LMFDB - Embedded newform 4730.2.a.bb.1.1

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			1.1
Root			$2.87555$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.87555 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.87555 q^{6} -0.638121 q^{7} -1.00000 q^{8} +5.26880 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.87555 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.87555 q^{6} -0.638121 q^{7} -1.00000 q^{8} +5.26880 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.87555 q^{12} -4.59700 q^{13} +0.638121 q^{14} +2.87555 q^{15} +1.00000 q^{16} +2.19981 q^{17} -5.26880 q^{18} +8.48677 q^{19} -1.00000 q^{20} +1.83495 q^{21} +1.00000 q^{22} -6.59700 q^{23} +2.87555 q^{24} +1.00000 q^{25} +4.59700 q^{26} -6.52406 q^{27} -0.638121 q^{28} -7.34651 q^{29} -2.87555 q^{30} -2.58878 q^{31} -1.00000 q^{32} +2.87555 q^{33} -2.19981 q^{34} +0.638121 q^{35} +5.26880 q^{36} +8.68495 q^{37} -8.48677 q^{38} +13.2189 q^{39} +1.00000 q^{40} +5.97606 q^{41} -1.83495 q^{42} +1.00000 q^{43} -1.00000 q^{44} -5.26880 q^{45} +6.59700 q^{46} -7.43235 q^{47} -2.87555 q^{48} -6.59280 q^{49} -1.00000 q^{50} -6.32566 q^{51} -4.59700 q^{52} -1.66793 q^{53} +6.52406 q^{54} +1.00000 q^{55} +0.638121 q^{56} -24.4042 q^{57} +7.34651 q^{58} +9.08082 q^{59} +2.87555 q^{60} -7.07567 q^{61} +2.58878 q^{62} -3.36213 q^{63} +1.00000 q^{64} +4.59700 q^{65} -2.87555 q^{66} +3.07549 q^{67} +2.19981 q^{68} +18.9700 q^{69} -0.638121 q^{70} -2.59759 q^{71} -5.26880 q^{72} -16.2362 q^{73} -8.68495 q^{74} -2.87555 q^{75} +8.48677 q^{76} +0.638121 q^{77} -13.2189 q^{78} +6.29306 q^{79} -1.00000 q^{80} +2.95388 q^{81} -5.97606 q^{82} -2.36375 q^{83} +1.83495 q^{84} -2.19981 q^{85} -1.00000 q^{86} +21.1253 q^{87} +1.00000 q^{88} +3.41566 q^{89} +5.26880 q^{90} +2.93344 q^{91} -6.59700 q^{92} +7.44416 q^{93} +7.43235 q^{94} -8.48677 q^{95} +2.87555 q^{96} +6.87292 q^{97} +6.59280 q^{98} -5.26880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.87555	−1.66020	−0.830101	−	0.557614i	$-0.811717\pi$
$3$	−2.87555	−1.66020	−0.830101	+	0.557614i	$0.811717\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.87555	1.17394
$7$	−0.638121	−0.241187	−0.120594	−	0.992702i	$-0.538480\pi$
$7$	−0.638121	−0.241187	−0.120594	+	0.992702i	$0.538480\pi$
$8$	−1.00000	−0.353553
$9$	5.26880	1.75627
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.87555	−0.830101
$13$	−4.59700	−1.27498	−0.637489	−	0.770460i	$-0.720027\pi$
$13$	−4.59700	−1.27498	−0.637489	+	0.770460i	$0.720027\pi$
$14$	0.638121	0.170545
$15$	2.87555	0.742465
$16$	1.00000	0.250000
$17$	2.19981	0.533531	0.266766	−	0.963761i	$-0.414045\pi$
$17$	2.19981	0.533531	0.266766	+	0.963761i	$0.414045\pi$
$18$	−5.26880	−1.24187
$19$	8.48677	1.94700	0.973499	−	0.228690i	$-0.0734442\pi$
$19$	8.48677	1.94700	0.973499	+	0.228690i	$0.0734442\pi$
$20$	−1.00000	−0.223607
$21$	1.83495	0.400419
$22$	1.00000	0.213201
$23$	−6.59700	−1.37557	−0.687785	−	0.725915i	$-0.741417\pi$
$23$	−6.59700	−1.37557	−0.687785	+	0.725915i	$0.741417\pi$
$24$	2.87555	0.586970
$25$	1.00000	0.200000
$26$	4.59700	0.901545
$27$	−6.52406	−1.25556
$28$	−0.638121	−0.120594
$29$	−7.34651	−1.36421	−0.682107	−	0.731253i	$-0.738936\pi$
$29$	−7.34651	−1.36421	−0.682107	+	0.731253i	$0.738936\pi$
$30$	−2.87555	−0.525002
$31$	−2.58878	−0.464958	−0.232479	−	0.972601i	$-0.574684\pi$
$31$	−2.58878	−0.464958	−0.232479	+	0.972601i	$0.574684\pi$
$32$	−1.00000	−0.176777
$33$	2.87555	0.500569
$34$	−2.19981	−0.377264
$35$	0.638121	0.107862
$36$	5.26880	0.878134
$37$	8.68495	1.42780	0.713899	−	0.700249i	$-0.246928\pi$
$37$	8.68495	1.42780	0.713899	+	0.700249i	$0.246928\pi$
$38$	−8.48677	−1.37674
$39$	13.2189	2.11672
$40$	1.00000	0.158114
$41$	5.97606	0.933304	0.466652	−	0.884441i	$-0.345460\pi$
$41$	5.97606	0.933304	0.466652	+	0.884441i	$0.345460\pi$
$42$	−1.83495	−0.283139
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−5.26880	−0.785427
$46$	6.59700	0.972674
$47$	−7.43235	−1.08412	−0.542060	−	0.840340i	$-0.682355\pi$
$47$	−7.43235	−1.08412	−0.542060	+	0.840340i	$0.682355\pi$
$48$	−2.87555	−0.415050
$49$	−6.59280	−0.941829
$50$	−1.00000	−0.141421
$51$	−6.32566	−0.885769
$52$	−4.59700	−0.637489
$53$	−1.66793	−0.229108	−0.114554	−	0.993417i	$-0.536544\pi$
$53$	−1.66793	−0.229108	−0.114554	+	0.993417i	$0.536544\pi$
$54$	6.52406	0.887813
$55$	1.00000	0.134840
$56$	0.638121	0.0852725
$57$	−24.4042	−3.23241
$58$	7.34651	0.964644
$59$	9.08082	1.18222	0.591111	−	0.806590i	$-0.298689\pi$
$59$	9.08082	1.18222	0.591111	+	0.806590i	$0.298689\pi$
$60$	2.87555	0.371232
$61$	−7.07567	−0.905947	−0.452973	−	0.891524i	$-0.649637\pi$
$61$	−7.07567	−0.905947	−0.452973	+	0.891524i	$0.649637\pi$
$62$	2.58878	0.328775
$63$	−3.36213	−0.423589
$64$	1.00000	0.125000
$65$	4.59700	0.570187
$66$	−2.87555	−0.353956
$67$	3.07549	0.375731	0.187866	−	0.982195i	$-0.439843\pi$
$67$	3.07549	0.375731	0.187866	+	0.982195i	$0.439843\pi$
$68$	2.19981	0.266766
$69$	18.9700	2.28372
$70$	−0.638121	−0.0762701
$71$	−2.59759	−0.308278	−0.154139	−	0.988049i	$-0.549260\pi$
$71$	−2.59759	−0.308278	−0.154139	+	0.988049i	$0.549260\pi$
$72$	−5.26880	−0.620934
$73$	−16.2362	−1.90030	−0.950149	−	0.311796i	$-0.899070\pi$
$73$	−16.2362	−1.90030	−0.950149	+	0.311796i	$0.899070\pi$
$74$	−8.68495	−1.00961
$75$	−2.87555	−0.332040
$76$	8.48677	0.973499
$77$	0.638121	0.0727207
$78$	−13.2189	−1.49675
$79$	6.29306	0.708024	0.354012	−	0.935241i	$-0.384817\pi$
$79$	6.29306	0.708024	0.354012	+	0.935241i	$0.384817\pi$
$80$	−1.00000	−0.111803
$81$	2.95388	0.328209
$82$	−5.97606	−0.659946
$83$	−2.36375	−0.259455	−0.129728	−	0.991550i	$-0.541410\pi$
$83$	−2.36375	−0.259455	−0.129728	+	0.991550i	$0.541410\pi$
$84$	1.83495	0.200210
$85$	−2.19981	−0.238602
$86$	−1.00000	−0.107833
$87$	21.1253	2.26487
$88$	1.00000	0.106600
$89$	3.41566	0.362059	0.181030	−	0.983478i	$-0.442057\pi$
$89$	3.41566	0.362059	0.181030	+	0.983478i	$0.442057\pi$
$90$	5.26880	0.555381
$91$	2.93344	0.307508
$92$	−6.59700	−0.687785
$93$	7.44416	0.771924
$94$	7.43235	0.766588
$95$	−8.48677	−0.870724
$96$	2.87555	0.293485
$97$	6.87292	0.697840	0.348920	−	0.937153i	$-0.386549\pi$
$97$	6.87292	0.697840	0.348920	+	0.937153i	$0.386549\pi$
$98$	6.59280	0.665974
$99$	−5.26880	−0.529535
$100$	1.00000	0.100000
$101$	−3.48201	−0.346473	−0.173237	−	0.984880i	$-0.555423\pi$
$101$	−3.48201	−0.346473	−0.173237	+	0.984880i	$0.555423\pi$
$102$	6.32566	0.626333
$103$	−2.39572	−0.236057	−0.118028	−	0.993010i	$-0.537657\pi$
$103$	−2.39572	−0.236057	−0.118028	+	0.993010i	$0.537657\pi$
$104$	4.59700	0.450773
$105$	−1.83495	−0.179073
$106$	1.66793	0.162004
$107$	−2.44388	−0.236259	−0.118130	−	0.992998i	$-0.537690\pi$
$107$	−2.44388	−0.236259	−0.118130	+	0.992998i	$0.537690\pi$
$108$	−6.52406	−0.627778
$109$	−17.0063	−1.62891	−0.814453	−	0.580229i	$-0.802963\pi$
$109$	−17.0063	−1.62891	−0.814453	+	0.580229i	$0.802963\pi$
$110$	−1.00000	−0.0953463
$111$	−24.9740	−2.37043
$112$	−0.638121	−0.0602968
$113$	−19.3050	−1.81606	−0.908031	−	0.418903i	$-0.862415\pi$
$113$	−19.3050	−1.81606	−0.908031	+	0.418903i	$0.862415\pi$
$114$	24.4042	2.28566
$115$	6.59700	0.615173
$116$	−7.34651	−0.682107
$117$	−24.2207	−2.23920
$118$	−9.08082	−0.835958
$119$	−1.40374	−0.128681
$120$	−2.87555	−0.262501
$121$	1.00000	0.0909091
$122$	7.07567	0.640601
$123$	−17.1845	−1.54947
$124$	−2.58878	−0.232479
$125$	−1.00000	−0.0894427
$126$	3.36213	0.299523
$127$	14.3223	1.27089	0.635447	−	0.772144i	$-0.280816\pi$
$127$	14.3223	1.27089	0.635447	+	0.772144i	$0.280816\pi$
$128$	−1.00000	−0.0883883
$129$	−2.87555	−0.253178
$130$	−4.59700	−0.403183
$131$	−20.3247	−1.77577	−0.887887	−	0.460062i	$-0.847827\pi$
$131$	−20.3247	−1.77577	−0.887887	+	0.460062i	$0.847827\pi$
$132$	2.87555	0.250285
$133$	−5.41559	−0.469591
$134$	−3.07549	−0.265682
$135$	6.52406	0.561502
$136$	−2.19981	−0.188632
$137$	−1.83433	−0.156717	−0.0783586	−	0.996925i	$-0.524968\pi$
$137$	−1.83433	−0.156717	−0.0783586	+	0.996925i	$0.524968\pi$
$138$	−18.9700	−1.61483
$139$	19.0091	1.61233	0.806167	−	0.591688i	$-0.201538\pi$
$139$	19.0091	1.61233	0.806167	+	0.591688i	$0.201538\pi$
$140$	0.638121	0.0539311
$141$	21.3721	1.79986
$142$	2.59759	0.217985
$143$	4.59700	0.384420
$144$	5.26880	0.439067
$145$	7.34651	0.610095
$146$	16.2362	1.34371
$147$	18.9579	1.56363
$148$	8.68495	0.713899
$149$	−5.64636	−0.462568	−0.231284	−	0.972886i	$-0.574293\pi$
$149$	−5.64636	−0.462568	−0.231284	+	0.972886i	$0.574293\pi$
$150$	2.87555	0.234788
$151$	−12.7081	−1.03417	−0.517084	−	0.855935i	$-0.672982\pi$
$151$	−12.7081	−1.03417	−0.517084	+	0.855935i	$0.672982\pi$
$152$	−8.48677	−0.688368
$153$	11.5903	0.937024
$154$	−0.638121	−0.0514213
$155$	2.58878	0.207936
$156$	13.2189	1.05836
$157$	−8.30966	−0.663183	−0.331592	−	0.943423i	$-0.607586\pi$
$157$	−8.30966	−0.663183	−0.331592	+	0.943423i	$0.607586\pi$
$158$	−6.29306	−0.500649
$159$	4.79623	0.380366
$160$	1.00000	0.0790569
$161$	4.20968	0.331770
$162$	−2.95388	−0.232079
$163$	1.36870	0.107205	0.0536025	−	0.998562i	$-0.482930\pi$
$163$	1.36870	0.107205	0.0536025	+	0.998562i	$0.482930\pi$
$164$	5.97606	0.466652
$165$	−2.87555	−0.223861
$166$	2.36375	0.183463
$167$	−0.269910	−0.0208863	−0.0104431	−	0.999945i	$-0.503324\pi$
$167$	−0.269910	−0.0208863	−0.0104431	+	0.999945i	$0.503324\pi$
$168$	−1.83495	−0.141570
$169$	8.13238	0.625568
$170$	2.19981	0.168717
$171$	44.7151	3.41945
$172$	1.00000	0.0762493
$173$	0.646448	0.0491486	0.0245743	−	0.999698i	$-0.492177\pi$
$173$	0.646448	0.0491486	0.0245743	+	0.999698i	$0.492177\pi$
$174$	−21.1253	−1.60150
$175$	−0.638121	−0.0482374
$176$	−1.00000	−0.0753778
$177$	−26.1124	−1.96273
$178$	−3.41566	−0.256014
$179$	−9.33927	−0.698050	−0.349025	−	0.937113i	$-0.613487\pi$
$179$	−9.33927	−0.698050	−0.349025	+	0.937113i	$0.613487\pi$
$180$	−5.26880	−0.392713
$181$	23.1945	1.72403	0.862017	−	0.506879i	$-0.169201\pi$
$181$	23.1945	1.72403	0.862017	+	0.506879i	$0.169201\pi$
$182$	−2.93344	−0.217441
$183$	20.3465	1.50405
$184$	6.59700	0.486337
$185$	−8.68495	−0.638530
$186$	−7.44416	−0.545832
$187$	−2.19981	−0.160866
$188$	−7.43235	−0.542060
$189$	4.16314	0.302824
$190$	8.48677	0.615695
$191$	1.40312	0.101526	0.0507631	−	0.998711i	$-0.483835\pi$
$191$	1.40312	0.101526	0.0507631	+	0.998711i	$0.483835\pi$
$192$	−2.87555	−0.207525
$193$	−12.2988	−0.885287	−0.442644	−	0.896698i	$-0.645959\pi$
$193$	−12.2988	−0.885287	−0.442644	+	0.896698i	$0.645959\pi$
$194$	−6.87292	−0.493447
$195$	−13.2189	−0.946626
$196$	−6.59280	−0.470914
$197$	11.3866	0.811260	0.405630	−	0.914037i	$-0.367052\pi$
$197$	11.3866	0.811260	0.405630	+	0.914037i	$0.367052\pi$
$198$	5.26880	0.374438
$199$	−0.348978	−0.0247384	−0.0123692	−	0.999923i	$-0.503937\pi$
$199$	−0.348978	−0.0247384	−0.0123692	+	0.999923i	$0.503937\pi$
$200$	−1.00000	−0.0707107
$201$	−8.84375	−0.623790
$202$	3.48201	0.244994
$203$	4.68797	0.329031
$204$	−6.32566	−0.442885
$205$	−5.97606	−0.417386
$206$	2.39572	0.166917
$207$	−34.7583	−2.41587
$208$	−4.59700	−0.318744
$209$	−8.48677	−0.587042
$210$	1.83495	0.126624
$211$	16.2045	1.11556	0.557781	−	0.829988i	$-0.311653\pi$
$211$	16.2045	1.11556	0.557781	+	0.829988i	$0.311653\pi$
$212$	−1.66793	−0.114554
$213$	7.46952	0.511803
$214$	2.44388	0.167060
$215$	−1.00000	−0.0681994
$216$	6.52406	0.443906
$217$	1.65195	0.112142
$218$	17.0063	1.15181
$219$	46.6879	3.15488
$220$	1.00000	0.0674200
$221$	−10.1125	−0.680240
$222$	24.9740	1.67615
$223$	−7.27004	−0.486838	−0.243419	−	0.969921i	$-0.578269\pi$
$223$	−7.27004	−0.486838	−0.243419	+	0.969921i	$0.578269\pi$
$224$	0.638121	0.0426363
$225$	5.26880	0.351254
$226$	19.3050	1.28415
$227$	−22.9239	−1.52151	−0.760756	−	0.649038i	$-0.775172\pi$
$227$	−22.9239	−1.52151	−0.760756	+	0.649038i	$0.775172\pi$
$228$	−24.4042	−1.61620
$229$	−17.3301	−1.14520	−0.572602	−	0.819834i	$-0.694066\pi$
$229$	−17.3301	−1.14520	−0.572602	+	0.819834i	$0.694066\pi$
$230$	−6.59700	−0.434993
$231$	−1.83495	−0.120731
$232$	7.34651	0.482322
$233$	16.5045	1.08124	0.540622	−	0.841265i	$-0.318189\pi$
$233$	16.5045	1.08124	0.540622	+	0.841265i	$0.318189\pi$
$234$	24.2207	1.58335
$235$	7.43235	0.484833
$236$	9.08082	0.591111
$237$	−18.0960	−1.17546
$238$	1.40374	0.0909911
$239$	19.8684	1.28518	0.642591	−	0.766209i	$-0.277859\pi$
$239$	19.8684	1.28518	0.642591	+	0.766209i	$0.277859\pi$
$240$	2.87555	0.185616
$241$	−26.6728	−1.71814	−0.859072	−	0.511855i	$-0.828959\pi$
$241$	−26.6728	−1.71814	−0.859072	+	0.511855i	$0.828959\pi$
$242$	−1.00000	−0.0642824
$243$	11.0782	0.710664
$244$	−7.07567	−0.452973
$245$	6.59280	0.421199
$246$	17.1845	1.09564
$247$	−39.0137	−2.48238
$248$	2.58878	0.164387
$249$	6.79709	0.430748
$250$	1.00000	0.0632456
$251$	4.27840	0.270050	0.135025	−	0.990842i	$-0.456889\pi$
$251$	4.27840	0.270050	0.135025	+	0.990842i	$0.456889\pi$
$252$	−3.36213	−0.211795
$253$	6.59700	0.414750
$254$	−14.3223	−0.898658
$255$	6.32566	0.396128
$256$	1.00000	0.0625000
$257$	14.5985	0.910628	0.455314	−	0.890331i	$-0.349527\pi$
$257$	14.5985	0.910628	0.455314	+	0.890331i	$0.349527\pi$
$258$	2.87555	0.179024
$259$	−5.54205	−0.344366
$260$	4.59700	0.285094
$261$	−38.7073	−2.39592
$262$	20.3247	1.25566
$263$	0.0322302	0.00198740	0.000993700	−	1.00000i	$-0.499684\pi$
$263$	0.0322302	0.00198740	0.000993700		1.00000i	$0.499684\pi$
$264$	−2.87555	−0.176978
$265$	1.66793	0.102460
$266$	5.41559	0.332051
$267$	−9.82191	−0.601091
$268$	3.07549	0.187866
$269$	−0.394595	−0.0240589	−0.0120294	−	0.999928i	$-0.503829\pi$
$269$	−0.394595	−0.0240589	−0.0120294	+	0.999928i	$0.503829\pi$
$270$	−6.52406	−0.397042
$271$	28.5263	1.73285	0.866423	−	0.499310i	$-0.166413\pi$
$271$	28.5263	1.73285	0.866423	+	0.499310i	$0.166413\pi$
$272$	2.19981	0.133383
$273$	−8.43526	−0.510525
$274$	1.83433	0.110816
$275$	−1.00000	−0.0603023
$276$	18.9700	1.14186
$277$	30.2610	1.81821	0.909105	−	0.416567i	$-0.136767\pi$
$277$	30.2610	1.81821	0.909105	+	0.416567i	$0.136767\pi$
$278$	−19.0091	−1.14009
$279$	−13.6398	−0.816591
$280$	−0.638121	−0.0381350
$281$	15.4840	0.923695	0.461848	−	0.886959i	$-0.347187\pi$
$281$	15.4840	0.923695	0.461848	+	0.886959i	$0.347187\pi$
$282$	−21.3721	−1.27269
$283$	−10.0140	−0.595271	−0.297636	−	0.954680i	$-0.596198\pi$
$283$	−10.0140	−0.595271	−0.297636	+	0.954680i	$0.596198\pi$
$284$	−2.59759	−0.154139
$285$	24.4042	1.44558
$286$	−4.59700	−0.271826
$287$	−3.81345	−0.225101
$288$	−5.26880	−0.310467
$289$	−12.1609	−0.715344
$290$	−7.34651	−0.431402
$291$	−19.7635	−1.15855
$292$	−16.2362	−0.950149
$293$	10.6641	0.623002	0.311501	−	0.950246i	$-0.399168\pi$
$293$	10.6641	0.623002	0.311501	+	0.950246i	$0.399168\pi$
$294$	−18.9579	−1.10565
$295$	−9.08082	−0.528706
$296$	−8.68495	−0.504803
$297$	6.52406	0.378565
$298$	5.64636	0.327085
$299$	30.3264	1.75382
$300$	−2.87555	−0.166020
$301$	−0.638121	−0.0367807
$302$	12.7081	0.731267
$303$	10.0127	0.575215
$304$	8.48677	0.486750
$305$	7.07567	0.405152
$306$	−11.5903	−0.662576
$307$	15.1916	0.867029	0.433515	−	0.901147i	$-0.357273\pi$
$307$	15.1916	0.867029	0.433515	+	0.901147i	$0.357273\pi$
$308$	0.638121	0.0363603
$309$	6.88901	0.391902
$310$	−2.58878	−0.147033
$311$	−21.3131	−1.20855	−0.604277	−	0.796774i	$-0.706538\pi$
$311$	−21.3131	−1.20855	−0.604277	+	0.796774i	$0.706538\pi$
$312$	−13.2189	−0.748373
$313$	3.96895	0.224339	0.112169	−	0.993689i	$-0.464220\pi$
$313$	3.96895	0.224339	0.112169	+	0.993689i	$0.464220\pi$
$314$	8.30966	0.468941
$315$	3.36213	0.189435
$316$	6.29306	0.354012
$317$	1.66920	0.0937514	0.0468757	−	0.998901i	$-0.485074\pi$
$317$	1.66920	0.0937514	0.0468757	+	0.998901i	$0.485074\pi$
$318$	−4.79623	−0.268959
$319$	7.34651	0.411326
$320$	−1.00000	−0.0559017
$321$	7.02752	0.392238
$322$	−4.20968	−0.234596
$323$	18.6692	1.03878
$324$	2.95388	0.164104
$325$	−4.59700	−0.254996
$326$	−1.36870	−0.0758054
$327$	48.9025	2.70431
$328$	−5.97606	−0.329973
$329$	4.74274	0.261476
$330$	2.87555	0.158294
$331$	28.2235	1.55131	0.775653	−	0.631160i	$-0.217421\pi$
$331$	28.2235	1.55131	0.775653	+	0.631160i	$0.217421\pi$
$332$	−2.36375	−0.129728
$333$	45.7593	2.50759
$334$	0.269910	0.0147688
$335$	−3.07549	−0.168032
$336$	1.83495	0.100105
$337$	−19.2662	−1.04950	−0.524750	−	0.851257i	$-0.675841\pi$
$337$	−19.2662	−1.04950	−0.524750	+	0.851257i	$0.675841\pi$
$338$	−8.13238	−0.442343
$339$	55.5126	3.01503
$340$	−2.19981	−0.119301
$341$	2.58878	0.140190
$342$	−44.7151	−2.41792
$343$	8.67385	0.468344
$344$	−1.00000	−0.0539164
$345$	−18.9700	−1.02131
$346$	−0.646448	−0.0347533
$347$	28.1125	1.50916	0.754580	−	0.656208i	$-0.227840\pi$
$347$	28.1125	1.50916	0.754580	+	0.656208i	$0.227840\pi$
$348$	21.1253	1.13243
$349$	−18.4755	−0.988972	−0.494486	−	0.869186i	$-0.664644\pi$
$349$	−18.4755	−0.988972	−0.494486	+	0.869186i	$0.664644\pi$
$350$	0.638121	0.0341090
$351$	29.9911	1.60081
$352$	1.00000	0.0533002
$353$	35.2433	1.87581	0.937905	−	0.346893i	$-0.112763\pi$
$353$	35.2433	1.87581	0.937905	+	0.346893i	$0.112763\pi$
$354$	26.1124	1.38786
$355$	2.59759	0.137866
$356$	3.41566	0.181030
$357$	4.03654	0.213636
$358$	9.33927	0.493596
$359$	−7.85867	−0.414765	−0.207382	−	0.978260i	$-0.566494\pi$
$359$	−7.85867	−0.414765	−0.207382	+	0.978260i	$0.566494\pi$
$360$	5.26880	0.277690
$361$	53.0253	2.79080
$362$	−23.1945	−1.21908
$363$	−2.87555	−0.150927
$364$	2.93344	0.153754
$365$	16.2362	0.849839
$366$	−20.3465	−1.06353
$367$	24.1696	1.26164	0.630820	−	0.775929i	$-0.282718\pi$
$367$	24.1696	1.26164	0.630820	+	0.775929i	$0.282718\pi$
$368$	−6.59700	−0.343892
$369$	31.4867	1.63913
$370$	8.68495	0.451509
$371$	1.06434	0.0552579
$372$	7.44416	0.385962
$373$	31.4941	1.63070	0.815352	−	0.578966i	$-0.196543\pi$
$373$	31.4941	1.63070	0.815352	+	0.578966i	$0.196543\pi$
$374$	2.19981	0.113749
$375$	2.87555	0.148493
$376$	7.43235	0.383294
$377$	33.7719	1.73934
$378$	−4.16314	−0.214129
$379$	20.1041	1.03268	0.516340	−	0.856384i	$-0.327294\pi$
$379$	20.1041	1.03268	0.516340	+	0.856384i	$0.327294\pi$
$380$	−8.48677	−0.435362
$381$	−41.1844	−2.10994
$382$	−1.40312	−0.0717899
$383$	5.85924	0.299393	0.149696	−	0.988732i	$-0.452170\pi$
$383$	5.85924	0.299393	0.149696	+	0.988732i	$0.452170\pi$
$384$	2.87555	0.146742
$385$	−0.638121	−0.0325217
$386$	12.2988	0.625993
$387$	5.26880	0.267828
$388$	6.87292	0.348920
$389$	23.6324	1.19821	0.599104	−	0.800671i	$-0.295524\pi$
$389$	23.6324	1.19821	0.599104	+	0.800671i	$0.295524\pi$
$390$	13.2189	0.669365
$391$	−14.5121	−0.733909
$392$	6.59280	0.332987
$393$	58.4446	2.94814
$394$	−11.3866	−0.573648
$395$	−6.29306	−0.316638
$396$	−5.26880	−0.264767
$397$	−0.614338	−0.0308328	−0.0154164	−	0.999881i	$-0.504907\pi$
$397$	−0.614338	−0.0308328	−0.0154164	+	0.999881i	$0.504907\pi$
$398$	0.348978	0.0174927
$399$	15.5728	0.779616
$400$	1.00000	0.0500000
$401$	−14.0403	−0.701137	−0.350569	−	0.936537i	$-0.614012\pi$
$401$	−14.0403	−0.701137	−0.350569	+	0.936537i	$0.614012\pi$
$402$	8.84375	0.441086
$403$	11.9006	0.592811
$404$	−3.48201	−0.173237
$405$	−2.95388	−0.146779
$406$	−4.68797	−0.232660
$407$	−8.68495	−0.430497
$408$	6.32566	0.313167
$409$	15.3070	0.756885	0.378442	−	0.925625i	$-0.376460\pi$
$409$	15.3070	0.756885	0.378442	+	0.925625i	$0.376460\pi$
$410$	5.97606	0.295137
$411$	5.27471	0.260182
$412$	−2.39572	−0.118028
$413$	−5.79467	−0.285137
$414$	34.7583	1.70828
$415$	2.36375	0.116032
$416$	4.59700	0.225386
$417$	−54.6618	−2.67680
$418$	8.48677	0.415102
$419$	8.77181	0.428531	0.214266	−	0.976775i	$-0.431264\pi$
$419$	8.77181	0.428531	0.214266	+	0.976775i	$0.431264\pi$
$420$	−1.83495	−0.0895364
$421$	−25.5129	−1.24342	−0.621711	−	0.783247i	$-0.713562\pi$
$421$	−25.5129	−1.24342	−0.621711	+	0.783247i	$0.713562\pi$
$422$	−16.2045	−0.788822
$423$	−39.1596	−1.90400
$424$	1.66793	0.0810019
$425$	2.19981	0.106706
$426$	−7.46952	−0.361899
$427$	4.51514	0.218503
$428$	−2.44388	−0.118130
$429$	−13.2189	−0.638215
$430$	1.00000	0.0482243
$431$	26.6342	1.28292	0.641462	−	0.767155i	$-0.278328\pi$
$431$	26.6342	1.28292	0.641462	+	0.767155i	$0.278328\pi$
$432$	−6.52406	−0.313889
$433$	23.1169	1.11093	0.555464	−	0.831541i	$-0.312541\pi$
$433$	23.1169	1.11093	0.555464	+	0.831541i	$0.312541\pi$
$434$	−1.65195	−0.0792963
$435$	−21.1253	−1.01288
$436$	−17.0063	−0.814453
$437$	−55.9872	−2.67823
$438$	−46.6879	−2.23084
$439$	−6.45373	−0.308020	−0.154010	−	0.988069i	$-0.549219\pi$
$439$	−6.45373	−0.308020	−0.154010	+	0.988069i	$0.549219\pi$
$440$	−1.00000	−0.0476731
$441$	−34.7362	−1.65410
$442$	10.1125	0.481003
$443$	20.2055	0.959990	0.479995	−	0.877271i	$-0.340638\pi$
$443$	20.2055	0.959990	0.479995	+	0.877271i	$0.340638\pi$
$444$	−24.9740	−1.18522
$445$	−3.41566	−0.161918
$446$	7.27004	0.344247
$447$	16.2364	0.767955
$448$	−0.638121	−0.0301484
$449$	−8.99123	−0.424322	−0.212161	−	0.977235i	$-0.568050\pi$
$449$	−8.99123	−0.424322	−0.212161	+	0.977235i	$0.568050\pi$
$450$	−5.26880	−0.248374
$451$	−5.97606	−0.281402
$452$	−19.3050	−0.908031
$453$	36.5427	1.71693
$454$	22.9239	1.07587
$455$	−2.93344	−0.137522
$456$	24.4042	1.14283
$457$	−4.97783	−0.232853	−0.116427	−	0.993199i	$-0.537144\pi$
$457$	−4.97783	−0.232853	−0.116427	+	0.993199i	$0.537144\pi$
$458$	17.3301	0.809781
$459$	−14.3517	−0.669879
$460$	6.59700	0.307587
$461$	−4.25819	−0.198324	−0.0991619	−	0.995071i	$-0.531616\pi$
$461$	−4.25819	−0.198324	−0.0991619	+	0.995071i	$0.531616\pi$
$462$	1.83495	0.0853697
$463$	−1.78970	−0.0831742	−0.0415871	−	0.999135i	$-0.513241\pi$
$463$	−1.78970	−0.0831742	−0.0415871	+	0.999135i	$0.513241\pi$
$464$	−7.34651	−0.341053
$465$	−7.44416	−0.345215
$466$	−16.5045	−0.764555
$467$	4.04228	0.187055	0.0935273	−	0.995617i	$-0.470186\pi$
$467$	4.04228	0.187055	0.0935273	+	0.995617i	$0.470186\pi$
$468$	−24.2207	−1.11960
$469$	−1.96254	−0.0906216
$470$	−7.43235	−0.342829
$471$	23.8949	1.10102
$472$	−9.08082	−0.417979
$473$	−1.00000	−0.0459800
$474$	18.0960	0.831177
$475$	8.48677	0.389400
$476$	−1.40374	−0.0643404
$477$	−8.78801	−0.402375
$478$	−19.8684	−0.908761
$479$	−0.426479	−0.0194863	−0.00974315	−	0.999953i	$-0.503101\pi$
$479$	−0.426479	−0.0194863	−0.00974315	+	0.999953i	$0.503101\pi$
$480$	−2.87555	−0.131250
$481$	−39.9247	−1.82041
$482$	26.6728	1.21491
$483$	−12.1052	−0.550804
$484$	1.00000	0.0454545
$485$	−6.87292	−0.312083
$486$	−11.0782	−0.502515
$487$	−11.7826	−0.533919	−0.266960	−	0.963708i	$-0.586019\pi$
$487$	−11.7826	−0.533919	−0.266960	+	0.963708i	$0.586019\pi$
$488$	7.07567	0.320301
$489$	−3.93578	−0.177982
$490$	−6.59280	−0.297832
$491$	20.4651	0.923576	0.461788	−	0.886990i	$-0.347208\pi$
$491$	20.4651	0.923576	0.461788	+	0.886990i	$0.347208\pi$
$492$	−17.1845	−0.774736
$493$	−16.1609	−0.727850
$494$	39.0137	1.75531
$495$	5.26880	0.236815
$496$	−2.58878	−0.116239
$497$	1.65758	0.0743526
$498$	−6.79709	−0.304585
$499$	31.3220	1.40217	0.701083	−	0.713079i	$-0.252700\pi$
$499$	31.3220	1.40217	0.701083	+	0.713079i	$0.252700\pi$
$500$	−1.00000	−0.0447214
$501$	0.776140	0.0346754
$502$	−4.27840	−0.190954
$503$	−37.4072	−1.66790	−0.833952	−	0.551837i	$-0.813927\pi$
$503$	−37.4072	−1.66790	−0.833952	+	0.551837i	$0.813927\pi$
$504$	3.36213	0.149761
$505$	3.48201	0.154948
$506$	−6.59700	−0.293272
$507$	−23.3851	−1.03857
$508$	14.3223	0.635447
$509$	−8.27957	−0.366986	−0.183493	−	0.983021i	$-0.558740\pi$
$509$	−8.27957	−0.366986	−0.183493	+	0.983021i	$0.558740\pi$
$510$	−6.32566	−0.280105
$511$	10.3606	0.458328
$512$	−1.00000	−0.0441942
$513$	−55.3682	−2.44457
$514$	−14.5985	−0.643911
$515$	2.39572	0.105568
$516$	−2.87555	−0.126589
$517$	7.43235	0.326874
$518$	5.54205	0.243504
$519$	−1.85890	−0.0815965
$520$	−4.59700	−0.201592
$521$	−30.4036	−1.33201	−0.666003	−	0.745949i	$-0.731996\pi$
$521$	−30.4036	−1.33201	−0.666003	+	0.745949i	$0.731996\pi$
$522$	38.7073	1.69417
$523$	13.3889	0.585457	0.292728	−	0.956196i	$-0.405437\pi$
$523$	13.3889	0.585457	0.292728	+	0.956196i	$0.405437\pi$
$524$	−20.3247	−0.887887
$525$	1.83495	0.0800838
$526$	−0.0322302	−0.00140530
$527$	−5.69481	−0.248070
$528$	2.87555	0.125142
$529$	20.5204	0.892190
$530$	−1.66793	−0.0724503
$531$	47.8451	2.07630
$532$	−5.41559	−0.234796
$533$	−27.4719	−1.18994
$534$	9.82191	0.425035
$535$	2.44388	0.105658
$536$	−3.07549	−0.132841
$537$	26.8556	1.15890
$538$	0.394595	0.0170122
$539$	6.59280	0.283972
$540$	6.52406	0.280751
$541$	41.4011	1.77997	0.889987	−	0.455986i	$-0.150713\pi$
$541$	41.4011	1.77997	0.889987	+	0.455986i	$0.150713\pi$
$542$	−28.5263	−1.22531
$543$	−66.6970	−2.86224
$544$	−2.19981	−0.0943159
$545$	17.0063	0.728469
$546$	8.43526	0.360996
$547$	20.5225	0.877477	0.438738	−	0.898615i	$-0.355425\pi$
$547$	20.5225	0.877477	0.438738	+	0.898615i	$0.355425\pi$
$548$	−1.83433	−0.0783586
$549$	−37.2803	−1.59109
$550$	1.00000	0.0426401
$551$	−62.3482	−2.65612
$552$	−18.9700	−0.807417
$553$	−4.01573	−0.170766
$554$	−30.2610	−1.28567
$555$	24.9740	1.06009
$556$	19.0091	0.806167
$557$	4.70330	0.199285	0.0996425	−	0.995023i	$-0.468230\pi$
$557$	4.70330	0.199285	0.0996425	+	0.995023i	$0.468230\pi$
$558$	13.6398	0.577417
$559$	−4.59700	−0.194432
$560$	0.638121	0.0269655
$561$	6.32566	0.267069
$562$	−15.4840	−0.653151
$563$	41.0955	1.73197	0.865984	−	0.500072i	$-0.166693\pi$
$563$	41.0955	1.73197	0.865984	+	0.500072i	$0.166693\pi$
$564$	21.3721	0.899928
$565$	19.3050	0.812168
$566$	10.0140	0.420920
$567$	−1.88493	−0.0791597
$568$	2.59759	0.108993
$569$	−22.3293	−0.936091	−0.468046	−	0.883704i	$-0.655042\pi$
$569$	−22.3293	−0.936091	−0.468046	+	0.883704i	$0.655042\pi$
$570$	−24.4042	−1.02218
$571$	44.2211	1.85060	0.925298	−	0.379240i	$-0.123814\pi$
$571$	44.2211	1.85060	0.925298	+	0.379240i	$0.123814\pi$
$572$	4.59700	0.192210
$573$	−4.03475	−0.168554
$574$	3.81345	0.159170
$575$	−6.59700	−0.275114
$576$	5.26880	0.219533
$577$	21.3812	0.890112	0.445056	−	0.895503i	$-0.353184\pi$
$577$	21.3812	0.890112	0.445056	+	0.895503i	$0.353184\pi$
$578$	12.1609	0.505825
$579$	35.3659	1.46975
$580$	7.34651	0.305047
$581$	1.50836	0.0625773
$582$	19.7635	0.819222
$583$	1.66793	0.0690787
$584$	16.2362	0.671857
$585$	24.2207	1.00140
$586$	−10.6641	−0.440529
$587$	−32.8265	−1.35489	−0.677447	−	0.735571i	$-0.736914\pi$
$587$	−32.8265	−1.35489	−0.677447	+	0.735571i	$0.736914\pi$
$588$	18.9579	0.781813
$589$	−21.9703	−0.905272
$590$	9.08082	0.373852
$591$	−32.7427	−1.34686
$592$	8.68495	0.356949
$593$	−12.7659	−0.524233	−0.262116	−	0.965036i	$-0.584420\pi$
$593$	−12.7659	−0.524233	−0.262116	+	0.965036i	$0.584420\pi$
$594$	−6.52406	−0.267686
$595$	1.40374	0.0575478
$596$	−5.64636	−0.231284
$597$	1.00350	0.0410707
$598$	−30.3264	−1.24014
$599$	18.3086	0.748069	0.374035	−	0.927415i	$-0.377974\pi$
$599$	18.3086	0.748069	0.374035	+	0.927415i	$0.377974\pi$
$600$	2.87555	0.117394
$601$	−31.3338	−1.27813	−0.639066	−	0.769152i	$-0.720679\pi$
$601$	−31.3338	−1.27813	−0.639066	+	0.769152i	$0.720679\pi$
$602$	0.638121	0.0260079
$603$	16.2042	0.659885
$604$	−12.7081	−0.517084
$605$	−1.00000	−0.0406558
$606$	−10.0127	−0.406739
$607$	−25.5715	−1.03791	−0.518957	−	0.854800i	$-0.673680\pi$
$607$	−25.5715	−1.03791	−0.518957	+	0.854800i	$0.673680\pi$
$608$	−8.48677	−0.344184
$609$	−13.4805	−0.546257
$610$	−7.07567	−0.286486
$611$	34.1665	1.38223
$612$	11.5903	0.468512
$613$	−15.0173	−0.606542	−0.303271	−	0.952904i	$-0.598079\pi$
$613$	−15.0173	−0.606542	−0.303271	+	0.952904i	$0.598079\pi$
$614$	−15.1916	−0.613082
$615$	17.1845	0.692945
$616$	−0.638121	−0.0257106
$617$	−34.3038	−1.38102	−0.690510	−	0.723323i	$-0.742614\pi$
$617$	−34.3038	−1.38102	−0.690510	+	0.723323i	$0.742614\pi$
$618$	−6.88901	−0.277116
$619$	15.2296	0.612131	0.306065	−	0.952010i	$-0.400987\pi$
$619$	15.2296	0.612131	0.306065	+	0.952010i	$0.400987\pi$
$620$	2.58878	0.103968
$621$	43.0392	1.72710
$622$	21.3131	0.854577
$623$	−2.17960	−0.0873240
$624$	13.2189	0.529180
$625$	1.00000	0.0400000
$626$	−3.96895	−0.158631
$627$	24.4042	0.974608
$628$	−8.30966	−0.331592
$629$	19.1052	0.761775
$630$	−3.36213	−0.133951
$631$	−4.96641	−0.197710	−0.0988548	−	0.995102i	$-0.531518\pi$
$631$	−4.96641	−0.197710	−0.0988548	+	0.995102i	$0.531518\pi$
$632$	−6.29306	−0.250324
$633$	−46.5968	−1.85206
$634$	−1.66920	−0.0662922
$635$	−14.3223	−0.568361
$636$	4.79623	0.190183
$637$	30.3071	1.20081
$638$	−7.34651	−0.290851
$639$	−13.6862	−0.541418
$640$	1.00000	0.0395285
$641$	−37.0352	−1.46280	−0.731400	−	0.681948i	$-0.761133\pi$
$641$	−37.0352	−1.46280	−0.731400	+	0.681948i	$0.761133\pi$
$642$	−7.02752	−0.277354
$643$	11.1674	0.440400	0.220200	−	0.975455i	$-0.429329\pi$
$643$	11.1674	0.440400	0.220200	+	0.975455i	$0.429329\pi$
$644$	4.20968	0.165885
$645$	2.87555	0.113225
$646$	−18.6692	−0.734532
$647$	−22.4095	−0.881007	−0.440503	−	0.897751i	$-0.645200\pi$
$647$	−22.4095	−0.881007	−0.440503	+	0.897751i	$0.645200\pi$
$648$	−2.95388	−0.116039
$649$	−9.08082	−0.356454
$650$	4.59700	0.180309
$651$	−4.75028	−0.186178
$652$	1.36870	0.0536025
$653$	6.15856	0.241003	0.120502	−	0.992713i	$-0.461550\pi$
$653$	6.15856	0.241003	0.120502	+	0.992713i	$0.461550\pi$
$654$	−48.9025	−1.91224
$655$	20.3247	0.794150
$656$	5.97606	0.233326
$657$	−85.5451	−3.33743
$658$	−4.74274	−0.184891
$659$	−34.8201	−1.35640	−0.678199	−	0.734879i	$-0.737239\pi$
$659$	−34.8201	−1.35640	−0.678199	+	0.734879i	$0.737239\pi$
$660$	−2.87555	−0.111931
$661$	2.11984	0.0824521	0.0412260	−	0.999150i	$-0.486874\pi$
$661$	2.11984	0.0824521	0.0412260	+	0.999150i	$0.486874\pi$
$662$	−28.2235	−1.09694
$663$	29.0790	1.12934
$664$	2.36375	0.0917313
$665$	5.41559	0.210007
$666$	−45.7593	−1.77314
$667$	48.4649	1.87657
$668$	−0.269910	−0.0104431
$669$	20.9054	0.808249
$670$	3.07549	0.118817
$671$	7.07567	0.273153
$672$	−1.83495	−0.0707848
$673$	8.62867	0.332611	0.166305	−	0.986074i	$-0.446816\pi$
$673$	8.62867	0.332611	0.166305	+	0.986074i	$0.446816\pi$
$674$	19.2662	0.742108
$675$	−6.52406	−0.251111
$676$	8.13238	0.312784
$677$	−27.1640	−1.04400	−0.521999	−	0.852946i	$-0.674814\pi$
$677$	−27.1640	−1.04400	−0.521999	+	0.852946i	$0.674814\pi$
$678$	−55.5126	−2.13195
$679$	−4.38576	−0.168310
$680$	2.19981	0.0843587
$681$	65.9188	2.52602
$682$	−2.58878	−0.0991294
$683$	5.82198	0.222772	0.111386	−	0.993777i	$-0.464471\pi$
$683$	5.82198	0.222772	0.111386	+	0.993777i	$0.464471\pi$
$684$	44.7151	1.70973
$685$	1.83433	0.0700861
$686$	−8.67385	−0.331169
$687$	49.8335	1.90127
$688$	1.00000	0.0381246
$689$	7.66748	0.292108
$690$	18.9700	0.722176
$691$	27.9562	1.06350	0.531752	−	0.846900i	$-0.321534\pi$
$691$	27.9562	1.06350	0.531752	+	0.846900i	$0.321534\pi$
$692$	0.646448	0.0245743
$693$	3.36213	0.127717
$694$	−28.1125	−1.06714
$695$	−19.0091	−0.721058
$696$	−21.1253	−0.800752
$697$	13.1462	0.497947
$698$	18.4755	0.699309
$699$	−47.4595	−1.79508
$700$	−0.638121	−0.0241187
$701$	−11.7301	−0.443040	−0.221520	−	0.975156i	$-0.571102\pi$
$701$	−11.7301	−0.443040	−0.221520	+	0.975156i	$0.571102\pi$
$702$	−29.9911	−1.13194
$703$	73.7072	2.77992
$704$	−1.00000	−0.0376889
$705$	−21.3721	−0.804920
$706$	−35.2433	−1.32640
$707$	2.22195	0.0835649
$708$	−26.1124	−0.981364
$709$	17.2242	0.646867	0.323434	−	0.946251i	$-0.395163\pi$
$709$	17.2242	0.646867	0.323434	+	0.946251i	$0.395163\pi$
$710$	−2.59759	−0.0974860
$711$	33.1569	1.24348
$712$	−3.41566	−0.128007
$713$	17.0781	0.639582
$714$	−4.03654	−0.151064
$715$	−4.59700	−0.171918
$716$	−9.33927	−0.349025
$717$	−57.1327	−2.13366
$718$	7.85867	0.293283
$719$	48.5029	1.80885	0.904426	−	0.426630i	$-0.140299\pi$
$719$	48.5029	1.80885	0.904426	+	0.426630i	$0.140299\pi$
$720$	−5.26880	−0.196357
$721$	1.52876	0.0569339
$722$	−53.0253	−1.97340
$723$	76.6990	2.85247
$724$	23.1945	0.862017
$725$	−7.34651	−0.272843
$726$	2.87555	0.106722
$727$	−27.2863	−1.01199	−0.505997	−	0.862535i	$-0.668875\pi$
$727$	−27.2863	−1.01199	−0.505997	+	0.862535i	$0.668875\pi$
$728$	−2.93344	−0.108721
$729$	−40.7175	−1.50805
$730$	−16.2362	−0.600927
$731$	2.19981	0.0813628
$732$	20.3465	0.752027
$733$	−25.3697	−0.937052	−0.468526	−	0.883450i	$-0.655215\pi$
$733$	−25.3697	−0.937052	−0.468526	+	0.883450i	$0.655215\pi$
$734$	−24.1696	−0.892115
$735$	−18.9579	−0.699274
$736$	6.59700	0.243169
$737$	−3.07549	−0.113287
$738$	−31.4867	−1.15904
$739$	30.1802	1.11019	0.555097	−	0.831785i	$-0.312681\pi$
$739$	30.1802	1.11019	0.555097	+	0.831785i	$0.312681\pi$
$740$	−8.68495	−0.319265
$741$	112.186	4.12125
$742$	−1.06434	−0.0390733
$743$	−7.83477	−0.287430	−0.143715	−	0.989619i	$-0.545905\pi$
$743$	−7.83477	−0.287430	−0.143715	+	0.989619i	$0.545905\pi$
$744$	−7.44416	−0.272916
$745$	5.64636	0.206867
$746$	−31.4941	−1.15308
$747$	−12.4541	−0.455673
$748$	−2.19981	−0.0804329
$749$	1.55949	0.0569827
$750$	−2.87555	−0.105000
$751$	19.6346	0.716477	0.358239	−	0.933630i	$-0.383377\pi$
$751$	19.6346	0.716477	0.358239	+	0.933630i	$0.383377\pi$
$752$	−7.43235	−0.271030
$753$	−12.3028	−0.448338
$754$	−33.7719	−1.22990
$755$	12.7081	0.462494
$756$	4.16314	0.151412
$757$	−5.29850	−0.192577	−0.0962886	−	0.995353i	$-0.530697\pi$
$757$	−5.29850	−0.192577	−0.0962886	+	0.995353i	$0.530697\pi$
$758$	−20.1041	−0.730215
$759$	−18.9700	−0.688568
$760$	8.48677	0.307848
$761$	11.2280	0.407013	0.203507	−	0.979074i	$-0.434766\pi$
$761$	11.2280	0.407013	0.203507	+	0.979074i	$0.434766\pi$
$762$	41.1844	1.49195
$763$	10.8521	0.392871
$764$	1.40312	0.0507631
$765$	−11.5903	−0.419050
$766$	−5.85924	−0.211703
$767$	−41.7445	−1.50731
$768$	−2.87555	−0.103763
$769$	−29.2911	−1.05626	−0.528132	−	0.849162i	$-0.677107\pi$
$769$	−29.2911	−1.05626	−0.528132	+	0.849162i	$0.677107\pi$
$770$	0.638121	0.0229963
$771$	−41.9787	−1.51183
$772$	−12.2988	−0.442644
$773$	−29.7669	−1.07064	−0.535321	−	0.844649i	$-0.679809\pi$
$773$	−29.7669	−1.07064	−0.535321	+	0.844649i	$0.679809\pi$
$774$	−5.26880	−0.189383
$775$	−2.58878	−0.0929916
$776$	−6.87292	−0.246724
$777$	15.9365	0.571717
$778$	−23.6324	−0.847261
$779$	50.7175	1.81714
$780$	−13.2189	−0.473313
$781$	2.59759	0.0929492
$782$	14.5121	0.518952
$783$	47.9291	1.71285
$784$	−6.59280	−0.235457
$785$	8.30966	0.296585
$786$	−58.4446	−2.08465
$787$	4.95817	0.176740	0.0883698	−	0.996088i	$-0.471834\pi$
$787$	4.95817	0.176740	0.0883698	+	0.996088i	$0.471834\pi$
$788$	11.3866	0.405630
$789$	−0.0926797	−0.00329948
$790$	6.29306	0.223897
$791$	12.3189	0.438011
$792$	5.26880	0.187219
$793$	32.5268	1.15506
$794$	0.614338	0.0218020
$795$	−4.79623	−0.170105
$796$	−0.348978	−0.0123692
$797$	16.1850	0.573303	0.286652	−	0.958035i	$-0.407458\pi$
$797$	16.1850	0.573303	0.286652	+	0.958035i	$0.407458\pi$
$798$	−15.5728	−0.551271
$799$	−16.3497	−0.578412
$800$	−1.00000	−0.0353553
$801$	17.9964	0.635873
$802$	14.0403	0.495779
$803$	16.2362	0.572962
$804$	−8.84375	−0.311895
$805$	−4.20968	−0.148372
$806$	−11.9006	−0.419181
$807$	1.13468	0.0399426
$808$	3.48201	0.122497
$809$	45.7892	1.60986	0.804931	−	0.593369i	$-0.202202\pi$
$809$	45.7892	1.60986	0.804931	+	0.593369i	$0.202202\pi$
$810$	2.95388	0.103789
$811$	−27.5186	−0.966307	−0.483154	−	0.875536i	$-0.660509\pi$
$811$	−27.5186	−0.966307	−0.483154	+	0.875536i	$0.660509\pi$
$812$	4.68797	0.164515
$813$	−82.0288	−2.87687
$814$	8.68495	0.304407
$815$	−1.36870	−0.0479436
$816$	−6.32566	−0.221442
$817$	8.48677	0.296915
$818$	−15.3070	−0.535198
$819$	15.4557	0.540067
$820$	−5.97606	−0.208693
$821$	−16.0882	−0.561483	−0.280742	−	0.959783i	$-0.590580\pi$
$821$	−16.0882	−0.561483	−0.280742	+	0.959783i	$0.590580\pi$
$822$	−5.27471	−0.183977
$823$	22.2062	0.774059	0.387029	−	0.922067i	$-0.373501\pi$
$823$	22.2062	0.774059	0.387029	+	0.922067i	$0.373501\pi$
$824$	2.39572	0.0834587
$825$	2.87555	0.100114
$826$	5.79467	0.201622
$827$	−40.2921	−1.40109	−0.700546	−	0.713607i	$-0.747060\pi$
$827$	−40.2921	−1.40109	−0.700546	+	0.713607i	$0.747060\pi$
$828$	−34.7583	−1.20793
$829$	0.540032	0.0187561	0.00937805	−	0.999956i	$-0.497015\pi$
$829$	0.540032	0.0187561	0.00937805	+	0.999956i	$0.497015\pi$
$830$	−2.36375	−0.0820469
$831$	−87.0172	−3.01859
$832$	−4.59700	−0.159372
$833$	−14.5029	−0.502495
$834$	54.6618	1.89278
$835$	0.269910	0.00934062
$836$	−8.48677	−0.293521
$837$	16.8893	0.583781
$838$	−8.77181	−0.303017
$839$	−49.6637	−1.71458	−0.857290	−	0.514833i	$-0.827854\pi$
$839$	−49.6637	−1.71458	−0.857290	+	0.514833i	$0.827854\pi$
$840$	1.83495	0.0633118
$841$	24.9713	0.861078
$842$	25.5129	0.879232
$843$	−44.5249	−1.53352
$844$	16.2045	0.557781
$845$	−8.13238	−0.279762
$846$	39.1596	1.34633
$847$	−0.638121	−0.0219261
$848$	−1.66793	−0.0572770
$849$	28.7958	0.988270
$850$	−2.19981	−0.0754527
$851$	−57.2946	−1.96403
$852$	7.46952	0.255901
$853$	−30.6175	−1.04832	−0.524162	−	0.851619i	$-0.675621\pi$
$853$	−30.6175	−1.04832	−0.524162	+	0.851619i	$0.675621\pi$
$854$	−4.51514	−0.154505
$855$	−44.7151	−1.52922
$856$	2.44388	0.0835302
$857$	−15.4649	−0.528271	−0.264136	−	0.964486i	$-0.585087\pi$
$857$	−15.4649	−0.528271	−0.264136	+	0.964486i	$0.585087\pi$
$858$	13.2189	0.451286
$859$	37.7982	1.28966	0.644830	−	0.764326i	$-0.276928\pi$
$859$	37.7982	1.28966	0.644830	+	0.764326i	$0.276928\pi$
$860$	−1.00000	−0.0340997
$861$	10.9658	0.373713
$862$	−26.6342	−0.907164
$863$	18.7929	0.639716	0.319858	−	0.947465i	$-0.396365\pi$
$863$	18.7929	0.639716	0.319858	+	0.947465i	$0.396365\pi$
$864$	6.52406	0.221953
$865$	−0.646448	−0.0219799
$866$	−23.1169	−0.785545
$867$	34.9692	1.18762
$868$	1.65195	0.0560709
$869$	−6.29306	−0.213477
$870$	21.1253	0.716214
$871$	−14.1380	−0.479049
$872$	17.0063	0.575905
$873$	36.2121	1.22559
$874$	55.9872	1.89380
$875$	0.638121	0.0215724
$876$	46.6879	1.57744
$877$	29.4637	0.994918	0.497459	−	0.867487i	$-0.334266\pi$
$877$	29.4637	0.994918	0.497459	+	0.867487i	$0.334266\pi$
$878$	6.45373	0.217803
$879$	−30.6651	−1.03431
$880$	1.00000	0.0337100
$881$	−26.4214	−0.890160	−0.445080	−	0.895491i	$-0.646825\pi$
$881$	−26.4214	−0.890160	−0.445080	+	0.895491i	$0.646825\pi$
$882$	34.7362	1.16963
$883$	48.0012	1.61537	0.807684	−	0.589615i	$-0.200721\pi$
$883$	48.0012	1.61537	0.807684	+	0.589615i	$0.200721\pi$
$884$	−10.1125	−0.340120
$885$	26.1124	0.877758
$886$	−20.2055	−0.678816
$887$	34.6035	1.16187	0.580937	−	0.813949i	$-0.302686\pi$
$887$	34.6035	1.16187	0.580937	+	0.813949i	$0.302686\pi$
$888$	24.9740	0.838074
$889$	−9.13933	−0.306523
$890$	3.41566	0.114493
$891$	−2.95388	−0.0989586
$892$	−7.27004	−0.243419
$893$	−63.0766	−2.11078
$894$	−16.2364	−0.543026
$895$	9.33927	0.312177
$896$	0.638121	0.0213181
$897$	−87.2051	−2.91169
$898$	8.99123	0.300041
$899$	19.0185	0.634302
$900$	5.26880	0.175627
$901$	−3.66913	−0.122236
$902$	5.97606	0.198981
$903$	1.83495	0.0610633
$904$	19.3050	0.642075
$905$	−23.1945	−0.771012
$906$	−36.5427	−1.21405
$907$	−45.9937	−1.52719	−0.763597	−	0.645693i	$-0.776569\pi$
$907$	−45.9937	−1.52719	−0.763597	+	0.645693i	$0.776569\pi$
$908$	−22.9239	−0.760756
$909$	−18.3460	−0.608500
$910$	2.93344	0.0972426
$911$	20.1996	0.669242	0.334621	−	0.942353i	$-0.391392\pi$
$911$	20.1996	0.669242	0.334621	+	0.942353i	$0.391392\pi$
$912$	−24.4042	−0.808102
$913$	2.36375	0.0782287
$914$	4.97783	0.164652
$915$	−20.3465	−0.672633
$916$	−17.3301	−0.572602
$917$	12.9696	0.428294
$918$	14.3517	0.473676
$919$	8.01951	0.264539	0.132270	−	0.991214i	$-0.457774\pi$
$919$	8.01951	0.264539	0.132270	+	0.991214i	$0.457774\pi$
$920$	−6.59700	−0.217497
$921$	−43.6842	−1.43944
$922$	4.25819	0.140236
$923$	11.9411	0.393047
$924$	−1.83495	−0.0603655
$925$	8.68495	0.285560
$926$	1.78970	0.0588131
$927$	−12.6226	−0.414579
$928$	7.34651	0.241161
$929$	−3.02292	−0.0991789	−0.0495894	−	0.998770i	$-0.515791\pi$
$929$	−3.02292	−0.0991789	−0.0495894	+	0.998770i	$0.515791\pi$
$930$	7.44416	0.244104
$931$	−55.9516	−1.83374
$932$	16.5045	0.540622
$933$	61.2869	2.00644
$934$	−4.04228	−0.132268
$935$	2.19981	0.0719413
$936$	24.2207	0.791677
$937$	−9.41462	−0.307562	−0.153781	−	0.988105i	$-0.549145\pi$
$937$	−9.41462	−0.307562	−0.153781	+	0.988105i	$0.549145\pi$
$938$	1.96254	0.0640791
$939$	−11.4129	−0.372447
$940$	7.43235	0.242417
$941$	49.3505	1.60878	0.804390	−	0.594101i	$-0.202492\pi$
$941$	49.3505	1.60878	0.804390	+	0.594101i	$0.202492\pi$
$942$	−23.8949	−0.778537
$943$	−39.4241	−1.28382
$944$	9.08082	0.295556
$945$	−4.16314	−0.135427
$946$	1.00000	0.0325128
$947$	−22.6328	−0.735466	−0.367733	−	0.929931i	$-0.619866\pi$
$947$	−22.6328	−0.735466	−0.367733	+	0.929931i	$0.619866\pi$
$948$	−18.0960	−0.587731
$949$	74.6376	2.42284
$950$	−8.48677	−0.275347
$951$	−4.79986	−0.155646
$952$	1.40374	0.0454956
$953$	28.2361	0.914656	0.457328	−	0.889298i	$-0.348807\pi$
$953$	28.2361	0.914656	0.457328	+	0.889298i	$0.348807\pi$
$954$	8.78801	0.284522
$955$	−1.40312	−0.0454039
$956$	19.8684	0.642591
$957$	−21.1253	−0.682884
$958$	0.426479	0.0137789
$959$	1.17052	0.0377982
$960$	2.87555	0.0928081
$961$	−24.2982	−0.783814
$962$	39.9247	1.28722
$963$	−12.8763	−0.414934
$964$	−26.6728	−0.859072
$965$	12.2988	0.395912
$966$	12.1052	0.389477
$967$	−12.8001	−0.411625	−0.205812	−	0.978591i	$-0.565984\pi$
$967$	−12.8001	−0.411625	−0.205812	+	0.978591i	$0.565984\pi$
$968$	−1.00000	−0.0321412
$969$	−53.6844	−1.72459
$970$	6.87292	0.220676
$971$	41.1070	1.31919	0.659593	−	0.751623i	$-0.270729\pi$
$971$	41.1070	1.31919	0.659593	+	0.751623i	$0.270729\pi$
$972$	11.0782	0.355332
$973$	−12.1301	−0.388874
$974$	11.7826	0.377538
$975$	13.2189	0.423344
$976$	−7.07567	−0.226487
$977$	25.6163	0.819538	0.409769	−	0.912189i	$-0.365609\pi$
$977$	25.6163	0.819538	0.409769	+	0.912189i	$0.365609\pi$
$978$	3.93578	0.125852
$979$	−3.41566	−0.109165
$980$	6.59280	0.210599
$981$	−89.6027	−2.86080
$982$	−20.4651	−0.653067
$983$	−18.1604	−0.579227	−0.289614	−	0.957144i	$-0.593527\pi$
$983$	−18.1604	−0.579227	−0.289614	+	0.957144i	$0.593527\pi$
$984$	17.1845	0.547821
$985$	−11.3866	−0.362807
$986$	16.1609	0.514668
$987$	−13.6380	−0.434102
$988$	−39.0137	−1.24119
$989$	−6.59700	−0.209772
$990$	−5.26880	−0.167454
$991$	−37.9311	−1.20492	−0.602461	−	0.798148i	$-0.705813\pi$
$991$	−37.9311	−1.20492	−0.602461	+	0.798148i	$0.705813\pi$
$992$	2.58878	0.0821937
$993$	−81.1582	−2.57548
$994$	−1.65758	−0.0525752
$995$	0.348978	0.0110633
$996$	6.79709	0.215374
$997$	14.8104	0.469051	0.234526	−	0.972110i	$-0.424646\pi$
$997$	14.8104	0.469051	0.234526	+	0.972110i	$0.424646\pi$
$998$	−31.3220	−0.991482
$999$	−56.6612	−1.79268

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.87555 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.87555 q^{6} -0.638121 q^{7} -1.00000 q^{8} +5.26880 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.87555 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.87555 q^{6} -0.638121 q^{7} -1.00000 q^{8} +5.26880 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.87555 q^{12} -4.59700 q^{13} +0.638121 q^{14} +2.87555 q^{15} +1.00000 q^{16} +2.19981 q^{17} -5.26880 q^{18} +8.48677 q^{19} -1.00000 q^{20} +1.83495 q^{21} +1.00000 q^{22} -6.59700 q^{23} +2.87555 q^{24} +1.00000 q^{25} +4.59700 q^{26} -6.52406 q^{27} -0.638121 q^{28} -7.34651 q^{29} -2.87555 q^{30} -2.58878 q^{31} -1.00000 q^{32} +2.87555 q^{33} -2.19981 q^{34} +0.638121 q^{35} +5.26880 q^{36} +8.68495 q^{37} -8.48677 q^{38} +13.2189 q^{39} +1.00000 q^{40} +5.97606 q^{41} -1.83495 q^{42} +1.00000 q^{43} -1.00000 q^{44} -5.26880 q^{45} +6.59700 q^{46} -7.43235 q^{47} -2.87555 q^{48} -6.59280 q^{49} -1.00000 q^{50} -6.32566 q^{51} -4.59700 q^{52} -1.66793 q^{53} +6.52406 q^{54} +1.00000 q^{55} +0.638121 q^{56} -24.4042 q^{57} +7.34651 q^{58} +9.08082 q^{59} +2.87555 q^{60} -7.07567 q^{61} +2.58878 q^{62} -3.36213 q^{63} +1.00000 q^{64} +4.59700 q^{65} -2.87555 q^{66} +3.07549 q^{67} +2.19981 q^{68} +18.9700 q^{69} -0.638121 q^{70} -2.59759 q^{71} -5.26880 q^{72} -16.2362 q^{73} -8.68495 q^{74} -2.87555 q^{75} +8.48677 q^{76} +0.638121 q^{77} -13.2189 q^{78} +6.29306 q^{79} -1.00000 q^{80} +2.95388 q^{81} -5.97606 q^{82} -2.36375 q^{83} +1.83495 q^{84} -2.19981 q^{85} -1.00000 q^{86} +21.1253 q^{87} +1.00000 q^{88} +3.41566 q^{89} +5.26880 q^{90} +2.93344 q^{91} -6.59700 q^{92} +7.44416 q^{93} +7.43235 q^{94} -8.48677 q^{95} +2.87555 q^{96} +6.87292 q^{97} +6.59280 q^{98} -5.26880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 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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