LMFDB - Embedded newform 4730.2.a.bb.1.3

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
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			1.3
Root			$2.17792$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.17792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.17792 q^{6} +4.63803 q^{7} -1.00000 q^{8} +1.74332 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.17792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.17792 q^{6} +4.63803 q^{7} -1.00000 q^{8} +1.74332 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.17792 q^{12} -5.80630 q^{13} -4.63803 q^{14} +2.17792 q^{15} +1.00000 q^{16} -7.18366 q^{17} -1.74332 q^{18} -6.16042 q^{19} -1.00000 q^{20} -10.1012 q^{21} +1.00000 q^{22} -7.80630 q^{23} +2.17792 q^{24} +1.00000 q^{25} +5.80630 q^{26} +2.73694 q^{27} +4.63803 q^{28} +1.51070 q^{29} -2.17792 q^{30} -3.25777 q^{31} -1.00000 q^{32} +2.17792 q^{33} +7.18366 q^{34} -4.63803 q^{35} +1.74332 q^{36} +3.52240 q^{37} +6.16042 q^{38} +12.6456 q^{39} +1.00000 q^{40} -8.02297 q^{41} +10.1012 q^{42} +1.00000 q^{43} -1.00000 q^{44} -1.74332 q^{45} +7.80630 q^{46} -7.28953 q^{47} -2.17792 q^{48} +14.5113 q^{49} -1.00000 q^{50} +15.6454 q^{51} -5.80630 q^{52} -0.333481 q^{53} -2.73694 q^{54} +1.00000 q^{55} -4.63803 q^{56} +13.4169 q^{57} -1.51070 q^{58} -1.57764 q^{59} +2.17792 q^{60} +14.7118 q^{61} +3.25777 q^{62} +8.08559 q^{63} +1.00000 q^{64} +5.80630 q^{65} -2.17792 q^{66} +3.48438 q^{67} -7.18366 q^{68} +17.0015 q^{69} +4.63803 q^{70} -9.42285 q^{71} -1.74332 q^{72} -3.01257 q^{73} -3.52240 q^{74} -2.17792 q^{75} -6.16042 q^{76} -4.63803 q^{77} -12.6456 q^{78} +5.06019 q^{79} -1.00000 q^{80} -11.1908 q^{81} +8.02297 q^{82} +13.5518 q^{83} -10.1012 q^{84} +7.18366 q^{85} -1.00000 q^{86} -3.29018 q^{87} +1.00000 q^{88} +13.5086 q^{89} +1.74332 q^{90} -26.9298 q^{91} -7.80630 q^{92} +7.09514 q^{93} +7.28953 q^{94} +6.16042 q^{95} +2.17792 q^{96} -15.3042 q^{97} -14.5113 q^{98} -1.74332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * 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
$3$	−2.17792	−1.25742	−0.628711	−	0.777639i	$-0.716417\pi$
$3$	−2.17792	−1.25742	−0.628711	+	0.777639i	$0.716417\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.17792	0.889131
$7$	4.63803	1.75301	0.876505	−	0.481392i	$-0.159869\pi$
$7$	4.63803	1.75301	0.876505	+	0.481392i	$0.159869\pi$
$8$	−1.00000	−0.353553
$9$	1.74332	0.581108
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.17792	−0.628711
$13$	−5.80630	−1.61038	−0.805189	−	0.593018i	$-0.797936\pi$
$13$	−5.80630	−1.61038	−0.805189	+	0.593018i	$0.797936\pi$
$14$	−4.63803	−1.23957
$15$	2.17792	0.562336
$16$	1.00000	0.250000
$17$	−7.18366	−1.74229	−0.871146	−	0.491024i	$-0.836623\pi$
$17$	−7.18366	−1.74229	−0.871146	+	0.491024i	$0.836623\pi$
$18$	−1.74332	−0.410905
$19$	−6.16042	−1.41330	−0.706649	−	0.707565i	$-0.749794\pi$
$19$	−6.16042	−1.41330	−0.706649	+	0.707565i	$0.749794\pi$
$20$	−1.00000	−0.223607
$21$	−10.1012	−2.20427
$22$	1.00000	0.213201
$23$	−7.80630	−1.62773	−0.813863	−	0.581057i	$-0.802639\pi$
$23$	−7.80630	−1.62773	−0.813863	+	0.581057i	$0.802639\pi$
$24$	2.17792	0.444565
$25$	1.00000	0.200000
$26$	5.80630	1.13871
$27$	2.73694	0.526724
$28$	4.63803	0.876505
$29$	1.51070	0.280530	0.140265	−	0.990114i	$-0.455205\pi$
$29$	1.51070	0.280530	0.140265	+	0.990114i	$0.455205\pi$
$30$	−2.17792	−0.397631
$31$	−3.25777	−0.585112	−0.292556	−	0.956248i	$-0.594506\pi$
$31$	−3.25777	−0.585112	−0.292556	+	0.956248i	$0.594506\pi$
$32$	−1.00000	−0.176777
$33$	2.17792	0.379127
$34$	7.18366	1.23199
$35$	−4.63803	−0.783970
$36$	1.74332	0.290554
$37$	3.52240	0.579079	0.289540	−	0.957166i	$-0.406498\pi$
$37$	3.52240	0.579079	0.289540	+	0.957166i	$0.406498\pi$
$38$	6.16042	0.999352
$39$	12.6456	2.02492
$40$	1.00000	0.158114
$41$	−8.02297	−1.25298	−0.626489	−	0.779431i	$-0.715509\pi$
$41$	−8.02297	−1.25298	−0.626489	+	0.779431i	$0.715509\pi$
$42$	10.1012	1.55866
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−1.74332	−0.259879
$46$	7.80630	1.15098
$47$	−7.28953	−1.06329	−0.531644	−	0.846968i	$-0.678425\pi$
$47$	−7.28953	−1.06329	−0.531644	+	0.846968i	$0.678425\pi$
$48$	−2.17792	−0.314355
$49$	14.5113	2.07305
$50$	−1.00000	−0.141421
$51$	15.6454	2.19080
$52$	−5.80630	−0.805189
$53$	−0.333481	−0.0458072	−0.0229036	−	0.999738i	$-0.507291\pi$
$53$	−0.333481	−0.0458072	−0.0229036	+	0.999738i	$0.507291\pi$
$54$	−2.73694	−0.372450
$55$	1.00000	0.134840
$56$	−4.63803	−0.619783
$57$	13.4169	1.77711
$58$	−1.51070	−0.198365
$59$	−1.57764	−0.205391	−0.102696	−	0.994713i	$-0.532747\pi$
$59$	−1.57764	−0.205391	−0.102696	+	0.994713i	$0.532747\pi$
$60$	2.17792	0.281168
$61$	14.7118	1.88366	0.941829	−	0.336092i	$-0.109105\pi$
$61$	14.7118	1.88366	0.941829	+	0.336092i	$0.109105\pi$
$62$	3.25777	0.413737
$63$	8.08559	1.01869
$64$	1.00000	0.125000
$65$	5.80630	0.720183
$66$	−2.17792	−0.268083
$67$	3.48438	0.425685	0.212842	−	0.977087i	$-0.431728\pi$
$67$	3.48438	0.425685	0.212842	+	0.977087i	$0.431728\pi$
$68$	−7.18366	−0.871146
$69$	17.0015	2.04674
$70$	4.63803	0.554351
$71$	−9.42285	−1.11829	−0.559144	−	0.829071i	$-0.688870\pi$
$71$	−9.42285	−1.11829	−0.559144	+	0.829071i	$0.688870\pi$
$72$	−1.74332	−0.205453
$73$	−3.01257	−0.352595	−0.176297	−	0.984337i	$-0.556412\pi$
$73$	−3.01257	−0.352595	−0.176297	+	0.984337i	$0.556412\pi$
$74$	−3.52240	−0.409471
$75$	−2.17792	−0.251484
$76$	−6.16042	−0.706649
$77$	−4.63803	−0.528553
$78$	−12.6456	−1.43184
$79$	5.06019	0.569316	0.284658	−	0.958629i	$-0.408120\pi$
$79$	5.06019	0.569316	0.284658	+	0.958629i	$0.408120\pi$
$80$	−1.00000	−0.111803
$81$	−11.1908	−1.24342
$82$	8.02297	0.885989
$83$	13.5518	1.48750	0.743749	−	0.668459i	$-0.233046\pi$
$83$	13.5518	1.48750	0.743749	+	0.668459i	$0.233046\pi$
$84$	−10.1012	−1.10214
$85$	7.18366	0.779177
$86$	−1.00000	−0.107833
$87$	−3.29018	−0.352745
$88$	1.00000	0.106600
$89$	13.5086	1.43191	0.715955	−	0.698146i	$-0.245991\pi$
$89$	13.5086	1.43191	0.715955	+	0.698146i	$0.245991\pi$
$90$	1.74332	0.183762
$91$	−26.9298	−2.82301
$92$	−7.80630	−0.813863
$93$	7.09514	0.735732
$94$	7.28953	0.751858
$95$	6.16042	0.632046
$96$	2.17792	0.222283
$97$	−15.3042	−1.55391	−0.776954	−	0.629557i	$-0.783236\pi$
$97$	−15.3042	−1.55391	−0.776954	+	0.629557i	$0.783236\pi$
$98$	−14.5113	−1.46586
$99$	−1.74332	−0.175211
$100$	1.00000	0.100000
$101$	4.61357	0.459068	0.229534	−	0.973301i	$-0.426280\pi$
$101$	4.61357	0.459068	0.229534	+	0.973301i	$0.426280\pi$
$102$	−15.6454	−1.54913
$103$	−4.67551	−0.460692	−0.230346	−	0.973109i	$-0.573986\pi$
$103$	−4.67551	−0.460692	−0.230346	+	0.973109i	$0.573986\pi$
$104$	5.80630	0.569355
$105$	10.1012	0.985781
$106$	0.333481	0.0323906
$107$	−13.4710	−1.30229	−0.651146	−	0.758952i	$-0.725712\pi$
$107$	−13.4710	−1.30229	−0.651146	+	0.758952i	$0.725712\pi$
$108$	2.73694	0.263362
$109$	10.6732	1.02231	0.511155	−	0.859488i	$-0.329218\pi$
$109$	10.6732	1.02231	0.511155	+	0.859488i	$0.329218\pi$
$110$	−1.00000	−0.0953463
$111$	−7.67150	−0.728146
$112$	4.63803	0.438253
$113$	9.96108	0.937060	0.468530	−	0.883448i	$-0.344784\pi$
$113$	9.96108	0.937060	0.468530	+	0.883448i	$0.344784\pi$
$114$	−13.4169	−1.25661
$115$	7.80630	0.727941
$116$	1.51070	0.140265
$117$	−10.1223	−0.935803
$118$	1.57764	0.145233
$119$	−33.3180	−3.05426
$120$	−2.17792	−0.198816
$121$	1.00000	0.0909091
$122$	−14.7118	−1.33195
$123$	17.4734	1.57552
$124$	−3.25777	−0.292556
$125$	−1.00000	−0.0894427
$126$	−8.08559	−0.720321
$127$	7.03779	0.624503	0.312251	−	0.950000i	$-0.398917\pi$
$127$	7.03779	0.624503	0.312251	+	0.950000i	$0.398917\pi$
$128$	−1.00000	−0.0883883
$129$	−2.17792	−0.191755
$130$	−5.80630	−0.509246
$131$	13.0432	1.13959	0.569793	−	0.821788i	$-0.307023\pi$
$131$	13.0432	1.13959	0.569793	+	0.821788i	$0.307023\pi$
$132$	2.17792	0.189563
$133$	−28.5722	−2.47753
$134$	−3.48438	−0.301004
$135$	−2.73694	−0.235558
$136$	7.18366	0.615993
$137$	−10.7505	−0.918478	−0.459239	−	0.888313i	$-0.651878\pi$
$137$	−10.7505	−0.918478	−0.459239	+	0.888313i	$0.651878\pi$
$138$	−17.0015	−1.44726
$139$	−16.6220	−1.40986	−0.704930	−	0.709277i	$-0.749022\pi$
$139$	−16.6220	−1.40986	−0.704930	+	0.709277i	$0.749022\pi$
$140$	−4.63803	−0.391985
$141$	15.8760	1.33700
$142$	9.42285	0.790748
$143$	5.80630	0.485547
$144$	1.74332	0.145277
$145$	−1.51070	−0.125457
$146$	3.01257	0.249322
$147$	−31.6045	−2.60669
$148$	3.52240	0.289540
$149$	8.69614	0.712415	0.356208	−	0.934407i	$-0.384070\pi$
$149$	8.69614	0.712415	0.356208	+	0.934407i	$0.384070\pi$
$150$	2.17792	0.177826
$151$	−8.11885	−0.660703	−0.330351	−	0.943858i	$-0.607167\pi$
$151$	−8.11885	−0.660703	−0.330351	+	0.943858i	$0.607167\pi$
$152$	6.16042	0.499676
$153$	−12.5234	−1.01246
$154$	4.63803	0.373743
$155$	3.25777	0.261670
$156$	12.6456	1.01246
$157$	6.54941	0.522700	0.261350	−	0.965244i	$-0.415832\pi$
$157$	6.54941	0.522700	0.261350	+	0.965244i	$0.415832\pi$
$158$	−5.06019	−0.402567
$159$	0.726295	0.0575989
$160$	1.00000	0.0790569
$161$	−36.2059	−2.85342
$162$	11.1908	0.879232
$163$	4.34472	0.340305	0.170152	−	0.985418i	$-0.445574\pi$
$163$	4.34472	0.340305	0.170152	+	0.985418i	$0.445574\pi$
$164$	−8.02297	−0.626489
$165$	−2.17792	−0.169551
$166$	−13.5518	−1.05182
$167$	−10.6765	−0.826176	−0.413088	−	0.910691i	$-0.635550\pi$
$167$	−10.6765	−0.826176	−0.413088	+	0.910691i	$0.635550\pi$
$168$	10.1012	0.779328
$169$	20.7131	1.59332
$170$	−7.18366	−0.550961
$171$	−10.7396	−0.821278
$172$	1.00000	0.0762493
$173$	−15.2008	−1.15569	−0.577847	−	0.816145i	$-0.696107\pi$
$173$	−15.2008	−1.15569	−0.577847	+	0.816145i	$0.696107\pi$
$174$	3.29018	0.249428
$175$	4.63803	0.350602
$176$	−1.00000	−0.0753778
$177$	3.43597	0.258263
$178$	−13.5086	−1.01251
$179$	17.0492	1.27431	0.637157	−	0.770734i	$-0.280110\pi$
$179$	17.0492	1.27431	0.637157	+	0.770734i	$0.280110\pi$
$180$	−1.74332	−0.129940
$181$	−22.8842	−1.70097	−0.850484	−	0.526001i	$-0.823691\pi$
$181$	−22.8842	−1.70097	−0.850484	+	0.526001i	$0.823691\pi$
$182$	26.9298	1.99617
$183$	−32.0412	−2.36855
$184$	7.80630	0.575488
$185$	−3.52240	−0.258972
$186$	−7.09514	−0.520241
$187$	7.18366	0.525321
$188$	−7.28953	−0.531644
$189$	12.6940	0.923352
$190$	−6.16042	−0.446924
$191$	9.36038	0.677293	0.338647	−	0.940914i	$-0.390031\pi$
$191$	9.36038	0.677293	0.338647	+	0.940914i	$0.390031\pi$
$192$	−2.17792	−0.157178
$193$	−5.84595	−0.420801	−0.210400	−	0.977615i	$-0.567477\pi$
$193$	−5.84595	−0.420801	−0.210400	+	0.977615i	$0.567477\pi$
$194$	15.3042	1.09878
$195$	−12.6456	−0.905573
$196$	14.5113	1.03652
$197$	5.86569	0.417913	0.208956	−	0.977925i	$-0.432993\pi$
$197$	5.86569	0.417913	0.208956	+	0.977925i	$0.432993\pi$
$198$	1.74332	0.123893
$199$	13.5383	0.959705	0.479853	−	0.877349i	$-0.340690\pi$
$199$	13.5383	0.959705	0.479853	+	0.877349i	$0.340690\pi$
$200$	−1.00000	−0.0707107
$201$	−7.58869	−0.535265
$202$	−4.61357	−0.324610
$203$	7.00668	0.491773
$204$	15.6454	1.09540
$205$	8.02297	0.560348
$206$	4.67551	0.325758
$207$	−13.6089	−0.945884
$208$	−5.80630	−0.402594
$209$	6.16042	0.426125
$210$	−10.1012	−0.697052
$211$	10.7018	0.736740	0.368370	−	0.929679i	$-0.379916\pi$
$211$	10.7018	0.736740	0.368370	+	0.929679i	$0.379916\pi$
$212$	−0.333481	−0.0229036
$213$	20.5222	1.40616
$214$	13.4710	0.920860
$215$	−1.00000	−0.0681994
$216$	−2.73694	−0.186225
$217$	−15.1096	−1.02571
$218$	−10.6732	−0.722883
$219$	6.56113	0.443360
$220$	1.00000	0.0674200
$221$	41.7105	2.80575
$222$	7.67150	0.514877
$223$	0.474339	0.0317641	0.0158820	−	0.999874i	$-0.494944\pi$
$223$	0.474339	0.0317641	0.0158820	+	0.999874i	$0.494944\pi$
$224$	−4.63803	−0.309891
$225$	1.74332	0.116222
$226$	−9.96108	−0.662601
$227$	22.9170	1.52105	0.760526	−	0.649308i	$-0.224941\pi$
$227$	22.9170	1.52105	0.760526	+	0.649308i	$0.224941\pi$
$228$	13.4169	0.888555
$229$	−1.74361	−0.115221	−0.0576107	−	0.998339i	$-0.518348\pi$
$229$	−1.74361	−0.115221	−0.0576107	+	0.998339i	$0.518348\pi$
$230$	−7.80630	−0.514732
$231$	10.1012	0.664613
$232$	−1.51070	−0.0991824
$233$	−14.1046	−0.924023	−0.462011	−	0.886874i	$-0.652872\pi$
$233$	−14.1046	−0.924023	−0.462011	+	0.886874i	$0.652872\pi$
$234$	10.1223	0.661713
$235$	7.28953	0.475517
$236$	−1.57764	−0.102696
$237$	−11.0207	−0.715870
$238$	33.3180	2.15969
$239$	22.2167	1.43708	0.718538	−	0.695488i	$-0.244812\pi$
$239$	22.2167	1.43708	0.718538	+	0.695488i	$0.244812\pi$
$240$	2.17792	0.140584
$241$	15.9469	1.02723	0.513615	−	0.858021i	$-0.328306\pi$
$241$	15.9469	1.02723	0.513615	+	0.858021i	$0.328306\pi$
$242$	−1.00000	−0.0642824
$243$	16.1618	1.03678
$244$	14.7118	0.941829
$245$	−14.5113	−0.927094
$246$	−17.4734	−1.11406
$247$	35.7692	2.27594
$248$	3.25777	0.206868
$249$	−29.5146	−1.87041
$250$	1.00000	0.0632456
$251$	−2.78403	−0.175726	−0.0878632	−	0.996133i	$-0.528004\pi$
$251$	−2.78403	−0.175726	−0.0878632	+	0.996133i	$0.528004\pi$
$252$	8.08559	0.509344
$253$	7.80630	0.490778
$254$	−7.03779	−0.441590
$255$	−15.6454	−0.979753
$256$	1.00000	0.0625000
$257$	15.5851	0.972173	0.486086	−	0.873911i	$-0.338424\pi$
$257$	15.5851	0.972173	0.486086	+	0.873911i	$0.338424\pi$
$258$	2.17792	0.135591
$259$	16.3370	1.01513
$260$	5.80630	0.360091
$261$	2.63364	0.163018
$262$	−13.0432	−0.805810
$263$	−11.5563	−0.712590	−0.356295	−	0.934373i	$-0.615960\pi$
$263$	−11.5563	−0.712590	−0.356295	+	0.934373i	$0.615960\pi$
$264$	−2.17792	−0.134042
$265$	0.333481	0.0204856
$266$	28.5722	1.75187
$267$	−29.4206	−1.80051
$268$	3.48438	0.212842
$269$	7.46417	0.455098	0.227549	−	0.973767i	$-0.426929\pi$
$269$	7.46417	0.455098	0.227549	+	0.973767i	$0.426929\pi$
$270$	2.73694	0.166565
$271$	−5.60803	−0.340663	−0.170332	−	0.985387i	$-0.554484\pi$
$271$	−5.60803	−0.340663	−0.170332	+	0.985387i	$0.554484\pi$
$272$	−7.18366	−0.435573
$273$	58.6509	3.54971
$274$	10.7505	0.649462
$275$	−1.00000	−0.0603023
$276$	17.0015	1.02337
$277$	−13.3255	−0.800654	−0.400327	−	0.916372i	$-0.631103\pi$
$277$	−13.3255	−0.800654	−0.400327	+	0.916372i	$0.631103\pi$
$278$	16.6220	0.996922
$279$	−5.67934	−0.340013
$280$	4.63803	0.277175
$281$	−24.1984	−1.44356	−0.721779	−	0.692124i	$-0.756675\pi$
$281$	−24.1984	−1.44356	−0.721779	+	0.692124i	$0.756675\pi$
$282$	−15.8760	−0.945402
$283$	−3.49895	−0.207991	−0.103996	−	0.994578i	$-0.533163\pi$
$283$	−3.49895	−0.207991	−0.103996	+	0.994578i	$0.533163\pi$
$284$	−9.42285	−0.559144
$285$	−13.4169	−0.794748
$286$	−5.80630	−0.343334
$287$	−37.2108	−2.19648
$288$	−1.74332	−0.102726
$289$	34.6049	2.03558
$290$	1.51070	0.0887115
$291$	33.3313	1.95392
$292$	−3.01257	−0.176297
$293$	−11.9897	−0.700444	−0.350222	−	0.936667i	$-0.613894\pi$
$293$	−11.9897	−0.700444	−0.350222	+	0.936667i	$0.613894\pi$
$294$	31.6045	1.84321
$295$	1.57764	0.0918537
$296$	−3.52240	−0.204735
$297$	−2.73694	−0.158813
$298$	−8.69614	−0.503754
$299$	45.3257	2.62125
$300$	−2.17792	−0.125742
$301$	4.63803	0.267332
$302$	8.11885	0.467187
$303$	−10.0480	−0.577242
$304$	−6.16042	−0.353324
$305$	−14.7118	−0.842397
$306$	12.5234	0.715917
$307$	6.33882	0.361775	0.180888	−	0.983504i	$-0.442103\pi$
$307$	6.33882	0.361775	0.180888	+	0.983504i	$0.442103\pi$
$308$	−4.63803	−0.264276
$309$	10.1829	0.579283
$310$	−3.25777	−0.185029
$311$	20.2786	1.14989	0.574946	−	0.818191i	$-0.305023\pi$
$311$	20.2786	1.14989	0.574946	+	0.818191i	$0.305023\pi$
$312$	−12.6456	−0.715918
$313$	−17.7146	−1.00129	−0.500644	−	0.865653i	$-0.666903\pi$
$313$	−17.7146	−1.00129	−0.500644	+	0.865653i	$0.666903\pi$
$314$	−6.54941	−0.369605
$315$	−8.08559	−0.455571
$316$	5.06019	0.284658
$317$	9.14582	0.513681	0.256840	−	0.966454i	$-0.417319\pi$
$317$	9.14582	0.513681	0.256840	+	0.966454i	$0.417319\pi$
$318$	−0.726295	−0.0407286
$319$	−1.51070	−0.0845831
$320$	−1.00000	−0.0559017
$321$	29.3388	1.63753
$322$	36.2059	2.01767
$323$	44.2543	2.46238
$324$	−11.1908	−0.621711
$325$	−5.80630	−0.322076
$326$	−4.34472	−0.240632
$327$	−23.2454	−1.28547
$328$	8.02297	0.442994
$329$	−33.8091	−1.86395
$330$	2.17792	0.119890
$331$	−7.20057	−0.395779	−0.197890	−	0.980224i	$-0.563409\pi$
$331$	−7.20057	−0.395779	−0.197890	+	0.980224i	$0.563409\pi$
$332$	13.5518	0.743749
$333$	6.14068	0.336507
$334$	10.6765	0.584195
$335$	−3.48438	−0.190372
$336$	−10.1012	−0.551068
$337$	3.67433	0.200154	0.100077	−	0.994980i	$-0.468091\pi$
$337$	3.67433	0.200154	0.100077	+	0.994980i	$0.468091\pi$
$338$	−20.7131	−1.12665
$339$	−21.6944	−1.17828
$340$	7.18366	0.389588
$341$	3.25777	0.176418
$342$	10.7396	0.580731
$343$	34.8377	1.88106
$344$	−1.00000	−0.0539164
$345$	−17.0015	−0.915329
$346$	15.2008	0.817199
$347$	1.54550	0.0829668	0.0414834	−	0.999139i	$-0.486792\pi$
$347$	1.54550	0.0829668	0.0414834	+	0.999139i	$0.486792\pi$
$348$	−3.29018	−0.176372
$349$	−15.3442	−0.821354	−0.410677	−	0.911781i	$-0.634708\pi$
$349$	−15.3442	−0.821354	−0.410677	+	0.911781i	$0.634708\pi$
$350$	−4.63803	−0.247913
$351$	−15.8915	−0.848224
$352$	1.00000	0.0533002
$353$	20.4471	1.08829	0.544146	−	0.838991i	$-0.316854\pi$
$353$	20.4471	1.08829	0.544146	+	0.838991i	$0.316854\pi$
$354$	−3.43597	−0.182620
$355$	9.42285	0.500113
$356$	13.5086	0.715955
$357$	72.5639	3.84049
$358$	−17.0492	−0.901076
$359$	35.1254	1.85385	0.926923	−	0.375252i	$-0.122444\pi$
$359$	35.1254	1.85385	0.926923	+	0.375252i	$0.122444\pi$
$360$	1.74332	0.0918812
$361$	18.9508	0.997409
$362$	22.8842	1.20277
$363$	−2.17792	−0.114311
$364$	−26.9298	−1.41150
$365$	3.01257	0.157685
$366$	32.0412	1.67482
$367$	−23.0698	−1.20424	−0.602118	−	0.798407i	$-0.705676\pi$
$367$	−23.0698	−1.20424	−0.602118	+	0.798407i	$0.705676\pi$
$368$	−7.80630	−0.406932
$369$	−13.9866	−0.728115
$370$	3.52240	0.183121
$371$	−1.54670	−0.0803005
$372$	7.09514	0.367866
$373$	11.3400	0.587160	0.293580	−	0.955934i	$-0.405153\pi$
$373$	11.3400	0.587160	0.293580	+	0.955934i	$0.405153\pi$
$374$	−7.18366	−0.371458
$375$	2.17792	0.112467
$376$	7.28953	0.375929
$377$	−8.77159	−0.451760
$378$	−12.6940	−0.652909
$379$	20.2144	1.03834	0.519171	−	0.854670i	$-0.326241\pi$
$379$	20.2144	1.03834	0.519171	+	0.854670i	$0.326241\pi$
$380$	6.16042	0.316023
$381$	−15.3277	−0.785263
$382$	−9.36038	−0.478919
$383$	−35.3883	−1.80826	−0.904129	−	0.427260i	$-0.859479\pi$
$383$	−35.3883	−1.80826	−0.904129	+	0.427260i	$0.859479\pi$
$384$	2.17792	0.111141
$385$	4.63803	0.236376
$386$	5.84595	0.297551
$387$	1.74332	0.0886181
$388$	−15.3042	−0.776954
$389$	−36.6686	−1.85917	−0.929586	−	0.368606i	$-0.879835\pi$
$389$	−36.6686	−1.85917	−0.929586	+	0.368606i	$0.879835\pi$
$390$	12.6456	0.640337
$391$	56.0778	2.83597
$392$	−14.5113	−0.732932
$393$	−28.4069	−1.43294
$394$	−5.86569	−0.295509
$395$	−5.06019	−0.254606
$396$	−1.74332	−0.0876053
$397$	9.61333	0.482479	0.241240	−	0.970466i	$-0.422446\pi$
$397$	9.61333	0.482479	0.241240	+	0.970466i	$0.422446\pi$
$398$	−13.5383	−0.678614
$399$	62.2279	3.11529
$400$	1.00000	0.0500000
$401$	−29.2222	−1.45929	−0.729643	−	0.683828i	$-0.760314\pi$
$401$	−29.2222	−1.45929	−0.729643	+	0.683828i	$0.760314\pi$
$402$	7.58869	0.378489
$403$	18.9156	0.942251
$404$	4.61357	0.229534
$405$	11.1908	0.556075
$406$	−7.00668	−0.347736
$407$	−3.52240	−0.174599
$408$	−15.6454	−0.774563
$409$	38.3348	1.89553	0.947767	−	0.318963i	$-0.103335\pi$
$409$	38.3348	1.89553	0.947767	+	0.318963i	$0.103335\pi$
$410$	−8.02297	−0.396226
$411$	23.4137	1.15491
$412$	−4.67551	−0.230346
$413$	−7.31714	−0.360053
$414$	13.6089	0.668841
$415$	−13.5518	−0.665230
$416$	5.80630	0.284677
$417$	36.2014	1.77279
$418$	−6.16042	−0.301316
$419$	−20.7961	−1.01596	−0.507978	−	0.861370i	$-0.669607\pi$
$419$	−20.7961	−1.01596	−0.507978	+	0.861370i	$0.669607\pi$
$420$	10.1012	0.492890
$421$	12.0941	0.589432	0.294716	−	0.955585i	$-0.404775\pi$
$421$	12.0941	0.589432	0.294716	+	0.955585i	$0.404775\pi$
$422$	−10.7018	−0.520954
$423$	−12.7080	−0.617885
$424$	0.333481	0.0161953
$425$	−7.18366	−0.348458
$426$	−20.5222	−0.994304
$427$	68.2340	3.30207
$428$	−13.4710	−0.651146
$429$	−12.6456	−0.610537
$430$	1.00000	0.0482243
$431$	3.40970	0.164240	0.0821198	−	0.996622i	$-0.473831\pi$
$431$	3.40970	0.164240	0.0821198	+	0.996622i	$0.473831\pi$
$432$	2.73694	0.131681
$433$	−29.8176	−1.43294	−0.716471	−	0.697617i	$-0.754244\pi$
$433$	−29.8176	−1.43294	−0.716471	+	0.697617i	$0.754244\pi$
$434$	15.1096	0.725285
$435$	3.29018	0.157752
$436$	10.6732	0.511155
$437$	48.0901	2.30046
$438$	−6.56113	−0.313503
$439$	−18.5112	−0.883492	−0.441746	−	0.897140i	$-0.645641\pi$
$439$	−18.5112	−0.883492	−0.441746	+	0.897140i	$0.645641\pi$
$440$	−1.00000	−0.0476731
$441$	25.2979	1.20466
$442$	−41.7105	−1.98396
$443$	−4.84563	−0.230223	−0.115111	−	0.993353i	$-0.536722\pi$
$443$	−4.84563	−0.230223	−0.115111	+	0.993353i	$0.536722\pi$
$444$	−7.67150	−0.364073
$445$	−13.5086	−0.640370
$446$	−0.474339	−0.0224606
$447$	−18.9395	−0.895806
$448$	4.63803	0.219126
$449$	1.78702	0.0843349	0.0421674	−	0.999111i	$-0.486574\pi$
$449$	1.78702	0.0843349	0.0421674	+	0.999111i	$0.486574\pi$
$450$	−1.74332	−0.0821811
$451$	8.02297	0.377787
$452$	9.96108	0.468530
$453$	17.6822	0.830781
$454$	−22.9170	−1.07555
$455$	26.9298	1.26249
$456$	−13.4169	−0.628303
$457$	15.6591	0.732503	0.366252	−	0.930516i	$-0.380641\pi$
$457$	15.6591	0.732503	0.366252	+	0.930516i	$0.380641\pi$
$458$	1.74361	0.0814738
$459$	−19.6612	−0.917707
$460$	7.80630	0.363971
$461$	1.93745	0.0902358	0.0451179	−	0.998982i	$-0.485634\pi$
$461$	1.93745	0.0902358	0.0451179	+	0.998982i	$0.485634\pi$
$462$	−10.1012	−0.469952
$463$	31.1924	1.44963	0.724816	−	0.688942i	$-0.241925\pi$
$463$	31.1924	1.44963	0.724816	+	0.688942i	$0.241925\pi$
$464$	1.51070	0.0701326
$465$	−7.09514	−0.329029
$466$	14.1046	0.653383
$467$	−33.1793	−1.53536	−0.767678	−	0.640836i	$-0.778588\pi$
$467$	−33.1793	−1.53536	−0.767678	+	0.640836i	$0.778588\pi$
$468$	−10.1223	−0.467902
$469$	16.1607	0.746230
$470$	−7.28953	−0.336241
$471$	−14.2641	−0.657254
$472$	1.57764	0.0726167
$473$	−1.00000	−0.0459800
$474$	11.0207	0.506197
$475$	−6.16042	−0.282659
$476$	−33.3180	−1.52713
$477$	−0.581366	−0.0266189
$478$	−22.2167	−1.01617
$479$	−24.9337	−1.13925	−0.569625	−	0.821905i	$-0.692911\pi$
$479$	−24.9337	−1.13925	−0.569625	+	0.821905i	$0.692911\pi$
$480$	−2.17792	−0.0994079
$481$	−20.4521	−0.932536
$482$	−15.9469	−0.726361
$483$	78.8534	3.58795
$484$	1.00000	0.0454545
$485$	15.3042	0.694929
$486$	−16.1618	−0.733115
$487$	27.1636	1.23090	0.615451	−	0.788175i	$-0.288974\pi$
$487$	27.1636	1.23090	0.615451	+	0.788175i	$0.288974\pi$
$488$	−14.7118	−0.665974
$489$	−9.46244	−0.427906
$490$	14.5113	0.655555
$491$	−31.2621	−1.41084	−0.705420	−	0.708789i	$-0.749242\pi$
$491$	−31.2621	−1.41084	−0.705420	+	0.708789i	$0.749242\pi$
$492$	17.4734	0.787760
$493$	−10.8524	−0.488766
$494$	−35.7692	−1.60933
$495$	1.74332	0.0783566
$496$	−3.25777	−0.146278
$497$	−43.7035	−1.96037
$498$	29.5146	1.32258
$499$	22.5838	1.01099	0.505496	−	0.862829i	$-0.331310\pi$
$499$	22.5838	1.01099	0.505496	+	0.862829i	$0.331310\pi$
$500$	−1.00000	−0.0447214
$501$	23.2526	1.03885
$502$	2.78403	0.124257
$503$	37.9353	1.69145	0.845726	−	0.533618i	$-0.179168\pi$
$503$	37.9353	1.69145	0.845726	+	0.533618i	$0.179168\pi$
$504$	−8.08559	−0.360161
$505$	−4.61357	−0.205301
$506$	−7.80630	−0.347032
$507$	−45.1115	−2.00347
$508$	7.03779	0.312251
$509$	4.31530	0.191272	0.0956361	−	0.995416i	$-0.469511\pi$
$509$	4.31530	0.191272	0.0956361	+	0.995416i	$0.469511\pi$
$510$	15.6454	0.692790
$511$	−13.9724	−0.618102
$512$	−1.00000	−0.0441942
$513$	−16.8607	−0.744417
$514$	−15.5851	−0.687430
$515$	4.67551	0.206028
$516$	−2.17792	−0.0958775
$517$	7.28953	0.320593
$518$	−16.3370	−0.717807
$519$	33.1060	1.45319
$520$	−5.80630	−0.254623
$521$	−5.38821	−0.236062	−0.118031	−	0.993010i	$-0.537658\pi$
$521$	−5.38821	−0.236062	−0.118031	+	0.993010i	$0.537658\pi$
$522$	−2.63364	−0.115271
$523$	34.3705	1.50292	0.751459	−	0.659779i	$-0.229350\pi$
$523$	34.3705	1.50292	0.751459	+	0.659779i	$0.229350\pi$
$524$	13.0432	0.569793
$525$	−10.1012	−0.440855
$526$	11.5563	0.503877
$527$	23.4027	1.01944
$528$	2.17792	0.0947817
$529$	37.9383	1.64949
$530$	−0.333481	−0.0144855
$531$	−2.75034	−0.119354
$532$	−28.5722	−1.23876
$533$	46.5838	2.01777
$534$	29.4206	1.27316
$535$	13.4710	0.582403
$536$	−3.48438	−0.150502
$537$	−37.1317	−1.60235
$538$	−7.46417	−0.321803
$539$	−14.5113	−0.625047
$540$	−2.73694	−0.117779
$541$	21.7848	0.936603	0.468301	−	0.883569i	$-0.344866\pi$
$541$	21.7848	0.936603	0.468301	+	0.883569i	$0.344866\pi$
$542$	5.60803	0.240885
$543$	49.8399	2.13883
$544$	7.18366	0.307997
$545$	−10.6732	−0.457191
$546$	−58.6509	−2.51003
$547$	−40.0504	−1.71243	−0.856216	−	0.516618i	$-0.827191\pi$
$547$	−40.0504	−1.71243	−0.856216	+	0.516618i	$0.827191\pi$
$548$	−10.7505	−0.459239
$549$	25.6475	1.09461
$550$	1.00000	0.0426401
$551$	−9.30656	−0.396473
$552$	−17.0015	−0.723631
$553$	23.4693	0.998017
$554$	13.3255	0.566148
$555$	7.67150	0.325637
$556$	−16.6220	−0.704930
$557$	−16.6440	−0.705230	−0.352615	−	0.935769i	$-0.614707\pi$
$557$	−16.6440	−0.705230	−0.352615	+	0.935769i	$0.614707\pi$
$558$	5.67934	0.240426
$559$	−5.80630	−0.245580
$560$	−4.63803	−0.195993
$561$	−15.6454	−0.660550
$562$	24.1984	1.02075
$563$	19.3161	0.814075	0.407038	−	0.913411i	$-0.366562\pi$
$563$	19.3161	0.814075	0.407038	+	0.913411i	$0.366562\pi$
$564$	15.8760	0.668500
$565$	−9.96108	−0.419066
$566$	3.49895	0.147072
$567$	−51.9032	−2.17973
$568$	9.42285	0.395374
$569$	−19.1536	−0.802963	−0.401481	−	0.915867i	$-0.631505\pi$
$569$	−19.1536	−0.802963	−0.401481	+	0.915867i	$0.631505\pi$
$570$	13.4169	0.561971
$571$	41.8316	1.75060	0.875299	−	0.483583i	$-0.160665\pi$
$571$	41.8316	1.75060	0.875299	+	0.483583i	$0.160665\pi$
$572$	5.80630	0.242774
$573$	−20.3861	−0.851643
$574$	37.2108	1.55315
$575$	−7.80630	−0.325545
$576$	1.74332	0.0726385
$577$	−2.64311	−0.110034	−0.0550171	−	0.998485i	$-0.517521\pi$
$577$	−2.64311	−0.110034	−0.0550171	+	0.998485i	$0.517521\pi$
$578$	−34.6049	−1.43937
$579$	12.7320	0.529124
$580$	−1.51070	−0.0627285
$581$	62.8535	2.60760
$582$	−33.3313	−1.38163
$583$	0.333481	0.0138114
$584$	3.01257	0.124661
$585$	10.1223	0.418504
$586$	11.9897	0.495288
$587$	37.1898	1.53499	0.767494	−	0.641056i	$-0.221503\pi$
$587$	37.1898	1.53499	0.767494	+	0.641056i	$0.221503\pi$
$588$	−31.6045	−1.30335
$589$	20.0692	0.826937
$590$	−1.57764	−0.0649504
$591$	−12.7750	−0.525492
$592$	3.52240	0.144770
$593$	−47.9818	−1.97038	−0.985188	−	0.171478i	$-0.945146\pi$
$593$	−47.9818	−1.97038	−0.985188	+	0.171478i	$0.945146\pi$
$594$	2.73694	0.112298
$595$	33.3180	1.36591
$596$	8.69614	0.356208
$597$	−29.4853	−1.20675
$598$	−45.3257	−1.85351
$599$	14.1921	0.579872	0.289936	−	0.957046i	$-0.406366\pi$
$599$	14.1921	0.579872	0.289936	+	0.957046i	$0.406366\pi$
$600$	2.17792	0.0889131
$601$	−6.37582	−0.260075	−0.130038	−	0.991509i	$-0.541510\pi$
$601$	−6.37582	−0.260075	−0.130038	+	0.991509i	$0.541510\pi$
$602$	−4.63803	−0.189032
$603$	6.07440	0.247369
$604$	−8.11885	−0.330351
$605$	−1.00000	−0.0406558
$606$	10.0480	0.408171
$607$	28.5905	1.16045	0.580227	−	0.814455i	$-0.302964\pi$
$607$	28.5905	1.16045	0.580227	+	0.814455i	$0.302964\pi$
$608$	6.16042	0.249838
$609$	−15.2600	−0.618365
$610$	14.7118	0.595665
$611$	42.3252	1.71229
$612$	−12.5234	−0.506230
$613$	−28.2920	−1.14270	−0.571351	−	0.820706i	$-0.693581\pi$
$613$	−28.2920	−1.14270	−0.571351	+	0.820706i	$0.693581\pi$
$614$	−6.33882	−0.255814
$615$	−17.4734	−0.704594
$616$	4.63803	0.186872
$617$	−40.6714	−1.63737	−0.818685	−	0.574243i	$-0.805296\pi$
$617$	−40.6714	−1.63737	−0.818685	+	0.574243i	$0.805296\pi$
$618$	−10.1829	−0.409615
$619$	−12.0151	−0.482927	−0.241463	−	0.970410i	$-0.577627\pi$
$619$	−12.0151	−0.482927	−0.241463	+	0.970410i	$0.577627\pi$
$620$	3.25777	0.130835
$621$	−21.3654	−0.857362
$622$	−20.2786	−0.813096
$623$	62.6534	2.51015
$624$	12.6456	0.506231
$625$	1.00000	0.0400000
$626$	17.7146	0.708017
$627$	−13.4169	−0.535819
$628$	6.54941	0.261350
$629$	−25.3037	−1.00893
$630$	8.08559	0.322138
$631$	−30.7436	−1.22388	−0.611942	−	0.790903i	$-0.709611\pi$
$631$	−30.7436	−1.22388	−0.611942	+	0.790903i	$0.709611\pi$
$632$	−5.06019	−0.201284
$633$	−23.3075	−0.926392
$634$	−9.14582	−0.363227
$635$	−7.03779	−0.279286
$636$	0.726295	0.0287995
$637$	−84.2571	−3.33839
$638$	1.51070	0.0598093
$639$	−16.4271	−0.649845
$640$	1.00000	0.0395285
$641$	−11.4765	−0.453295	−0.226648	−	0.973977i	$-0.572777\pi$
$641$	−11.4765	−0.453295	−0.226648	+	0.973977i	$0.572777\pi$
$642$	−29.3388	−1.15791
$643$	−18.8176	−0.742095	−0.371048	−	0.928614i	$-0.621001\pi$
$643$	−18.8176	−0.742095	−0.371048	+	0.928614i	$0.621001\pi$
$644$	−36.2059	−1.42671
$645$	2.17792	0.0857554
$646$	−44.2543	−1.74116
$647$	−13.6044	−0.534844	−0.267422	−	0.963579i	$-0.586172\pi$
$647$	−13.6044	−0.534844	−0.267422	+	0.963579i	$0.586172\pi$
$648$	11.1908	0.439616
$649$	1.57764	0.0619277
$650$	5.80630	0.227742
$651$	32.9075	1.28975
$652$	4.34472	0.170152
$653$	40.9051	1.60074	0.800371	−	0.599505i	$-0.204636\pi$
$653$	40.9051	1.60074	0.800371	+	0.599505i	$0.204636\pi$
$654$	23.2454	0.908968
$655$	−13.0432	−0.509639
$656$	−8.02297	−0.313244
$657$	−5.25189	−0.204896
$658$	33.8091	1.31801
$659$	−6.14372	−0.239325	−0.119663	−	0.992815i	$-0.538181\pi$
$659$	−6.14372	−0.239325	−0.119663	+	0.992815i	$0.538181\pi$
$660$	−2.17792	−0.0847753
$661$	11.6935	0.454824	0.227412	−	0.973799i	$-0.426974\pi$
$661$	11.6935	0.454824	0.227412	+	0.973799i	$0.426974\pi$
$662$	7.20057	0.279858
$663$	−90.8419	−3.52801
$664$	−13.5518	−0.525910
$665$	28.5722	1.10798
$666$	−6.14068	−0.237947
$667$	−11.7930	−0.456626
$668$	−10.6765	−0.413088
$669$	−1.03307	−0.0399408
$670$	3.48438	0.134613
$671$	−14.7118	−0.567944
$672$	10.1012	0.389664
$673$	−0.279963	−0.0107918	−0.00539589	−	0.999985i	$-0.501718\pi$
$673$	−0.279963	−0.0107918	−0.00539589	+	0.999985i	$0.501718\pi$
$674$	−3.67433	−0.141530
$675$	2.73694	0.105345
$676$	20.7131	0.796658
$677$	−43.8456	−1.68512	−0.842561	−	0.538601i	$-0.818953\pi$
$677$	−43.8456	−1.68512	−0.842561	+	0.538601i	$0.818953\pi$
$678$	21.6944	0.833169
$679$	−70.9814	−2.72402
$680$	−7.18366	−0.275481
$681$	−49.9112	−1.91260
$682$	−3.25777	−0.124746
$683$	−20.5824	−0.787562	−0.393781	−	0.919204i	$-0.628833\pi$
$683$	−20.5824	−0.787562	−0.393781	+	0.919204i	$0.628833\pi$
$684$	−10.7396	−0.410639
$685$	10.7505	0.410756
$686$	−34.8377	−1.33011
$687$	3.79745	0.144882
$688$	1.00000	0.0381246
$689$	1.93629	0.0737669
$690$	17.0015	0.647235
$691$	39.6324	1.50769	0.753844	−	0.657053i	$-0.228197\pi$
$691$	39.6324	1.50769	0.753844	+	0.657053i	$0.228197\pi$
$692$	−15.2008	−0.577847
$693$	−8.08559	−0.307146
$694$	−1.54550	−0.0586664
$695$	16.6220	0.630509
$696$	3.29018	0.124714
$697$	57.6342	2.18305
$698$	15.3442	0.580785
$699$	30.7186	1.16189
$700$	4.63803	0.175301
$701$	19.7081	0.744365	0.372182	−	0.928160i	$-0.378610\pi$
$701$	19.7081	0.744365	0.372182	+	0.928160i	$0.378610\pi$
$702$	15.8915	0.599785
$703$	−21.6995	−0.818411
$704$	−1.00000	−0.0376889
$705$	−15.8760	−0.597925
$706$	−20.4471	−0.769539
$707$	21.3979	0.804751
$708$	3.43597	0.129132
$709$	7.36825	0.276720	0.138360	−	0.990382i	$-0.455817\pi$
$709$	7.36825	0.276720	0.138360	+	0.990382i	$0.455817\pi$
$710$	−9.42285	−0.353633
$711$	8.82155	0.330834
$712$	−13.5086	−0.506257
$713$	25.4311	0.952402
$714$	−72.5639	−2.71563
$715$	−5.80630	−0.217143
$716$	17.0492	0.637157
$717$	−48.3860	−1.80701
$718$	−35.1254	−1.31087
$719$	−10.3342	−0.385399	−0.192700	−	0.981258i	$-0.561724\pi$
$719$	−10.3342	−0.385399	−0.192700	+	0.981258i	$0.561724\pi$
$720$	−1.74332	−0.0649698
$721$	−21.6852	−0.807597
$722$	−18.9508	−0.705275
$723$	−34.7310	−1.29166
$724$	−22.8842	−0.850484
$725$	1.51070	0.0561061
$726$	2.17792	0.0808301
$727$	−31.5464	−1.16999	−0.584996	−	0.811036i	$-0.698904\pi$
$727$	−31.5464	−1.16999	−0.584996	+	0.811036i	$0.698904\pi$
$728$	26.9298	0.998085
$729$	−1.62671	−0.0602484
$730$	−3.01257	−0.111500
$731$	−7.18366	−0.265697
$732$	−32.0412	−1.18428
$733$	−9.14996	−0.337961	−0.168981	−	0.985619i	$-0.554048\pi$
$733$	−9.14996	−0.337961	−0.168981	+	0.985619i	$0.554048\pi$
$734$	23.0698	0.851524
$735$	31.6045	1.16575
$736$	7.80630	0.287744
$737$	−3.48438	−0.128349
$738$	13.9866	0.514855
$739$	16.8841	0.621090	0.310545	−	0.950559i	$-0.399488\pi$
$739$	16.8841	0.621090	0.310545	+	0.950559i	$0.399488\pi$
$740$	−3.52240	−0.129486
$741$	−77.9025	−2.86182
$742$	1.54670	0.0567810
$743$	38.1690	1.40028	0.700142	−	0.714004i	$-0.253120\pi$
$743$	38.1690	1.40028	0.700142	+	0.714004i	$0.253120\pi$
$744$	−7.09514	−0.260121
$745$	−8.69614	−0.318602
$746$	−11.3400	−0.415185
$747$	23.6251	0.864397
$748$	7.18366	0.262660
$749$	−62.4790	−2.28293
$750$	−2.17792	−0.0795263
$751$	2.04969	0.0747944	0.0373972	−	0.999300i	$-0.488093\pi$
$751$	2.04969	0.0747944	0.0373972	+	0.999300i	$0.488093\pi$
$752$	−7.28953	−0.265822
$753$	6.06339	0.220962
$754$	8.77159	0.319442
$755$	8.11885	0.295475
$756$	12.6940	0.461676
$757$	14.8304	0.539019	0.269510	−	0.962998i	$-0.413138\pi$
$757$	14.8304	0.539019	0.269510	+	0.962998i	$0.413138\pi$
$758$	−20.2144	−0.734219
$759$	−17.0015	−0.617114
$760$	−6.16042	−0.223462
$761$	12.1243	0.439506	0.219753	−	0.975556i	$-0.429475\pi$
$761$	12.1243	0.439506	0.219753	+	0.975556i	$0.429475\pi$
$762$	15.3277	0.555265
$763$	49.5028	1.79212
$764$	9.36038	0.338647
$765$	12.5234	0.452786
$766$	35.3883	1.27863
$767$	9.16024	0.330757
$768$	−2.17792	−0.0785888
$769$	42.9199	1.54773	0.773866	−	0.633349i	$-0.218320\pi$
$769$	42.9199	1.54773	0.773866	+	0.633349i	$0.218320\pi$
$770$	−4.63803	−0.167143
$771$	−33.9431	−1.22243
$772$	−5.84595	−0.210400
$773$	10.9632	0.394320	0.197160	−	0.980371i	$-0.436828\pi$
$773$	10.9632	0.394320	0.197160	+	0.980371i	$0.436828\pi$
$774$	−1.74332	−0.0626625
$775$	−3.25777	−0.117022
$776$	15.3042	0.549389
$777$	−35.5806	−1.27645
$778$	36.6686	1.31463
$779$	49.4249	1.77083
$780$	−12.6456	−0.452787
$781$	9.42285	0.337176
$782$	−56.0778	−2.00534
$783$	4.13470	0.147762
$784$	14.5113	0.518262
$785$	−6.54941	−0.233758
$786$	28.4069	1.01324
$787$	−49.9397	−1.78016	−0.890079	−	0.455807i	$-0.849351\pi$
$787$	−49.9397	−1.78016	−0.890079	+	0.455807i	$0.849351\pi$
$788$	5.86569	0.208956
$789$	25.1686	0.896026
$790$	5.06019	0.180034
$791$	46.1998	1.64268
$792$	1.74332	0.0619463
$793$	−85.4214	−3.03340
$794$	−9.61333	−0.341164
$795$	−0.726295	−0.0257590
$796$	13.5383	0.479853
$797$	41.1063	1.45606	0.728030	−	0.685545i	$-0.240436\pi$
$797$	41.1063	1.45606	0.728030	+	0.685545i	$0.240436\pi$
$798$	−62.2279	−2.20284
$799$	52.3655	1.85256
$800$	−1.00000	−0.0353553
$801$	23.5499	0.832094
$802$	29.2222	1.03187
$803$	3.01257	0.106311
$804$	−7.58869	−0.267632
$805$	36.2059	1.27609
$806$	−18.9156	−0.666272
$807$	−16.2563	−0.572250
$808$	−4.61357	−0.162305
$809$	21.5610	0.758045	0.379023	−	0.925387i	$-0.376260\pi$
$809$	21.5610	0.758045	0.379023	+	0.925387i	$0.376260\pi$
$810$	−11.1908	−0.393204
$811$	−5.47442	−0.192233	−0.0961164	−	0.995370i	$-0.530642\pi$
$811$	−5.47442	−0.192233	−0.0961164	+	0.995370i	$0.530642\pi$
$812$	7.00668	0.245886
$813$	12.2138	0.428357
$814$	3.52240	0.123460
$815$	−4.34472	−0.152189
$816$	15.6454	0.547699
$817$	−6.16042	−0.215526
$818$	−38.3348	−1.34035
$819$	−46.9473	−1.64047
$820$	8.02297	0.280174
$821$	46.1977	1.61231	0.806155	−	0.591705i	$-0.201545\pi$
$821$	46.1977	1.61231	0.806155	+	0.591705i	$0.201545\pi$
$822$	−23.4137	−0.816647
$823$	16.7693	0.584540	0.292270	−	0.956336i	$-0.405589\pi$
$823$	16.7693	0.584540	0.292270	+	0.956336i	$0.405589\pi$
$824$	4.67551	0.162879
$825$	2.17792	0.0758253
$826$	7.31714	0.254596
$827$	−16.5294	−0.574784	−0.287392	−	0.957813i	$-0.592788\pi$
$827$	−16.5294	−0.574784	−0.287392	+	0.957813i	$0.592788\pi$
$828$	−13.6089	−0.472942
$829$	0.371395	0.0128991	0.00644954	−	0.999979i	$-0.497947\pi$
$829$	0.371395	0.0128991	0.00644954	+	0.999979i	$0.497947\pi$
$830$	13.5518	0.470388
$831$	29.0219	1.00676
$832$	−5.80630	−0.201297
$833$	−104.244	−3.61185
$834$	−36.2014	−1.25355
$835$	10.6765	0.369477
$836$	6.16042	0.213063
$837$	−8.91630	−0.308192
$838$	20.7961	0.718389
$839$	−40.4614	−1.39688	−0.698442	−	0.715667i	$-0.746123\pi$
$839$	−40.4614	−1.39688	−0.698442	+	0.715667i	$0.746123\pi$
$840$	−10.1012	−0.348526
$841$	−26.7178	−0.921303
$842$	−12.0941	−0.416791
$843$	52.7022	1.81516
$844$	10.7018	0.368370
$845$	−20.7131	−0.712553
$846$	12.7080	0.436910
$847$	4.63803	0.159365
$848$	−0.333481	−0.0114518
$849$	7.62042	0.261532
$850$	7.18366	0.246397
$851$	−27.4969	−0.942582
$852$	20.5222	0.703079
$853$	−21.1766	−0.725071	−0.362536	−	0.931970i	$-0.618089\pi$
$853$	−21.1766	−0.725071	−0.362536	+	0.931970i	$0.618089\pi$
$854$	−68.2340	−2.33492
$855$	10.7396	0.367287
$856$	13.4710	0.460430
$857$	43.4091	1.48283	0.741413	−	0.671049i	$-0.234156\pi$
$857$	43.4091	1.48283	0.741413	+	0.671049i	$0.234156\pi$
$858$	12.6456	0.431715
$859$	23.0665	0.787020	0.393510	−	0.919320i	$-0.371261\pi$
$859$	23.0665	0.787020	0.393510	+	0.919320i	$0.371261\pi$
$860$	−1.00000	−0.0340997
$861$	81.0420	2.76190
$862$	−3.40970	−0.116135
$863$	23.7305	0.807797	0.403898	−	0.914804i	$-0.367655\pi$
$863$	23.7305	0.807797	0.403898	+	0.914804i	$0.367655\pi$
$864$	−2.73694	−0.0931125
$865$	15.2008	0.516842
$866$	29.8176	1.01324
$867$	−75.3666	−2.55959
$868$	−15.1096	−0.512854
$869$	−5.06019	−0.171655
$870$	−3.29018	−0.111548
$871$	−20.2313	−0.685513
$872$	−10.6732	−0.361441
$873$	−26.6802	−0.902988
$874$	−48.0901	−1.62667
$875$	−4.63803	−0.156794
$876$	6.56113	0.221680
$877$	−38.5945	−1.30324	−0.651622	−	0.758544i	$-0.725911\pi$
$877$	−38.5945	−1.30324	−0.651622	+	0.758544i	$0.725911\pi$
$878$	18.5112	0.624723
$879$	26.1125	0.880753
$880$	1.00000	0.0337100
$881$	−7.88757	−0.265739	−0.132870	−	0.991134i	$-0.542419\pi$
$881$	−7.88757	−0.265739	−0.132870	+	0.991134i	$0.542419\pi$
$882$	−25.2979	−0.851826
$883$	11.1519	0.375290	0.187645	−	0.982237i	$-0.439915\pi$
$883$	11.1519	0.375290	0.187645	+	0.982237i	$0.439915\pi$
$884$	41.7105	1.40287
$885$	−3.43597	−0.115499
$886$	4.84563	0.162792
$887$	30.6592	1.02944	0.514718	−	0.857359i	$-0.327897\pi$
$887$	30.6592	1.02944	0.514718	+	0.857359i	$0.327897\pi$
$888$	7.67150	0.257439
$889$	32.6415	1.09476
$890$	13.5086	0.452810
$891$	11.1908	0.374906
$892$	0.474339	0.0158820
$893$	44.9066	1.50274
$894$	18.9395	0.633430
$895$	−17.0492	−0.569891
$896$	−4.63803	−0.154946
$897$	−98.7157	−3.29602
$898$	−1.78702	−0.0596338
$899$	−4.92151	−0.164142
$900$	1.74332	0.0581108
$901$	2.39562	0.0798095
$902$	−8.02297	−0.267136
$903$	−10.1012	−0.336148
$904$	−9.96108	−0.331301
$905$	22.8842	0.760696
$906$	−17.6822	−0.587451
$907$	39.7812	1.32091	0.660456	−	0.750865i	$-0.270363\pi$
$907$	39.7812	1.32091	0.660456	+	0.750865i	$0.270363\pi$
$908$	22.9170	0.760526
$909$	8.04295	0.266768
$910$	−26.9298	−0.892714
$911$	−31.7767	−1.05281	−0.526405	−	0.850234i	$-0.676461\pi$
$911$	−31.7767	−1.05281	−0.526405	+	0.850234i	$0.676461\pi$
$912$	13.4169	0.444277
$913$	−13.5518	−0.448498
$914$	−15.6591	−0.517958
$915$	32.0412	1.05925
$916$	−1.74361	−0.0576107
$917$	60.4946	1.99771
$918$	19.6612	0.648917
$919$	32.8697	1.08427	0.542136	−	0.840291i	$-0.317616\pi$
$919$	32.8697	1.08427	0.542136	+	0.840291i	$0.317616\pi$
$920$	−7.80630	−0.257366
$921$	−13.8054	−0.454904
$922$	−1.93745	−0.0638064
$923$	54.7119	1.80086
$924$	10.1012	0.332307
$925$	3.52240	0.115816
$926$	−31.1924	−1.02504
$927$	−8.15093	−0.267712
$928$	−1.51070	−0.0495912
$929$	−52.8939	−1.73539	−0.867697	−	0.497094i	$-0.834400\pi$
$929$	−52.8939	−1.73539	−0.867697	+	0.497094i	$0.834400\pi$
$930$	7.09514	0.232659
$931$	−89.3958	−2.92983
$932$	−14.1046	−0.462011
$933$	−44.1650	−1.44590
$934$	33.1793	1.08566
$935$	−7.18366	−0.234931
$936$	10.1223	0.330856
$937$	2.67168	0.0872799	0.0436399	−	0.999047i	$-0.486105\pi$
$937$	2.67168	0.0872799	0.0436399	+	0.999047i	$0.486105\pi$
$938$	−16.1607	−0.527664
$939$	38.5809	1.25904
$940$	7.28953	0.237758
$941$	40.5921	1.32326	0.661632	−	0.749829i	$-0.269864\pi$
$941$	40.5921	1.32326	0.661632	+	0.749829i	$0.269864\pi$
$942$	14.2641	0.464749
$943$	62.6297	2.03950
$944$	−1.57764	−0.0513478
$945$	−12.6940	−0.412936
$946$	1.00000	0.0325128
$947$	4.30856	0.140009	0.0700047	−	0.997547i	$-0.477699\pi$
$947$	4.30856	0.140009	0.0700047	+	0.997547i	$0.477699\pi$
$948$	−11.0207	−0.357935
$949$	17.4919	0.567811
$950$	6.16042	0.199870
$951$	−19.9188	−0.645913
$952$	33.3180	1.07984
$953$	29.9630	0.970596	0.485298	−	0.874349i	$-0.338711\pi$
$953$	29.9630	0.970596	0.485298	+	0.874349i	$0.338711\pi$
$954$	0.581366	0.0188224
$955$	−9.36038	−0.302895
$956$	22.2167	0.718538
$957$	3.29018	0.106357
$958$	24.9337	0.805571
$959$	−49.8612	−1.61010
$960$	2.17792	0.0702920
$961$	−20.3870	−0.657644
$962$	20.4521	0.659403
$963$	−23.4843	−0.756772
$964$	15.9469	0.513615
$965$	5.84595	0.188188
$966$	−78.8534	−2.53707
$967$	32.5276	1.04602	0.523008	−	0.852328i	$-0.324810\pi$
$967$	32.5276	1.04602	0.523008	+	0.852328i	$0.324810\pi$
$968$	−1.00000	−0.0321412
$969$	−96.3823	−3.09625
$970$	−15.3042	−0.491389
$971$	26.9186	0.863860	0.431930	−	0.901907i	$-0.357833\pi$
$971$	26.9186	0.863860	0.431930	+	0.901907i	$0.357833\pi$
$972$	16.1618	0.518390
$973$	−77.0934	−2.47150
$974$	−27.1636	−0.870379
$975$	12.6456	0.404985
$976$	14.7118	0.470915
$977$	1.86491	0.0596638	0.0298319	−	0.999555i	$-0.490503\pi$
$977$	1.86491	0.0596638	0.0298319	+	0.999555i	$0.490503\pi$
$978$	9.46244	0.302575
$979$	−13.5086	−0.431737
$980$	−14.5113	−0.463547
$981$	18.6069	0.594073
$982$	31.2621	0.997615
$983$	46.1847	1.47306	0.736531	−	0.676404i	$-0.236463\pi$
$983$	46.1847	1.47306	0.736531	+	0.676404i	$0.236463\pi$
$984$	−17.4734	−0.557030
$985$	−5.86569	−0.186896
$986$	10.8524	0.345610
$987$	73.6333	2.34377
$988$	35.7692	1.13797
$989$	−7.80630	−0.248226
$990$	−1.74332	−0.0554065
$991$	−0.401128	−0.0127422	−0.00637112	−	0.999980i	$-0.502028\pi$
$991$	−0.401128	−0.0127422	−0.00637112	+	0.999980i	$0.502028\pi$
$992$	3.25777	0.103434
$993$	15.6823	0.497661
$994$	43.7035	1.38619
$995$	−13.5383	−0.429193
$996$	−29.5146	−0.935206
$997$	21.6030	0.684175	0.342087	−	0.939668i	$-0.388866\pi$
$997$	21.6030	0.684175	0.342087	+	0.939668i	$0.388866\pi$
$998$	−22.5838	−0.714879
$999$	9.64059	0.305015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.3	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.17792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.17792 q^{6} +4.63803 q^{7} -1.00000 q^{8} +1.74332 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.17792 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.17792 q^{6} +4.63803 q^{7} -1.00000 q^{8} +1.74332 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.17792 q^{12} -5.80630 q^{13} -4.63803 q^{14} +2.17792 q^{15} +1.00000 q^{16} -7.18366 q^{17} -1.74332 q^{18} -6.16042 q^{19} -1.00000 q^{20} -10.1012 q^{21} +1.00000 q^{22} -7.80630 q^{23} +2.17792 q^{24} +1.00000 q^{25} +5.80630 q^{26} +2.73694 q^{27} +4.63803 q^{28} +1.51070 q^{29} -2.17792 q^{30} -3.25777 q^{31} -1.00000 q^{32} +2.17792 q^{33} +7.18366 q^{34} -4.63803 q^{35} +1.74332 q^{36} +3.52240 q^{37} +6.16042 q^{38} +12.6456 q^{39} +1.00000 q^{40} -8.02297 q^{41} +10.1012 q^{42} +1.00000 q^{43} -1.00000 q^{44} -1.74332 q^{45} +7.80630 q^{46} -7.28953 q^{47} -2.17792 q^{48} +14.5113 q^{49} -1.00000 q^{50} +15.6454 q^{51} -5.80630 q^{52} -0.333481 q^{53} -2.73694 q^{54} +1.00000 q^{55} -4.63803 q^{56} +13.4169 q^{57} -1.51070 q^{58} -1.57764 q^{59} +2.17792 q^{60} +14.7118 q^{61} +3.25777 q^{62} +8.08559 q^{63} +1.00000 q^{64} +5.80630 q^{65} -2.17792 q^{66} +3.48438 q^{67} -7.18366 q^{68} +17.0015 q^{69} +4.63803 q^{70} -9.42285 q^{71} -1.74332 q^{72} -3.01257 q^{73} -3.52240 q^{74} -2.17792 q^{75} -6.16042 q^{76} -4.63803 q^{77} -12.6456 q^{78} +5.06019 q^{79} -1.00000 q^{80} -11.1908 q^{81} +8.02297 q^{82} +13.5518 q^{83} -10.1012 q^{84} +7.18366 q^{85} -1.00000 q^{86} -3.29018 q^{87} +1.00000 q^{88} +13.5086 q^{89} +1.74332 q^{90} -26.9298 q^{91} -7.80630 q^{92} +7.09514 q^{93} +7.28953 q^{94} +6.16042 q^{95} +2.17792 q^{96} -15.3042 q^{97} -14.5113 q^{98} -1.74332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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