LMFDB - Embedded newform 4730.2.a.z.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.10
Root			$-2.42851$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.42851 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42851 q^{6} -0.184466 q^{7} -1.00000 q^{8} +8.75468 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.42851 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42851 q^{6} -0.184466 q^{7} -1.00000 q^{8} +8.75468 q^{9} -1.00000 q^{10} +1.00000 q^{11} +3.42851 q^{12} -1.86739 q^{13} +0.184466 q^{14} +3.42851 q^{15} +1.00000 q^{16} +1.38300 q^{17} -8.75468 q^{18} +2.95225 q^{19} +1.00000 q^{20} -0.632445 q^{21} -1.00000 q^{22} +4.77865 q^{23} -3.42851 q^{24} +1.00000 q^{25} +1.86739 q^{26} +19.7300 q^{27} -0.184466 q^{28} -2.99075 q^{29} -3.42851 q^{30} +10.5154 q^{31} -1.00000 q^{32} +3.42851 q^{33} -1.38300 q^{34} -0.184466 q^{35} +8.75468 q^{36} -8.37690 q^{37} -2.95225 q^{38} -6.40237 q^{39} -1.00000 q^{40} -4.20340 q^{41} +0.632445 q^{42} +1.00000 q^{43} +1.00000 q^{44} +8.75468 q^{45} -4.77865 q^{46} -8.11982 q^{47} +3.42851 q^{48} -6.96597 q^{49} -1.00000 q^{50} +4.74164 q^{51} -1.86739 q^{52} +8.47957 q^{53} -19.7300 q^{54} +1.00000 q^{55} +0.184466 q^{56} +10.1218 q^{57} +2.99075 q^{58} +0.668546 q^{59} +3.42851 q^{60} -1.18222 q^{61} -10.5154 q^{62} -1.61495 q^{63} +1.00000 q^{64} -1.86739 q^{65} -3.42851 q^{66} -7.72801 q^{67} +1.38300 q^{68} +16.3837 q^{69} +0.184466 q^{70} -13.0883 q^{71} -8.75468 q^{72} +13.7339 q^{73} +8.37690 q^{74} +3.42851 q^{75} +2.95225 q^{76} -0.184466 q^{77} +6.40237 q^{78} -17.0422 q^{79} +1.00000 q^{80} +41.3804 q^{81} +4.20340 q^{82} +9.61476 q^{83} -0.632445 q^{84} +1.38300 q^{85} -1.00000 q^{86} -10.2538 q^{87} -1.00000 q^{88} +9.80120 q^{89} -8.75468 q^{90} +0.344471 q^{91} +4.77865 q^{92} +36.0520 q^{93} +8.11982 q^{94} +2.95225 q^{95} -3.42851 q^{96} +10.6985 q^{97} +6.96597 q^{98} +8.75468 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.42851	1.97945	0.989726	−	0.142979i	$-0.0456681\pi$
$3$	3.42851	1.97945	0.989726	+	0.142979i	$0.0456681\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.42851	−1.39968
$7$	−0.184466	−0.0697218	−0.0348609	−	0.999392i	$-0.511099\pi$
$7$	−0.184466	−0.0697218	−0.0348609	+	0.999392i	$0.511099\pi$
$8$	−1.00000	−0.353553
$9$	8.75468	2.91823
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.42851	0.989726
$13$	−1.86739	−0.517921	−0.258960	−	0.965888i	$-0.583380\pi$
$13$	−1.86739	−0.517921	−0.258960	+	0.965888i	$0.583380\pi$
$14$	0.184466	0.0493007
$15$	3.42851	0.885238
$16$	1.00000	0.250000
$17$	1.38300	0.335427	0.167714	−	0.985836i	$-0.446362\pi$
$17$	1.38300	0.335427	0.167714	+	0.985836i	$0.446362\pi$
$18$	−8.75468	−2.06350
$19$	2.95225	0.677293	0.338647	−	0.940914i	$-0.390031\pi$
$19$	2.95225	0.677293	0.338647	+	0.940914i	$0.390031\pi$
$20$	1.00000	0.223607
$21$	−0.632445	−0.138011
$22$	−1.00000	−0.213201
$23$	4.77865	0.996418	0.498209	−	0.867057i	$-0.333991\pi$
$23$	4.77865	0.996418	0.498209	+	0.867057i	$0.333991\pi$
$24$	−3.42851	−0.699842
$25$	1.00000	0.200000
$26$	1.86739	0.366225
$27$	19.7300	3.79704
$28$	−0.184466	−0.0348609
$29$	−2.99075	−0.555369	−0.277684	−	0.960672i	$-0.589567\pi$
$29$	−2.99075	−0.555369	−0.277684	+	0.960672i	$0.589567\pi$
$30$	−3.42851	−0.625958
$31$	10.5154	1.88861	0.944307	−	0.329065i	$-0.106734\pi$
$31$	10.5154	1.88861	0.944307	+	0.329065i	$0.106734\pi$
$32$	−1.00000	−0.176777
$33$	3.42851	0.596827
$34$	−1.38300	−0.237183
$35$	−0.184466	−0.0311805
$36$	8.75468	1.45911
$37$	−8.37690	−1.37715	−0.688577	−	0.725163i	$-0.741764\pi$
$37$	−8.37690	−1.37715	−0.688577	+	0.725163i	$0.741764\pi$
$38$	−2.95225	−0.478919
$39$	−6.40237	−1.02520
$40$	−1.00000	−0.158114
$41$	−4.20340	−0.656461	−0.328231	−	0.944598i	$-0.606452\pi$
$41$	−4.20340	−0.656461	−0.328231	+	0.944598i	$0.606452\pi$
$42$	0.632445	0.0975884
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	8.75468	1.30507
$46$	−4.77865	−0.704574
$47$	−8.11982	−1.18440	−0.592198	−	0.805792i	$-0.701740\pi$
$47$	−8.11982	−1.18440	−0.592198	+	0.805792i	$0.701740\pi$
$48$	3.42851	0.494863
$49$	−6.96597	−0.995139
$50$	−1.00000	−0.141421
$51$	4.74164	0.663962
$52$	−1.86739	−0.258960
$53$	8.47957	1.16476	0.582380	−	0.812917i	$-0.302122\pi$
$53$	8.47957	1.16476	0.582380	+	0.812917i	$0.302122\pi$
$54$	−19.7300	−2.68491
$55$	1.00000	0.134840
$56$	0.184466	0.0246504
$57$	10.1218	1.34067
$58$	2.99075	0.392705
$59$	0.668546	0.0870373	0.0435187	−	0.999053i	$-0.486143\pi$
$59$	0.668546	0.0870373	0.0435187	+	0.999053i	$0.486143\pi$
$60$	3.42851	0.442619
$61$	−1.18222	−0.151368	−0.0756840	−	0.997132i	$-0.524114\pi$
$61$	−1.18222	−0.151368	−0.0756840	+	0.997132i	$0.524114\pi$
$62$	−10.5154	−1.33545
$63$	−1.61495	−0.203464
$64$	1.00000	0.125000
$65$	−1.86739	−0.231621
$66$	−3.42851	−0.422020
$67$	−7.72801	−0.944127	−0.472063	−	0.881565i	$-0.656491\pi$
$67$	−7.72801	−0.944127	−0.472063	+	0.881565i	$0.656491\pi$
$68$	1.38300	0.167714
$69$	16.3837	1.97236
$70$	0.184466	0.0220480
$71$	−13.0883	−1.55329	−0.776646	−	0.629937i	$-0.783081\pi$
$71$	−13.0883	−1.55329	−0.776646	+	0.629937i	$0.783081\pi$
$72$	−8.75468	−1.03175
$73$	13.7339	1.60743	0.803713	−	0.595017i	$-0.202855\pi$
$73$	13.7339	1.60743	0.803713	+	0.595017i	$0.202855\pi$
$74$	8.37690	0.973795
$75$	3.42851	0.395890
$76$	2.95225	0.338647
$77$	−0.184466	−0.0210219
$78$	6.40237	0.724925
$79$	−17.0422	−1.91740	−0.958698	−	0.284425i	$-0.908197\pi$
$79$	−17.0422	−1.91740	−0.958698	+	0.284425i	$0.908197\pi$
$80$	1.00000	0.111803
$81$	41.3804	4.59783
$82$	4.20340	0.464188
$83$	9.61476	1.05536	0.527679	−	0.849444i	$-0.323063\pi$
$83$	9.61476	1.05536	0.527679	+	0.849444i	$0.323063\pi$
$84$	−0.632445	−0.0690054
$85$	1.38300	0.150008
$86$	−1.00000	−0.107833
$87$	−10.2538	−1.09933
$88$	−1.00000	−0.106600
$89$	9.80120	1.03892	0.519462	−	0.854493i	$-0.326132\pi$
$89$	9.80120	1.03892	0.519462	+	0.854493i	$0.326132\pi$
$90$	−8.75468	−0.922825
$91$	0.344471	0.0361104
$92$	4.77865	0.498209
$93$	36.0520	3.73842
$94$	8.11982	0.837495
$95$	2.95225	0.302895
$96$	−3.42851	−0.349921
$97$	10.6985	1.08627	0.543137	−	0.839644i	$-0.317237\pi$
$97$	10.6985	1.08627	0.543137	+	0.839644i	$0.317237\pi$
$98$	6.96597	0.703669
$99$	8.75468	0.879879
$100$	1.00000	0.100000
$101$	−11.2581	−1.12022	−0.560109	−	0.828419i	$-0.689241\pi$
$101$	−11.2581	−1.12022	−0.560109	+	0.828419i	$0.689241\pi$
$102$	−4.74164	−0.469492
$103$	−10.9672	−1.08063	−0.540313	−	0.841464i	$-0.681694\pi$
$103$	−10.9672	−1.08063	−0.540313	+	0.841464i	$0.681694\pi$
$104$	1.86739	0.183113
$105$	−0.632445	−0.0617203
$106$	−8.47957	−0.823609
$107$	−13.3494	−1.29053	−0.645267	−	0.763958i	$-0.723254\pi$
$107$	−13.3494	−1.29053	−0.645267	+	0.763958i	$0.723254\pi$
$108$	19.7300	1.89852
$109$	−11.5308	−1.10445	−0.552226	−	0.833694i	$-0.686222\pi$
$109$	−11.5308	−1.10445	−0.552226	+	0.833694i	$0.686222\pi$
$110$	−1.00000	−0.0953463
$111$	−28.7203	−2.72601
$112$	−0.184466	−0.0174304
$113$	2.29281	0.215689	0.107845	−	0.994168i	$-0.465605\pi$
$113$	2.29281	0.215689	0.107845	+	0.994168i	$0.465605\pi$
$114$	−10.1218	−0.947996
$115$	4.77865	0.445612
$116$	−2.99075	−0.277684
$117$	−16.3484	−1.51141
$118$	−0.668546	−0.0615447
$119$	−0.255117	−0.0233866
$120$	−3.42851	−0.312979
$121$	1.00000	0.0909091
$122$	1.18222	0.107033
$123$	−14.4114	−1.29943
$124$	10.5154	0.944307
$125$	1.00000	0.0894427
$126$	1.61495	0.143871
$127$	10.6919	0.948752	0.474376	−	0.880322i	$-0.342674\pi$
$127$	10.6919	0.948752	0.474376	+	0.880322i	$0.342674\pi$
$128$	−1.00000	−0.0883883
$129$	3.42851	0.301864
$130$	1.86739	0.163781
$131$	−17.2083	−1.50349	−0.751746	−	0.659453i	$-0.770788\pi$
$131$	−17.2083	−1.50349	−0.751746	+	0.659453i	$0.770788\pi$
$132$	3.42851	0.298414
$133$	−0.544592	−0.0472221
$134$	7.72801	0.667598
$135$	19.7300	1.69809
$136$	−1.38300	−0.118591
$137$	3.49548	0.298639	0.149320	−	0.988789i	$-0.452292\pi$
$137$	3.49548	0.298639	0.149320	+	0.988789i	$0.452292\pi$
$138$	−16.3837	−1.39467
$139$	4.60638	0.390708	0.195354	−	0.980733i	$-0.437414\pi$
$139$	4.60638	0.390708	0.195354	+	0.980733i	$0.437414\pi$
$140$	−0.184466	−0.0155903
$141$	−27.8389	−2.34446
$142$	13.0883	1.09834
$143$	−1.86739	−0.156159
$144$	8.75468	0.729557
$145$	−2.99075	−0.248368
$146$	−13.7339	−1.13662
$147$	−23.8829	−1.96983
$148$	−8.37690	−0.688577
$149$	11.1739	0.915405	0.457702	−	0.889105i	$-0.348673\pi$
$149$	11.1739	0.915405	0.457702	+	0.889105i	$0.348673\pi$
$150$	−3.42851	−0.279937
$151$	21.3949	1.74109	0.870546	−	0.492087i	$-0.163766\pi$
$151$	21.3949	1.74109	0.870546	+	0.492087i	$0.163766\pi$
$152$	−2.95225	−0.239459
$153$	12.1077	0.978853
$154$	0.184466	0.0148647
$155$	10.5154	0.844614
$156$	−6.40237	−0.512600
$157$	1.88759	0.150646	0.0753232	−	0.997159i	$-0.476001\pi$
$157$	1.88759	0.150646	0.0753232	+	0.997159i	$0.476001\pi$
$158$	17.0422	1.35580
$159$	29.0723	2.30558
$160$	−1.00000	−0.0790569
$161$	−0.881502	−0.0694721
$162$	−41.3804	−3.25115
$163$	8.28406	0.648858	0.324429	−	0.945910i	$-0.394828\pi$
$163$	8.28406	0.648858	0.324429	+	0.945910i	$0.394828\pi$
$164$	−4.20340	−0.328231
$165$	3.42851	0.266909
$166$	−9.61476	−0.746250
$167$	14.6096	1.13052	0.565261	−	0.824912i	$-0.308776\pi$
$167$	14.6096	1.13052	0.565261	+	0.824912i	$0.308776\pi$
$168$	0.632445	0.0487942
$169$	−9.51285	−0.731758
$170$	−1.38300	−0.106071
$171$	25.8460	1.97650
$172$	1.00000	0.0762493
$173$	17.7273	1.34779	0.673893	−	0.738829i	$-0.264621\pi$
$173$	17.7273	1.34779	0.673893	+	0.738829i	$0.264621\pi$
$174$	10.2538	0.777340
$175$	−0.184466	−0.0139444
$176$	1.00000	0.0753778
$177$	2.29212	0.172286
$178$	−9.80120	−0.734631
$179$	8.47601	0.633526	0.316763	−	0.948505i	$-0.397404\pi$
$179$	8.47601	0.633526	0.316763	+	0.948505i	$0.397404\pi$
$180$	8.75468	0.652536
$181$	13.9575	1.03746	0.518728	−	0.854940i	$-0.326406\pi$
$181$	13.9575	1.03746	0.518728	+	0.854940i	$0.326406\pi$
$182$	−0.344471	−0.0255339
$183$	−4.05326	−0.299626
$184$	−4.77865	−0.352287
$185$	−8.37690	−0.615882
$186$	−36.0520	−2.64346
$187$	1.38300	0.101135
$188$	−8.11982	−0.592198
$189$	−3.63952	−0.264736
$190$	−2.95225	−0.214179
$191$	−4.20514	−0.304273	−0.152137	−	0.988359i	$-0.548615\pi$
$191$	−4.20514	−0.304273	−0.152137	+	0.988359i	$0.548615\pi$
$192$	3.42851	0.247431
$193$	4.54871	0.327423	0.163711	−	0.986508i	$-0.447653\pi$
$193$	4.54871	0.327423	0.163711	+	0.986508i	$0.447653\pi$
$194$	−10.6985	−0.768111
$195$	−6.40237	−0.458483
$196$	−6.96597	−0.497569
$197$	6.70590	0.477776	0.238888	−	0.971047i	$-0.423217\pi$
$197$	6.70590	0.477776	0.238888	+	0.971047i	$0.423217\pi$
$198$	−8.75468	−0.622168
$199$	−4.34710	−0.308158	−0.154079	−	0.988059i	$-0.549241\pi$
$199$	−4.34710	−0.308158	−0.154079	+	0.988059i	$0.549241\pi$
$200$	−1.00000	−0.0707107
$201$	−26.4956	−1.86885
$202$	11.2581	0.792114
$203$	0.551693	0.0387213
$204$	4.74164	0.331981
$205$	−4.20340	−0.293578
$206$	10.9672	0.764118
$207$	41.8356	2.90778
$208$	−1.86739	−0.129480
$209$	2.95225	0.204212
$210$	0.632445	0.0436429
$211$	−17.4496	−1.20128	−0.600639	−	0.799520i	$-0.705087\pi$
$211$	−17.4496	−1.20128	−0.600639	+	0.799520i	$0.705087\pi$
$212$	8.47957	0.582380
$213$	−44.8733	−3.07467
$214$	13.3494	0.912545
$215$	1.00000	0.0681994
$216$	−19.7300	−1.34246
$217$	−1.93973	−0.131678
$218$	11.5308	0.780966
$219$	47.0867	3.18182
$220$	1.00000	0.0674200
$221$	−2.58260	−0.173725
$222$	28.7203	1.92758
$223$	9.03133	0.604783	0.302391	−	0.953184i	$-0.402215\pi$
$223$	9.03133	0.604783	0.302391	+	0.953184i	$0.402215\pi$
$224$	0.184466	0.0123252
$225$	8.75468	0.583646
$226$	−2.29281	−0.152515
$227$	6.69594	0.444425	0.222213	−	0.974998i	$-0.428672\pi$
$227$	6.69594	0.444425	0.222213	+	0.974998i	$0.428672\pi$
$228$	10.1218	0.670335
$229$	14.1110	0.932483	0.466242	−	0.884657i	$-0.345608\pi$
$229$	14.1110	0.932483	0.466242	+	0.884657i	$0.345608\pi$
$230$	−4.77865	−0.315095
$231$	−0.632445	−0.0416118
$232$	2.99075	0.196352
$233$	−10.6897	−0.700303	−0.350152	−	0.936693i	$-0.613870\pi$
$233$	−10.6897	−0.700303	−0.350152	+	0.936693i	$0.613870\pi$
$234$	16.3484	1.06873
$235$	−8.11982	−0.529678
$236$	0.668546	0.0435187
$237$	−58.4293	−3.79539
$238$	0.255117	0.0165368
$239$	−18.7181	−1.21077	−0.605387	−	0.795931i	$-0.706982\pi$
$239$	−18.7181	−1.21077	−0.605387	+	0.795931i	$0.706982\pi$
$240$	3.42851	0.221309
$241$	13.0392	0.839929	0.419965	−	0.907540i	$-0.362042\pi$
$241$	13.0392	0.839929	0.419965	+	0.907540i	$0.362042\pi$
$242$	−1.00000	−0.0642824
$243$	82.6833	5.30414
$244$	−1.18222	−0.0756840
$245$	−6.96597	−0.445040
$246$	14.4114	0.918838
$247$	−5.51301	−0.350784
$248$	−10.5154	−0.667726
$249$	32.9643	2.08903
$250$	−1.00000	−0.0632456
$251$	−3.25282	−0.205316	−0.102658	−	0.994717i	$-0.532735\pi$
$251$	−3.25282	−0.205316	−0.102658	+	0.994717i	$0.532735\pi$
$252$	−1.61495	−0.101732
$253$	4.77865	0.300431
$254$	−10.6919	−0.670869
$255$	4.74164	0.296933
$256$	1.00000	0.0625000
$257$	−2.88382	−0.179888	−0.0899439	−	0.995947i	$-0.528669\pi$
$257$	−2.88382	−0.179888	−0.0899439	+	0.995947i	$0.528669\pi$
$258$	−3.42851	−0.213450
$259$	1.54526	0.0960176
$260$	−1.86739	−0.115811
$261$	−26.1831	−1.62069
$262$	17.2083	1.06313
$263$	−27.2673	−1.68138	−0.840688	−	0.541520i	$-0.817849\pi$
$263$	−27.2673	−1.68138	−0.840688	+	0.541520i	$0.817849\pi$
$264$	−3.42851	−0.211010
$265$	8.47957	0.520896
$266$	0.544592	0.0333911
$267$	33.6035	2.05650
$268$	−7.72801	−0.472063
$269$	−24.3978	−1.48756	−0.743779	−	0.668426i	$-0.766968\pi$
$269$	−24.3978	−1.48756	−0.743779	+	0.668426i	$0.766968\pi$
$270$	−19.7300	−1.20073
$271$	−5.30420	−0.322207	−0.161104	−	0.986937i	$-0.551505\pi$
$271$	−5.30420	−0.322207	−0.161104	+	0.986937i	$0.551505\pi$
$272$	1.38300	0.0838568
$273$	1.18102	0.0714787
$274$	−3.49548	−0.211170
$275$	1.00000	0.0603023
$276$	16.3837	0.986181
$277$	−11.8561	−0.712364	−0.356182	−	0.934417i	$-0.615922\pi$
$277$	−11.8561	−0.712364	−0.356182	+	0.934417i	$0.615922\pi$
$278$	−4.60638	−0.276272
$279$	92.0586	5.51141
$280$	0.184466	0.0110240
$281$	17.2792	1.03079	0.515396	−	0.856952i	$-0.327645\pi$
$281$	17.2792	1.03079	0.515396	+	0.856952i	$0.327645\pi$
$282$	27.8389	1.65778
$283$	−6.28973	−0.373886	−0.186943	−	0.982371i	$-0.559858\pi$
$283$	−6.28973	−0.373886	−0.186943	+	0.982371i	$0.559858\pi$
$284$	−13.0883	−0.776646
$285$	10.1218	0.599566
$286$	1.86739	0.110421
$287$	0.775387	0.0457696
$288$	−8.75468	−0.515875
$289$	−15.0873	−0.887489
$290$	2.99075	0.175623
$291$	36.6801	2.15022
$292$	13.7339	0.803713
$293$	12.3915	0.723916	0.361958	−	0.932194i	$-0.382108\pi$
$293$	12.3915	0.723916	0.361958	+	0.932194i	$0.382108\pi$
$294$	23.8829	1.39288
$295$	0.668546	0.0389243
$296$	8.37690	0.486897
$297$	19.7300	1.14485
$298$	−11.1739	−0.647289
$299$	−8.92361	−0.516066
$300$	3.42851	0.197945
$301$	−0.184466	−0.0106325
$302$	−21.3949	−1.23114
$303$	−38.5984	−2.21742
$304$	2.95225	0.169323
$305$	−1.18222	−0.0676938
$306$	−12.1077	−0.692154
$307$	−20.3927	−1.16387	−0.581936	−	0.813234i	$-0.697705\pi$
$307$	−20.3927	−1.16387	−0.581936	+	0.813234i	$0.697705\pi$
$308$	−0.184466	−0.0105110
$309$	−37.6010	−2.13905
$310$	−10.5154	−0.597232
$311$	−7.49923	−0.425243	−0.212621	−	0.977135i	$-0.568200\pi$
$311$	−7.49923	−0.425243	−0.212621	+	0.977135i	$0.568200\pi$
$312$	6.40237	0.362463
$313$	7.80151	0.440967	0.220484	−	0.975391i	$-0.429236\pi$
$313$	7.80151	0.440967	0.220484	+	0.975391i	$0.429236\pi$
$314$	−1.88759	−0.106523
$315$	−1.61495	−0.0909919
$316$	−17.0422	−0.958698
$317$	7.28303	0.409056	0.204528	−	0.978861i	$-0.434434\pi$
$317$	7.28303	0.409056	0.204528	+	0.978861i	$0.434434\pi$
$318$	−29.0723	−1.63029
$319$	−2.99075	−0.167450
$320$	1.00000	0.0559017
$321$	−45.7685	−2.55455
$322$	0.881502	0.0491242
$323$	4.08297	0.227183
$324$	41.3804	2.29891
$325$	−1.86739	−0.103584
$326$	−8.28406	−0.458812
$327$	−39.5336	−2.18621
$328$	4.20340	0.232094
$329$	1.49783	0.0825782
$330$	−3.42851	−0.188733
$331$	6.13299	0.337100	0.168550	−	0.985693i	$-0.446092\pi$
$331$	6.13299	0.337100	0.168550	+	0.985693i	$0.446092\pi$
$332$	9.61476	0.527679
$333$	−73.3371	−4.01885
$334$	−14.6096	−0.799399
$335$	−7.72801	−0.422226
$336$	−0.632445	−0.0345027
$337$	−18.2108	−0.992004	−0.496002	−	0.868321i	$-0.665199\pi$
$337$	−18.2108	−0.992004	−0.496002	+	0.868321i	$0.665199\pi$
$338$	9.51285	0.517431
$339$	7.86092	0.426947
$340$	1.38300	0.0750038
$341$	10.5154	0.569439
$342$	−25.8460	−1.39759
$343$	2.57625	0.139105
$344$	−1.00000	−0.0539164
$345$	16.3837	0.882067
$346$	−17.7273	−0.953028
$347$	−5.17920	−0.278034	−0.139017	−	0.990290i	$-0.544394\pi$
$347$	−5.17920	−0.278034	−0.139017	+	0.990290i	$0.544394\pi$
$348$	−10.2538	−0.549663
$349$	9.30012	0.497824	0.248912	−	0.968526i	$-0.419927\pi$
$349$	9.30012	0.497824	0.248912	+	0.968526i	$0.419927\pi$
$350$	0.184466	0.00986015
$351$	−36.8436	−1.96657
$352$	−1.00000	−0.0533002
$353$	−0.645416	−0.0343520	−0.0171760	−	0.999852i	$-0.505468\pi$
$353$	−0.645416	−0.0343520	−0.0171760	+	0.999852i	$0.505468\pi$
$354$	−2.29212	−0.121825
$355$	−13.0883	−0.694654
$356$	9.80120	0.519462
$357$	−0.874673	−0.0462926
$358$	−8.47601	−0.447971
$359$	26.5913	1.40344	0.701718	−	0.712455i	$-0.252417\pi$
$359$	26.5913	1.40344	0.701718	+	0.712455i	$0.252417\pi$
$360$	−8.75468	−0.461412
$361$	−10.2842	−0.541274
$362$	−13.9575	−0.733592
$363$	3.42851	0.179950
$364$	0.344471	0.0180552
$365$	13.7339	0.718863
$366$	4.05326	0.211867
$367$	−14.7740	−0.771196	−0.385598	−	0.922667i	$-0.626005\pi$
$367$	−14.7740	−0.771196	−0.385598	+	0.922667i	$0.626005\pi$
$368$	4.77865	0.249105
$369$	−36.7995	−1.91570
$370$	8.37690	0.435494
$371$	−1.56420	−0.0812091
$372$	36.0520	1.86921
$373$	−15.2156	−0.787833	−0.393916	−	0.919146i	$-0.628880\pi$
$373$	−15.2156	−0.787833	−0.393916	+	0.919146i	$0.628880\pi$
$374$	−1.38300	−0.0715133
$375$	3.42851	0.177048
$376$	8.11982	0.418747
$377$	5.58490	0.287637
$378$	3.63952	0.187197
$379$	28.3159	1.45449	0.727244	−	0.686379i	$-0.240801\pi$
$379$	28.3159	1.45449	0.727244	+	0.686379i	$0.240801\pi$
$380$	2.95225	0.151447
$381$	36.6573	1.87801
$382$	4.20514	0.215154
$383$	−32.8852	−1.68035	−0.840177	−	0.542313i	$-0.817549\pi$
$383$	−32.8852	−1.68035	−0.840177	+	0.542313i	$0.817549\pi$
$384$	−3.42851	−0.174960
$385$	−0.184466	−0.00940128
$386$	−4.54871	−0.231523
$387$	8.75468	0.445026
$388$	10.6985	0.543137
$389$	−14.7176	−0.746212	−0.373106	−	0.927789i	$-0.621707\pi$
$389$	−14.7176	−0.746212	−0.373106	+	0.927789i	$0.621707\pi$
$390$	6.40237	0.324196
$391$	6.60889	0.334226
$392$	6.96597	0.351835
$393$	−58.9987	−2.97609
$394$	−6.70590	−0.337839
$395$	−17.0422	−0.857486
$396$	8.75468	0.439939
$397$	24.4872	1.22898	0.614489	−	0.788925i	$-0.289362\pi$
$397$	24.4872	1.22898	0.614489	+	0.788925i	$0.289362\pi$
$398$	4.34710	0.217900
$399$	−1.86714	−0.0934739
$400$	1.00000	0.0500000
$401$	−28.2812	−1.41229	−0.706147	−	0.708065i	$-0.749568\pi$
$401$	−28.2812	−1.41229	−0.706147	+	0.708065i	$0.749568\pi$
$402$	26.4956	1.32148
$403$	−19.6363	−0.978153
$404$	−11.2581	−0.560109
$405$	41.3804	2.05621
$406$	−0.551693	−0.0273801
$407$	−8.37690	−0.415228
$408$	−4.74164	−0.234746
$409$	4.72448	0.233610	0.116805	−	0.993155i	$-0.462735\pi$
$409$	4.72448	0.233610	0.116805	+	0.993155i	$0.462735\pi$
$410$	4.20340	0.207591
$411$	11.9843	0.591142
$412$	−10.9672	−0.540313
$413$	−0.123324	−0.00606840
$414$	−41.8356	−2.05611
$415$	9.61476	0.471970
$416$	1.86739	0.0915563
$417$	15.7930	0.773388
$418$	−2.95225	−0.144399
$419$	−16.7677	−0.819156	−0.409578	−	0.912275i	$-0.634324\pi$
$419$	−16.7677	−0.819156	−0.409578	+	0.912275i	$0.634324\pi$
$420$	−0.632445	−0.0308602
$421$	−38.1148	−1.85760	−0.928800	−	0.370581i	$-0.879159\pi$
$421$	−38.1148	−1.85760	−0.928800	+	0.370581i	$0.879159\pi$
$422$	17.4496	0.849432
$423$	−71.0864	−3.45634
$424$	−8.47957	−0.411805
$425$	1.38300	0.0670854
$426$	44.8733	2.17412
$427$	0.218080	0.0105536
$428$	−13.3494	−0.645267
$429$	−6.40237	−0.309109
$430$	−1.00000	−0.0482243
$431$	−1.60385	−0.0772547	−0.0386274	−	0.999254i	$-0.512299\pi$
$431$	−1.60385	−0.0772547	−0.0386274	+	0.999254i	$0.512299\pi$
$432$	19.7300	0.949260
$433$	27.9656	1.34394	0.671971	−	0.740577i	$-0.265448\pi$
$433$	27.9656	1.34394	0.671971	+	0.740577i	$0.265448\pi$
$434$	1.93973	0.0931101
$435$	−10.2538	−0.491633
$436$	−11.5308	−0.552226
$437$	14.1078	0.674868
$438$	−47.0867	−2.24989
$439$	32.6484	1.55822	0.779111	−	0.626886i	$-0.215671\pi$
$439$	32.6484	1.55822	0.779111	+	0.626886i	$0.215671\pi$
$440$	−1.00000	−0.0476731
$441$	−60.9849	−2.90404
$442$	2.58260	0.122842
$443$	−26.0337	−1.23690	−0.618450	−	0.785824i	$-0.712239\pi$
$443$	−26.0337	−1.23690	−0.618450	+	0.785824i	$0.712239\pi$
$444$	−28.7203	−1.36300
$445$	9.80120	0.464621
$446$	−9.03133	−0.427646
$447$	38.3100	1.81200
$448$	−0.184466	−0.00871522
$449$	−15.2249	−0.718509	−0.359254	−	0.933240i	$-0.616969\pi$
$449$	−15.2249	−0.718509	−0.359254	+	0.933240i	$0.616969\pi$
$450$	−8.75468	−0.412700
$451$	−4.20340	−0.197931
$452$	2.29281	0.107845
$453$	73.3526	3.44641
$454$	−6.69594	−0.314256
$455$	0.344471	0.0161490
$456$	−10.1218	−0.473998
$457$	−31.6495	−1.48050	−0.740251	−	0.672331i	$-0.765293\pi$
$457$	−31.6495	−1.48050	−0.740251	+	0.672331i	$0.765293\pi$
$458$	−14.1110	−0.659365
$459$	27.2866	1.27363
$460$	4.77865	0.222806
$461$	−3.73982	−0.174181	−0.0870905	−	0.996200i	$-0.527757\pi$
$461$	−3.73982	−0.174181	−0.0870905	+	0.996200i	$0.527757\pi$
$462$	0.632445	0.0294240
$463$	−17.8767	−0.830800	−0.415400	−	0.909639i	$-0.636358\pi$
$463$	−17.8767	−0.830800	−0.415400	+	0.909639i	$0.636358\pi$
$464$	−2.99075	−0.138842
$465$	36.0520	1.67187
$466$	10.6897	0.495189
$467$	−5.29123	−0.244849	−0.122424	−	0.992478i	$-0.539067\pi$
$467$	−5.29123	−0.244849	−0.122424	+	0.992478i	$0.539067\pi$
$468$	−16.3484	−0.755706
$469$	1.42556	0.0658262
$470$	8.11982	0.374539
$471$	6.47163	0.298197
$472$	−0.668546	−0.0307723
$473$	1.00000	0.0459800
$474$	58.4293	2.68375
$475$	2.95225	0.135459
$476$	−0.255117	−0.0116933
$477$	74.2360	3.39903
$478$	18.7181	0.856146
$479$	−27.4380	−1.25367	−0.626837	−	0.779150i	$-0.715651\pi$
$479$	−27.4380	−1.25367	−0.626837	+	0.779150i	$0.715651\pi$
$480$	−3.42851	−0.156489
$481$	15.6429	0.713257
$482$	−13.0392	−0.593920
$483$	−3.02224	−0.137517
$484$	1.00000	0.0454545
$485$	10.6985	0.485796
$486$	−82.6833	−3.75059
$487$	−3.14932	−0.142710	−0.0713548	−	0.997451i	$-0.522732\pi$
$487$	−3.14932	−0.142710	−0.0713548	+	0.997451i	$0.522732\pi$
$488$	1.18222	0.0535167
$489$	28.4020	1.28438
$490$	6.96597	0.314691
$491$	−18.2086	−0.821741	−0.410871	−	0.911694i	$-0.634775\pi$
$491$	−18.2086	−0.821741	−0.410871	+	0.911694i	$0.634775\pi$
$492$	−14.4114	−0.649717
$493$	−4.13621	−0.186286
$494$	5.51301	0.248042
$495$	8.75468	0.393494
$496$	10.5154	0.472154
$497$	2.41435	0.108298
$498$	−32.9643	−1.47717
$499$	7.55692	0.338294	0.169147	−	0.985591i	$-0.445899\pi$
$499$	7.55692	0.338294	0.169147	+	0.985591i	$0.445899\pi$
$500$	1.00000	0.0447214
$501$	50.0890	2.23781
$502$	3.25282	0.145181
$503$	−35.2791	−1.57302	−0.786508	−	0.617580i	$-0.788113\pi$
$503$	−35.2791	−1.57302	−0.786508	+	0.617580i	$0.788113\pi$
$504$	1.61495	0.0719354
$505$	−11.2581	−0.500977
$506$	−4.77865	−0.212437
$507$	−32.6149	−1.44848
$508$	10.6919	0.474376
$509$	−30.6656	−1.35923	−0.679614	−	0.733570i	$-0.737853\pi$
$509$	−30.6656	−1.35923	−0.679614	+	0.733570i	$0.737853\pi$
$510$	−4.74164	−0.209963
$511$	−2.53344	−0.112073
$512$	−1.00000	−0.0441942
$513$	58.2480	2.57171
$514$	2.88382	0.127200
$515$	−10.9672	−0.483270
$516$	3.42851	0.150932
$517$	−8.11982	−0.357109
$518$	−1.54526	−0.0678947
$519$	60.7784	2.66788
$520$	1.86739	0.0818905
$521$	10.2281	0.448101	0.224051	−	0.974578i	$-0.428072\pi$
$521$	10.2281	0.448101	0.224051	+	0.974578i	$0.428072\pi$
$522$	26.1831	1.14600
$523$	33.9426	1.48421	0.742104	−	0.670285i	$-0.233828\pi$
$523$	33.9426	1.48421	0.742104	+	0.670285i	$0.233828\pi$
$524$	−17.2083	−0.751746
$525$	−0.632445	−0.0276022
$526$	27.2673	1.18891
$527$	14.5428	0.633492
$528$	3.42851	0.149207
$529$	−0.164461	−0.00715046
$530$	−8.47957	−0.368329
$531$	5.85291	0.253995
$532$	−0.544592	−0.0236111
$533$	7.84939	0.339995
$534$	−33.6035	−1.45417
$535$	−13.3494	−0.577144
$536$	7.72801	0.333799
$537$	29.0601	1.25403
$538$	24.3978	1.05186
$539$	−6.96597	−0.300046
$540$	19.7300	0.849044
$541$	38.7747	1.66706	0.833528	−	0.552477i	$-0.186317\pi$
$541$	38.7747	1.66706	0.833528	+	0.552477i	$0.186317\pi$
$542$	5.30420	0.227835
$543$	47.8535	2.05359
$544$	−1.38300	−0.0592957
$545$	−11.5308	−0.493926
$546$	−1.18102	−0.0505431
$547$	14.9174	0.637822	0.318911	−	0.947785i	$-0.396683\pi$
$547$	14.9174	0.637822	0.318911	+	0.947785i	$0.396683\pi$
$548$	3.49548	0.149320
$549$	−10.3500	−0.441726
$550$	−1.00000	−0.0426401
$551$	−8.82946	−0.376147
$552$	−16.3837	−0.697335
$553$	3.14371	0.133684
$554$	11.8561	0.503717
$555$	−28.7203	−1.21911
$556$	4.60638	0.195354
$557$	−20.8782	−0.884639	−0.442320	−	0.896858i	$-0.645844\pi$
$557$	−20.8782	−0.884639	−0.442320	+	0.896858i	$0.645844\pi$
$558$	−92.0586	−3.89715
$559$	−1.86739	−0.0789822
$560$	−0.184466	−0.00779513
$561$	4.74164	0.200192
$562$	−17.2792	−0.728881
$563$	35.6253	1.50143	0.750713	−	0.660629i	$-0.229710\pi$
$563$	35.6253	1.50143	0.750713	+	0.660629i	$0.229710\pi$
$564$	−27.8389	−1.17223
$565$	2.29281	0.0964592
$566$	6.28973	0.264377
$567$	−7.63331	−0.320569
$568$	13.0883	0.549172
$569$	−19.0655	−0.799267	−0.399633	−	0.916675i	$-0.630863\pi$
$569$	−19.0655	−0.799267	−0.399633	+	0.916675i	$0.630863\pi$
$570$	−10.1218	−0.423957
$571$	−4.86908	−0.203765	−0.101882	−	0.994796i	$-0.532487\pi$
$571$	−4.86908	−0.203765	−0.101882	+	0.994796i	$0.532487\pi$
$572$	−1.86739	−0.0780795
$573$	−14.4174	−0.602294
$574$	−0.775387	−0.0323640
$575$	4.77865	0.199284
$576$	8.75468	0.364779
$577$	−16.2337	−0.675816	−0.337908	−	0.941179i	$-0.609719\pi$
$577$	−16.2337	−0.675816	−0.337908	+	0.941179i	$0.609719\pi$
$578$	15.0873	0.627549
$579$	15.5953	0.648118
$580$	−2.99075	−0.124184
$581$	−1.77360	−0.0735814
$582$	−36.6801	−1.52044
$583$	8.47957	0.351188
$584$	−13.7339	−0.568311
$585$	−16.3484	−0.675924
$586$	−12.3915	−0.511886
$587$	22.9307	0.946452	0.473226	−	0.880941i	$-0.343089\pi$
$587$	22.9307	0.946452	0.473226	+	0.880941i	$0.343089\pi$
$588$	−23.8829	−0.984915
$589$	31.0440	1.27915
$590$	−0.668546	−0.0275236
$591$	22.9913	0.945734
$592$	−8.37690	−0.344289
$593$	37.6810	1.54737	0.773686	−	0.633569i	$-0.218411\pi$
$593$	37.6810	1.54737	0.773686	+	0.633569i	$0.218411\pi$
$594$	−19.7300	−0.809532
$595$	−0.255117	−0.0104588
$596$	11.1739	0.457702
$597$	−14.9041	−0.609983
$598$	8.92361	0.364914
$599$	16.5054	0.674390	0.337195	−	0.941435i	$-0.390522\pi$
$599$	16.5054	0.674390	0.337195	+	0.941435i	$0.390522\pi$
$600$	−3.42851	−0.139968
$601$	22.7227	0.926877	0.463439	−	0.886129i	$-0.346615\pi$
$601$	22.7227	0.926877	0.463439	+	0.886129i	$0.346615\pi$
$602$	0.184466	0.00751829
$603$	−67.6563	−2.75518
$604$	21.3949	0.870546
$605$	1.00000	0.0406558
$606$	38.5984	1.56795
$607$	−4.59208	−0.186387	−0.0931935	−	0.995648i	$-0.529708\pi$
$607$	−4.59208	−0.186387	−0.0931935	+	0.995648i	$0.529708\pi$
$608$	−2.95225	−0.119730
$609$	1.89149	0.0766469
$610$	1.18222	0.0478668
$611$	15.1629	0.613424
$612$	12.1077	0.489426
$613$	−44.7721	−1.80833	−0.904164	−	0.427186i	$-0.859505\pi$
$613$	−44.7721	−1.80833	−0.904164	+	0.427186i	$0.859505\pi$
$614$	20.3927	0.822982
$615$	−14.4114	−0.581124
$616$	0.184466	0.00743237
$617$	−37.9235	−1.52674	−0.763372	−	0.645959i	$-0.776458\pi$
$617$	−37.9235	−1.52674	−0.763372	+	0.645959i	$0.776458\pi$
$618$	37.6010	1.51253
$619$	28.5741	1.14849	0.574245	−	0.818684i	$-0.305296\pi$
$619$	28.5741	1.14849	0.574245	+	0.818684i	$0.305296\pi$
$620$	10.5154	0.422307
$621$	94.2828	3.78344
$622$	7.49923	0.300692
$623$	−1.80799	−0.0724357
$624$	−6.40237	−0.256300
$625$	1.00000	0.0400000
$626$	−7.80151	−0.311811
$627$	10.1218	0.404227
$628$	1.88759	0.0753232
$629$	−11.5853	−0.461935
$630$	1.61495	0.0643410
$631$	39.1470	1.55842	0.779209	−	0.626764i	$-0.215621\pi$
$631$	39.1470	1.55842	0.779209	+	0.626764i	$0.215621\pi$
$632$	17.0422	0.677902
$633$	−59.8260	−2.37787
$634$	−7.28303	−0.289246
$635$	10.6919	0.424295
$636$	29.0723	1.15279
$637$	13.0082	0.515403
$638$	2.99075	0.118405
$639$	−114.584	−4.53286
$640$	−1.00000	−0.0395285
$641$	−49.5520	−1.95719	−0.978594	−	0.205802i	$-0.934020\pi$
$641$	−49.5520	−1.95719	−0.978594	+	0.205802i	$0.934020\pi$
$642$	45.7685	1.80634
$643$	28.1755	1.11113	0.555567	−	0.831472i	$-0.312501\pi$
$643$	28.1755	1.11113	0.555567	+	0.831472i	$0.312501\pi$
$644$	−0.881502	−0.0347360
$645$	3.42851	0.134997
$646$	−4.08297	−0.160642
$647$	−25.7087	−1.01071	−0.505356	−	0.862911i	$-0.668639\pi$
$647$	−25.7087	−1.01071	−0.505356	+	0.862911i	$0.668639\pi$
$648$	−41.3804	−1.62558
$649$	0.668546	0.0262427
$650$	1.86739	0.0732451
$651$	−6.65039	−0.260649
$652$	8.28406	0.324429
$653$	14.8029	0.579284	0.289642	−	0.957135i	$-0.406464\pi$
$653$	14.8029	0.579284	0.289642	+	0.957135i	$0.406464\pi$
$654$	39.5336	1.54588
$655$	−17.2083	−0.672382
$656$	−4.20340	−0.164115
$657$	120.236	4.69084
$658$	−1.49783	−0.0583916
$659$	43.8772	1.70921	0.854607	−	0.519275i	$-0.173798\pi$
$659$	43.8772	1.70921	0.854607	+	0.519275i	$0.173798\pi$
$660$	3.42851	0.133455
$661$	−42.2923	−1.64498	−0.822490	−	0.568779i	$-0.807416\pi$
$661$	−42.2923	−1.64498	−0.822490	+	0.568779i	$0.807416\pi$
$662$	−6.13299	−0.238366
$663$	−8.85448	−0.343880
$664$	−9.61476	−0.373125
$665$	−0.544592	−0.0211184
$666$	73.3371	2.84176
$667$	−14.2918	−0.553379
$668$	14.6096	0.565261
$669$	30.9640	1.19714
$670$	7.72801	0.298559
$671$	−1.18222	−0.0456392
$672$	0.632445	0.0243971
$673$	−24.1133	−0.929500	−0.464750	−	0.885442i	$-0.653856\pi$
$673$	−24.1133	−0.929500	−0.464750	+	0.885442i	$0.653856\pi$
$674$	18.2108	0.701452
$675$	19.7300	0.759408
$676$	−9.51285	−0.365879
$677$	22.3245	0.858001	0.429000	−	0.903304i	$-0.358866\pi$
$677$	22.3245	0.858001	0.429000	+	0.903304i	$0.358866\pi$
$678$	−7.86092	−0.301897
$679$	−1.97352	−0.0757369
$680$	−1.38300	−0.0530357
$681$	22.9571	0.879718
$682$	−10.5154	−0.402654
$683$	−20.8228	−0.796763	−0.398382	−	0.917220i	$-0.630428\pi$
$683$	−20.8228	−0.796763	−0.398382	+	0.917220i	$0.630428\pi$
$684$	25.8460	0.988248
$685$	3.49548	0.133556
$686$	−2.57625	−0.0983618
$687$	48.3798	1.84581
$688$	1.00000	0.0381246
$689$	−15.8347	−0.603253
$690$	−16.3837	−0.623716
$691$	−39.3969	−1.49873	−0.749365	−	0.662157i	$-0.769641\pi$
$691$	−39.3969	−1.49873	−0.749365	+	0.662157i	$0.769641\pi$
$692$	17.7273	0.673893
$693$	−1.61495	−0.0613467
$694$	5.17920	0.196600
$695$	4.60638	0.174730
$696$	10.2538	0.388670
$697$	−5.81331	−0.220195
$698$	−9.30012	−0.352015
$699$	−36.6496	−1.38622
$700$	−0.184466	−0.00697218
$701$	−43.8307	−1.65546	−0.827731	−	0.561125i	$-0.810369\pi$
$701$	−43.8307	−1.65546	−0.827731	+	0.561125i	$0.810369\pi$
$702$	36.8436	1.39057
$703$	−24.7307	−0.932737
$704$	1.00000	0.0376889
$705$	−27.8389	−1.04847
$706$	0.645416	0.0242906
$707$	2.07673	0.0781036
$708$	2.29212	0.0861431
$709$	17.7070	0.665000	0.332500	−	0.943103i	$-0.392108\pi$
$709$	17.7070	0.665000	0.332500	+	0.943103i	$0.392108\pi$
$710$	13.0883	0.491194
$711$	−149.199	−5.59540
$712$	−9.80120	−0.367315
$713$	50.2493	1.88185
$714$	0.874673	0.0327338
$715$	−1.86739	−0.0698364
$716$	8.47601	0.316763
$717$	−64.1752	−2.39667
$718$	−26.5913	−0.992379
$719$	−8.39883	−0.313224	−0.156612	−	0.987660i	$-0.550057\pi$
$719$	−8.39883	−0.313224	−0.156612	+	0.987660i	$0.550057\pi$
$720$	8.75468	0.326268
$721$	2.02307	0.0753431
$722$	10.2842	0.382738
$723$	44.7051	1.66260
$724$	13.9575	0.518728
$725$	−2.99075	−0.111074
$726$	−3.42851	−0.127244
$727$	48.1774	1.78680	0.893401	−	0.449261i	$-0.148313\pi$
$727$	48.1774	1.78680	0.893401	+	0.449261i	$0.148313\pi$
$728$	−0.344471	−0.0127669
$729$	159.339	5.90145
$730$	−13.7339	−0.508313
$731$	1.38300	0.0511522
$732$	−4.05326	−0.149813
$733$	9.45432	0.349203	0.174602	−	0.984639i	$-0.444136\pi$
$733$	9.45432	0.349203	0.174602	+	0.984639i	$0.444136\pi$
$734$	14.7740	0.545318
$735$	−23.8829	−0.880934
$736$	−4.77865	−0.176144
$737$	−7.72801	−0.284665
$738$	36.7995	1.35461
$739$	28.3743	1.04376	0.521882	−	0.853018i	$-0.325230\pi$
$739$	28.3743	1.04376	0.521882	+	0.853018i	$0.325230\pi$
$740$	−8.37690	−0.307941
$741$	−18.9014	−0.694361
$742$	1.56420	0.0574235
$743$	−24.0323	−0.881659	−0.440829	−	0.897591i	$-0.645316\pi$
$743$	−24.0323	−0.881659	−0.440829	+	0.897591i	$0.645316\pi$
$744$	−36.0520	−1.32173
$745$	11.1739	0.409381
$746$	15.2156	0.557082
$747$	84.1742	3.07977
$748$	1.38300	0.0505675
$749$	2.46251	0.0899783
$750$	−3.42851	−0.125192
$751$	−4.35455	−0.158900	−0.0794499	−	0.996839i	$-0.525316\pi$
$751$	−4.35455	−0.158900	−0.0794499	+	0.996839i	$0.525316\pi$
$752$	−8.11982	−0.296099
$753$	−11.1523	−0.406414
$754$	−5.58490	−0.203390
$755$	21.3949	0.778640
$756$	−3.63952	−0.132368
$757$	44.4631	1.61604	0.808020	−	0.589155i	$-0.200539\pi$
$757$	44.4631	1.61604	0.808020	+	0.589155i	$0.200539\pi$
$758$	−28.3159	−1.02848
$759$	16.3837	0.594689
$760$	−2.95225	−0.107089
$761$	−48.0020	−1.74007	−0.870036	−	0.492988i	$-0.835904\pi$
$761$	−48.0020	−1.74007	−0.870036	+	0.492988i	$0.835904\pi$
$762$	−36.6573	−1.32795
$763$	2.12705	0.0770044
$764$	−4.20514	−0.152137
$765$	12.1077	0.437756
$766$	32.8852	1.18819
$767$	−1.24844	−0.0450784
$768$	3.42851	0.123716
$769$	28.8769	1.04133	0.520665	−	0.853761i	$-0.325684\pi$
$769$	28.8769	1.04133	0.520665	+	0.853761i	$0.325684\pi$
$770$	0.184466	0.00664771
$771$	−9.88721	−0.356079
$772$	4.54871	0.163711
$773$	−28.1242	−1.01156	−0.505779	−	0.862663i	$-0.668795\pi$
$773$	−28.1242	−1.01156	−0.505779	+	0.862663i	$0.668795\pi$
$774$	−8.75468	−0.314681
$775$	10.5154	0.377723
$776$	−10.6985	−0.384056
$777$	5.29793	0.190062
$778$	14.7176	0.527652
$779$	−12.4095	−0.444617
$780$	−6.40237	−0.229242
$781$	−13.0883	−0.468335
$782$	−6.60889	−0.236333
$783$	−59.0075	−2.10876
$784$	−6.96597	−0.248785
$785$	1.88759	0.0673711
$786$	58.9987	2.10441
$787$	2.47731	0.0883065	0.0441532	−	0.999025i	$-0.485941\pi$
$787$	2.47731	0.0883065	0.0441532	+	0.999025i	$0.485941\pi$
$788$	6.70590	0.238888
$789$	−93.4863	−3.32820
$790$	17.0422	0.606334
$791$	−0.422947	−0.0150382
$792$	−8.75468	−0.311084
$793$	2.20767	0.0783967
$794$	−24.4872	−0.869019
$795$	29.0723	1.03109
$796$	−4.34710	−0.154079
$797$	38.3325	1.35781	0.678903	−	0.734228i	$-0.262456\pi$
$797$	38.3325	1.35781	0.678903	+	0.734228i	$0.262456\pi$
$798$	1.86714	0.0660960
$799$	−11.2297	−0.397279
$800$	−1.00000	−0.0353553
$801$	85.8064	3.03182
$802$	28.2812	0.998643
$803$	13.7339	0.484657
$804$	−26.4956	−0.934427
$805$	−0.881502	−0.0310688
$806$	19.6363	0.691658
$807$	−83.6480	−2.94455
$808$	11.2581	0.396057
$809$	−38.7940	−1.36392	−0.681962	−	0.731387i	$-0.738873\pi$
$809$	−38.7940	−1.36392	−0.681962	+	0.731387i	$0.738873\pi$
$810$	−41.3804	−1.45396
$811$	8.02415	0.281766	0.140883	−	0.990026i	$-0.455006\pi$
$811$	8.02415	0.281766	0.140883	+	0.990026i	$0.455006\pi$
$812$	0.551693	0.0193606
$813$	−18.1855	−0.637794
$814$	8.37690	0.293610
$815$	8.28406	0.290178
$816$	4.74164	0.165990
$817$	2.95225	0.103286
$818$	−4.72448	−0.165188
$819$	3.01573	0.105378
$820$	−4.20340	−0.146789
$821$	19.8993	0.694490	0.347245	−	0.937775i	$-0.387117\pi$
$821$	19.8993	0.694490	0.347245	+	0.937775i	$0.387117\pi$
$822$	−11.9843	−0.418001
$823$	10.1533	0.353923	0.176961	−	0.984218i	$-0.443373\pi$
$823$	10.1533	0.353923	0.176961	+	0.984218i	$0.443373\pi$
$824$	10.9672	0.382059
$825$	3.42851	0.119365
$826$	0.123324	0.00429100
$827$	26.6730	0.927510	0.463755	−	0.885963i	$-0.346502\pi$
$827$	26.6730	0.927510	0.463755	+	0.885963i	$0.346502\pi$
$828$	41.8356	1.45389
$829$	−45.8403	−1.59210	−0.796050	−	0.605231i	$-0.793081\pi$
$829$	−45.8403	−1.59210	−0.796050	+	0.605231i	$0.793081\pi$
$830$	−9.61476	−0.333733
$831$	−40.6488	−1.41009
$832$	−1.86739	−0.0647401
$833$	−9.63395	−0.333797
$834$	−15.7930	−0.546868
$835$	14.6096	0.505584
$836$	2.95225	0.102106
$837$	207.468	7.17114
$838$	16.7677	0.579231
$839$	−10.9506	−0.378055	−0.189028	−	0.981972i	$-0.560534\pi$
$839$	−10.9506	−0.378055	−0.189028	+	0.981972i	$0.560534\pi$
$840$	0.632445	0.0218214
$841$	−20.0554	−0.691566
$842$	38.1148	1.31352
$843$	59.2420	2.04040
$844$	−17.4496	−0.600639
$845$	−9.51285	−0.327252
$846$	71.0864	2.44400
$847$	−0.184466	−0.00633834
$848$	8.47957	0.291190
$849$	−21.5644	−0.740088
$850$	−1.38300	−0.0474366
$851$	−40.0303	−1.37222
$852$	−44.8733	−1.53733
$853$	46.6945	1.59879	0.799394	−	0.600807i	$-0.205154\pi$
$853$	46.6945	1.59879	0.799394	+	0.600807i	$0.205154\pi$
$854$	−0.218080	−0.00746256
$855$	25.8460	0.883916
$856$	13.3494	0.456272
$857$	30.4220	1.03920	0.519598	−	0.854411i	$-0.326082\pi$
$857$	30.4220	1.03920	0.519598	+	0.854411i	$0.326082\pi$
$858$	6.40237	0.218573
$859$	13.6881	0.467031	0.233515	−	0.972353i	$-0.424977\pi$
$859$	13.6881	0.467031	0.233515	+	0.972353i	$0.424977\pi$
$860$	1.00000	0.0340997
$861$	2.65842	0.0905988
$862$	1.60385	0.0546274
$863$	−19.0802	−0.649498	−0.324749	−	0.945800i	$-0.605280\pi$
$863$	−19.0802	−0.649498	−0.324749	+	0.945800i	$0.605280\pi$
$864$	−19.7300	−0.671228
$865$	17.7273	0.602748
$866$	−27.9656	−0.950311
$867$	−51.7270	−1.75674
$868$	−1.93973	−0.0658388
$869$	−17.0422	−0.578117
$870$	10.2538	0.347637
$871$	14.4312	0.488983
$872$	11.5308	0.390483
$873$	93.6624	3.16999
$874$	−14.1078	−0.477203
$875$	−0.184466	−0.00623611
$876$	47.0867	1.59091
$877$	1.98680	0.0670895	0.0335448	−	0.999437i	$-0.489320\pi$
$877$	1.98680	0.0670895	0.0335448	+	0.999437i	$0.489320\pi$
$878$	−32.6484	−1.10183
$879$	42.4842	1.43296
$880$	1.00000	0.0337100
$881$	−33.5881	−1.13161	−0.565805	−	0.824539i	$-0.691435\pi$
$881$	−33.5881	−1.13161	−0.565805	+	0.824539i	$0.691435\pi$
$882$	60.9849	2.05347
$883$	4.62390	0.155607	0.0778033	−	0.996969i	$-0.475209\pi$
$883$	4.62390	0.155607	0.0778033	+	0.996969i	$0.475209\pi$
$884$	−2.58260	−0.0868624
$885$	2.29212	0.0770487
$886$	26.0337	0.874620
$887$	−48.6666	−1.63406	−0.817032	−	0.576593i	$-0.804382\pi$
$887$	−48.6666	−1.63406	−0.817032	+	0.576593i	$0.804382\pi$
$888$	28.7203	0.963790
$889$	−1.97230	−0.0661487
$890$	−9.80120	−0.328537
$891$	41.3804	1.38630
$892$	9.03133	0.302391
$893$	−23.9718	−0.802184
$894$	−38.3100	−1.28128
$895$	8.47601	0.283322
$896$	0.184466	0.00616259
$897$	−30.5947	−1.02153
$898$	15.2249	0.508062
$899$	−31.4488	−1.04888
$900$	8.75468	0.291823
$901$	11.7273	0.390692
$902$	4.20340	0.139958
$903$	−0.632445	−0.0210465
$904$	−2.29281	−0.0762577
$905$	13.9575	0.463964
$906$	−73.3526	−2.43698
$907$	−13.6309	−0.452605	−0.226303	−	0.974057i	$-0.572664\pi$
$907$	−13.6309	−0.452605	−0.226303	+	0.974057i	$0.572664\pi$
$908$	6.69594	0.222213
$909$	−98.5608	−3.26905
$910$	−0.344471	−0.0114191
$911$	−31.0975	−1.03031	−0.515154	−	0.857098i	$-0.672265\pi$
$911$	−31.0975	−1.03031	−0.515154	+	0.857098i	$0.672265\pi$
$912$	10.1218	0.335167
$913$	9.61476	0.318202
$914$	31.6495	1.04687
$915$	−4.05326	−0.133997
$916$	14.1110	0.466242
$917$	3.17435	0.104826
$918$	−27.2866	−0.900592
$919$	−37.5417	−1.23839	−0.619194	−	0.785238i	$-0.712541\pi$
$919$	−37.5417	−1.23839	−0.619194	+	0.785238i	$0.712541\pi$
$920$	−4.77865	−0.157548
$921$	−69.9166	−2.30383
$922$	3.73982	0.123165
$923$	24.4409	0.804483
$924$	−0.632445	−0.0208059
$925$	−8.37690	−0.275431
$926$	17.8767	0.587464
$927$	−96.0140	−3.15351
$928$	2.99075	0.0981762
$929$	39.9446	1.31054	0.655269	−	0.755395i	$-0.272555\pi$
$929$	39.9446	1.31054	0.655269	+	0.755395i	$0.272555\pi$
$930$	−36.0520	−1.18219
$931$	−20.5653	−0.674001
$932$	−10.6897	−0.350152
$933$	−25.7112	−0.841747
$934$	5.29123	0.173134
$935$	1.38300	0.0452290
$936$	16.3484	0.534365
$937$	39.5559	1.29224	0.646118	−	0.763238i	$-0.276392\pi$
$937$	39.5559	1.29224	0.646118	+	0.763238i	$0.276392\pi$
$938$	−1.42556	−0.0465461
$939$	26.7476	0.872873
$940$	−8.11982	−0.264839
$941$	−24.8616	−0.810467	−0.405233	−	0.914213i	$-0.632810\pi$
$941$	−24.8616	−0.810467	−0.405233	+	0.914213i	$0.632810\pi$
$942$	−6.47163	−0.210857
$943$	−20.0866	−0.654110
$944$	0.668546	0.0217593
$945$	−3.63952	−0.118394
$946$	−1.00000	−0.0325128
$947$	40.0629	1.30187	0.650935	−	0.759133i	$-0.274377\pi$
$947$	40.0629	1.30187	0.650935	+	0.759133i	$0.274377\pi$
$948$	−58.4293	−1.89770
$949$	−25.6465	−0.832520
$950$	−2.95225	−0.0957838
$951$	24.9699	0.809706
$952$	0.255117	0.00826840
$953$	3.50313	0.113478	0.0567388	−	0.998389i	$-0.481930\pi$
$953$	3.50313	0.113478	0.0567388	+	0.998389i	$0.481930\pi$
$954$	−74.2360	−2.40348
$955$	−4.20514	−0.136075
$956$	−18.7181	−0.605387
$957$	−10.2538	−0.331459
$958$	27.4380	0.886482
$959$	−0.644800	−0.0208217
$960$	3.42851	0.110655
$961$	79.5728	2.56686
$962$	−15.6429	−0.504349
$963$	−116.870	−3.76607
$964$	13.0392	0.419965
$965$	4.54871	0.146428
$966$	3.02224	0.0972389
$967$	37.3781	1.20200	0.600999	−	0.799250i	$-0.294769\pi$
$967$	37.3781	1.20200	0.600999	+	0.799250i	$0.294769\pi$
$968$	−1.00000	−0.0321412
$969$	13.9985	0.449697
$970$	−10.6985	−0.343510
$971$	−15.7634	−0.505872	−0.252936	−	0.967483i	$-0.581396\pi$
$971$	−15.7634	−0.505872	−0.252936	+	0.967483i	$0.581396\pi$
$972$	82.6833	2.65207
$973$	−0.849723	−0.0272409
$974$	3.14932	0.100911
$975$	−6.40237	−0.205040
$976$	−1.18222	−0.0378420
$977$	39.0346	1.24883	0.624414	−	0.781094i	$-0.285338\pi$
$977$	39.0346	1.24883	0.624414	+	0.781094i	$0.285338\pi$
$978$	−28.4020	−0.908195
$979$	9.80120	0.313248
$980$	−6.96597	−0.222520
$981$	−100.949	−3.22304
$982$	18.2086	0.581059
$983$	31.9350	1.01857	0.509284	−	0.860598i	$-0.329910\pi$
$983$	31.9350	1.01857	0.509284	+	0.860598i	$0.329910\pi$
$984$	14.4114	0.459419
$985$	6.70590	0.213668
$986$	4.13621	0.131724
$987$	5.13534	0.163460
$988$	−5.51301	−0.175392
$989$	4.77865	0.151952
$990$	−8.75468	−0.278242
$991$	−31.5856	−1.00335	−0.501674	−	0.865057i	$-0.667282\pi$
$991$	−31.5856	−1.00335	−0.501674	+	0.865057i	$0.667282\pi$
$992$	−10.5154	−0.333863
$993$	21.0270	0.667273
$994$	−2.41435	−0.0765785
$995$	−4.34710	−0.137812
$996$	32.9643	1.04451
$997$	−0.395014	−0.0125102	−0.00625511	−	0.999980i	$-0.501991\pi$
$997$	−0.395014	−0.0125102	−0.00625511	+	0.999980i	$0.501991\pi$
$998$	−7.55692	−0.239210
$999$	−165.276	−5.22911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.10	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.42851 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42851 q^{6} -0.184466 q^{7} -1.00000 q^{8} +8.75468 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.42851 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.42851 q^{6} -0.184466 q^{7} -1.00000 q^{8} +8.75468 q^{9} -1.00000 q^{10} +1.00000 q^{11} +3.42851 q^{12} -1.86739 q^{13} +0.184466 q^{14} +3.42851 q^{15} +1.00000 q^{16} +1.38300 q^{17} -8.75468 q^{18} +2.95225 q^{19} +1.00000 q^{20} -0.632445 q^{21} -1.00000 q^{22} +4.77865 q^{23} -3.42851 q^{24} +1.00000 q^{25} +1.86739 q^{26} +19.7300 q^{27} -0.184466 q^{28} -2.99075 q^{29} -3.42851 q^{30} +10.5154 q^{31} -1.00000 q^{32} +3.42851 q^{33} -1.38300 q^{34} -0.184466 q^{35} +8.75468 q^{36} -8.37690 q^{37} -2.95225 q^{38} -6.40237 q^{39} -1.00000 q^{40} -4.20340 q^{41} +0.632445 q^{42} +1.00000 q^{43} +1.00000 q^{44} +8.75468 q^{45} -4.77865 q^{46} -8.11982 q^{47} +3.42851 q^{48} -6.96597 q^{49} -1.00000 q^{50} +4.74164 q^{51} -1.86739 q^{52} +8.47957 q^{53} -19.7300 q^{54} +1.00000 q^{55} +0.184466 q^{56} +10.1218 q^{57} +2.99075 q^{58} +0.668546 q^{59} +3.42851 q^{60} -1.18222 q^{61} -10.5154 q^{62} -1.61495 q^{63} +1.00000 q^{64} -1.86739 q^{65} -3.42851 q^{66} -7.72801 q^{67} +1.38300 q^{68} +16.3837 q^{69} +0.184466 q^{70} -13.0883 q^{71} -8.75468 q^{72} +13.7339 q^{73} +8.37690 q^{74} +3.42851 q^{75} +2.95225 q^{76} -0.184466 q^{77} +6.40237 q^{78} -17.0422 q^{79} +1.00000 q^{80} +41.3804 q^{81} +4.20340 q^{82} +9.61476 q^{83} -0.632445 q^{84} +1.38300 q^{85} -1.00000 q^{86} -10.2538 q^{87} -1.00000 q^{88} +9.80120 q^{89} -8.75468 q^{90} +0.344471 q^{91} +4.77865 q^{92} +36.0520 q^{93} +8.11982 q^{94} +2.95225 q^{95} -3.42851 q^{96} +10.6985 q^{97} +6.96597 q^{98} +8.75468 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

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