LMFDB - Embedded newform 799.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, 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("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 22 x^{15} + 70 x^{14} + 184 x^{13} - 644 x^{12} - 713 x^{11} + 2975 x^{10} + \cdots + 11 $ x^17 - 3x^16 - 22x^15 + 70x^14 + 184x^13 - 644x^12 - 713x^11 + 2975x^10 + 1130x^9 - 7241x^8 + 309x^7 + 8675x^6 - 2943x^5 - 3739x^4 + 2446x^3 - 300x^2 - 60x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.54005$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.54005 q^{2} -1.81435 q^{3} +4.45187 q^{4} +0.588316 q^{5} -4.60855 q^{6} +4.54595 q^{7} +6.22788 q^{8} +0.291871 q^{9} +O(q^{10})$	\(q+2.54005 q^{2} -1.81435 q^{3} +4.45187 q^{4} +0.588316 q^{5} -4.60855 q^{6} +4.54595 q^{7} +6.22788 q^{8} +0.291871 q^{9} +1.49435 q^{10} -0.0560242 q^{11} -8.07725 q^{12} -3.99371 q^{13} +11.5470 q^{14} -1.06741 q^{15} +6.91540 q^{16} +1.00000 q^{17} +0.741367 q^{18} +7.36434 q^{19} +2.61911 q^{20} -8.24795 q^{21} -0.142305 q^{22} -4.23898 q^{23} -11.2996 q^{24} -4.65388 q^{25} -10.1442 q^{26} +4.91350 q^{27} +20.2380 q^{28} +7.03119 q^{29} -2.71128 q^{30} +2.26324 q^{31} +5.10972 q^{32} +0.101648 q^{33} +2.54005 q^{34} +2.67446 q^{35} +1.29937 q^{36} -7.39959 q^{37} +18.7058 q^{38} +7.24599 q^{39} +3.66396 q^{40} +6.72284 q^{41} -20.9502 q^{42} -9.36347 q^{43} -0.249413 q^{44} +0.171712 q^{45} -10.7672 q^{46} -1.00000 q^{47} -12.5470 q^{48} +13.6657 q^{49} -11.8211 q^{50} -1.81435 q^{51} -17.7795 q^{52} -8.23828 q^{53} +12.4805 q^{54} -0.0329600 q^{55} +28.3116 q^{56} -13.3615 q^{57} +17.8596 q^{58} -0.0665683 q^{59} -4.75198 q^{60} -5.89974 q^{61} +5.74875 q^{62} +1.32683 q^{63} -0.851835 q^{64} -2.34956 q^{65} +0.258190 q^{66} +0.798029 q^{67} +4.45187 q^{68} +7.69100 q^{69} +6.79326 q^{70} -0.897400 q^{71} +1.81773 q^{72} +12.1754 q^{73} -18.7953 q^{74} +8.44378 q^{75} +32.7851 q^{76} -0.254683 q^{77} +18.4052 q^{78} -9.09343 q^{79} +4.06844 q^{80} -9.79042 q^{81} +17.0764 q^{82} -13.2624 q^{83} -36.7188 q^{84} +0.588316 q^{85} -23.7837 q^{86} -12.7570 q^{87} -0.348912 q^{88} +8.78234 q^{89} +0.436158 q^{90} -18.1552 q^{91} -18.8714 q^{92} -4.10631 q^{93} -2.54005 q^{94} +4.33256 q^{95} -9.27083 q^{96} -0.738938 q^{97} +34.7115 q^{98} -0.0163518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9	\( 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9} + 12 q^{10} + 8 q^{11} + 12 q^{12} + q^{13} + 11 q^{14} - 7 q^{15} + 15 q^{16} + 17 q^{17} - 26 q^{18} - q^{19} + 13 q^{20} + 14 q^{21} + 3 q^{22} + 12 q^{23} - 24 q^{24} + 33 q^{26} + 22 q^{27} + q^{28} + 10 q^{29} + q^{30} + 2 q^{31} - q^{32} + 3 q^{33} + 3 q^{34} + 9 q^{35} + 50 q^{36} + 10 q^{37} + 23 q^{38} + 13 q^{39} + q^{40} + 65 q^{41} - 41 q^{42} - 3 q^{43} + 10 q^{44} + 31 q^{45} - 17 q^{47} - 16 q^{48} + 14 q^{49} + 5 q^{50} + q^{51} - 32 q^{52} - 13 q^{53} - 15 q^{54} - 11 q^{55} + 46 q^{56} + 36 q^{57} - q^{58} + 39 q^{59} + 43 q^{60} + 23 q^{61} + 33 q^{62} - 15 q^{63} - 27 q^{64} - 10 q^{65} - 86 q^{66} - 14 q^{67} + 19 q^{68} + 45 q^{69} - 13 q^{70} + 21 q^{71} - 42 q^{72} + 24 q^{73} + 25 q^{74} - 32 q^{75} - 5 q^{76} - 2 q^{77} + 36 q^{78} - 26 q^{79} - 14 q^{80} + 41 q^{81} - 37 q^{82} - 5 q^{83} - 60 q^{84} + 11 q^{85} - 24 q^{86} - 5 q^{87} - 25 q^{88} + 61 q^{89} + 6 q^{90} + 29 q^{91} - 12 q^{92} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 12 q^{96} + 3 q^{97} + 36 q^{98} - 27 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9 + 12 * q^10 + 8 * q^11 + 12 * q^12 + q^13 + 11 * q^14 - 7 * q^15 + 15 * q^16 + 17 * q^17 - 26 * q^18 - q^19 + 13 * q^20 + 14 * q^21 + 3 * q^22 + 12 * q^23 - 24 * q^24 + 33 * q^26 + 22 * q^27 + q^28 + 10 * q^29 + q^30 + 2 * q^31 - q^32 + 3 * q^33 + 3 * q^34 + 9 * q^35 + 50 * q^36 + 10 * q^37 + 23 * q^38 + 13 * q^39 + q^40 + 65 * q^41 - 41 * q^42 - 3 * q^43 + 10 * q^44 + 31 * q^45 - 17 * q^47 - 16 * q^48 + 14 * q^49 + 5 * q^50 + q^51 - 32 * q^52 - 13 * q^53 - 15 * q^54 - 11 * q^55 + 46 * q^56 + 36 * q^57 - q^58 + 39 * q^59 + 43 * q^60 + 23 * q^61 + 33 * q^62 - 15 * q^63 - 27 * q^64 - 10 * q^65 - 86 * q^66 - 14 * q^67 + 19 * q^68 + 45 * q^69 - 13 * q^70 + 21 * q^71 - 42 * q^72 + 24 * q^73 + 25 * q^74 - 32 * q^75 - 5 * q^76 - 2 * q^77 + 36 * q^78 - 26 * q^79 - 14 * q^80 + 41 * q^81 - 37 * q^82 - 5 * q^83 - 60 * q^84 + 11 * q^85 - 24 * q^86 - 5 * q^87 - 25 * q^88 + 61 * q^89 + 6 * q^90 + 29 * q^91 - 12 * q^92 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 12 * q^96 + 3 * q^97 + 36 * q^98 - 27 * 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 $

$2$	2.54005	1.79609	0.898044	−	0.439905i	$-0.144988\pi$
$2$	2.54005	1.79609	0.898044	+	0.439905i	$0.144988\pi$
$3$	−1.81435	−1.04752	−0.523758	−	0.851867i	$-0.675470\pi$
$3$	−1.81435	−1.04752	−0.523758	+	0.851867i	$0.675470\pi$
$4$	4.45187	2.22593
$5$	0.588316	0.263103	0.131552	−	0.991309i	$-0.458004\pi$
$5$	0.588316	0.263103	0.131552	+	0.991309i	$0.458004\pi$
$6$	−4.60855	−1.88143
$7$	4.54595	1.71821	0.859104	−	0.511802i	$-0.171022\pi$
$7$	4.54595	1.71821	0.859104	+	0.511802i	$0.171022\pi$
$8$	6.22788	2.20189
$9$	0.291871	0.0972902
$10$	1.49435	0.472556
$11$	−0.0560242	−0.0168919	−0.00844597	−	0.999964i	$-0.502688\pi$
$11$	−0.0560242	−0.0168919	−0.00844597	+	0.999964i	$0.502688\pi$
$12$	−8.07725	−2.33170
$13$	−3.99371	−1.10765	−0.553827	−	0.832632i	$-0.686833\pi$
$13$	−3.99371	−1.10765	−0.553827	+	0.832632i	$0.686833\pi$
$14$	11.5470	3.08605
$15$	−1.06741	−0.275605
$16$	6.91540	1.72885
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.741367	0.174742
$19$	7.36434	1.68949	0.844747	−	0.535166i	$-0.179751\pi$
$19$	7.36434	1.68949	0.844747	+	0.535166i	$0.179751\pi$
$20$	2.61911	0.585650
$21$	−8.24795	−1.79985
$22$	−0.142305	−0.0303394
$23$	−4.23898	−0.883888	−0.441944	−	0.897043i	$-0.645711\pi$
$23$	−4.23898	−0.883888	−0.441944	+	0.897043i	$0.645711\pi$
$24$	−11.2996	−2.30651
$25$	−4.65388	−0.930777
$26$	−10.1442	−1.98945
$27$	4.91350	0.945603
$28$	20.2380	3.82462
$29$	7.03119	1.30566	0.652829	−	0.757505i	$-0.273582\pi$
$29$	7.03119	1.30566	0.652829	+	0.757505i	$0.273582\pi$
$30$	−2.71128	−0.495011
$31$	2.26324	0.406490	0.203245	−	0.979128i	$-0.434851\pi$
$31$	2.26324	0.406490	0.203245	+	0.979128i	$0.434851\pi$
$32$	5.10972	0.903279
$33$	0.101648	0.0176946
$34$	2.54005	0.435615
$35$	2.67446	0.452066
$36$	1.29937	0.216562
$37$	−7.39959	−1.21648	−0.608242	−	0.793751i	$-0.708125\pi$
$37$	−7.39959	−1.21648	−0.608242	+	0.793751i	$0.708125\pi$
$38$	18.7058	3.03448
$39$	7.24599	1.16029
$40$	3.66396	0.579323
$41$	6.72284	1.04993	0.524966	−	0.851123i	$-0.324078\pi$
$41$	6.72284	1.04993	0.524966	+	0.851123i	$0.324078\pi$
$42$	−20.9502	−3.23269
$43$	−9.36347	−1.42792	−0.713958	−	0.700189i	$-0.753099\pi$
$43$	−9.36347	−1.42792	−0.713958	+	0.700189i	$0.753099\pi$
$44$	−0.249413	−0.0376004
$45$	0.171712	0.0255974
$46$	−10.7672	−1.58754
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−12.5470	−1.81100
$49$	13.6657	1.95224
$50$	−11.8211	−1.67176
$51$	−1.81435	−0.254060
$52$	−17.7795	−2.46557
$53$	−8.23828	−1.13161	−0.565807	−	0.824537i	$-0.691435\pi$
$53$	−8.23828	−1.13161	−0.565807	+	0.824537i	$0.691435\pi$
$54$	12.4805	1.69839
$55$	−0.0329600	−0.00444432
$56$	28.3116	3.78330
$57$	−13.3615	−1.76977
$58$	17.8596	2.34508
$59$	−0.0665683	−0.00866646	−0.00433323	−	0.999991i	$-0.501379\pi$
$59$	−0.0665683	−0.00866646	−0.00433323	+	0.999991i	$0.501379\pi$
$60$	−4.75198	−0.613478
$61$	−5.89974	−0.755384	−0.377692	−	0.925931i	$-0.623282\pi$
$61$	−5.89974	−0.755384	−0.377692	+	0.925931i	$0.623282\pi$
$62$	5.74875	0.730092
$63$	1.32683	0.167165
$64$	−0.851835	−0.106479
$65$	−2.34956	−0.291427
$66$	0.258190	0.0317810
$67$	0.798029	0.0974948	0.0487474	−	0.998811i	$-0.484477\pi$
$67$	0.798029	0.0974948	0.0487474	+	0.998811i	$0.484477\pi$
$68$	4.45187	0.539868
$69$	7.69100	0.925887
$70$	6.79326	0.811950
$71$	−0.897400	−0.106502	−0.0532509	−	0.998581i	$-0.516958\pi$
$71$	−0.897400	−0.106502	−0.0532509	+	0.998581i	$0.516958\pi$
$72$	1.81773	0.214222
$73$	12.1754	1.42502	0.712511	−	0.701661i	$-0.247558\pi$
$73$	12.1754	1.42502	0.712511	+	0.701661i	$0.247558\pi$
$74$	−18.7953	−2.18491
$75$	8.44378	0.975004
$76$	32.7851	3.76070
$77$	−0.254683	−0.0290239
$78$	18.4052	2.08398
$79$	−9.09343	−1.02309	−0.511545	−	0.859256i	$-0.670927\pi$
$79$	−9.09343	−1.02309	−0.511545	+	0.859256i	$0.670927\pi$
$80$	4.06844	0.454865
$81$	−9.79042	−1.08782
$82$	17.0764	1.88577
$83$	−13.2624	−1.45573	−0.727867	−	0.685719i	$-0.759488\pi$
$83$	−13.2624	−1.45573	−0.727867	+	0.685719i	$0.759488\pi$
$84$	−36.7188	−4.00635
$85$	0.588316	0.0638119
$86$	−23.7837	−2.56466
$87$	−12.7570	−1.36770
$88$	−0.348912	−0.0371941
$89$	8.78234	0.930926	0.465463	−	0.885067i	$-0.345888\pi$
$89$	8.78234	0.930926	0.465463	+	0.885067i	$0.345888\pi$
$90$	0.436158	0.0459751
$91$	−18.1552	−1.90318
$92$	−18.8714	−1.96748
$93$	−4.10631	−0.425805
$94$	−2.54005	−0.261986
$95$	4.33256	0.444511
$96$	−9.27083	−0.946200
$97$	−0.738938	−0.0750278	−0.0375139	−	0.999296i	$-0.511944\pi$
$97$	−0.738938	−0.0750278	−0.0375139	+	0.999296i	$0.511944\pi$
$98$	34.7115	3.50639
$99$	−0.0163518	−0.00164342
$100$	−20.7185	−2.07185
$101$	−12.5027	−1.24407	−0.622034	−	0.782990i	$-0.713693\pi$
$101$	−12.5027	−1.24407	−0.622034	+	0.782990i	$0.713693\pi$
$102$	−4.60855	−0.456314
$103$	−19.2245	−1.89424	−0.947122	−	0.320872i	$-0.896024\pi$
$103$	−19.2245	−1.89424	−0.947122	+	0.320872i	$0.896024\pi$
$104$	−24.8723	−2.43893
$105$	−4.85240	−0.473546
$106$	−20.9257	−2.03248
$107$	9.89787	0.956863	0.478432	−	0.878125i	$-0.341205\pi$
$107$	9.89787	0.956863	0.478432	+	0.878125i	$0.341205\pi$
$108$	21.8742	2.10485
$109$	−9.91905	−0.950072	−0.475036	−	0.879966i	$-0.657565\pi$
$109$	−9.91905	−0.950072	−0.475036	+	0.879966i	$0.657565\pi$
$110$	−0.0837201	−0.00798240
$111$	13.4255	1.27429
$112$	31.4370	2.97052
$113$	4.72745	0.444722	0.222361	−	0.974964i	$-0.428624\pi$
$113$	4.72745	0.444722	0.222361	+	0.974964i	$0.428624\pi$
$114$	−33.9389	−3.17867
$115$	−2.49386	−0.232554
$116$	31.3019	2.90631
$117$	−1.16565	−0.107764
$118$	−0.169087	−0.0155657
$119$	4.54595	0.416726
$120$	−6.64771	−0.606850
$121$	−10.9969	−0.999715
$122$	−14.9856	−1.35674
$123$	−12.1976	−1.09982
$124$	10.0756	0.904820
$125$	−5.67954	−0.507993
$126$	3.37022	0.300243
$127$	−15.4897	−1.37449	−0.687243	−	0.726428i	$-0.741179\pi$
$127$	−15.4897	−1.37449	−0.687243	+	0.726428i	$0.741179\pi$
$128$	−12.3831	−1.09453
$129$	16.9886	1.49576
$130$	−5.96801	−0.523429
$131$	8.83262	0.771710	0.385855	−	0.922560i	$-0.373907\pi$
$131$	8.83262	0.771710	0.385855	+	0.922560i	$0.373907\pi$
$132$	0.452522	0.0393870
$133$	33.4779	2.90290
$134$	2.02704	0.175109
$135$	2.89069	0.248791
$136$	6.22788	0.534036
$137$	21.7492	1.85816	0.929080	−	0.369880i	$-0.120601\pi$
$137$	21.7492	1.85816	0.929080	+	0.369880i	$0.120601\pi$
$138$	19.5355	1.66298
$139$	−1.95418	−0.165752	−0.0828759	−	0.996560i	$-0.526410\pi$
$139$	−1.95418	−0.165752	−0.0828759	+	0.996560i	$0.526410\pi$
$140$	11.9063	1.00627
$141$	1.81435	0.152796
$142$	−2.27944	−0.191287
$143$	0.223744	0.0187104
$144$	2.01840	0.168200
$145$	4.13656	0.343523
$146$	30.9261	2.55947
$147$	−24.7943	−2.04500
$148$	−32.9420	−2.70782
$149$	5.98396	0.490225	0.245113	−	0.969495i	$-0.421175\pi$
$149$	5.98396	0.490225	0.245113	+	0.969495i	$0.421175\pi$
$150$	21.4476	1.75119
$151$	−7.72326	−0.628510	−0.314255	−	0.949339i	$-0.601755\pi$
$151$	−7.72326	−0.628510	−0.314255	+	0.949339i	$0.601755\pi$
$152$	45.8642	3.72007
$153$	0.291871	0.0235963
$154$	−0.646909	−0.0521294
$155$	1.33150	0.106949
$156$	32.2582	2.58272
$157$	4.71325	0.376158	0.188079	−	0.982154i	$-0.439774\pi$
$157$	4.71325	0.376158	0.188079	+	0.982154i	$0.439774\pi$
$158$	−23.0978	−1.83756
$159$	14.9471	1.18538
$160$	3.00613	0.237656
$161$	−19.2702	−1.51870
$162$	−24.8682	−1.95383
$163$	−9.98634	−0.782191	−0.391095	−	0.920350i	$-0.627904\pi$
$163$	−9.98634	−0.782191	−0.391095	+	0.920350i	$0.627904\pi$
$164$	29.9292	2.33708
$165$	0.0598010	0.00465550
$166$	−33.6871	−2.61463
$167$	−9.88066	−0.764589	−0.382294	−	0.924041i	$-0.624866\pi$
$167$	−9.88066	−0.764589	−0.382294	+	0.924041i	$0.624866\pi$
$168$	−51.3672	−3.96307
$169$	2.94969	0.226899
$170$	1.49435	0.114612
$171$	2.14943	0.164371
$172$	−41.6849	−3.17845
$173$	8.36003	0.635601	0.317801	−	0.948158i	$-0.397056\pi$
$173$	8.36003	0.635601	0.317801	+	0.948158i	$0.397056\pi$
$174$	−32.4036	−2.45651
$175$	−21.1563	−1.59927
$176$	−0.387430	−0.0292036
$177$	0.120778	0.00907826
$178$	22.3076	1.67203
$179$	7.99276	0.597407	0.298703	−	0.954346i	$-0.403446\pi$
$179$	7.99276	0.597407	0.298703	+	0.954346i	$0.403446\pi$
$180$	0.764441	0.0569780
$181$	−5.12939	−0.381264	−0.190632	−	0.981662i	$-0.561054\pi$
$181$	−5.12939	−0.381264	−0.190632	+	0.981662i	$0.561054\pi$
$182$	−46.1151	−3.41828
$183$	10.7042	0.791277
$184$	−26.3998	−1.94622
$185$	−4.35330	−0.320061
$186$	−10.4303	−0.764783
$187$	−0.0560242	−0.00409690
$188$	−4.45187	−0.324686
$189$	22.3365	1.62474
$190$	11.0049	0.798381
$191$	23.6215	1.70919	0.854595	−	0.519295i	$-0.173805\pi$
$191$	23.6215	1.70919	0.854595	+	0.519295i	$0.173805\pi$
$192$	1.54553	0.111539
$193$	21.7254	1.56383	0.781914	−	0.623387i	$-0.214244\pi$
$193$	21.7254	1.56383	0.781914	+	0.623387i	$0.214244\pi$
$194$	−1.87694	−0.134757
$195$	4.26293	0.305275
$196$	60.8377	4.34555
$197$	−8.26043	−0.588531	−0.294265	−	0.955724i	$-0.595075\pi$
$197$	−8.26043	−0.588531	−0.294265	+	0.955724i	$0.595075\pi$
$198$	−0.0415345	−0.00295173
$199$	−3.50063	−0.248153	−0.124077	−	0.992273i	$-0.539597\pi$
$199$	−3.50063	−0.248153	−0.124077	+	0.992273i	$0.539597\pi$
$200$	−28.9838	−2.04946
$201$	−1.44791	−0.102127
$202$	−31.7576	−2.23446
$203$	31.9634	2.24339
$204$	−8.07725	−0.565521
$205$	3.95516	0.276240
$206$	−48.8312	−3.40223
$207$	−1.23723	−0.0859937
$208$	−27.6181	−1.91497
$209$	−0.412581	−0.0285388
$210$	−12.3254	−0.850531
$211$	15.6985	1.08073	0.540363	−	0.841432i	$-0.318287\pi$
$211$	15.6985	1.08073	0.540363	+	0.841432i	$0.318287\pi$
$212$	−36.6757	−2.51890
$213$	1.62820	0.111562
$214$	25.1411	1.71861
$215$	−5.50868	−0.375689
$216$	30.6007	2.08211
$217$	10.2886	0.698434
$218$	−25.1949	−1.70641
$219$	−22.0904	−1.49273
$220$	−0.146734	−0.00989277
$221$	−3.99371	−0.268646
$222$	34.1014	2.28873
$223$	16.3338	1.09379	0.546896	−	0.837201i	$-0.315809\pi$
$223$	16.3338	1.09379	0.546896	+	0.837201i	$0.315809\pi$
$224$	23.2285	1.55202
$225$	−1.35833	−0.0905555
$226$	12.0080	0.798759
$227$	−11.6436	−0.772816	−0.386408	−	0.922328i	$-0.626284\pi$
$227$	−11.6436	−0.772816	−0.386408	+	0.922328i	$0.626284\pi$
$228$	−59.4836	−3.93940
$229$	25.5016	1.68519	0.842596	−	0.538547i	$-0.181026\pi$
$229$	25.5016	1.68519	0.842596	+	0.538547i	$0.181026\pi$
$230$	−6.33454	−0.417687
$231$	0.462085	0.0304030
$232$	43.7893	2.87491
$233$	11.6979	0.766356	0.383178	−	0.923675i	$-0.374830\pi$
$233$	11.6979	0.766356	0.383178	+	0.923675i	$0.374830\pi$
$234$	−2.96080	−0.193554
$235$	−0.588316	−0.0383775
$236$	−0.296353	−0.0192910
$237$	16.4987	1.07170
$238$	11.5470	0.748478
$239$	9.68148	0.626243	0.313121	−	0.949713i	$-0.398625\pi$
$239$	9.68148	0.626243	0.313121	+	0.949713i	$0.398625\pi$
$240$	−7.38158	−0.476479
$241$	15.7440	1.01416	0.507080	−	0.861899i	$-0.330725\pi$
$241$	15.7440	1.01416	0.507080	+	0.861899i	$0.330725\pi$
$242$	−27.9326	−1.79558
$243$	3.02277	0.193911
$244$	−26.2649	−1.68144
$245$	8.03973	0.513639
$246$	−30.9825	−1.97537
$247$	−29.4110	−1.87138
$248$	14.0952	0.895045
$249$	24.0626	1.52490
$250$	−14.4263	−0.912401
$251$	4.11382	0.259662	0.129831	−	0.991536i	$-0.458556\pi$
$251$	4.11382	0.259662	0.129831	+	0.991536i	$0.458556\pi$
$252$	5.90687	0.372098
$253$	0.237486	0.0149306
$254$	−39.3446	−2.46870
$255$	−1.06741	−0.0668440
$256$	−29.7502	−1.85939
$257$	8.37994	0.522727	0.261363	−	0.965241i	$-0.415828\pi$
$257$	8.37994	0.522727	0.261363	+	0.965241i	$0.415828\pi$
$258$	43.1520	2.68653
$259$	−33.6382	−2.09017
$260$	−10.4599	−0.648698
$261$	2.05220	0.127028
$262$	22.4353	1.38606
$263$	14.5444	0.896846	0.448423	−	0.893821i	$-0.351986\pi$
$263$	14.5444	0.896846	0.448423	+	0.893821i	$0.351986\pi$
$264$	0.633049	0.0389615
$265$	−4.84671	−0.297731
$266$	85.0356	5.21387
$267$	−15.9342	−0.975160
$268$	3.55272	0.217017
$269$	−22.5966	−1.37774	−0.688870	−	0.724885i	$-0.741893\pi$
$269$	−22.5966	−1.37774	−0.688870	+	0.724885i	$0.741893\pi$
$270$	7.34251	0.446851
$271$	15.3566	0.932846	0.466423	−	0.884562i	$-0.345543\pi$
$271$	15.3566	0.932846	0.466423	+	0.884562i	$0.345543\pi$
$272$	6.91540	0.419307
$273$	32.9399	1.99361
$274$	55.2441	3.33742
$275$	0.260730	0.0157226
$276$	34.2393	2.06096
$277$	26.4378	1.58849	0.794247	−	0.607595i	$-0.207866\pi$
$277$	26.4378	1.58849	0.794247	+	0.607595i	$0.207866\pi$
$278$	−4.96373	−0.297705
$279$	0.660574	0.0395475
$280$	16.6562	0.995397
$281$	20.2928	1.21057	0.605285	−	0.796009i	$-0.293059\pi$
$281$	20.2928	1.21057	0.605285	+	0.796009i	$0.293059\pi$
$282$	4.60855	0.274435
$283$	1.87527	0.111473	0.0557367	−	0.998446i	$-0.482249\pi$
$283$	1.87527	0.111473	0.0557367	+	0.998446i	$0.482249\pi$
$284$	−3.99511	−0.237066
$285$	−7.86078	−0.465633
$286$	0.568322	0.0336056
$287$	30.5617	1.80400
$288$	1.49138	0.0878802
$289$	1.00000	0.0588235
$290$	10.5071	0.616997
$291$	1.34069	0.0785928
$292$	54.2033	3.17201
$293$	−1.54784	−0.0904256	−0.0452128	−	0.998977i	$-0.514397\pi$
$293$	−1.54784	−0.0904256	−0.0452128	+	0.998977i	$0.514397\pi$
$294$	−62.9788	−3.67300
$295$	−0.0391632	−0.00228017
$296$	−46.0837	−2.67856
$297$	−0.275275	−0.0159731
$298$	15.1996	0.880488
$299$	16.9292	0.979043
$300$	37.5906	2.17029
$301$	−42.5658	−2.45345
$302$	−19.6175	−1.12886
$303$	22.6843	1.30318
$304$	50.9273	2.92088
$305$	−3.47091	−0.198744
$306$	0.741367	0.0423811
$307$	26.6104	1.51873	0.759367	−	0.650662i	$-0.225509\pi$
$307$	26.6104	1.51873	0.759367	+	0.650662i	$0.225509\pi$
$308$	−1.13382	−0.0646052
$309$	34.8800	1.98425
$310$	3.38208	0.192089
$311$	−14.0396	−0.796113	−0.398056	−	0.917361i	$-0.630315\pi$
$311$	−14.0396	−0.796113	−0.398056	+	0.917361i	$0.630315\pi$
$312$	45.1271	2.55482
$313$	−7.34365	−0.415088	−0.207544	−	0.978226i	$-0.566547\pi$
$313$	−7.34365	−0.415088	−0.207544	+	0.978226i	$0.566547\pi$
$314$	11.9719	0.675614
$315$	0.780595	0.0439816
$316$	−40.4827	−2.27733
$317$	1.23605	0.0694233	0.0347117	−	0.999397i	$-0.488949\pi$
$317$	1.23605	0.0694233	0.0347117	+	0.999397i	$0.488949\pi$
$318$	37.9665	2.12906
$319$	−0.393917	−0.0220551
$320$	−0.501148	−0.0280150
$321$	−17.9582	−1.00233
$322$	−48.9473	−2.72772
$323$	7.36434	0.409763
$324$	−43.5857	−2.42143
$325$	18.5862	1.03098
$326$	−25.3658	−1.40488
$327$	17.9966	0.995216
$328$	41.8690	2.31183
$329$	−4.54595	−0.250626
$330$	0.151898	0.00836169
$331$	−20.7410	−1.14003	−0.570014	−	0.821635i	$-0.693062\pi$
$331$	−20.7410	−1.14003	−0.570014	+	0.821635i	$0.693062\pi$
$332$	−59.0423	−3.24037
$333$	−2.15972	−0.118352
$334$	−25.0974	−1.37327
$335$	0.469494	0.0256512
$336$	−57.0378	−3.11167
$337$	−3.75734	−0.204676	−0.102338	−	0.994750i	$-0.532632\pi$
$337$	−3.75734	−0.204676	−0.102338	+	0.994750i	$0.532632\pi$
$338$	7.49236	0.407531
$339$	−8.57726	−0.465853
$340$	2.61911	0.142041
$341$	−0.126796	−0.00686641
$342$	5.45968	0.295225
$343$	30.3017	1.63614
$344$	−58.3145	−3.14411
$345$	4.52474	0.243604
$346$	21.2349	1.14160
$347$	18.1170	0.972569	0.486284	−	0.873801i	$-0.338352\pi$
$347$	18.1170	0.972569	0.486284	+	0.873801i	$0.338352\pi$
$348$	−56.7927	−3.04441
$349$	−17.3092	−0.926542	−0.463271	−	0.886217i	$-0.653324\pi$
$349$	−17.3092	−0.926542	−0.463271	+	0.886217i	$0.653324\pi$
$350$	−53.7382	−2.87243
$351$	−19.6231	−1.04740
$352$	−0.286268	−0.0152581
$353$	−3.29255	−0.175245	−0.0876225	−	0.996154i	$-0.527927\pi$
$353$	−3.29255	−0.175245	−0.0876225	+	0.996154i	$0.527927\pi$
$354$	0.306783	0.0163054
$355$	−0.527955	−0.0280209
$356$	39.0978	2.07218
$357$	−8.24795	−0.436528
$358$	20.3020	1.07300
$359$	−10.1442	−0.535392	−0.267696	−	0.963503i	$-0.586262\pi$
$359$	−10.1442	−0.535392	−0.267696	+	0.963503i	$0.586262\pi$
$360$	1.06940	0.0563625
$361$	35.2334	1.85439
$362$	−13.0289	−0.684785
$363$	19.9522	1.04722
$364$	−80.8245	−4.23635
$365$	7.16299	0.374928
$366$	27.1892	1.42120
$367$	9.42463	0.491962	0.245981	−	0.969275i	$-0.420890\pi$
$367$	9.42463	0.491962	0.245981	+	0.969275i	$0.420890\pi$
$368$	−29.3142	−1.52811
$369$	1.96220	0.102148
$370$	−11.0576	−0.574858
$371$	−37.4508	−1.94435
$372$	−18.2808	−0.947814
$373$	−37.3921	−1.93609	−0.968045	−	0.250775i	$-0.919315\pi$
$373$	−37.3921	−1.93609	−0.968045	+	0.250775i	$0.919315\pi$
$374$	−0.142305	−0.00735839
$375$	10.3047	0.532131
$376$	−6.22788	−0.321178
$377$	−28.0805	−1.44622
$378$	56.7359	2.91818
$379$	−31.6959	−1.62811	−0.814054	−	0.580789i	$-0.802744\pi$
$379$	−31.6959	−1.62811	−0.814054	+	0.580789i	$0.802744\pi$
$380$	19.2880	0.989453
$381$	28.1037	1.43980
$382$	59.9998	3.06986
$383$	−5.52800	−0.282468	−0.141234	−	0.989976i	$-0.545107\pi$
$383$	−5.52800	−0.282468	−0.141234	+	0.989976i	$0.545107\pi$
$384$	22.4674	1.14653
$385$	−0.149834	−0.00763627
$386$	55.1836	2.80877
$387$	−2.73292	−0.138922
$388$	−3.28966	−0.167007
$389$	6.48337	0.328720	0.164360	−	0.986400i	$-0.447444\pi$
$389$	6.48337	0.328720	0.164360	+	0.986400i	$0.447444\pi$
$390$	10.8281	0.548301
$391$	−4.23898	−0.214374
$392$	85.1080	4.29860
$393$	−16.0255	−0.808378
$394$	−20.9819	−1.05705
$395$	−5.34981	−0.269178
$396$	−0.0727962	−0.00365815
$397$	4.36990	0.219319	0.109659	−	0.993969i	$-0.465024\pi$
$397$	4.36990	0.219319	0.109659	+	0.993969i	$0.465024\pi$
$398$	−8.89179	−0.445705
$399$	−60.7407	−3.04084
$400$	−32.1834	−1.60917
$401$	−18.5251	−0.925100	−0.462550	−	0.886593i	$-0.653065\pi$
$401$	−18.5251	−0.925100	−0.462550	+	0.886593i	$0.653065\pi$
$402$	−3.67776	−0.183430
$403$	−9.03872	−0.450251
$404$	−55.6605	−2.76921
$405$	−5.75987	−0.286210
$406$	81.1888	4.02933
$407$	0.414556	0.0205488
$408$	−11.2996	−0.559411
$409$	18.0064	0.890357	0.445179	−	0.895442i	$-0.353140\pi$
$409$	18.0064	0.890357	0.445179	+	0.895442i	$0.353140\pi$
$410$	10.0463	0.496152
$411$	−39.4607	−1.94645
$412$	−85.5849	−4.21646
$413$	−0.302616	−0.0148908
$414$	−3.14264	−0.154452
$415$	−7.80247	−0.383008
$416$	−20.4067	−1.00052
$417$	3.54558	0.173628
$418$	−1.04798	−0.0512583
$419$	−19.7940	−0.966998	−0.483499	−	0.875345i	$-0.660634\pi$
$419$	−19.7940	−0.966998	−0.483499	+	0.875345i	$0.660634\pi$
$420$	−21.6023	−1.05408
$421$	31.1769	1.51947	0.759734	−	0.650234i	$-0.225329\pi$
$421$	31.1769	1.51947	0.759734	+	0.650234i	$0.225329\pi$
$422$	39.8749	1.94108
$423$	−0.291871	−0.0141912
$424$	−51.3070	−2.49169
$425$	−4.65388	−0.225747
$426$	4.13571	0.200376
$427$	−26.8199	−1.29791
$428$	44.0640	2.12992
$429$	−0.405951	−0.0195995
$430$	−13.9923	−0.674771
$431$	26.5933	1.28095	0.640476	−	0.767978i	$-0.278737\pi$
$431$	26.5933	1.28095	0.640476	+	0.767978i	$0.278737\pi$
$432$	33.9788	1.63480
$433$	−25.5366	−1.22721	−0.613605	−	0.789613i	$-0.710281\pi$
$433$	−25.5366	−1.22721	−0.613605	+	0.789613i	$0.710281\pi$
$434$	26.1335	1.25445
$435$	−7.50518	−0.359846
$436$	−44.1583	−2.11480
$437$	−31.2173	−1.49332
$438$	−56.1109	−2.68108
$439$	−25.7679	−1.22984	−0.614918	−	0.788591i	$-0.710811\pi$
$439$	−25.7679	−1.22984	−0.614918	+	0.788591i	$0.710811\pi$
$440$	−0.205271	−0.00978589
$441$	3.98860	0.189934
$442$	−10.1442	−0.482512
$443$	−24.8117	−1.17884	−0.589419	−	0.807827i	$-0.700643\pi$
$443$	−24.8117	−1.17884	−0.589419	+	0.807827i	$0.700643\pi$
$444$	59.7684	2.83648
$445$	5.16679	0.244930
$446$	41.4887	1.96455
$447$	−10.8570	−0.513519
$448$	−3.87240	−0.182954
$449$	−1.53385	−0.0723870	−0.0361935	−	0.999345i	$-0.511523\pi$
$449$	−1.53385	−0.0723870	−0.0361935	+	0.999345i	$0.511523\pi$
$450$	−3.45024	−0.162646
$451$	−0.376642	−0.0177354
$452$	21.0460	0.989921
$453$	14.0127	0.658374
$454$	−29.5755	−1.38805
$455$	−10.6810	−0.500733
$456$	−83.2137	−3.89684
$457$	10.1028	0.472589	0.236295	−	0.971681i	$-0.424067\pi$
$457$	10.1028	0.472589	0.236295	+	0.971681i	$0.424067\pi$
$458$	64.7753	3.02675
$459$	4.91350	0.229342
$460$	−11.1023	−0.517649
$461$	−3.73710	−0.174054	−0.0870270	−	0.996206i	$-0.527737\pi$
$461$	−3.73710	−0.174054	−0.0870270	+	0.996206i	$0.527737\pi$
$462$	1.17372	0.0546064
$463$	−4.98366	−0.231610	−0.115805	−	0.993272i	$-0.536945\pi$
$463$	−4.98366	−0.231610	−0.115805	+	0.993272i	$0.536945\pi$
$464$	48.6234	2.25729
$465$	−2.41581	−0.112031
$466$	29.7133	1.37644
$467$	−40.0596	−1.85374	−0.926869	−	0.375386i	$-0.877510\pi$
$467$	−40.0596	−1.85374	−0.926869	+	0.375386i	$0.877510\pi$
$468$	−5.18930	−0.239876
$469$	3.62780	0.167516
$470$	−1.49435	−0.0689294
$471$	−8.55150	−0.394032
$472$	−0.414579	−0.0190826
$473$	0.524581	0.0241203
$474$	41.9075	1.92487
$475$	−34.2728	−1.57254
$476$	20.2380	0.927606
$477$	−2.40451	−0.110095
$478$	24.5915	1.12479
$479$	37.6724	1.72130	0.860648	−	0.509200i	$-0.170059\pi$
$479$	37.6724	1.72130	0.860648	+	0.509200i	$0.170059\pi$
$480$	−5.45418	−0.248948
$481$	29.5518	1.34745
$482$	39.9906	1.82152
$483$	34.9629	1.59087
$484$	−48.9566	−2.22530
$485$	−0.434729	−0.0197400
$486$	7.67801	0.348281
$487$	−9.18073	−0.416019	−0.208009	−	0.978127i	$-0.566698\pi$
$487$	−9.18073	−0.416019	−0.208009	+	0.978127i	$0.566698\pi$
$488$	−36.7428	−1.66327
$489$	18.1187	0.819357
$490$	20.4213	0.922542
$491$	−7.67005	−0.346145	−0.173072	−	0.984909i	$-0.555369\pi$
$491$	−7.67005	−0.346145	−0.173072	+	0.984909i	$0.555369\pi$
$492$	−54.3021	−2.44813
$493$	7.03119	0.316669
$494$	−74.7055	−3.36116
$495$	−0.00962005	−0.000432389 0
$496$	15.6512	0.702760
$497$	−4.07953	−0.182992
$498$	61.1202	2.73886
$499$	−17.5643	−0.786286	−0.393143	−	0.919477i	$-0.628612\pi$
$499$	−17.5643	−0.786286	−0.393143	+	0.919477i	$0.628612\pi$
$500$	−25.2846	−1.13076
$501$	17.9270	0.800919
$502$	10.4493	0.466376
$503$	27.6446	1.23261	0.616306	−	0.787507i	$-0.288628\pi$
$503$	27.6446	1.23261	0.616306	+	0.787507i	$0.288628\pi$
$504$	8.26333	0.368078
$505$	−7.35556	−0.327318
$506$	0.603226	0.0268167
$507$	−5.35177	−0.237680
$508$	−68.9580	−3.05952
$509$	13.9321	0.617530	0.308765	−	0.951138i	$-0.400084\pi$
$509$	13.9321	0.617530	0.308765	+	0.951138i	$0.400084\pi$
$510$	−2.71128	−0.120058
$511$	55.3487	2.44848
$512$	−50.8007	−2.24510
$513$	36.1846	1.59759
$514$	21.2855	0.938863
$515$	−11.3101	−0.498382
$516$	75.6311	3.32947
$517$	0.0560242	0.00246394
$518$	−85.4427	−3.75414
$519$	−15.1680	−0.665802
$520$	−14.6328	−0.641690
$521$	33.9964	1.48941	0.744704	−	0.667395i	$-0.232591\pi$
$521$	33.9964	1.48941	0.744704	+	0.667395i	$0.232591\pi$
$522$	5.21269	0.228153
$523$	5.87014	0.256683	0.128342	−	0.991730i	$-0.459035\pi$
$523$	5.87014	0.256683	0.128342	+	0.991730i	$0.459035\pi$
$524$	39.3217	1.71777
$525$	38.3850	1.67526
$526$	36.9435	1.61081
$527$	2.26324	0.0985883
$528$	0.702934	0.0305913
$529$	−5.03106	−0.218742
$530$	−12.3109	−0.534752
$531$	−0.0194293	−0.000843162 0
$532$	149.039	6.46167
$533$	−26.8491	−1.16296
$534$	−40.4738	−1.75147
$535$	5.82308	0.251754
$536$	4.97003	0.214672
$537$	−14.5017	−0.625793
$538$	−57.3966	−2.47454
$539$	−0.765608	−0.0329771
$540$	12.8690	0.553793
$541$	19.1645	0.823945	0.411972	−	0.911196i	$-0.364840\pi$
$541$	19.1645	0.823945	0.411972	+	0.911196i	$0.364840\pi$
$542$	39.0065	1.67547
$543$	9.30651	0.399381
$544$	5.10972	0.219077
$545$	−5.83554	−0.249967
$546$	83.6690	3.58070
$547$	13.4998	0.577208	0.288604	−	0.957449i	$-0.406809\pi$
$547$	13.4998	0.577208	0.288604	+	0.957449i	$0.406809\pi$
$548$	96.8246	4.13614
$549$	−1.72196	−0.0734915
$550$	0.662269	0.0282392
$551$	51.7800	2.20590
$552$	47.8986	2.03870
$553$	−41.3383	−1.75788
$554$	67.1534	2.85308
$555$	7.89841	0.335269
$556$	−8.69977	−0.368952
$557$	−28.7177	−1.21681	−0.608405	−	0.793627i	$-0.708190\pi$
$557$	−28.7177	−1.21681	−0.608405	+	0.793627i	$0.708190\pi$
$558$	1.67789	0.0710308
$559$	37.3949	1.58164
$560$	18.4949	0.781553
$561$	0.101648	0.00429157
$562$	51.5449	2.17429
$563$	−30.6578	−1.29207	−0.646035	−	0.763307i	$-0.723574\pi$
$563$	−30.6578	−1.29207	−0.646035	+	0.763307i	$0.723574\pi$
$564$	8.07725	0.340114
$565$	2.78124	0.117008
$566$	4.76329	0.200216
$567$	−44.5068	−1.86911
$568$	−5.58889	−0.234505
$569$	34.5766	1.44952	0.724762	−	0.688999i	$-0.241949\pi$
$569$	34.5766	1.44952	0.724762	+	0.688999i	$0.241949\pi$
$570$	−19.9668	−0.836318
$571$	−20.4470	−0.855679	−0.427839	−	0.903855i	$-0.640725\pi$
$571$	−20.4470	−0.855679	−0.427839	+	0.903855i	$0.640725\pi$
$572$	0.996080	0.0416482
$573$	−42.8577	−1.79040
$574$	77.6283	3.24014
$575$	19.7277	0.822702
$576$	−0.248626	−0.0103594
$577$	1.61857	0.0673821	0.0336910	−	0.999432i	$-0.489274\pi$
$577$	1.61857	0.0673821	0.0336910	+	0.999432i	$0.489274\pi$
$578$	2.54005	0.105652
$579$	−39.4175	−1.63813
$580$	18.4154	0.764659
$581$	−60.2900	−2.50125
$582$	3.40543	0.141160
$583$	0.461543	0.0191152
$584$	75.8268	3.13774
$585$	−0.685769	−0.0283530
$586$	−3.93159	−0.162412
$587$	−10.2797	−0.424287	−0.212144	−	0.977238i	$-0.568044\pi$
$587$	−10.2797	−0.424287	−0.212144	+	0.977238i	$0.568044\pi$
$588$	−110.381	−4.55203
$589$	16.6673	0.686763
$590$	−0.0994767	−0.00409539
$591$	14.9873	0.616496
$592$	−51.1711	−2.10312
$593$	31.0143	1.27360	0.636802	−	0.771028i	$-0.280257\pi$
$593$	31.0143	1.27360	0.636802	+	0.771028i	$0.280257\pi$
$594$	−0.699213	−0.0286891
$595$	2.67446	0.109642
$596$	26.6398	1.09121
$597$	6.35137	0.259944
$598$	43.0011	1.75845
$599$	−8.49857	−0.347242	−0.173621	−	0.984813i	$-0.555547\pi$
$599$	−8.49857	−0.347242	−0.173621	+	0.984813i	$0.555547\pi$
$600$	52.5868	2.14685
$601$	−12.6823	−0.517322	−0.258661	−	0.965968i	$-0.583281\pi$
$601$	−12.6823	−0.517322	−0.258661	+	0.965968i	$0.583281\pi$
$602$	−108.119	−4.40662
$603$	0.232921	0.00948529
$604$	−34.3829	−1.39902
$605$	−6.46963	−0.263028
$606$	57.6194	2.34063
$607$	29.8737	1.21254	0.606268	−	0.795261i	$-0.292666\pi$
$607$	29.8737	1.21254	0.606268	+	0.795261i	$0.292666\pi$
$608$	37.6297	1.52609
$609$	−57.9929	−2.34999
$610$	−8.81630	−0.356962
$611$	3.99371	0.161568
$612$	1.29937	0.0525239
$613$	23.0588	0.931338	0.465669	−	0.884959i	$-0.345814\pi$
$613$	23.0588	0.931338	0.465669	+	0.884959i	$0.345814\pi$
$614$	67.5918	2.72778
$615$	−7.17605	−0.289366
$616$	−1.58614	−0.0639072
$617$	−37.6011	−1.51376	−0.756882	−	0.653551i	$-0.773278\pi$
$617$	−37.6011	−1.51376	−0.756882	+	0.653551i	$0.773278\pi$
$618$	88.5970	3.56389
$619$	21.2557	0.854339	0.427170	−	0.904172i	$-0.359511\pi$
$619$	21.2557	0.854339	0.427170	+	0.904172i	$0.359511\pi$
$620$	5.92767	0.238061
$621$	−20.8282	−0.835807
$622$	−35.6613	−1.42989
$623$	39.9241	1.59952
$624$	50.1089	2.00596
$625$	19.9281	0.797122
$626$	−18.6533	−0.745534
$627$	0.748568	0.0298949
$628$	20.9828	0.837304
$629$	−7.39959	−0.295041
$630$	1.98275	0.0789948
$631$	−17.9320	−0.713861	−0.356931	−	0.934131i	$-0.616177\pi$
$631$	−17.9320	−0.713861	−0.356931	+	0.934131i	$0.616177\pi$
$632$	−56.6327	−2.25273
$633$	−28.4825	−1.13208
$634$	3.13963	0.124690
$635$	−9.11283	−0.361632
$636$	66.5427	2.63859
$637$	−54.5766	−2.16240
$638$	−1.00057	−0.0396129
$639$	−0.261925	−0.0103616
$640$	−7.28521	−0.287973
$641$	42.2256	1.66781	0.833906	−	0.551907i	$-0.186100\pi$
$641$	42.2256	1.66781	0.833906	+	0.551907i	$0.186100\pi$
$642$	−45.6148	−1.80027
$643$	−15.0887	−0.595040	−0.297520	−	0.954716i	$-0.596160\pi$
$643$	−15.0887	−0.595040	−0.297520	+	0.954716i	$0.596160\pi$
$644$	−85.7883	−3.38053
$645$	9.99468	0.393540
$646$	18.7058	0.735970
$647$	37.6284	1.47932	0.739662	−	0.672979i	$-0.234986\pi$
$647$	37.6284	1.47932	0.739662	+	0.672979i	$0.234986\pi$
$648$	−60.9735	−2.39527
$649$	0.00372944	0.000146393 0
$650$	47.2100	1.85173
$651$	−18.6671	−0.731621
$652$	−44.4579	−1.74110
$653$	−6.07073	−0.237566	−0.118783	−	0.992920i	$-0.537899\pi$
$653$	−6.07073	−0.237566	−0.118783	+	0.992920i	$0.537899\pi$
$654$	45.7124	1.78750
$655$	5.19638	0.203039
$656$	46.4911	1.81517
$657$	3.55364	0.138641
$658$	−11.5470	−0.450147
$659$	16.0698	0.625990	0.312995	−	0.949755i	$-0.398668\pi$
$659$	16.0698	0.625990	0.312995	+	0.949755i	$0.398668\pi$
$660$	0.266226	0.0103628
$661$	23.4600	0.912490	0.456245	−	0.889854i	$-0.349194\pi$
$661$	23.4600	0.912490	0.456245	+	0.889854i	$0.349194\pi$
$662$	−52.6833	−2.04759
$663$	7.24599	0.281411
$664$	−82.5963	−3.20536
$665$	19.6956	0.763762
$666$	−5.48581	−0.212571
$667$	−29.8050	−1.15406
$668$	−43.9874	−1.70192
$669$	−29.6352	−1.14576
$670$	1.19254	0.0460718
$671$	0.330528	0.0127599
$672$	−42.1447	−1.62577
$673$	−21.6719	−0.835390	−0.417695	−	0.908587i	$-0.637162\pi$
$673$	−21.6719	−0.835390	−0.417695	+	0.908587i	$0.637162\pi$
$674$	−9.54385	−0.367615
$675$	−22.8668	−0.880145
$676$	13.1316	0.505062
$677$	7.55027	0.290180	0.145090	−	0.989418i	$-0.453653\pi$
$677$	7.55027	0.290180	0.145090	+	0.989418i	$0.453653\pi$
$678$	−21.7867	−0.836713
$679$	−3.35918	−0.128913
$680$	3.66396	0.140506
$681$	21.1257	0.809537
$682$	−0.322069	−0.0123327
$683$	25.9841	0.994253	0.497127	−	0.867678i	$-0.334388\pi$
$683$	25.9841	0.994253	0.497127	+	0.867678i	$0.334388\pi$
$684$	9.56900	0.365880
$685$	12.7954	0.488887
$686$	76.9680	2.93865
$687$	−46.2688	−1.76527
$688$	−64.7521	−2.46865
$689$	32.9013	1.25344
$690$	11.4931	0.437534
$691$	−22.0863	−0.840201	−0.420101	−	0.907477i	$-0.638005\pi$
$691$	−22.0863	−0.840201	−0.420101	+	0.907477i	$0.638005\pi$
$692$	37.2177	1.41481
$693$	−0.0743346	−0.00282374
$694$	46.0180	1.74682
$695$	−1.14968	−0.0436098
$696$	−79.4493	−3.01152
$697$	6.72284	0.254646
$698$	−43.9663	−1.66415
$699$	−21.2241	−0.802770
$700$	−94.1851	−3.55986
$701$	−1.62200	−0.0612623	−0.0306311	−	0.999531i	$-0.509752\pi$
$701$	−1.62200	−0.0612623	−0.0306311	+	0.999531i	$0.509752\pi$
$702$	−49.8436	−1.88123
$703$	−54.4931	−2.05524
$704$	0.0477234	0.00179864
$705$	1.06741	0.0402011
$706$	−8.36326	−0.314755
$707$	−56.8368	−2.13757
$708$	0.537689	0.0202076
$709$	−30.9591	−1.16269	−0.581346	−	0.813656i	$-0.697474\pi$
$709$	−30.9591	−1.16269	−0.581346	+	0.813656i	$0.697474\pi$
$710$	−1.34103	−0.0503281
$711$	−2.65410	−0.0995367
$712$	54.6953	2.04979
$713$	−9.59383	−0.359292
$714$	−20.9502	−0.784042
$715$	0.131632	0.00492278
$716$	35.5827	1.32979
$717$	−17.5656	−0.655999
$718$	−25.7669	−0.961611
$719$	−26.7876	−0.999009	−0.499504	−	0.866311i	$-0.666485\pi$
$719$	−26.7876	−0.999009	−0.499504	+	0.866311i	$0.666485\pi$
$720$	1.18746	0.0442540
$721$	−87.3935	−3.25471
$722$	89.4948	3.33065
$723$	−28.5652	−1.06235
$724$	−22.8354	−0.848670
$725$	−32.7223	−1.21528
$726$	50.6796	1.88090
$727$	−5.20449	−0.193024	−0.0965119	−	0.995332i	$-0.530769\pi$
$727$	−5.20449	−0.193024	−0.0965119	+	0.995332i	$0.530769\pi$
$728$	−113.068	−4.19059
$729$	23.8869	0.884700
$730$	18.1944	0.673404
$731$	−9.36347	−0.346320
$732$	47.6537	1.76133
$733$	−10.8548	−0.400931	−0.200466	−	0.979701i	$-0.564246\pi$
$733$	−10.8548	−0.400931	−0.200466	+	0.979701i	$0.564246\pi$
$734$	23.9391	0.883607
$735$	−14.5869	−0.538046
$736$	−21.6600	−0.798398
$737$	−0.0447090	−0.00164688
$738$	4.98409	0.183467
$739$	50.7176	1.86568	0.932839	−	0.360294i	$-0.117324\pi$
$739$	50.7176	1.86568	0.932839	+	0.360294i	$0.117324\pi$
$740$	−19.3803	−0.712435
$741$	53.3619	1.96030
$742$	−95.1270	−3.49222
$743$	−23.0422	−0.845335	−0.422667	−	0.906285i	$-0.638906\pi$
$743$	−23.0422	−0.845335	−0.422667	+	0.906285i	$0.638906\pi$
$744$	−25.5736	−0.937574
$745$	3.52046	0.128980
$746$	−94.9780	−3.47739
$747$	−3.87090	−0.141629
$748$	−0.249413	−0.00911943
$749$	44.9952	1.64409
$750$	26.1744	0.955755
$751$	44.3120	1.61697	0.808485	−	0.588517i	$-0.200288\pi$
$751$	44.3120	1.61697	0.808485	+	0.588517i	$0.200288\pi$
$752$	−6.91540	−0.252179
$753$	−7.46392	−0.272000
$754$	−71.3259	−2.59754
$755$	−4.54372	−0.165363
$756$	99.4392	3.61657
$757$	2.79052	0.101423	0.0507115	−	0.998713i	$-0.483851\pi$
$757$	2.79052	0.101423	0.0507115	+	0.998713i	$0.483851\pi$
$758$	−80.5092	−2.92423
$759$	−0.430882	−0.0156400
$760$	26.9826	0.978763
$761$	35.0132	1.26923	0.634613	−	0.772830i	$-0.281159\pi$
$761$	35.0132	1.26923	0.634613	+	0.772830i	$0.281159\pi$
$762$	71.3849	2.58600
$763$	−45.0915	−1.63242
$764$	105.160	3.80454
$765$	0.171712	0.00620827
$766$	−14.0414	−0.507337
$767$	0.265854	0.00959944
$768$	53.9773	1.94774
$769$	−48.8236	−1.76062	−0.880312	−	0.474395i	$-0.842667\pi$
$769$	−48.8236	−1.76062	−0.880312	+	0.474395i	$0.842667\pi$
$770$	−0.380587	−0.0137154
$771$	−15.2042	−0.547565
$772$	96.7185	3.48098
$773$	51.9508	1.86854	0.934271	−	0.356564i	$-0.116052\pi$
$773$	51.9508	1.86854	0.934271	+	0.356564i	$0.116052\pi$
$774$	−6.94177	−0.249517
$775$	−10.5329	−0.378351
$776$	−4.60201	−0.165203
$777$	61.0314	2.18949
$778$	16.4681	0.590410
$779$	49.5093	1.77385
$780$	18.9780	0.679522
$781$	0.0502761	0.00179902
$782$	−10.7672	−0.385035
$783$	34.5477	1.23463
$784$	94.5034	3.37512
$785$	2.77288	0.0989685
$786$	−40.7056	−1.45192
$787$	37.5483	1.33845	0.669227	−	0.743058i	$-0.266625\pi$
$787$	37.5483	1.33845	0.669227	+	0.743058i	$0.266625\pi$
$788$	−36.7743	−1.31003
$789$	−26.3886	−0.939461
$790$	−13.5888	−0.483468
$791$	21.4908	0.764124
$792$	−0.101837	−0.00361863
$793$	23.5618	0.836705
$794$	11.0998	0.393916
$795$	8.79364	0.311878
$796$	−15.5843	−0.552373
$797$	6.99027	0.247608	0.123804	−	0.992307i	$-0.460491\pi$
$797$	6.99027	0.247608	0.123804	+	0.992307i	$0.460491\pi$
$798$	−154.284	−5.46161
$799$	−1.00000	−0.0353775
$800$	−23.7800	−0.840751
$801$	2.56331	0.0905700
$802$	−47.0548	−1.66156
$803$	−0.682117	−0.0240714
$804$	−6.44588	−0.227329
$805$	−11.3370	−0.399575
$806$	−22.9588	−0.808690
$807$	40.9982	1.44320
$808$	−77.8654	−2.73930
$809$	−21.2450	−0.746935	−0.373468	−	0.927643i	$-0.621831\pi$
$809$	−21.2450	−0.746935	−0.373468	+	0.927643i	$0.621831\pi$
$810$	−14.6304	−0.514059
$811$	41.3445	1.45180	0.725901	−	0.687799i	$-0.241423\pi$
$811$	41.3445	1.45180	0.725901	+	0.687799i	$0.241423\pi$
$812$	142.297	4.99364
$813$	−27.8622	−0.977171
$814$	1.05300	0.0369075
$815$	−5.87513	−0.205797
$816$	−12.5470	−0.439231
$817$	−68.9557	−2.41245
$818$	45.7371	1.59916
$819$	−5.29897	−0.185161
$820$	17.6078	0.614893
$821$	−13.3190	−0.464835	−0.232417	−	0.972616i	$-0.574664\pi$
$821$	−13.3190	−0.464835	−0.232417	+	0.972616i	$0.574664\pi$
$822$	−100.232	−3.49600
$823$	−13.6721	−0.476580	−0.238290	−	0.971194i	$-0.576587\pi$
$823$	−13.6721	−0.476580	−0.238290	+	0.971194i	$0.576587\pi$
$824$	−119.728	−4.17091
$825$	−0.473056	−0.0164697
$826$	−0.768661	−0.0267451
$827$	44.9658	1.56362	0.781808	−	0.623520i	$-0.214298\pi$
$827$	44.9658	1.56362	0.781808	+	0.623520i	$0.214298\pi$
$828$	−5.50800	−0.191416
$829$	25.0742	0.870861	0.435431	−	0.900222i	$-0.356596\pi$
$829$	25.0742	0.870861	0.435431	+	0.900222i	$0.356596\pi$
$830$	−19.8187	−0.687916
$831$	−47.9675	−1.66397
$832$	3.40198	0.117942
$833$	13.6657	0.473487
$834$	9.00595	0.311851
$835$	−5.81296	−0.201166
$836$	−1.83676	−0.0635256
$837$	11.1204	0.384378
$838$	−50.2777	−1.73681
$839$	42.6648	1.47295	0.736476	−	0.676464i	$-0.236488\pi$
$839$	42.6648	1.47295	0.736476	+	0.676464i	$0.236488\pi$
$840$	−30.2202	−1.04269
$841$	20.4376	0.704744
$842$	79.1909	2.72910
$843$	−36.8183	−1.26809
$844$	69.8875	2.40563
$845$	1.73535	0.0596978
$846$	−0.741367	−0.0254887
$847$	−49.9912	−1.71772
$848$	−56.9710	−1.95639
$849$	−3.40240	−0.116770
$850$	−11.8211	−0.405461
$851$	31.3667	1.07524
$852$	7.24853	0.248330
$853$	−2.73523	−0.0936524	−0.0468262	−	0.998903i	$-0.514911\pi$
$853$	−2.73523	−0.0936524	−0.0468262	+	0.998903i	$0.514911\pi$
$854$	−68.1240	−2.33116
$855$	1.26455	0.0432466
$856$	61.6427	2.10690
$857$	39.8834	1.36239	0.681196	−	0.732101i	$-0.261460\pi$
$857$	39.8834	1.36239	0.681196	+	0.732101i	$0.261460\pi$
$858$	−1.03114	−0.0352024
$859$	−18.0399	−0.615512	−0.307756	−	0.951465i	$-0.599578\pi$
$859$	−18.0399	−0.615512	−0.307756	+	0.951465i	$0.599578\pi$
$860$	−24.5239	−0.836259
$861$	−55.4496	−1.88972
$862$	67.5483	2.30070
$863$	−20.1977	−0.687536	−0.343768	−	0.939055i	$-0.611703\pi$
$863$	−20.1977	−0.687536	−0.343768	+	0.939055i	$0.611703\pi$
$864$	25.1066	0.854144
$865$	4.91834	0.167229
$866$	−64.8643	−2.20418
$867$	−1.81435	−0.0616186
$868$	45.8034	1.55467
$869$	0.509452	0.0172820
$870$	−19.0635	−0.646315
$871$	−3.18709	−0.107991
$872$	−61.7746	−2.09195
$873$	−0.215674	−0.00729947
$874$	−79.2935	−2.68214
$875$	−25.8189	−0.872838
$876$	−98.3438	−3.32273
$877$	−26.2170	−0.885284	−0.442642	−	0.896698i	$-0.645959\pi$
$877$	−26.2170	−0.885284	−0.442642	+	0.896698i	$0.645959\pi$
$878$	−65.4519	−2.20889
$879$	2.80832	0.0947223
$880$	−0.227931	−0.00768356
$881$	−2.41044	−0.0812097	−0.0406048	−	0.999175i	$-0.512928\pi$
$881$	−2.41044	−0.0812097	−0.0406048	+	0.999175i	$0.512928\pi$
$882$	10.1313	0.341137
$883$	−10.8787	−0.366097	−0.183048	−	0.983104i	$-0.558596\pi$
$883$	−10.8787	−0.366097	−0.183048	+	0.983104i	$0.558596\pi$
$884$	−17.7795	−0.597988
$885$	0.0710559	0.00238852
$886$	−63.0230	−2.11730
$887$	33.1803	1.11408	0.557042	−	0.830484i	$-0.311936\pi$
$887$	33.1803	1.11408	0.557042	+	0.830484i	$0.311936\pi$
$888$	83.6120	2.80584
$889$	−70.4153	−2.36165
$890$	13.1239	0.439915
$891$	0.548501	0.0183755
$892$	72.7159	2.43471
$893$	−7.36434	−0.246438
$894$	−27.5774	−0.922325
$895$	4.70227	0.157180
$896$	−56.2931	−1.88062
$897$	−30.7156	−1.02556
$898$	−3.89607	−0.130013
$899$	15.9133	0.530737
$900$	−6.04712	−0.201571
$901$	−8.23828	−0.274457
$902$	−0.956691	−0.0318543
$903$	77.2294	2.57003
$904$	29.4420	0.979226
$905$	−3.01770	−0.100312
$906$	35.5930	1.18250
$907$	−35.1380	−1.16674	−0.583370	−	0.812207i	$-0.698266\pi$
$907$	−35.1380	−1.16674	−0.583370	+	0.812207i	$0.698266\pi$
$908$	−51.8360	−1.72024
$909$	−3.64918	−0.121036
$910$	−27.1303	−0.899360
$911$	−9.48624	−0.314293	−0.157147	−	0.987575i	$-0.550230\pi$
$911$	−9.48624	−0.314293	−0.157147	+	0.987575i	$0.550230\pi$
$912$	−92.4000	−3.05967
$913$	0.743014	0.0245902
$914$	25.6617	0.848812
$915$	6.29746	0.208187
$916$	113.530	3.75113
$917$	40.1526	1.32596
$918$	12.4805	0.411919
$919$	−21.2377	−0.700567	−0.350283	−	0.936644i	$-0.613915\pi$
$919$	−21.2377	−0.700567	−0.350283	+	0.936644i	$0.613915\pi$
$920$	−15.5315	−0.512057
$921$	−48.2806	−1.59090
$922$	−9.49242	−0.312616
$923$	3.58395	0.117967
$924$	2.05714	0.0676750
$925$	34.4368	1.13228
$926$	−12.6588	−0.415993
$927$	−5.61106	−0.184292
$928$	35.9274	1.17937
$929$	51.4251	1.68720	0.843602	−	0.536970i	$-0.180431\pi$
$929$	51.4251	1.68720	0.843602	+	0.536970i	$0.180431\pi$
$930$	−6.13629	−0.201217
$931$	100.638	3.29829
$932$	52.0776	1.70586
$933$	25.4728	0.833941
$934$	−101.753	−3.32948
$935$	−0.0329600	−0.00107791
$936$	−7.25950	−0.237284
$937$	−31.6880	−1.03520	−0.517602	−	0.855622i	$-0.673175\pi$
$937$	−31.6880	−1.03520	−0.517602	+	0.855622i	$0.673175\pi$
$938$	9.21480	0.300874
$939$	13.3240	0.434811
$940$	−2.61911	−0.0854259
$941$	19.8865	0.648282	0.324141	−	0.946009i	$-0.394925\pi$
$941$	19.8865	0.648282	0.324141	+	0.946009i	$0.394925\pi$
$942$	−21.7212	−0.707717
$943$	−28.4980	−0.928022
$944$	−0.460346	−0.0149830
$945$	13.1409	0.427475
$946$	1.33246	0.0433221
$947$	−6.71524	−0.218216	−0.109108	−	0.994030i	$-0.534799\pi$
$947$	−6.71524	−0.218216	−0.109108	+	0.994030i	$0.534799\pi$
$948$	73.4499	2.38554
$949$	−48.6250	−1.57843
$950$	−87.0546	−2.82442
$951$	−2.24262	−0.0727221
$952$	28.3116	0.917584
$953$	−3.82632	−0.123947	−0.0619733	−	0.998078i	$-0.519739\pi$
$953$	−3.82632	−0.123947	−0.0619733	+	0.998078i	$0.519739\pi$
$954$	−6.10759	−0.197740
$955$	13.8969	0.449693
$956$	43.1007	1.39398
$957$	0.714704	0.0231031
$958$	95.6899	3.09160
$959$	98.8707	3.19270
$960$	0.909259	0.0293462
$961$	−25.8777	−0.834766
$962$	75.0631	2.42013
$963$	2.88890	0.0930935
$964$	70.0902	2.25745
$965$	12.7814	0.411448
$966$	88.8075	2.85734
$967$	−8.81760	−0.283555	−0.141777	−	0.989899i	$-0.545282\pi$
$967$	−8.81760	−0.283555	−0.141777	+	0.989899i	$0.545282\pi$
$968$	−68.4871	−2.20126
$969$	−13.3615	−0.429233
$970$	−1.10424	−0.0354549
$971$	−51.2783	−1.64560	−0.822799	−	0.568332i	$-0.807589\pi$
$971$	−51.2783	−1.64560	−0.822799	+	0.568332i	$0.807589\pi$
$972$	13.4570	0.431633
$973$	−8.88362	−0.284796
$974$	−23.3195	−0.747206
$975$	−33.7220	−1.07997
$976$	−40.7990	−1.30595
$977$	−51.0942	−1.63465	−0.817325	−	0.576177i	$-0.804544\pi$
$977$	−51.0942	−1.63465	−0.817325	+	0.576177i	$0.804544\pi$
$978$	46.0225	1.47164
$979$	−0.492024	−0.0157252
$980$	35.7918	1.14333
$981$	−2.89508	−0.0924328
$982$	−19.4823	−0.621706
$983$	0.0957544	0.00305409	0.00152705	−	0.999999i	$-0.499514\pi$
$983$	0.0957544	0.00305409	0.00152705	+	0.999999i	$0.499514\pi$
$984$	−75.9651	−2.42168
$985$	−4.85974	−0.154844
$986$	17.8596	0.568765
$987$	8.24795	0.262535
$988$	−130.934	−4.16556
$989$	39.6915	1.26212
$990$	−0.0244354	−0.000776609 0
$991$	−18.2404	−0.579424	−0.289712	−	0.957114i	$-0.593560\pi$
$991$	−18.2404	−0.579424	−0.289712	+	0.957114i	$0.593560\pi$
$992$	11.5645	0.367174
$993$	37.6315	1.19420
$994$	−10.3622	−0.328670
$995$	−2.05948	−0.0652899
$996$	107.123	3.39434
$997$	16.9248	0.536015	0.268007	−	0.963417i	$-0.413635\pi$
$997$	16.9248	0.536015	0.268007	+	0.963417i	$0.413635\pi$
$998$	−44.6143	−1.41224
$999$	−36.3579	−1.15031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.f.1.16	✓	17
3.2	odd	2		7191.2.a.y.1.2		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.f.1.16	✓	17	1.1	even	1	trivial
7191.2.a.y.1.2		17	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q+2.54005 q^{2} -1.81435 q^{3} +4.45187 q^{4} +0.588316 q^{5} -4.60855 q^{6} +4.54595 q^{7} +6.22788 q^{8} +0.291871 q^{9} +O(q^{10})\)	\(q+2.54005 q^{2} -1.81435 q^{3} +4.45187 q^{4} +0.588316 q^{5} -4.60855 q^{6} +4.54595 q^{7} +6.22788 q^{8} +0.291871 q^{9} +1.49435 q^{10} -0.0560242 q^{11} -8.07725 q^{12} -3.99371 q^{13} +11.5470 q^{14} -1.06741 q^{15} +6.91540 q^{16} +1.00000 q^{17} +0.741367 q^{18} +7.36434 q^{19} +2.61911 q^{20} -8.24795 q^{21} -0.142305 q^{22} -4.23898 q^{23} -11.2996 q^{24} -4.65388 q^{25} -10.1442 q^{26} +4.91350 q^{27} +20.2380 q^{28} +7.03119 q^{29} -2.71128 q^{30} +2.26324 q^{31} +5.10972 q^{32} +0.101648 q^{33} +2.54005 q^{34} +2.67446 q^{35} +1.29937 q^{36} -7.39959 q^{37} +18.7058 q^{38} +7.24599 q^{39} +3.66396 q^{40} +6.72284 q^{41} -20.9502 q^{42} -9.36347 q^{43} -0.249413 q^{44} +0.171712 q^{45} -10.7672 q^{46} -1.00000 q^{47} -12.5470 q^{48} +13.6657 q^{49} -11.8211 q^{50} -1.81435 q^{51} -17.7795 q^{52} -8.23828 q^{53} +12.4805 q^{54} -0.0329600 q^{55} +28.3116 q^{56} -13.3615 q^{57} +17.8596 q^{58} -0.0665683 q^{59} -4.75198 q^{60} -5.89974 q^{61} +5.74875 q^{62} +1.32683 q^{63} -0.851835 q^{64} -2.34956 q^{65} +0.258190 q^{66} +0.798029 q^{67} +4.45187 q^{68} +7.69100 q^{69} +6.79326 q^{70} -0.897400 q^{71} +1.81773 q^{72} +12.1754 q^{73} -18.7953 q^{74} +8.44378 q^{75} +32.7851 q^{76} -0.254683 q^{77} +18.4052 q^{78} -9.09343 q^{79} +4.06844 q^{80} -9.79042 q^{81} +17.0764 q^{82} -13.2624 q^{83} -36.7188 q^{84} +0.588316 q^{85} -23.7837 q^{86} -12.7570 q^{87} -0.348912 q^{88} +8.78234 q^{89} +0.436158 q^{90} -18.1552 q^{91} -18.8714 q^{92} -4.10631 q^{93} -2.54005 q^{94} +4.33256 q^{95} -9.27083 q^{96} -0.738938 q^{97} +34.7115 q^{98} -0.0163518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9	\( 17 q + 3 q^{2} + q^{3} + 19 q^{4} + 11 q^{5} + 5 q^{6} + q^{7} + 3 q^{8} + 30 q^{9} + 12 q^{10} + 8 q^{11} + 12 q^{12} + q^{13} + 11 q^{14} - 7 q^{15} + 15 q^{16} + 17 q^{17} - 26 q^{18} - q^{19} + 13 q^{20} + 14 q^{21} + 3 q^{22} + 12 q^{23} - 24 q^{24} + 33 q^{26} + 22 q^{27} + q^{28} + 10 q^{29} + q^{30} + 2 q^{31} - q^{32} + 3 q^{33} + 3 q^{34} + 9 q^{35} + 50 q^{36} + 10 q^{37} + 23 q^{38} + 13 q^{39} + q^{40} + 65 q^{41} - 41 q^{42} - 3 q^{43} + 10 q^{44} + 31 q^{45} - 17 q^{47} - 16 q^{48} + 14 q^{49} + 5 q^{50} + q^{51} - 32 q^{52} - 13 q^{53} - 15 q^{54} - 11 q^{55} + 46 q^{56} + 36 q^{57} - q^{58} + 39 q^{59} + 43 q^{60} + 23 q^{61} + 33 q^{62} - 15 q^{63} - 27 q^{64} - 10 q^{65} - 86 q^{66} - 14 q^{67} + 19 q^{68} + 45 q^{69} - 13 q^{70} + 21 q^{71} - 42 q^{72} + 24 q^{73} + 25 q^{74} - 32 q^{75} - 5 q^{76} - 2 q^{77} + 36 q^{78} - 26 q^{79} - 14 q^{80} + 41 q^{81} - 37 q^{82} - 5 q^{83} - 60 q^{84} + 11 q^{85} - 24 q^{86} - 5 q^{87} - 25 q^{88} + 61 q^{89} + 6 q^{90} + 29 q^{91} - 12 q^{92} - 3 q^{93} - 3 q^{94} - 6 q^{95} + 12 q^{96} + 3 q^{97} + 36 q^{98} - 27 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 + q^3 + 19 * q^4 + 11 * q^5 + 5 * q^6 + q^7 + 3 * q^8 + 30 * q^9 + 12 * q^10 + 8 * q^11 + 12 * q^12 + q^13 + 11 * q^14 - 7 * q^15 + 15 * q^16 + 17 * q^17 - 26 * q^18 - q^19 + 13 * q^20 + 14 * q^21 + 3 * q^22 + 12 * q^23 - 24 * q^24 + 33 * q^26 + 22 * q^27 + q^28 + 10 * q^29 + q^30 + 2 * q^31 - q^32 + 3 * q^33 + 3 * q^34 + 9 * q^35 + 50 * q^36 + 10 * q^37 + 23 * q^38 + 13 * q^39 + q^40 + 65 * q^41 - 41 * q^42 - 3 * q^43 + 10 * q^44 + 31 * q^45 - 17 * q^47 - 16 * q^48 + 14 * q^49 + 5 * q^50 + q^51 - 32 * q^52 - 13 * q^53 - 15 * q^54 - 11 * q^55 + 46 * q^56 + 36 * q^57 - q^58 + 39 * q^59 + 43 * q^60 + 23 * q^61 + 33 * q^62 - 15 * q^63 - 27 * q^64 - 10 * q^65 - 86 * q^66 - 14 * q^67 + 19 * q^68 + 45 * q^69 - 13 * q^70 + 21 * q^71 - 42 * q^72 + 24 * q^73 + 25 * q^74 - 32 * q^75 - 5 * q^76 - 2 * q^77 + 36 * q^78 - 26 * q^79 - 14 * q^80 + 41 * q^81 - 37 * q^82 - 5 * q^83 - 60 * q^84 + 11 * q^85 - 24 * q^86 - 5 * q^87 - 25 * q^88 + 61 * q^89 + 6 * q^90 + 29 * q^91 - 12 * q^92 - 3 * q^93 - 3 * q^94 - 6 * q^95 + 12 * q^96 + 3 * q^97 + 36 * q^98 - 27 * q^99

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