LMFDB - Embedded newform 4030.2.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 48x^{6} + 66x^{5} - 202x^{4} - 75x^{3} + 210x^{2} + 68x - 16 $ x^9 - 3x^8 - 16x^7 + 48x^6 + 66x^5 - 202x^4 - 75x^3 + 210x^2 + 68x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.522486$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.522486 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.522486 q^{6} -4.13215 q^{7} +1.00000 q^{8} -2.72701 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.522486 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.522486 q^{6} -4.13215 q^{7} +1.00000 q^{8} -2.72701 q^{9} -1.00000 q^{10} -2.97727 q^{11} -0.522486 q^{12} +1.00000 q^{13} -4.13215 q^{14} +0.522486 q^{15} +1.00000 q^{16} -2.04611 q^{17} -2.72701 q^{18} +3.17257 q^{19} -1.00000 q^{20} +2.15899 q^{21} -2.97727 q^{22} +2.85380 q^{23} -0.522486 q^{24} +1.00000 q^{25} +1.00000 q^{26} +2.99228 q^{27} -4.13215 q^{28} -4.68130 q^{29} +0.522486 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.55558 q^{33} -2.04611 q^{34} +4.13215 q^{35} -2.72701 q^{36} -3.69333 q^{37} +3.17257 q^{38} -0.522486 q^{39} -1.00000 q^{40} -1.87034 q^{41} +2.15899 q^{42} +3.10089 q^{43} -2.97727 q^{44} +2.72701 q^{45} +2.85380 q^{46} +0.104842 q^{47} -0.522486 q^{48} +10.0747 q^{49} +1.00000 q^{50} +1.06907 q^{51} +1.00000 q^{52} +11.5528 q^{53} +2.99228 q^{54} +2.97727 q^{55} -4.13215 q^{56} -1.65762 q^{57} -4.68130 q^{58} +2.27633 q^{59} +0.522486 q^{60} +6.29020 q^{61} +1.00000 q^{62} +11.2684 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.55558 q^{66} -3.65780 q^{67} -2.04611 q^{68} -1.49107 q^{69} +4.13215 q^{70} +0.272695 q^{71} -2.72701 q^{72} -4.97851 q^{73} -3.69333 q^{74} -0.522486 q^{75} +3.17257 q^{76} +12.3025 q^{77} -0.522486 q^{78} -6.74165 q^{79} -1.00000 q^{80} +6.61760 q^{81} -1.87034 q^{82} -3.77412 q^{83} +2.15899 q^{84} +2.04611 q^{85} +3.10089 q^{86} +2.44592 q^{87} -2.97727 q^{88} +16.9121 q^{89} +2.72701 q^{90} -4.13215 q^{91} +2.85380 q^{92} -0.522486 q^{93} +0.104842 q^{94} -3.17257 q^{95} -0.522486 q^{96} -5.39312 q^{97} +10.0747 q^{98} +8.11903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.522486	−0.301658	−0.150829	−	0.988560i	$-0.548194\pi$
$3$	−0.522486	−0.301658	−0.150829	+	0.988560i	$0.548194\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.522486	−0.213304
$7$	−4.13215	−1.56181	−0.780903	−	0.624652i	$-0.785241\pi$
$7$	−4.13215	−1.56181	−0.780903	+	0.624652i	$0.785241\pi$
$8$	1.00000	0.353553
$9$	−2.72701	−0.909003
$10$	−1.00000	−0.316228
$11$	−2.97727	−0.897680	−0.448840	−	0.893612i	$-0.648163\pi$
$11$	−2.97727	−0.897680	−0.448840	+	0.893612i	$0.648163\pi$
$12$	−0.522486	−0.150829
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.13215	−1.10436
$15$	0.522486	0.134905
$16$	1.00000	0.250000
$17$	−2.04611	−0.496256	−0.248128	−	0.968727i	$-0.579815\pi$
$17$	−2.04611	−0.496256	−0.248128	+	0.968727i	$0.579815\pi$
$18$	−2.72701	−0.642762
$19$	3.17257	0.727837	0.363919	−	0.931431i	$-0.381439\pi$
$19$	3.17257	0.727837	0.363919	+	0.931431i	$0.381439\pi$
$20$	−1.00000	−0.223607
$21$	2.15899	0.471131
$22$	−2.97727	−0.634756
$23$	2.85380	0.595058	0.297529	−	0.954713i	$-0.403837\pi$
$23$	2.85380	0.595058	0.297529	+	0.954713i	$0.403837\pi$
$24$	−0.522486	−0.106652
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	2.99228	0.575865
$28$	−4.13215	−0.780903
$29$	−4.68130	−0.869296	−0.434648	−	0.900600i	$-0.643127\pi$
$29$	−4.68130	−0.869296	−0.434648	+	0.900600i	$0.643127\pi$
$30$	0.522486	0.0953925
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	1.55558	0.270792
$34$	−2.04611	−0.350906
$35$	4.13215	0.698461
$36$	−2.72701	−0.454501
$37$	−3.69333	−0.607180	−0.303590	−	0.952803i	$-0.598185\pi$
$37$	−3.69333	−0.607180	−0.303590	+	0.952803i	$0.598185\pi$
$38$	3.17257	0.514659
$39$	−0.522486	−0.0836648
$40$	−1.00000	−0.158114
$41$	−1.87034	−0.292098	−0.146049	−	0.989277i	$-0.546656\pi$
$41$	−1.87034	−0.292098	−0.146049	+	0.989277i	$0.546656\pi$
$42$	2.15899	0.333140
$43$	3.10089	0.472882	0.236441	−	0.971646i	$-0.424019\pi$
$43$	3.10089	0.472882	0.236441	+	0.971646i	$0.424019\pi$
$44$	−2.97727	−0.448840
$45$	2.72701	0.406518
$46$	2.85380	0.420770
$47$	0.104842	0.0152928	0.00764642	−	0.999971i	$-0.497566\pi$
$47$	0.104842	0.0152928	0.00764642	+	0.999971i	$0.497566\pi$
$48$	−0.522486	−0.0754144
$49$	10.0747	1.43924
$50$	1.00000	0.141421
$51$	1.06907	0.149699
$52$	1.00000	0.138675
$53$	11.5528	1.58690	0.793449	−	0.608637i	$-0.208283\pi$
$53$	11.5528	1.58690	0.793449	+	0.608637i	$0.208283\pi$
$54$	2.99228	0.407198
$55$	2.97727	0.401455
$56$	−4.13215	−0.552182
$57$	−1.65762	−0.219558
$58$	−4.68130	−0.614685
$59$	2.27633	0.296354	0.148177	−	0.988961i	$-0.452660\pi$
$59$	2.27633	0.296354	0.148177	+	0.988961i	$0.452660\pi$
$60$	0.522486	0.0674527
$61$	6.29020	0.805378	0.402689	−	0.915337i	$-0.368076\pi$
$61$	6.29020	0.805378	0.402689	+	0.915337i	$0.368076\pi$
$62$	1.00000	0.127000
$63$	11.2684	1.41969
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	1.55558	0.191479
$67$	−3.65780	−0.446872	−0.223436	−	0.974719i	$-0.571727\pi$
$67$	−3.65780	−0.446872	−0.223436	+	0.974719i	$0.571727\pi$
$68$	−2.04611	−0.248128
$69$	−1.49107	−0.179504
$70$	4.13215	0.493887
$71$	0.272695	0.0323629	0.0161815	−	0.999869i	$-0.494849\pi$
$71$	0.272695	0.0323629	0.0161815	+	0.999869i	$0.494849\pi$
$72$	−2.72701	−0.321381
$73$	−4.97851	−0.582690	−0.291345	−	0.956618i	$-0.594103\pi$
$73$	−4.97851	−0.582690	−0.291345	+	0.956618i	$0.594103\pi$
$74$	−3.69333	−0.429341
$75$	−0.522486	−0.0603315
$76$	3.17257	0.363919
$77$	12.3025	1.40200
$78$	−0.522486	−0.0591599
$79$	−6.74165	−0.758495	−0.379247	−	0.925295i	$-0.623817\pi$
$79$	−6.74165	−0.758495	−0.379247	+	0.925295i	$0.623817\pi$
$80$	−1.00000	−0.111803
$81$	6.61760	0.735289
$82$	−1.87034	−0.206545
$83$	−3.77412	−0.414263	−0.207132	−	0.978313i	$-0.566413\pi$
$83$	−3.77412	−0.414263	−0.207132	+	0.978313i	$0.566413\pi$
$84$	2.15899	0.235565
$85$	2.04611	0.221932
$86$	3.10089	0.334378
$87$	2.44592	0.262230
$88$	−2.97727	−0.317378
$89$	16.9121	1.79267	0.896337	−	0.443373i	$-0.146218\pi$
$89$	16.9121	1.79267	0.896337	+	0.443373i	$0.146218\pi$
$90$	2.72701	0.287452
$91$	−4.13215	−0.433167
$92$	2.85380	0.297529
$93$	−0.522486	−0.0541793
$94$	0.104842	0.0108137
$95$	−3.17257	−0.325499
$96$	−0.522486	−0.0533260
$97$	−5.39312	−0.547588	−0.273794	−	0.961788i	$-0.588279\pi$
$97$	−5.39312	−0.547588	−0.273794	+	0.961788i	$0.588279\pi$
$98$	10.0747	1.01770
$99$	8.11903	0.815994
$100$	1.00000	0.100000
$101$	10.3609	1.03095	0.515473	−	0.856906i	$-0.327616\pi$
$101$	10.3609	1.03095	0.515473	+	0.856906i	$0.327616\pi$
$102$	1.06907	0.105853
$103$	8.65141	0.852448	0.426224	−	0.904618i	$-0.359843\pi$
$103$	8.65141	0.852448	0.426224	+	0.904618i	$0.359843\pi$
$104$	1.00000	0.0980581
$105$	−2.15899	−0.210696
$106$	11.5528	1.12211
$107$	4.62951	0.447552	0.223776	−	0.974641i	$-0.428162\pi$
$107$	4.62951	0.447552	0.223776	+	0.974641i	$0.428162\pi$
$108$	2.99228	0.287933
$109$	6.92245	0.663050	0.331525	−	0.943446i	$-0.392437\pi$
$109$	6.92245	0.663050	0.331525	+	0.943446i	$0.392437\pi$
$110$	2.97727	0.283871
$111$	1.92971	0.183160
$112$	−4.13215	−0.390452
$113$	17.7257	1.66749	0.833747	−	0.552146i	$-0.186191\pi$
$113$	17.7257	1.66749	0.833747	+	0.552146i	$0.186191\pi$
$114$	−1.65762	−0.155251
$115$	−2.85380	−0.266118
$116$	−4.68130	−0.434648
$117$	−2.72701	−0.252112
$118$	2.27633	0.209554
$119$	8.45486	0.775056
$120$	0.522486	0.0476963
$121$	−2.13587	−0.194170
$122$	6.29020	0.569488
$123$	0.977227	0.0881136
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	11.2684	1.00387
$127$	6.32457	0.561215	0.280607	−	0.959823i	$-0.409464\pi$
$127$	6.32457	0.561215	0.280607	+	0.959823i	$0.409464\pi$
$128$	1.00000	0.0883883
$129$	−1.62017	−0.142648
$130$	−1.00000	−0.0877058
$131$	8.06738	0.704851	0.352425	−	0.935840i	$-0.385357\pi$
$131$	8.06738	0.704851	0.352425	+	0.935840i	$0.385357\pi$
$132$	1.55558	0.135396
$133$	−13.1095	−1.13674
$134$	−3.65780	−0.315986
$135$	−2.99228	−0.257535
$136$	−2.04611	−0.175453
$137$	2.48768	0.212537	0.106269	−	0.994337i	$-0.466110\pi$
$137$	2.48768	0.212537	0.106269	+	0.994337i	$0.466110\pi$
$138$	−1.49107	−0.126928
$139$	9.97772	0.846299	0.423149	−	0.906060i	$-0.360925\pi$
$139$	9.97772	0.846299	0.423149	+	0.906060i	$0.360925\pi$
$140$	4.13215	0.349231
$141$	−0.0547787	−0.00461320
$142$	0.272695	0.0228840
$143$	−2.97727	−0.248972
$144$	−2.72701	−0.227251
$145$	4.68130	0.388761
$146$	−4.97851	−0.412024
$147$	−5.26389	−0.434158
$148$	−3.69333	−0.303590
$149$	−14.6505	−1.20021	−0.600107	−	0.799919i	$-0.704876\pi$
$149$	−14.6505	−1.20021	−0.600107	+	0.799919i	$0.704876\pi$
$150$	−0.522486	−0.0426608
$151$	20.4558	1.66467	0.832334	−	0.554275i	$-0.187004\pi$
$151$	20.4558	1.66467	0.832334	+	0.554275i	$0.187004\pi$
$152$	3.17257	0.257329
$153$	5.57977	0.451098
$154$	12.3025	0.991366
$155$	−1.00000	−0.0803219
$156$	−0.522486	−0.0418324
$157$	−9.18738	−0.733233	−0.366616	−	0.930372i	$-0.619484\pi$
$157$	−9.18738	−0.733233	−0.366616	+	0.930372i	$0.619484\pi$
$158$	−6.74165	−0.536337
$159$	−6.03617	−0.478700
$160$	−1.00000	−0.0790569
$161$	−11.7923	−0.929366
$162$	6.61760	0.519928
$163$	−6.86511	−0.537717	−0.268859	−	0.963180i	$-0.586646\pi$
$163$	−6.86511	−0.537717	−0.268859	+	0.963180i	$0.586646\pi$
$164$	−1.87034	−0.146049
$165$	−1.55558	−0.121102
$166$	−3.77412	−0.292928
$167$	6.25871	0.484313	0.242157	−	0.970237i	$-0.422145\pi$
$167$	6.25871	0.484313	0.242157	+	0.970237i	$0.422145\pi$
$168$	2.15899	0.166570
$169$	1.00000	0.0769231
$170$	2.04611	0.156930
$171$	−8.65162	−0.661606
$172$	3.10089	0.236441
$173$	−11.9608	−0.909362	−0.454681	−	0.890654i	$-0.650247\pi$
$173$	−11.9608	−0.909362	−0.454681	+	0.890654i	$0.650247\pi$
$174$	2.44592	0.185424
$175$	−4.13215	−0.312361
$176$	−2.97727	−0.224420
$177$	−1.18935	−0.0893973
$178$	16.9121	1.26761
$179$	7.98138	0.596556	0.298278	−	0.954479i	$-0.403588\pi$
$179$	7.98138	0.596556	0.298278	+	0.954479i	$0.403588\pi$
$180$	2.72701	0.203259
$181$	−2.74918	−0.204345	−0.102173	−	0.994767i	$-0.532579\pi$
$181$	−2.74918	−0.204345	−0.102173	+	0.994767i	$0.532579\pi$
$182$	−4.13215	−0.306296
$183$	−3.28654	−0.242948
$184$	2.85380	0.210385
$185$	3.69333	0.271539
$186$	−0.522486	−0.0383106
$187$	6.09183	0.445479
$188$	0.104842	0.00764642
$189$	−12.3646	−0.899390
$190$	−3.17257	−0.230162
$191$	4.23668	0.306556	0.153278	−	0.988183i	$-0.451017\pi$
$191$	4.23668	0.306556	0.153278	+	0.988183i	$0.451017\pi$
$192$	−0.522486	−0.0377072
$193$	−2.10390	−0.151442	−0.0757210	−	0.997129i	$-0.524126\pi$
$193$	−2.10390	−0.151442	−0.0757210	+	0.997129i	$0.524126\pi$
$194$	−5.39312	−0.387203
$195$	0.522486	0.0374160
$196$	10.0747	0.719620
$197$	−27.4366	−1.95478	−0.977389	−	0.211450i	$-0.932182\pi$
$197$	−27.4366	−1.95478	−0.977389	+	0.211450i	$0.932182\pi$
$198$	8.11903	0.576995
$199$	−0.304610	−0.0215933	−0.0107966	−	0.999942i	$-0.503437\pi$
$199$	−0.304610	−0.0215933	−0.0107966	+	0.999942i	$0.503437\pi$
$200$	1.00000	0.0707107
$201$	1.91115	0.134802
$202$	10.3609	0.728989
$203$	19.3439	1.35767
$204$	1.06907	0.0748497
$205$	1.87034	0.130630
$206$	8.65141	0.602772
$207$	−7.78233	−0.540910
$208$	1.00000	0.0693375
$209$	−9.44559	−0.653365
$210$	−2.15899	−0.148985
$211$	−10.6560	−0.733591	−0.366796	−	0.930302i	$-0.619545\pi$
$211$	−10.6560	−0.733591	−0.366796	+	0.930302i	$0.619545\pi$
$212$	11.5528	0.793449
$213$	−0.142479	−0.00976252
$214$	4.62951	0.316467
$215$	−3.10089	−0.211479
$216$	2.99228	0.203599
$217$	−4.13215	−0.280509
$218$	6.92245	0.468847
$219$	2.60120	0.175773
$220$	2.97727	0.200727
$221$	−2.04611	−0.137637
$222$	1.92971	0.129514
$223$	−14.0918	−0.943656	−0.471828	−	0.881691i	$-0.656406\pi$
$223$	−14.0918	−0.943656	−0.471828	+	0.881691i	$0.656406\pi$
$224$	−4.13215	−0.276091
$225$	−2.72701	−0.181801
$226$	17.7257	1.17910
$227$	21.7237	1.44185	0.720926	−	0.693012i	$-0.243717\pi$
$227$	21.7237	1.44185	0.720926	+	0.693012i	$0.243717\pi$
$228$	−1.65762	−0.109779
$229$	5.52308	0.364975	0.182488	−	0.983208i	$-0.441585\pi$
$229$	5.52308	0.364975	0.182488	+	0.983208i	$0.441585\pi$
$230$	−2.85380	−0.188174
$231$	−6.42790	−0.422925
$232$	−4.68130	−0.307343
$233$	−22.9051	−1.50056	−0.750281	−	0.661120i	$-0.770082\pi$
$233$	−22.9051	−1.50056	−0.750281	+	0.661120i	$0.770082\pi$
$234$	−2.72701	−0.178270
$235$	−0.104842	−0.00683917
$236$	2.27633	0.148177
$237$	3.52242	0.228806
$238$	8.45486	0.548047
$239$	12.0879	0.781900	0.390950	−	0.920412i	$-0.372147\pi$
$239$	12.0879	0.781900	0.390950	+	0.920412i	$0.372147\pi$
$240$	0.522486	0.0337263
$241$	−9.70431	−0.625109	−0.312555	−	0.949900i	$-0.601185\pi$
$241$	−9.70431	−0.625109	−0.312555	+	0.949900i	$0.601185\pi$
$242$	−2.13587	−0.137299
$243$	−12.4345	−0.797671
$244$	6.29020	0.402689
$245$	−10.0747	−0.643648
$246$	0.977227	0.0623057
$247$	3.17257	0.201866
$248$	1.00000	0.0635001
$249$	1.97193	0.124966
$250$	−1.00000	−0.0632456
$251$	−15.2584	−0.963100	−0.481550	−	0.876419i	$-0.659926\pi$
$251$	−15.2584	−0.963100	−0.481550	+	0.876419i	$0.659926\pi$
$252$	11.2684	0.709843
$253$	−8.49652	−0.534172
$254$	6.32457	0.396839
$255$	−1.06907	−0.0669476
$256$	1.00000	0.0625000
$257$	7.81256	0.487334	0.243667	−	0.969859i	$-0.421650\pi$
$257$	7.81256	0.487334	0.243667	+	0.969859i	$0.421650\pi$
$258$	−1.62017	−0.100868
$259$	15.2614	0.948297
$260$	−1.00000	−0.0620174
$261$	12.7660	0.790193
$262$	8.06738	0.498405
$263$	11.0433	0.680962	0.340481	−	0.940251i	$-0.389410\pi$
$263$	11.0433	0.680962	0.340481	+	0.940251i	$0.389410\pi$
$264$	1.55558	0.0957394
$265$	−11.5528	−0.709682
$266$	−13.1095	−0.803797
$267$	−8.83632	−0.540774
$268$	−3.65780	−0.223436
$269$	−13.2643	−0.808740	−0.404370	−	0.914595i	$-0.632509\pi$
$269$	−13.2643	−0.808740	−0.404370	+	0.914595i	$0.632509\pi$
$270$	−2.99228	−0.182105
$271$	19.6314	1.19252	0.596261	−	0.802791i	$-0.296652\pi$
$271$	19.6314	1.19252	0.596261	+	0.802791i	$0.296652\pi$
$272$	−2.04611	−0.124064
$273$	2.15899	0.130668
$274$	2.48768	0.150286
$275$	−2.97727	−0.179536
$276$	−1.49107	−0.0897519
$277$	−32.3891	−1.94607	−0.973037	−	0.230651i	$-0.925915\pi$
$277$	−32.3891	−1.94607	−0.973037	+	0.230651i	$0.925915\pi$
$278$	9.97772	0.598424
$279$	−2.72701	−0.163262
$280$	4.13215	0.246943
$281$	5.53679	0.330297	0.165149	−	0.986269i	$-0.447190\pi$
$281$	5.53679	0.330297	0.165149	+	0.986269i	$0.447190\pi$
$282$	−0.0547787	−0.00326203
$283$	3.08926	0.183637	0.0918187	−	0.995776i	$-0.470732\pi$
$283$	3.08926	0.183637	0.0918187	+	0.995776i	$0.470732\pi$
$284$	0.272695	0.0161815
$285$	1.65762	0.0981892
$286$	−2.97727	−0.176050
$287$	7.72853	0.456201
$288$	−2.72701	−0.160690
$289$	−12.8134	−0.753730
$290$	4.68130	0.274896
$291$	2.81783	0.165184
$292$	−4.97851	−0.291345
$293$	24.9488	1.45753	0.728763	−	0.684766i	$-0.240096\pi$
$293$	24.9488	1.45753	0.728763	+	0.684766i	$0.240096\pi$
$294$	−5.26389	−0.306996
$295$	−2.27633	−0.132533
$296$	−3.69333	−0.214670
$297$	−8.90883	−0.516943
$298$	−14.6505	−0.848680
$299$	2.85380	0.165039
$300$	−0.522486	−0.0301658
$301$	−12.8134	−0.738550
$302$	20.4558	1.17710
$303$	−5.41342	−0.310993
$304$	3.17257	0.181959
$305$	−6.29020	−0.360176
$306$	5.57977	0.318974
$307$	−4.32593	−0.246894	−0.123447	−	0.992351i	$-0.539395\pi$
$307$	−4.32593	−0.246894	−0.123447	+	0.992351i	$0.539395\pi$
$308$	12.3025	0.701002
$309$	−4.52024	−0.257148
$310$	−1.00000	−0.0567962
$311$	15.6313	0.886367	0.443184	−	0.896431i	$-0.353849\pi$
$311$	15.6313	0.886367	0.443184	+	0.896431i	$0.353849\pi$
$312$	−0.522486	−0.0295800
$313$	−4.27565	−0.241674	−0.120837	−	0.992672i	$-0.538558\pi$
$313$	−4.27565	−0.241674	−0.120837	+	0.992672i	$0.538558\pi$
$314$	−9.18738	−0.518474
$315$	−11.2684	−0.634903
$316$	−6.74165	−0.379247
$317$	7.67198	0.430901	0.215451	−	0.976515i	$-0.430878\pi$
$317$	7.67198	0.430901	0.215451	+	0.976515i	$0.430878\pi$
$318$	−6.03617	−0.338492
$319$	13.9375	0.780350
$320$	−1.00000	−0.0559017
$321$	−2.41886	−0.135007
$322$	−11.7923	−0.657161
$323$	−6.49144	−0.361193
$324$	6.61760	0.367644
$325$	1.00000	0.0554700
$326$	−6.86511	−0.380224
$327$	−3.61688	−0.200014
$328$	−1.87034	−0.103272
$329$	−0.433225	−0.0238845
$330$	−1.55558	−0.0856320
$331$	−14.9397	−0.821160	−0.410580	−	0.911824i	$-0.634674\pi$
$331$	−14.9397	−0.821160	−0.410580	+	0.911824i	$0.634674\pi$
$332$	−3.77412	−0.207132
$333$	10.0717	0.551928
$334$	6.25871	0.342461
$335$	3.65780	0.199847
$336$	2.15899	0.117783
$337$	22.1452	1.20633	0.603163	−	0.797618i	$-0.293907\pi$
$337$	22.1452	1.20633	0.603163	+	0.797618i	$0.293907\pi$
$338$	1.00000	0.0543928
$339$	−9.26144	−0.503012
$340$	2.04611	0.110966
$341$	−2.97727	−0.161228
$342$	−8.65162	−0.467826
$343$	−12.7051	−0.686010
$344$	3.10089	0.167189
$345$	1.49107	0.0802766
$346$	−11.9608	−0.643016
$347$	−8.54606	−0.458777	−0.229388	−	0.973335i	$-0.573673\pi$
$347$	−8.54606	−0.458777	−0.229388	+	0.973335i	$0.573673\pi$
$348$	2.44592	0.131115
$349$	24.2343	1.29723	0.648617	−	0.761115i	$-0.275348\pi$
$349$	24.2343	1.29723	0.648617	+	0.761115i	$0.275348\pi$
$350$	−4.13215	−0.220873
$351$	2.99228	0.159716
$352$	−2.97727	−0.158689
$353$	−26.4097	−1.40565	−0.702823	−	0.711365i	$-0.748077\pi$
$353$	−26.4097	−1.40565	−0.702823	+	0.711365i	$0.748077\pi$
$354$	−1.18935	−0.0632134
$355$	−0.272695	−0.0144731
$356$	16.9121	0.896337
$357$	−4.41755	−0.233801
$358$	7.98138	0.421829
$359$	30.4588	1.60755	0.803777	−	0.594930i	$-0.202820\pi$
$359$	30.4588	1.60755	0.803777	+	0.594930i	$0.202820\pi$
$360$	2.72701	0.143726
$361$	−8.93481	−0.470253
$362$	−2.74918	−0.144494
$363$	1.11597	0.0585730
$364$	−4.13215	−0.216584
$365$	4.97851	0.260587
$366$	−3.28654	−0.171790
$367$	−0.616087	−0.0321595	−0.0160797	−	0.999871i	$-0.505119\pi$
$367$	−0.616087	−0.0321595	−0.0160797	+	0.999871i	$0.505119\pi$
$368$	2.85380	0.148765
$369$	5.10043	0.265518
$370$	3.69333	0.192007
$371$	−47.7379	−2.47843
$372$	−0.522486	−0.0270897
$373$	21.8835	1.13309	0.566543	−	0.824032i	$-0.308281\pi$
$373$	21.8835	1.13309	0.566543	+	0.824032i	$0.308281\pi$
$374$	6.09183	0.315001
$375$	0.522486	0.0269811
$376$	0.104842	0.00540683
$377$	−4.68130	−0.241099
$378$	−12.3646	−0.635965
$379$	36.3420	1.86676	0.933381	−	0.358886i	$-0.116843\pi$
$379$	36.3420	1.86676	0.933381	+	0.358886i	$0.116843\pi$
$380$	−3.17257	−0.162749
$381$	−3.30450	−0.169295
$382$	4.23668	0.216768
$383$	−14.1355	−0.722288	−0.361144	−	0.932510i	$-0.617614\pi$
$383$	−14.1355	−0.722288	−0.361144	+	0.932510i	$0.617614\pi$
$384$	−0.522486	−0.0266630
$385$	−12.3025	−0.626995
$386$	−2.10390	−0.107086
$387$	−8.45616	−0.429851
$388$	−5.39312	−0.273794
$389$	21.8694	1.10882	0.554412	−	0.832242i	$-0.312943\pi$
$389$	21.8694	1.10882	0.554412	+	0.832242i	$0.312943\pi$
$390$	0.522486	0.0264571
$391$	−5.83920	−0.295301
$392$	10.0747	0.508849
$393$	−4.21510	−0.212624
$394$	−27.4366	−1.38224
$395$	6.74165	0.339209
$396$	8.11903	0.407997
$397$	−16.4329	−0.824744	−0.412372	−	0.911016i	$-0.635300\pi$
$397$	−16.4329	−0.824744	−0.412372	+	0.911016i	$0.635300\pi$
$398$	−0.304610	−0.0152687
$399$	6.84955	0.342907
$400$	1.00000	0.0500000
$401$	−6.63293	−0.331233	−0.165616	−	0.986190i	$-0.552961\pi$
$401$	−6.63293	−0.331233	−0.165616	+	0.986190i	$0.552961\pi$
$402$	1.91115	0.0953196
$403$	1.00000	0.0498135
$404$	10.3609	0.515473
$405$	−6.61760	−0.328831
$406$	19.3439	0.960020
$407$	10.9960	0.545053
$408$	1.06907	0.0529267
$409$	5.51901	0.272898	0.136449	−	0.990647i	$-0.456431\pi$
$409$	5.51901	0.272898	0.136449	+	0.990647i	$0.456431\pi$
$410$	1.87034	0.0923695
$411$	−1.29978	−0.0641134
$412$	8.65141	0.426224
$413$	−9.40616	−0.462847
$414$	−7.78233	−0.382481
$415$	3.77412	0.185264
$416$	1.00000	0.0490290
$417$	−5.21322	−0.255292
$418$	−9.44559	−0.461999
$419$	28.6925	1.40172	0.700861	−	0.713298i	$-0.252799\pi$
$419$	28.6925	1.40172	0.700861	+	0.713298i	$0.252799\pi$
$420$	−2.15899	−0.105348
$421$	3.12918	0.152507	0.0762534	−	0.997088i	$-0.475704\pi$
$421$	3.12918	0.152507	0.0762534	+	0.997088i	$0.475704\pi$
$422$	−10.6560	−0.518727
$423$	−0.285906	−0.0139012
$424$	11.5528	0.561053
$425$	−2.04611	−0.0992512
$426$	−0.142479	−0.00690314
$427$	−25.9921	−1.25784
$428$	4.62951	0.223776
$429$	1.55558	0.0751042
$430$	−3.10089	−0.149538
$431$	−38.1310	−1.83671	−0.918353	−	0.395762i	$-0.870481\pi$
$431$	−38.1310	−1.83671	−0.918353	+	0.395762i	$0.870481\pi$
$432$	2.99228	0.143966
$433$	−9.30745	−0.447287	−0.223644	−	0.974671i	$-0.571795\pi$
$433$	−9.30745	−0.447287	−0.223644	+	0.974671i	$0.571795\pi$
$434$	−4.13215	−0.198350
$435$	−2.44592	−0.117273
$436$	6.92245	0.331525
$437$	9.05387	0.433105
$438$	2.60120	0.124290
$439$	34.5078	1.64697	0.823485	−	0.567338i	$-0.192027\pi$
$439$	34.5078	1.64697	0.823485	+	0.567338i	$0.192027\pi$
$440$	2.97727	0.141936
$441$	−27.4738	−1.30827
$442$	−2.04611	−0.0973238
$443$	−6.66311	−0.316574	−0.158287	−	0.987393i	$-0.550597\pi$
$443$	−6.66311	−0.316574	−0.158287	+	0.987393i	$0.550597\pi$
$444$	1.92971	0.0915802
$445$	−16.9121	−0.801708
$446$	−14.0918	−0.667265
$447$	7.65468	0.362054
$448$	−4.13215	−0.195226
$449$	−0.373542	−0.0176285	−0.00881427	−	0.999961i	$-0.502806\pi$
$449$	−0.373542	−0.0176285	−0.00881427	+	0.999961i	$0.502806\pi$
$450$	−2.72701	−0.128552
$451$	5.56851	0.262211
$452$	17.7257	0.833747
$453$	−10.6879	−0.502160
$454$	21.7237	1.01954
$455$	4.13215	0.193718
$456$	−1.65762	−0.0776253
$457$	12.2633	0.573655	0.286827	−	0.957982i	$-0.407399\pi$
$457$	12.2633	0.573655	0.286827	+	0.957982i	$0.407399\pi$
$458$	5.52308	0.258076
$459$	−6.12256	−0.285776
$460$	−2.85380	−0.133059
$461$	23.6144	1.09983	0.549916	−	0.835220i	$-0.314660\pi$
$461$	23.6144	1.09983	0.549916	+	0.835220i	$0.314660\pi$
$462$	−6.42790	−0.299053
$463$	−3.45526	−0.160580	−0.0802898	−	0.996772i	$-0.525585\pi$
$463$	−3.45526	−0.160580	−0.0802898	+	0.996772i	$0.525585\pi$
$464$	−4.68130	−0.217324
$465$	0.522486	0.0242297
$466$	−22.9051	−1.06106
$467$	−12.7975	−0.592196	−0.296098	−	0.955158i	$-0.595686\pi$
$467$	−12.7975	−0.592196	−0.296098	+	0.955158i	$0.595686\pi$
$468$	−2.72701	−0.126056
$469$	15.1146	0.697928
$470$	−0.104842	−0.00483602
$471$	4.80028	0.221185
$472$	2.27633	0.104777
$473$	−9.23219	−0.424497
$474$	3.52242	0.161790
$475$	3.17257	0.145567
$476$	8.45486	0.387528
$477$	−31.5045	−1.44249
$478$	12.0879	0.552887
$479$	−19.0395	−0.869935	−0.434967	−	0.900446i	$-0.643240\pi$
$479$	−19.0395	−0.869935	−0.434967	+	0.900446i	$0.643240\pi$
$480$	0.522486	0.0238481
$481$	−3.69333	−0.168401
$482$	−9.70431	−0.442019
$483$	6.16133	0.280350
$484$	−2.13587	−0.0970852
$485$	5.39312	0.244889
$486$	−12.4345	−0.564038
$487$	−22.5046	−1.01978	−0.509891	−	0.860239i	$-0.670314\pi$
$487$	−22.5046	−1.01978	−0.509891	+	0.860239i	$0.670314\pi$
$488$	6.29020	0.284744
$489$	3.58693	0.162206
$490$	−10.0747	−0.455128
$491$	14.2934	0.645050	0.322525	−	0.946561i	$-0.395468\pi$
$491$	14.2934	0.645050	0.322525	+	0.946561i	$0.395468\pi$
$492$	0.977227	0.0440568
$493$	9.57849	0.431393
$494$	3.17257	0.142741
$495$	−8.11903	−0.364923
$496$	1.00000	0.0449013
$497$	−1.12682	−0.0505446
$498$	1.97193	0.0883641
$499$	37.5606	1.68144	0.840722	−	0.541467i	$-0.182131\pi$
$499$	37.5606	1.68144	0.840722	+	0.541467i	$0.182131\pi$
$500$	−1.00000	−0.0447214
$501$	−3.27009	−0.146097
$502$	−15.2584	−0.681015
$503$	6.08883	0.271488	0.135744	−	0.990744i	$-0.456658\pi$
$503$	6.08883	0.271488	0.135744	+	0.990744i	$0.456658\pi$
$504$	11.2684	0.501935
$505$	−10.3609	−0.461053
$506$	−8.49652	−0.377717
$507$	−0.522486	−0.0232044
$508$	6.32457	0.280607
$509$	−32.3335	−1.43316	−0.716579	−	0.697506i	$-0.754293\pi$
$509$	−32.3335	−1.43316	−0.716579	+	0.697506i	$0.754293\pi$
$510$	−1.06907	−0.0473391
$511$	20.5720	0.910050
$512$	1.00000	0.0441942
$513$	9.49322	0.419136
$514$	7.81256	0.344597
$515$	−8.65141	−0.381226
$516$	−1.62017	−0.0713242
$517$	−0.312144	−0.0137281
$518$	15.2614	0.670547
$519$	6.24935	0.274316
$520$	−1.00000	−0.0438529
$521$	23.1282	1.01326	0.506632	−	0.862162i	$-0.330890\pi$
$521$	23.1282	1.01326	0.506632	+	0.862162i	$0.330890\pi$
$522$	12.7660	0.558751
$523$	15.4330	0.674836	0.337418	−	0.941355i	$-0.390446\pi$
$523$	15.4330	0.674836	0.337418	+	0.941355i	$0.390446\pi$
$524$	8.06738	0.352425
$525$	2.15899	0.0942262
$526$	11.0433	0.481513
$527$	−2.04611	−0.0891302
$528$	1.55558	0.0676980
$529$	−14.8558	−0.645906
$530$	−11.5528	−0.501821
$531$	−6.20758	−0.269386
$532$	−13.1095	−0.568371
$533$	−1.87034	−0.0810134
$534$	−8.83632	−0.382385
$535$	−4.62951	−0.200151
$536$	−3.65780	−0.157993
$537$	−4.17016	−0.179956
$538$	−13.2643	−0.571866
$539$	−29.9950	−1.29198
$540$	−2.99228	−0.128767
$541$	24.0368	1.03342	0.516711	−	0.856160i	$-0.327156\pi$
$541$	24.0368	1.03342	0.516711	+	0.856160i	$0.327156\pi$
$542$	19.6314	0.843240
$543$	1.43641	0.0616423
$544$	−2.04611	−0.0877265
$545$	−6.92245	−0.296525
$546$	2.15899	0.0923964
$547$	21.9287	0.937603	0.468801	−	0.883304i	$-0.344686\pi$
$547$	21.9287	0.937603	0.468801	+	0.883304i	$0.344686\pi$
$548$	2.48768	0.106269
$549$	−17.1534	−0.732091
$550$	−2.97727	−0.126951
$551$	−14.8518	−0.632706
$552$	−1.49107	−0.0634642
$553$	27.8575	1.18462
$554$	−32.3891	−1.37608
$555$	−1.92971	−0.0819118
$556$	9.97772	0.423149
$557$	−9.09176	−0.385230	−0.192615	−	0.981274i	$-0.561697\pi$
$557$	−9.09176	−0.385230	−0.192615	+	0.981274i	$0.561697\pi$
$558$	−2.72701	−0.115443
$559$	3.10089	0.131154
$560$	4.13215	0.174615
$561$	−3.18290	−0.134382
$562$	5.53679	0.233555
$563$	−31.0819	−1.30995	−0.654973	−	0.755652i	$-0.727320\pi$
$563$	−31.0819	−1.30995	−0.654973	+	0.755652i	$0.727320\pi$
$564$	−0.0547787	−0.00230660
$565$	−17.7257	−0.745726
$566$	3.08926	0.129851
$567$	−27.3449	−1.14838
$568$	0.272695	0.0114420
$569$	37.0257	1.55220	0.776099	−	0.630611i	$-0.217195\pi$
$569$	37.0257	1.55220	0.776099	+	0.630611i	$0.217195\pi$
$570$	1.65762	0.0694302
$571$	6.02221	0.252022	0.126011	−	0.992029i	$-0.459783\pi$
$571$	6.02221	0.252022	0.126011	+	0.992029i	$0.459783\pi$
$572$	−2.97727	−0.124486
$573$	−2.21361	−0.0924749
$574$	7.72853	0.322583
$575$	2.85380	0.119012
$576$	−2.72701	−0.113625
$577$	0.147834	0.00615443	0.00307721	−	0.999995i	$-0.499020\pi$
$577$	0.147834	0.00615443	0.00307721	+	0.999995i	$0.499020\pi$
$578$	−12.8134	−0.532968
$579$	1.09926	0.0456836
$580$	4.68130	0.194381
$581$	15.5952	0.646999
$582$	2.81783	0.116803
$583$	−34.3957	−1.42453
$584$	−4.97851	−0.206012
$585$	2.72701	0.112748
$586$	24.9488	1.03063
$587$	24.9482	1.02972	0.514860	−	0.857274i	$-0.327844\pi$
$587$	24.9482	1.02972	0.514860	+	0.857274i	$0.327844\pi$
$588$	−5.26389	−0.217079
$589$	3.17257	0.130723
$590$	−2.27633	−0.0937152
$591$	14.3353	0.589674
$592$	−3.69333	−0.151795
$593$	−2.61925	−0.107560	−0.0537799	−	0.998553i	$-0.517127\pi$
$593$	−2.61925	−0.107560	−0.0537799	+	0.998553i	$0.517127\pi$
$594$	−8.90883	−0.365534
$595$	−8.45486	−0.346615
$596$	−14.6505	−0.600107
$597$	0.159155	0.00651377
$598$	2.85380	0.116701
$599$	25.9840	1.06168	0.530839	−	0.847473i	$-0.321877\pi$
$599$	25.9840	1.06168	0.530839	+	0.847473i	$0.321877\pi$
$600$	−0.522486	−0.0213304
$601$	−23.8496	−0.972845	−0.486422	−	0.873724i	$-0.661698\pi$
$601$	−23.8496	−0.972845	−0.486422	+	0.873724i	$0.661698\pi$
$602$	−12.8134	−0.522234
$603$	9.97486	0.406208
$604$	20.4558	0.832334
$605$	2.13587	0.0868357
$606$	−5.41342	−0.219905
$607$	38.6872	1.57027	0.785133	−	0.619328i	$-0.212595\pi$
$607$	38.6872	1.57027	0.785133	+	0.619328i	$0.212595\pi$
$608$	3.17257	0.128665
$609$	−10.1069	−0.409552
$610$	−6.29020	−0.254683
$611$	0.104842	0.00424147
$612$	5.57977	0.225549
$613$	−10.8228	−0.437131	−0.218565	−	0.975822i	$-0.570138\pi$
$613$	−10.8228	−0.437131	−0.218565	+	0.975822i	$0.570138\pi$
$614$	−4.32593	−0.174580
$615$	−0.977227	−0.0394056
$616$	12.3025	0.495683
$617$	−21.2541	−0.855658	−0.427829	−	0.903860i	$-0.640721\pi$
$617$	−21.2541	−0.855658	−0.427829	+	0.903860i	$0.640721\pi$
$618$	−4.52024	−0.181831
$619$	38.6365	1.55293	0.776467	−	0.630159i	$-0.217010\pi$
$619$	38.6365	1.55293	0.776467	+	0.630159i	$0.217010\pi$
$620$	−1.00000	−0.0401610
$621$	8.53937	0.342673
$622$	15.6313	0.626756
$623$	−69.8832	−2.79981
$624$	−0.522486	−0.0209162
$625$	1.00000	0.0400000
$626$	−4.27565	−0.170889
$627$	4.93519	0.197093
$628$	−9.18738	−0.366616
$629$	7.55698	0.301316
$630$	−11.2684	−0.448944
$631$	−9.70437	−0.386325	−0.193162	−	0.981167i	$-0.561874\pi$
$631$	−9.70437	−0.386325	−0.193162	+	0.981167i	$0.561874\pi$
$632$	−6.74165	−0.268168
$633$	5.56763	0.221293
$634$	7.67198	0.304693
$635$	−6.32457	−0.250983
$636$	−6.03617	−0.239350
$637$	10.0747	0.399174
$638$	13.9375	0.551791
$639$	−0.743641	−0.0294180
$640$	−1.00000	−0.0395285
$641$	−4.18262	−0.165204	−0.0826019	−	0.996583i	$-0.526323\pi$
$641$	−4.18262	−0.165204	−0.0826019	+	0.996583i	$0.526323\pi$
$642$	−2.41886	−0.0954646
$643$	−24.5266	−0.967235	−0.483617	−	0.875280i	$-0.660677\pi$
$643$	−24.5266	−0.967235	−0.483617	+	0.875280i	$0.660677\pi$
$644$	−11.7923	−0.464683
$645$	1.62017	0.0637943
$646$	−6.49144	−0.255402
$647$	11.6243	0.456998	0.228499	−	0.973544i	$-0.426618\pi$
$647$	11.6243	0.456998	0.228499	+	0.973544i	$0.426618\pi$
$648$	6.61760	0.259964
$649$	−6.77726	−0.266031
$650$	1.00000	0.0392232
$651$	2.15899	0.0846176
$652$	−6.86511	−0.268859
$653$	37.3850	1.46299	0.731494	−	0.681848i	$-0.238824\pi$
$653$	37.3850	1.46299	0.731494	+	0.681848i	$0.238824\pi$
$654$	−3.61688	−0.141431
$655$	−8.06738	−0.315219
$656$	−1.87034	−0.0730245
$657$	13.5764	0.529667
$658$	−0.433225	−0.0168889
$659$	−11.6813	−0.455039	−0.227520	−	0.973773i	$-0.573062\pi$
$659$	−11.6813	−0.455039	−0.227520	+	0.973773i	$0.573062\pi$
$660$	−1.55558	−0.0605509
$661$	−42.1795	−1.64059	−0.820296	−	0.571939i	$-0.806191\pi$
$661$	−42.1795	−1.64059	−0.820296	+	0.571939i	$0.806191\pi$
$662$	−14.9397	−0.580648
$663$	1.06907	0.0415191
$664$	−3.77412	−0.146464
$665$	13.1095	0.508366
$666$	10.0717	0.390272
$667$	−13.3595	−0.517282
$668$	6.25871	0.242157
$669$	7.36277	0.284661
$670$	3.65780	0.141313
$671$	−18.7276	−0.722972
$672$	2.15899	0.0832850
$673$	5.14683	0.198396	0.0991979	−	0.995068i	$-0.468372\pi$
$673$	5.14683	0.198396	0.0991979	+	0.995068i	$0.468372\pi$
$674$	22.1452	0.853002
$675$	2.99228	0.115173
$676$	1.00000	0.0384615
$677$	−0.960644	−0.0369206	−0.0184603	−	0.999830i	$-0.505876\pi$
$677$	−0.960644	−0.0369206	−0.0184603	+	0.999830i	$0.505876\pi$
$678$	−9.26144	−0.355684
$679$	22.2852	0.855227
$680$	2.04611	0.0784649
$681$	−11.3503	−0.434946
$682$	−2.97727	−0.114005
$683$	28.7675	1.10076	0.550378	−	0.834916i	$-0.314484\pi$
$683$	28.7675	1.10076	0.550378	+	0.834916i	$0.314484\pi$
$684$	−8.65162	−0.330803
$685$	−2.48768	−0.0950495
$686$	−12.7051	−0.485082
$687$	−2.88573	−0.110098
$688$	3.10089	0.118220
$689$	11.5528	0.440126
$690$	1.49107	0.0567641
$691$	−11.7046	−0.445262	−0.222631	−	0.974903i	$-0.571465\pi$
$691$	−11.7046	−0.445262	−0.222631	+	0.974903i	$0.571465\pi$
$692$	−11.9608	−0.454681
$693$	−33.5491	−1.27442
$694$	−8.54606	−0.324404
$695$	−9.97772	−0.378476
$696$	2.44592	0.0927122
$697$	3.82693	0.144955
$698$	24.2343	0.917283
$699$	11.9676	0.452656
$700$	−4.13215	−0.156181
$701$	−18.2655	−0.689877	−0.344939	−	0.938625i	$-0.612100\pi$
$701$	−18.2655	−0.689877	−0.344939	+	0.938625i	$0.612100\pi$
$702$	2.99228	0.112936
$703$	−11.7173	−0.441928
$704$	−2.97727	−0.112210
$705$	0.0547787	0.00206309
$706$	−26.4097	−0.993942
$707$	−42.8127	−1.61014
$708$	−1.18935	−0.0446986
$709$	15.0134	0.563841	0.281921	−	0.959438i	$-0.409029\pi$
$709$	15.0134	0.563841	0.281921	+	0.959438i	$0.409029\pi$
$710$	−0.272695	−0.0102341
$711$	18.3845	0.689474
$712$	16.9121	0.633806
$713$	2.85380	0.106876
$714$	−4.41755	−0.165323
$715$	2.97727	0.111344
$716$	7.98138	0.298278
$717$	−6.31575	−0.235866
$718$	30.4588	1.13671
$719$	17.9327	0.668775	0.334388	−	0.942436i	$-0.391470\pi$
$719$	17.9327	0.668775	0.334388	+	0.942436i	$0.391470\pi$
$720$	2.72701	0.101630
$721$	−35.7489	−1.33136
$722$	−8.93481	−0.332519
$723$	5.07037	0.188569
$724$	−2.74918	−0.102173
$725$	−4.68130	−0.173859
$726$	1.11597	0.0414174
$727$	−24.6101	−0.912738	−0.456369	−	0.889791i	$-0.650850\pi$
$727$	−24.6101	−0.912738	−0.456369	+	0.889791i	$0.650850\pi$
$728$	−4.13215	−0.153148
$729$	−13.3560	−0.494665
$730$	4.97851	0.184263
$731$	−6.34478	−0.234670
$732$	−3.28654	−0.121474
$733$	−21.6900	−0.801140	−0.400570	−	0.916266i	$-0.631188\pi$
$733$	−21.6900	−0.801140	−0.400570	+	0.916266i	$0.631188\pi$
$734$	−0.616087	−0.0227402
$735$	5.26389	0.194161
$736$	2.85380	0.105192
$737$	10.8903	0.401148
$738$	5.10043	0.187750
$739$	−1.64998	−0.0606955	−0.0303478	−	0.999539i	$-0.509661\pi$
$739$	−1.64998	−0.0606955	−0.0303478	+	0.999539i	$0.509661\pi$
$740$	3.69333	0.135769
$741$	−1.65762	−0.0608943
$742$	−47.7379	−1.75251
$743$	10.3142	0.378392	0.189196	−	0.981939i	$-0.439412\pi$
$743$	10.3142	0.378392	0.189196	+	0.981939i	$0.439412\pi$
$744$	−0.522486	−0.0191553
$745$	14.6505	0.536752
$746$	21.8835	0.801212
$747$	10.2921	0.376566
$748$	6.09183	0.222739
$749$	−19.1298	−0.698989
$750$	0.522486	0.0190785
$751$	−4.39326	−0.160312	−0.0801561	−	0.996782i	$-0.525542\pi$
$751$	−4.39326	−0.160312	−0.0801561	+	0.996782i	$0.525542\pi$
$752$	0.104842	0.00382321
$753$	7.97229	0.290526
$754$	−4.68130	−0.170483
$755$	−20.4558	−0.744462
$756$	−12.3646	−0.449695
$757$	−19.0103	−0.690940	−0.345470	−	0.938430i	$-0.612281\pi$
$757$	−19.0103	−0.690940	−0.345470	+	0.938430i	$0.612281\pi$
$758$	36.3420	1.32000
$759$	4.43932	0.161137
$760$	−3.17257	−0.115081
$761$	29.6854	1.07610	0.538048	−	0.842914i	$-0.319162\pi$
$761$	29.6854	1.07610	0.538048	+	0.842914i	$0.319162\pi$
$762$	−3.30450	−0.119709
$763$	−28.6046	−1.03556
$764$	4.23668	0.153278
$765$	−5.57977	−0.201737
$766$	−14.1355	−0.510735
$767$	2.27633	0.0821937
$768$	−0.522486	−0.0188536
$769$	−20.9815	−0.756614	−0.378307	−	0.925680i	$-0.623494\pi$
$769$	−20.9815	−0.756614	−0.378307	+	0.925680i	$0.623494\pi$
$770$	−12.3025	−0.443352
$771$	−4.08195	−0.147008
$772$	−2.10390	−0.0757210
$773$	−0.771925	−0.0277642	−0.0138821	−	0.999904i	$-0.504419\pi$
$773$	−0.771925	−0.0277642	−0.0138821	+	0.999904i	$0.504419\pi$
$774$	−8.45616	−0.303950
$775$	1.00000	0.0359211
$776$	−5.39312	−0.193602
$777$	−7.97387	−0.286061
$778$	21.8694	0.784058
$779$	−5.93378	−0.212600
$780$	0.522486	0.0187080
$781$	−0.811886	−0.0290515
$782$	−5.83920	−0.208809
$783$	−14.0078	−0.500597
$784$	10.0747	0.359810
$785$	9.18738	0.327912
$786$	−4.21510	−0.150348
$787$	−9.97044	−0.355408	−0.177704	−	0.984084i	$-0.556867\pi$
$787$	−9.97044	−0.355408	−0.177704	+	0.984084i	$0.556867\pi$
$788$	−27.4366	−0.977389
$789$	−5.77000	−0.205417
$790$	6.74165	0.239857
$791$	−73.2454	−2.60430
$792$	8.11903	0.288497
$793$	6.29020	0.223372
$794$	−16.4329	−0.583182
$795$	6.03617	0.214081
$796$	−0.304610	−0.0107966
$797$	6.10096	0.216107	0.108054	−	0.994145i	$-0.465538\pi$
$797$	6.10096	0.216107	0.108054	+	0.994145i	$0.465538\pi$
$798$	6.84955	0.242472
$799$	−0.214520	−0.00758916
$800$	1.00000	0.0353553
$801$	−46.1193	−1.62955
$802$	−6.63293	−0.234217
$803$	14.8224	0.523069
$804$	1.91115	0.0674012
$805$	11.7923	0.415625
$806$	1.00000	0.0352235
$807$	6.93043	0.243963
$808$	10.3609	0.364494
$809$	25.6816	0.902915	0.451458	−	0.892293i	$-0.350904\pi$
$809$	25.6816	0.902915	0.451458	+	0.892293i	$0.350904\pi$
$810$	−6.61760	−0.232519
$811$	−37.9595	−1.33294	−0.666469	−	0.745533i	$-0.732195\pi$
$811$	−37.9595	−1.33294	−0.666469	+	0.745533i	$0.732195\pi$
$812$	19.3439	0.678837
$813$	−10.2571	−0.359733
$814$	10.9960	0.385411
$815$	6.86511	0.240474
$816$	1.06907	0.0374248
$817$	9.83780	0.344181
$818$	5.51901	0.192968
$819$	11.2684	0.393750
$820$	1.87034	0.0653151
$821$	44.2606	1.54471	0.772353	−	0.635193i	$-0.219080\pi$
$821$	44.2606	1.54471	0.772353	+	0.635193i	$0.219080\pi$
$822$	−1.29978	−0.0453350
$823$	14.0851	0.490975	0.245488	−	0.969400i	$-0.421052\pi$
$823$	14.0851	0.490975	0.245488	+	0.969400i	$0.421052\pi$
$824$	8.65141	0.301386
$825$	1.55558	0.0541584
$826$	−9.40616	−0.327282
$827$	−2.23699	−0.0777877	−0.0388939	−	0.999243i	$-0.512383\pi$
$827$	−2.23699	−0.0777877	−0.0388939	+	0.999243i	$0.512383\pi$
$828$	−7.78233	−0.270455
$829$	−8.64963	−0.300414	−0.150207	−	0.988655i	$-0.547994\pi$
$829$	−8.64963	−0.300414	−0.150207	+	0.988655i	$0.547994\pi$
$830$	3.77412	0.131002
$831$	16.9229	0.587048
$832$	1.00000	0.0346688
$833$	−20.6140	−0.714232
$834$	−5.21322	−0.180519
$835$	−6.25871	−0.216591
$836$	−9.44559	−0.326682
$837$	2.99228	0.103428
$838$	28.6925	0.991167
$839$	−15.9280	−0.549896	−0.274948	−	0.961459i	$-0.588661\pi$
$839$	−15.9280	−0.549896	−0.274948	+	0.961459i	$0.588661\pi$
$840$	−2.15899	−0.0744923
$841$	−7.08539	−0.244324
$842$	3.12918	0.107839
$843$	−2.89290	−0.0996367
$844$	−10.6560	−0.366796
$845$	−1.00000	−0.0344010
$846$	−0.285906	−0.00982965
$847$	8.82576	0.303257
$848$	11.5528	0.396724
$849$	−1.61409	−0.0553956
$850$	−2.04611	−0.0701812
$851$	−10.5400	−0.361307
$852$	−0.142479	−0.00488126
$853$	18.5242	0.634258	0.317129	−	0.948382i	$-0.397281\pi$
$853$	18.5242	0.634258	0.317129	+	0.948382i	$0.397281\pi$
$854$	−25.9921	−0.889431
$855$	8.65162	0.295879
$856$	4.62951	0.158233
$857$	44.2374	1.51112	0.755560	−	0.655079i	$-0.227365\pi$
$857$	44.2374	1.51112	0.755560	+	0.655079i	$0.227365\pi$
$858$	1.55558	0.0531067
$859$	36.8806	1.25835	0.629175	−	0.777264i	$-0.283393\pi$
$859$	36.8806	1.25835	0.629175	+	0.777264i	$0.283393\pi$
$860$	−3.10089	−0.105740
$861$	−4.03805	−0.137616
$862$	−38.1310	−1.29875
$863$	22.1974	0.755610	0.377805	−	0.925885i	$-0.376679\pi$
$863$	22.1974	0.755610	0.377805	+	0.925885i	$0.376679\pi$
$864$	2.99228	0.101800
$865$	11.9608	0.406679
$866$	−9.30745	−0.316280
$867$	6.69483	0.227368
$868$	−4.13215	−0.140254
$869$	20.0717	0.680886
$870$	−2.44592	−0.0829244
$871$	−3.65780	−0.123940
$872$	6.92245	0.234424
$873$	14.7071	0.497759
$874$	9.05387	0.306252
$875$	4.13215	0.139692
$876$	2.60120	0.0878865
$877$	−1.50124	−0.0506933	−0.0253466	−	0.999679i	$-0.508069\pi$
$877$	−1.50124	−0.0506933	−0.0253466	+	0.999679i	$0.508069\pi$
$878$	34.5078	1.16458
$879$	−13.0354	−0.439674
$880$	2.97727	0.100364
$881$	−12.9813	−0.437352	−0.218676	−	0.975797i	$-0.570174\pi$
$881$	−12.9813	−0.437352	−0.218676	+	0.975797i	$0.570174\pi$
$882$	−27.4738	−0.925089
$883$	−9.15536	−0.308102	−0.154051	−	0.988063i	$-0.549232\pi$
$883$	−9.15536	−0.308102	−0.154051	+	0.988063i	$0.549232\pi$
$884$	−2.04611	−0.0688183
$885$	1.18935	0.0399797
$886$	−6.66311	−0.223852
$887$	17.0779	0.573420	0.286710	−	0.958017i	$-0.407438\pi$
$887$	17.0779	0.573420	0.286710	+	0.958017i	$0.407438\pi$
$888$	1.92971	0.0647569
$889$	−26.1341	−0.876509
$890$	−16.9121	−0.566893
$891$	−19.7024	−0.660054
$892$	−14.0918	−0.471828
$893$	0.332620	0.0111307
$894$	7.65468	0.256011
$895$	−7.98138	−0.266788
$896$	−4.13215	−0.138046
$897$	−1.49107	−0.0497854
$898$	−0.373542	−0.0124653
$899$	−4.68130	−0.156130
$900$	−2.72701	−0.0909003
$901$	−23.6383	−0.787507
$902$	5.56851	0.185411
$903$	6.69481	0.222789
$904$	17.7257	0.589548
$905$	2.74918	0.0913860
$906$	−10.6879	−0.355080
$907$	48.7376	1.61831	0.809153	−	0.587597i	$-0.199926\pi$
$907$	48.7376	1.61831	0.809153	+	0.587597i	$0.199926\pi$
$908$	21.7237	0.720926
$909$	−28.2542	−0.937133
$910$	4.13215	0.136980
$911$	39.2003	1.29876	0.649382	−	0.760463i	$-0.275028\pi$
$911$	39.2003	1.29876	0.649382	+	0.760463i	$0.275028\pi$
$912$	−1.65762	−0.0548894
$913$	11.2366	0.371876
$914$	12.2633	0.405635
$915$	3.28654	0.108650
$916$	5.52308	0.182488
$917$	−33.3357	−1.10084
$918$	−6.12256	−0.202074
$919$	15.8263	0.522061	0.261031	−	0.965331i	$-0.415938\pi$
$919$	15.8263	0.522061	0.261031	+	0.965331i	$0.415938\pi$
$920$	−2.85380	−0.0940870
$921$	2.26024	0.0744775
$922$	23.6144	0.777699
$923$	0.272695	0.00897586
$924$	−6.42790	−0.211462
$925$	−3.69333	−0.121436
$926$	−3.45526	−0.113547
$927$	−23.5925	−0.774878
$928$	−4.68130	−0.153671
$929$	5.38902	0.176808	0.0884041	−	0.996085i	$-0.471823\pi$
$929$	5.38902	0.176808	0.0884041	+	0.996085i	$0.471823\pi$
$930$	0.522486	0.0171330
$931$	31.9626	1.04753
$932$	−22.9051	−0.750281
$933$	−8.16712	−0.267379
$934$	−12.7975	−0.418746
$935$	−6.09183	−0.199224
$936$	−2.72701	−0.0891350
$937$	−48.5071	−1.58466	−0.792328	−	0.610095i	$-0.791131\pi$
$937$	−48.5071	−1.58466	−0.792328	+	0.610095i	$0.791131\pi$
$938$	15.1146	0.493509
$939$	2.23397	0.0729027
$940$	−0.104842	−0.00341958
$941$	−38.9430	−1.26950	−0.634752	−	0.772716i	$-0.718898\pi$
$941$	−38.9430	−1.26950	−0.634752	+	0.772716i	$0.718898\pi$
$942$	4.80028	0.156402
$943$	−5.33758	−0.173815
$944$	2.27633	0.0740884
$945$	12.3646	0.402220
$946$	−9.23219	−0.300164
$947$	−24.4750	−0.795330	−0.397665	−	0.917531i	$-0.630179\pi$
$947$	−24.4750	−0.795330	−0.397665	+	0.917531i	$0.630179\pi$
$948$	3.52242	0.114403
$949$	−4.97851	−0.161609
$950$	3.17257	0.102932
$951$	−4.00850	−0.129985
$952$	8.45486	0.274024
$953$	44.2622	1.43379	0.716897	−	0.697179i	$-0.245562\pi$
$953$	44.2622	1.43379	0.716897	+	0.697179i	$0.245562\pi$
$954$	−31.5045	−1.02000
$955$	−4.23668	−0.137096
$956$	12.0879	0.390950
$957$	−7.28215	−0.235399
$958$	−19.0395	−0.615137
$959$	−10.2795	−0.331942
$960$	0.522486	0.0168632
$961$	1.00000	0.0322581
$962$	−3.69333	−0.119078
$963$	−12.6247	−0.406826
$964$	−9.70431	−0.312555
$965$	2.10390	0.0677269
$966$	6.16133	0.198238
$967$	31.3234	1.00729	0.503646	−	0.863910i	$-0.331992\pi$
$967$	31.3234	1.00729	0.503646	+	0.863910i	$0.331992\pi$
$968$	−2.13587	−0.0686496
$969$	3.39169	0.108957
$970$	5.39312	0.173163
$971$	−50.2539	−1.61272	−0.806362	−	0.591422i	$-0.798567\pi$
$971$	−50.2539	−1.61272	−0.806362	+	0.591422i	$0.798567\pi$
$972$	−12.4345	−0.398835
$973$	−41.2294	−1.32176
$974$	−22.5046	−0.721094
$975$	−0.522486	−0.0167330
$976$	6.29020	0.201344
$977$	−47.1534	−1.50857	−0.754285	−	0.656547i	$-0.772016\pi$
$977$	−47.1534	−1.50857	−0.754285	+	0.656547i	$0.772016\pi$
$978$	3.58693	0.114697
$979$	−50.3517	−1.60925
$980$	−10.0747	−0.321824
$981$	−18.8776	−0.602714
$982$	14.2934	0.456120
$983$	−2.27331	−0.0725073	−0.0362536	−	0.999343i	$-0.511542\pi$
$983$	−2.27331	−0.0725073	−0.0362536	+	0.999343i	$0.511542\pi$
$984$	0.977227	0.0311529
$985$	27.4366	0.874203
$986$	9.57849	0.305041
$987$	0.226354	0.00720493
$988$	3.17257	0.100933
$989$	8.84933	0.281392
$990$	−8.11903	−0.258040
$991$	10.5770	0.335988	0.167994	−	0.985788i	$-0.446271\pi$
$991$	10.5770	0.335988	0.167994	+	0.985788i	$0.446271\pi$
$992$	1.00000	0.0317500
$993$	7.80579	0.247709
$994$	−1.12682	−0.0357405
$995$	0.304610	0.00965680
$996$	1.97193	0.0624828
$997$	−29.0841	−0.921101	−0.460551	−	0.887633i	$-0.652348\pi$
$997$	−29.0841	−0.921101	−0.460551	+	0.887633i	$0.652348\pi$
$998$	37.5606	1.18896
$999$	−11.0515	−0.349654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.q.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.q.1.4	✓	9	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.522486 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.522486 q^{6} -4.13215 q^{7} +1.00000 q^{8} -2.72701 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.522486 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.522486 q^{6} -4.13215 q^{7} +1.00000 q^{8} -2.72701 q^{9} -1.00000 q^{10} -2.97727 q^{11} -0.522486 q^{12} +1.00000 q^{13} -4.13215 q^{14} +0.522486 q^{15} +1.00000 q^{16} -2.04611 q^{17} -2.72701 q^{18} +3.17257 q^{19} -1.00000 q^{20} +2.15899 q^{21} -2.97727 q^{22} +2.85380 q^{23} -0.522486 q^{24} +1.00000 q^{25} +1.00000 q^{26} +2.99228 q^{27} -4.13215 q^{28} -4.68130 q^{29} +0.522486 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.55558 q^{33} -2.04611 q^{34} +4.13215 q^{35} -2.72701 q^{36} -3.69333 q^{37} +3.17257 q^{38} -0.522486 q^{39} -1.00000 q^{40} -1.87034 q^{41} +2.15899 q^{42} +3.10089 q^{43} -2.97727 q^{44} +2.72701 q^{45} +2.85380 q^{46} +0.104842 q^{47} -0.522486 q^{48} +10.0747 q^{49} +1.00000 q^{50} +1.06907 q^{51} +1.00000 q^{52} +11.5528 q^{53} +2.99228 q^{54} +2.97727 q^{55} -4.13215 q^{56} -1.65762 q^{57} -4.68130 q^{58} +2.27633 q^{59} +0.522486 q^{60} +6.29020 q^{61} +1.00000 q^{62} +11.2684 q^{63} +1.00000 q^{64} -1.00000 q^{65} +1.55558 q^{66} -3.65780 q^{67} -2.04611 q^{68} -1.49107 q^{69} +4.13215 q^{70} +0.272695 q^{71} -2.72701 q^{72} -4.97851 q^{73} -3.69333 q^{74} -0.522486 q^{75} +3.17257 q^{76} +12.3025 q^{77} -0.522486 q^{78} -6.74165 q^{79} -1.00000 q^{80} +6.61760 q^{81} -1.87034 q^{82} -3.77412 q^{83} +2.15899 q^{84} +2.04611 q^{85} +3.10089 q^{86} +2.44592 q^{87} -2.97727 q^{88} +16.9121 q^{89} +2.72701 q^{90} -4.13215 q^{91} +2.85380 q^{92} -0.522486 q^{93} +0.104842 q^{94} -3.17257 q^{95} -0.522486 q^{96} -5.39312 q^{97} +10.0747 q^{98} +8.11903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} - 9 q^{5} + 3 q^{6} + 3 q^{7} + 9 q^{8} + 14 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{12} + 9 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 14 q^{18} + 6 q^{19} - 9 q^{20} - q^{21} + 6 q^{22} + 14 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 9 q^{27} + 3 q^{28} + 17 q^{29} - 3 q^{30} + 9 q^{31} + 9 q^{32} - 8 q^{33} + 3 q^{34} - 3 q^{35} + 14 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 9 q^{40} + 4 q^{41} - q^{42} + 5 q^{43} + 6 q^{44} - 14 q^{45} + 14 q^{46} + 25 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} + 15 q^{51} + 9 q^{52} + 18 q^{53} + 9 q^{54} - 6 q^{55} + 3 q^{56} + 13 q^{57} + 17 q^{58} - 6 q^{59} - 3 q^{60} + 26 q^{61} + 9 q^{62} + 8 q^{63} + 9 q^{64} - 9 q^{65} - 8 q^{66} - 2 q^{67} + 3 q^{68} + 8 q^{69} - 3 q^{70} + 18 q^{71} + 14 q^{72} - 5 q^{73} - 3 q^{74} + 3 q^{75} + 6 q^{76} + 19 q^{77} + 3 q^{78} + 18 q^{79} - 9 q^{80} + 41 q^{81} + 4 q^{82} + 13 q^{83} - q^{84} - 3 q^{85} + 5 q^{86} + 19 q^{87} + 6 q^{88} + 9 q^{89} - 14 q^{90} + 3 q^{91} + 14 q^{92} + 3 q^{93} + 25 q^{94} - 6 q^{95} + 3 q^{96} - 18 q^{97} + 8 q^{98} + 21 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 - 9 * q^5 + 3 * q^6 + 3 * q^7 + 9 * q^8 + 14 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^12 + 9 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 14 * q^18 + 6 * q^19 - 9 * q^20 - q^21 + 6 * q^22 + 14 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 9 * q^27 + 3 * q^28 + 17 * q^29 - 3 * q^30 + 9 * q^31 + 9 * q^32 - 8 * q^33 + 3 * q^34 - 3 * q^35 + 14 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 9 * q^40 + 4 * q^41 - q^42 + 5 * q^43 + 6 * q^44 - 14 * q^45 + 14 * q^46 + 25 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 + 15 * q^51 + 9 * q^52 + 18 * q^53 + 9 * q^54 - 6 * q^55 + 3 * q^56 + 13 * q^57 + 17 * q^58 - 6 * q^59 - 3 * q^60 + 26 * q^61 + 9 * q^62 + 8 * q^63 + 9 * q^64 - 9 * q^65 - 8 * q^66 - 2 * q^67 + 3 * q^68 + 8 * q^69 - 3 * q^70 + 18 * q^71 + 14 * q^72 - 5 * q^73 - 3 * q^74 + 3 * q^75 + 6 * q^76 + 19 * q^77 + 3 * q^78 + 18 * q^79 - 9 * q^80 + 41 * q^81 + 4 * q^82 + 13 * q^83 - q^84 - 3 * q^85 + 5 * q^86 + 19 * q^87 + 6 * q^88 + 9 * q^89 - 14 * q^90 + 3 * q^91 + 14 * q^92 + 3 * q^93 + 25 * q^94 - 6 * q^95 + 3 * q^96 - 18 * q^97 + 8 * q^98 + 21 * q^99

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