LMFDB - Embedded newform 8038.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8038,2,Mod(1,8038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8038 = 2 \cdot 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8038.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:	$64.1837531447$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.28450 q^{3} +1.00000 q^{4} -2.56431 q^{5} -2.28450 q^{6} +0.255204 q^{7} +1.00000 q^{8} +2.21893 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.28450 q^{3} +1.00000 q^{4} -2.56431 q^{5} -2.28450 q^{6} +0.255204 q^{7} +1.00000 q^{8} +2.21893 q^{9} -2.56431 q^{10} +4.07877 q^{11} -2.28450 q^{12} -5.76477 q^{13} +0.255204 q^{14} +5.85817 q^{15} +1.00000 q^{16} +5.95375 q^{17} +2.21893 q^{18} -0.319890 q^{19} -2.56431 q^{20} -0.583012 q^{21} +4.07877 q^{22} +0.259893 q^{23} -2.28450 q^{24} +1.57571 q^{25} -5.76477 q^{26} +1.78436 q^{27} +0.255204 q^{28} -2.79065 q^{29} +5.85817 q^{30} -7.26993 q^{31} +1.00000 q^{32} -9.31793 q^{33} +5.95375 q^{34} -0.654422 q^{35} +2.21893 q^{36} -7.38326 q^{37} -0.319890 q^{38} +13.1696 q^{39} -2.56431 q^{40} -10.7965 q^{41} -0.583012 q^{42} +8.27836 q^{43} +4.07877 q^{44} -5.69002 q^{45} +0.259893 q^{46} +9.32881 q^{47} -2.28450 q^{48} -6.93487 q^{49} +1.57571 q^{50} -13.6013 q^{51} -5.76477 q^{52} +7.10517 q^{53} +1.78436 q^{54} -10.4592 q^{55} +0.255204 q^{56} +0.730788 q^{57} -2.79065 q^{58} +2.80328 q^{59} +5.85817 q^{60} +11.1715 q^{61} -7.26993 q^{62} +0.566278 q^{63} +1.00000 q^{64} +14.7827 q^{65} -9.31793 q^{66} +4.70141 q^{67} +5.95375 q^{68} -0.593725 q^{69} -0.654422 q^{70} +12.3658 q^{71} +2.21893 q^{72} -1.79465 q^{73} -7.38326 q^{74} -3.59969 q^{75} -0.319890 q^{76} +1.04092 q^{77} +13.1696 q^{78} +11.0041 q^{79} -2.56431 q^{80} -10.7331 q^{81} -10.7965 q^{82} -7.28607 q^{83} -0.583012 q^{84} -15.2673 q^{85} +8.27836 q^{86} +6.37523 q^{87} +4.07877 q^{88} +12.5902 q^{89} -5.69002 q^{90} -1.47119 q^{91} +0.259893 q^{92} +16.6081 q^{93} +9.32881 q^{94} +0.820298 q^{95} -2.28450 q^{96} -12.7617 q^{97} -6.93487 q^{98} +9.05048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q + 75 q^{2} - 30 q^{3} + 75 q^{4} - 29 q^{5} - 30 q^{6} - 31 q^{7} + 75 q^{8} + 55 q^{9}+O(q^{10}) $ 75 * q + 75 * q^2 - 30 * q^3 + 75 * q^4 - 29 * q^5 - 30 * q^6 - 31 * q^7 + 75 * q^8 + 55 * q^9	\( 75 q + 75 q^{2} - 30 q^{3} + 75 q^{4} - 29 q^{5} - 30 q^{6} - 31 q^{7} + 75 q^{8} + 55 q^{9} - 29 q^{10} - 30 q^{11} - 30 q^{12} - 23 q^{13} - 31 q^{14} - 22 q^{15} + 75 q^{16} - 48 q^{17} + 55 q^{18} - 58 q^{19} - 29 q^{20} - 5 q^{21} - 30 q^{22} - 79 q^{23} - 30 q^{24} + 42 q^{25} - 23 q^{26} - 108 q^{27} - 31 q^{28} - 39 q^{29} - 22 q^{30} - 95 q^{31} + 75 q^{32} - 44 q^{33} - 48 q^{34} - 60 q^{35} + 55 q^{36} - 16 q^{37} - 58 q^{38} - 57 q^{39} - 29 q^{40} - 85 q^{41} - 5 q^{42} - 55 q^{43} - 30 q^{44} - 48 q^{45} - 79 q^{46} - 88 q^{47} - 30 q^{48} + 26 q^{49} + 42 q^{50} - 39 q^{51} - 23 q^{52} - 79 q^{53} - 108 q^{54} - 78 q^{55} - 31 q^{56} - 40 q^{57} - 39 q^{58} - 74 q^{59} - 22 q^{60} - 21 q^{61} - 95 q^{62} - 97 q^{63} + 75 q^{64} - 63 q^{65} - 44 q^{66} - 59 q^{67} - 48 q^{68} + 3 q^{69} - 60 q^{70} - 72 q^{71} + 55 q^{72} - 91 q^{73} - 16 q^{74} - 95 q^{75} - 58 q^{76} - 60 q^{77} - 57 q^{78} - 64 q^{79} - 29 q^{80} + 47 q^{81} - 85 q^{82} - 105 q^{83} - 5 q^{84} + 14 q^{85} - 55 q^{86} - 75 q^{87} - 30 q^{88} - 78 q^{89} - 48 q^{90} - 89 q^{91} - 79 q^{92} + 27 q^{93} - 88 q^{94} - 53 q^{95} - 30 q^{96} - 79 q^{97} + 26 q^{98} - 57 q^{99}+O(q^{100}) \) 75 * q + 75 * q^2 - 30 * q^3 + 75 * q^4 - 29 * q^5 - 30 * q^6 - 31 * q^7 + 75 * q^8 + 55 * q^9 - 29 * q^10 - 30 * q^11 - 30 * q^12 - 23 * q^13 - 31 * q^14 - 22 * q^15 + 75 * q^16 - 48 * q^17 + 55 * q^18 - 58 * q^19 - 29 * q^20 - 5 * q^21 - 30 * q^22 - 79 * q^23 - 30 * q^24 + 42 * q^25 - 23 * q^26 - 108 * q^27 - 31 * q^28 - 39 * q^29 - 22 * q^30 - 95 * q^31 + 75 * q^32 - 44 * q^33 - 48 * q^34 - 60 * q^35 + 55 * q^36 - 16 * q^37 - 58 * q^38 - 57 * q^39 - 29 * q^40 - 85 * q^41 - 5 * q^42 - 55 * q^43 - 30 * q^44 - 48 * q^45 - 79 * q^46 - 88 * q^47 - 30 * q^48 + 26 * q^49 + 42 * q^50 - 39 * q^51 - 23 * q^52 - 79 * q^53 - 108 * q^54 - 78 * q^55 - 31 * q^56 - 40 * q^57 - 39 * q^58 - 74 * q^59 - 22 * q^60 - 21 * q^61 - 95 * q^62 - 97 * q^63 + 75 * q^64 - 63 * q^65 - 44 * q^66 - 59 * q^67 - 48 * q^68 + 3 * q^69 - 60 * q^70 - 72 * q^71 + 55 * q^72 - 91 * q^73 - 16 * q^74 - 95 * q^75 - 58 * q^76 - 60 * q^77 - 57 * q^78 - 64 * q^79 - 29 * q^80 + 47 * q^81 - 85 * q^82 - 105 * q^83 - 5 * q^84 + 14 * q^85 - 55 * q^86 - 75 * q^87 - 30 * q^88 - 78 * q^89 - 48 * q^90 - 89 * q^91 - 79 * q^92 + 27 * q^93 - 88 * q^94 - 53 * q^95 - 30 * q^96 - 79 * q^97 + 26 * q^98 - 57 * 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
$3$	−2.28450	−1.31895	−0.659477	−	0.751724i	$-0.729222\pi$
$3$	−2.28450	−1.31895	−0.659477	+	0.751724i	$0.729222\pi$
$4$	1.00000	0.500000
$5$	−2.56431	−1.14680	−0.573398	−	0.819277i	$-0.694375\pi$
$5$	−2.56431	−1.14680	−0.573398	+	0.819277i	$0.694375\pi$
$6$	−2.28450	−0.932642
$7$	0.255204	0.0964579	0.0482290	−	0.998836i	$-0.484642\pi$
$7$	0.255204	0.0964579	0.0482290	+	0.998836i	$0.484642\pi$
$8$	1.00000	0.353553
$9$	2.21893	0.739642
$10$	−2.56431	−0.810907
$11$	4.07877	1.22979	0.614897	−	0.788607i	$-0.289197\pi$
$11$	4.07877	1.22979	0.614897	+	0.788607i	$0.289197\pi$
$12$	−2.28450	−0.659477
$13$	−5.76477	−1.59886	−0.799430	−	0.600759i	$-0.794865\pi$
$13$	−5.76477	−1.59886	−0.799430	+	0.600759i	$0.794865\pi$
$14$	0.255204	0.0682061
$15$	5.85817	1.51257
$16$	1.00000	0.250000
$17$	5.95375	1.44400	0.721999	−	0.691894i	$-0.243224\pi$
$17$	5.95375	1.44400	0.721999	+	0.691894i	$0.243224\pi$
$18$	2.21893	0.523006
$19$	−0.319890	−0.0733878	−0.0366939	−	0.999327i	$-0.511683\pi$
$19$	−0.319890	−0.0733878	−0.0366939	+	0.999327i	$0.511683\pi$
$20$	−2.56431	−0.573398
$21$	−0.583012	−0.127224
$22$	4.07877	0.869596
$23$	0.259893	0.0541915	0.0270957	−	0.999633i	$-0.491374\pi$
$23$	0.259893	0.0541915	0.0270957	+	0.999633i	$0.491374\pi$
$24$	−2.28450	−0.466321
$25$	1.57571	0.315141
$26$	−5.76477	−1.13057
$27$	1.78436	0.343400
$28$	0.255204	0.0482290
$29$	−2.79065	−0.518210	−0.259105	−	0.965849i	$-0.583428\pi$
$29$	−2.79065	−0.518210	−0.259105	+	0.965849i	$0.583428\pi$
$30$	5.85817	1.06955
$31$	−7.26993	−1.30572	−0.652859	−	0.757480i	$-0.726430\pi$
$31$	−7.26993	−1.30572	−0.652859	+	0.757480i	$0.726430\pi$
$32$	1.00000	0.176777
$33$	−9.31793	−1.62204
$34$	5.95375	1.02106
$35$	−0.654422	−0.110618
$36$	2.21893	0.369821
$37$	−7.38326	−1.21380	−0.606900	−	0.794778i	$-0.707587\pi$
$37$	−7.38326	−1.21380	−0.606900	+	0.794778i	$0.707587\pi$
$38$	−0.319890	−0.0518930
$39$	13.1696	2.10883
$40$	−2.56431	−0.405454
$41$	−10.7965	−1.68613	−0.843067	−	0.537809i	$-0.819252\pi$
$41$	−10.7965	−1.68613	−0.843067	+	0.537809i	$0.819252\pi$
$42$	−0.583012	−0.0899607
$43$	8.27836	1.26244	0.631219	−	0.775605i	$-0.282555\pi$
$43$	8.27836	1.26244	0.631219	+	0.775605i	$0.282555\pi$
$44$	4.07877	0.614897
$45$	−5.69002	−0.848219
$46$	0.259893	0.0383191
$47$	9.32881	1.36075	0.680373	−	0.732866i	$-0.261818\pi$
$47$	9.32881	1.36075	0.680373	+	0.732866i	$0.261818\pi$
$48$	−2.28450	−0.329739
$49$	−6.93487	−0.990696
$50$	1.57571	0.222838
$51$	−13.6013	−1.90457
$52$	−5.76477	−0.799430
$53$	7.10517	0.975970	0.487985	−	0.872852i	$-0.337732\pi$
$53$	7.10517	0.975970	0.487985	+	0.872852i	$0.337732\pi$
$54$	1.78436	0.242821
$55$	−10.4592	−1.41032
$56$	0.255204	0.0341030
$57$	0.730788	0.0967952
$58$	−2.79065	−0.366430
$59$	2.80328	0.364956	0.182478	−	0.983210i	$-0.441588\pi$
$59$	2.80328	0.364956	0.182478	+	0.983210i	$0.441588\pi$
$60$	5.85817	0.756286
$61$	11.1715	1.43036	0.715181	−	0.698940i	$-0.246344\pi$
$61$	11.1715	1.43036	0.715181	+	0.698940i	$0.246344\pi$
$62$	−7.26993	−0.923282
$63$	0.566278	0.0713443
$64$	1.00000	0.125000
$65$	14.7827	1.83357
$66$	−9.31793	−1.14696
$67$	4.70141	0.574368	0.287184	−	0.957875i	$-0.407281\pi$
$67$	4.70141	0.574368	0.287184	+	0.957875i	$0.407281\pi$
$68$	5.95375	0.721999
$69$	−0.593725	−0.0714761
$70$	−0.654422	−0.0782184
$71$	12.3658	1.46755	0.733775	−	0.679393i	$-0.237757\pi$
$71$	12.3658	1.46755	0.733775	+	0.679393i	$0.237757\pi$
$72$	2.21893	0.261503
$73$	−1.79465	−0.210048	−0.105024	−	0.994470i	$-0.533492\pi$
$73$	−1.79465	−0.210048	−0.105024	+	0.994470i	$0.533492\pi$
$74$	−7.38326	−0.858286
$75$	−3.59969	−0.415657
$76$	−0.319890	−0.0366939
$77$	1.04092	0.118623
$78$	13.1696	1.49116
$79$	11.0041	1.23806	0.619030	−	0.785367i	$-0.287526\pi$
$79$	11.0041	1.23806	0.619030	+	0.785367i	$0.287526\pi$
$80$	−2.56431	−0.286699
$81$	−10.7331	−1.19257
$82$	−10.7965	−1.19228
$83$	−7.28607	−0.799750	−0.399875	−	0.916570i	$-0.630947\pi$
$83$	−7.28607	−0.799750	−0.399875	+	0.916570i	$0.630947\pi$
$84$	−0.583012	−0.0636118
$85$	−15.2673	−1.65597
$86$	8.27836	0.892679
$87$	6.37523	0.683496
$88$	4.07877	0.434798
$89$	12.5902	1.33456	0.667280	−	0.744807i	$-0.267459\pi$
$89$	12.5902	1.33456	0.667280	+	0.744807i	$0.267459\pi$
$90$	−5.69002	−0.599781
$91$	−1.47119	−0.154223
$92$	0.259893	0.0270957
$93$	16.6081	1.72218
$94$	9.32881	0.962193
$95$	0.820298	0.0841608
$96$	−2.28450	−0.233160
$97$	−12.7617	−1.29575	−0.647877	−	0.761745i	$-0.724343\pi$
$97$	−12.7617	−1.29575	−0.647877	+	0.761745i	$0.724343\pi$
$98$	−6.93487	−0.700528
$99$	9.05048	0.909608
$100$	1.57571	0.157571
$101$	14.4285	1.43569	0.717843	−	0.696205i	$-0.245130\pi$
$101$	14.4285	1.43569	0.717843	+	0.696205i	$0.245130\pi$
$102$	−13.6013	−1.34673
$103$	−10.8654	−1.07060	−0.535299	−	0.844663i	$-0.679801\pi$
$103$	−10.8654	−1.07060	−0.535299	+	0.844663i	$0.679801\pi$
$104$	−5.76477	−0.565283
$105$	1.49503	0.145900
$106$	7.10517	0.690115
$107$	19.6364	1.89832	0.949160	−	0.314794i	$-0.101936\pi$
$107$	19.6364	1.89832	0.949160	+	0.314794i	$0.101936\pi$
$108$	1.78436	0.171700
$109$	7.89489	0.756193	0.378097	−	0.925766i	$-0.376579\pi$
$109$	7.89489	0.756193	0.378097	+	0.925766i	$0.376579\pi$
$110$	−10.4592	−0.997249
$111$	16.8670	1.60095
$112$	0.255204	0.0241145
$113$	−20.0211	−1.88342	−0.941711	−	0.336422i	$-0.890783\pi$
$113$	−20.0211	−1.88342	−0.941711	+	0.336422i	$0.890783\pi$
$114$	0.730788	0.0684445
$115$	−0.666448	−0.0621466
$116$	−2.79065	−0.259105
$117$	−12.7916	−1.18258
$118$	2.80328	0.258063
$119$	1.51942	0.139285
$120$	5.85817	0.534775
$121$	5.63634	0.512394
$122$	11.1715	1.01142
$123$	24.6646	2.22393
$124$	−7.26993	−0.652859
$125$	8.78097	0.785393
$126$	0.566278	0.0504481
$127$	3.18501	0.282624	0.141312	−	0.989965i	$-0.454868\pi$
$127$	3.18501	0.282624	0.141312	+	0.989965i	$0.454868\pi$
$128$	1.00000	0.0883883
$129$	−18.9119	−1.66510
$130$	14.7827	1.29653
$131$	−13.7231	−1.19899	−0.599497	−	0.800377i	$-0.704633\pi$
$131$	−13.7231	−1.19899	−0.599497	+	0.800377i	$0.704633\pi$
$132$	−9.31793	−0.811022
$133$	−0.0816371	−0.00707883
$134$	4.70141	0.406140
$135$	−4.57566	−0.393810
$136$	5.95375	0.510530
$137$	−7.54170	−0.644331	−0.322165	−	0.946683i	$-0.604411\pi$
$137$	−7.54170	−0.644331	−0.322165	+	0.946683i	$0.604411\pi$
$138$	−0.593725	−0.0505412
$139$	−2.25320	−0.191114	−0.0955571	−	0.995424i	$-0.530463\pi$
$139$	−2.25320	−0.191114	−0.0955571	+	0.995424i	$0.530463\pi$
$140$	−0.654422	−0.0553088
$141$	−21.3116	−1.79476
$142$	12.3658	1.03771
$143$	−23.5132	−1.96627
$144$	2.21893	0.184910
$145$	7.15610	0.594282
$146$	−1.79465	−0.148526
$147$	15.8427	1.30668
$148$	−7.38326	−0.606900
$149$	−3.31923	−0.271922	−0.135961	−	0.990714i	$-0.543412\pi$
$149$	−3.31923	−0.271922	−0.135961	+	0.990714i	$0.543412\pi$
$150$	−3.59969	−0.293914
$151$	−8.30197	−0.675605	−0.337803	−	0.941217i	$-0.609684\pi$
$151$	−8.30197	−0.675605	−0.337803	+	0.941217i	$0.609684\pi$
$152$	−0.319890	−0.0259465
$153$	13.2109	1.06804
$154$	1.04092	0.0838794
$155$	18.6424	1.49739
$156$	13.1696	1.05441
$157$	−20.3457	−1.62376	−0.811880	−	0.583824i	$-0.801556\pi$
$157$	−20.3457	−1.62376	−0.811880	+	0.583824i	$0.801556\pi$
$158$	11.0041	0.875441
$159$	−16.2317	−1.28726
$160$	−2.56431	−0.202727
$161$	0.0663257	0.00522720
$162$	−10.7331	−0.843276
$163$	−22.2605	−1.74358	−0.871789	−	0.489882i	$-0.837040\pi$
$163$	−22.2605	−1.74358	−0.871789	+	0.489882i	$0.837040\pi$
$164$	−10.7965	−0.843067
$165$	23.8941	1.86015
$166$	−7.28607	−0.565509
$167$	7.61974	0.589633	0.294817	−	0.955554i	$-0.404741\pi$
$167$	7.61974	0.589633	0.294817	+	0.955554i	$0.404741\pi$
$168$	−0.583012	−0.0449804
$169$	20.2326	1.55636
$170$	−15.2673	−1.17095
$171$	−0.709812	−0.0542807
$172$	8.27836	0.631219
$173$	−6.06223	−0.460903	−0.230451	−	0.973084i	$-0.574020\pi$
$173$	−6.06223	−0.460903	−0.230451	+	0.973084i	$0.574020\pi$
$174$	6.37523	0.483305
$175$	0.402126	0.0303979
$176$	4.07877	0.307449
$177$	−6.40408	−0.481360
$178$	12.5902	0.943676
$179$	−15.5518	−1.16240	−0.581199	−	0.813761i	$-0.697416\pi$
$179$	−15.5518	−1.16240	−0.581199	+	0.813761i	$0.697416\pi$
$180$	−5.69002	−0.424109
$181$	−22.4443	−1.66827	−0.834135	−	0.551560i	$-0.814033\pi$
$181$	−22.4443	−1.66827	−0.834135	+	0.551560i	$0.814033\pi$
$182$	−1.47119	−0.109052
$183$	−25.5212	−1.88658
$184$	0.259893	0.0191596
$185$	18.9330	1.39198
$186$	16.6081	1.21777
$187$	24.2840	1.77582
$188$	9.32881	0.680373
$189$	0.455376	0.0331237
$190$	0.820298	0.0595107
$191$	7.73222	0.559484	0.279742	−	0.960075i	$-0.409751\pi$
$191$	7.73222	0.559484	0.279742	+	0.960075i	$0.409751\pi$
$192$	−2.28450	−0.164869
$193$	−7.50867	−0.540486	−0.270243	−	0.962792i	$-0.587104\pi$
$193$	−7.50867	−0.540486	−0.270243	+	0.962792i	$0.587104\pi$
$194$	−12.7617	−0.916237
$195$	−33.7710	−2.41839
$196$	−6.93487	−0.495348
$197$	7.49558	0.534038	0.267019	−	0.963691i	$-0.413961\pi$
$197$	7.49558	0.534038	0.267019	+	0.963691i	$0.413961\pi$
$198$	9.05048	0.643190
$199$	−17.2343	−1.22171	−0.610853	−	0.791744i	$-0.709173\pi$
$199$	−17.2343	−1.22171	−0.610853	+	0.791744i	$0.709173\pi$
$200$	1.57571	0.111419
$201$	−10.7403	−0.757566
$202$	14.4285	1.01518
$203$	−0.712184	−0.0499855
$204$	−13.6013	−0.952284
$205$	27.6857	1.93365
$206$	−10.8654	−0.757027
$207$	0.576684	0.0400823
$208$	−5.76477	−0.399715
$209$	−1.30476	−0.0902519
$210$	1.49503	0.103167
$211$	−11.7222	−0.806992	−0.403496	−	0.914982i	$-0.632205\pi$
$211$	−11.7222	−0.806992	−0.403496	+	0.914982i	$0.632205\pi$
$212$	7.10517	0.487985
$213$	−28.2496	−1.93563
$214$	19.6364	1.34231
$215$	−21.2283	−1.44776
$216$	1.78436	0.121410
$217$	−1.85531	−0.125947
$218$	7.89489	0.534709
$219$	4.09987	0.277044
$220$	−10.4592	−0.705162
$221$	−34.3220	−2.30875
$222$	16.8670	1.13204
$223$	−23.1931	−1.55313	−0.776564	−	0.630039i	$-0.783039\pi$
$223$	−23.1931	−1.55313	−0.776564	+	0.630039i	$0.783039\pi$
$224$	0.255204	0.0170515
$225$	3.49637	0.233092
$226$	−20.0211	−1.33178
$227$	−20.5323	−1.36278	−0.681388	−	0.731922i	$-0.738624\pi$
$227$	−20.5323	−1.36278	−0.681388	+	0.731922i	$0.738624\pi$
$228$	0.730788	0.0483976
$229$	18.8443	1.24526	0.622632	−	0.782515i	$-0.286063\pi$
$229$	18.8443	1.24526	0.622632	+	0.782515i	$0.286063\pi$
$230$	−0.666448	−0.0439442
$231$	−2.37797	−0.156459
$232$	−2.79065	−0.183215
$233$	−20.6005	−1.34958	−0.674790	−	0.738009i	$-0.735766\pi$
$233$	−20.6005	−1.34958	−0.674790	+	0.738009i	$0.735766\pi$
$234$	−12.7916	−0.836213
$235$	−23.9220	−1.56050
$236$	2.80328	0.182478
$237$	−25.1389	−1.63295
$238$	1.51942	0.0984894
$239$	16.7046	1.08053	0.540266	−	0.841494i	$-0.318324\pi$
$239$	16.7046	1.08053	0.540266	+	0.841494i	$0.318324\pi$
$240$	5.85817	0.378143
$241$	−23.7105	−1.52733	−0.763663	−	0.645615i	$-0.776601\pi$
$241$	−23.7105	−1.52733	−0.763663	+	0.645615i	$0.776601\pi$
$242$	5.63634	0.362318
$243$	19.1668	1.22955
$244$	11.1715	0.715181
$245$	17.7832	1.13613
$246$	24.6646	1.57256
$247$	1.84409	0.117337
$248$	−7.26993	−0.461641
$249$	16.6450	1.05483
$250$	8.78097	0.555357
$251$	27.3011	1.72323	0.861615	−	0.507562i	$-0.169453\pi$
$251$	27.3011	1.72323	0.861615	+	0.507562i	$0.169453\pi$
$252$	0.566278	0.0356722
$253$	1.06004	0.0666444
$254$	3.18501	0.199845
$255$	34.8781	2.18415
$256$	1.00000	0.0625000
$257$	−17.8261	−1.11196	−0.555982	−	0.831194i	$-0.687658\pi$
$257$	−17.8261	−1.11196	−0.555982	+	0.831194i	$0.687658\pi$
$258$	−18.9119	−1.17740
$259$	−1.88423	−0.117081
$260$	14.7827	0.916784
$261$	−6.19224	−0.383290
$262$	−13.7231	−0.847817
$263$	−4.21896	−0.260153	−0.130076	−	0.991504i	$-0.541522\pi$
$263$	−4.21896	−0.260153	−0.130076	+	0.991504i	$0.541522\pi$
$264$	−9.31793	−0.573479
$265$	−18.2199	−1.11924
$266$	−0.0816371	−0.00500549
$267$	−28.7623	−1.76022
$268$	4.70141	0.287184
$269$	−29.8771	−1.82164	−0.910820	−	0.412803i	$-0.864550\pi$
$269$	−29.8771	−1.82164	−0.910820	+	0.412803i	$0.864550\pi$
$270$	−4.57566	−0.278466
$271$	−11.8364	−0.719008	−0.359504	−	0.933144i	$-0.617054\pi$
$271$	−11.8364	−0.719008	−0.359504	+	0.933144i	$0.617054\pi$
$272$	5.95375	0.360999
$273$	3.36093	0.203413
$274$	−7.54170	−0.455611
$275$	6.42694	0.387559
$276$	−0.593725	−0.0357380
$277$	5.81784	0.349560	0.174780	−	0.984607i	$-0.444079\pi$
$277$	5.81784	0.349560	0.174780	+	0.984607i	$0.444079\pi$
$278$	−2.25320	−0.135138
$279$	−16.1314	−0.965763
$280$	−0.654422	−0.0391092
$281$	−16.5580	−0.987768	−0.493884	−	0.869528i	$-0.664423\pi$
$281$	−16.5580	−0.987768	−0.493884	+	0.869528i	$0.664423\pi$
$282$	−21.3116	−1.26909
$283$	31.3520	1.86369	0.931843	−	0.362863i	$-0.118201\pi$
$283$	31.3520	1.86369	0.931843	+	0.362863i	$0.118201\pi$
$284$	12.3658	0.733775
$285$	−1.87397	−0.111004
$286$	−23.5132	−1.39036
$287$	−2.75531	−0.162641
$288$	2.21893	0.130751
$289$	18.4472	1.08513
$290$	7.15610	0.420221
$291$	29.1541	1.70904
$292$	−1.79465	−0.105024
$293$	6.15410	0.359526	0.179763	−	0.983710i	$-0.442467\pi$
$293$	6.15410	0.359526	0.179763	+	0.983710i	$0.442467\pi$
$294$	15.8427	0.923965
$295$	−7.18848	−0.418530
$296$	−7.38326	−0.429143
$297$	7.27799	0.422312
$298$	−3.31923	−0.192278
$299$	−1.49823	−0.0866446
$300$	−3.59969	−0.207828
$301$	2.11267	0.121772
$302$	−8.30197	−0.477725
$303$	−32.9618	−1.89360
$304$	−0.319890	−0.0183469
$305$	−28.6472	−1.64033
$306$	13.2109	0.755219
$307$	−4.83500	−0.275948	−0.137974	−	0.990436i	$-0.544059\pi$
$307$	−4.83500	−0.275948	−0.137974	+	0.990436i	$0.544059\pi$
$308$	1.04092	0.0593117
$309$	24.8219	1.41207
$310$	18.6424	1.05882
$311$	−21.9959	−1.24727	−0.623637	−	0.781714i	$-0.714346\pi$
$311$	−21.9959	−1.24727	−0.623637	+	0.781714i	$0.714346\pi$
$312$	13.1696	0.745582
$313$	18.5597	1.04906	0.524529	−	0.851393i	$-0.324242\pi$
$313$	18.5597	1.04906	0.524529	+	0.851393i	$0.324242\pi$
$314$	−20.3457	−1.14817
$315$	−1.45211	−0.0818174
$316$	11.0041	0.619030
$317$	6.61469	0.371518	0.185759	−	0.982595i	$-0.440526\pi$
$317$	6.61469	0.371518	0.185759	+	0.982595i	$0.440526\pi$
$318$	−16.2317	−0.910230
$319$	−11.3824	−0.637292
$320$	−2.56431	−0.143350
$321$	−44.8592	−2.50380
$322$	0.0663257	0.00369619
$323$	−1.90455	−0.105972
$324$	−10.7331	−0.596286
$325$	−9.08359	−0.503867
$326$	−22.2605	−1.23290
$327$	−18.0359	−0.997385
$328$	−10.7965	−0.596138
$329$	2.38075	0.131255
$330$	23.8941	1.31533
$331$	7.82998	0.430375	0.215187	−	0.976573i	$-0.430964\pi$
$331$	7.82998	0.430375	0.215187	+	0.976573i	$0.430964\pi$
$332$	−7.28607	−0.399875
$333$	−16.3829	−0.897777
$334$	7.61974	0.416934
$335$	−12.0559	−0.658683
$336$	−0.583012	−0.0318059
$337$	22.7537	1.23947	0.619737	−	0.784810i	$-0.287239\pi$
$337$	22.7537	1.23947	0.619737	+	0.784810i	$0.287239\pi$
$338$	20.2326	1.10051
$339$	45.7380	2.48415
$340$	−15.2673	−0.827985
$341$	−29.6523	−1.60576
$342$	−0.709812	−0.0383822
$343$	−3.55623	−0.192018
$344$	8.27836	0.446339
$345$	1.52250	0.0819685
$346$	−6.06223	−0.325907
$347$	−8.47561	−0.454994	−0.227497	−	0.973779i	$-0.573054\pi$
$347$	−8.47561	−0.454994	−0.227497	+	0.973779i	$0.573054\pi$
$348$	6.37523	0.341748
$349$	−10.3512	−0.554089	−0.277045	−	0.960857i	$-0.589355\pi$
$349$	−10.3512	−0.554089	−0.277045	+	0.960857i	$0.589355\pi$
$350$	0.402126	0.0214945
$351$	−10.2864	−0.549049
$352$	4.07877	0.217399
$353$	−7.63263	−0.406244	−0.203122	−	0.979153i	$-0.565109\pi$
$353$	−7.63263	−0.406244	−0.203122	+	0.979153i	$0.565109\pi$
$354$	−6.40408	−0.340373
$355$	−31.7098	−1.68298
$356$	12.5902	0.667280
$357$	−3.47111	−0.183711
$358$	−15.5518	−0.821940
$359$	−9.80734	−0.517612	−0.258806	−	0.965929i	$-0.583329\pi$
$359$	−9.80734	−0.517612	−0.258806	+	0.965929i	$0.583329\pi$
$360$	−5.69002	−0.299891
$361$	−18.8977	−0.994614
$362$	−22.4443	−1.17965
$363$	−12.8762	−0.675825
$364$	−1.47119	−0.0771114
$365$	4.60204	0.240882
$366$	−25.5212	−1.33401
$367$	15.4151	0.804662	0.402331	−	0.915494i	$-0.368200\pi$
$367$	15.4151	0.804662	0.402331	+	0.915494i	$0.368200\pi$
$368$	0.259893	0.0135479
$369$	−23.9567	−1.24714
$370$	18.9330	0.984279
$371$	1.81326	0.0941400
$372$	16.6081	0.861091
$373$	−1.89148	−0.0979371	−0.0489685	−	0.998800i	$-0.515593\pi$
$373$	−1.89148	−0.0979371	−0.0489685	+	0.998800i	$0.515593\pi$
$374$	24.2840	1.25569
$375$	−20.0601	−1.03590
$376$	9.32881	0.481097
$377$	16.0875	0.828546
$378$	0.455376	0.0234220
$379$	−25.8045	−1.32549	−0.662743	−	0.748847i	$-0.730608\pi$
$379$	−25.8045	−1.32549	−0.662743	+	0.748847i	$0.730608\pi$
$380$	0.820298	0.0420804
$381$	−7.27614	−0.372768
$382$	7.73222	0.395615
$383$	22.4355	1.14640	0.573201	−	0.819414i	$-0.305701\pi$
$383$	22.4355	1.14640	0.573201	+	0.819414i	$0.305701\pi$
$384$	−2.28450	−0.116580
$385$	−2.66924	−0.136037
$386$	−7.50867	−0.382181
$387$	18.3691	0.933752
$388$	−12.7617	−0.647877
$389$	33.6258	1.70490	0.852448	−	0.522813i	$-0.175117\pi$
$389$	33.6258	1.70490	0.852448	+	0.522813i	$0.175117\pi$
$390$	−33.7710	−1.71006
$391$	1.54734	0.0782523
$392$	−6.93487	−0.350264
$393$	31.3504	1.58142
$394$	7.49558	0.377622
$395$	−28.2180	−1.41980
$396$	9.05048	0.454804
$397$	−6.22430	−0.312389	−0.156194	−	0.987726i	$-0.549923\pi$
$397$	−6.22430	−0.312389	−0.156194	+	0.987726i	$0.549923\pi$
$398$	−17.2343	−0.863877
$399$	0.186500	0.00933666
$400$	1.57571	0.0787853
$401$	18.6485	0.931263	0.465631	−	0.884979i	$-0.345827\pi$
$401$	18.6485	0.931263	0.465631	+	0.884979i	$0.345827\pi$
$402$	−10.7403	−0.535680
$403$	41.9095	2.08766
$404$	14.4285	0.717843
$405$	27.5232	1.36764
$406$	−0.712184	−0.0353451
$407$	−30.1146	−1.49272
$408$	−13.6013	−0.673366
$409$	−2.11010	−0.104338	−0.0521690	−	0.998638i	$-0.516613\pi$
$409$	−2.11010	−0.104338	−0.0521690	+	0.998638i	$0.516613\pi$
$410$	27.6857	1.36730
$411$	17.2290	0.849843
$412$	−10.8654	−0.535299
$413$	0.715407	0.0352029
$414$	0.576684	0.0283425
$415$	18.6838	0.917150
$416$	−5.76477	−0.282641
$417$	5.14744	0.252071
$418$	−1.30476	−0.0638177
$419$	27.3093	1.33415	0.667073	−	0.744993i	$-0.267547\pi$
$419$	27.3093	1.33415	0.667073	+	0.744993i	$0.267547\pi$
$420$	1.49503	0.0729498
$421$	8.48658	0.413611	0.206805	−	0.978382i	$-0.433693\pi$
$421$	8.48658	0.413611	0.206805	+	0.978382i	$0.433693\pi$
$422$	−11.7222	−0.570629
$423$	20.6999	1.00647
$424$	7.10517	0.345057
$425$	9.38136	0.455063
$426$	−28.2496	−1.36870
$427$	2.85100	0.137970
$428$	19.6364	0.949160
$429$	53.7158	2.59342
$430$	−21.2283	−1.02372
$431$	1.21701	0.0586212	0.0293106	−	0.999570i	$-0.490669\pi$
$431$	1.21701	0.0586212	0.0293106	+	0.999570i	$0.490669\pi$
$432$	1.78436	0.0858501
$433$	−27.2661	−1.31032	−0.655162	−	0.755489i	$-0.727399\pi$
$433$	−27.2661	−1.31032	−0.655162	+	0.755489i	$0.727399\pi$
$434$	−1.85531	−0.0890578
$435$	−16.3481	−0.783831
$436$	7.89489	0.378097
$437$	−0.0831372	−0.00397699
$438$	4.09987	0.195899
$439$	−0.417201	−0.0199119	−0.00995597	−	0.999950i	$-0.503169\pi$
$439$	−0.417201	−0.0199119	−0.00995597	+	0.999950i	$0.503169\pi$
$440$	−10.4592	−0.498625
$441$	−15.3880	−0.732760
$442$	−34.3220	−1.63253
$443$	−38.9974	−1.85282	−0.926411	−	0.376513i	$-0.877123\pi$
$443$	−38.9974	−1.85282	−0.926411	+	0.376513i	$0.877123\pi$
$444$	16.8670	0.800474
$445$	−32.2853	−1.53047
$446$	−23.1931	−1.09823
$447$	7.58278	0.358653
$448$	0.255204	0.0120572
$449$	9.74665	0.459973	0.229986	−	0.973194i	$-0.426132\pi$
$449$	9.74665	0.459973	0.229986	+	0.973194i	$0.426132\pi$
$450$	3.49637	0.164821
$451$	−44.0365	−2.07360
$452$	−20.0211	−0.941711
$453$	18.9658	0.891093
$454$	−20.5323	−0.963629
$455$	3.77260	0.176862
$456$	0.730788	0.0342223
$457$	−38.1677	−1.78541	−0.892704	−	0.450643i	$-0.851195\pi$
$457$	−38.1677	−1.78541	−0.892704	+	0.450643i	$0.851195\pi$
$458$	18.8443	0.880534
$459$	10.6236	0.495869
$460$	−0.666448	−0.0310733
$461$	38.0492	1.77213	0.886065	−	0.463561i	$-0.153428\pi$
$461$	38.0492	1.77213	0.886065	+	0.463561i	$0.153428\pi$
$462$	−2.37797	−0.110633
$463$	14.8335	0.689370	0.344685	−	0.938718i	$-0.387986\pi$
$463$	14.8335	0.689370	0.344685	+	0.938718i	$0.387986\pi$
$464$	−2.79065	−0.129553
$465$	−42.5884	−1.97499
$466$	−20.6005	−0.954298
$467$	−1.78187	−0.0824551	−0.0412276	−	0.999150i	$-0.513127\pi$
$467$	−1.78187	−0.0824551	−0.0412276	+	0.999150i	$0.513127\pi$
$468$	−12.7916	−0.591292
$469$	1.19982	0.0554024
$470$	−23.9220	−1.10344
$471$	46.4796	2.14167
$472$	2.80328	0.129031
$473$	33.7655	1.55254
$474$	−25.1389	−1.15467
$475$	−0.504052	−0.0231275
$476$	1.51942	0.0696425
$477$	15.7658	0.721868
$478$	16.7046	0.764051
$479$	−24.0042	−1.09678	−0.548389	−	0.836223i	$-0.684759\pi$
$479$	−24.0042	−1.09678	−0.548389	+	0.836223i	$0.684759\pi$
$480$	5.85817	0.267388
$481$	42.5628	1.94070
$482$	−23.7105	−1.07998
$483$	−0.151521	−0.00689444
$484$	5.63634	0.256197
$485$	32.7250	1.48597
$486$	19.1668	0.869422
$487$	36.2555	1.64289	0.821446	−	0.570286i	$-0.193168\pi$
$487$	36.2555	1.64289	0.821446	+	0.570286i	$0.193168\pi$
$488$	11.1715	0.505709
$489$	50.8541	2.29970
$490$	17.7832	0.803362
$491$	11.5051	0.519220	0.259610	−	0.965714i	$-0.416406\pi$
$491$	11.5051	0.519220	0.259610	+	0.965714i	$0.416406\pi$
$492$	24.6646	1.11197
$493$	−16.6148	−0.748294
$494$	1.84409	0.0829697
$495$	−23.2083	−1.04313
$496$	−7.26993	−0.326429
$497$	3.15580	0.141557
$498$	16.6450	0.745881
$499$	−44.5542	−1.99452	−0.997261	−	0.0739654i	$-0.976435\pi$
$499$	−44.5542	−1.99452	−0.997261	+	0.0739654i	$0.976435\pi$
$500$	8.78097	0.392697
$501$	−17.4073	−0.777700
$502$	27.3011	1.21851
$503$	−8.26921	−0.368706	−0.184353	−	0.982860i	$-0.559019\pi$
$503$	−8.26921	−0.368706	−0.184353	+	0.982860i	$0.559019\pi$
$504$	0.566278	0.0252240
$505$	−36.9991	−1.64644
$506$	1.06004	0.0471247
$507$	−46.2214	−2.05276
$508$	3.18501	0.141312
$509$	21.3457	0.946130	0.473065	−	0.881028i	$-0.343148\pi$
$509$	21.3457	0.946130	0.473065	+	0.881028i	$0.343148\pi$
$510$	34.8781	1.54443
$511$	−0.458001	−0.0202608
$512$	1.00000	0.0441942
$513$	−0.570799	−0.0252014
$514$	−17.8261	−0.786277
$515$	27.8622	1.22776
$516$	−18.9119	−0.832550
$517$	38.0500	1.67344
$518$	−1.88423	−0.0827885
$519$	13.8491	0.607910
$520$	14.7827	0.648264
$521$	3.35561	0.147012	0.0735060	−	0.997295i	$-0.476581\pi$
$521$	3.35561	0.147012	0.0735060	+	0.997295i	$0.476581\pi$
$522$	−6.19224	−0.271027
$523$	−35.7861	−1.56482	−0.782408	−	0.622766i	$-0.786009\pi$
$523$	−35.7861	−1.56482	−0.782408	+	0.622766i	$0.786009\pi$
$524$	−13.7231	−0.599497
$525$	−0.918655	−0.0400934
$526$	−4.21896	−0.183956
$527$	−43.2834	−1.88545
$528$	−9.31793	−0.405511
$529$	−22.9325	−0.997063
$530$	−18.2199	−0.791421
$531$	6.22027	0.269937
$532$	−0.0816371	−0.00353942
$533$	62.2395	2.69589
$534$	−28.7623	−1.24467
$535$	−50.3538	−2.17699
$536$	4.70141	0.203070
$537$	35.5281	1.53315
$538$	−29.8771	−1.28809
$539$	−28.2857	−1.21835
$540$	−4.57566	−0.196905
$541$	−22.9748	−0.987762	−0.493881	−	0.869529i	$-0.664422\pi$
$541$	−22.9748	−0.987762	−0.493881	+	0.869529i	$0.664422\pi$
$542$	−11.8364	−0.508415
$543$	51.2739	2.20037
$544$	5.95375	0.255265
$545$	−20.2450	−0.867200
$546$	3.36093	0.143835
$547$	20.9360	0.895160	0.447580	−	0.894244i	$-0.352286\pi$
$547$	20.9360	0.895160	0.447580	+	0.894244i	$0.352286\pi$
$548$	−7.54170	−0.322165
$549$	24.7887	1.05796
$550$	6.42694	0.274045
$551$	0.892700	0.0380303
$552$	−0.593725	−0.0252706
$553$	2.80829	0.119421
$554$	5.81784	0.247176
$555$	−43.2524	−1.83596
$556$	−2.25320	−0.0955571
$557$	−6.97242	−0.295431	−0.147715	−	0.989030i	$-0.547192\pi$
$557$	−6.97242	−0.295431	−0.147715	+	0.989030i	$0.547192\pi$
$558$	−16.1314	−0.682898
$559$	−47.7229	−2.01846
$560$	−0.654422	−0.0276544
$561$	−55.4767	−2.34223
$562$	−16.5580	−0.698457
$563$	12.9899	0.547459	0.273729	−	0.961807i	$-0.411743\pi$
$563$	12.9899	0.547459	0.273729	+	0.961807i	$0.411743\pi$
$564$	−21.3116	−0.897382
$565$	51.3403	2.15990
$566$	31.3520	1.31782
$567$	−2.73914	−0.115033
$568$	12.3658	0.518857
$569$	−26.2266	−1.09948	−0.549739	−	0.835337i	$-0.685273\pi$
$569$	−26.2266	−1.09948	−0.549739	+	0.835337i	$0.685273\pi$
$570$	−1.87397	−0.0784919
$571$	−3.56133	−0.149037	−0.0745184	−	0.997220i	$-0.523742\pi$
$571$	−3.56133	−0.149037	−0.0745184	+	0.997220i	$0.523742\pi$
$572$	−23.5132	−0.983135
$573$	−17.6642	−0.737934
$574$	−2.75531	−0.115005
$575$	0.409515	0.0170780
$576$	2.21893	0.0924552
$577$	−40.5961	−1.69004	−0.845020	−	0.534735i	$-0.820411\pi$
$577$	−40.5961	−1.69004	−0.845020	+	0.534735i	$0.820411\pi$
$578$	18.4472	0.767302
$579$	17.1535	0.712877
$580$	7.15610	0.297141
$581$	−1.85943	−0.0771423
$582$	29.1541	1.20848
$583$	28.9803	1.20024
$584$	−1.79465	−0.0742631
$585$	32.8017	1.35618
$586$	6.15410	0.254224
$587$	−20.8406	−0.860182	−0.430091	−	0.902785i	$-0.641519\pi$
$587$	−20.8406	−0.860182	−0.430091	+	0.902785i	$0.641519\pi$
$588$	15.8427	0.653342
$589$	2.32558	0.0958237
$590$	−7.18848	−0.295945
$591$	−17.1236	−0.704372
$592$	−7.38326	−0.303450
$593$	−4.08118	−0.167594	−0.0837969	−	0.996483i	$-0.526705\pi$
$593$	−4.08118	−0.167594	−0.0837969	+	0.996483i	$0.526705\pi$
$594$	7.27799	0.298620
$595$	−3.89627	−0.159731
$596$	−3.31923	−0.135961
$597$	39.3717	1.61138
$598$	−1.49823	−0.0612670
$599$	−18.1516	−0.741653	−0.370826	−	0.928702i	$-0.620926\pi$
$599$	−18.1516	−0.741653	−0.370826	+	0.928702i	$0.620926\pi$
$600$	−3.59969	−0.146957
$601$	−14.6235	−0.596504	−0.298252	−	0.954487i	$-0.596404\pi$
$601$	−14.6235	−0.596504	−0.298252	+	0.954487i	$0.596404\pi$
$602$	2.11267	0.0861059
$603$	10.4321	0.424827
$604$	−8.30197	−0.337803
$605$	−14.4533	−0.587612
$606$	−32.9618	−1.33898
$607$	7.18651	0.291691	0.145846	−	0.989307i	$-0.453410\pi$
$607$	7.18651	0.291691	0.145846	+	0.989307i	$0.453410\pi$
$608$	−0.319890	−0.0129733
$609$	1.62698	0.0659286
$610$	−28.6472	−1.15989
$611$	−53.7785	−2.17564
$612$	13.2109	0.534021
$613$	15.9200	0.643002	0.321501	−	0.946909i	$-0.395813\pi$
$613$	15.9200	0.643002	0.321501	+	0.946909i	$0.395813\pi$
$614$	−4.83500	−0.195125
$615$	−63.2478	−2.55040
$616$	1.04092	0.0419397
$617$	−4.15338	−0.167209	−0.0836044	−	0.996499i	$-0.526643\pi$
$617$	−4.15338	−0.167209	−0.0836044	+	0.996499i	$0.526643\pi$
$618$	24.8219	0.998484
$619$	19.3524	0.777837	0.388918	−	0.921272i	$-0.372849\pi$
$619$	19.3524	0.777837	0.388918	+	0.921272i	$0.372849\pi$
$620$	18.6424	0.748696
$621$	0.463743	0.0186094
$622$	−21.9959	−0.881956
$623$	3.21307	0.128729
$624$	13.1696	0.527206
$625$	−30.3957	−1.21583
$626$	18.5597	0.741795
$627$	2.98071	0.119038
$628$	−20.3457	−0.811880
$629$	−43.9581	−1.75272
$630$	−1.45211	−0.0578536
$631$	−30.3555	−1.20843	−0.604216	−	0.796821i	$-0.706514\pi$
$631$	−30.3555	−1.20843	−0.604216	+	0.796821i	$0.706514\pi$
$632$	11.0041	0.437721
$633$	26.7794	1.06439
$634$	6.61469	0.262703
$635$	−8.16736	−0.324112
$636$	−16.2317	−0.643630
$637$	39.9780	1.58398
$638$	−11.3824	−0.450634
$639$	27.4388	1.08546
$640$	−2.56431	−0.101363
$641$	−11.9802	−0.473189	−0.236595	−	0.971608i	$-0.576031\pi$
$641$	−11.9802	−0.473189	−0.236595	+	0.971608i	$0.576031\pi$
$642$	−44.8592	−1.77045
$643$	−0.798201	−0.0314780	−0.0157390	−	0.999876i	$-0.505010\pi$
$643$	−0.798201	−0.0314780	−0.0157390	+	0.999876i	$0.505010\pi$
$644$	0.0663257	0.00261360
$645$	48.4960	1.90953
$646$	−1.90455	−0.0749334
$647$	−32.5996	−1.28162	−0.640810	−	0.767699i	$-0.721402\pi$
$647$	−32.5996	−1.28162	−0.640810	+	0.767699i	$0.721402\pi$
$648$	−10.7331	−0.421638
$649$	11.4339	0.448820
$650$	−9.08359	−0.356288
$651$	4.23846	0.166118
$652$	−22.2605	−0.871789
$653$	−33.8249	−1.32367	−0.661835	−	0.749650i	$-0.730222\pi$
$653$	−33.8249	−1.32367	−0.661835	+	0.749650i	$0.730222\pi$
$654$	−18.0359	−0.705258
$655$	35.1904	1.37500
$656$	−10.7965	−0.421533
$657$	−3.98219	−0.155360
$658$	2.38075	0.0928112
$659$	0.876590	0.0341471	0.0170735	−	0.999854i	$-0.494565\pi$
$659$	0.876590	0.0341471	0.0170735	+	0.999854i	$0.494565\pi$
$660$	23.8941	0.930076
$661$	−24.8911	−0.968153	−0.484077	−	0.875026i	$-0.660844\pi$
$661$	−24.8911	−0.968153	−0.484077	+	0.875026i	$0.660844\pi$
$662$	7.82998	0.304321
$663$	78.4086	3.04514
$664$	−7.28607	−0.282754
$665$	0.209343	0.00811798
$666$	−16.3829	−0.634825
$667$	−0.725270	−0.0280826
$668$	7.61974	0.294817
$669$	52.9847	2.04851
$670$	−12.0559	−0.465759
$671$	45.5658	1.75905
$672$	−0.583012	−0.0224902
$673$	−20.2277	−0.779721	−0.389861	−	0.920874i	$-0.627477\pi$
$673$	−20.2277	−0.779721	−0.389861	+	0.920874i	$0.627477\pi$
$674$	22.7537	0.876440
$675$	2.81163	0.108220
$676$	20.2326	0.778178
$677$	−43.3122	−1.66462	−0.832311	−	0.554309i	$-0.812983\pi$
$677$	−43.3122	−1.66462	−0.832311	+	0.554309i	$0.812983\pi$
$678$	45.7380	1.75656
$679$	−3.25683	−0.124986
$680$	−15.2673	−0.585474
$681$	46.9060	1.79744
$682$	−29.6523	−1.13545
$683$	7.87875	0.301472	0.150736	−	0.988574i	$-0.451836\pi$
$683$	7.87875	0.301472	0.150736	+	0.988574i	$0.451836\pi$
$684$	−0.709812	−0.0271403
$685$	19.3393	0.738916
$686$	−3.55623	−0.135778
$687$	−43.0496	−1.64245
$688$	8.27836	0.315610
$689$	−40.9597	−1.56044
$690$	1.52250	0.0579605
$691$	−12.6599	−0.481604	−0.240802	−	0.970574i	$-0.577410\pi$
$691$	−12.6599	−0.481604	−0.240802	+	0.970574i	$0.577410\pi$
$692$	−6.06223	−0.230451
$693$	2.30972	0.0877389
$694$	−8.47561	−0.321730
$695$	5.77792	0.219169
$696$	6.37523	0.241652
$697$	−64.2798	−2.43477
$698$	−10.3512	−0.391800
$699$	47.0617	1.78004
$700$	0.402126	0.0151989
$701$	23.6078	0.891653	0.445826	−	0.895120i	$-0.352910\pi$
$701$	23.6078	0.891653	0.445826	+	0.895120i	$0.352910\pi$
$702$	−10.2864	−0.388237
$703$	2.36183	0.0890781
$704$	4.07877	0.153724
$705$	54.6497	2.05823
$706$	−7.63263	−0.287258
$707$	3.68220	0.138483
$708$	−6.40408	−0.240680
$709$	22.4005	0.841269	0.420635	−	0.907230i	$-0.361807\pi$
$709$	22.4005	0.841269	0.420635	+	0.907230i	$0.361807\pi$
$710$	−31.7098	−1.19005
$711$	24.4173	0.915722
$712$	12.5902	0.471838
$713$	−1.88940	−0.0707587
$714$	−3.47111	−0.129903
$715$	60.2951	2.25491
$716$	−15.5518	−0.581199
$717$	−38.1616	−1.42517
$718$	−9.80734	−0.366007
$719$	−7.74402	−0.288803	−0.144402	−	0.989519i	$-0.546126\pi$
$719$	−7.74402	−0.288803	−0.144402	+	0.989519i	$0.546126\pi$
$720$	−5.69002	−0.212055
$721$	−2.77288	−0.103268
$722$	−18.8977	−0.703298
$723$	54.1665	2.01447
$724$	−22.4443	−0.834135
$725$	−4.39724	−0.163309
$726$	−12.8762	−0.477880
$727$	5.97631	0.221649	0.110825	−	0.993840i	$-0.464651\pi$
$727$	5.97631	0.221649	0.110825	+	0.993840i	$0.464651\pi$
$728$	−1.47119	−0.0545260
$729$	−11.5870	−0.429146
$730$	4.60204	0.170329
$731$	49.2873	1.82296
$732$	−25.5212	−0.943291
$733$	−6.03672	−0.222971	−0.111486	−	0.993766i	$-0.535561\pi$
$733$	−6.03672	−0.222971	−0.111486	+	0.993766i	$0.535561\pi$
$734$	15.4151	0.568982
$735$	−40.6256	−1.49850
$736$	0.259893	0.00957979
$737$	19.1759	0.706355
$738$	−23.9567	−0.881858
$739$	−31.7729	−1.16879	−0.584393	−	0.811471i	$-0.698667\pi$
$739$	−31.7729	−1.16879	−0.584393	+	0.811471i	$0.698667\pi$
$740$	18.9330	0.695991
$741$	−4.21283	−0.154762
$742$	1.81326	0.0665670
$743$	−29.4041	−1.07873	−0.539365	−	0.842072i	$-0.681336\pi$
$743$	−29.4041	−1.07873	−0.539365	+	0.842072i	$0.681336\pi$
$744$	16.6081	0.608883
$745$	8.51155	0.311839
$746$	−1.89148	−0.0692520
$747$	−16.1673	−0.591529
$748$	24.2840	0.887910
$749$	5.01128	0.183108
$750$	−20.0601	−0.732491
$751$	13.7513	0.501794	0.250897	−	0.968014i	$-0.419274\pi$
$751$	13.7513	0.501794	0.250897	+	0.968014i	$0.419274\pi$
$752$	9.32881	0.340187
$753$	−62.3693	−2.27286
$754$	16.0875	0.585871
$755$	21.2889	0.774781
$756$	0.455376	0.0165619
$757$	34.3648	1.24901	0.624505	−	0.781021i	$-0.285301\pi$
$757$	34.3648	1.24901	0.624505	+	0.781021i	$0.285301\pi$
$758$	−25.8045	−0.937260
$759$	−2.42167	−0.0879009
$760$	0.820298	0.0297553
$761$	27.9820	1.01435	0.507174	−	0.861844i	$-0.330690\pi$
$761$	27.9820	1.01435	0.507174	+	0.861844i	$0.330690\pi$
$762$	−7.27614	−0.263587
$763$	2.01481	0.0729408
$764$	7.73222	0.279742
$765$	−33.8770	−1.22483
$766$	22.4355	0.810629
$767$	−16.1603	−0.583513
$768$	−2.28450	−0.0824347
$769$	23.7344	0.855885	0.427942	−	0.903806i	$-0.359239\pi$
$769$	23.7344	0.855885	0.427942	+	0.903806i	$0.359239\pi$
$770$	−2.66924	−0.0961926
$771$	40.7238	1.46663
$772$	−7.50867	−0.270243
$773$	−8.81966	−0.317221	−0.158611	−	0.987341i	$-0.550701\pi$
$773$	−8.81966	−0.317221	−0.158611	+	0.987341i	$0.550701\pi$
$774$	18.3691	0.660263
$775$	−11.4553	−0.411485
$776$	−12.7617	−0.458118
$777$	4.30453	0.154424
$778$	33.6258	1.20554
$779$	3.45370	0.123742
$780$	−33.7710	−1.20920
$781$	50.4372	1.80478
$782$	1.54734	0.0553327
$783$	−4.97952	−0.177954
$784$	−6.93487	−0.247674
$785$	52.1727	1.86212
$786$	31.3504	1.11823
$787$	0.634933	0.0226329	0.0113165	−	0.999936i	$-0.496398\pi$
$787$	0.634933	0.0226329	0.0113165	+	0.999936i	$0.496398\pi$
$788$	7.49558	0.267019
$789$	9.63821	0.343129
$790$	−28.2180	−1.00395
$791$	−5.10945	−0.181671
$792$	9.05048	0.321595
$793$	−64.4010	−2.28695
$794$	−6.22430	−0.220892
$795$	41.6233	1.47622
$796$	−17.2343	−0.610853
$797$	19.1814	0.679439	0.339720	−	0.940527i	$-0.389668\pi$
$797$	19.1814	0.679439	0.339720	+	0.940527i	$0.389668\pi$
$798$	0.186500	0.00660202
$799$	55.5414	1.96491
$800$	1.57571	0.0557096
$801$	27.9367	0.987096
$802$	18.6485	0.658502
$803$	−7.31996	−0.258316
$804$	−10.7403	−0.378783
$805$	−0.170080	−0.00599453
$806$	41.9095	1.47620
$807$	68.2542	2.40266
$808$	14.4285	0.507591
$809$	37.8378	1.33031	0.665153	−	0.746707i	$-0.268366\pi$
$809$	37.8378	1.33031	0.665153	+	0.746707i	$0.268366\pi$
$810$	27.5232	0.967065
$811$	18.5838	0.652566	0.326283	−	0.945272i	$-0.394204\pi$
$811$	18.5838	0.652566	0.326283	+	0.945272i	$0.394204\pi$
$812$	−0.712184	−0.0249928
$813$	27.0401	0.948339
$814$	−30.1146	−1.05552
$815$	57.0829	1.99953
$816$	−13.6013	−0.476142
$817$	−2.64816	−0.0926476
$818$	−2.11010	−0.0737781
$819$	−3.26447	−0.114070
$820$	27.6857	0.966826
$821$	−17.2601	−0.602380	−0.301190	−	0.953564i	$-0.597384\pi$
$821$	−17.2601	−0.602380	−0.301190	+	0.953564i	$0.597384\pi$
$822$	17.2290	0.600930
$823$	25.2637	0.880636	0.440318	−	0.897842i	$-0.354866\pi$
$823$	25.2637	0.880636	0.440318	+	0.897842i	$0.354866\pi$
$824$	−10.8654	−0.378513
$825$	−14.6823	−0.511173
$826$	0.715407	0.0248922
$827$	16.2604	0.565428	0.282714	−	0.959204i	$-0.408765\pi$
$827$	16.2604	0.565428	0.282714	+	0.959204i	$0.408765\pi$
$828$	0.576684	0.0200411
$829$	26.6744	0.926441	0.463220	−	0.886243i	$-0.346694\pi$
$829$	26.6744	0.926441	0.463220	+	0.886243i	$0.346694\pi$
$830$	18.6838	0.648523
$831$	−13.2908	−0.461054
$832$	−5.76477	−0.199858
$833$	−41.2885	−1.43056
$834$	5.14744	0.178241
$835$	−19.5394	−0.676189
$836$	−1.30476	−0.0451259
$837$	−12.9722	−0.448384
$838$	27.3093	0.943383
$839$	−35.1866	−1.21478	−0.607388	−	0.794405i	$-0.707783\pi$
$839$	−35.1866	−1.21478	−0.607388	+	0.794405i	$0.707783\pi$
$840$	1.49503	0.0515833
$841$	−21.2123	−0.731458
$842$	8.48658	0.292467
$843$	37.8267	1.30282
$844$	−11.7222	−0.403496
$845$	−51.8828	−1.78482
$846$	20.6999	0.711679
$847$	1.43841	0.0494245
$848$	7.10517	0.243992
$849$	−71.6236	−2.45812
$850$	9.38136	0.321778
$851$	−1.91886	−0.0657776
$852$	−28.2496	−0.967816
$853$	−3.58702	−0.122817	−0.0614087	−	0.998113i	$-0.519559\pi$
$853$	−3.58702	−0.122817	−0.0614087	+	0.998113i	$0.519559\pi$
$854$	2.85100	0.0975593
$855$	1.82018	0.0622489
$856$	19.6364	0.671157
$857$	−51.6407	−1.76401	−0.882007	−	0.471236i	$-0.843808\pi$
$857$	−51.6407	−1.76401	−0.882007	+	0.471236i	$0.843808\pi$
$858$	53.7158	1.83383
$859$	46.3537	1.58157	0.790784	−	0.612095i	$-0.209673\pi$
$859$	46.3537	1.58157	0.790784	+	0.612095i	$0.209673\pi$
$860$	−21.2283	−0.723880
$861$	6.29450	0.214516
$862$	1.21701	0.0414514
$863$	34.0968	1.16067	0.580335	−	0.814378i	$-0.302922\pi$
$863$	34.0968	1.16067	0.580335	+	0.814378i	$0.302922\pi$
$864$	1.78436	0.0607052
$865$	15.5455	0.528561
$866$	−27.2661	−0.926538
$867$	−42.1425	−1.43124
$868$	−1.85531	−0.0629734
$869$	44.8833	1.52256
$870$	−16.3481	−0.554252
$871$	−27.1025	−0.918335
$872$	7.89489	0.267355
$873$	−28.3173	−0.958395
$874$	−0.0831372	−0.00281216
$875$	2.24093	0.0757574
$876$	4.09987	0.138522
$877$	−8.48598	−0.286551	−0.143276	−	0.989683i	$-0.545764\pi$
$877$	−8.48598	−0.286551	−0.143276	+	0.989683i	$0.545764\pi$
$878$	−0.417201	−0.0140799
$879$	−14.0590	−0.474199
$880$	−10.4592	−0.352581
$881$	−2.62909	−0.0885763	−0.0442882	−	0.999019i	$-0.514102\pi$
$881$	−2.62909	−0.0885763	−0.0442882	+	0.999019i	$0.514102\pi$
$882$	−15.3880	−0.518140
$883$	−44.8076	−1.50790	−0.753948	−	0.656934i	$-0.771853\pi$
$883$	−44.8076	−1.50790	−0.753948	+	0.656934i	$0.771853\pi$
$884$	−34.3220	−1.15438
$885$	16.4221	0.552022
$886$	−38.9974	−1.31014
$887$	−23.9610	−0.804532	−0.402266	−	0.915523i	$-0.631777\pi$
$887$	−23.9610	−0.804532	−0.402266	+	0.915523i	$0.631777\pi$
$888$	16.8670	0.566020
$889$	0.812826	0.0272613
$890$	−32.2853	−1.08220
$891$	−43.7780	−1.46662
$892$	−23.1931	−0.776564
$893$	−2.98419	−0.0998622
$894$	7.58278	0.253606
$895$	39.8798	1.33303
$896$	0.255204	0.00852576
$897$	3.42269	0.114280
$898$	9.74665	0.325250
$899$	20.2878	0.676636
$900$	3.49637	0.116546
$901$	42.3024	1.40930
$902$	−44.0365	−1.46626
$903$	−4.82639	−0.160612
$904$	−20.0211	−0.665890
$905$	57.5542	1.91317
$906$	18.9658	0.630098
$907$	−17.7409	−0.589077	−0.294538	−	0.955640i	$-0.595166\pi$
$907$	−17.7409	−0.589077	−0.294538	+	0.955640i	$0.595166\pi$
$908$	−20.5323	−0.681388
$909$	32.0157	1.06189
$910$	3.77260	0.125060
$911$	35.8654	1.18827	0.594137	−	0.804364i	$-0.297494\pi$
$911$	35.8654	1.18827	0.594137	+	0.804364i	$0.297494\pi$
$912$	0.730788	0.0241988
$913$	−29.7182	−0.983528
$914$	−38.1677	−1.26247
$915$	65.4444	2.16352
$916$	18.8443	0.622632
$917$	−3.50219	−0.115652
$918$	10.6236	0.350633
$919$	−0.653687	−0.0215631	−0.0107816	−	0.999942i	$-0.503432\pi$
$919$	−0.653687	−0.0215631	−0.0107816	+	0.999942i	$0.503432\pi$
$920$	−0.666448	−0.0219721
$921$	11.0455	0.363963
$922$	38.0492	1.25309
$923$	−71.2860	−2.34641
$924$	−2.37797	−0.0782295
$925$	−11.6338	−0.382518
$926$	14.8335	0.487458
$927$	−24.1095	−0.791859
$928$	−2.79065	−0.0916075
$929$	39.7419	1.30389	0.651945	−	0.758266i	$-0.273953\pi$
$929$	39.7419	1.30389	0.651945	+	0.758266i	$0.273953\pi$
$930$	−42.5884	−1.39653
$931$	2.21840	0.0727050
$932$	−20.6005	−0.674790
$933$	50.2496	1.64510
$934$	−1.78187	−0.0583046
$935$	−62.2717	−2.03650
$936$	−12.7916	−0.418107
$937$	50.9011	1.66287	0.831434	−	0.555624i	$-0.187520\pi$
$937$	50.9011	1.66287	0.831434	+	0.555624i	$0.187520\pi$
$938$	1.19982	0.0391754
$939$	−42.3996	−1.38366
$940$	−23.9220	−0.780249
$941$	−51.9395	−1.69318	−0.846589	−	0.532247i	$-0.821348\pi$
$941$	−51.9395	−1.69318	−0.846589	+	0.532247i	$0.821348\pi$
$942$	46.4796	1.51439
$943$	−2.80594	−0.0913740
$944$	2.80328	0.0912389
$945$	−1.16773	−0.0379861
$946$	33.7655	1.09781
$947$	−18.3467	−0.596187	−0.298093	−	0.954537i	$-0.596351\pi$
$947$	−18.3467	−0.596187	−0.298093	+	0.954537i	$0.596351\pi$
$948$	−25.1389	−0.816473
$949$	10.3457	0.335837
$950$	−0.504052	−0.0163536
$951$	−15.1112	−0.490016
$952$	1.51942	0.0492447
$953$	−37.3949	−1.21134	−0.605669	−	0.795717i	$-0.707094\pi$
$953$	−37.3949	−1.21134	−0.605669	+	0.795717i	$0.707094\pi$
$954$	15.7658	0.510438
$955$	−19.8278	−0.641614
$956$	16.7046	0.540266
$957$	26.0031	0.840560
$958$	−24.0042	−0.775539
$959$	−1.92467	−0.0621508
$960$	5.85817	0.189072
$961$	21.8518	0.704898
$962$	42.5628	1.37228
$963$	43.5717	1.40408
$964$	−23.7105	−0.763663
$965$	19.2546	0.619827
$966$	−0.151521	−0.00487510
$967$	20.8153	0.669375	0.334687	−	0.942329i	$-0.391369\pi$
$967$	20.8153	0.669375	0.334687	+	0.942329i	$0.391369\pi$
$968$	5.63634	0.181159
$969$	4.35093	0.139772
$970$	32.7250	1.05074
$971$	6.37347	0.204535	0.102267	−	0.994757i	$-0.467390\pi$
$971$	6.37347	0.204535	0.102267	+	0.994757i	$0.467390\pi$
$972$	19.1668	0.614774
$973$	−0.575026	−0.0184345
$974$	36.2555	1.16170
$975$	20.7514	0.664578
$976$	11.1715	0.357590
$977$	8.46705	0.270885	0.135442	−	0.990785i	$-0.456754\pi$
$977$	8.46705	0.270885	0.135442	+	0.990785i	$0.456754\pi$
$978$	50.8541	1.62613
$979$	51.3525	1.64123
$980$	17.7832	0.568063
$981$	17.5182	0.559312
$982$	11.5051	0.367144
$983$	33.1310	1.05672	0.528358	−	0.849022i	$-0.322808\pi$
$983$	33.1310	1.05672	0.528358	+	0.849022i	$0.322808\pi$
$984$	24.6646	0.786279
$985$	−19.2210	−0.612432
$986$	−16.6148	−0.529124
$987$	−5.43881	−0.173119
$988$	1.84409	0.0586684
$989$	2.15149	0.0684134
$990$	−23.2083	−0.737607
$991$	33.2504	1.05623	0.528116	−	0.849172i	$-0.322899\pi$
$991$	33.2504	1.05623	0.528116	+	0.849172i	$0.322899\pi$
$992$	−7.26993	−0.230820
$993$	−17.8876	−0.567645
$994$	3.15580	0.100096
$995$	44.1941	1.40105
$996$	16.6450	0.527417
$997$	29.5032	0.934375	0.467188	−	0.884158i	$-0.345267\pi$
$997$	29.5032	0.934375	0.467188	+	0.884158i	$0.345267\pi$
$998$	−44.5542	−1.41034
$999$	−13.1744	−0.416819

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8038.2.a.a.1.16	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8038.2.a.a.1.16	✓	75	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:	\( N \)	\(=\)	\( 8038 = 2 \cdot 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.28450 q^{3} +1.00000 q^{4} -2.56431 q^{5} -2.28450 q^{6} +0.255204 q^{7} +1.00000 q^{8} +2.21893 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.28450 q^{3} +1.00000 q^{4} -2.56431 q^{5} -2.28450 q^{6} +0.255204 q^{7} +1.00000 q^{8} +2.21893 q^{9} -2.56431 q^{10} +4.07877 q^{11} -2.28450 q^{12} -5.76477 q^{13} +0.255204 q^{14} +5.85817 q^{15} +1.00000 q^{16} +5.95375 q^{17} +2.21893 q^{18} -0.319890 q^{19} -2.56431 q^{20} -0.583012 q^{21} +4.07877 q^{22} +0.259893 q^{23} -2.28450 q^{24} +1.57571 q^{25} -5.76477 q^{26} +1.78436 q^{27} +0.255204 q^{28} -2.79065 q^{29} +5.85817 q^{30} -7.26993 q^{31} +1.00000 q^{32} -9.31793 q^{33} +5.95375 q^{34} -0.654422 q^{35} +2.21893 q^{36} -7.38326 q^{37} -0.319890 q^{38} +13.1696 q^{39} -2.56431 q^{40} -10.7965 q^{41} -0.583012 q^{42} +8.27836 q^{43} +4.07877 q^{44} -5.69002 q^{45} +0.259893 q^{46} +9.32881 q^{47} -2.28450 q^{48} -6.93487 q^{49} +1.57571 q^{50} -13.6013 q^{51} -5.76477 q^{52} +7.10517 q^{53} +1.78436 q^{54} -10.4592 q^{55} +0.255204 q^{56} +0.730788 q^{57} -2.79065 q^{58} +2.80328 q^{59} +5.85817 q^{60} +11.1715 q^{61} -7.26993 q^{62} +0.566278 q^{63} +1.00000 q^{64} +14.7827 q^{65} -9.31793 q^{66} +4.70141 q^{67} +5.95375 q^{68} -0.593725 q^{69} -0.654422 q^{70} +12.3658 q^{71} +2.21893 q^{72} -1.79465 q^{73} -7.38326 q^{74} -3.59969 q^{75} -0.319890 q^{76} +1.04092 q^{77} +13.1696 q^{78} +11.0041 q^{79} -2.56431 q^{80} -10.7331 q^{81} -10.7965 q^{82} -7.28607 q^{83} -0.583012 q^{84} -15.2673 q^{85} +8.27836 q^{86} +6.37523 q^{87} +4.07877 q^{88} +12.5902 q^{89} -5.69002 q^{90} -1.47119 q^{91} +0.259893 q^{92} +16.6081 q^{93} +9.32881 q^{94} +0.820298 q^{95} -2.28450 q^{96} -12.7617 q^{97} -6.93487 q^{98} +9.05048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q + 75 q^{2} - 30 q^{3} + 75 q^{4} - 29 q^{5} - 30 q^{6} - 31 q^{7} + 75 q^{8} + 55 q^{9}+O(q^{10}) \) 75 * q + 75 * q^2 - 30 * q^3 + 75 * q^4 - 29 * q^5 - 30 * q^6 - 31 * q^7 + 75 * q^8 + 55 * q^9	\( 75 q + 75 q^{2} - 30 q^{3} + 75 q^{4} - 29 q^{5} - 30 q^{6} - 31 q^{7} + 75 q^{8} + 55 q^{9} - 29 q^{10} - 30 q^{11} - 30 q^{12} - 23 q^{13} - 31 q^{14} - 22 q^{15} + 75 q^{16} - 48 q^{17} + 55 q^{18} - 58 q^{19} - 29 q^{20} - 5 q^{21} - 30 q^{22} - 79 q^{23} - 30 q^{24} + 42 q^{25} - 23 q^{26} - 108 q^{27} - 31 q^{28} - 39 q^{29} - 22 q^{30} - 95 q^{31} + 75 q^{32} - 44 q^{33} - 48 q^{34} - 60 q^{35} + 55 q^{36} - 16 q^{37} - 58 q^{38} - 57 q^{39} - 29 q^{40} - 85 q^{41} - 5 q^{42} - 55 q^{43} - 30 q^{44} - 48 q^{45} - 79 q^{46} - 88 q^{47} - 30 q^{48} + 26 q^{49} + 42 q^{50} - 39 q^{51} - 23 q^{52} - 79 q^{53} - 108 q^{54} - 78 q^{55} - 31 q^{56} - 40 q^{57} - 39 q^{58} - 74 q^{59} - 22 q^{60} - 21 q^{61} - 95 q^{62} - 97 q^{63} + 75 q^{64} - 63 q^{65} - 44 q^{66} - 59 q^{67} - 48 q^{68} + 3 q^{69} - 60 q^{70} - 72 q^{71} + 55 q^{72} - 91 q^{73} - 16 q^{74} - 95 q^{75} - 58 q^{76} - 60 q^{77} - 57 q^{78} - 64 q^{79} - 29 q^{80} + 47 q^{81} - 85 q^{82} - 105 q^{83} - 5 q^{84} + 14 q^{85} - 55 q^{86} - 75 q^{87} - 30 q^{88} - 78 q^{89} - 48 q^{90} - 89 q^{91} - 79 q^{92} + 27 q^{93} - 88 q^{94} - 53 q^{95} - 30 q^{96} - 79 q^{97} + 26 q^{98} - 57 q^{99}+O(q^{100}) \) 75 * q + 75 * q^2 - 30 * q^3 + 75 * q^4 - 29 * q^5 - 30 * q^6 - 31 * q^7 + 75 * q^8 + 55 * q^9 - 29 * q^10 - 30 * q^11 - 30 * q^12 - 23 * q^13 - 31 * q^14 - 22 * q^15 + 75 * q^16 - 48 * q^17 + 55 * q^18 - 58 * q^19 - 29 * q^20 - 5 * q^21 - 30 * q^22 - 79 * q^23 - 30 * q^24 + 42 * q^25 - 23 * q^26 - 108 * q^27 - 31 * q^28 - 39 * q^29 - 22 * q^30 - 95 * q^31 + 75 * q^32 - 44 * q^33 - 48 * q^34 - 60 * q^35 + 55 * q^36 - 16 * q^37 - 58 * q^38 - 57 * q^39 - 29 * q^40 - 85 * q^41 - 5 * q^42 - 55 * q^43 - 30 * q^44 - 48 * q^45 - 79 * q^46 - 88 * q^47 - 30 * q^48 + 26 * q^49 + 42 * q^50 - 39 * q^51 - 23 * q^52 - 79 * q^53 - 108 * q^54 - 78 * q^55 - 31 * q^56 - 40 * q^57 - 39 * q^58 - 74 * q^59 - 22 * q^60 - 21 * q^61 - 95 * q^62 - 97 * q^63 + 75 * q^64 - 63 * q^65 - 44 * q^66 - 59 * q^67 - 48 * q^68 + 3 * q^69 - 60 * q^70 - 72 * q^71 + 55 * q^72 - 91 * q^73 - 16 * q^74 - 95 * q^75 - 58 * q^76 - 60 * q^77 - 57 * q^78 - 64 * q^79 - 29 * q^80 + 47 * q^81 - 85 * q^82 - 105 * q^83 - 5 * q^84 + 14 * q^85 - 55 * q^86 - 75 * q^87 - 30 * q^88 - 78 * q^89 - 48 * q^90 - 89 * q^91 - 79 * q^92 + 27 * q^93 - 88 * q^94 - 53 * q^95 - 30 * q^96 - 79 * q^97 + 26 * q^98 - 57 * q^99

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