LMFDB - Embedded newform 6026.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} + \cdots - 18 $ x^20 - 5x^19 - 17x^18 + 115x^17 + 78x^16 - 1083x^15 + 248x^14 + 5359x^13 - 3723x^12 - 14776x^11 + 14837x^10 + 21886x^9 - 28084x^8 - 14682x^7 + 25315x^6 + 2042x^5 - 9137x^4 + 576x^3 + 1159x^2 - 78*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-1.95611$ of defining polynomial
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.95611 q^{3} +1.00000 q^{4} -3.19910 q^{5} +1.95611 q^{6} +0.785940 q^{7} +1.00000 q^{8} +0.826384 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.95611 q^{3} +1.00000 q^{4} -3.19910 q^{5} +1.95611 q^{6} +0.785940 q^{7} +1.00000 q^{8} +0.826384 q^{9} -3.19910 q^{10} -2.79655 q^{11} +1.95611 q^{12} -1.12153 q^{13} +0.785940 q^{14} -6.25780 q^{15} +1.00000 q^{16} +6.29137 q^{17} +0.826384 q^{18} -5.77980 q^{19} -3.19910 q^{20} +1.53739 q^{21} -2.79655 q^{22} +1.00000 q^{23} +1.95611 q^{24} +5.23422 q^{25} -1.12153 q^{26} -4.25184 q^{27} +0.785940 q^{28} +0.967528 q^{29} -6.25780 q^{30} -3.26606 q^{31} +1.00000 q^{32} -5.47037 q^{33} +6.29137 q^{34} -2.51430 q^{35} +0.826384 q^{36} +7.66151 q^{37} -5.77980 q^{38} -2.19385 q^{39} -3.19910 q^{40} -7.03756 q^{41} +1.53739 q^{42} +7.26539 q^{43} -2.79655 q^{44} -2.64368 q^{45} +1.00000 q^{46} -6.60397 q^{47} +1.95611 q^{48} -6.38230 q^{49} +5.23422 q^{50} +12.3066 q^{51} -1.12153 q^{52} -6.69887 q^{53} -4.25184 q^{54} +8.94643 q^{55} +0.785940 q^{56} -11.3060 q^{57} +0.967528 q^{58} -1.83857 q^{59} -6.25780 q^{60} -4.80854 q^{61} -3.26606 q^{62} +0.649488 q^{63} +1.00000 q^{64} +3.58789 q^{65} -5.47037 q^{66} -0.232592 q^{67} +6.29137 q^{68} +1.95611 q^{69} -2.51430 q^{70} -15.2779 q^{71} +0.826384 q^{72} -5.03780 q^{73} +7.66151 q^{74} +10.2387 q^{75} -5.77980 q^{76} -2.19792 q^{77} -2.19385 q^{78} -12.2273 q^{79} -3.19910 q^{80} -10.7962 q^{81} -7.03756 q^{82} +0.286919 q^{83} +1.53739 q^{84} -20.1267 q^{85} +7.26539 q^{86} +1.89260 q^{87} -2.79655 q^{88} +5.71106 q^{89} -2.64368 q^{90} -0.881457 q^{91} +1.00000 q^{92} -6.38879 q^{93} -6.60397 q^{94} +18.4901 q^{95} +1.95611 q^{96} -12.3659 q^{97} -6.38230 q^{98} -2.31102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.95611	1.12936	0.564682	−	0.825309i	$-0.308999\pi$
$3$	1.95611	1.12936	0.564682	+	0.825309i	$0.308999\pi$
$4$	1.00000	0.500000
$5$	−3.19910	−1.43068	−0.715340	−	0.698777i	$-0.753728\pi$
$5$	−3.19910	−1.43068	−0.715340	+	0.698777i	$0.753728\pi$
$6$	1.95611	0.798580
$7$	0.785940	0.297057	0.148529	−	0.988908i	$-0.452546\pi$
$7$	0.785940	0.297057	0.148529	+	0.988908i	$0.452546\pi$
$8$	1.00000	0.353553
$9$	0.826384	0.275461
$10$	−3.19910	−1.01164
$11$	−2.79655	−0.843192	−0.421596	−	0.906784i	$-0.638530\pi$
$11$	−2.79655	−0.843192	−0.421596	+	0.906784i	$0.638530\pi$
$12$	1.95611	0.564682
$13$	−1.12153	−0.311057	−0.155529	−	0.987831i	$-0.549708\pi$
$13$	−1.12153	−0.311057	−0.155529	+	0.987831i	$0.549708\pi$
$14$	0.785940	0.210051
$15$	−6.25780	−1.61576
$16$	1.00000	0.250000
$17$	6.29137	1.52588	0.762941	−	0.646468i	$-0.223755\pi$
$17$	6.29137	1.52588	0.762941	+	0.646468i	$0.223755\pi$
$18$	0.826384	0.194781
$19$	−5.77980	−1.32598	−0.662989	−	0.748629i	$-0.730712\pi$
$19$	−5.77980	−1.32598	−0.662989	+	0.748629i	$0.730712\pi$
$20$	−3.19910	−0.715340
$21$	1.53739	0.335486
$22$	−2.79655	−0.596226
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.95611	0.399290
$25$	5.23422	1.04684
$26$	−1.12153	−0.219951
$27$	−4.25184	−0.818267
$28$	0.785940	0.148529
$29$	0.967528	0.179665	0.0898327	−	0.995957i	$-0.471367\pi$
$29$	0.967528	0.179665	0.0898327	+	0.995957i	$0.471367\pi$
$30$	−6.25780	−1.14251
$31$	−3.26606	−0.586602	−0.293301	−	0.956020i	$-0.594754\pi$
$31$	−3.26606	−0.586602	−0.293301	+	0.956020i	$0.594754\pi$
$32$	1.00000	0.176777
$33$	−5.47037	−0.952270
$34$	6.29137	1.07896
$35$	−2.51430	−0.424994
$36$	0.826384	0.137731
$37$	7.66151	1.25954	0.629772	−	0.776780i	$-0.283148\pi$
$37$	7.66151	1.25954	0.629772	+	0.776780i	$0.283148\pi$
$38$	−5.77980	−0.937608
$39$	−2.19385	−0.351297
$40$	−3.19910	−0.505822
$41$	−7.03756	−1.09908	−0.549541	−	0.835466i	$-0.685198\pi$
$41$	−7.03756	−1.09908	−0.549541	+	0.835466i	$0.685198\pi$
$42$	1.53739	0.237224
$43$	7.26539	1.10796	0.553981	−	0.832529i	$-0.313108\pi$
$43$	7.26539	1.10796	0.553981	+	0.832529i	$0.313108\pi$
$44$	−2.79655	−0.421596
$45$	−2.64368	−0.394097
$46$	1.00000	0.147442
$47$	−6.60397	−0.963288	−0.481644	−	0.876367i	$-0.659960\pi$
$47$	−6.60397	−0.963288	−0.481644	+	0.876367i	$0.659960\pi$
$48$	1.95611	0.282341
$49$	−6.38230	−0.911757
$50$	5.23422	0.740230
$51$	12.3066	1.72327
$52$	−1.12153	−0.155529
$53$	−6.69887	−0.920161	−0.460081	−	0.887877i	$-0.652179\pi$
$53$	−6.69887	−0.920161	−0.460081	+	0.887877i	$0.652179\pi$
$54$	−4.25184	−0.578602
$55$	8.94643	1.20634
$56$	0.785940	0.105026
$57$	−11.3060	−1.49751
$58$	0.967528	0.127043
$59$	−1.83857	−0.239362	−0.119681	−	0.992812i	$-0.538187\pi$
$59$	−1.83857	−0.239362	−0.119681	+	0.992812i	$0.538187\pi$
$60$	−6.25780	−0.807878
$61$	−4.80854	−0.615670	−0.307835	−	0.951440i	$-0.599605\pi$
$61$	−4.80854	−0.615670	−0.307835	+	0.951440i	$0.599605\pi$
$62$	−3.26606	−0.414790
$63$	0.649488	0.0818278
$64$	1.00000	0.125000
$65$	3.58789	0.445023
$66$	−5.47037	−0.673356
$67$	−0.232592	−0.0284157	−0.0142078	−	0.999899i	$-0.504523\pi$
$67$	−0.232592	−0.0284157	−0.0142078	+	0.999899i	$0.504523\pi$
$68$	6.29137	0.762941
$69$	1.95611	0.235489
$70$	−2.51430	−0.300516
$71$	−15.2779	−1.81315	−0.906576	−	0.422043i	$-0.861313\pi$
$71$	−15.2779	−1.81315	−0.906576	+	0.422043i	$0.861313\pi$
$72$	0.826384	0.0973903
$73$	−5.03780	−0.589630	−0.294815	−	0.955554i	$-0.595258\pi$
$73$	−5.03780	−0.589630	−0.294815	+	0.955554i	$0.595258\pi$
$74$	7.66151	0.890633
$75$	10.2387	1.18227
$76$	−5.77980	−0.662989
$77$	−2.19792	−0.250476
$78$	−2.19385	−0.248404
$79$	−12.2273	−1.37568	−0.687839	−	0.725864i	$-0.741440\pi$
$79$	−12.2273	−1.37568	−0.687839	+	0.725864i	$0.741440\pi$
$80$	−3.19910	−0.357670
$81$	−10.7962	−1.19958
$82$	−7.03756	−0.777169
$83$	0.286919	0.0314934	0.0157467	−	0.999876i	$-0.494987\pi$
$83$	0.286919	0.0314934	0.0157467	+	0.999876i	$0.494987\pi$
$84$	1.53739	0.167743
$85$	−20.1267	−2.18305
$86$	7.26539	0.783447
$87$	1.89260	0.202908
$88$	−2.79655	−0.298113
$89$	5.71106	0.605371	0.302686	−	0.953090i	$-0.402117\pi$
$89$	5.71106	0.605371	0.302686	+	0.953090i	$0.402117\pi$
$90$	−2.64368	−0.278669
$91$	−0.881457	−0.0924018
$92$	1.00000	0.104257
$93$	−6.38879	−0.662487
$94$	−6.60397	−0.681147
$95$	18.4901	1.89705
$96$	1.95611	0.199645
$97$	−12.3659	−1.25557	−0.627786	−	0.778386i	$-0.716039\pi$
$97$	−12.3659	−1.25557	−0.627786	+	0.778386i	$0.716039\pi$
$98$	−6.38230	−0.644710
$99$	−2.31102	−0.232267
$100$	5.23422	0.523422
$101$	4.17753	0.415679	0.207840	−	0.978163i	$-0.433357\pi$
$101$	4.17753	0.415679	0.207840	+	0.978163i	$0.433357\pi$
$102$	12.3066	1.21854
$103$	−1.61463	−0.159094	−0.0795470	−	0.996831i	$-0.525347\pi$
$103$	−1.61463	−0.159094	−0.0795470	+	0.996831i	$0.525347\pi$
$104$	−1.12153	−0.109975
$105$	−4.91825	−0.479972
$106$	−6.69887	−0.650652
$107$	−0.210986	−0.0203968	−0.0101984	−	0.999948i	$-0.503246\pi$
$107$	−0.210986	−0.0203968	−0.0101984	+	0.999948i	$0.503246\pi$
$108$	−4.25184	−0.409134
$109$	−13.8005	−1.32184	−0.660922	−	0.750454i	$-0.729835\pi$
$109$	−13.8005	−1.32184	−0.660922	+	0.750454i	$0.729835\pi$
$110$	8.94643	0.853009
$111$	14.9868	1.42248
$112$	0.785940	0.0742643
$113$	9.58577	0.901753	0.450877	−	0.892586i	$-0.351111\pi$
$113$	9.58577	0.901753	0.450877	+	0.892586i	$0.351111\pi$
$114$	−11.3060	−1.05890
$115$	−3.19910	−0.298317
$116$	0.967528	0.0898327
$117$	−0.926817	−0.0856843
$118$	−1.83857	−0.169254
$119$	4.94464	0.453274
$120$	−6.25780	−0.571256
$121$	−3.17931	−0.289028
$122$	−4.80854	−0.435345
$123$	−13.7663	−1.24126
$124$	−3.26606	−0.293301
$125$	−0.749282	−0.0670178
$126$	0.649488	0.0578610
$127$	0.0806456	0.00715614	0.00357807	−	0.999994i	$-0.498861\pi$
$127$	0.0806456	0.00715614	0.00357807	+	0.999994i	$0.498861\pi$
$128$	1.00000	0.0883883
$129$	14.2119	1.25129
$130$	3.58789	0.314679
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−5.47037	−0.476135
$133$	−4.54258	−0.393891
$134$	−0.232592	−0.0200929
$135$	13.6021	1.17068
$136$	6.29137	0.539481
$137$	−12.4755	−1.06586	−0.532928	−	0.846161i	$-0.678908\pi$
$137$	−12.4755	−1.06586	−0.532928	+	0.846161i	$0.678908\pi$
$138$	1.95611	0.166516
$139$	5.87012	0.497897	0.248949	−	0.968517i	$-0.419915\pi$
$139$	5.87012	0.497897	0.248949	+	0.968517i	$0.419915\pi$
$140$	−2.51430	−0.212497
$141$	−12.9181	−1.08790
$142$	−15.2779	−1.28209
$143$	3.13642	0.262281
$144$	0.826384	0.0688653
$145$	−3.09521	−0.257044
$146$	−5.03780	−0.416932
$147$	−12.4845	−1.02970
$148$	7.66151	0.629772
$149$	−7.11836	−0.583159	−0.291579	−	0.956547i	$-0.594181\pi$
$149$	−7.11836	−0.583159	−0.291579	+	0.956547i	$0.594181\pi$
$150$	10.2387	0.835989
$151$	−13.7047	−1.11527	−0.557637	−	0.830085i	$-0.688292\pi$
$151$	−13.7047	−1.11527	−0.557637	+	0.830085i	$0.688292\pi$
$152$	−5.77980	−0.468804
$153$	5.19909	0.420322
$154$	−2.19792	−0.177113
$155$	10.4484	0.839239
$156$	−2.19385	−0.175648
$157$	0.914056	0.0729496	0.0364748	−	0.999335i	$-0.488387\pi$
$157$	0.914056	0.0729496	0.0364748	+	0.999335i	$0.488387\pi$
$158$	−12.2273	−0.972751
$159$	−13.1038	−1.03920
$160$	−3.19910	−0.252911
$161$	0.785940	0.0619407
$162$	−10.7962	−0.848233
$163$	−12.9696	−1.01586	−0.507930	−	0.861398i	$-0.669589\pi$
$163$	−12.9696	−1.01586	−0.507930	+	0.861398i	$0.669589\pi$
$164$	−7.03756	−0.549541
$165$	17.5002	1.36239
$166$	0.286919	0.0222692
$167$	22.7235	1.75839	0.879197	−	0.476458i	$-0.158080\pi$
$167$	22.7235	1.75839	0.879197	+	0.476458i	$0.158080\pi$
$168$	1.53739	0.118612
$169$	−11.7422	−0.903243
$170$	−20.1267	−1.54365
$171$	−4.77634	−0.365256
$172$	7.26539	0.553981
$173$	−0.660557	−0.0502212	−0.0251106	−	0.999685i	$-0.507994\pi$
$173$	−0.660557	−0.0502212	−0.0251106	+	0.999685i	$0.507994\pi$
$174$	1.89260	0.143477
$175$	4.11378	0.310972
$176$	−2.79655	−0.210798
$177$	−3.59646	−0.270327
$178$	5.71106	0.428062
$179$	20.5615	1.53684	0.768419	−	0.639947i	$-0.221044\pi$
$179$	20.5615	1.53684	0.768419	+	0.639947i	$0.221044\pi$
$180$	−2.64368	−0.197048
$181$	14.3313	1.06524	0.532619	−	0.846355i	$-0.321208\pi$
$181$	14.3313	1.06524	0.532619	+	0.846355i	$0.321208\pi$
$182$	−0.881457	−0.0653380
$183$	−9.40605	−0.695315
$184$	1.00000	0.0737210
$185$	−24.5099	−1.80200
$186$	−6.38879	−0.468449
$187$	−17.5941	−1.28661
$188$	−6.60397	−0.481644
$189$	−3.34169	−0.243072
$190$	18.4901	1.34142
$191$	14.3260	1.03659	0.518297	−	0.855201i	$-0.326566\pi$
$191$	14.3260	1.03659	0.518297	+	0.855201i	$0.326566\pi$
$192$	1.95611	0.141170
$193$	−20.3072	−1.46175	−0.730873	−	0.682514i	$-0.760887\pi$
$193$	−20.3072	−1.46175	−0.730873	+	0.682514i	$0.760887\pi$
$194$	−12.3659	−0.887823
$195$	7.01833	0.502593
$196$	−6.38230	−0.455878
$197$	−7.12965	−0.507967	−0.253983	−	0.967209i	$-0.581741\pi$
$197$	−7.12965	−0.507967	−0.253983	+	0.967209i	$0.581741\pi$
$198$	−2.31102	−0.164237
$199$	16.9172	1.19923	0.599615	−	0.800289i	$-0.295320\pi$
$199$	16.9172	1.19923	0.599615	+	0.800289i	$0.295320\pi$
$200$	5.23422	0.370115
$201$	−0.454978	−0.0320916
$202$	4.17753	0.293930
$203$	0.760419	0.0533709
$204$	12.3066	0.861637
$205$	22.5138	1.57244
$206$	−1.61463	−0.112497
$207$	0.826384	0.0574377
$208$	−1.12153	−0.0777643
$209$	16.1635	1.11805
$210$	−4.91825	−0.339392
$211$	13.4830	0.928210	0.464105	−	0.885780i	$-0.346376\pi$
$211$	13.4830	0.928210	0.464105	+	0.885780i	$0.346376\pi$
$212$	−6.69887	−0.460081
$213$	−29.8853	−2.04771
$214$	−0.210986	−0.0144227
$215$	−23.2427	−1.58514
$216$	−4.25184	−0.289301
$217$	−2.56693	−0.174254
$218$	−13.8005	−0.934685
$219$	−9.85452	−0.665907
$220$	8.94643	0.603168
$221$	−7.05598	−0.474637
$222$	14.9868	1.00585
$223$	12.0237	0.805170	0.402585	−	0.915383i	$-0.368112\pi$
$223$	12.0237	0.805170	0.402585	+	0.915383i	$0.368112\pi$
$224$	0.785940	0.0525128
$225$	4.32547	0.288365
$226$	9.58577	0.637636
$227$	10.7042	0.710463	0.355231	−	0.934778i	$-0.384402\pi$
$227$	10.7042	0.710463	0.355231	+	0.934778i	$0.384402\pi$
$228$	−11.3060	−0.748755
$229$	−2.88268	−0.190493	−0.0952464	−	0.995454i	$-0.530364\pi$
$229$	−2.88268	−0.190493	−0.0952464	+	0.995454i	$0.530364\pi$
$230$	−3.19910	−0.210942
$231$	−4.29938	−0.282879
$232$	0.967528	0.0635213
$233$	25.5318	1.67264	0.836322	−	0.548239i	$-0.184701\pi$
$233$	25.5318	1.67264	0.836322	+	0.548239i	$0.184701\pi$
$234$	−0.926817	−0.0605879
$235$	21.1267	1.37816
$236$	−1.83857	−0.119681
$237$	−23.9180	−1.55364
$238$	4.94464	0.320513
$239$	1.30907	0.0846765	0.0423382	−	0.999103i	$-0.486519\pi$
$239$	1.30907	0.0846765	0.0423382	+	0.999103i	$0.486519\pi$
$240$	−6.25780	−0.403939
$241$	13.6848	0.881515	0.440757	−	0.897626i	$-0.354710\pi$
$241$	13.6848	0.881515	0.440757	+	0.897626i	$0.354710\pi$
$242$	−3.17931	−0.204374
$243$	−8.36316	−0.536497
$244$	−4.80854	−0.307835
$245$	20.4176	1.30443
$246$	−13.7663	−0.877706
$247$	6.48224	0.412455
$248$	−3.26606	−0.207395
$249$	0.561245	0.0355675
$250$	−0.749282	−0.0473887
$251$	10.7185	0.676548	0.338274	−	0.941048i	$-0.390157\pi$
$251$	10.7185	0.676548	0.338274	+	0.941048i	$0.390157\pi$
$252$	0.649488	0.0409139
$253$	−2.79655	−0.175818
$254$	0.0806456	0.00506015
$255$	−39.3701	−2.46545
$256$	1.00000	0.0625000
$257$	−8.63324	−0.538527	−0.269264	−	0.963067i	$-0.586780\pi$
$257$	−8.63324	−0.538527	−0.269264	+	0.963067i	$0.586780\pi$
$258$	14.2119	0.884796
$259$	6.02149	0.374157
$260$	3.58789	0.222512
$261$	0.799550	0.0494909
$262$	−1.00000	−0.0617802
$263$	−5.87098	−0.362020	−0.181010	−	0.983481i	$-0.557937\pi$
$263$	−5.87098	−0.362020	−0.181010	+	0.983481i	$0.557937\pi$
$264$	−5.47037	−0.336678
$265$	21.4303	1.31646
$266$	−4.54258	−0.278523
$267$	11.1715	0.683684
$268$	−0.232592	−0.0142078
$269$	−22.6524	−1.38114	−0.690570	−	0.723265i	$-0.742640\pi$
$269$	−22.6524	−1.38114	−0.690570	+	0.723265i	$0.742640\pi$
$270$	13.6021	0.827794
$271$	2.70174	0.164119	0.0820596	−	0.996627i	$-0.473850\pi$
$271$	2.70174	0.164119	0.0820596	+	0.996627i	$0.473850\pi$
$272$	6.29137	0.381470
$273$	−1.72423	−0.104355
$274$	−12.4755	−0.753674
$275$	−14.6377	−0.882689
$276$	1.95611	0.117744
$277$	−18.2099	−1.09413	−0.547064	−	0.837091i	$-0.684255\pi$
$277$	−18.2099	−1.09413	−0.547064	+	0.837091i	$0.684255\pi$
$278$	5.87012	0.352067
$279$	−2.69902	−0.161586
$280$	−2.51430	−0.150258
$281$	2.45464	0.146432	0.0732159	−	0.997316i	$-0.476674\pi$
$281$	2.45464	0.146432	0.0732159	+	0.997316i	$0.476674\pi$
$282$	−12.9181	−0.769263
$283$	24.9238	1.48157	0.740784	−	0.671743i	$-0.234454\pi$
$283$	24.9238	1.48157	0.740784	+	0.671743i	$0.234454\pi$
$284$	−15.2779	−0.906576
$285$	36.1688	2.14246
$286$	3.13642	0.185461
$287$	−5.53110	−0.326491
$288$	0.826384	0.0486952
$289$	22.5814	1.32832
$290$	−3.09521	−0.181757
$291$	−24.1892	−1.41800
$292$	−5.03780	−0.294815
$293$	−6.59731	−0.385419	−0.192710	−	0.981256i	$-0.561728\pi$
$293$	−6.59731	−0.385419	−0.192710	+	0.981256i	$0.561728\pi$
$294$	−12.4845	−0.728111
$295$	5.88178	0.342450
$296$	7.66151	0.445316
$297$	11.8905	0.689956
$298$	−7.11836	−0.412355
$299$	−1.12153	−0.0648599
$300$	10.2387	0.591133
$301$	5.71016	0.329128
$302$	−13.7047	−0.788618
$303$	8.17172	0.469453
$304$	−5.77980	−0.331494
$305$	15.3830	0.880827
$306$	5.19909	0.297212
$307$	−4.63858	−0.264738	−0.132369	−	0.991201i	$-0.542258\pi$
$307$	−4.63858	−0.264738	−0.132369	+	0.991201i	$0.542258\pi$
$308$	−2.19792	−0.125238
$309$	−3.15840	−0.179675
$310$	10.4484	0.593432
$311$	−0.251448	−0.0142583	−0.00712915	−	0.999975i	$-0.502269\pi$
$311$	−0.251448	−0.0142583	−0.00712915	+	0.999975i	$0.502269\pi$
$312$	−2.19385	−0.124202
$313$	23.7512	1.34250	0.671249	−	0.741232i	$-0.265758\pi$
$313$	23.7512	1.34250	0.671249	+	0.741232i	$0.265758\pi$
$314$	0.914056	0.0515831
$315$	−2.07778	−0.117069
$316$	−12.2273	−0.687839
$317$	10.7572	0.604182	0.302091	−	0.953279i	$-0.402315\pi$
$317$	10.7572	0.604182	0.302091	+	0.953279i	$0.402315\pi$
$318$	−13.1038	−0.734823
$319$	−2.70574	−0.151492
$320$	−3.19910	−0.178835
$321$	−0.412714	−0.0230354
$322$	0.785940	0.0437987
$323$	−36.3629	−2.02329
$324$	−10.7962	−0.599791
$325$	−5.87035	−0.325628
$326$	−12.9696	−0.718322
$327$	−26.9953	−1.49284
$328$	−7.03756	−0.388584
$329$	−5.19032	−0.286152
$330$	17.5002	0.963357
$331$	−4.14159	−0.227642	−0.113821	−	0.993501i	$-0.536309\pi$
$331$	−4.14159	−0.227642	−0.113821	+	0.993501i	$0.536309\pi$
$332$	0.286919	0.0157467
$333$	6.33135	0.346956
$334$	22.7235	1.24337
$335$	0.744086	0.0406537
$336$	1.53739	0.0838714
$337$	17.9499	0.977796	0.488898	−	0.872341i	$-0.337399\pi$
$337$	17.9499	0.977796	0.488898	+	0.872341i	$0.337399\pi$
$338$	−11.7422	−0.638690
$339$	18.7509	1.01841
$340$	−20.1267	−1.09152
$341$	9.13370	0.494618
$342$	−4.77634	−0.258275
$343$	−10.5177	−0.567901
$344$	7.26539	0.391724
$345$	−6.25780	−0.336909
$346$	−0.660557	−0.0355118
$347$	−2.85009	−0.153001	−0.0765005	−	0.997070i	$-0.524375\pi$
$347$	−2.85009	−0.153001	−0.0765005	+	0.997070i	$0.524375\pi$
$348$	1.89260	0.101454
$349$	5.21034	0.278903	0.139451	−	0.990229i	$-0.455466\pi$
$349$	5.21034	0.278903	0.139451	+	0.990229i	$0.455466\pi$
$350$	4.11378	0.219891
$351$	4.76858	0.254528
$352$	−2.79655	−0.149057
$353$	20.3154	1.08128	0.540640	−	0.841254i	$-0.318182\pi$
$353$	20.3154	1.08128	0.540640	+	0.841254i	$0.318182\pi$
$354$	−3.59646	−0.191150
$355$	48.8754	2.59404
$356$	5.71106	0.302686
$357$	9.67228	0.511911
$358$	20.5615	1.08671
$359$	−12.5527	−0.662505	−0.331252	−	0.943542i	$-0.607471\pi$
$359$	−12.5527	−0.662505	−0.331252	+	0.943542i	$0.607471\pi$
$360$	−2.64368	−0.139334
$361$	14.4061	0.758216
$362$	14.3313	0.753237
$363$	−6.21909	−0.326418
$364$	−0.881457	−0.0462009
$365$	16.1164	0.843572
$366$	−9.40605	−0.491662
$367$	−26.5995	−1.38848	−0.694241	−	0.719742i	$-0.744260\pi$
$367$	−26.5995	−1.38848	−0.694241	+	0.719742i	$0.744260\pi$
$368$	1.00000	0.0521286
$369$	−5.81573	−0.302755
$370$	−24.5099	−1.27421
$371$	−5.26491	−0.273341
$372$	−6.38879	−0.331243
$373$	−15.0190	−0.777655	−0.388828	−	0.921311i	$-0.627120\pi$
$373$	−15.0190	−0.777655	−0.388828	+	0.921311i	$0.627120\pi$
$374$	−17.5941	−0.909771
$375$	−1.46568	−0.0756874
$376$	−6.60397	−0.340574
$377$	−1.08511	−0.0558862
$378$	−3.34169	−0.171878
$379$	−28.3834	−1.45796	−0.728980	−	0.684535i	$-0.760005\pi$
$379$	−28.3834	−1.45796	−0.728980	+	0.684535i	$0.760005\pi$
$380$	18.4901	0.948524
$381$	0.157752	0.00808188
$382$	14.3260	0.732982
$383$	−14.3119	−0.731302	−0.365651	−	0.930752i	$-0.619154\pi$
$383$	−14.3119	−0.731302	−0.365651	+	0.930752i	$0.619154\pi$
$384$	1.95611	0.0998226
$385$	7.03136	0.358351
$386$	−20.3072	−1.03361
$387$	6.00400	0.305201
$388$	−12.3659	−0.627786
$389$	−24.0904	−1.22143	−0.610717	−	0.791849i	$-0.709119\pi$
$389$	−24.0904	−1.22143	−0.610717	+	0.791849i	$0.709119\pi$
$390$	7.01833	0.355387
$391$	6.29137	0.318168
$392$	−6.38230	−0.322355
$393$	−1.95611	−0.0986729
$394$	−7.12965	−0.359187
$395$	39.1163	1.96815
$396$	−2.31102	−0.116133
$397$	−10.9123	−0.547673	−0.273837	−	0.961776i	$-0.588293\pi$
$397$	−10.9123	−0.547673	−0.273837	+	0.961776i	$0.588293\pi$
$398$	16.9172	0.847983
$399$	−8.88580	−0.444846
$400$	5.23422	0.261711
$401$	−2.73051	−0.136355	−0.0681776	−	0.997673i	$-0.521718\pi$
$401$	−2.73051	−0.136355	−0.0681776	+	0.997673i	$0.521718\pi$
$402$	−0.454978	−0.0226922
$403$	3.66299	0.182467
$404$	4.17753	0.207840
$405$	34.5382	1.71622
$406$	0.760419	0.0377389
$407$	−21.4258	−1.06204
$408$	12.3066	0.609270
$409$	5.68020	0.280868	0.140434	−	0.990090i	$-0.455150\pi$
$409$	5.68020	0.280868	0.140434	+	0.990090i	$0.455150\pi$
$410$	22.5138	1.11188
$411$	−24.4036	−1.20374
$412$	−1.61463	−0.0795470
$413$	−1.44501	−0.0711042
$414$	0.826384	0.0406146
$415$	−0.917880	−0.0450570
$416$	−1.12153	−0.0549877
$417$	11.4826	0.562307
$418$	16.1635	0.790583
$419$	−3.23286	−0.157936	−0.0789678	−	0.996877i	$-0.525162\pi$
$419$	−3.23286	−0.157936	−0.0789678	+	0.996877i	$0.525162\pi$
$420$	−4.91825	−0.239986
$421$	28.6372	1.39569	0.697845	−	0.716249i	$-0.254142\pi$
$421$	28.6372	1.39569	0.697845	+	0.716249i	$0.254142\pi$
$422$	13.4830	0.656343
$423$	−5.45741	−0.265349
$424$	−6.69887	−0.325326
$425$	32.9304	1.59736
$426$	−29.8853	−1.44795
$427$	−3.77922	−0.182889
$428$	−0.210986	−0.0101984
$429$	6.13520	0.296210
$430$	−23.2427	−1.12086
$431$	14.6322	0.704806	0.352403	−	0.935848i	$-0.385365\pi$
$431$	14.6322	0.704806	0.352403	+	0.935848i	$0.385365\pi$
$432$	−4.25184	−0.204567
$433$	19.7108	0.947243	0.473621	−	0.880729i	$-0.342947\pi$
$433$	19.7108	0.947243	0.473621	+	0.880729i	$0.342947\pi$
$434$	−2.56693	−0.123216
$435$	−6.05459	−0.290296
$436$	−13.8005	−0.660922
$437$	−5.77980	−0.276485
$438$	−9.85452	−0.470867
$439$	−7.21839	−0.344515	−0.172258	−	0.985052i	$-0.555106\pi$
$439$	−7.21839	−0.344515	−0.172258	+	0.985052i	$0.555106\pi$
$440$	8.94643	0.426504
$441$	−5.27423	−0.251154
$442$	−7.05598	−0.335619
$443$	−36.9943	−1.75765	−0.878827	−	0.477140i	$-0.841673\pi$
$443$	−36.9943	−1.75765	−0.878827	+	0.477140i	$0.841673\pi$
$444$	14.9868	0.711242
$445$	−18.2702	−0.866092
$446$	12.0237	0.569341
$447$	−13.9243	−0.658598
$448$	0.785940	0.0371322
$449$	3.77298	0.178058	0.0890291	−	0.996029i	$-0.471624\pi$
$449$	3.77298	0.178058	0.0890291	+	0.996029i	$0.471624\pi$
$450$	4.32547	0.203905
$451$	19.6809	0.926737
$452$	9.58577	0.450877
$453$	−26.8080	−1.25955
$454$	10.7042	0.502373
$455$	2.81987	0.132197
$456$	−11.3060	−0.529450
$457$	−28.6537	−1.34036	−0.670181	−	0.742197i	$-0.733784\pi$
$457$	−28.6537	−1.34036	−0.670181	+	0.742197i	$0.733784\pi$
$458$	−2.88268	−0.134699
$459$	−26.7499	−1.24858
$460$	−3.19910	−0.149159
$461$	19.6878	0.916952	0.458476	−	0.888707i	$-0.348396\pi$
$461$	19.6878	0.916952	0.458476	+	0.888707i	$0.348396\pi$
$462$	−4.29938	−0.200025
$463$	−21.0455	−0.978065	−0.489033	−	0.872265i	$-0.662650\pi$
$463$	−21.0455	−0.978065	−0.489033	+	0.872265i	$0.662650\pi$
$464$	0.967528	0.0449164
$465$	20.4383	0.947806
$466$	25.5318	1.18274
$467$	26.8392	1.24197	0.620984	−	0.783823i	$-0.286733\pi$
$467$	26.8392	1.24197	0.620984	+	0.783823i	$0.286733\pi$
$468$	−0.926817	−0.0428421
$469$	−0.182804	−0.00844109
$470$	21.1267	0.974503
$471$	1.78800	0.0823866
$472$	−1.83857	−0.0846272
$473$	−20.3180	−0.934224
$474$	−23.9180	−1.09859
$475$	−30.2527	−1.38809
$476$	4.94464	0.226637
$477$	−5.53584	−0.253469
$478$	1.30907	0.0598753
$479$	2.72533	0.124523	0.0622617	−	0.998060i	$-0.480169\pi$
$479$	2.72533	0.124523	0.0622617	+	0.998060i	$0.480169\pi$
$480$	−6.25780	−0.285628
$481$	−8.59264	−0.391791
$482$	13.6848	0.623325
$483$	1.53739	0.0699536
$484$	−3.17931	−0.144514
$485$	39.5599	1.79632
$486$	−8.36316	−0.379361
$487$	−31.5655	−1.43037	−0.715184	−	0.698936i	$-0.753657\pi$
$487$	−31.5655	−1.43037	−0.715184	+	0.698936i	$0.753657\pi$
$488$	−4.80854	−0.217672
$489$	−25.3701	−1.14728
$490$	20.4176	0.922373
$491$	1.10905	0.0500509	0.0250255	−	0.999687i	$-0.492033\pi$
$491$	1.10905	0.0500509	0.0250255	+	0.999687i	$0.492033\pi$
$492$	−13.7663	−0.620632
$493$	6.08708	0.274148
$494$	6.48224	0.291650
$495$	7.39319	0.332299
$496$	−3.26606	−0.146650
$497$	−12.0075	−0.538610
$498$	0.561245	0.0251500
$499$	39.0820	1.74955	0.874775	−	0.484530i	$-0.161009\pi$
$499$	39.0820	1.74955	0.874775	+	0.484530i	$0.161009\pi$
$500$	−0.749282	−0.0335089
$501$	44.4497	1.98587
$502$	10.7185	0.478392
$503$	32.5169	1.44986	0.724928	−	0.688825i	$-0.241873\pi$
$503$	32.5169	1.44986	0.724928	+	0.688825i	$0.241873\pi$
$504$	0.649488	0.0289305
$505$	−13.3643	−0.594704
$506$	−2.79655	−0.124322
$507$	−22.9690	−1.02009
$508$	0.0806456	0.00357807
$509$	27.2923	1.20971	0.604855	−	0.796335i	$-0.293231\pi$
$509$	27.2923	1.20971	0.604855	+	0.796335i	$0.293231\pi$
$510$	−39.3701	−1.74334
$511$	−3.95941	−0.175154
$512$	1.00000	0.0441942
$513$	24.5748	1.08500
$514$	−8.63324	−0.380796
$515$	5.16535	0.227613
$516$	14.2119	0.625646
$517$	18.4683	0.812236
$518$	6.02149	0.264569
$519$	−1.29213	−0.0567180
$520$	3.58789	0.157339
$521$	−5.47724	−0.239962	−0.119981	−	0.992776i	$-0.538283\pi$
$521$	−5.47724	−0.239962	−0.119981	+	0.992776i	$0.538283\pi$
$522$	0.799550	0.0349953
$523$	10.1154	0.442313	0.221157	−	0.975238i	$-0.429017\pi$
$523$	10.1154	0.442313	0.221157	+	0.975238i	$0.429017\pi$
$524$	−1.00000	−0.0436852
$525$	8.04702	0.351201
$526$	−5.87098	−0.255987
$527$	−20.5480	−0.895085
$528$	−5.47037	−0.238067
$529$	1.00000	0.0434783
$530$	21.4303	0.930875
$531$	−1.51937	−0.0659350
$532$	−4.54258	−0.196946
$533$	7.89286	0.341878
$534$	11.1715	0.483438
$535$	0.674966	0.0291813
$536$	−0.232592	−0.0100465
$537$	40.2207	1.73565
$538$	−22.6524	−0.976614
$539$	17.8484	0.768786
$540$	13.6021	0.585339
$541$	−30.2401	−1.30012	−0.650061	−	0.759882i	$-0.725257\pi$
$541$	−30.2401	−1.30012	−0.650061	+	0.759882i	$0.725257\pi$
$542$	2.70174	0.116050
$543$	28.0337	1.20304
$544$	6.29137	0.269740
$545$	44.1490	1.89114
$546$	−1.72423	−0.0737903
$547$	21.7549	0.930172	0.465086	−	0.885265i	$-0.346023\pi$
$547$	21.7549	0.930172	0.465086	+	0.885265i	$0.346023\pi$
$548$	−12.4755	−0.532928
$549$	−3.97370	−0.169593
$550$	−14.6377	−0.624156
$551$	−5.59212	−0.238232
$552$	1.95611	0.0832578
$553$	−9.60991	−0.408655
$554$	−18.2099	−0.773666
$555$	−47.9442	−2.03512
$556$	5.87012	0.248949
$557$	37.1414	1.57373	0.786866	−	0.617124i	$-0.211702\pi$
$557$	37.1414	1.57373	0.786866	+	0.617124i	$0.211702\pi$
$558$	−2.69902	−0.114259
$559$	−8.14837	−0.344640
$560$	−2.51430	−0.106248
$561$	−34.4161	−1.45305
$562$	2.45464	0.103543
$563$	11.5856	0.488276	0.244138	−	0.969740i	$-0.421495\pi$
$563$	11.5856	0.488276	0.244138	+	0.969740i	$0.421495\pi$
$564$	−12.9181	−0.543951
$565$	−30.6658	−1.29012
$566$	24.9238	1.04763
$567$	−8.48519	−0.356345
$568$	−15.2779	−0.641046
$569$	16.5982	0.695833	0.347917	−	0.937525i	$-0.386889\pi$
$569$	16.5982	0.695833	0.347917	+	0.937525i	$0.386889\pi$
$570$	36.1688	1.51495
$571$	1.74839	0.0731679	0.0365839	−	0.999331i	$-0.488352\pi$
$571$	1.74839	0.0731679	0.0365839	+	0.999331i	$0.488352\pi$
$572$	3.13642	0.131140
$573$	28.0233	1.17069
$574$	−5.53110	−0.230864
$575$	5.23422	0.218282
$576$	0.826384	0.0344327
$577$	−28.4834	−1.18578	−0.592891	−	0.805283i	$-0.702013\pi$
$577$	−28.4834	−1.18578	−0.592891	+	0.805283i	$0.702013\pi$
$578$	22.5814	0.939261
$579$	−39.7233	−1.65084
$580$	−3.09521	−0.128522
$581$	0.225501	0.00935534
$582$	−24.1892	−1.00267
$583$	18.7337	0.775872
$584$	−5.03780	−0.208466
$585$	2.96498	0.122587
$586$	−6.59731	−0.272532
$587$	17.2586	0.712338	0.356169	−	0.934422i	$-0.384083\pi$
$587$	17.2586	0.712338	0.356169	+	0.934422i	$0.384083\pi$
$588$	−12.4845	−0.514852
$589$	18.8772	0.777821
$590$	5.88178	0.242149
$591$	−13.9464	−0.573679
$592$	7.66151	0.314886
$593$	−13.9170	−0.571503	−0.285752	−	0.958304i	$-0.592243\pi$
$593$	−13.9170	−0.571503	−0.285752	+	0.958304i	$0.592243\pi$
$594$	11.8905	0.487873
$595$	−15.8184	−0.648490
$596$	−7.11836	−0.291579
$597$	33.0920	1.35437
$598$	−1.12153	−0.0458629
$599$	−20.6502	−0.843742	−0.421871	−	0.906656i	$-0.638627\pi$
$599$	−20.6502	−0.843742	−0.421871	+	0.906656i	$0.638627\pi$
$600$	10.2387	0.417994
$601$	−8.44629	−0.344531	−0.172266	−	0.985051i	$-0.555109\pi$
$601$	−8.44629	−0.344531	−0.172266	+	0.985051i	$0.555109\pi$
$602$	5.71016	0.232729
$603$	−0.192211	−0.00782743
$604$	−13.7047	−0.557637
$605$	10.1709	0.413506
$606$	8.17172	0.331953
$607$	−31.6536	−1.28478	−0.642391	−	0.766377i	$-0.722057\pi$
$607$	−31.6536	−1.28478	−0.642391	+	0.766377i	$0.722057\pi$
$608$	−5.77980	−0.234402
$609$	1.48747	0.0602752
$610$	15.3830	0.622839
$611$	7.40657	0.299638
$612$	5.19909	0.210161
$613$	34.5417	1.39513	0.697563	−	0.716523i	$-0.254268\pi$
$613$	34.5417	1.39513	0.697563	+	0.716523i	$0.254268\pi$
$614$	−4.63858	−0.187198
$615$	44.0397	1.77585
$616$	−2.19792	−0.0885567
$617$	13.8259	0.556610	0.278305	−	0.960493i	$-0.410227\pi$
$617$	13.8259	0.556610	0.278305	+	0.960493i	$0.410227\pi$
$618$	−3.15840	−0.127049
$619$	−10.5789	−0.425202	−0.212601	−	0.977139i	$-0.568193\pi$
$619$	−10.5789	−0.425202	−0.212601	+	0.977139i	$0.568193\pi$
$620$	10.4484	0.419620
$621$	−4.25184	−0.170621
$622$	−0.251448	−0.0100821
$623$	4.48855	0.179830
$624$	−2.19385	−0.0878242
$625$	−23.7741	−0.950962
$626$	23.7512	0.949290
$627$	31.6177	1.26269
$628$	0.914056	0.0364748
$629$	48.2014	1.92192
$630$	−2.07778	−0.0827805
$631$	4.11135	0.163670	0.0818352	−	0.996646i	$-0.473922\pi$
$631$	4.11135	0.163670	0.0818352	+	0.996646i	$0.473922\pi$
$632$	−12.2273	−0.486375
$633$	26.3743	1.04829
$634$	10.7572	0.427221
$635$	−0.257993	−0.0102381
$636$	−13.1038	−0.519598
$637$	7.15796	0.283609
$638$	−2.70574	−0.107121
$639$	−12.6254	−0.499453
$640$	−3.19910	−0.126455
$641$	18.6504	0.736646	0.368323	−	0.929698i	$-0.379932\pi$
$641$	18.6504	0.736646	0.368323	+	0.929698i	$0.379932\pi$
$642$	−0.412714	−0.0162885
$643$	−40.6918	−1.60473	−0.802365	−	0.596834i	$-0.796425\pi$
$643$	−40.6918	−1.60473	−0.802365	+	0.596834i	$0.796425\pi$
$644$	0.785940	0.0309704
$645$	−45.4654	−1.79020
$646$	−36.3629	−1.43068
$647$	−2.86254	−0.112538	−0.0562691	−	0.998416i	$-0.517920\pi$
$647$	−2.86254	−0.112538	−0.0562691	+	0.998416i	$0.517920\pi$
$648$	−10.7962	−0.424116
$649$	5.14166	0.201828
$650$	−5.87035	−0.230254
$651$	−5.02120	−0.196796
$652$	−12.9696	−0.507930
$653$	−43.6781	−1.70925	−0.854627	−	0.519242i	$-0.826214\pi$
$653$	−43.6781	−1.70925	−0.854627	+	0.519242i	$0.826214\pi$
$654$	−26.9953	−1.05560
$655$	3.19910	0.124999
$656$	−7.03756	−0.274771
$657$	−4.16316	−0.162420
$658$	−5.19032	−0.202340
$659$	−31.5877	−1.23048	−0.615241	−	0.788339i	$-0.710941\pi$
$659$	−31.5877	−1.23048	−0.615241	+	0.788339i	$0.710941\pi$
$660$	17.5002	0.681196
$661$	2.48767	0.0967592	0.0483796	−	0.998829i	$-0.484594\pi$
$661$	2.48767	0.0967592	0.0483796	+	0.998829i	$0.484594\pi$
$662$	−4.14159	−0.160967
$663$	−13.8023	−0.536037
$664$	0.286919	0.0111346
$665$	14.5321	0.563532
$666$	6.33135	0.245335
$667$	0.967528	0.0374628
$668$	22.7235	0.879197
$669$	23.5198	0.909329
$670$	0.744086	0.0287465
$671$	13.4473	0.519128
$672$	1.53739	0.0593060
$673$	−25.2208	−0.972190	−0.486095	−	0.873906i	$-0.661579\pi$
$673$	−25.2208	−0.972190	−0.486095	+	0.873906i	$0.661579\pi$
$674$	17.9499	0.691406
$675$	−22.2551	−0.856598
$676$	−11.7422	−0.451622
$677$	18.9103	0.726780	0.363390	−	0.931637i	$-0.381619\pi$
$677$	18.9103	0.726780	0.363390	+	0.931637i	$0.381619\pi$
$678$	18.7509	0.720122
$679$	−9.71889	−0.372977
$680$	−20.1267	−0.771824
$681$	20.9386	0.802371
$682$	9.13370	0.349747
$683$	−6.07699	−0.232529	−0.116265	−	0.993218i	$-0.537092\pi$
$683$	−6.07699	−0.232529	−0.116265	+	0.993218i	$0.537092\pi$
$684$	−4.77634	−0.182628
$685$	39.9104	1.52490
$686$	−10.5177	−0.401567
$687$	−5.63885	−0.215136
$688$	7.26539	0.276990
$689$	7.51301	0.286223
$690$	−6.25780	−0.238230
$691$	14.7041	0.559369	0.279685	−	0.960092i	$-0.409770\pi$
$691$	14.7041	0.559369	0.279685	+	0.960092i	$0.409770\pi$
$692$	−0.660557	−0.0251106
$693$	−1.81633	−0.0689965
$694$	−2.85009	−0.108188
$695$	−18.7791	−0.712332
$696$	1.89260	0.0717386
$697$	−44.2759	−1.67707
$698$	5.21034	0.197214
$699$	49.9431	1.88902
$700$	4.11378	0.155486
$701$	51.1785	1.93299	0.966493	−	0.256695i	$-0.0826334\pi$
$701$	51.1785	1.93299	0.966493	+	0.256695i	$0.0826334\pi$
$702$	4.76858	0.179978
$703$	−44.2820	−1.67013
$704$	−2.79655	−0.105399
$705$	41.3263	1.55644
$706$	20.3154	0.764580
$707$	3.28328	0.123481
$708$	−3.59646	−0.135163
$709$	30.6650	1.15165	0.575824	−	0.817574i	$-0.304681\pi$
$709$	30.6650	1.15165	0.575824	+	0.817574i	$0.304681\pi$
$710$	48.8754	1.83426
$711$	−10.1044	−0.378946
$712$	5.71106	0.214031
$713$	−3.26606	−0.122315
$714$	9.67228	0.361976
$715$	−10.0337	−0.375240
$716$	20.5615	0.768419
$717$	2.56068	0.0956305
$718$	−12.5527	−0.468462
$719$	−37.7921	−1.40941	−0.704703	−	0.709502i	$-0.748920\pi$
$719$	−37.7921	−1.40941	−0.704703	+	0.709502i	$0.748920\pi$
$720$	−2.64368	−0.0985242
$721$	−1.26900	−0.0472601
$722$	14.4061	0.536140
$723$	26.7690	0.995551
$724$	14.3313	0.532619
$725$	5.06425	0.188082
$726$	−6.21909	−0.230812
$727$	47.4241	1.75886	0.879430	−	0.476028i	$-0.157924\pi$
$727$	47.4241	1.75886	0.879430	+	0.476028i	$0.157924\pi$
$728$	−0.881457	−0.0326690
$729$	16.0294	0.593682
$730$	16.1164	0.596495
$731$	45.7093	1.69062
$732$	−9.40605	−0.347658
$733$	−18.6792	−0.689932	−0.344966	−	0.938615i	$-0.612110\pi$
$733$	−18.6792	−0.689932	−0.344966	+	0.938615i	$0.612110\pi$
$734$	−26.5995	−0.981805
$735$	39.9391	1.47318
$736$	1.00000	0.0368605
$737$	0.650456	0.0239599
$738$	−5.81573	−0.214080
$739$	0.0216047	0.000794741 0	0.000397371	−	1.00000i	$-0.499874\pi$
$739$	0.0216047	0.000794741 0	0.000397371		1.00000i	$0.499874\pi$
$740$	−24.5099	−0.901002
$741$	12.6800	0.465811
$742$	−5.26491	−0.193281
$743$	32.5312	1.19345	0.596727	−	0.802445i	$-0.296468\pi$
$743$	32.5312	1.19345	0.596727	+	0.802445i	$0.296468\pi$
$744$	−6.38879	−0.234224
$745$	22.7723	0.834313
$746$	−15.0190	−0.549885
$747$	0.237105	0.00867522
$748$	−17.5941	−0.643305
$749$	−0.165823	−0.00605903
$750$	−1.46568	−0.0535191
$751$	−17.4936	−0.638350	−0.319175	−	0.947696i	$-0.603406\pi$
$751$	−17.4936	−0.638350	−0.319175	+	0.947696i	$0.603406\pi$
$752$	−6.60397	−0.240822
$753$	20.9667	0.764069
$754$	−1.08511	−0.0395175
$755$	43.8427	1.59560
$756$	−3.34169	−0.121536
$757$	−36.5938	−1.33003	−0.665013	−	0.746832i	$-0.731574\pi$
$757$	−36.5938	−1.33003	−0.665013	+	0.746832i	$0.731574\pi$
$758$	−28.3834	−1.03093
$759$	−5.47037	−0.198562
$760$	18.4901	0.670708
$761$	9.33884	0.338533	0.169266	−	0.985570i	$-0.445860\pi$
$761$	9.33884	0.338533	0.169266	+	0.985570i	$0.445860\pi$
$762$	0.157752	0.00571475
$763$	−10.8463	−0.392664
$764$	14.3260	0.518297
$765$	−16.6324	−0.601345
$766$	−14.3119	−0.517109
$767$	2.06202	0.0744553
$768$	1.95611	0.0705852
$769$	2.35132	0.0847908	0.0423954	−	0.999101i	$-0.486501\pi$
$769$	2.35132	0.0847908	0.0423954	+	0.999101i	$0.486501\pi$
$770$	7.03136	0.253392
$771$	−16.8876	−0.608193
$772$	−20.3072	−0.730873
$773$	−24.2194	−0.871112	−0.435556	−	0.900162i	$-0.643448\pi$
$773$	−24.2194	−0.871112	−0.435556	+	0.900162i	$0.643448\pi$
$774$	6.00400	0.215809
$775$	−17.0953	−0.614080
$776$	−12.3659	−0.443912
$777$	11.7787	0.422559
$778$	−24.0904	−0.863684
$779$	40.6757	1.45736
$780$	7.01833	0.251296
$781$	42.7254	1.52883
$782$	6.29137	0.224979
$783$	−4.11377	−0.147014
$784$	−6.38230	−0.227939
$785$	−2.92415	−0.104367
$786$	−1.95611	−0.0697723
$787$	−3.22014	−0.114786	−0.0573928	−	0.998352i	$-0.518279\pi$
$787$	−3.22014	−0.114786	−0.0573928	+	0.998352i	$0.518279\pi$
$788$	−7.12965	−0.253983
$789$	−11.4843	−0.408852
$790$	39.1163	1.39169
$791$	7.53384	0.267872
$792$	−2.31102	−0.0821187
$793$	5.39293	0.191509
$794$	−10.9123	−0.387263
$795$	41.9202	1.48676
$796$	16.9172	0.599615
$797$	−43.2263	−1.53115	−0.765577	−	0.643345i	$-0.777546\pi$
$797$	−43.2263	−1.53115	−0.765577	+	0.643345i	$0.777546\pi$
$798$	−8.88580	−0.314554
$799$	−41.5480	−1.46986
$800$	5.23422	0.185058
$801$	4.71953	0.166756
$802$	−2.73051	−0.0964177
$803$	14.0885	0.497171
$804$	−0.454978	−0.0160458
$805$	−2.51430	−0.0886173
$806$	3.66299	0.129023
$807$	−44.3107	−1.55981
$808$	4.17753	0.146965
$809$	9.77399	0.343635	0.171818	−	0.985129i	$-0.445036\pi$
$809$	9.77399	0.343635	0.171818	+	0.985129i	$0.445036\pi$
$810$	34.5382	1.21355
$811$	49.2585	1.72970	0.864850	−	0.502031i	$-0.167414\pi$
$811$	49.2585	1.72970	0.864850	+	0.502031i	$0.167414\pi$
$812$	0.760419	0.0266855
$813$	5.28492	0.185350
$814$	−21.4258	−0.750974
$815$	41.4911	1.45337
$816$	12.3066	0.430819
$817$	−41.9925	−1.46913
$818$	5.68020	0.198603
$819$	−0.728422	−0.0254531
$820$	22.5138	0.786218
$821$	−28.5625	−0.996837	−0.498418	−	0.866937i	$-0.666086\pi$
$821$	−28.5625	−0.996837	−0.498418	+	0.866937i	$0.666086\pi$
$822$	−24.4036	−0.851172
$823$	−10.7977	−0.376384	−0.188192	−	0.982132i	$-0.560263\pi$
$823$	−10.7977	−0.376384	−0.188192	+	0.982132i	$0.560263\pi$
$824$	−1.61463	−0.0562483
$825$	−28.6331	−0.996877
$826$	−1.44501	−0.0502783
$827$	25.5183	0.887359	0.443680	−	0.896185i	$-0.353673\pi$
$827$	25.5183	0.887359	0.443680	+	0.896185i	$0.353673\pi$
$828$	0.826384	0.0287188
$829$	46.7022	1.62204	0.811018	−	0.585021i	$-0.198914\pi$
$829$	46.7022	1.62204	0.811018	+	0.585021i	$0.198914\pi$
$830$	−0.917880	−0.0318601
$831$	−35.6207	−1.23567
$832$	−1.12153	−0.0388822
$833$	−40.1534	−1.39123
$834$	11.4826	0.397611
$835$	−72.6946	−2.51570
$836$	16.1635	0.559026
$837$	13.8868	0.479997
$838$	−3.23286	−0.111677
$839$	−10.0026	−0.345328	−0.172664	−	0.984981i	$-0.555238\pi$
$839$	−10.0026	−0.345328	−0.172664	+	0.984981i	$0.555238\pi$
$840$	−4.91825	−0.169696
$841$	−28.0639	−0.967720
$842$	28.6372	0.986902
$843$	4.80156	0.165375
$844$	13.4830	0.464105
$845$	37.5643	1.29225
$846$	−5.45741	−0.187630
$847$	−2.49875	−0.0858579
$848$	−6.69887	−0.230040
$849$	48.7539	1.67323
$850$	32.9304	1.12950
$851$	7.66151	0.262633
$852$	−29.8853	−1.02385
$853$	23.2794	0.797070	0.398535	−	0.917153i	$-0.369519\pi$
$853$	23.2794	0.797070	0.398535	+	0.917153i	$0.369519\pi$
$854$	−3.77922	−0.129322
$855$	15.2800	0.522564
$856$	−0.210986	−0.00721137
$857$	−15.3981	−0.525988	−0.262994	−	0.964797i	$-0.584710\pi$
$857$	−15.3981	−0.525988	−0.262994	+	0.964797i	$0.584710\pi$
$858$	6.13520	0.209452
$859$	30.5539	1.04249	0.521243	−	0.853409i	$-0.325469\pi$
$859$	30.5539	1.04249	0.521243	+	0.853409i	$0.325469\pi$
$860$	−23.2427	−0.792569
$861$	−10.8195	−0.368726
$862$	14.6322	0.498373
$863$	−13.3138	−0.453207	−0.226604	−	0.973987i	$-0.572762\pi$
$863$	−13.3138	−0.453207	−0.226604	+	0.973987i	$0.572762\pi$
$864$	−4.25184	−0.144651
$865$	2.11319	0.0718505
$866$	19.7108	0.669802
$867$	44.1717	1.50015
$868$	−2.56693	−0.0871272
$869$	34.1942	1.15996
$870$	−6.05459	−0.205270
$871$	0.260860	0.00883891
$872$	−13.8005	−0.467343
$873$	−10.2190	−0.345862
$874$	−5.77980	−0.195505
$875$	−0.588890	−0.0199081
$876$	−9.85452	−0.332953
$877$	−26.3929	−0.891224	−0.445612	−	0.895226i	$-0.647014\pi$
$877$	−26.3929	−0.891224	−0.445612	+	0.895226i	$0.647014\pi$
$878$	−7.21839	−0.243609
$879$	−12.9051	−0.435278
$880$	8.94643	0.301584
$881$	−24.7447	−0.833669	−0.416835	−	0.908982i	$-0.636861\pi$
$881$	−24.7447	−0.833669	−0.416835	+	0.908982i	$0.636861\pi$
$882$	−5.27423	−0.177593
$883$	16.0827	0.541227	0.270613	−	0.962688i	$-0.412774\pi$
$883$	16.0827	0.541227	0.270613	+	0.962688i	$0.412774\pi$
$884$	−7.05598	−0.237318
$885$	11.5054	0.386751
$886$	−36.9943	−1.24285
$887$	−44.0182	−1.47799	−0.738994	−	0.673712i	$-0.764699\pi$
$887$	−44.0182	−1.47799	−0.738994	+	0.673712i	$0.764699\pi$
$888$	14.9868	0.502924
$889$	0.0633826	0.00212578
$890$	−18.2702	−0.612420
$891$	30.1922	1.01148
$892$	12.0237	0.402585
$893$	38.1696	1.27730
$894$	−13.9243	−0.465699
$895$	−65.7782	−2.19872
$896$	0.785940	0.0262564
$897$	−2.19385	−0.0732504
$898$	3.77298	0.125906
$899$	−3.16000	−0.105392
$900$	4.32547	0.144182
$901$	−42.1451	−1.40406
$902$	19.6809	0.655302
$903$	11.1697	0.371705
$904$	9.58577	0.318818
$905$	−45.8473	−1.52401
$906$	−26.8080	−0.890636
$907$	29.9049	0.992976	0.496488	−	0.868044i	$-0.334623\pi$
$907$	29.9049	0.992976	0.496488	+	0.868044i	$0.334623\pi$
$908$	10.7042	0.355231
$909$	3.45224	0.114504
$910$	2.81987	0.0934777
$911$	−0.439802	−0.0145713	−0.00728564	−	0.999973i	$-0.502319\pi$
$911$	−0.439802	−0.0145713	−0.00728564	+	0.999973i	$0.502319\pi$
$912$	−11.3060	−0.374378
$913$	−0.802382	−0.0265550
$914$	−28.6537	−0.947779
$915$	30.0909	0.994773
$916$	−2.88268	−0.0952464
$917$	−0.785940	−0.0259540
$918$	−26.7499	−0.882879
$919$	−25.2074	−0.831515	−0.415757	−	0.909476i	$-0.636483\pi$
$919$	−25.2074	−0.831515	−0.415757	+	0.909476i	$0.636483\pi$
$920$	−3.19910	−0.105471
$921$	−9.07360	−0.298985
$922$	19.6878	0.648383
$923$	17.1347	0.563994
$924$	−4.29938	−0.141439
$925$	40.1020	1.31855
$926$	−21.0455	−0.691597
$927$	−1.33430	−0.0438243
$928$	0.967528	0.0317607
$929$	20.0501	0.657823	0.328912	−	0.944361i	$-0.393318\pi$
$929$	20.0501	0.657823	0.328912	+	0.944361i	$0.393318\pi$
$930$	20.4383	0.670200
$931$	36.8884	1.20897
$932$	25.5318	0.836322
$933$	−0.491861	−0.0161028
$934$	26.8392	0.878204
$935$	56.2853	1.84073
$936$	−0.926817	−0.0302940
$937$	16.3609	0.534486	0.267243	−	0.963629i	$-0.413887\pi$
$937$	16.3609	0.534486	0.267243	+	0.963629i	$0.413887\pi$
$938$	−0.182804	−0.00596875
$939$	46.4601	1.51617
$940$	21.1267	0.689078
$941$	−51.1799	−1.66842	−0.834209	−	0.551448i	$-0.814075\pi$
$941$	−51.1799	−1.66842	−0.834209	+	0.551448i	$0.814075\pi$
$942$	1.78800	0.0582561
$943$	−7.03756	−0.229175
$944$	−1.83857	−0.0598405
$945$	10.6904	0.347758
$946$	−20.3180	−0.660596
$947$	53.9233	1.75227	0.876136	−	0.482063i	$-0.160113\pi$
$947$	53.9233	1.75227	0.876136	+	0.482063i	$0.160113\pi$
$948$	−23.9180	−0.776820
$949$	5.65006	0.183409
$950$	−30.2527	−0.981528
$951$	21.0422	0.682341
$952$	4.94464	0.160257
$953$	−47.5729	−1.54104	−0.770519	−	0.637417i	$-0.780003\pi$
$953$	−47.5729	−1.54104	−0.770519	+	0.637417i	$0.780003\pi$
$954$	−5.53584	−0.179230
$955$	−45.8303	−1.48303
$956$	1.30907	0.0423382
$957$	−5.29274	−0.171090
$958$	2.72533	0.0880513
$959$	−9.80501	−0.316620
$960$	−6.25780	−0.201970
$961$	−20.3328	−0.655898
$962$	−8.59264	−0.277038
$963$	−0.174356	−0.00561854
$964$	13.6848	0.440757
$965$	64.9648	2.09129
$966$	1.53739	0.0494647
$967$	31.7967	1.02251	0.511257	−	0.859428i	$-0.329180\pi$
$967$	31.7967	1.02251	0.511257	+	0.859428i	$0.329180\pi$
$968$	−3.17931	−0.102187
$969$	−71.1300	−2.28502
$970$	39.5599	1.27019
$971$	−16.2285	−0.520797	−0.260399	−	0.965501i	$-0.583854\pi$
$971$	−16.2285	−0.520797	−0.260399	+	0.965501i	$0.583854\pi$
$972$	−8.36316	−0.268249
$973$	4.61356	0.147904
$974$	−31.5655	−1.01142
$975$	−11.4831	−0.367753
$976$	−4.80854	−0.153918
$977$	−13.9233	−0.445446	−0.222723	−	0.974882i	$-0.571494\pi$
$977$	−13.9233	−0.445446	−0.222723	+	0.974882i	$0.571494\pi$
$978$	−25.3701	−0.811246
$979$	−15.9713	−0.510444
$980$	20.4176	0.652216
$981$	−11.4045	−0.364117
$982$	1.10905	0.0353913
$983$	59.2904	1.89107	0.945536	−	0.325519i	$-0.105539\pi$
$983$	59.2904	1.89107	0.945536	+	0.325519i	$0.105539\pi$
$984$	−13.7663	−0.438853
$985$	22.8085	0.726738
$986$	6.08708	0.193852
$987$	−10.1529	−0.323169
$988$	6.48224	0.206227
$989$	7.26539	0.231026
$990$	7.39319	0.234971
$991$	−10.6935	−0.339691	−0.169846	−	0.985471i	$-0.554327\pi$
$991$	−10.6935	−0.339691	−0.169846	+	0.985471i	$0.554327\pi$
$992$	−3.26606	−0.103698
$993$	−8.10142	−0.257091
$994$	−12.0075	−0.380855
$995$	−54.1198	−1.71571
$996$	0.561245	0.0177837
$997$	4.65249	0.147346	0.0736730	−	0.997282i	$-0.476528\pi$
$997$	4.65249	0.147346	0.0736730	+	0.997282i	$0.476528\pi$
$998$	39.0820	1.23712
$999$	−32.5755	−1.03064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.18	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.18	✓	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.95611 q^{3} +1.00000 q^{4} -3.19910 q^{5} +1.95611 q^{6} +0.785940 q^{7} +1.00000 q^{8} +0.826384 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.95611 q^{3} +1.00000 q^{4} -3.19910 q^{5} +1.95611 q^{6} +0.785940 q^{7} +1.00000 q^{8} +0.826384 q^{9} -3.19910 q^{10} -2.79655 q^{11} +1.95611 q^{12} -1.12153 q^{13} +0.785940 q^{14} -6.25780 q^{15} +1.00000 q^{16} +6.29137 q^{17} +0.826384 q^{18} -5.77980 q^{19} -3.19910 q^{20} +1.53739 q^{21} -2.79655 q^{22} +1.00000 q^{23} +1.95611 q^{24} +5.23422 q^{25} -1.12153 q^{26} -4.25184 q^{27} +0.785940 q^{28} +0.967528 q^{29} -6.25780 q^{30} -3.26606 q^{31} +1.00000 q^{32} -5.47037 q^{33} +6.29137 q^{34} -2.51430 q^{35} +0.826384 q^{36} +7.66151 q^{37} -5.77980 q^{38} -2.19385 q^{39} -3.19910 q^{40} -7.03756 q^{41} +1.53739 q^{42} +7.26539 q^{43} -2.79655 q^{44} -2.64368 q^{45} +1.00000 q^{46} -6.60397 q^{47} +1.95611 q^{48} -6.38230 q^{49} +5.23422 q^{50} +12.3066 q^{51} -1.12153 q^{52} -6.69887 q^{53} -4.25184 q^{54} +8.94643 q^{55} +0.785940 q^{56} -11.3060 q^{57} +0.967528 q^{58} -1.83857 q^{59} -6.25780 q^{60} -4.80854 q^{61} -3.26606 q^{62} +0.649488 q^{63} +1.00000 q^{64} +3.58789 q^{65} -5.47037 q^{66} -0.232592 q^{67} +6.29137 q^{68} +1.95611 q^{69} -2.51430 q^{70} -15.2779 q^{71} +0.826384 q^{72} -5.03780 q^{73} +7.66151 q^{74} +10.2387 q^{75} -5.77980 q^{76} -2.19792 q^{77} -2.19385 q^{78} -12.2273 q^{79} -3.19910 q^{80} -10.7962 q^{81} -7.03756 q^{82} +0.286919 q^{83} +1.53739 q^{84} -20.1267 q^{85} +7.26539 q^{86} +1.89260 q^{87} -2.79655 q^{88} +5.71106 q^{89} -2.64368 q^{90} -0.881457 q^{91} +1.00000 q^{92} -6.38879 q^{93} -6.60397 q^{94} +18.4901 q^{95} +1.95611 q^{96} -12.3659 q^{97} -6.38230 q^{98} -2.31102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

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