LMFDB - Embedded newform 8034.2.a.bb.1.1

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.19123$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.19123 q^{5} -1.00000 q^{6} -2.48485 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.19123 q^{5} -1.00000 q^{6} -2.48485 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.19123 q^{10} -3.45337 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.48485 q^{14} -4.19123 q^{15} +1.00000 q^{16} +4.15125 q^{17} -1.00000 q^{18} -1.49203 q^{19} -4.19123 q^{20} -2.48485 q^{21} +3.45337 q^{22} -1.16579 q^{23} -1.00000 q^{24} +12.5664 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.48485 q^{28} +3.97697 q^{29} +4.19123 q^{30} +6.19959 q^{31} -1.00000 q^{32} -3.45337 q^{33} -4.15125 q^{34} +10.4146 q^{35} +1.00000 q^{36} +0.938276 q^{37} +1.49203 q^{38} -1.00000 q^{39} +4.19123 q^{40} -8.24288 q^{41} +2.48485 q^{42} -1.09636 q^{43} -3.45337 q^{44} -4.19123 q^{45} +1.16579 q^{46} +1.91281 q^{47} +1.00000 q^{48} -0.825500 q^{49} -12.5664 q^{50} +4.15125 q^{51} -1.00000 q^{52} -3.82574 q^{53} -1.00000 q^{54} +14.4739 q^{55} +2.48485 q^{56} -1.49203 q^{57} -3.97697 q^{58} +8.10947 q^{59} -4.19123 q^{60} +5.11955 q^{61} -6.19959 q^{62} -2.48485 q^{63} +1.00000 q^{64} +4.19123 q^{65} +3.45337 q^{66} +13.0998 q^{67} +4.15125 q^{68} -1.16579 q^{69} -10.4146 q^{70} +0.896009 q^{71} -1.00000 q^{72} -0.857920 q^{73} -0.938276 q^{74} +12.5664 q^{75} -1.49203 q^{76} +8.58112 q^{77} +1.00000 q^{78} +4.36696 q^{79} -4.19123 q^{80} +1.00000 q^{81} +8.24288 q^{82} -1.28939 q^{83} -2.48485 q^{84} -17.3989 q^{85} +1.09636 q^{86} +3.97697 q^{87} +3.45337 q^{88} +1.33376 q^{89} +4.19123 q^{90} +2.48485 q^{91} -1.16579 q^{92} +6.19959 q^{93} -1.91281 q^{94} +6.25345 q^{95} -1.00000 q^{96} -1.09589 q^{97} +0.825500 q^{98} -3.45337 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * 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
$5$	−4.19123	−1.87438	−0.937188	−	0.348824i	$-0.886581\pi$
$5$	−4.19123	−1.87438	−0.937188	+	0.348824i	$0.886581\pi$
$6$	−1.00000	−0.408248
$7$	−2.48485	−0.939187	−0.469593	−	0.882883i	$-0.655599\pi$
$7$	−2.48485	−0.939187	−0.469593	+	0.882883i	$0.655599\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.19123	1.32538
$11$	−3.45337	−1.04123	−0.520615	−	0.853791i	$-0.674297\pi$
$11$	−3.45337	−1.04123	−0.520615	+	0.853791i	$0.674297\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.48485	0.664105
$15$	−4.19123	−1.08217
$16$	1.00000	0.250000
$17$	4.15125	1.00683	0.503413	−	0.864046i	$-0.332077\pi$
$17$	4.15125	1.00683	0.503413	+	0.864046i	$0.332077\pi$
$18$	−1.00000	−0.235702
$19$	−1.49203	−0.342295	−0.171148	−	0.985245i	$-0.554748\pi$
$19$	−1.49203	−0.342295	−0.171148	+	0.985245i	$0.554748\pi$
$20$	−4.19123	−0.937188
$21$	−2.48485	−0.542240
$22$	3.45337	0.736261
$23$	−1.16579	−0.243084	−0.121542	−	0.992586i	$-0.538784\pi$
$23$	−1.16579	−0.243084	−0.121542	+	0.992586i	$0.538784\pi$
$24$	−1.00000	−0.204124
$25$	12.5664	2.51329
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−2.48485	−0.469593
$29$	3.97697	0.738505	0.369253	−	0.929329i	$-0.379614\pi$
$29$	3.97697	0.738505	0.369253	+	0.929329i	$0.379614\pi$
$30$	4.19123	0.765211
$31$	6.19959	1.11348	0.556740	−	0.830687i	$-0.312052\pi$
$31$	6.19959	1.11348	0.556740	+	0.830687i	$0.312052\pi$
$32$	−1.00000	−0.176777
$33$	−3.45337	−0.601155
$34$	−4.15125	−0.711933
$35$	10.4146	1.76039
$36$	1.00000	0.166667
$37$	0.938276	0.154252	0.0771258	−	0.997021i	$-0.475426\pi$
$37$	0.938276	0.154252	0.0771258	+	0.997021i	$0.475426\pi$
$38$	1.49203	0.242039
$39$	−1.00000	−0.160128
$40$	4.19123	0.662692
$41$	−8.24288	−1.28732	−0.643661	−	0.765311i	$-0.722585\pi$
$41$	−8.24288	−1.28732	−0.643661	+	0.765311i	$0.722585\pi$
$42$	2.48485	0.383421
$43$	−1.09636	−0.167193	−0.0835964	−	0.996500i	$-0.526641\pi$
$43$	−1.09636	−0.167193	−0.0835964	+	0.996500i	$0.526641\pi$
$44$	−3.45337	−0.520615
$45$	−4.19123	−0.624792
$46$	1.16579	0.171886
$47$	1.91281	0.279012	0.139506	−	0.990221i	$-0.455448\pi$
$47$	1.91281	0.279012	0.139506	+	0.990221i	$0.455448\pi$
$48$	1.00000	0.144338
$49$	−0.825500	−0.117929
$50$	−12.5664	−1.77716
$51$	4.15125	0.581291
$52$	−1.00000	−0.138675
$53$	−3.82574	−0.525505	−0.262753	−	0.964863i	$-0.584630\pi$
$53$	−3.82574	−0.525505	−0.262753	+	0.964863i	$0.584630\pi$
$54$	−1.00000	−0.136083
$55$	14.4739	1.95166
$56$	2.48485	0.332053
$57$	−1.49203	−0.197624
$58$	−3.97697	−0.522202
$59$	8.10947	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$59$	8.10947	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$60$	−4.19123	−0.541086
$61$	5.11955	0.655491	0.327745	−	0.944766i	$-0.393711\pi$
$61$	5.11955	0.655491	0.327745	+	0.944766i	$0.393711\pi$
$62$	−6.19959	−0.787349
$63$	−2.48485	−0.313062
$64$	1.00000	0.125000
$65$	4.19123	0.519859
$66$	3.45337	0.425080
$67$	13.0998	1.60040	0.800198	−	0.599736i	$-0.204728\pi$
$67$	13.0998	1.60040	0.800198	+	0.599736i	$0.204728\pi$
$68$	4.15125	0.503413
$69$	−1.16579	−0.140345
$70$	−10.4146	−1.24478
$71$	0.896009	0.106337	0.0531683	−	0.998586i	$-0.483068\pi$
$71$	0.896009	0.106337	0.0531683	+	0.998586i	$0.483068\pi$
$72$	−1.00000	−0.117851
$73$	−0.857920	−0.100412	−0.0502059	−	0.998739i	$-0.515988\pi$
$73$	−0.857920	−0.100412	−0.0502059	+	0.998739i	$0.515988\pi$
$74$	−0.938276	−0.109072
$75$	12.5664	1.45105
$76$	−1.49203	−0.171148
$77$	8.58112	0.977909
$78$	1.00000	0.113228
$79$	4.36696	0.491322	0.245661	−	0.969356i	$-0.420995\pi$
$79$	4.36696	0.491322	0.245661	+	0.969356i	$0.420995\pi$
$80$	−4.19123	−0.468594
$81$	1.00000	0.111111
$82$	8.24288	0.910274
$83$	−1.28939	−0.141529	−0.0707644	−	0.997493i	$-0.522544\pi$
$83$	−1.28939	−0.141529	−0.0707644	+	0.997493i	$0.522544\pi$
$84$	−2.48485	−0.271120
$85$	−17.3989	−1.88717
$86$	1.09636	0.118223
$87$	3.97697	0.426376
$88$	3.45337	0.368130
$89$	1.33376	0.141378	0.0706891	−	0.997498i	$-0.477480\pi$
$89$	1.33376	0.141378	0.0706891	+	0.997498i	$0.477480\pi$
$90$	4.19123	0.441795
$91$	2.48485	0.260483
$92$	−1.16579	−0.121542
$93$	6.19959	0.642868
$94$	−1.91281	−0.197292
$95$	6.25345	0.641590
$96$	−1.00000	−0.102062
$97$	−1.09589	−0.111271	−0.0556355	−	0.998451i	$-0.517718\pi$
$97$	−1.09589	−0.111271	−0.0556355	+	0.998451i	$0.517718\pi$
$98$	0.825500	0.0833881
$99$	−3.45337	−0.347077
$100$	12.5664	1.25664
$101$	−12.2271	−1.21664	−0.608320	−	0.793692i	$-0.708156\pi$
$101$	−12.2271	−1.21664	−0.608320	+	0.793692i	$0.708156\pi$
$102$	−4.15125	−0.411035
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	10.4146	1.01636
$106$	3.82574	0.371588
$107$	−17.9304	−1.73340	−0.866700	−	0.498830i	$-0.833763\pi$
$107$	−17.9304	−1.73340	−0.866700	+	0.498830i	$0.833763\pi$
$108$	1.00000	0.0962250
$109$	18.1175	1.73534	0.867670	−	0.497140i	$-0.165617\pi$
$109$	18.1175	1.73534	0.867670	+	0.497140i	$0.165617\pi$
$110$	−14.4739	−1.38003
$111$	0.938276	0.0890572
$112$	−2.48485	−0.234797
$113$	16.6258	1.56402	0.782011	−	0.623264i	$-0.214194\pi$
$113$	16.6258	1.56402	0.782011	+	0.623264i	$0.214194\pi$
$114$	1.49203	0.139741
$115$	4.88610	0.455631
$116$	3.97697	0.369253
$117$	−1.00000	−0.0924500
$118$	−8.10947	−0.746538
$119$	−10.3152	−0.945597
$120$	4.19123	0.382606
$121$	0.925764	0.0841604
$122$	−5.11955	−0.463502
$123$	−8.24288	−0.743236
$124$	6.19959	0.556740
$125$	−31.7127	−2.83647
$126$	2.48485	0.221368
$127$	−6.45305	−0.572615	−0.286308	−	0.958138i	$-0.592428\pi$
$127$	−6.45305	−0.572615	−0.286308	+	0.958138i	$0.592428\pi$
$128$	−1.00000	−0.0883883
$129$	−1.09636	−0.0965288
$130$	−4.19123	−0.367596
$131$	−5.48297	−0.479049	−0.239525	−	0.970890i	$-0.576992\pi$
$131$	−5.48297	−0.479049	−0.239525	+	0.970890i	$0.576992\pi$
$132$	−3.45337	−0.300577
$133$	3.70748	0.321479
$134$	−13.0998	−1.13165
$135$	−4.19123	−0.360724
$136$	−4.15125	−0.355967
$137$	9.92674	0.848098	0.424049	−	0.905639i	$-0.360608\pi$
$137$	9.92674	0.848098	0.424049	+	0.905639i	$0.360608\pi$
$138$	1.16579	0.0992386
$139$	3.44571	0.292261	0.146131	−	0.989265i	$-0.453318\pi$
$139$	3.44571	0.292261	0.146131	+	0.989265i	$0.453318\pi$
$140$	10.4146	0.880195
$141$	1.91281	0.161088
$142$	−0.896009	−0.0751914
$143$	3.45337	0.288785
$144$	1.00000	0.0833333
$145$	−16.6684	−1.38424
$146$	0.857920	0.0710019
$147$	−0.825500	−0.0680861
$148$	0.938276	0.0771258
$149$	−4.22838	−0.346403	−0.173201	−	0.984886i	$-0.555411\pi$
$149$	−4.22838	−0.346403	−0.173201	+	0.984886i	$0.555411\pi$
$150$	−12.5664	−1.02605
$151$	−14.8402	−1.20768	−0.603840	−	0.797106i	$-0.706363\pi$
$151$	−14.8402	−1.20768	−0.603840	+	0.797106i	$0.706363\pi$
$152$	1.49203	0.121020
$153$	4.15125	0.335609
$154$	−8.58112	−0.691486
$155$	−25.9839	−2.08708
$156$	−1.00000	−0.0800641
$157$	11.3687	0.907322	0.453661	−	0.891174i	$-0.350118\pi$
$157$	11.3687	0.907322	0.453661	+	0.891174i	$0.350118\pi$
$158$	−4.36696	−0.347417
$159$	−3.82574	−0.303401
$160$	4.19123	0.331346
$161$	2.89682	0.228301
$162$	−1.00000	−0.0785674
$163$	17.4080	1.36350	0.681750	−	0.731585i	$-0.261219\pi$
$163$	17.4080	1.36350	0.681750	+	0.731585i	$0.261219\pi$
$164$	−8.24288	−0.643661
$165$	14.4739	1.12679
$166$	1.28939	0.100076
$167$	−19.8534	−1.53630	−0.768151	−	0.640268i	$-0.778823\pi$
$167$	−19.8534	−1.53630	−0.768151	+	0.640268i	$0.778823\pi$
$168$	2.48485	0.191711
$169$	1.00000	0.0769231
$170$	17.3989	1.33443
$171$	−1.49203	−0.114098
$172$	−1.09636	−0.0835964
$173$	8.38483	0.637487	0.318744	−	0.947841i	$-0.396739\pi$
$173$	8.38483	0.637487	0.318744	+	0.947841i	$0.396739\pi$
$174$	−3.97697	−0.301493
$175$	−31.2258	−2.36045
$176$	−3.45337	−0.260308
$177$	8.10947	0.609545
$178$	−1.33376	−0.0999695
$179$	24.2415	1.81189	0.905946	−	0.423394i	$-0.139161\pi$
$179$	24.2415	1.81189	0.905946	+	0.423394i	$0.139161\pi$
$180$	−4.19123	−0.312396
$181$	1.00614	0.0747858	0.0373929	−	0.999301i	$-0.488095\pi$
$181$	1.00614	0.0747858	0.0373929	+	0.999301i	$0.488095\pi$
$182$	−2.48485	−0.184190
$183$	5.11955	0.378448
$184$	1.16579	0.0859431
$185$	−3.93253	−0.289126
$186$	−6.19959	−0.454576
$187$	−14.3358	−1.04834
$188$	1.91281	0.139506
$189$	−2.48485	−0.180747
$190$	−6.25345	−0.453673
$191$	−17.7258	−1.28259	−0.641295	−	0.767294i	$-0.721603\pi$
$191$	−17.7258	−1.28259	−0.641295	+	0.767294i	$0.721603\pi$
$192$	1.00000	0.0721688
$193$	−8.92394	−0.642359	−0.321180	−	0.947018i	$-0.604079\pi$
$193$	−8.92394	−0.642359	−0.321180	+	0.947018i	$0.604079\pi$
$194$	1.09589	0.0786805
$195$	4.19123	0.300140
$196$	−0.825500	−0.0589643
$197$	−5.72916	−0.408186	−0.204093	−	0.978952i	$-0.565425\pi$
$197$	−5.72916	−0.408186	−0.204093	+	0.978952i	$0.565425\pi$
$198$	3.45337	0.245420
$199$	4.04033	0.286412	0.143206	−	0.989693i	$-0.454259\pi$
$199$	4.04033	0.286412	0.143206	+	0.989693i	$0.454259\pi$
$200$	−12.5664	−0.888582
$201$	13.0998	0.923989
$202$	12.2271	0.860295
$203$	−9.88220	−0.693594
$204$	4.15125	0.290646
$205$	34.5479	2.41293
$206$	−1.00000	−0.0696733
$207$	−1.16579	−0.0810279
$208$	−1.00000	−0.0693375
$209$	5.15253	0.356408
$210$	−10.4146	−0.718676
$211$	−18.1802	−1.25158	−0.625789	−	0.779992i	$-0.715223\pi$
$211$	−18.1802	−1.25158	−0.625789	+	0.779992i	$0.715223\pi$
$212$	−3.82574	−0.262753
$213$	0.896009	0.0613935
$214$	17.9304	1.22570
$215$	4.59509	0.313382
$216$	−1.00000	−0.0680414
$217$	−15.4051	−1.04577
$218$	−18.1175	−1.22707
$219$	−0.857920	−0.0579728
$220$	14.4739	0.975829
$221$	−4.15125	−0.279243
$222$	−0.938276	−0.0629730
$223$	−15.7232	−1.05290	−0.526452	−	0.850205i	$-0.676478\pi$
$223$	−15.7232	−1.05290	−0.526452	+	0.850205i	$0.676478\pi$
$224$	2.48485	0.166026
$225$	12.5664	0.837763
$226$	−16.6258	−1.10593
$227$	5.43218	0.360546	0.180273	−	0.983617i	$-0.442302\pi$
$227$	5.43218	0.360546	0.180273	+	0.983617i	$0.442302\pi$
$228$	−1.49203	−0.0988121
$229$	14.2912	0.944386	0.472193	−	0.881495i	$-0.343462\pi$
$229$	14.2912	0.944386	0.472193	+	0.881495i	$0.343462\pi$
$230$	−4.88610	−0.322180
$231$	8.58112	0.564596
$232$	−3.97697	−0.261101
$233$	−15.7787	−1.03370	−0.516848	−	0.856077i	$-0.672895\pi$
$233$	−15.7787	−1.03370	−0.516848	+	0.856077i	$0.672895\pi$
$234$	1.00000	0.0653720
$235$	−8.01704	−0.522974
$236$	8.10947	0.527882
$237$	4.36696	0.283665
$238$	10.3152	0.668638
$239$	−24.0758	−1.55733	−0.778667	−	0.627438i	$-0.784104\pi$
$239$	−24.0758	−1.55733	−0.778667	+	0.627438i	$0.784104\pi$
$240$	−4.19123	−0.270543
$241$	−24.3323	−1.56738	−0.783689	−	0.621153i	$-0.786665\pi$
$241$	−24.3323	−1.56738	−0.783689	+	0.621153i	$0.786665\pi$
$242$	−0.925764	−0.0595104
$243$	1.00000	0.0641500
$244$	5.11955	0.327745
$245$	3.45987	0.221043
$246$	8.24288	0.525547
$247$	1.49203	0.0949356
$248$	−6.19959	−0.393675
$249$	−1.28939	−0.0817117
$250$	31.7127	2.00569
$251$	8.22652	0.519253	0.259627	−	0.965709i	$-0.416400\pi$
$251$	8.22652	0.519253	0.259627	+	0.965709i	$0.416400\pi$
$252$	−2.48485	−0.156531
$253$	4.02590	0.253106
$254$	6.45305	0.404900
$255$	−17.3989	−1.08956
$256$	1.00000	0.0625000
$257$	19.2253	1.19924	0.599620	−	0.800285i	$-0.295319\pi$
$257$	19.2253	1.19924	0.599620	+	0.800285i	$0.295319\pi$
$258$	1.09636	0.0682562
$259$	−2.33148	−0.144871
$260$	4.19123	0.259929
$261$	3.97697	0.246168
$262$	5.48297	0.338739
$263$	−26.5673	−1.63821	−0.819104	−	0.573644i	$-0.805529\pi$
$263$	−26.5673	−1.63821	−0.819104	+	0.573644i	$0.805529\pi$
$264$	3.45337	0.212540
$265$	16.0346	0.984995
$266$	−3.70748	−0.227320
$267$	1.33376	0.0816248
$268$	13.0998	0.800198
$269$	3.93881	0.240154	0.120077	−	0.992765i	$-0.461686\pi$
$269$	3.93881	0.240154	0.120077	+	0.992765i	$0.461686\pi$
$270$	4.19123	0.255070
$271$	−6.13049	−0.372401	−0.186200	−	0.982512i	$-0.559617\pi$
$271$	−6.13049	−0.372401	−0.186200	+	0.982512i	$0.559617\pi$
$272$	4.15125	0.251706
$273$	2.48485	0.150390
$274$	−9.92674	−0.599696
$275$	−43.3966	−2.61691
$276$	−1.16579	−0.0701723
$277$	−3.38074	−0.203129	−0.101564	−	0.994829i	$-0.532385\pi$
$277$	−3.38074	−0.203129	−0.101564	+	0.994829i	$0.532385\pi$
$278$	−3.44571	−0.206660
$279$	6.19959	0.371160
$280$	−10.4146	−0.622392
$281$	−5.93074	−0.353798	−0.176899	−	0.984229i	$-0.556607\pi$
$281$	−5.93074	−0.353798	−0.176899	+	0.984229i	$0.556607\pi$
$282$	−1.91281	−0.113906
$283$	23.4537	1.39418	0.697088	−	0.716985i	$-0.254479\pi$
$283$	23.4537	1.39418	0.697088	+	0.716985i	$0.254479\pi$
$284$	0.896009	0.0531683
$285$	6.25345	0.370422
$286$	−3.45337	−0.204202
$287$	20.4824	1.20904
$288$	−1.00000	−0.0589256
$289$	0.232872	0.0136984
$290$	16.6684	0.978803
$291$	−1.09589	−0.0642424
$292$	−0.857920	−0.0502059
$293$	−29.0023	−1.69433	−0.847167	−	0.531327i	$-0.821693\pi$
$293$	−29.0023	−1.69433	−0.847167	+	0.531327i	$0.821693\pi$
$294$	0.825500	0.0481442
$295$	−33.9887	−1.97890
$296$	−0.938276	−0.0545362
$297$	−3.45337	−0.200385
$298$	4.22838	0.244944
$299$	1.16579	0.0674193
$300$	12.5664	0.725524
$301$	2.72429	0.157025
$302$	14.8402	0.853959
$303$	−12.2271	−0.702428
$304$	−1.49203	−0.0855738
$305$	−21.4572	−1.22864
$306$	−4.15125	−0.237311
$307$	25.5987	1.46100	0.730499	−	0.682914i	$-0.239288\pi$
$307$	25.5987	1.46100	0.730499	+	0.682914i	$0.239288\pi$
$308$	8.58112	0.488955
$309$	1.00000	0.0568880
$310$	25.9839	1.47579
$311$	−14.8637	−0.842842	−0.421421	−	0.906865i	$-0.638468\pi$
$311$	−14.8637	−0.842842	−0.421421	+	0.906865i	$0.638468\pi$
$312$	1.00000	0.0566139
$313$	11.2838	0.637798	0.318899	−	0.947789i	$-0.396687\pi$
$313$	11.2838	0.637798	0.318899	+	0.947789i	$0.396687\pi$
$314$	−11.3687	−0.641574
$315$	10.4146	0.586796
$316$	4.36696	0.245661
$317$	3.43988	0.193203	0.0966013	−	0.995323i	$-0.469203\pi$
$317$	3.43988	0.193203	0.0966013	+	0.995323i	$0.469203\pi$
$318$	3.82574	0.214537
$319$	−13.7340	−0.768954
$320$	−4.19123	−0.234297
$321$	−17.9304	−1.00078
$322$	−2.89682	−0.161433
$323$	−6.19379	−0.344632
$324$	1.00000	0.0555556
$325$	−12.5664	−0.697061
$326$	−17.4080	−0.964140
$327$	18.1175	1.00190
$328$	8.24288	0.455137
$329$	−4.75306	−0.262045
$330$	−14.4739	−0.796761
$331$	−6.84967	−0.376492	−0.188246	−	0.982122i	$-0.560280\pi$
$331$	−6.84967	−0.376492	−0.188246	+	0.982122i	$0.560280\pi$
$332$	−1.28939	−0.0707644
$333$	0.938276	0.0514172
$334$	19.8534	1.08633
$335$	−54.9043	−2.99974
$336$	−2.48485	−0.135560
$337$	8.11014	0.441788	0.220894	−	0.975298i	$-0.429103\pi$
$337$	8.11014	0.441788	0.220894	+	0.975298i	$0.429103\pi$
$338$	−1.00000	−0.0543928
$339$	16.6258	0.902989
$340$	−17.3989	−0.943586
$341$	−21.4095	−1.15939
$342$	1.49203	0.0806798
$343$	19.4452	1.04994
$344$	1.09636	0.0591116
$345$	4.88610	0.263059
$346$	−8.38483	−0.450772
$347$	−15.6913	−0.842351	−0.421176	−	0.906979i	$-0.638382\pi$
$347$	−15.6913	−0.842351	−0.421176	+	0.906979i	$0.638382\pi$
$348$	3.97697	0.213188
$349$	−16.5396	−0.885347	−0.442673	−	0.896683i	$-0.645970\pi$
$349$	−16.5396	−0.885347	−0.442673	+	0.896683i	$0.645970\pi$
$350$	31.2258	1.66909
$351$	−1.00000	−0.0533761
$352$	3.45337	0.184065
$353$	−28.2812	−1.50525	−0.752627	−	0.658447i	$-0.771214\pi$
$353$	−28.2812	−1.50525	−0.752627	+	0.658447i	$0.771214\pi$
$354$	−8.10947	−0.431014
$355$	−3.75538	−0.199315
$356$	1.33376	0.0706891
$357$	−10.3152	−0.545941
$358$	−24.2415	−1.28120
$359$	−21.2405	−1.12103	−0.560516	−	0.828143i	$-0.689397\pi$
$359$	−21.2405	−1.12103	−0.560516	+	0.828143i	$0.689397\pi$
$360$	4.19123	0.220897
$361$	−16.7738	−0.882834
$362$	−1.00614	−0.0528815
$363$	0.925764	0.0485900
$364$	2.48485	0.130242
$365$	3.59574	0.188210
$366$	−5.11955	−0.267603
$367$	−4.96807	−0.259331	−0.129666	−	0.991558i	$-0.541390\pi$
$367$	−4.96807	−0.259331	−0.129666	+	0.991558i	$0.541390\pi$
$368$	−1.16579	−0.0607710
$369$	−8.24288	−0.429107
$370$	3.93253	0.204443
$371$	9.50640	0.493547
$372$	6.19959	0.321434
$373$	−1.35351	−0.0700822	−0.0350411	−	0.999386i	$-0.511156\pi$
$373$	−1.35351	−0.0700822	−0.0350411	+	0.999386i	$0.511156\pi$
$374$	14.3358	0.741287
$375$	−31.7127	−1.63764
$376$	−1.91281	−0.0986458
$377$	−3.97697	−0.204824
$378$	2.48485	0.127807
$379$	1.33194	0.0684173	0.0342086	−	0.999415i	$-0.489109\pi$
$379$	1.33194	0.0684173	0.0342086	+	0.999415i	$0.489109\pi$
$380$	6.25345	0.320795
$381$	−6.45305	−0.330600
$382$	17.7258	0.906929
$383$	−5.46332	−0.279162	−0.139581	−	0.990211i	$-0.544576\pi$
$383$	−5.46332	−0.279162	−0.139581	+	0.990211i	$0.544576\pi$
$384$	−1.00000	−0.0510310
$385$	−35.9655	−1.83297
$386$	8.92394	0.454217
$387$	−1.09636	−0.0557309
$388$	−1.09589	−0.0556355
$389$	5.47837	0.277764	0.138882	−	0.990309i	$-0.455649\pi$
$389$	5.47837	0.277764	0.138882	+	0.990309i	$0.455649\pi$
$390$	−4.19123	−0.212231
$391$	−4.83948	−0.244743
$392$	0.825500	0.0416941
$393$	−5.48297	−0.276579
$394$	5.72916	0.288631
$395$	−18.3030	−0.920922
$396$	−3.45337	−0.173538
$397$	−32.9394	−1.65318	−0.826589	−	0.562806i	$-0.809722\pi$
$397$	−32.9394	−1.65318	−0.826589	+	0.562806i	$0.809722\pi$
$398$	−4.04033	−0.202524
$399$	3.70748	0.185606
$400$	12.5664	0.628322
$401$	7.80301	0.389664	0.194832	−	0.980837i	$-0.437584\pi$
$401$	7.80301	0.389664	0.194832	+	0.980837i	$0.437584\pi$
$402$	−13.0998	−0.653359
$403$	−6.19959	−0.308824
$404$	−12.2271	−0.608320
$405$	−4.19123	−0.208264
$406$	9.88220	0.490445
$407$	−3.24021	−0.160611
$408$	−4.15125	−0.205517
$409$	25.9347	1.28239	0.641194	−	0.767378i	$-0.278439\pi$
$409$	25.9347	1.28239	0.641194	+	0.767378i	$0.278439\pi$
$410$	−34.5479	−1.70620
$411$	9.92674	0.489650
$412$	1.00000	0.0492665
$413$	−20.1509	−0.991559
$414$	1.16579	0.0572954
$415$	5.40413	0.265278
$416$	1.00000	0.0490290
$417$	3.44571	0.168737
$418$	−5.15253	−0.252019
$419$	−11.8178	−0.577339	−0.288670	−	0.957429i	$-0.593213\pi$
$419$	−11.8178	−0.577339	−0.288670	+	0.957429i	$0.593213\pi$
$420$	10.4146	0.508181
$421$	−28.3038	−1.37944	−0.689720	−	0.724076i	$-0.742267\pi$
$421$	−28.3038	−1.37944	−0.689720	+	0.724076i	$0.742267\pi$
$422$	18.1802	0.884999
$423$	1.91281	0.0930041
$424$	3.82574	0.185794
$425$	52.1664	2.53044
$426$	−0.896009	−0.0434118
$427$	−12.7213	−0.615628
$428$	−17.9304	−0.866700
$429$	3.45337	0.166730
$430$	−4.59509	−0.221595
$431$	−11.3047	−0.544528	−0.272264	−	0.962223i	$-0.587772\pi$
$431$	−11.3047	−0.544528	−0.272264	+	0.962223i	$0.587772\pi$
$432$	1.00000	0.0481125
$433$	−13.6585	−0.656385	−0.328193	−	0.944611i	$-0.606439\pi$
$433$	−13.6585	−0.656385	−0.328193	+	0.944611i	$0.606439\pi$
$434$	15.4051	0.739468
$435$	−16.6684	−0.799190
$436$	18.1175	0.867670
$437$	1.73939	0.0832064
$438$	0.857920	0.0409930
$439$	−10.1305	−0.483503	−0.241751	−	0.970338i	$-0.577722\pi$
$439$	−10.1305	−0.483503	−0.241751	+	0.970338i	$0.577722\pi$
$440$	−14.4739	−0.690015
$441$	−0.825500	−0.0393095
$442$	4.15125	0.197455
$443$	−24.1352	−1.14670	−0.573348	−	0.819312i	$-0.694356\pi$
$443$	−24.1352	−1.14670	−0.573348	+	0.819312i	$0.694356\pi$
$444$	0.938276	0.0445286
$445$	−5.59010	−0.264996
$446$	15.7232	0.744515
$447$	−4.22838	−0.199996
$448$	−2.48485	−0.117398
$449$	34.6217	1.63390	0.816951	−	0.576708i	$-0.195663\pi$
$449$	34.6217	1.63390	0.816951	+	0.576708i	$0.195663\pi$
$450$	−12.5664	−0.592388
$451$	28.4657	1.34040
$452$	16.6258	0.782011
$453$	−14.8402	−0.697254
$454$	−5.43218	−0.254945
$455$	−10.4146	−0.488244
$456$	1.49203	0.0698707
$457$	−31.4318	−1.47032	−0.735158	−	0.677896i	$-0.762892\pi$
$457$	−31.4318	−1.47032	−0.735158	+	0.677896i	$0.762892\pi$
$458$	−14.2912	−0.667782
$459$	4.15125	0.193764
$460$	4.88610	0.227815
$461$	17.5107	0.815554	0.407777	−	0.913082i	$-0.366304\pi$
$461$	17.5107	0.815554	0.407777	+	0.913082i	$0.366304\pi$
$462$	−8.58112	−0.399230
$463$	10.4776	0.486933	0.243467	−	0.969909i	$-0.421715\pi$
$463$	10.4776	0.486933	0.243467	+	0.969909i	$0.421715\pi$
$464$	3.97697	0.184626
$465$	−25.9839	−1.20498
$466$	15.7787	0.730934
$467$	0.734108	0.0339705	0.0169852	−	0.999856i	$-0.494593\pi$
$467$	0.734108	0.0339705	0.0169852	+	0.999856i	$0.494593\pi$
$468$	−1.00000	−0.0462250
$469$	−32.5511	−1.50307
$470$	8.01704	0.369799
$471$	11.3687	0.523843
$472$	−8.10947	−0.373269
$473$	3.78613	0.174086
$474$	−4.36696	−0.200581
$475$	−18.7495	−0.860287
$476$	−10.3152	−0.472799
$477$	−3.82574	−0.175168
$478$	24.0758	1.10120
$479$	40.2600	1.83952	0.919762	−	0.392475i	$-0.128381\pi$
$479$	40.2600	1.83952	0.919762	+	0.392475i	$0.128381\pi$
$480$	4.19123	0.191303
$481$	−0.938276	−0.0427817
$482$	24.3323	1.10830
$483$	2.89682	0.131810
$484$	0.925764	0.0420802
$485$	4.59314	0.208564
$486$	−1.00000	−0.0453609
$487$	10.8019	0.489482	0.244741	−	0.969589i	$-0.421297\pi$
$487$	10.8019	0.489482	0.244741	+	0.969589i	$0.421297\pi$
$488$	−5.11955	−0.231751
$489$	17.4080	0.787217
$490$	−3.45987	−0.156301
$491$	21.2973	0.961134	0.480567	−	0.876958i	$-0.340431\pi$
$491$	21.2973	0.961134	0.480567	+	0.876958i	$0.340431\pi$
$492$	−8.24288	−0.371618
$493$	16.5094	0.743546
$494$	−1.49203	−0.0671296
$495$	14.4739	0.650553
$496$	6.19959	0.278370
$497$	−2.22645	−0.0998700
$498$	1.28939	0.0577789
$499$	−26.0360	−1.16553	−0.582765	−	0.812640i	$-0.698029\pi$
$499$	−26.0360	−1.16553	−0.582765	+	0.812640i	$0.698029\pi$
$500$	−31.7127	−1.41824
$501$	−19.8534	−0.886985
$502$	−8.22652	−0.367168
$503$	−16.2381	−0.724020	−0.362010	−	0.932174i	$-0.617909\pi$
$503$	−16.2381	−0.724020	−0.362010	+	0.932174i	$0.617909\pi$
$504$	2.48485	0.110684
$505$	51.2466	2.28044
$506$	−4.02590	−0.178973
$507$	1.00000	0.0444116
$508$	−6.45305	−0.286308
$509$	2.48262	0.110040	0.0550202	−	0.998485i	$-0.482478\pi$
$509$	2.48262	0.110040	0.0550202	+	0.998485i	$0.482478\pi$
$510$	17.3989	0.770434
$511$	2.13180	0.0943055
$512$	−1.00000	−0.0441942
$513$	−1.49203	−0.0658747
$514$	−19.2253	−0.847990
$515$	−4.19123	−0.184688
$516$	−1.09636	−0.0482644
$517$	−6.60565	−0.290516
$518$	2.33148	0.102439
$519$	8.38483	0.368053
$520$	−4.19123	−0.183798
$521$	−1.51427	−0.0663415	−0.0331707	−	0.999450i	$-0.510561\pi$
$521$	−1.51427	−0.0663415	−0.0331707	+	0.999450i	$0.510561\pi$
$522$	−3.97697	−0.174067
$523$	11.1517	0.487628	0.243814	−	0.969822i	$-0.421601\pi$
$523$	11.1517	0.487628	0.243814	+	0.969822i	$0.421601\pi$
$524$	−5.48297	−0.239525
$525$	−31.2258	−1.36280
$526$	26.5673	1.15839
$527$	25.7361	1.12108
$528$	−3.45337	−0.150289
$529$	−21.6409	−0.940910
$530$	−16.0346	−0.696497
$531$	8.10947	0.351921
$532$	3.70748	0.160740
$533$	8.24288	0.357039
$534$	−1.33376	−0.0577174
$535$	75.1506	3.24904
$536$	−13.0998	−0.565825
$537$	24.2415	1.04610
$538$	−3.93881	−0.169814
$539$	2.85076	0.122791
$540$	−4.19123	−0.180362
$541$	23.9397	1.02925	0.514623	−	0.857416i	$-0.327932\pi$
$541$	23.9397	1.02925	0.514623	+	0.857416i	$0.327932\pi$
$542$	6.13049	0.263327
$543$	1.00614	0.0431776
$544$	−4.15125	−0.177983
$545$	−75.9346	−3.25268
$546$	−2.48485	−0.106342
$547$	26.2096	1.12064	0.560321	−	0.828275i	$-0.310678\pi$
$547$	26.2096	1.12064	0.560321	+	0.828275i	$0.310678\pi$
$548$	9.92674	0.424049
$549$	5.11955	0.218497
$550$	43.3966	1.85044
$551$	−5.93376	−0.252787
$552$	1.16579	0.0496193
$553$	−10.8513	−0.461443
$554$	3.38074	0.143634
$555$	−3.93253	−0.166927
$556$	3.44571	0.146131
$557$	−8.02154	−0.339884	−0.169942	−	0.985454i	$-0.554358\pi$
$557$	−8.02154	−0.339884	−0.169942	+	0.985454i	$0.554358\pi$
$558$	−6.19959	−0.262450
$559$	1.09636	0.0463709
$560$	10.4146	0.440097
$561$	−14.3358	−0.605258
$562$	5.93074	0.250173
$563$	13.6134	0.573736	0.286868	−	0.957970i	$-0.407386\pi$
$563$	13.6134	0.573736	0.286868	+	0.957970i	$0.407386\pi$
$564$	1.91281	0.0805439
$565$	−69.6826	−2.93157
$566$	−23.4537	−0.985831
$567$	−2.48485	−0.104354
$568$	−0.896009	−0.0375957
$569$	41.8088	1.75272	0.876358	−	0.481659i	$-0.159966\pi$
$569$	41.8088	1.75272	0.876358	+	0.481659i	$0.159966\pi$
$570$	−6.25345	−0.261928
$571$	3.05692	0.127928	0.0639640	−	0.997952i	$-0.479626\pi$
$571$	3.05692	0.127928	0.0639640	+	0.997952i	$0.479626\pi$
$572$	3.45337	0.144393
$573$	−17.7258	−0.740504
$574$	−20.4824	−0.854917
$575$	−14.6498	−0.610940
$576$	1.00000	0.0416667
$577$	5.43693	0.226342	0.113171	−	0.993576i	$-0.463899\pi$
$577$	5.43693	0.226342	0.113171	+	0.993576i	$0.463899\pi$
$578$	−0.232872	−0.00968622
$579$	−8.92394	−0.370866
$580$	−16.6684	−0.692118
$581$	3.20394	0.132922
$582$	1.09589	0.0454262
$583$	13.2117	0.547172
$584$	0.857920	0.0355010
$585$	4.19123	0.173286
$586$	29.0023	1.19807
$587$	20.2161	0.834406	0.417203	−	0.908813i	$-0.363010\pi$
$587$	20.2161	0.834406	0.417203	+	0.908813i	$0.363010\pi$
$588$	−0.825500	−0.0340431
$589$	−9.24998	−0.381139
$590$	33.9887	1.39929
$591$	−5.72916	−0.235666
$592$	0.938276	0.0385629
$593$	36.5479	1.50084	0.750422	−	0.660959i	$-0.229850\pi$
$593$	36.5479	1.50084	0.750422	+	0.660959i	$0.229850\pi$
$594$	3.45337	0.141693
$595$	43.2336	1.77241
$596$	−4.22838	−0.173201
$597$	4.04033	0.165360
$598$	−1.16579	−0.0476727
$599$	5.09064	0.207998	0.103999	−	0.994577i	$-0.466836\pi$
$599$	5.09064	0.207998	0.103999	+	0.994577i	$0.466836\pi$
$600$	−12.5664	−0.513023
$601$	4.56186	0.186082	0.0930410	−	0.995662i	$-0.470341\pi$
$601$	4.56186	0.186082	0.0930410	+	0.995662i	$0.470341\pi$
$602$	−2.72429	−0.111034
$603$	13.0998	0.533465
$604$	−14.8402	−0.603840
$605$	−3.88010	−0.157748
$606$	12.2271	0.496691
$607$	−20.6660	−0.838806	−0.419403	−	0.907800i	$-0.637761\pi$
$607$	−20.6660	−0.838806	−0.419403	+	0.907800i	$0.637761\pi$
$608$	1.49203	0.0605098
$609$	−9.88220	−0.400447
$610$	21.4572	0.868777
$611$	−1.91281	−0.0773841
$612$	4.15125	0.167804
$613$	27.3650	1.10526	0.552630	−	0.833426i	$-0.313624\pi$
$613$	27.3650	1.10526	0.552630	+	0.833426i	$0.313624\pi$
$614$	−25.5987	−1.03308
$615$	34.5479	1.39310
$616$	−8.58112	−0.345743
$617$	−42.5586	−1.71334	−0.856672	−	0.515861i	$-0.827472\pi$
$617$	−42.5586	−1.71334	−0.856672	+	0.515861i	$0.827472\pi$
$618$	−1.00000	−0.0402259
$619$	−15.1000	−0.606920	−0.303460	−	0.952844i	$-0.598142\pi$
$619$	−15.1000	−0.606920	−0.303460	+	0.952844i	$0.598142\pi$
$620$	−25.9839	−1.04354
$621$	−1.16579	−0.0467815
$622$	14.8637	0.595979
$623$	−3.31420	−0.132781
$624$	−1.00000	−0.0400320
$625$	70.0832	2.80333
$626$	−11.2838	−0.450992
$627$	5.15253	0.205772
$628$	11.3687	0.453661
$629$	3.89502	0.155305
$630$	−10.4146	−0.414928
$631$	−11.6996	−0.465755	−0.232878	−	0.972506i	$-0.574814\pi$
$631$	−11.6996	−0.465755	−0.232878	+	0.972506i	$0.574814\pi$
$632$	−4.36696	−0.173708
$633$	−18.1802	−0.722599
$634$	−3.43988	−0.136615
$635$	27.0462	1.07330
$636$	−3.82574	−0.151700
$637$	0.825500	0.0327075
$638$	13.7340	0.543733
$639$	0.896009	0.0354456
$640$	4.19123	0.165673
$641$	6.02988	0.238166	0.119083	−	0.992884i	$-0.462005\pi$
$641$	6.02988	0.238166	0.119083	+	0.992884i	$0.462005\pi$
$642$	17.9304	0.707657
$643$	40.2778	1.58840	0.794201	−	0.607655i	$-0.207890\pi$
$643$	40.2778	1.58840	0.794201	+	0.607655i	$0.207890\pi$
$644$	2.89682	0.114151
$645$	4.59509	0.180931
$646$	6.19379	0.243691
$647$	34.4114	1.35285	0.676426	−	0.736511i	$-0.263528\pi$
$647$	34.4114	1.35285	0.676426	+	0.736511i	$0.263528\pi$
$648$	−1.00000	−0.0392837
$649$	−28.0050	−1.09929
$650$	12.5664	0.492896
$651$	−15.4051	−0.603773
$652$	17.4080	0.681750
$653$	−18.8545	−0.737835	−0.368917	−	0.929462i	$-0.620272\pi$
$653$	−18.8545	−0.737835	−0.368917	+	0.929462i	$0.620272\pi$
$654$	−18.1175	−0.708450
$655$	22.9804	0.897918
$656$	−8.24288	−0.321831
$657$	−0.857920	−0.0334706
$658$	4.75306	0.185294
$659$	−33.2202	−1.29408	−0.647038	−	0.762458i	$-0.723992\pi$
$659$	−33.2202	−1.29408	−0.647038	+	0.762458i	$0.723992\pi$
$660$	14.4739	0.563395
$661$	16.0955	0.626041	0.313021	−	0.949746i	$-0.398659\pi$
$661$	16.0955	0.626041	0.313021	+	0.949746i	$0.398659\pi$
$662$	6.84967	0.266220
$663$	−4.15125	−0.161221
$664$	1.28939	0.0500380
$665$	−15.5389	−0.602573
$666$	−0.938276	−0.0363575
$667$	−4.63631	−0.179519
$668$	−19.8534	−0.768151
$669$	−15.7232	−0.607894
$670$	54.9043	2.12114
$671$	−17.6797	−0.682517
$672$	2.48485	0.0958553
$673$	16.4323	0.633419	0.316709	−	0.948523i	$-0.397422\pi$
$673$	16.4323	0.633419	0.316709	+	0.948523i	$0.397422\pi$
$674$	−8.11014	−0.312391
$675$	12.5664	0.483683
$676$	1.00000	0.0384615
$677$	−14.8423	−0.570436	−0.285218	−	0.958463i	$-0.592066\pi$
$677$	−14.8423	−0.570436	−0.285218	+	0.958463i	$0.592066\pi$
$678$	−16.6258	−0.638509
$679$	2.72313	0.104504
$680$	17.3989	0.667216
$681$	5.43218	0.208162
$682$	21.4095	0.819812
$683$	30.6457	1.17262	0.586312	−	0.810086i	$-0.300579\pi$
$683$	30.6457	1.17262	0.586312	+	0.810086i	$0.300579\pi$
$684$	−1.49203	−0.0570492
$685$	−41.6053	−1.58966
$686$	−19.4452	−0.742422
$687$	14.2912	0.545242
$688$	−1.09636	−0.0417982
$689$	3.82574	0.145749
$690$	−4.88610	−0.186010
$691$	9.94855	0.378461	0.189230	−	0.981933i	$-0.439401\pi$
$691$	9.94855	0.378461	0.189230	+	0.981933i	$0.439401\pi$
$692$	8.38483	0.318744
$693$	8.58112	0.325970
$694$	15.6913	0.595632
$695$	−14.4418	−0.547808
$696$	−3.97697	−0.150747
$697$	−34.2183	−1.29611
$698$	16.5396	0.626035
$699$	−15.7787	−0.596805
$700$	−31.2258	−1.18022
$701$	0.606614	0.0229115	0.0114557	−	0.999934i	$-0.496353\pi$
$701$	0.606614	0.0229115	0.0114557	+	0.999934i	$0.496353\pi$
$702$	1.00000	0.0377426
$703$	−1.39994	−0.0527996
$704$	−3.45337	−0.130154
$705$	−8.01704	−0.301939
$706$	28.2812	1.06438
$707$	30.3825	1.14265
$708$	8.10947	0.304773
$709$	−12.3399	−0.463436	−0.231718	−	0.972783i	$-0.574435\pi$
$709$	−12.3399	−0.463436	−0.231718	+	0.972783i	$0.574435\pi$
$710$	3.75538	0.140937
$711$	4.36696	0.163774
$712$	−1.33376	−0.0499848
$713$	−7.22742	−0.270669
$714$	10.3152	0.386038
$715$	−14.4739	−0.541292
$716$	24.2415	0.905946
$717$	−24.0758	−0.899127
$718$	21.2405	0.792690
$719$	−25.0439	−0.933980	−0.466990	−	0.884263i	$-0.654662\pi$
$719$	−25.0439	−0.933980	−0.466990	+	0.884263i	$0.654662\pi$
$720$	−4.19123	−0.156198
$721$	−2.48485	−0.0925408
$722$	16.7738	0.624258
$723$	−24.3323	−0.904926
$724$	1.00614	0.0373929
$725$	49.9764	1.85608
$726$	−0.925764	−0.0343583
$727$	−36.0438	−1.33679	−0.668396	−	0.743806i	$-0.733019\pi$
$727$	−36.0438	−1.33679	−0.668396	+	0.743806i	$0.733019\pi$
$728$	−2.48485	−0.0920948
$729$	1.00000	0.0370370
$730$	−3.59574	−0.133084
$731$	−4.55125	−0.168334
$732$	5.11955	0.189224
$733$	34.1416	1.26105	0.630525	−	0.776169i	$-0.282840\pi$
$733$	34.1416	1.26105	0.630525	+	0.776169i	$0.282840\pi$
$734$	4.96807	0.183375
$735$	3.45987	0.127619
$736$	1.16579	0.0429716
$737$	−45.2385	−1.66638
$738$	8.24288	0.303425
$739$	−34.8852	−1.28327	−0.641636	−	0.767010i	$-0.721744\pi$
$739$	−34.8852	−1.28327	−0.641636	+	0.767010i	$0.721744\pi$
$740$	−3.93253	−0.144563
$741$	1.49203	0.0548111
$742$	−9.50640	−0.348991
$743$	−28.9668	−1.06269	−0.531345	−	0.847156i	$-0.678313\pi$
$743$	−28.9668	−1.06269	−0.531345	+	0.847156i	$0.678313\pi$
$744$	−6.19959	−0.227288
$745$	17.7221	0.649289
$746$	1.35351	0.0495556
$747$	−1.28939	−0.0471763
$748$	−14.3358	−0.524169
$749$	44.5545	1.62799
$750$	31.7127	1.15798
$751$	−19.0257	−0.694258	−0.347129	−	0.937817i	$-0.612843\pi$
$751$	−19.0257	−0.694258	−0.347129	+	0.937817i	$0.612843\pi$
$752$	1.91281	0.0697531
$753$	8.22652	0.299791
$754$	3.97697	0.144833
$755$	62.1988	2.26365
$756$	−2.48485	−0.0903733
$757$	53.9813	1.96198	0.980991	−	0.194052i	$-0.0621631\pi$
$757$	53.9813	1.96198	0.980991	+	0.194052i	$0.0621631\pi$
$758$	−1.33194	−0.0483783
$759$	4.02590	0.146131
$760$	−6.25345	−0.226836
$761$	−2.12579	−0.0770600	−0.0385300	−	0.999257i	$-0.512268\pi$
$761$	−2.12579	−0.0770600	−0.0385300	+	0.999257i	$0.512268\pi$
$762$	6.45305	0.233769
$763$	−45.0193	−1.62981
$764$	−17.7258	−0.641295
$765$	−17.3989	−0.629057
$766$	5.46332	0.197398
$767$	−8.10947	−0.292816
$768$	1.00000	0.0360844
$769$	−25.5752	−0.922264	−0.461132	−	0.887332i	$-0.652557\pi$
$769$	−25.5752	−0.922264	−0.461132	+	0.887332i	$0.652557\pi$
$770$	35.9655	1.29611
$771$	19.2253	0.692381
$772$	−8.92394	−0.321180
$773$	10.8883	0.391626	0.195813	−	0.980641i	$-0.437265\pi$
$773$	10.8883	0.391626	0.195813	+	0.980641i	$0.437265\pi$
$774$	1.09636	0.0394077
$775$	77.9068	2.79850
$776$	1.09589	0.0393403
$777$	−2.33148	−0.0836414
$778$	−5.47837	−0.196409
$779$	12.2986	0.440644
$780$	4.19123	0.150070
$781$	−3.09425	−0.110721
$782$	4.83948	0.173060
$783$	3.97697	0.142125
$784$	−0.825500	−0.0294822
$785$	−47.6489	−1.70066
$786$	5.48297	0.195571
$787$	8.06590	0.287518	0.143759	−	0.989613i	$-0.454081\pi$
$787$	8.06590	0.287518	0.143759	+	0.989613i	$0.454081\pi$
$788$	−5.72916	−0.204093
$789$	−26.5673	−0.945820
$790$	18.3030	0.651190
$791$	−41.3126	−1.46891
$792$	3.45337	0.122710
$793$	−5.11955	−0.181800
$794$	32.9394	1.16897
$795$	16.0346	0.568687
$796$	4.04033	0.143206
$797$	−9.83867	−0.348503	−0.174252	−	0.984701i	$-0.555751\pi$
$797$	−9.83867	−0.348503	−0.174252	+	0.984701i	$0.555751\pi$
$798$	−3.70748	−0.131243
$799$	7.94056	0.280917
$800$	−12.5664	−0.444291
$801$	1.33376	0.0471261
$802$	−7.80301	−0.275534
$803$	2.96271	0.104552
$804$	13.0998	0.461994
$805$	−12.1412	−0.427922
$806$	6.19959	0.218371
$807$	3.93881	0.138653
$808$	12.2271	0.430147
$809$	−23.3970	−0.822595	−0.411298	−	0.911501i	$-0.634924\pi$
$809$	−23.3970	−0.822595	−0.411298	+	0.911501i	$0.634924\pi$
$810$	4.19123	0.147265
$811$	24.8923	0.874087	0.437044	−	0.899440i	$-0.356026\pi$
$811$	24.8923	0.874087	0.437044	+	0.899440i	$0.356026\pi$
$812$	−9.88220	−0.346797
$813$	−6.13049	−0.215006
$814$	3.24021	0.113569
$815$	−72.9610	−2.55571
$816$	4.15125	0.145323
$817$	1.63580	0.0572293
$818$	−25.9347	−0.906786
$819$	2.48485	0.0868278
$820$	34.5479	1.20646
$821$	7.39290	0.258014	0.129007	−	0.991644i	$-0.458821\pi$
$821$	7.39290	0.258014	0.129007	+	0.991644i	$0.458821\pi$
$822$	−9.92674	−0.346235
$823$	−37.2278	−1.29768	−0.648839	−	0.760925i	$-0.724745\pi$
$823$	−37.2278	−1.29768	−0.648839	+	0.760925i	$0.724745\pi$
$824$	−1.00000	−0.0348367
$825$	−43.3966	−1.51087
$826$	20.1509	0.701138
$827$	37.7529	1.31280	0.656399	−	0.754414i	$-0.272079\pi$
$827$	37.7529	1.31280	0.656399	+	0.754414i	$0.272079\pi$
$828$	−1.16579	−0.0405140
$829$	−17.6399	−0.612660	−0.306330	−	0.951925i	$-0.599101\pi$
$829$	−17.6399	−0.612660	−0.306330	+	0.951925i	$0.599101\pi$
$830$	−5.40413	−0.187580
$831$	−3.38074	−0.117277
$832$	−1.00000	−0.0346688
$833$	−3.42686	−0.118734
$834$	−3.44571	−0.119315
$835$	83.2103	2.87961
$836$	5.15253	0.178204
$837$	6.19959	0.214289
$838$	11.8178	0.408241
$839$	−36.9424	−1.27539	−0.637696	−	0.770288i	$-0.720112\pi$
$839$	−36.9424	−1.27539	−0.637696	+	0.770288i	$0.720112\pi$
$840$	−10.4146	−0.359338
$841$	−13.1837	−0.454610
$842$	28.3038	0.975412
$843$	−5.93074	−0.204265
$844$	−18.1802	−0.625789
$845$	−4.19123	−0.144183
$846$	−1.91281	−0.0657638
$847$	−2.30039	−0.0790423
$848$	−3.82574	−0.131376
$849$	23.4537	0.804928
$850$	−52.1664	−1.78929
$851$	−1.09383	−0.0374961
$852$	0.896009	0.0306967
$853$	−37.4443	−1.28207	−0.641034	−	0.767512i	$-0.721494\pi$
$853$	−37.4443	−1.28207	−0.641034	+	0.767512i	$0.721494\pi$
$854$	12.7213	0.435315
$855$	6.25345	0.213863
$856$	17.9304	0.612849
$857$	−9.08161	−0.310222	−0.155111	−	0.987897i	$-0.549574\pi$
$857$	−9.08161	−0.310222	−0.155111	+	0.987897i	$0.549574\pi$
$858$	−3.45337	−0.117896
$859$	−17.8016	−0.607384	−0.303692	−	0.952770i	$-0.598219\pi$
$859$	−17.8016	−0.607384	−0.303692	+	0.952770i	$0.598219\pi$
$860$	4.59509	0.156691
$861$	20.4824	0.698037
$862$	11.3047	0.385040
$863$	57.5943	1.96053	0.980266	−	0.197681i	$-0.0633410\pi$
$863$	57.5943	1.96053	0.980266	+	0.197681i	$0.0633410\pi$
$864$	−1.00000	−0.0340207
$865$	−35.1428	−1.19489
$866$	13.6585	0.464134
$867$	0.232872	0.00790876
$868$	−15.4051	−0.522883
$869$	−15.0807	−0.511579
$870$	16.6684	0.565112
$871$	−13.0998	−0.443870
$872$	−18.1175	−0.613535
$873$	−1.09589	−0.0370904
$874$	−1.73939	−0.0588358
$875$	78.8015	2.66398
$876$	−0.857920	−0.0289864
$877$	−29.6978	−1.00282	−0.501412	−	0.865208i	$-0.667186\pi$
$877$	−29.6978	−1.00282	−0.501412	+	0.865208i	$0.667186\pi$
$878$	10.1305	0.341888
$879$	−29.0023	−0.978224
$880$	14.4739	0.487914
$881$	48.3041	1.62741	0.813703	−	0.581281i	$-0.197448\pi$
$881$	48.3041	1.62741	0.813703	+	0.581281i	$0.197448\pi$
$882$	0.825500	0.0277960
$883$	−22.8351	−0.768463	−0.384231	−	0.923237i	$-0.625534\pi$
$883$	−22.8351	−0.768463	−0.384231	+	0.923237i	$0.625534\pi$
$884$	−4.15125	−0.139622
$885$	−33.9887	−1.14252
$886$	24.1352	0.810837
$887$	−32.2578	−1.08311	−0.541556	−	0.840664i	$-0.682165\pi$
$887$	−32.2578	−1.08311	−0.541556	+	0.840664i	$0.682165\pi$
$888$	−0.938276	−0.0314865
$889$	16.0349	0.537793
$890$	5.59010	0.187381
$891$	−3.45337	−0.115692
$892$	−15.7232	−0.526452
$893$	−2.85397	−0.0955046
$894$	4.22838	0.141418
$895$	−101.602	−3.39617
$896$	2.48485	0.0830131
$897$	1.16579	0.0389246
$898$	−34.6217	−1.15534
$899$	24.6556	0.822311
$900$	12.5664	0.418881
$901$	−15.8816	−0.529092
$902$	−28.4657	−0.947805
$903$	2.72429	0.0906586
$904$	−16.6258	−0.552965
$905$	−4.21697	−0.140177
$906$	14.8402	0.493033
$907$	−1.51747	−0.0503868	−0.0251934	−	0.999683i	$-0.508020\pi$
$907$	−1.51747	−0.0503868	−0.0251934	+	0.999683i	$0.508020\pi$
$908$	5.43218	0.180273
$909$	−12.2271	−0.405547
$910$	10.4146	0.345241
$911$	37.8108	1.25273	0.626364	−	0.779531i	$-0.284543\pi$
$911$	37.8108	1.25273	0.626364	+	0.779531i	$0.284543\pi$
$912$	−1.49203	−0.0494061
$913$	4.45274	0.147364
$914$	31.4318	1.03967
$915$	−21.4572	−0.709354
$916$	14.2912	0.472193
$917$	13.6244	0.449916
$918$	−4.15125	−0.137012
$919$	58.1081	1.91681	0.958405	−	0.285412i	$-0.0921304\pi$
$919$	58.1081	1.91681	0.958405	+	0.285412i	$0.0921304\pi$
$920$	−4.88610	−0.161090
$921$	25.5987	0.843507
$922$	−17.5107	−0.576684
$923$	−0.896009	−0.0294925
$924$	8.58112	0.282298
$925$	11.7908	0.387679
$926$	−10.4776	−0.344314
$927$	1.00000	0.0328443
$928$	−3.97697	−0.130551
$929$	8.37459	0.274761	0.137381	−	0.990518i	$-0.456132\pi$
$929$	8.37459	0.274761	0.137381	+	0.990518i	$0.456132\pi$
$930$	25.9839	0.852047
$931$	1.23167	0.0403664
$932$	−15.7787	−0.516848
$933$	−14.8637	−0.486615
$934$	−0.734108	−0.0240207
$935$	60.0847	1.96498
$936$	1.00000	0.0326860
$937$	12.3552	0.403625	0.201813	−	0.979424i	$-0.435317\pi$
$937$	12.3552	0.403625	0.201813	+	0.979424i	$0.435317\pi$
$938$	32.5511	1.06283
$939$	11.2838	0.368233
$940$	−8.01704	−0.261487
$941$	20.5177	0.668859	0.334429	−	0.942421i	$-0.391456\pi$
$941$	20.5177	0.668859	0.334429	+	0.942421i	$0.391456\pi$
$942$	−11.3687	−0.370413
$943$	9.60946	0.312927
$944$	8.10947	0.263941
$945$	10.4146	0.338787
$946$	−3.78613	−0.123098
$947$	−7.31607	−0.237740	−0.118870	−	0.992910i	$-0.537927\pi$
$947$	−7.31607	−0.237740	−0.118870	+	0.992910i	$0.537927\pi$
$948$	4.36696	0.141832
$949$	0.857920	0.0278492
$950$	18.7495	0.608314
$951$	3.43988	0.111546
$952$	10.3152	0.334319
$953$	25.3981	0.822726	0.411363	−	0.911471i	$-0.365053\pi$
$953$	25.3981	0.822726	0.411363	+	0.911471i	$0.365053\pi$
$954$	3.82574	0.123863
$955$	74.2928	2.40406
$956$	−24.0758	−0.778667
$957$	−13.7340	−0.443956
$958$	−40.2600	−1.30074
$959$	−24.6665	−0.796523
$960$	−4.19123	−0.135271
$961$	7.43497	0.239838
$962$	0.938276	0.0302512
$963$	−17.9304	−0.577800
$964$	−24.3323	−0.783689
$965$	37.4023	1.20402
$966$	−2.89682	−0.0932035
$967$	−46.8399	−1.50627	−0.753134	−	0.657867i	$-0.771459\pi$
$967$	−46.8399	−1.50627	−0.753134	+	0.657867i	$0.771459\pi$
$968$	−0.925764	−0.0297552
$969$	−6.19379	−0.198973
$970$	−4.59314	−0.147477
$971$	−40.4508	−1.29813	−0.649063	−	0.760734i	$-0.724839\pi$
$971$	−40.4508	−1.29813	−0.649063	+	0.760734i	$0.724839\pi$
$972$	1.00000	0.0320750
$973$	−8.56209	−0.274488
$974$	−10.8019	−0.346116
$975$	−12.5664	−0.402448
$976$	5.11955	0.163873
$977$	7.12306	0.227887	0.113943	−	0.993487i	$-0.463652\pi$
$977$	7.12306	0.227887	0.113943	+	0.993487i	$0.463652\pi$
$978$	−17.4080	−0.556647
$979$	−4.60597	−0.147207
$980$	3.45987	0.110521
$981$	18.1175	0.578447
$982$	−21.2973	−0.679624
$983$	−35.6158	−1.13597	−0.567984	−	0.823040i	$-0.692276\pi$
$983$	−35.6158	−1.13597	−0.567984	+	0.823040i	$0.692276\pi$
$984$	8.24288	0.262774
$985$	24.0123	0.765094
$986$	−16.5094	−0.525767
$987$	−4.75306	−0.151292
$988$	1.49203	0.0474678
$989$	1.27812	0.0406419
$990$	−14.4739	−0.460010
$991$	5.41675	0.172069	0.0860344	−	0.996292i	$-0.472581\pi$
$991$	5.41675	0.172069	0.0860344	+	0.996292i	$0.472581\pi$
$992$	−6.19959	−0.196837
$993$	−6.84967	−0.217368
$994$	2.22645	0.0706187
$995$	−16.9340	−0.536843
$996$	−1.28939	−0.0408558
$997$	−49.4466	−1.56599	−0.782995	−	0.622028i	$-0.786309\pi$
$997$	−49.4466	−1.56599	−0.782995	+	0.622028i	$0.786309\pi$
$998$	26.0360	0.824155
$999$	0.938276	0.0296857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.1	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.1	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.19123 q^{5} -1.00000 q^{6} -2.48485 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.19123 q^{5} -1.00000 q^{6} -2.48485 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.19123 q^{10} -3.45337 q^{11} +1.00000 q^{12} -1.00000 q^{13} +2.48485 q^{14} -4.19123 q^{15} +1.00000 q^{16} +4.15125 q^{17} -1.00000 q^{18} -1.49203 q^{19} -4.19123 q^{20} -2.48485 q^{21} +3.45337 q^{22} -1.16579 q^{23} -1.00000 q^{24} +12.5664 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.48485 q^{28} +3.97697 q^{29} +4.19123 q^{30} +6.19959 q^{31} -1.00000 q^{32} -3.45337 q^{33} -4.15125 q^{34} +10.4146 q^{35} +1.00000 q^{36} +0.938276 q^{37} +1.49203 q^{38} -1.00000 q^{39} +4.19123 q^{40} -8.24288 q^{41} +2.48485 q^{42} -1.09636 q^{43} -3.45337 q^{44} -4.19123 q^{45} +1.16579 q^{46} +1.91281 q^{47} +1.00000 q^{48} -0.825500 q^{49} -12.5664 q^{50} +4.15125 q^{51} -1.00000 q^{52} -3.82574 q^{53} -1.00000 q^{54} +14.4739 q^{55} +2.48485 q^{56} -1.49203 q^{57} -3.97697 q^{58} +8.10947 q^{59} -4.19123 q^{60} +5.11955 q^{61} -6.19959 q^{62} -2.48485 q^{63} +1.00000 q^{64} +4.19123 q^{65} +3.45337 q^{66} +13.0998 q^{67} +4.15125 q^{68} -1.16579 q^{69} -10.4146 q^{70} +0.896009 q^{71} -1.00000 q^{72} -0.857920 q^{73} -0.938276 q^{74} +12.5664 q^{75} -1.49203 q^{76} +8.58112 q^{77} +1.00000 q^{78} +4.36696 q^{79} -4.19123 q^{80} +1.00000 q^{81} +8.24288 q^{82} -1.28939 q^{83} -2.48485 q^{84} -17.3989 q^{85} +1.09636 q^{86} +3.97697 q^{87} +3.45337 q^{88} +1.33376 q^{89} +4.19123 q^{90} +2.48485 q^{91} -1.16579 q^{92} +6.19959 q^{93} -1.91281 q^{94} +6.25345 q^{95} -1.00000 q^{96} -1.09589 q^{97} +0.825500 q^{98} -3.45337 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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