060	−0.206786
$753$	1.14712	0.0418035
$754$	11.6487	0.424221
$755$	1.52919	0.0556531
$756$	17.7859	0.646868
$757$	16.8467	0.612302	0.306151	−	0.951983i	$-0.400959\pi$
$757$	16.8467	0.612302	0.306151	+	0.951983i	$0.400959\pi$
$758$	3.98720	0.144822
$759$	−5.81240	−0.210977
$760$	−0.229283	−0.00831698
$761$	26.6047	0.964419	0.482210	−	0.876056i	$-0.339834\pi$
$761$	26.6047	0.964419	0.482210	+	0.876056i	$0.339834\pi$
$762$	−0.494343	−0.0179082
$763$	67.2320	2.43396
$764$	3.85269	0.139385
$765$	−21.2186	−0.767160
$766$	1.59572	0.0576556
$767$	11.7815	0.425407
$768$	−1.00049	−0.0361020
$769$	34.5581	1.24620	0.623099	−	0.782143i	$-0.285873\pi$
$769$	34.5581	1.24620	0.623099	+	0.782143i	$0.285873\pi$
$770$	−54.6584	−1.96975
$771$	14.7623	0.531650
$772$	−15.9928	−0.575594
$773$	−13.5558	−0.487568	−0.243784	−	0.969830i	$-0.578389\pi$
$773$	−13.5558	−0.487568	−0.243784	+	0.969830i	$0.578389\pi$
$774$	−19.8528	−0.713596
$775$	1.70279	0.0611659
$776$	−9.89517	−0.355216
$777$	0	0
$778$	−7.42233	−0.266104
$779$	−1.01177	−0.0362506
$780$	−8.30285	−0.297290
$781$	−6.84879	−0.245069
$782$	−4.01203	−0.143470
$783$	16.5903	0.592890
$784$	5.64617	0.201649
$785$	30.3752	1.08414
$786$	−0.159905	−0.00570361
$787$	44.0193	1.56912	0.784560	−	0.620053i	$-0.212889\pi$
$787$	44.0193	1.56912	0.784560	+	0.620053i	$0.212889\pi$
$788$	−9.80398	−0.349252
$789$	3.51429	0.125112
$790$	−33.9375	−1.20744
$791$	29.0529	1.03300
$792$	13.0017	0.461995
$793$	−22.9109	−0.813589
$794$	−14.8046	−0.525394
$795$	−26.8312	−0.951605
$796$	−13.8114	−0.489533
$797$	−44.9813	−1.59332	−0.796660	−	0.604428i	$-0.793402\pi$
$797$	−44.9813	−1.59332	−0.796660	+	0.604428i	$0.793402\pi$
$798$	0.345198	0.0122199
$799$	−25.4702	−0.901070
$800$	0.584595	0.0206686
$801$	−2.83180	−0.100057
$802$	−27.9814	−0.988059
$803$	8.87190	0.313082
$804$	−2.64705	−0.0933542
$805$	−7.50650	−0.264569
$806$	10.2288	0.360294
$807$	−5.32343	−0.187394
$808$	−17.7542	−0.624589
$809$	16.1187	0.566704	0.283352	−	0.959016i	$-0.408553\pi$
$809$	16.1187	0.566704	0.283352	+	0.959016i	$0.408553\pi$
$810$	2.34703	0.0824663
$811$	−27.9550	−0.981634	−0.490817	−	0.871263i	$-0.663302\pi$
$811$	−27.9550	−0.981634	−0.490817	+	0.871263i	$0.663302\pi$
$812$	11.7961	0.413961
$813$	−22.9688	−0.805551
$814$	0	0
$815$	−33.6071	−1.17721
$816$	−4.49381	−0.157315
$817$	−0.963566	−0.0337109
$818$	32.0567	1.12084
$819$	−24.9642	−0.872319
$820$	24.6435	0.860588
$821$	−42.0111	−1.46620	−0.733099	−	0.680122i	$-0.761927\pi$
$821$	−42.0111	−1.46620	−0.733099	+	0.680122i	$0.761927\pi$
$822$	−9.13070	−0.318470
$823$	−34.9154	−1.21707	−0.608537	−	0.793526i	$-0.708243\pi$
$823$	−34.9154	−1.21707	−0.608537	+	0.793526i	$0.708243\pi$
$824$	9.78820	0.340988
$825$	3.80407	0.132441
$826$	11.9306	0.415119
$827$	−29.5702	−1.02826	−0.514129	−	0.857713i	$-0.671885\pi$
$827$	−29.5702	−1.02826	−0.514129	+	0.857713i	$0.671885\pi$
$828$	1.78558	0.0620533
$829$	27.8818	0.968375	0.484187	−	0.874964i	$-0.339115\pi$
$829$	27.8818	0.968375	0.484187	+	0.874964i	$0.339115\pi$
$830$	−27.6801	−0.960791
$831$	−18.8421	−0.653626
$832$	3.51172	0.121747
$833$	25.3604	0.878687
$834$	−8.19960	−0.283929
$835$	−9.97618	−0.345240
$836$	0.631042	0.0218251
$837$	14.5681	0.503546
$838$	−17.9414	−0.619775
$839$	1.34231	0.0463417	0.0231709	−	0.999732i	$-0.492624\pi$
$839$	1.34231	0.0463417	0.0231709	+	0.999732i	$0.492624\pi$
$840$	−8.40789	−0.290100
$841$	−17.9969	−0.620582
$842$	7.77982	0.268110
$843$	27.6744	0.953156
$844$	23.8026	0.819321
$845$	−1.57821	−0.0542920
$846$	11.3357	0.389728
$847$	111.315	3.82484
$848$	11.3483	0.389704
$849$	−8.31598	−0.285404
$850$	2.62578	0.0900635
$851$	0	0
$852$	−1.05352	−0.0360931
$853$	54.0994	1.85233	0.926164	−	0.377120i	$-0.123086\pi$
$853$	54.0994	1.85233	0.926164	+	0.377120i	$0.123086\pi$
$854$	−23.2007	−0.793913
$855$	0.458343	0.0156750
$856$	−5.00740	−0.171150
$857$	−33.3747	−1.14006	−0.570029	−	0.821625i	$-0.693068\pi$
$857$	−33.3747	−1.14006	−0.570029	+	0.821625i	$0.693068\pi$
$858$	22.8514	0.780135
$859$	−55.9910	−1.91039	−0.955194	−	0.295979i	$-0.904354\pi$
$859$	−55.9910	−1.91039	−0.955194	+	0.295979i	$0.904354\pi$
$860$	23.4693	0.800297
$861$	−37.1020	−1.26443
$862$	15.9195	0.542221
$863$	−12.0345	−0.409660	−0.204830	−	0.978798i	$-0.565664\pi$
$863$	−12.0345	−0.409660	−0.204830	+	0.978798i	$0.565664\pi$
$864$	5.00146	0.170153
$865$	3.67158	0.124838
$866$	4.27498	0.145270
$867$	−3.17618	−0.107869
$868$	10.3582	0.351580
$869$	93.4040	3.16851
$870$	−7.84270	−0.265892
$871$	9.29115	0.314819
$872$	18.9059	0.640233
$873$	19.7807	0.669475
$874$	0.0866640	0.00293145
$875$	−37.1061	−1.25442
$876$	1.36473	0.0461099
$877$	20.1198	0.679399	0.339699	−	0.940534i	$-0.389675\pi$
$877$	20.1198	0.679399	0.339699	+	0.940534i	$0.389675\pi$
$878$	−8.24455	−0.278240
$879$	13.1599	0.443874
$880$	−15.3701	−0.518127
$881$	−18.0268	−0.607338	−0.303669	−	0.952778i	$-0.598212\pi$
$881$	−18.0268	−0.607338	−0.303669	+	0.952778i	$0.598212\pi$
$882$	−11.2868	−0.380047
$883$	25.1384	0.845975	0.422987	−	0.906136i	$-0.360981\pi$
$883$	25.1384	0.845975	0.422987	+	0.906136i	$0.360981\pi$
$884$	15.7733	0.530513
$885$	−7.93214	−0.266636
$886$	7.74272	0.260122
$887$	37.1006	1.24572	0.622858	−	0.782335i	$-0.285972\pi$
$887$	37.1006	1.24572	0.622858	+	0.782335i	$0.285972\pi$
$888$	0	0
$889$	1.75710	0.0589312
$890$	3.34765	0.112214
$891$	−6.45959	−0.216404
$892$	1.79531	0.0601113
$893$	0.550181	0.0184111
$894$	−0.0392295	−0.00131203
$895$	−14.6785	−0.490647
$896$	3.55615	0.118802
$897$	3.13829	0.104785
$898$	−3.70290	−0.123567
$899$	9.66191	0.322243
$900$	−1.16862	−0.0389540
$901$	50.9724	1.69814
$902$	−67.8248	−2.25832
$903$	−35.3343	−1.17585
$904$	8.16977	0.271723
$905$	5.13796	0.170792
$906$	−0.647409	−0.0215087
$907$	43.5955	1.44756	0.723782	−	0.690029i	$-0.242402\pi$
$907$	43.5955	1.44756	0.723782	+	0.690029i	$0.242402\pi$
$908$	−25.8385	−0.857482
$909$	35.4910	1.17716
$910$	29.5118	0.978305
$911$	−49.0366	−1.62466	−0.812328	−	0.583201i	$-0.801800\pi$
$911$	−49.0366	−1.62466	−0.812328	+	0.583201i	$0.801800\pi$
$912$	0.0970708	0.00321434
$913$	76.1823	2.52127
$914$	−10.2275	−0.338297
$915$	15.4252	0.509940
$916$	9.04832	0.298965
$917$	0.568367	0.0187691
$918$	22.4647	0.741444
$919$	15.7023	0.517971	0.258986	−	0.965881i	$-0.416612\pi$
$919$	15.7023	0.517971	0.258986	+	0.965881i	$0.416612\pi$
$920$	−2.11085	−0.0695927
$921$	−16.4284	−0.541333
$922$	22.9629	0.756242
$923$	3.69787	0.121717
$924$	23.1405	0.761267
$925$	0	0
$926$	−28.7681	−0.945378
$927$	−19.5668	−0.642659
$928$	3.31710	0.108889
$929$	34.7032	1.13858	0.569288	−	0.822138i	$-0.307219\pi$
$929$	34.7032	1.13858	0.569288	+	0.822138i	$0.307219\pi$
$930$	−6.88672	−0.225825
$931$	−0.547811	−0.0179538
$932$	−22.4890	−0.736652
$933$	4.14027	0.135546
$934$	−18.8665	−0.617331
$935$	−69.0368	−2.25774
$936$	−7.02001	−0.229456
$937$	9.27548	0.303017	0.151508	−	0.988456i	$-0.451587\pi$
$937$	9.27548	0.303017	0.151508	+	0.988456i	$0.451587\pi$
$938$	9.40870	0.307205
$939$	24.8416	0.810673
$940$	−13.4006	−0.437080
$941$	28.6248	0.933142	0.466571	−	0.884484i	$-0.345489\pi$
$941$	28.6248	0.933142	0.466571	+	0.884484i	$0.345489\pi$
$942$	−12.8598	−0.418996
$943$	−9.31469	−0.303328
$944$	3.35492	0.109193
$945$	42.0313	1.36728
$946$	−64.5931	−2.10010
$947$	−10.7536	−0.349445	−0.174722	−	0.984618i	$-0.555903\pi$
$947$	−10.7536	−0.349445	−0.174722	+	0.984618i	$0.555903\pi$
$948$	14.3680	0.466650
$949$	−4.79021	−0.155497
$950$	−0.0567195	−0.00184022
$951$	−28.9833	−0.939848
$952$	15.9728	0.517683
$953$	−21.4192	−0.693835	−0.346918	−	0.937896i	$-0.612772\pi$
$953$	−21.4192	−0.693835	−0.346918	+	0.937896i	$0.612772\pi$
$954$	−22.6856	−0.734474
$955$	9.10457	0.294617
$956$	−8.26614	−0.267346
$957$	21.5850	0.697743
$958$	−25.2986	−0.817359
$959$	32.4543	1.04800
$960$	−2.36433	−0.0763083
$961$	−22.5158	−0.726317
$962$	0	0
$963$	10.0099	0.322565
$964$	21.5829	0.695137
$965$	−37.7938	−1.21663
$966$	3.17799	0.102250
$967$	12.9914	0.417774	0.208887	−	0.977940i	$-0.433016\pi$
$967$	12.9914	0.417774	0.208887	+	0.977940i	$0.433016\pi$
$968$	31.3022	1.00609
$969$	0.436005	0.0140065
$970$	−23.3840	−0.750816
$971$	23.1028	0.741403	0.370701	−	0.928752i	$-0.379117\pi$
$971$	23.1028	0.741403	0.370701	+	0.928752i	$0.379117\pi$
$972$	−15.9980	−0.513137
$973$	29.1447	0.934338
$974$	−25.6291	−0.821209
$975$	−2.05394	−0.0657786
$976$	−6.52412	−0.208832
$977$	44.0689	1.40989	0.704944	−	0.709263i	$-0.250972\pi$
$977$	44.0689	1.40989	0.704944	+	0.709263i	$0.250972\pi$
$978$	14.2281	0.454965
$979$	−9.21354	−0.294466
$980$	13.3429	0.426223
$981$	−37.7933	−1.20665
$982$	−9.79999	−0.312730
$983$	48.1765	1.53659	0.768295	−	0.640095i	$-0.221105\pi$
$983$	48.1765	1.53659	0.768295	+	0.640095i	$0.221105\pi$
$984$	−10.4332	−0.332599
$985$	−23.1685	−0.738211
$986$	14.8991	0.474485
$987$	20.1753	0.642187
$988$	−0.340719	−0.0108397
$989$	−8.87088	−0.282077
$990$	30.7253	0.976513
$991$	11.6221	0.369188	0.184594	−	0.982815i	$-0.440903\pi$
$991$	11.6221	0.369188	0.184594	+	0.982815i	$0.440903\pi$
$992$	2.91276	0.0924803
$993$	−17.0466	−0.540958
$994$	3.74466	0.118773
$995$	−32.6388	−1.03472
$996$	11.7188	0.371325
$997$	2.08705	0.0660975	0.0330488	−	0.999454i	$-0.489478\pi$
$997$	2.08705	0.0660975	0.0330488	+	0.999454i	$0.489478\pi$
$998$	−3.61306	−0.114369
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.x.1.5	yes	18
37.36	even	2		2738.2.a.w.1.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2738.2.a.w.1.5	✓	18	37.36	even	2
2738.2.a.x.1.5	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00049 q^{3} +1.00000 q^{4} +2.36317 q^{5} -1.00049 q^{6} +3.55615 q^{7} +1.00000 q^{8} -1.99902 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00049 q^{3} +1.00000 q^{4} +2.36317 q^{5} -1.00049 q^{6} +3.55615 q^{7} +1.00000 q^{8} -1.99902 q^{9} +2.36317 q^{10} -6.50402 q^{11} -1.00049 q^{12} +3.51172 q^{13} +3.55615 q^{14} -2.36433 q^{15} +1.00000 q^{16} +4.49162 q^{17} -1.99902 q^{18} -0.0970235 q^{19} +2.36317 q^{20} -3.55788 q^{21} -6.50402 q^{22} -0.893227 q^{23} -1.00049 q^{24} +0.584595 q^{25} +3.51172 q^{26} +5.00146 q^{27} +3.55615 q^{28} +3.31710 q^{29} -2.36433 q^{30} +2.91276 q^{31} +1.00000 q^{32} +6.50719 q^{33} +4.49162 q^{34} +8.40379 q^{35} -1.99902 q^{36} -0.0970235 q^{38} -3.51343 q^{39} +2.36317 q^{40} +10.4281 q^{41} -3.55788 q^{42} +9.93127 q^{43} -6.50402 q^{44} -4.72404 q^{45} -0.893227 q^{46} -5.67060 q^{47} -1.00049 q^{48} +5.64617 q^{49} +0.584595 q^{50} -4.49381 q^{51} +3.51172 q^{52} +11.3483 q^{53} +5.00146 q^{54} -15.3701 q^{55} +3.55615 q^{56} +0.0970708 q^{57} +3.31710 q^{58} +3.35492 q^{59} -2.36433 q^{60} -6.52412 q^{61} +2.91276 q^{62} -7.10882 q^{63} +1.00000 q^{64} +8.29880 q^{65} +6.50719 q^{66} +2.64576 q^{67} +4.49162 q^{68} +0.893663 q^{69} +8.40379 q^{70} +1.05301 q^{71} -1.99902 q^{72} -1.36406 q^{73} -0.584881 q^{75} -0.0970235 q^{76} -23.1292 q^{77} -3.51343 q^{78} -14.3610 q^{79} +2.36317 q^{80} +0.993169 q^{81} +10.4281 q^{82} -11.7131 q^{83} -3.55788 q^{84} +10.6145 q^{85} +9.93127 q^{86} -3.31871 q^{87} -6.50402 q^{88} +1.41659 q^{89} -4.72404 q^{90} +12.4882 q^{91} -0.893227 q^{92} -2.91418 q^{93} -5.67060 q^{94} -0.229283 q^{95} -1.00049 q^{96} -9.89517 q^{97} +5.64617 q^{98} +13.0017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 8 q^{3} + 18 q^{4} + 9 q^{5} + 8 q^{6} + 18 q^{7} + 18 q^{8} + 26 q^{9}+O(q^{10}) \) 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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