LMFDB - Embedded newform 4730.2.a.be.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 $ x^12 - 3x^11 - 26x^10 + 79x^9 + 247x^8 - 766x^7 - 1023x^6 + 3281x^5 + 1634x^4 - 5557x^3 - 483x^2 + 1648*x + 392
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.03435$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.03435 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.03435 q^{6} -3.44511 q^{7} +1.00000 q^{8} +6.20730 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.03435 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.03435 q^{6} -3.44511 q^{7} +1.00000 q^{8} +6.20730 q^{9} +1.00000 q^{10} -1.00000 q^{11} -3.03435 q^{12} +3.01153 q^{13} -3.44511 q^{14} -3.03435 q^{15} +1.00000 q^{16} +8.05622 q^{17} +6.20730 q^{18} -1.97164 q^{19} +1.00000 q^{20} +10.4537 q^{21} -1.00000 q^{22} -1.01153 q^{23} -3.03435 q^{24} +1.00000 q^{25} +3.01153 q^{26} -9.73209 q^{27} -3.44511 q^{28} -7.47434 q^{29} -3.03435 q^{30} +3.58845 q^{31} +1.00000 q^{32} +3.03435 q^{33} +8.05622 q^{34} -3.44511 q^{35} +6.20730 q^{36} +0.814968 q^{37} -1.97164 q^{38} -9.13803 q^{39} +1.00000 q^{40} -8.79033 q^{41} +10.4537 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.20730 q^{45} -1.01153 q^{46} -2.28907 q^{47} -3.03435 q^{48} +4.86875 q^{49} +1.00000 q^{50} -24.4454 q^{51} +3.01153 q^{52} -4.19135 q^{53} -9.73209 q^{54} -1.00000 q^{55} -3.44511 q^{56} +5.98266 q^{57} -7.47434 q^{58} -0.747496 q^{59} -3.03435 q^{60} -0.594147 q^{61} +3.58845 q^{62} -21.3848 q^{63} +1.00000 q^{64} +3.01153 q^{65} +3.03435 q^{66} +3.95796 q^{67} +8.05622 q^{68} +3.06933 q^{69} -3.44511 q^{70} -5.26792 q^{71} +6.20730 q^{72} +6.70688 q^{73} +0.814968 q^{74} -3.03435 q^{75} -1.97164 q^{76} +3.44511 q^{77} -9.13803 q^{78} +7.02527 q^{79} +1.00000 q^{80} +10.9087 q^{81} -8.79033 q^{82} +12.1548 q^{83} +10.4537 q^{84} +8.05622 q^{85} +1.00000 q^{86} +22.6798 q^{87} -1.00000 q^{88} +11.2814 q^{89} +6.20730 q^{90} -10.3750 q^{91} -1.01153 q^{92} -10.8886 q^{93} -2.28907 q^{94} -1.97164 q^{95} -3.03435 q^{96} -13.1215 q^{97} +4.86875 q^{98} -6.20730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.03435	−1.75188	−0.875942	−	0.482416i	$-0.839760\pi$
$3$	−3.03435	−1.75188	−0.875942	+	0.482416i	$0.839760\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.03435	−1.23877
$7$	−3.44511	−1.30213	−0.651064	−	0.759023i	$-0.725677\pi$
$7$	−3.44511	−1.30213	−0.651064	+	0.759023i	$0.725677\pi$
$8$	1.00000	0.353553
$9$	6.20730	2.06910
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.03435	−0.875942
$13$	3.01153	0.835247	0.417623	−	0.908620i	$-0.362863\pi$
$13$	3.01153	0.835247	0.417623	+	0.908620i	$0.362863\pi$
$14$	−3.44511	−0.920743
$15$	−3.03435	−0.783467
$16$	1.00000	0.250000
$17$	8.05622	1.95392	0.976961	−	0.213420i	$-0.0684602\pi$
$17$	8.05622	1.95392	0.976961	+	0.213420i	$0.0684602\pi$
$18$	6.20730	1.46308
$19$	−1.97164	−0.452326	−0.226163	−	0.974090i	$-0.572618\pi$
$19$	−1.97164	−0.452326	−0.226163	+	0.974090i	$0.572618\pi$
$20$	1.00000	0.223607
$21$	10.4537	2.28118
$22$	−1.00000	−0.213201
$23$	−1.01153	−0.210918	−0.105459	−	0.994424i	$-0.533631\pi$
$23$	−1.01153	−0.210918	−0.105459	+	0.994424i	$0.533631\pi$
$24$	−3.03435	−0.619385
$25$	1.00000	0.200000
$26$	3.01153	0.590609
$27$	−9.73209	−1.87294
$28$	−3.44511	−0.651064
$29$	−7.47434	−1.38795	−0.693975	−	0.719999i	$-0.744142\pi$
$29$	−7.47434	−1.38795	−0.693975	+	0.719999i	$0.744142\pi$
$30$	−3.03435	−0.553995
$31$	3.58845	0.644504	0.322252	−	0.946654i	$-0.395560\pi$
$31$	3.58845	0.644504	0.322252	+	0.946654i	$0.395560\pi$
$32$	1.00000	0.176777
$33$	3.03435	0.528213
$34$	8.05622	1.38163
$35$	−3.44511	−0.582329
$36$	6.20730	1.03455
$37$	0.814968	0.133980	0.0669900	−	0.997754i	$-0.478660\pi$
$37$	0.814968	0.133980	0.0669900	+	0.997754i	$0.478660\pi$
$38$	−1.97164	−0.319843
$39$	−9.13803	−1.46326
$40$	1.00000	0.158114
$41$	−8.79033	−1.37282	−0.686410	−	0.727215i	$-0.740814\pi$
$41$	−8.79033	−1.37282	−0.686410	+	0.727215i	$0.740814\pi$
$42$	10.4537	1.61304
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	6.20730	0.925330
$46$	−1.01153	−0.149141
$47$	−2.28907	−0.333895	−0.166948	−	0.985966i	$-0.553391\pi$
$47$	−2.28907	−0.333895	−0.166948	+	0.985966i	$0.553391\pi$
$48$	−3.03435	−0.437971
$49$	4.86875	0.695536
$50$	1.00000	0.141421
$51$	−24.4454	−3.42305
$52$	3.01153	0.417623
$53$	−4.19135	−0.575726	−0.287863	−	0.957672i	$-0.592945\pi$
$53$	−4.19135	−0.575726	−0.287863	+	0.957672i	$0.592945\pi$
$54$	−9.73209	−1.32437
$55$	−1.00000	−0.134840
$56$	−3.44511	−0.460372
$57$	5.98266	0.792422
$58$	−7.47434	−0.981429
$59$	−0.747496	−0.0973156	−0.0486578	−	0.998816i	$-0.515494\pi$
$59$	−0.747496	−0.0973156	−0.0486578	+	0.998816i	$0.515494\pi$
$60$	−3.03435	−0.391733
$61$	−0.594147	−0.0760727	−0.0380363	−	0.999276i	$-0.512110\pi$
$61$	−0.594147	−0.0760727	−0.0380363	+	0.999276i	$0.512110\pi$
$62$	3.58845	0.455733
$63$	−21.3848	−2.69423
$64$	1.00000	0.125000
$65$	3.01153	0.373534
$66$	3.03435	0.373503
$67$	3.95796	0.483541	0.241771	−	0.970333i	$-0.422272\pi$
$67$	3.95796	0.483541	0.241771	+	0.970333i	$0.422272\pi$
$68$	8.05622	0.976961
$69$	3.06933	0.369503
$70$	−3.44511	−0.411769
$71$	−5.26792	−0.625187	−0.312594	−	0.949887i	$-0.601198\pi$
$71$	−5.26792	−0.625187	−0.312594	+	0.949887i	$0.601198\pi$
$72$	6.20730	0.731538
$73$	6.70688	0.784981	0.392491	−	0.919756i	$-0.371614\pi$
$73$	6.70688	0.784981	0.392491	+	0.919756i	$0.371614\pi$
$74$	0.814968	0.0947381
$75$	−3.03435	−0.350377
$76$	−1.97164	−0.226163
$77$	3.44511	0.392606
$78$	−9.13803	−1.03468
$79$	7.02527	0.790404	0.395202	−	0.918594i	$-0.370675\pi$
$79$	7.02527	0.790404	0.395202	+	0.918594i	$0.370675\pi$
$80$	1.00000	0.111803
$81$	10.9087	1.21208
$82$	−8.79033	−0.970730
$83$	12.1548	1.33416	0.667079	−	0.744987i	$-0.267544\pi$
$83$	12.1548	1.33416	0.667079	+	0.744987i	$0.267544\pi$
$84$	10.4537	1.14059
$85$	8.05622	0.873820
$86$	1.00000	0.107833
$87$	22.6798	2.43153
$88$	−1.00000	−0.106600
$89$	11.2814	1.19583	0.597914	−	0.801560i	$-0.295996\pi$
$89$	11.2814	1.19583	0.597914	+	0.801560i	$0.295996\pi$
$90$	6.20730	0.654307
$91$	−10.3750	−1.08760
$92$	−1.01153	−0.105459
$93$	−10.8886	−1.12910
$94$	−2.28907	−0.236099
$95$	−1.97164	−0.202286
$96$	−3.03435	−0.309692
$97$	−13.1215	−1.33229	−0.666143	−	0.745824i	$-0.732056\pi$
$97$	−13.1215	−1.33229	−0.666143	+	0.745824i	$0.732056\pi$
$98$	4.86875	0.491818
$99$	−6.20730	−0.623857
$100$	1.00000	0.100000
$101$	2.38586	0.237402	0.118701	−	0.992930i	$-0.462127\pi$
$101$	2.38586	0.237402	0.118701	+	0.992930i	$0.462127\pi$
$102$	−24.4454	−2.42046
$103$	8.69704	0.856945	0.428472	−	0.903555i	$-0.359052\pi$
$103$	8.69704	0.856945	0.428472	+	0.903555i	$0.359052\pi$
$104$	3.01153	0.295304
$105$	10.4537	1.02017
$106$	−4.19135	−0.407100
$107$	−0.158326	−0.0153060	−0.00765299	−	0.999971i	$-0.502436\pi$
$107$	−0.158326	−0.0153060	−0.00765299	+	0.999971i	$0.502436\pi$
$108$	−9.73209	−0.936471
$109$	17.8523	1.70994	0.854970	−	0.518678i	$-0.173575\pi$
$109$	17.8523	1.70994	0.854970	+	0.518678i	$0.173575\pi$
$110$	−1.00000	−0.0953463
$111$	−2.47290	−0.234717
$112$	−3.44511	−0.325532
$113$	14.1561	1.33169	0.665847	−	0.746089i	$-0.268070\pi$
$113$	14.1561	1.33169	0.665847	+	0.746089i	$0.268070\pi$
$114$	5.98266	0.560327
$115$	−1.01153	−0.0943252
$116$	−7.47434	−0.693975
$117$	18.6935	1.72821
$118$	−0.747496	−0.0688125
$119$	−27.7545	−2.54425
$120$	−3.03435	−0.276997
$121$	1.00000	0.0909091
$122$	−0.594147	−0.0537915
$123$	26.6730	2.40502
$124$	3.58845	0.322252
$125$	1.00000	0.0894427
$126$	−21.3848	−1.90511
$127$	5.67047	0.503173	0.251586	−	0.967835i	$-0.419048\pi$
$127$	5.67047	0.503173	0.251586	+	0.967835i	$0.419048\pi$
$128$	1.00000	0.0883883
$129$	−3.03435	−0.267160
$130$	3.01153	0.264128
$131$	−7.81393	−0.682707	−0.341353	−	0.939935i	$-0.610885\pi$
$131$	−7.81393	−0.682707	−0.341353	+	0.939935i	$0.610885\pi$
$132$	3.03435	0.264107
$133$	6.79251	0.588986
$134$	3.95796	0.341915
$135$	−9.73209	−0.837605
$136$	8.05622	0.690815
$137$	11.7760	1.00609	0.503045	−	0.864260i	$-0.332213\pi$
$137$	11.7760	1.00609	0.503045	+	0.864260i	$0.332213\pi$
$138$	3.06933	0.261278
$139$	−14.3383	−1.21616	−0.608078	−	0.793877i	$-0.708059\pi$
$139$	−14.3383	−1.21616	−0.608078	+	0.793877i	$0.708059\pi$
$140$	−3.44511	−0.291165
$141$	6.94585	0.584946
$142$	−5.26792	−0.442074
$143$	−3.01153	−0.251836
$144$	6.20730	0.517275
$145$	−7.47434	−0.620710
$146$	6.70688	0.555066
$147$	−14.7735	−1.21850
$148$	0.814968	0.0669900
$149$	−8.21509	−0.673006	−0.336503	−	0.941682i	$-0.609244\pi$
$149$	−8.21509	−0.673006	−0.336503	+	0.941682i	$0.609244\pi$
$150$	−3.03435	−0.247754
$151$	9.95698	0.810288	0.405144	−	0.914253i	$-0.367221\pi$
$151$	9.95698	0.810288	0.405144	+	0.914253i	$0.367221\pi$
$152$	−1.97164	−0.159921
$153$	50.0074	4.04286
$154$	3.44511	0.277615
$155$	3.58845	0.288231
$156$	−9.13803	−0.731628
$157$	1.44307	0.115169	0.0575846	−	0.998341i	$-0.481660\pi$
$157$	1.44307	0.115169	0.0575846	+	0.998341i	$0.481660\pi$
$158$	7.02527	0.558900
$159$	12.7180	1.00861
$160$	1.00000	0.0790569
$161$	3.48481	0.274642
$162$	10.9087	0.857068
$163$	−3.41087	−0.267160	−0.133580	−	0.991038i	$-0.542647\pi$
$163$	−3.41087	−0.267160	−0.133580	+	0.991038i	$0.542647\pi$
$164$	−8.79033	−0.686410
$165$	3.03435	0.236224
$166$	12.1548	0.943392
$167$	1.97518	0.152844	0.0764222	−	0.997076i	$-0.475650\pi$
$167$	1.97518	0.152844	0.0764222	+	0.997076i	$0.475650\pi$
$168$	10.4537	0.806518
$169$	−3.93071	−0.302363
$170$	8.05622	0.617884
$171$	−12.2386	−0.935907
$172$	1.00000	0.0762493
$173$	9.06789	0.689419	0.344709	−	0.938709i	$-0.387977\pi$
$173$	9.06789	0.689419	0.344709	+	0.938709i	$0.387977\pi$
$174$	22.6798	1.71935
$175$	−3.44511	−0.260425
$176$	−1.00000	−0.0753778
$177$	2.26817	0.170486
$178$	11.2814	0.845579
$179$	4.50260	0.336540	0.168270	−	0.985741i	$-0.446182\pi$
$179$	4.50260	0.336540	0.168270	+	0.985741i	$0.446182\pi$
$180$	6.20730	0.462665
$181$	21.3984	1.59053	0.795264	−	0.606263i	$-0.207332\pi$
$181$	21.3984	1.59053	0.795264	+	0.606263i	$0.207332\pi$
$182$	−10.3750	−0.769048
$183$	1.80285	0.133271
$184$	−1.01153	−0.0745707
$185$	0.814968	0.0599176
$186$	−10.8886	−0.798392
$187$	−8.05622	−0.589129
$188$	−2.28907	−0.166948
$189$	33.5281	2.43881
$190$	−1.97164	−0.143038
$191$	23.5905	1.70695	0.853474	−	0.521136i	$-0.174492\pi$
$191$	23.5905	1.70695	0.853474	+	0.521136i	$0.174492\pi$
$192$	−3.03435	−0.218986
$193$	18.2524	1.31383	0.656917	−	0.753963i	$-0.271860\pi$
$193$	18.2524	1.31383	0.656917	+	0.753963i	$0.271860\pi$
$194$	−13.1215	−0.942068
$195$	−9.13803	−0.654388
$196$	4.86875	0.347768
$197$	−16.3169	−1.16253	−0.581265	−	0.813714i	$-0.697442\pi$
$197$	−16.3169	−1.16253	−0.581265	+	0.813714i	$0.697442\pi$
$198$	−6.20730	−0.441134
$199$	1.88014	0.133279	0.0666397	−	0.997777i	$-0.478772\pi$
$199$	1.88014	0.133279	0.0666397	+	0.997777i	$0.478772\pi$
$200$	1.00000	0.0707107
$201$	−12.0098	−0.847109
$202$	2.38586	0.167868
$203$	25.7499	1.80729
$204$	−24.4454	−1.71152
$205$	−8.79033	−0.613944
$206$	8.69704	0.605951
$207$	−6.27885	−0.436410
$208$	3.01153	0.208812
$209$	1.97164	0.136381
$210$	10.4537	0.721372
$211$	−5.48675	−0.377724	−0.188862	−	0.982004i	$-0.560480\pi$
$211$	−5.48675	−0.377724	−0.188862	+	0.982004i	$0.560480\pi$
$212$	−4.19135	−0.287863
$213$	15.9847	1.09526
$214$	−0.158326	−0.0108230
$215$	1.00000	0.0681994
$216$	−9.73209	−0.662185
$217$	−12.3626	−0.839227
$218$	17.8523	1.20911
$219$	−20.3511	−1.37520
$220$	−1.00000	−0.0674200
$221$	24.2615	1.63201
$222$	−2.47290	−0.165970
$223$	−5.95482	−0.398764	−0.199382	−	0.979922i	$-0.563894\pi$
$223$	−5.95482	−0.398764	−0.199382	+	0.979922i	$0.563894\pi$
$224$	−3.44511	−0.230186
$225$	6.20730	0.413820
$226$	14.1561	0.941649
$227$	16.6824	1.10725	0.553623	−	0.832767i	$-0.313245\pi$
$227$	16.6824	1.10725	0.553623	+	0.832767i	$0.313245\pi$
$228$	5.98266	0.396211
$229$	−20.8066	−1.37494	−0.687469	−	0.726214i	$-0.741278\pi$
$229$	−20.8066	−1.37494	−0.687469	+	0.726214i	$0.741278\pi$
$230$	−1.01153	−0.0666980
$231$	−10.4537	−0.687801
$232$	−7.47434	−0.490715
$233$	6.22241	0.407643	0.203822	−	0.979008i	$-0.434664\pi$
$233$	6.22241	0.407643	0.203822	+	0.979008i	$0.434664\pi$
$234$	18.6935	1.22203
$235$	−2.28907	−0.149322
$236$	−0.747496	−0.0486578
$237$	−21.3171	−1.38470
$238$	−27.7545	−1.79906
$239$	1.42446	0.0921408	0.0460704	−	0.998938i	$-0.485330\pi$
$239$	1.42446	0.0921408	0.0460704	+	0.998938i	$0.485330\pi$
$240$	−3.03435	−0.195867
$241$	−13.8015	−0.889034	−0.444517	−	0.895770i	$-0.646625\pi$
$241$	−13.8015	−0.889034	−0.444517	+	0.895770i	$0.646625\pi$
$242$	1.00000	0.0642824
$243$	−3.90458	−0.250479
$244$	−0.594147	−0.0380363
$245$	4.86875	0.311053
$246$	26.6730	1.70061
$247$	−5.93765	−0.377804
$248$	3.58845	0.227867
$249$	−36.8818	−2.33729
$250$	1.00000	0.0632456
$251$	11.7815	0.743642	0.371821	−	0.928305i	$-0.378734\pi$
$251$	11.7815	0.743642	0.371821	+	0.928305i	$0.378734\pi$
$252$	−21.3848	−1.34712
$253$	1.01153	0.0635941
$254$	5.67047	0.355797
$255$	−24.4454	−1.53083
$256$	1.00000	0.0625000
$257$	2.93713	0.183213	0.0916066	−	0.995795i	$-0.470800\pi$
$257$	2.93713	0.183213	0.0916066	+	0.995795i	$0.470800\pi$
$258$	−3.03435	−0.188911
$259$	−2.80765	−0.174459
$260$	3.01153	0.186767
$261$	−46.3955	−2.87181
$262$	−7.81393	−0.482746
$263$	16.1661	0.996842	0.498421	−	0.866935i	$-0.333913\pi$
$263$	16.1661	0.996842	0.498421	+	0.866935i	$0.333913\pi$
$264$	3.03435	0.186752
$265$	−4.19135	−0.257473
$266$	6.79251	0.416476
$267$	−34.2318	−2.09495
$268$	3.95796	0.241771
$269$	−7.51028	−0.457910	−0.228955	−	0.973437i	$-0.573531\pi$
$269$	−7.51028	−0.457910	−0.228955	+	0.973437i	$0.573531\pi$
$270$	−9.73209	−0.592276
$271$	−5.81531	−0.353255	−0.176628	−	0.984278i	$-0.556519\pi$
$271$	−5.81531	−0.353255	−0.176628	+	0.984278i	$0.556519\pi$
$272$	8.05622	0.488480
$273$	31.4815	1.90535
$274$	11.7760	0.711412
$275$	−1.00000	−0.0603023
$276$	3.06933	0.184752
$277$	−14.0947	−0.846868	−0.423434	−	0.905927i	$-0.639175\pi$
$277$	−14.0947	−0.846868	−0.423434	+	0.905927i	$0.639175\pi$
$278$	−14.3383	−0.859952
$279$	22.2746	1.33354
$280$	−3.44511	−0.205884
$281$	28.9769	1.72862	0.864310	−	0.502960i	$-0.167756\pi$
$281$	28.9769	1.72862	0.864310	+	0.502960i	$0.167756\pi$
$282$	6.94585	0.413619
$283$	−5.85843	−0.348248	−0.174124	−	0.984724i	$-0.555709\pi$
$283$	−5.85843	−0.348248	−0.174124	+	0.984724i	$0.555709\pi$
$284$	−5.26792	−0.312594
$285$	5.98266	0.354382
$286$	−3.01153	−0.178075
$287$	30.2836	1.78759
$288$	6.20730	0.365769
$289$	47.9027	2.81781
$290$	−7.47434	−0.438908
$291$	39.8152	2.33401
$292$	6.70688	0.392491
$293$	22.6998	1.32614	0.663068	−	0.748559i	$-0.269254\pi$
$293$	22.6998	1.32614	0.663068	+	0.748559i	$0.269254\pi$
$294$	−14.7735	−0.861609
$295$	−0.747496	−0.0435209
$296$	0.814968	0.0473690
$297$	9.73209	0.564713
$298$	−8.21509	−0.475887
$299$	−3.04623	−0.176168
$300$	−3.03435	−0.175188
$301$	−3.44511	−0.198573
$302$	9.95698	0.572960
$303$	−7.23954	−0.415901
$304$	−1.97164	−0.113081
$305$	−0.594147	−0.0340207
$306$	50.0074	2.85873
$307$	23.5995	1.34690	0.673448	−	0.739234i	$-0.264812\pi$
$307$	23.5995	1.34690	0.673448	+	0.739234i	$0.264812\pi$
$308$	3.44511	0.196303
$309$	−26.3899	−1.50127
$310$	3.58845	0.203810
$311$	−33.5297	−1.90130	−0.950649	−	0.310269i	$-0.899581\pi$
$311$	−33.5297	−1.90130	−0.950649	+	0.310269i	$0.899581\pi$
$312$	−9.13803	−0.517339
$313$	13.5130	0.763801	0.381901	−	0.924203i	$-0.375270\pi$
$313$	13.5130	0.763801	0.381901	+	0.924203i	$0.375270\pi$
$314$	1.44307	0.0814370
$315$	−21.3848	−1.20490
$316$	7.02527	0.395202
$317$	32.4963	1.82518	0.912588	−	0.408881i	$-0.134081\pi$
$317$	32.4963	1.82518	0.912588	+	0.408881i	$0.134081\pi$
$318$	12.7180	0.713192
$319$	7.47434	0.418483
$320$	1.00000	0.0559017
$321$	0.480418	0.0268143
$322$	3.48481	0.194201
$323$	−15.8840	−0.883809
$324$	10.9087	0.606039
$325$	3.01153	0.167049
$326$	−3.41087	−0.188911
$327$	−54.1702	−2.99562
$328$	−8.79033	−0.485365
$329$	7.88608	0.434774
$330$	3.03435	0.167036
$331$	−4.30112	−0.236411	−0.118206	−	0.992989i	$-0.537714\pi$
$331$	−4.30112	−0.236411	−0.118206	+	0.992989i	$0.537714\pi$
$332$	12.1548	0.667079
$333$	5.05875	0.277218
$334$	1.97518	0.108077
$335$	3.95796	0.216246
$336$	10.4537	0.570294
$337$	−1.53439	−0.0835837	−0.0417919	−	0.999126i	$-0.513307\pi$
$337$	−1.53439	−0.0835837	−0.0417919	+	0.999126i	$0.513307\pi$
$338$	−3.93071	−0.213803
$339$	−42.9546	−2.33297
$340$	8.05622	0.436910
$341$	−3.58845	−0.194325
$342$	−12.2386	−0.661786
$343$	7.34238	0.396451
$344$	1.00000	0.0539164
$345$	3.06933	0.165247
$346$	9.06789	0.487493
$347$	−11.3937	−0.611645	−0.305823	−	0.952089i	$-0.598931\pi$
$347$	−11.3937	−0.611645	−0.305823	+	0.952089i	$0.598931\pi$
$348$	22.6798	1.21576
$349$	19.2716	1.03159	0.515793	−	0.856713i	$-0.327497\pi$
$349$	19.2716	1.03159	0.515793	+	0.856713i	$0.327497\pi$
$350$	−3.44511	−0.184149
$351$	−29.3084	−1.56437
$352$	−1.00000	−0.0533002
$353$	17.3056	0.921086	0.460543	−	0.887637i	$-0.347655\pi$
$353$	17.3056	0.921086	0.460543	+	0.887637i	$0.347655\pi$
$354$	2.26817	0.120552
$355$	−5.26792	−0.279592
$356$	11.2814	0.597914
$357$	84.2171	4.45724
$358$	4.50260	0.237970
$359$	31.0300	1.63770	0.818850	−	0.574007i	$-0.194612\pi$
$359$	31.0300	1.63770	0.818850	+	0.574007i	$0.194612\pi$
$360$	6.20730	0.327154
$361$	−15.1126	−0.795402
$362$	21.3984	1.12467
$363$	−3.03435	−0.159262
$364$	−10.3750	−0.543799
$365$	6.70688	0.351054
$366$	1.80285	0.0942365
$367$	26.2176	1.36855	0.684273	−	0.729226i	$-0.260119\pi$
$367$	26.2176	1.36855	0.684273	+	0.729226i	$0.260119\pi$
$368$	−1.01153	−0.0527294
$369$	−54.5643	−2.84050
$370$	0.814968	0.0423682
$371$	14.4396	0.749669
$372$	−10.8886	−0.564549
$373$	3.10048	0.160537	0.0802685	−	0.996773i	$-0.474422\pi$
$373$	3.10048	0.160537	0.0802685	+	0.996773i	$0.474422\pi$
$374$	−8.05622	−0.416577
$375$	−3.03435	−0.156693
$376$	−2.28907	−0.118050
$377$	−22.5092	−1.15928
$378$	33.5281	1.72450
$379$	16.3697	0.840855	0.420427	−	0.907326i	$-0.361880\pi$
$379$	16.3697	0.840855	0.420427	+	0.907326i	$0.361880\pi$
$380$	−1.97164	−0.101143
$381$	−17.2062	−0.881501
$382$	23.5905	1.20699
$383$	1.84411	0.0942298	0.0471149	−	0.998889i	$-0.484997\pi$
$383$	1.84411	0.0942298	0.0471149	+	0.998889i	$0.484997\pi$
$384$	−3.03435	−0.154846
$385$	3.44511	0.175579
$386$	18.2524	0.929021
$387$	6.20730	0.315535
$388$	−13.1215	−0.666143
$389$	−2.69523	−0.136654	−0.0683269	−	0.997663i	$-0.521766\pi$
$389$	−2.69523	−0.136654	−0.0683269	+	0.997663i	$0.521766\pi$
$390$	−9.13803	−0.462722
$391$	−8.14908	−0.412116
$392$	4.86875	0.245909
$393$	23.7102	1.19602
$394$	−16.3169	−0.822033
$395$	7.02527	0.353480
$396$	−6.20730	−0.311929
$397$	31.5646	1.58418	0.792092	−	0.610402i	$-0.208992\pi$
$397$	31.5646	1.58418	0.792092	+	0.610402i	$0.208992\pi$
$398$	1.88014	0.0942428
$399$	−20.6109	−1.03184
$400$	1.00000	0.0500000
$401$	−20.9312	−1.04525	−0.522626	−	0.852562i	$-0.675048\pi$
$401$	−20.9312	−1.04525	−0.522626	+	0.852562i	$0.675048\pi$
$402$	−12.0098	−0.598996
$403$	10.8067	0.538320
$404$	2.38586	0.118701
$405$	10.9087	0.542058
$406$	25.7499	1.27795
$407$	−0.814968	−0.0403965
$408$	−24.4454	−1.21023
$409$	−26.4274	−1.30675	−0.653376	−	0.757034i	$-0.726648\pi$
$409$	−26.4274	−1.30675	−0.653376	+	0.757034i	$0.726648\pi$
$410$	−8.79033	−0.434124
$411$	−35.7325	−1.76255
$412$	8.69704	0.428472
$413$	2.57520	0.126717
$414$	−6.27885	−0.308588
$415$	12.1548	0.596653
$416$	3.01153	0.147652
$417$	43.5074	2.13056
$418$	1.97164	0.0964361
$419$	−21.0841	−1.03003	−0.515014	−	0.857182i	$-0.672213\pi$
$419$	−21.0841	−1.03003	−0.515014	+	0.857182i	$0.672213\pi$
$420$	10.4537	0.510087
$421$	−30.4110	−1.48214	−0.741070	−	0.671428i	$-0.765681\pi$
$421$	−30.4110	−1.48214	−0.741070	+	0.671428i	$0.765681\pi$
$422$	−5.48675	−0.267091
$423$	−14.2089	−0.690863
$424$	−4.19135	−0.203550
$425$	8.05622	0.390784
$426$	15.9847	0.774463
$427$	2.04690	0.0990563
$428$	−0.158326	−0.00765299
$429$	9.13803	0.441188
$430$	1.00000	0.0482243
$431$	21.1977	1.02106	0.510529	−	0.859861i	$-0.329450\pi$
$431$	21.1977	1.02106	0.510529	+	0.859861i	$0.329450\pi$
$432$	−9.73209	−0.468235
$433$	25.0369	1.20320	0.601599	−	0.798798i	$-0.294530\pi$
$433$	25.0369	1.20320	0.601599	+	0.798798i	$0.294530\pi$
$434$	−12.3626	−0.593423
$435$	22.6798	1.08741
$436$	17.8523	0.854970
$437$	1.99437	0.0954035
$438$	−20.3511	−0.972411
$439$	17.1204	0.817113	0.408557	−	0.912733i	$-0.366032\pi$
$439$	17.1204	0.817113	0.408557	+	0.912733i	$0.366032\pi$
$440$	−1.00000	−0.0476731
$441$	30.2218	1.43913
$442$	24.2615	1.15400
$443$	−26.7844	−1.27256	−0.636282	−	0.771457i	$-0.719528\pi$
$443$	−26.7844	−1.27256	−0.636282	+	0.771457i	$0.719528\pi$
$444$	−2.47290	−0.117359
$445$	11.2814	0.534791
$446$	−5.95482	−0.281969
$447$	24.9275	1.17903
$448$	−3.44511	−0.162766
$449$	−37.7530	−1.78167	−0.890837	−	0.454323i	$-0.849881\pi$
$449$	−37.7530	−1.78167	−0.890837	+	0.454323i	$0.849881\pi$
$450$	6.20730	0.292615
$451$	8.79033	0.413921
$452$	14.1561	0.665847
$453$	−30.2130	−1.41953
$454$	16.6824	0.782942
$455$	−10.3750	−0.486389
$456$	5.98266	0.280164
$457$	−35.4827	−1.65981	−0.829905	−	0.557904i	$-0.811606\pi$
$457$	−35.4827	−1.65981	−0.829905	+	0.557904i	$0.811606\pi$
$458$	−20.8066	−0.972228
$459$	−78.4039	−3.65958
$460$	−1.01153	−0.0471626
$461$	−31.8589	−1.48381	−0.741907	−	0.670502i	$-0.766079\pi$
$461$	−31.8589	−1.48381	−0.741907	+	0.670502i	$0.766079\pi$
$462$	−10.4537	−0.486349
$463$	25.0415	1.16378	0.581888	−	0.813269i	$-0.302314\pi$
$463$	25.0415	1.16378	0.581888	+	0.813269i	$0.302314\pi$
$464$	−7.47434	−0.346988
$465$	−10.8886	−0.504948
$466$	6.22241	0.288247
$467$	7.52638	0.348279	0.174140	−	0.984721i	$-0.444286\pi$
$467$	7.52638	0.348279	0.174140	+	0.984721i	$0.444286\pi$
$468$	18.6935	0.864105
$469$	−13.6356	−0.629632
$470$	−2.28907	−0.105587
$471$	−4.37878	−0.201763
$472$	−0.747496	−0.0344063
$473$	−1.00000	−0.0459800
$474$	−21.3171	−0.979129
$475$	−1.97164	−0.0904651
$476$	−27.7545	−1.27213
$477$	−26.0170	−1.19124
$478$	1.42446	0.0651534
$479$	−8.55601	−0.390934	−0.195467	−	0.980710i	$-0.562622\pi$
$479$	−8.55601	−0.390934	−0.195467	+	0.980710i	$0.562622\pi$
$480$	−3.03435	−0.138499
$481$	2.45430	0.111906
$482$	−13.8015	−0.628642
$483$	−10.5742	−0.481141
$484$	1.00000	0.0454545
$485$	−13.1215	−0.595816
$486$	−3.90458	−0.177115
$487$	−9.24248	−0.418817	−0.209408	−	0.977828i	$-0.567154\pi$
$487$	−9.24248	−0.418817	−0.209408	+	0.977828i	$0.567154\pi$
$488$	−0.594147	−0.0268957
$489$	10.3498	0.468033
$490$	4.86875	0.219948
$491$	34.7025	1.56610	0.783050	−	0.621958i	$-0.213663\pi$
$491$	34.7025	1.56610	0.783050	+	0.621958i	$0.213663\pi$
$492$	26.6730	1.20251
$493$	−60.2150	−2.71195
$494$	−5.93765	−0.267147
$495$	−6.20730	−0.278998
$496$	3.58845	0.161126
$497$	18.1485	0.814074
$498$	−36.8818	−1.65271
$499$	13.6098	0.609259	0.304629	−	0.952471i	$-0.401467\pi$
$499$	13.6098	0.609259	0.304629	+	0.952471i	$0.401467\pi$
$500$	1.00000	0.0447214
$501$	−5.99341	−0.267766
$502$	11.7815	0.525834
$503$	−10.9154	−0.486691	−0.243346	−	0.969940i	$-0.578245\pi$
$503$	−10.9154	−0.486691	−0.243346	+	0.969940i	$0.578245\pi$
$504$	−21.3848	−0.952555
$505$	2.38586	0.106169
$506$	1.01153	0.0449678
$507$	11.9272	0.529705
$508$	5.67047	0.251586
$509$	−38.3303	−1.69896	−0.849479	−	0.527622i	$-0.823084\pi$
$509$	−38.3303	−1.69896	−0.849479	+	0.527622i	$0.823084\pi$
$510$	−24.4454	−1.08246
$511$	−23.1059	−1.02215
$512$	1.00000	0.0441942
$513$	19.1882	0.847180
$514$	2.93713	0.129551
$515$	8.69704	0.383237
$516$	−3.03435	−0.133580
$517$	2.28907	0.100673
$518$	−2.80765	−0.123361
$519$	−27.5152	−1.20778
$520$	3.01153	0.132064
$521$	21.4920	0.941583	0.470792	−	0.882244i	$-0.343968\pi$
$521$	21.4920	0.941583	0.470792	+	0.882244i	$0.343968\pi$
$522$	−46.3955	−2.03068
$523$	−45.0225	−1.96870	−0.984348	−	0.176235i	$-0.943608\pi$
$523$	−45.0225	−1.96870	−0.984348	+	0.176235i	$0.943608\pi$
$524$	−7.81393	−0.341353
$525$	10.4537	0.456236
$526$	16.1661	0.704874
$527$	28.9093	1.25931
$528$	3.03435	0.132053
$529$	−21.9768	−0.955514
$530$	−4.19135	−0.182061
$531$	−4.63993	−0.201356
$532$	6.79251	0.294493
$533$	−26.4723	−1.14664
$534$	−34.2318	−1.48136
$535$	−0.158326	−0.00684504
$536$	3.95796	0.170958
$537$	−13.6625	−0.589579
$538$	−7.51028	−0.323791
$539$	−4.86875	−0.209712
$540$	−9.73209	−0.418803
$541$	43.5568	1.87265	0.936327	−	0.351128i	$-0.114202\pi$
$541$	43.5568	1.87265	0.936327	+	0.351128i	$0.114202\pi$
$542$	−5.81531	−0.249789
$543$	−64.9302	−2.78642
$544$	8.05622	0.345408
$545$	17.8523	0.764708
$546$	31.4815	1.34728
$547$	−1.74771	−0.0747267	−0.0373633	−	0.999302i	$-0.511896\pi$
$547$	−1.74771	−0.0747267	−0.0373633	+	0.999302i	$0.511896\pi$
$548$	11.7760	0.503045
$549$	−3.68805	−0.157402
$550$	−1.00000	−0.0426401
$551$	14.7367	0.627805
$552$	3.06933	0.130639
$553$	−24.2028	−1.02921
$554$	−14.0947	−0.598826
$555$	−2.47290	−0.104969
$556$	−14.3383	−0.608078
$557$	27.7103	1.17412	0.587061	−	0.809542i	$-0.300285\pi$
$557$	27.7103	1.17412	0.587061	+	0.809542i	$0.300285\pi$
$558$	22.2746	0.942958
$559$	3.01153	0.127374
$560$	−3.44511	−0.145582
$561$	24.4454	1.03209
$562$	28.9769	1.22232
$563$	31.7218	1.33691	0.668457	−	0.743751i	$-0.266955\pi$
$563$	31.7218	1.33691	0.668457	+	0.743751i	$0.266955\pi$
$564$	6.94585	0.292473
$565$	14.1561	0.595551
$566$	−5.85843	−0.246248
$567$	−37.5816	−1.57828
$568$	−5.26792	−0.221037
$569$	−27.2360	−1.14179	−0.570895	−	0.821023i	$-0.693404\pi$
$569$	−27.2360	−1.14179	−0.570895	+	0.821023i	$0.693404\pi$
$570$	5.98266	0.250586
$571$	32.7621	1.37105	0.685526	−	0.728048i	$-0.259572\pi$
$571$	32.7621	1.37105	0.685526	+	0.728048i	$0.259572\pi$
$572$	−3.01153	−0.125918
$573$	−71.5819	−2.99038
$574$	30.2836	1.26401
$575$	−1.01153	−0.0421835
$576$	6.20730	0.258638
$577$	−13.0091	−0.541576	−0.270788	−	0.962639i	$-0.587284\pi$
$577$	−13.0091	−0.541576	−0.270788	+	0.962639i	$0.587284\pi$
$578$	47.9027	1.99249
$579$	−55.3841	−2.30169
$580$	−7.47434	−0.310355
$581$	−41.8744	−1.73724
$582$	39.8152	1.65040
$583$	4.19135	0.173588
$584$	6.70688	0.277533
$585$	18.6935	0.772879
$586$	22.6998	0.937719
$587$	−15.4139	−0.636199	−0.318100	−	0.948057i	$-0.603045\pi$
$587$	−15.4139	−0.636199	−0.318100	+	0.948057i	$0.603045\pi$
$588$	−14.7735	−0.609249
$589$	−7.07513	−0.291526
$590$	−0.747496	−0.0307739
$591$	49.5112	2.03662
$592$	0.814968	0.0334950
$593$	16.4405	0.675129	0.337564	−	0.941302i	$-0.390397\pi$
$593$	16.4405	0.675129	0.337564	+	0.941302i	$0.390397\pi$
$594$	9.73209	0.399313
$595$	−27.7545	−1.13783
$596$	−8.21509	−0.336503
$597$	−5.70500	−0.233490
$598$	−3.04623	−0.124570
$599$	4.52286	0.184799	0.0923995	−	0.995722i	$-0.470546\pi$
$599$	4.52286	0.184799	0.0923995	+	0.995722i	$0.470546\pi$
$600$	−3.03435	−0.123877
$601$	−37.8833	−1.54529	−0.772646	−	0.634837i	$-0.781067\pi$
$601$	−37.8833	−1.54529	−0.772646	+	0.634837i	$0.781067\pi$
$602$	−3.44511	−0.140412
$603$	24.5682	1.00050
$604$	9.95698	0.405144
$605$	1.00000	0.0406558
$606$	−7.23954	−0.294086
$607$	−27.3697	−1.11090	−0.555450	−	0.831550i	$-0.687454\pi$
$607$	−27.3697	−1.11090	−0.555450	+	0.831550i	$0.687454\pi$
$608$	−1.97164	−0.0799606
$609$	−78.1343	−3.16616
$610$	−0.594147	−0.0240563
$611$	−6.89359	−0.278885
$612$	50.0074	2.02143
$613$	−9.72740	−0.392886	−0.196443	−	0.980515i	$-0.562939\pi$
$613$	−9.72740	−0.392886	−0.196443	+	0.980515i	$0.562939\pi$
$614$	23.5995	0.952400
$615$	26.6730	1.07556
$616$	3.44511	0.138807
$617$	−26.8861	−1.08239	−0.541197	−	0.840896i	$-0.682029\pi$
$617$	−26.8861	−1.08239	−0.541197	+	0.840896i	$0.682029\pi$
$618$	−26.3899	−1.06156
$619$	15.1651	0.609538	0.304769	−	0.952426i	$-0.401421\pi$
$619$	15.1651	0.609538	0.304769	+	0.952426i	$0.401421\pi$
$620$	3.58845	0.144116
$621$	9.84426	0.395037
$622$	−33.5297	−1.34442
$623$	−38.8657	−1.55712
$624$	−9.13803	−0.365814
$625$	1.00000	0.0400000
$626$	13.5130	0.540089
$627$	−5.98266	−0.238924
$628$	1.44307	0.0575846
$629$	6.56556	0.261786
$630$	−21.3848	−0.851991
$631$	40.8146	1.62480	0.812402	−	0.583098i	$-0.198160\pi$
$631$	40.8146	1.62480	0.812402	+	0.583098i	$0.198160\pi$
$632$	7.02527	0.279450
$633$	16.6488	0.661729
$634$	32.4963	1.29059
$635$	5.67047	0.225026
$636$	12.7180	0.504303
$637$	14.6624	0.580944
$638$	7.47434	0.295912
$639$	−32.6996	−1.29358
$640$	1.00000	0.0395285
$641$	10.5834	0.418017	0.209009	−	0.977914i	$-0.432976\pi$
$641$	10.5834	0.418017	0.209009	+	0.977914i	$0.432976\pi$
$642$	0.480418	0.0189606
$643$	26.6338	1.05033	0.525167	−	0.850999i	$-0.324003\pi$
$643$	26.6338	1.05033	0.525167	+	0.850999i	$0.324003\pi$
$644$	3.48481	0.137321
$645$	−3.03435	−0.119478
$646$	−15.8840	−0.624947
$647$	−24.4855	−0.962624	−0.481312	−	0.876549i	$-0.659840\pi$
$647$	−24.4855	−0.962624	−0.481312	+	0.876549i	$0.659840\pi$
$648$	10.9087	0.428534
$649$	0.747496	0.0293418
$650$	3.01153	0.118122
$651$	37.5124	1.47023
$652$	−3.41087	−0.133580
$653$	−6.10760	−0.239009	−0.119504	−	0.992834i	$-0.538131\pi$
$653$	−6.10760	−0.239009	−0.119504	+	0.992834i	$0.538131\pi$
$654$	−54.1702	−2.11822
$655$	−7.81393	−0.305316
$656$	−8.79033	−0.343205
$657$	41.6317	1.62421
$658$	7.88608	0.307432
$659$	−1.81431	−0.0706755	−0.0353377	−	0.999375i	$-0.511251\pi$
$659$	−1.81431	−0.0706755	−0.0353377	+	0.999375i	$0.511251\pi$
$660$	3.03435	0.118112
$661$	−4.07311	−0.158425	−0.0792127	−	0.996858i	$-0.525241\pi$
$661$	−4.07311	−0.158425	−0.0792127	+	0.996858i	$0.525241\pi$
$662$	−4.30112	−0.167168
$663$	−73.6180	−2.85909
$664$	12.1548	0.471696
$665$	6.79251	0.263402
$666$	5.05875	0.196023
$667$	7.56049	0.292743
$668$	1.97518	0.0764222
$669$	18.0690	0.698589
$670$	3.95796	0.152909
$671$	0.594147	0.0229368
$672$	10.4537	0.403259
$673$	37.7126	1.45372	0.726858	−	0.686788i	$-0.240980\pi$
$673$	37.7126	1.45372	0.726858	+	0.686788i	$0.240980\pi$
$674$	−1.53439	−0.0591026
$675$	−9.73209	−0.374588
$676$	−3.93071	−0.151181
$677$	−41.5508	−1.59693	−0.798463	−	0.602043i	$-0.794353\pi$
$677$	−41.5508	−1.59693	−0.798463	+	0.602043i	$0.794353\pi$
$678$	−42.9546	−1.64966
$679$	45.2049	1.73481
$680$	8.05622	0.308942
$681$	−50.6202	−1.93977
$682$	−3.58845	−0.137409
$683$	16.0110	0.612642	0.306321	−	0.951928i	$-0.400902\pi$
$683$	16.0110	0.612642	0.306321	+	0.951928i	$0.400902\pi$
$684$	−12.2386	−0.467954
$685$	11.7760	0.449937
$686$	7.34238	0.280333
$687$	63.1345	2.40873
$688$	1.00000	0.0381246
$689$	−12.6224	−0.480873
$690$	3.06933	0.116847
$691$	−10.1084	−0.384540	−0.192270	−	0.981342i	$-0.561585\pi$
$691$	−10.1084	−0.384540	−0.192270	+	0.981342i	$0.561585\pi$
$692$	9.06789	0.344709
$693$	21.3848	0.812342
$694$	−11.3937	−0.432498
$695$	−14.3383	−0.543881
$696$	22.6798	0.859675
$697$	−70.8169	−2.68238
$698$	19.2716	0.729442
$699$	−18.8810	−0.714144
$700$	−3.44511	−0.130213
$701$	38.0510	1.43717	0.718583	−	0.695441i	$-0.244791\pi$
$701$	38.0510	1.43717	0.718583	+	0.695441i	$0.244791\pi$
$702$	−29.3084	−1.10618
$703$	−1.60682	−0.0606025
$704$	−1.00000	−0.0376889
$705$	6.94585	0.261596
$706$	17.3056	0.651306
$707$	−8.21953	−0.309127
$708$	2.26817	0.0852429
$709$	49.2891	1.85109	0.925545	−	0.378638i	$-0.123607\pi$
$709$	49.2891	1.85109	0.925545	+	0.378638i	$0.123607\pi$
$710$	−5.26792	−0.197702
$711$	43.6080	1.63543
$712$	11.2814	0.422789
$713$	−3.62981	−0.135937
$714$	84.2171	3.15175
$715$	−3.01153	−0.112625
$716$	4.50260	0.168270
$717$	−4.32232	−0.161420
$718$	31.0300	1.15803
$719$	−28.1770	−1.05083	−0.525413	−	0.850847i	$-0.676089\pi$
$719$	−28.1770	−1.05083	−0.525413	+	0.850847i	$0.676089\pi$
$720$	6.20730	0.231333
$721$	−29.9622	−1.11585
$722$	−15.1126	−0.562434
$723$	41.8787	1.55749
$724$	21.3984	0.795264
$725$	−7.47434	−0.277590
$726$	−3.03435	−0.112615
$727$	43.0471	1.59653	0.798264	−	0.602308i	$-0.205752\pi$
$727$	43.0471	1.59653	0.798264	+	0.602308i	$0.205752\pi$
$728$	−10.3750	−0.384524
$729$	−20.8782	−0.773267
$730$	6.70688	0.248233
$731$	8.05622	0.297970
$732$	1.80285	0.0666353
$733$	17.3492	0.640807	0.320403	−	0.947281i	$-0.396182\pi$
$733$	17.3492	0.640807	0.320403	+	0.947281i	$0.396182\pi$
$734$	26.2176	0.967709
$735$	−14.7735	−0.544929
$736$	−1.01153	−0.0372853
$737$	−3.95796	−0.145793
$738$	−54.5643	−2.00854
$739$	−14.8976	−0.548018	−0.274009	−	0.961727i	$-0.588350\pi$
$739$	−14.8976	−0.548018	−0.274009	+	0.961727i	$0.588350\pi$
$740$	0.814968	0.0299588
$741$	18.0169	0.661868
$742$	14.4396	0.530096
$743$	38.5777	1.41528	0.707639	−	0.706575i	$-0.249761\pi$
$743$	38.5777	1.41528	0.707639	+	0.706575i	$0.249761\pi$
$744$	−10.8886	−0.399196
$745$	−8.21509	−0.300978
$746$	3.10048	0.113517
$747$	75.4482	2.76051
$748$	−8.05622	−0.294565
$749$	0.545451	0.0199303
$750$	−3.03435	−0.110799
$751$	9.30941	0.339705	0.169853	−	0.985469i	$-0.445671\pi$
$751$	9.30941	0.339705	0.169853	+	0.985469i	$0.445671\pi$
$752$	−2.28907	−0.0834738
$753$	−35.7492	−1.30277
$754$	−22.5092	−0.819736
$755$	9.95698	0.362372
$756$	33.5281	1.21940
$757$	35.2626	1.28164	0.640820	−	0.767691i	$-0.278594\pi$
$757$	35.2626	1.28164	0.640820	+	0.767691i	$0.278594\pi$
$758$	16.3697	0.594574
$759$	−3.06933	−0.111409
$760$	−1.97164	−0.0715190
$761$	36.1965	1.31212	0.656062	−	0.754707i	$-0.272221\pi$
$761$	36.1965	1.31212	0.656062	+	0.754707i	$0.272221\pi$
$762$	−17.2062	−0.623315
$763$	−61.5030	−2.22656
$764$	23.5905	0.853474
$765$	50.0074	1.80802
$766$	1.84411	0.0666305
$767$	−2.25110	−0.0812826
$768$	−3.03435	−0.109493
$769$	−26.5292	−0.956667	−0.478334	−	0.878178i	$-0.658759\pi$
$769$	−26.5292	−0.956667	−0.478334	+	0.878178i	$0.658759\pi$
$770$	3.44511	0.124153
$771$	−8.91229	−0.320968
$772$	18.2524	0.656917
$773$	−33.2115	−1.19453	−0.597267	−	0.802043i	$-0.703747\pi$
$773$	−33.2115	−1.19453	−0.597267	+	0.802043i	$0.703747\pi$
$774$	6.20730	0.223117
$775$	3.58845	0.128901
$776$	−13.1215	−0.471034
$777$	8.51940	0.305632
$778$	−2.69523	−0.0966288
$779$	17.3314	0.620961
$780$	−9.13803	−0.327194
$781$	5.26792	0.188501
$782$	−8.14908	−0.291410
$783$	72.7410	2.59955
$784$	4.86875	0.173884
$785$	1.44307	0.0515053
$786$	23.7102	0.845716
$787$	−15.6797	−0.558922	−0.279461	−	0.960157i	$-0.590156\pi$
$787$	−15.6797	−0.558922	−0.279461	+	0.960157i	$0.590156\pi$
$788$	−16.3169	−0.581265
$789$	−49.0535	−1.74635
$790$	7.02527	0.249948
$791$	−48.7692	−1.73403
$792$	−6.20730	−0.220567
$793$	−1.78929	−0.0635395
$794$	31.5646	1.12019
$795$	12.7180	0.451062
$796$	1.88014	0.0666397
$797$	16.3162	0.577951	0.288975	−	0.957337i	$-0.406685\pi$
$797$	16.3162	0.577951	0.288975	+	0.957337i	$0.406685\pi$
$798$	−20.6109	−0.729618
$799$	−18.4413	−0.652405
$800$	1.00000	0.0353553
$801$	70.0272	2.47429
$802$	−20.9312	−0.739105
$803$	−6.70688	−0.236681
$804$	−12.0098	−0.423554
$805$	3.48481	0.122823
$806$	10.8067	0.380650
$807$	22.7889	0.802206
$808$	2.38586	0.0839342
$809$	10.8237	0.380543	0.190271	−	0.981732i	$-0.439063\pi$
$809$	10.8237	0.380543	0.190271	+	0.981732i	$0.439063\pi$
$810$	10.9087	0.383293
$811$	−14.4504	−0.507424	−0.253712	−	0.967280i	$-0.581651\pi$
$811$	−14.4504	−0.507424	−0.253712	+	0.967280i	$0.581651\pi$
$812$	25.7499	0.903644
$813$	17.6457	0.618862
$814$	−0.814968	−0.0285646
$815$	−3.41087	−0.119478
$816$	−24.4454	−0.855761
$817$	−1.97164	−0.0689790
$818$	−26.4274	−0.924013
$819$	−64.4009	−2.25035
$820$	−8.79033	−0.306972
$821$	39.2959	1.37144	0.685718	−	0.727867i	$-0.259488\pi$
$821$	39.2959	1.37144	0.685718	+	0.727867i	$0.259488\pi$
$822$	−35.7325	−1.24631
$823$	−23.6733	−0.825199	−0.412600	−	0.910913i	$-0.635379\pi$
$823$	−23.6733	−0.825199	−0.412600	+	0.910913i	$0.635379\pi$
$824$	8.69704	0.302976
$825$	3.03435	0.105643
$826$	2.57520	0.0896027
$827$	−42.8341	−1.48949	−0.744744	−	0.667351i	$-0.767428\pi$
$827$	−42.8341	−1.48949	−0.744744	+	0.667351i	$0.767428\pi$
$828$	−6.27885	−0.218205
$829$	−25.9312	−0.900628	−0.450314	−	0.892870i	$-0.648688\pi$
$829$	−25.9312	−0.900628	−0.450314	+	0.892870i	$0.648688\pi$
$830$	12.1548	0.421898
$831$	42.7683	1.48362
$832$	3.01153	0.104406
$833$	39.2237	1.35902
$834$	43.5074	1.50654
$835$	1.97518	0.0683541
$836$	1.97164	0.0681907
$837$	−34.9231	−1.20712
$838$	−21.0841	−0.728339
$839$	−3.95871	−0.136670	−0.0683350	−	0.997662i	$-0.521769\pi$
$839$	−3.95871	−0.136670	−0.0683350	+	0.997662i	$0.521769\pi$
$840$	10.4537	0.360686
$841$	26.8658	0.926406
$842$	−30.4110	−1.04803
$843$	−87.9263	−3.02834
$844$	−5.48675	−0.188862
$845$	−3.93071	−0.135221
$846$	−14.2089	−0.488514
$847$	−3.44511	−0.118375
$848$	−4.19135	−0.143932
$849$	17.7766	0.610090
$850$	8.05622	0.276326
$851$	−0.824361	−0.0282587
$852$	15.9847	0.547628
$853$	−37.4187	−1.28119	−0.640595	−	0.767879i	$-0.721312\pi$
$853$	−37.4187	−1.28119	−0.640595	+	0.767879i	$0.721312\pi$
$854$	2.04690	0.0700434
$855$	−12.2386	−0.418551
$856$	−0.158326	−0.00541148
$857$	27.3132	0.933003	0.466501	−	0.884521i	$-0.345514\pi$
$857$	27.3132	0.933003	0.466501	+	0.884521i	$0.345514\pi$
$858$	9.13803	0.311967
$859$	13.2220	0.451130	0.225565	−	0.974228i	$-0.427577\pi$
$859$	13.2220	0.451130	0.225565	+	0.974228i	$0.427577\pi$
$860$	1.00000	0.0340997
$861$	−91.8912	−3.13164
$862$	21.1977	0.721997
$863$	−8.08216	−0.275120	−0.137560	−	0.990493i	$-0.543926\pi$
$863$	−8.08216	−0.275120	−0.137560	+	0.990493i	$0.543926\pi$
$864$	−9.73209	−0.331092
$865$	9.06789	0.308317
$866$	25.0369	0.850790
$867$	−145.354	−4.93648
$868$	−12.3626	−0.419613
$869$	−7.02527	−0.238316
$870$	22.6798	0.768917
$871$	11.9195	0.403876
$872$	17.8523	0.604555
$873$	−81.4491	−2.75663
$874$	1.99437	0.0674604
$875$	−3.44511	−0.116466
$876$	−20.3511	−0.687599
$877$	−44.3666	−1.49815	−0.749076	−	0.662484i	$-0.769502\pi$
$877$	−44.3666	−1.49815	−0.749076	+	0.662484i	$0.769502\pi$
$878$	17.1204	0.577786
$879$	−68.8792	−2.32324
$880$	−1.00000	−0.0337100
$881$	−1.04662	−0.0352615	−0.0176307	−	0.999845i	$-0.505612\pi$
$881$	−1.04662	−0.0352615	−0.0176307	+	0.999845i	$0.505612\pi$
$882$	30.2218	1.01762
$883$	−15.4009	−0.518281	−0.259140	−	0.965840i	$-0.583439\pi$
$883$	−15.4009	−0.518281	−0.259140	+	0.965840i	$0.583439\pi$
$884$	24.2615	0.816003
$885$	2.26817	0.0762436
$886$	−26.7844	−0.899838
$887$	−52.4559	−1.76130	−0.880648	−	0.473771i	$-0.842892\pi$
$887$	−52.4559	−1.76130	−0.880648	+	0.473771i	$0.842892\pi$
$888$	−2.47290	−0.0829851
$889$	−19.5354	−0.655195
$890$	11.2814	0.378154
$891$	−10.9087	−0.365455
$892$	−5.95482	−0.199382
$893$	4.51322	0.151029
$894$	24.9275	0.833700
$895$	4.50260	0.150505
$896$	−3.44511	−0.115093
$897$	9.24335	0.308627
$898$	−37.7530	−1.25983
$899$	−26.8213	−0.894540
$900$	6.20730	0.206910
$901$	−33.7664	−1.12492
$902$	8.79033	0.292686
$903$	10.4537	0.347876
$904$	14.1561	0.470825
$905$	21.3984	0.711306
$906$	−30.2130	−1.00376
$907$	−35.8803	−1.19139	−0.595694	−	0.803212i	$-0.703123\pi$
$907$	−35.8803	−1.19139	−0.595694	+	0.803212i	$0.703123\pi$
$908$	16.6824	0.553623
$909$	14.8097	0.491208
$910$	−10.3750	−0.343929
$911$	40.0836	1.32803	0.664015	−	0.747720i	$-0.268851\pi$
$911$	40.0836	1.32803	0.664015	+	0.747720i	$0.268851\pi$
$912$	5.98266	0.198106
$913$	−12.1548	−0.402264
$914$	−35.4827	−1.17366
$915$	1.80285	0.0596004
$916$	−20.8066	−0.687469
$917$	26.9198	0.888971
$918$	−78.4039	−2.58771
$919$	48.9039	1.61319	0.806596	−	0.591104i	$-0.201308\pi$
$919$	48.9039	1.61319	0.806596	+	0.591104i	$0.201308\pi$
$920$	−1.01153	−0.0333490
$921$	−71.6093	−2.35961
$922$	−31.8589	−1.04922
$923$	−15.8645	−0.522186
$924$	−10.4537	−0.343900
$925$	0.814968	0.0267960
$926$	25.0415	0.822914
$927$	53.9852	1.77311
$928$	−7.47434	−0.245357
$929$	−35.4865	−1.16427	−0.582137	−	0.813091i	$-0.697783\pi$
$929$	−35.4865	−1.16427	−0.582137	+	0.813091i	$0.697783\pi$
$930$	−10.8886	−0.357052
$931$	−9.59943	−0.314609
$932$	6.22241	0.203822
$933$	101.741	3.33085
$934$	7.52638	0.246271
$935$	−8.05622	−0.263467
$936$	18.6935	0.611015
$937$	−5.43303	−0.177489	−0.0887446	−	0.996054i	$-0.528285\pi$
$937$	−5.43303	−0.177489	−0.0887446	+	0.996054i	$0.528285\pi$
$938$	−13.6356	−0.445217
$939$	−41.0033	−1.33809
$940$	−2.28907	−0.0746612
$941$	0.702205	0.0228912	0.0114456	−	0.999934i	$-0.496357\pi$
$941$	0.702205	0.0228912	0.0114456	+	0.999934i	$0.496357\pi$
$942$	−4.37878	−0.142668
$943$	8.89165	0.289552
$944$	−0.747496	−0.0243289
$945$	33.5281	1.09067
$946$	−1.00000	−0.0325128
$947$	−46.2283	−1.50222	−0.751110	−	0.660178i	$-0.770481\pi$
$947$	−46.2283	−1.50222	−0.751110	+	0.660178i	$0.770481\pi$
$948$	−21.3171	−0.692349
$949$	20.1980	0.655653
$950$	−1.97164	−0.0639685
$951$	−98.6053	−3.19750
$952$	−27.7545	−0.899530
$953$	−47.7755	−1.54760	−0.773800	−	0.633430i	$-0.781646\pi$
$953$	−47.7755	−1.54760	−0.773800	+	0.633430i	$0.781646\pi$
$954$	−26.0170	−0.842331
$955$	23.5905	0.763370
$956$	1.42446	0.0460704
$957$	−22.6798	−0.733134
$958$	−8.55601	−0.276432
$959$	−40.5695	−1.31006
$960$	−3.03435	−0.0979333
$961$	−18.1230	−0.584614
$962$	2.45430	0.0791297
$963$	−0.982780	−0.0316696
$964$	−13.8015	−0.444517
$965$	18.2524	0.587564
$966$	−10.5742	−0.340218
$967$	55.6766	1.79044	0.895220	−	0.445625i	$-0.147019\pi$
$967$	55.6766	1.79044	0.895220	+	0.445625i	$0.147019\pi$
$968$	1.00000	0.0321412
$969$	48.1976	1.54833
$970$	−13.1215	−0.421306
$971$	34.5148	1.10763	0.553816	−	0.832639i	$-0.313171\pi$
$971$	34.5148	1.10763	0.553816	+	0.832639i	$0.313171\pi$
$972$	−3.90458	−0.125240
$973$	49.3968	1.58359
$974$	−9.24248	−0.296148
$975$	−9.13803	−0.292651
$976$	−0.594147	−0.0190182
$977$	5.20212	0.166431	0.0832153	−	0.996532i	$-0.473481\pi$
$977$	5.20212	0.166431	0.0832153	+	0.996532i	$0.473481\pi$
$978$	10.3498	0.330950
$979$	−11.2814	−0.360556
$980$	4.86875	0.155527
$981$	110.815	3.53804
$982$	34.7025	1.10740
$983$	4.79649	0.152984	0.0764921	−	0.997070i	$-0.475628\pi$
$983$	4.79649	0.152984	0.0764921	+	0.997070i	$0.475628\pi$
$984$	26.6730	0.850304
$985$	−16.3169	−0.519899
$986$	−60.2150	−1.91763
$987$	−23.9292	−0.761674
$988$	−5.93765	−0.188902
$989$	−1.01153	−0.0321646
$990$	−6.20730	−0.197281
$991$	32.7118	1.03912	0.519562	−	0.854433i	$-0.326095\pi$
$991$	32.7118	1.03912	0.519562	+	0.854433i	$0.326095\pi$
$992$	3.58845	0.113933
$993$	13.0511	0.414165
$994$	18.1485	0.575637
$995$	1.88014	0.0596044
$996$	−36.8818	−1.16865
$997$	−22.3139	−0.706688	−0.353344	−	0.935493i	$-0.614956\pi$
$997$	−22.3139	−0.706688	−0.353344	+	0.935493i	$0.614956\pi$
$998$	13.6098	0.430811
$999$	−7.93134	−0.250937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.be.1.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.be.1.1	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.03435 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.03435 q^{6} -3.44511 q^{7} +1.00000 q^{8} +6.20730 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.03435 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.03435 q^{6} -3.44511 q^{7} +1.00000 q^{8} +6.20730 q^{9} +1.00000 q^{10} -1.00000 q^{11} -3.03435 q^{12} +3.01153 q^{13} -3.44511 q^{14} -3.03435 q^{15} +1.00000 q^{16} +8.05622 q^{17} +6.20730 q^{18} -1.97164 q^{19} +1.00000 q^{20} +10.4537 q^{21} -1.00000 q^{22} -1.01153 q^{23} -3.03435 q^{24} +1.00000 q^{25} +3.01153 q^{26} -9.73209 q^{27} -3.44511 q^{28} -7.47434 q^{29} -3.03435 q^{30} +3.58845 q^{31} +1.00000 q^{32} +3.03435 q^{33} +8.05622 q^{34} -3.44511 q^{35} +6.20730 q^{36} +0.814968 q^{37} -1.97164 q^{38} -9.13803 q^{39} +1.00000 q^{40} -8.79033 q^{41} +10.4537 q^{42} +1.00000 q^{43} -1.00000 q^{44} +6.20730 q^{45} -1.01153 q^{46} -2.28907 q^{47} -3.03435 q^{48} +4.86875 q^{49} +1.00000 q^{50} -24.4454 q^{51} +3.01153 q^{52} -4.19135 q^{53} -9.73209 q^{54} -1.00000 q^{55} -3.44511 q^{56} +5.98266 q^{57} -7.47434 q^{58} -0.747496 q^{59} -3.03435 q^{60} -0.594147 q^{61} +3.58845 q^{62} -21.3848 q^{63} +1.00000 q^{64} +3.01153 q^{65} +3.03435 q^{66} +3.95796 q^{67} +8.05622 q^{68} +3.06933 q^{69} -3.44511 q^{70} -5.26792 q^{71} +6.20730 q^{72} +6.70688 q^{73} +0.814968 q^{74} -3.03435 q^{75} -1.97164 q^{76} +3.44511 q^{77} -9.13803 q^{78} +7.02527 q^{79} +1.00000 q^{80} +10.9087 q^{81} -8.79033 q^{82} +12.1548 q^{83} +10.4537 q^{84} +8.05622 q^{85} +1.00000 q^{86} +22.6798 q^{87} -1.00000 q^{88} +11.2814 q^{89} +6.20730 q^{90} -10.3750 q^{91} -1.01153 q^{92} -10.8886 q^{93} -2.28907 q^{94} -1.97164 q^{95} -3.03435 q^{96} -13.1215 q^{97} +4.86875 q^{98} -6.20730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

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