LMFDB - Embedded newform 4830.2.a.cc.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.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:	$38.5677441763$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.53209$ of defining polynomial
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.06418 q^{11} +1.00000 q^{12} +4.82295 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.36959 q^{17} +1.00000 q^{18} -7.14796 q^{19} -1.00000 q^{20} -1.00000 q^{21} -5.06418 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.82295 q^{26} +1.00000 q^{27} -1.00000 q^{28} +1.67499 q^{29} -1.00000 q^{30} -2.24123 q^{31} +1.00000 q^{32} -5.06418 q^{33} -2.36959 q^{34} +1.00000 q^{35} +1.00000 q^{36} +4.12836 q^{37} -7.14796 q^{38} +4.82295 q^{39} -1.00000 q^{40} -0.610815 q^{41} -1.00000 q^{42} -10.4534 q^{43} -5.06418 q^{44} -1.00000 q^{45} -1.00000 q^{46} -2.24123 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.36959 q^{51} +4.82295 q^{52} -0.128356 q^{53} +1.00000 q^{54} +5.06418 q^{55} -1.00000 q^{56} -7.14796 q^{57} +1.67499 q^{58} -8.00000 q^{59} -1.00000 q^{60} +3.38919 q^{61} -2.24123 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.82295 q^{65} -5.06418 q^{66} -7.67499 q^{67} -2.36959 q^{68} -1.00000 q^{69} +1.00000 q^{70} -11.1925 q^{71} +1.00000 q^{72} -13.0351 q^{73} +4.12836 q^{74} +1.00000 q^{75} -7.14796 q^{76} +5.06418 q^{77} +4.82295 q^{78} +8.90673 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.610815 q^{82} -17.2763 q^{83} -1.00000 q^{84} +2.36959 q^{85} -10.4534 q^{86} +1.67499 q^{87} -5.06418 q^{88} +13.7297 q^{89} -1.00000 q^{90} -4.82295 q^{91} -1.00000 q^{92} -2.24123 q^{93} -2.24123 q^{94} +7.14796 q^{95} +1.00000 q^{96} +6.95130 q^{97} +1.00000 q^{98} -5.06418 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{21} - 6 q^{22} - 3 q^{23} + 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{30} - 18 q^{31} + 3 q^{32} - 6 q^{33} + 3 q^{35} + 3 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} - 3 q^{40} - 6 q^{41} - 3 q^{42} - 18 q^{43} - 6 q^{44} - 3 q^{45} - 3 q^{46} - 18 q^{47} + 3 q^{48} + 3 q^{49} + 3 q^{50} - 6 q^{52} + 18 q^{53} + 3 q^{54} + 6 q^{55} - 3 q^{56} - 6 q^{57} - 24 q^{59} - 3 q^{60} + 6 q^{61} - 18 q^{62} - 3 q^{63} + 3 q^{64} + 6 q^{65} - 6 q^{66} - 18 q^{67} - 3 q^{69} + 3 q^{70} - 6 q^{71} + 3 q^{72} + 6 q^{73} - 6 q^{74} + 3 q^{75} - 6 q^{76} + 6 q^{77} - 6 q^{78} - 3 q^{80} + 3 q^{81} - 6 q^{82} - 18 q^{83} - 3 q^{84} - 18 q^{86} - 6 q^{88} - 6 q^{89} - 3 q^{90} + 6 q^{91} - 3 q^{92} - 18 q^{93} - 18 q^{94} + 6 q^{95} + 3 q^{96} - 18 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^21 - 6 * q^22 - 3 * q^23 + 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^30 - 18 * q^31 + 3 * q^32 - 6 * q^33 + 3 * q^35 + 3 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 - 3 * q^40 - 6 * q^41 - 3 * q^42 - 18 * q^43 - 6 * q^44 - 3 * q^45 - 3 * q^46 - 18 * q^47 + 3 * q^48 + 3 * q^49 + 3 * q^50 - 6 * q^52 + 18 * q^53 + 3 * q^54 + 6 * q^55 - 3 * q^56 - 6 * q^57 - 24 * q^59 - 3 * q^60 + 6 * q^61 - 18 * q^62 - 3 * q^63 + 3 * q^64 + 6 * q^65 - 6 * q^66 - 18 * q^67 - 3 * q^69 + 3 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 6 * q^74 + 3 * q^75 - 6 * q^76 + 6 * q^77 - 6 * q^78 - 3 * q^80 + 3 * q^81 - 6 * q^82 - 18 * q^83 - 3 * q^84 - 18 * q^86 - 6 * q^88 - 6 * q^89 - 3 * q^90 + 6 * q^91 - 3 * q^92 - 18 * q^93 - 18 * q^94 + 6 * q^95 + 3 * q^96 - 18 * q^97 + 3 * q^98 - 6 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−5.06418	−1.52691	−0.763454	−	0.645863i	$-0.776498\pi$
$11$	−5.06418	−1.52691	−0.763454	+	0.645863i	$0.776498\pi$
$12$	1.00000	0.288675
$13$	4.82295	1.33765	0.668823	−	0.743422i	$-0.266799\pi$
$13$	4.82295	1.33765	0.668823	+	0.743422i	$0.266799\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−2.36959	−0.574709	−0.287354	−	0.957824i	$-0.592776\pi$
$17$	−2.36959	−0.574709	−0.287354	+	0.957824i	$0.592776\pi$
$18$	1.00000	0.235702
$19$	−7.14796	−1.63985	−0.819927	−	0.572468i	$-0.805986\pi$
$19$	−7.14796	−1.63985	−0.819927	+	0.572468i	$0.805986\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	−5.06418	−1.07969
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.82295	0.945858
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	1.67499	0.311038	0.155519	−	0.987833i	$-0.450295\pi$
$29$	1.67499	0.311038	0.155519	+	0.987833i	$0.450295\pi$
$30$	−1.00000	−0.182574
$31$	−2.24123	−0.402537	−0.201268	−	0.979536i	$-0.564506\pi$
$31$	−2.24123	−0.402537	−0.201268	+	0.979536i	$0.564506\pi$
$32$	1.00000	0.176777
$33$	−5.06418	−0.881560
$34$	−2.36959	−0.406380
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	4.12836	0.678697	0.339349	−	0.940661i	$-0.389793\pi$
$37$	4.12836	0.678697	0.339349	+	0.940661i	$0.389793\pi$
$38$	−7.14796	−1.15955
$39$	4.82295	0.772290
$40$	−1.00000	−0.158114
$41$	−0.610815	−0.0953932	−0.0476966	−	0.998862i	$-0.515188\pi$
$41$	−0.610815	−0.0953932	−0.0476966	+	0.998862i	$0.515188\pi$
$42$	−1.00000	−0.154303
$43$	−10.4534	−1.59412	−0.797061	−	0.603898i	$-0.793613\pi$
$43$	−10.4534	−1.59412	−0.797061	+	0.603898i	$0.793613\pi$
$44$	−5.06418	−0.763454
$45$	−1.00000	−0.149071
$46$	−1.00000	−0.147442
$47$	−2.24123	−0.326917	−0.163458	−	0.986550i	$-0.552265\pi$
$47$	−2.24123	−0.326917	−0.163458	+	0.986550i	$0.552265\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−2.36959	−0.331808
$52$	4.82295	0.668823
$53$	−0.128356	−0.0176310	−0.00881550	−	0.999961i	$-0.502806\pi$
$53$	−0.128356	−0.0176310	−0.00881550	+	0.999961i	$0.502806\pi$
$54$	1.00000	0.136083
$55$	5.06418	0.682854
$56$	−1.00000	−0.133631
$57$	−7.14796	−0.946770
$58$	1.67499	0.219937
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	−1.00000	−0.129099
$61$	3.38919	0.433941	0.216970	−	0.976178i	$-0.430383\pi$
$61$	3.38919	0.433941	0.216970	+	0.976178i	$0.430383\pi$
$62$	−2.24123	−0.284636
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−4.82295	−0.598213
$66$	−5.06418	−0.623357
$67$	−7.67499	−0.937650	−0.468825	−	0.883291i	$-0.655322\pi$
$67$	−7.67499	−0.937650	−0.468825	+	0.883291i	$0.655322\pi$
$68$	−2.36959	−0.287354
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	−11.1925	−1.32831	−0.664155	−	0.747595i	$-0.731208\pi$
$71$	−11.1925	−1.32831	−0.664155	+	0.747595i	$0.731208\pi$
$72$	1.00000	0.117851
$73$	−13.0351	−1.52564	−0.762820	−	0.646610i	$-0.776186\pi$
$73$	−13.0351	−1.52564	−0.762820	+	0.646610i	$0.776186\pi$
$74$	4.12836	0.479912
$75$	1.00000	0.115470
$76$	−7.14796	−0.819927
$77$	5.06418	0.577117
$78$	4.82295	0.546091
$79$	8.90673	1.00209	0.501043	−	0.865423i	$-0.332950\pi$
$79$	8.90673	1.00209	0.501043	+	0.865423i	$0.332950\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−0.610815	−0.0674532
$83$	−17.2763	−1.89632	−0.948161	−	0.317791i	$-0.897059\pi$
$83$	−17.2763	−1.89632	−0.948161	+	0.317791i	$0.897059\pi$
$84$	−1.00000	−0.109109
$85$	2.36959	0.257018
$86$	−10.4534	−1.12722
$87$	1.67499	0.179578
$88$	−5.06418	−0.539843
$89$	13.7297	1.45534	0.727671	−	0.685926i	$-0.240603\pi$
$89$	13.7297	1.45534	0.727671	+	0.685926i	$0.240603\pi$
$90$	−1.00000	−0.105409
$91$	−4.82295	−0.505582
$92$	−1.00000	−0.104257
$93$	−2.24123	−0.232405
$94$	−2.24123	−0.231165
$95$	7.14796	0.733365
$96$	1.00000	0.102062
$97$	6.95130	0.705798	0.352899	−	0.935661i	$-0.385196\pi$
$97$	6.95130	0.705798	0.352899	+	0.935661i	$0.385196\pi$
$98$	1.00000	0.101015
$99$	−5.06418	−0.508969
$100$	1.00000	0.100000
$101$	−10.0446	−0.999473	−0.499736	−	0.866178i	$-0.666570\pi$
$101$	−10.0446	−0.999473	−0.499736	+	0.866178i	$0.666570\pi$
$102$	−2.36959	−0.234624
$103$	2.61081	0.257251	0.128626	−	0.991693i	$-0.458943\pi$
$103$	2.61081	0.257251	0.128626	+	0.991693i	$0.458943\pi$
$104$	4.82295	0.472929
$105$	1.00000	0.0975900
$106$	−0.128356	−0.0124670
$107$	−13.6459	−1.31920	−0.659599	−	0.751617i	$-0.729274\pi$
$107$	−13.6459	−1.31920	−0.659599	+	0.751617i	$0.729274\pi$
$108$	1.00000	0.0962250
$109$	−0.610815	−0.0585054	−0.0292527	−	0.999572i	$-0.509313\pi$
$109$	−0.610815	−0.0585054	−0.0292527	+	0.999572i	$0.509313\pi$
$110$	5.06418	0.482850
$111$	4.12836	0.391846
$112$	−1.00000	−0.0944911
$113$	−2.48246	−0.233530	−0.116765	−	0.993160i	$-0.537252\pi$
$113$	−2.48246	−0.233530	−0.116765	+	0.993160i	$0.537252\pi$
$114$	−7.14796	−0.669467
$115$	1.00000	0.0932505
$116$	1.67499	0.155519
$117$	4.82295	0.445882
$118$	−8.00000	−0.736460
$119$	2.36959	0.217220
$120$	−1.00000	−0.0912871
$121$	14.6459	1.33145
$122$	3.38919	0.306842
$123$	−0.610815	−0.0550753
$124$	−2.24123	−0.201268
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	2.28581	0.202833	0.101416	−	0.994844i	$-0.467663\pi$
$127$	2.28581	0.202833	0.101416	+	0.994844i	$0.467663\pi$
$128$	1.00000	0.0883883
$129$	−10.4534	−0.920367
$130$	−4.82295	−0.423001
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	−5.06418	−0.440780
$133$	7.14796	0.619806
$134$	−7.67499	−0.663018
$135$	−1.00000	−0.0860663
$136$	−2.36959	−0.203190
$137$	−13.0351	−1.11366	−0.556831	−	0.830626i	$-0.687983\pi$
$137$	−13.0351	−1.11366	−0.556831	+	0.830626i	$0.687983\pi$
$138$	−1.00000	−0.0851257
$139$	14.8675	1.26105	0.630524	−	0.776170i	$-0.282840\pi$
$139$	14.8675	1.26105	0.630524	+	0.776170i	$0.282840\pi$
$140$	1.00000	0.0845154
$141$	−2.24123	−0.188746
$142$	−11.1925	−0.939257
$143$	−24.4243	−2.04246
$144$	1.00000	0.0833333
$145$	−1.67499	−0.139101
$146$	−13.0351	−1.07879
$147$	1.00000	0.0824786
$148$	4.12836	0.339349
$149$	11.1634	0.914544	0.457272	−	0.889327i	$-0.348827\pi$
$149$	11.1634	0.914544	0.457272	+	0.889327i	$0.348827\pi$
$150$	1.00000	0.0816497
$151$	16.4243	1.33659	0.668294	−	0.743897i	$-0.267025\pi$
$151$	16.4243	1.33659	0.668294	+	0.743897i	$0.267025\pi$
$152$	−7.14796	−0.579776
$153$	−2.36959	−0.191570
$154$	5.06418	0.408083
$155$	2.24123	0.180020
$156$	4.82295	0.386145
$157$	7.38919	0.589721	0.294861	−	0.955540i	$-0.404727\pi$
$157$	7.38919	0.589721	0.294861	+	0.955540i	$0.404727\pi$
$158$	8.90673	0.708581
$159$	−0.128356	−0.0101793
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−5.38919	−0.422114	−0.211057	−	0.977474i	$-0.567691\pi$
$163$	−5.38919	−0.422114	−0.211057	+	0.977474i	$0.567691\pi$
$164$	−0.610815	−0.0476966
$165$	5.06418	0.394246
$166$	−17.2763	−1.34090
$167$	−10.6655	−0.825321	−0.412660	−	0.910885i	$-0.635400\pi$
$167$	−10.6655	−0.825321	−0.412660	+	0.910885i	$0.635400\pi$
$168$	−1.00000	−0.0771517
$169$	10.2608	0.789295
$170$	2.36959	0.181739
$171$	−7.14796	−0.546618
$172$	−10.4534	−0.797061
$173$	26.1438	1.98768	0.993840	−	0.110828i	$-0.0353504\pi$
$173$	26.1438	1.98768	0.993840	+	0.110828i	$0.0353504\pi$
$174$	1.67499	0.126981
$175$	−1.00000	−0.0755929
$176$	−5.06418	−0.381727
$177$	−8.00000	−0.601317
$178$	13.7297	1.02908
$179$	−13.1634	−0.983882	−0.491941	−	0.870629i	$-0.663712\pi$
$179$	−13.1634	−0.983882	−0.491941	+	0.870629i	$0.663712\pi$
$180$	−1.00000	−0.0745356
$181$	−10.1676	−0.755749	−0.377874	−	0.925857i	$-0.623345\pi$
$181$	−10.1676	−0.755749	−0.377874	+	0.925857i	$0.623345\pi$
$182$	−4.82295	−0.357501
$183$	3.38919	0.250536
$184$	−1.00000	−0.0737210
$185$	−4.12836	−0.303523
$186$	−2.24123	−0.164335
$187$	12.0000	0.877527
$188$	−2.24123	−0.163458
$189$	−1.00000	−0.0727393
$190$	7.14796	0.518567
$191$	15.7743	1.14138	0.570692	−	0.821164i	$-0.306675\pi$
$191$	15.7743	1.14138	0.570692	+	0.821164i	$0.306675\pi$
$192$	1.00000	0.0721688
$193$	−14.2567	−1.02622	−0.513110	−	0.858323i	$-0.671507\pi$
$193$	−14.2567	−1.02622	−0.513110	+	0.858323i	$0.671507\pi$
$194$	6.95130	0.499075
$195$	−4.82295	−0.345378
$196$	1.00000	0.0714286
$197$	2.48246	0.176868	0.0884339	−	0.996082i	$-0.471814\pi$
$197$	2.48246	0.176868	0.0884339	+	0.996082i	$0.471814\pi$
$198$	−5.06418	−0.359895
$199$	2.12836	0.150875	0.0754376	−	0.997151i	$-0.475965\pi$
$199$	2.12836	0.150875	0.0754376	+	0.997151i	$0.475965\pi$
$200$	1.00000	0.0707107
$201$	−7.67499	−0.541352
$202$	−10.0446	−0.706734
$203$	−1.67499	−0.117561
$204$	−2.36959	−0.165904
$205$	0.610815	0.0426611
$206$	2.61081	0.181904
$207$	−1.00000	−0.0695048
$208$	4.82295	0.334411
$209$	36.1985	2.50390
$210$	1.00000	0.0690066
$211$	−9.16344	−0.630837	−0.315419	−	0.948953i	$-0.602145\pi$
$211$	−9.16344	−0.630837	−0.315419	+	0.948953i	$0.602145\pi$
$212$	−0.128356	−0.00881550
$213$	−11.1925	−0.766900
$214$	−13.6459	−0.932814
$215$	10.4534	0.712913
$216$	1.00000	0.0680414
$217$	2.24123	0.152145
$218$	−0.610815	−0.0413696
$219$	−13.0351	−0.880829
$220$	5.06418	0.341427
$221$	−11.4284	−0.768756
$222$	4.12836	0.277077
$223$	−9.43376	−0.631731	−0.315866	−	0.948804i	$-0.602295\pi$
$223$	−9.43376	−0.631731	−0.315866	+	0.948804i	$0.602295\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	−2.48246	−0.165131
$227$	−11.6304	−0.771938	−0.385969	−	0.922512i	$-0.626133\pi$
$227$	−11.6304	−0.771938	−0.385969	+	0.922512i	$0.626133\pi$
$228$	−7.14796	−0.473385
$229$	−21.6851	−1.43299	−0.716496	−	0.697591i	$-0.754255\pi$
$229$	−21.6851	−1.43299	−0.716496	+	0.697591i	$0.754255\pi$
$230$	1.00000	0.0659380
$231$	5.06418	0.333198
$232$	1.67499	0.109969
$233$	12.6108	0.826162	0.413081	−	0.910694i	$-0.364453\pi$
$233$	12.6108	0.826162	0.413081	+	0.910694i	$0.364453\pi$
$234$	4.82295	0.315286
$235$	2.24123	0.146202
$236$	−8.00000	−0.520756
$237$	8.90673	0.578554
$238$	2.36959	0.153597
$239$	−11.1925	−0.723985	−0.361992	−	0.932181i	$-0.617903\pi$
$239$	−11.1925	−0.723985	−0.361992	+	0.932181i	$0.617903\pi$
$240$	−1.00000	−0.0645497
$241$	−2.36959	−0.152638	−0.0763192	−	0.997083i	$-0.524317\pi$
$241$	−2.36959	−0.152638	−0.0763192	+	0.997083i	$0.524317\pi$
$242$	14.6459	0.941474
$243$	1.00000	0.0641500
$244$	3.38919	0.216970
$245$	−1.00000	−0.0638877
$246$	−0.610815	−0.0389441
$247$	−34.4742	−2.19354
$248$	−2.24123	−0.142318
$249$	−17.2763	−1.09484
$250$	−1.00000	−0.0632456
$251$	−1.34461	−0.0848709	−0.0424355	−	0.999099i	$-0.513512\pi$
$251$	−1.34461	−0.0848709	−0.0424355	+	0.999099i	$0.513512\pi$
$252$	−1.00000	−0.0629941
$253$	5.06418	0.318382
$254$	2.28581	0.143424
$255$	2.36959	0.148389
$256$	1.00000	0.0625000
$257$	5.09327	0.317710	0.158855	−	0.987302i	$-0.449220\pi$
$257$	5.09327	0.317710	0.158855	+	0.987302i	$0.449220\pi$
$258$	−10.4534	−0.650798
$259$	−4.12836	−0.256524
$260$	−4.82295	−0.299107
$261$	1.67499	0.103679
$262$	−4.00000	−0.247121
$263$	0.482459	0.0297497	0.0148748	−	0.999889i	$-0.495265\pi$
$263$	0.482459	0.0297497	0.0148748	+	0.999889i	$0.495265\pi$
$264$	−5.06418	−0.311679
$265$	0.128356	0.00788482
$266$	7.14796	0.438269
$267$	13.7297	0.840242
$268$	−7.67499	−0.468825
$269$	−2.69459	−0.164292	−0.0821461	−	0.996620i	$-0.526177\pi$
$269$	−2.69459	−0.164292	−0.0821461	+	0.996620i	$0.526177\pi$
$270$	−1.00000	−0.0608581
$271$	24.5371	1.49053	0.745263	−	0.666771i	$-0.232324\pi$
$271$	24.5371	1.49053	0.745263	+	0.666771i	$0.232324\pi$
$272$	−2.36959	−0.143677
$273$	−4.82295	−0.291898
$274$	−13.0351	−0.787478
$275$	−5.06418	−0.305381
$276$	−1.00000	−0.0601929
$277$	24.4534	1.46926	0.734630	−	0.678468i	$-0.237356\pi$
$277$	24.4534	1.46926	0.734630	+	0.678468i	$0.237356\pi$
$278$	14.8675	0.891695
$279$	−2.24123	−0.134179
$280$	1.00000	0.0597614
$281$	6.58172	0.392632	0.196316	−	0.980541i	$-0.437102\pi$
$281$	6.58172	0.392632	0.196316	+	0.980541i	$0.437102\pi$
$282$	−2.24123	−0.133463
$283$	−4.04458	−0.240425	−0.120213	−	0.992748i	$-0.538358\pi$
$283$	−4.04458	−0.240425	−0.120213	+	0.992748i	$0.538358\pi$
$284$	−11.1925	−0.664155
$285$	7.14796	0.423408
$286$	−24.4243	−1.44424
$287$	0.610815	0.0360552
$288$	1.00000	0.0589256
$289$	−11.3851	−0.669710
$290$	−1.67499	−0.0983589
$291$	6.95130	0.407493
$292$	−13.0351	−0.762820
$293$	−14.7392	−0.861072	−0.430536	−	0.902574i	$-0.641675\pi$
$293$	−14.7392	−0.861072	−0.430536	+	0.902574i	$0.641675\pi$
$294$	1.00000	0.0583212
$295$	8.00000	0.465778
$296$	4.12836	0.239956
$297$	−5.06418	−0.293853
$298$	11.1634	0.646681
$299$	−4.82295	−0.278918
$300$	1.00000	0.0577350
$301$	10.4534	0.602522
$302$	16.4243	0.945110
$303$	−10.0446	−0.577046
$304$	−7.14796	−0.409963
$305$	−3.38919	−0.194064
$306$	−2.36959	−0.135460
$307$	9.38919	0.535869	0.267935	−	0.963437i	$-0.413659\pi$
$307$	9.38919	0.535869	0.267935	+	0.963437i	$0.413659\pi$
$308$	5.06418	0.288558
$309$	2.61081	0.148524
$310$	2.24123	0.127293
$311$	−24.9513	−1.41486	−0.707429	−	0.706784i	$-0.750145\pi$
$311$	−24.9513	−1.41486	−0.707429	+	0.706784i	$0.750145\pi$
$312$	4.82295	0.273046
$313$	−6.69459	−0.378401	−0.189200	−	0.981938i	$-0.560590\pi$
$313$	−6.69459	−0.378401	−0.189200	+	0.981938i	$0.560590\pi$
$314$	7.38919	0.416996
$315$	1.00000	0.0563436
$316$	8.90673	0.501043
$317$	23.9026	1.34250	0.671252	−	0.741229i	$-0.265757\pi$
$317$	23.9026	1.34250	0.671252	+	0.741229i	$0.265757\pi$
$318$	−0.128356	−0.00719782
$319$	−8.48246	−0.474927
$320$	−1.00000	−0.0559017
$321$	−13.6459	−0.761640
$322$	1.00000	0.0557278
$323$	16.9377	0.942438
$324$	1.00000	0.0555556
$325$	4.82295	0.267529
$326$	−5.38919	−0.298479
$327$	−0.610815	−0.0337781
$328$	−0.610815	−0.0337266
$329$	2.24123	0.123563
$330$	5.06418	0.278774
$331$	28.9959	1.59376	0.796879	−	0.604139i	$-0.206483\pi$
$331$	28.9959	1.59376	0.796879	+	0.604139i	$0.206483\pi$
$332$	−17.2763	−0.948161
$333$	4.12836	0.226232
$334$	−10.6655	−0.583590
$335$	7.67499	0.419330
$336$	−1.00000	−0.0545545
$337$	0.0290958	0.00158495	0.000792476	−	1.00000i	$-0.499748\pi$
$337$	0.0290958	0.00158495	0.000792476		1.00000i	$0.499748\pi$
$338$	10.2608	0.558116
$339$	−2.48246	−0.134829
$340$	2.36959	0.128509
$341$	11.3500	0.614636
$342$	−7.14796	−0.386517
$343$	−1.00000	−0.0539949
$344$	−10.4534	−0.563608
$345$	1.00000	0.0538382
$346$	26.1438	1.40550
$347$	25.6459	1.37674	0.688372	−	0.725358i	$-0.258326\pi$
$347$	25.6459	1.37674	0.688372	+	0.725358i	$0.258326\pi$
$348$	1.67499	0.0897890
$349$	−26.6263	−1.42527	−0.712636	−	0.701533i	$-0.752499\pi$
$349$	−26.6263	−1.42527	−0.712636	+	0.701533i	$0.752499\pi$
$350$	−1.00000	−0.0534522
$351$	4.82295	0.257430
$352$	−5.06418	−0.269922
$353$	10.6500	0.566843	0.283422	−	0.958995i	$-0.408530\pi$
$353$	10.6500	0.566843	0.283422	+	0.958995i	$0.408530\pi$
$354$	−8.00000	−0.425195
$355$	11.1925	0.594038
$356$	13.7297	0.727671
$357$	2.36959	0.125412
$358$	−13.1634	−0.695709
$359$	−4.48246	−0.236575	−0.118288	−	0.992979i	$-0.537740\pi$
$359$	−4.48246	−0.236575	−0.118288	+	0.992979i	$0.537740\pi$
$360$	−1.00000	−0.0527046
$361$	32.0933	1.68912
$362$	−10.1676	−0.534395
$363$	14.6459	0.768710
$364$	−4.82295	−0.252791
$365$	13.0351	0.682287
$366$	3.38919	0.177156
$367$	24.6810	1.28834	0.644168	−	0.764884i	$-0.277204\pi$
$367$	24.6810	1.28834	0.644168	+	0.764884i	$0.277204\pi$
$368$	−1.00000	−0.0521286
$369$	−0.610815	−0.0317977
$370$	−4.12836	−0.214623
$371$	0.128356	0.00666389
$372$	−2.24123	−0.116202
$373$	29.6067	1.53298	0.766488	−	0.642258i	$-0.222002\pi$
$373$	29.6067	1.53298	0.766488	+	0.642258i	$0.222002\pi$
$374$	12.0000	0.620505
$375$	−1.00000	−0.0516398
$376$	−2.24123	−0.115583
$377$	8.07840	0.416059
$378$	−1.00000	−0.0514344
$379$	9.38919	0.482290	0.241145	−	0.970489i	$-0.422477\pi$
$379$	9.38919	0.482290	0.241145	+	0.970489i	$0.422477\pi$
$380$	7.14796	0.366682
$381$	2.28581	0.117105
$382$	15.7743	0.807081
$383$	27.9418	1.42776	0.713880	−	0.700268i	$-0.246936\pi$
$383$	27.9418	1.42776	0.713880	+	0.700268i	$0.246936\pi$
$384$	1.00000	0.0510310
$385$	−5.06418	−0.258094
$386$	−14.2567	−0.725647
$387$	−10.4534	−0.531374
$388$	6.95130	0.352899
$389$	−7.22163	−0.366151	−0.183076	−	0.983099i	$-0.558605\pi$
$389$	−7.22163	−0.366151	−0.183076	+	0.983099i	$0.558605\pi$
$390$	−4.82295	−0.244219
$391$	2.36959	0.119835
$392$	1.00000	0.0505076
$393$	−4.00000	−0.201773
$394$	2.48246	0.125064
$395$	−8.90673	−0.448146
$396$	−5.06418	−0.254485
$397$	−25.2472	−1.26712	−0.633561	−	0.773693i	$-0.718407\pi$
$397$	−25.2472	−1.26712	−0.633561	+	0.773693i	$0.718407\pi$
$398$	2.12836	0.106685
$399$	7.14796	0.357845
$400$	1.00000	0.0500000
$401$	−5.02498	−0.250935	−0.125468	−	0.992098i	$-0.540043\pi$
$401$	−5.02498	−0.250935	−0.125468	+	0.992098i	$0.540043\pi$
$402$	−7.67499	−0.382794
$403$	−10.8093	−0.538451
$404$	−10.0446	−0.499736
$405$	−1.00000	−0.0496904
$406$	−1.67499	−0.0831285
$407$	−20.9067	−1.03631
$408$	−2.36959	−0.117312
$409$	−13.2608	−0.655706	−0.327853	−	0.944729i	$-0.606325\pi$
$409$	−13.2608	−0.655706	−0.327853	+	0.944729i	$0.606325\pi$
$410$	0.610815	0.0301660
$411$	−13.0351	−0.642973
$412$	2.61081	0.128626
$413$	8.00000	0.393654
$414$	−1.00000	−0.0491473
$415$	17.2763	0.848061
$416$	4.82295	0.236464
$417$	14.8675	0.728066
$418$	36.1985	1.77053
$419$	12.8621	0.628357	0.314179	−	0.949364i	$-0.398271\pi$
$419$	12.8621	0.628357	0.314179	+	0.949364i	$0.398271\pi$
$420$	1.00000	0.0487950
$421$	11.4783	0.559420	0.279710	−	0.960085i	$-0.409762\pi$
$421$	11.4783	0.559420	0.279710	+	0.960085i	$0.409762\pi$
$422$	−9.16344	−0.446069
$423$	−2.24123	−0.108972
$424$	−0.128356	−0.00623350
$425$	−2.36959	−0.114942
$426$	−11.1925	−0.542280
$427$	−3.38919	−0.164014
$428$	−13.6459	−0.659599
$429$	−24.4243	−1.17921
$430$	10.4534	0.504106
$431$	−4.00000	−0.192673	−0.0963366	−	0.995349i	$-0.530713\pi$
$431$	−4.00000	−0.192673	−0.0963366	+	0.995349i	$0.530713\pi$
$432$	1.00000	0.0481125
$433$	−14.7837	−0.710462	−0.355231	−	0.934779i	$-0.615598\pi$
$433$	−14.7837	−0.710462	−0.355231	+	0.934779i	$0.615598\pi$
$434$	2.24123	0.107582
$435$	−1.67499	−0.0803097
$436$	−0.610815	−0.0292527
$437$	7.14796	0.341933
$438$	−13.0351	−0.622840
$439$	−7.88713	−0.376432	−0.188216	−	0.982128i	$-0.560270\pi$
$439$	−7.88713	−0.376432	−0.188216	+	0.982128i	$0.560270\pi$
$440$	5.06418	0.241425
$441$	1.00000	0.0476190
$442$	−11.4284	−0.543593
$443$	−9.64590	−0.458290	−0.229145	−	0.973392i	$-0.573593\pi$
$443$	−9.64590	−0.458290	−0.229145	+	0.973392i	$0.573593\pi$
$444$	4.12836	0.195923
$445$	−13.7297	−0.650849
$446$	−9.43376	−0.446702
$447$	11.1634	0.528012
$448$	−1.00000	−0.0472456
$449$	−21.9418	−1.03550	−0.517749	−	0.855533i	$-0.673230\pi$
$449$	−21.9418	−1.03550	−0.517749	+	0.855533i	$0.673230\pi$
$450$	1.00000	0.0471405
$451$	3.09327	0.145657
$452$	−2.48246	−0.116765
$453$	16.4243	0.771679
$454$	−11.6304	−0.545842
$455$	4.82295	0.226103
$456$	−7.14796	−0.334734
$457$	−4.76827	−0.223050	−0.111525	−	0.993762i	$-0.535574\pi$
$457$	−4.76827	−0.223050	−0.111525	+	0.993762i	$0.535574\pi$
$458$	−21.6851	−1.01328
$459$	−2.36959	−0.110603
$460$	1.00000	0.0466252
$461$	−41.0797	−1.91327	−0.956635	−	0.291289i	$-0.905916\pi$
$461$	−41.0797	−1.91327	−0.956635	+	0.291289i	$0.905916\pi$
$462$	5.06418	0.235607
$463$	9.23173	0.429035	0.214518	−	0.976720i	$-0.431182\pi$
$463$	9.23173	0.429035	0.214518	+	0.976720i	$0.431182\pi$
$464$	1.67499	0.0777596
$465$	2.24123	0.103935
$466$	12.6108	0.584185
$467$	15.7980	0.731043	0.365521	−	0.930803i	$-0.380891\pi$
$467$	15.7980	0.731043	0.365521	+	0.930803i	$0.380891\pi$
$468$	4.82295	0.222941
$469$	7.67499	0.354398
$470$	2.24123	0.103380
$471$	7.38919	0.340476
$472$	−8.00000	−0.368230
$473$	52.9377	2.43408
$474$	8.90673	0.409099
$475$	−7.14796	−0.327971
$476$	2.36959	0.108610
$477$	−0.128356	−0.00587700
$478$	−11.1925	−0.511935
$479$	−13.3892	−0.611767	−0.305884	−	0.952069i	$-0.598952\pi$
$479$	−13.3892	−0.611767	−0.305884	+	0.952069i	$0.598952\pi$
$480$	−1.00000	−0.0456435
$481$	19.9108	0.907856
$482$	−2.36959	−0.107932
$483$	1.00000	0.0455016
$484$	14.6459	0.665723
$485$	−6.95130	−0.315642
$486$	1.00000	0.0453609
$487$	23.9317	1.08445	0.542224	−	0.840234i	$-0.317582\pi$
$487$	23.9317	1.08445	0.542224	+	0.840234i	$0.317582\pi$
$488$	3.38919	0.153421
$489$	−5.38919	−0.243707
$490$	−1.00000	−0.0451754
$491$	10.5526	0.476233	0.238117	−	0.971237i	$-0.423470\pi$
$491$	10.5526	0.476233	0.238117	+	0.971237i	$0.423470\pi$
$492$	−0.610815	−0.0275376
$493$	−3.96904	−0.178756
$494$	−34.4742	−1.55107
$495$	5.06418	0.227618
$496$	−2.24123	−0.100634
$497$	11.1925	0.502054
$498$	−17.2763	−0.774170
$499$	11.0933	0.496603	0.248302	−	0.968683i	$-0.420128\pi$
$499$	11.0933	0.496603	0.248302	+	0.968683i	$0.420128\pi$
$500$	−1.00000	−0.0447214
$501$	−10.6655	−0.476499
$502$	−1.34461	−0.0600128
$503$	−15.7743	−0.703339	−0.351670	−	0.936124i	$-0.614386\pi$
$503$	−15.7743	−0.703339	−0.351670	+	0.936124i	$0.614386\pi$
$504$	−1.00000	−0.0445435
$505$	10.0446	0.446978
$506$	5.06418	0.225130
$507$	10.2608	0.455699
$508$	2.28581	0.101416
$509$	−42.8931	−1.90120	−0.950602	−	0.310413i	$-0.899533\pi$
$509$	−42.8931	−1.90120	−0.950602	+	0.310413i	$0.899533\pi$
$510$	2.36959	0.104927
$511$	13.0351	0.576638
$512$	1.00000	0.0441942
$513$	−7.14796	−0.315590
$514$	5.09327	0.224655
$515$	−2.61081	−0.115046
$516$	−10.4534	−0.460184
$517$	11.3500	0.499172
$518$	−4.12836	−0.181390
$519$	26.1438	1.14759
$520$	−4.82295	−0.211500
$521$	−8.00538	−0.350722	−0.175361	−	0.984504i	$-0.556109\pi$
$521$	−8.00538	−0.350722	−0.175361	+	0.984504i	$0.556109\pi$
$522$	1.67499	0.0733124
$523$	−23.1581	−1.01263	−0.506316	−	0.862348i	$-0.668993\pi$
$523$	−23.1581	−1.01263	−0.506316	+	0.862348i	$0.668993\pi$
$524$	−4.00000	−0.174741
$525$	−1.00000	−0.0436436
$526$	0.482459	0.0210362
$527$	5.31078	0.231341
$528$	−5.06418	−0.220390
$529$	1.00000	0.0434783
$530$	0.128356	0.00557541
$531$	−8.00000	−0.347170
$532$	7.14796	0.309903
$533$	−2.94593	−0.127602
$534$	13.7297	0.594141
$535$	13.6459	0.589964
$536$	−7.67499	−0.331509
$537$	−13.1634	−0.568044
$538$	−2.69459	−0.116172
$539$	−5.06418	−0.218130
$540$	−1.00000	−0.0430331
$541$	9.42839	0.405358	0.202679	−	0.979245i	$-0.435035\pi$
$541$	9.42839	0.405358	0.202679	+	0.979245i	$0.435035\pi$
$542$	24.5371	1.05396
$543$	−10.1676	−0.436332
$544$	−2.36959	−0.101595
$545$	0.610815	0.0261644
$546$	−4.82295	−0.206403
$547$	33.8135	1.44576	0.722879	−	0.690974i	$-0.242818\pi$
$547$	33.8135	1.44576	0.722879	+	0.690974i	$0.242818\pi$
$548$	−13.0351	−0.556831
$549$	3.38919	0.144647
$550$	−5.06418	−0.215937
$551$	−11.9728	−0.510057
$552$	−1.00000	−0.0425628
$553$	−8.90673	−0.378753
$554$	24.4534	1.03892
$555$	−4.12836	−0.175239
$556$	14.8675	0.630524
$557$	−6.16756	−0.261328	−0.130664	−	0.991427i	$-0.541711\pi$
$557$	−6.16756	−0.261328	−0.130664	+	0.991427i	$0.541711\pi$
$558$	−2.24123	−0.0948788
$559$	−50.4160	−2.13237
$560$	1.00000	0.0422577
$561$	12.0000	0.506640
$562$	6.58172	0.277633
$563$	23.2371	0.979327	0.489664	−	0.871911i	$-0.337120\pi$
$563$	23.2371	0.979327	0.489664	+	0.871911i	$0.337120\pi$
$564$	−2.24123	−0.0943728
$565$	2.48246	0.104438
$566$	−4.04458	−0.170006
$567$	−1.00000	−0.0419961
$568$	−11.1925	−0.469628
$569$	−5.36009	−0.224707	−0.112353	−	0.993668i	$-0.535839\pi$
$569$	−5.36009	−0.224707	−0.112353	+	0.993668i	$0.535839\pi$
$570$	7.14796	0.299395
$571$	11.0933	0.464239	0.232120	−	0.972687i	$-0.425434\pi$
$571$	11.0933	0.464239	0.232120	+	0.972687i	$0.425434\pi$
$572$	−24.4243	−1.02123
$573$	15.7743	0.658979
$574$	0.610815	0.0254949
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	4.83656	0.201349	0.100674	−	0.994919i	$-0.467900\pi$
$577$	4.83656	0.201349	0.100674	+	0.994919i	$0.467900\pi$
$578$	−11.3851	−0.473556
$579$	−14.2567	−0.592489
$580$	−1.67499	−0.0695503
$581$	17.2763	0.716742
$582$	6.95130	0.288141
$583$	0.650015	0.0269209
$584$	−13.0351	−0.539396
$585$	−4.82295	−0.199404
$586$	−14.7392	−0.608870
$587$	12.6500	0.522122	0.261061	−	0.965322i	$-0.415928\pi$
$587$	12.6500	0.522122	0.261061	+	0.965322i	$0.415928\pi$
$588$	1.00000	0.0412393
$589$	16.0202	0.660101
$590$	8.00000	0.329355
$591$	2.48246	0.102115
$592$	4.12836	0.169674
$593$	−33.9418	−1.39382	−0.696912	−	0.717157i	$-0.745443\pi$
$593$	−33.9418	−1.39382	−0.696912	+	0.717157i	$0.745443\pi$
$594$	−5.06418	−0.207786
$595$	−2.36959	−0.0971435
$596$	11.1634	0.457272
$597$	2.12836	0.0871078
$598$	−4.82295	−0.197225
$599$	6.71007	0.274166	0.137083	−	0.990560i	$-0.456227\pi$
$599$	6.71007	0.274166	0.137083	+	0.990560i	$0.456227\pi$
$600$	1.00000	0.0408248
$601$	−24.7784	−1.01073	−0.505365	−	0.862905i	$-0.668642\pi$
$601$	−24.7784	−1.01073	−0.505365	+	0.862905i	$0.668642\pi$
$602$	10.4534	0.426047
$603$	−7.67499	−0.312550
$604$	16.4243	0.668294
$605$	−14.6459	−0.595440
$606$	−10.0446	−0.408033
$607$	22.3405	0.906772	0.453386	−	0.891314i	$-0.350216\pi$
$607$	22.3405	0.906772	0.453386	+	0.891314i	$0.350216\pi$
$608$	−7.14796	−0.289888
$609$	−1.67499	−0.0678741
$610$	−3.38919	−0.137224
$611$	−10.8093	−0.437299
$612$	−2.36959	−0.0957848
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	9.38919	0.378917
$615$	0.610815	0.0246304
$616$	5.06418	0.204042
$617$	18.6500	0.750821	0.375411	−	0.926859i	$-0.377502\pi$
$617$	18.6500	0.750821	0.375411	+	0.926859i	$0.377502\pi$
$618$	2.61081	0.105022
$619$	46.6965	1.87689	0.938445	−	0.345430i	$-0.112267\pi$
$619$	46.6965	1.87689	0.938445	+	0.345430i	$0.112267\pi$
$620$	2.24123	0.0900099
$621$	−1.00000	−0.0401286
$622$	−24.9513	−1.00046
$623$	−13.7297	−0.550068
$624$	4.82295	0.193072
$625$	1.00000	0.0400000
$626$	−6.69459	−0.267570
$627$	36.1985	1.44563
$628$	7.38919	0.294861
$629$	−9.78249	−0.390053
$630$	1.00000	0.0398410
$631$	44.1985	1.75952	0.879758	−	0.475422i	$-0.157705\pi$
$631$	44.1985	1.75952	0.879758	+	0.475422i	$0.157705\pi$
$632$	8.90673	0.354291
$633$	−9.16344	−0.364214
$634$	23.9026	0.949294
$635$	−2.28581	−0.0907095
$636$	−0.128356	−0.00508963
$637$	4.82295	0.191092
$638$	−8.48246	−0.335824
$639$	−11.1925	−0.442770
$640$	−1.00000	−0.0395285
$641$	35.1735	1.38927	0.694636	−	0.719362i	$-0.255566\pi$
$641$	35.1735	1.38927	0.694636	+	0.719362i	$0.255566\pi$
$642$	−13.6459	−0.538561
$643$	−35.8188	−1.41256	−0.706278	−	0.707934i	$-0.749627\pi$
$643$	−35.8188	−1.41256	−0.706278	+	0.707934i	$0.749627\pi$
$644$	1.00000	0.0394055
$645$	10.4534	0.411601
$646$	16.9377	0.666404
$647$	31.3465	1.23236	0.616179	−	0.787606i	$-0.288680\pi$
$647$	31.3465	1.23236	0.616179	+	0.787606i	$0.288680\pi$
$648$	1.00000	0.0392837
$649$	40.5134	1.59029
$650$	4.82295	0.189172
$651$	2.24123	0.0878407
$652$	−5.38919	−0.211057
$653$	2.57161	0.100635	0.0503175	−	0.998733i	$-0.483977\pi$
$653$	2.57161	0.100635	0.0503175	+	0.998733i	$0.483977\pi$
$654$	−0.610815	−0.0238847
$655$	4.00000	0.156293
$656$	−0.610815	−0.0238483
$657$	−13.0351	−0.508547
$658$	2.24123	0.0873722
$659$	−27.3601	−1.06580	−0.532899	−	0.846179i	$-0.678897\pi$
$659$	−27.3601	−1.06580	−0.532899	+	0.846179i	$0.678897\pi$
$660$	5.06418	0.197123
$661$	−36.3851	−1.41522	−0.707608	−	0.706606i	$-0.750225\pi$
$661$	−36.3851	−1.41522	−0.707608	+	0.706606i	$0.750225\pi$
$662$	28.9959	1.12696
$663$	−11.4284	−0.443842
$664$	−17.2763	−0.670451
$665$	−7.14796	−0.277186
$666$	4.12836	0.159971
$667$	−1.67499	−0.0648560
$668$	−10.6655	−0.412660
$669$	−9.43376	−0.364730
$670$	7.67499	0.296511
$671$	−17.1634	−0.662587
$672$	−1.00000	−0.0385758
$673$	−28.1284	−1.08427	−0.542134	−	0.840292i	$-0.682384\pi$
$673$	−28.1284	−1.08427	−0.542134	+	0.840292i	$0.682384\pi$
$674$	0.0290958	0.00112073
$675$	1.00000	0.0384900
$676$	10.2608	0.394647
$677$	−7.47834	−0.287416	−0.143708	−	0.989620i	$-0.545903\pi$
$677$	−7.47834	−0.287416	−0.143708	+	0.989620i	$0.545903\pi$
$678$	−2.48246	−0.0953383
$679$	−6.95130	−0.266767
$680$	2.36959	0.0908694
$681$	−11.6304	−0.445678
$682$	11.3500	0.434613
$683$	−10.6108	−0.406012	−0.203006	−	0.979178i	$-0.565071\pi$
$683$	−10.6108	−0.406012	−0.203006	+	0.979178i	$0.565071\pi$
$684$	−7.14796	−0.273309
$685$	13.0351	0.498045
$686$	−1.00000	−0.0381802
$687$	−21.6851	−0.827338
$688$	−10.4534	−0.398531
$689$	−0.619052	−0.0235840
$690$	1.00000	0.0380693
$691$	9.22163	0.350807	0.175404	−	0.984497i	$-0.443877\pi$
$691$	9.22163	0.350807	0.175404	+	0.984497i	$0.443877\pi$
$692$	26.1438	0.993840
$693$	5.06418	0.192372
$694$	25.6459	0.973505
$695$	−14.8675	−0.563957
$696$	1.67499	0.0634904
$697$	1.44738	0.0548233
$698$	−26.6263	−1.00782
$699$	12.6108	0.476985
$700$	−1.00000	−0.0377964
$701$	−11.2216	−0.423835	−0.211918	−	0.977288i	$-0.567971\pi$
$701$	−11.2216	−0.423835	−0.211918	+	0.977288i	$0.567971\pi$
$702$	4.82295	0.182030
$703$	−29.5093	−1.11296
$704$	−5.06418	−0.190863
$705$	2.24123	0.0844096
$706$	10.6500	0.400819
$707$	10.0446	0.377765
$708$	−8.00000	−0.300658
$709$	42.0310	1.57851	0.789253	−	0.614068i	$-0.210468\pi$
$709$	42.0310	1.57851	0.789253	+	0.614068i	$0.210468\pi$
$710$	11.1925	0.420048
$711$	8.90673	0.334028
$712$	13.7297	0.514541
$713$	2.24123	0.0839347
$714$	2.36959	0.0886795
$715$	24.4243	0.913416
$716$	−13.1634	−0.491941
$717$	−11.1925	−0.417993
$718$	−4.48246	−0.167284
$719$	−35.8188	−1.33582	−0.667908	−	0.744243i	$-0.732810\pi$
$719$	−35.8188	−1.33582	−0.667908	+	0.744243i	$0.732810\pi$
$720$	−1.00000	−0.0372678
$721$	−2.61081	−0.0972318
$722$	32.0933	1.19439
$723$	−2.36959	−0.0881258
$724$	−10.1676	−0.377874
$725$	1.67499	0.0622077
$726$	14.6459	0.543560
$727$	24.9377	0.924888	0.462444	−	0.886649i	$-0.346973\pi$
$727$	24.9377	0.924888	0.462444	+	0.886649i	$0.346973\pi$
$728$	−4.82295	−0.178750
$729$	1.00000	0.0370370
$730$	13.0351	0.482450
$731$	24.7701	0.916156
$732$	3.38919	0.125268
$733$	−10.4825	−0.387178	−0.193589	−	0.981083i	$-0.562013\pi$
$733$	−10.4825	−0.387178	−0.193589	+	0.981083i	$0.562013\pi$
$734$	24.6810	0.910992
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	38.8675	1.43170
$738$	−0.610815	−0.0224844
$739$	44.9377	1.65306	0.826530	−	0.562893i	$-0.190312\pi$
$739$	44.9377	1.65306	0.826530	+	0.562893i	$0.190312\pi$
$740$	−4.12836	−0.151761
$741$	−34.4742	−1.26644
$742$	0.128356	0.00471208
$743$	36.1985	1.32799	0.663997	−	0.747735i	$-0.268859\pi$
$743$	36.1985	1.32799	0.663997	+	0.747735i	$0.268859\pi$
$744$	−2.24123	−0.0821675
$745$	−11.1634	−0.408997
$746$	29.6067	1.08398
$747$	−17.2763	−0.632107
$748$	12.0000	0.438763
$749$	13.6459	0.498610
$750$	−1.00000	−0.0365148
$751$	1.47834	0.0539454	0.0269727	−	0.999636i	$-0.491413\pi$
$751$	1.47834	0.0539454	0.0269727	+	0.999636i	$0.491413\pi$
$752$	−2.24123	−0.0817292
$753$	−1.34461	−0.0490002
$754$	8.07840	0.294198
$755$	−16.4243	−0.597740
$756$	−1.00000	−0.0363696
$757$	12.5217	0.455107	0.227554	−	0.973766i	$-0.426927\pi$
$757$	12.5217	0.455107	0.227554	+	0.973766i	$0.426927\pi$
$758$	9.38919	0.341031
$759$	5.06418	0.183818
$760$	7.14796	0.259284
$761$	−4.20676	−0.152495	−0.0762474	−	0.997089i	$-0.524294\pi$
$761$	−4.20676	−0.152495	−0.0762474	+	0.997089i	$0.524294\pi$
$762$	2.28581	0.0828060
$763$	0.610815	0.0221130
$764$	15.7743	0.570692
$765$	2.36959	0.0856725
$766$	27.9418	1.00958
$767$	−38.5836	−1.39317
$768$	1.00000	0.0360844
$769$	37.4938	1.35206	0.676031	−	0.736873i	$-0.263699\pi$
$769$	37.4938	1.35206	0.676031	+	0.736873i	$0.263699\pi$
$770$	−5.06418	−0.182500
$771$	5.09327	0.183430
$772$	−14.2567	−0.513110
$773$	25.0351	0.900449	0.450225	−	0.892915i	$-0.351344\pi$
$773$	25.0351	0.900449	0.450225	+	0.892915i	$0.351344\pi$
$774$	−10.4534	−0.375738
$775$	−2.24123	−0.0805073
$776$	6.95130	0.249537
$777$	−4.12836	−0.148104
$778$	−7.22163	−0.258908
$779$	4.36608	0.156431
$780$	−4.82295	−0.172689
$781$	56.6810	2.02820
$782$	2.36959	0.0847362
$783$	1.67499	0.0598593
$784$	1.00000	0.0357143
$785$	−7.38919	−0.263731
$786$	−4.00000	−0.142675
$787$	−34.3405	−1.22411	−0.612053	−	0.790817i	$-0.709656\pi$
$787$	−34.3405	−1.22411	−0.612053	+	0.790817i	$0.709656\pi$
$788$	2.48246	0.0884339
$789$	0.482459	0.0171760
$790$	−8.90673	−0.316887
$791$	2.48246	0.0882661
$792$	−5.06418	−0.179948
$793$	16.3459	0.580459
$794$	−25.2472	−0.895990
$795$	0.128356	0.00455230
$796$	2.12836	0.0754376
$797$	−18.9959	−0.672869	−0.336434	−	0.941707i	$-0.609221\pi$
$797$	−18.9959	−0.672869	−0.336434	+	0.941707i	$0.609221\pi$
$798$	7.14796	0.253035
$799$	5.31078	0.187882
$800$	1.00000	0.0353553
$801$	13.7297	0.485114
$802$	−5.02498	−0.177438
$803$	66.0120	2.32951
$804$	−7.67499	−0.270676
$805$	−1.00000	−0.0352454
$806$	−10.8093	−0.380743
$807$	−2.69459	−0.0948542
$808$	−10.0446	−0.353367
$809$	−32.0702	−1.12753	−0.563763	−	0.825936i	$-0.690647\pi$
$809$	−32.0702	−1.12753	−0.563763	+	0.825936i	$0.690647\pi$
$810$	−1.00000	−0.0351364
$811$	14.5526	0.511012	0.255506	−	0.966808i	$-0.417758\pi$
$811$	14.5526	0.511012	0.255506	+	0.966808i	$0.417758\pi$
$812$	−1.67499	−0.0587807
$813$	24.5371	0.860555
$814$	−20.9067	−0.732780
$815$	5.38919	0.188775
$816$	−2.36959	−0.0829521
$817$	74.7202	2.61413
$818$	−13.2608	−0.463654
$819$	−4.82295	−0.168527
$820$	0.610815	0.0213306
$821$	−19.9709	−0.696989	−0.348495	−	0.937311i	$-0.613307\pi$
$821$	−19.9709	−0.696989	−0.348495	+	0.937311i	$0.613307\pi$
$822$	−13.0351	−0.454651
$823$	20.0993	0.700616	0.350308	−	0.936635i	$-0.386077\pi$
$823$	20.0993	0.700616	0.350308	+	0.936635i	$0.386077\pi$
$824$	2.61081	0.0909520
$825$	−5.06418	−0.176312
$826$	8.00000	0.278356
$827$	4.68098	0.162774	0.0813868	−	0.996683i	$-0.474065\pi$
$827$	4.68098	0.162774	0.0813868	+	0.996683i	$0.474065\pi$
$828$	−1.00000	−0.0347524
$829$	−26.8520	−0.932610	−0.466305	−	0.884624i	$-0.654415\pi$
$829$	−26.8520	−0.932610	−0.466305	+	0.884624i	$0.654415\pi$
$830$	17.2763	0.599670
$831$	24.4534	0.848278
$832$	4.82295	0.167206
$833$	−2.36959	−0.0821013
$834$	14.8675	0.514820
$835$	10.6655	0.369095
$836$	36.1985	1.25195
$837$	−2.24123	−0.0774682
$838$	12.8621	0.444316
$839$	28.5134	0.984393	0.492196	−	0.870484i	$-0.336194\pi$
$839$	28.5134	0.984393	0.492196	+	0.870484i	$0.336194\pi$
$840$	1.00000	0.0345033
$841$	−26.1944	−0.903255
$842$	11.4783	0.395570
$843$	6.58172	0.226686
$844$	−9.16344	−0.315419
$845$	−10.2608	−0.352983
$846$	−2.24123	−0.0770551
$847$	−14.6459	−0.503239
$848$	−0.128356	−0.00440775
$849$	−4.04458	−0.138810
$850$	−2.36959	−0.0812761
$851$	−4.12836	−0.141518
$852$	−11.1925	−0.383450
$853$	−33.2472	−1.13836	−0.569181	−	0.822212i	$-0.692740\pi$
$853$	−33.2472	−1.13836	−0.569181	+	0.822212i	$0.692740\pi$
$854$	−3.38919	−0.115976
$855$	7.14796	0.244455
$856$	−13.6459	−0.466407
$857$	−46.1985	−1.57811	−0.789056	−	0.614322i	$-0.789430\pi$
$857$	−46.1985	−1.57811	−0.789056	+	0.614322i	$0.789430\pi$
$858$	−24.4243	−0.833831
$859$	−20.9649	−0.715314	−0.357657	−	0.933853i	$-0.616424\pi$
$859$	−20.9649	−0.715314	−0.357657	+	0.933853i	$0.616424\pi$
$860$	10.4534	0.356457
$861$	0.610815	0.0208165
$862$	−4.00000	−0.136241
$863$	53.0161	1.80469	0.902344	−	0.431016i	$-0.141845\pi$
$863$	53.0161	1.80469	0.902344	+	0.431016i	$0.141845\pi$
$864$	1.00000	0.0340207
$865$	−26.1438	−0.888917
$866$	−14.7837	−0.502372
$867$	−11.3851	−0.386657
$868$	2.24123	0.0760723
$869$	−45.1052	−1.53009
$870$	−1.67499	−0.0567876
$871$	−37.0161	−1.25424
$872$	−0.610815	−0.0206848
$873$	6.95130	0.235266
$874$	7.14796	0.241783
$875$	1.00000	0.0338062
$876$	−13.0351	−0.440415
$877$	−50.9478	−1.72038	−0.860192	−	0.509970i	$-0.829657\pi$
$877$	−50.9478	−1.72038	−0.860192	+	0.509970i	$0.829657\pi$
$878$	−7.88713	−0.266178
$879$	−14.7392	−0.497140
$880$	5.06418	0.170713
$881$	29.1688	0.982722	0.491361	−	0.870956i	$-0.336500\pi$
$881$	29.1688	0.982722	0.491361	+	0.870956i	$0.336500\pi$
$882$	1.00000	0.0336718
$883$	−33.6459	−1.13227	−0.566137	−	0.824311i	$-0.691563\pi$
$883$	−33.6459	−1.13227	−0.566137	+	0.824311i	$0.691563\pi$
$884$	−11.4284	−0.384378
$885$	8.00000	0.268917
$886$	−9.64590	−0.324060
$887$	2.75465	0.0924922	0.0462461	−	0.998930i	$-0.485274\pi$
$887$	2.75465	0.0924922	0.0462461	+	0.998930i	$0.485274\pi$
$888$	4.12836	0.138539
$889$	−2.28581	−0.0766635
$890$	−13.7297	−0.460220
$891$	−5.06418	−0.169656
$892$	−9.43376	−0.315866
$893$	16.0202	0.536096
$894$	11.1634	0.373361
$895$	13.1634	0.440005
$896$	−1.00000	−0.0334077
$897$	−4.82295	−0.161034
$898$	−21.9418	−0.732208
$899$	−3.75404	−0.125204
$900$	1.00000	0.0333333
$901$	0.304149	0.0101327
$902$	3.09327	0.102995
$903$	10.4534	0.347866
$904$	−2.48246	−0.0825654
$905$	10.1676	0.337981
$906$	16.4243	0.545660
$907$	−18.2276	−0.605238	−0.302619	−	0.953112i	$-0.597861\pi$
$907$	−18.2276	−0.605238	−0.302619	+	0.953112i	$0.597861\pi$
$908$	−11.6304	−0.385969
$909$	−10.0446	−0.333158
$910$	4.82295	0.159879
$911$	18.3541	0.608099	0.304049	−	0.952656i	$-0.401661\pi$
$911$	18.3541	0.608099	0.304049	+	0.952656i	$0.401661\pi$
$912$	−7.14796	−0.236692
$913$	87.4903	2.89551
$914$	−4.76827	−0.157720
$915$	−3.38919	−0.112043
$916$	−21.6851	−0.716496
$917$	4.00000	0.132092
$918$	−2.36959	−0.0782080
$919$	−50.7511	−1.67413	−0.837063	−	0.547107i	$-0.815729\pi$
$919$	−50.7511	−1.67413	−0.837063	+	0.547107i	$0.815729\pi$
$920$	1.00000	0.0329690
$921$	9.38919	0.309384
$922$	−41.0797	−1.35289
$923$	−53.9810	−1.77681
$924$	5.06418	0.166599
$925$	4.12836	0.135739
$926$	9.23173	0.303374
$927$	2.61081	0.0857504
$928$	1.67499	0.0549843
$929$	−10.8176	−0.354913	−0.177457	−	0.984129i	$-0.556787\pi$
$929$	−10.8176	−0.354913	−0.177457	+	0.984129i	$0.556787\pi$
$930$	2.24123	0.0734928
$931$	−7.14796	−0.234265
$932$	12.6108	0.413081
$933$	−24.9513	−0.816869
$934$	15.7980	0.516925
$935$	−12.0000	−0.392442
$936$	4.82295	0.157643
$937$	5.87702	0.191994	0.0959970	−	0.995382i	$-0.469396\pi$
$937$	5.87702	0.191994	0.0959970	+	0.995382i	$0.469396\pi$
$938$	7.67499	0.250597
$939$	−6.69459	−0.218470
$940$	2.24123	0.0731008
$941$	−5.03508	−0.164139	−0.0820695	−	0.996627i	$-0.526153\pi$
$941$	−5.03508	−0.164139	−0.0820695	+	0.996627i	$0.526153\pi$
$942$	7.38919	0.240753
$943$	0.610815	0.0198909
$944$	−8.00000	−0.260378
$945$	1.00000	0.0325300
$946$	52.9377	1.72115
$947$	3.94181	0.128092	0.0640458	−	0.997947i	$-0.479600\pi$
$947$	3.94181	0.128092	0.0640458	+	0.997947i	$0.479600\pi$
$948$	8.90673	0.289277
$949$	−62.8675	−2.04077
$950$	−7.14796	−0.231910
$951$	23.9026	0.775095
$952$	2.36959	0.0767987
$953$	−46.2877	−1.49940	−0.749702	−	0.661775i	$-0.769803\pi$
$953$	−46.2877	−1.49940	−0.749702	+	0.661775i	$0.769803\pi$
$954$	−0.128356	−0.00415566
$955$	−15.7743	−0.510443
$956$	−11.1925	−0.361992
$957$	−8.48246	−0.274199
$958$	−13.3892	−0.432585
$959$	13.0351	0.420925
$960$	−1.00000	−0.0322749
$961$	−25.9769	−0.837964
$962$	19.9108	0.641951
$963$	−13.6459	−0.439733
$964$	−2.36959	−0.0763192
$965$	14.2567	0.458940
$966$	1.00000	0.0321745
$967$	−40.1302	−1.29050	−0.645250	−	0.763971i	$-0.723247\pi$
$967$	−40.1302	−1.29050	−0.645250	+	0.763971i	$0.723247\pi$
$968$	14.6459	0.470737
$969$	16.9377	0.544117
$970$	−6.95130	−0.223193
$971$	23.5039	0.754277	0.377138	−	0.926157i	$-0.376908\pi$
$971$	23.5039	0.754277	0.377138	+	0.926157i	$0.376908\pi$
$972$	1.00000	0.0320750
$973$	−14.8675	−0.476631
$974$	23.9317	0.766821
$975$	4.82295	0.154458
$976$	3.38919	0.108485
$977$	16.7202	0.534926	0.267463	−	0.963568i	$-0.413815\pi$
$977$	16.7202	0.534926	0.267463	+	0.963568i	$0.413815\pi$
$978$	−5.38919	−0.172327
$979$	−69.5295	−2.22217
$980$	−1.00000	−0.0319438
$981$	−0.610815	−0.0195018
$982$	10.5526	0.336748
$983$	−20.9067	−0.666821	−0.333411	−	0.942782i	$-0.608200\pi$
$983$	−20.9067	−0.666821	−0.333411	+	0.942782i	$0.608200\pi$
$984$	−0.610815	−0.0194721
$985$	−2.48246	−0.0790977
$986$	−3.96904	−0.126400
$987$	2.24123	0.0713391
$988$	−34.4742	−1.09677
$989$	10.4534	0.332398
$990$	5.06418	0.160950
$991$	53.9810	1.71476	0.857382	−	0.514681i	$-0.172090\pi$
$991$	53.9810	1.71476	0.857382	+	0.514681i	$0.172090\pi$
$992$	−2.24123	−0.0711591
$993$	28.9959	0.920156
$994$	11.1925	0.355006
$995$	−2.12836	−0.0674734
$996$	−17.2763	−0.547421
$997$	19.5229	0.618297	0.309149	−	0.951014i	$-0.399956\pi$
$997$	19.5229	0.618297	0.309149	+	0.951014i	$0.399956\pi$
$998$	11.0933	0.351151
$999$	4.12836	0.130615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.cc.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.cc.1.1	✓	3	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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.06418 q^{11} +1.00000 q^{12} +4.82295 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.36959 q^{17} +1.00000 q^{18} -7.14796 q^{19} -1.00000 q^{20} -1.00000 q^{21} -5.06418 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.82295 q^{26} +1.00000 q^{27} -1.00000 q^{28} +1.67499 q^{29} -1.00000 q^{30} -2.24123 q^{31} +1.00000 q^{32} -5.06418 q^{33} -2.36959 q^{34} +1.00000 q^{35} +1.00000 q^{36} +4.12836 q^{37} -7.14796 q^{38} +4.82295 q^{39} -1.00000 q^{40} -0.610815 q^{41} -1.00000 q^{42} -10.4534 q^{43} -5.06418 q^{44} -1.00000 q^{45} -1.00000 q^{46} -2.24123 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.36959 q^{51} +4.82295 q^{52} -0.128356 q^{53} +1.00000 q^{54} +5.06418 q^{55} -1.00000 q^{56} -7.14796 q^{57} +1.67499 q^{58} -8.00000 q^{59} -1.00000 q^{60} +3.38919 q^{61} -2.24123 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.82295 q^{65} -5.06418 q^{66} -7.67499 q^{67} -2.36959 q^{68} -1.00000 q^{69} +1.00000 q^{70} -11.1925 q^{71} +1.00000 q^{72} -13.0351 q^{73} +4.12836 q^{74} +1.00000 q^{75} -7.14796 q^{76} +5.06418 q^{77} +4.82295 q^{78} +8.90673 q^{79} -1.00000 q^{80} +1.00000 q^{81} -0.610815 q^{82} -17.2763 q^{83} -1.00000 q^{84} +2.36959 q^{85} -10.4534 q^{86} +1.67499 q^{87} -5.06418 q^{88} +13.7297 q^{89} -1.00000 q^{90} -4.82295 q^{91} -1.00000 q^{92} -2.24123 q^{93} -2.24123 q^{94} +7.14796 q^{95} +1.00000 q^{96} +6.95130 q^{97} +1.00000 q^{98} -5.06418 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{21} - 6 q^{22} - 3 q^{23} + 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{30} - 18 q^{31} + 3 q^{32} - 6 q^{33} + 3 q^{35} + 3 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{39} - 3 q^{40} - 6 q^{41} - 3 q^{42} - 18 q^{43} - 6 q^{44} - 3 q^{45} - 3 q^{46} - 18 q^{47} + 3 q^{48} + 3 q^{49} + 3 q^{50} - 6 q^{52} + 18 q^{53} + 3 q^{54} + 6 q^{55} - 3 q^{56} - 6 q^{57} - 24 q^{59} - 3 q^{60} + 6 q^{61} - 18 q^{62} - 3 q^{63} + 3 q^{64} + 6 q^{65} - 6 q^{66} - 18 q^{67} - 3 q^{69} + 3 q^{70} - 6 q^{71} + 3 q^{72} + 6 q^{73} - 6 q^{74} + 3 q^{75} - 6 q^{76} + 6 q^{77} - 6 q^{78} - 3 q^{80} + 3 q^{81} - 6 q^{82} - 18 q^{83} - 3 q^{84} - 18 q^{86} - 6 q^{88} - 6 q^{89} - 3 q^{90} + 6 q^{91} - 3 q^{92} - 18 q^{93} - 18 q^{94} + 6 q^{95} + 3 q^{96} - 18 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^21 - 6 * q^22 - 3 * q^23 + 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^30 - 18 * q^31 + 3 * q^32 - 6 * q^33 + 3 * q^35 + 3 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 - 3 * q^40 - 6 * q^41 - 3 * q^42 - 18 * q^43 - 6 * q^44 - 3 * q^45 - 3 * q^46 - 18 * q^47 + 3 * q^48 + 3 * q^49 + 3 * q^50 - 6 * q^52 + 18 * q^53 + 3 * q^54 + 6 * q^55 - 3 * q^56 - 6 * q^57 - 24 * q^59 - 3 * q^60 + 6 * q^61 - 18 * q^62 - 3 * q^63 + 3 * q^64 + 6 * q^65 - 6 * q^66 - 18 * q^67 - 3 * q^69 + 3 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 6 * q^74 + 3 * q^75 - 6 * q^76 + 6 * q^77 - 6 * q^78 - 3 * q^80 + 3 * q^81 - 6 * q^82 - 18 * q^83 - 3 * q^84 - 18 * q^86 - 6 * q^88 - 6 * q^89 - 3 * q^90 + 6 * q^91 - 3 * q^92 - 18 * q^93 - 18 * q^94 + 6 * q^95 + 3 * q^96 - 18 * q^97 + 3 * q^98 - 6 * q^99

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