LMFDB - Embedded newform 9251.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.78145$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78145 q^{2} -1.92907 q^{3} +1.17356 q^{4} -0.848076 q^{5} +3.43654 q^{6} +2.45497 q^{7} +1.47226 q^{8} +0.721313 q^{9} +O(q^{10})$	\(q-1.78145 q^{2} -1.92907 q^{3} +1.17356 q^{4} -0.848076 q^{5} +3.43654 q^{6} +2.45497 q^{7} +1.47226 q^{8} +0.721313 q^{9} +1.51080 q^{10} +1.00000 q^{11} -2.26388 q^{12} -2.27043 q^{13} -4.37340 q^{14} +1.63600 q^{15} -4.96988 q^{16} -6.53754 q^{17} -1.28498 q^{18} +7.80252 q^{19} -0.995267 q^{20} -4.73581 q^{21} -1.78145 q^{22} -2.66317 q^{23} -2.84010 q^{24} -4.28077 q^{25} +4.04466 q^{26} +4.39575 q^{27} +2.88105 q^{28} -2.91445 q^{30} -2.88571 q^{31} +5.90906 q^{32} -1.92907 q^{33} +11.6463 q^{34} -2.08200 q^{35} +0.846503 q^{36} +6.95308 q^{37} -13.8998 q^{38} +4.37983 q^{39} -1.24859 q^{40} +7.15083 q^{41} +8.43660 q^{42} -1.97256 q^{43} +1.17356 q^{44} -0.611729 q^{45} +4.74430 q^{46} +8.46322 q^{47} +9.58724 q^{48} -0.973131 q^{49} +7.62597 q^{50} +12.6114 q^{51} -2.66449 q^{52} +10.0192 q^{53} -7.83080 q^{54} -0.848076 q^{55} +3.61436 q^{56} -15.0516 q^{57} -1.67078 q^{59} +1.91994 q^{60} +7.62442 q^{61} +5.14074 q^{62} +1.77080 q^{63} -0.586923 q^{64} +1.92550 q^{65} +3.43654 q^{66} -6.65145 q^{67} -7.67219 q^{68} +5.13744 q^{69} +3.70898 q^{70} -16.3246 q^{71} +1.06196 q^{72} -13.3077 q^{73} -12.3866 q^{74} +8.25790 q^{75} +9.15671 q^{76} +2.45497 q^{77} -7.80243 q^{78} -14.2486 q^{79} +4.21484 q^{80} -10.6436 q^{81} -12.7388 q^{82} +5.56435 q^{83} -5.55775 q^{84} +5.54433 q^{85} +3.51401 q^{86} +1.47226 q^{88} -5.14212 q^{89} +1.08976 q^{90} -5.57384 q^{91} -3.12539 q^{92} +5.56674 q^{93} -15.0768 q^{94} -6.61713 q^{95} -11.3990 q^{96} -18.0058 q^{97} +1.73358 q^{98} +0.721313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q - 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 9 * q^9	\( 18 q - 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 9 q^{9} - 5 q^{10} + 18 q^{11} - 3 q^{12} - 15 q^{13} + 12 q^{14} - 27 q^{15} + 4 q^{16} + 6 q^{17} - 12 q^{18} + 11 q^{19} - 18 q^{20} + 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} - 10 q^{26} + 6 q^{27} - 6 q^{28} - 19 q^{30} - 8 q^{31} - 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} + 9 q^{37} - 3 q^{38} - 8 q^{39} - 36 q^{40} + 3 q^{41} + 28 q^{42} + 13 q^{43} + 12 q^{44} - q^{45} + 37 q^{46} - q^{47} + 46 q^{48} - 23 q^{49} + 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} - 6 q^{55} + 10 q^{56} + 14 q^{57} - 16 q^{59} + 3 q^{60} - 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} - q^{66} + 9 q^{67} + 5 q^{68} - 47 q^{69} - 69 q^{70} - 13 q^{71} + 22 q^{72} - 57 q^{73} + 33 q^{74} - q^{75} - 26 q^{76} - 5 q^{77} + 5 q^{78} + 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} + 35 q^{84} + 40 q^{85} + 4 q^{86} + 3 q^{88} - 80 q^{89} + 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} + 7 q^{95} + 8 q^{96} + 20 q^{97} - 78 q^{98} + 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 9 * q^9 - 5 * q^10 + 18 * q^11 - 3 * q^12 - 15 * q^13 + 12 * q^14 - 27 * q^15 + 4 * q^16 + 6 * q^17 - 12 * q^18 + 11 * q^19 - 18 * q^20 + 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 - 10 * q^26 + 6 * q^27 - 6 * q^28 - 19 * q^30 - 8 * q^31 - 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 + 9 * q^37 - 3 * q^38 - 8 * q^39 - 36 * q^40 + 3 * q^41 + 28 * q^42 + 13 * q^43 + 12 * q^44 - q^45 + 37 * q^46 - q^47 + 46 * q^48 - 23 * q^49 + 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 - 6 * q^55 + 10 * q^56 + 14 * q^57 - 16 * q^59 + 3 * q^60 - 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 - q^66 + 9 * q^67 + 5 * q^68 - 47 * q^69 - 69 * q^70 - 13 * q^71 + 22 * q^72 - 57 * q^73 + 33 * q^74 - q^75 - 26 * q^76 - 5 * q^77 + 5 * q^78 + 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 + 35 * q^84 + 40 * q^85 + 4 * q^86 + 3 * q^88 - 80 * q^89 + 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 + 7 * q^95 + 8 * q^96 + 20 * q^97 - 78 * q^98 + 9 * 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 $

$2$	−1.78145	−1.25967	−0.629837	−	0.776727i	$-0.716878\pi$
$2$	−1.78145	−1.25967	−0.629837	+	0.776727i	$0.716878\pi$
$3$	−1.92907	−1.11375	−0.556875	−	0.830597i	$-0.688000\pi$
$3$	−1.92907	−1.11375	−0.556875	+	0.830597i	$0.688000\pi$
$4$	1.17356	0.586779
$5$	−0.848076	−0.379271	−0.189636	−	0.981855i	$-0.560731\pi$
$5$	−0.848076	−0.379271	−0.189636	+	0.981855i	$0.560731\pi$
$6$	3.43654	1.40296
$7$	2.45497	0.927891	0.463945	−	0.885864i	$-0.346433\pi$
$7$	2.45497	0.927891	0.463945	+	0.885864i	$0.346433\pi$
$8$	1.47226	0.520523
$9$	0.721313	0.240438
$10$	1.51080	0.477758
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.26388	−0.653525
$13$	−2.27043	−0.629705	−0.314852	−	0.949141i	$-0.601955\pi$
$13$	−2.27043	−0.629705	−0.314852	+	0.949141i	$0.601955\pi$
$14$	−4.37340	−1.16884
$15$	1.63600	0.422413
$16$	−4.96988	−1.24247
$17$	−6.53754	−1.58559	−0.792793	−	0.609491i	$-0.791374\pi$
$17$	−6.53754	−1.58559	−0.792793	+	0.609491i	$0.791374\pi$
$18$	−1.28498	−0.302873
$19$	7.80252	1.79002	0.895010	−	0.446046i	$-0.147168\pi$
$19$	7.80252	1.79002	0.895010	+	0.446046i	$0.147168\pi$
$20$	−0.995267	−0.222549
$21$	−4.73581	−1.03344
$22$	−1.78145	−0.379806
$23$	−2.66317	−0.555309	−0.277655	−	0.960681i	$-0.589557\pi$
$23$	−2.66317	−0.555309	−0.277655	+	0.960681i	$0.589557\pi$
$24$	−2.84010	−0.579733
$25$	−4.28077	−0.856153
$26$	4.04466	0.793223
$27$	4.39575	0.845962
$28$	2.88105	0.544467
$29$	0	0
$29$	0	0
$30$	−2.91445	−0.532103
$31$	−2.88571	−0.518289	−0.259144	−	0.965839i	$-0.583441\pi$
$31$	−2.88571	−0.518289	−0.259144	+	0.965839i	$0.583441\pi$
$32$	5.90906	1.04458
$33$	−1.92907	−0.335808
$34$	11.6463	1.99732
$35$	−2.08200	−0.351922
$36$	0.846503	0.141084
$37$	6.95308	1.14308	0.571540	−	0.820574i	$-0.306346\pi$
$37$	6.95308	1.14308	0.571540	+	0.820574i	$0.306346\pi$
$38$	−13.8998	−2.25484
$39$	4.37983	0.701333
$40$	−1.24859	−0.197420
$41$	7.15083	1.11677	0.558386	−	0.829581i	$-0.311421\pi$
$41$	7.15083	1.11677	0.558386	+	0.829581i	$0.311421\pi$
$42$	8.43660	1.30180
$43$	−1.97256	−0.300812	−0.150406	−	0.988624i	$-0.548058\pi$
$43$	−1.97256	−0.300812	−0.150406	+	0.988624i	$0.548058\pi$
$44$	1.17356	0.176921
$45$	−0.611729	−0.0911911
$46$	4.74430	0.699509
$47$	8.46322	1.23449	0.617244	−	0.786772i	$-0.288249\pi$
$47$	8.46322	1.23449	0.617244	+	0.786772i	$0.288249\pi$
$48$	9.58724	1.38380
$49$	−0.973131	−0.139019
$50$	7.62597	1.07847
$51$	12.6114	1.76595
$52$	−2.66449	−0.369498
$53$	10.0192	1.37625	0.688125	−	0.725593i	$-0.258434\pi$
$53$	10.0192	1.37625	0.688125	+	0.725593i	$0.258434\pi$
$54$	−7.83080	−1.06564
$55$	−0.848076	−0.114355
$56$	3.61436	0.482989
$57$	−15.0516	−1.99363
$58$	0	0
$59$	−1.67078	−0.217517	−0.108759	−	0.994068i	$-0.534688\pi$
$59$	−1.67078	−0.217517	−0.108759	+	0.994068i	$0.534688\pi$
$60$	1.91994	0.247863
$61$	7.62442	0.976207	0.488103	−	0.872786i	$-0.337689\pi$
$61$	7.62442	0.976207	0.488103	+	0.872786i	$0.337689\pi$
$62$	5.14074	0.652875
$63$	1.77080	0.223100
$64$	−0.586923	−0.0733653
$65$	1.92550	0.238829
$66$	3.43654	0.423009
$67$	−6.65145	−0.812604	−0.406302	−	0.913739i	$-0.633182\pi$
$67$	−6.65145	−0.812604	−0.406302	+	0.913739i	$0.633182\pi$
$68$	−7.67219	−0.930389
$69$	5.13744	0.618475
$70$	3.70898	0.443307
$71$	−16.3246	−1.93737	−0.968687	−	0.248285i	$-0.920133\pi$
$71$	−16.3246	−1.93737	−0.968687	+	0.248285i	$0.920133\pi$
$72$	1.06196	0.125153
$73$	−13.3077	−1.55755	−0.778774	−	0.627305i	$-0.784158\pi$
$73$	−13.3077	−1.55755	−0.778774	+	0.627305i	$0.784158\pi$
$74$	−12.3866	−1.43991
$75$	8.25790	0.953540
$76$	9.15671	1.05035
$77$	2.45497	0.279770
$78$	−7.80243	−0.883452
$79$	−14.2486	−1.60309	−0.801545	−	0.597935i	$-0.795988\pi$
$79$	−14.2486	−1.60309	−0.801545	+	0.597935i	$0.795988\pi$
$80$	4.21484	0.471233
$81$	−10.6436	−1.18263
$82$	−12.7388	−1.40677
$83$	5.56435	0.610766	0.305383	−	0.952230i	$-0.401215\pi$
$83$	5.56435	0.610766	0.305383	+	0.952230i	$0.401215\pi$
$84$	−5.55775	−0.606400
$85$	5.54433	0.601367
$86$	3.51401	0.378925
$87$	0	0
$88$	1.47226	0.156944
$89$	−5.14212	−0.545064	−0.272532	−	0.962147i	$-0.587861\pi$
$89$	−5.14212	−0.545064	−0.272532	+	0.962147i	$0.587861\pi$
$90$	1.08976	0.114871
$91$	−5.57384	−0.584297
$92$	−3.12539	−0.325844
$93$	5.56674	0.577244
$94$	−15.0768	−1.55505
$95$	−6.61713	−0.678903
$96$	−11.3990	−1.16340
$97$	−18.0058	−1.82821	−0.914104	−	0.405479i	$-0.867105\pi$
$97$	−18.0058	−1.82821	−0.914104	+	0.405479i	$0.867105\pi$
$98$	1.73358	0.175118
$99$	0.721313	0.0724947
$100$	−5.02373	−0.502373
$101$	−2.22234	−0.221131	−0.110566	−	0.993869i	$-0.535266\pi$
$101$	−2.22234	−0.221131	−0.110566	+	0.993869i	$0.535266\pi$
$102$	−22.4665	−2.22452
$103$	−6.13391	−0.604392	−0.302196	−	0.953246i	$-0.597720\pi$
$103$	−6.13391	−0.604392	−0.302196	+	0.953246i	$0.597720\pi$
$104$	−3.34267	−0.327776
$105$	4.01633	0.391953
$106$	−17.8488	−1.73363
$107$	6.66721	0.644543	0.322272	−	0.946647i	$-0.395554\pi$
$107$	6.66721	0.644543	0.322272	+	0.946647i	$0.395554\pi$
$108$	5.15867	0.496393
$109$	6.96016	0.666662	0.333331	−	0.942810i	$-0.391827\pi$
$109$	6.96016	0.666662	0.333331	+	0.942810i	$0.391827\pi$
$110$	1.51080	0.144050
$111$	−13.4130	−1.27310
$112$	−12.2009	−1.15288
$113$	12.8702	1.21073	0.605366	−	0.795948i	$-0.293027\pi$
$113$	12.8702	1.21073	0.605366	+	0.795948i	$0.293027\pi$
$114$	26.8137	2.51133
$115$	2.25857	0.210613
$116$	0	0
$117$	−1.63769	−0.151405
$118$	2.97641	0.274001
$119$	−16.0495	−1.47125
$120$	2.40862	0.219876
$121$	1.00000	0.0909091
$122$	−13.5825	−1.22970
$123$	−13.7945	−1.24380
$124$	−3.38655	−0.304121
$125$	7.87080	0.703986
$126$	−3.15459	−0.281033
$127$	−1.79718	−0.159474	−0.0797369	−	0.996816i	$-0.525408\pi$
$127$	−1.79718	−0.159474	−0.0797369	+	0.996816i	$0.525408\pi$
$128$	−10.7725	−0.952167
$129$	3.80520	0.335029
$130$	−3.43018	−0.300847
$131$	9.92738	0.867360	0.433680	−	0.901067i	$-0.357215\pi$
$131$	9.92738	0.867360	0.433680	+	0.901067i	$0.357215\pi$
$132$	−2.26388	−0.197045
$133$	19.1549	1.66094
$134$	11.8492	1.02362
$135$	−3.72793	−0.320849
$136$	−9.62498	−0.825335
$137$	11.2435	0.960598	0.480299	−	0.877105i	$-0.340528\pi$
$137$	11.2435	0.960598	0.480299	+	0.877105i	$0.340528\pi$
$138$	−9.15209	−0.779077
$139$	−7.85311	−0.666092	−0.333046	−	0.942911i	$-0.608076\pi$
$139$	−7.85311	−0.666092	−0.333046	+	0.942911i	$0.608076\pi$
$140$	−2.44335	−0.206501
$141$	−16.3262	−1.37491
$142$	29.0814	2.44046
$143$	−2.27043	−0.189863
$144$	−3.58484	−0.298736
$145$	0	0
$146$	23.7070	1.96200
$147$	1.87724	0.154832
$148$	8.15985	0.670735
$149$	−1.28162	−0.104994	−0.0524971	−	0.998621i	$-0.516718\pi$
$149$	−1.28162	−0.104994	−0.0524971	+	0.998621i	$0.516718\pi$
$150$	−14.7110	−1.20115
$151$	6.34789	0.516584	0.258292	−	0.966067i	$-0.416840\pi$
$151$	6.34789	0.516584	0.258292	+	0.966067i	$0.416840\pi$
$152$	11.4874	0.931747
$153$	−4.71561	−0.381235
$154$	−4.37340	−0.352419
$155$	2.44730	0.196572
$156$	5.13998	0.411528
$157$	19.7780	1.57845	0.789227	−	0.614102i	$-0.210481\pi$
$157$	19.7780	1.57845	0.789227	+	0.614102i	$0.210481\pi$
$158$	25.3831	2.01937
$159$	−19.3278	−1.53280
$160$	−5.01133	−0.396180
$161$	−6.53800	−0.515266
$162$	18.9611	1.48973
$163$	−0.717552	−0.0562030	−0.0281015	−	0.999605i	$-0.508946\pi$
$163$	−0.717552	−0.0562030	−0.0281015	+	0.999605i	$0.508946\pi$
$164$	8.39192	0.655299
$165$	1.63600	0.127362
$166$	−9.91260	−0.769367
$167$	20.2382	1.56608	0.783039	−	0.621973i	$-0.213669\pi$
$167$	20.2382	1.56608	0.783039	+	0.621973i	$0.213669\pi$
$168$	−6.97235	−0.537929
$169$	−7.84513	−0.603472
$170$	−9.87694	−0.757527
$171$	5.62806	0.430388
$172$	−2.31491	−0.176510
$173$	7.29179	0.554384	0.277192	−	0.960814i	$-0.410596\pi$
$173$	7.29179	0.554384	0.277192	+	0.960814i	$0.410596\pi$
$174$	0	0
$175$	−10.5091	−0.794417
$176$	−4.96988	−0.374619
$177$	3.22306	0.242260
$178$	9.16043	0.686603
$179$	−5.63972	−0.421532	−0.210766	−	0.977537i	$-0.567596\pi$
$179$	−5.63972	−0.421532	−0.210766	+	0.977537i	$0.567596\pi$
$180$	−0.717899	−0.0535091
$181$	20.4124	1.51725	0.758623	−	0.651530i	$-0.225873\pi$
$181$	20.4124	1.51725	0.758623	+	0.651530i	$0.225873\pi$
$182$	9.92951	0.736024
$183$	−14.7080	−1.08725
$184$	−3.92088	−0.289051
$185$	−5.89674	−0.433537
$186$	−9.91686	−0.727139
$187$	−6.53754	−0.478072
$188$	9.93209	0.724372
$189$	10.7914	0.784960
$190$	11.7881	0.855197
$191$	5.94507	0.430170	0.215085	−	0.976595i	$-0.430997\pi$
$191$	5.94507	0.430170	0.215085	+	0.976595i	$0.430997\pi$
$192$	1.13222	0.0817106
$193$	1.86066	0.133933	0.0669666	−	0.997755i	$-0.478668\pi$
$193$	1.86066	0.133933	0.0669666	+	0.997755i	$0.478668\pi$
$194$	32.0763	2.30295
$195$	−3.71443	−0.265996
$196$	−1.14203	−0.0815733
$197$	−10.5367	−0.750706	−0.375353	−	0.926882i	$-0.622479\pi$
$197$	−10.5367	−0.750706	−0.375353	+	0.926882i	$0.622479\pi$
$198$	−1.28498	−0.0913197
$199$	−9.88442	−0.700688	−0.350344	−	0.936621i	$-0.613935\pi$
$199$	−9.88442	−0.700688	−0.350344	+	0.936621i	$0.613935\pi$
$200$	−6.30241	−0.445648
$201$	12.8311	0.905038
$202$	3.95899	0.278553
$203$	0	0
$204$	14.8002	1.03622
$205$	−6.06445	−0.423560
$206$	10.9272	0.761337
$207$	−1.92098	−0.133517
$208$	11.2838	0.782389
$209$	7.80252	0.539711
$210$	−7.15488	−0.493733
$211$	−19.6653	−1.35381	−0.676906	−	0.736069i	$-0.736680\pi$
$211$	−19.6653	−1.35381	−0.676906	+	0.736069i	$0.736680\pi$
$212$	11.7582	0.807555
$213$	31.4913	2.15775
$214$	−11.8773	−0.811914
$215$	1.67288	0.114089
$216$	6.47170	0.440343
$217$	−7.08433	−0.480915
$218$	−12.3992	−0.839777
$219$	25.6715	1.73472
$220$	−0.995267	−0.0671009
$221$	14.8430	0.998451
$222$	23.8945	1.60370
$223$	15.2289	1.01980	0.509901	−	0.860233i	$-0.329682\pi$
$223$	15.2289	1.01980	0.509901	+	0.860233i	$0.329682\pi$
$224$	14.5065	0.969259
$225$	−3.08777	−0.205852
$226$	−22.9277	−1.52513
$227$	−5.95105	−0.394985	−0.197492	−	0.980304i	$-0.563280\pi$
$227$	−5.95105	−0.394985	−0.197492	+	0.980304i	$0.563280\pi$
$228$	−17.6639	−1.16982
$229$	18.8853	1.24798	0.623989	−	0.781433i	$-0.285511\pi$
$229$	18.8853	1.24798	0.623989	+	0.781433i	$0.285511\pi$
$230$	−4.02353	−0.265304
$231$	−4.73581	−0.311593
$232$	0	0
$233$	−20.1830	−1.32223	−0.661115	−	0.750284i	$-0.729917\pi$
$233$	−20.1830	−1.32223	−0.661115	+	0.750284i	$0.729917\pi$
$234$	2.91747	0.190721
$235$	−7.17746	−0.468206
$236$	−1.96076	−0.127635
$237$	27.4865	1.78544
$238$	28.5913	1.85330
$239$	−10.0674	−0.651206	−0.325603	−	0.945507i	$-0.605567\pi$
$239$	−10.0674	−0.651206	−0.325603	+	0.945507i	$0.605567\pi$
$240$	−8.13071	−0.524835
$241$	−24.1592	−1.55623	−0.778116	−	0.628121i	$-0.783824\pi$
$241$	−24.1592	−1.55623	−0.778116	+	0.628121i	$0.783824\pi$
$242$	−1.78145	−0.114516
$243$	7.34510	0.471189
$244$	8.94770	0.572818
$245$	0.825289	0.0527258
$246$	24.5741	1.56679
$247$	−17.7151	−1.12718
$248$	−4.24852	−0.269781
$249$	−10.7340	−0.680241
$250$	−14.0214	−0.886793
$251$	4.74546	0.299531	0.149765	−	0.988722i	$-0.452148\pi$
$251$	4.74546	0.299531	0.149765	+	0.988722i	$0.452148\pi$
$252$	2.07814	0.130910
$253$	−2.66317	−0.167432
$254$	3.20158	0.200885
$255$	−10.6954	−0.669772
$256$	20.3646	1.27279
$257$	14.4146	0.899159	0.449579	−	0.893240i	$-0.351574\pi$
$257$	14.4146	0.899159	0.449579	+	0.893240i	$0.351574\pi$
$258$	−6.77877	−0.422028
$259$	17.0696	1.06065
$260$	2.25969	0.140140
$261$	0	0
$262$	−17.6851	−1.09259
$263$	−1.64890	−0.101676	−0.0508378	−	0.998707i	$-0.516189\pi$
$263$	−1.64890	−0.101676	−0.0508378	+	0.998707i	$0.516189\pi$
$264$	−2.84010	−0.174796
$265$	−8.49708	−0.521972
$266$	−34.1235	−2.09225
$267$	9.91952	0.607065
$268$	−7.80587	−0.476819
$269$	−2.23892	−0.136509	−0.0682547	−	0.997668i	$-0.521743\pi$
$269$	−2.23892	−0.136509	−0.0682547	+	0.997668i	$0.521743\pi$
$270$	6.64111	0.404165
$271$	23.3206	1.41663	0.708314	−	0.705898i	$-0.249456\pi$
$271$	23.3206	1.41663	0.708314	+	0.705898i	$0.249456\pi$
$272$	32.4908	1.97004
$273$	10.7523	0.650761
$274$	−20.0297	−1.21004
$275$	−4.28077	−0.258140
$276$	6.02909	0.362909
$277$	−6.13143	−0.368402	−0.184201	−	0.982889i	$-0.558970\pi$
$277$	−6.13143	−0.368402	−0.184201	+	0.982889i	$0.558970\pi$
$278$	13.9899	0.839059
$279$	−2.08150	−0.124616
$280$	−3.06525	−0.183184
$281$	17.6475	1.05276	0.526381	−	0.850249i	$-0.323548\pi$
$281$	17.6475	1.05276	0.526381	+	0.850249i	$0.323548\pi$
$282$	29.0842	1.73194
$283$	12.7175	0.755974	0.377987	−	0.925811i	$-0.376616\pi$
$283$	12.7175	0.755974	0.377987	+	0.925811i	$0.376616\pi$
$284$	−19.1579	−1.13681
$285$	12.7649	0.756128
$286$	4.04466	0.239166
$287$	17.5551	1.03624
$288$	4.26228	0.251157
$289$	25.7394	1.51408
$290$	0	0
$291$	34.7344	2.03617
$292$	−15.6174	−0.913937
$293$	25.3501	1.48097	0.740483	−	0.672075i	$-0.234597\pi$
$293$	25.3501	1.48097	0.740483	+	0.672075i	$0.234597\pi$
$294$	−3.34420	−0.195038
$295$	1.41695	0.0824981
$296$	10.2368	0.595000
$297$	4.39575	0.255067
$298$	2.28314	0.132259
$299$	6.04655	0.349681
$300$	9.69113	0.559518
$301$	−4.84256	−0.279121
$302$	−11.3084	−0.650728
$303$	4.28705	0.246285
$304$	−38.7776	−2.22405
$305$	−6.46609	−0.370247
$306$	8.40062	0.480232
$307$	−6.70484	−0.382665	−0.191333	−	0.981525i	$-0.561281\pi$
$307$	−6.70484	−0.382665	−0.191333	+	0.981525i	$0.561281\pi$
$308$	2.88105	0.164163
$309$	11.8327	0.673141
$310$	−4.35974	−0.247617
$311$	−7.62827	−0.432560	−0.216280	−	0.976331i	$-0.569392\pi$
$311$	−7.62827	−0.432560	−0.216280	+	0.976331i	$0.569392\pi$
$312$	6.44825	0.365060
$313$	−20.4075	−1.15350	−0.576750	−	0.816921i	$-0.695679\pi$
$313$	−20.4075	−1.15350	−0.576750	+	0.816921i	$0.695679\pi$
$314$	−35.2334	−1.98834
$315$	−1.50177	−0.0846154
$316$	−16.7215	−0.940660
$317$	17.3671	0.975432	0.487716	−	0.873002i	$-0.337830\pi$
$317$	17.3671	0.975432	0.487716	+	0.873002i	$0.337830\pi$
$318$	34.4315	1.93082
$319$	0	0
$320$	0.497755	0.0278254
$321$	−12.8615	−0.717860
$322$	11.6471	0.649068
$323$	−51.0093	−2.83823
$324$	−12.4909	−0.693941
$325$	9.71919	0.539124
$326$	1.27828	0.0707975
$327$	−13.4266	−0.742495
$328$	10.5279	0.581306
$329$	20.7769	1.14547
$330$	−2.91445	−0.160435
$331$	−7.05722	−0.387900	−0.193950	−	0.981011i	$-0.562130\pi$
$331$	−7.05722	−0.387900	−0.193950	+	0.981011i	$0.562130\pi$
$332$	6.53009	0.358385
$333$	5.01535	0.274839
$334$	−36.0533	−1.97275
$335$	5.64094	0.308197
$336$	23.5364	1.28401
$337$	−7.74779	−0.422049	−0.211024	−	0.977481i	$-0.567680\pi$
$337$	−7.74779	−0.422049	−0.211024	+	0.977481i	$0.567680\pi$
$338$	13.9757	0.760178
$339$	−24.8276	−1.34845
$340$	6.50660	0.352870
$341$	−2.88571	−0.156270
$342$	−10.0261	−0.542149
$343$	−19.5738	−1.05688
$344$	−2.90412	−0.156580
$345$	−4.35694	−0.234570
$346$	−12.9899	−0.698344
$347$	−25.4257	−1.36492	−0.682461	−	0.730922i	$-0.739090\pi$
$347$	−25.4257	−1.36492	−0.682461	+	0.730922i	$0.739090\pi$
$348$	0	0
$349$	−21.0704	−1.12787	−0.563936	−	0.825818i	$-0.690714\pi$
$349$	−21.0704	−1.12787	−0.563936	+	0.825818i	$0.690714\pi$
$350$	18.7215	1.00071
$351$	−9.98025	−0.532706
$352$	5.90906	0.314954
$353$	15.1578	0.806768	0.403384	−	0.915031i	$-0.367834\pi$
$353$	15.1578	0.806768	0.403384	+	0.915031i	$0.367834\pi$
$354$	−5.74171	−0.305169
$355$	13.8445	0.734790
$356$	−6.03458	−0.319832
$357$	30.9605	1.63860
$358$	10.0469	0.530993
$359$	4.19544	0.221427	0.110714	−	0.993852i	$-0.464686\pi$
$359$	4.19544	0.221427	0.110714	+	0.993852i	$0.464686\pi$
$360$	−0.900625	−0.0474671
$361$	41.8793	2.20417
$362$	−36.3637	−1.91123
$363$	−1.92907	−0.101250
$364$	−6.54123	−0.342854
$365$	11.2859	0.590733
$366$	26.2016	1.36958
$367$	−6.66570	−0.347947	−0.173973	−	0.984750i	$-0.555661\pi$
$367$	−6.66570	−0.347947	−0.173973	+	0.984750i	$0.555661\pi$
$368$	13.2356	0.689955
$369$	5.15799	0.268514
$370$	10.5047	0.546116
$371$	24.5969	1.27701
$372$	6.53289	0.338715
$373$	20.3265	1.05246	0.526232	−	0.850341i	$-0.323604\pi$
$373$	20.3265	1.05246	0.526232	+	0.850341i	$0.323604\pi$
$374$	11.6463	0.602215
$375$	−15.1833	−0.784064
$376$	12.4601	0.642580
$377$	0	0
$378$	−19.2244	−0.988794
$379$	7.00197	0.359667	0.179833	−	0.983697i	$-0.442444\pi$
$379$	7.00197	0.359667	0.179833	+	0.983697i	$0.442444\pi$
$380$	−7.76559	−0.398366
$381$	3.46688	0.177614
$382$	−10.5908	−0.541874
$383$	29.1043	1.48716	0.743581	−	0.668646i	$-0.233126\pi$
$383$	29.1043	1.48716	0.743581	+	0.668646i	$0.233126\pi$
$384$	20.7810	1.06048
$385$	−2.08200	−0.106109
$386$	−3.31467	−0.168712
$387$	−1.42283	−0.0723265
$388$	−21.1308	−1.07276
$389$	−17.1971	−0.871928	−0.435964	−	0.899964i	$-0.643592\pi$
$389$	−17.1971	−0.871928	−0.435964	+	0.899964i	$0.643592\pi$
$390$	6.61706	0.335068
$391$	17.4106	0.880491
$392$	−1.43270	−0.0723625
$393$	−19.1506	−0.966021
$394$	18.7705	0.945645
$395$	12.0839	0.608006
$396$	0.846503	0.0425384
$397$	−8.40364	−0.421767	−0.210883	−	0.977511i	$-0.567634\pi$
$397$	−8.40364	−0.421767	−0.210883	+	0.977511i	$0.567634\pi$
$398$	17.6086	0.882638
$399$	−36.9512	−1.84987
$400$	21.2749	1.06374
$401$	−21.5339	−1.07535	−0.537677	−	0.843151i	$-0.680698\pi$
$401$	−21.5339	−1.07535	−0.537677	+	0.843151i	$0.680698\pi$
$402$	−22.8580	−1.14005
$403$	6.55181	0.326369
$404$	−2.60805	−0.129755
$405$	9.02662	0.448537
$406$	0	0
$407$	6.95308	0.344651
$408$	18.5673	0.919216
$409$	−26.6309	−1.31681	−0.658405	−	0.752663i	$-0.728769\pi$
$409$	−26.6309	−1.31681	−0.658405	+	0.752663i	$0.728769\pi$
$410$	10.8035	0.533547
$411$	−21.6895	−1.06987
$412$	−7.19850	−0.354645
$413$	−4.10172	−0.201832
$414$	3.42213	0.168188
$415$	−4.71899	−0.231646
$416$	−13.4161	−0.657779
$417$	15.1492	0.741859
$418$	−13.8998	−0.679861
$419$	7.39201	0.361123	0.180562	−	0.983564i	$-0.442208\pi$
$419$	7.39201	0.361123	0.180562	+	0.983564i	$0.442208\pi$
$420$	4.71339	0.229990
$421$	21.6379	1.05456	0.527282	−	0.849690i	$-0.323211\pi$
$421$	21.6379	1.05456	0.527282	+	0.849690i	$0.323211\pi$
$422$	35.0326	1.70536
$423$	6.10463	0.296817
$424$	14.7510	0.716370
$425$	27.9857	1.35750
$426$	−56.1001	−2.71806
$427$	18.7177	0.905813
$428$	7.82436	0.378205
$429$	4.37983	0.211460
$430$	−2.98015	−0.143715
$431$	14.5472	0.700715	0.350358	−	0.936616i	$-0.386060\pi$
$431$	14.5472	0.700715	0.350358	+	0.936616i	$0.386060\pi$
$432$	−21.8463	−1.05108
$433$	0.496922	0.0238806	0.0119403	−	0.999929i	$-0.496199\pi$
$433$	0.496922	0.0238806	0.0119403	+	0.999929i	$0.496199\pi$
$434$	12.6204	0.605797
$435$	0	0
$436$	8.16816	0.391184
$437$	−20.7794	−0.994015
$438$	−45.7324	−2.18518
$439$	−37.5541	−1.79236	−0.896180	−	0.443691i	$-0.853669\pi$
$439$	−37.5541	−1.79236	−0.896180	+	0.443691i	$0.853669\pi$
$440$	−1.24859	−0.0595242
$441$	−0.701932	−0.0334253
$442$	−26.4421	−1.25772
$443$	−31.0408	−1.47479	−0.737396	−	0.675461i	$-0.763945\pi$
$443$	−31.0408	−1.47479	−0.737396	+	0.675461i	$0.763945\pi$
$444$	−15.7409	−0.747031
$445$	4.36091	0.206727
$446$	−27.1295	−1.28462
$447$	2.47233	0.116937
$448$	−1.44088	−0.0680750
$449$	23.4475	1.10655	0.553277	−	0.832997i	$-0.313377\pi$
$449$	23.4475	1.10655	0.553277	+	0.832997i	$0.313377\pi$
$450$	5.50071	0.259306
$451$	7.15083	0.336720
$452$	15.1040	0.710432
$453$	−12.2455	−0.575345
$454$	10.6015	0.497552
$455$	4.72704	0.221607
$456$	−22.1599	−1.03773
$457$	6.53081	0.305498	0.152749	−	0.988265i	$-0.451187\pi$
$457$	6.53081	0.305498	0.152749	+	0.988265i	$0.451187\pi$
$458$	−33.6433	−1.57205
$459$	−28.7374	−1.34135
$460$	2.65057	0.123583
$461$	−33.9899	−1.58307	−0.791535	−	0.611124i	$-0.790717\pi$
$461$	−33.9899	−1.58307	−0.791535	+	0.611124i	$0.790717\pi$
$462$	8.43660	0.392506
$463$	9.24762	0.429773	0.214887	−	0.976639i	$-0.431062\pi$
$463$	9.24762	0.429773	0.214887	+	0.976639i	$0.431062\pi$
$464$	0	0
$465$	−4.72102	−0.218932
$466$	35.9549	1.66558
$467$	27.5893	1.27668	0.638341	−	0.769754i	$-0.279621\pi$
$467$	27.5893	1.27668	0.638341	+	0.769754i	$0.279621\pi$
$468$	−1.92193	−0.0888412
$469$	−16.3291	−0.754008
$470$	12.7863	0.589787
$471$	−38.1531	−1.75800
$472$	−2.45983	−0.113223
$473$	−1.97256	−0.0906982
$474$	−48.9658	−2.24907
$475$	−33.4008	−1.53253
$476$	−18.8350	−0.863300
$477$	7.22701	0.330902
$478$	17.9346	0.820308
$479$	−16.3173	−0.745557	−0.372778	−	0.927920i	$-0.621595\pi$
$479$	−16.3173	−0.745557	−0.372778	+	0.927920i	$0.621595\pi$
$480$	9.66721	0.441246
$481$	−15.7865	−0.719803
$482$	43.0384	1.96035
$483$	12.6123	0.573877
$484$	1.17356	0.0533436
$485$	15.2703	0.693387
$486$	−13.0849	−0.593544
$487$	22.8961	1.03752	0.518760	−	0.854920i	$-0.326394\pi$
$487$	22.8961	1.03752	0.518760	+	0.854920i	$0.326394\pi$
$488$	11.2251	0.508139
$489$	1.38421	0.0625961
$490$	−1.47021	−0.0664173
$491$	−22.7150	−1.02511	−0.512556	−	0.858654i	$-0.671301\pi$
$491$	−22.7150	−1.02511	−0.512556	+	0.858654i	$0.671301\pi$
$492$	−16.1886	−0.729839
$493$	0	0
$494$	31.5585	1.41989
$495$	−0.611729	−0.0274952
$496$	14.3416	0.643958
$497$	−40.0764	−1.79767
$498$	19.1221	0.856882
$499$	2.60721	0.116715	0.0583574	−	0.998296i	$-0.481414\pi$
$499$	2.60721	0.116715	0.0583574	+	0.998296i	$0.481414\pi$
$500$	9.23684	0.413084
$501$	−39.0409	−1.74422
$502$	−8.45379	−0.377311
$503$	−9.64698	−0.430137	−0.215069	−	0.976599i	$-0.568998\pi$
$503$	−9.64698	−0.430137	−0.215069	+	0.976599i	$0.568998\pi$
$504$	2.60708	0.116129
$505$	1.88472	0.0838687
$506$	4.74430	0.210910
$507$	15.1338	0.672116
$508$	−2.10909	−0.0935759
$509$	8.80063	0.390081	0.195040	−	0.980795i	$-0.437516\pi$
$509$	8.80063	0.390081	0.195040	+	0.980795i	$0.437516\pi$
$510$	19.0533	0.843695
$511$	−32.6700	−1.44523
$512$	−14.7334	−0.651128
$513$	34.2979	1.51429
$514$	−25.6789	−1.13265
$515$	5.20202	0.229229
$516$	4.46563	0.196588
$517$	8.46322	0.372212
$518$	−30.4086	−1.33608
$519$	−14.0664	−0.617445
$520$	2.83484	0.124316
$521$	−36.8285	−1.61349	−0.806744	−	0.590901i	$-0.798772\pi$
$521$	−36.8285	−1.61349	−0.806744	+	0.590901i	$0.798772\pi$
$522$	0	0
$523$	24.3453	1.06455	0.532273	−	0.846573i	$-0.321338\pi$
$523$	24.3453	1.06455	0.532273	+	0.846573i	$0.321338\pi$
$524$	11.6504	0.508949
$525$	20.2729	0.884781
$526$	2.93743	0.128078
$527$	18.8654	0.821791
$528$	9.58724	0.417231
$529$	−15.9075	−0.691632
$530$	15.1371	0.657514
$531$	−1.20516	−0.0522994
$532$	22.4794	0.974607
$533$	−16.2355	−0.703237
$534$	−17.6711	−0.764704
$535$	−5.65430	−0.244457
$536$	−9.79269	−0.422980
$537$	10.8794	0.469481
$538$	3.98852	0.171957
$539$	−0.973131	−0.0419157
$540$	−4.37494	−0.188268
$541$	−17.6971	−0.760856	−0.380428	−	0.924810i	$-0.624223\pi$
$541$	−17.6971	−0.760856	−0.380428	+	0.924810i	$0.624223\pi$
$542$	−41.5445	−1.78449
$543$	−39.3770	−1.68983
$544$	−38.6307	−1.65628
$545$	−5.90275	−0.252846
$546$	−19.1547	−0.819747
$547$	9.86507	0.421800	0.210900	−	0.977508i	$-0.432361\pi$
$547$	9.86507	0.421800	0.210900	+	0.977508i	$0.432361\pi$
$548$	13.1949	0.563659
$549$	5.49959	0.234717
$550$	7.62597	0.325172
$551$	0	0
$552$	7.56366	0.321931
$553$	−34.9798	−1.48749
$554$	10.9228	0.464066
$555$	11.3752	0.482852
$556$	−9.21608	−0.390849
$557$	−15.7332	−0.666636	−0.333318	−	0.942814i	$-0.608168\pi$
$557$	−15.7332	−0.666636	−0.333318	+	0.942814i	$0.608168\pi$
$558$	3.70809	0.156976
$559$	4.47856	0.189423
$560$	10.3473	0.437253
$561$	12.6114	0.532453
$562$	−31.4381	−1.32614
$563$	42.5873	1.79484	0.897420	−	0.441177i	$-0.145439\pi$
$563$	42.5873	1.79484	0.897420	+	0.441177i	$0.145439\pi$
$564$	−19.1597	−0.806769
$565$	−10.9150	−0.459196
$566$	−22.6555	−0.952281
$567$	−26.1298	−1.09735
$568$	−24.0341	−1.00845
$569$	39.4283	1.65292	0.826459	−	0.562997i	$-0.190352\pi$
$569$	39.4283	1.65292	0.826459	+	0.562997i	$0.190352\pi$
$570$	−22.7400	−0.952475
$571$	40.4567	1.69306	0.846530	−	0.532342i	$-0.178688\pi$
$571$	40.4567	1.69306	0.846530	+	0.532342i	$0.178688\pi$
$572$	−2.66449	−0.111408
$573$	−11.4685	−0.479102
$574$	−31.2734	−1.30533
$575$	11.4004	0.475430
$576$	−0.423355	−0.0176398
$577$	−18.6305	−0.775597	−0.387798	−	0.921744i	$-0.626764\pi$
$577$	−18.6305	−0.775597	−0.387798	+	0.921744i	$0.626764\pi$
$578$	−45.8535	−1.90725
$579$	−3.58934	−0.149168
$580$	0	0
$581$	13.6603	0.566724
$582$	−61.8775	−2.56491
$583$	10.0192	0.414955
$584$	−19.5924	−0.810740
$585$	1.38889	0.0574235
$586$	−45.1598	−1.86554
$587$	−28.2511	−1.16605	−0.583024	−	0.812455i	$-0.698130\pi$
$587$	−28.2511	−1.16605	−0.583024	+	0.812455i	$0.698130\pi$
$588$	2.20305	0.0908522
$589$	−22.5158	−0.927747
$590$	−2.52423	−0.103921
$591$	20.3260	0.836098
$592$	−34.5560	−1.42024
$593$	−21.8860	−0.898749	−0.449374	−	0.893344i	$-0.648353\pi$
$593$	−21.8860	−0.898749	−0.449374	+	0.893344i	$0.648353\pi$
$594$	−7.83080	−0.321302
$595$	13.6112	0.558003
$596$	−1.50405	−0.0616084
$597$	19.0677	0.780391
$598$	−10.7716	−0.440484
$599$	−4.19515	−0.171409	−0.0857046	−	0.996321i	$-0.527314\pi$
$599$	−4.19515	−0.171409	−0.0857046	+	0.996321i	$0.527314\pi$
$600$	12.1578	0.496340
$601$	−27.4535	−1.11985	−0.559927	−	0.828542i	$-0.689171\pi$
$601$	−27.4535	−1.11985	−0.559927	+	0.828542i	$0.689171\pi$
$602$	8.62678	0.351601
$603$	−4.79778	−0.195381
$604$	7.44962	0.303121
$605$	−0.848076	−0.0344792
$606$	−7.63716	−0.310239
$607$	−33.8834	−1.37529	−0.687643	−	0.726049i	$-0.741355\pi$
$607$	−33.8834	−1.37529	−0.687643	+	0.726049i	$0.741355\pi$
$608$	46.1055	1.86983
$609$	0	0
$610$	11.5190	0.466391
$611$	−19.2152	−0.777363
$612$	−5.53405	−0.223701
$613$	3.94951	0.159519	0.0797597	−	0.996814i	$-0.474585\pi$
$613$	3.94951	0.159519	0.0797597	+	0.996814i	$0.474585\pi$
$614$	11.9443	0.482034
$615$	11.6988	0.471739
$616$	3.61436	0.145627
$617$	−17.3211	−0.697320	−0.348660	−	0.937249i	$-0.613363\pi$
$617$	−17.3211	−0.697320	−0.348660	+	0.937249i	$0.613363\pi$
$618$	−21.0794	−0.847939
$619$	−26.6581	−1.07148	−0.535740	−	0.844383i	$-0.679967\pi$
$619$	−26.6581	−1.07148	−0.535740	+	0.844383i	$0.679967\pi$
$620$	2.87205	0.115344
$621$	−11.7066	−0.469770
$622$	13.5894	0.544884
$623$	−12.6237	−0.505760
$624$	−21.7672	−0.871385
$625$	14.7288	0.589152
$626$	36.3549	1.45303
$627$	−15.0516	−0.601103
$628$	23.2106	0.926204
$629$	−45.4560	−1.81245
$630$	2.67533	0.106588
$631$	29.0215	1.15533	0.577663	−	0.816275i	$-0.303965\pi$
$631$	29.0215	1.15533	0.577663	+	0.816275i	$0.303965\pi$
$632$	−20.9776	−0.834446
$633$	37.9357	1.50781
$634$	−30.9385	−1.22873
$635$	1.52414	0.0604838
$636$	−22.6823	−0.899413
$637$	2.20943	0.0875408
$638$	0	0
$639$	−11.7751	−0.465818
$640$	9.13593	0.361130
$641$	38.1853	1.50823	0.754114	−	0.656743i	$-0.228066\pi$
$641$	38.1853	1.50823	0.754114	+	0.656743i	$0.228066\pi$
$642$	22.9121	0.904269
$643$	−47.9079	−1.88930	−0.944652	−	0.328075i	$-0.893600\pi$
$643$	−47.9079	−1.88930	−0.944652	+	0.328075i	$0.893600\pi$
$644$	−7.67272	−0.302348
$645$	−3.22710	−0.127067
$646$	90.8704	3.57525
$647$	−0.128175	−0.00503907	−0.00251954	−	0.999997i	$-0.500802\pi$
$647$	−0.128175	−0.00503907	−0.00251954	+	0.999997i	$0.500802\pi$
$648$	−15.6702	−0.615585
$649$	−1.67078	−0.0655840
$650$	−17.3142	−0.679120
$651$	13.6662	0.535619
$652$	−0.842089	−0.0329788
$653$	36.1102	1.41310	0.706550	−	0.707663i	$-0.250251\pi$
$653$	36.1102	1.41310	0.706550	+	0.707663i	$0.250251\pi$
$654$	23.9189	0.935302
$655$	−8.41918	−0.328965
$656$	−35.5388	−1.38756
$657$	−9.59902	−0.374493
$658$	−37.0131	−1.44292
$659$	−30.0440	−1.17035	−0.585173	−	0.810908i	$-0.698974\pi$
$659$	−30.0440	−1.17035	−0.585173	+	0.810908i	$0.698974\pi$
$660$	1.91994	0.0747336
$661$	35.5408	1.38238	0.691188	−	0.722675i	$-0.257088\pi$
$661$	35.5408	1.38238	0.691188	+	0.722675i	$0.257088\pi$
$662$	12.5721	0.488628
$663$	−28.6333	−1.11202
$664$	8.19218	0.317918
$665$	−16.2448	−0.629948
$666$	−8.93458	−0.346208
$667$	0	0
$668$	23.7507	0.918942
$669$	−29.3776	−1.13580
$670$	−10.0490	−0.388228
$671$	7.62442	0.294337
$672$	−27.9841	−1.07951
$673$	17.2593	0.665298	0.332649	−	0.943051i	$-0.392058\pi$
$673$	17.2593	0.665298	0.332649	+	0.943051i	$0.392058\pi$
$674$	13.8023	0.531644
$675$	−18.8172	−0.724273
$676$	−9.20672	−0.354105
$677$	−40.7109	−1.56465	−0.782324	−	0.622871i	$-0.785966\pi$
$677$	−40.7109	−1.56465	−0.782324	+	0.622871i	$0.785966\pi$
$678$	44.2291	1.69861
$679$	−44.2036	−1.69638
$680$	8.16271	0.313026
$681$	11.4800	0.439914
$682$	5.14074	0.196849
$683$	3.01801	0.115481	0.0577404	−	0.998332i	$-0.481610\pi$
$683$	3.01801	0.115481	0.0577404	+	0.998332i	$0.481610\pi$
$684$	6.60486	0.252543
$685$	−9.53536	−0.364327
$686$	34.8697	1.33133
$687$	−36.4311	−1.38993
$688$	9.80336	0.373750
$689$	−22.7480	−0.866631
$690$	7.76167	0.295482
$691$	−32.0386	−1.21881	−0.609403	−	0.792860i	$-0.708591\pi$
$691$	−32.0386	−1.21881	−0.609403	+	0.792860i	$0.708591\pi$
$692$	8.55734	0.325301
$693$	1.77080	0.0672672
$694$	45.2945	1.71936
$695$	6.66003	0.252629
$696$	0	0
$697$	−46.7488	−1.77074
$698$	37.5358	1.42075
$699$	38.9344	1.47263
$700$	−12.3331	−0.466147
$701$	−34.4196	−1.30001	−0.650005	−	0.759930i	$-0.725233\pi$
$701$	−34.4196	−1.30001	−0.650005	+	0.759930i	$0.725233\pi$
$702$	17.7793	0.671037
$703$	54.2515	2.04613
$704$	−0.586923	−0.0221205
$705$	13.8458	0.521464
$706$	−27.0028	−1.01626
$707$	−5.45578	−0.205186
$708$	3.78245	0.142153
$709$	−44.7279	−1.67979	−0.839896	−	0.542747i	$-0.817384\pi$
$709$	−44.7279	−1.67979	−0.839896	+	0.542747i	$0.817384\pi$
$710$	−24.6633	−0.925596
$711$	−10.2777	−0.385443
$712$	−7.57055	−0.283719
$713$	7.68513	0.287810
$714$	−55.1546	−2.06411
$715$	1.92550	0.0720096
$716$	−6.61854	−0.247346
$717$	19.4207	0.725280
$718$	−7.47397	−0.278926
$719$	18.8534	0.703115	0.351557	−	0.936166i	$-0.385652\pi$
$719$	18.8534	0.703115	0.351557	+	0.936166i	$0.385652\pi$
$720$	3.04022	0.113302
$721$	−15.0586	−0.560810
$722$	−74.6058	−2.77654
$723$	46.6048	1.73325
$724$	23.9552	0.890288
$725$	0	0
$726$	3.43654	0.127542
$727$	18.6087	0.690158	0.345079	−	0.938574i	$-0.387852\pi$
$727$	18.6087	0.690158	0.345079	+	0.938574i	$0.387852\pi$
$728$	−8.20616	−0.304140
$729$	17.7617	0.657841
$730$	−20.1053	−0.744131
$731$	12.8957	0.476963
$732$	−17.2607	−0.637976
$733$	21.9510	0.810777	0.405388	−	0.914145i	$-0.367136\pi$
$733$	21.9510	0.810777	0.405388	+	0.914145i	$0.367136\pi$
$734$	11.8746	0.438300
$735$	−1.59204	−0.0587233
$736$	−15.7368	−0.580067
$737$	−6.65145	−0.245009
$738$	−9.18869	−0.338240
$739$	22.2525	0.818573	0.409286	−	0.912406i	$-0.365778\pi$
$739$	22.2525	0.818573	0.409286	+	0.912406i	$0.365778\pi$
$740$	−6.92017	−0.254391
$741$	34.1737	1.25540
$742$	−43.8182	−1.60862
$743$	−2.12726	−0.0780417	−0.0390208	−	0.999238i	$-0.512424\pi$
$743$	−2.12726	−0.0780417	−0.0390208	+	0.999238i	$0.512424\pi$
$744$	8.19570	0.300469
$745$	1.08691	0.0398213
$746$	−36.2105	−1.32576
$747$	4.01364	0.146851
$748$	−7.67219	−0.280523
$749$	16.3678	0.598066
$750$	27.0483	0.987665
$751$	48.9374	1.78575	0.892876	−	0.450303i	$-0.148684\pi$
$751$	48.9374	1.78575	0.892876	+	0.450303i	$0.148684\pi$
$752$	−42.0612	−1.53381
$753$	−9.15433	−0.333602
$754$	0	0
$755$	−5.38350	−0.195926
$756$	12.6644	0.460599
$757$	28.7611	1.04534	0.522671	−	0.852535i	$-0.324936\pi$
$757$	28.7611	1.04534	0.522671	+	0.852535i	$0.324936\pi$
$758$	−12.4736	−0.453063
$759$	5.13744	0.186477
$760$	−9.74215	−0.353385
$761$	13.7023	0.496709	0.248354	−	0.968669i	$-0.420110\pi$
$761$	13.7023	0.496709	0.248354	+	0.968669i	$0.420110\pi$
$762$	−6.17607	−0.223736
$763$	17.0870	0.618590
$764$	6.97689	0.252415
$765$	3.99920	0.144591
$766$	−51.8479	−1.87334
$767$	3.79340	0.136972
$768$	−39.2847	−1.41756
$769$	30.1249	1.08633	0.543166	−	0.839625i	$-0.317225\pi$
$769$	30.1249	1.08633	0.543166	+	0.839625i	$0.317225\pi$
$770$	3.70898	0.133662
$771$	−27.8068	−1.00144
$772$	2.18359	0.0785892
$773$	−31.1971	−1.12208	−0.561041	−	0.827788i	$-0.689599\pi$
$773$	−31.1971	−1.12208	−0.561041	+	0.827788i	$0.689599\pi$
$774$	2.53470	0.0911079
$775$	12.3530	0.443735
$776$	−26.5092	−0.951626
$777$	−32.9284	−1.18130
$778$	30.6357	1.09834
$779$	55.7945	1.99904
$780$	−4.35910	−0.156081
$781$	−16.3246	−0.584140
$782$	−31.0160	−1.10913
$783$	0	0
$784$	4.83634	0.172727
$785$	−16.7732	−0.598662
$786$	34.1158	1.21687
$787$	−16.7312	−0.596404	−0.298202	−	0.954503i	$-0.596387\pi$
$787$	−16.7312	−0.596404	−0.298202	+	0.954503i	$0.596387\pi$
$788$	−12.3654	−0.440499
$789$	3.18085	0.113241
$790$	−21.5268	−0.765889
$791$	31.5961	1.12343
$792$	1.06196	0.0377352
$793$	−17.3107	−0.614722
$794$	14.9707	0.531289
$795$	16.3915	0.581346
$796$	−11.5999	−0.411149
$797$	9.08294	0.321734	0.160867	−	0.986976i	$-0.448571\pi$
$797$	9.08294	0.321734	0.160867	+	0.986976i	$0.448571\pi$
$798$	65.8267	2.33024
$799$	−55.3287	−1.95739
$800$	−25.2953	−0.894323
$801$	−3.70908	−0.131054
$802$	38.3616	1.35460
$803$	−13.3077	−0.469618
$804$	15.0581	0.531057
$805$	5.54472	0.195426
$806$	−11.6717	−0.411119
$807$	4.31904	0.152037
$808$	−3.27187	−0.115104
$809$	31.8513	1.11983	0.559915	−	0.828550i	$-0.310834\pi$
$809$	31.8513	1.11983	0.559915	+	0.828550i	$0.310834\pi$
$810$	−16.0805	−0.565010
$811$	−9.46359	−0.332312	−0.166156	−	0.986100i	$-0.553135\pi$
$811$	−9.46359	−0.332312	−0.166156	+	0.986100i	$0.553135\pi$
$812$	0	0
$813$	−44.9871	−1.57777
$814$	−12.3866	−0.434148
$815$	0.608539	0.0213162
$816$	−62.6770	−2.19413
$817$	−15.3909	−0.538459
$818$	47.4415	1.65875
$819$	−4.02048	−0.140487
$820$	−7.11699	−0.248536
$821$	45.9200	1.60262	0.801310	−	0.598249i	$-0.204137\pi$
$821$	45.9200	1.60262	0.801310	+	0.598249i	$0.204137\pi$
$822$	38.6388	1.34768
$823$	−34.5510	−1.20437	−0.602187	−	0.798355i	$-0.705704\pi$
$823$	−34.5510	−1.20437	−0.602187	+	0.798355i	$0.705704\pi$
$824$	−9.03073	−0.314600
$825$	8.25790	0.287503
$826$	7.30700	0.254243
$827$	5.54741	0.192902	0.0964512	−	0.995338i	$-0.469251\pi$
$827$	5.54741	0.192902	0.0964512	+	0.995338i	$0.469251\pi$
$828$	−2.25438	−0.0783452
$829$	11.7610	0.408476	0.204238	−	0.978921i	$-0.434528\pi$
$829$	11.7610	0.408476	0.204238	+	0.978921i	$0.434528\pi$
$830$	8.40664	0.291799
$831$	11.8280	0.410307
$832$	1.33257	0.0461985
$833$	6.36188	0.220426
$834$	−26.9875	−0.934501
$835$	−17.1635	−0.593968
$836$	9.15671	0.316691
$837$	−12.6849	−0.438453
$838$	−13.1685	−0.454898
$839$	21.8446	0.754159	0.377080	−	0.926181i	$-0.376928\pi$
$839$	21.8446	0.754159	0.377080	+	0.926181i	$0.376928\pi$
$840$	5.91309	0.204021
$841$	0	0
$842$	−38.5467	−1.32841
$843$	−34.0433	−1.17251
$844$	−23.0783	−0.794389
$845$	6.65327	0.228880
$846$	−10.8751	−0.373893
$847$	2.45497	0.0843537
$848$	−49.7944	−1.70995
$849$	−24.5329	−0.841966
$850$	−49.8550	−1.71001
$851$	−18.5172	−0.634762
$852$	36.9569	1.26612
$853$	−18.0234	−0.617110	−0.308555	−	0.951206i	$-0.599845\pi$
$853$	−18.0234	−0.617110	−0.308555	+	0.951206i	$0.599845\pi$
$854$	−33.3446	−1.14103
$855$	−4.77302	−0.163234
$856$	9.81588	0.335500
$857$	36.3010	1.24002	0.620009	−	0.784595i	$-0.287129\pi$
$857$	36.3010	1.24002	0.620009	+	0.784595i	$0.287129\pi$
$858$	−7.80243	−0.266371
$859$	−4.89319	−0.166953	−0.0834767	−	0.996510i	$-0.526602\pi$
$859$	−4.89319	−0.166953	−0.0834767	+	0.996510i	$0.526602\pi$
$860$	1.96322	0.0669453
$861$	−33.8650	−1.15411
$862$	−25.9151	−0.882673
$863$	−3.46670	−0.118008	−0.0590038	−	0.998258i	$-0.518792\pi$
$863$	−3.46670	−0.118008	−0.0590038	+	0.998258i	$0.518792\pi$
$864$	25.9747	0.883678
$865$	−6.18399	−0.210262
$866$	−0.885241	−0.0300817
$867$	−49.6532	−1.68631
$868$	−8.31387	−0.282191
$869$	−14.2486	−0.483350
$870$	0	0
$871$	15.1017	0.511701
$872$	10.2472	0.347013
$873$	−12.9878	−0.439570
$874$	37.0175	1.25213
$875$	19.3226	0.653222
$876$	30.1270	1.01790
$877$	18.5138	0.625168	0.312584	−	0.949890i	$-0.398805\pi$
$877$	18.5138	0.625168	0.312584	+	0.949890i	$0.398805\pi$
$878$	66.9007	2.25779
$879$	−48.9021	−1.64943
$880$	4.21484	0.142082
$881$	−34.6831	−1.16850	−0.584252	−	0.811572i	$-0.698612\pi$
$881$	−34.6831	−1.16850	−0.584252	+	0.811572i	$0.698612\pi$
$882$	1.25046	0.0421050
$883$	−51.6039	−1.73661	−0.868305	−	0.496030i	$-0.834791\pi$
$883$	−51.6039	−1.73661	−0.868305	+	0.496030i	$0.834791\pi$
$884$	17.4192	0.585871
$885$	−2.73340	−0.0918822
$886$	55.2975	1.85776
$887$	−42.4340	−1.42479	−0.712397	−	0.701777i	$-0.752390\pi$
$887$	−42.4340	−1.42479	−0.712397	+	0.701777i	$0.752390\pi$
$888$	−19.7474	−0.662680
$889$	−4.41201	−0.147974
$890$	−7.76874	−0.260409
$891$	−10.6436	−0.356576
$892$	17.8720	0.598398
$893$	66.0344	2.20976
$894$	−4.40433	−0.147303
$895$	4.78291	0.159875
$896$	−26.4462	−0.883507
$897$	−11.6642	−0.389457
$898$	−41.7704	−1.39390
$899$	0	0
$900$	−3.62368	−0.120789
$901$	−65.5012	−2.18216
$902$	−12.7388	−0.424157
$903$	9.34164	0.310870
$904$	18.9484	0.630214
$905$	−17.3113	−0.575447
$906$	21.8148	0.724748
$907$	−49.1581	−1.63227	−0.816133	−	0.577864i	$-0.803887\pi$
$907$	−49.1581	−1.63227	−0.816133	+	0.577864i	$0.803887\pi$
$908$	−6.98390	−0.231769
$909$	−1.60300	−0.0531683
$910$	−8.42098	−0.279153
$911$	30.5305	1.01152	0.505760	−	0.862674i	$-0.331212\pi$
$911$	30.5305	1.01152	0.505760	+	0.862674i	$0.331212\pi$
$912$	74.8046	2.47703
$913$	5.56435	0.184153
$914$	−11.6343	−0.384829
$915$	12.4735	0.412363
$916$	22.1630	0.732288
$917$	24.3714	0.804815
$918$	51.1942	1.68966
$919$	−37.8847	−1.24970	−0.624850	−	0.780745i	$-0.714840\pi$
$919$	−37.8847	−1.24970	−0.624850	+	0.780745i	$0.714840\pi$
$920$	3.32521	0.109629
$921$	12.9341	0.426193
$922$	60.5513	1.99415
$923$	37.0639	1.21997
$924$	−5.55775	−0.182836
$925$	−29.7645	−0.978651
$926$	−16.4742	−0.541374
$927$	−4.42447	−0.145319
$928$	0	0
$929$	31.0388	1.01835	0.509176	−	0.860663i	$-0.329950\pi$
$929$	31.0388	1.01835	0.509176	+	0.860663i	$0.329950\pi$
$930$	8.41025	0.275783
$931$	−7.59287	−0.248846
$932$	−23.6859	−0.775857
$933$	14.7155	0.481763
$934$	−49.1490	−1.60820
$935$	5.54433	0.181319
$936$	−2.41111	−0.0788097
$937$	−14.1913	−0.463608	−0.231804	−	0.972762i	$-0.574463\pi$
$937$	−14.1913	−0.463608	−0.231804	+	0.972762i	$0.574463\pi$
$938$	29.0895	0.949804
$939$	39.3675	1.28471
$940$	−8.42317	−0.274733
$941$	−39.6260	−1.29177	−0.645885	−	0.763434i	$-0.723512\pi$
$941$	−39.6260	−1.29177	−0.645885	+	0.763434i	$0.723512\pi$
$942$	67.9678	2.21451
$943$	−19.0439	−0.620154
$944$	8.30359	0.270259
$945$	−9.15195	−0.297713
$946$	3.51401	0.114250
$947$	−43.2822	−1.40648	−0.703240	−	0.710952i	$-0.748264\pi$
$947$	−43.2822	−1.40648	−0.703240	+	0.710952i	$0.748264\pi$
$948$	32.2570	1.04766
$949$	30.2142	0.980796
$950$	59.5017	1.93049
$951$	−33.5023	−1.08639
$952$	−23.6290	−0.765821
$953$	1.66999	0.0540964	0.0270482	−	0.999634i	$-0.491389\pi$
$953$	1.66999	0.0540964	0.0270482	+	0.999634i	$0.491389\pi$
$954$	−12.8746	−0.416829
$955$	−5.04187	−0.163151
$956$	−11.8147	−0.382114
$957$	0	0
$958$	29.0684	0.939159
$959$	27.6025	0.891330
$960$	−0.960205	−0.0309905
$961$	−22.6727	−0.731377
$962$	28.1228	0.906717
$963$	4.80914	0.154972
$964$	−28.3523	−0.913165
$965$	−1.57798	−0.0507970
$966$	−22.4681	−0.722899
$967$	54.4782	1.75190	0.875950	−	0.482401i	$-0.160235\pi$
$967$	54.4782	1.75190	0.875950	+	0.482401i	$0.160235\pi$
$968$	1.47226	0.0473203
$969$	98.4005	3.16108
$970$	−27.2032	−0.873442
$971$	−51.2275	−1.64397	−0.821984	−	0.569511i	$-0.807133\pi$
$971$	−51.2275	−1.64397	−0.821984	+	0.569511i	$0.807133\pi$
$972$	8.61991	0.276484
$973$	−19.2791	−0.618060
$974$	−40.7882	−1.30694
$975$	−18.7490	−0.600449
$976$	−37.8924	−1.21291
$977$	−43.7917	−1.40102	−0.700510	−	0.713642i	$-0.747044\pi$
$977$	−43.7917	−1.40102	−0.700510	+	0.713642i	$0.747044\pi$
$978$	−2.46590	−0.0788507
$979$	−5.14212	−0.164343
$980$	0.968526	0.0309384
$981$	5.02045	0.160291
$982$	40.4655	1.29131
$983$	−36.5283	−1.16507	−0.582535	−	0.812805i	$-0.697939\pi$
$983$	−36.5283	−1.16507	−0.582535	+	0.812805i	$0.697939\pi$
$984$	−20.3091	−0.647429
$985$	8.93589	0.284721
$986$	0	0
$987$	−40.0802	−1.27577
$988$	−20.7897	−0.661408
$989$	5.25325	0.167044
$990$	1.08976	0.0346349
$991$	−14.8345	−0.471232	−0.235616	−	0.971846i	$-0.575711\pi$
$991$	−14.8345	−0.471232	−0.235616	+	0.971846i	$0.575711\pi$
$992$	−17.0518	−0.541396
$993$	13.6139	0.432023
$994$	71.3940	2.26448
$995$	8.38274	0.265751
$996$	−12.5970	−0.399151
$997$	49.8939	1.58015	0.790077	−	0.613007i	$-0.210040\pi$
$997$	49.8939	1.58015	0.790077	+	0.613007i	$0.210040\pi$
$998$	−4.64461	−0.147023
$999$	30.5640	0.967002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.s.1.3	✓	18
29.28	even	2		9251.2.a.t.1.16	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.3	✓	18	1.1	even	1	trivial
9251.2.a.t.1.16	yes	18	29.28	even	2

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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-1.78145 q^{2} -1.92907 q^{3} +1.17356 q^{4} -0.848076 q^{5} +3.43654 q^{6} +2.45497 q^{7} +1.47226 q^{8} +0.721313 q^{9} +O(q^{10})\)	\(q-1.78145 q^{2} -1.92907 q^{3} +1.17356 q^{4} -0.848076 q^{5} +3.43654 q^{6} +2.45497 q^{7} +1.47226 q^{8} +0.721313 q^{9} +1.51080 q^{10} +1.00000 q^{11} -2.26388 q^{12} -2.27043 q^{13} -4.37340 q^{14} +1.63600 q^{15} -4.96988 q^{16} -6.53754 q^{17} -1.28498 q^{18} +7.80252 q^{19} -0.995267 q^{20} -4.73581 q^{21} -1.78145 q^{22} -2.66317 q^{23} -2.84010 q^{24} -4.28077 q^{25} +4.04466 q^{26} +4.39575 q^{27} +2.88105 q^{28} -2.91445 q^{30} -2.88571 q^{31} +5.90906 q^{32} -1.92907 q^{33} +11.6463 q^{34} -2.08200 q^{35} +0.846503 q^{36} +6.95308 q^{37} -13.8998 q^{38} +4.37983 q^{39} -1.24859 q^{40} +7.15083 q^{41} +8.43660 q^{42} -1.97256 q^{43} +1.17356 q^{44} -0.611729 q^{45} +4.74430 q^{46} +8.46322 q^{47} +9.58724 q^{48} -0.973131 q^{49} +7.62597 q^{50} +12.6114 q^{51} -2.66449 q^{52} +10.0192 q^{53} -7.83080 q^{54} -0.848076 q^{55} +3.61436 q^{56} -15.0516 q^{57} -1.67078 q^{59} +1.91994 q^{60} +7.62442 q^{61} +5.14074 q^{62} +1.77080 q^{63} -0.586923 q^{64} +1.92550 q^{65} +3.43654 q^{66} -6.65145 q^{67} -7.67219 q^{68} +5.13744 q^{69} +3.70898 q^{70} -16.3246 q^{71} +1.06196 q^{72} -13.3077 q^{73} -12.3866 q^{74} +8.25790 q^{75} +9.15671 q^{76} +2.45497 q^{77} -7.80243 q^{78} -14.2486 q^{79} +4.21484 q^{80} -10.6436 q^{81} -12.7388 q^{82} +5.56435 q^{83} -5.55775 q^{84} +5.54433 q^{85} +3.51401 q^{86} +1.47226 q^{88} -5.14212 q^{89} +1.08976 q^{90} -5.57384 q^{91} -3.12539 q^{92} +5.56674 q^{93} -15.0768 q^{94} -6.61713 q^{95} -11.3990 q^{96} -18.0058 q^{97} +1.73358 q^{98} +0.721313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q - 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 9 * q^9	\( 18 q - 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 9 q^{9} - 5 q^{10} + 18 q^{11} - 3 q^{12} - 15 q^{13} + 12 q^{14} - 27 q^{15} + 4 q^{16} + 6 q^{17} - 12 q^{18} + 11 q^{19} - 18 q^{20} + 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} - 10 q^{26} + 6 q^{27} - 6 q^{28} - 19 q^{30} - 8 q^{31} - 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} + 9 q^{37} - 3 q^{38} - 8 q^{39} - 36 q^{40} + 3 q^{41} + 28 q^{42} + 13 q^{43} + 12 q^{44} - q^{45} + 37 q^{46} - q^{47} + 46 q^{48} - 23 q^{49} + 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} - 6 q^{55} + 10 q^{56} + 14 q^{57} - 16 q^{59} + 3 q^{60} - 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} - q^{66} + 9 q^{67} + 5 q^{68} - 47 q^{69} - 69 q^{70} - 13 q^{71} + 22 q^{72} - 57 q^{73} + 33 q^{74} - q^{75} - 26 q^{76} - 5 q^{77} + 5 q^{78} + 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} + 35 q^{84} + 40 q^{85} + 4 q^{86} + 3 q^{88} - 80 q^{89} + 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} + 7 q^{95} + 8 q^{96} + 20 q^{97} - 78 q^{98} + 9 q^{99}+O(q^{100}) \) 18 * q - 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 9 * q^9 - 5 * q^10 + 18 * q^11 - 3 * q^12 - 15 * q^13 + 12 * q^14 - 27 * q^15 + 4 * q^16 + 6 * q^17 - 12 * q^18 + 11 * q^19 - 18 * q^20 + 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 - 10 * q^26 + 6 * q^27 - 6 * q^28 - 19 * q^30 - 8 * q^31 - 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 + 9 * q^37 - 3 * q^38 - 8 * q^39 - 36 * q^40 + 3 * q^41 + 28 * q^42 + 13 * q^43 + 12 * q^44 - q^45 + 37 * q^46 - q^47 + 46 * q^48 - 23 * q^49 + 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 - 6 * q^55 + 10 * q^56 + 14 * q^57 - 16 * q^59 + 3 * q^60 - 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 - q^66 + 9 * q^67 + 5 * q^68 - 47 * q^69 - 69 * q^70 - 13 * q^71 + 22 * q^72 - 57 * q^73 + 33 * q^74 - q^75 - 26 * q^76 - 5 * q^77 + 5 * q^78 + 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 + 35 * q^84 + 40 * q^85 + 4 * q^86 + 3 * q^88 - 80 * q^89 + 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 + 7 * q^95 + 8 * q^96 + 20 * q^97 - 78 * q^98 + 9 * q^99

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