LMFDB - Embedded newform 667.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 $ x^12 - 3x^11 - 13x^10 + 41x^9 + 54x^8 - 188x^7 - 77x^6 + 342x^5 + 13x^4 - 215x^3 + 9x^2 + 37*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.89304$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.89304 q^{2} -0.392615 q^{3} +1.58359 q^{4} -4.13664 q^{5} -0.743235 q^{6} +2.17357 q^{7} -0.788273 q^{8} -2.84585 q^{9} +O(q^{10})$	\(q+1.89304 q^{2} -0.392615 q^{3} +1.58359 q^{4} -4.13664 q^{5} -0.743235 q^{6} +2.17357 q^{7} -0.788273 q^{8} -2.84585 q^{9} -7.83081 q^{10} -2.90288 q^{11} -0.621743 q^{12} +3.60532 q^{13} +4.11464 q^{14} +1.62411 q^{15} -4.65942 q^{16} -6.33191 q^{17} -5.38731 q^{18} -2.54061 q^{19} -6.55075 q^{20} -0.853375 q^{21} -5.49525 q^{22} -1.00000 q^{23} +0.309488 q^{24} +12.1118 q^{25} +6.82502 q^{26} +2.29517 q^{27} +3.44205 q^{28} -1.00000 q^{29} +3.07449 q^{30} -0.623156 q^{31} -7.24391 q^{32} +1.13971 q^{33} -11.9865 q^{34} -8.99125 q^{35} -4.50668 q^{36} +1.79544 q^{37} -4.80948 q^{38} -1.41550 q^{39} +3.26080 q^{40} -5.90209 q^{41} -1.61547 q^{42} -1.37819 q^{43} -4.59698 q^{44} +11.7723 q^{45} -1.89304 q^{46} +9.54531 q^{47} +1.82936 q^{48} -2.27561 q^{49} +22.9280 q^{50} +2.48600 q^{51} +5.70937 q^{52} +11.4616 q^{53} +4.34484 q^{54} +12.0081 q^{55} -1.71336 q^{56} +0.997483 q^{57} -1.89304 q^{58} -6.14493 q^{59} +2.57192 q^{60} +0.927645 q^{61} -1.17966 q^{62} -6.18565 q^{63} -4.39416 q^{64} -14.9139 q^{65} +2.15752 q^{66} -10.5188 q^{67} -10.0272 q^{68} +0.392615 q^{69} -17.0208 q^{70} +5.20091 q^{71} +2.24331 q^{72} +11.9900 q^{73} +3.39884 q^{74} -4.75526 q^{75} -4.02330 q^{76} -6.30959 q^{77} -2.67960 q^{78} +0.490191 q^{79} +19.2743 q^{80} +7.63644 q^{81} -11.1729 q^{82} -17.8520 q^{83} -1.35140 q^{84} +26.1928 q^{85} -2.60896 q^{86} +0.392615 q^{87} +2.28826 q^{88} -14.8674 q^{89} +22.2853 q^{90} +7.83641 q^{91} -1.58359 q^{92} +0.244660 q^{93} +18.0696 q^{94} +10.5096 q^{95} +2.84407 q^{96} +7.45263 q^{97} -4.30782 q^{98} +8.26116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * 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 $

$2$	1.89304	1.33858	0.669290	−	0.743001i	$-0.266598\pi$
$2$	1.89304	1.33858	0.669290	+	0.743001i	$0.266598\pi$
$3$	−0.392615	−0.226676	−0.113338	−	0.993556i	$-0.536154\pi$
$3$	−0.392615	−0.226676	−0.113338	+	0.993556i	$0.536154\pi$
$4$	1.58359	0.791797
$5$	−4.13664	−1.84996	−0.924980	−	0.380016i	$-0.875919\pi$
$5$	−4.13664	−1.84996	−0.924980	+	0.380016i	$0.875919\pi$
$6$	−0.743235	−0.303424
$7$	2.17357	0.821531	0.410765	−	0.911741i	$-0.365262\pi$
$7$	2.17357	0.821531	0.410765	+	0.911741i	$0.365262\pi$
$8$	−0.788273	−0.278697
$9$	−2.84585	−0.948618
$10$	−7.83081	−2.47632
$11$	−2.90288	−0.875250	−0.437625	−	0.899158i	$-0.644180\pi$
$11$	−2.90288	−0.875250	−0.437625	+	0.899158i	$0.644180\pi$
$12$	−0.621743	−0.179482
$13$	3.60532	0.999937	0.499968	−	0.866044i	$-0.333345\pi$
$13$	3.60532	0.999937	0.499968	+	0.866044i	$0.333345\pi$
$14$	4.11464	1.09968
$15$	1.62411	0.419342
$16$	−4.65942	−1.16485
$17$	−6.33191	−1.53571	−0.767856	−	0.640622i	$-0.778677\pi$
$17$	−6.33191	−1.53571	−0.767856	+	0.640622i	$0.778677\pi$
$18$	−5.38731	−1.26980
$19$	−2.54061	−0.582857	−0.291428	−	0.956593i	$-0.594131\pi$
$19$	−2.54061	−0.582857	−0.291428	+	0.956593i	$0.594131\pi$
$20$	−6.55075	−1.46479
$21$	−0.853375	−0.186222
$22$	−5.49525	−1.17159
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.309488	0.0631739
$25$	12.1118	2.42235
$26$	6.82502	1.33850
$27$	2.29517	0.441706
$28$	3.44205	0.650486
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.07449	0.561323
$31$	−0.623156	−0.111922	−0.0559611	−	0.998433i	$-0.517822\pi$
$31$	−0.623156	−0.111922	−0.0559611	+	0.998433i	$0.517822\pi$
$32$	−7.24391	−1.28055
$33$	1.13971	0.198398
$34$	−11.9865	−2.05567
$35$	−8.99125	−1.51980
$36$	−4.50668	−0.751113
$37$	1.79544	0.295169	0.147585	−	0.989049i	$-0.452850\pi$
$37$	1.79544	0.295169	0.147585	+	0.989049i	$0.452850\pi$
$38$	−4.80948	−0.780201
$39$	−1.41550	−0.226662
$40$	3.26080	0.515578
$41$	−5.90209	−0.921751	−0.460875	−	0.887465i	$-0.652465\pi$
$41$	−5.90209	−0.921751	−0.460875	+	0.887465i	$0.652465\pi$
$42$	−1.61547	−0.249273
$43$	−1.37819	−0.210171	−0.105086	−	0.994463i	$-0.533512\pi$
$43$	−1.37819	−0.210171	−0.105086	+	0.994463i	$0.533512\pi$
$44$	−4.59698	−0.693020
$45$	11.7723	1.75491
$46$	−1.89304	−0.279113
$47$	9.54531	1.39233	0.696163	−	0.717883i	$-0.254889\pi$
$47$	9.54531	1.39233	0.696163	+	0.717883i	$0.254889\pi$
$48$	1.82936	0.264045
$49$	−2.27561	−0.325087
$50$	22.9280	3.24251
$51$	2.48600	0.348110
$52$	5.70937	0.791747
$53$	11.4616	1.57437	0.787186	−	0.616715i	$-0.211537\pi$
$53$	11.4616	1.57437	0.787186	+	0.616715i	$0.211537\pi$
$54$	4.34484	0.591258
$55$	12.0081	1.61918
$56$	−1.71336	−0.228958
$57$	0.997483	0.132120
$58$	−1.89304	−0.248568
$59$	−6.14493	−0.800002	−0.400001	−	0.916515i	$-0.630990\pi$
$59$	−6.14493	−0.800002	−0.400001	+	0.916515i	$0.630990\pi$
$60$	2.57192	0.332034
$61$	0.927645	0.118773	0.0593864	−	0.998235i	$-0.481086\pi$
$61$	0.927645	0.118773	0.0593864	+	0.998235i	$0.481086\pi$
$62$	−1.17966	−0.149817
$63$	−6.18565	−0.779319
$64$	−4.39416	−0.549271
$65$	−14.9139	−1.84984
$66$	2.15752	0.265572
$67$	−10.5188	−1.28508	−0.642540	−	0.766252i	$-0.722119\pi$
$67$	−10.5188	−1.28508	−0.642540	+	0.766252i	$0.722119\pi$
$68$	−10.0272	−1.21597
$69$	0.392615	0.0472653
$70$	−17.0208	−2.03437
$71$	5.20091	0.617234	0.308617	−	0.951186i	$-0.400134\pi$
$71$	5.20091	0.617234	0.308617	+	0.951186i	$0.400134\pi$
$72$	2.24331	0.264377
$73$	11.9900	1.40333	0.701663	−	0.712509i	$-0.252441\pi$
$73$	11.9900	1.40333	0.701663	+	0.712509i	$0.252441\pi$
$74$	3.39884	0.395107
$75$	−4.75526	−0.549090
$76$	−4.02330	−0.461504
$77$	−6.30959	−0.719045
$78$	−2.67960	−0.303405
$79$	0.490191	0.0551508	0.0275754	−	0.999620i	$-0.491221\pi$
$79$	0.490191	0.0551508	0.0275754	+	0.999620i	$0.491221\pi$
$80$	19.2743	2.15493
$81$	7.63644	0.848494
$82$	−11.1729	−1.23384
$83$	−17.8520	−1.95951	−0.979754	−	0.200204i	$-0.935839\pi$
$83$	−17.8520	−1.95951	−0.979754	+	0.200204i	$0.935839\pi$
$84$	−1.35140	−0.147450
$85$	26.1928	2.84101
$86$	−2.60896	−0.281331
$87$	0.392615	0.0420927
$88$	2.28826	0.243929
$89$	−14.8674	−1.57594	−0.787969	−	0.615715i	$-0.788867\pi$
$89$	−14.8674	−1.57594	−0.787969	+	0.615715i	$0.788867\pi$
$90$	22.2853	2.34908
$91$	7.83641	0.821479
$92$	−1.58359	−0.165101
$93$	0.244660	0.0253701
$94$	18.0696	1.86374
$95$	10.5096	1.07826
$96$	2.84407	0.290271
$97$	7.45263	0.756700	0.378350	−	0.925663i	$-0.376492\pi$
$97$	7.45263	0.756700	0.378350	+	0.925663i	$0.376492\pi$
$98$	−4.30782	−0.435155
$99$	8.26116	0.830278
$100$	19.1801	1.91801
$101$	−2.54775	−0.253511	−0.126755	−	0.991934i	$-0.540456\pi$
$101$	−2.54775	−0.253511	−0.126755	+	0.991934i	$0.540456\pi$
$102$	4.70609	0.465973
$103$	−14.3457	−1.41352	−0.706762	−	0.707451i	$-0.749845\pi$
$103$	−14.3457	−1.41352	−0.706762	+	0.707451i	$0.749845\pi$
$104$	−2.84198	−0.278679
$105$	3.53010	0.344503
$106$	21.6973	2.10742
$107$	9.36779	0.905618	0.452809	−	0.891607i	$-0.350422\pi$
$107$	9.36779	0.905618	0.452809	+	0.891607i	$0.350422\pi$
$108$	3.63462	0.349741
$109$	2.25163	0.215667	0.107834	−	0.994169i	$-0.465609\pi$
$109$	2.25163	0.215667	0.107834	+	0.994169i	$0.465609\pi$
$110$	22.7319	2.16740
$111$	−0.704918	−0.0669078
$112$	−10.1276	−0.956964
$113$	7.52268	0.707674	0.353837	−	0.935307i	$-0.384877\pi$
$113$	7.52268	0.707674	0.353837	+	0.935307i	$0.384877\pi$
$114$	1.88827	0.176853
$115$	4.13664	0.385743
$116$	−1.58359	−0.147033
$117$	−10.2602	−0.948558
$118$	−11.6326	−1.07087
$119$	−13.7628	−1.26164
$120$	−1.28024	−0.116869
$121$	−2.57331	−0.233938
$122$	1.75607	0.158987
$123$	2.31725	0.208939
$124$	−0.986826	−0.0886196
$125$	−29.4188	−2.63130
$126$	−11.7097	−1.04318
$127$	4.88569	0.433535	0.216767	−	0.976223i	$-0.430449\pi$
$127$	4.88569	0.433535	0.216767	+	0.976223i	$0.430449\pi$
$128$	6.16950	0.545312
$129$	0.541096	0.0476409
$130$	−28.2326	−2.47616
$131$	−7.66514	−0.669706	−0.334853	−	0.942270i	$-0.608687\pi$
$131$	−7.66514	−0.669706	−0.334853	+	0.942270i	$0.608687\pi$
$132$	1.80484	0.157091
$133$	−5.52219	−0.478835
$134$	−19.9126	−1.72018
$135$	−9.49428	−0.817138
$136$	4.99127	0.427998
$137$	14.4595	1.23536	0.617681	−	0.786429i	$-0.288072\pi$
$137$	14.4595	1.23536	0.617681	+	0.786429i	$0.288072\pi$
$138$	0.743235	0.0632684
$139$	−20.3694	−1.72771	−0.863856	−	0.503740i	$-0.831957\pi$
$139$	−20.3694	−1.72771	−0.863856	+	0.503740i	$0.831957\pi$
$140$	−14.2385	−1.20337
$141$	−3.74763	−0.315608
$142$	9.84552	0.826218
$143$	−10.4658	−0.875195
$144$	13.2600	1.10500
$145$	4.13664	0.343529
$146$	22.6976	1.87847
$147$	0.893438	0.0736896
$148$	2.84325	0.233714
$149$	−15.0000	−1.22885	−0.614426	−	0.788974i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614426	+	0.788974i	$0.710612\pi$
$150$	−9.00189	−0.735001
$151$	−6.07420	−0.494311	−0.247156	−	0.968976i	$-0.579496\pi$
$151$	−6.07420	−0.494311	−0.247156	+	0.968976i	$0.579496\pi$
$152$	2.00270	0.162440
$153$	18.0197	1.45680
$154$	−11.9443	−0.962499
$155$	2.57777	0.207052
$156$	−2.24158	−0.179470
$157$	−11.5417	−0.921126	−0.460563	−	0.887627i	$-0.652353\pi$
$157$	−11.5417	−0.921126	−0.460563	+	0.887627i	$0.652353\pi$
$158$	0.927950	0.0738238
$159$	−4.50000	−0.356873
$160$	29.9654	2.36898
$161$	−2.17357	−0.171301
$162$	14.4561	1.13578
$163$	−9.23786	−0.723565	−0.361782	−	0.932263i	$-0.617832\pi$
$163$	−9.23786	−0.723565	−0.361782	+	0.932263i	$0.617832\pi$
$164$	−9.34651	−0.729840
$165$	−4.71458	−0.367029
$166$	−33.7945	−2.62296
$167$	8.72322	0.675023	0.337512	−	0.941321i	$-0.390415\pi$
$167$	8.72322	0.675023	0.337512	+	0.941321i	$0.390415\pi$
$168$	0.672692	0.0518993
$169$	−0.00164176	−0.000126289 0
$170$	49.5840	3.80292
$171$	7.23022	0.552909
$172$	−2.18249	−0.166413
$173$	−19.7976	−1.50518	−0.752592	−	0.658488i	$-0.771196\pi$
$173$	−19.7976	−1.50518	−0.752592	+	0.658488i	$0.771196\pi$
$174$	0.743235	0.0563445
$175$	26.3257	1.99004
$176$	13.5257	1.01954
$177$	2.41259	0.181341
$178$	−28.1445	−2.10952
$179$	0.260507	0.0194712	0.00973559	−	0.999953i	$-0.496901\pi$
$179$	0.260507	0.0194712	0.00973559	+	0.999953i	$0.496901\pi$
$180$	18.6425	1.38953
$181$	−21.7810	−1.61897	−0.809486	−	0.587140i	$-0.800254\pi$
$181$	−21.7810	−1.61897	−0.809486	+	0.587140i	$0.800254\pi$
$182$	14.8346	1.09962
$183$	−0.364207	−0.0269230
$184$	0.788273	0.0581123
$185$	−7.42710	−0.546051
$186$	0.463152	0.0339599
$187$	18.3807	1.34413
$188$	15.1159	1.10244
$189$	4.98870	0.362875
$190$	19.8951	1.44334
$191$	−9.64983	−0.698237	−0.349119	−	0.937079i	$-0.613519\pi$
$191$	−9.64983	−0.698237	−0.349119	+	0.937079i	$0.613519\pi$
$192$	1.72521	0.124507
$193$	−5.73866	−0.413078	−0.206539	−	0.978438i	$-0.566220\pi$
$193$	−5.73866	−0.413078	−0.206539	+	0.978438i	$0.566220\pi$
$194$	14.1081	1.01290
$195$	5.85543	0.419316
$196$	−3.60364	−0.257403
$197$	5.96435	0.424942	0.212471	−	0.977167i	$-0.431849\pi$
$197$	5.96435	0.424942	0.212471	+	0.977167i	$0.431849\pi$
$198$	15.6387	1.11139
$199$	−7.57249	−0.536799	−0.268400	−	0.963308i	$-0.586495\pi$
$199$	−7.57249	−0.536799	−0.268400	+	0.963308i	$0.586495\pi$
$200$	−9.54738	−0.675101
$201$	4.12985	0.291297
$202$	−4.82299	−0.339345
$203$	−2.17357	−0.152554
$204$	3.93682	0.275632
$205$	24.4148	1.70520
$206$	−27.1570	−1.89212
$207$	2.84585	0.197800
$208$	−16.7987	−1.16478
$209$	7.37509	0.510145
$210$	6.68262	0.461144
$211$	21.2652	1.46396	0.731978	−	0.681328i	$-0.238597\pi$
$211$	21.2652	1.46396	0.731978	+	0.681328i	$0.238597\pi$
$212$	18.1505	1.24658
$213$	−2.04195	−0.139912
$214$	17.7336	1.21224
$215$	5.70105	0.388809
$216$	−1.80922	−0.123102
$217$	−1.35447	−0.0919475
$218$	4.26243	0.288688
$219$	−4.70746	−0.318101
$220$	19.0160	1.28206
$221$	−22.8286	−1.53562
$222$	−1.33444	−0.0895615
$223$	18.7155	1.25328	0.626640	−	0.779309i	$-0.284430\pi$
$223$	18.7155	1.25328	0.626640	+	0.779309i	$0.284430\pi$
$224$	−15.7451	−1.05202
$225$	−34.4683	−2.29789
$226$	14.2407	0.947278
$227$	26.9571	1.78921	0.894603	−	0.446861i	$-0.147458\pi$
$227$	26.9571	1.78921	0.894603	+	0.446861i	$0.147458\pi$
$228$	1.57961	0.104612
$229$	−28.9721	−1.91453	−0.957264	−	0.289214i	$-0.906606\pi$
$229$	−28.9721	−1.91453	−0.957264	+	0.289214i	$0.906606\pi$
$230$	7.83081	0.516348
$231$	2.47724	0.162990
$232$	0.788273	0.0517527
$233$	4.49108	0.294220	0.147110	−	0.989120i	$-0.453003\pi$
$233$	4.49108	0.294220	0.147110	+	0.989120i	$0.453003\pi$
$234$	−19.4230	−1.26972
$235$	−39.4855	−2.57575
$236$	−9.73107	−0.633439
$237$	−0.192456	−0.0125014
$238$	−26.0535	−1.68880
$239$	−3.47110	−0.224527	−0.112263	−	0.993678i	$-0.535810\pi$
$239$	−3.47110	−0.224527	−0.112263	+	0.993678i	$0.535810\pi$
$240$	−7.56739	−0.488473
$241$	−9.27826	−0.597665	−0.298833	−	0.954306i	$-0.596597\pi$
$241$	−9.27826	−0.597665	−0.298833	+	0.954306i	$0.596597\pi$
$242$	−4.87138	−0.313144
$243$	−9.88369	−0.634039
$244$	1.46901	0.0940439
$245$	9.41337	0.601398
$246$	4.38664	0.279682
$247$	−9.15974	−0.582820
$248$	0.491217	0.0311923
$249$	7.00895	0.444174
$250$	−55.6909	−3.52220
$251$	23.6609	1.49346	0.746732	−	0.665125i	$-0.231622\pi$
$251$	23.6609	1.49346	0.746732	+	0.665125i	$0.231622\pi$
$252$	−9.79556	−0.617062
$253$	2.90288	0.182502
$254$	9.24880	0.580321
$255$	−10.2837	−0.643989
$256$	20.4674	1.27921
$257$	−1.76852	−0.110317	−0.0551586	−	0.998478i	$-0.517566\pi$
$257$	−1.76852	−0.110317	−0.0551586	+	0.998478i	$0.517566\pi$
$258$	1.02432	0.0637711
$259$	3.90251	0.242490
$260$	−23.6176	−1.46470
$261$	2.84585	0.176154
$262$	−14.5104	−0.896455
$263$	9.44640	0.582490	0.291245	−	0.956648i	$-0.405930\pi$
$263$	9.44640	0.582490	0.291245	+	0.956648i	$0.405930\pi$
$264$	−0.898404	−0.0552930
$265$	−47.4125	−2.91253
$266$	−10.4537	−0.640959
$267$	5.83715	0.357228
$268$	−16.6576	−1.01752
$269$	13.4217	0.818335	0.409168	−	0.912459i	$-0.365819\pi$
$269$	13.4217	0.818335	0.409168	+	0.912459i	$0.365819\pi$
$270$	−17.9730	−1.09380
$271$	25.0505	1.52171	0.760854	−	0.648923i	$-0.224780\pi$
$271$	25.0505	1.52171	0.760854	+	0.648923i	$0.224780\pi$
$272$	29.5030	1.78888
$273$	−3.07669	−0.186210
$274$	27.3725	1.65363
$275$	−35.1589	−2.12016
$276$	0.621743	0.0374245
$277$	13.0000	0.781097	0.390548	−	0.920582i	$-0.372285\pi$
$277$	13.0000	0.781097	0.390548	+	0.920582i	$0.372285\pi$
$278$	−38.5601	−2.31268
$279$	1.77341	0.106171
$280$	7.08756	0.423563
$281$	6.21024	0.370472	0.185236	−	0.982694i	$-0.440695\pi$
$281$	6.21024	0.370472	0.185236	+	0.982694i	$0.440695\pi$
$282$	−7.09441	−0.422466
$283$	−28.5623	−1.69785	−0.848925	−	0.528513i	$-0.822750\pi$
$283$	−28.5623	−1.69785	−0.848925	+	0.528513i	$0.822750\pi$
$284$	8.23613	0.488724
$285$	−4.12623	−0.244417
$286$	−19.8122	−1.17152
$287$	−12.8286	−0.757247
$288$	20.6151	1.21476
$289$	23.0930	1.35841
$290$	7.83081	0.459841
$291$	−2.92601	−0.171526
$292$	18.9873	1.11115
$293$	15.3281	0.895476	0.447738	−	0.894165i	$-0.352230\pi$
$293$	15.3281	0.895476	0.447738	+	0.894165i	$0.352230\pi$
$294$	1.69131	0.0986394
$295$	25.4193	1.47997
$296$	−1.41530	−0.0822626
$297$	−6.66259	−0.386603
$298$	−28.3957	−1.64492
$299$	−3.60532	−0.208501
$300$	−7.53040	−0.434768
$301$	−2.99558	−0.172662
$302$	−11.4987	−0.661675
$303$	1.00029	0.0574649
$304$	11.8378	0.678944
$305$	−3.83733	−0.219725
$306$	34.1119	1.95005
$307$	9.42800	0.538085	0.269042	−	0.963128i	$-0.413293\pi$
$307$	9.42800	0.538085	0.269042	+	0.963128i	$0.413293\pi$
$308$	−9.99183	−0.569337
$309$	5.63234	0.320412
$310$	4.87982	0.277155
$311$	11.7826	0.668131	0.334065	−	0.942550i	$-0.391579\pi$
$311$	11.7826	0.668131	0.334065	+	0.942550i	$0.391579\pi$
$312$	1.11580	0.0631699
$313$	−8.28597	−0.468350	−0.234175	−	0.972194i	$-0.575239\pi$
$313$	−8.28597	−0.468350	−0.234175	+	0.972194i	$0.575239\pi$
$314$	−21.8488	−1.23300
$315$	25.5878	1.44171
$316$	0.776263	0.0436682
$317$	−12.1509	−0.682462	−0.341231	−	0.939979i	$-0.610844\pi$
$317$	−12.1509	−0.682462	−0.341231	+	0.939979i	$0.610844\pi$
$318$	−8.51867	−0.477703
$319$	2.90288	0.162530
$320$	18.1771	1.01613
$321$	−3.67793	−0.205282
$322$	−4.11464	−0.229300
$323$	16.0869	0.895101
$324$	12.0930	0.671835
$325$	43.6668	2.42220
$326$	−17.4876	−0.968549
$327$	−0.884025	−0.0488867
$328$	4.65245	0.256889
$329$	20.7474	1.14384
$330$	−8.92487	−0.491298
$331$	−28.5702	−1.57036	−0.785179	−	0.619269i	$-0.787429\pi$
$331$	−28.5702	−1.57036	−0.785179	+	0.619269i	$0.787429\pi$
$332$	−28.2703	−1.55153
$333$	−5.10957	−0.280003
$334$	16.5134	0.903573
$335$	43.5126	2.37735
$336$	3.97623	0.216921
$337$	−11.8439	−0.645181	−0.322590	−	0.946539i	$-0.604554\pi$
$337$	−11.8439	−0.645181	−0.322590	+	0.946539i	$0.604554\pi$
$338$	−0.00310791	−0.000169048 0
$339$	−2.95351	−0.160413
$340$	41.4787	2.24950
$341$	1.80894	0.0979598
$342$	13.6871	0.740112
$343$	−20.1612	−1.08860
$344$	1.08639	0.0585741
$345$	−1.62411	−0.0874389
$346$	−37.4776	−2.01481
$347$	18.9200	1.01568	0.507839	−	0.861452i	$-0.330444\pi$
$347$	18.9200	1.01568	0.507839	+	0.861452i	$0.330444\pi$
$348$	0.621743	0.0333289
$349$	−16.0609	−0.859720	−0.429860	−	0.902896i	$-0.641437\pi$
$349$	−16.0609	−0.859720	−0.429860	+	0.902896i	$0.641437\pi$
$350$	49.8356	2.66382
$351$	8.27483	0.441678
$352$	21.0282	1.12081
$353$	−3.99382	−0.212570	−0.106285	−	0.994336i	$-0.533896\pi$
$353$	−3.99382	−0.212570	−0.106285	+	0.994336i	$0.533896\pi$
$354$	4.56713	0.242740
$355$	−21.5143	−1.14186
$356$	−23.5439	−1.24782
$357$	5.40349	0.285983
$358$	0.493149	0.0260637
$359$	−8.41768	−0.444268	−0.222134	−	0.975016i	$-0.571302\pi$
$359$	−8.41768	−0.444268	−0.222134	+	0.975016i	$0.571302\pi$
$360$	−9.27976	−0.489086
$361$	−12.5453	−0.660278
$362$	−41.2323	−2.16712
$363$	1.01032	0.0530281
$364$	12.4097	0.650444
$365$	−49.5984	−2.59610
$366$	−0.689458	−0.0360386
$367$	−4.87150	−0.254290	−0.127145	−	0.991884i	$-0.540581\pi$
$367$	−4.87150	−0.254290	−0.127145	+	0.991884i	$0.540581\pi$
$368$	4.65942	0.242889
$369$	16.7965	0.874389
$370$	−14.0598	−0.730933
$371$	24.9126	1.29340
$372$	0.387443	0.0200880
$373$	−30.3229	−1.57006	−0.785031	−	0.619456i	$-0.787353\pi$
$373$	−30.3229	−1.57006	−0.785031	+	0.619456i	$0.787353\pi$
$374$	34.7954	1.79923
$375$	11.5503	0.596452
$376$	−7.52431	−0.388037
$377$	−3.60532	−0.185684
$378$	9.44381	0.485737
$379$	20.2411	1.03972	0.519859	−	0.854252i	$-0.325985\pi$
$379$	20.2411	1.03972	0.519859	+	0.854252i	$0.325985\pi$
$380$	16.6429	0.853765
$381$	−1.91819	−0.0982721
$382$	−18.2675	−0.934647
$383$	17.8879	0.914031	0.457016	−	0.889459i	$-0.348918\pi$
$383$	17.8879	0.914031	0.457016	+	0.889459i	$0.348918\pi$
$384$	−2.42224	−0.123609
$385$	26.1005	1.33020
$386$	−10.8635	−0.552937
$387$	3.92212	0.199372
$388$	11.8019	0.599153
$389$	−36.7234	−1.86195	−0.930975	−	0.365082i	$-0.881041\pi$
$389$	−36.7234	−1.86195	−0.930975	+	0.365082i	$0.881041\pi$
$390$	11.0845	0.561288
$391$	6.33191	0.320218
$392$	1.79380	0.0906007
$393$	3.00945	0.151806
$394$	11.2907	0.568819
$395$	−2.02774	−0.102027
$396$	13.0823	0.657411
$397$	2.26436	0.113645	0.0568226	−	0.998384i	$-0.481903\pi$
$397$	2.26436	0.113645	0.0568226	+	0.998384i	$0.481903\pi$
$398$	−14.3350	−0.718549
$399$	2.16810	0.108541
$400$	−56.4338	−2.82169
$401$	19.2023	0.958916	0.479458	−	0.877565i	$-0.340833\pi$
$401$	19.2023	0.958916	0.479458	+	0.877565i	$0.340833\pi$
$402$	7.81797	0.389925
$403$	−2.24668	−0.111915
$404$	−4.03460	−0.200729
$405$	−31.5892	−1.56968
$406$	−4.11464	−0.204206
$407$	−5.21195	−0.258347
$408$	−1.95965	−0.0970170
$409$	−6.56665	−0.324700	−0.162350	−	0.986733i	$-0.551907\pi$
$409$	−6.56665	−0.324700	−0.162350	+	0.986733i	$0.551907\pi$
$410$	46.2181	2.28255
$411$	−5.67703	−0.280027
$412$	−22.7178	−1.11922
$413$	−13.3564	−0.657226
$414$	5.38731	0.264772
$415$	73.8471	3.62501
$416$	−26.1166	−1.28047
$417$	7.99734	0.391631
$418$	13.9613	0.682871
$419$	−8.45752	−0.413177	−0.206588	−	0.978428i	$-0.566236\pi$
$419$	−8.45752	−0.413177	−0.206588	+	0.978428i	$0.566236\pi$
$420$	5.59025	0.272776
$421$	16.3679	0.797724	0.398862	−	0.917011i	$-0.369405\pi$
$421$	16.3679	0.797724	0.398862	+	0.917011i	$0.369405\pi$
$422$	40.2558	1.95962
$423$	−27.1646	−1.32079
$424$	−9.03488	−0.438772
$425$	−76.6906	−3.72004
$426$	−3.86550	−0.187284
$427$	2.01630	0.0975755
$428$	14.8348	0.717066
$429$	4.10903	0.198386
$430$	10.7923	0.520452
$431$	33.5196	1.61458	0.807292	−	0.590153i	$-0.200932\pi$
$431$	33.5196	1.61458	0.807292	+	0.590153i	$0.200932\pi$
$432$	−10.6942	−0.514523
$433$	3.79071	0.182170	0.0910850	−	0.995843i	$-0.470966\pi$
$433$	3.79071	0.182170	0.0910850	+	0.995843i	$0.470966\pi$
$434$	−2.56407	−0.123079
$435$	−1.62411	−0.0778699
$436$	3.56567	0.170765
$437$	2.54061	0.121534
$438$	−8.91141	−0.425804
$439$	−13.1475	−0.627498	−0.313749	−	0.949506i	$-0.601585\pi$
$439$	−13.1475	−0.627498	−0.313749	+	0.949506i	$0.601585\pi$
$440$	−9.46569	−0.451259
$441$	6.47605	0.308383
$442$	−43.2154	−2.05555
$443$	4.85308	0.230577	0.115288	−	0.993332i	$-0.463221\pi$
$443$	4.85308	0.230577	0.115288	+	0.993332i	$0.463221\pi$
$444$	−1.11630	−0.0529774
$445$	61.5009	2.91542
$446$	35.4291	1.67761
$447$	5.88924	0.278552
$448$	−9.55101	−0.451243
$449$	−17.7095	−0.835761	−0.417881	−	0.908502i	$-0.637227\pi$
$449$	−17.7095	−0.835761	−0.417881	+	0.908502i	$0.637227\pi$
$450$	−65.2498	−3.07591
$451$	17.1330	0.806762
$452$	11.9129	0.560334
$453$	2.38482	0.112049
$454$	51.0308	2.39500
$455$	−32.4164	−1.51970
$456$	−0.786289	−0.0368214
$457$	−9.62192	−0.450094	−0.225047	−	0.974348i	$-0.572254\pi$
$457$	−9.62192	−0.450094	−0.225047	+	0.974348i	$0.572254\pi$
$458$	−54.8453	−2.56275
$459$	−14.5328	−0.678333
$460$	6.55075	0.305430
$461$	8.04370	0.374633	0.187316	−	0.982300i	$-0.440021\pi$
$461$	8.04370	0.374633	0.187316	+	0.982300i	$0.440021\pi$
$462$	4.68951	0.218176
$463$	15.2951	0.710826	0.355413	−	0.934709i	$-0.384340\pi$
$463$	15.2951	0.710826	0.355413	+	0.934709i	$0.384340\pi$
$464$	4.65942	0.216308
$465$	−1.01207	−0.0469337
$466$	8.50179	0.393838
$467$	−30.1456	−1.39497	−0.697486	−	0.716599i	$-0.745698\pi$
$467$	−30.1456	−1.39497	−0.697486	+	0.716599i	$0.745698\pi$
$468$	−16.2480	−0.751065
$469$	−22.8634	−1.05573
$470$	−74.7475	−3.44785
$471$	4.53144	0.208798
$472$	4.84388	0.222958
$473$	4.00070	0.183952
$474$	−0.364327	−0.0167341
$475$	−30.7713	−1.41189
$476$	−21.7947	−0.998959
$477$	−32.6181	−1.49348
$478$	−6.57093	−0.300547
$479$	31.8526	1.45538	0.727691	−	0.685905i	$-0.240593\pi$
$479$	31.8526	1.45538	0.727691	+	0.685905i	$0.240593\pi$
$480$	−11.7649	−0.536991
$481$	6.47315	0.295150
$482$	−17.5641	−0.800023
$483$	0.853375	0.0388299
$484$	−4.07509	−0.185231
$485$	−30.8288	−1.39987
$486$	−18.7102	−0.848712
$487$	18.3382	0.830983	0.415491	−	0.909597i	$-0.363610\pi$
$487$	18.3382	0.830983	0.415491	+	0.909597i	$0.363610\pi$
$488$	−0.731237	−0.0331016
$489$	3.62692	0.164015
$490$	17.8199	0.805020
$491$	−32.8491	−1.48246	−0.741230	−	0.671251i	$-0.765757\pi$
$491$	−32.8491	−1.48246	−0.741230	+	0.671251i	$0.765757\pi$
$492$	3.66958	0.165437
$493$	6.33191	0.285175
$494$	−17.3397	−0.780152
$495$	−34.1734	−1.53598
$496$	2.90355	0.130373
$497$	11.3045	0.507077
$498$	13.2682	0.594563
$499$	1.97698	0.0885019	0.0442510	−	0.999020i	$-0.485910\pi$
$499$	1.97698	0.0885019	0.0442510	+	0.999020i	$0.485910\pi$
$500$	−46.5874	−2.08345
$501$	−3.42487	−0.153012
$502$	44.7910	1.99912
$503$	−23.7496	−1.05894	−0.529470	−	0.848328i	$-0.677609\pi$
$503$	−23.7496	−1.05894	−0.529470	+	0.848328i	$0.677609\pi$
$504$	4.87598	0.217193
$505$	10.5391	0.468985
$506$	5.49525	0.244294
$507$	0.000644579 0	2.86268e−5 0
$508$	7.73695	0.343272
$509$	−29.5397	−1.30933	−0.654663	−	0.755921i	$-0.727189\pi$
$509$	−29.5397	−1.30933	−0.654663	+	0.755921i	$0.727189\pi$
$510$	−19.4674	−0.862031
$511$	26.0611	1.15288
$512$	26.4066	1.16702
$513$	−5.83114	−0.257451
$514$	−3.34788	−0.147668
$515$	59.3430	2.61496
$516$	0.856877	0.0377219
$517$	−27.7089	−1.21863
$518$	7.38761	0.324593
$519$	7.77283	0.341189
$520$	11.7562	0.515545
$521$	16.3314	0.715492	0.357746	−	0.933819i	$-0.383545\pi$
$521$	16.3314	0.715492	0.357746	+	0.933819i	$0.383545\pi$
$522$	5.38731	0.235796
$523$	32.3855	1.41612	0.708059	−	0.706153i	$-0.249571\pi$
$523$	32.3855	1.41612	0.708059	+	0.706153i	$0.249571\pi$
$524$	−12.1385	−0.530271
$525$	−10.3359	−0.451094
$526$	17.8824	0.779710
$527$	3.94577	0.171880
$528$	−5.31040	−0.231105
$529$	1.00000	0.0434783
$530$	−89.7537	−3.89865
$531$	17.4876	0.758896
$532$	−8.74491	−0.379140
$533$	−21.2789	−0.921693
$534$	11.0500	0.478178
$535$	−38.7511	−1.67536
$536$	8.29171	0.358148
$537$	−0.102279	−0.00441365
$538$	25.4078	1.09541
$539$	6.60581	0.284532
$540$	−15.0351	−0.647007
$541$	28.7175	1.23466	0.617330	−	0.786704i	$-0.288214\pi$
$541$	28.7175	1.23466	0.617330	+	0.786704i	$0.288214\pi$
$542$	47.4215	2.03693
$543$	8.55156	0.366982
$544$	45.8678	1.96656
$545$	−9.31419	−0.398976
$546$	−5.82429	−0.249257
$547$	36.2106	1.54825	0.774127	−	0.633031i	$-0.218189\pi$
$547$	36.2106	1.54825	0.774127	+	0.633031i	$0.218189\pi$
$548$	22.8980	0.978156
$549$	−2.63994	−0.112670
$550$	−66.5572	−2.83801
$551$	2.54061	0.108234
$552$	−0.309488	−0.0131727
$553$	1.06546	0.0453081
$554$	24.6096	1.04556
$555$	2.91599	0.123777
$556$	−32.2569	−1.36800
$557$	−24.2398	−1.02707	−0.513537	−	0.858067i	$-0.671665\pi$
$557$	−24.2398	−1.02707	−0.513537	+	0.858067i	$0.671665\pi$
$558$	3.35714	0.142119
$559$	−4.96881	−0.210158
$560$	41.8940	1.77035
$561$	−7.21655	−0.304683
$562$	11.7562	0.495906
$563$	15.1645	0.639109	0.319554	−	0.947568i	$-0.396467\pi$
$563$	15.1645	0.639109	0.319554	+	0.947568i	$0.396467\pi$
$564$	−5.93473	−0.249897
$565$	−31.1186	−1.30917
$566$	−54.0695	−2.27271
$567$	16.5983	0.697064
$568$	−4.09974	−0.172021
$569$	35.1519	1.47365	0.736823	−	0.676086i	$-0.236325\pi$
$569$	35.1519	1.47365	0.736823	+	0.676086i	$0.236325\pi$
$570$	−7.81110	−0.327171
$571$	−16.7166	−0.699567	−0.349784	−	0.936830i	$-0.613745\pi$
$571$	−16.7166	−0.699567	−0.349784	+	0.936830i	$0.613745\pi$
$572$	−16.5736	−0.692976
$573$	3.78867	0.158274
$574$	−24.2850	−1.01364
$575$	−12.1118	−0.505095
$576$	12.5051	0.521048
$577$	−10.8562	−0.451950	−0.225975	−	0.974133i	$-0.572557\pi$
$577$	−10.8562	−0.451950	−0.225975	+	0.974133i	$0.572557\pi$
$578$	43.7160	1.81835
$579$	2.25308	0.0936349
$580$	6.55075	0.272005
$581$	−38.8024	−1.60980
$582$	−5.53906	−0.229601
$583$	−33.2716	−1.37797
$584$	−9.45141	−0.391102
$585$	42.4428	1.75479
$586$	29.0166	1.19867
$587$	11.6245	0.479796	0.239898	−	0.970798i	$-0.422886\pi$
$587$	11.6245	0.479796	0.239898	+	0.970798i	$0.422886\pi$
$588$	1.41484	0.0583472
$589$	1.58320	0.0652346
$590$	48.1198	1.98106
$591$	−2.34169	−0.0963244
$592$	−8.36572	−0.343829
$593$	−45.4704	−1.86725	−0.933623	−	0.358257i	$-0.883371\pi$
$593$	−45.4704	−1.86725	−0.933623	+	0.358257i	$0.883371\pi$
$594$	−12.6125	−0.517499
$595$	56.9318	2.33398
$596$	−23.7540	−0.973001
$597$	2.97307	0.121680
$598$	−6.82502	−0.279096
$599$	5.44584	0.222511	0.111255	−	0.993792i	$-0.464513\pi$
$599$	5.44584	0.222511	0.111255	+	0.993792i	$0.464513\pi$
$600$	3.74844	0.153030
$601$	33.4537	1.36461	0.682303	−	0.731070i	$-0.260979\pi$
$601$	33.4537	1.36461	0.682303	+	0.731070i	$0.260979\pi$
$602$	−5.67074	−0.231122
$603$	29.9351	1.21905
$604$	−9.61906	−0.391394
$605$	10.6449	0.432775
$606$	1.89358	0.0769214
$607$	3.73539	0.151615	0.0758075	−	0.997122i	$-0.475847\pi$
$607$	3.73539	0.151615	0.0758075	+	0.997122i	$0.475847\pi$
$608$	18.4040	0.746380
$609$	0.853375	0.0345805
$610$	−7.26421	−0.294119
$611$	34.4139	1.39224
$612$	28.5358	1.15349
$613$	7.08936	0.286337	0.143168	−	0.989698i	$-0.454271\pi$
$613$	7.08936	0.286337	0.143168	+	0.989698i	$0.454271\pi$
$614$	17.8476	0.720269
$615$	−9.58561	−0.386529
$616$	4.97368	0.200395
$617$	11.2960	0.454761	0.227381	−	0.973806i	$-0.426984\pi$
$617$	11.2960	0.454761	0.227381	+	0.973806i	$0.426984\pi$
$618$	10.6622	0.428898
$619$	−26.6328	−1.07046	−0.535231	−	0.844706i	$-0.679775\pi$
$619$	−26.6328	−1.07046	−0.535231	+	0.844706i	$0.679775\pi$
$620$	4.08214	0.163943
$621$	−2.29517	−0.0921020
$622$	22.3049	0.894347
$623$	−32.3152	−1.29468
$624$	6.59542	0.264028
$625$	61.1360	2.44544
$626$	−15.6856	−0.626925
$627$	−2.89557	−0.115638
$628$	−18.2773	−0.729345
$629$	−11.3686	−0.453295
$630$	48.4387	1.92984
$631$	−2.87228	−0.114344	−0.0571719	−	0.998364i	$-0.518208\pi$
$631$	−2.87228	−0.114344	−0.0571719	+	0.998364i	$0.518208\pi$
$632$	−0.386404	−0.0153703
$633$	−8.34904	−0.331844
$634$	−23.0021	−0.913530
$635$	−20.2103	−0.802022
$636$	−7.12617	−0.282571
$637$	−8.20431	−0.325067
$638$	5.49525	0.217559
$639$	−14.8010	−0.585519
$640$	−25.5210	−1.00881
$641$	27.6468	1.09198	0.545991	−	0.837791i	$-0.316153\pi$
$641$	27.6468	1.09198	0.545991	+	0.837791i	$0.316153\pi$
$642$	−6.96247	−0.274787
$643$	43.5745	1.71841	0.859204	−	0.511632i	$-0.170959\pi$
$643$	43.5745	1.71841	0.859204	+	0.511632i	$0.170959\pi$
$644$	−3.44205	−0.135636
$645$	−2.23832	−0.0881337
$646$	30.4532	1.19816
$647$	8.79866	0.345911	0.172956	−	0.984930i	$-0.444668\pi$
$647$	8.79866	0.345911	0.172956	+	0.984930i	$0.444668\pi$
$648$	−6.01960	−0.236472
$649$	17.8380	0.700201
$650$	82.6630	3.24231
$651$	0.531786	0.0208423
$652$	−14.6290	−0.572916
$653$	29.0231	1.13576	0.567881	−	0.823111i	$-0.307764\pi$
$653$	29.0231	1.13576	0.567881	+	0.823111i	$0.307764\pi$
$654$	−1.67349	−0.0654388
$655$	31.7079	1.23893
$656$	27.5003	1.07371
$657$	−34.1219	−1.33122
$658$	39.2756	1.53112
$659$	−11.3575	−0.442424	−0.221212	−	0.975226i	$-0.571001\pi$
$659$	−11.3575	−0.442424	−0.221212	+	0.975226i	$0.571001\pi$
$660$	−7.46597	−0.290613
$661$	45.4983	1.76968	0.884840	−	0.465895i	$-0.154268\pi$
$661$	45.4983	1.76968	0.884840	+	0.465895i	$0.154268\pi$
$662$	−54.0844	−2.10205
$663$	8.96284	0.348088
$664$	14.0722	0.546108
$665$	22.8433	0.885826
$666$	−9.67261	−0.374806
$667$	1.00000	0.0387202
$668$	13.8140	0.534481
$669$	−7.34797	−0.284089
$670$	82.3710	3.18227
$671$	−2.69284	−0.103956
$672$	6.18177	0.238467
$673$	−22.3750	−0.862494	−0.431247	−	0.902234i	$-0.641926\pi$
$673$	−22.3750	−0.862494	−0.431247	+	0.902234i	$0.641926\pi$
$674$	−22.4210	−0.863626
$675$	27.7985	1.06997
$676$	−0.00259988	−9.99954e−5 0
$677$	8.84186	0.339820	0.169910	−	0.985460i	$-0.445652\pi$
$677$	8.84186	0.339820	0.169910	+	0.985460i	$0.445652\pi$
$678$	−5.59112	−0.214726
$679$	16.1988	0.621652
$680$	−20.6471	−0.791779
$681$	−10.5838	−0.405571
$682$	3.42440	0.131127
$683$	−37.9258	−1.45119	−0.725595	−	0.688122i	$-0.758435\pi$
$683$	−37.9258	−1.45119	−0.725595	+	0.688122i	$0.758435\pi$
$684$	11.4497	0.437791
$685$	−59.8139	−2.28537
$686$	−38.1658	−1.45718
$687$	11.3749	0.433978
$688$	6.42155	0.244819
$689$	41.3228	1.57427
$690$	−3.07449	−0.117044
$691$	−34.4601	−1.31092	−0.655461	−	0.755229i	$-0.727526\pi$
$691$	−34.4601	−1.31092	−0.655461	+	0.755229i	$0.727526\pi$
$692$	−31.3513	−1.19180
$693$	17.9562	0.682099
$694$	35.8163	1.35957
$695$	84.2609	3.19620
$696$	−0.309488	−0.0117311
$697$	37.3715	1.41554
$698$	−30.4039	−1.15080
$699$	−1.76327	−0.0666928
$700$	41.6892	1.57571
$701$	−6.09855	−0.230339	−0.115169	−	0.993346i	$-0.536741\pi$
$701$	−6.09855	−0.230339	−0.115169	+	0.993346i	$0.536741\pi$
$702$	15.6646	0.591221
$703$	−4.56153	−0.172041
$704$	12.7557	0.480749
$705$	15.5026	0.583861
$706$	−7.56046	−0.284542
$707$	−5.53771	−0.208267
$708$	3.82056	0.143586
$709$	51.3717	1.92930	0.964652	−	0.263528i	$-0.0848860\pi$
$709$	51.3717	1.92930	0.964652	+	0.263528i	$0.0848860\pi$
$710$	−40.7273	−1.52847
$711$	−1.39501	−0.0523170
$712$	11.7195	0.439209
$713$	0.623156	0.0233374
$714$	10.2290	0.382811
$715$	43.2932	1.61908
$716$	0.412537	0.0154172
$717$	1.36281	0.0508949
$718$	−15.9350	−0.594688
$719$	2.25180	0.0839779	0.0419890	−	0.999118i	$-0.486631\pi$
$719$	2.25180	0.0839779	0.0419890	+	0.999118i	$0.486631\pi$
$720$	−54.8519	−2.04421
$721$	−31.1813	−1.16125
$722$	−23.7487	−0.883835
$723$	3.64278	0.135477
$724$	−34.4923	−1.28190
$725$	−12.1118	−0.449820
$726$	1.91258	0.0709824
$727$	33.5034	1.24257	0.621286	−	0.783584i	$-0.286611\pi$
$727$	33.5034	1.24257	0.621286	+	0.783584i	$0.286611\pi$
$728$	−6.17723	−0.228943
$729$	−19.0288	−0.704772
$730$	−93.8916	−3.47509
$731$	8.72655	0.322763
$732$	−0.576756	−0.0213175
$733$	43.1646	1.59432	0.797161	−	0.603767i	$-0.206334\pi$
$733$	43.1646	1.59432	0.797161	+	0.603767i	$0.206334\pi$
$734$	−9.22193	−0.340388
$735$	−3.69583	−0.136323
$736$	7.24391	0.267014
$737$	30.5349	1.12477
$738$	31.7964	1.17044
$739$	21.7361	0.799577	0.399788	−	0.916607i	$-0.369084\pi$
$739$	21.7361	0.799577	0.399788	+	0.916607i	$0.369084\pi$
$740$	−11.7615	−0.432361
$741$	3.59625	0.132112
$742$	47.1604	1.73131
$743$	−9.31252	−0.341643	−0.170822	−	0.985302i	$-0.554642\pi$
$743$	−9.31252	−0.341643	−0.170822	+	0.985302i	$0.554642\pi$
$744$	−0.192859	−0.00707056
$745$	62.0498	2.27333
$746$	−57.4025	−2.10165
$747$	50.8041	1.85882
$748$	29.1076	1.06428
$749$	20.3615	0.743994
$750$	21.8651	0.798399
$751$	−30.0386	−1.09612	−0.548062	−	0.836437i	$-0.684634\pi$
$751$	−30.0386	−1.09612	−0.548062	+	0.836437i	$0.684634\pi$
$752$	−44.4756	−1.62186
$753$	−9.28963	−0.338533
$754$	−6.82502	−0.248552
$755$	25.1268	0.914456
$756$	7.90008	0.287323
$757$	−22.1458	−0.804903	−0.402452	−	0.915441i	$-0.631842\pi$
$757$	−22.1458	−0.804903	−0.402452	+	0.915441i	$0.631842\pi$
$758$	38.3173	1.39175
$759$	−1.13971	−0.0413689
$760$	−8.28443	−0.300508
$761$	−28.4979	−1.03305	−0.516523	−	0.856273i	$-0.672774\pi$
$761$	−28.4979	−1.03305	−0.516523	+	0.856273i	$0.672774\pi$
$762$	−3.63122	−0.131545
$763$	4.89408	0.177177
$764$	−15.2814	−0.552862
$765$	−74.5409	−2.69503
$766$	33.8626	1.22350
$767$	−22.1545	−0.799951
$768$	−8.03582	−0.289968
$769$	16.3508	0.589627	0.294813	−	0.955555i	$-0.404743\pi$
$769$	16.3508	0.589627	0.294813	+	0.955555i	$0.404743\pi$
$770$	49.4092	1.78058
$771$	0.694347	0.0250063
$772$	−9.08770	−0.327074
$773$	−36.5135	−1.31330	−0.656650	−	0.754195i	$-0.728027\pi$
$773$	−36.5135	−1.31330	−0.656650	+	0.754195i	$0.728027\pi$
$774$	7.42471	0.266876
$775$	−7.54752	−0.271115
$776$	−5.87471	−0.210890
$777$	−1.53219	−0.0549668
$778$	−69.5188	−2.49237
$779$	14.9949	0.537249
$780$	9.27261	0.332013
$781$	−15.0976	−0.540234
$782$	11.9865	0.428638
$783$	−2.29517	−0.0820227
$784$	10.6030	0.378679
$785$	47.7437	1.70405
$786$	5.69700	0.203205
$787$	−50.2240	−1.79029	−0.895146	−	0.445773i	$-0.852929\pi$
$787$	−50.2240	−1.79029	−0.895146	+	0.445773i	$0.852929\pi$
$788$	9.44511	0.336468
$789$	−3.70880	−0.132037
$790$	−3.83859	−0.136571
$791$	16.3510	0.581376
$792$	−6.51205	−0.231396
$793$	3.34446	0.118765
$794$	4.28653	0.152123
$795$	18.6149	0.660201
$796$	−11.9917	−0.425036
$797$	−1.43285	−0.0507542	−0.0253771	−	0.999678i	$-0.508079\pi$
$797$	−1.43285	−0.0507542	−0.0253771	+	0.999678i	$0.508079\pi$
$798$	4.10429	0.145290
$799$	−60.4400	−2.13821
$800$	−87.7365	−3.10196
$801$	42.3104	1.49496
$802$	36.3506	1.28359
$803$	−34.8056	−1.22826
$804$	6.54001	0.230648
$805$	8.99125	0.316900
$806$	−4.25305	−0.149807
$807$	−5.26956	−0.185497
$808$	2.00832	0.0706526
$809$	40.7853	1.43393	0.716967	−	0.697108i	$-0.245530\pi$
$809$	40.7853	1.43393	0.716967	+	0.697108i	$0.245530\pi$
$810$	−59.7995	−2.10114
$811$	−45.2569	−1.58919	−0.794593	−	0.607143i	$-0.792316\pi$
$811$	−45.2569	−1.58919	−0.794593	+	0.607143i	$0.792316\pi$
$812$	−3.44205	−0.120792
$813$	−9.83519	−0.344935
$814$	−9.86642	−0.345818
$815$	38.2137	1.33857
$816$	−11.5833	−0.405497
$817$	3.50144	0.122500
$818$	−12.4309	−0.434637
$819$	−22.3013	−0.779270
$820$	38.6631	1.35017
$821$	−30.8490	−1.07664	−0.538319	−	0.842741i	$-0.680940\pi$
$821$	−30.8490	−1.07664	−0.538319	+	0.842741i	$0.680940\pi$
$822$	−10.7468	−0.374839
$823$	46.6436	1.62589	0.812946	−	0.582339i	$-0.197862\pi$
$823$	46.6436	1.62589	0.812946	+	0.582339i	$0.197862\pi$
$824$	11.3083	0.393944
$825$	13.8039	0.480591
$826$	−25.2842	−0.879750
$827$	−37.6666	−1.30980	−0.654898	−	0.755718i	$-0.727288\pi$
$827$	−37.6666	−1.30980	−0.654898	+	0.755718i	$0.727288\pi$
$828$	4.50668	0.156618
$829$	−13.0797	−0.454276	−0.227138	−	0.973863i	$-0.572937\pi$
$829$	−13.0797	−0.454276	−0.227138	+	0.973863i	$0.572937\pi$
$830$	139.795	4.85237
$831$	−5.10401	−0.177056
$832$	−15.8424	−0.549236
$833$	14.4089	0.499240
$834$	15.1393	0.524230
$835$	−36.0848	−1.24877
$836$	11.6791	0.403932
$837$	−1.43025	−0.0494366
$838$	−16.0104	−0.553070
$839$	−50.3656	−1.73881	−0.869406	−	0.494098i	$-0.835499\pi$
$839$	−50.3656	−1.73881	−0.869406	+	0.494098i	$0.835499\pi$
$840$	−2.78268	−0.0960117
$841$	1.00000	0.0344828
$842$	30.9851	1.06782
$843$	−2.43823	−0.0839772
$844$	33.6754	1.15916
$845$	0.00679136	0.000233630 0
$846$	−51.4236	−1.76798
$847$	−5.59327	−0.192187
$848$	−53.4044	−1.83392
$849$	11.2140	0.384863
$850$	−145.178	−4.97957
$851$	−1.79544	−0.0615470
$852$	−3.23363	−0.110782
$853$	−13.5345	−0.463411	−0.231705	−	0.972786i	$-0.574431\pi$
$853$	−13.5345	−0.463411	−0.231705	+	0.972786i	$0.574431\pi$
$854$	3.81693	0.130613
$855$	−29.9088	−1.02286
$856$	−7.38438	−0.252393
$857$	−15.3725	−0.525115	−0.262558	−	0.964916i	$-0.584566\pi$
$857$	−15.3725	−0.525115	−0.262558	+	0.964916i	$0.584566\pi$
$858$	7.77855	0.265555
$859$	37.4269	1.27699	0.638495	−	0.769626i	$-0.279557\pi$
$859$	37.4269	1.27699	0.638495	+	0.769626i	$0.279557\pi$
$860$	9.02816	0.307858
$861$	5.03669	0.171650
$862$	63.4539	2.16125
$863$	−39.8598	−1.35684	−0.678422	−	0.734673i	$-0.737336\pi$
$863$	−39.8598	−1.35684	−0.678422	+	0.734673i	$0.737336\pi$
$864$	−16.6260	−0.565628
$865$	81.8954	2.78453
$866$	7.17597	0.243849
$867$	−9.06667	−0.307920
$868$	−2.14493	−0.0728037
$869$	−1.42296	−0.0482707
$870$	−3.07449	−0.104235
$871$	−37.9238	−1.28500
$872$	−1.77490	−0.0601058
$873$	−21.2091	−0.717819
$874$	4.80948	0.162683
$875$	−63.9437	−2.16169
$876$	−7.45471	−0.251871
$877$	−11.7747	−0.397604	−0.198802	−	0.980040i	$-0.563705\pi$
$877$	−11.7747	−0.397604	−0.198802	+	0.980040i	$0.563705\pi$
$878$	−24.8888	−0.839956
$879$	−6.01803	−0.202983
$880$	−55.9510	−1.88611
$881$	10.1889	0.343272	0.171636	−	0.985160i	$-0.445095\pi$
$881$	10.1889	0.343272	0.171636	+	0.985160i	$0.445095\pi$
$882$	12.2594	0.412796
$883$	48.0068	1.61556	0.807779	−	0.589485i	$-0.200669\pi$
$883$	48.0068	1.61556	0.807779	+	0.589485i	$0.200669\pi$
$884$	−36.1512	−1.21590
$885$	−9.98001	−0.335474
$886$	9.18706	0.308645
$887$	20.3833	0.684405	0.342202	−	0.939626i	$-0.388827\pi$
$887$	20.3833	0.684405	0.342202	+	0.939626i	$0.388827\pi$
$888$	0.555668	0.0186470
$889$	10.6194	0.356162
$890$	116.424	3.90253
$891$	−22.1676	−0.742644
$892$	29.6377	0.992343
$893$	−24.2510	−0.811527
$894$	11.1486	0.372864
$895$	−1.07762	−0.0360209
$896$	13.4098	0.447991
$897$	1.41550	0.0472623
$898$	−33.5247	−1.11873
$899$	0.623156	0.0207834
$900$	−54.5838	−1.81946
$901$	−72.5738	−2.41778
$902$	32.4335	1.07992
$903$	1.17611	0.0391385
$904$	−5.92992	−0.197226
$905$	90.1002	2.99503
$906$	4.51456	0.149986
$907$	−58.8464	−1.95396	−0.976982	−	0.213322i	$-0.931572\pi$
$907$	−58.8464	−1.95396	−0.976982	+	0.213322i	$0.931572\pi$
$908$	42.6891	1.41669
$909$	7.25053	0.240485
$910$	−61.3654	−2.03424
$911$	11.8082	0.391225	0.195612	−	0.980681i	$-0.437331\pi$
$911$	11.8082	0.391225	0.195612	+	0.980681i	$0.437331\pi$
$912$	−4.64769	−0.153900
$913$	51.8220	1.71506
$914$	−18.2147	−0.602487
$915$	1.50659	0.0498064
$916$	−45.8800	−1.51592
$917$	−16.6607	−0.550184
$918$	−27.5111	−0.908003
$919$	33.0243	1.08937	0.544686	−	0.838640i	$-0.316649\pi$
$919$	33.0243	1.08937	0.544686	+	0.838640i	$0.316649\pi$
$920$	−3.26080	−0.107505
$921$	−3.70157	−0.121971
$922$	15.2270	0.501476
$923$	18.7510	0.617195
$924$	3.92294	0.129055
$925$	21.7460	0.715004
$926$	28.9543	0.951497
$927$	40.8258	1.34089
$928$	7.24391	0.237793
$929$	30.2213	0.991529	0.495765	−	0.868457i	$-0.334888\pi$
$929$	30.2213	0.991529	0.495765	+	0.868457i	$0.334888\pi$
$930$	−1.91589	−0.0628245
$931$	5.78145	0.189479
$932$	7.11205	0.232963
$933$	−4.62603	−0.151449
$934$	−57.0668	−1.86728
$935$	−76.0344	−2.48659
$936$	8.08786	0.264360
$937$	21.1832	0.692024	0.346012	−	0.938230i	$-0.387536\pi$
$937$	21.1832	0.692024	0.346012	+	0.938230i	$0.387536\pi$
$938$	−43.2813	−1.41318
$939$	3.25319	0.106164
$940$	−62.5290	−2.03947
$941$	29.9197	0.975354	0.487677	−	0.873024i	$-0.337844\pi$
$941$	29.9197	0.975354	0.487677	+	0.873024i	$0.337844\pi$
$942$	8.57818	0.279492
$943$	5.90209	0.192198
$944$	28.6318	0.931886
$945$	−20.6365	−0.671304
$946$	7.57348	0.246235
$947$	36.9299	1.20006	0.600030	−	0.799977i	$-0.295155\pi$
$947$	36.9299	1.20006	0.600030	+	0.799977i	$0.295155\pi$
$948$	−0.304773	−0.00989855
$949$	43.2279	1.40324
$950$	−58.2513	−1.88992
$951$	4.77062	0.154698
$952$	10.8489	0.351613
$953$	9.86914	0.319693	0.159846	−	0.987142i	$-0.448900\pi$
$953$	9.86914	0.319693	0.159846	+	0.987142i	$0.448900\pi$
$954$	−61.7472	−1.99914
$955$	39.9179	1.29171
$956$	−5.49681	−0.177780
$957$	−1.13971	−0.0368417
$958$	60.2982	1.94815
$959$	31.4288	1.01489
$960$	−7.13659	−0.230332
$961$	−30.6117	−0.987473
$962$	12.2539	0.395082
$963$	−26.6594	−0.859086
$964$	−14.6930	−0.473230
$965$	23.7387	0.764177
$966$	1.61547	0.0519769
$967$	−14.9617	−0.481135	−0.240567	−	0.970632i	$-0.577333\pi$
$967$	−14.9617	−0.481135	−0.240567	+	0.970632i	$0.577333\pi$
$968$	2.02847	0.0651976
$969$	−6.31597	−0.202898
$970$	−58.3602	−1.87383
$971$	−14.7355	−0.472885	−0.236442	−	0.971646i	$-0.575981\pi$
$971$	−14.7355	−0.472885	−0.236442	+	0.971646i	$0.575981\pi$
$972$	−15.6517	−0.502030
$973$	−44.2743	−1.41937
$974$	34.7149	1.11234
$975$	−17.1442	−0.549055
$976$	−4.32229	−0.138353
$977$	17.1304	0.548049	0.274025	−	0.961723i	$-0.411645\pi$
$977$	17.1304	0.548049	0.274025	+	0.961723i	$0.411645\pi$
$978$	6.86590	0.219547
$979$	43.1581	1.37934
$980$	14.9070	0.476185
$981$	−6.40782	−0.204586
$982$	−62.1847	−1.98439
$983$	18.4641	0.588912	0.294456	−	0.955665i	$-0.404862\pi$
$983$	18.4641	0.588912	0.294456	+	0.955665i	$0.404862\pi$
$984$	−1.82662	−0.0582306
$985$	−24.6723	−0.786126
$986$	11.9865	0.381729
$987$	−8.14573	−0.259281
$988$	−14.5053	−0.461475
$989$	1.37819	0.0438238
$990$	−64.6916	−2.05603
$991$	−7.20886	−0.228997	−0.114498	−	0.993423i	$-0.536526\pi$
$991$	−7.20886	−0.228997	−0.114498	+	0.993423i	$0.536526\pi$
$992$	4.51409	0.143322
$993$	11.2171	0.355963
$994$	21.3999	0.678763
$995$	31.3246	0.993057
$996$	11.0993	0.351696
$997$	17.8282	0.564623	0.282312	−	0.959323i	$-0.408899\pi$
$997$	17.8282	0.564623	0.282312	+	0.959323i	$0.408899\pi$
$998$	3.74250	0.118467
$999$	4.12085	0.130378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.b.1.11	✓	12
3.2	odd	2		6003.2.a.n.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.b.1.11	✓	12	1.1	even	1	trivial
6003.2.a.n.1.2		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.89304 q^{2} -0.392615 q^{3} +1.58359 q^{4} -4.13664 q^{5} -0.743235 q^{6} +2.17357 q^{7} -0.788273 q^{8} -2.84585 q^{9} +O(q^{10})\)	\(q+1.89304 q^{2} -0.392615 q^{3} +1.58359 q^{4} -4.13664 q^{5} -0.743235 q^{6} +2.17357 q^{7} -0.788273 q^{8} -2.84585 q^{9} -7.83081 q^{10} -2.90288 q^{11} -0.621743 q^{12} +3.60532 q^{13} +4.11464 q^{14} +1.62411 q^{15} -4.65942 q^{16} -6.33191 q^{17} -5.38731 q^{18} -2.54061 q^{19} -6.55075 q^{20} -0.853375 q^{21} -5.49525 q^{22} -1.00000 q^{23} +0.309488 q^{24} +12.1118 q^{25} +6.82502 q^{26} +2.29517 q^{27} +3.44205 q^{28} -1.00000 q^{29} +3.07449 q^{30} -0.623156 q^{31} -7.24391 q^{32} +1.13971 q^{33} -11.9865 q^{34} -8.99125 q^{35} -4.50668 q^{36} +1.79544 q^{37} -4.80948 q^{38} -1.41550 q^{39} +3.26080 q^{40} -5.90209 q^{41} -1.61547 q^{42} -1.37819 q^{43} -4.59698 q^{44} +11.7723 q^{45} -1.89304 q^{46} +9.54531 q^{47} +1.82936 q^{48} -2.27561 q^{49} +22.9280 q^{50} +2.48600 q^{51} +5.70937 q^{52} +11.4616 q^{53} +4.34484 q^{54} +12.0081 q^{55} -1.71336 q^{56} +0.997483 q^{57} -1.89304 q^{58} -6.14493 q^{59} +2.57192 q^{60} +0.927645 q^{61} -1.17966 q^{62} -6.18565 q^{63} -4.39416 q^{64} -14.9139 q^{65} +2.15752 q^{66} -10.5188 q^{67} -10.0272 q^{68} +0.392615 q^{69} -17.0208 q^{70} +5.20091 q^{71} +2.24331 q^{72} +11.9900 q^{73} +3.39884 q^{74} -4.75526 q^{75} -4.02330 q^{76} -6.30959 q^{77} -2.67960 q^{78} +0.490191 q^{79} +19.2743 q^{80} +7.63644 q^{81} -11.1729 q^{82} -17.8520 q^{83} -1.35140 q^{84} +26.1928 q^{85} -2.60896 q^{86} +0.392615 q^{87} +2.28826 q^{88} -14.8674 q^{89} +22.2853 q^{90} +7.83641 q^{91} -1.58359 q^{92} +0.244660 q^{93} +18.0696 q^{94} +10.5096 q^{95} +2.84407 q^{96} +7.45263 q^{97} -4.30782 q^{98} +8.26116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

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