LMFDB - Embedded newform 5239.2.a.u.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, 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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.33972 q^{2} +0.118285 q^{3} -0.205154 q^{4} +0.202435 q^{5} -0.158469 q^{6} +4.70921 q^{7} +2.95429 q^{8} -2.98601 q^{9} +O(q^{10})$	\(q-1.33972 q^{2} +0.118285 q^{3} -0.205154 q^{4} +0.202435 q^{5} -0.158469 q^{6} +4.70921 q^{7} +2.95429 q^{8} -2.98601 q^{9} -0.271205 q^{10} +2.81601 q^{11} -0.0242667 q^{12} -6.30902 q^{14} +0.0239451 q^{15} -3.54760 q^{16} -1.69766 q^{17} +4.00041 q^{18} -1.56366 q^{19} -0.0415303 q^{20} +0.557031 q^{21} -3.77266 q^{22} +1.98053 q^{23} +0.349449 q^{24} -4.95902 q^{25} -0.708058 q^{27} -0.966113 q^{28} +7.44053 q^{29} -0.0320796 q^{30} -1.00000 q^{31} -1.15578 q^{32} +0.333093 q^{33} +2.27438 q^{34} +0.953307 q^{35} +0.612592 q^{36} +8.73766 q^{37} +2.09487 q^{38} +0.598050 q^{40} -1.99546 q^{41} -0.746265 q^{42} -1.07177 q^{43} -0.577715 q^{44} -0.604471 q^{45} -2.65336 q^{46} -0.861407 q^{47} -0.419630 q^{48} +15.1767 q^{49} +6.64369 q^{50} -0.200808 q^{51} -10.1667 q^{53} +0.948598 q^{54} +0.570057 q^{55} +13.9124 q^{56} -0.184959 q^{57} -9.96822 q^{58} +10.0236 q^{59} -0.00491242 q^{60} +13.3800 q^{61} +1.33972 q^{62} -14.0617 q^{63} +8.64363 q^{64} -0.446250 q^{66} +5.66757 q^{67} +0.348281 q^{68} +0.234268 q^{69} -1.27716 q^{70} -2.34523 q^{71} -8.82152 q^{72} -1.28714 q^{73} -11.7060 q^{74} -0.586580 q^{75} +0.320792 q^{76} +13.2612 q^{77} -7.62076 q^{79} -0.718158 q^{80} +8.87427 q^{81} +2.67336 q^{82} +13.5045 q^{83} -0.114277 q^{84} -0.343664 q^{85} +1.43587 q^{86} +0.880107 q^{87} +8.31929 q^{88} -13.4913 q^{89} +0.809821 q^{90} -0.406314 q^{92} -0.118285 q^{93} +1.15404 q^{94} -0.316540 q^{95} -0.136712 q^{96} -11.4021 q^{97} -20.3325 q^{98} -8.40862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) $ 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.33972	−0.947324	−0.473662	−	0.880707i	$-0.657068\pi$
$2$	−1.33972	−0.947324	−0.473662	+	0.880707i	$0.657068\pi$
$3$	0.118285	0.0682921	0.0341461	−	0.999417i	$-0.489129\pi$
$3$	0.118285	0.0682921	0.0341461	+	0.999417i	$0.489129\pi$
$4$	−0.205154	−0.102577
$5$	0.202435	0.0905315	0.0452657	−	0.998975i	$-0.485587\pi$
$5$	0.202435	0.0905315	0.0452657	+	0.998975i	$0.485587\pi$
$6$	−0.158469	−0.0646948
$7$	4.70921	1.77991	0.889957	−	0.456044i	$-0.150734\pi$
$7$	4.70921	1.77991	0.889957	+	0.456044i	$0.150734\pi$
$8$	2.95429	1.04450
$9$	−2.98601	−0.995336
$10$	−0.271205	−0.0857627
$11$	2.81601	0.849058	0.424529	−	0.905414i	$-0.360440\pi$
$11$	2.81601	0.849058	0.424529	+	0.905414i	$0.360440\pi$
$12$	−0.0242667	−0.00700520
$13$	0	0
$13$	0	0
$14$	−6.30902	−1.68616
$15$	0.0239451	0.00618259
$16$	−3.54760	−0.886901
$17$	−1.69766	−0.411742	−0.205871	−	0.978579i	$-0.566003\pi$
$17$	−1.69766	−0.411742	−0.205871	+	0.978579i	$0.566003\pi$
$18$	4.00041	0.942906
$19$	−1.56366	−0.358729	−0.179365	−	0.983783i	$-0.557404\pi$
$19$	−1.56366	−0.358729	−0.179365	+	0.983783i	$0.557404\pi$
$20$	−0.0415303	−0.00928645
$21$	0.557031	0.121554
$22$	−3.77266	−0.804333
$23$	1.98053	0.412970	0.206485	−	0.978450i	$-0.433798\pi$
$23$	1.98053	0.412970	0.206485	+	0.978450i	$0.433798\pi$
$24$	0.349449	0.0713310
$25$	−4.95902	−0.991804
$26$	0	0
$27$	−0.708058	−0.136266
$28$	−0.966113	−0.182578
$29$	7.44053	1.38167	0.690836	−	0.723011i	$-0.257243\pi$
$29$	7.44053	1.38167	0.690836	+	0.723011i	$0.257243\pi$
$30$	−0.0320796	−0.00585692
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.15578	−0.204315
$33$	0.333093	0.0579840
$34$	2.27438	0.390053
$35$	0.953307	0.161138
$36$	0.612592	0.102099
$37$	8.73766	1.43646	0.718231	−	0.695805i	$-0.244952\pi$
$37$	8.73766	1.43646	0.718231	+	0.695805i	$0.244952\pi$
$38$	2.09487	0.339833
$39$	0	0
$40$	0.598050	0.0945599
$41$	−1.99546	−0.311639	−0.155820	−	0.987786i	$-0.549802\pi$
$41$	−1.99546	−0.311639	−0.155820	+	0.987786i	$0.549802\pi$
$42$	−0.746265	−0.115151
$43$	−1.07177	−0.163443	−0.0817214	−	0.996655i	$-0.526042\pi$
$43$	−1.07177	−0.163443	−0.0817214	+	0.996655i	$0.526042\pi$
$44$	−0.577715	−0.0870938
$45$	−0.604471	−0.0901093
$46$	−2.65336	−0.391216
$47$	−0.861407	−0.125649	−0.0628246	−	0.998025i	$-0.520011\pi$
$47$	−0.861407	−0.125649	−0.0628246	+	0.998025i	$0.520011\pi$
$48$	−0.419630	−0.0605684
$49$	15.1767	2.16810
$50$	6.64369	0.939560
$51$	−0.200808	−0.0281188
$52$	0	0
$53$	−10.1667	−1.39650	−0.698250	−	0.715854i	$-0.746038\pi$
$53$	−10.1667	−1.39650	−0.698250	+	0.715854i	$0.746038\pi$
$54$	0.948598	0.129088
$55$	0.570057	0.0768665
$56$	13.9124	1.85912
$57$	−0.184959	−0.0244984
$58$	−9.96822	−1.30889
$59$	10.0236	1.30496	0.652479	−	0.757807i	$-0.273729\pi$
$59$	10.0236	1.30496	0.652479	+	0.757807i	$0.273729\pi$
$60$	−0.00491242	−0.000634191 0
$61$	13.3800	1.71313	0.856566	−	0.516038i	$-0.172594\pi$
$61$	13.3800	1.71313	0.856566	+	0.516038i	$0.172594\pi$
$62$	1.33972	0.170144
$63$	−14.0617	−1.77161
$64$	8.64363	1.08045
$65$	0	0
$66$	−0.446250	−0.0549296
$67$	5.66757	0.692404	0.346202	−	0.938160i	$-0.387471\pi$
$67$	5.66757	0.692404	0.346202	+	0.938160i	$0.387471\pi$
$68$	0.348281	0.0422353
$69$	0.234268	0.0282026
$70$	−1.27716	−0.152650
$71$	−2.34523	−0.278327	−0.139164	−	0.990269i	$-0.544441\pi$
$71$	−2.34523	−0.278327	−0.139164	+	0.990269i	$0.544441\pi$
$72$	−8.82152	−1.03963
$73$	−1.28714	−0.150648	−0.0753241	−	0.997159i	$-0.523999\pi$
$73$	−1.28714	−0.150648	−0.0753241	+	0.997159i	$0.523999\pi$
$74$	−11.7060	−1.36080
$75$	−0.586580	−0.0677324
$76$	0.320792	0.0367974
$77$	13.2612	1.51125
$78$	0	0
$79$	−7.62076	−0.857402	−0.428701	−	0.903446i	$-0.641029\pi$
$79$	−7.62076	−0.857402	−0.428701	+	0.903446i	$0.641029\pi$
$80$	−0.718158	−0.0802925
$81$	8.87427	0.986030
$82$	2.67336	0.295223
$83$	13.5045	1.48231	0.741153	−	0.671336i	$-0.234279\pi$
$83$	13.5045	1.48231	0.741153	+	0.671336i	$0.234279\pi$
$84$	−0.114277	−0.0124687
$85$	−0.343664	−0.0372756
$86$	1.43587	0.154833
$87$	0.880107	0.0943574
$88$	8.31929	0.886839
$89$	−13.4913	−1.43008	−0.715040	−	0.699084i	$-0.753591\pi$
$89$	−13.4913	−1.43008	−0.715040	+	0.699084i	$0.753591\pi$
$90$	0.809821	0.0853627
$91$	0	0
$92$	−0.406314	−0.0423612
$93$	−0.118285	−0.0122656
$94$	1.15404	0.119031
$95$	−0.316540	−0.0324763
$96$	−0.136712	−0.0139531
$97$	−11.4021	−1.15770	−0.578852	−	0.815433i	$-0.696499\pi$
$97$	−11.4021	−1.15770	−0.578852	+	0.815433i	$0.696499\pi$
$98$	−20.3325	−2.05389
$99$	−8.40862	−0.845098
$100$	1.01736	0.101736
$101$	7.59542	0.755772	0.377886	−	0.925852i	$-0.376651\pi$
$101$	7.59542	0.755772	0.377886	+	0.925852i	$0.376651\pi$
$102$	0.269026	0.0266376
$103$	6.27969	0.618757	0.309378	−	0.950939i	$-0.399879\pi$
$103$	6.27969	0.618757	0.309378	+	0.950939i	$0.399879\pi$
$104$	0	0
$105$	0.112762	0.0110045
$106$	13.6205	1.32294
$107$	13.6953	1.32398	0.661988	−	0.749514i	$-0.269713\pi$
$107$	13.6953	1.32398	0.661988	+	0.749514i	$0.269713\pi$
$108$	0.145261	0.0139777
$109$	8.28199	0.793270	0.396635	−	0.917976i	$-0.370178\pi$
$109$	8.28199	0.793270	0.396635	+	0.917976i	$0.370178\pi$
$110$	−0.763716	−0.0728174
$111$	1.03354	0.0980991
$112$	−16.7064	−1.57861
$113$	−8.39462	−0.789700	−0.394850	−	0.918746i	$-0.629203\pi$
$113$	−8.39462	−0.789700	−0.394850	+	0.918746i	$0.629203\pi$
$114$	0.247793	0.0232079
$115$	0.400928	0.0373867
$116$	−1.52646	−0.141728
$117$	0	0
$118$	−13.4288	−1.23622
$119$	−7.99463	−0.732866
$120$	0.0707406	0.00645770
$121$	−3.07011	−0.279101
$122$	−17.9254	−1.62289
$123$	−0.236034	−0.0212825
$124$	0.205154	0.0184234
$125$	−2.01605	−0.180321
$126$	18.8388	1.67829
$127$	5.08165	0.450924	0.225462	−	0.974252i	$-0.427611\pi$
$127$	5.08165	0.450924	0.225462	+	0.974252i	$0.427611\pi$
$128$	−9.26847	−0.819225
$129$	−0.126774	−0.0111619
$130$	0	0
$131$	8.39456	0.733436	0.366718	−	0.930332i	$-0.380481\pi$
$131$	8.39456	0.733436	0.366718	+	0.930332i	$0.380481\pi$
$132$	−0.0683353	−0.00594782
$133$	−7.36363	−0.638507
$134$	−7.59295	−0.655931
$135$	−0.143335	−0.0123363
$136$	−5.01536	−0.430064
$137$	−6.23889	−0.533024	−0.266512	−	0.963832i	$-0.585871\pi$
$137$	−6.23889	−0.533024	−0.266512	+	0.963832i	$0.585871\pi$
$138$	−0.313853	−0.0267170
$139$	1.18972	0.100911	0.0504556	−	0.998726i	$-0.483933\pi$
$139$	1.18972	0.100911	0.0504556	+	0.998726i	$0.483933\pi$
$140$	−0.195575	−0.0165291
$141$	−0.101892	−0.00858085
$142$	3.14195	0.263666
$143$	0	0
$144$	10.5932	0.882765
$145$	1.50622	0.125085
$146$	1.72440	0.142713
$147$	1.79518	0.148064
$148$	−1.79257	−0.147348
$149$	−4.60419	−0.377190	−0.188595	−	0.982055i	$-0.560393\pi$
$149$	−4.60419	−0.377190	−0.188595	+	0.982055i	$0.560393\pi$
$150$	0.785852	0.0641646
$151$	−19.4856	−1.58572	−0.792859	−	0.609405i	$-0.791408\pi$
$151$	−19.4856	−1.58572	−0.792859	+	0.609405i	$0.791408\pi$
$152$	−4.61951	−0.374692
$153$	5.06922	0.409822
$154$	−17.7662	−1.43164
$155$	−0.202435	−0.0162599
$156$	0	0
$157$	6.33376	0.505489	0.252745	−	0.967533i	$-0.418667\pi$
$157$	6.33376	0.505489	0.252745	+	0.967533i	$0.418667\pi$
$158$	10.2097	0.812238
$159$	−1.20257	−0.0953700
$160$	−0.233970	−0.0184969
$161$	9.32675	0.735050
$162$	−11.8890	−0.934090
$163$	22.2477	1.74257	0.871287	−	0.490773i	$-0.163286\pi$
$163$	22.2477	1.74257	0.871287	+	0.490773i	$0.163286\pi$
$164$	0.409377	0.0319670
$165$	0.0674294	0.00524937
$166$	−18.0922	−1.40422
$167$	1.82665	0.141350	0.0706751	−	0.997499i	$-0.477485\pi$
$167$	1.82665	0.141350	0.0706751	+	0.997499i	$0.477485\pi$
$168$	1.64563	0.126963
$169$	0	0
$170$	0.460414	0.0353121
$171$	4.66912	0.357056
$172$	0.219877	0.0167655
$173$	−23.9074	−1.81765	−0.908823	−	0.417182i	$-0.863018\pi$
$173$	−23.9074	−1.81765	−0.908823	+	0.417182i	$0.863018\pi$
$174$	−1.17910	−0.0893870
$175$	−23.3531	−1.76533
$176$	−9.99007	−0.753030
$177$	1.18564	0.0891183
$178$	18.0746	1.35475
$179$	5.31492	0.397256	0.198628	−	0.980075i	$-0.436351\pi$
$179$	5.31492	0.397256	0.198628	+	0.980075i	$0.436351\pi$
$180$	0.124010	0.00924314
$181$	−4.49290	−0.333955	−0.166977	−	0.985961i	$-0.553401\pi$
$181$	−4.49290	−0.333955	−0.166977	+	0.985961i	$0.553401\pi$
$182$	0	0
$183$	1.58266	0.116993
$184$	5.85106	0.431346
$185$	1.76880	0.130045
$186$	0.158469	0.0116195
$187$	−4.78061	−0.349593
$188$	0.176721	0.0128887
$189$	−3.33439	−0.242541
$190$	0.424074	0.0307656
$191$	−20.9046	−1.51260	−0.756301	−	0.654224i	$-0.772995\pi$
$191$	−20.9046	−1.51260	−0.756301	+	0.654224i	$0.772995\pi$
$192$	1.02242	0.0737865
$193$	−8.50639	−0.612304	−0.306152	−	0.951983i	$-0.599042\pi$
$193$	−8.50639	−0.612304	−0.306152	+	0.951983i	$0.599042\pi$
$194$	15.2755	1.09672
$195$	0	0
$196$	−3.11355	−0.222397
$197$	25.6672	1.82871	0.914356	−	0.404912i	$-0.132698\pi$
$197$	25.6672	1.82871	0.914356	+	0.404912i	$0.132698\pi$
$198$	11.2652	0.800582
$199$	13.4844	0.955882	0.477941	−	0.878392i	$-0.341383\pi$
$199$	13.4844	0.955882	0.477941	+	0.878392i	$0.341383\pi$
$200$	−14.6504	−1.03594
$201$	0.670391	0.0472857
$202$	−10.1757	−0.715961
$203$	35.0390	2.45926
$204$	0.0411966	0.00288434
$205$	−0.403951	−0.0282132
$206$	−8.41302	−0.586163
$207$	−5.91389	−0.411044
$208$	0	0
$209$	−4.40329	−0.304582
$210$	−0.151070	−0.0104248
$211$	−10.5851	−0.728709	−0.364355	−	0.931260i	$-0.618710\pi$
$211$	−10.5851	−0.728709	−0.364355	+	0.931260i	$0.618710\pi$
$212$	2.08573	0.143249
$213$	−0.277406	−0.0190076
$214$	−18.3479	−1.25424
$215$	−0.216963	−0.0147967
$216$	−2.09180	−0.142329
$217$	−4.70921	−0.319682
$218$	−11.0955	−0.751484
$219$	−0.152250	−0.0102881
$220$	−0.116949	−0.00788473
$221$	0	0
$222$	−1.38465	−0.0929316
$223$	2.47569	0.165785	0.0828924	−	0.996559i	$-0.473584\pi$
$223$	2.47569	0.165785	0.0828924	+	0.996559i	$0.473584\pi$
$224$	−5.44282	−0.363663
$225$	14.8077	0.987178
$226$	11.2464	0.748101
$227$	7.17504	0.476224	0.238112	−	0.971238i	$-0.423471\pi$
$227$	7.17504	0.476224	0.238112	+	0.971238i	$0.423471\pi$
$228$	0.0379450	0.00251297
$229$	−23.5622	−1.55703	−0.778517	−	0.627624i	$-0.784028\pi$
$229$	−23.5622	−1.55703	−0.778517	+	0.627624i	$0.784028\pi$
$230$	−0.537131	−0.0354174
$231$	1.56860	0.103206
$232$	21.9815	1.44315
$233$	−0.311648	−0.0204167	−0.0102084	−	0.999948i	$-0.503249\pi$
$233$	−0.311648	−0.0204167	−0.0102084	+	0.999948i	$0.503249\pi$
$234$	0	0
$235$	−0.174379	−0.0113752
$236$	−2.05638	−0.133859
$237$	−0.901425	−0.0585538
$238$	10.7105	0.694262
$239$	5.12149	0.331282	0.165641	−	0.986186i	$-0.447031\pi$
$239$	5.12149	0.331282	0.165641	+	0.986186i	$0.447031\pi$
$240$	−0.0849476	−0.00548334
$241$	−10.9326	−0.704231	−0.352116	−	0.935957i	$-0.614538\pi$
$241$	−10.9326	−0.704231	−0.352116	+	0.935957i	$0.614538\pi$
$242$	4.11309	0.264399
$243$	3.17387	0.203604
$244$	−2.74496	−0.175728
$245$	3.07228	0.196281
$246$	0.316220	0.0201614
$247$	0	0
$248$	−2.95429	−0.187597
$249$	1.59738	0.101230
$250$	2.70094	0.170822
$251$	5.73808	0.362185	0.181092	−	0.983466i	$-0.442037\pi$
$251$	5.73808	0.362185	0.181092	+	0.983466i	$0.442037\pi$
$252$	2.88482	0.181727
$253$	5.57719	0.350635
$254$	−6.80798	−0.427171
$255$	−0.0406505	−0.00254563
$256$	−4.87012	−0.304382
$257$	14.9267	0.931100	0.465550	−	0.885021i	$-0.345856\pi$
$257$	14.9267	0.931100	0.465550	+	0.885021i	$0.345856\pi$
$258$	0.169842	0.0105739
$259$	41.1475	2.55678
$260$	0	0
$261$	−22.2175	−1.37523
$262$	−11.2464	−0.694802
$263$	20.2998	1.25174	0.625870	−	0.779927i	$-0.284744\pi$
$263$	20.2998	1.25174	0.625870	+	0.779927i	$0.284744\pi$
$264$	0.984050	0.0605641
$265$	−2.05809	−0.126427
$266$	9.86519	0.604874
$267$	−1.59583	−0.0976632
$268$	−1.16272	−0.0710247
$269$	25.6497	1.56389	0.781945	−	0.623347i	$-0.214228\pi$
$269$	25.6497	1.56389	0.781945	+	0.623347i	$0.214228\pi$
$270$	0.192029	0.0116865
$271$	8.66743	0.526509	0.263254	−	0.964726i	$-0.415204\pi$
$271$	8.66743	0.526509	0.263254	+	0.964726i	$0.415204\pi$
$272$	6.02262	0.365175
$273$	0	0
$274$	8.35836	0.504947
$275$	−13.9646	−0.842099
$276$	−0.0480610	−0.00289294
$277$	−5.05791	−0.303900	−0.151950	−	0.988388i	$-0.548555\pi$
$277$	−5.05791	−0.303900	−0.151950	+	0.988388i	$0.548555\pi$
$278$	−1.59390	−0.0955956
$279$	2.98601	0.178768
$280$	2.81634	0.168309
$281$	2.72907	0.162803	0.0814013	−	0.996681i	$-0.474060\pi$
$281$	2.72907	0.162803	0.0814013	+	0.996681i	$0.474060\pi$
$282$	0.136507	0.00812885
$283$	−2.41595	−0.143613	−0.0718066	−	0.997419i	$-0.522876\pi$
$283$	−2.41595	−0.143613	−0.0718066	+	0.997419i	$0.522876\pi$
$284$	0.481133	0.0285500
$285$	−0.0374420	−0.00221788
$286$	0	0
$287$	−9.39706	−0.554691
$288$	3.45117	0.203362
$289$	−14.1180	−0.830468
$290$	−2.01791	−0.118496
$291$	−1.34870	−0.0790620
$292$	0.264062	0.0154530
$293$	15.7681	0.921182	0.460591	−	0.887613i	$-0.347638\pi$
$293$	15.7681	0.921182	0.460591	+	0.887613i	$0.347638\pi$
$294$	−2.40503	−0.140264
$295$	2.02912	0.118140
$296$	25.8135	1.50038
$297$	−1.99389	−0.115697
$298$	6.16832	0.357321
$299$	0	0
$300$	0.120339	0.00694779
$301$	−5.04717	−0.290914
$302$	26.1053	1.50219
$303$	0.898428	0.0516133
$304$	5.54726	0.318157
$305$	2.70857	0.155092
$306$	−6.79133	−0.388234
$307$	30.1931	1.72321	0.861607	−	0.507576i	$-0.169458\pi$
$307$	30.1931	1.72321	0.861607	+	0.507576i	$0.169458\pi$
$308$	−2.72058	−0.155019
$309$	0.742796	0.0422562
$310$	0.271205	0.0154034
$311$	28.7863	1.63232	0.816162	−	0.577823i	$-0.196098\pi$
$311$	28.7863	1.63232	0.816162	+	0.577823i	$0.196098\pi$
$312$	0	0
$313$	−19.0497	−1.07675	−0.538377	−	0.842704i	$-0.680962\pi$
$313$	−19.0497	−1.07675	−0.538377	+	0.842704i	$0.680962\pi$
$314$	−8.48546	−0.478862
$315$	−2.84658	−0.160387
$316$	1.56343	0.0879497
$317$	28.5436	1.60317	0.801584	−	0.597882i	$-0.203991\pi$
$317$	28.5436	1.60317	0.801584	+	0.597882i	$0.203991\pi$
$318$	1.61111	0.0903463
$319$	20.9526	1.17312
$320$	1.74977	0.0978151
$321$	1.61996	0.0904172
$322$	−12.4952	−0.696331
$323$	2.65457	0.147704
$324$	−1.82059	−0.101144
$325$	0	0
$326$	−29.8057	−1.65078
$327$	0.979638	0.0541741
$328$	−5.89517	−0.325506
$329$	−4.05655	−0.223645
$330$	−0.0903365	−0.00497286
$331$	−15.5223	−0.853181	−0.426591	−	0.904445i	$-0.640285\pi$
$331$	−15.5223	−0.853181	−0.426591	+	0.904445i	$0.640285\pi$
$332$	−2.77049	−0.152051
$333$	−26.0907	−1.42976
$334$	−2.44719	−0.133904
$335$	1.14731	0.0626843
$336$	−1.97613	−0.107806
$337$	−32.8187	−1.78775	−0.893874	−	0.448317i	$-0.852023\pi$
$337$	−32.8187	−1.78775	−0.893874	+	0.448317i	$0.852023\pi$
$338$	0	0
$339$	−0.992962	−0.0539303
$340$	0.0705041	0.00382362
$341$	−2.81601	−0.152495
$342$	−6.25530	−0.338248
$343$	38.5057	2.07911
$344$	−3.16630	−0.170716
$345$	0.0474240	0.00255322
$346$	32.0292	1.72190
$347$	11.2699	0.604999	0.302500	−	0.953150i	$-0.402179\pi$
$347$	11.2699	0.604999	0.302500	+	0.953150i	$0.402179\pi$
$348$	−0.180557	−0.00967889
$349$	32.8342	1.75758	0.878788	−	0.477212i	$-0.158353\pi$
$349$	32.8342	1.75758	0.878788	+	0.477212i	$0.158353\pi$
$350$	31.2865	1.67234
$351$	0	0
$352$	−3.25469	−0.173475
$353$	−0.465659	−0.0247845	−0.0123923	−	0.999923i	$-0.503945\pi$
$353$	−0.465659	−0.0247845	−0.0123923	+	0.999923i	$0.503945\pi$
$354$	−1.58843	−0.0844240
$355$	−0.474755	−0.0251974
$356$	2.76780	0.146693
$357$	−0.945648	−0.0500490
$358$	−7.12050	−0.376330
$359$	20.9081	1.10349	0.551744	−	0.834014i	$-0.313963\pi$
$359$	20.9081	1.10349	0.551744	+	0.834014i	$0.313963\pi$
$360$	−1.78578	−0.0941189
$361$	−16.5550	−0.871313
$362$	6.01922	0.316363
$363$	−0.363150	−0.0190604
$364$	0	0
$365$	−0.260561	−0.0136384
$366$	−2.12032	−0.110831
$367$	31.0339	1.61996	0.809979	−	0.586459i	$-0.199478\pi$
$367$	31.0339	1.61996	0.809979	+	0.586459i	$0.199478\pi$
$368$	−7.02614	−0.366263
$369$	5.95847	0.310186
$370$	−2.36970	−0.123195
$371$	−47.8770	−2.48565
$372$	0.0242667	0.00125817
$373$	19.8415	1.02735	0.513676	−	0.857984i	$-0.328283\pi$
$373$	19.8415	1.02735	0.513676	+	0.857984i	$0.328283\pi$
$374$	6.40468	0.331178
$375$	−0.238469	−0.0123145
$376$	−2.54484	−0.131240
$377$	0	0
$378$	4.46715	0.229765
$379$	−9.37772	−0.481701	−0.240850	−	0.970562i	$-0.577426\pi$
$379$	−9.37772	−0.481701	−0.240850	+	0.970562i	$0.577426\pi$
$380$	0.0649394	0.00333132
$381$	0.601085	0.0307945
$382$	28.0062	1.43292
$383$	−0.851961	−0.0435332	−0.0217666	−	0.999763i	$-0.506929\pi$
$383$	−0.851961	−0.0435332	−0.0217666	+	0.999763i	$0.506929\pi$
$384$	−1.09633	−0.0559466
$385$	2.68452	0.136816
$386$	11.3962	0.580050
$387$	3.20030	0.162681
$388$	2.33918	0.118754
$389$	22.0367	1.11731	0.558653	−	0.829401i	$-0.311318\pi$
$389$	22.0367	1.11731	0.558653	+	0.829401i	$0.311318\pi$
$390$	0	0
$391$	−3.36227	−0.170037
$392$	44.8362	2.26457
$393$	0.992954	0.0500879
$394$	−34.3868	−1.73238
$395$	−1.54270	−0.0776219
$396$	1.72506	0.0866876
$397$	−9.42347	−0.472950	−0.236475	−	0.971638i	$-0.575992\pi$
$397$	−9.42347	−0.472950	−0.236475	+	0.971638i	$0.575992\pi$
$398$	−18.0653	−0.905530
$399$	−0.871010	−0.0436050
$400$	17.5926	0.879632
$401$	13.1885	0.658602	0.329301	−	0.944225i	$-0.393187\pi$
$401$	13.1885	0.658602	0.329301	+	0.944225i	$0.393187\pi$
$402$	−0.898135	−0.0447949
$403$	0	0
$404$	−1.55823	−0.0775249
$405$	1.79646	0.0892668
$406$	−46.9425	−2.32972
$407$	24.6053	1.21964
$408$	−0.593245	−0.0293700
$409$	−22.0952	−1.09254	−0.546269	−	0.837610i	$-0.683952\pi$
$409$	−22.0952	−1.09254	−0.546269	+	0.837610i	$0.683952\pi$
$410$	0.541180	0.0267270
$411$	−0.737970	−0.0364014
$412$	−1.28830	−0.0634702
$413$	47.2031	2.32271
$414$	7.92294	0.389391
$415$	2.73377	0.134195
$416$	0	0
$417$	0.140727	0.00689144
$418$	5.89917	0.288538
$419$	−21.8881	−1.06931	−0.534653	−	0.845072i	$-0.679558\pi$
$419$	−21.8881	−1.06931	−0.534653	+	0.845072i	$0.679558\pi$
$420$	−0.0231336	−0.00112881
$421$	−23.9021	−1.16492	−0.582460	−	0.812860i	$-0.697910\pi$
$421$	−23.9021	−1.16492	−0.582460	+	0.812860i	$0.697910\pi$
$422$	14.1811	0.690324
$423$	2.57217	0.125063
$424$	−30.0353	−1.45864
$425$	8.41872	0.408368
$426$	0.371646	0.0180063
$427$	63.0092	3.04923
$428$	−2.80965	−0.135810
$429$	0	0
$430$	0.290669	0.0140173
$431$	1.45183	0.0699323	0.0349662	−	0.999388i	$-0.488868\pi$
$431$	1.45183	0.0699323	0.0349662	+	0.999388i	$0.488868\pi$
$432$	2.51191	0.120854
$433$	−6.56647	−0.315565	−0.157782	−	0.987474i	$-0.550434\pi$
$433$	−6.56647	−0.315565	−0.157782	+	0.987474i	$0.550434\pi$
$434$	6.30902	0.302843
$435$	0.178164	0.00854231
$436$	−1.69908	−0.0813713
$437$	−3.09689	−0.148144
$438$	0.203972	0.00974615
$439$	30.9979	1.47945	0.739724	−	0.672911i	$-0.234956\pi$
$439$	30.9979	1.47945	0.739724	+	0.672911i	$0.234956\pi$
$440$	1.68411	0.0802868
$441$	−45.3177	−2.15798
$442$	0	0
$443$	−2.70050	−0.128305	−0.0641524	−	0.997940i	$-0.520434\pi$
$443$	−2.70050	−0.128305	−0.0641524	+	0.997940i	$0.520434\pi$
$444$	−0.212034	−0.0100627
$445$	−2.73111	−0.129467
$446$	−3.31673	−0.157052
$447$	−0.544609	−0.0257591
$448$	40.7047	1.92311
$449$	6.40312	0.302182	0.151091	−	0.988520i	$-0.451721\pi$
$449$	6.40312	0.302182	0.151091	+	0.988520i	$0.451721\pi$
$450$	−19.8381	−0.935178
$451$	−5.61924	−0.264600
$452$	1.72219	0.0810050
$453$	−2.30487	−0.108292
$454$	−9.61254	−0.451139
$455$	0	0
$456$	−0.546421	−0.0255885
$457$	−27.9706	−1.30841	−0.654205	−	0.756318i	$-0.726996\pi$
$457$	−27.9706	−1.30841	−0.654205	+	0.756318i	$0.726996\pi$
$458$	31.5667	1.47502
$459$	1.20204	0.0561064
$460$	−0.0822520	−0.00383502
$461$	18.7518	0.873358	0.436679	−	0.899617i	$-0.356155\pi$
$461$	18.7518	0.873358	0.436679	+	0.899617i	$0.356155\pi$
$462$	−2.10149	−0.0977700
$463$	29.6529	1.37809	0.689045	−	0.724719i	$-0.258030\pi$
$463$	29.6529	1.37809	0.689045	+	0.724719i	$0.258030\pi$
$464$	−26.3961	−1.22541
$465$	−0.0239451	−0.00111043
$466$	0.417521	0.0193413
$467$	11.4822	0.531332	0.265666	−	0.964065i	$-0.414408\pi$
$467$	11.4822	0.531332	0.265666	+	0.964065i	$0.414408\pi$
$468$	0	0
$469$	26.6898	1.23242
$470$	0.233618	0.0107760
$471$	0.749192	0.0345209
$472$	29.6125	1.36303
$473$	−3.01810	−0.138772
$474$	1.20766	0.0554694
$475$	7.75425	0.355789
$476$	1.64013	0.0751752
$477$	30.3578	1.38999
$478$	−6.86136	−0.313831
$479$	27.2817	1.24653	0.623267	−	0.782009i	$-0.285805\pi$
$479$	27.2817	1.24653	0.623267	+	0.782009i	$0.285805\pi$
$480$	−0.0276752	−0.00126320
$481$	0	0
$482$	14.6466	0.667135
$483$	1.10322	0.0501982
$484$	0.629846	0.0286293
$485$	−2.30817	−0.104809
$486$	−4.25209	−0.192879
$487$	7.68242	0.348124	0.174062	−	0.984735i	$-0.444311\pi$
$487$	7.68242	0.348124	0.174062	+	0.984735i	$0.444311\pi$
$488$	39.5283	1.78936
$489$	2.63158	0.119004
$490$	−4.11599	−0.185942
$491$	−29.7141	−1.34098	−0.670490	−	0.741919i	$-0.733916\pi$
$491$	−29.7141	−1.34098	−0.670490	+	0.741919i	$0.733916\pi$
$492$	0.0484234	0.00218309
$493$	−12.6315	−0.568893
$494$	0	0
$495$	−1.70219	−0.0765080
$496$	3.54760	0.159292
$497$	−11.0442	−0.495399
$498$	−2.14004	−0.0958975
$499$	26.1725	1.17164	0.585820	−	0.810441i	$-0.300772\pi$
$499$	26.1725	1.17164	0.585820	+	0.810441i	$0.300772\pi$
$500$	0.413601	0.0184968
$501$	0.216066	0.00965310
$502$	−7.68742	−0.343106
$503$	32.6955	1.45782	0.728911	−	0.684609i	$-0.240027\pi$
$503$	32.6955	1.45782	0.728911	+	0.684609i	$0.240027\pi$
$504$	−41.5424	−1.85045
$505$	1.53758	0.0684212
$506$	−7.47187	−0.332165
$507$	0	0
$508$	−1.04252	−0.0462544
$509$	−25.0621	−1.11086	−0.555429	−	0.831564i	$-0.687446\pi$
$509$	−25.0621	−1.11086	−0.555429	+	0.831564i	$0.687446\pi$
$510$	0.0544602	0.00241154
$511$	−6.06141	−0.268141
$512$	25.0615	1.10757
$513$	1.10716	0.0488825
$514$	−19.9975	−0.882054
$515$	1.27123	0.0560170
$516$	0.0260083	0.00114495
$517$	−2.42573	−0.106683
$518$	−55.1260	−2.42210
$519$	−2.82790	−0.124131
$520$	0	0
$521$	37.1709	1.62849	0.814244	−	0.580523i	$-0.197152\pi$
$521$	37.1709	1.62849	0.814244	+	0.580523i	$0.197152\pi$
$522$	29.7652	1.30279
$523$	−32.6176	−1.42627	−0.713133	−	0.701029i	$-0.752724\pi$
$523$	−32.6176	−1.42627	−0.713133	+	0.701029i	$0.752724\pi$
$524$	−1.72218	−0.0752337
$525$	−2.76233	−0.120558
$526$	−27.1961	−1.18580
$527$	1.69766	0.0739511
$528$	−1.18168	−0.0514260
$529$	−19.0775	−0.829456
$530$	2.75726	0.119768
$531$	−29.9305	−1.29887
$532$	1.51068	0.0654962
$533$	0	0
$534$	2.13796	0.0925187
$535$	2.77241	0.119862
$536$	16.7436	0.723214
$537$	0.628678	0.0271294
$538$	−34.3634	−1.48151
$539$	42.7376	1.84084
$540$	0.0294058	0.00126542
$541$	−20.6902	−0.889543	−0.444772	−	0.895644i	$-0.646715\pi$
$541$	−20.6902	−0.889543	−0.444772	+	0.895644i	$0.646715\pi$
$542$	−11.6119	−0.498775
$543$	−0.531445	−0.0228065
$544$	1.96212	0.0841252
$545$	1.67656	0.0718159
$546$	0	0
$547$	32.0295	1.36948	0.684741	−	0.728787i	$-0.259915\pi$
$547$	32.0295	1.36948	0.684741	+	0.728787i	$0.259915\pi$
$548$	1.27993	0.0546760
$549$	−39.9527	−1.70514
$550$	18.7087	0.797741
$551$	−11.6345	−0.495646
$552$	0.692095	0.0294575
$553$	−35.8877	−1.52610
$554$	6.77618	0.287892
$555$	0.209224	0.00888105
$556$	−0.244077	−0.0103512
$557$	−5.86544	−0.248527	−0.124263	−	0.992249i	$-0.539657\pi$
$557$	−5.86544	−0.248527	−0.124263	+	0.992249i	$0.539657\pi$
$558$	−4.00041	−0.169351
$559$	0	0
$560$	−3.38196	−0.142914
$561$	−0.565477	−0.0238745
$562$	−3.65619	−0.154227
$563$	−20.1520	−0.849306	−0.424653	−	0.905356i	$-0.639604\pi$
$563$	−20.1520	−0.849306	−0.424653	+	0.905356i	$0.639604\pi$
$564$	0.0209035	0.000880198 0
$565$	−1.69936	−0.0714927
$566$	3.23669	0.136048
$567$	41.7908	1.75505
$568$	−6.92847	−0.290712
$569$	−5.94196	−0.249100	−0.124550	−	0.992213i	$-0.539749\pi$
$569$	−5.94196	−0.249100	−0.124550	+	0.992213i	$0.539749\pi$
$570$	0.0501618	0.00210105
$571$	6.20391	0.259625	0.129813	−	0.991539i	$-0.458562\pi$
$571$	6.20391	0.259625	0.129813	+	0.991539i	$0.458562\pi$
$572$	0	0
$573$	−2.47271	−0.103299
$574$	12.5894	0.525472
$575$	−9.82150	−0.409585
$576$	−25.8099	−1.07541
$577$	−28.0603	−1.16817	−0.584083	−	0.811694i	$-0.698546\pi$
$577$	−28.0603	−1.16817	−0.584083	+	0.811694i	$0.698546\pi$
$578$	18.9141	0.786723
$579$	−1.00618	−0.0418155
$580$	−0.309007	−0.0128308
$581$	63.5953	2.63838
$582$	1.80688	0.0748974
$583$	−28.6294	−1.18571
$584$	−3.80257	−0.157352
$585$	0	0
$586$	−21.1248	−0.872658
$587$	−22.6976	−0.936832	−0.468416	−	0.883508i	$-0.655175\pi$
$587$	−22.6976	−0.936832	−0.468416	+	0.883508i	$0.655175\pi$
$588$	−0.368288	−0.0151879
$589$	1.56366	0.0644297
$590$	−2.71845	−0.111917
$591$	3.03606	0.124887
$592$	−30.9978	−1.27400
$593$	−44.2485	−1.81707	−0.908534	−	0.417812i	$-0.862797\pi$
$593$	−44.2485	−1.81707	−0.908534	+	0.417812i	$0.862797\pi$
$594$	2.67126	0.109603
$595$	−1.61839	−0.0663475
$596$	0.944569	0.0386910
$597$	1.59501	0.0652793
$598$	0	0
$599$	0.237064	0.00968619	0.00484309	−	0.999988i	$-0.498458\pi$
$599$	0.237064	0.00968619	0.00484309	+	0.999988i	$0.498458\pi$
$600$	−1.73292	−0.0707464
$601$	32.6796	1.33303	0.666515	−	0.745492i	$-0.267785\pi$
$601$	32.6796	1.33303	0.666515	+	0.745492i	$0.267785\pi$
$602$	6.76179	0.275590
$603$	−16.9234	−0.689174
$604$	3.99755	0.162658
$605$	−0.621497	−0.0252674
$606$	−1.20364	−0.0488945
$607$	0.245054	0.00994642	0.00497321	−	0.999988i	$-0.498417\pi$
$607$	0.245054	0.00994642	0.00497321	+	0.999988i	$0.498417\pi$
$608$	1.80725	0.0732938
$609$	4.14461	0.167948
$610$	−3.62872	−0.146923
$611$	0	0
$612$	−1.03997	−0.0420383
$613$	−13.9043	−0.561589	−0.280795	−	0.959768i	$-0.590598\pi$
$613$	−13.9043	−0.561589	−0.280795	+	0.959768i	$0.590598\pi$
$614$	−40.4503	−1.63244
$615$	−0.0477815	−0.00192674
$616$	39.1773	1.57850
$617$	43.0243	1.73209	0.866047	−	0.499963i	$-0.166653\pi$
$617$	43.0243	1.73209	0.866047	+	0.499963i	$0.166653\pi$
$618$	−0.995138	−0.0400303
$619$	−31.5371	−1.26758	−0.633792	−	0.773503i	$-0.718503\pi$
$619$	−31.5371	−1.26758	−0.633792	+	0.773503i	$0.718503\pi$
$620$	0.0415303	0.00166790
$621$	−1.40233	−0.0562736
$622$	−38.5656	−1.54634
$623$	−63.5336	−2.54542
$624$	0	0
$625$	24.3870	0.975479
$626$	25.5213	1.02003
$627$	−0.520845	−0.0208005
$628$	−1.29940	−0.0518515
$629$	−14.8335	−0.591452
$630$	3.81362	0.151938
$631$	32.6923	1.30146	0.650730	−	0.759309i	$-0.274463\pi$
$631$	32.6923	1.30146	0.650730	+	0.759309i	$0.274463\pi$
$632$	−22.5139	−0.895555
$633$	−1.25206	−0.0497651
$634$	−38.2404	−1.51872
$635$	1.02870	0.0408228
$636$	0.246712	0.00978277
$637$	0	0
$638$	−28.0706	−1.11132
$639$	7.00287	0.277029
$640$	−1.87626	−0.0741656
$641$	44.6404	1.76319	0.881595	−	0.472006i	$-0.156470\pi$
$641$	44.6404	1.76319	0.881595	+	0.472006i	$0.156470\pi$
$642$	−2.17029	−0.0856544
$643$	−35.8886	−1.41531	−0.707655	−	0.706558i	$-0.750247\pi$
$643$	−35.8886	−1.41531	−0.707655	+	0.706558i	$0.750247\pi$
$644$	−1.91342	−0.0753993
$645$	−0.0256635	−0.00101050
$646$	−3.55637	−0.139924
$647$	−4.64801	−0.182732	−0.0913660	−	0.995817i	$-0.529123\pi$
$647$	−4.64801	−0.182732	−0.0913660	+	0.995817i	$0.529123\pi$
$648$	26.2171	1.02991
$649$	28.2264	1.10798
$650$	0	0
$651$	−0.557031	−0.0218318
$652$	−4.56420	−0.178748
$653$	19.0429	0.745205	0.372602	−	0.927991i	$-0.378466\pi$
$653$	19.0429	0.745205	0.372602	+	0.927991i	$0.378466\pi$
$654$	−1.31244	−0.0513205
$655$	1.69935	0.0663991
$656$	7.07912	0.276393
$657$	3.84341	0.149946
$658$	5.43463	0.211864
$659$	−13.6123	−0.530260	−0.265130	−	0.964213i	$-0.585415\pi$
$659$	−13.6123	−0.530260	−0.265130	+	0.964213i	$0.585415\pi$
$660$	−0.0138334	−0.000538465 0
$661$	−26.7501	−1.04046	−0.520230	−	0.854026i	$-0.674154\pi$
$661$	−26.7501	−1.04046	−0.520230	+	0.854026i	$0.674154\pi$
$662$	20.7955	0.808239
$663$	0	0
$664$	39.8960	1.54827
$665$	−1.49065	−0.0578050
$666$	34.9542	1.35445
$667$	14.7362	0.570589
$668$	−0.374744	−0.0144993
$669$	0.292839	0.0113218
$670$	−1.53707	−0.0593824
$671$	37.6781	1.45455
$672$	−0.643806	−0.0248353
$673$	15.3676	0.592378	0.296189	−	0.955129i	$-0.404284\pi$
$673$	15.3676	0.592378	0.296189	+	0.955129i	$0.404284\pi$
$674$	43.9678	1.69358
$675$	3.51127	0.135149
$676$	0	0
$677$	39.3521	1.51242	0.756212	−	0.654326i	$-0.227048\pi$
$677$	39.3521	1.51242	0.756212	+	0.654326i	$0.227048\pi$
$678$	1.33029	0.0510894
$679$	−53.6947	−2.06061
$680$	−1.01528	−0.0389343
$681$	0.848703	0.0325224
$682$	3.77266	0.144462
$683$	2.16391	0.0827996	0.0413998	−	0.999143i	$-0.486818\pi$
$683$	2.16391	0.0827996	0.0413998	+	0.999143i	$0.486818\pi$
$684$	−0.957888	−0.0366258
$685$	−1.26297	−0.0482555
$686$	−51.5867	−1.96959
$687$	−2.78706	−0.106333
$688$	3.80220	0.144958
$689$	0	0
$690$	−0.0635348	−0.00241873
$691$	−4.08682	−0.155470	−0.0777349	−	0.996974i	$-0.524769\pi$
$691$	−4.08682	−0.155470	−0.0777349	+	0.996974i	$0.524769\pi$
$692$	4.90470	0.186449
$693$	−39.5980	−1.50420
$694$	−15.0985	−0.573130
$695$	0.240841	0.00913564
$696$	2.60009	0.0985561
$697$	3.38761	0.128315
$698$	−43.9886	−1.66499
$699$	−0.0368634	−0.00139430
$700$	4.79098	0.181082
$701$	4.25935	0.160874	0.0804368	−	0.996760i	$-0.474368\pi$
$701$	4.25935	0.160874	0.0804368	+	0.996760i	$0.474368\pi$
$702$	0	0
$703$	−13.6628	−0.515301
$704$	24.3405	0.917367
$705$	−0.0206265	−0.000776837 0
$706$	0.623851	0.0234790
$707$	35.7684	1.34521
$708$	−0.243239	−0.00914149
$709$	3.54395	0.133096	0.0665480	−	0.997783i	$-0.478801\pi$
$709$	3.54395	0.133096	0.0665480	+	0.997783i	$0.478801\pi$
$710$	0.636038	0.0238701
$711$	22.7556	0.853403
$712$	−39.8573	−1.49372
$713$	−1.98053	−0.0741715
$714$	1.26690	0.0474126
$715$	0	0
$716$	−1.09038	−0.0407493
$717$	0.605798	0.0226239
$718$	−28.0110	−1.04536
$719$	19.4717	0.726173	0.363087	−	0.931755i	$-0.381723\pi$
$719$	19.4717	0.726173	0.363087	+	0.931755i	$0.381723\pi$
$720$	2.14442	0.0799180
$721$	29.5724	1.10133
$722$	22.1790	0.825416
$723$	−1.29317	−0.0480934
$724$	0.921736	0.0342561
$725$	−36.8978	−1.37035
$726$	0.486518	0.0180564
$727$	43.9668	1.63064	0.815320	−	0.579011i	$-0.196561\pi$
$727$	43.9668	1.63064	0.815320	+	0.579011i	$0.196561\pi$
$728$	0	0
$729$	−26.2474	−0.972126
$730$	0.349079	0.0129200
$731$	1.81949	0.0672963
$732$	−0.324688	−0.0120008
$733$	−21.9574	−0.811014	−0.405507	−	0.914092i	$-0.632905\pi$
$733$	−21.9574	−0.811014	−0.405507	+	0.914092i	$0.632905\pi$
$734$	−41.5767	−1.53463
$735$	0.363406	0.0134044
$736$	−2.28906	−0.0843759
$737$	15.9599	0.587891
$738$	−7.98268	−0.293846
$739$	−24.7472	−0.910340	−0.455170	−	0.890405i	$-0.650421\pi$
$739$	−24.7472	−0.910340	−0.455170	+	0.890405i	$0.650421\pi$
$740$	−0.362877	−0.0133396
$741$	0	0
$742$	64.1418	2.35472
$743$	6.10010	0.223791	0.111896	−	0.993720i	$-0.464308\pi$
$743$	6.10010	0.223791	0.111896	+	0.993720i	$0.464308\pi$
$744$	−0.349449	−0.0128114
$745$	−0.932048	−0.0341476
$746$	−26.5820	−0.973235
$747$	−40.3244	−1.47539
$748$	0.980762	0.0358602
$749$	64.4942	2.35657
$750$	0.319482	0.0116658
$751$	−43.7295	−1.59571	−0.797856	−	0.602848i	$-0.794033\pi$
$751$	−43.7295	−1.59571	−0.797856	+	0.602848i	$0.794033\pi$
$752$	3.05593	0.111438
$753$	0.678732	0.0247344
$754$	0	0
$755$	−3.94456	−0.143557
$756$	0.684064	0.0248792
$757$	49.0002	1.78094	0.890471	−	0.455039i	$-0.150375\pi$
$757$	49.0002	1.78094	0.890471	+	0.455039i	$0.150375\pi$
$758$	12.5635	0.456327
$759$	0.659701	0.0239456
$760$	−0.935149	−0.0339214
$761$	−32.9397	−1.19406	−0.597031	−	0.802218i	$-0.703653\pi$
$761$	−32.9397	−1.19406	−0.597031	+	0.802218i	$0.703653\pi$
$762$	−0.805285	−0.0291724
$763$	39.0016	1.41195
$764$	4.28865	0.155158
$765$	1.02619	0.0371018
$766$	1.14139	0.0412400
$767$	0	0
$768$	−0.576064	−0.0207869
$769$	−42.4130	−1.52945	−0.764727	−	0.644355i	$-0.777126\pi$
$769$	−42.4130	−1.52945	−0.764727	+	0.644355i	$0.777126\pi$
$770$	−3.59650	−0.129609
$771$	1.76561	0.0635868
$772$	1.74512	0.0628083
$773$	3.73872	0.134472	0.0672362	−	0.997737i	$-0.478582\pi$
$773$	3.73872	0.134472	0.0672362	+	0.997737i	$0.478582\pi$
$774$	−4.28751	−0.154111
$775$	4.95902	0.178133
$776$	−33.6849	−1.20922
$777$	4.86715	0.174608
$778$	−29.5230	−1.05845
$779$	3.12024	0.111794
$780$	0	0
$781$	−6.60418	−0.236316
$782$	4.50449	0.161080
$783$	−5.26833	−0.188275
$784$	−53.8408	−1.92289
$785$	1.28217	0.0457627
$786$	−1.33028	−0.0474495
$787$	17.3985	0.620191	0.310095	−	0.950705i	$-0.399639\pi$
$787$	17.3985	0.620191	0.310095	+	0.950705i	$0.399639\pi$
$788$	−5.26573	−0.187584
$789$	2.40117	0.0854841
$790$	2.06679	0.0735331
$791$	−39.5320	−1.40560
$792$	−24.8415	−0.882703
$793$	0	0
$794$	12.6248	0.448037
$795$	−0.243442	−0.00863399
$796$	−2.76637	−0.0980515
$797$	−24.0225	−0.850921	−0.425461	−	0.904977i	$-0.639888\pi$
$797$	−24.0225	−0.850921	−0.425461	+	0.904977i	$0.639888\pi$
$798$	1.16691	0.0413081
$799$	1.46237	0.0517351
$800$	5.73154	0.202641
$801$	40.2853	1.42341
$802$	−17.6689	−0.623909
$803$	−3.62459	−0.127909
$804$	−0.137533	−0.00485043
$805$	1.88806	0.0665452
$806$	0	0
$807$	3.03399	0.106801
$808$	22.4390	0.789403
$809$	−33.3545	−1.17268	−0.586341	−	0.810065i	$-0.699432\pi$
$809$	−33.3545	−1.17268	−0.586341	+	0.810065i	$0.699432\pi$
$810$	−2.40675	−0.0845646
$811$	18.9502	0.665431	0.332716	−	0.943027i	$-0.392035\pi$
$811$	18.9502	0.665431	0.332716	+	0.943027i	$0.392035\pi$
$812$	−7.18840	−0.252263
$813$	1.02523	0.0359564
$814$	−32.9642	−1.15539
$815$	4.50370	0.157758
$816$	0.712388	0.0249386
$817$	1.67588	0.0586317
$818$	29.6014	1.03499
$819$	0	0
$820$	0.0828721	0.00289402
$821$	−12.8755	−0.449358	−0.224679	−	0.974433i	$-0.572133\pi$
$821$	−12.8755	−0.449358	−0.224679	+	0.974433i	$0.572133\pi$
$822$	0.988672	0.0344839
$823$	−5.73400	−0.199875	−0.0999374	−	0.994994i	$-0.531864\pi$
$823$	−5.73400	−0.199875	−0.0999374	+	0.994994i	$0.531864\pi$
$824$	18.5520	0.646290
$825$	−1.65181	−0.0575087
$826$	−63.2389	−2.20036
$827$	0.0433533	0.00150754	0.000753771	−	1.00000i	$-0.499760\pi$
$827$	0.0433533	0.00150754	0.000753771		1.00000i	$0.499760\pi$
$828$	1.21326	0.0421636
$829$	15.1688	0.526834	0.263417	−	0.964682i	$-0.415150\pi$
$829$	15.1688	0.526834	0.263417	+	0.964682i	$0.415150\pi$
$830$	−3.66248	−0.127127
$831$	−0.598277	−0.0207540
$832$	0	0
$833$	−25.7648	−0.892697
$834$	−0.188535	−0.00652842
$835$	0.369776	0.0127966
$836$	0.903352	0.0312431
$837$	0.708058	0.0244741
$838$	29.3240	1.01298
$839$	25.9984	0.897565	0.448783	−	0.893641i	$-0.351858\pi$
$839$	25.9984	0.897565	0.448783	+	0.893641i	$0.351858\pi$
$840$	0.333132	0.0114942
$841$	26.3615	0.909019
$842$	32.0221	1.10356
$843$	0.322809	0.0111181
$844$	2.17158	0.0747488
$845$	0	0
$846$	−3.44598	−0.118475
$847$	−14.4578	−0.496776
$848$	36.0674	1.23856
$849$	−0.285772	−0.00980766
$850$	−11.2787	−0.386857
$851$	17.3052	0.593215
$852$	0.0569110	0.00194974
$853$	−0.970188	−0.0332186	−0.0166093	−	0.999862i	$-0.505287\pi$
$853$	−0.970188	−0.0332186	−0.0166093	+	0.999862i	$0.505287\pi$
$854$	−84.4145	−2.88861
$855$	0.945190	0.0323248
$856$	40.4599	1.38289
$857$	−45.9538	−1.56975	−0.784875	−	0.619654i	$-0.787273\pi$
$857$	−45.9538	−1.56975	−0.784875	+	0.619654i	$0.787273\pi$
$858$	0	0
$859$	15.0913	0.514909	0.257454	−	0.966290i	$-0.417116\pi$
$859$	15.0913	0.514909	0.257454	+	0.966290i	$0.417116\pi$
$860$	0.0445107	0.00151780
$861$	−1.11154	−0.0378810
$862$	−1.94505	−0.0662486
$863$	18.3546	0.624796	0.312398	−	0.949951i	$-0.398868\pi$
$863$	18.3546	0.624796	0.312398	+	0.949951i	$0.398868\pi$
$864$	0.818359	0.0278412
$865$	−4.83968	−0.164554
$866$	8.79723	0.298942
$867$	−1.66995	−0.0567144
$868$	0.966113	0.0327920
$869$	−21.4601	−0.727984
$870$	−0.238690	−0.00809234
$871$	0	0
$872$	24.4674	0.828569
$873$	34.0466	1.15230
$874$	4.14896	0.140341
$875$	−9.49400	−0.320956
$876$	0.0312346	0.00105532
$877$	39.2011	1.32373	0.661863	−	0.749625i	$-0.269766\pi$
$877$	39.2011	1.32373	0.661863	+	0.749625i	$0.269766\pi$
$878$	−41.5284	−1.40152
$879$	1.86514	0.0629095
$880$	−2.02234	−0.0681729
$881$	50.3010	1.69468	0.847342	−	0.531048i	$-0.178201\pi$
$881$	50.3010	1.69468	0.847342	+	0.531048i	$0.178201\pi$
$882$	60.7129	2.04431
$883$	36.4707	1.22734	0.613669	−	0.789563i	$-0.289693\pi$
$883$	36.4707	1.22734	0.613669	+	0.789563i	$0.289693\pi$
$884$	0	0
$885$	0.240015	0.00806802
$886$	3.61792	0.121546
$887$	44.5895	1.49717	0.748584	−	0.663040i	$-0.230734\pi$
$887$	44.5895	1.49717	0.748584	+	0.663040i	$0.230734\pi$
$888$	3.05337	0.102464
$889$	23.9306	0.802605
$890$	3.65893	0.122647
$891$	24.9900	0.837197
$892$	−0.507899	−0.0170057
$893$	1.34695	0.0450740
$894$	0.729623	0.0244022
$895$	1.07592	0.0359642
$896$	−43.6472	−1.45815
$897$	0	0
$898$	−8.57838	−0.286264
$899$	−7.44053	−0.248156
$900$	−3.03785	−0.101262
$901$	17.2595	0.574999
$902$	7.52820	0.250662
$903$	−0.597007	−0.0198672
$904$	−24.8001	−0.824839
$905$	−0.909518	−0.0302334
$906$	3.08787	0.102588
$907$	4.65455	0.154552	0.0772758	−	0.997010i	$-0.475378\pi$
$907$	4.65455	0.154552	0.0772758	+	0.997010i	$0.475378\pi$
$908$	−1.47199	−0.0488496
$909$	−22.6800	−0.752248
$910$	0	0
$911$	−3.07618	−0.101918	−0.0509591	−	0.998701i	$-0.516228\pi$
$911$	−3.07618	−0.101918	−0.0509591	+	0.998701i	$0.516228\pi$
$912$	0.656161	0.0217276
$913$	38.0286	1.25856
$914$	37.4727	1.23949
$915$	0.320385	0.0105916
$916$	4.83388	0.159716
$917$	39.5318	1.30545
$918$	−1.61039	−0.0531509
$919$	−5.25601	−0.173380	−0.0866900	−	0.996235i	$-0.527629\pi$
$919$	−5.25601	−0.173380	−0.0866900	+	0.996235i	$0.527629\pi$
$920$	1.18446	0.0390504
$921$	3.57141	0.117682
$922$	−25.1221	−0.827353
$923$	0	0
$924$	−0.321805	−0.0105866
$925$	−43.3302	−1.42469
$926$	−39.7266	−1.30550
$927$	−18.7512	−0.615871
$928$	−8.59963	−0.282297
$929$	1.40191	0.0459951	0.0229975	−	0.999736i	$-0.492679\pi$
$929$	1.40191	0.0459951	0.0229975	+	0.999736i	$0.492679\pi$
$930$	0.0320796	0.00105193
$931$	−23.7312	−0.777759
$932$	0.0639358	0.00209429
$933$	3.40501	0.111475
$934$	−15.3829	−0.503344
$935$	−0.967761	−0.0316492
$936$	0	0
$937$	37.2364	1.21646	0.608230	−	0.793761i	$-0.291880\pi$
$937$	37.2364	1.21646	0.608230	+	0.793761i	$0.291880\pi$
$938$	−35.7568	−1.16750
$939$	−2.25330	−0.0735338
$940$	0.0357745	0.00116683
$941$	−44.1056	−1.43780	−0.718901	−	0.695112i	$-0.755355\pi$
$941$	−44.1056	−1.43780	−0.718901	+	0.695112i	$0.755355\pi$
$942$	−1.00371	−0.0327025
$943$	−3.95208	−0.128697
$944$	−35.5597	−1.15737
$945$	−0.674996	−0.0219576
$946$	4.04341	0.131462
$947$	2.08162	0.0676436	0.0338218	−	0.999428i	$-0.489232\pi$
$947$	2.08162	0.0676436	0.0338218	+	0.999428i	$0.489232\pi$
$948$	0.184931	0.00600627
$949$	0	0
$950$	−10.3885	−0.337048
$951$	3.37629	0.109484
$952$	−23.6184	−0.765477
$953$	−6.81701	−0.220824	−0.110412	−	0.993886i	$-0.535217\pi$
$953$	−6.81701	−0.220824	−0.110412	+	0.993886i	$0.535217\pi$
$954$	−40.6709	−1.31677
$955$	−4.23181	−0.136938
$956$	−1.05069	−0.0339819
$957$	2.47839	0.0801148
$958$	−36.5499	−1.18087
$959$	−29.3803	−0.948738
$960$	0.206972	0.00668000
$961$	1.00000	0.0322581
$962$	0	0
$963$	−40.8944	−1.31780
$964$	2.24287	0.0722379
$965$	−1.72199	−0.0554328
$966$	−1.47800	−0.0475539
$967$	−58.1703	−1.87063	−0.935315	−	0.353816i	$-0.884884\pi$
$967$	−58.1703	−1.87063	−0.935315	+	0.353816i	$0.884884\pi$
$968$	−9.06999	−0.291520
$969$	0.313997	0.0100870
$970$	3.09230	0.0992877
$971$	−23.5053	−0.754321	−0.377161	−	0.926148i	$-0.623100\pi$
$971$	−23.5053	−0.754321	−0.377161	+	0.926148i	$0.623100\pi$
$972$	−0.651132	−0.0208851
$973$	5.60267	0.179613
$974$	−10.2923	−0.329786
$975$	0	0
$976$	−47.4669	−1.51938
$977$	−8.54005	−0.273220	−0.136610	−	0.990625i	$-0.543621\pi$
$977$	−8.54005	−0.273220	−0.136610	+	0.990625i	$0.543621\pi$
$978$	−3.52558	−0.112735
$979$	−37.9917	−1.21422
$980$	−0.630291	−0.0201339
$981$	−24.7301	−0.789571
$982$	39.8086	1.27034
$983$	15.1003	0.481625	0.240812	−	0.970572i	$-0.422586\pi$
$983$	15.1003	0.481625	0.240812	+	0.970572i	$0.422586\pi$
$984$	−0.697313	−0.0222295
$985$	5.19593	0.165556
$986$	16.9226	0.538926
$987$	−0.479831	−0.0152732
$988$	0	0
$989$	−2.12267	−0.0674969
$990$	2.28046	0.0724778
$991$	−25.5201	−0.810672	−0.405336	−	0.914168i	$-0.632846\pi$
$991$	−25.5201	−0.810672	−0.405336	+	0.914168i	$0.632846\pi$
$992$	1.15578	0.0366961
$993$	−1.83606	−0.0582656
$994$	14.7961	0.469303
$995$	2.72970	0.0865375
$996$	−0.327709	−0.0103839
$997$	−50.4640	−1.59821	−0.799105	−	0.601192i	$-0.794693\pi$
$997$	−50.4640	−1.59821	−0.799105	+	0.601192i	$0.794693\pi$
$998$	−35.0637	−1.10992
$999$	−6.18677	−0.195741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.u.1.17	✓	54
13.12	even	2		5239.2.a.v.1.38	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.17	✓	54	1.1	even	1	trivial
5239.2.a.v.1.38	yes	54	13.12	even	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-1.33972 q^{2} +0.118285 q^{3} -0.205154 q^{4} +0.202435 q^{5} -0.158469 q^{6} +4.70921 q^{7} +2.95429 q^{8} -2.98601 q^{9} +O(q^{10})\)	\(q-1.33972 q^{2} +0.118285 q^{3} -0.205154 q^{4} +0.202435 q^{5} -0.158469 q^{6} +4.70921 q^{7} +2.95429 q^{8} -2.98601 q^{9} -0.271205 q^{10} +2.81601 q^{11} -0.0242667 q^{12} -6.30902 q^{14} +0.0239451 q^{15} -3.54760 q^{16} -1.69766 q^{17} +4.00041 q^{18} -1.56366 q^{19} -0.0415303 q^{20} +0.557031 q^{21} -3.77266 q^{22} +1.98053 q^{23} +0.349449 q^{24} -4.95902 q^{25} -0.708058 q^{27} -0.966113 q^{28} +7.44053 q^{29} -0.0320796 q^{30} -1.00000 q^{31} -1.15578 q^{32} +0.333093 q^{33} +2.27438 q^{34} +0.953307 q^{35} +0.612592 q^{36} +8.73766 q^{37} +2.09487 q^{38} +0.598050 q^{40} -1.99546 q^{41} -0.746265 q^{42} -1.07177 q^{43} -0.577715 q^{44} -0.604471 q^{45} -2.65336 q^{46} -0.861407 q^{47} -0.419630 q^{48} +15.1767 q^{49} +6.64369 q^{50} -0.200808 q^{51} -10.1667 q^{53} +0.948598 q^{54} +0.570057 q^{55} +13.9124 q^{56} -0.184959 q^{57} -9.96822 q^{58} +10.0236 q^{59} -0.00491242 q^{60} +13.3800 q^{61} +1.33972 q^{62} -14.0617 q^{63} +8.64363 q^{64} -0.446250 q^{66} +5.66757 q^{67} +0.348281 q^{68} +0.234268 q^{69} -1.27716 q^{70} -2.34523 q^{71} -8.82152 q^{72} -1.28714 q^{73} -11.7060 q^{74} -0.586580 q^{75} +0.320792 q^{76} +13.2612 q^{77} -7.62076 q^{79} -0.718158 q^{80} +8.87427 q^{81} +2.67336 q^{82} +13.5045 q^{83} -0.114277 q^{84} -0.343664 q^{85} +1.43587 q^{86} +0.880107 q^{87} +8.31929 q^{88} -13.4913 q^{89} +0.809821 q^{90} -0.406314 q^{92} -0.118285 q^{93} +1.15404 q^{94} -0.316540 q^{95} -0.136712 q^{96} -11.4021 q^{97} -20.3325 q^{98} -8.40862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * q^99

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