LMFDB - Embedded newform 8005.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30625 q^{2} +1.53084 q^{3} +3.31877 q^{4} +1.00000 q^{5} -3.53050 q^{6} -2.53384 q^{7} -3.04142 q^{8} -0.656523 q^{9} +O(q^{10})$	\(q-2.30625 q^{2} +1.53084 q^{3} +3.31877 q^{4} +1.00000 q^{5} -3.53050 q^{6} -2.53384 q^{7} -3.04142 q^{8} -0.656523 q^{9} -2.30625 q^{10} +3.26090 q^{11} +5.08052 q^{12} -5.86353 q^{13} +5.84365 q^{14} +1.53084 q^{15} +0.376717 q^{16} +3.56890 q^{17} +1.51410 q^{18} +3.68285 q^{19} +3.31877 q^{20} -3.87890 q^{21} -7.52044 q^{22} +7.17615 q^{23} -4.65593 q^{24} +1.00000 q^{25} +13.5228 q^{26} -5.59756 q^{27} -8.40923 q^{28} +0.473452 q^{29} -3.53050 q^{30} +0.165097 q^{31} +5.21404 q^{32} +4.99192 q^{33} -8.23077 q^{34} -2.53384 q^{35} -2.17885 q^{36} -0.0844805 q^{37} -8.49355 q^{38} -8.97614 q^{39} -3.04142 q^{40} -2.07321 q^{41} +8.94571 q^{42} -12.4427 q^{43} +10.8222 q^{44} -0.656523 q^{45} -16.5500 q^{46} -8.06024 q^{47} +0.576694 q^{48} -0.579673 q^{49} -2.30625 q^{50} +5.46343 q^{51} -19.4597 q^{52} +6.78139 q^{53} +12.9094 q^{54} +3.26090 q^{55} +7.70646 q^{56} +5.63785 q^{57} -1.09190 q^{58} -3.22775 q^{59} +5.08052 q^{60} -11.4336 q^{61} -0.380755 q^{62} +1.66352 q^{63} -12.7783 q^{64} -5.86353 q^{65} -11.5126 q^{66} +3.11827 q^{67} +11.8444 q^{68} +10.9856 q^{69} +5.84365 q^{70} +8.03001 q^{71} +1.99676 q^{72} -10.6967 q^{73} +0.194833 q^{74} +1.53084 q^{75} +12.2225 q^{76} -8.26258 q^{77} +20.7012 q^{78} +2.74763 q^{79} +0.376717 q^{80} -6.59941 q^{81} +4.78134 q^{82} +4.48249 q^{83} -12.8732 q^{84} +3.56890 q^{85} +28.6960 q^{86} +0.724780 q^{87} -9.91776 q^{88} -9.29048 q^{89} +1.51410 q^{90} +14.8572 q^{91} +23.8160 q^{92} +0.252738 q^{93} +18.5889 q^{94} +3.68285 q^{95} +7.98187 q^{96} -15.3425 q^{97} +1.33687 q^{98} -2.14086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) $ 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * 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 $

$2$	−2.30625	−1.63076	−0.815381	−	0.578924i	$-0.803473\pi$
$2$	−2.30625	−1.63076	−0.815381	+	0.578924i	$0.803473\pi$
$3$	1.53084	0.883832	0.441916	−	0.897056i	$-0.354299\pi$
$3$	1.53084	0.883832	0.441916	+	0.897056i	$0.354299\pi$
$4$	3.31877	1.65939
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.53050	−1.44132
$7$	−2.53384	−0.957700	−0.478850	−	0.877897i	$-0.658946\pi$
$7$	−2.53384	−0.957700	−0.478850	+	0.877897i	$0.658946\pi$
$8$	−3.04142	−1.07530
$9$	−0.656523	−0.218841
$10$	−2.30625	−0.729299
$11$	3.26090	0.983198	0.491599	−	0.870822i	$-0.336413\pi$
$11$	3.26090	0.983198	0.491599	+	0.870822i	$0.336413\pi$
$12$	5.08052	1.46662
$13$	−5.86353	−1.62625	−0.813126	−	0.582088i	$-0.802236\pi$
$13$	−5.86353	−1.62625	−0.813126	+	0.582088i	$0.802236\pi$
$14$	5.84365	1.56178
$15$	1.53084	0.395262
$16$	0.376717	0.0941792
$17$	3.56890	0.865586	0.432793	−	0.901493i	$-0.357528\pi$
$17$	3.56890	0.865586	0.432793	+	0.901493i	$0.357528\pi$
$18$	1.51410	0.356878
$19$	3.68285	0.844903	0.422451	−	0.906386i	$-0.361170\pi$
$19$	3.68285	0.844903	0.422451	+	0.906386i	$0.361170\pi$
$20$	3.31877	0.742101
$21$	−3.87890	−0.846446
$22$	−7.52044	−1.60336
$23$	7.17615	1.49633	0.748166	−	0.663512i	$-0.230935\pi$
$23$	7.17615	1.49633	0.748166	+	0.663512i	$0.230935\pi$
$24$	−4.65593	−0.950388
$25$	1.00000	0.200000
$26$	13.5228	2.65203
$27$	−5.59756	−1.07725
$28$	−8.40923	−1.58920
$29$	0.473452	0.0879178	0.0439589	−	0.999033i	$-0.486003\pi$
$29$	0.473452	0.0879178	0.0439589	+	0.999033i	$0.486003\pi$
$30$	−3.53050	−0.644578
$31$	0.165097	0.0296524	0.0148262	−	0.999890i	$-0.495281\pi$
$31$	0.165097	0.0296524	0.0148262	+	0.999890i	$0.495281\pi$
$32$	5.21404	0.921721
$33$	4.99192	0.868982
$34$	−8.23077	−1.41157
$35$	−2.53384	−0.428297
$36$	−2.17885	−0.363142
$37$	−0.0844805	−0.0138885	−0.00694425	−	0.999976i	$-0.502210\pi$
$37$	−0.0844805	−0.0138885	−0.00694425	+	0.999976i	$0.502210\pi$
$38$	−8.49355	−1.37784
$39$	−8.97614	−1.43733
$40$	−3.04142	−0.480891
$41$	−2.07321	−0.323781	−0.161891	−	0.986809i	$-0.551759\pi$
$41$	−2.07321	−0.323781	−0.161891	+	0.986809i	$0.551759\pi$
$42$	8.94571	1.38035
$43$	−12.4427	−1.89749	−0.948747	−	0.316035i	$-0.897648\pi$
$43$	−12.4427	−1.89749	−0.948747	+	0.316035i	$0.897648\pi$
$44$	10.8222	1.63151
$45$	−0.656523	−0.0978687
$46$	−16.5500	−2.44016
$47$	−8.06024	−1.17571	−0.587853	−	0.808968i	$-0.700027\pi$
$47$	−8.06024	−1.17571	−0.587853	+	0.808968i	$0.700027\pi$
$48$	0.576694	0.0832386
$49$	−0.579673	−0.0828105
$50$	−2.30625	−0.326153
$51$	5.46343	0.765033
$52$	−19.4597	−2.69858
$53$	6.78139	0.931495	0.465748	−	0.884918i	$-0.345785\pi$
$53$	6.78139	0.931495	0.465748	+	0.884918i	$0.345785\pi$
$54$	12.9094	1.75674
$55$	3.26090	0.439700
$56$	7.70646	1.02982
$57$	5.63785	0.746752
$58$	−1.09190	−0.143373
$59$	−3.22775	−0.420217	−0.210109	−	0.977678i	$-0.567382\pi$
$59$	−3.22775	−0.420217	−0.210109	+	0.977678i	$0.567382\pi$
$60$	5.08052	0.655892
$61$	−11.4336	−1.46393	−0.731963	−	0.681345i	$-0.761396\pi$
$61$	−11.4336	−1.46393	−0.731963	+	0.681345i	$0.761396\pi$
$62$	−0.380755	−0.0483560
$63$	1.66352	0.209584
$64$	−12.7783	−1.59729
$65$	−5.86353	−0.727282
$66$	−11.5126	−1.41710
$67$	3.11827	0.380958	0.190479	−	0.981691i	$-0.438996\pi$
$67$	3.11827	0.380958	0.190479	+	0.981691i	$0.438996\pi$
$68$	11.8444	1.43634
$69$	10.9856	1.32251
$70$	5.84365	0.698450
$71$	8.03001	0.952987	0.476493	−	0.879178i	$-0.341908\pi$
$71$	8.03001	0.952987	0.476493	+	0.879178i	$0.341908\pi$
$72$	1.99676	0.235321
$73$	−10.6967	−1.25195	−0.625976	−	0.779842i	$-0.715299\pi$
$73$	−10.6967	−1.25195	−0.625976	+	0.779842i	$0.715299\pi$
$74$	0.194833	0.0226489
$75$	1.53084	0.176766
$76$	12.2225	1.40202
$77$	−8.26258	−0.941609
$78$	20.7012	2.34395
$79$	2.74763	0.309133	0.154566	−	0.987982i	$-0.450602\pi$
$79$	2.74763	0.309133	0.154566	+	0.987982i	$0.450602\pi$
$80$	0.376717	0.0421182
$81$	−6.59941	−0.733267
$82$	4.78134	0.528010
$83$	4.48249	0.492017	0.246008	−	0.969268i	$-0.420881\pi$
$83$	4.48249	0.492017	0.246008	+	0.969268i	$0.420881\pi$
$84$	−12.8732	−1.40458
$85$	3.56890	0.387102
$86$	28.6960	3.09436
$87$	0.724780	0.0777046
$88$	−9.91776	−1.05724
$89$	−9.29048	−0.984788	−0.492394	−	0.870372i	$-0.663878\pi$
$89$	−9.29048	−0.984788	−0.492394	+	0.870372i	$0.663878\pi$
$90$	1.51410	0.159601
$91$	14.8572	1.55746
$92$	23.8160	2.48299
$93$	0.252738	0.0262077
$94$	18.5889	1.91730
$95$	3.68285	0.377852
$96$	7.98187	0.814646
$97$	−15.3425	−1.55779	−0.778896	−	0.627153i	$-0.784220\pi$
$97$	−15.3425	−1.55779	−0.778896	+	0.627153i	$0.784220\pi$
$98$	1.33687	0.135044
$99$	−2.14086	−0.215164
$100$	3.31877	0.331877
$101$	16.6463	1.65637	0.828186	−	0.560454i	$-0.189373\pi$
$101$	16.6463	1.65637	0.828186	+	0.560454i	$0.189373\pi$
$102$	−12.6000	−1.24759
$103$	−15.1366	−1.49145	−0.745726	−	0.666253i	$-0.767897\pi$
$103$	−15.1366	−1.49145	−0.745726	+	0.666253i	$0.767897\pi$
$104$	17.8335	1.74872
$105$	−3.87890	−0.378542
$106$	−15.6396	−1.51905
$107$	13.5741	1.31226	0.656129	−	0.754648i	$-0.272193\pi$
$107$	13.5741	1.31226	0.656129	+	0.754648i	$0.272193\pi$
$108$	−18.5770	−1.78758
$109$	6.90380	0.661265	0.330632	−	0.943760i	$-0.392738\pi$
$109$	6.90380	0.661265	0.330632	+	0.943760i	$0.392738\pi$
$110$	−7.52044	−0.717046
$111$	−0.129326	−0.0122751
$112$	−0.954538	−0.0901954
$113$	−7.53645	−0.708969	−0.354485	−	0.935062i	$-0.615344\pi$
$113$	−7.53645	−0.708969	−0.354485	+	0.935062i	$0.615344\pi$
$114$	−13.0023	−1.21778
$115$	7.17615	0.669180
$116$	1.57128	0.145890
$117$	3.84955	0.355891
$118$	7.44399	0.685274
$119$	−9.04302	−0.828972
$120$	−4.65593	−0.425027
$121$	−0.366538	−0.0333217
$122$	26.3688	2.38732
$123$	−3.17376	−0.286168
$124$	0.547921	0.0492048
$125$	1.00000	0.0894427
$126$	−3.83649	−0.341782
$127$	4.48270	0.397775	0.198888	−	0.980022i	$-0.436267\pi$
$127$	4.48270	0.397775	0.198888	+	0.980022i	$0.436267\pi$
$128$	19.0418	1.68308
$129$	−19.0478	−1.67707
$130$	13.5228	1.18602
$131$	14.3669	1.25524	0.627620	−	0.778520i	$-0.284029\pi$
$131$	14.3669	1.25524	0.627620	+	0.778520i	$0.284029\pi$
$132$	16.5671	1.44198
$133$	−9.33173	−0.809163
$134$	−7.19151	−0.621252
$135$	−5.59756	−0.481761
$136$	−10.8545	−0.930769
$137$	−14.0919	−1.20396	−0.601978	−	0.798513i	$-0.705620\pi$
$137$	−14.0919	−1.20396	−0.601978	+	0.798513i	$0.705620\pi$
$138$	−25.3354	−2.15669
$139$	23.3208	1.97805	0.989024	−	0.147754i	$-0.0472043\pi$
$139$	23.3208	1.97805	0.989024	+	0.147754i	$0.0472043\pi$
$140$	−8.40923	−0.710710
$141$	−12.3389	−1.03913
$142$	−18.5192	−1.55410
$143$	−19.1204	−1.59893
$144$	−0.247323	−0.0206103
$145$	0.473452	0.0393180
$146$	24.6692	2.04164
$147$	−0.887388	−0.0731906
$148$	−0.280372	−0.0230464
$149$	7.02616	0.575605	0.287803	−	0.957690i	$-0.407075\pi$
$149$	7.02616	0.575605	0.287803	+	0.957690i	$0.407075\pi$
$150$	−3.53050	−0.288264
$151$	5.87274	0.477917	0.238958	−	0.971030i	$-0.423194\pi$
$151$	5.87274	0.477917	0.238958	+	0.971030i	$0.423194\pi$
$152$	−11.2011	−0.908528
$153$	−2.34307	−0.189426
$154$	19.0556	1.53554
$155$	0.165097	0.0132609
$156$	−29.7898	−2.38509
$157$	2.52481	0.201502	0.100751	−	0.994912i	$-0.467875\pi$
$157$	2.52481	0.201502	0.100751	+	0.994912i	$0.467875\pi$
$158$	−6.33672	−0.504123
$159$	10.3812	0.823285
$160$	5.21404	0.412206
$161$	−18.1832	−1.43304
$162$	15.2199	1.19579
$163$	−13.4433	−1.05296	−0.526480	−	0.850187i	$-0.676489\pi$
$163$	−13.4433	−1.05296	−0.526480	+	0.850187i	$0.676489\pi$
$164$	−6.88052	−0.537279
$165$	4.99192	0.388620
$166$	−10.3377	−0.802363
$167$	20.1747	1.56117	0.780584	−	0.625051i	$-0.214922\pi$
$167$	20.1747	1.56117	0.780584	+	0.625051i	$0.214922\pi$
$168$	11.7974	0.910187
$169$	21.3810	1.64469
$170$	−8.23077	−0.631271
$171$	−2.41787	−0.184899
$172$	−41.2945	−3.14868
$173$	−19.7494	−1.50152	−0.750761	−	0.660574i	$-0.770313\pi$
$173$	−19.7494	−1.50152	−0.750761	+	0.660574i	$0.770313\pi$
$174$	−1.67152	−0.126718
$175$	−2.53384	−0.191540
$176$	1.22844	0.0925968
$177$	−4.94117	−0.371401
$178$	21.4261	1.60596
$179$	−0.807940	−0.0603883	−0.0301941	−	0.999544i	$-0.509613\pi$
$179$	−0.807940	−0.0603883	−0.0301941	+	0.999544i	$0.509613\pi$
$180$	−2.17885	−0.162402
$181$	11.5018	0.854921	0.427461	−	0.904034i	$-0.359408\pi$
$181$	11.5018	0.854921	0.427461	+	0.904034i	$0.359408\pi$
$182$	−34.2645	−2.53985
$183$	−17.5031	−1.29386
$184$	−21.8257	−1.60901
$185$	−0.0844805	−0.00621113
$186$	−0.582876	−0.0427386
$187$	11.6378	0.851043
$188$	−26.7501	−1.95095
$189$	14.1833	1.03168
$190$	−8.49355	−0.616187
$191$	−17.1860	−1.24354	−0.621768	−	0.783201i	$-0.713585\pi$
$191$	−17.1860	−1.24354	−0.621768	+	0.783201i	$0.713585\pi$
$192$	−19.5615	−1.41173
$193$	−1.67594	−0.120637	−0.0603186	−	0.998179i	$-0.519212\pi$
$193$	−1.67594	−0.120637	−0.0603186	+	0.998179i	$0.519212\pi$
$194$	35.3835	2.54039
$195$	−8.97614	−0.642795
$196$	−1.92381	−0.137415
$197$	24.7261	1.76166	0.880832	−	0.473430i	$-0.156984\pi$
$197$	24.7261	1.76166	0.880832	+	0.473430i	$0.156984\pi$
$198$	4.93734	0.350882
$199$	−15.0653	−1.06795	−0.533974	−	0.845501i	$-0.679302\pi$
$199$	−15.0653	−1.06795	−0.533974	+	0.845501i	$0.679302\pi$
$200$	−3.04142	−0.215061
$201$	4.77358	0.336703
$202$	−38.3905	−2.70115
$203$	−1.19965	−0.0841989
$204$	18.1319	1.26949
$205$	−2.07321	−0.144799
$206$	34.9087	2.43220
$207$	−4.71131	−0.327459
$208$	−2.20889	−0.153159
$209$	12.0094	0.830707
$210$	8.94571	0.617312
$211$	3.38501	0.233034	0.116517	−	0.993189i	$-0.462827\pi$
$211$	3.38501	0.233034	0.116517	+	0.993189i	$0.462827\pi$
$212$	22.5059	1.54571
$213$	12.2927	0.842280
$214$	−31.3053	−2.13998
$215$	−12.4427	−0.848586
$216$	17.0245	1.15837
$217$	−0.418330	−0.0283981
$218$	−15.9219	−1.07837
$219$	−16.3749	−1.10652
$220$	10.8222	0.729632
$221$	−20.9264	−1.40766
$222$	0.298258	0.0200178
$223$	−20.4103	−1.36677	−0.683386	−	0.730057i	$-0.739493\pi$
$223$	−20.4103	−1.36677	−0.683386	+	0.730057i	$0.739493\pi$
$224$	−13.2115	−0.882732
$225$	−0.656523	−0.0437682
$226$	17.3809	1.15616
$227$	21.3368	1.41618	0.708088	−	0.706124i	$-0.249558\pi$
$227$	21.3368	1.41618	0.708088	+	0.706124i	$0.249558\pi$
$228$	18.7108	1.23915
$229$	10.0612	0.664862	0.332431	−	0.943128i	$-0.392131\pi$
$229$	10.0612	0.664862	0.332431	+	0.943128i	$0.392131\pi$
$230$	−16.5500	−1.09127
$231$	−12.6487	−0.832224
$232$	−1.43997	−0.0945384
$233$	−0.927968	−0.0607932	−0.0303966	−	0.999538i	$-0.509677\pi$
$233$	−0.927968	−0.0607932	−0.0303966	+	0.999538i	$0.509677\pi$
$234$	−8.87800	−0.580373
$235$	−8.06024	−0.525792
$236$	−10.7122	−0.697303
$237$	4.20619	0.273222
$238$	20.8554	1.35186
$239$	−27.9804	−1.80990	−0.904951	−	0.425515i	$-0.860093\pi$
$239$	−27.9804	−1.80990	−0.904951	+	0.425515i	$0.860093\pi$
$240$	0.576694	0.0372254
$241$	−9.57441	−0.616742	−0.308371	−	0.951266i	$-0.599784\pi$
$241$	−9.57441	−0.616742	−0.308371	+	0.951266i	$0.599784\pi$
$242$	0.845328	0.0543398
$243$	6.69003	0.429165
$244$	−37.9456	−2.42922
$245$	−0.579673	−0.0370340
$246$	7.31947	0.466673
$247$	−21.5945	−1.37402
$248$	−0.502131	−0.0318853
$249$	6.86198	0.434860
$250$	−2.30625	−0.145860
$251$	−1.17812	−0.0743622	−0.0371811	−	0.999309i	$-0.511838\pi$
$251$	−1.17812	−0.0743622	−0.0371811	+	0.999309i	$0.511838\pi$
$252$	5.52086	0.347781
$253$	23.4007	1.47119
$254$	−10.3382	−0.648677
$255$	5.46343	0.342133
$256$	−18.3586	−1.14741
$257$	1.22908	0.0766681	0.0383341	−	0.999265i	$-0.487795\pi$
$257$	1.22908	0.0766681	0.0383341	+	0.999265i	$0.487795\pi$
$258$	43.9290	2.73490
$259$	0.214060	0.0133010
$260$	−19.4597	−1.20684
$261$	−0.310832	−0.0192400
$262$	−33.1336	−2.04700
$263$	−16.2712	−1.00333	−0.501663	−	0.865063i	$-0.667278\pi$
$263$	−16.2712	−1.00333	−0.501663	+	0.865063i	$0.667278\pi$
$264$	−15.1825	−0.934420
$265$	6.78139	0.416577
$266$	21.5213	1.31955
$267$	−14.2222	−0.870388
$268$	10.3488	0.632156
$269$	−13.8728	−0.845840	−0.422920	−	0.906167i	$-0.638995\pi$
$269$	−13.8728	−0.845840	−0.422920	+	0.906167i	$0.638995\pi$
$270$	12.9094	0.785638
$271$	−23.3205	−1.41662	−0.708311	−	0.705900i	$-0.750543\pi$
$271$	−23.3205	−1.41662	−0.708311	+	0.705900i	$0.750543\pi$
$272$	1.34447	0.0815202
$273$	22.7441	1.37653
$274$	32.4995	1.96337
$275$	3.26090	0.196640
$276$	36.4586	2.19455
$277$	−24.9155	−1.49703	−0.748513	−	0.663120i	$-0.769232\pi$
$277$	−24.9155	−1.49703	−0.748513	+	0.663120i	$0.769232\pi$
$278$	−53.7836	−3.22573
$279$	−0.108390	−0.00648916
$280$	7.70646	0.460549
$281$	−27.0220	−1.61200	−0.805998	−	0.591919i	$-0.798371\pi$
$281$	−27.0220	−1.61200	−0.805998	+	0.591919i	$0.798371\pi$
$282$	28.4567	1.69457
$283$	−25.4018	−1.50998	−0.754992	−	0.655734i	$-0.772359\pi$
$283$	−25.4018	−1.50998	−0.754992	+	0.655734i	$0.772359\pi$
$284$	26.6498	1.58137
$285$	5.63785	0.333958
$286$	44.0963	2.60747
$287$	5.25318	0.310085
$288$	−3.42314	−0.201710
$289$	−4.26293	−0.250761
$290$	−1.09190	−0.0641184
$291$	−23.4869	−1.37683
$292$	−35.4999	−2.07747
$293$	5.91991	0.345845	0.172922	−	0.984935i	$-0.444679\pi$
$293$	5.91991	0.345845	0.172922	+	0.984935i	$0.444679\pi$
$294$	2.04654	0.119356
$295$	−3.22775	−0.187927
$296$	0.256941	0.0149344
$297$	−18.2531	−1.05915
$298$	−16.2041	−0.938676
$299$	−42.0776	−2.43341
$300$	5.08052	0.293324
$301$	31.5278	1.81723
$302$	−13.5440	−0.779369
$303$	25.4829	1.46395
$304$	1.38739	0.0795722
$305$	−11.4336	−0.654687
$306$	5.40369	0.308909
$307$	23.2103	1.32468	0.662339	−	0.749204i	$-0.269564\pi$
$307$	23.2103	1.32468	0.662339	+	0.749204i	$0.269564\pi$
$308$	−27.4217	−1.56249
$309$	−23.1717	−1.31819
$310$	−0.380755	−0.0216254
$311$	1.32715	0.0752558	0.0376279	−	0.999292i	$-0.488020\pi$
$311$	1.32715	0.0752558	0.0376279	+	0.999292i	$0.488020\pi$
$312$	27.3002	1.54557
$313$	−8.84644	−0.500030	−0.250015	−	0.968242i	$-0.580436\pi$
$313$	−8.84644	−0.500030	−0.250015	+	0.968242i	$0.580436\pi$
$314$	−5.82283	−0.328602
$315$	1.66352	0.0937289
$316$	9.11878	0.512971
$317$	−8.57616	−0.481685	−0.240843	−	0.970564i	$-0.577424\pi$
$317$	−8.57616	−0.481685	−0.240843	+	0.970564i	$0.577424\pi$
$318$	−23.9417	−1.34258
$319$	1.54388	0.0864406
$320$	−12.7783	−0.714328
$321$	20.7798	1.15982
$322$	41.9350	2.33694
$323$	13.1437	0.731336
$324$	−21.9019	−1.21677
$325$	−5.86353	−0.325250
$326$	31.0036	1.71713
$327$	10.5686	0.584447
$328$	6.30551	0.348163
$329$	20.4233	1.12597
$330$	−11.5126	−0.633748
$331$	−13.4549	−0.739546	−0.369773	−	0.929122i	$-0.620565\pi$
$331$	−13.4549	−0.739546	−0.369773	+	0.929122i	$0.620565\pi$
$332$	14.8764	0.816446
$333$	0.0554634	0.00303937
$334$	−46.5279	−2.54590
$335$	3.11827	0.170369
$336$	−1.46125	−0.0797176
$337$	−3.39059	−0.184697	−0.0923485	−	0.995727i	$-0.529437\pi$
$337$	−3.39059	−0.184697	−0.0923485	+	0.995727i	$0.529437\pi$
$338$	−49.3099	−2.68211
$339$	−11.5371	−0.626610
$340$	11.8444	0.642352
$341$	0.538366	0.0291541
$342$	5.57621	0.301527
$343$	19.2057	1.03701
$344$	37.8435	2.04038
$345$	10.9856	0.591443
$346$	45.5471	2.44863
$347$	−6.30128	−0.338270	−0.169135	−	0.985593i	$-0.554097\pi$
$347$	−6.30128	−0.338270	−0.169135	+	0.985593i	$0.554097\pi$
$348$	2.40538	0.128942
$349$	22.1141	1.18374	0.591871	−	0.806033i	$-0.298390\pi$
$349$	22.1141	1.18374	0.591871	+	0.806033i	$0.298390\pi$
$350$	5.84365	0.312356
$351$	32.8215	1.75188
$352$	17.0025	0.906234
$353$	−29.8105	−1.58665	−0.793325	−	0.608798i	$-0.791652\pi$
$353$	−29.8105	−1.58665	−0.793325	+	0.608798i	$0.791652\pi$
$354$	11.3956	0.605667
$355$	8.03001	0.426189
$356$	−30.8330	−1.63415
$357$	−13.8434	−0.732672
$358$	1.86331	0.0984789
$359$	5.58800	0.294923	0.147462	−	0.989068i	$-0.452890\pi$
$359$	5.58800	0.294923	0.147462	+	0.989068i	$0.452890\pi$
$360$	1.99676	0.105239
$361$	−5.43665	−0.286139
$362$	−26.5260	−1.39417
$363$	−0.561112	−0.0294508
$364$	49.3078	2.58443
$365$	−10.6967	−0.559890
$366$	40.3664	2.10999
$367$	16.0507	0.837838	0.418919	−	0.908024i	$-0.362409\pi$
$367$	16.0507	0.837838	0.418919	+	0.908024i	$0.362409\pi$
$368$	2.70338	0.140923
$369$	1.36111	0.0708566
$370$	0.194833	0.0101289
$371$	−17.1829	−0.892093
$372$	0.838780	0.0434887
$373$	−19.3800	−1.00346	−0.501729	−	0.865025i	$-0.667303\pi$
$373$	−19.3800	−1.00346	−0.501729	+	0.865025i	$0.667303\pi$
$374$	−26.8397	−1.38785
$375$	1.53084	0.0790523
$376$	24.5146	1.26424
$377$	−2.77610	−0.142976
$378$	−32.7102	−1.68243
$379$	3.80590	0.195496	0.0977480	−	0.995211i	$-0.468836\pi$
$379$	3.80590	0.195496	0.0977480	+	0.995211i	$0.468836\pi$
$380$	12.2225	0.627003
$381$	6.86230	0.351566
$382$	39.6352	2.02791
$383$	−32.2822	−1.64955	−0.824773	−	0.565464i	$-0.808697\pi$
$383$	−32.2822	−1.64955	−0.824773	+	0.565464i	$0.808697\pi$
$384$	29.1500	1.48756
$385$	−8.26258	−0.421100
$386$	3.86514	0.196731
$387$	8.16893	0.415250
$388$	−50.9182	−2.58498
$389$	−12.8963	−0.653866	−0.326933	−	0.945047i	$-0.606015\pi$
$389$	−12.8963	−0.653866	−0.326933	+	0.945047i	$0.606015\pi$
$390$	20.7012	1.04825
$391$	25.6110	1.29520
$392$	1.76303	0.0890465
$393$	21.9934	1.10942
$394$	−57.0245	−2.87285
$395$	2.74763	0.138248
$396$	−7.10502	−0.357041
$397$	−11.5455	−0.579451	−0.289725	−	0.957110i	$-0.593564\pi$
$397$	−11.5455	−0.579451	−0.289725	+	0.957110i	$0.593564\pi$
$398$	34.7442	1.74157
$399$	−14.2854	−0.715165
$400$	0.376717	0.0188358
$401$	19.0379	0.950706	0.475353	−	0.879795i	$-0.342320\pi$
$401$	19.0379	0.950706	0.475353	+	0.879795i	$0.342320\pi$
$402$	−11.0091	−0.549082
$403$	−0.968054	−0.0482222
$404$	55.2454	2.74856
$405$	−6.59941	−0.327927
$406$	2.76669	0.137308
$407$	−0.275482	−0.0136551
$408$	−16.6166	−0.822643
$409$	−24.0380	−1.18860	−0.594302	−	0.804242i	$-0.702572\pi$
$409$	−24.0380	−1.18860	−0.594302	+	0.804242i	$0.702572\pi$
$410$	4.78134	0.236133
$411$	−21.5725	−1.06409
$412$	−50.2349	−2.47490
$413$	8.17859	0.402442
$414$	10.8654	0.534008
$415$	4.48249	0.220037
$416$	−30.5727	−1.49895
$417$	35.7005	1.74826
$418$	−27.6966	−1.35469
$419$	−20.5712	−1.00497	−0.502485	−	0.864586i	$-0.667581\pi$
$419$	−20.5712	−1.00497	−0.502485	+	0.864586i	$0.667581\pi$
$420$	−12.8732	−0.628148
$421$	18.1519	0.884671	0.442336	−	0.896850i	$-0.354150\pi$
$421$	18.1519	0.884671	0.442336	+	0.896850i	$0.354150\pi$
$422$	−7.80667	−0.380023
$423$	5.29173	0.257293
$424$	−20.6250	−1.00164
$425$	3.56890	0.173117
$426$	−28.3499	−1.37356
$427$	28.9709	1.40200
$428$	45.0494	2.17755
$429$	−29.2703	−1.41318
$430$	28.6960	1.38384
$431$	−7.79069	−0.375264	−0.187632	−	0.982239i	$-0.560081\pi$
$431$	−7.79069	−0.375264	−0.187632	+	0.982239i	$0.560081\pi$
$432$	−2.10869	−0.101455
$433$	−31.3391	−1.50606	−0.753031	−	0.657985i	$-0.771409\pi$
$433$	−31.3391	−1.50606	−0.753031	+	0.657985i	$0.771409\pi$
$434$	0.964772	0.0463105
$435$	0.724780	0.0347505
$436$	22.9122	1.09729
$437$	26.4287	1.26425
$438$	37.7647	1.80446
$439$	−16.1937	−0.772881	−0.386441	−	0.922314i	$-0.626296\pi$
$439$	−16.1937	−0.772881	−0.386441	+	0.922314i	$0.626296\pi$
$440$	−9.91776	−0.472811
$441$	0.380569	0.0181223
$442$	48.2614	2.29556
$443$	36.0108	1.71092	0.855462	−	0.517866i	$-0.173273\pi$
$443$	36.0108	1.71092	0.855462	+	0.517866i	$0.173273\pi$
$444$	−0.429205	−0.0203691
$445$	−9.29048	−0.440411
$446$	47.0711	2.22888
$447$	10.7559	0.508738
$448$	32.3781	1.52972
$449$	−3.28207	−0.154890	−0.0774451	−	0.996997i	$-0.524676\pi$
$449$	−3.28207	−0.154890	−0.0774451	+	0.996997i	$0.524676\pi$
$450$	1.51410	0.0713756
$451$	−6.76053	−0.318341
$452$	−25.0118	−1.17645
$453$	8.99023	0.422398
$454$	−49.2080	−2.30945
$455$	14.8572	0.696518
$456$	−17.1471	−0.802986
$457$	−24.3559	−1.13932	−0.569660	−	0.821881i	$-0.692925\pi$
$457$	−24.3559	−1.13932	−0.569660	+	0.821881i	$0.692925\pi$
$458$	−23.2036	−1.08423
$459$	−19.9771	−0.932453
$460$	23.8160	1.11043
$461$	20.7673	0.967231	0.483616	−	0.875280i	$-0.339323\pi$
$461$	20.7673	0.967231	0.483616	+	0.875280i	$0.339323\pi$
$462$	29.1710	1.35716
$463$	9.60367	0.446321	0.223160	−	0.974782i	$-0.428363\pi$
$463$	9.60367	0.446321	0.223160	+	0.974782i	$0.428363\pi$
$464$	0.178357	0.00828003
$465$	0.252738	0.0117204
$466$	2.14012	0.0991393
$467$	−30.1966	−1.39733	−0.698666	−	0.715448i	$-0.746223\pi$
$467$	−30.1966	−1.39733	−0.698666	+	0.715448i	$0.746223\pi$
$468$	12.7758	0.590561
$469$	−7.90119	−0.364843
$470$	18.5889	0.857442
$471$	3.86508	0.178094
$472$	9.81694	0.451861
$473$	−40.5744	−1.86561
$474$	−9.70052	−0.445560
$475$	3.68285	0.168981
$476$	−30.0117	−1.37559
$477$	−4.45214	−0.203849
$478$	64.5297	2.95152
$479$	−7.56834	−0.345806	−0.172903	−	0.984939i	$-0.555315\pi$
$479$	−7.56834	−0.345806	−0.172903	+	0.984939i	$0.555315\pi$
$480$	7.98187	0.364321
$481$	0.495354	0.0225862
$482$	22.0809	1.00576
$483$	−27.8356	−1.26656
$484$	−1.21646	−0.0552936
$485$	−15.3425	−0.696666
$486$	−15.4289	−0.699867
$487$	−3.63187	−0.164576	−0.0822878	−	0.996609i	$-0.526223\pi$
$487$	−3.63187	−0.164576	−0.0822878	+	0.996609i	$0.526223\pi$
$488$	34.7745	1.57417
$489$	−20.5796	−0.930640
$490$	1.33687	0.0603936
$491$	25.1494	1.13498	0.567488	−	0.823382i	$-0.307915\pi$
$491$	25.1494	1.13498	0.567488	+	0.823382i	$0.307915\pi$
$492$	−10.5330	−0.474864
$493$	1.68970	0.0761004
$494$	49.8022	2.24071
$495$	−2.14086	−0.0962243
$496$	0.0621949	0.00279264
$497$	−20.3467	−0.912676
$498$	−15.8254	−0.709154
$499$	36.5133	1.63456	0.817279	−	0.576242i	$-0.195481\pi$
$499$	36.5133	1.63456	0.817279	+	0.576242i	$0.195481\pi$
$500$	3.31877	0.148420
$501$	30.8843	1.37981
$502$	2.71703	0.121267
$503$	10.3409	0.461077	0.230538	−	0.973063i	$-0.425951\pi$
$503$	10.3409	0.461077	0.230538	+	0.973063i	$0.425951\pi$
$504$	−5.05947	−0.225367
$505$	16.6463	0.740752
$506$	−53.9678	−2.39916
$507$	32.7310	1.45363
$508$	14.8771	0.660063
$509$	−26.0153	−1.15311	−0.576554	−	0.817059i	$-0.695603\pi$
$509$	−26.0153	−1.15311	−0.576554	+	0.817059i	$0.695603\pi$
$510$	−12.6000	−0.557938
$511$	27.1037	1.19900
$512$	4.25572	0.188078
$513$	−20.6149	−0.910172
$514$	−2.83457	−0.125028
$515$	−15.1366	−0.666998
$516$	−63.2154	−2.78290
$517$	−26.2836	−1.15595
$518$	−0.493674	−0.0216908
$519$	−30.2333	−1.32709
$520$	17.8335	0.782049
$521$	23.0929	1.01172	0.505860	−	0.862616i	$-0.331175\pi$
$521$	23.0929	1.01172	0.505860	+	0.862616i	$0.331175\pi$
$522$	0.716856	0.0313759
$523$	−19.1365	−0.836780	−0.418390	−	0.908268i	$-0.637405\pi$
$523$	−19.1365	−0.836780	−0.418390	+	0.908268i	$0.637405\pi$
$524$	47.6805	2.08293
$525$	−3.87890	−0.169289
$526$	37.5255	1.63619
$527$	0.589217	0.0256667
$528$	1.88054	0.0818400
$529$	28.4972	1.23901
$530$	−15.6396	−0.679339
$531$	2.11909	0.0919608
$532$	−30.9699	−1.34272
$533$	12.1563	0.526550
$534$	32.8000	1.41940
$535$	13.5741	0.586860
$536$	−9.48398	−0.409645
$537$	−1.23683	−0.0533731
$538$	31.9941	1.37936
$539$	−1.89026	−0.0814191
$540$	−18.5770	−0.799428
$541$	−10.3461	−0.444815	−0.222407	−	0.974954i	$-0.571391\pi$
$541$	−10.3461	−0.444815	−0.222407	+	0.974954i	$0.571391\pi$
$542$	53.7829	2.31018
$543$	17.6074	0.755607
$544$	18.6084	0.797829
$545$	6.90380	0.295726
$546$	−52.4535	−2.24480
$547$	−0.0523120	−0.00223670	−0.00111835	−	0.999999i	$-0.500356\pi$
$547$	−0.0523120	−0.00223670	−0.00111835	+	0.999999i	$0.500356\pi$
$548$	−46.7680	−1.99783
$549$	7.50644	0.320367
$550$	−7.52044	−0.320673
$551$	1.74365	0.0742820
$552$	−33.4117	−1.42210
$553$	−6.96206	−0.296057
$554$	57.4612	2.44129
$555$	−0.129326	−0.00548959
$556$	77.3966	3.28235
$557$	−25.4638	−1.07893	−0.539467	−	0.842007i	$-0.681374\pi$
$557$	−25.4638	−1.07893	−0.539467	+	0.842007i	$0.681374\pi$
$558$	0.249975	0.0105823
$559$	72.9582	3.08580
$560$	−0.954538	−0.0403366
$561$	17.8157	0.752179
$562$	62.3193	2.62878
$563$	−3.27057	−0.137838	−0.0689190	−	0.997622i	$-0.521955\pi$
$563$	−3.27057	−0.137838	−0.0689190	+	0.997622i	$0.521955\pi$
$564$	−40.9502	−1.72431
$565$	−7.53645	−0.317061
$566$	58.5829	2.46242
$567$	16.7218	0.702250
$568$	−24.4226	−1.02475
$569$	20.8675	0.874809	0.437405	−	0.899265i	$-0.355898\pi$
$569$	20.8675	0.874809	0.437405	+	0.899265i	$0.355898\pi$
$570$	−13.0023	−0.544606
$571$	6.41248	0.268354	0.134177	−	0.990957i	$-0.457161\pi$
$571$	6.41248	0.268354	0.134177	+	0.990957i	$0.457161\pi$
$572$	−63.4563	−2.65324
$573$	−26.3091	−1.09908
$574$	−12.1151	−0.505676
$575$	7.17615	0.299266
$576$	8.38925	0.349552
$577$	−36.8305	−1.53327	−0.766637	−	0.642081i	$-0.778071\pi$
$577$	−36.8305	−1.53327	−0.766637	+	0.642081i	$0.778071\pi$
$578$	9.83137	0.408931
$579$	−2.56561	−0.106623
$580$	1.57128	0.0652439
$581$	−11.3579	−0.471204
$582$	54.1666	2.24528
$583$	22.1134	0.915844
$584$	32.5331	1.34623
$585$	3.84955	0.159159
$586$	−13.6528	−0.563991
$587$	23.2644	0.960225	0.480113	−	0.877207i	$-0.340596\pi$
$587$	23.2644	0.960225	0.480113	+	0.877207i	$0.340596\pi$
$588$	−2.94504	−0.121451
$589$	0.608028	0.0250534
$590$	7.44399	0.306464
$591$	37.8518	1.55701
$592$	−0.0318252	−0.00130801
$593$	−28.5819	−1.17372	−0.586858	−	0.809690i	$-0.699635\pi$
$593$	−28.5819	−1.17372	−0.586858	+	0.809690i	$0.699635\pi$
$594$	42.0961	1.72722
$595$	−9.04302	−0.370728
$596$	23.3182	0.955152
$597$	−23.0625	−0.943887
$598$	97.0414	3.96832
$599$	14.5271	0.593563	0.296782	−	0.954945i	$-0.404087\pi$
$599$	14.5271	0.593563	0.296782	+	0.954945i	$0.404087\pi$
$600$	−4.65593	−0.190078
$601$	3.06290	0.124938	0.0624692	−	0.998047i	$-0.480102\pi$
$601$	3.06290	0.124938	0.0624692	+	0.998047i	$0.480102\pi$
$602$	−72.7108	−2.96347
$603$	−2.04722	−0.0833692
$604$	19.4903	0.793049
$605$	−0.366538	−0.0149019
$606$	−58.7698	−2.38736
$607$	4.02372	0.163318	0.0816589	−	0.996660i	$-0.473978\pi$
$607$	4.02372	0.163318	0.0816589	+	0.996660i	$0.473978\pi$
$608$	19.2025	0.778764
$609$	−1.83647	−0.0744177
$610$	26.3688	1.06764
$611$	47.2615	1.91199
$612$	−7.77611	−0.314331
$613$	−23.2620	−0.939542	−0.469771	−	0.882788i	$-0.655664\pi$
$613$	−23.2620	−0.939542	−0.469771	+	0.882788i	$0.655664\pi$
$614$	−53.5286	−2.16024
$615$	−3.17376	−0.127978
$616$	25.1300	1.01252
$617$	11.1927	0.450600	0.225300	−	0.974289i	$-0.427664\pi$
$617$	11.1927	0.450600	0.225300	+	0.974289i	$0.427664\pi$
$618$	53.4397	2.14966
$619$	2.52232	0.101381	0.0506904	−	0.998714i	$-0.483858\pi$
$619$	2.52232	0.101381	0.0506904	+	0.998714i	$0.483858\pi$
$620$	0.547921	0.0220050
$621$	−40.1689	−1.61192
$622$	−3.06074	−0.122724
$623$	23.5405	0.943132
$624$	−3.38146	−0.135367
$625$	1.00000	0.0400000
$626$	20.4021	0.815431
$627$	18.3845	0.734205
$628$	8.37928	0.334369
$629$	−0.301503	−0.0120217
$630$	−3.83649	−0.152850
$631$	−23.7952	−0.947273	−0.473636	−	0.880720i	$-0.657059\pi$
$631$	−23.7952	−0.947273	−0.473636	+	0.880720i	$0.657059\pi$
$632$	−8.35671	−0.332412
$633$	5.18191	0.205963
$634$	19.7787	0.785514
$635$	4.48270	0.177891
$636$	34.4530	1.36615
$637$	3.39894	0.134671
$638$	−3.56057	−0.140964
$639$	−5.27189	−0.208553
$640$	19.0418	0.752694
$641$	−38.6752	−1.52758	−0.763789	−	0.645466i	$-0.776663\pi$
$641$	−38.6752	−1.52758	−0.763789	+	0.645466i	$0.776663\pi$
$642$	−47.9234	−1.89139
$643$	0.130012	0.00512717	0.00256358	−	0.999997i	$-0.499184\pi$
$643$	0.130012	0.00512717	0.00256358	+	0.999997i	$0.499184\pi$
$644$	−60.3459	−2.37796
$645$	−19.0478	−0.750007
$646$	−30.3127	−1.19264
$647$	−30.5089	−1.19943	−0.599714	−	0.800214i	$-0.704719\pi$
$647$	−30.5089	−1.19943	−0.599714	+	0.800214i	$0.704719\pi$
$648$	20.0716	0.788486
$649$	−10.5254	−0.413157
$650$	13.5228	0.530406
$651$	−0.640397	−0.0250991
$652$	−44.6153	−1.74727
$653$	−6.77173	−0.264998	−0.132499	−	0.991183i	$-0.542300\pi$
$653$	−6.77173	−0.264998	−0.132499	+	0.991183i	$0.542300\pi$
$654$	−24.3739	−0.953094
$655$	14.3669	0.561361
$656$	−0.781013	−0.0304935
$657$	7.02263	0.273979
$658$	−47.1012	−1.83620
$659$	−0.640851	−0.0249640	−0.0124820	−	0.999922i	$-0.503973\pi$
$659$	−0.640851	−0.0249640	−0.0124820	+	0.999922i	$0.503973\pi$
$660$	16.5671	0.644872
$661$	0.205062	0.00797597	0.00398799	−	0.999992i	$-0.498731\pi$
$661$	0.205062	0.00797597	0.00398799	+	0.999992i	$0.498731\pi$
$662$	31.0302	1.20602
$663$	−32.0350	−1.24414
$664$	−13.6331	−0.529068
$665$	−9.33173	−0.361869
$666$	−0.127912	−0.00495650
$667$	3.39756	0.131554
$668$	66.9554	2.59058
$669$	−31.2449	−1.20800
$670$	−7.19151	−0.277832
$671$	−37.2839	−1.43933
$672$	−20.2247	−0.780187
$673$	40.9762	1.57952	0.789758	−	0.613418i	$-0.210206\pi$
$673$	40.9762	1.57952	0.789758	+	0.613418i	$0.210206\pi$
$674$	7.81953	0.301197
$675$	−5.59756	−0.215450
$676$	70.9588	2.72919
$677$	−33.4362	−1.28506	−0.642529	−	0.766262i	$-0.722115\pi$
$677$	−33.4362	−1.28506	−0.642529	+	0.766262i	$0.722115\pi$
$678$	26.6074	1.02185
$679$	38.8753	1.49190
$680$	−10.8545	−0.416252
$681$	32.6633	1.25166
$682$	−1.24160	−0.0475435
$683$	10.4123	0.398416	0.199208	−	0.979957i	$-0.436163\pi$
$683$	10.4123	0.398416	0.199208	+	0.979957i	$0.436163\pi$
$684$	−8.02438	−0.306820
$685$	−14.0919	−0.538425
$686$	−44.2930	−1.69111
$687$	15.4021	0.587626
$688$	−4.68738	−0.178705
$689$	−39.7629	−1.51485
$690$	−25.3354	−0.964503
$691$	−2.25028	−0.0856049	−0.0428024	−	0.999084i	$-0.513629\pi$
$691$	−2.25028	−0.0856049	−0.0428024	+	0.999084i	$0.513629\pi$
$692$	−65.5439	−2.49161
$693$	5.42458	0.206063
$694$	14.5323	0.551639
$695$	23.3208	0.884610
$696$	−2.20436	−0.0835561
$697$	−7.39909	−0.280261
$698$	−51.0006	−1.93040
$699$	−1.42057	−0.0537310
$700$	−8.40923	−0.317839
$701$	3.63753	0.137388	0.0686938	−	0.997638i	$-0.478117\pi$
$701$	3.63753	0.137388	0.0686938	+	0.997638i	$0.478117\pi$
$702$	−75.6944	−2.85690
$703$	−0.311128	−0.0117344
$704$	−41.6687	−1.57045
$705$	−12.3389	−0.464712
$706$	68.7503	2.58745
$707$	−42.1791	−1.58631
$708$	−16.3986	−0.616299
$709$	−45.8197	−1.72079	−0.860397	−	0.509625i	$-0.829784\pi$
$709$	−45.8197	−1.72079	−0.860397	+	0.509625i	$0.829784\pi$
$710$	−18.5192	−0.695013
$711$	−1.80389	−0.0676510
$712$	28.2562	1.05895
$713$	1.18476	0.0443698
$714$	31.9264	1.19481
$715$	−19.1204	−0.715062
$716$	−2.68137	−0.100208
$717$	−42.8336	−1.59965
$718$	−12.8873	−0.480950
$719$	−18.6368	−0.695034	−0.347517	−	0.937674i	$-0.612975\pi$
$719$	−18.6368	−0.695034	−0.347517	+	0.937674i	$0.612975\pi$
$720$	−0.247323	−0.00921719
$721$	38.3536	1.42836
$722$	12.5383	0.466625
$723$	−14.6569	−0.545096
$724$	38.1718	1.41865
$725$	0.473452	0.0175836
$726$	1.29406	0.0480272
$727$	28.2413	1.04741	0.523705	−	0.851899i	$-0.324549\pi$
$727$	28.2413	1.04741	0.523705	+	0.851899i	$0.324549\pi$
$728$	−45.1871	−1.67475
$729$	30.0396	1.11258
$730$	24.6692	0.913048
$731$	−44.4068	−1.64245
$732$	−58.0887	−2.14702
$733$	23.1258	0.854171	0.427085	−	0.904211i	$-0.359540\pi$
$733$	23.1258	0.854171	0.427085	+	0.904211i	$0.359540\pi$
$734$	−37.0168	−1.36632
$735$	−0.887388	−0.0327318
$736$	37.4167	1.37920
$737$	10.1684	0.374557
$738$	−3.13906	−0.115550
$739$	28.9267	1.06409	0.532043	−	0.846717i	$-0.321424\pi$
$739$	28.9267	1.06409	0.532043	+	0.846717i	$0.321424\pi$
$740$	−0.280372	−0.0103067
$741$	−33.0577	−1.21441
$742$	39.6281	1.45479
$743$	−27.2426	−0.999432	−0.499716	−	0.866189i	$-0.666562\pi$
$743$	−27.2426	−0.999432	−0.499716	+	0.866189i	$0.666562\pi$
$744$	−0.768682	−0.0281813
$745$	7.02616	0.257418
$746$	44.6950	1.63640
$747$	−2.94286	−0.107673
$748$	38.6233	1.41221
$749$	−34.3946	−1.25675
$750$	−3.53050	−0.128916
$751$	−49.4436	−1.80422	−0.902112	−	0.431502i	$-0.857984\pi$
$751$	−49.4436	−1.80422	−0.902112	+	0.431502i	$0.857984\pi$
$752$	−3.03643	−0.110727
$753$	−1.80351	−0.0657237
$754$	6.40237	0.233161
$755$	5.87274	0.213731
$756$	47.0712	1.71196
$757$	43.7942	1.59173	0.795863	−	0.605477i	$-0.207018\pi$
$757$	43.7942	1.59173	0.795863	+	0.605477i	$0.207018\pi$
$758$	−8.77735	−0.318808
$759$	35.8228	1.30028
$760$	−11.2011	−0.406306
$761$	36.5312	1.32425	0.662127	−	0.749392i	$-0.269654\pi$
$761$	36.5312	1.32425	0.662127	+	0.749392i	$0.269654\pi$
$762$	−15.8262	−0.573322
$763$	−17.4931	−0.633293
$764$	−57.0365	−2.06351
$765$	−2.34307	−0.0847138
$766$	74.4508	2.69002
$767$	18.9260	0.683379
$768$	−28.1041	−1.01412
$769$	−24.7260	−0.891644	−0.445822	−	0.895122i	$-0.647088\pi$
$769$	−24.7260	−0.891644	−0.445822	+	0.895122i	$0.647088\pi$
$770$	19.0556	0.686715
$771$	1.88153	0.0677617
$772$	−5.56208	−0.200184
$773$	15.9129	0.572347	0.286173	−	0.958178i	$-0.407617\pi$
$773$	15.9129	0.572347	0.286173	+	0.958178i	$0.407617\pi$
$774$	−18.8396	−0.677174
$775$	0.165097	0.00593047
$776$	46.6629	1.67510
$777$	0.327691	0.0117559
$778$	29.7420	1.06630
$779$	−7.63532	−0.273564
$780$	−29.7898	−1.06665
$781$	26.1850	0.936975
$782$	−59.0653	−2.11217
$783$	−2.65017	−0.0947095
$784$	−0.218373	−0.00779902
$785$	2.52481	0.0901143
$786$	−50.7223	−1.80920
$787$	−29.0262	−1.03467	−0.517336	−	0.855782i	$-0.673076\pi$
$787$	−29.0262	−1.03467	−0.517336	+	0.855782i	$0.673076\pi$
$788$	82.0604	2.92328
$789$	−24.9087	−0.886772
$790$	−6.33672	−0.225450
$791$	19.0961	0.678980
$792$	6.51124	0.231367
$793$	67.0414	2.38071
$794$	26.6267	0.944946
$795$	10.3812	0.368184
$796$	−49.9982	−1.77214
$797$	−55.1272	−1.95271	−0.976353	−	0.216181i	$-0.930640\pi$
$797$	−55.1272	−1.95271	−0.976353	+	0.216181i	$0.930640\pi$
$798$	32.9457	1.16626
$799$	−28.7662	−1.01767
$800$	5.21404	0.184344
$801$	6.09941	0.215512
$802$	−43.9061	−1.55038
$803$	−34.8808	−1.23092
$804$	15.8424	0.558720
$805$	−18.1832	−0.640874
$806$	2.23257	0.0786390
$807$	−21.2371	−0.747581
$808$	−50.6285	−1.78110
$809$	−46.6415	−1.63983	−0.819914	−	0.572487i	$-0.805979\pi$
$809$	−46.6415	−1.63983	−0.819914	+	0.572487i	$0.805979\pi$
$810$	15.2199	0.534771
$811$	−11.0458	−0.387872	−0.193936	−	0.981014i	$-0.562125\pi$
$811$	−11.0458	−0.387872	−0.193936	+	0.981014i	$0.562125\pi$
$812$	−3.98137	−0.139719
$813$	−35.7001	−1.25206
$814$	0.635330	0.0222683
$815$	−13.4433	−0.470898
$816$	2.05816	0.0720501
$817$	−45.8246	−1.60320
$818$	55.4376	1.93833
$819$	−9.75412	−0.340837
$820$	−6.88052	−0.240278
$821$	23.2937	0.812956	0.406478	−	0.913661i	$-0.366757\pi$
$821$	23.2937	0.812956	0.406478	+	0.913661i	$0.366757\pi$
$822$	49.7516	1.73529
$823$	−49.2935	−1.71826	−0.859132	−	0.511754i	$-0.828996\pi$
$823$	−49.2935	−1.71826	−0.859132	+	0.511754i	$0.828996\pi$
$824$	46.0367	1.60377
$825$	4.99192	0.173796
$826$	−18.8618	−0.656287
$827$	−36.6182	−1.27334	−0.636670	−	0.771136i	$-0.719689\pi$
$827$	−36.6182	−1.27334	−0.636670	+	0.771136i	$0.719689\pi$
$828$	−15.6358	−0.543381
$829$	20.7386	0.720280	0.360140	−	0.932898i	$-0.382729\pi$
$829$	20.7386	0.720280	0.360140	+	0.932898i	$0.382729\pi$
$830$	−10.3377	−0.358827
$831$	−38.1417	−1.32312
$832$	74.9260	2.59759
$833$	−2.06880	−0.0716796
$834$	−82.3342	−2.85100
$835$	20.1747	0.698176
$836$	39.8565	1.37846
$837$	−0.924142	−0.0319430
$838$	47.4423	1.63887
$839$	−1.34404	−0.0464015	−0.0232008	−	0.999731i	$-0.507386\pi$
$839$	−1.34404	−0.0464015	−0.0232008	+	0.999731i	$0.507386\pi$
$840$	11.7974	0.407048
$841$	−28.7758	−0.992270
$842$	−41.8628	−1.44269
$843$	−41.3663	−1.42473
$844$	11.2341	0.386693
$845$	21.3810	0.735530
$846$	−12.2040	−0.419584
$847$	0.928748	0.0319122
$848$	2.55466	0.0877274
$849$	−38.8862	−1.33457
$850$	−8.23077	−0.282313
$851$	−0.606245	−0.0207818
$852$	40.7966	1.39767
$853$	−5.14150	−0.176041	−0.0880207	−	0.996119i	$-0.528054\pi$
$853$	−5.14150	−0.176041	−0.0880207	+	0.996119i	$0.528054\pi$
$854$	−66.8141	−2.28633
$855$	−2.41787	−0.0826895
$856$	−41.2846	−1.41108
$857$	38.5853	1.31805	0.659024	−	0.752122i	$-0.270970\pi$
$857$	38.5853	1.31805	0.659024	+	0.752122i	$0.270970\pi$
$858$	67.5045	2.30457
$859$	5.33017	0.181863	0.0909315	−	0.995857i	$-0.471016\pi$
$859$	5.33017	0.181863	0.0909315	+	0.995857i	$0.471016\pi$
$860$	−41.2945	−1.40813
$861$	8.04179	0.274063
$862$	17.9672	0.611967
$863$	−9.72153	−0.330925	−0.165462	−	0.986216i	$-0.552912\pi$
$863$	−9.72153	−0.330925	−0.165462	+	0.986216i	$0.552912\pi$
$864$	−29.1859	−0.992924
$865$	−19.7494	−0.671501
$866$	72.2757	2.45603
$867$	−6.52587	−0.221630
$868$	−1.38834	−0.0471234
$869$	8.95976	0.303939
$870$	−1.67152	−0.0566699
$871$	−18.2841	−0.619533
$872$	−20.9974	−0.711061
$873$	10.0727	0.340909
$874$	−60.9510	−2.06170
$875$	−2.53384	−0.0856593
$876$	−54.3447	−1.83614
$877$	16.6655	0.562752	0.281376	−	0.959598i	$-0.409209\pi$
$877$	16.6655	0.562752	0.281376	+	0.959598i	$0.409209\pi$
$878$	37.3466	1.26039
$879$	9.06244	0.305669
$880$	1.22844	0.0414105
$881$	3.98189	0.134153	0.0670767	−	0.997748i	$-0.478633\pi$
$881$	3.98189	0.134153	0.0670767	+	0.997748i	$0.478633\pi$
$882$	−0.877686	−0.0295532
$883$	15.3272	0.515801	0.257900	−	0.966172i	$-0.416969\pi$
$883$	15.3272	0.515801	0.257900	+	0.966172i	$0.416969\pi$
$884$	−69.4500	−2.33585
$885$	−4.94117	−0.166096
$886$	−83.0497	−2.79011
$887$	5.81627	0.195291	0.0976456	−	0.995221i	$-0.468869\pi$
$887$	5.81627	0.195291	0.0976456	+	0.995221i	$0.468869\pi$
$888$	0.393335	0.0131995
$889$	−11.3584	−0.380949
$890$	21.4261	0.718206
$891$	−21.5200	−0.720947
$892$	−67.7371	−2.26800
$893$	−29.6846	−0.993357
$894$	−24.8058	−0.829631
$895$	−0.807940	−0.0270065
$896$	−48.2489	−1.61188
$897$	−64.4142	−2.15073
$898$	7.56925	0.252589
$899$	0.0781657	0.00260697
$900$	−2.17885	−0.0726284
$901$	24.2021	0.806289
$902$	15.5915	0.519139
$903$	48.2640	1.60613
$904$	22.9215	0.762358
$905$	11.5018	0.382332
$906$	−20.7337	−0.688831
$907$	−52.2391	−1.73457	−0.867285	−	0.497812i	$-0.834137\pi$
$907$	−52.2391	−1.73457	−0.867285	+	0.497812i	$0.834137\pi$
$908$	70.8122	2.34998
$909$	−10.9287	−0.362482
$910$	−34.2645	−1.13586
$911$	37.9334	1.25679	0.628395	−	0.777894i	$-0.283712\pi$
$911$	37.9334	1.25679	0.628395	+	0.777894i	$0.283712\pi$
$912$	2.12387	0.0703285
$913$	14.6169	0.483750
$914$	56.1706	1.85796
$915$	−17.5031	−0.578634
$916$	33.3908	1.10326
$917$	−36.4033	−1.20214
$918$	46.0722	1.52061
$919$	−44.7637	−1.47662	−0.738309	−	0.674463i	$-0.764375\pi$
$919$	−44.7637	−1.47662	−0.738309	+	0.674463i	$0.764375\pi$
$920$	−21.8257	−0.719572
$921$	35.5312	1.17079
$922$	−47.8946	−1.57733
$923$	−47.0842	−1.54980
$924$	−41.9782	−1.38098
$925$	−0.0844805	−0.00277770
$926$	−22.1484	−0.727843
$927$	9.93752	0.326391
$928$	2.46860	0.0810357
$929$	−42.4094	−1.39141	−0.695704	−	0.718329i	$-0.744907\pi$
$929$	−42.4094	−1.39141	−0.695704	+	0.718329i	$0.744907\pi$
$930$	−0.582876	−0.0191133
$931$	−2.13485	−0.0699668
$932$	−3.07972	−0.100880
$933$	2.03166	0.0665135
$934$	69.6408	2.27872
$935$	11.6378	0.380598
$936$	−11.7081	−0.382691
$937$	−19.6875	−0.643164	−0.321582	−	0.946882i	$-0.604215\pi$
$937$	−19.6875	−0.643164	−0.321582	+	0.946882i	$0.604215\pi$
$938$	18.2221	0.594973
$939$	−13.5425	−0.441943
$940$	−26.7501	−0.872492
$941$	−13.5153	−0.440586	−0.220293	−	0.975434i	$-0.570701\pi$
$941$	−13.5153	−0.440586	−0.220293	+	0.975434i	$0.570701\pi$
$942$	−8.91384	−0.290429
$943$	−14.8777	−0.484484
$944$	−1.21595	−0.0395757
$945$	14.1833	0.461383
$946$	93.5746	3.04237
$947$	−31.4168	−1.02091	−0.510454	−	0.859905i	$-0.670523\pi$
$947$	−31.4168	−1.02091	−0.510454	+	0.859905i	$0.670523\pi$
$948$	13.9594	0.453381
$949$	62.7204	2.03599
$950$	−8.49355	−0.275567
$951$	−13.1287	−0.425729
$952$	27.5036	0.891397
$953$	19.3962	0.628304	0.314152	−	0.949373i	$-0.398280\pi$
$953$	19.3962	0.628304	0.314152	+	0.949373i	$0.398280\pi$
$954$	10.2677	0.332430
$955$	−17.1860	−0.556126
$956$	−92.8607	−3.00333
$957$	2.36343	0.0763990
$958$	17.4545	0.563928
$959$	35.7067	1.15303
$960$	−19.5615	−0.631346
$961$	−30.9727	−0.999121
$962$	−1.14241	−0.0368327
$963$	−8.91172	−0.287176
$964$	−31.7753	−1.02341
$965$	−1.67594	−0.0539506
$966$	64.1958	2.06547
$967$	47.9194	1.54098	0.770491	−	0.637451i	$-0.220011\pi$
$967$	47.9194	1.54098	0.770491	+	0.637451i	$0.220011\pi$
$968$	1.11480	0.0358309
$969$	20.1210	0.646378
$970$	35.3835	1.13610
$971$	−1.49448	−0.0479600	−0.0239800	−	0.999712i	$-0.507634\pi$
$971$	−1.49448	−0.0479600	−0.0239800	+	0.999712i	$0.507634\pi$
$972$	22.2027	0.712152
$973$	−59.0912	−1.89438
$974$	8.37598	0.268384
$975$	−8.97614	−0.287467
$976$	−4.30724	−0.137871
$977$	−6.92523	−0.221558	−0.110779	−	0.993845i	$-0.535335\pi$
$977$	−6.92523	−0.221558	−0.110779	+	0.993845i	$0.535335\pi$
$978$	47.4616	1.51765
$979$	−30.2953	−0.968242
$980$	−1.92381	−0.0614537
$981$	−4.53251	−0.144712
$982$	−58.0007	−1.85088
$983$	7.24693	0.231141	0.115571	−	0.993299i	$-0.463130\pi$
$983$	7.24693	0.231141	0.115571	+	0.993299i	$0.463130\pi$
$984$	9.65274	0.307718
$985$	24.7261	0.787840
$986$	−3.89687	−0.124102
$987$	31.2649	0.995172
$988$	−71.6673	−2.28004
$989$	−89.2908	−2.83928
$990$	4.93734	0.156919
$991$	36.3823	1.15572	0.577862	−	0.816135i	$-0.303887\pi$
$991$	36.3823	1.15572	0.577862	+	0.816135i	$0.303887\pi$
$992$	0.860824	0.0273312
$993$	−20.5973	−0.653634
$994$	46.9246	1.48836
$995$	−15.0653	−0.477601
$996$	22.7734	0.721601
$997$	−6.12033	−0.193833	−0.0969164	−	0.995293i	$-0.530898\pi$
$997$	−6.12033	−0.193833	−0.0969164	+	0.995293i	$0.530898\pi$
$998$	−84.2086	−2.66558
$999$	0.472884	0.0149614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.e.1.17	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.e.1.17	✓	126	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30625 q^{2} +1.53084 q^{3} +3.31877 q^{4} +1.00000 q^{5} -3.53050 q^{6} -2.53384 q^{7} -3.04142 q^{8} -0.656523 q^{9} +O(q^{10})\)	\(q-2.30625 q^{2} +1.53084 q^{3} +3.31877 q^{4} +1.00000 q^{5} -3.53050 q^{6} -2.53384 q^{7} -3.04142 q^{8} -0.656523 q^{9} -2.30625 q^{10} +3.26090 q^{11} +5.08052 q^{12} -5.86353 q^{13} +5.84365 q^{14} +1.53084 q^{15} +0.376717 q^{16} +3.56890 q^{17} +1.51410 q^{18} +3.68285 q^{19} +3.31877 q^{20} -3.87890 q^{21} -7.52044 q^{22} +7.17615 q^{23} -4.65593 q^{24} +1.00000 q^{25} +13.5228 q^{26} -5.59756 q^{27} -8.40923 q^{28} +0.473452 q^{29} -3.53050 q^{30} +0.165097 q^{31} +5.21404 q^{32} +4.99192 q^{33} -8.23077 q^{34} -2.53384 q^{35} -2.17885 q^{36} -0.0844805 q^{37} -8.49355 q^{38} -8.97614 q^{39} -3.04142 q^{40} -2.07321 q^{41} +8.94571 q^{42} -12.4427 q^{43} +10.8222 q^{44} -0.656523 q^{45} -16.5500 q^{46} -8.06024 q^{47} +0.576694 q^{48} -0.579673 q^{49} -2.30625 q^{50} +5.46343 q^{51} -19.4597 q^{52} +6.78139 q^{53} +12.9094 q^{54} +3.26090 q^{55} +7.70646 q^{56} +5.63785 q^{57} -1.09190 q^{58} -3.22775 q^{59} +5.08052 q^{60} -11.4336 q^{61} -0.380755 q^{62} +1.66352 q^{63} -12.7783 q^{64} -5.86353 q^{65} -11.5126 q^{66} +3.11827 q^{67} +11.8444 q^{68} +10.9856 q^{69} +5.84365 q^{70} +8.03001 q^{71} +1.99676 q^{72} -10.6967 q^{73} +0.194833 q^{74} +1.53084 q^{75} +12.2225 q^{76} -8.26258 q^{77} +20.7012 q^{78} +2.74763 q^{79} +0.376717 q^{80} -6.59941 q^{81} +4.78134 q^{82} +4.48249 q^{83} -12.8732 q^{84} +3.56890 q^{85} +28.6960 q^{86} +0.724780 q^{87} -9.91776 q^{88} -9.29048 q^{89} +1.51410 q^{90} +14.8572 q^{91} +23.8160 q^{92} +0.252738 q^{93} +18.5889 q^{94} +3.68285 q^{95} +7.98187 q^{96} -15.3425 q^{97} +1.33687 q^{98} -2.14086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9	\( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 126 * q - 15 * q^2 - 46 * q^3 + 119 * q^4 + 126 * q^5 - 10 * q^6 - 60 * q^7 - 57 * q^8 + 112 * q^9 - 15 * q^10 - 35 * q^11 - 86 * q^12 - 36 * q^13 - 31 * q^14 - 46 * q^15 + 101 * q^16 - 62 * q^17 - 45 * q^18 - 29 * q^19 + 119 * q^20 - 16 * q^21 - 67 * q^22 - 107 * q^23 - 9 * q^24 + 126 * q^25 - 53 * q^26 - 181 * q^27 - 100 * q^28 - 39 * q^29 - 10 * q^30 - 29 * q^31 - 99 * q^32 - 72 * q^33 - 18 * q^34 - 60 * q^35 + 93 * q^36 - 72 * q^37 - 93 * q^38 - 8 * q^39 - 57 * q^40 - 28 * q^41 - 22 * q^42 - 103 * q^43 - 47 * q^44 + 112 * q^45 + q^46 - 130 * q^47 - 134 * q^48 + 116 * q^49 - 15 * q^50 - 46 * q^51 - 117 * q^52 - 103 * q^53 + 11 * q^54 - 35 * q^55 - 84 * q^56 - 70 * q^57 - 77 * q^58 - 219 * q^59 - 86 * q^60 - 4 * q^61 - 77 * q^62 - 145 * q^63 + 51 * q^64 - 36 * q^65 + 16 * q^66 - 150 * q^67 - 130 * q^68 - 21 * q^69 - 31 * q^70 - 92 * q^71 - 115 * q^72 - 79 * q^73 - 57 * q^74 - 46 * q^75 - 38 * q^76 - 75 * q^77 - 23 * q^78 - 20 * q^79 + 101 * q^80 + 142 * q^81 - 63 * q^82 - 243 * q^83 - 2 * q^84 - 62 * q^85 - 14 * q^86 - 107 * q^87 - 121 * q^88 - 84 * q^89 - 45 * q^90 - 82 * q^91 - 228 * q^92 - 149 * q^93 - 29 * q^95 + 38 * q^96 - 85 * q^97 - 48 * q^98 - 33 * q^99

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