LMFDB - Embedded newform 4730.2.a.z.1.4

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			1.4
Root			$0.523103$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.476897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.476897 q^{6} +2.32668 q^{7} -1.00000 q^{8} -2.77257 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.476897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.476897 q^{6} +2.32668 q^{7} -1.00000 q^{8} -2.77257 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.476897 q^{12} +7.04755 q^{13} -2.32668 q^{14} +0.476897 q^{15} +1.00000 q^{16} +2.62579 q^{17} +2.77257 q^{18} +2.34216 q^{19} +1.00000 q^{20} +1.10959 q^{21} -1.00000 q^{22} -1.69414 q^{23} -0.476897 q^{24} +1.00000 q^{25} -7.04755 q^{26} -2.75292 q^{27} +2.32668 q^{28} +7.70842 q^{29} -0.476897 q^{30} +1.97951 q^{31} -1.00000 q^{32} +0.476897 q^{33} -2.62579 q^{34} +2.32668 q^{35} -2.77257 q^{36} -3.78694 q^{37} -2.34216 q^{38} +3.36095 q^{39} -1.00000 q^{40} +6.55376 q^{41} -1.10959 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.77257 q^{45} +1.69414 q^{46} +0.404355 q^{47} +0.476897 q^{48} -1.58657 q^{49} -1.00000 q^{50} +1.25223 q^{51} +7.04755 q^{52} -9.69344 q^{53} +2.75292 q^{54} +1.00000 q^{55} -2.32668 q^{56} +1.11697 q^{57} -7.70842 q^{58} +14.0213 q^{59} +0.476897 q^{60} -6.27911 q^{61} -1.97951 q^{62} -6.45088 q^{63} +1.00000 q^{64} +7.04755 q^{65} -0.476897 q^{66} +0.865830 q^{67} +2.62579 q^{68} -0.807929 q^{69} -2.32668 q^{70} -11.9711 q^{71} +2.77257 q^{72} -7.72080 q^{73} +3.78694 q^{74} +0.476897 q^{75} +2.34216 q^{76} +2.32668 q^{77} -3.36095 q^{78} +4.49996 q^{79} +1.00000 q^{80} +7.00485 q^{81} -6.55376 q^{82} -3.11305 q^{83} +1.10959 q^{84} +2.62579 q^{85} -1.00000 q^{86} +3.67612 q^{87} -1.00000 q^{88} -10.1704 q^{89} +2.77257 q^{90} +16.3974 q^{91} -1.69414 q^{92} +0.944022 q^{93} -0.404355 q^{94} +2.34216 q^{95} -0.476897 q^{96} +11.1245 q^{97} +1.58657 q^{98} -2.77257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.476897	0.275336	0.137668	−	0.990478i	$-0.456039\pi$
$3$	0.476897	0.275336	0.137668	+	0.990478i	$0.456039\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.476897	−0.194692
$7$	2.32668	0.879402	0.439701	−	0.898144i	$-0.355084\pi$
$7$	2.32668	0.879402	0.439701	+	0.898144i	$0.355084\pi$
$8$	−1.00000	−0.353553
$9$	−2.77257	−0.924190
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.476897	0.137668
$13$	7.04755	1.95464	0.977319	−	0.211774i	$-0.0679239\pi$
$13$	7.04755	1.95464	0.977319	+	0.211774i	$0.0679239\pi$
$14$	−2.32668	−0.621831
$15$	0.476897	0.123134
$16$	1.00000	0.250000
$17$	2.62579	0.636847	0.318424	−	0.947949i	$-0.396847\pi$
$17$	2.62579	0.636847	0.318424	+	0.947949i	$0.396847\pi$
$18$	2.77257	0.653501
$19$	2.34216	0.537328	0.268664	−	0.963234i	$-0.413418\pi$
$19$	2.34216	0.537328	0.268664	+	0.963234i	$0.413418\pi$
$20$	1.00000	0.223607
$21$	1.10959	0.242131
$22$	−1.00000	−0.213201
$23$	−1.69414	−0.353252	−0.176626	−	0.984278i	$-0.556518\pi$
$23$	−1.69414	−0.353252	−0.176626	+	0.984278i	$0.556518\pi$
$24$	−0.476897	−0.0973461
$25$	1.00000	0.200000
$26$	−7.04755	−1.38214
$27$	−2.75292	−0.529800
$28$	2.32668	0.439701
$29$	7.70842	1.43142	0.715709	−	0.698399i	$-0.246104\pi$
$29$	7.70842	1.43142	0.715709	+	0.698399i	$0.246104\pi$
$30$	−0.476897	−0.0870690
$31$	1.97951	0.355531	0.177765	−	0.984073i	$-0.443113\pi$
$31$	1.97951	0.355531	0.177765	+	0.984073i	$0.443113\pi$
$32$	−1.00000	−0.176777
$33$	0.476897	0.0830171
$34$	−2.62579	−0.450319
$35$	2.32668	0.393280
$36$	−2.77257	−0.462095
$37$	−3.78694	−0.622569	−0.311284	−	0.950317i	$-0.600759\pi$
$37$	−3.78694	−0.622569	−0.311284	+	0.950317i	$0.600759\pi$
$38$	−2.34216	−0.379948
$39$	3.36095	0.538183
$40$	−1.00000	−0.158114
$41$	6.55376	1.02353	0.511763	−	0.859127i	$-0.328993\pi$
$41$	6.55376	1.02353	0.511763	+	0.859127i	$0.328993\pi$
$42$	−1.10959	−0.171213
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−2.77257	−0.413310
$46$	1.69414	0.249787
$47$	0.404355	0.0589813	0.0294906	−	0.999565i	$-0.490611\pi$
$47$	0.404355	0.0589813	0.0294906	+	0.999565i	$0.490611\pi$
$48$	0.476897	0.0688341
$49$	−1.58657	−0.226653
$50$	−1.00000	−0.141421
$51$	1.25223	0.175347
$52$	7.04755	0.977319
$53$	−9.69344	−1.33150	−0.665748	−	0.746176i	$-0.731888\pi$
$53$	−9.69344	−1.33150	−0.665748	+	0.746176i	$0.731888\pi$
$54$	2.75292	0.374625
$55$	1.00000	0.134840
$56$	−2.32668	−0.310915
$57$	1.11697	0.147946
$58$	−7.70842	−1.01217
$59$	14.0213	1.82541	0.912706	−	0.408616i	$-0.133988\pi$
$59$	14.0213	1.82541	0.912706	+	0.408616i	$0.133988\pi$
$60$	0.476897	0.0615671
$61$	−6.27911	−0.803957	−0.401979	−	0.915649i	$-0.631677\pi$
$61$	−6.27911	−0.803957	−0.401979	+	0.915649i	$0.631677\pi$
$62$	−1.97951	−0.251398
$63$	−6.45088	−0.812734
$64$	1.00000	0.125000
$65$	7.04755	0.874140
$66$	−0.476897	−0.0587019
$67$	0.865830	0.105778	0.0528890	−	0.998600i	$-0.483157\pi$
$67$	0.865830	0.105778	0.0528890	+	0.998600i	$0.483157\pi$
$68$	2.62579	0.318424
$69$	−0.807929	−0.0972632
$70$	−2.32668	−0.278091
$71$	−11.9711	−1.42071	−0.710355	−	0.703843i	$-0.751466\pi$
$71$	−11.9711	−1.42071	−0.710355	+	0.703843i	$0.751466\pi$
$72$	2.77257	0.326750
$73$	−7.72080	−0.903652	−0.451826	−	0.892106i	$-0.649227\pi$
$73$	−7.72080	−0.903652	−0.451826	+	0.892106i	$0.649227\pi$
$74$	3.78694	0.440223
$75$	0.476897	0.0550673
$76$	2.34216	0.268664
$77$	2.32668	0.265150
$78$	−3.36095	−0.380553
$79$	4.49996	0.506285	0.253142	−	0.967429i	$-0.418536\pi$
$79$	4.49996	0.506285	0.253142	+	0.967429i	$0.418536\pi$
$80$	1.00000	0.111803
$81$	7.00485	0.778317
$82$	−6.55376	−0.723742
$83$	−3.11305	−0.341702	−0.170851	−	0.985297i	$-0.554652\pi$
$83$	−3.11305	−0.341702	−0.170851	+	0.985297i	$0.554652\pi$
$84$	1.10959	0.121066
$85$	2.62579	0.284807
$86$	−1.00000	−0.107833
$87$	3.67612	0.394122
$88$	−1.00000	−0.106600
$89$	−10.1704	−1.07806	−0.539031	−	0.842286i	$-0.681209\pi$
$89$	−10.1704	−1.07806	−0.539031	+	0.842286i	$0.681209\pi$
$90$	2.77257	0.292254
$91$	16.3974	1.71891
$92$	−1.69414	−0.176626
$93$	0.944022	0.0978906
$94$	−0.404355	−0.0417061
$95$	2.34216	0.240300
$96$	−0.476897	−0.0486731
$97$	11.1245	1.12952	0.564761	−	0.825255i	$-0.308968\pi$
$97$	11.1245	1.12952	0.564761	+	0.825255i	$0.308968\pi$
$98$	1.58657	0.160268
$99$	−2.77257	−0.278654
$100$	1.00000	0.100000
$101$	−13.9538	−1.38846	−0.694229	−	0.719754i	$-0.744255\pi$
$101$	−13.9538	−1.38846	−0.694229	+	0.719754i	$0.744255\pi$
$102$	−1.25223	−0.123989
$103$	−1.01319	−0.0998325	−0.0499163	−	0.998753i	$-0.515895\pi$
$103$	−1.01319	−0.0998325	−0.0499163	+	0.998753i	$0.515895\pi$
$104$	−7.04755	−0.691069
$105$	1.10959	0.108284
$106$	9.69344	0.941510
$107$	2.27925	0.220343	0.110171	−	0.993913i	$-0.464860\pi$
$107$	2.27925	0.220343	0.110171	+	0.993913i	$0.464860\pi$
$108$	−2.75292	−0.264900
$109$	10.6639	1.02142	0.510708	−	0.859754i	$-0.329383\pi$
$109$	10.6639	1.02142	0.510708	+	0.859754i	$0.329383\pi$
$110$	−1.00000	−0.0953463
$111$	−1.80598	−0.171416
$112$	2.32668	0.219850
$113$	−4.26341	−0.401068	−0.200534	−	0.979687i	$-0.564268\pi$
$113$	−4.26341	−0.401068	−0.200534	+	0.979687i	$0.564268\pi$
$114$	−1.11697	−0.104614
$115$	−1.69414	−0.157979
$116$	7.70842	0.715709
$117$	−19.5398	−1.80646
$118$	−14.0213	−1.29076
$119$	6.10936	0.560044
$120$	−0.476897	−0.0435345
$121$	1.00000	0.0909091
$122$	6.27911	0.568484
$123$	3.12547	0.281814
$124$	1.97951	0.177765
$125$	1.00000	0.0894427
$126$	6.45088	0.574690
$127$	19.4909	1.72954	0.864769	−	0.502170i	$-0.167465\pi$
$127$	19.4909	1.72954	0.864769	+	0.502170i	$0.167465\pi$
$128$	−1.00000	−0.0883883
$129$	0.476897	0.0419884
$130$	−7.04755	−0.618111
$131$	2.91551	0.254729	0.127365	−	0.991856i	$-0.459348\pi$
$131$	2.91551	0.254729	0.127365	+	0.991856i	$0.459348\pi$
$132$	0.476897	0.0415085
$133$	5.44945	0.472527
$134$	−0.865830	−0.0747963
$135$	−2.75292	−0.236934
$136$	−2.62579	−0.225159
$137$	−11.1721	−0.954500	−0.477250	−	0.878767i	$-0.658366\pi$
$137$	−11.1721	−0.954500	−0.477250	+	0.878767i	$0.658366\pi$
$138$	0.807929	0.0687755
$139$	−8.95267	−0.759355	−0.379678	−	0.925119i	$-0.623965\pi$
$139$	−8.95267	−0.759355	−0.379678	+	0.925119i	$0.623965\pi$
$140$	2.32668	0.196640
$141$	0.192836	0.0162397
$142$	11.9711	1.00459
$143$	7.04755	0.589345
$144$	−2.77257	−0.231047
$145$	7.70842	0.640150
$146$	7.72080	0.638978
$147$	−0.756630	−0.0624058
$148$	−3.78694	−0.311284
$149$	6.07096	0.497352	0.248676	−	0.968587i	$-0.420004\pi$
$149$	6.07096	0.497352	0.248676	+	0.968587i	$0.420004\pi$
$150$	−0.476897	−0.0389385
$151$	23.4818	1.91092	0.955460	−	0.295119i	$-0.0953593\pi$
$151$	23.4818	1.91092	0.955460	+	0.295119i	$0.0953593\pi$
$152$	−2.34216	−0.189974
$153$	−7.28018	−0.588568
$154$	−2.32668	−0.187489
$155$	1.97951	0.158998
$156$	3.36095	0.269092
$157$	18.2090	1.45323	0.726617	−	0.687043i	$-0.241092\pi$
$157$	18.2090	1.45323	0.726617	+	0.687043i	$0.241092\pi$
$158$	−4.49996	−0.357998
$159$	−4.62277	−0.366610
$160$	−1.00000	−0.0790569
$161$	−3.94171	−0.310651
$162$	−7.00485	−0.550353
$163$	6.69530	0.524416	0.262208	−	0.965011i	$-0.415549\pi$
$163$	6.69530	0.524416	0.262208	+	0.965011i	$0.415549\pi$
$164$	6.55376	0.511763
$165$	0.476897	0.0371264
$166$	3.11305	0.241619
$167$	0.205327	0.0158887	0.00794435	−	0.999968i	$-0.497471\pi$
$167$	0.205327	0.0158887	0.00794435	+	0.999968i	$0.497471\pi$
$168$	−1.10959	−0.0856064
$169$	36.6679	2.82061
$170$	−2.62579	−0.201389
$171$	−6.49380	−0.496593
$172$	1.00000	0.0762493
$173$	13.6703	1.03933	0.519667	−	0.854369i	$-0.326056\pi$
$173$	13.6703	1.03933	0.519667	+	0.854369i	$0.326056\pi$
$174$	−3.67612	−0.278686
$175$	2.32668	0.175880
$176$	1.00000	0.0753778
$177$	6.68670	0.502603
$178$	10.1704	0.762305
$179$	−20.1848	−1.50868	−0.754340	−	0.656484i	$-0.772043\pi$
$179$	−20.1848	−1.50868	−0.754340	+	0.656484i	$0.772043\pi$
$180$	−2.77257	−0.206655
$181$	−12.4760	−0.927333	−0.463667	−	0.886010i	$-0.653466\pi$
$181$	−12.4760	−0.927333	−0.463667	+	0.886010i	$0.653466\pi$
$182$	−16.3974	−1.21545
$183$	−2.99449	−0.221359
$184$	1.69414	0.124894
$185$	−3.78694	−0.278421
$186$	−0.944022	−0.0692191
$187$	2.62579	0.192017
$188$	0.404355	0.0294906
$189$	−6.40516	−0.465907
$190$	−2.34216	−0.169918
$191$	−4.28012	−0.309699	−0.154849	−	0.987938i	$-0.549489\pi$
$191$	−4.28012	−0.309699	−0.154849	+	0.987938i	$0.549489\pi$
$192$	0.476897	0.0344171
$193$	0.604686	0.0435263	0.0217631	−	0.999763i	$-0.493072\pi$
$193$	0.604686	0.0435263	0.0217631	+	0.999763i	$0.493072\pi$
$194$	−11.1245	−0.798693
$195$	3.36095	0.240683
$196$	−1.58657	−0.113326
$197$	−16.6949	−1.18947	−0.594733	−	0.803924i	$-0.702742\pi$
$197$	−16.6949	−1.18947	−0.594733	+	0.803924i	$0.702742\pi$
$198$	2.77257	0.197038
$199$	−9.73334	−0.689978	−0.344989	−	0.938607i	$-0.612117\pi$
$199$	−9.73334	−0.689978	−0.344989	+	0.938607i	$0.612117\pi$
$200$	−1.00000	−0.0707107
$201$	0.412911	0.0291245
$202$	13.9538	0.981788
$203$	17.9350	1.25879
$204$	1.25223	0.0876736
$205$	6.55376	0.457735
$206$	1.01319	0.0705923
$207$	4.69712	0.326472
$208$	7.04755	0.488659
$209$	2.34216	0.162010
$210$	−1.10959	−0.0765687
$211$	−8.06797	−0.555422	−0.277711	−	0.960665i	$-0.589576\pi$
$211$	−8.06797	−0.555422	−0.277711	+	0.960665i	$0.589576\pi$
$212$	−9.69344	−0.665748
$213$	−5.70899	−0.391173
$214$	−2.27925	−0.155806
$215$	1.00000	0.0681994
$216$	2.75292	0.187312
$217$	4.60568	0.312654
$218$	−10.6639	−0.722250
$219$	−3.68203	−0.248808
$220$	1.00000	0.0674200
$221$	18.5054	1.24481
$222$	1.80598	0.121209
$223$	−3.23734	−0.216788	−0.108394	−	0.994108i	$-0.534571\pi$
$223$	−3.23734	−0.216788	−0.108394	+	0.994108i	$0.534571\pi$
$224$	−2.32668	−0.155458
$225$	−2.77257	−0.184838
$226$	4.26341	0.283598
$227$	−2.83604	−0.188235	−0.0941174	−	0.995561i	$-0.530003\pi$
$227$	−2.83604	−0.188235	−0.0941174	+	0.995561i	$0.530003\pi$
$228$	1.11697	0.0739730
$229$	−6.39965	−0.422900	−0.211450	−	0.977389i	$-0.567819\pi$
$229$	−6.39965	−0.422900	−0.211450	+	0.977389i	$0.567819\pi$
$230$	1.69414	0.111708
$231$	1.10959	0.0730053
$232$	−7.70842	−0.506083
$233$	−5.32076	−0.348575	−0.174287	−	0.984695i	$-0.555762\pi$
$233$	−5.32076	−0.348575	−0.174287	+	0.984695i	$0.555762\pi$
$234$	19.5398	1.27736
$235$	0.404355	0.0263772
$236$	14.0213	0.912706
$237$	2.14602	0.139399
$238$	−6.10936	−0.396011
$239$	−24.2525	−1.56876	−0.784382	−	0.620277i	$-0.787020\pi$
$239$	−24.2525	−1.56876	−0.784382	+	0.620277i	$0.787020\pi$
$240$	0.476897	0.0307836
$241$	−4.25285	−0.273950	−0.136975	−	0.990574i	$-0.543738\pi$
$241$	−4.25285	−0.273950	−0.136975	+	0.990574i	$0.543738\pi$
$242$	−1.00000	−0.0642824
$243$	11.5993	0.744099
$244$	−6.27911	−0.401979
$245$	−1.58657	−0.101362
$246$	−3.12547	−0.199273
$247$	16.5065	1.05028
$248$	−1.97951	−0.125699
$249$	−1.48460	−0.0940829
$250$	−1.00000	−0.0632456
$251$	−15.2758	−0.964197	−0.482099	−	0.876117i	$-0.660125\pi$
$251$	−15.2758	−0.964197	−0.482099	+	0.876117i	$0.660125\pi$
$252$	−6.45088	−0.406367
$253$	−1.69414	−0.106510
$254$	−19.4909	−1.22297
$255$	1.25223	0.0784177
$256$	1.00000	0.0625000
$257$	19.5264	1.21803	0.609013	−	0.793160i	$-0.291566\pi$
$257$	19.5264	1.21803	0.609013	+	0.793160i	$0.291566\pi$
$258$	−0.476897	−0.0296903
$259$	−8.81099	−0.547488
$260$	7.04755	0.437070
$261$	−21.3721	−1.32290
$262$	−2.91551	−0.180121
$263$	4.73224	0.291803	0.145901	−	0.989299i	$-0.453392\pi$
$263$	4.73224	0.291803	0.145901	+	0.989299i	$0.453392\pi$
$264$	−0.476897	−0.0293510
$265$	−9.69344	−0.595463
$266$	−5.44945	−0.334127
$267$	−4.85024	−0.296830
$268$	0.865830	0.0528890
$269$	17.3602	1.05847	0.529235	−	0.848475i	$-0.322479\pi$
$269$	17.3602	1.05847	0.529235	+	0.848475i	$0.322479\pi$
$270$	2.75292	0.167537
$271$	−22.7272	−1.38058	−0.690290	−	0.723533i	$-0.742517\pi$
$271$	−22.7272	−1.38058	−0.690290	+	0.723533i	$0.742517\pi$
$272$	2.62579	0.159212
$273$	7.81985	0.473279
$274$	11.1721	0.674934
$275$	1.00000	0.0603023
$276$	−0.807929	−0.0486316
$277$	14.9688	0.899389	0.449694	−	0.893183i	$-0.351533\pi$
$277$	14.9688	0.899389	0.449694	+	0.893183i	$0.351533\pi$
$278$	8.95267	0.536945
$279$	−5.48833	−0.328578
$280$	−2.32668	−0.139046
$281$	−15.0273	−0.896451	−0.448225	−	0.893921i	$-0.647944\pi$
$281$	−15.0273	−0.896451	−0.448225	+	0.893921i	$0.647944\pi$
$282$	−0.192836	−0.0114832
$283$	20.2670	1.20475	0.602375	−	0.798213i	$-0.294221\pi$
$283$	20.2670	1.20475	0.602375	+	0.798213i	$0.294221\pi$
$284$	−11.9711	−0.710355
$285$	1.11697	0.0661635
$286$	−7.04755	−0.416730
$287$	15.2485	0.900090
$288$	2.77257	0.163375
$289$	−10.1052	−0.594426
$290$	−7.70842	−0.452654
$291$	5.30524	0.310999
$292$	−7.72080	−0.451826
$293$	−8.35048	−0.487840	−0.243920	−	0.969795i	$-0.578433\pi$
$293$	−8.35048	−0.487840	−0.243920	+	0.969795i	$0.578433\pi$
$294$	0.756630	0.0441276
$295$	14.0213	0.816350
$296$	3.78694	0.220111
$297$	−2.75292	−0.159741
$298$	−6.07096	−0.351681
$299$	−11.9395	−0.690480
$300$	0.476897	0.0275336
$301$	2.32668	0.134107
$302$	−23.4818	−1.35123
$303$	−6.65454	−0.382293
$304$	2.34216	0.134332
$305$	−6.27911	−0.359541
$306$	7.28018	0.416180
$307$	13.3580	0.762383	0.381192	−	0.924496i	$-0.375514\pi$
$307$	13.3580	0.762383	0.381192	+	0.924496i	$0.375514\pi$
$308$	2.32668	0.132575
$309$	−0.483187	−0.0274875
$310$	−1.97951	−0.112429
$311$	27.7455	1.57331	0.786653	−	0.617396i	$-0.211812\pi$
$311$	27.7455	1.57331	0.786653	+	0.617396i	$0.211812\pi$
$312$	−3.36095	−0.190276
$313$	−6.36553	−0.359801	−0.179900	−	0.983685i	$-0.557578\pi$
$313$	−6.36553	−0.359801	−0.179900	+	0.983685i	$0.557578\pi$
$314$	−18.2090	−1.02759
$315$	−6.45088	−0.363466
$316$	4.49996	0.253142
$317$	−7.55401	−0.424275	−0.212138	−	0.977240i	$-0.568043\pi$
$317$	−7.55401	−0.424275	−0.212138	+	0.977240i	$0.568043\pi$
$318$	4.62277	0.259232
$319$	7.70842	0.431589
$320$	1.00000	0.0559017
$321$	1.08696	0.0606685
$322$	3.94171	0.219663
$323$	6.15001	0.342196
$324$	7.00485	0.389158
$325$	7.04755	0.390928
$326$	−6.69530	−0.370818
$327$	5.08557	0.281233
$328$	−6.55376	−0.361871
$329$	0.940805	0.0518682
$330$	−0.476897	−0.0262523
$331$	2.99224	0.164468	0.0822341	−	0.996613i	$-0.473794\pi$
$331$	2.99224	0.164468	0.0822341	+	0.996613i	$0.473794\pi$
$332$	−3.11305	−0.170851
$333$	10.4996	0.575372
$334$	−0.205327	−0.0112350
$335$	0.865830	0.0473053
$336$	1.10959	0.0605328
$337$	25.7076	1.40038	0.700191	−	0.713956i	$-0.253098\pi$
$337$	25.7076	1.40038	0.700191	+	0.713956i	$0.253098\pi$
$338$	−36.6679	−1.99447
$339$	−2.03321	−0.110429
$340$	2.62579	0.142403
$341$	1.97951	0.107197
$342$	6.49380	0.351144
$343$	−19.9782	−1.07872
$344$	−1.00000	−0.0539164
$345$	−0.807929	−0.0434974
$346$	−13.6703	−0.734921
$347$	−12.4899	−0.670492	−0.335246	−	0.942131i	$-0.608820\pi$
$347$	−12.4899	−0.670492	−0.335246	+	0.942131i	$0.608820\pi$
$348$	3.67612	0.197061
$349$	−9.63365	−0.515677	−0.257839	−	0.966188i	$-0.583010\pi$
$349$	−9.63365	−0.515677	−0.257839	+	0.966188i	$0.583010\pi$
$350$	−2.32668	−0.124366
$351$	−19.4013	−1.03557
$352$	−1.00000	−0.0533002
$353$	26.7862	1.42568	0.712842	−	0.701325i	$-0.247408\pi$
$353$	26.7862	1.42568	0.712842	+	0.701325i	$0.247408\pi$
$354$	−6.68670	−0.355394
$355$	−11.9711	−0.635361
$356$	−10.1704	−0.539031
$357$	2.91354	0.154201
$358$	20.1848	1.06680
$359$	16.2503	0.857657	0.428828	−	0.903386i	$-0.358927\pi$
$359$	16.2503	0.857657	0.428828	+	0.903386i	$0.358927\pi$
$360$	2.77257	0.146127
$361$	−13.5143	−0.711279
$362$	12.4760	0.655724
$363$	0.476897	0.0250306
$364$	16.3974	0.859456
$365$	−7.72080	−0.404125
$366$	2.99449	0.156524
$367$	28.3485	1.47978	0.739891	−	0.672727i	$-0.234877\pi$
$367$	28.3485	1.47978	0.739891	+	0.672727i	$0.234877\pi$
$368$	−1.69414	−0.0883131
$369$	−18.1708	−0.945932
$370$	3.78694	0.196874
$371$	−22.5535	−1.17092
$372$	0.944022	0.0489453
$373$	−28.7795	−1.49015	−0.745073	−	0.666982i	$-0.767586\pi$
$373$	−28.7795	−1.49015	−0.745073	+	0.666982i	$0.767586\pi$
$374$	−2.62579	−0.135776
$375$	0.476897	0.0246268
$376$	−0.404355	−0.0208530
$377$	54.3255	2.79790
$378$	6.40516	0.329446
$379$	−16.6520	−0.855355	−0.427677	−	0.903932i	$-0.640668\pi$
$379$	−16.6520	−0.855355	−0.427677	+	0.903932i	$0.640668\pi$
$380$	2.34216	0.120150
$381$	9.29515	0.476205
$382$	4.28012	0.218990
$383$	11.6186	0.593683	0.296841	−	0.954927i	$-0.404067\pi$
$383$	11.6186	0.593683	0.296841	+	0.954927i	$0.404067\pi$
$384$	−0.476897	−0.0243365
$385$	2.32668	0.118578
$386$	−0.604686	−0.0307777
$387$	−2.77257	−0.140938
$388$	11.1245	0.564761
$389$	37.9528	1.92429	0.962143	−	0.272547i	$-0.0878659\pi$
$389$	37.9528	1.92429	0.962143	+	0.272547i	$0.0878659\pi$
$390$	−3.36095	−0.170188
$391$	−4.44845	−0.224968
$392$	1.58657	0.0801339
$393$	1.39040	0.0701363
$394$	16.6949	0.841079
$395$	4.49996	0.226418
$396$	−2.77257	−0.139327
$397$	20.9977	1.05385	0.526923	−	0.849913i	$-0.323346\pi$
$397$	20.9977	1.05385	0.526923	+	0.849913i	$0.323346\pi$
$398$	9.73334	0.487888
$399$	2.59882	0.130104
$400$	1.00000	0.0500000
$401$	3.10478	0.155045	0.0775227	−	0.996991i	$-0.475299\pi$
$401$	3.10478	0.155045	0.0775227	+	0.996991i	$0.475299\pi$
$402$	−0.412911	−0.0205942
$403$	13.9507	0.694934
$404$	−13.9538	−0.694229
$405$	7.00485	0.348074
$406$	−17.9350	−0.890100
$407$	−3.78694	−0.187712
$408$	−1.25223	−0.0619946
$409$	29.5312	1.46022	0.730112	−	0.683327i	$-0.239468\pi$
$409$	29.5312	1.46022	0.730112	+	0.683327i	$0.239468\pi$
$410$	−6.55376	−0.323667
$411$	−5.32796	−0.262809
$412$	−1.01319	−0.0499163
$413$	32.6230	1.60527
$414$	−4.69712	−0.230851
$415$	−3.11305	−0.152814
$416$	−7.04755	−0.345534
$417$	−4.26950	−0.209078
$418$	−2.34216	−0.114559
$419$	13.9595	0.681967	0.340983	−	0.940069i	$-0.389240\pi$
$419$	13.9595	0.681967	0.340983	+	0.940069i	$0.389240\pi$
$420$	1.10959	0.0541422
$421$	−13.6258	−0.664081	−0.332040	−	0.943265i	$-0.607737\pi$
$421$	−13.6258	−0.664081	−0.332040	+	0.943265i	$0.607737\pi$
$422$	8.06797	0.392743
$423$	−1.12110	−0.0545099
$424$	9.69344	0.470755
$425$	2.62579	0.127369
$426$	5.70899	0.276601
$427$	−14.6095	−0.707001
$428$	2.27925	0.110171
$429$	3.36095	0.162268
$430$	−1.00000	−0.0482243
$431$	−7.75827	−0.373703	−0.186851	−	0.982388i	$-0.559828\pi$
$431$	−7.75827	−0.373703	−0.186851	+	0.982388i	$0.559828\pi$
$432$	−2.75292	−0.132450
$433$	14.9588	0.718875	0.359437	−	0.933169i	$-0.382969\pi$
$433$	14.9588	0.718875	0.359437	+	0.933169i	$0.382969\pi$
$434$	−4.60568	−0.221080
$435$	3.67612	0.176257
$436$	10.6639	0.510708
$437$	−3.96794	−0.189812
$438$	3.68203	0.175934
$439$	34.4724	1.64528	0.822638	−	0.568565i	$-0.192501\pi$
$439$	34.4724	1.64528	0.822638	+	0.568565i	$0.192501\pi$
$440$	−1.00000	−0.0476731
$441$	4.39888	0.209470
$442$	−18.5054	−0.880210
$443$	−37.5405	−1.78360	−0.891802	−	0.452426i	$-0.850559\pi$
$443$	−37.5405	−1.78360	−0.891802	+	0.452426i	$0.850559\pi$
$444$	−1.80598	−0.0857080
$445$	−10.1704	−0.482124
$446$	3.23734	0.153292
$447$	2.89522	0.136939
$448$	2.32668	0.109925
$449$	−17.1835	−0.810938	−0.405469	−	0.914109i	$-0.632892\pi$
$449$	−17.1835	−0.810938	−0.405469	+	0.914109i	$0.632892\pi$
$450$	2.77257	0.130700
$451$	6.55376	0.308605
$452$	−4.26341	−0.200534
$453$	11.1984	0.526146
$454$	2.83604	0.133102
$455$	16.3974	0.768720
$456$	−1.11697	−0.0523068
$457$	−9.28066	−0.434131	−0.217065	−	0.976157i	$-0.569649\pi$
$457$	−9.28066	−0.434131	−0.217065	+	0.976157i	$0.569649\pi$
$458$	6.39965	0.299036
$459$	−7.22858	−0.337401
$460$	−1.69414	−0.0789896
$461$	10.9558	0.510264	0.255132	−	0.966906i	$-0.417881\pi$
$461$	10.9558	0.510264	0.255132	+	0.966906i	$0.417881\pi$
$462$	−1.10959	−0.0516226
$463$	30.5108	1.41796	0.708978	−	0.705231i	$-0.249157\pi$
$463$	30.5108	1.41796	0.708978	+	0.705231i	$0.249157\pi$
$464$	7.70842	0.357855
$465$	0.944022	0.0437780
$466$	5.32076	0.246479
$467$	−2.77066	−0.128211	−0.0641054	−	0.997943i	$-0.520419\pi$
$467$	−2.77066	−0.128211	−0.0641054	+	0.997943i	$0.520419\pi$
$468$	−19.5398	−0.903228
$469$	2.01451	0.0930213
$470$	−0.404355	−0.0186515
$471$	8.68380	0.400128
$472$	−14.0213	−0.645381
$473$	1.00000	0.0459800
$474$	−2.14602	−0.0985698
$475$	2.34216	0.107466
$476$	6.10936	0.280022
$477$	26.8757	1.23056
$478$	24.2525	1.10928
$479$	13.0437	0.595981	0.297990	−	0.954569i	$-0.403684\pi$
$479$	13.0437	0.595981	0.297990	+	0.954569i	$0.403684\pi$
$480$	−0.476897	−0.0217673
$481$	−26.6886	−1.21690
$482$	4.25285	0.193712
$483$	−1.87979	−0.0855334
$484$	1.00000	0.0454545
$485$	11.1245	0.505138
$486$	−11.5993	−0.526157
$487$	28.4023	1.28703	0.643515	−	0.765433i	$-0.277475\pi$
$487$	28.4023	1.28703	0.643515	+	0.765433i	$0.277475\pi$
$488$	6.27911	0.284242
$489$	3.19297	0.144391
$490$	1.58657	0.0716740
$491$	28.6023	1.29080	0.645402	−	0.763843i	$-0.276690\pi$
$491$	28.6023	1.29080	0.645402	+	0.763843i	$0.276690\pi$
$492$	3.12547	0.140907
$493$	20.2407	0.911594
$494$	−16.5065	−0.742661
$495$	−2.77257	−0.124618
$496$	1.97951	0.0888827
$497$	−27.8529	−1.24937
$498$	1.48460	0.0665267
$499$	−39.0599	−1.74856	−0.874281	−	0.485420i	$-0.838667\pi$
$499$	−39.0599	−1.74856	−0.874281	+	0.485420i	$0.838667\pi$
$500$	1.00000	0.0447214
$501$	0.0979200	0.00437474
$502$	15.2758	0.681790
$503$	−14.9314	−0.665760	−0.332880	−	0.942969i	$-0.608020\pi$
$503$	−14.9314	−0.665760	−0.332880	+	0.942969i	$0.608020\pi$
$504$	6.45088	0.287345
$505$	−13.9538	−0.620938
$506$	1.69414	0.0753136
$507$	17.4868	0.776616
$508$	19.4909	0.864769
$509$	24.8904	1.10325	0.551625	−	0.834093i	$-0.314008\pi$
$509$	24.8904	1.10325	0.551625	+	0.834093i	$0.314008\pi$
$510$	−1.25223	−0.0554497
$511$	−17.9638	−0.794673
$512$	−1.00000	−0.0441942
$513$	−6.44777	−0.284676
$514$	−19.5264	−0.861275
$515$	−1.01319	−0.0446465
$516$	0.476897	0.0209942
$517$	0.404355	0.0177835
$518$	8.81099	0.387133
$519$	6.51933	0.286167
$520$	−7.04755	−0.309055
$521$	16.3972	0.718375	0.359188	−	0.933265i	$-0.383054\pi$
$521$	16.3972	0.718375	0.359188	+	0.933265i	$0.383054\pi$
$522$	21.3721	0.935433
$523$	29.2945	1.28096	0.640480	−	0.767975i	$-0.278736\pi$
$523$	29.2945	1.28096	0.640480	+	0.767975i	$0.278736\pi$
$524$	2.91551	0.127365
$525$	1.10959	0.0484263
$526$	−4.73224	−0.206336
$527$	5.19778	0.226419
$528$	0.476897	0.0207543
$529$	−20.1299	−0.875213
$530$	9.69344	0.421056
$531$	−38.8749	−1.68703
$532$	5.44945	0.236264
$533$	46.1879	2.00062
$534$	4.85024	0.209890
$535$	2.27925	0.0985404
$536$	−0.865830	−0.0373981
$537$	−9.62604	−0.415394
$538$	−17.3602	−0.748451
$539$	−1.58657	−0.0683384
$540$	−2.75292	−0.118467
$541$	−9.43178	−0.405504	−0.202752	−	0.979230i	$-0.564989\pi$
$541$	−9.43178	−0.405504	−0.202752	+	0.979230i	$0.564989\pi$
$542$	22.7272	0.976218
$543$	−5.94976	−0.255329
$544$	−2.62579	−0.112580
$545$	10.6639	0.456791
$546$	−7.81985	−0.334659
$547$	12.2655	0.524435	0.262218	−	0.965009i	$-0.415546\pi$
$547$	12.2655	0.524435	0.262218	+	0.965009i	$0.415546\pi$
$548$	−11.1721	−0.477250
$549$	17.4093	0.743009
$550$	−1.00000	−0.0426401
$551$	18.0543	0.769141
$552$	0.807929	0.0343877
$553$	10.4700	0.445228
$554$	−14.9688	−0.635964
$555$	−1.80598	−0.0766595
$556$	−8.95267	−0.379678
$557$	−1.98873	−0.0842650	−0.0421325	−	0.999112i	$-0.513415\pi$
$557$	−1.98873	−0.0842650	−0.0421325	+	0.999112i	$0.513415\pi$
$558$	5.48833	0.232340
$559$	7.04755	0.298079
$560$	2.32668	0.0983201
$561$	1.25223	0.0528692
$562$	15.0273	0.633887
$563$	−31.6444	−1.33365	−0.666827	−	0.745213i	$-0.732348\pi$
$563$	−31.6444	−1.33365	−0.666827	+	0.745213i	$0.732348\pi$
$564$	0.192836	0.00811985
$565$	−4.26341	−0.179363
$566$	−20.2670	−0.851887
$567$	16.2980	0.684453
$568$	11.9711	0.502297
$569$	−18.1051	−0.759005	−0.379503	−	0.925191i	$-0.623905\pi$
$569$	−18.1051	−0.759005	−0.379503	+	0.925191i	$0.623905\pi$
$570$	−1.11697	−0.0467846
$571$	−8.19280	−0.342858	−0.171429	−	0.985196i	$-0.554838\pi$
$571$	−8.19280	−0.342858	−0.171429	+	0.985196i	$0.554838\pi$
$572$	7.04755	0.294673
$573$	−2.04118	−0.0852714
$574$	−15.2485	−0.636460
$575$	−1.69414	−0.0706505
$576$	−2.77257	−0.115524
$577$	−22.2259	−0.925278	−0.462639	−	0.886547i	$-0.653097\pi$
$577$	−22.2259	−0.925278	−0.462639	+	0.886547i	$0.653097\pi$
$578$	10.1052	0.420322
$579$	0.288373	0.0119844
$580$	7.70842	0.320075
$581$	−7.24306	−0.300493
$582$	−5.30524	−0.219909
$583$	−9.69344	−0.401461
$584$	7.72080	0.319489
$585$	−19.5398	−0.807872
$586$	8.35048	0.344955
$587$	0.838924	0.0346261	0.0173131	−	0.999850i	$-0.494489\pi$
$587$	0.838924	0.0346261	0.0173131	+	0.999850i	$0.494489\pi$
$588$	−0.756630	−0.0312029
$589$	4.63633	0.191037
$590$	−14.0213	−0.577246
$591$	−7.96176	−0.327503
$592$	−3.78694	−0.155642
$593$	24.9303	1.02376	0.511882	−	0.859056i	$-0.328949\pi$
$593$	24.9303	1.02376	0.511882	+	0.859056i	$0.328949\pi$
$594$	2.75292	0.112954
$595$	6.10936	0.250459
$596$	6.07096	0.248676
$597$	−4.64180	−0.189976
$598$	11.9395	0.488243
$599$	−0.617976	−0.0252498	−0.0126249	−	0.999920i	$-0.504019\pi$
$599$	−0.617976	−0.0252498	−0.0126249	+	0.999920i	$0.504019\pi$
$600$	−0.476897	−0.0194692
$601$	−28.1235	−1.14718	−0.573592	−	0.819141i	$-0.694450\pi$
$601$	−28.1235	−1.14718	−0.573592	+	0.819141i	$0.694450\pi$
$602$	−2.32668	−0.0948283
$603$	−2.40057	−0.0977589
$604$	23.4818	0.955460
$605$	1.00000	0.0406558
$606$	6.65454	0.270322
$607$	13.8770	0.563249	0.281624	−	0.959525i	$-0.409127\pi$
$607$	13.8770	0.563249	0.281624	+	0.959525i	$0.409127\pi$
$608$	−2.34216	−0.0949871
$609$	8.55315	0.346591
$610$	6.27911	0.254234
$611$	2.84971	0.115287
$612$	−7.28018	−0.294284
$613$	−8.03130	−0.324381	−0.162191	−	0.986759i	$-0.551856\pi$
$613$	−8.03130	−0.324381	−0.162191	+	0.986759i	$0.551856\pi$
$614$	−13.3580	−0.539086
$615$	3.12547	0.126031
$616$	−2.32668	−0.0937445
$617$	−29.4567	−1.18588	−0.592942	−	0.805245i	$-0.702034\pi$
$617$	−29.4567	−1.18588	−0.592942	+	0.805245i	$0.702034\pi$
$618$	0.483187	0.0194366
$619$	−12.6746	−0.509435	−0.254717	−	0.967016i	$-0.581982\pi$
$619$	−12.6746	−0.509435	−0.254717	+	0.967016i	$0.581982\pi$
$620$	1.97951	0.0794991
$621$	4.66383	0.187153
$622$	−27.7455	−1.11250
$623$	−23.6633	−0.948049
$624$	3.36095	0.134546
$625$	1.00000	0.0400000
$626$	6.36553	0.254418
$627$	1.11697	0.0446074
$628$	18.2090	0.726617
$629$	−9.94370	−0.396481
$630$	6.45088	0.257009
$631$	−30.3570	−1.20849	−0.604247	−	0.796797i	$-0.706526\pi$
$631$	−30.3570	−1.20849	−0.604247	+	0.796797i	$0.706526\pi$
$632$	−4.49996	−0.178999
$633$	−3.84759	−0.152928
$634$	7.55401	0.300008
$635$	19.4909	0.773473
$636$	−4.62277	−0.183305
$637$	−11.1814	−0.443024
$638$	−7.70842	−0.305179
$639$	33.1908	1.31301
$640$	−1.00000	−0.0395285
$641$	−23.2486	−0.918265	−0.459133	−	0.888368i	$-0.651840\pi$
$641$	−23.2486	−0.918265	−0.459133	+	0.888368i	$0.651840\pi$
$642$	−1.08696	−0.0428991
$643$	22.7244	0.896163	0.448082	−	0.893993i	$-0.352107\pi$
$643$	22.7244	0.896163	0.448082	+	0.893993i	$0.352107\pi$
$644$	−3.94171	−0.155325
$645$	0.476897	0.0187778
$646$	−6.15001	−0.241969
$647$	−4.40142	−0.173037	−0.0865187	−	0.996250i	$-0.527574\pi$
$647$	−4.40142	−0.173037	−0.0865187	+	0.996250i	$0.527574\pi$
$648$	−7.00485	−0.275176
$649$	14.0213	0.550383
$650$	−7.04755	−0.276427
$651$	2.19644	0.0860851
$652$	6.69530	0.262208
$653$	−38.5393	−1.50816	−0.754080	−	0.656783i	$-0.771917\pi$
$653$	−38.5393	−1.50816	−0.754080	+	0.656783i	$0.771917\pi$
$654$	−5.08557	−0.198862
$655$	2.91551	0.113918
$656$	6.55376	0.255881
$657$	21.4065	0.835146
$658$	−0.940805	−0.0366764
$659$	31.5267	1.22811	0.614053	−	0.789265i	$-0.289538\pi$
$659$	31.5267	1.22811	0.614053	+	0.789265i	$0.289538\pi$
$660$	0.476897	0.0185632
$661$	35.9155	1.39695	0.698476	−	0.715634i	$-0.253862\pi$
$661$	35.9155	1.39695	0.698476	+	0.715634i	$0.253862\pi$
$662$	−2.99224	−0.116297
$663$	8.82515	0.342740
$664$	3.11305	0.120810
$665$	5.44945	0.211321
$666$	−10.4996	−0.406849
$667$	−13.0591	−0.505652
$668$	0.205327	0.00794435
$669$	−1.54387	−0.0596897
$670$	−0.865830	−0.0334499
$671$	−6.27911	−0.242402
$672$	−1.10959	−0.0428032
$673$	2.22906	0.0859240	0.0429620	−	0.999077i	$-0.486321\pi$
$673$	2.22906	0.0859240	0.0429620	+	0.999077i	$0.486321\pi$
$674$	−25.7076	−0.990219
$675$	−2.75292	−0.105960
$676$	36.6679	1.41030
$677$	−29.3982	−1.12986	−0.564932	−	0.825137i	$-0.691098\pi$
$677$	−29.3982	−1.12986	−0.564932	+	0.825137i	$0.691098\pi$
$678$	2.03321	0.0780849
$679$	25.8831	0.993303
$680$	−2.62579	−0.100694
$681$	−1.35250	−0.0518279
$682$	−1.97951	−0.0757994
$683$	−39.0011	−1.49234	−0.746168	−	0.665758i	$-0.768108\pi$
$683$	−39.0011	−1.49234	−0.746168	+	0.665758i	$0.768108\pi$
$684$	−6.49380	−0.248297
$685$	−11.1721	−0.426866
$686$	19.9782	0.762771
$687$	−3.05197	−0.116440
$688$	1.00000	0.0381246
$689$	−68.3150	−2.60259
$690$	0.807929	0.0307573
$691$	25.0073	0.951323	0.475662	−	0.879628i	$-0.342209\pi$
$691$	25.0073	0.951323	0.475662	+	0.879628i	$0.342209\pi$
$692$	13.6703	0.519667
$693$	−6.45088	−0.245049
$694$	12.4899	0.474110
$695$	−8.95267	−0.339594
$696$	−3.67612	−0.139343
$697$	17.2088	0.651829
$698$	9.63365	0.364639
$699$	−2.53745	−0.0959753
$700$	2.32668	0.0879402
$701$	−38.0425	−1.43684	−0.718422	−	0.695608i	$-0.755135\pi$
$701$	−38.0425	−1.43684	−0.718422	+	0.695608i	$0.755135\pi$
$702$	19.4013	0.732256
$703$	−8.86961	−0.334524
$704$	1.00000	0.0376889
$705$	0.192836	0.00726262
$706$	−26.7862	−1.00811
$707$	−32.4661	−1.22101
$708$	6.68670	0.251301
$709$	−7.90126	−0.296738	−0.148369	−	0.988932i	$-0.547402\pi$
$709$	−7.90126	−0.296738	−0.148369	+	0.988932i	$0.547402\pi$
$710$	11.9711	0.449268
$711$	−12.4764	−0.467903
$712$	10.1704	0.381152
$713$	−3.35357	−0.125592
$714$	−2.91354	−0.109036
$715$	7.04755	0.263563
$716$	−20.1848	−0.754340
$717$	−11.5659	−0.431938
$718$	−16.2503	−0.606455
$719$	20.1417	0.751159	0.375579	−	0.926790i	$-0.377444\pi$
$719$	20.1417	0.751159	0.375579	+	0.926790i	$0.377444\pi$
$720$	−2.77257	−0.103328
$721$	−2.35737	−0.0877929
$722$	13.5143	0.502950
$723$	−2.02817	−0.0754285
$724$	−12.4760	−0.463667
$725$	7.70842	0.286284
$726$	−0.476897	−0.0176993
$727$	48.4601	1.79729	0.898644	−	0.438679i	$-0.144554\pi$
$727$	48.4601	1.79729	0.898644	+	0.438679i	$0.144554\pi$
$728$	−16.3974	−0.607727
$729$	−15.4829	−0.573439
$730$	7.72080	0.285760
$731$	2.62579	0.0971183
$732$	−2.99449	−0.110679
$733$	−30.8907	−1.14097	−0.570486	−	0.821307i	$-0.693245\pi$
$733$	−30.8907	−1.14097	−0.570486	+	0.821307i	$0.693245\pi$
$734$	−28.3485	−1.04636
$735$	−0.756630	−0.0279087
$736$	1.69414	0.0624468
$737$	0.865830	0.0318932
$738$	18.1708	0.668875
$739$	−16.4501	−0.605127	−0.302563	−	0.953129i	$-0.597842\pi$
$739$	−16.4501	−0.605127	−0.302563	+	0.953129i	$0.597842\pi$
$740$	−3.78694	−0.139211
$741$	7.87188	0.289181
$742$	22.5535	0.827965
$743$	−4.53455	−0.166357	−0.0831783	−	0.996535i	$-0.526507\pi$
$743$	−4.53455	−0.166357	−0.0831783	+	0.996535i	$0.526507\pi$
$744$	−0.944022	−0.0346095
$745$	6.07096	0.222423
$746$	28.7795	1.05369
$747$	8.63115	0.315797
$748$	2.62579	0.0960083
$749$	5.30307	0.193770
$750$	−0.476897	−0.0174138
$751$	25.4131	0.927335	0.463668	−	0.886009i	$-0.346533\pi$
$751$	25.4131	0.927335	0.463668	+	0.886009i	$0.346533\pi$
$752$	0.404355	0.0147453
$753$	−7.28496	−0.265479
$754$	−54.3255	−1.97842
$755$	23.4818	0.854590
$756$	−6.40516	−0.232953
$757$	19.8231	0.720483	0.360241	−	0.932859i	$-0.382694\pi$
$757$	19.8231	0.720483	0.360241	+	0.932859i	$0.382694\pi$
$758$	16.6520	0.604827
$759$	−0.807929	−0.0293260
$760$	−2.34216	−0.0849590
$761$	−25.2338	−0.914724	−0.457362	−	0.889281i	$-0.651206\pi$
$761$	−25.2338	−0.914724	−0.457362	+	0.889281i	$0.651206\pi$
$762$	−9.29515	−0.336728
$763$	24.8114	0.898234
$764$	−4.28012	−0.154849
$765$	−7.28018	−0.263215
$766$	−11.6186	−0.419797
$767$	98.8155	3.56802
$768$	0.476897	0.0172085
$769$	24.1913	0.872360	0.436180	−	0.899859i	$-0.356331\pi$
$769$	24.1913	0.872360	0.436180	+	0.899859i	$0.356331\pi$
$770$	−2.32668	−0.0838476
$771$	9.31210	0.335367
$772$	0.604686	0.0217631
$773$	−39.7438	−1.42949	−0.714743	−	0.699387i	$-0.753456\pi$
$773$	−39.7438	−1.42949	−0.714743	+	0.699387i	$0.753456\pi$
$774$	2.77257	0.0996580
$775$	1.97951	0.0711061
$776$	−11.1245	−0.399346
$777$	−4.20193	−0.150743
$778$	−37.9528	−1.36068
$779$	15.3500	0.549969
$780$	3.36095	0.120341
$781$	−11.9711	−0.428360
$782$	4.44845	0.159076
$783$	−21.2207	−0.758365
$784$	−1.58657	−0.0566632
$785$	18.2090	0.649906
$786$	−1.39040	−0.0495939
$787$	44.4381	1.58405	0.792024	−	0.610490i	$-0.209028\pi$
$787$	44.4381	1.58405	0.792024	+	0.610490i	$0.209028\pi$
$788$	−16.6949	−0.594733
$789$	2.25679	0.0803439
$790$	−4.49996	−0.160101
$791$	−9.91959	−0.352700
$792$	2.77257	0.0985190
$793$	−44.2523	−1.57145
$794$	−20.9977	−0.745182
$795$	−4.62277	−0.163953
$796$	−9.73334	−0.344989
$797$	19.6040	0.694411	0.347205	−	0.937789i	$-0.387131\pi$
$797$	19.6040	0.694411	0.347205	+	0.937789i	$0.387131\pi$
$798$	−2.59882	−0.0919974
$799$	1.06175	0.0375621
$800$	−1.00000	−0.0353553
$801$	28.1982	0.996333
$802$	−3.10478	−0.109634
$803$	−7.72080	−0.272461
$804$	0.412911	0.0145623
$805$	−3.94171	−0.138927
$806$	−13.9507	−0.491392
$807$	8.27902	0.291435
$808$	13.9538	0.490894
$809$	−12.9903	−0.456714	−0.228357	−	0.973578i	$-0.573335\pi$
$809$	−12.9903	−0.456714	−0.228357	+	0.973578i	$0.573335\pi$
$810$	−7.00485	−0.246125
$811$	−7.38962	−0.259485	−0.129742	−	0.991548i	$-0.541415\pi$
$811$	−7.38962	−0.259485	−0.129742	+	0.991548i	$0.541415\pi$
$812$	17.9350	0.629396
$813$	−10.8385	−0.380124
$814$	3.78694	0.132732
$815$	6.69530	0.234526
$816$	1.25223	0.0438368
$817$	2.34216	0.0819417
$818$	−29.5312	−1.03253
$819$	−45.4628	−1.58860
$820$	6.55376	0.228867
$821$	1.76990	0.0617699	0.0308849	−	0.999523i	$-0.490167\pi$
$821$	1.76990	0.0617699	0.0308849	+	0.999523i	$0.490167\pi$
$822$	5.32796	0.185834
$823$	−16.4345	−0.572872	−0.286436	−	0.958099i	$-0.592471\pi$
$823$	−16.4345	−0.572872	−0.286436	+	0.958099i	$0.592471\pi$
$824$	1.01319	0.0352961
$825$	0.476897	0.0166034
$826$	−32.6230	−1.13510
$827$	−7.86264	−0.273411	−0.136705	−	0.990612i	$-0.543651\pi$
$827$	−7.86264	−0.273411	−0.136705	+	0.990612i	$0.543651\pi$
$828$	4.69712	0.163236
$829$	13.3539	0.463801	0.231900	−	0.972740i	$-0.425506\pi$
$829$	13.3539	0.463801	0.231900	+	0.972740i	$0.425506\pi$
$830$	3.11305	0.108056
$831$	7.13858	0.247635
$832$	7.04755	0.244330
$833$	−4.16600	−0.144343
$834$	4.26950	0.147841
$835$	0.205327	0.00710565
$836$	2.34216	0.0810052
$837$	−5.44943	−0.188360
$838$	−13.9595	−0.482223
$839$	−24.0343	−0.829756	−0.414878	−	0.909877i	$-0.636176\pi$
$839$	−24.0343	−0.829756	−0.414878	+	0.909877i	$0.636176\pi$
$840$	−1.10959	−0.0382843
$841$	30.4198	1.04896
$842$	13.6258	0.469576
$843$	−7.16645	−0.246826
$844$	−8.06797	−0.277711
$845$	36.6679	1.26141
$846$	1.12110	0.0385443
$847$	2.32668	0.0799456
$848$	−9.69344	−0.332874
$849$	9.66529	0.331712
$850$	−2.62579	−0.0900638
$851$	6.41560	0.219924
$852$	−5.70899	−0.195587
$853$	−47.7368	−1.63448	−0.817238	−	0.576300i	$-0.804496\pi$
$853$	−47.7368	−1.63448	−0.817238	+	0.576300i	$0.804496\pi$
$854$	14.6095	0.499926
$855$	−6.49380	−0.222083
$856$	−2.27925	−0.0779030
$857$	−6.92293	−0.236483	−0.118241	−	0.992985i	$-0.537726\pi$
$857$	−6.92293	−0.236483	−0.118241	+	0.992985i	$0.537726\pi$
$858$	−3.36095	−0.114741
$859$	−45.1445	−1.54031	−0.770156	−	0.637856i	$-0.779822\pi$
$859$	−45.1445	−1.54031	−0.770156	+	0.637856i	$0.779822\pi$
$860$	1.00000	0.0340997
$861$	7.27196	0.247828
$862$	7.75827	0.264248
$863$	32.2578	1.09807	0.549034	−	0.835800i	$-0.314996\pi$
$863$	32.2578	1.09807	0.549034	+	0.835800i	$0.314996\pi$
$864$	2.75292	0.0936562
$865$	13.6703	0.464805
$866$	−14.9588	−0.508321
$867$	−4.81916	−0.163667
$868$	4.60568	0.156327
$869$	4.49996	0.152651
$870$	−3.67612	−0.124632
$871$	6.10197	0.206758
$872$	−10.6639	−0.361125
$873$	−30.8434	−1.04389
$874$	3.96794	0.134218
$875$	2.32668	0.0786561
$876$	−3.68203	−0.124404
$877$	−22.6334	−0.764275	−0.382138	−	0.924105i	$-0.624812\pi$
$877$	−22.6334	−0.764275	−0.382138	+	0.924105i	$0.624812\pi$
$878$	−34.4724	−1.16339
$879$	−3.98232	−0.134320
$880$	1.00000	0.0337100
$881$	−31.3590	−1.05651	−0.528257	−	0.849085i	$-0.677154\pi$
$881$	−31.3590	−1.05651	−0.528257	+	0.849085i	$0.677154\pi$
$882$	−4.39888	−0.148118
$883$	−52.9153	−1.78074	−0.890372	−	0.455234i	$-0.849555\pi$
$883$	−52.9153	−1.78074	−0.890372	+	0.455234i	$0.849555\pi$
$884$	18.5054	0.622403
$885$	6.68670	0.224771
$886$	37.5405	1.26120
$887$	43.0907	1.44684	0.723422	−	0.690406i	$-0.242568\pi$
$887$	43.0907	1.44684	0.723422	+	0.690406i	$0.242568\pi$
$888$	1.80598	0.0606047
$889$	45.3490	1.52096
$890$	10.1704	0.340913
$891$	7.00485	0.234671
$892$	−3.23734	−0.108394
$893$	0.947064	0.0316923
$894$	−2.89522	−0.0968307
$895$	−20.1848	−0.674702
$896$	−2.32668	−0.0777288
$897$	−5.69392	−0.190114
$898$	17.1835	0.573420
$899$	15.2589	0.508913
$900$	−2.77257	−0.0924190
$901$	−25.4529	−0.847960
$902$	−6.55376	−0.218216
$903$	1.10959	0.0369247
$904$	4.26341	0.141799
$905$	−12.4760	−0.414716
$906$	−11.1984	−0.372042
$907$	−13.8566	−0.460101	−0.230051	−	0.973179i	$-0.573889\pi$
$907$	−13.8566	−0.460101	−0.230051	+	0.973179i	$0.573889\pi$
$908$	−2.83604	−0.0941174
$909$	38.6880	1.28320
$910$	−16.3974	−0.543567
$911$	−16.5938	−0.549776	−0.274888	−	0.961476i	$-0.588641\pi$
$911$	−16.5938	−0.549776	−0.274888	+	0.961476i	$0.588641\pi$
$912$	1.11697	0.0369865
$913$	−3.11305	−0.103027
$914$	9.28066	0.306977
$915$	−2.99449	−0.0989947
$916$	−6.39965	−0.211450
$917$	6.78346	0.224009
$918$	7.22858	0.238579
$919$	3.52513	0.116283	0.0581416	−	0.998308i	$-0.481483\pi$
$919$	3.52513	0.116283	0.0581416	+	0.998308i	$0.481483\pi$
$920$	1.69414	0.0558541
$921$	6.37040	0.209912
$922$	−10.9558	−0.360811
$923$	−84.3670	−2.77697
$924$	1.10959	0.0365027
$925$	−3.78694	−0.124514
$926$	−30.5108	−1.00265
$927$	2.80914	0.0922642
$928$	−7.70842	−0.253041
$929$	0.233203	0.00765113	0.00382557	−	0.999993i	$-0.498782\pi$
$929$	0.233203	0.00765113	0.00382557	+	0.999993i	$0.498782\pi$
$930$	−0.944022	−0.0309557
$931$	−3.71600	−0.121787
$932$	−5.32076	−0.174287
$933$	13.2318	0.433188
$934$	2.77066	0.0906587
$935$	2.62579	0.0858724
$936$	19.5398	0.638679
$937$	3.06613	0.100166	0.0500830	−	0.998745i	$-0.484051\pi$
$937$	3.06613	0.100166	0.0500830	+	0.998745i	$0.484051\pi$
$938$	−2.01451	−0.0657760
$939$	−3.03570	−0.0990663
$940$	0.404355	0.0131886
$941$	−14.7301	−0.480187	−0.240094	−	0.970750i	$-0.577178\pi$
$941$	−14.7301	−0.480187	−0.240094	+	0.970750i	$0.577178\pi$
$942$	−8.68380	−0.282933
$943$	−11.1030	−0.361563
$944$	14.0213	0.456353
$945$	−6.40516	−0.208360
$946$	−1.00000	−0.0325128
$947$	11.4472	0.371985	0.185993	−	0.982551i	$-0.440450\pi$
$947$	11.4472	0.371985	0.185993	+	0.982551i	$0.440450\pi$
$948$	2.14602	0.0696994
$949$	−54.4127	−1.76631
$950$	−2.34216	−0.0759897
$951$	−3.60248	−0.116818
$952$	−6.10936	−0.198006
$953$	−29.8676	−0.967507	−0.483753	−	0.875204i	$-0.660727\pi$
$953$	−29.8676	−0.967507	−0.483753	+	0.875204i	$0.660727\pi$
$954$	−26.8757	−0.870134
$955$	−4.28012	−0.138501
$956$	−24.2525	−0.784382
$957$	3.67612	0.118832
$958$	−13.0437	−0.421422
$959$	−25.9940	−0.839389
$960$	0.476897	0.0153918
$961$	−27.0815	−0.873598
$962$	26.6886	0.860476
$963$	−6.31937	−0.203639
$964$	−4.25285	−0.136975
$965$	0.604686	0.0194655
$966$	1.87979	0.0604813
$967$	−4.95197	−0.159245	−0.0796223	−	0.996825i	$-0.525371\pi$
$967$	−4.95197	−0.159245	−0.0796223	+	0.996825i	$0.525371\pi$
$968$	−1.00000	−0.0321412
$969$	2.93292	0.0942190
$970$	−11.1245	−0.357186
$971$	4.15205	0.133246	0.0666228	−	0.997778i	$-0.478778\pi$
$971$	4.15205	0.133246	0.0666228	+	0.997778i	$0.478778\pi$
$972$	11.5993	0.372049
$973$	−20.8300	−0.667778
$974$	−28.4023	−0.910068
$975$	3.36095	0.107637
$976$	−6.27911	−0.200989
$977$	−11.6724	−0.373434	−0.186717	−	0.982414i	$-0.559785\pi$
$977$	−11.6724	−0.373434	−0.186717	+	0.982414i	$0.559785\pi$
$978$	−3.19297	−0.102100
$979$	−10.1704	−0.325048
$980$	−1.58657	−0.0506811
$981$	−29.5664	−0.943982
$982$	−28.6023	−0.912736
$983$	24.3674	0.777200	0.388600	−	0.921407i	$-0.372959\pi$
$983$	24.3674	0.777200	0.388600	+	0.921407i	$0.372959\pi$
$984$	−3.12547	−0.0996363
$985$	−16.6949	−0.531945
$986$	−20.2407	−0.644595
$987$	0.448667	0.0142812
$988$	16.5065	0.525141
$989$	−1.69414	−0.0538705
$990$	2.77257	0.0881180
$991$	35.8652	1.13930	0.569648	−	0.821889i	$-0.307080\pi$
$991$	35.8652	1.13930	0.569648	+	0.821889i	$0.307080\pi$
$992$	−1.97951	−0.0628495
$993$	1.42699	0.0452841
$994$	27.8529	0.883441
$995$	−9.73334	−0.308568
$996$	−1.48460	−0.0470415
$997$	−51.5221	−1.63172	−0.815861	−	0.578248i	$-0.803737\pi$
$997$	−51.5221	−1.63172	−0.815861	+	0.578248i	$0.803737\pi$
$998$	39.0599	1.23642
$999$	10.4251	0.329837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.476897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.476897 q^{6} +2.32668 q^{7} -1.00000 q^{8} -2.77257 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.476897 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.476897 q^{6} +2.32668 q^{7} -1.00000 q^{8} -2.77257 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.476897 q^{12} +7.04755 q^{13} -2.32668 q^{14} +0.476897 q^{15} +1.00000 q^{16} +2.62579 q^{17} +2.77257 q^{18} +2.34216 q^{19} +1.00000 q^{20} +1.10959 q^{21} -1.00000 q^{22} -1.69414 q^{23} -0.476897 q^{24} +1.00000 q^{25} -7.04755 q^{26} -2.75292 q^{27} +2.32668 q^{28} +7.70842 q^{29} -0.476897 q^{30} +1.97951 q^{31} -1.00000 q^{32} +0.476897 q^{33} -2.62579 q^{34} +2.32668 q^{35} -2.77257 q^{36} -3.78694 q^{37} -2.34216 q^{38} +3.36095 q^{39} -1.00000 q^{40} +6.55376 q^{41} -1.10959 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.77257 q^{45} +1.69414 q^{46} +0.404355 q^{47} +0.476897 q^{48} -1.58657 q^{49} -1.00000 q^{50} +1.25223 q^{51} +7.04755 q^{52} -9.69344 q^{53} +2.75292 q^{54} +1.00000 q^{55} -2.32668 q^{56} +1.11697 q^{57} -7.70842 q^{58} +14.0213 q^{59} +0.476897 q^{60} -6.27911 q^{61} -1.97951 q^{62} -6.45088 q^{63} +1.00000 q^{64} +7.04755 q^{65} -0.476897 q^{66} +0.865830 q^{67} +2.62579 q^{68} -0.807929 q^{69} -2.32668 q^{70} -11.9711 q^{71} +2.77257 q^{72} -7.72080 q^{73} +3.78694 q^{74} +0.476897 q^{75} +2.34216 q^{76} +2.32668 q^{77} -3.36095 q^{78} +4.49996 q^{79} +1.00000 q^{80} +7.00485 q^{81} -6.55376 q^{82} -3.11305 q^{83} +1.10959 q^{84} +2.62579 q^{85} -1.00000 q^{86} +3.67612 q^{87} -1.00000 q^{88} -10.1704 q^{89} +2.77257 q^{90} +16.3974 q^{91} -1.69414 q^{92} +0.944022 q^{93} -0.404355 q^{94} +2.34216 q^{95} -0.476897 q^{96} +11.1245 q^{97} +1.58657 q^{98} -2.77257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 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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