LMFDB - Embedded newform 4730.2.a.z.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 21x^{7} + 107x^{6} - 45x^{5} - 262x^{4} - 47x^{3} + 120x^{2} - 2x - 6 $ x^10 - 2x^9 - 17x^8 + 21x^7 + 107x^6 - 45x^5 - 262x^4 - 47x^3 + 120x^2 - 2*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.68568$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.68568 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.68568 q^{6} +4.03613 q^{7} -1.00000 q^{8} +4.21287 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.68568 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.68568 q^{6} +4.03613 q^{7} -1.00000 q^{8} +4.21287 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.68568 q^{12} +4.50732 q^{13} -4.03613 q^{14} +2.68568 q^{15} +1.00000 q^{16} -5.71882 q^{17} -4.21287 q^{18} +0.726777 q^{19} +1.00000 q^{20} +10.8397 q^{21} -1.00000 q^{22} -3.76465 q^{23} -2.68568 q^{24} +1.00000 q^{25} -4.50732 q^{26} +3.25739 q^{27} +4.03613 q^{28} +0.439002 q^{29} -2.68568 q^{30} -0.158220 q^{31} -1.00000 q^{32} +2.68568 q^{33} +5.71882 q^{34} +4.03613 q^{35} +4.21287 q^{36} +2.90049 q^{37} -0.726777 q^{38} +12.1052 q^{39} -1.00000 q^{40} -9.05460 q^{41} -10.8397 q^{42} +1.00000 q^{43} +1.00000 q^{44} +4.21287 q^{45} +3.76465 q^{46} +12.3291 q^{47} +2.68568 q^{48} +9.29031 q^{49} -1.00000 q^{50} -15.3589 q^{51} +4.50732 q^{52} +5.86744 q^{53} -3.25739 q^{54} +1.00000 q^{55} -4.03613 q^{56} +1.95189 q^{57} -0.439002 q^{58} -4.85755 q^{59} +2.68568 q^{60} +8.76979 q^{61} +0.158220 q^{62} +17.0037 q^{63} +1.00000 q^{64} +4.50732 q^{65} -2.68568 q^{66} -5.33538 q^{67} -5.71882 q^{68} -10.1106 q^{69} -4.03613 q^{70} +13.1410 q^{71} -4.21287 q^{72} +5.57033 q^{73} -2.90049 q^{74} +2.68568 q^{75} +0.726777 q^{76} +4.03613 q^{77} -12.1052 q^{78} -0.750555 q^{79} +1.00000 q^{80} -3.89033 q^{81} +9.05460 q^{82} -1.03270 q^{83} +10.8397 q^{84} -5.71882 q^{85} -1.00000 q^{86} +1.17902 q^{87} -1.00000 q^{88} -1.17265 q^{89} -4.21287 q^{90} +18.1921 q^{91} -3.76465 q^{92} -0.424928 q^{93} -12.3291 q^{94} +0.726777 q^{95} -2.68568 q^{96} -5.36406 q^{97} -9.29031 q^{98} +4.21287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * 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
$3$	2.68568	1.55058	0.775289	−	0.631607i	$-0.217604\pi$
$3$	2.68568	1.55058	0.775289	+	0.631607i	$0.217604\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.68568	−1.09642
$7$	4.03613	1.52551	0.762756	−	0.646686i	$-0.223846\pi$
$7$	4.03613	1.52551	0.762756	+	0.646686i	$0.223846\pi$
$8$	−1.00000	−0.353553
$9$	4.21287	1.40429
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.68568	0.775289
$13$	4.50732	1.25011	0.625053	−	0.780582i	$-0.285077\pi$
$13$	4.50732	1.25011	0.625053	+	0.780582i	$0.285077\pi$
$14$	−4.03613	−1.07870
$15$	2.68568	0.693439
$16$	1.00000	0.250000
$17$	−5.71882	−1.38702	−0.693509	−	0.720448i	$-0.743936\pi$
$17$	−5.71882	−1.38702	−0.693509	+	0.720448i	$0.743936\pi$
$18$	−4.21287	−0.992983
$19$	0.726777	0.166734	0.0833671	−	0.996519i	$-0.473433\pi$
$19$	0.726777	0.166734	0.0833671	+	0.996519i	$0.473433\pi$
$20$	1.00000	0.223607
$21$	10.8397	2.36542
$22$	−1.00000	−0.213201
$23$	−3.76465	−0.784984	−0.392492	−	0.919755i	$-0.628387\pi$
$23$	−3.76465	−0.784984	−0.392492	+	0.919755i	$0.628387\pi$
$24$	−2.68568	−0.548212
$25$	1.00000	0.200000
$26$	−4.50732	−0.883958
$27$	3.25739	0.626884
$28$	4.03613	0.762756
$29$	0.439002	0.0815206	0.0407603	−	0.999169i	$-0.487022\pi$
$29$	0.439002	0.0815206	0.0407603	+	0.999169i	$0.487022\pi$
$30$	−2.68568	−0.490336
$31$	−0.158220	−0.0284171	−0.0142086	−	0.999899i	$-0.504523\pi$
$31$	−0.158220	−0.0284171	−0.0142086	+	0.999899i	$0.504523\pi$
$32$	−1.00000	−0.176777
$33$	2.68568	0.467517
$34$	5.71882	0.980770
$35$	4.03613	0.682230
$36$	4.21287	0.702145
$37$	2.90049	0.476837	0.238419	−	0.971162i	$-0.423371\pi$
$37$	2.90049	0.476837	0.238419	+	0.971162i	$0.423371\pi$
$38$	−0.726777	−0.117899
$39$	12.1052	1.93839
$40$	−1.00000	−0.158114
$41$	−9.05460	−1.41409	−0.707045	−	0.707168i	$-0.749972\pi$
$41$	−9.05460	−1.41409	−0.707045	+	0.707168i	$0.749972\pi$
$42$	−10.8397	−1.67261
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	4.21287	0.628018
$46$	3.76465	0.555068
$47$	12.3291	1.79839	0.899195	−	0.437548i	$-0.144153\pi$
$47$	12.3291	1.79839	0.899195	+	0.437548i	$0.144153\pi$
$48$	2.68568	0.387644
$49$	9.29031	1.32719
$50$	−1.00000	−0.141421
$51$	−15.3589	−2.15068
$52$	4.50732	0.625053
$53$	5.86744	0.805955	0.402978	−	0.915210i	$-0.367975\pi$
$53$	5.86744	0.805955	0.402978	+	0.915210i	$0.367975\pi$
$54$	−3.25739	−0.443274
$55$	1.00000	0.134840
$56$	−4.03613	−0.539350
$57$	1.95189	0.258534
$58$	−0.439002	−0.0576438
$59$	−4.85755	−0.632399	−0.316199	−	0.948693i	$-0.602407\pi$
$59$	−4.85755	−0.632399	−0.316199	+	0.948693i	$0.602407\pi$
$60$	2.68568	0.346720
$61$	8.76979	1.12286	0.561429	−	0.827525i	$-0.310252\pi$
$61$	8.76979	1.12286	0.561429	+	0.827525i	$0.310252\pi$
$62$	0.158220	0.0200939
$63$	17.0037	2.14226
$64$	1.00000	0.125000
$65$	4.50732	0.559064
$66$	−2.68568	−0.330584
$67$	−5.33538	−0.651821	−0.325910	−	0.945401i	$-0.605671\pi$
$67$	−5.33538	−0.651821	−0.325910	+	0.945401i	$0.605671\pi$
$68$	−5.71882	−0.693509
$69$	−10.1106	−1.21718
$70$	−4.03613	−0.482409
$71$	13.1410	1.55955	0.779773	−	0.626062i	$-0.215334\pi$
$71$	13.1410	1.55955	0.779773	+	0.626062i	$0.215334\pi$
$72$	−4.21287	−0.496492
$73$	5.57033	0.651958	0.325979	−	0.945377i	$-0.394306\pi$
$73$	5.57033	0.651958	0.325979	+	0.945377i	$0.394306\pi$
$74$	−2.90049	−0.337175
$75$	2.68568	0.310116
$76$	0.726777	0.0833671
$77$	4.03613	0.459959
$78$	−12.1052	−1.37065
$79$	−0.750555	−0.0844441	−0.0422220	−	0.999108i	$-0.513444\pi$
$79$	−0.750555	−0.0844441	−0.0422220	+	0.999108i	$0.513444\pi$
$80$	1.00000	0.111803
$81$	−3.89033	−0.432258
$82$	9.05460	0.999913
$83$	−1.03270	−0.113354	−0.0566770	−	0.998393i	$-0.518051\pi$
$83$	−1.03270	−0.113354	−0.0566770	+	0.998393i	$0.518051\pi$
$84$	10.8397	1.18271
$85$	−5.71882	−0.620293
$86$	−1.00000	−0.107833
$87$	1.17902	0.126404
$88$	−1.00000	−0.106600
$89$	−1.17265	−0.124300	−0.0621502	−	0.998067i	$-0.519796\pi$
$89$	−1.17265	−0.124300	−0.0621502	+	0.998067i	$0.519796\pi$
$90$	−4.21287	−0.444076
$91$	18.1921	1.90705
$92$	−3.76465	−0.392492
$93$	−0.424928	−0.0440629
$94$	−12.3291	−1.27165
$95$	0.726777	0.0745658
$96$	−2.68568	−0.274106
$97$	−5.36406	−0.544637	−0.272319	−	0.962207i	$-0.587790\pi$
$97$	−5.36406	−0.544637	−0.272319	+	0.962207i	$0.587790\pi$
$98$	−9.29031	−0.938463
$99$	4.21287	0.423410
$100$	1.00000	0.100000
$101$	−10.0398	−0.998998	−0.499499	−	0.866314i	$-0.666483\pi$
$101$	−10.0398	−0.998998	−0.499499	+	0.866314i	$0.666483\pi$
$102$	15.3589	1.52076
$103$	3.78461	0.372909	0.186454	−	0.982464i	$-0.440300\pi$
$103$	3.78461	0.372909	0.186454	+	0.982464i	$0.440300\pi$
$104$	−4.50732	−0.441979
$105$	10.8397	1.05785
$106$	−5.86744	−0.569896
$107$	−9.75462	−0.943015	−0.471507	−	0.881862i	$-0.656290\pi$
$107$	−9.75462	−0.943015	−0.471507	+	0.881862i	$0.656290\pi$
$108$	3.25739	0.313442
$109$	8.38098	0.802753	0.401376	−	0.915913i	$-0.368532\pi$
$109$	8.38098	0.802753	0.401376	+	0.915913i	$0.368532\pi$
$110$	−1.00000	−0.0953463
$111$	7.78978	0.739373
$112$	4.03613	0.381378
$113$	−0.886368	−0.0833825	−0.0416912	−	0.999131i	$-0.513275\pi$
$113$	−0.886368	−0.0833825	−0.0416912	+	0.999131i	$0.513275\pi$
$114$	−1.95189	−0.182811
$115$	−3.76465	−0.351056
$116$	0.439002	0.0407603
$117$	18.9888	1.75551
$118$	4.85755	0.447173
$119$	−23.0819	−2.11591
$120$	−2.68568	−0.245168
$121$	1.00000	0.0909091
$122$	−8.76979	−0.793980
$123$	−24.3178	−2.19266
$124$	−0.158220	−0.0142086
$125$	1.00000	0.0894427
$126$	−17.0037	−1.51481
$127$	−12.4763	−1.10709	−0.553545	−	0.832819i	$-0.686725\pi$
$127$	−12.4763	−1.10709	−0.553545	+	0.832819i	$0.686725\pi$
$128$	−1.00000	−0.0883883
$129$	2.68568	0.236461
$130$	−4.50732	−0.395318
$131$	−2.00453	−0.175136	−0.0875681	−	0.996159i	$-0.527910\pi$
$131$	−2.00453	−0.175136	−0.0875681	+	0.996159i	$0.527910\pi$
$132$	2.68568	0.233758
$133$	2.93336	0.254355
$134$	5.33538	0.460907
$135$	3.25739	0.280351
$136$	5.71882	0.490385
$137$	−18.3974	−1.57180	−0.785900	−	0.618354i	$-0.787800\pi$
$137$	−18.3974	−1.57180	−0.785900	+	0.618354i	$0.787800\pi$
$138$	10.1106	0.860676
$139$	11.5109	0.976343	0.488172	−	0.872748i	$-0.337664\pi$
$139$	11.5109	0.976343	0.488172	+	0.872748i	$0.337664\pi$
$140$	4.03613	0.341115
$141$	33.1121	2.78854
$142$	−13.1410	−1.10277
$143$	4.50732	0.376921
$144$	4.21287	0.351073
$145$	0.439002	0.0364571
$146$	−5.57033	−0.461004
$147$	24.9508	2.05791
$148$	2.90049	0.238419
$149$	−2.50497	−0.205215	−0.102608	−	0.994722i	$-0.532719\pi$
$149$	−2.50497	−0.205215	−0.102608	+	0.994722i	$0.532719\pi$
$150$	−2.68568	−0.219285
$151$	−4.31360	−0.351036	−0.175518	−	0.984476i	$-0.556160\pi$
$151$	−4.31360	−0.351036	−0.175518	+	0.984476i	$0.556160\pi$
$152$	−0.726777	−0.0589494
$153$	−24.0927	−1.94778
$154$	−4.03613	−0.325240
$155$	−0.158220	−0.0127085
$156$	12.1052	0.969193
$157$	22.8158	1.82090	0.910451	−	0.413616i	$-0.135735\pi$
$157$	22.8158	1.82090	0.910451	+	0.413616i	$0.135735\pi$
$158$	0.750555	0.0597110
$159$	15.7581	1.24970
$160$	−1.00000	−0.0790569
$161$	−15.1946	−1.19750
$162$	3.89033	0.305653
$163$	−9.31122	−0.729311	−0.364655	−	0.931143i	$-0.618813\pi$
$163$	−9.31122	−0.729311	−0.364655	+	0.931143i	$0.618813\pi$
$164$	−9.05460	−0.707045
$165$	2.68568	0.209080
$166$	1.03270	0.0801534
$167$	−17.8990	−1.38507	−0.692534	−	0.721385i	$-0.743506\pi$
$167$	−17.8990	−1.38507	−0.692534	+	0.721385i	$0.743506\pi$
$168$	−10.8397	−0.836304
$169$	7.31595	0.562765
$170$	5.71882	0.438614
$171$	3.06182	0.234143
$172$	1.00000	0.0762493
$173$	−19.3800	−1.47343	−0.736715	−	0.676203i	$-0.763624\pi$
$173$	−19.3800	−1.47343	−0.736715	+	0.676203i	$0.763624\pi$
$174$	−1.17902	−0.0893812
$175$	4.03613	0.305102
$176$	1.00000	0.0753778
$177$	−13.0458	−0.980583
$178$	1.17265	0.0878937
$179$	10.4063	0.777806	0.388903	−	0.921279i	$-0.372854\pi$
$179$	10.4063	0.777806	0.388903	+	0.921279i	$0.372854\pi$
$180$	4.21287	0.314009
$181$	−14.6822	−1.09132	−0.545661	−	0.838006i	$-0.683721\pi$
$181$	−14.6822	−1.09132	−0.545661	+	0.838006i	$0.683721\pi$
$182$	−18.1921	−1.34849
$183$	23.5529	1.74108
$184$	3.76465	0.277534
$185$	2.90049	0.213248
$186$	0.424928	0.0311572
$187$	−5.71882	−0.418202
$188$	12.3291	0.899195
$189$	13.1472	0.956319
$190$	−0.726777	−0.0527260
$191$	20.8338	1.50748	0.753740	−	0.657173i	$-0.228248\pi$
$191$	20.8338	1.50748	0.753740	+	0.657173i	$0.228248\pi$
$192$	2.68568	0.193822
$193$	2.97751	0.214326	0.107163	−	0.994241i	$-0.465823\pi$
$193$	2.97751	0.214326	0.107163	+	0.994241i	$0.465823\pi$
$194$	5.36406	0.385117
$195$	12.1052	0.866873
$196$	9.29031	0.663593
$197$	−4.35502	−0.310282	−0.155141	−	0.987892i	$-0.549583\pi$
$197$	−4.35502	−0.310282	−0.155141	+	0.987892i	$0.549583\pi$
$198$	−4.21287	−0.299396
$199$	12.0519	0.854335	0.427168	−	0.904172i	$-0.359511\pi$
$199$	12.0519	0.854335	0.427168	+	0.904172i	$0.359511\pi$
$200$	−1.00000	−0.0707107
$201$	−14.3291	−1.01070
$202$	10.0398	0.706399
$203$	1.77187	0.124361
$204$	−15.3589	−1.07534
$205$	−9.05460	−0.632401
$206$	−3.78461	−0.263686
$207$	−15.8600	−1.10235
$208$	4.50732	0.312527
$209$	0.726777	0.0502722
$210$	−10.8397	−0.748013
$211$	−11.7432	−0.808432	−0.404216	−	0.914664i	$-0.632456\pi$
$211$	−11.7432	−0.808432	−0.404216	+	0.914664i	$0.632456\pi$
$212$	5.86744	0.402978
$213$	35.2924	2.41820
$214$	9.75462	0.666812
$215$	1.00000	0.0681994
$216$	−3.25739	−0.221637
$217$	−0.638595	−0.0433506
$218$	−8.38098	−0.567632
$219$	14.9601	1.01091
$220$	1.00000	0.0674200
$221$	−25.7766	−1.73392
$222$	−7.78978	−0.522816
$223$	−25.6670	−1.71879	−0.859395	−	0.511313i	$-0.829159\pi$
$223$	−25.6670	−1.71879	−0.859395	+	0.511313i	$0.829159\pi$
$224$	−4.03613	−0.269675
$225$	4.21287	0.280858
$226$	0.886368	0.0589603
$227$	4.46614	0.296428	0.148214	−	0.988955i	$-0.452648\pi$
$227$	4.46614	0.296428	0.148214	+	0.988955i	$0.452648\pi$
$228$	1.95189	0.129267
$229$	13.9524	0.921998	0.460999	−	0.887401i	$-0.347491\pi$
$229$	13.9524	0.921998	0.460999	+	0.887401i	$0.347491\pi$
$230$	3.76465	0.248234
$231$	10.8397	0.713202
$232$	−0.439002	−0.0288219
$233$	8.04351	0.526948	0.263474	−	0.964667i	$-0.415132\pi$
$233$	8.04351	0.526948	0.263474	+	0.964667i	$0.415132\pi$
$234$	−18.9888	−1.24133
$235$	12.3291	0.804264
$236$	−4.85755	−0.316199
$237$	−2.01575	−0.130937
$238$	23.0819	1.49618
$239$	13.1546	0.850903	0.425451	−	0.904981i	$-0.360115\pi$
$239$	13.1546	0.850903	0.425451	+	0.904981i	$0.360115\pi$
$240$	2.68568	0.173360
$241$	−3.94270	−0.253971	−0.126986	−	0.991905i	$-0.540530\pi$
$241$	−3.94270	−0.253971	−0.126986	+	0.991905i	$0.540530\pi$
$242$	−1.00000	−0.0642824
$243$	−20.2203	−1.29713
$244$	8.76979	0.561429
$245$	9.29031	0.593536
$246$	24.3178	1.55044
$247$	3.27582	0.208435
$248$	0.158220	0.0100470
$249$	−2.77351	−0.175764
$250$	−1.00000	−0.0632456
$251$	5.58605	0.352588	0.176294	−	0.984338i	$-0.443589\pi$
$251$	5.58605	0.352588	0.176294	+	0.984338i	$0.443589\pi$
$252$	17.0037	1.07113
$253$	−3.76465	−0.236682
$254$	12.4763	0.782831
$255$	−15.3589	−0.961813
$256$	1.00000	0.0625000
$257$	1.66810	0.104053	0.0520266	−	0.998646i	$-0.483432\pi$
$257$	1.66810	0.104053	0.0520266	+	0.998646i	$0.483432\pi$
$258$	−2.68568	−0.167203
$259$	11.7067	0.727421
$260$	4.50732	0.279532
$261$	1.84946	0.114479
$262$	2.00453	0.123840
$263$	0.235369	0.0145135	0.00725674	−	0.999974i	$-0.497690\pi$
$263$	0.235369	0.0145135	0.00725674	+	0.999974i	$0.497690\pi$
$264$	−2.68568	−0.165292
$265$	5.86744	0.360434
$266$	−2.93336	−0.179856
$267$	−3.14936	−0.192738
$268$	−5.33538	−0.325910
$269$	7.77021	0.473758	0.236879	−	0.971539i	$-0.423875\pi$
$269$	7.77021	0.473758	0.236879	+	0.971539i	$0.423875\pi$
$270$	−3.25739	−0.198238
$271$	−8.68735	−0.527719	−0.263859	−	0.964561i	$-0.584995\pi$
$271$	−8.68735	−0.527719	−0.263859	+	0.964561i	$0.584995\pi$
$272$	−5.71882	−0.346755
$273$	48.8582	2.95703
$274$	18.3974	1.11143
$275$	1.00000	0.0603023
$276$	−10.1106	−0.608590
$277$	−23.3828	−1.40493	−0.702467	−	0.711717i	$-0.747918\pi$
$277$	−23.3828	−1.40493	−0.702467	+	0.711717i	$0.747918\pi$
$278$	−11.5109	−0.690379
$279$	−0.666560	−0.0399059
$280$	−4.03613	−0.241205
$281$	−22.9108	−1.36674	−0.683372	−	0.730070i	$-0.739487\pi$
$281$	−22.9108	−1.36674	−0.683372	+	0.730070i	$0.739487\pi$
$282$	−33.1121	−1.97180
$283$	−25.9531	−1.54275	−0.771375	−	0.636381i	$-0.780431\pi$
$283$	−25.9531	−1.54275	−0.771375	+	0.636381i	$0.780431\pi$
$284$	13.1410	0.779773
$285$	1.95189	0.115620
$286$	−4.50732	−0.266524
$287$	−36.5455	−2.15721
$288$	−4.21287	−0.248246
$289$	15.7049	0.923820
$290$	−0.439002	−0.0257791
$291$	−14.4061	−0.844502
$292$	5.57033	0.325979
$293$	30.7157	1.79443	0.897214	−	0.441596i	$-0.145588\pi$
$293$	30.7157	1.79443	0.897214	+	0.441596i	$0.145588\pi$
$294$	−24.9508	−1.45516
$295$	−4.85755	−0.282817
$296$	−2.90049	−0.168587
$297$	3.25739	0.189013
$298$	2.50497	0.145109
$299$	−16.9685	−0.981314
$300$	2.68568	0.155058
$301$	4.03613	0.232638
$302$	4.31360	0.248220
$303$	−26.9637	−1.54902
$304$	0.726777	0.0416835
$305$	8.76979	0.502157
$306$	24.0927	1.37729
$307$	−31.3822	−1.79108	−0.895539	−	0.444984i	$-0.853209\pi$
$307$	−31.3822	−1.79108	−0.895539	+	0.444984i	$0.853209\pi$
$308$	4.03613	0.229980
$309$	10.1642	0.578224
$310$	0.158220	0.00898628
$311$	0.0582887	0.00330525	0.00165262	−	0.999999i	$-0.499474\pi$
$311$	0.0582887	0.00330525	0.00165262	+	0.999999i	$0.499474\pi$
$312$	−12.1052	−0.685323
$313$	34.8463	1.96963	0.984814	−	0.173613i	$-0.0555443\pi$
$313$	34.8463	1.96963	0.984814	+	0.173613i	$0.0555443\pi$
$314$	−22.8158	−1.28757
$315$	17.0037	0.958049
$316$	−0.750555	−0.0422220
$317$	4.32945	0.243166	0.121583	−	0.992581i	$-0.461203\pi$
$317$	4.32945	0.243166	0.121583	+	0.992581i	$0.461203\pi$
$318$	−15.7581	−0.883669
$319$	0.439002	0.0245794
$320$	1.00000	0.0559017
$321$	−26.1978	−1.46222
$322$	15.1946	0.846762
$323$	−4.15631	−0.231263
$324$	−3.89033	−0.216129
$325$	4.50732	0.250021
$326$	9.31122	0.515701
$327$	22.5086	1.24473
$328$	9.05460	0.499957
$329$	49.7620	2.74347
$330$	−2.68568	−0.147842
$331$	−34.2982	−1.88520	−0.942599	−	0.333928i	$-0.891626\pi$
$331$	−34.2982	−1.88520	−0.942599	+	0.333928i	$0.891626\pi$
$332$	−1.03270	−0.0566770
$333$	12.2194	0.669618
$334$	17.8990	0.979391
$335$	−5.33538	−0.291503
$336$	10.8397	0.591356
$337$	2.85858	0.155717	0.0778583	−	0.996964i	$-0.475192\pi$
$337$	2.85858	0.155717	0.0778583	+	0.996964i	$0.475192\pi$
$338$	−7.31595	−0.397935
$339$	−2.38050	−0.129291
$340$	−5.71882	−0.310147
$341$	−0.158220	−0.00856808
$342$	−3.06182	−0.165564
$343$	9.24396	0.499127
$344$	−1.00000	−0.0539164
$345$	−10.1106	−0.544339
$346$	19.3800	1.04187
$347$	35.0563	1.88192	0.940959	−	0.338520i	$-0.109926\pi$
$347$	35.0563	1.88192	0.940959	+	0.338520i	$0.109926\pi$
$348$	1.17902	0.0632020
$349$	−6.80924	−0.364490	−0.182245	−	0.983253i	$-0.558336\pi$
$349$	−6.80924	−0.364490	−0.182245	+	0.983253i	$0.558336\pi$
$350$	−4.03613	−0.215740
$351$	14.6821	0.783672
$352$	−1.00000	−0.0533002
$353$	3.46593	0.184473	0.0922363	−	0.995737i	$-0.470598\pi$
$353$	3.46593	0.184473	0.0922363	+	0.995737i	$0.470598\pi$
$354$	13.0458	0.693377
$355$	13.1410	0.697451
$356$	−1.17265	−0.0621502
$357$	−61.9905	−3.28089
$358$	−10.4063	−0.549992
$359$	−1.81960	−0.0960348	−0.0480174	−	0.998846i	$-0.515290\pi$
$359$	−1.81960	−0.0960348	−0.0480174	+	0.998846i	$0.515290\pi$
$360$	−4.21287	−0.222038
$361$	−18.4718	−0.972200
$362$	14.6822	0.771681
$363$	2.68568	0.140962
$364$	18.1921	0.953526
$365$	5.57033	0.291564
$366$	−23.5529	−1.23113
$367$	29.3384	1.53145	0.765726	−	0.643167i	$-0.222380\pi$
$367$	29.3384	1.53145	0.765726	+	0.643167i	$0.222380\pi$
$368$	−3.76465	−0.196246
$369$	−38.1459	−1.98579
$370$	−2.90049	−0.150789
$371$	23.6817	1.22949
$372$	−0.424928	−0.0220315
$373$	−12.0503	−0.623942	−0.311971	−	0.950092i	$-0.600989\pi$
$373$	−12.0503	−0.623942	−0.311971	+	0.950092i	$0.600989\pi$
$374$	5.71882	0.295713
$375$	2.68568	0.138688
$376$	−12.3291	−0.635827
$377$	1.97872	0.101909
$378$	−13.1472	−0.676220
$379$	−28.7165	−1.47507	−0.737534	−	0.675310i	$-0.764010\pi$
$379$	−28.7165	−1.47507	−0.737534	+	0.675310i	$0.764010\pi$
$380$	0.726777	0.0372829
$381$	−33.5073	−1.71663
$382$	−20.8338	−1.06595
$383$	8.14499	0.416189	0.208095	−	0.978109i	$-0.433274\pi$
$383$	8.14499	0.416189	0.208095	+	0.978109i	$0.433274\pi$
$384$	−2.68568	−0.137053
$385$	4.03613	0.205700
$386$	−2.97751	−0.151552
$387$	4.21287	0.214152
$388$	−5.36406	−0.272319
$389$	14.1842	0.719166	0.359583	−	0.933113i	$-0.382919\pi$
$389$	14.1842	0.719166	0.359583	+	0.933113i	$0.382919\pi$
$390$	−12.1052	−0.612972
$391$	21.5294	1.08879
$392$	−9.29031	−0.469231
$393$	−5.38351	−0.271562
$394$	4.35502	0.219403
$395$	−0.750555	−0.0377645
$396$	4.21287	0.211705
$397$	1.83752	0.0922223	0.0461111	−	0.998936i	$-0.485317\pi$
$397$	1.83752	0.0922223	0.0461111	+	0.998936i	$0.485317\pi$
$398$	−12.0519	−0.604106
$399$	7.87807	0.394397
$400$	1.00000	0.0500000
$401$	−20.3011	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$401$	−20.3011	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$402$	14.3291	0.714672
$403$	−0.713147	−0.0355244
$404$	−10.0398	−0.499499
$405$	−3.89033	−0.193312
$406$	−1.77187	−0.0879363
$407$	2.90049	0.143772
$408$	15.3589	0.760380
$409$	−17.9381	−0.886984	−0.443492	−	0.896278i	$-0.646261\pi$
$409$	−17.9381	−0.886984	−0.443492	+	0.896278i	$0.646261\pi$
$410$	9.05460	0.447175
$411$	−49.4096	−2.43720
$412$	3.78461	0.186454
$413$	−19.6057	−0.964731
$414$	15.8600	0.779476
$415$	−1.03270	−0.0506935
$416$	−4.50732	−0.220990
$417$	30.9146	1.51390
$418$	−0.726777	−0.0355478
$419$	−36.3304	−1.77486	−0.887428	−	0.460947i	$-0.847510\pi$
$419$	−36.3304	−1.77486	−0.887428	+	0.460947i	$0.847510\pi$
$420$	10.8397	0.528925
$421$	3.41690	0.166529	0.0832647	−	0.996527i	$-0.473465\pi$
$421$	3.41690	0.166529	0.0832647	+	0.996527i	$0.473465\pi$
$422$	11.7432	0.571648
$423$	51.9411	2.52546
$424$	−5.86744	−0.284948
$425$	−5.71882	−0.277404
$426$	−35.2924	−1.70992
$427$	35.3960	1.71293
$428$	−9.75462	−0.471507
$429$	12.1052	0.584445
$430$	−1.00000	−0.0482243
$431$	−2.97747	−0.143420	−0.0717099	−	0.997426i	$-0.522846\pi$
$431$	−2.97747	−0.143420	−0.0717099	+	0.997426i	$0.522846\pi$
$432$	3.25739	0.156721
$433$	12.5958	0.605316	0.302658	−	0.953099i	$-0.402126\pi$
$433$	12.5958	0.605316	0.302658	+	0.953099i	$0.402126\pi$
$434$	0.638595	0.0306535
$435$	1.17902	0.0565296
$436$	8.38098	0.401376
$437$	−2.73606	−0.130884
$438$	−14.9601	−0.714822
$439$	−12.4899	−0.596109	−0.298055	−	0.954549i	$-0.596338\pi$
$439$	−12.4899	−0.596109	−0.298055	+	0.954549i	$0.596338\pi$
$440$	−1.00000	−0.0476731
$441$	39.1389	1.86376
$442$	25.7766	1.22607
$443$	−5.84964	−0.277925	−0.138962	−	0.990298i	$-0.544377\pi$
$443$	−5.84964	−0.277925	−0.138962	+	0.990298i	$0.544377\pi$
$444$	7.78978	0.369687
$445$	−1.17265	−0.0555889
$446$	25.6670	1.21537
$447$	−6.72755	−0.318202
$448$	4.03613	0.190689
$449$	19.1094	0.901830	0.450915	−	0.892567i	$-0.351098\pi$
$449$	19.1094	0.901830	0.450915	+	0.892567i	$0.351098\pi$
$450$	−4.21287	−0.198597
$451$	−9.05460	−0.426364
$452$	−0.886368	−0.0416912
$453$	−11.5849	−0.544308
$454$	−4.46614	−0.209606
$455$	18.1921	0.852859
$456$	−1.95189	−0.0914056
$457$	11.4338	0.534853	0.267426	−	0.963578i	$-0.413827\pi$
$457$	11.4338	0.534853	0.267426	+	0.963578i	$0.413827\pi$
$458$	−13.9524	−0.651951
$459$	−18.6284	−0.869500
$460$	−3.76465	−0.175528
$461$	−22.6868	−1.05663	−0.528315	−	0.849049i	$-0.677176\pi$
$461$	−22.6868	−1.05663	−0.528315	+	0.849049i	$0.677176\pi$
$462$	−10.8397	−0.504310
$463$	6.36213	0.295673	0.147837	−	0.989012i	$-0.452769\pi$
$463$	6.36213	0.295673	0.147837	+	0.989012i	$0.452769\pi$
$464$	0.439002	0.0203802
$465$	−0.424928	−0.0197055
$466$	−8.04351	−0.372608
$467$	26.9634	1.24772	0.623859	−	0.781537i	$-0.285564\pi$
$467$	26.9634	1.24772	0.623859	+	0.781537i	$0.285564\pi$
$468$	18.9888	0.877756
$469$	−21.5343	−0.994360
$470$	−12.3291	−0.568701
$471$	61.2760	2.82345
$472$	4.85755	0.223587
$473$	1.00000	0.0459800
$474$	2.01575	0.0925865
$475$	0.726777	0.0333468
$476$	−23.0819	−1.05796
$477$	24.7188	1.13180
$478$	−13.1546	−0.601679
$479$	−21.1574	−0.966706	−0.483353	−	0.875426i	$-0.660581\pi$
$479$	−21.1574	−0.966706	−0.483353	+	0.875426i	$0.660581\pi$
$480$	−2.68568	−0.122584
$481$	13.0734	0.596097
$482$	3.94270	0.179585
$483$	−40.8078	−1.85682
$484$	1.00000	0.0454545
$485$	−5.36406	−0.243569
$486$	20.2203	0.917212
$487$	−4.38219	−0.198576	−0.0992880	−	0.995059i	$-0.531657\pi$
$487$	−4.38219	−0.198576	−0.0992880	+	0.995059i	$0.531657\pi$
$488$	−8.76979	−0.396990
$489$	−25.0069	−1.13085
$490$	−9.29031	−0.419693
$491$	−36.4434	−1.64467	−0.822334	−	0.569005i	$-0.807329\pi$
$491$	−36.4434	−1.64467	−0.822334	+	0.569005i	$0.807329\pi$
$492$	−24.3178	−1.09633
$493$	−2.51057	−0.113071
$494$	−3.27582	−0.147386
$495$	4.21287	0.189355
$496$	−0.158220	−0.00710428
$497$	53.0386	2.37911
$498$	2.77351	0.124284
$499$	24.1642	1.08174	0.540869	−	0.841107i	$-0.318095\pi$
$499$	24.1642	1.08174	0.540869	+	0.841107i	$0.318095\pi$
$500$	1.00000	0.0447214
$501$	−48.0711	−2.14766
$502$	−5.58605	−0.249318
$503$	−1.04078	−0.0464060	−0.0232030	−	0.999731i	$-0.507386\pi$
$503$	−1.04078	−0.0464060	−0.0232030	+	0.999731i	$0.507386\pi$
$504$	−17.0037	−0.757404
$505$	−10.0398	−0.446766
$506$	3.76465	0.167359
$507$	19.6483	0.872611
$508$	−12.4763	−0.553545
$509$	−17.6057	−0.780358	−0.390179	−	0.920739i	$-0.627587\pi$
$509$	−17.6057	−0.780358	−0.390179	+	0.920739i	$0.627587\pi$
$510$	15.3589	0.680105
$511$	22.4825	0.994569
$512$	−1.00000	−0.0441942
$513$	2.36739	0.104523
$514$	−1.66810	−0.0735767
$515$	3.78461	0.166770
$516$	2.68568	0.118230
$517$	12.3291	0.542235
$518$	−11.7067	−0.514364
$519$	−52.0483	−2.28467
$520$	−4.50732	−0.197659
$521$	15.5035	0.679219	0.339609	−	0.940567i	$-0.389705\pi$
$521$	15.5035	0.679219	0.339609	+	0.940567i	$0.389705\pi$
$522$	−1.84946	−0.0809486
$523$	−23.2595	−1.01707	−0.508533	−	0.861042i	$-0.669812\pi$
$523$	−23.2595	−1.01707	−0.508533	+	0.861042i	$0.669812\pi$
$524$	−2.00453	−0.0875681
$525$	10.8397	0.473085
$526$	−0.235369	−0.0102626
$527$	0.904831	0.0394151
$528$	2.68568	0.116879
$529$	−8.82739	−0.383800
$530$	−5.86744	−0.254865
$531$	−20.4642	−0.888071
$532$	2.93336	0.127177
$533$	−40.8120	−1.76776
$534$	3.14936	0.136286
$535$	−9.75462	−0.421729
$536$	5.33538	0.230453
$537$	27.9481	1.20605
$538$	−7.77021	−0.334998
$539$	9.29031	0.400162
$540$	3.25739	0.140176
$541$	17.4581	0.750582	0.375291	−	0.926907i	$-0.377543\pi$
$541$	17.4581	0.750582	0.375291	+	0.926907i	$0.377543\pi$
$542$	8.68735	0.373154
$543$	−39.4318	−1.69218
$544$	5.71882	0.245193
$545$	8.38098	0.359002
$546$	−48.8582	−2.09094
$547$	34.1394	1.45970	0.729848	−	0.683609i	$-0.239591\pi$
$547$	34.1394	1.45970	0.729848	+	0.683609i	$0.239591\pi$
$548$	−18.3974	−0.785900
$549$	36.9460	1.57682
$550$	−1.00000	−0.0426401
$551$	0.319057	0.0135923
$552$	10.1106	0.430338
$553$	−3.02934	−0.128820
$554$	23.3828	0.993438
$555$	7.78978	0.330658
$556$	11.5109	0.488172
$557$	15.2381	0.645661	0.322830	−	0.946457i	$-0.395366\pi$
$557$	15.2381	0.645661	0.322830	+	0.946457i	$0.395366\pi$
$558$	0.666560	0.0282177
$559$	4.50732	0.190639
$560$	4.03613	0.170557
$561$	−15.3589	−0.648454
$562$	22.9108	0.966434
$563$	−28.4428	−1.19872	−0.599360	−	0.800480i	$-0.704578\pi$
$563$	−28.4428	−1.19872	−0.599360	+	0.800480i	$0.704578\pi$
$564$	33.1121	1.39427
$565$	−0.886368	−0.0372898
$566$	25.9531	1.09089
$567$	−15.7018	−0.659415
$568$	−13.1410	−0.551383
$569$	−0.174420	−0.00731208	−0.00365604	−	0.999993i	$-0.501164\pi$
$569$	−0.174420	−0.00731208	−0.00365604	+	0.999993i	$0.501164\pi$
$570$	−1.95189	−0.0817557
$571$	−9.83697	−0.411664	−0.205832	−	0.978587i	$-0.565990\pi$
$571$	−9.83697	−0.411664	−0.205832	+	0.978587i	$0.565990\pi$
$572$	4.50732	0.188461
$573$	55.9528	2.33746
$574$	36.5455	1.52538
$575$	−3.76465	−0.156997
$576$	4.21287	0.175536
$577$	11.5851	0.482294	0.241147	−	0.970489i	$-0.422476\pi$
$577$	11.5851	0.482294	0.241147	+	0.970489i	$0.422476\pi$
$578$	−15.7049	−0.653239
$579$	7.99665	0.332329
$580$	0.439002	0.0182286
$581$	−4.16812	−0.172923
$582$	14.4061	0.597153
$583$	5.86744	0.243005
$584$	−5.57033	−0.230502
$585$	18.9888	0.785089
$586$	−30.7157	−1.26885
$587$	9.48513	0.391493	0.195747	−	0.980655i	$-0.437287\pi$
$587$	9.48513	0.391493	0.195747	+	0.980655i	$0.437287\pi$
$588$	24.9508	1.02895
$589$	−0.114991	−0.00473810
$590$	4.85755	0.199982
$591$	−11.6962	−0.481117
$592$	2.90049	0.119209
$593$	−34.0358	−1.39768	−0.698841	−	0.715277i	$-0.746301\pi$
$593$	−34.0358	−1.39768	−0.698841	+	0.715277i	$0.746301\pi$
$594$	−3.25739	−0.133652
$595$	−23.0819	−0.946265
$596$	−2.50497	−0.102608
$597$	32.3675	1.32471
$598$	16.9685	0.693894
$599$	42.3037	1.72848	0.864240	−	0.503079i	$-0.167800\pi$
$599$	42.3037	1.72848	0.864240	+	0.503079i	$0.167800\pi$
$600$	−2.68568	−0.109642
$601$	−11.6708	−0.476063	−0.238031	−	0.971257i	$-0.576502\pi$
$601$	−11.6708	−0.476063	−0.238031	+	0.971257i	$0.576502\pi$
$602$	−4.03613	−0.164500
$603$	−22.4773	−0.915346
$604$	−4.31360	−0.175518
$605$	1.00000	0.0406558
$606$	26.9637	1.09533
$607$	16.6101	0.674183	0.337091	−	0.941472i	$-0.390557\pi$
$607$	16.6101	0.674183	0.337091	+	0.941472i	$0.390557\pi$
$608$	−0.726777	−0.0294747
$609$	4.75867	0.192831
$610$	−8.76979	−0.355079
$611$	55.5714	2.24818
$612$	−24.0927	−0.973888
$613$	18.1911	0.734730	0.367365	−	0.930077i	$-0.380260\pi$
$613$	18.1911	0.734730	0.367365	+	0.930077i	$0.380260\pi$
$614$	31.3822	1.26648
$615$	−24.3178	−0.980586
$616$	−4.03613	−0.162620
$617$	18.5577	0.747104	0.373552	−	0.927609i	$-0.378140\pi$
$617$	18.5577	0.747104	0.373552	+	0.927609i	$0.378140\pi$
$618$	−10.1642	−0.408866
$619$	−22.1186	−0.889021	−0.444511	−	0.895774i	$-0.646622\pi$
$619$	−22.1186	−0.889021	−0.444511	+	0.895774i	$0.646622\pi$
$620$	−0.158220	−0.00635426
$621$	−12.2629	−0.492094
$622$	−0.0582887	−0.00233716
$623$	−4.73296	−0.189622
$624$	12.1052	0.484597
$625$	1.00000	0.0400000
$626$	−34.8463	−1.39274
$627$	1.95189	0.0779510
$628$	22.8158	0.910451
$629$	−16.5874	−0.661382
$630$	−17.0037	−0.677443
$631$	24.7453	0.985097	0.492548	−	0.870285i	$-0.336065\pi$
$631$	24.7453	0.985097	0.492548	+	0.870285i	$0.336065\pi$
$632$	0.750555	0.0298555
$633$	−31.5383	−1.25354
$634$	−4.32945	−0.171944
$635$	−12.4763	−0.495106
$636$	15.7581	0.624848
$637$	41.8744	1.65912
$638$	−0.439002	−0.0173803
$639$	55.3612	2.19006
$640$	−1.00000	−0.0395285
$641$	6.11770	0.241635	0.120817	−	0.992675i	$-0.461448\pi$
$641$	6.11770	0.241635	0.120817	+	0.992675i	$0.461448\pi$
$642$	26.1978	1.03394
$643$	33.7504	1.33098	0.665492	−	0.746405i	$-0.268222\pi$
$643$	33.7504	1.33098	0.665492	+	0.746405i	$0.268222\pi$
$644$	−15.1946	−0.598751
$645$	2.68568	0.105749
$646$	4.15631	0.163528
$647$	−15.7248	−0.618204	−0.309102	−	0.951029i	$-0.600029\pi$
$647$	−15.7248	−0.618204	−0.309102	+	0.951029i	$0.600029\pi$
$648$	3.89033	0.152826
$649$	−4.85755	−0.190675
$650$	−4.50732	−0.176792
$651$	−1.71506	−0.0672185
$652$	−9.31122	−0.364655
$653$	15.3568	0.600959	0.300479	−	0.953788i	$-0.402853\pi$
$653$	15.3568	0.600959	0.300479	+	0.953788i	$0.402853\pi$
$654$	−22.5086	−0.880157
$655$	−2.00453	−0.0783233
$656$	−9.05460	−0.353523
$657$	23.4671	0.915538
$658$	−49.7620	−1.93992
$659$	17.9440	0.698999	0.349499	−	0.936937i	$-0.386352\pi$
$659$	17.9440	0.698999	0.349499	+	0.936937i	$0.386352\pi$
$660$	2.68568	0.104540
$661$	12.1764	0.473606	0.236803	−	0.971558i	$-0.423900\pi$
$661$	12.1764	0.473606	0.236803	+	0.971558i	$0.423900\pi$
$662$	34.2982	1.33304
$663$	−69.2276	−2.68858
$664$	1.03270	0.0400767
$665$	2.93336	0.113751
$666$	−12.2194	−0.473492
$667$	−1.65269	−0.0639924
$668$	−17.8990	−0.692534
$669$	−68.9333	−2.66512
$670$	5.33538	0.206124
$671$	8.76979	0.338554
$672$	−10.8397	−0.418152
$673$	40.8234	1.57363	0.786813	−	0.617192i	$-0.211730\pi$
$673$	40.8234	1.57363	0.786813	+	0.617192i	$0.211730\pi$
$674$	−2.85858	−0.110108
$675$	3.25739	0.125377
$676$	7.31595	0.281383
$677$	10.8623	0.417473	0.208737	−	0.977972i	$-0.433065\pi$
$677$	10.8623	0.417473	0.208737	+	0.977972i	$0.433065\pi$
$678$	2.38050	0.0914225
$679$	−21.6500	−0.830851
$680$	5.71882	0.219307
$681$	11.9946	0.459635
$682$	0.158220	0.00605855
$683$	16.2402	0.621413	0.310706	−	0.950506i	$-0.399434\pi$
$683$	16.2402	0.621413	0.310706	+	0.950506i	$0.399434\pi$
$684$	3.06182	0.117072
$685$	−18.3974	−0.702930
$686$	−9.24396	−0.352936
$687$	37.4715	1.42963
$688$	1.00000	0.0381246
$689$	26.4464	1.00753
$690$	10.1106	0.384906
$691$	−24.0637	−0.915426	−0.457713	−	0.889100i	$-0.651331\pi$
$691$	−24.0637	−0.915426	−0.457713	+	0.889100i	$0.651331\pi$
$692$	−19.3800	−0.736715
$693$	17.0037	0.645916
$694$	−35.0563	−1.33072
$695$	11.5109	0.436634
$696$	−1.17902	−0.0446906
$697$	51.7817	1.96137
$698$	6.80924	0.257734
$699$	21.6023	0.817073
$700$	4.03613	0.152551
$701$	−38.7175	−1.46234	−0.731170	−	0.682195i	$-0.761025\pi$
$701$	−38.7175	−1.46234	−0.731170	+	0.682195i	$0.761025\pi$
$702$	−14.6821	−0.554139
$703$	2.10801	0.0795051
$704$	1.00000	0.0376889
$705$	33.1121	1.24707
$706$	−3.46593	−0.130442
$707$	−40.5219	−1.52398
$708$	−13.0458	−0.490291
$709$	32.5123	1.22103	0.610513	−	0.792006i	$-0.290963\pi$
$709$	32.5123	1.22103	0.610513	+	0.792006i	$0.290963\pi$
$710$	−13.1410	−0.493172
$711$	−3.16199	−0.118584
$712$	1.17265	0.0439469
$713$	0.595643	0.0223070
$714$	61.9905	2.31994
$715$	4.50732	0.168564
$716$	10.4063	0.388903
$717$	35.3291	1.31939
$718$	1.81960	0.0679069
$719$	1.84506	0.0688093	0.0344046	−	0.999408i	$-0.489046\pi$
$719$	1.84506	0.0688093	0.0344046	+	0.999408i	$0.489046\pi$
$720$	4.21287	0.157004
$721$	15.2752	0.568877
$722$	18.4718	0.687449
$723$	−10.5888	−0.393802
$724$	−14.6822	−0.545661
$725$	0.439002	0.0163041
$726$	−2.68568	−0.0996749
$727$	32.0720	1.18948	0.594742	−	0.803917i	$-0.297254\pi$
$727$	32.0720	1.18948	0.594742	+	0.803917i	$0.297254\pi$
$728$	−18.1921	−0.674245
$729$	−42.6343	−1.57905
$730$	−5.57033	−0.206167
$731$	−5.71882	−0.211518
$732$	23.5529	0.870538
$733$	16.2652	0.600768	0.300384	−	0.953818i	$-0.402885\pi$
$733$	16.2652	0.600768	0.300384	+	0.953818i	$0.402885\pi$
$734$	−29.3384	−1.08290
$735$	24.9508	0.920323
$736$	3.76465	0.138767
$737$	−5.33538	−0.196531
$738$	38.1459	1.40417
$739$	−29.6931	−1.09228	−0.546139	−	0.837695i	$-0.683903\pi$
$739$	−29.6931	−1.09228	−0.546139	+	0.837695i	$0.683903\pi$
$740$	2.90049	0.106624
$741$	8.79780	0.323195
$742$	−23.6817	−0.869384
$743$	−7.35234	−0.269731	−0.134866	−	0.990864i	$-0.543060\pi$
$743$	−7.35234	−0.269731	−0.134866	+	0.990864i	$0.543060\pi$
$744$	0.424928	0.0155786
$745$	−2.50497	−0.0917751
$746$	12.0503	0.441194
$747$	−4.35065	−0.159182
$748$	−5.71882	−0.209101
$749$	−39.3709	−1.43858
$750$	−2.68568	−0.0980671
$751$	4.81681	0.175768	0.0878839	−	0.996131i	$-0.471990\pi$
$751$	4.81681	0.175768	0.0878839	+	0.996131i	$0.471990\pi$
$752$	12.3291	0.449597
$753$	15.0023	0.546715
$754$	−1.97872	−0.0720608
$755$	−4.31360	−0.156988
$756$	13.1472	0.478160
$757$	−51.1734	−1.85993	−0.929965	−	0.367648i	$-0.880163\pi$
$757$	−51.1734	−1.85993	−0.929965	+	0.367648i	$0.880163\pi$
$758$	28.7165	1.04303
$759$	−10.1106	−0.366993
$760$	−0.726777	−0.0263630
$761$	42.4115	1.53742	0.768708	−	0.639599i	$-0.220900\pi$
$761$	42.4115	1.53742	0.768708	+	0.639599i	$0.220900\pi$
$762$	33.5073	1.21384
$763$	33.8267	1.22461
$764$	20.8338	0.753740
$765$	−24.0927	−0.871072
$766$	−8.14499	−0.294290
$767$	−21.8945	−0.790565
$768$	2.68568	0.0969111
$769$	47.1086	1.69878	0.849390	−	0.527765i	$-0.176970\pi$
$769$	47.1086	1.69878	0.849390	+	0.527765i	$0.176970\pi$
$770$	−4.03613	−0.145452
$771$	4.47998	0.161342
$772$	2.97751	0.107163
$773$	−3.71435	−0.133596	−0.0667979	−	0.997767i	$-0.521278\pi$
$773$	−3.71435	−0.133596	−0.0667979	+	0.997767i	$0.521278\pi$
$774$	−4.21287	−0.151429
$775$	−0.158220	−0.00568342
$776$	5.36406	0.192558
$777$	31.4405	1.12792
$778$	−14.1842	−0.508527
$779$	−6.58068	−0.235777
$780$	12.1052	0.433436
$781$	13.1410	0.470221
$782$	−21.5294	−0.769889
$783$	1.43000	0.0511040
$784$	9.29031	0.331797
$785$	22.8158	0.814332
$786$	5.38351	0.192024
$787$	−40.9548	−1.45988	−0.729940	−	0.683511i	$-0.760452\pi$
$787$	−40.9548	−1.45988	−0.729940	+	0.683511i	$0.760452\pi$
$788$	−4.35502	−0.155141
$789$	0.632126	0.0225043
$790$	0.750555	0.0267036
$791$	−3.57749	−0.127201
$792$	−4.21287	−0.149698
$793$	39.5283	1.40369
$794$	−1.83752	−0.0652110
$795$	15.7581	0.558881
$796$	12.0519	0.427168
$797$	−21.3456	−0.756101	−0.378050	−	0.925785i	$-0.623405\pi$
$797$	−21.3456	−0.756101	−0.378050	+	0.925785i	$0.623405\pi$
$798$	−7.87807	−0.278881
$799$	−70.5082	−2.49440
$800$	−1.00000	−0.0353553
$801$	−4.94022	−0.174554
$802$	20.3011	0.716855
$803$	5.57033	0.196573
$804$	−14.3291	−0.505349
$805$	−15.1946	−0.535540
$806$	0.713147	0.0251195
$807$	20.8683	0.734599
$808$	10.0398	0.353199
$809$	−2.73636	−0.0962052	−0.0481026	−	0.998842i	$-0.515317\pi$
$809$	−2.73636	−0.0962052	−0.0481026	+	0.998842i	$0.515317\pi$
$810$	3.89033	0.136692
$811$	6.38436	0.224185	0.112093	−	0.993698i	$-0.464245\pi$
$811$	6.38436	0.224185	0.112093	+	0.993698i	$0.464245\pi$
$812$	1.77187	0.0621803
$813$	−23.3314	−0.818269
$814$	−2.90049	−0.101662
$815$	−9.31122	−0.326158
$816$	−15.3589	−0.537670
$817$	0.726777	0.0254267
$818$	17.9381	0.627192
$819$	76.6410	2.67805
$820$	−9.05460	−0.316200
$821$	−41.9648	−1.46458	−0.732290	−	0.680993i	$-0.761549\pi$
$821$	−41.9648	−1.46458	−0.732290	+	0.680993i	$0.761549\pi$
$822$	49.4096	1.72336
$823$	−37.0796	−1.29251	−0.646257	−	0.763120i	$-0.723667\pi$
$823$	−37.0796	−1.29251	−0.646257	+	0.763120i	$0.723667\pi$
$824$	−3.78461	−0.131843
$825$	2.68568	0.0935033
$826$	19.6057	0.682168
$827$	18.9230	0.658016	0.329008	−	0.944327i	$-0.393286\pi$
$827$	18.9230	0.658016	0.329008	+	0.944327i	$0.393286\pi$
$828$	−15.8600	−0.551173
$829$	17.0586	0.592471	0.296235	−	0.955115i	$-0.404269\pi$
$829$	17.0586	0.592471	0.296235	+	0.955115i	$0.404269\pi$
$830$	1.03270	0.0358457
$831$	−62.7986	−2.17846
$832$	4.50732	0.156263
$833$	−53.1296	−1.84083
$834$	−30.9146	−1.07049
$835$	−17.8990	−0.619422
$836$	0.726777	0.0251361
$837$	−0.515383	−0.0178142
$838$	36.3304	1.25501
$839$	37.6563	1.30004	0.650021	−	0.759917i	$-0.274760\pi$
$839$	37.6563	1.30004	0.650021	+	0.759917i	$0.274760\pi$
$840$	−10.8397	−0.374006
$841$	−28.8073	−0.993354
$842$	−3.41690	−0.117754
$843$	−61.5311	−2.11924
$844$	−11.7432	−0.404216
$845$	7.31595	0.251676
$846$	−51.9411	−1.78577
$847$	4.03613	0.138683
$848$	5.86744	0.201489
$849$	−69.7016	−2.39215
$850$	5.71882	0.196154
$851$	−10.9193	−0.374310
$852$	35.2924	1.20910
$853$	1.72578	0.0590895	0.0295447	−	0.999563i	$-0.490594\pi$
$853$	1.72578	0.0590895	0.0295447	+	0.999563i	$0.490594\pi$
$854$	−35.3960	−1.21123
$855$	3.06182	0.104712
$856$	9.75462	0.333406
$857$	38.2570	1.30683	0.653417	−	0.756998i	$-0.273335\pi$
$857$	38.2570	1.30683	0.653417	+	0.756998i	$0.273335\pi$
$858$	−12.1052	−0.413265
$859$	7.43934	0.253827	0.126913	−	0.991914i	$-0.459493\pi$
$859$	7.43934	0.253827	0.126913	+	0.991914i	$0.459493\pi$
$860$	1.00000	0.0340997
$861$	−98.1495	−3.34493
$862$	2.97747	0.101413
$863$	−29.9446	−1.01933	−0.509664	−	0.860374i	$-0.670230\pi$
$863$	−29.9446	−1.01933	−0.509664	+	0.860374i	$0.670230\pi$
$864$	−3.25739	−0.110818
$865$	−19.3800	−0.658938
$866$	−12.5958	−0.428023
$867$	42.1784	1.43245
$868$	−0.638595	−0.0216753
$869$	−0.750555	−0.0254609
$870$	−1.17902	−0.0399725
$871$	−24.0483	−0.814845
$872$	−8.38098	−0.283816
$873$	−22.5981	−0.764829
$874$	2.73606	0.0925487
$875$	4.03613	0.136446
$876$	14.9601	0.505456
$877$	−18.1849	−0.614059	−0.307030	−	0.951700i	$-0.599335\pi$
$877$	−18.1849	−0.614059	−0.307030	+	0.951700i	$0.599335\pi$
$878$	12.4899	0.421513
$879$	82.4924	2.78240
$880$	1.00000	0.0337100
$881$	−32.8103	−1.10541	−0.552704	−	0.833378i	$-0.686404\pi$
$881$	−32.8103	−1.10541	−0.552704	+	0.833378i	$0.686404\pi$
$882$	−39.1389	−1.31787
$883$	−26.1867	−0.881253	−0.440626	−	0.897691i	$-0.645244\pi$
$883$	−26.1867	−0.881253	−0.440626	+	0.897691i	$0.645244\pi$
$884$	−25.7766	−0.866960
$885$	−13.0458	−0.438530
$886$	5.84964	0.196523
$887$	5.30684	0.178186	0.0890931	−	0.996023i	$-0.471603\pi$
$887$	5.30684	0.178186	0.0890931	+	0.996023i	$0.471603\pi$
$888$	−7.78978	−0.261408
$889$	−50.3558	−1.68888
$890$	1.17265	0.0393073
$891$	−3.89033	−0.130331
$892$	−25.6670	−0.859395
$893$	8.96054	0.299853
$894$	6.72755	0.225003
$895$	10.4063	0.347846
$896$	−4.03613	−0.134837
$897$	−45.5719	−1.52160
$898$	−19.1094	−0.637690
$899$	−0.0694588	−0.00231658
$900$	4.21287	0.140429
$901$	−33.5549	−1.11787
$902$	9.05460	0.301485
$903$	10.8397	0.360724
$904$	0.886368	0.0294801
$905$	−14.6822	−0.488054
$906$	11.5849	0.384884
$907$	50.5027	1.67692	0.838458	−	0.544967i	$-0.183458\pi$
$907$	50.5027	1.67692	0.838458	+	0.544967i	$0.183458\pi$
$908$	4.46614	0.148214
$909$	−42.2964	−1.40288
$910$	−18.1921	−0.603063
$911$	30.6067	1.01404	0.507022	−	0.861933i	$-0.330746\pi$
$911$	30.6067	1.01404	0.507022	+	0.861933i	$0.330746\pi$
$912$	1.95189	0.0646335
$913$	−1.03270	−0.0341775
$914$	−11.4338	−0.378198
$915$	23.5529	0.778633
$916$	13.9524	0.460999
$917$	−8.09052	−0.267172
$918$	18.6284	0.614829
$919$	−49.0686	−1.61862	−0.809312	−	0.587379i	$-0.800160\pi$
$919$	−49.0686	−1.61862	−0.809312	+	0.587379i	$0.800160\pi$
$920$	3.76465	0.124117
$921$	−84.2825	−2.77720
$922$	22.6868	0.747150
$923$	59.2306	1.94960
$924$	10.8397	0.356601
$925$	2.90049	0.0953675
$926$	−6.36213	−0.209072
$927$	15.9441	0.523672
$928$	−0.439002	−0.0144109
$929$	41.1118	1.34884	0.674418	−	0.738350i	$-0.264395\pi$
$929$	41.1118	1.34884	0.674418	+	0.738350i	$0.264395\pi$
$930$	0.424928	0.0139339
$931$	6.75198	0.221287
$932$	8.04351	0.263474
$933$	0.156545	0.00512504
$934$	−26.9634	−0.882270
$935$	−5.71882	−0.187026
$936$	−18.9888	−0.620667
$937$	−4.27589	−0.139687	−0.0698436	−	0.997558i	$-0.522250\pi$
$937$	−4.27589	−0.139687	−0.0698436	+	0.997558i	$0.522250\pi$
$938$	21.5343	0.703119
$939$	93.5859	3.05406
$940$	12.3291	0.402132
$941$	15.9630	0.520378	0.260189	−	0.965558i	$-0.416215\pi$
$941$	15.9630	0.520378	0.260189	+	0.965558i	$0.416215\pi$
$942$	−61.2760	−1.99648
$943$	34.0874	1.11004
$944$	−4.85755	−0.158100
$945$	13.1472	0.427679
$946$	−1.00000	−0.0325128
$947$	31.3512	1.01878	0.509388	−	0.860537i	$-0.329872\pi$
$947$	31.3512	1.01878	0.509388	+	0.860537i	$0.329872\pi$
$948$	−2.01575	−0.0654686
$949$	25.1073	0.815016
$950$	−0.726777	−0.0235798
$951$	11.6275	0.377048
$952$	23.0819	0.748088
$953$	−23.5895	−0.764139	−0.382070	−	0.924134i	$-0.624789\pi$
$953$	−23.5895	−0.764139	−0.382070	+	0.924134i	$0.624789\pi$
$954$	−24.7188	−0.800300
$955$	20.8338	0.674165
$956$	13.1546	0.425451
$957$	1.17902	0.0381123
$958$	21.1574	0.683564
$959$	−74.2544	−2.39780
$960$	2.68568	0.0866799
$961$	−30.9750	−0.999192
$962$	−13.0734	−0.421504
$963$	−41.0950	−1.32427
$964$	−3.94270	−0.126986
$965$	2.97751	0.0958496
$966$	40.8078	1.31297
$967$	−5.42913	−0.174589	−0.0872945	−	0.996183i	$-0.527822\pi$
$967$	−5.42913	−0.174589	−0.0872945	+	0.996183i	$0.527822\pi$
$968$	−1.00000	−0.0321412
$969$	−11.1625	−0.358592
$970$	5.36406	0.172229
$971$	−21.0286	−0.674841	−0.337421	−	0.941354i	$-0.609554\pi$
$971$	−21.0286	−0.674841	−0.337421	+	0.941354i	$0.609554\pi$
$972$	−20.2203	−0.648567
$973$	46.4595	1.48942
$974$	4.38219	0.140414
$975$	12.1052	0.387677
$976$	8.76979	0.280714
$977$	−34.1625	−1.09295	−0.546477	−	0.837474i	$-0.684031\pi$
$977$	−34.1625	−1.09295	−0.546477	+	0.837474i	$0.684031\pi$
$978$	25.0069	0.799634
$979$	−1.17265	−0.0374780
$980$	9.29031	0.296768
$981$	35.3080	1.12730
$982$	36.4434	1.16296
$983$	−59.3476	−1.89290	−0.946448	−	0.322857i	$-0.895357\pi$
$983$	−59.3476	−1.89290	−0.946448	+	0.322857i	$0.895357\pi$
$984$	24.3178	0.775222
$985$	−4.35502	−0.138763
$986$	2.51057	0.0799530
$987$	133.645	4.25396
$988$	3.27582	0.104218
$989$	−3.76465	−0.119709
$990$	−4.21287	−0.133894
$991$	−37.0321	−1.17636	−0.588181	−	0.808729i	$-0.700156\pi$
$991$	−37.0321	−1.17636	−0.588181	+	0.808729i	$0.700156\pi$
$992$	0.158220	0.00502348
$993$	−92.1138	−2.92314
$994$	−53.0386	−1.68228
$995$	12.0519	0.382070
$996$	−2.77351	−0.0878821
$997$	31.7866	1.00669	0.503345	−	0.864085i	$-0.332102\pi$
$997$	31.7866	1.00669	0.503345	+	0.864085i	$0.332102\pi$
$998$	−24.1642	−0.764905
$999$	9.44801	0.298922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.9	✓	10	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.68568 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.68568 q^{6} +4.03613 q^{7} -1.00000 q^{8} +4.21287 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.68568 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.68568 q^{6} +4.03613 q^{7} -1.00000 q^{8} +4.21287 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.68568 q^{12} +4.50732 q^{13} -4.03613 q^{14} +2.68568 q^{15} +1.00000 q^{16} -5.71882 q^{17} -4.21287 q^{18} +0.726777 q^{19} +1.00000 q^{20} +10.8397 q^{21} -1.00000 q^{22} -3.76465 q^{23} -2.68568 q^{24} +1.00000 q^{25} -4.50732 q^{26} +3.25739 q^{27} +4.03613 q^{28} +0.439002 q^{29} -2.68568 q^{30} -0.158220 q^{31} -1.00000 q^{32} +2.68568 q^{33} +5.71882 q^{34} +4.03613 q^{35} +4.21287 q^{36} +2.90049 q^{37} -0.726777 q^{38} +12.1052 q^{39} -1.00000 q^{40} -9.05460 q^{41} -10.8397 q^{42} +1.00000 q^{43} +1.00000 q^{44} +4.21287 q^{45} +3.76465 q^{46} +12.3291 q^{47} +2.68568 q^{48} +9.29031 q^{49} -1.00000 q^{50} -15.3589 q^{51} +4.50732 q^{52} +5.86744 q^{53} -3.25739 q^{54} +1.00000 q^{55} -4.03613 q^{56} +1.95189 q^{57} -0.439002 q^{58} -4.85755 q^{59} +2.68568 q^{60} +8.76979 q^{61} +0.158220 q^{62} +17.0037 q^{63} +1.00000 q^{64} +4.50732 q^{65} -2.68568 q^{66} -5.33538 q^{67} -5.71882 q^{68} -10.1106 q^{69} -4.03613 q^{70} +13.1410 q^{71} -4.21287 q^{72} +5.57033 q^{73} -2.90049 q^{74} +2.68568 q^{75} +0.726777 q^{76} +4.03613 q^{77} -12.1052 q^{78} -0.750555 q^{79} +1.00000 q^{80} -3.89033 q^{81} +9.05460 q^{82} -1.03270 q^{83} +10.8397 q^{84} -5.71882 q^{85} -1.00000 q^{86} +1.17902 q^{87} -1.00000 q^{88} -1.17265 q^{89} -4.21287 q^{90} +18.1921 q^{91} -3.76465 q^{92} -0.424928 q^{93} -12.3291 q^{94} +0.726777 q^{95} -2.68568 q^{96} -5.36406 q^{97} -9.29031 q^{98} +4.21287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

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