LMFDB - Embedded newform 4830.2.a.bx.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:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*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			$1.80194$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.60388 q^{11} -1.00000 q^{12} -1.10992 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +0.493959 q^{17} -1.00000 q^{18} -2.49396 q^{19} +1.00000 q^{20} +1.00000 q^{21} +1.60388 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.10992 q^{26} -1.00000 q^{27} -1.00000 q^{28} +1.82371 q^{29} +1.00000 q^{30} +9.70171 q^{31} -1.00000 q^{32} +1.60388 q^{33} -0.493959 q^{34} -1.00000 q^{35} +1.00000 q^{36} -8.76809 q^{37} +2.49396 q^{38} +1.10992 q^{39} -1.00000 q^{40} -2.98792 q^{41} -1.00000 q^{42} +1.60388 q^{43} -1.60388 q^{44} +1.00000 q^{45} -1.00000 q^{46} +5.70171 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -0.493959 q^{51} -1.10992 q^{52} -0.219833 q^{53} +1.00000 q^{54} -1.60388 q^{55} +1.00000 q^{56} +2.49396 q^{57} -1.82371 q^{58} +3.20775 q^{59} -1.00000 q^{60} +4.76809 q^{61} -9.70171 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.10992 q^{65} -1.60388 q^{66} -12.8116 q^{67} +0.493959 q^{68} -1.00000 q^{69} +1.00000 q^{70} -6.59179 q^{71} -1.00000 q^{72} -6.00000 q^{73} +8.76809 q^{74} -1.00000 q^{75} -2.49396 q^{76} +1.60388 q^{77} -1.10992 q^{78} +8.98792 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.98792 q^{82} +8.27413 q^{83} +1.00000 q^{84} +0.493959 q^{85} -1.60388 q^{86} -1.82371 q^{87} +1.60388 q^{88} -10.5375 q^{89} -1.00000 q^{90} +1.10992 q^{91} +1.00000 q^{92} -9.70171 q^{93} -5.70171 q^{94} -2.49396 q^{95} +1.00000 q^{96} -4.67025 q^{97} -1.00000 q^{98} -1.60388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 4 q^{11} - 3 q^{12} - 4 q^{13} + 3 q^{14} - 3 q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 4 q^{26} - 3 q^{27} - 3 q^{28} - 2 q^{29} + 3 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 2 q^{38} + 4 q^{39} - 3 q^{40} + 10 q^{41} - 3 q^{42} - 4 q^{43} + 4 q^{44} + 3 q^{45} - 3 q^{46} - 10 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 8 q^{51} - 4 q^{52} - 2 q^{53} + 3 q^{54} + 4 q^{55} + 3 q^{56} - 2 q^{57} + 2 q^{58} - 8 q^{59} - 3 q^{60} - 6 q^{61} - 2 q^{62} - 3 q^{63} + 3 q^{64} - 4 q^{65} + 4 q^{66} - 12 q^{67} - 8 q^{68} - 3 q^{69} + 3 q^{70} + 8 q^{71} - 3 q^{72} - 18 q^{73} + 6 q^{74} - 3 q^{75} + 2 q^{76} - 4 q^{77} - 4 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 10 q^{82} + 14 q^{83} + 3 q^{84} - 8 q^{85} + 4 q^{86} + 2 q^{87} - 4 q^{88} - 16 q^{89} - 3 q^{90} + 4 q^{91} + 3 q^{92} - 2 q^{93} + 10 q^{94} + 2 q^{95} + 3 q^{96} - 12 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 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 + 4 * q^11 - 3 * q^12 - 4 * q^13 + 3 * q^14 - 3 * q^15 + 3 * q^16 - 8 * q^17 - 3 * q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 4 * q^26 - 3 * q^27 - 3 * q^28 - 2 * q^29 + 3 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 2 * q^38 + 4 * q^39 - 3 * q^40 + 10 * q^41 - 3 * q^42 - 4 * q^43 + 4 * q^44 + 3 * q^45 - 3 * q^46 - 10 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 8 * q^51 - 4 * q^52 - 2 * q^53 + 3 * q^54 + 4 * q^55 + 3 * q^56 - 2 * q^57 + 2 * q^58 - 8 * q^59 - 3 * q^60 - 6 * q^61 - 2 * q^62 - 3 * q^63 + 3 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 - 8 * q^68 - 3 * q^69 + 3 * q^70 + 8 * q^71 - 3 * q^72 - 18 * q^73 + 6 * q^74 - 3 * q^75 + 2 * q^76 - 4 * q^77 - 4 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 10 * q^82 + 14 * q^83 + 3 * q^84 - 8 * q^85 + 4 * q^86 + 2 * q^87 - 4 * q^88 - 16 * q^89 - 3 * q^90 + 4 * q^91 + 3 * q^92 - 2 * q^93 + 10 * q^94 + 2 * q^95 + 3 * q^96 - 12 * q^97 - 3 * q^98 + 4 * 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
$11$	−1.60388	−0.483587	−0.241793	−	0.970328i	$-0.577736\pi$
$11$	−1.60388	−0.483587	−0.241793	+	0.970328i	$0.577736\pi$
$12$	−1.00000	−0.288675
$13$	−1.10992	−0.307835	−0.153918	−	0.988084i	$-0.549189\pi$
$13$	−1.10992	−0.307835	−0.153918	+	0.988084i	$0.549189\pi$
$14$	1.00000	0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	0.493959	0.119803	0.0599014	−	0.998204i	$-0.480921\pi$
$17$	0.493959	0.119803	0.0599014	+	0.998204i	$0.480921\pi$
$18$	−1.00000	−0.235702
$19$	−2.49396	−0.572153	−0.286077	−	0.958207i	$-0.592351\pi$
$19$	−2.49396	−0.572153	−0.286077	+	0.958207i	$0.592351\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	1.60388	0.341947
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	1.10992	0.217672
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	1.82371	0.338654	0.169327	−	0.985560i	$-0.445841\pi$
$29$	1.82371	0.338654	0.169327	+	0.985560i	$0.445841\pi$
$30$	1.00000	0.182574
$31$	9.70171	1.74248	0.871239	−	0.490859i	$-0.163317\pi$
$31$	9.70171	1.74248	0.871239	+	0.490859i	$0.163317\pi$
$32$	−1.00000	−0.176777
$33$	1.60388	0.279199
$34$	−0.493959	−0.0847133
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−8.76809	−1.44146	−0.720732	−	0.693214i	$-0.756194\pi$
$37$	−8.76809	−1.44146	−0.720732	+	0.693214i	$0.756194\pi$
$38$	2.49396	0.404574
$39$	1.10992	0.177729
$40$	−1.00000	−0.158114
$41$	−2.98792	−0.466634	−0.233317	−	0.972401i	$-0.574958\pi$
$41$	−2.98792	−0.466634	−0.233317	+	0.972401i	$0.574958\pi$
$42$	−1.00000	−0.154303
$43$	1.60388	0.244589	0.122294	−	0.992494i	$-0.460975\pi$
$43$	1.60388	0.244589	0.122294	+	0.992494i	$0.460975\pi$
$44$	−1.60388	−0.241793
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	5.70171	0.831680	0.415840	−	0.909438i	$-0.363488\pi$
$47$	5.70171	0.831680	0.415840	+	0.909438i	$0.363488\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−0.493959	−0.0691681
$52$	−1.10992	−0.153918
$53$	−0.219833	−0.0301963	−0.0150982	−	0.999886i	$-0.504806\pi$
$53$	−0.219833	−0.0301963	−0.0150982	+	0.999886i	$0.504806\pi$
$54$	1.00000	0.136083
$55$	−1.60388	−0.216267
$56$	1.00000	0.133631
$57$	2.49396	0.330333
$58$	−1.82371	−0.239465
$59$	3.20775	0.417614	0.208807	−	0.977957i	$-0.433042\pi$
$59$	3.20775	0.417614	0.208807	+	0.977957i	$0.433042\pi$
$60$	−1.00000	−0.129099
$61$	4.76809	0.610491	0.305245	−	0.952274i	$-0.401262\pi$
$61$	4.76809	0.610491	0.305245	+	0.952274i	$0.401262\pi$
$62$	−9.70171	−1.23212
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−1.10992	−0.137668
$66$	−1.60388	−0.197423
$67$	−12.8116	−1.56519	−0.782595	−	0.622532i	$-0.786104\pi$
$67$	−12.8116	−1.56519	−0.782595	+	0.622532i	$0.786104\pi$
$68$	0.493959	0.0599014
$69$	−1.00000	−0.120386
$70$	1.00000	0.119523
$71$	−6.59179	−0.782302	−0.391151	−	0.920327i	$-0.627923\pi$
$71$	−6.59179	−0.782302	−0.391151	+	0.920327i	$0.627923\pi$
$72$	−1.00000	−0.117851
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	8.76809	1.01927
$75$	−1.00000	−0.115470
$76$	−2.49396	−0.286077
$77$	1.60388	0.182779
$78$	−1.10992	−0.125673
$79$	8.98792	1.01122	0.505610	−	0.862762i	$-0.331268\pi$
$79$	8.98792	1.01122	0.505610	+	0.862762i	$0.331268\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.98792	0.329960
$83$	8.27413	0.908203	0.454102	−	0.890950i	$-0.349960\pi$
$83$	8.27413	0.908203	0.454102	+	0.890950i	$0.349960\pi$
$84$	1.00000	0.109109
$85$	0.493959	0.0535774
$86$	−1.60388	−0.172950
$87$	−1.82371	−0.195522
$88$	1.60388	0.170974
$89$	−10.5375	−1.11697	−0.558486	−	0.829514i	$-0.688618\pi$
$89$	−10.5375	−1.11697	−0.558486	+	0.829514i	$0.688618\pi$
$90$	−1.00000	−0.105409
$91$	1.10992	0.116351
$92$	1.00000	0.104257
$93$	−9.70171	−1.00602
$94$	−5.70171	−0.588086
$95$	−2.49396	−0.255875
$96$	1.00000	0.102062
$97$	−4.67025	−0.474192	−0.237096	−	0.971486i	$-0.576196\pi$
$97$	−4.67025	−0.474192	−0.237096	+	0.971486i	$0.576196\pi$
$98$	−1.00000	−0.101015
$99$	−1.60388	−0.161196
$100$	1.00000	0.100000
$101$	−7.87800	−0.783891	−0.391945	−	0.919989i	$-0.628198\pi$
$101$	−7.87800	−0.783891	−0.391945	+	0.919989i	$0.628198\pi$
$102$	0.493959	0.0489092
$103$	−12.5483	−1.23642	−0.618208	−	0.786014i	$-0.712141\pi$
$103$	−12.5483	−1.23642	−0.618208	+	0.786014i	$0.712141\pi$
$104$	1.10992	0.108836
$105$	1.00000	0.0975900
$106$	0.219833	0.0213520
$107$	12.6353	1.22150	0.610752	−	0.791822i	$-0.290867\pi$
$107$	12.6353	1.22150	0.610752	+	0.791822i	$0.290867\pi$
$108$	−1.00000	−0.0962250
$109$	−6.98792	−0.669321	−0.334661	−	0.942339i	$-0.608622\pi$
$109$	−6.98792	−0.669321	−0.334661	+	0.942339i	$0.608622\pi$
$110$	1.60388	0.152924
$111$	8.76809	0.832230
$112$	−1.00000	−0.0944911
$113$	−10.5483	−0.992296	−0.496148	−	0.868238i	$-0.665253\pi$
$113$	−10.5483	−0.992296	−0.496148	+	0.868238i	$0.665253\pi$
$114$	−2.49396	−0.233581
$115$	1.00000	0.0932505
$116$	1.82371	0.169327
$117$	−1.10992	−0.102612
$118$	−3.20775	−0.295297
$119$	−0.493959	−0.0452812
$120$	1.00000	0.0912871
$121$	−8.42758	−0.766144
$122$	−4.76809	−0.431682
$123$	2.98792	0.269412
$124$	9.70171	0.871239
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	−6.04354	−0.536278	−0.268139	−	0.963380i	$-0.586409\pi$
$127$	−6.04354	−0.536278	−0.268139	+	0.963380i	$0.586409\pi$
$128$	−1.00000	−0.0883883
$129$	−1.60388	−0.141213
$130$	1.10992	0.0973461
$131$	−0.439665	−0.0384137	−0.0192069	−	0.999816i	$-0.506114\pi$
$131$	−0.439665	−0.0384137	−0.0192069	+	0.999816i	$0.506114\pi$
$132$	1.60388	0.139599
$133$	2.49396	0.216254
$134$	12.8116	1.10676
$135$	−1.00000	−0.0860663
$136$	−0.493959	−0.0423567
$137$	15.9758	1.36491	0.682454	−	0.730929i	$-0.260913\pi$
$137$	15.9758	1.36491	0.682454	+	0.730929i	$0.260913\pi$
$138$	1.00000	0.0851257
$139$	6.76809	0.574062	0.287031	−	0.957921i	$-0.407332\pi$
$139$	6.76809	0.574062	0.287031	+	0.957921i	$0.407332\pi$
$140$	−1.00000	−0.0845154
$141$	−5.70171	−0.480171
$142$	6.59179	0.553171
$143$	1.78017	0.148865
$144$	1.00000	0.0833333
$145$	1.82371	0.151451
$146$	6.00000	0.496564
$147$	−1.00000	−0.0824786
$148$	−8.76809	−0.720732
$149$	12.7681	1.04600	0.523001	−	0.852332i	$-0.324812\pi$
$149$	12.7681	1.04600	0.523001	+	0.852332i	$0.324812\pi$
$150$	1.00000	0.0816497
$151$	−6.21983	−0.506163	−0.253081	−	0.967445i	$-0.581444\pi$
$151$	−6.21983	−0.506163	−0.253081	+	0.967445i	$0.581444\pi$
$152$	2.49396	0.202287
$153$	0.493959	0.0399342
$154$	−1.60388	−0.129244
$155$	9.70171	0.779260
$156$	1.10992	0.0888644
$157$	−14.9879	−1.19617	−0.598083	−	0.801434i	$-0.704071\pi$
$157$	−14.9879	−1.19617	−0.598083	+	0.801434i	$0.704071\pi$
$158$	−8.98792	−0.715040
$159$	0.219833	0.0174339
$160$	−1.00000	−0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	20.6353	1.61628	0.808142	−	0.588988i	$-0.200473\pi$
$163$	20.6353	1.61628	0.808142	+	0.588988i	$0.200473\pi$
$164$	−2.98792	−0.233317
$165$	1.60388	0.124862
$166$	−8.27413	−0.642197
$167$	−20.4698	−1.58400	−0.792000	−	0.610521i	$-0.790960\pi$
$167$	−20.4698	−1.58400	−0.792000	+	0.610521i	$0.790960\pi$
$168$	−1.00000	−0.0771517
$169$	−11.7681	−0.905237
$170$	−0.493959	−0.0378849
$171$	−2.49396	−0.190718
$172$	1.60388	0.122294
$173$	−15.3491	−1.16697	−0.583486	−	0.812123i	$-0.698312\pi$
$173$	−15.3491	−1.16697	−0.583486	+	0.812123i	$0.698312\pi$
$174$	1.82371	0.138255
$175$	−1.00000	−0.0755929
$176$	−1.60388	−0.120897
$177$	−3.20775	−0.241109
$178$	10.5375	0.789819
$179$	11.6474	0.870569	0.435284	−	0.900293i	$-0.356648\pi$
$179$	11.6474	0.870569	0.435284	+	0.900293i	$0.356648\pi$
$180$	1.00000	0.0745356
$181$	25.5991	1.90277	0.951383	−	0.308011i	$-0.0996635\pi$
$181$	25.5991	1.90277	0.951383	+	0.308011i	$0.0996635\pi$
$182$	−1.10992	−0.0822725
$183$	−4.76809	−0.352467
$184$	−1.00000	−0.0737210
$185$	−8.76809	−0.644642
$186$	9.70171	0.711364
$187$	−0.792249	−0.0579350
$188$	5.70171	0.415840
$189$	1.00000	0.0727393
$190$	2.49396	0.180931
$191$	7.01208	0.507376	0.253688	−	0.967286i	$-0.418356\pi$
$191$	7.01208	0.507376	0.253688	+	0.967286i	$0.418356\pi$
$192$	−1.00000	−0.0721688
$193$	−22.6353	−1.62933	−0.814664	−	0.579934i	$-0.803078\pi$
$193$	−22.6353	−1.62933	−0.814664	+	0.579934i	$0.803078\pi$
$194$	4.67025	0.335304
$195$	1.10992	0.0794828
$196$	1.00000	0.0714286
$197$	2.54825	0.181556	0.0907778	−	0.995871i	$-0.471065\pi$
$197$	2.54825	0.181556	0.0907778	+	0.995871i	$0.471065\pi$
$198$	1.60388	0.113982
$199$	−17.6233	−1.24928	−0.624640	−	0.780913i	$-0.714754\pi$
$199$	−17.6233	−1.24928	−0.624640	+	0.780913i	$0.714754\pi$
$200$	−1.00000	−0.0707107
$201$	12.8116	0.903662
$202$	7.87800	0.554294
$203$	−1.82371	−0.127999
$204$	−0.493959	−0.0345841
$205$	−2.98792	−0.208685
$206$	12.5483	0.874278
$207$	1.00000	0.0695048
$208$	−1.10992	−0.0769588
$209$	4.00000	0.276686
$210$	−1.00000	−0.0690066
$211$	14.9638	1.03015	0.515074	−	0.857146i	$-0.327765\pi$
$211$	14.9638	1.03015	0.515074	+	0.857146i	$0.327765\pi$
$212$	−0.219833	−0.0150982
$213$	6.59179	0.451662
$214$	−12.6353	−0.863734
$215$	1.60388	0.109383
$216$	1.00000	0.0680414
$217$	−9.70171	−0.658595
$218$	6.98792	0.473282
$219$	6.00000	0.405442
$220$	−1.60388	−0.108133
$221$	−0.548253	−0.0368795
$222$	−8.76809	−0.588475
$223$	−24.2935	−1.62681	−0.813407	−	0.581695i	$-0.802390\pi$
$223$	−24.2935	−1.62681	−0.813407	+	0.581695i	$0.802390\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	10.5483	0.701659
$227$	12.9095	0.856831	0.428416	−	0.903582i	$-0.359072\pi$
$227$	12.9095	0.856831	0.428416	+	0.903582i	$0.359072\pi$
$228$	2.49396	0.165166
$229$	6.19567	0.409421	0.204711	−	0.978823i	$-0.434375\pi$
$229$	6.19567	0.409421	0.204711	+	0.978823i	$0.434375\pi$
$230$	−1.00000	−0.0659380
$231$	−1.60388	−0.105527
$232$	−1.82371	−0.119732
$233$	14.9879	0.981891	0.490946	−	0.871190i	$-0.336651\pi$
$233$	14.9879	0.981891	0.490946	+	0.871190i	$0.336651\pi$
$234$	1.10992	0.0725575
$235$	5.70171	0.371939
$236$	3.20775	0.208807
$237$	−8.98792	−0.583828
$238$	0.493959	0.0320186
$239$	3.38404	0.218896	0.109448	−	0.993993i	$-0.465092\pi$
$239$	3.38404	0.218896	0.109448	+	0.993993i	$0.465092\pi$
$240$	−1.00000	−0.0645497
$241$	−21.0422	−1.35545	−0.677724	−	0.735316i	$-0.737034\pi$
$241$	−21.0422	−1.35545	−0.677724	+	0.735316i	$0.737034\pi$
$242$	8.42758	0.541746
$243$	−1.00000	−0.0641500
$244$	4.76809	0.305245
$245$	1.00000	0.0638877
$246$	−2.98792	−0.190503
$247$	2.76809	0.176129
$248$	−9.70171	−0.616059
$249$	−8.27413	−0.524351
$250$	−1.00000	−0.0632456
$251$	14.5133	0.916074	0.458037	−	0.888933i	$-0.348553\pi$
$251$	14.5133	0.916074	0.458037	+	0.888933i	$0.348553\pi$
$252$	−1.00000	−0.0629941
$253$	−1.60388	−0.100835
$254$	6.04354	0.379205
$255$	−0.493959	−0.0309329
$256$	1.00000	0.0625000
$257$	−21.3163	−1.32968	−0.664838	−	0.746987i	$-0.731500\pi$
$257$	−21.3163	−1.32968	−0.664838	+	0.746987i	$0.731500\pi$
$258$	1.60388	0.0998529
$259$	8.76809	0.544822
$260$	−1.10992	−0.0688341
$261$	1.82371	0.112885
$262$	0.439665	0.0271626
$263$	−12.1957	−0.752017	−0.376009	−	0.926616i	$-0.622704\pi$
$263$	−12.1957	−0.752017	−0.376009	+	0.926616i	$0.622704\pi$
$264$	−1.60388	−0.0987117
$265$	−0.219833	−0.0135042
$266$	−2.49396	−0.152914
$267$	10.5375	0.644885
$268$	−12.8116	−0.782595
$269$	−15.5254	−0.946601	−0.473301	−	0.880901i	$-0.656938\pi$
$269$	−15.5254	−0.946601	−0.473301	+	0.880901i	$0.656938\pi$
$270$	1.00000	0.0608581
$271$	−29.1051	−1.76801	−0.884005	−	0.467477i	$-0.845163\pi$
$271$	−29.1051	−1.76801	−0.884005	+	0.467477i	$0.845163\pi$
$272$	0.493959	0.0299507
$273$	−1.10992	−0.0671752
$274$	−15.9758	−0.965136
$275$	−1.60388	−0.0967173
$276$	−1.00000	−0.0601929
$277$	−19.6039	−1.17788	−0.588941	−	0.808176i	$-0.700455\pi$
$277$	−19.6039	−1.17788	−0.588941	+	0.808176i	$0.700455\pi$
$278$	−6.76809	−0.405923
$279$	9.70171	0.580826
$280$	1.00000	0.0597614
$281$	−8.04354	−0.479837	−0.239919	−	0.970793i	$-0.577121\pi$
$281$	−8.04354	−0.479837	−0.239919	+	0.970793i	$0.577121\pi$
$282$	5.70171	0.339532
$283$	1.08575	0.0645413	0.0322707	−	0.999479i	$-0.489726\pi$
$283$	1.08575	0.0645413	0.0322707	+	0.999479i	$0.489726\pi$
$284$	−6.59179	−0.391151
$285$	2.49396	0.147729
$286$	−1.78017	−0.105264
$287$	2.98792	0.176371
$288$	−1.00000	−0.0589256
$289$	−16.7560	−0.985647
$290$	−1.82371	−0.107092
$291$	4.67025	0.273775
$292$	−6.00000	−0.351123
$293$	−6.10859	−0.356868	−0.178434	−	0.983952i	$-0.557103\pi$
$293$	−6.10859	−0.356868	−0.178434	+	0.983952i	$0.557103\pi$
$294$	1.00000	0.0583212
$295$	3.20775	0.186762
$296$	8.76809	0.509635
$297$	1.60388	0.0930663
$298$	−12.7681	−0.739635
$299$	−1.10992	−0.0641881
$300$	−1.00000	−0.0577350
$301$	−1.60388	−0.0924458
$302$	6.21983	0.357911
$303$	7.87800	0.452579
$304$	−2.49396	−0.143038
$305$	4.76809	0.273020
$306$	−0.493959	−0.0282378
$307$	−17.4276	−0.994645	−0.497322	−	0.867566i	$-0.665683\pi$
$307$	−17.4276	−0.994645	−0.497322	+	0.867566i	$0.665683\pi$
$308$	1.60388	0.0913893
$309$	12.5483	0.713845
$310$	−9.70171	−0.551020
$311$	32.0495	1.81736	0.908680	−	0.417492i	$-0.137091\pi$
$311$	32.0495	1.81736	0.908680	+	0.417492i	$0.137091\pi$
$312$	−1.10992	−0.0628366
$313$	21.5013	1.21532	0.607661	−	0.794196i	$-0.292108\pi$
$313$	21.5013	1.21532	0.607661	+	0.794196i	$0.292108\pi$
$314$	14.9879	0.845817
$315$	−1.00000	−0.0563436
$316$	8.98792	0.505610
$317$	−30.5870	−1.71794	−0.858969	−	0.512028i	$-0.828894\pi$
$317$	−30.5870	−1.71794	−0.858969	+	0.512028i	$0.828894\pi$
$318$	−0.219833	−0.0123276
$319$	−2.92500	−0.163769
$320$	1.00000	0.0559017
$321$	−12.6353	−0.705236
$322$	1.00000	0.0557278
$323$	−1.23191	−0.0685455
$324$	1.00000	0.0555556
$325$	−1.10992	−0.0615671
$326$	−20.6353	−1.14289
$327$	6.98792	0.386433
$328$	2.98792	0.164980
$329$	−5.70171	−0.314345
$330$	−1.60388	−0.0882904
$331$	−3.75600	−0.206449	−0.103224	−	0.994658i	$-0.532916\pi$
$331$	−3.75600	−0.206449	−0.103224	+	0.994658i	$0.532916\pi$
$332$	8.27413	0.454102
$333$	−8.76809	−0.480488
$334$	20.4698	1.12006
$335$	−12.8116	−0.699974
$336$	1.00000	0.0545545
$337$	−17.1884	−0.936310	−0.468155	−	0.883646i	$-0.655081\pi$
$337$	−17.1884	−0.936310	−0.468155	+	0.883646i	$0.655081\pi$
$338$	11.7681	0.640099
$339$	10.5483	0.572902
$340$	0.493959	0.0267887
$341$	−15.5603	−0.842639
$342$	2.49396	0.134858
$343$	−1.00000	−0.0539949
$344$	−1.60388	−0.0864752
$345$	−1.00000	−0.0538382
$346$	15.3491	0.825174
$347$	−13.6233	−0.731335	−0.365667	−	0.930746i	$-0.619159\pi$
$347$	−13.6233	−0.731335	−0.365667	+	0.930746i	$0.619159\pi$
$348$	−1.82371	−0.0977610
$349$	−6.07846	−0.325372	−0.162686	−	0.986678i	$-0.552016\pi$
$349$	−6.07846	−0.325372	−0.162686	+	0.986678i	$0.552016\pi$
$350$	1.00000	0.0534522
$351$	1.10992	0.0592429
$352$	1.60388	0.0854868
$353$	6.63533	0.353163	0.176582	−	0.984286i	$-0.443496\pi$
$353$	6.63533	0.353163	0.176582	+	0.984286i	$0.443496\pi$
$354$	3.20775	0.170490
$355$	−6.59179	−0.349856
$356$	−10.5375	−0.558486
$357$	0.493959	0.0261431
$358$	−11.6474	−0.615585
$359$	34.9638	1.84532	0.922658	−	0.385619i	$-0.126012\pi$
$359$	34.9638	1.84532	0.922658	+	0.385619i	$0.126012\pi$
$360$	−1.00000	−0.0527046
$361$	−12.7802	−0.672640
$362$	−25.5991	−1.34546
$363$	8.42758	0.442333
$364$	1.10992	0.0581754
$365$	−6.00000	−0.314054
$366$	4.76809	0.249232
$367$	−11.8431	−0.618204	−0.309102	−	0.951029i	$-0.600028\pi$
$367$	−11.8431	−0.618204	−0.309102	+	0.951029i	$0.600028\pi$
$368$	1.00000	0.0521286
$369$	−2.98792	−0.155545
$370$	8.76809	0.455831
$371$	0.219833	0.0114131
$372$	−9.70171	−0.503010
$373$	25.5991	1.32547	0.662735	−	0.748854i	$-0.269395\pi$
$373$	25.5991	1.32547	0.662735	+	0.748854i	$0.269395\pi$
$374$	0.792249	0.0409662
$375$	−1.00000	−0.0516398
$376$	−5.70171	−0.294043
$377$	−2.02416	−0.104250
$378$	−1.00000	−0.0514344
$379$	−6.21983	−0.319491	−0.159746	−	0.987158i	$-0.551067\pi$
$379$	−6.21983	−0.319491	−0.159746	+	0.987158i	$0.551067\pi$
$380$	−2.49396	−0.127937
$381$	6.04354	0.309620
$382$	−7.01208	−0.358769
$383$	13.7802	0.704134	0.352067	−	0.935975i	$-0.385479\pi$
$383$	13.7802	0.704134	0.352067	+	0.935975i	$0.385479\pi$
$384$	1.00000	0.0510310
$385$	1.60388	0.0817411
$386$	22.6353	1.15211
$387$	1.60388	0.0815296
$388$	−4.67025	−0.237096
$389$	9.31634	0.472357	0.236179	−	0.971710i	$-0.424105\pi$
$389$	9.31634	0.472357	0.236179	+	0.971710i	$0.424105\pi$
$390$	−1.10992	−0.0562028
$391$	0.493959	0.0249806
$392$	−1.00000	−0.0505076
$393$	0.439665	0.0221782
$394$	−2.54825	−0.128379
$395$	8.98792	0.452231
$396$	−1.60388	−0.0805978
$397$	−17.1099	−0.858722	−0.429361	−	0.903133i	$-0.641261\pi$
$397$	−17.1099	−0.858722	−0.429361	+	0.903133i	$0.641261\pi$
$398$	17.6233	0.883374
$399$	−2.49396	−0.124854
$400$	1.00000	0.0500000
$401$	14.7245	0.735309	0.367654	−	0.929963i	$-0.380161\pi$
$401$	14.7245	0.735309	0.367654	+	0.929963i	$0.380161\pi$
$402$	−12.8116	−0.638986
$403$	−10.7681	−0.536397
$404$	−7.87800	−0.391945
$405$	1.00000	0.0496904
$406$	1.82371	0.0905091
$407$	14.0629	0.697073
$408$	0.493959	0.0244546
$409$	19.8189	0.979983	0.489991	−	0.871727i	$-0.337000\pi$
$409$	19.8189	0.979983	0.489991	+	0.871727i	$0.337000\pi$
$410$	2.98792	0.147563
$411$	−15.9758	−0.788030
$412$	−12.5483	−0.618208
$413$	−3.20775	−0.157843
$414$	−1.00000	−0.0491473
$415$	8.27413	0.406161
$416$	1.10992	0.0544181
$417$	−6.76809	−0.331435
$418$	−4.00000	−0.195646
$419$	−31.0616	−1.51746	−0.758729	−	0.651406i	$-0.774179\pi$
$419$	−31.0616	−1.51746	−0.758729	+	0.651406i	$0.774179\pi$
$420$	1.00000	0.0487950
$421$	−18.4397	−0.898694	−0.449347	−	0.893357i	$-0.648343\pi$
$421$	−18.4397	−0.898694	−0.449347	+	0.893357i	$0.648343\pi$
$422$	−14.9638	−0.728424
$423$	5.70171	0.277227
$424$	0.219833	0.0106760
$425$	0.493959	0.0239605
$426$	−6.59179	−0.319373
$427$	−4.76809	−0.230744
$428$	12.6353	0.610752
$429$	−1.78017	−0.0859473
$430$	−1.60388	−0.0773457
$431$	−8.19567	−0.394772	−0.197386	−	0.980326i	$-0.563245\pi$
$431$	−8.19567	−0.394772	−0.197386	+	0.980326i	$0.563245\pi$
$432$	−1.00000	−0.0481125
$433$	−31.5254	−1.51501	−0.757507	−	0.652827i	$-0.773583\pi$
$433$	−31.5254	−1.51501	−0.757507	+	0.652827i	$0.773583\pi$
$434$	9.70171	0.465697
$435$	−1.82371	−0.0874401
$436$	−6.98792	−0.334661
$437$	−2.49396	−0.119302
$438$	−6.00000	−0.286691
$439$	−4.90946	−0.234316	−0.117158	−	0.993113i	$-0.537378\pi$
$439$	−4.90946	−0.234316	−0.117158	+	0.993113i	$0.537378\pi$
$440$	1.60388	0.0764618
$441$	1.00000	0.0476190
$442$	0.548253	0.0260778
$443$	−15.5991	−0.741135	−0.370568	−	0.928806i	$-0.620837\pi$
$443$	−15.5991	−0.741135	−0.370568	+	0.928806i	$0.620837\pi$
$444$	8.76809	0.416115
$445$	−10.5375	−0.499525
$446$	24.2935	1.15033
$447$	−12.7681	−0.603910
$448$	−1.00000	−0.0472456
$449$	−33.8431	−1.59715	−0.798577	−	0.601893i	$-0.794413\pi$
$449$	−33.8431	−1.59715	−0.798577	+	0.601893i	$0.794413\pi$
$450$	−1.00000	−0.0471405
$451$	4.79225	0.225658
$452$	−10.5483	−0.496148
$453$	6.21983	0.292233
$454$	−12.9095	−0.605871
$455$	1.10992	0.0520337
$456$	−2.49396	−0.116790
$457$	−13.8237	−0.646646	−0.323323	−	0.946289i	$-0.604800\pi$
$457$	−13.8237	−0.646646	−0.323323	+	0.946289i	$0.604800\pi$
$458$	−6.19567	−0.289505
$459$	−0.493959	−0.0230560
$460$	1.00000	0.0466252
$461$	−12.3177	−0.573691	−0.286845	−	0.957977i	$-0.592607\pi$
$461$	−12.3177	−0.573691	−0.286845	+	0.957977i	$0.592607\pi$
$462$	1.60388	0.0746190
$463$	−24.2150	−1.12537	−0.562684	−	0.826672i	$-0.690231\pi$
$463$	−24.2150	−1.12537	−0.562684	+	0.826672i	$0.690231\pi$
$464$	1.82371	0.0846635
$465$	−9.70171	−0.449906
$466$	−14.9879	−0.694302
$467$	−5.59312	−0.258819	−0.129409	−	0.991591i	$-0.541308\pi$
$467$	−5.59312	−0.258819	−0.129409	+	0.991591i	$0.541308\pi$
$468$	−1.10992	−0.0513059
$469$	12.8116	0.591586
$470$	−5.70171	−0.263000
$471$	14.9879	0.690607
$472$	−3.20775	−0.147649
$473$	−2.57242	−0.118280
$474$	8.98792	0.412829
$475$	−2.49396	−0.114431
$476$	−0.493959	−0.0226406
$477$	−0.219833	−0.0100654
$478$	−3.38404	−0.154783
$479$	−26.0844	−1.19183	−0.595914	−	0.803048i	$-0.703210\pi$
$479$	−26.0844	−1.19183	−0.595914	+	0.803048i	$0.703210\pi$
$480$	1.00000	0.0456435
$481$	9.73184	0.443734
$482$	21.0422	0.958447
$483$	1.00000	0.0455016
$484$	−8.42758	−0.383072
$485$	−4.67025	−0.212065
$486$	1.00000	0.0453609
$487$	−20.2634	−0.918221	−0.459111	−	0.888379i	$-0.651832\pi$
$487$	−20.2634	−0.918221	−0.459111	+	0.888379i	$0.651832\pi$
$488$	−4.76809	−0.215841
$489$	−20.6353	−0.933162
$490$	−1.00000	−0.0451754
$491$	−13.8888	−0.626791	−0.313395	−	0.949623i	$-0.601467\pi$
$491$	−13.8888	−0.626791	−0.313395	+	0.949623i	$0.601467\pi$
$492$	2.98792	0.134706
$493$	0.900837	0.0405717
$494$	−2.76809	−0.124542
$495$	−1.60388	−0.0720888
$496$	9.70171	0.435620
$497$	6.59179	0.295682
$498$	8.27413	0.370772
$499$	7.84309	0.351105	0.175552	−	0.984470i	$-0.443829\pi$
$499$	7.84309	0.351105	0.175552	+	0.984470i	$0.443829\pi$
$500$	1.00000	0.0447214
$501$	20.4698	0.914523
$502$	−14.5133	−0.647762
$503$	−27.5120	−1.22670	−0.613350	−	0.789811i	$-0.710178\pi$
$503$	−27.5120	−1.22670	−0.613350	+	0.789811i	$0.710178\pi$
$504$	1.00000	0.0445435
$505$	−7.87800	−0.350566
$506$	1.60388	0.0713010
$507$	11.7681	0.522639
$508$	−6.04354	−0.268139
$509$	−5.90217	−0.261609	−0.130804	−	0.991408i	$-0.541756\pi$
$509$	−5.90217	−0.261609	−0.130804	+	0.991408i	$0.541756\pi$
$510$	0.493959	0.0218729
$511$	6.00000	0.265424
$512$	−1.00000	−0.0441942
$513$	2.49396	0.110111
$514$	21.3163	0.940223
$515$	−12.5483	−0.552942
$516$	−1.60388	−0.0706067
$517$	−9.14483	−0.402189
$518$	−8.76809	−0.385248
$519$	15.3491	0.673752
$520$	1.10992	0.0486730
$521$	13.8538	0.606948	0.303474	−	0.952840i	$-0.401853\pi$
$521$	13.8538	0.606948	0.303474	+	0.952840i	$0.401853\pi$
$522$	−1.82371	−0.0798215
$523$	37.5254	1.64087	0.820436	−	0.571738i	$-0.193731\pi$
$523$	37.5254	1.64087	0.820436	+	0.571738i	$0.193731\pi$
$524$	−0.439665	−0.0192069
$525$	1.00000	0.0436436
$526$	12.1957	0.531756
$527$	4.79225	0.208754
$528$	1.60388	0.0697997
$529$	1.00000	0.0434783
$530$	0.219833	0.00954891
$531$	3.20775	0.139205
$532$	2.49396	0.108127
$533$	3.31634	0.143647
$534$	−10.5375	−0.456002
$535$	12.6353	0.546273
$536$	12.8116	0.553378
$537$	−11.6474	−0.502623
$538$	15.5254	0.669348
$539$	−1.60388	−0.0690838
$540$	−1.00000	−0.0430331
$541$	2.08708	0.0897306	0.0448653	−	0.998993i	$-0.485714\pi$
$541$	2.08708	0.0897306	0.0448653	+	0.998993i	$0.485714\pi$
$542$	29.1051	1.25017
$543$	−25.5991	−1.09856
$544$	−0.493959	−0.0211783
$545$	−6.98792	−0.299330
$546$	1.10992	0.0475000
$547$	−38.1715	−1.63210	−0.816048	−	0.577984i	$-0.803839\pi$
$547$	−38.1715	−1.63210	−0.816048	+	0.577984i	$0.803839\pi$
$548$	15.9758	0.682454
$549$	4.76809	0.203497
$550$	1.60388	0.0683895
$551$	−4.54825	−0.193762
$552$	1.00000	0.0425628
$553$	−8.98792	−0.382205
$554$	19.6039	0.832889
$555$	8.76809	0.372185
$556$	6.76809	0.287031
$557$	−3.69309	−0.156481	−0.0782405	−	0.996935i	$-0.524930\pi$
$557$	−3.69309	−0.156481	−0.0782405	+	0.996935i	$0.524930\pi$
$558$	−9.70171	−0.410706
$559$	−1.78017	−0.0752931
$560$	−1.00000	−0.0422577
$561$	0.792249	0.0334488
$562$	8.04354	0.339296
$563$	−30.1414	−1.27031	−0.635154	−	0.772386i	$-0.719063\pi$
$563$	−30.1414	−1.27031	−0.635154	+	0.772386i	$0.719063\pi$
$564$	−5.70171	−0.240085
$565$	−10.5483	−0.443768
$566$	−1.08575	−0.0456376
$567$	−1.00000	−0.0419961
$568$	6.59179	0.276586
$569$	39.9952	1.67669	0.838343	−	0.545143i	$-0.183525\pi$
$569$	39.9952	1.67669	0.838343	+	0.545143i	$0.183525\pi$
$570$	−2.49396	−0.104460
$571$	−24.3526	−1.01912	−0.509562	−	0.860434i	$-0.670193\pi$
$571$	−24.3526	−1.01912	−0.509562	+	0.860434i	$0.670193\pi$
$572$	1.78017	0.0744325
$573$	−7.01208	−0.292934
$574$	−2.98792	−0.124713
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	20.4155	0.849908	0.424954	−	0.905215i	$-0.360290\pi$
$577$	20.4155	0.849908	0.424954	+	0.905215i	$0.360290\pi$
$578$	16.7560	0.696958
$579$	22.6353	0.940692
$580$	1.82371	0.0757254
$581$	−8.27413	−0.343269
$582$	−4.67025	−0.193588
$583$	0.352584	0.0146025
$584$	6.00000	0.248282
$585$	−1.10992	−0.0458894
$586$	6.10859	0.252343
$587$	−24.7922	−1.02329	−0.511643	−	0.859198i	$-0.670963\pi$
$587$	−24.7922	−1.02329	−0.511643	+	0.859198i	$0.670963\pi$
$588$	−1.00000	−0.0412393
$589$	−24.1957	−0.996965
$590$	−3.20775	−0.132061
$591$	−2.54825	−0.104821
$592$	−8.76809	−0.360366
$593$	25.4905	1.04677	0.523385	−	0.852096i	$-0.324669\pi$
$593$	25.4905	1.04677	0.523385	+	0.852096i	$0.324669\pi$
$594$	−1.60388	−0.0658078
$595$	−0.493959	−0.0202504
$596$	12.7681	0.523001
$597$	17.6233	0.721272
$598$	1.10992	0.0453879
$599$	39.5314	1.61521	0.807604	−	0.589725i	$-0.200764\pi$
$599$	39.5314	1.61521	0.807604	+	0.589725i	$0.200764\pi$
$600$	1.00000	0.0408248
$601$	−28.4155	−1.15909	−0.579546	−	0.814939i	$-0.696770\pi$
$601$	−28.4155	−1.15909	−0.579546	+	0.814939i	$0.696770\pi$
$602$	1.60388	0.0653691
$603$	−12.8116	−0.521730
$604$	−6.21983	−0.253081
$605$	−8.42758	−0.342630
$606$	−7.87800	−0.320022
$607$	−31.7453	−1.28850	−0.644250	−	0.764815i	$-0.722830\pi$
$607$	−31.7453	−1.28850	−0.644250	+	0.764815i	$0.722830\pi$
$608$	2.49396	0.101143
$609$	1.82371	0.0739004
$610$	−4.76809	−0.193054
$611$	−6.32842	−0.256021
$612$	0.493959	0.0199671
$613$	5.75600	0.232483	0.116241	−	0.993221i	$-0.462915\pi$
$613$	5.75600	0.232483	0.116241	+	0.993221i	$0.462915\pi$
$614$	17.4276	0.703320
$615$	2.98792	0.120484
$616$	−1.60388	−0.0646220
$617$	−14.0871	−0.567125	−0.283562	−	0.958954i	$-0.591516\pi$
$617$	−14.0871	−0.567125	−0.283562	+	0.958954i	$0.591516\pi$
$618$	−12.5483	−0.504765
$619$	−14.7767	−0.593926	−0.296963	−	0.954889i	$-0.595974\pi$
$619$	−14.7767	−0.593926	−0.296963	+	0.954889i	$0.595974\pi$
$620$	9.70171	0.389630
$621$	−1.00000	−0.0401286
$622$	−32.0495	−1.28507
$623$	10.5375	0.422176
$624$	1.10992	0.0444322
$625$	1.00000	0.0400000
$626$	−21.5013	−0.859363
$627$	−4.00000	−0.159745
$628$	−14.9879	−0.598083
$629$	−4.33108	−0.172691
$630$	1.00000	0.0398410
$631$	−20.9396	−0.833592	−0.416796	−	0.909000i	$-0.636847\pi$
$631$	−20.9396	−0.833592	−0.416796	+	0.909000i	$0.636847\pi$
$632$	−8.98792	−0.357520
$633$	−14.9638	−0.594756
$634$	30.5870	1.21477
$635$	−6.04354	−0.239831
$636$	0.219833	0.00871693
$637$	−1.10992	−0.0439765
$638$	2.92500	0.115802
$639$	−6.59179	−0.260767
$640$	−1.00000	−0.0395285
$641$	1.93230	0.0763211	0.0381606	−	0.999272i	$-0.487850\pi$
$641$	1.93230	0.0763211	0.0381606	+	0.999272i	$0.487850\pi$
$642$	12.6353	0.498677
$643$	40.0495	1.57940	0.789699	−	0.613494i	$-0.210237\pi$
$643$	40.0495	1.57940	0.789699	+	0.613494i	$0.210237\pi$
$644$	−1.00000	−0.0394055
$645$	−1.60388	−0.0631525
$646$	1.23191	0.0484690
$647$	−31.6775	−1.24537	−0.622686	−	0.782471i	$-0.713959\pi$
$647$	−31.6775	−1.24537	−0.622686	+	0.782471i	$0.713959\pi$
$648$	−1.00000	−0.0392837
$649$	−5.14483	−0.201952
$650$	1.10992	0.0435345
$651$	9.70171	0.380240
$652$	20.6353	0.808142
$653$	50.7439	1.98576	0.992882	−	0.119106i	$-0.0380028\pi$
$653$	50.7439	1.98576	0.992882	+	0.119106i	$0.0380028\pi$
$654$	−6.98792	−0.273249
$655$	−0.439665	−0.0171791
$656$	−2.98792	−0.116659
$657$	−6.00000	−0.234082
$658$	5.70171	0.222276
$659$	20.6547	0.804593	0.402297	−	0.915509i	$-0.368212\pi$
$659$	20.6547	0.804593	0.402297	+	0.915509i	$0.368212\pi$
$660$	1.60388	0.0624308
$661$	0.659498	0.0256515	0.0128257	−	0.999918i	$-0.495917\pi$
$661$	0.659498	0.0256515	0.0128257	+	0.999918i	$0.495917\pi$
$662$	3.75600	0.145981
$663$	0.548253	0.0212924
$664$	−8.27413	−0.321098
$665$	2.49396	0.0967116
$666$	8.76809	0.339756
$667$	1.82371	0.0706143
$668$	−20.4698	−0.792000
$669$	24.2935	0.939241
$670$	12.8116	0.494956
$671$	−7.64742	−0.295225
$672$	−1.00000	−0.0385758
$673$	17.4034	0.670853	0.335426	−	0.942066i	$-0.391120\pi$
$673$	17.4034	0.670853	0.335426	+	0.942066i	$0.391120\pi$
$674$	17.1884	0.662071
$675$	−1.00000	−0.0384900
$676$	−11.7681	−0.452619
$677$	8.85517	0.340332	0.170166	−	0.985415i	$-0.445570\pi$
$677$	8.85517	0.340332	0.170166	+	0.985415i	$0.445570\pi$
$678$	−10.5483	−0.405103
$679$	4.67025	0.179228
$680$	−0.493959	−0.0189425
$681$	−12.9095	−0.494692
$682$	15.5603	0.595836
$683$	17.1836	0.657512	0.328756	−	0.944415i	$-0.393371\pi$
$683$	17.1836	0.657512	0.328756	+	0.944415i	$0.393371\pi$
$684$	−2.49396	−0.0953589
$685$	15.9758	0.610405
$686$	1.00000	0.0381802
$687$	−6.19567	−0.236380
$688$	1.60388	0.0611472
$689$	0.243996	0.00929550
$690$	1.00000	0.0380693
$691$	19.0121	0.723254	0.361627	−	0.932323i	$-0.382221\pi$
$691$	19.0121	0.723254	0.361627	+	0.932323i	$0.382221\pi$
$692$	−15.3491	−0.583486
$693$	1.60388	0.0609262
$694$	13.6233	0.517132
$695$	6.76809	0.256728
$696$	1.82371	0.0691275
$697$	−1.47591	−0.0559041
$698$	6.07846	0.230073
$699$	−14.9879	−0.566895
$700$	−1.00000	−0.0377964
$701$	−3.58450	−0.135385	−0.0676923	−	0.997706i	$-0.521564\pi$
$701$	−3.58450	−0.135385	−0.0676923	+	0.997706i	$0.521564\pi$
$702$	−1.10992	−0.0418911
$703$	21.8672	0.824739
$704$	−1.60388	−0.0604483
$705$	−5.70171	−0.214739
$706$	−6.63533	−0.249724
$707$	7.87800	0.296283
$708$	−3.20775	−0.120555
$709$	−25.6474	−0.963209	−0.481604	−	0.876389i	$-0.659946\pi$
$709$	−25.6474	−0.963209	−0.481604	+	0.876389i	$0.659946\pi$
$710$	6.59179	0.247386
$711$	8.98792	0.337073
$712$	10.5375	0.394909
$713$	9.70171	0.363332
$714$	−0.493959	−0.0184860
$715$	1.78017	0.0665745
$716$	11.6474	0.435284
$717$	−3.38404	−0.126379
$718$	−34.9638	−1.30484
$719$	−12.0978	−0.451173	−0.225587	−	0.974223i	$-0.572430\pi$
$719$	−12.0978	−0.451173	−0.225587	+	0.974223i	$0.572430\pi$
$720$	1.00000	0.0372678
$721$	12.5483	0.467321
$722$	12.7802	0.475629
$723$	21.0422	0.782568
$724$	25.5991	0.951383
$725$	1.82371	0.0677308
$726$	−8.42758	−0.312777
$727$	42.5628	1.57857	0.789284	−	0.614028i	$-0.210452\pi$
$727$	42.5628	1.57857	0.789284	+	0.614028i	$0.210452\pi$
$728$	−1.10992	−0.0411362
$729$	1.00000	0.0370370
$730$	6.00000	0.222070
$731$	0.792249	0.0293024
$732$	−4.76809	−0.176234
$733$	−48.2103	−1.78069	−0.890343	−	0.455290i	$-0.849536\pi$
$733$	−48.2103	−1.78069	−0.890343	+	0.455290i	$0.849536\pi$
$734$	11.8431	0.437136
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	20.5483	0.756905
$738$	2.98792	0.109987
$739$	3.64742	0.134172	0.0670862	−	0.997747i	$-0.478630\pi$
$739$	3.64742	0.134172	0.0670862	+	0.997747i	$0.478630\pi$
$740$	−8.76809	−0.322321
$741$	−2.76809	−0.101688
$742$	−0.219833	−0.00807031
$743$	24.2828	0.890848	0.445424	−	0.895320i	$-0.353053\pi$
$743$	24.2828	0.890848	0.445424	+	0.895320i	$0.353053\pi$
$744$	9.70171	0.355682
$745$	12.7681	0.467786
$746$	−25.5991	−0.937249
$747$	8.27413	0.302734
$748$	−0.792249	−0.0289675
$749$	−12.6353	−0.461685
$750$	1.00000	0.0365148
$751$	−29.9275	−1.09207	−0.546035	−	0.837762i	$-0.683864\pi$
$751$	−29.9275	−1.09207	−0.546035	+	0.837762i	$0.683864\pi$
$752$	5.70171	0.207920
$753$	−14.5133	−0.528895
$754$	2.02416	0.0737157
$755$	−6.21983	−0.226363
$756$	1.00000	0.0363696
$757$	31.7318	1.15331	0.576657	−	0.816987i	$-0.304357\pi$
$757$	31.7318	1.15331	0.576657	+	0.816987i	$0.304357\pi$
$758$	6.21983	0.225914
$759$	1.60388	0.0582170
$760$	2.49396	0.0904654
$761$	6.35258	0.230281	0.115140	−	0.993349i	$-0.463268\pi$
$761$	6.35258	0.230281	0.115140	+	0.993349i	$0.463268\pi$
$762$	−6.04354	−0.218934
$763$	6.98792	0.252980
$764$	7.01208	0.253688
$765$	0.493959	0.0178591
$766$	−13.7802	−0.497898
$767$	−3.56033	−0.128556
$768$	−1.00000	−0.0360844
$769$	−32.6413	−1.17708	−0.588538	−	0.808470i	$-0.700296\pi$
$769$	−32.6413	−1.17708	−0.588538	+	0.808470i	$0.700296\pi$
$770$	−1.60388	−0.0577997
$771$	21.3163	0.767689
$772$	−22.6353	−0.814664
$773$	50.8310	1.82826	0.914132	−	0.405417i	$-0.132874\pi$
$773$	50.8310	1.82826	0.914132	+	0.405417i	$0.132874\pi$
$774$	−1.60388	−0.0576501
$775$	9.70171	0.348496
$776$	4.67025	0.167652
$777$	−8.76809	−0.314553
$778$	−9.31634	−0.334007
$779$	7.45175	0.266987
$780$	1.10992	0.0397414
$781$	10.5724	0.378311
$782$	−0.493959	−0.0176639
$783$	−1.82371	−0.0651740
$784$	1.00000	0.0357143
$785$	−14.9879	−0.534942
$786$	−0.439665	−0.0156823
$787$	−4.99867	−0.178183	−0.0890917	−	0.996023i	$-0.528396\pi$
$787$	−4.99867	−0.178183	−0.0890917	+	0.996023i	$0.528396\pi$
$788$	2.54825	0.0907778
$789$	12.1957	0.434177
$790$	−8.98792	−0.319776
$791$	10.5483	0.375053
$792$	1.60388	0.0569912
$793$	−5.29218	−0.187931
$794$	17.1099	0.607208
$795$	0.219833	0.00779666
$796$	−17.6233	−0.624640
$797$	9.40342	0.333086	0.166543	−	0.986034i	$-0.446740\pi$
$797$	9.40342	0.333086	0.166543	+	0.986034i	$0.446740\pi$
$798$	2.49396	0.0882852
$799$	2.81641	0.0996375
$800$	−1.00000	−0.0353553
$801$	−10.5375	−0.372324
$802$	−14.7245	−0.519942
$803$	9.62325	0.339597
$804$	12.8116	0.451831
$805$	−1.00000	−0.0352454
$806$	10.7681	0.379290
$807$	15.5254	0.546521
$808$	7.87800	0.277147
$809$	−52.5628	−1.84801	−0.924006	−	0.382379i	$-0.875105\pi$
$809$	−52.5628	−1.84801	−0.924006	+	0.382379i	$0.875105\pi$
$810$	−1.00000	−0.0351364
$811$	−5.53617	−0.194401	−0.0972006	−	0.995265i	$-0.530989\pi$
$811$	−5.53617	−0.194401	−0.0972006	+	0.995265i	$0.530989\pi$
$812$	−1.82371	−0.0639996
$813$	29.1051	1.02076
$814$	−14.0629	−0.492905
$815$	20.6353	0.722824
$816$	−0.493959	−0.0172920
$817$	−4.00000	−0.139942
$818$	−19.8189	−0.692952
$819$	1.10992	0.0387836
$820$	−2.98792	−0.104343
$821$	17.1400	0.598192	0.299096	−	0.954223i	$-0.403315\pi$
$821$	17.1400	0.598192	0.299096	+	0.954223i	$0.403315\pi$
$822$	15.9758	0.557221
$823$	−6.92287	−0.241316	−0.120658	−	0.992694i	$-0.538500\pi$
$823$	−6.92287	−0.241316	−0.120658	+	0.992694i	$0.538500\pi$
$824$	12.5483	0.437139
$825$	1.60388	0.0558398
$826$	3.20775	0.111612
$827$	−11.0508	−0.384275	−0.192138	−	0.981368i	$-0.561542\pi$
$827$	−11.0508	−0.384275	−0.192138	+	0.981368i	$0.561542\pi$
$828$	1.00000	0.0347524
$829$	8.10262	0.281416	0.140708	−	0.990051i	$-0.455062\pi$
$829$	8.10262	0.281416	0.140708	+	0.990051i	$0.455062\pi$
$830$	−8.27413	−0.287199
$831$	19.6039	0.680051
$832$	−1.10992	−0.0384794
$833$	0.493959	0.0171147
$834$	6.76809	0.234360
$835$	−20.4698	−0.708387
$836$	4.00000	0.138343
$837$	−9.70171	−0.335340
$838$	31.0616	1.07300
$839$	−36.0388	−1.24420	−0.622098	−	0.782939i	$-0.713719\pi$
$839$	−36.0388	−1.24420	−0.622098	+	0.782939i	$0.713719\pi$
$840$	−1.00000	−0.0345033
$841$	−25.6741	−0.885313
$842$	18.4397	0.635473
$843$	8.04354	0.277034
$844$	14.9638	0.515074
$845$	−11.7681	−0.404834
$846$	−5.70171	−0.196029
$847$	8.42758	0.289575
$848$	−0.219833	−0.00754908
$849$	−1.08575	−0.0372629
$850$	−0.493959	−0.0169427
$851$	−8.76809	−0.300566
$852$	6.59179	0.225831
$853$	−27.4771	−0.940798	−0.470399	−	0.882454i	$-0.655890\pi$
$853$	−27.4771	−0.940798	−0.470399	+	0.882454i	$0.655890\pi$
$854$	4.76809	0.163161
$855$	−2.49396	−0.0852916
$856$	−12.6353	−0.431867
$857$	−32.6595	−1.11563	−0.557814	−	0.829966i	$-0.688360\pi$
$857$	−32.6595	−1.11563	−0.557814	+	0.829966i	$0.688360\pi$
$858$	1.78017	0.0607739
$859$	1.03624	0.0353562	0.0176781	−	0.999844i	$-0.494373\pi$
$859$	1.03624	0.0353562	0.0176781	+	0.999844i	$0.494373\pi$
$860$	1.60388	0.0546917
$861$	−2.98792	−0.101828
$862$	8.19567	0.279146
$863$	52.6353	1.79173	0.895864	−	0.444329i	$-0.146558\pi$
$863$	52.6353	1.79173	0.895864	+	0.444329i	$0.146558\pi$
$864$	1.00000	0.0340207
$865$	−15.3491	−0.521886
$866$	31.5254	1.07128
$867$	16.7560	0.569064
$868$	−9.70171	−0.329297
$869$	−14.4155	−0.489012
$870$	1.82371	0.0618295
$871$	14.2198	0.481821
$872$	6.98792	0.236641
$873$	−4.67025	−0.158064
$874$	2.49396	0.0843594
$875$	−1.00000	−0.0338062
$876$	6.00000	0.202721
$877$	−15.4953	−0.523239	−0.261619	−	0.965171i	$-0.584256\pi$
$877$	−15.4953	−0.523239	−0.261619	+	0.965171i	$0.584256\pi$
$878$	4.90946	0.165686
$879$	6.10859	0.206038
$880$	−1.60388	−0.0540666
$881$	0.474582	0.0159891	0.00799453	−	0.999968i	$-0.497455\pi$
$881$	0.474582	0.0159891	0.00799453	+	0.999968i	$0.497455\pi$
$882$	−1.00000	−0.0336718
$883$	25.0750	0.843841	0.421920	−	0.906633i	$-0.361356\pi$
$883$	25.0750	0.843841	0.421920	+	0.906633i	$0.361356\pi$
$884$	−0.548253	−0.0184398
$885$	−3.20775	−0.107827
$886$	15.5991	0.524062
$887$	27.7861	0.932967	0.466484	−	0.884530i	$-0.345521\pi$
$887$	27.7861	0.932967	0.466484	+	0.884530i	$0.345521\pi$
$888$	−8.76809	−0.294238
$889$	6.04354	0.202694
$890$	10.5375	0.353218
$891$	−1.60388	−0.0537318
$892$	−24.2935	−0.813407
$893$	−14.2198	−0.475849
$894$	12.7681	0.427029
$895$	11.6474	0.389330
$896$	1.00000	0.0334077
$897$	1.10992	0.0370590
$898$	33.8431	1.12936
$899$	17.6931	0.590097
$900$	1.00000	0.0333333
$901$	−0.108588	−0.00361760
$902$	−4.79225	−0.159564
$903$	1.60388	0.0533736
$904$	10.5483	0.350830
$905$	25.5991	0.850943
$906$	−6.21983	−0.206640
$907$	37.0073	1.22881	0.614404	−	0.788992i	$-0.289397\pi$
$907$	37.0073	1.22881	0.614404	+	0.788992i	$0.289397\pi$
$908$	12.9095	0.428416
$909$	−7.87800	−0.261297
$910$	−1.10992	−0.0367934
$911$	1.82849	0.0605807	0.0302904	−	0.999541i	$-0.490357\pi$
$911$	1.82849	0.0605807	0.0302904	+	0.999541i	$0.490357\pi$
$912$	2.49396	0.0825832
$913$	−13.2707	−0.439195
$914$	13.8237	0.457248
$915$	−4.76809	−0.157628
$916$	6.19567	0.204711
$917$	0.439665	0.0145190
$918$	0.493959	0.0163031
$919$	50.7198	1.67309	0.836545	−	0.547898i	$-0.184572\pi$
$919$	50.7198	1.67309	0.836545	+	0.547898i	$0.184572\pi$
$920$	−1.00000	−0.0329690
$921$	17.4276	0.574258
$922$	12.3177	0.405661
$923$	7.31634	0.240820
$924$	−1.60388	−0.0527636
$925$	−8.76809	−0.288293
$926$	24.2150	0.795756
$927$	−12.5483	−0.412139
$928$	−1.82371	−0.0598661
$929$	16.3069	0.535012	0.267506	−	0.963556i	$-0.413800\pi$
$929$	16.3069	0.535012	0.267506	+	0.963556i	$0.413800\pi$
$930$	9.70171	0.318132
$931$	−2.49396	−0.0817362
$932$	14.9879	0.490946
$933$	−32.0495	−1.04925
$934$	5.59312	0.183013
$935$	−0.792249	−0.0259093
$936$	1.10992	0.0362787
$937$	8.70901	0.284511	0.142255	−	0.989830i	$-0.454565\pi$
$937$	8.70901	0.284511	0.142255	+	0.989830i	$0.454565\pi$
$938$	−12.8116	−0.418314
$939$	−21.5013	−0.701667
$940$	5.70171	0.185969
$941$	−20.8552	−0.679859	−0.339930	−	0.940451i	$-0.610403\pi$
$941$	−20.8552	−0.679859	−0.339930	+	0.940451i	$0.610403\pi$
$942$	−14.9879	−0.488333
$943$	−2.98792	−0.0973000
$944$	3.20775	0.104403
$945$	1.00000	0.0325300
$946$	2.57242	0.0836365
$947$	10.1328	0.329270	0.164635	−	0.986355i	$-0.447355\pi$
$947$	10.1328	0.329270	0.164635	+	0.986355i	$0.447355\pi$
$948$	−8.98792	−0.291914
$949$	6.65950	0.216176
$950$	2.49396	0.0809147
$951$	30.5870	0.991852
$952$	0.493959	0.0160093
$953$	20.9638	0.679083	0.339541	−	0.940591i	$-0.389728\pi$
$953$	20.9638	0.679083	0.339541	+	0.940591i	$0.389728\pi$
$954$	0.219833	0.00711734
$955$	7.01208	0.226906
$956$	3.38404	0.109448
$957$	2.92500	0.0945518
$958$	26.0844	0.842750
$959$	−15.9758	−0.515887
$960$	−1.00000	−0.0322749
$961$	63.1232	2.03623
$962$	−9.73184	−0.313767
$963$	12.6353	0.407168
$964$	−21.0422	−0.677724
$965$	−22.6353	−0.728657
$966$	−1.00000	−0.0321745
$967$	−4.48055	−0.144085	−0.0720424	−	0.997402i	$-0.522952\pi$
$967$	−4.48055	−0.144085	−0.0720424	+	0.997402i	$0.522952\pi$
$968$	8.42758	0.270873
$969$	1.23191	0.0395748
$970$	4.67025	0.149953
$971$	−7.19700	−0.230963	−0.115481	−	0.993310i	$-0.536841\pi$
$971$	−7.19700	−0.230963	−0.115481	+	0.993310i	$0.536841\pi$
$972$	−1.00000	−0.0320750
$973$	−6.76809	−0.216975
$974$	20.2634	0.649280
$975$	1.10992	0.0355458
$976$	4.76809	0.152623
$977$	52.4543	1.67816	0.839080	−	0.544008i	$-0.183094\pi$
$977$	52.4543	1.67816	0.839080	+	0.544008i	$0.183094\pi$
$978$	20.6353	0.659845
$979$	16.9008	0.540153
$980$	1.00000	0.0319438
$981$	−6.98792	−0.223107
$982$	13.8888	0.443208
$983$	1.34050	0.0427554	0.0213777	−	0.999771i	$-0.493195\pi$
$983$	1.34050	0.0427554	0.0213777	+	0.999771i	$0.493195\pi$
$984$	−2.98792	−0.0952514
$985$	2.54825	0.0811941
$986$	−0.900837	−0.0286885
$987$	5.70171	0.181487
$988$	2.76809	0.0880645
$989$	1.60388	0.0510003
$990$	1.60388	0.0509745
$991$	57.6835	1.83238	0.916189	−	0.400747i	$-0.131249\pi$
$991$	57.6835	1.83238	0.916189	+	0.400747i	$0.131249\pi$
$992$	−9.70171	−0.308030
$993$	3.75600	0.119193
$994$	−6.59179	−0.209079
$995$	−17.6233	−0.558695
$996$	−8.27413	−0.262176
$997$	−49.0133	−1.55227	−0.776133	−	0.630569i	$-0.782821\pi$
$997$	−49.0133	−1.55227	−0.776133	+	0.630569i	$0.782821\pi$
$998$	−7.84309	−0.248269
$999$	8.76809	0.277410

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bx.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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.60388 q^{11} -1.00000 q^{12} -1.10992 q^{13} +1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +0.493959 q^{17} -1.00000 q^{18} -2.49396 q^{19} +1.00000 q^{20} +1.00000 q^{21} +1.60388 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.10992 q^{26} -1.00000 q^{27} -1.00000 q^{28} +1.82371 q^{29} +1.00000 q^{30} +9.70171 q^{31} -1.00000 q^{32} +1.60388 q^{33} -0.493959 q^{34} -1.00000 q^{35} +1.00000 q^{36} -8.76809 q^{37} +2.49396 q^{38} +1.10992 q^{39} -1.00000 q^{40} -2.98792 q^{41} -1.00000 q^{42} +1.60388 q^{43} -1.60388 q^{44} +1.00000 q^{45} -1.00000 q^{46} +5.70171 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -0.493959 q^{51} -1.10992 q^{52} -0.219833 q^{53} +1.00000 q^{54} -1.60388 q^{55} +1.00000 q^{56} +2.49396 q^{57} -1.82371 q^{58} +3.20775 q^{59} -1.00000 q^{60} +4.76809 q^{61} -9.70171 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.10992 q^{65} -1.60388 q^{66} -12.8116 q^{67} +0.493959 q^{68} -1.00000 q^{69} +1.00000 q^{70} -6.59179 q^{71} -1.00000 q^{72} -6.00000 q^{73} +8.76809 q^{74} -1.00000 q^{75} -2.49396 q^{76} +1.60388 q^{77} -1.10992 q^{78} +8.98792 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.98792 q^{82} +8.27413 q^{83} +1.00000 q^{84} +0.493959 q^{85} -1.60388 q^{86} -1.82371 q^{87} +1.60388 q^{88} -10.5375 q^{89} -1.00000 q^{90} +1.10992 q^{91} +1.00000 q^{92} -9.70171 q^{93} -5.70171 q^{94} -2.49396 q^{95} +1.00000 q^{96} -4.67025 q^{97} -1.00000 q^{98} -1.60388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} + 4 q^{11} - 3 q^{12} - 4 q^{13} + 3 q^{14} - 3 q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - 4 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 4 q^{26} - 3 q^{27} - 3 q^{28} - 2 q^{29} + 3 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 2 q^{38} + 4 q^{39} - 3 q^{40} + 10 q^{41} - 3 q^{42} - 4 q^{43} + 4 q^{44} + 3 q^{45} - 3 q^{46} - 10 q^{47} - 3 q^{48} + 3 q^{49} - 3 q^{50} + 8 q^{51} - 4 q^{52} - 2 q^{53} + 3 q^{54} + 4 q^{55} + 3 q^{56} - 2 q^{57} + 2 q^{58} - 8 q^{59} - 3 q^{60} - 6 q^{61} - 2 q^{62} - 3 q^{63} + 3 q^{64} - 4 q^{65} + 4 q^{66} - 12 q^{67} - 8 q^{68} - 3 q^{69} + 3 q^{70} + 8 q^{71} - 3 q^{72} - 18 q^{73} + 6 q^{74} - 3 q^{75} + 2 q^{76} - 4 q^{77} - 4 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} - 10 q^{82} + 14 q^{83} + 3 q^{84} - 8 q^{85} + 4 q^{86} + 2 q^{87} - 4 q^{88} - 16 q^{89} - 3 q^{90} + 4 q^{91} + 3 q^{92} - 2 q^{93} + 10 q^{94} + 2 q^{95} + 3 q^{96} - 12 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) 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 + 4 * q^11 - 3 * q^12 - 4 * q^13 + 3 * q^14 - 3 * q^15 + 3 * q^16 - 8 * q^17 - 3 * q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - 4 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 4 * q^26 - 3 * q^27 - 3 * q^28 - 2 * q^29 + 3 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 2 * q^38 + 4 * q^39 - 3 * q^40 + 10 * q^41 - 3 * q^42 - 4 * q^43 + 4 * q^44 + 3 * q^45 - 3 * q^46 - 10 * q^47 - 3 * q^48 + 3 * q^49 - 3 * q^50 + 8 * q^51 - 4 * q^52 - 2 * q^53 + 3 * q^54 + 4 * q^55 + 3 * q^56 - 2 * q^57 + 2 * q^58 - 8 * q^59 - 3 * q^60 - 6 * q^61 - 2 * q^62 - 3 * q^63 + 3 * q^64 - 4 * q^65 + 4 * q^66 - 12 * q^67 - 8 * q^68 - 3 * q^69 + 3 * q^70 + 8 * q^71 - 3 * q^72 - 18 * q^73 + 6 * q^74 - 3 * q^75 + 2 * q^76 - 4 * q^77 - 4 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 - 10 * q^82 + 14 * q^83 + 3 * q^84 - 8 * q^85 + 4 * q^86 + 2 * q^87 - 4 * q^88 - 16 * q^89 - 3 * q^90 + 4 * q^91 + 3 * q^92 - 2 * q^93 + 10 * q^94 + 2 * q^95 + 3 * q^96 - 12 * q^97 - 3 * q^98 + 4 * q^99

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