LMFDB - Embedded newform 8034.2.a.u.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 $ x^11 - 4x^10 - 18x^9 + 64x^8 + 85x^7 - 249x^6 - 109x^5 + 230x^4 + 97x^3 - 53x^2 - 32x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.218590$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.47956 q^{5} -1.00000 q^{6} -2.89002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.47956 q^{5} -1.00000 q^{6} -2.89002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.47956 q^{10} +2.90081 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.89002 q^{14} -2.47956 q^{15} +1.00000 q^{16} +0.600515 q^{17} +1.00000 q^{18} -5.25953 q^{19} +2.47956 q^{20} +2.89002 q^{21} +2.90081 q^{22} +3.98263 q^{23} -1.00000 q^{24} +1.14823 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.89002 q^{28} -3.18067 q^{29} -2.47956 q^{30} -3.32455 q^{31} +1.00000 q^{32} -2.90081 q^{33} +0.600515 q^{34} -7.16599 q^{35} +1.00000 q^{36} -10.9890 q^{37} -5.25953 q^{38} +1.00000 q^{39} +2.47956 q^{40} -11.7100 q^{41} +2.89002 q^{42} +2.64798 q^{43} +2.90081 q^{44} +2.47956 q^{45} +3.98263 q^{46} -11.4015 q^{47} -1.00000 q^{48} +1.35223 q^{49} +1.14823 q^{50} -0.600515 q^{51} -1.00000 q^{52} -3.86641 q^{53} -1.00000 q^{54} +7.19273 q^{55} -2.89002 q^{56} +5.25953 q^{57} -3.18067 q^{58} +1.08168 q^{59} -2.47956 q^{60} -10.2622 q^{61} -3.32455 q^{62} -2.89002 q^{63} +1.00000 q^{64} -2.47956 q^{65} -2.90081 q^{66} +7.96532 q^{67} +0.600515 q^{68} -3.98263 q^{69} -7.16599 q^{70} +10.2926 q^{71} +1.00000 q^{72} +12.4630 q^{73} -10.9890 q^{74} -1.14823 q^{75} -5.25953 q^{76} -8.38339 q^{77} +1.00000 q^{78} +4.57087 q^{79} +2.47956 q^{80} +1.00000 q^{81} -11.7100 q^{82} -2.92067 q^{83} +2.89002 q^{84} +1.48901 q^{85} +2.64798 q^{86} +3.18067 q^{87} +2.90081 q^{88} +8.74202 q^{89} +2.47956 q^{90} +2.89002 q^{91} +3.98263 q^{92} +3.32455 q^{93} -11.4015 q^{94} -13.0413 q^{95} -1.00000 q^{96} +15.8595 q^{97} +1.35223 q^{98} +2.90081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.47956	1.10889	0.554447	−	0.832219i	$-0.312930\pi$
$5$	2.47956	1.10889	0.554447	+	0.832219i	$0.312930\pi$
$6$	−1.00000	−0.408248
$7$	−2.89002	−1.09233	−0.546163	−	0.837679i	$-0.683912\pi$
$7$	−2.89002	−1.09233	−0.546163	+	0.837679i	$0.683912\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.47956	0.784107
$11$	2.90081	0.874626	0.437313	−	0.899309i	$-0.355930\pi$
$11$	2.90081	0.874626	0.437313	+	0.899309i	$0.355930\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.89002	−0.772391
$15$	−2.47956	−0.640220
$16$	1.00000	0.250000
$17$	0.600515	0.145646	0.0728232	−	0.997345i	$-0.476799\pi$
$17$	0.600515	0.145646	0.0728232	+	0.997345i	$0.476799\pi$
$18$	1.00000	0.235702
$19$	−5.25953	−1.20662	−0.603310	−	0.797507i	$-0.706152\pi$
$19$	−5.25953	−1.20662	−0.603310	+	0.797507i	$0.706152\pi$
$20$	2.47956	0.554447
$21$	2.89002	0.630655
$22$	2.90081	0.618454
$23$	3.98263	0.830435	0.415217	−	0.909722i	$-0.363705\pi$
$23$	3.98263	0.830435	0.415217	+	0.909722i	$0.363705\pi$
$24$	−1.00000	−0.204124
$25$	1.14823	0.229646
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−2.89002	−0.546163
$29$	−3.18067	−0.590636	−0.295318	−	0.955399i	$-0.595426\pi$
$29$	−3.18067	−0.590636	−0.295318	+	0.955399i	$0.595426\pi$
$30$	−2.47956	−0.452704
$31$	−3.32455	−0.597106	−0.298553	−	0.954393i	$-0.596504\pi$
$31$	−3.32455	−0.597106	−0.298553	+	0.954393i	$0.596504\pi$
$32$	1.00000	0.176777
$33$	−2.90081	−0.504965
$34$	0.600515	0.102987
$35$	−7.16599	−1.21127
$36$	1.00000	0.166667
$37$	−10.9890	−1.80658	−0.903291	−	0.429029i	$-0.858856\pi$
$37$	−10.9890	−1.80658	−0.903291	+	0.429029i	$0.858856\pi$
$38$	−5.25953	−0.853209
$39$	1.00000	0.160128
$40$	2.47956	0.392053
$41$	−11.7100	−1.82880	−0.914400	−	0.404811i	$-0.867337\pi$
$41$	−11.7100	−1.82880	−0.914400	+	0.404811i	$0.867337\pi$
$42$	2.89002	0.445940
$43$	2.64798	0.403813	0.201907	−	0.979405i	$-0.435286\pi$
$43$	2.64798	0.403813	0.201907	+	0.979405i	$0.435286\pi$
$44$	2.90081	0.437313
$45$	2.47956	0.369631
$46$	3.98263	0.587206
$47$	−11.4015	−1.66308	−0.831540	−	0.555465i	$-0.812540\pi$
$47$	−11.4015	−1.66308	−0.831540	+	0.555465i	$0.812540\pi$
$48$	−1.00000	−0.144338
$49$	1.35223	0.193175
$50$	1.14823	0.162384
$51$	−0.600515	−0.0840889
$52$	−1.00000	−0.138675
$53$	−3.86641	−0.531092	−0.265546	−	0.964098i	$-0.585552\pi$
$53$	−3.86641	−0.531092	−0.265546	+	0.964098i	$0.585552\pi$
$54$	−1.00000	−0.136083
$55$	7.19273	0.969867
$56$	−2.89002	−0.386195
$57$	5.25953	0.696642
$58$	−3.18067	−0.417643
$59$	1.08168	0.140823	0.0704113	−	0.997518i	$-0.477569\pi$
$59$	1.08168	0.140823	0.0704113	+	0.997518i	$0.477569\pi$
$60$	−2.47956	−0.320110
$61$	−10.2622	−1.31394	−0.656972	−	0.753915i	$-0.728163\pi$
$61$	−10.2622	−1.31394	−0.656972	+	0.753915i	$0.728163\pi$
$62$	−3.32455	−0.422218
$63$	−2.89002	−0.364109
$64$	1.00000	0.125000
$65$	−2.47956	−0.307552
$66$	−2.90081	−0.357064
$67$	7.96532	0.973119	0.486559	−	0.873648i	$-0.338252\pi$
$67$	7.96532	0.973119	0.486559	+	0.873648i	$0.338252\pi$
$68$	0.600515	0.0728232
$69$	−3.98263	−0.479452
$70$	−7.16599	−0.856500
$71$	10.2926	1.22151	0.610756	−	0.791819i	$-0.290866\pi$
$71$	10.2926	1.22151	0.610756	+	0.791819i	$0.290866\pi$
$72$	1.00000	0.117851
$73$	12.4630	1.45868	0.729342	−	0.684150i	$-0.239826\pi$
$73$	12.4630	1.45868	0.729342	+	0.684150i	$0.239826\pi$
$74$	−10.9890	−1.27745
$75$	−1.14823	−0.132586
$76$	−5.25953	−0.603310
$77$	−8.38339	−0.955376
$78$	1.00000	0.113228
$79$	4.57087	0.514263	0.257131	−	0.966376i	$-0.417223\pi$
$79$	4.57087	0.514263	0.257131	+	0.966376i	$0.417223\pi$
$80$	2.47956	0.277224
$81$	1.00000	0.111111
$82$	−11.7100	−1.29316
$83$	−2.92067	−0.320585	−0.160292	−	0.987070i	$-0.551244\pi$
$83$	−2.92067	−0.320585	−0.160292	+	0.987070i	$0.551244\pi$
$84$	2.89002	0.315327
$85$	1.48901	0.161506
$86$	2.64798	0.285539
$87$	3.18067	0.341004
$88$	2.90081	0.309227
$89$	8.74202	0.926652	0.463326	−	0.886188i	$-0.346656\pi$
$89$	8.74202	0.926652	0.463326	+	0.886188i	$0.346656\pi$
$90$	2.47956	0.261369
$91$	2.89002	0.302957
$92$	3.98263	0.415217
$93$	3.32455	0.344739
$94$	−11.4015	−1.17598
$95$	−13.0413	−1.33801
$96$	−1.00000	−0.102062
$97$	15.8595	1.61029	0.805143	−	0.593081i	$-0.202089\pi$
$97$	15.8595	1.61029	0.805143	+	0.593081i	$0.202089\pi$
$98$	1.35223	0.136596
$99$	2.90081	0.291542
$100$	1.14823	0.114823
$101$	1.20794	0.120195	0.0600975	−	0.998193i	$-0.480859\pi$
$101$	1.20794	0.120195	0.0600975	+	0.998193i	$0.480859\pi$
$102$	−0.600515	−0.0594599
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	7.16599	0.699329
$106$	−3.86641	−0.375539
$107$	−9.24442	−0.893692	−0.446846	−	0.894611i	$-0.647453\pi$
$107$	−9.24442	−0.893692	−0.446846	+	0.894611i	$0.647453\pi$
$108$	−1.00000	−0.0962250
$109$	−13.5565	−1.29848	−0.649238	−	0.760586i	$-0.724912\pi$
$109$	−13.5565	−1.29848	−0.649238	+	0.760586i	$0.724912\pi$
$110$	7.19273	0.685800
$111$	10.9890	1.04303
$112$	−2.89002	−0.273081
$113$	−12.6546	−1.19044	−0.595220	−	0.803563i	$-0.702935\pi$
$113$	−12.6546	−1.19044	−0.595220	+	0.803563i	$0.702935\pi$
$114$	5.25953	0.492600
$115$	9.87517	0.920864
$116$	−3.18067	−0.295318
$117$	−1.00000	−0.0924500
$118$	1.08168	0.0995766
$119$	−1.73550	−0.159093
$120$	−2.47956	−0.226352
$121$	−2.58533	−0.235030
$122$	−10.2622	−0.929099
$123$	11.7100	1.05586
$124$	−3.32455	−0.298553
$125$	−9.55070	−0.854241
$126$	−2.89002	−0.257464
$127$	5.06260	0.449233	0.224617	−	0.974447i	$-0.427887\pi$
$127$	5.06260	0.449233	0.224617	+	0.974447i	$0.427887\pi$
$128$	1.00000	0.0883883
$129$	−2.64798	−0.233142
$130$	−2.47956	−0.217472
$131$	−11.1754	−0.976402	−0.488201	−	0.872731i	$-0.662347\pi$
$131$	−11.1754	−0.976402	−0.488201	+	0.872731i	$0.662347\pi$
$132$	−2.90081	−0.252483
$133$	15.2002	1.31802
$134$	7.96532	0.688099
$135$	−2.47956	−0.213407
$136$	0.600515	0.0514937
$137$	−8.70375	−0.743612	−0.371806	−	0.928310i	$-0.621261\pi$
$137$	−8.70375	−0.743612	−0.371806	+	0.928310i	$0.621261\pi$
$138$	−3.98263	−0.339024
$139$	10.6963	0.907245	0.453623	−	0.891194i	$-0.350131\pi$
$139$	10.6963	0.907245	0.453623	+	0.891194i	$0.350131\pi$
$140$	−7.16599	−0.605637
$141$	11.4015	0.960180
$142$	10.2926	0.863739
$143$	−2.90081	−0.242578
$144$	1.00000	0.0833333
$145$	−7.88668	−0.654953
$146$	12.4630	1.03144
$147$	−1.35223	−0.111530
$148$	−10.9890	−0.903291
$149$	−5.28604	−0.433049	−0.216525	−	0.976277i	$-0.569472\pi$
$149$	−5.28604	−0.433049	−0.216525	+	0.976277i	$0.569472\pi$
$150$	−1.14823	−0.0937526
$151$	−5.72306	−0.465736	−0.232868	−	0.972508i	$-0.574811\pi$
$151$	−5.72306	−0.465736	−0.232868	+	0.972508i	$0.574811\pi$
$152$	−5.25953	−0.426604
$153$	0.600515	0.0485488
$154$	−8.38339	−0.675553
$155$	−8.24342	−0.662127
$156$	1.00000	0.0800641
$157$	−5.76483	−0.460084	−0.230042	−	0.973181i	$-0.573886\pi$
$157$	−5.76483	−0.460084	−0.230042	+	0.973181i	$0.573886\pi$
$158$	4.57087	0.363639
$159$	3.86641	0.306626
$160$	2.47956	0.196027
$161$	−11.5099	−0.907105
$162$	1.00000	0.0785674
$163$	−18.5101	−1.44983	−0.724913	−	0.688840i	$-0.758120\pi$
$163$	−18.5101	−1.44983	−0.724913	+	0.688840i	$0.758120\pi$
$164$	−11.7100	−0.914400
$165$	−7.19273	−0.559953
$166$	−2.92067	−0.226688
$167$	14.0116	1.08425	0.542127	−	0.840297i	$-0.317619\pi$
$167$	14.0116	1.08425	0.542127	+	0.840297i	$0.317619\pi$
$168$	2.89002	0.222970
$169$	1.00000	0.0769231
$170$	1.48901	0.114202
$171$	−5.25953	−0.402206
$172$	2.64798	0.201907
$173$	15.6516	1.18997	0.594985	−	0.803737i	$-0.297158\pi$
$173$	15.6516	1.18997	0.594985	+	0.803737i	$0.297158\pi$
$174$	3.18067	0.241126
$175$	−3.31841	−0.250848
$176$	2.90081	0.218656
$177$	−1.08168	−0.0813040
$178$	8.74202	0.655242
$179$	−4.66202	−0.348456	−0.174228	−	0.984705i	$-0.555743\pi$
$179$	−4.66202	−0.348456	−0.174228	+	0.984705i	$0.555743\pi$
$180$	2.47956	0.184816
$181$	25.9795	1.93104	0.965519	−	0.260331i	$-0.0838317\pi$
$181$	25.9795	1.93104	0.965519	+	0.260331i	$0.0838317\pi$
$182$	2.89002	0.214223
$183$	10.2622	0.758606
$184$	3.98263	0.293603
$185$	−27.2479	−2.00331
$186$	3.32455	0.243768
$187$	1.74198	0.127386
$188$	−11.4015	−0.831540
$189$	2.89002	0.210218
$190$	−13.0413	−0.946118
$191$	−3.81922	−0.276349	−0.138175	−	0.990408i	$-0.544123\pi$
$191$	−3.81922	−0.276349	−0.138175	+	0.990408i	$0.544123\pi$
$192$	−1.00000	−0.0721688
$193$	−21.2978	−1.53305	−0.766525	−	0.642215i	$-0.778016\pi$
$193$	−21.2978	−1.53305	−0.766525	+	0.642215i	$0.778016\pi$
$194$	15.8595	1.13864
$195$	2.47956	0.177565
$196$	1.35223	0.0965877
$197$	−3.38264	−0.241003	−0.120502	−	0.992713i	$-0.538450\pi$
$197$	−3.38264	−0.241003	−0.120502	+	0.992713i	$0.538450\pi$
$198$	2.90081	0.206151
$199$	9.71031	0.688345	0.344173	−	0.938906i	$-0.388159\pi$
$199$	9.71031	0.688345	0.344173	+	0.938906i	$0.388159\pi$
$200$	1.14823	0.0811921
$201$	−7.96532	−0.561830
$202$	1.20794	0.0849907
$203$	9.19222	0.645167
$204$	−0.600515	−0.0420445
$205$	−29.0358	−2.02795
$206$	1.00000	0.0696733
$207$	3.98263	0.276812
$208$	−1.00000	−0.0693375
$209$	−15.2569	−1.05534
$210$	7.16599	0.494500
$211$	0.302633	0.0208341	0.0104171	−	0.999946i	$-0.496684\pi$
$211$	0.302633	0.0208341	0.0104171	+	0.999946i	$0.496684\pi$
$212$	−3.86641	−0.265546
$213$	−10.2926	−0.705240
$214$	−9.24442	−0.631936
$215$	6.56583	0.447786
$216$	−1.00000	−0.0680414
$217$	9.60801	0.652234
$218$	−13.5565	−0.918161
$219$	−12.4630	−0.842171
$220$	7.19273	0.484934
$221$	−0.600515	−0.0403950
$222$	10.9890	0.737534
$223$	−1.73371	−0.116098	−0.0580489	−	0.998314i	$-0.518488\pi$
$223$	−1.73371	−0.116098	−0.0580489	+	0.998314i	$0.518488\pi$
$224$	−2.89002	−0.193098
$225$	1.14823	0.0765487
$226$	−12.6546	−0.841768
$227$	−19.0851	−1.26672	−0.633361	−	0.773857i	$-0.718325\pi$
$227$	−19.0851	−1.26672	−0.633361	+	0.773857i	$0.718325\pi$
$228$	5.25953	0.348321
$229$	−11.5942	−0.766165	−0.383083	−	0.923714i	$-0.625138\pi$
$229$	−11.5942	−0.766165	−0.383083	+	0.923714i	$0.625138\pi$
$230$	9.87517	0.651149
$231$	8.38339	0.551587
$232$	−3.18067	−0.208821
$233$	−25.1780	−1.64947	−0.824733	−	0.565523i	$-0.808675\pi$
$233$	−25.1780	−1.64947	−0.824733	+	0.565523i	$0.808675\pi$
$234$	−1.00000	−0.0653720
$235$	−28.2707	−1.84418
$236$	1.08168	0.0704113
$237$	−4.57087	−0.296910
$238$	−1.73550	−0.112496
$239$	−11.7062	−0.757212	−0.378606	−	0.925558i	$-0.623596\pi$
$239$	−11.7062	−0.757212	−0.378606	+	0.925558i	$0.623596\pi$
$240$	−2.47956	−0.160055
$241$	−16.6536	−1.07276	−0.536378	−	0.843978i	$-0.680208\pi$
$241$	−16.6536	−1.07276	−0.536378	+	0.843978i	$0.680208\pi$
$242$	−2.58533	−0.166191
$243$	−1.00000	−0.0641500
$244$	−10.2622	−0.656972
$245$	3.35293	0.214211
$246$	11.7100	0.746605
$247$	5.25953	0.334656
$248$	−3.32455	−0.211109
$249$	2.92067	0.185090
$250$	−9.55070	−0.604040
$251$	6.06402	0.382757	0.191379	−	0.981516i	$-0.438704\pi$
$251$	6.06402	0.382757	0.191379	+	0.981516i	$0.438704\pi$
$252$	−2.89002	−0.182054
$253$	11.5528	0.726320
$254$	5.06260	0.317656
$255$	−1.48901	−0.0932457
$256$	1.00000	0.0625000
$257$	9.94524	0.620367	0.310184	−	0.950677i	$-0.399609\pi$
$257$	9.94524	0.620367	0.310184	+	0.950677i	$0.399609\pi$
$258$	−2.64798	−0.164856
$259$	31.7585	1.97338
$260$	−2.47956	−0.153776
$261$	−3.18067	−0.196879
$262$	−11.1754	−0.690421
$263$	15.4285	0.951365	0.475682	−	0.879617i	$-0.342201\pi$
$263$	15.4285	0.951365	0.475682	+	0.879617i	$0.342201\pi$
$264$	−2.90081	−0.178532
$265$	−9.58701	−0.588925
$266$	15.2002	0.931982
$267$	−8.74202	−0.535003
$268$	7.96532	0.486559
$269$	14.2747	0.870342	0.435171	−	0.900348i	$-0.356688\pi$
$269$	14.2747	0.870342	0.435171	+	0.900348i	$0.356688\pi$
$270$	−2.47956	−0.150901
$271$	28.1851	1.71212	0.856062	−	0.516872i	$-0.172904\pi$
$271$	28.1851	1.71212	0.856062	+	0.516872i	$0.172904\pi$
$272$	0.600515	0.0364116
$273$	−2.89002	−0.174912
$274$	−8.70375	−0.525813
$275$	3.33079	0.200854
$276$	−3.98263	−0.239726
$277$	−13.7238	−0.824582	−0.412291	−	0.911052i	$-0.635271\pi$
$277$	−13.7238	−0.824582	−0.412291	+	0.911052i	$0.635271\pi$
$278$	10.6963	0.641519
$279$	−3.32455	−0.199035
$280$	−7.16599	−0.428250
$281$	−11.0717	−0.660480	−0.330240	−	0.943897i	$-0.607130\pi$
$281$	−11.0717	−0.660480	−0.330240	+	0.943897i	$0.607130\pi$
$282$	11.4015	0.678950
$283$	14.9927	0.891224	0.445612	−	0.895226i	$-0.352986\pi$
$283$	14.9927	0.891224	0.445612	+	0.895226i	$0.352986\pi$
$284$	10.2926	0.610756
$285$	13.0413	0.772502
$286$	−2.90081	−0.171528
$287$	33.8423	1.99765
$288$	1.00000	0.0589256
$289$	−16.6394	−0.978787
$290$	−7.88668	−0.463122
$291$	−15.8595	−0.929699
$292$	12.4630	0.729342
$293$	14.3300	0.837167	0.418583	−	0.908178i	$-0.362527\pi$
$293$	14.3300	0.837167	0.418583	+	0.908178i	$0.362527\pi$
$294$	−1.35223	−0.0788635
$295$	2.68209	0.156157
$296$	−10.9890	−0.638723
$297$	−2.90081	−0.168322
$298$	−5.28604	−0.306212
$299$	−3.98263	−0.230321
$300$	−1.14823	−0.0662931
$301$	−7.65272	−0.441096
$302$	−5.72306	−0.329325
$303$	−1.20794	−0.0693946
$304$	−5.25953	−0.301655
$305$	−25.4458	−1.45702
$306$	0.600515	0.0343292
$307$	−29.9350	−1.70848	−0.854241	−	0.519878i	$-0.825978\pi$
$307$	−29.9350	−1.70848	−0.854241	+	0.519878i	$0.825978\pi$
$308$	−8.38339	−0.477688
$309$	−1.00000	−0.0568880
$310$	−8.24342	−0.468195
$311$	18.7887	1.06541	0.532706	−	0.846300i	$-0.321175\pi$
$311$	18.7887	1.06541	0.532706	+	0.846300i	$0.321175\pi$
$312$	1.00000	0.0566139
$313$	−6.00068	−0.339179	−0.169589	−	0.985515i	$-0.554244\pi$
$313$	−6.00068	−0.339179	−0.169589	+	0.985515i	$0.554244\pi$
$314$	−5.76483	−0.325328
$315$	−7.16599	−0.403758
$316$	4.57087	0.257131
$317$	−24.8356	−1.39491	−0.697454	−	0.716630i	$-0.745684\pi$
$317$	−24.8356	−1.39491	−0.697454	+	0.716630i	$0.745684\pi$
$318$	3.86641	0.216818
$319$	−9.22651	−0.516586
$320$	2.47956	0.138612
$321$	9.24442	0.515973
$322$	−11.5099	−0.641420
$323$	−3.15843	−0.175740
$324$	1.00000	0.0555556
$325$	−1.14823	−0.0636923
$326$	−18.5101	−1.02518
$327$	13.5565	0.749675
$328$	−11.7100	−0.646579
$329$	32.9506	1.81663
$330$	−7.19273	−0.395947
$331$	2.63869	0.145035	0.0725177	−	0.997367i	$-0.476897\pi$
$331$	2.63869	0.145035	0.0725177	+	0.997367i	$0.476897\pi$
$332$	−2.92067	−0.160292
$333$	−10.9890	−0.602194
$334$	14.0116	0.766683
$335$	19.7505	1.07909
$336$	2.89002	0.157664
$337$	26.3122	1.43332	0.716658	−	0.697424i	$-0.245671\pi$
$337$	26.3122	1.43332	0.716658	+	0.697424i	$0.245671\pi$
$338$	1.00000	0.0543928
$339$	12.6546	0.687301
$340$	1.48901	0.0807532
$341$	−9.64386	−0.522244
$342$	−5.25953	−0.284403
$343$	16.3222	0.881315
$344$	2.64798	0.142770
$345$	−9.87517	−0.531661
$346$	15.6516	0.841435
$347$	0.378755	0.0203326	0.0101663	−	0.999948i	$-0.496764\pi$
$347$	0.378755	0.0203326	0.0101663	+	0.999948i	$0.496764\pi$
$348$	3.18067	0.170502
$349$	−2.12315	−0.113650	−0.0568249	−	0.998384i	$-0.518098\pi$
$349$	−2.12315	−0.113650	−0.0568249	+	0.998384i	$0.518098\pi$
$350$	−3.31841	−0.177377
$351$	1.00000	0.0533761
$352$	2.90081	0.154613
$353$	26.9491	1.43435	0.717177	−	0.696891i	$-0.245434\pi$
$353$	26.9491	1.43435	0.717177	+	0.696891i	$0.245434\pi$
$354$	−1.08168	−0.0574906
$355$	25.5212	1.35453
$356$	8.74202	0.463326
$357$	1.73550	0.0918525
$358$	−4.66202	−0.246396
$359$	0.933539	0.0492703	0.0246352	−	0.999697i	$-0.492158\pi$
$359$	0.933539	0.0492703	0.0246352	+	0.999697i	$0.492158\pi$
$360$	2.47956	0.130684
$361$	8.66268	0.455931
$362$	25.9795	1.36545
$363$	2.58533	0.135695
$364$	2.89002	0.151478
$365$	30.9028	1.61753
$366$	10.2622	0.536415
$367$	1.13322	0.0591538	0.0295769	−	0.999563i	$-0.490584\pi$
$367$	1.13322	0.0591538	0.0295769	+	0.999563i	$0.490584\pi$
$368$	3.98263	0.207609
$369$	−11.7100	−0.609600
$370$	−27.2479	−1.41655
$371$	11.1740	0.580126
$372$	3.32455	0.172370
$373$	22.2711	1.15315	0.576576	−	0.817043i	$-0.304388\pi$
$373$	22.2711	1.15315	0.576576	+	0.817043i	$0.304388\pi$
$374$	1.74198	0.0900755
$375$	9.55070	0.493196
$376$	−11.4015	−0.587988
$377$	3.18067	0.163813
$378$	2.89002	0.148647
$379$	8.67947	0.445835	0.222917	−	0.974837i	$-0.428442\pi$
$379$	8.67947	0.445835	0.222917	+	0.974837i	$0.428442\pi$
$380$	−13.0413	−0.669007
$381$	−5.06260	−0.259365
$382$	−3.81922	−0.195408
$383$	−17.2227	−0.880038	−0.440019	−	0.897989i	$-0.645028\pi$
$383$	−17.2227	−0.880038	−0.440019	+	0.897989i	$0.645028\pi$
$384$	−1.00000	−0.0510310
$385$	−20.7871	−1.05941
$386$	−21.2978	−1.08403
$387$	2.64798	0.134604
$388$	15.8595	0.805143
$389$	−31.0210	−1.57283	−0.786414	−	0.617700i	$-0.788065\pi$
$389$	−31.0210	−1.57283	−0.786414	+	0.617700i	$0.788065\pi$
$390$	2.47956	0.125558
$391$	2.39163	0.120950
$392$	1.35223	0.0682978
$393$	11.1754	0.563726
$394$	−3.38264	−0.170415
$395$	11.3338	0.570263
$396$	2.90081	0.145771
$397$	−21.0848	−1.05821	−0.529107	−	0.848555i	$-0.677473\pi$
$397$	−21.0848	−1.05821	−0.529107	+	0.848555i	$0.677473\pi$
$398$	9.71031	0.486734
$399$	−15.2002	−0.760960
$400$	1.14823	0.0574115
$401$	3.49679	0.174621	0.0873106	−	0.996181i	$-0.472173\pi$
$401$	3.49679	0.174621	0.0873106	+	0.996181i	$0.472173\pi$
$402$	−7.96532	−0.397274
$403$	3.32455	0.165607
$404$	1.20794	0.0600975
$405$	2.47956	0.123210
$406$	9.19222	0.456202
$407$	−31.8770	−1.58008
$408$	−0.600515	−0.0297299
$409$	0.735549	0.0363705	0.0181853	−	0.999835i	$-0.494211\pi$
$409$	0.735549	0.0363705	0.0181853	+	0.999835i	$0.494211\pi$
$410$	−29.0358	−1.43397
$411$	8.70375	0.429324
$412$	1.00000	0.0492665
$413$	−3.12608	−0.153824
$414$	3.98263	0.195735
$415$	−7.24198	−0.355495
$416$	−1.00000	−0.0490290
$417$	−10.6963	−0.523798
$418$	−15.2569	−0.746238
$419$	−8.74164	−0.427057	−0.213529	−	0.976937i	$-0.568496\pi$
$419$	−8.74164	−0.427057	−0.213529	+	0.976937i	$0.568496\pi$
$420$	7.16599	0.349665
$421$	−40.0374	−1.95130	−0.975652	−	0.219324i	$-0.929615\pi$
$421$	−40.0374	−1.95130	−0.975652	+	0.219324i	$0.929615\pi$
$422$	0.302633	0.0147320
$423$	−11.4015	−0.554360
$424$	−3.86641	−0.187770
$425$	0.689530	0.0334471
$426$	−10.2926	−0.498680
$427$	29.6581	1.43525
$428$	−9.24442	−0.446846
$429$	2.90081	0.140052
$430$	6.56583	0.316633
$431$	−17.0381	−0.820697	−0.410349	−	0.911929i	$-0.634593\pi$
$431$	−17.0381	−0.820697	−0.410349	+	0.911929i	$0.634593\pi$
$432$	−1.00000	−0.0481125
$433$	10.5116	0.505157	0.252578	−	0.967576i	$-0.418721\pi$
$433$	10.5116	0.505157	0.252578	+	0.967576i	$0.418721\pi$
$434$	9.60801	0.461199
$435$	7.88668	0.378137
$436$	−13.5565	−0.649238
$437$	−20.9468	−1.00202
$438$	−12.4630	−0.595505
$439$	36.7323	1.75314	0.876568	−	0.481278i	$-0.159827\pi$
$439$	36.7323	1.75314	0.876568	+	0.481278i	$0.159827\pi$
$440$	7.19273	0.342900
$441$	1.35223	0.0643918
$442$	−0.600515	−0.0285636
$443$	−1.39731	−0.0663883	−0.0331941	−	0.999449i	$-0.510568\pi$
$443$	−1.39731	−0.0663883	−0.0331941	+	0.999449i	$0.510568\pi$
$444$	10.9890	0.521515
$445$	21.6764	1.02756
$446$	−1.73371	−0.0820935
$447$	5.28604	0.250021
$448$	−2.89002	−0.136541
$449$	−29.4721	−1.39088	−0.695438	−	0.718586i	$-0.744790\pi$
$449$	−29.4721	−1.39088	−0.695438	+	0.718586i	$0.744790\pi$
$450$	1.14823	0.0541281
$451$	−33.9685	−1.59952
$452$	−12.6546	−0.595220
$453$	5.72306	0.268893
$454$	−19.0851	−0.895707
$455$	7.16599	0.335947
$456$	5.25953	0.246300
$457$	−19.6913	−0.921121	−0.460560	−	0.887628i	$-0.652352\pi$
$457$	−19.6913	−0.921121	−0.460560	+	0.887628i	$0.652352\pi$
$458$	−11.5942	−0.541761
$459$	−0.600515	−0.0280296
$460$	9.87517	0.460432
$461$	10.6804	0.497437	0.248719	−	0.968576i	$-0.419991\pi$
$461$	10.6804	0.497437	0.248719	+	0.968576i	$0.419991\pi$
$462$	8.38339	0.390031
$463$	7.77142	0.361168	0.180584	−	0.983560i	$-0.442201\pi$
$463$	7.77142	0.361168	0.180584	+	0.983560i	$0.442201\pi$
$464$	−3.18067	−0.147659
$465$	8.24342	0.382279
$466$	−25.1780	−1.16635
$467$	−1.71116	−0.0791830	−0.0395915	−	0.999216i	$-0.512606\pi$
$467$	−1.71116	−0.0791830	−0.0395915	+	0.999216i	$0.512606\pi$
$468$	−1.00000	−0.0462250
$469$	−23.0199	−1.06296
$470$	−28.2707	−1.30403
$471$	5.76483	0.265629
$472$	1.08168	0.0497883
$473$	7.68127	0.353185
$474$	−4.57087	−0.209947
$475$	−6.03915	−0.277095
$476$	−1.73550	−0.0795466
$477$	−3.86641	−0.177031
$478$	−11.7062	−0.535430
$479$	10.2984	0.470548	0.235274	−	0.971929i	$-0.424401\pi$
$479$	10.2984	0.470548	0.235274	+	0.971929i	$0.424401\pi$
$480$	−2.47956	−0.113176
$481$	10.9890	0.501056
$482$	−16.6536	−0.758553
$483$	11.5099	0.523718
$484$	−2.58533	−0.117515
$485$	39.3245	1.78564
$486$	−1.00000	−0.0453609
$487$	19.6833	0.891937	0.445968	−	0.895049i	$-0.352859\pi$
$487$	19.6833	0.891937	0.445968	+	0.895049i	$0.352859\pi$
$488$	−10.2622	−0.464549
$489$	18.5101	0.837058
$490$	3.35293	0.151470
$491$	−25.0458	−1.13030	−0.565151	−	0.824987i	$-0.691182\pi$
$491$	−25.0458	−1.13030	−0.565151	+	0.824987i	$0.691182\pi$
$492$	11.7100	0.527929
$493$	−1.91004	−0.0860240
$494$	5.25953	0.236638
$495$	7.19273	0.323289
$496$	−3.32455	−0.149277
$497$	−29.7459	−1.33429
$498$	2.92067	0.130878
$499$	−6.10890	−0.273472	−0.136736	−	0.990608i	$-0.543661\pi$
$499$	−6.10890	−0.273472	−0.136736	+	0.990608i	$0.543661\pi$
$500$	−9.55070	−0.427120
$501$	−14.0116	−0.625994
$502$	6.06402	0.270650
$503$	−27.4405	−1.22351	−0.611755	−	0.791048i	$-0.709536\pi$
$503$	−27.4405	−1.22351	−0.611755	+	0.791048i	$0.709536\pi$
$504$	−2.89002	−0.128732
$505$	2.99517	0.133284
$506$	11.5528	0.513586
$507$	−1.00000	−0.0444116
$508$	5.06260	0.224617
$509$	8.76145	0.388344	0.194172	−	0.980967i	$-0.437798\pi$
$509$	8.76145	0.388344	0.194172	+	0.980967i	$0.437798\pi$
$510$	−1.48901	−0.0659347
$511$	−36.0183	−1.59336
$512$	1.00000	0.0441942
$513$	5.25953	0.232214
$514$	9.94524	0.438666
$515$	2.47956	0.109263
$516$	−2.64798	−0.116571
$517$	−33.0735	−1.45457
$518$	31.7585	1.39539
$519$	−15.6516	−0.687029
$520$	−2.47956	−0.108736
$521$	−41.9722	−1.83884	−0.919419	−	0.393280i	$-0.871340\pi$
$521$	−41.9722	−1.83884	−0.919419	+	0.393280i	$0.871340\pi$
$522$	−3.18067	−0.139214
$523$	5.80278	0.253738	0.126869	−	0.991919i	$-0.459507\pi$
$523$	5.80278	0.253738	0.126869	+	0.991919i	$0.459507\pi$
$524$	−11.1754	−0.488201
$525$	3.31841	0.144827
$526$	15.4285	0.672716
$527$	−1.99644	−0.0869663
$528$	−2.90081	−0.126241
$529$	−7.13869	−0.310378
$530$	−9.58701	−0.416433
$531$	1.08168	0.0469409
$532$	15.2002	0.659011
$533$	11.7100	0.507218
$534$	−8.74202	−0.378304
$535$	−22.9221	−0.991010
$536$	7.96532	0.344049
$537$	4.66202	0.201181
$538$	14.2747	0.615425
$539$	3.92255	0.168956
$540$	−2.47956	−0.106703
$541$	−35.5307	−1.52759	−0.763793	−	0.645461i	$-0.776665\pi$
$541$	−35.5307	−1.52759	−0.763793	+	0.645461i	$0.776665\pi$
$542$	28.1851	1.21066
$543$	−25.9795	−1.11489
$544$	0.600515	0.0257469
$545$	−33.6141	−1.43987
$546$	−2.89002	−0.123682
$547$	4.03026	0.172321	0.0861607	−	0.996281i	$-0.472540\pi$
$547$	4.03026	0.172321	0.0861607	+	0.996281i	$0.472540\pi$
$548$	−8.70375	−0.371806
$549$	−10.2622	−0.437981
$550$	3.33079	0.142025
$551$	16.7289	0.712673
$552$	−3.98263	−0.169512
$553$	−13.2099	−0.561743
$554$	−13.7238	−0.583068
$555$	27.2479	1.15661
$556$	10.6963	0.453623
$557$	5.74473	0.243412	0.121706	−	0.992566i	$-0.461164\pi$
$557$	5.74473	0.243412	0.121706	+	0.992566i	$0.461164\pi$
$558$	−3.32455	−0.140739
$559$	−2.64798	−0.111998
$560$	−7.16599	−0.302818
$561$	−1.74198	−0.0735463
$562$	−11.0717	−0.467030
$563$	−3.25748	−0.137286	−0.0686431	−	0.997641i	$-0.521867\pi$
$563$	−3.25748	−0.137286	−0.0686431	+	0.997641i	$0.521867\pi$
$564$	11.4015	0.480090
$565$	−31.3778	−1.32007
$566$	14.9927	0.630190
$567$	−2.89002	−0.121370
$568$	10.2926	0.431869
$569$	42.7839	1.79359	0.896796	−	0.442444i	$-0.145888\pi$
$569$	42.7839	1.79359	0.896796	+	0.442444i	$0.145888\pi$
$570$	13.0413	0.546242
$571$	4.76805	0.199537	0.0997683	−	0.995011i	$-0.468190\pi$
$571$	4.76805	0.199537	0.0997683	+	0.995011i	$0.468190\pi$
$572$	−2.90081	−0.121289
$573$	3.81922	0.159550
$574$	33.8423	1.41255
$575$	4.57297	0.190706
$576$	1.00000	0.0416667
$577$	23.7580	0.989060	0.494530	−	0.869161i	$-0.335340\pi$
$577$	23.7580	0.989060	0.494530	+	0.869161i	$0.335340\pi$
$578$	−16.6394	−0.692107
$579$	21.2978	0.885107
$580$	−7.88668	−0.327477
$581$	8.44079	0.350183
$582$	−15.8595	−0.657396
$583$	−11.2157	−0.464507
$584$	12.4630	0.515722
$585$	−2.47956	−0.102517
$586$	14.3300	0.591966
$587$	4.54740	0.187691	0.0938456	−	0.995587i	$-0.470084\pi$
$587$	4.54740	0.187691	0.0938456	+	0.995587i	$0.470084\pi$
$588$	−1.35223	−0.0557649
$589$	17.4856	0.720480
$590$	2.68209	0.110420
$591$	3.38264	0.139143
$592$	−10.9890	−0.451645
$593$	12.4189	0.509984	0.254992	−	0.966943i	$-0.417927\pi$
$593$	12.4189	0.509984	0.254992	+	0.966943i	$0.417927\pi$
$594$	−2.90081	−0.119021
$595$	−4.30329	−0.176418
$596$	−5.28604	−0.216525
$597$	−9.71031	−0.397416
$598$	−3.98263	−0.162862
$599$	7.98993	0.326460	0.163230	−	0.986588i	$-0.447809\pi$
$599$	7.98993	0.326460	0.163230	+	0.986588i	$0.447809\pi$
$600$	−1.14823	−0.0468763
$601$	−0.550756	−0.0224658	−0.0112329	−	0.999937i	$-0.503576\pi$
$601$	−0.550756	−0.0224658	−0.0112329	+	0.999937i	$0.503576\pi$
$602$	−7.65272	−0.311902
$603$	7.96532	0.324373
$604$	−5.72306	−0.232868
$605$	−6.41049	−0.260623
$606$	−1.20794	−0.0490694
$607$	−31.7955	−1.29054	−0.645270	−	0.763955i	$-0.723255\pi$
$607$	−31.7955	−1.29054	−0.645270	+	0.763955i	$0.723255\pi$
$608$	−5.25953	−0.213302
$609$	−9.19222	−0.372487
$610$	−25.4458	−1.03027
$611$	11.4015	0.461255
$612$	0.600515	0.0242744
$613$	−34.3879	−1.38891	−0.694457	−	0.719534i	$-0.744356\pi$
$613$	−34.3879	−1.38891	−0.694457	+	0.719534i	$0.744356\pi$
$614$	−29.9350	−1.20808
$615$	29.0358	1.17084
$616$	−8.38339	−0.337776
$617$	33.2991	1.34057	0.670285	−	0.742104i	$-0.266172\pi$
$617$	33.2991	1.34057	0.670285	+	0.742104i	$0.266172\pi$
$618$	−1.00000	−0.0402259
$619$	1.03396	0.0415583	0.0207792	−	0.999784i	$-0.493385\pi$
$619$	1.03396	0.0415583	0.0207792	+	0.999784i	$0.493385\pi$
$620$	−8.24342	−0.331064
$621$	−3.98263	−0.159817
$622$	18.7887	0.753360
$623$	−25.2646	−1.01221
$624$	1.00000	0.0400320
$625$	−29.4227	−1.17691
$626$	−6.00068	−0.239836
$627$	15.2569	0.609301
$628$	−5.76483	−0.230042
$629$	−6.59907	−0.263122
$630$	−7.16599	−0.285500
$631$	22.7363	0.905117	0.452558	−	0.891735i	$-0.350511\pi$
$631$	22.7363	0.905117	0.452558	+	0.891735i	$0.350511\pi$
$632$	4.57087	0.181819
$633$	−0.302633	−0.0120286
$634$	−24.8356	−0.986349
$635$	12.5530	0.498152
$636$	3.86641	0.153313
$637$	−1.35223	−0.0535772
$638$	−9.22651	−0.365281
$639$	10.2926	0.407170
$640$	2.47956	0.0980133
$641$	−17.2153	−0.679962	−0.339981	−	0.940432i	$-0.610421\pi$
$641$	−17.2153	−0.679962	−0.339981	+	0.940432i	$0.610421\pi$
$642$	9.24442	0.364848
$643$	36.2026	1.42769	0.713846	−	0.700303i	$-0.246952\pi$
$643$	36.2026	1.42769	0.713846	+	0.700303i	$0.246952\pi$
$644$	−11.5099	−0.453553
$645$	−6.56583	−0.258529
$646$	−3.15843	−0.124267
$647$	−11.7082	−0.460298	−0.230149	−	0.973155i	$-0.573921\pi$
$647$	−11.7082	−0.460298	−0.230149	+	0.973155i	$0.573921\pi$
$648$	1.00000	0.0392837
$649$	3.13774	0.123167
$650$	−1.14823	−0.0450373
$651$	−9.60801	−0.376568
$652$	−18.5101	−0.724913
$653$	41.2859	1.61564	0.807821	−	0.589428i	$-0.200647\pi$
$653$	41.2859	1.61564	0.807821	+	0.589428i	$0.200647\pi$
$654$	13.5565	0.530100
$655$	−27.7102	−1.08273
$656$	−11.7100	−0.457200
$657$	12.4630	0.486228
$658$	32.9506	1.28455
$659$	−17.7762	−0.692461	−0.346231	−	0.938149i	$-0.612538\pi$
$659$	−17.7762	−0.692461	−0.346231	+	0.938149i	$0.612538\pi$
$660$	−7.19273	−0.279977
$661$	45.8706	1.78416	0.892079	−	0.451879i	$-0.149246\pi$
$661$	45.8706	1.78416	0.892079	+	0.451879i	$0.149246\pi$
$662$	2.63869	0.102556
$663$	0.600515	0.0233221
$664$	−2.92067	−0.113344
$665$	37.6898	1.46155
$666$	−10.9890	−0.425815
$667$	−12.6674	−0.490485
$668$	14.0116	0.542127
$669$	1.73371	0.0670291
$670$	19.7505	0.763029
$671$	−29.7687	−1.14921
$672$	2.89002	0.111485
$673$	−8.59510	−0.331317	−0.165658	−	0.986183i	$-0.552975\pi$
$673$	−8.59510	−0.331317	−0.165658	+	0.986183i	$0.552975\pi$
$674$	26.3122	1.01351
$675$	−1.14823	−0.0441954
$676$	1.00000	0.0384615
$677$	9.42580	0.362263	0.181131	−	0.983459i	$-0.442024\pi$
$677$	9.42580	0.362263	0.181131	+	0.983459i	$0.442024\pi$
$678$	12.6546	0.485995
$679$	−45.8342	−1.75896
$680$	1.48901	0.0571011
$681$	19.0851	0.731342
$682$	−9.64386	−0.369282
$683$	30.3440	1.16108	0.580541	−	0.814231i	$-0.302841\pi$
$683$	30.3440	1.16108	0.580541	+	0.814231i	$0.302841\pi$
$684$	−5.25953	−0.201103
$685$	−21.5815	−0.824587
$686$	16.3222	0.623184
$687$	11.5942	0.442346
$688$	2.64798	0.100953
$689$	3.86641	0.147299
$690$	−9.87517	−0.375941
$691$	28.5095	1.08455	0.542276	−	0.840200i	$-0.317563\pi$
$691$	28.5095	1.08455	0.542276	+	0.840200i	$0.317563\pi$
$692$	15.6516	0.594985
$693$	−8.38339	−0.318459
$694$	0.378755	0.0143773
$695$	26.5220	1.00604
$696$	3.18067	0.120563
$697$	−7.03205	−0.266358
$698$	−2.12315	−0.0803625
$699$	25.1780	0.952319
$700$	−3.31841	−0.125424
$701$	−46.2456	−1.74667	−0.873337	−	0.487117i	$-0.838049\pi$
$701$	−46.2456	−1.74667	−0.873337	+	0.487117i	$0.838049\pi$
$702$	1.00000	0.0377426
$703$	57.7970	2.17986
$704$	2.90081	0.109328
$705$	28.2707	1.06474
$706$	26.9491	1.01424
$707$	−3.49099	−0.131292
$708$	−1.08168	−0.0406520
$709$	4.31897	0.162202	0.0811012	−	0.996706i	$-0.474156\pi$
$709$	4.31897	0.162202	0.0811012	+	0.996706i	$0.474156\pi$
$710$	25.5212	0.957795
$711$	4.57087	0.171421
$712$	8.74202	0.327621
$713$	−13.2404	−0.495858
$714$	1.73550	0.0649495
$715$	−7.19273	−0.268993
$716$	−4.66202	−0.174228
$717$	11.7062	0.437177
$718$	0.933539	0.0348394
$719$	−16.5659	−0.617804	−0.308902	−	0.951094i	$-0.599961\pi$
$719$	−16.5659	−0.617804	−0.308902	+	0.951094i	$0.599961\pi$
$720$	2.47956	0.0924078
$721$	−2.89002	−0.107630
$722$	8.66268	0.322392
$723$	16.6536	0.619356
$724$	25.9795	0.965519
$725$	−3.65215	−0.135637
$726$	2.58533	0.0959506
$727$	−22.0271	−0.816940	−0.408470	−	0.912772i	$-0.633938\pi$
$727$	−22.0271	−0.816940	−0.408470	+	0.912772i	$0.633938\pi$
$728$	2.89002	0.107111
$729$	1.00000	0.0370370
$730$	30.9028	1.14376
$731$	1.59015	0.0588139
$732$	10.2622	0.379303
$733$	−33.5101	−1.23772	−0.618862	−	0.785499i	$-0.712406\pi$
$733$	−33.5101	−1.23772	−0.618862	+	0.785499i	$0.712406\pi$
$734$	1.13322	0.0418280
$735$	−3.35293	−0.123675
$736$	3.98263	0.146802
$737$	23.1058	0.851114
$738$	−11.7100	−0.431052
$739$	21.9021	0.805683	0.402841	−	0.915270i	$-0.368023\pi$
$739$	21.9021	0.805683	0.402841	+	0.915270i	$0.368023\pi$
$740$	−27.2479	−1.00165
$741$	−5.25953	−0.193214
$742$	11.1740	0.410211
$743$	22.1421	0.812313	0.406157	−	0.913804i	$-0.366869\pi$
$743$	22.1421	0.812313	0.406157	+	0.913804i	$0.366869\pi$
$744$	3.32455	0.121884
$745$	−13.1071	−0.480206
$746$	22.2711	0.815402
$747$	−2.92067	−0.106862
$748$	1.74198	0.0636930
$749$	26.7166	0.976203
$750$	9.55070	0.348742
$751$	−41.3846	−1.51015	−0.755073	−	0.655641i	$-0.772399\pi$
$751$	−41.3846	−1.51015	−0.755073	+	0.655641i	$0.772399\pi$
$752$	−11.4015	−0.415770
$753$	−6.06402	−0.220985
$754$	3.18067	0.115833
$755$	−14.1907	−0.516452
$756$	2.89002	0.105109
$757$	33.2928	1.21005	0.605023	−	0.796208i	$-0.293164\pi$
$757$	33.2928	1.21005	0.605023	+	0.796208i	$0.293164\pi$
$758$	8.67947	0.315253
$759$	−11.5528	−0.419341
$760$	−13.0413	−0.473059
$761$	9.03610	0.327558	0.163779	−	0.986497i	$-0.447632\pi$
$761$	9.03610	0.327558	0.163779	+	0.986497i	$0.447632\pi$
$762$	−5.06260	−0.183399
$763$	39.1785	1.41836
$764$	−3.81922	−0.138175
$765$	1.48901	0.0538354
$766$	−17.2227	−0.622281
$767$	−1.08168	−0.0390572
$768$	−1.00000	−0.0360844
$769$	11.5004	0.414715	0.207357	−	0.978265i	$-0.433514\pi$
$769$	11.5004	0.414715	0.207357	+	0.978265i	$0.433514\pi$
$770$	−20.7871	−0.749117
$771$	−9.94524	−0.358169
$772$	−21.2978	−0.766525
$773$	35.6429	1.28199	0.640993	−	0.767547i	$-0.278523\pi$
$773$	35.6429	1.28199	0.640993	+	0.767547i	$0.278523\pi$
$774$	2.64798	0.0951797
$775$	−3.81734	−0.137123
$776$	15.8595	0.569322
$777$	−31.7585	−1.13933
$778$	−31.0210	−1.11216
$779$	61.5893	2.20667
$780$	2.47956	0.0887826
$781$	29.8569	1.06837
$782$	2.39163	0.0855244
$783$	3.18067	0.113668
$784$	1.35223	0.0482938
$785$	−14.2943	−0.510184
$786$	11.1754	0.398615
$787$	−50.1100	−1.78623	−0.893115	−	0.449828i	$-0.851485\pi$
$787$	−50.1100	−1.78623	−0.893115	+	0.449828i	$0.851485\pi$
$788$	−3.38264	−0.120502
$789$	−15.4285	−0.549271
$790$	11.3338	0.403237
$791$	36.5719	1.30035
$792$	2.90081	0.103076
$793$	10.2622	0.364422
$794$	−21.0848	−0.748270
$795$	9.58701	0.340016
$796$	9.71031	0.344173
$797$	50.7373	1.79721	0.898603	−	0.438762i	$-0.144583\pi$
$797$	50.7373	1.79721	0.898603	+	0.438762i	$0.144583\pi$
$798$	−15.2002	−0.538080
$799$	−6.84677	−0.242221
$800$	1.14823	0.0405961
$801$	8.74202	0.308884
$802$	3.49679	0.123476
$803$	36.1527	1.27580
$804$	−7.96532	−0.280915
$805$	−28.5395	−1.00588
$806$	3.32455	0.117102
$807$	−14.2747	−0.502492
$808$	1.20794	0.0424954
$809$	−15.2032	−0.534515	−0.267257	−	0.963625i	$-0.586117\pi$
$809$	−15.2032	−0.534515	−0.267257	+	0.963625i	$0.586117\pi$
$810$	2.47956	0.0871229
$811$	−10.1016	−0.354716	−0.177358	−	0.984146i	$-0.556755\pi$
$811$	−10.1016	−0.354716	−0.177358	+	0.984146i	$0.556755\pi$
$812$	9.19222	0.322584
$813$	−28.1851	−0.988496
$814$	−31.8770	−1.11729
$815$	−45.8971	−1.60770
$816$	−0.600515	−0.0210222
$817$	−13.9271	−0.487249
$818$	0.735549	0.0257179
$819$	2.89002	0.100986
$820$	−29.0358	−1.01397
$821$	51.1594	1.78548	0.892738	−	0.450576i	$-0.148781\pi$
$821$	51.1594	1.78548	0.892738	+	0.450576i	$0.148781\pi$
$822$	8.70375	0.303578
$823$	28.6065	0.997159	0.498579	−	0.866844i	$-0.333855\pi$
$823$	28.6065	0.997159	0.498579	+	0.866844i	$0.333855\pi$
$824$	1.00000	0.0348367
$825$	−3.33079	−0.115963
$826$	−3.12608	−0.108770
$827$	2.20603	0.0767112	0.0383556	−	0.999264i	$-0.487788\pi$
$827$	2.20603	0.0767112	0.0383556	+	0.999264i	$0.487788\pi$
$828$	3.98263	0.138406
$829$	5.29871	0.184032	0.0920159	−	0.995758i	$-0.470669\pi$
$829$	5.29871	0.184032	0.0920159	+	0.995758i	$0.470669\pi$
$830$	−7.24198	−0.251373
$831$	13.7238	0.476073
$832$	−1.00000	−0.0346688
$833$	0.812033	0.0281353
$834$	−10.6963	−0.370381
$835$	34.7427	1.20232
$836$	−15.2569	−0.527670
$837$	3.32455	0.114913
$838$	−8.74164	−0.301975
$839$	1.66068	0.0573329	0.0286665	−	0.999589i	$-0.490874\pi$
$839$	1.66068	0.0573329	0.0286665	+	0.999589i	$0.490874\pi$
$840$	7.16599	0.247250
$841$	−18.8833	−0.651149
$842$	−40.0374	−1.37978
$843$	11.0717	0.381328
$844$	0.302633	0.0104171
$845$	2.47956	0.0852995
$846$	−11.4015	−0.391992
$847$	7.47166	0.256729
$848$	−3.86641	−0.132773
$849$	−14.9927	−0.514548
$850$	0.689530	0.0236507
$851$	−43.7651	−1.50025
$852$	−10.2926	−0.352620
$853$	19.2521	0.659179	0.329589	−	0.944124i	$-0.393090\pi$
$853$	19.2521	0.659179	0.329589	+	0.944124i	$0.393090\pi$
$854$	29.6581	1.01488
$855$	−13.0413	−0.446004
$856$	−9.24442	−0.315968
$857$	−41.4673	−1.41650	−0.708248	−	0.705964i	$-0.750514\pi$
$857$	−41.4673	−1.41650	−0.708248	+	0.705964i	$0.750514\pi$
$858$	2.90081	0.0990319
$859$	20.7353	0.707478	0.353739	−	0.935344i	$-0.384910\pi$
$859$	20.7353	0.707478	0.353739	+	0.935344i	$0.384910\pi$
$860$	6.56583	0.223893
$861$	−33.8423	−1.15334
$862$	−17.0381	−0.580321
$863$	−45.8095	−1.55937	−0.779687	−	0.626170i	$-0.784622\pi$
$863$	−45.8095	−1.55937	−0.779687	+	0.626170i	$0.784622\pi$
$864$	−1.00000	−0.0340207
$865$	38.8091	1.31955
$866$	10.5116	0.357200
$867$	16.6394	0.565103
$868$	9.60801	0.326117
$869$	13.2592	0.449788
$870$	7.88668	0.267383
$871$	−7.96532	−0.269895
$872$	−13.5565	−0.459080
$873$	15.8595	0.536762
$874$	−20.9468	−0.708534
$875$	27.6017	0.933109
$876$	−12.4630	−0.421086
$877$	−19.5227	−0.659236	−0.329618	−	0.944114i	$-0.606920\pi$
$877$	−19.5227	−0.659236	−0.329618	+	0.944114i	$0.606920\pi$
$878$	36.7323	1.23965
$879$	−14.3300	−0.483339
$880$	7.19273	0.242467
$881$	−0.526259	−0.0177301	−0.00886506	−	0.999961i	$-0.502822\pi$
$881$	−0.526259	−0.0177301	−0.00886506	+	0.999961i	$0.502822\pi$
$882$	1.35223	0.0455319
$883$	17.9179	0.602985	0.301492	−	0.953469i	$-0.402515\pi$
$883$	17.9179	0.602985	0.301492	+	0.953469i	$0.402515\pi$
$884$	−0.600515	−0.0201975
$885$	−2.68209	−0.0901575
$886$	−1.39731	−0.0469436
$887$	42.3085	1.42058	0.710290	−	0.703909i	$-0.248564\pi$
$887$	42.3085	1.42058	0.710290	+	0.703909i	$0.248564\pi$
$888$	10.9890	0.368767
$889$	−14.6310	−0.490709
$890$	21.6764	0.726594
$891$	2.90081	0.0971806
$892$	−1.73371	−0.0580489
$893$	59.9666	2.00670
$894$	5.28604	0.176792
$895$	−11.5598	−0.386401
$896$	−2.89002	−0.0965489
$897$	3.98263	0.132976
$898$	−29.4721	−0.983498
$899$	10.5743	0.352672
$900$	1.14823	0.0382743
$901$	−2.32184	−0.0773516
$902$	−33.9685	−1.13103
$903$	7.65272	0.254667
$904$	−12.6546	−0.420884
$905$	64.4177	2.14132
$906$	5.72306	0.190136
$907$	−50.5270	−1.67772	−0.838861	−	0.544345i	$-0.816778\pi$
$907$	−50.5270	−1.67772	−0.838861	+	0.544345i	$0.816778\pi$
$908$	−19.0851	−0.633361
$909$	1.20794	0.0400650
$910$	7.16599	0.237550
$911$	44.7224	1.48172	0.740860	−	0.671660i	$-0.234418\pi$
$911$	44.7224	1.48172	0.740860	+	0.671660i	$0.234418\pi$
$912$	5.25953	0.174161
$913$	−8.47229	−0.280392
$914$	−19.6913	−0.651331
$915$	25.4458	0.841214
$916$	−11.5942	−0.383083
$917$	32.2973	1.06655
$918$	−0.600515	−0.0198200
$919$	41.8843	1.38163	0.690817	−	0.723030i	$-0.257251\pi$
$919$	41.8843	1.38163	0.690817	+	0.723030i	$0.257251\pi$
$920$	9.87517	0.325575
$921$	29.9350	0.986392
$922$	10.6804	0.351741
$923$	−10.2926	−0.338786
$924$	8.38339	0.275793
$925$	−12.6179	−0.414874
$926$	7.77142	0.255385
$927$	1.00000	0.0328443
$928$	−3.18067	−0.104411
$929$	−44.5454	−1.46149	−0.730743	−	0.682652i	$-0.760826\pi$
$929$	−44.5454	−1.46149	−0.730743	+	0.682652i	$0.760826\pi$
$930$	8.24342	0.270312
$931$	−7.11208	−0.233089
$932$	−25.1780	−0.824733
$933$	−18.7887	−0.615116
$934$	−1.71116	−0.0559908
$935$	4.31934	0.141258
$936$	−1.00000	−0.0326860
$937$	15.0441	0.491468	0.245734	−	0.969337i	$-0.420971\pi$
$937$	15.0441	0.491468	0.245734	+	0.969337i	$0.420971\pi$
$938$	−23.0199	−0.751628
$939$	6.00068	0.195825
$940$	−28.2707	−0.922090
$941$	−23.7604	−0.774568	−0.387284	−	0.921960i	$-0.626587\pi$
$941$	−23.7604	−0.774568	−0.387284	+	0.921960i	$0.626587\pi$
$942$	5.76483	0.187828
$943$	−46.6367	−1.51870
$944$	1.08168	0.0352056
$945$	7.16599	0.233110
$946$	7.68127	0.249740
$947$	26.0608	0.846862	0.423431	−	0.905928i	$-0.360826\pi$
$947$	26.0608	0.846862	0.423431	+	0.905928i	$0.360826\pi$
$948$	−4.57087	−0.148455
$949$	−12.4630	−0.404566
$950$	−6.03915	−0.195936
$951$	24.8356	0.805350
$952$	−1.73550	−0.0562479
$953$	−4.23637	−0.137229	−0.0686147	−	0.997643i	$-0.521858\pi$
$953$	−4.23637	−0.137229	−0.0686147	+	0.997643i	$0.521858\pi$
$954$	−3.86641	−0.125180
$955$	−9.46999	−0.306442
$956$	−11.7062	−0.378606
$957$	9.22651	0.298251
$958$	10.2984	0.332727
$959$	25.1540	0.812266
$960$	−2.47956	−0.0800275
$961$	−19.9474	−0.643464
$962$	10.9890	0.354300
$963$	−9.24442	−0.297897
$964$	−16.6536	−0.536378
$965$	−52.8092	−1.69999
$966$	11.5099	0.370324
$967$	−38.3270	−1.23251	−0.616257	−	0.787545i	$-0.711352\pi$
$967$	−38.3270	−1.23251	−0.616257	+	0.787545i	$0.711352\pi$
$968$	−2.58533	−0.0830957
$969$	3.15843	0.101463
$970$	39.3245	1.26264
$971$	11.1407	0.357521	0.178760	−	0.983893i	$-0.442791\pi$
$971$	11.1407	0.357521	0.178760	+	0.983893i	$0.442791\pi$
$972$	−1.00000	−0.0320750
$973$	−30.9124	−0.991007
$974$	19.6833	0.630695
$975$	1.14823	0.0367728
$976$	−10.2622	−0.328486
$977$	0.0230900	0.000738715 0	0.000369357	−	1.00000i	$-0.499882\pi$
$977$	0.0230900	0.000738715 0	0.000369357		1.00000i	$0.499882\pi$
$978$	18.5101	0.591889
$979$	25.3589	0.810474
$980$	3.35293	0.107105
$981$	−13.5565	−0.432825
$982$	−25.0458	−0.799245
$983$	2.19064	0.0698704	0.0349352	−	0.999390i	$-0.488878\pi$
$983$	2.19064	0.0698704	0.0349352	+	0.999390i	$0.488878\pi$
$984$	11.7100	0.373302
$985$	−8.38748	−0.267247
$986$	−1.91004	−0.0608282
$987$	−32.9506	−1.04883
$988$	5.25953	0.167328
$989$	10.5459	0.335341
$990$	7.19273	0.228600
$991$	40.6424	1.29105	0.645525	−	0.763739i	$-0.276639\pi$
$991$	40.6424	1.29105	0.645525	+	0.763739i	$0.276639\pi$
$992$	−3.32455	−0.105554
$993$	−2.63869	−0.0837363
$994$	−29.7459	−0.943484
$995$	24.0773	0.763302
$996$	2.92067	0.0925449
$997$	37.3247	1.18208	0.591042	−	0.806641i	$-0.298717\pi$
$997$	37.3247	1.18208	0.591042	+	0.806641i	$0.298717\pi$
$998$	−6.10890	−0.193374
$999$	10.9890	0.347677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.10	✓	11	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.47956 q^{5} -1.00000 q^{6} -2.89002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.47956 q^{5} -1.00000 q^{6} -2.89002 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.47956 q^{10} +2.90081 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.89002 q^{14} -2.47956 q^{15} +1.00000 q^{16} +0.600515 q^{17} +1.00000 q^{18} -5.25953 q^{19} +2.47956 q^{20} +2.89002 q^{21} +2.90081 q^{22} +3.98263 q^{23} -1.00000 q^{24} +1.14823 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.89002 q^{28} -3.18067 q^{29} -2.47956 q^{30} -3.32455 q^{31} +1.00000 q^{32} -2.90081 q^{33} +0.600515 q^{34} -7.16599 q^{35} +1.00000 q^{36} -10.9890 q^{37} -5.25953 q^{38} +1.00000 q^{39} +2.47956 q^{40} -11.7100 q^{41} +2.89002 q^{42} +2.64798 q^{43} +2.90081 q^{44} +2.47956 q^{45} +3.98263 q^{46} -11.4015 q^{47} -1.00000 q^{48} +1.35223 q^{49} +1.14823 q^{50} -0.600515 q^{51} -1.00000 q^{52} -3.86641 q^{53} -1.00000 q^{54} +7.19273 q^{55} -2.89002 q^{56} +5.25953 q^{57} -3.18067 q^{58} +1.08168 q^{59} -2.47956 q^{60} -10.2622 q^{61} -3.32455 q^{62} -2.89002 q^{63} +1.00000 q^{64} -2.47956 q^{65} -2.90081 q^{66} +7.96532 q^{67} +0.600515 q^{68} -3.98263 q^{69} -7.16599 q^{70} +10.2926 q^{71} +1.00000 q^{72} +12.4630 q^{73} -10.9890 q^{74} -1.14823 q^{75} -5.25953 q^{76} -8.38339 q^{77} +1.00000 q^{78} +4.57087 q^{79} +2.47956 q^{80} +1.00000 q^{81} -11.7100 q^{82} -2.92067 q^{83} +2.89002 q^{84} +1.48901 q^{85} +2.64798 q^{86} +3.18067 q^{87} +2.90081 q^{88} +8.74202 q^{89} +2.47956 q^{90} +2.89002 q^{91} +3.98263 q^{92} +3.32455 q^{93} -11.4015 q^{94} -13.0413 q^{95} -1.00000 q^{96} +15.8595 q^{97} +1.35223 q^{98} +2.90081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

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