LMFDB - Embedded newform 4730.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.23252.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 2 $ x^4 - x^3 - 6*x^2 + 2
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			1.2
Root			$-0.634868$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.63487 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.63487 q^{6} +1.96207 q^{7} +1.00000 q^{8} -0.327207 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.63487 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.63487 q^{6} +1.96207 q^{7} +1.00000 q^{8} -0.327207 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.63487 q^{12} -4.51539 q^{13} +1.96207 q^{14} -1.63487 q^{15} +1.00000 q^{16} +3.62773 q^{17} -0.327207 q^{18} -0.692339 q^{19} +1.00000 q^{20} -3.20773 q^{21} -1.00000 q^{22} -3.69234 q^{23} -1.63487 q^{24} +1.00000 q^{25} -4.51539 q^{26} +5.43954 q^{27} +1.96207 q^{28} -7.11234 q^{29} -1.63487 q^{30} -2.92415 q^{31} +1.00000 q^{32} +1.63487 q^{33} +3.62773 q^{34} +1.96207 q^{35} -0.327207 q^{36} +3.93539 q^{37} -0.692339 q^{38} +7.38207 q^{39} +1.00000 q^{40} -2.51539 q^{41} -3.20773 q^{42} -1.00000 q^{43} -1.00000 q^{44} -0.327207 q^{45} -3.69234 q^{46} -2.00000 q^{47} -1.63487 q^{48} -3.15026 q^{49} +1.00000 q^{50} -5.93086 q^{51} -4.51539 q^{52} -5.09279 q^{53} +5.43954 q^{54} -1.00000 q^{55} +1.96207 q^{56} +1.13188 q^{57} -7.11234 q^{58} -7.91701 q^{59} -1.63487 q^{60} +0.949239 q^{61} -2.92415 q^{62} -0.642005 q^{63} +1.00000 q^{64} -4.51539 q^{65} +1.63487 q^{66} +5.28215 q^{67} +3.62773 q^{68} +6.03649 q^{69} +1.96207 q^{70} +4.01124 q^{71} -0.327207 q^{72} -9.47747 q^{73} +3.93539 q^{74} -1.63487 q^{75} -0.692339 q^{76} -1.96207 q^{77} +7.38207 q^{78} -15.3554 q^{79} +1.00000 q^{80} -7.91131 q^{81} -2.51539 q^{82} -11.0995 q^{83} -3.20773 q^{84} +3.62773 q^{85} -1.00000 q^{86} +11.6277 q^{87} -1.00000 q^{88} +9.93086 q^{89} -0.327207 q^{90} -8.85954 q^{91} -3.69234 q^{92} +4.78060 q^{93} -2.00000 q^{94} -0.692339 q^{95} -1.63487 q^{96} -0.791840 q^{97} -3.15026 q^{98} +0.327207 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} - 3 q^{12} - 9 q^{13} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 3 q^{21} - 4 q^{22} - 14 q^{23} - 3 q^{24} + 4 q^{25} - 9 q^{26} - 3 q^{27} - 8 q^{29} - 3 q^{30} + 4 q^{31} + 4 q^{32} + 3 q^{33} - 15 q^{34} + 3 q^{36} - 13 q^{37} - 2 q^{38} + 2 q^{39} + 4 q^{40} - q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} + 3 q^{45} - 14 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{50} + 5 q^{51} - 9 q^{52} - 5 q^{53} - 3 q^{54} - 4 q^{55} - 21 q^{57} - 8 q^{58} + 10 q^{59} - 3 q^{60} - 12 q^{61} + 4 q^{62} - 25 q^{63} + 4 q^{64} - 9 q^{65} + 3 q^{66} - 17 q^{67} - 15 q^{68} - 12 q^{69} + 3 q^{71} + 3 q^{72} - 21 q^{73} - 13 q^{74} - 3 q^{75} - 2 q^{76} + 2 q^{78} - 13 q^{79} + 4 q^{80} - 8 q^{81} - q^{82} - 16 q^{83} - 3 q^{84} - 15 q^{85} - 4 q^{86} + 17 q^{87} - 4 q^{88} + 11 q^{89} + 3 q^{90} + 9 q^{91} - 14 q^{92} + 3 q^{93} - 8 q^{94} - 2 q^{95} - 3 q^{96} + 26 q^{97} - 3 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 - 3 * q^12 - 9 * q^13 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 3 * q^21 - 4 * q^22 - 14 * q^23 - 3 * q^24 + 4 * q^25 - 9 * q^26 - 3 * q^27 - 8 * q^29 - 3 * q^30 + 4 * q^31 + 4 * q^32 + 3 * q^33 - 15 * q^34 + 3 * q^36 - 13 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - q^41 - 3 * q^42 - 4 * q^43 - 4 * q^44 + 3 * q^45 - 14 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^50 + 5 * q^51 - 9 * q^52 - 5 * q^53 - 3 * q^54 - 4 * q^55 - 21 * q^57 - 8 * q^58 + 10 * q^59 - 3 * q^60 - 12 * q^61 + 4 * q^62 - 25 * q^63 + 4 * q^64 - 9 * q^65 + 3 * q^66 - 17 * q^67 - 15 * q^68 - 12 * q^69 + 3 * q^71 + 3 * q^72 - 21 * q^73 - 13 * q^74 - 3 * q^75 - 2 * q^76 + 2 * q^78 - 13 * q^79 + 4 * q^80 - 8 * q^81 - q^82 - 16 * q^83 - 3 * q^84 - 15 * q^85 - 4 * q^86 + 17 * q^87 - 4 * q^88 + 11 * q^89 + 3 * q^90 + 9 * q^91 - 14 * q^92 + 3 * q^93 - 8 * q^94 - 2 * q^95 - 3 * q^96 + 26 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.63487	−0.943891	−0.471946	−	0.881628i	$-0.656448\pi$
$3$	−1.63487	−0.943891	−0.471946	+	0.881628i	$0.656448\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.63487	−0.667432
$7$	1.96207	0.741595	0.370797	−	0.928714i	$-0.379084\pi$
$7$	1.96207	0.741595	0.370797	+	0.928714i	$0.379084\pi$
$8$	1.00000	0.353553
$9$	−0.327207	−0.109069
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.63487	−0.471946
$13$	−4.51539	−1.25234	−0.626172	−	0.779685i	$-0.715379\pi$
$13$	−4.51539	−1.25234	−0.626172	+	0.779685i	$0.715379\pi$
$14$	1.96207	0.524387
$15$	−1.63487	−0.422121
$16$	1.00000	0.250000
$17$	3.62773	0.879854	0.439927	−	0.898034i	$-0.355004\pi$
$17$	3.62773	0.879854	0.439927	+	0.898034i	$0.355004\pi$
$18$	−0.327207	−0.0771235
$19$	−0.692339	−0.158834	−0.0794168	−	0.996842i	$-0.525306\pi$
$19$	−0.692339	−0.158834	−0.0794168	+	0.996842i	$0.525306\pi$
$20$	1.00000	0.223607
$21$	−3.20773	−0.699985
$22$	−1.00000	−0.213201
$23$	−3.69234	−0.769906	−0.384953	−	0.922936i	$-0.625782\pi$
$23$	−3.69234	−0.769906	−0.384953	+	0.922936i	$0.625782\pi$
$24$	−1.63487	−0.333716
$25$	1.00000	0.200000
$26$	−4.51539	−0.885542
$27$	5.43954	1.04684
$28$	1.96207	0.370797
$29$	−7.11234	−1.32073	−0.660364	−	0.750946i	$-0.729598\pi$
$29$	−7.11234	−1.32073	−0.660364	+	0.750946i	$0.729598\pi$
$30$	−1.63487	−0.298485
$31$	−2.92415	−0.525193	−0.262596	−	0.964906i	$-0.584579\pi$
$31$	−2.92415	−0.525193	−0.262596	+	0.964906i	$0.584579\pi$
$32$	1.00000	0.176777
$33$	1.63487	0.284594
$34$	3.62773	0.622151
$35$	1.96207	0.331651
$36$	−0.327207	−0.0545345
$37$	3.93539	0.646974	0.323487	−	0.946233i	$-0.395145\pi$
$37$	3.93539	0.646974	0.323487	+	0.946233i	$0.395145\pi$
$38$	−0.692339	−0.112312
$39$	7.38207	1.18208
$40$	1.00000	0.158114
$41$	−2.51539	−0.392839	−0.196419	−	0.980520i	$-0.562931\pi$
$41$	−2.51539	−0.392839	−0.196419	+	0.980520i	$0.562931\pi$
$42$	−3.20773	−0.494964
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	−0.327207	−0.0487772
$46$	−3.69234	−0.544406
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	−1.63487	−0.235973
$49$	−3.15026	−0.450037
$50$	1.00000	0.141421
$51$	−5.93086	−0.830487
$52$	−4.51539	−0.626172
$53$	−5.09279	−0.699549	−0.349774	−	0.936834i	$-0.613742\pi$
$53$	−5.09279	−0.699549	−0.349774	+	0.936834i	$0.613742\pi$
$54$	5.43954	0.740228
$55$	−1.00000	−0.134840
$56$	1.96207	0.262193
$57$	1.13188	0.149922
$58$	−7.11234	−0.933896
$59$	−7.91701	−1.03071	−0.515354	−	0.856978i	$-0.672339\pi$
$59$	−7.91701	−1.03071	−0.515354	+	0.856978i	$0.672339\pi$
$60$	−1.63487	−0.211061
$61$	0.949239	0.121538	0.0607688	−	0.998152i	$-0.480645\pi$
$61$	0.949239	0.121538	0.0607688	+	0.998152i	$0.480645\pi$
$62$	−2.92415	−0.371367
$63$	−0.642005	−0.0808850
$64$	1.00000	0.125000
$65$	−4.51539	−0.560066
$66$	1.63487	0.201238
$67$	5.28215	0.645317	0.322658	−	0.946515i	$-0.395424\pi$
$67$	5.28215	0.645317	0.322658	+	0.946515i	$0.395424\pi$
$68$	3.62773	0.439927
$69$	6.03649	0.726708
$70$	1.96207	0.234513
$71$	4.01124	0.476047	0.238023	−	0.971259i	$-0.423501\pi$
$71$	4.01124	0.476047	0.238023	+	0.971259i	$0.423501\pi$
$72$	−0.327207	−0.0385617
$73$	−9.47747	−1.10925	−0.554627	−	0.832099i	$-0.687139\pi$
$73$	−9.47747	−1.10925	−0.554627	+	0.832099i	$0.687139\pi$
$74$	3.93539	0.457480
$75$	−1.63487	−0.188778
$76$	−0.692339	−0.0794168
$77$	−1.96207	−0.223599
$78$	7.38207	0.835855
$79$	−15.3554	−1.72762	−0.863808	−	0.503821i	$-0.831927\pi$
$79$	−15.3554	−1.72762	−0.863808	+	0.503821i	$0.831927\pi$
$80$	1.00000	0.111803
$81$	−7.91131	−0.879035
$82$	−2.51539	−0.277779
$83$	−11.0995	−1.21833	−0.609164	−	0.793044i	$-0.708495\pi$
$83$	−11.0995	−1.21833	−0.609164	+	0.793044i	$0.708495\pi$
$84$	−3.20773	−0.349992
$85$	3.62773	0.393483
$86$	−1.00000	−0.107833
$87$	11.6277	1.24662
$88$	−1.00000	−0.106600
$89$	9.93086	1.05267	0.526335	−	0.850278i	$-0.323566\pi$
$89$	9.93086	1.05267	0.526335	+	0.850278i	$0.323566\pi$
$90$	−0.327207	−0.0344907
$91$	−8.85954	−0.928732
$92$	−3.69234	−0.384953
$93$	4.78060	0.495725
$94$	−2.00000	−0.206284
$95$	−0.692339	−0.0710325
$96$	−1.63487	−0.166858
$97$	−0.791840	−0.0803992	−0.0401996	−	0.999192i	$-0.512799\pi$
$97$	−0.791840	−0.0803992	−0.0401996	+	0.999192i	$0.512799\pi$
$98$	−3.15026	−0.318225
$99$	0.327207	0.0328856
$100$	1.00000	0.100000
$101$	5.88053	0.585134	0.292567	−	0.956245i	$-0.405491\pi$
$101$	5.88053	0.585134	0.292567	+	0.956245i	$0.405491\pi$
$102$	−5.93086	−0.587243
$103$	−15.1796	−1.49569	−0.747846	−	0.663872i	$-0.768912\pi$
$103$	−15.1796	−1.49569	−0.747846	+	0.663872i	$0.768912\pi$
$104$	−4.51539	−0.442771
$105$	−3.20773	−0.313043
$106$	−5.09279	−0.494656
$107$	17.1236	1.65540	0.827699	−	0.561172i	$-0.189649\pi$
$107$	17.1236	1.65540	0.827699	+	0.561172i	$0.189649\pi$
$108$	5.43954	0.523420
$109$	4.04362	0.387309	0.193654	−	0.981070i	$-0.437966\pi$
$109$	4.04362	0.387309	0.193654	+	0.981070i	$0.437966\pi$
$110$	−1.00000	−0.0953463
$111$	−6.43385	−0.610674
$112$	1.96207	0.185399
$113$	14.6714	1.38016	0.690082	−	0.723731i	$-0.257574\pi$
$113$	14.6714	1.38016	0.690082	+	0.723731i	$0.257574\pi$
$114$	1.13188	0.106011
$115$	−3.69234	−0.344312
$116$	−7.11234	−0.660364
$117$	1.47747	0.136592
$118$	−7.91701	−0.728820
$119$	7.11788	0.652495
$120$	−1.63487	−0.149242
$121$	1.00000	0.0909091
$122$	0.949239	0.0859401
$123$	4.11234	0.370797
$124$	−2.92415	−0.262596
$125$	1.00000	0.0894427
$126$	−0.642005	−0.0571943
$127$	−14.8355	−1.31643	−0.658217	−	0.752828i	$-0.728689\pi$
$127$	−14.8355	−1.31643	−0.658217	+	0.752828i	$0.728689\pi$
$128$	1.00000	0.0883883
$129$	1.63487	0.143942
$130$	−4.51539	−0.396026
$131$	10.5898	0.925236	0.462618	−	0.886558i	$-0.346910\pi$
$131$	10.5898	0.925236	0.462618	+	0.886558i	$0.346910\pi$
$132$	1.63487	0.142297
$133$	−1.35842	−0.117790
$134$	5.28215	0.456308
$135$	5.43954	0.468161
$136$	3.62773	0.311075
$137$	−18.2667	−1.56063	−0.780315	−	0.625387i	$-0.784941\pi$
$137$	−18.2667	−1.56063	−0.780315	+	0.625387i	$0.784941\pi$
$138$	6.03649	0.513860
$139$	18.9227	1.60500	0.802502	−	0.596650i	$-0.203502\pi$
$139$	18.9227	1.60500	0.802502	+	0.596650i	$0.203502\pi$
$140$	1.96207	0.165826
$141$	3.26974	0.275361
$142$	4.01124	0.336616
$143$	4.51539	0.377596
$144$	−0.327207	−0.0272673
$145$	−7.11234	−0.590647
$146$	−9.47747	−0.784361
$147$	5.15026	0.424786
$148$	3.93539	0.323487
$149$	−11.2175	−0.918976	−0.459488	−	0.888184i	$-0.651967\pi$
$149$	−11.2175	−0.918976	−0.459488	+	0.888184i	$0.651967\pi$
$150$	−1.63487	−0.133486
$151$	3.33392	0.271310	0.135655	−	0.990756i	$-0.456686\pi$
$151$	3.33392	0.271310	0.135655	+	0.990756i	$0.456686\pi$
$152$	−0.692339	−0.0561561
$153$	−1.18702	−0.0959648
$154$	−1.96207	−0.158109
$155$	−2.92415	−0.234873
$156$	7.38207	0.591039
$157$	17.3816	1.38721	0.693603	−	0.720357i	$-0.256022\pi$
$157$	17.3816	1.38721	0.693603	+	0.720357i	$0.256022\pi$
$158$	−15.3554	−1.22161
$159$	8.32604	0.660298
$160$	1.00000	0.0790569
$161$	−7.24465	−0.570958
$162$	−7.91131	−0.621572
$163$	−5.91744	−0.463490	−0.231745	−	0.972777i	$-0.574443\pi$
$163$	−5.91744	−0.463490	−0.231745	+	0.972777i	$0.574443\pi$
$164$	−2.51539	−0.196419
$165$	1.63487	0.127274
$166$	−11.0995	−0.861488
$167$	−17.1107	−1.32407	−0.662035	−	0.749473i	$-0.730307\pi$
$167$	−17.1107	−1.32407	−0.662035	+	0.749473i	$0.730307\pi$
$168$	−3.20773	−0.247482
$169$	7.38878	0.568368
$170$	3.62773	0.278234
$171$	0.226538	0.0173238
$172$	−1.00000	−0.0762493
$173$	−18.5083	−1.40716	−0.703578	−	0.710618i	$-0.748416\pi$
$173$	−18.5083	−1.40716	−0.703578	+	0.710618i	$0.748416\pi$
$174$	11.6277	0.881496
$175$	1.96207	0.148319
$176$	−1.00000	−0.0753778
$177$	12.9433	0.972876
$178$	9.93086	0.744349
$179$	−8.39331	−0.627346	−0.313673	−	0.949531i	$-0.601560\pi$
$179$	−8.39331	−0.627346	−0.313673	+	0.949531i	$0.601560\pi$
$180$	−0.327207	−0.0243886
$181$	−24.4636	−1.81837	−0.909183	−	0.416396i	$-0.863293\pi$
$181$	−24.4636	−1.81837	−0.909183	+	0.416396i	$0.863293\pi$
$182$	−8.85954	−0.656713
$183$	−1.55188	−0.114718
$184$	−3.69234	−0.272203
$185$	3.93539	0.289336
$186$	4.78060	0.350531
$187$	−3.62773	−0.265286
$188$	−2.00000	−0.145865
$189$	10.6728	0.776331
$190$	−0.692339	−0.0502276
$191$	25.0601	1.81329	0.906644	−	0.421897i	$-0.138635\pi$
$191$	25.0601	1.81329	0.906644	+	0.421897i	$0.138635\pi$
$192$	−1.63487	−0.117986
$193$	−11.9103	−0.857322	−0.428661	−	0.903465i	$-0.641015\pi$
$193$	−11.9103	−0.857322	−0.428661	+	0.903465i	$0.641015\pi$
$194$	−0.791840	−0.0568508
$195$	7.38207	0.528641
$196$	−3.15026	−0.225019
$197$	−19.5000	−1.38931	−0.694657	−	0.719341i	$-0.744444\pi$
$197$	−19.5000	−1.38931	−0.694657	+	0.719341i	$0.744444\pi$
$198$	0.327207	0.0232536
$199$	−13.1615	−0.932994	−0.466497	−	0.884523i	$-0.654484\pi$
$199$	−13.1615	−0.932994	−0.466497	+	0.884523i	$0.654484\pi$
$200$	1.00000	0.0707107
$201$	−8.63561	−0.609109
$202$	5.88053	0.413752
$203$	−13.9549	−0.979445
$204$	−5.93086	−0.415243
$205$	−2.51539	−0.175683
$206$	−15.1796	−1.05761
$207$	1.20816	0.0839729
$208$	−4.51539	−0.313086
$209$	0.692339	0.0478901
$210$	−3.20773	−0.221355
$211$	−3.51539	−0.242010	−0.121005	−	0.992652i	$-0.538612\pi$
$211$	−3.51539	−0.242010	−0.121005	+	0.992652i	$0.538612\pi$
$212$	−5.09279	−0.349774
$213$	−6.55785	−0.449336
$214$	17.1236	1.17054
$215$	−1.00000	−0.0681994
$216$	5.43954	0.370114
$217$	−5.73740	−0.389480
$218$	4.04362	0.273869
$219$	15.4944	1.04702
$220$	−1.00000	−0.0674200
$221$	−16.3806	−1.10188
$222$	−6.43385	−0.431811
$223$	14.3986	0.964201	0.482100	−	0.876116i	$-0.339874\pi$
$223$	14.3986	0.964201	0.482100	+	0.876116i	$0.339874\pi$
$224$	1.96207	0.131097
$225$	−0.327207	−0.0218138
$226$	14.6714	0.975924
$227$	−1.30883	−0.0868700	−0.0434350	−	0.999056i	$-0.513830\pi$
$227$	−1.30883	−0.0868700	−0.0434350	+	0.999056i	$0.513830\pi$
$228$	1.13188	0.0749608
$229$	−12.7694	−0.843823	−0.421911	−	0.906637i	$-0.638641\pi$
$229$	−12.7694	−0.843823	−0.421911	+	0.906637i	$0.638641\pi$
$230$	−3.69234	−0.243466
$231$	3.20773	0.211053
$232$	−7.11234	−0.466948
$233$	−26.7754	−1.75411	−0.877057	−	0.480386i	$-0.840496\pi$
$233$	−26.7754	−1.75411	−0.877057	+	0.480386i	$0.840496\pi$
$234$	1.47747	0.0965852
$235$	−2.00000	−0.130466
$236$	−7.91701	−0.515354
$237$	25.1040	1.63068
$238$	7.11788	0.461384
$239$	−2.95227	−0.190967	−0.0954833	−	0.995431i	$-0.530440\pi$
$239$	−2.95227	−0.190967	−0.0954833	+	0.995431i	$0.530440\pi$
$240$	−1.63487	−0.105530
$241$	13.8591	0.892744	0.446372	−	0.894847i	$-0.352716\pi$
$241$	13.8591	0.892744	0.446372	+	0.894847i	$0.352716\pi$
$242$	1.00000	0.0642824
$243$	−3.38468	−0.217127
$244$	0.949239	0.0607688
$245$	−3.15026	−0.201263
$246$	4.11234	0.262193
$247$	3.12618	0.198914
$248$	−2.92415	−0.185684
$249$	18.1462	1.14997
$250$	1.00000	0.0632456
$251$	18.2934	1.15467	0.577334	−	0.816508i	$-0.304093\pi$
$251$	18.2934	1.15467	0.577334	+	0.816508i	$0.304093\pi$
$252$	−0.642005	−0.0404425
$253$	3.69234	0.232135
$254$	−14.8355	−0.930860
$255$	−5.93086	−0.371405
$256$	1.00000	0.0625000
$257$	−10.2693	−0.640582	−0.320291	−	0.947319i	$-0.603781\pi$
$257$	−10.2693	−0.640582	−0.320291	+	0.947319i	$0.603781\pi$
$258$	1.63487	0.101782
$259$	7.72153	0.479793
$260$	−4.51539	−0.280033
$261$	2.32721	0.144051
$262$	10.5898	0.654240
$263$	−5.49845	−0.339049	−0.169525	−	0.985526i	$-0.554223\pi$
$263$	−5.49845	−0.339049	−0.169525	+	0.985526i	$0.554223\pi$
$264$	1.63487	0.100619
$265$	−5.09279	−0.312848
$266$	−1.35842	−0.0832902
$267$	−16.2356	−0.993605
$268$	5.28215	0.322658
$269$	−13.4000	−0.817014	−0.408507	−	0.912755i	$-0.633950\pi$
$269$	−13.4000	−0.817014	−0.408507	+	0.912755i	$0.633950\pi$
$270$	5.43954	0.331040
$271$	12.8641	0.781437	0.390718	−	0.920510i	$-0.372227\pi$
$271$	12.8641	0.781437	0.390718	+	0.920510i	$0.372227\pi$
$272$	3.62773	0.219963
$273$	14.4842	0.876622
$274$	−18.2667	−1.10353
$275$	−1.00000	−0.0603023
$276$	6.03649	0.363354
$277$	−20.9575	−1.25922	−0.629608	−	0.776913i	$-0.716785\pi$
$277$	−20.9575	−1.25922	−0.629608	+	0.776913i	$0.716785\pi$
$278$	18.9227	1.13491
$279$	0.956803	0.0572823
$280$	1.96207	0.117256
$281$	14.9166	0.889849	0.444924	−	0.895568i	$-0.353231\pi$
$281$	14.9166	0.889849	0.444924	+	0.895568i	$0.353231\pi$
$282$	3.26974	0.194710
$283$	12.3452	0.733844	0.366922	−	0.930252i	$-0.380412\pi$
$283$	12.3452	0.733844	0.366922	+	0.930252i	$0.380412\pi$
$284$	4.01124	0.238023
$285$	1.13188	0.0670470
$286$	4.51539	0.267001
$287$	−4.93539	−0.291327
$288$	−0.327207	−0.0192809
$289$	−3.83957	−0.225857
$290$	−7.11234	−0.417651
$291$	1.29455	0.0758881
$292$	−9.47747	−0.554627
$293$	−5.95377	−0.347823	−0.173911	−	0.984761i	$-0.555641\pi$
$293$	−5.95377	−0.347823	−0.173911	+	0.984761i	$0.555641\pi$
$294$	5.15026	0.300369
$295$	−7.91701	−0.460946
$296$	3.93539	0.228740
$297$	−5.43954	−0.315634
$298$	−11.2175	−0.649814
$299$	16.6724	0.964188
$300$	−1.63487	−0.0943891
$301$	−1.96207	−0.113092
$302$	3.33392	0.191845
$303$	−9.61388	−0.552303
$304$	−0.692339	−0.0397084
$305$	0.949239	0.0543533
$306$	−1.18702	−0.0678574
$307$	29.1484	1.66359	0.831793	−	0.555085i	$-0.187314\pi$
$307$	29.1484	1.66359	0.831793	+	0.555085i	$0.187314\pi$
$308$	−1.96207	−0.111800
$309$	24.8167	1.41177
$310$	−2.92415	−0.166081
$311$	−26.8386	−1.52187	−0.760937	−	0.648825i	$-0.775261\pi$
$311$	−26.8386	−1.52187	−0.760937	+	0.648825i	$0.775261\pi$
$312$	7.38207	0.417928
$313$	−7.17961	−0.405816	−0.202908	−	0.979198i	$-0.565039\pi$
$313$	−7.17961	−0.405816	−0.202908	+	0.979198i	$0.565039\pi$
$314$	17.3816	0.980903
$315$	−0.642005	−0.0361729
$316$	−15.3554	−0.863808
$317$	30.7048	1.72455	0.862277	−	0.506437i	$-0.169038\pi$
$317$	30.7048	1.72455	0.862277	+	0.506437i	$0.169038\pi$
$318$	8.32604	0.466901
$319$	7.11234	0.398214
$320$	1.00000	0.0559017
$321$	−27.9948	−1.56252
$322$	−7.24465	−0.403728
$323$	−2.51162	−0.139750
$324$	−7.91131	−0.439517
$325$	−4.51539	−0.250469
$326$	−5.91744	−0.327737
$327$	−6.61079	−0.365578
$328$	−2.51539	−0.138889
$329$	−3.92415	−0.216345
$330$	1.63487	0.0899965
$331$	18.1622	0.998287	0.499144	−	0.866519i	$-0.333648\pi$
$331$	18.1622	0.998287	0.499144	+	0.866519i	$0.333648\pi$
$332$	−11.0995	−0.609164
$333$	−1.28769	−0.0705649
$334$	−17.1107	−0.936258
$335$	5.28215	0.288594
$336$	−3.20773	−0.174996
$337$	−20.3483	−1.10844	−0.554220	−	0.832370i	$-0.686983\pi$
$337$	−20.3483	−1.10844	−0.554220	+	0.832370i	$0.686983\pi$
$338$	7.38878	0.401897
$339$	−23.9857	−1.30273
$340$	3.62773	0.196741
$341$	2.92415	0.158352
$342$	0.226538	0.0122498
$343$	−19.9156	−1.07534
$344$	−1.00000	−0.0539164
$345$	6.03649	0.324994
$346$	−18.5083	−0.995010
$347$	30.5366	1.63929	0.819645	−	0.572872i	$-0.194171\pi$
$347$	30.5366	1.63929	0.819645	+	0.572872i	$0.194171\pi$
$348$	11.6277	0.623312
$349$	−32.0330	−1.71469	−0.857344	−	0.514743i	$-0.827887\pi$
$349$	−32.0330	−1.71469	−0.857344	+	0.514743i	$0.827887\pi$
$350$	1.96207	0.104877
$351$	−24.5617	−1.31101
$352$	−1.00000	−0.0533002
$353$	−34.7427	−1.84917	−0.924585	−	0.380977i	$-0.875588\pi$
$353$	−34.7427	−1.84917	−0.924585	+	0.380977i	$0.875588\pi$
$354$	12.9433	0.687927
$355$	4.01124	0.212895
$356$	9.93086	0.526335
$357$	−11.6368	−0.615884
$358$	−8.39331	−0.443600
$359$	−22.8704	−1.20705	−0.603526	−	0.797344i	$-0.706238\pi$
$359$	−22.8704	−1.20705	−0.603526	+	0.797344i	$0.706238\pi$
$360$	−0.327207	−0.0172453
$361$	−18.5207	−0.974772
$362$	−24.4636	−1.28578
$363$	−1.63487	−0.0858083
$364$	−8.85954	−0.464366
$365$	−9.47747	−0.496073
$366$	−1.55188	−0.0811181
$367$	−2.86055	−0.149320	−0.0746598	−	0.997209i	$-0.523787\pi$
$367$	−2.86055	−0.149320	−0.0746598	+	0.997209i	$0.523787\pi$
$368$	−3.69234	−0.192476
$369$	0.823055	0.0428465
$370$	3.93539	0.204591
$371$	−9.99244	−0.518781
$372$	4.78060	0.247862
$373$	22.6375	1.17213	0.586064	−	0.810265i	$-0.300677\pi$
$373$	22.6375	1.17213	0.586064	+	0.810265i	$0.300677\pi$
$374$	−3.62773	−0.187585
$375$	−1.63487	−0.0844242
$376$	−2.00000	−0.103142
$377$	32.1150	1.65401
$378$	10.6728	0.548949
$379$	−0.709706	−0.0364551	−0.0182276	−	0.999834i	$-0.505802\pi$
$379$	−0.709706	−0.0364551	−0.0182276	+	0.999834i	$0.505802\pi$
$380$	−0.692339	−0.0355163
$381$	24.2540	1.24257
$382$	25.0601	1.28219
$383$	−12.9129	−0.659819	−0.329909	−	0.944013i	$-0.607018\pi$
$383$	−12.9129	−0.659819	−0.329909	+	0.944013i	$0.607018\pi$
$384$	−1.63487	−0.0834290
$385$	−1.96207	−0.0999966
$386$	−11.9103	−0.606218
$387$	0.327207	0.0166329
$388$	−0.791840	−0.0401996
$389$	25.4918	1.29249	0.646243	−	0.763132i	$-0.276339\pi$
$389$	25.4918	1.29249	0.646243	+	0.763132i	$0.276339\pi$
$390$	7.38207	0.373806
$391$	−13.3948	−0.677405
$392$	−3.15026	−0.159112
$393$	−17.3129	−0.873322
$394$	−19.5000	−0.982393
$395$	−15.3554	−0.772613
$396$	0.327207	0.0164428
$397$	8.98716	0.451053	0.225526	−	0.974237i	$-0.427590\pi$
$397$	8.98716	0.451053	0.225526	+	0.974237i	$0.427590\pi$
$398$	−13.1615	−0.659727
$399$	2.22084	0.111181
$400$	1.00000	0.0500000
$401$	−22.7724	−1.13720	−0.568601	−	0.822614i	$-0.692515\pi$
$401$	−22.7724	−1.13720	−0.568601	+	0.822614i	$0.692515\pi$
$402$	−8.63561	−0.430705
$403$	13.2037	0.657723
$404$	5.88053	0.292567
$405$	−7.91131	−0.393116
$406$	−13.9549	−0.692572
$407$	−3.93539	−0.195070
$408$	−5.93086	−0.293621
$409$	32.1961	1.59200	0.795998	−	0.605299i	$-0.206947\pi$
$409$	32.1961	1.59200	0.795998	+	0.605299i	$0.206947\pi$
$410$	−2.51539	−0.124226
$411$	29.8636	1.47307
$412$	−15.1796	−0.747846
$413$	−15.5338	−0.764367
$414$	1.20816	0.0593778
$415$	−11.0995	−0.544853
$416$	−4.51539	−0.221385
$417$	−30.9361	−1.51495
$418$	0.692339	0.0338634
$419$	19.8174	0.968141	0.484071	−	0.875029i	$-0.339158\pi$
$419$	19.8174	0.968141	0.484071	+	0.875029i	$0.339158\pi$
$420$	−3.20773	−0.156521
$421$	−1.73069	−0.0843487	−0.0421744	−	0.999110i	$-0.513428\pi$
$421$	−1.73069	−0.0843487	−0.0421744	+	0.999110i	$0.513428\pi$
$422$	−3.51539	−0.171127
$423$	0.654414	0.0318187
$424$	−5.09279	−0.247328
$425$	3.62773	0.175971
$426$	−6.55785	−0.317729
$427$	1.86248	0.0901317
$428$	17.1236	0.827699
$429$	−7.38207	−0.356410
$430$	−1.00000	−0.0482243
$431$	−12.5600	−0.604995	−0.302498	−	0.953150i	$-0.597820\pi$
$431$	−12.5600	−0.604995	−0.302498	+	0.953150i	$0.597820\pi$
$432$	5.43954	0.261710
$433$	18.5083	0.889450	0.444725	−	0.895667i	$-0.353301\pi$
$433$	18.5083	0.889450	0.444725	+	0.895667i	$0.353301\pi$
$434$	−5.73740	−0.275404
$435$	11.6277	0.557507
$436$	4.04362	0.193654
$437$	2.55635	0.122287
$438$	15.4944	0.740352
$439$	−1.99286	−0.0951142	−0.0475571	−	0.998869i	$-0.515144\pi$
$439$	−1.99286	−0.0951142	−0.0475571	+	0.998869i	$0.515144\pi$
$440$	−1.00000	−0.0476731
$441$	1.03079	0.0490851
$442$	−16.3806	−0.779147
$443$	41.3662	1.96537	0.982684	−	0.185290i	$-0.0593225\pi$
$443$	41.3662	1.96537	0.982684	+	0.185290i	$0.0593225\pi$
$444$	−6.43385	−0.305337
$445$	9.93086	0.470768
$446$	14.3986	0.681793
$447$	18.3392	0.867414
$448$	1.96207	0.0926993
$449$	−4.73026	−0.223235	−0.111617	−	0.993751i	$-0.535603\pi$
$449$	−4.73026	−0.223235	−0.111617	+	0.993751i	$0.535603\pi$
$450$	−0.327207	−0.0154247
$451$	2.51539	0.118445
$452$	14.6714	0.690082
$453$	−5.45051	−0.256088
$454$	−1.30883	−0.0614264
$455$	−8.85954	−0.415342
$456$	1.13188	0.0530053
$457$	−13.6303	−0.637600	−0.318800	−	0.947822i	$-0.603280\pi$
$457$	−13.6303	−0.637600	−0.318800	+	0.947822i	$0.603280\pi$
$458$	−12.7694	−0.596673
$459$	19.7332	0.921067
$460$	−3.69234	−0.172156
$461$	−2.72163	−0.126759	−0.0633794	−	0.997990i	$-0.520188\pi$
$461$	−2.72163	−0.126759	−0.0633794	+	0.997990i	$0.520188\pi$
$462$	3.20773	0.149237
$463$	1.30095	0.0604603	0.0302301	−	0.999543i	$-0.490376\pi$
$463$	1.30095	0.0604603	0.0302301	+	0.999543i	$0.490376\pi$
$464$	−7.11234	−0.330182
$465$	4.78060	0.221695
$466$	−26.7754	−1.24035
$467$	−30.8949	−1.42964	−0.714822	−	0.699307i	$-0.753492\pi$
$467$	−30.8949	−1.42964	−0.714822	+	0.699307i	$0.753492\pi$
$468$	1.47747	0.0682960
$469$	10.3640	0.478563
$470$	−2.00000	−0.0922531
$471$	−28.4167	−1.30937
$472$	−7.91701	−0.364410
$473$	1.00000	0.0459800
$474$	25.1040	1.15307
$475$	−0.692339	−0.0317667
$476$	7.11788	0.326247
$477$	1.66640	0.0762991
$478$	−2.95227	−0.135034
$479$	23.0451	1.05296	0.526478	−	0.850189i	$-0.323512\pi$
$479$	23.0451	1.05296	0.526478	+	0.850189i	$0.323512\pi$
$480$	−1.63487	−0.0746212
$481$	−17.7698	−0.810235
$482$	13.8591	0.631265
$483$	11.8440	0.538922
$484$	1.00000	0.0454545
$485$	−0.791840	−0.0359556
$486$	−3.38468	−0.153532
$487$	−13.2002	−0.598157	−0.299078	−	0.954229i	$-0.596679\pi$
$487$	−13.2002	−0.598157	−0.299078	+	0.954229i	$0.596679\pi$
$488$	0.949239	0.0429700
$489$	9.67423	0.437484
$490$	−3.15026	−0.142314
$491$	−7.37025	−0.332615	−0.166307	−	0.986074i	$-0.553184\pi$
$491$	−7.37025	−0.332615	−0.166307	+	0.986074i	$0.553184\pi$
$492$	4.11234	0.185398
$493$	−25.8016	−1.16205
$494$	3.12618	0.140654
$495$	0.327207	0.0147069
$496$	−2.92415	−0.131298
$497$	7.87036	0.353034
$498$	18.1462	0.813151
$499$	8.03382	0.359643	0.179822	−	0.983699i	$-0.442448\pi$
$499$	8.03382	0.359643	0.179822	+	0.983699i	$0.442448\pi$
$500$	1.00000	0.0447214
$501$	27.9738	1.24978
$502$	18.2934	0.816474
$503$	36.7972	1.64070	0.820352	−	0.571858i	$-0.193777\pi$
$503$	36.7972	1.64070	0.820352	+	0.571858i	$0.193777\pi$
$504$	−0.642005	−0.0285972
$505$	5.88053	0.261680
$506$	3.69234	0.164145
$507$	−12.0797	−0.536478
$508$	−14.8355	−0.658217
$509$	13.6432	0.604726	0.302363	−	0.953193i	$-0.402225\pi$
$509$	13.6432	0.604726	0.302363	+	0.953193i	$0.402225\pi$
$510$	−5.93086	−0.262623
$511$	−18.5955	−0.822617
$512$	1.00000	0.0441942
$513$	−3.76601	−0.166273
$514$	−10.2693	−0.452960
$515$	−15.1796	−0.668894
$516$	1.63487	0.0719710
$517$	2.00000	0.0879599
$518$	7.72153	0.339265
$519$	30.2586	1.32820
$520$	−4.51539	−0.198013
$521$	32.0062	1.40222	0.701108	−	0.713055i	$-0.252689\pi$
$521$	32.0062	1.40222	0.701108	+	0.713055i	$0.252689\pi$
$522$	2.32721	0.101859
$523$	36.1229	1.57954	0.789772	−	0.613401i	$-0.210199\pi$
$523$	36.1229	1.57954	0.789772	+	0.613401i	$0.210199\pi$
$524$	10.5898	0.462618
$525$	−3.20773	−0.139997
$526$	−5.49845	−0.239744
$527$	−10.6080	−0.462093
$528$	1.63487	0.0711485
$529$	−9.36663	−0.407245
$530$	−5.09279	−0.221217
$531$	2.59050	0.112418
$532$	−1.35842	−0.0588950
$533$	11.3580	0.491969
$534$	−16.2356	−0.702585
$535$	17.1236	0.740317
$536$	5.28215	0.228154
$537$	13.7220	0.592146
$538$	−13.4000	−0.577716
$539$	3.15026	0.135691
$540$	5.43954	0.234081
$541$	−14.4820	−0.622630	−0.311315	−	0.950307i	$-0.600769\pi$
$541$	−14.4820	−0.622630	−0.311315	+	0.950307i	$0.600769\pi$
$542$	12.8641	0.552559
$543$	39.9948	1.71634
$544$	3.62773	0.155538
$545$	4.04362	0.173210
$546$	14.4842	0.619866
$547$	1.12091	0.0479267	0.0239634	−	0.999713i	$-0.492371\pi$
$547$	1.12091	0.0479267	0.0239634	+	0.999713i	$0.492371\pi$
$548$	−18.2667	−0.780315
$549$	−0.310598	−0.0132560
$550$	−1.00000	−0.0426401
$551$	4.92415	0.209776
$552$	6.03649	0.256930
$553$	−30.1284	−1.28119
$554$	−20.9575	−0.890401
$555$	−6.43385	−0.273102
$556$	18.9227	0.802502
$557$	−40.2416	−1.70509	−0.852546	−	0.522652i	$-0.824943\pi$
$557$	−40.2416	−1.70509	−0.852546	+	0.522652i	$0.824943\pi$
$558$	0.956803	0.0405047
$559$	4.51539	0.190981
$560$	1.96207	0.0829128
$561$	5.93086	0.250401
$562$	14.9166	0.629218
$563$	−10.1504	−0.427789	−0.213895	−	0.976857i	$-0.568615\pi$
$563$	−10.1504	−0.427789	−0.213895	+	0.976857i	$0.568615\pi$
$564$	3.26974	0.137681
$565$	14.6714	0.617229
$566$	12.3452	0.518906
$567$	−15.5226	−0.651888
$568$	4.01124	0.168308
$569$	41.5381	1.74137	0.870684	−	0.491843i	$-0.163677\pi$
$569$	41.5381	1.74137	0.870684	+	0.491843i	$0.163677\pi$
$570$	1.13188	0.0474094
$571$	1.39944	0.0585647	0.0292824	−	0.999571i	$-0.490678\pi$
$571$	1.39944	0.0585647	0.0292824	+	0.999571i	$0.490678\pi$
$572$	4.51539	0.188798
$573$	−40.9700	−1.71155
$574$	−4.93539	−0.205999
$575$	−3.69234	−0.153981
$576$	−0.327207	−0.0136336
$577$	−21.5895	−0.898784	−0.449392	−	0.893335i	$-0.648359\pi$
$577$	−21.5895	−0.898784	−0.449392	+	0.893335i	$0.648359\pi$
$578$	−3.83957	−0.159705
$579$	19.4718	0.809219
$580$	−7.11234	−0.295324
$581$	−21.7781	−0.903506
$582$	1.29455	0.0536610
$583$	5.09279	0.210922
$584$	−9.47747	−0.392180
$585$	1.47747	0.0610858
$586$	−5.95377	−0.245948
$587$	7.99329	0.329918	0.164959	−	0.986300i	$-0.447251\pi$
$587$	7.99329	0.329918	0.164959	+	0.986300i	$0.447251\pi$
$588$	5.15026	0.212393
$589$	2.02450	0.0834182
$590$	−7.91701	−0.325938
$591$	31.8798	1.31136
$592$	3.93539	0.161744
$593$	12.3790	0.508346	0.254173	−	0.967159i	$-0.418197\pi$
$593$	12.3790	0.508346	0.254173	+	0.967159i	$0.418197\pi$
$594$	−5.43954	−0.223187
$595$	7.11788	0.291805
$596$	−11.2175	−0.459488
$597$	21.5173	0.880645
$598$	16.6724	0.681784
$599$	1.99957	0.0817004	0.0408502	−	0.999165i	$-0.486993\pi$
$599$	1.99957	0.0817004	0.0408502	+	0.999165i	$0.486993\pi$
$600$	−1.63487	−0.0667432
$601$	9.26947	0.378109	0.189055	−	0.981967i	$-0.439458\pi$
$601$	9.26947	0.378109	0.189055	+	0.981967i	$0.439458\pi$
$602$	−1.96207	−0.0799682
$603$	−1.72836	−0.0703841
$604$	3.33392	0.135655
$605$	1.00000	0.0406558
$606$	−9.61388	−0.390537
$607$	12.5641	0.509962	0.254981	−	0.966946i	$-0.417931\pi$
$607$	12.5641	0.509962	0.254981	+	0.966946i	$0.417931\pi$
$608$	−0.692339	−0.0280781
$609$	22.8145	0.924489
$610$	0.949239	0.0384336
$611$	9.03079	0.365347
$612$	−1.18702	−0.0479824
$613$	3.23138	0.130514	0.0652572	−	0.997868i	$-0.479213\pi$
$613$	3.23138	0.130514	0.0652572	+	0.997868i	$0.479213\pi$
$614$	29.1484	1.17633
$615$	4.11234	0.165825
$616$	−1.96207	−0.0790543
$617$	−12.5046	−0.503418	−0.251709	−	0.967803i	$-0.580993\pi$
$617$	−12.5046	−0.503418	−0.251709	+	0.967803i	$0.580993\pi$
$618$	24.8167	0.998272
$619$	33.8494	1.36052	0.680261	−	0.732970i	$-0.261867\pi$
$619$	33.8494	1.36052	0.680261	+	0.732970i	$0.261867\pi$
$620$	−2.92415	−0.117437
$621$	−20.0846	−0.805969
$622$	−26.8386	−1.07613
$623$	19.4851	0.780654
$624$	7.38207	0.295519
$625$	1.00000	0.0400000
$626$	−7.17961	−0.286955
$627$	−1.13188	−0.0452031
$628$	17.3816	0.693603
$629$	14.2765	0.569243
$630$	−0.642005	−0.0255781
$631$	26.5755	1.05796	0.528978	−	0.848636i	$-0.322576\pi$
$631$	26.5755	1.05796	0.528978	+	0.848636i	$0.322576\pi$
$632$	−15.3554	−0.610805
$633$	5.74720	0.228431
$634$	30.7048	1.21944
$635$	−14.8355	−0.588727
$636$	8.32604	0.330149
$637$	14.2247	0.563602
$638$	7.11234	0.281580
$639$	−1.31251	−0.0519220
$640$	1.00000	0.0395285
$641$	20.2930	0.801524	0.400762	−	0.916182i	$-0.368745\pi$
$641$	20.2930	0.801524	0.400762	+	0.916182i	$0.368745\pi$
$642$	−27.9948	−1.10487
$643$	−48.7530	−1.92263	−0.961315	−	0.275453i	$-0.911172\pi$
$643$	−48.7530	−1.92263	−0.961315	+	0.275453i	$0.911172\pi$
$644$	−7.24465	−0.285479
$645$	1.63487	0.0643729
$646$	−2.51162	−0.0988184
$647$	−21.9662	−0.863580	−0.431790	−	0.901974i	$-0.642118\pi$
$647$	−21.9662	−0.863580	−0.431790	+	0.901974i	$0.642118\pi$
$648$	−7.91131	−0.310786
$649$	7.91701	0.310770
$650$	−4.51539	−0.177108
$651$	9.37989	0.367627
$652$	−5.91744	−0.231745
$653$	6.65879	0.260579	0.130289	−	0.991476i	$-0.458409\pi$
$653$	6.65879	0.260579	0.130289	+	0.991476i	$0.458409\pi$
$654$	−6.61079	−0.258502
$655$	10.5898	0.413778
$656$	−2.51539	−0.0982096
$657$	3.10110	0.120985
$658$	−3.92415	−0.152979
$659$	10.1883	0.396881	0.198441	−	0.980113i	$-0.436412\pi$
$659$	10.1883	0.396881	0.198441	+	0.980113i	$0.436412\pi$
$660$	1.63487	0.0636371
$661$	−8.80526	−0.342485	−0.171242	−	0.985229i	$-0.554778\pi$
$661$	−8.80526	−0.342485	−0.171242	+	0.985229i	$0.554778\pi$
$662$	18.1622	0.705896
$663$	26.7802	1.04006
$664$	−11.0995	−0.430744
$665$	−1.35842	−0.0526773
$666$	−1.28769	−0.0498969
$667$	26.2612	1.01684
$668$	−17.1107	−0.662035
$669$	−23.5398	−0.910101
$670$	5.28215	0.204067
$671$	−0.949239	−0.0366450
$672$	−3.20773	−0.123741
$673$	27.6233	1.06480	0.532399	−	0.846493i	$-0.321291\pi$
$673$	27.6233	1.06480	0.532399	+	0.846493i	$0.321291\pi$
$674$	−20.3483	−0.783785
$675$	5.43954	0.209368
$676$	7.38878	0.284184
$677$	11.2099	0.430832	0.215416	−	0.976522i	$-0.430889\pi$
$677$	11.2099	0.430832	0.215416	+	0.976522i	$0.430889\pi$
$678$	−23.9857	−0.921166
$679$	−1.55365	−0.0596236
$680$	3.62773	0.139117
$681$	2.13976	0.0819958
$682$	2.92415	0.111971
$683$	38.0012	1.45408	0.727038	−	0.686597i	$-0.240896\pi$
$683$	38.0012	1.45408	0.727038	+	0.686597i	$0.240896\pi$
$684$	0.226538	0.00866191
$685$	−18.2667	−0.697935
$686$	−19.9156	−0.760380
$687$	20.8762	0.796477
$688$	−1.00000	−0.0381246
$689$	22.9960	0.876076
$690$	6.03649	0.229805
$691$	10.1237	0.385125	0.192562	−	0.981285i	$-0.438320\pi$
$691$	10.1237	0.385125	0.192562	+	0.981285i	$0.438320\pi$
$692$	−18.5083	−0.703578
$693$	0.642005	0.0243877
$694$	30.5366	1.15915
$695$	18.9227	0.717779
$696$	11.6277	0.440748
$697$	−9.12517	−0.345641
$698$	−32.0330	−1.21247
$699$	43.7742	1.65569
$700$	1.96207	0.0741595
$701$	−16.4820	−0.622517	−0.311258	−	0.950325i	$-0.600750\pi$
$701$	−16.4820	−0.622517	−0.311258	+	0.950325i	$0.600750\pi$
$702$	−24.5617	−0.927021
$703$	−2.72463	−0.102761
$704$	−1.00000	−0.0376889
$705$	3.26974	0.123145
$706$	−34.7427	−1.30756
$707$	11.5380	0.433932
$708$	12.9433	0.486438
$709$	12.0019	0.450742	0.225371	−	0.974273i	$-0.427641\pi$
$709$	12.0019	0.450742	0.225371	+	0.974273i	$0.427641\pi$
$710$	4.01124	0.150539
$711$	5.02439	0.188429
$712$	9.93086	0.372175
$713$	10.7970	0.404349
$714$	−11.6368	−0.435496
$715$	4.51539	0.168866
$716$	−8.39331	−0.313673
$717$	4.82657	0.180252
$718$	−22.8704	−0.853514
$719$	−0.133321	−0.00497205	−0.00248603	−	0.999997i	$-0.500791\pi$
$719$	−0.133321	−0.00497205	−0.00248603	+	0.999997i	$0.500791\pi$
$720$	−0.327207	−0.0121943
$721$	−29.7835	−1.10920
$722$	−18.5207	−0.689268
$723$	−22.6578	−0.842653
$724$	−24.4636	−0.909183
$725$	−7.11234	−0.264146
$726$	−1.63487	−0.0606756
$727$	−24.8452	−0.921458	−0.460729	−	0.887541i	$-0.652412\pi$
$727$	−24.8452	−0.921458	−0.460729	+	0.887541i	$0.652412\pi$
$728$	−8.85954	−0.328356
$729$	29.2674	1.08398
$730$	−9.47747	−0.350777
$731$	−3.62773	−0.134176
$732$	−1.55188	−0.0573592
$733$	6.11755	0.225957	0.112978	−	0.993597i	$-0.463961\pi$
$733$	6.11755	0.225957	0.112978	+	0.993597i	$0.463961\pi$
$734$	−2.86055	−0.105585
$735$	5.15026	0.189970
$736$	−3.69234	−0.136101
$737$	−5.28215	−0.194570
$738$	0.823055	0.0302971
$739$	−12.9673	−0.477012	−0.238506	−	0.971141i	$-0.576658\pi$
$739$	−12.9673	−0.477012	−0.238506	+	0.971141i	$0.576658\pi$
$740$	3.93539	0.144668
$741$	−5.11090	−0.187754
$742$	−9.99244	−0.366834
$743$	−25.2559	−0.926551	−0.463275	−	0.886214i	$-0.653326\pi$
$743$	−25.2559	−0.926551	−0.463275	+	0.886214i	$0.653326\pi$
$744$	4.78060	0.175265
$745$	−11.2175	−0.410979
$746$	22.6375	0.828819
$747$	3.63184	0.132882
$748$	−3.62773	−0.132643
$749$	33.5977	1.22763
$750$	−1.63487	−0.0596969
$751$	14.3953	0.525293	0.262647	−	0.964892i	$-0.415405\pi$
$751$	14.3953	0.525293	0.262647	+	0.964892i	$0.415405\pi$
$752$	−2.00000	−0.0729325
$753$	−29.9073	−1.08988
$754$	32.1150	1.16956
$755$	3.33392	0.121334
$756$	10.6728	0.388166
$757$	−29.3704	−1.06749	−0.533743	−	0.845647i	$-0.679215\pi$
$757$	−29.3704	−1.06749	−0.533743	+	0.845647i	$0.679215\pi$
$758$	−0.709706	−0.0257777
$759$	−6.03649	−0.219111
$760$	−0.692339	−0.0251138
$761$	24.9966	0.906127	0.453064	−	0.891478i	$-0.350331\pi$
$761$	24.9966	0.906127	0.453064	+	0.891478i	$0.350331\pi$
$762$	24.2540	0.878631
$763$	7.93389	0.287226
$764$	25.0601	0.906644
$765$	−1.18702	−0.0429168
$766$	−12.9129	−0.466562
$767$	35.7484	1.29080
$768$	−1.63487	−0.0589932
$769$	−39.3115	−1.41761	−0.708804	−	0.705405i	$-0.750765\pi$
$769$	−39.3115	−1.41761	−0.708804	+	0.705405i	$0.750765\pi$
$770$	−1.96207	−0.0707083
$771$	16.7890	0.604640
$772$	−11.9103	−0.428661
$773$	49.7385	1.78897	0.894485	−	0.447097i	$-0.147542\pi$
$773$	49.7385	1.78897	0.894485	+	0.447097i	$0.147542\pi$
$774$	0.327207	0.0117612
$775$	−2.92415	−0.105039
$776$	−0.791840	−0.0284254
$777$	−12.6237	−0.452872
$778$	25.4918	0.913925
$779$	1.74151	0.0623959
$780$	7.38207	0.264321
$781$	−4.01124	−0.143534
$782$	−13.3948	−0.478998
$783$	−38.6879	−1.38259
$784$	−3.15026	−0.112509
$785$	17.3816	0.620378
$786$	−17.3129	−0.617532
$787$	38.8036	1.38320	0.691599	−	0.722282i	$-0.256907\pi$
$787$	38.8036	1.38320	0.691599	+	0.722282i	$0.256907\pi$
$788$	−19.5000	−0.694657
$789$	8.98925	0.320026
$790$	−15.3554	−0.546320
$791$	28.7863	1.02352
$792$	0.327207	0.0116268
$793$	−4.28619	−0.152207
$794$	8.98716	0.318943
$795$	8.32604	0.295294
$796$	−13.1615	−0.466497
$797$	15.7711	0.558642	0.279321	−	0.960198i	$-0.409891\pi$
$797$	15.7711	0.558642	0.279321	+	0.960198i	$0.409891\pi$
$798$	2.22084	0.0786169
$799$	−7.25546	−0.256680
$800$	1.00000	0.0353553
$801$	−3.24945	−0.114814
$802$	−22.7724	−0.804123
$803$	9.47747	0.334453
$804$	−8.63561	−0.304554
$805$	−7.24465	−0.255340
$806$	13.2037	0.465080
$807$	21.9073	0.771172
$808$	5.88053	0.206876
$809$	55.2795	1.94353	0.971763	−	0.235961i	$-0.0758237\pi$
$809$	55.2795	1.94353	0.971763	+	0.235961i	$0.0758237\pi$
$810$	−7.91131	−0.277975
$811$	10.2837	0.361111	0.180555	−	0.983565i	$-0.442210\pi$
$811$	10.2837	0.361111	0.180555	+	0.983565i	$0.442210\pi$
$812$	−13.9549	−0.489722
$813$	−21.0311	−0.737591
$814$	−3.93539	−0.137935
$815$	−5.91744	−0.207279
$816$	−5.93086	−0.207622
$817$	0.692339	0.0242219
$818$	32.1961	1.12571
$819$	2.89890	0.101296
$820$	−2.51539	−0.0878414
$821$	34.9791	1.22078	0.610389	−	0.792102i	$-0.291013\pi$
$821$	34.9791	1.22078	0.610389	+	0.792102i	$0.291013\pi$
$822$	29.8636	1.04161
$823$	−18.5743	−0.647460	−0.323730	−	0.946150i	$-0.604937\pi$
$823$	−18.5743	−0.647460	−0.323730	+	0.946150i	$0.604937\pi$
$824$	−15.1796	−0.528807
$825$	1.63487	0.0569188
$826$	−15.5338	−0.540489
$827$	−24.8202	−0.863082	−0.431541	−	0.902093i	$-0.642030\pi$
$827$	−24.8202	−0.863082	−0.431541	+	0.902093i	$0.642030\pi$
$828$	1.20816	0.0419864
$829$	40.5057	1.40682	0.703410	−	0.710785i	$-0.251660\pi$
$829$	40.5057	1.40682	0.703410	+	0.710785i	$0.251660\pi$
$830$	−11.0995	−0.385269
$831$	34.2628	1.18856
$832$	−4.51539	−0.156543
$833$	−11.4283	−0.395967
$834$	−30.9361	−1.07123
$835$	−17.1107	−0.592142
$836$	0.692339	0.0239451
$837$	−15.9060	−0.549793
$838$	19.8174	0.684579
$839$	37.1090	1.28114	0.640572	−	0.767898i	$-0.278697\pi$
$839$	37.1090	1.28114	0.640572	+	0.767898i	$0.278697\pi$
$840$	−3.20773	−0.110677
$841$	21.5853	0.744322
$842$	−1.73069	−0.0596435
$843$	−24.3866	−0.839921
$844$	−3.51539	−0.121005
$845$	7.38878	0.254182
$846$	0.654414	0.0224992
$847$	1.96207	0.0674177
$848$	−5.09279	−0.174887
$849$	−20.1827	−0.692669
$850$	3.62773	0.124430
$851$	−14.5308	−0.498109
$852$	−6.55785	−0.224668
$853$	32.3048	1.10609	0.553047	−	0.833150i	$-0.313465\pi$
$853$	32.3048	1.10609	0.553047	+	0.833150i	$0.313465\pi$
$854$	1.86248	0.0637327
$855$	0.226538	0.00774745
$856$	17.1236	0.585272
$857$	−18.5211	−0.632668	−0.316334	−	0.948648i	$-0.602452\pi$
$857$	−18.5211	−0.632668	−0.316334	+	0.948648i	$0.602452\pi$
$858$	−7.38207	−0.252020
$859$	−9.25194	−0.315672	−0.157836	−	0.987465i	$-0.550452\pi$
$859$	−9.25194	−0.315672	−0.157836	+	0.987465i	$0.550452\pi$
$860$	−1.00000	−0.0340997
$861$	8.06871	0.274981
$862$	−12.5600	−0.427796
$863$	10.2638	0.349383	0.174691	−	0.984623i	$-0.444107\pi$
$863$	10.2638	0.349383	0.174691	+	0.984623i	$0.444107\pi$
$864$	5.43954	0.185057
$865$	−18.5083	−0.629300
$866$	18.5083	0.628936
$867$	6.27719	0.213184
$868$	−5.73740	−0.194740
$869$	15.3554	0.520896
$870$	11.6277	0.394217
$871$	−23.8510	−0.808159
$872$	4.04362	0.136934
$873$	0.259096	0.00876906
$874$	2.55635	0.0864699
$875$	1.96207	0.0663302
$876$	15.4944	0.523508
$877$	−47.3395	−1.59854	−0.799271	−	0.600971i	$-0.794781\pi$
$877$	−47.3395	−1.59854	−0.799271	+	0.600971i	$0.794781\pi$
$878$	−1.99286	−0.0672559
$879$	9.73363	0.328307
$880$	−1.00000	−0.0337100
$881$	38.1960	1.28685	0.643427	−	0.765507i	$-0.277512\pi$
$881$	38.1960	1.28685	0.643427	+	0.765507i	$0.277512\pi$
$882$	1.03079	0.0347084
$883$	−20.9715	−0.705746	−0.352873	−	0.935671i	$-0.614795\pi$
$883$	−20.9715	−0.705746	−0.352873	+	0.935671i	$0.614795\pi$
$884$	−16.3806	−0.550940
$885$	12.9433	0.435083
$886$	41.3662	1.38972
$887$	7.67732	0.257779	0.128890	−	0.991659i	$-0.458859\pi$
$887$	7.67732	0.257779	0.128890	+	0.991659i	$0.458859\pi$
$888$	−6.43385	−0.215906
$889$	−29.1083	−0.976261
$890$	9.93086	0.332883
$891$	7.91131	0.265039
$892$	14.3986	0.482100
$893$	1.38468	0.0463365
$894$	18.3392	0.613354
$895$	−8.39331	−0.280558
$896$	1.96207	0.0655483
$897$	−27.2571	−0.910089
$898$	−4.73026	−0.157851
$899$	20.7975	0.693637
$900$	−0.327207	−0.0109069
$901$	−18.4753	−0.615501
$902$	2.51539	0.0837535
$903$	3.20773	0.106747
$904$	14.6714	0.487962
$905$	−24.4636	−0.813198
$906$	−5.45051	−0.181081
$907$	−47.7829	−1.58661	−0.793303	−	0.608828i	$-0.791640\pi$
$907$	−47.7829	−1.58661	−0.793303	+	0.608828i	$0.791640\pi$
$908$	−1.30883	−0.0434350
$909$	−1.92415	−0.0638200
$910$	−8.85954	−0.293691
$911$	26.0429	0.862841	0.431420	−	0.902151i	$-0.358013\pi$
$911$	26.0429	0.862841	0.431420	+	0.902151i	$0.358013\pi$
$912$	1.13188	0.0374804
$913$	11.0995	0.367340
$914$	−13.6303	−0.450851
$915$	−1.55188	−0.0513036
$916$	−12.7694	−0.421911
$917$	20.7780	0.686150
$918$	19.7332	0.651293
$919$	5.92063	0.195304	0.0976518	−	0.995221i	$-0.468867\pi$
$919$	5.92063	0.195304	0.0976518	+	0.995221i	$0.468867\pi$
$920$	−3.69234	−0.121733
$921$	−47.6538	−1.57025
$922$	−2.72163	−0.0896321
$923$	−18.1123	−0.596175
$924$	3.20773	0.105527
$925$	3.93539	0.129395
$926$	1.30095	0.0427519
$927$	4.96688	0.163134
$928$	−7.11234	−0.233474
$929$	−28.4247	−0.932584	−0.466292	−	0.884631i	$-0.654410\pi$
$929$	−28.4247	−0.932584	−0.466292	+	0.884631i	$0.654410\pi$
$930$	4.78060	0.156762
$931$	2.18105	0.0714810
$932$	−26.7754	−0.877057
$933$	43.8775	1.43648
$934$	−30.8949	−1.01091
$935$	−3.62773	−0.118639
$936$	1.47747	0.0482926
$937$	−24.1872	−0.790163	−0.395081	−	0.918646i	$-0.629284\pi$
$937$	−24.1872	−0.790163	−0.395081	+	0.918646i	$0.629284\pi$
$938$	10.3640	0.338395
$939$	11.7377	0.383046
$940$	−2.00000	−0.0652328
$941$	−14.9867	−0.488554	−0.244277	−	0.969706i	$-0.578551\pi$
$941$	−14.9867	−0.488554	−0.244277	+	0.969706i	$0.578551\pi$
$942$	−28.4167	−0.925866
$943$	9.28769	0.302449
$944$	−7.91701	−0.257677
$945$	10.6728	0.347186
$946$	1.00000	0.0325128
$947$	−12.1135	−0.393636	−0.196818	−	0.980440i	$-0.563061\pi$
$947$	−12.1135	−0.393636	−0.196818	+	0.980440i	$0.563061\pi$
$948$	25.1040	0.815341
$949$	42.7945	1.38917
$950$	−0.692339	−0.0224625
$951$	−50.1983	−1.62779
$952$	7.11788	0.230692
$953$	−29.1026	−0.942725	−0.471363	−	0.881939i	$-0.656238\pi$
$953$	−29.1026	−0.942725	−0.471363	+	0.881939i	$0.656238\pi$
$954$	1.66640	0.0539516
$955$	25.0601	0.810927
$956$	−2.95227	−0.0954833
$957$	−11.6277	−0.375871
$958$	23.0451	0.744552
$959$	−35.8406	−1.15735
$960$	−1.63487	−0.0527651
$961$	−22.4493	−0.724172
$962$	−17.7698	−0.572923
$963$	−5.60296	−0.180553
$964$	13.8591	0.446372
$965$	−11.9103	−0.383406
$966$	11.8440	0.381076
$967$	−53.0223	−1.70508	−0.852541	−	0.522661i	$-0.824939\pi$
$967$	−53.0223	−1.70508	−0.852541	+	0.522661i	$0.824939\pi$
$968$	1.00000	0.0321412
$969$	4.10617	0.131909
$970$	−0.791840	−0.0254245
$971$	36.5591	1.17324	0.586618	−	0.809864i	$-0.300459\pi$
$971$	36.5591	1.17324	0.586618	+	0.809864i	$0.300459\pi$
$972$	−3.38468	−0.108564
$973$	37.1278	1.19026
$974$	−13.2002	−0.422961
$975$	7.38207	0.236416
$976$	0.949239	0.0303844
$977$	15.5055	0.496065	0.248032	−	0.968752i	$-0.420216\pi$
$977$	15.5055	0.496065	0.248032	+	0.968752i	$0.420216\pi$
$978$	9.67423	0.309348
$979$	−9.93086	−0.317392
$980$	−3.15026	−0.100631
$981$	−1.32310	−0.0422434
$982$	−7.37025	−0.235194
$983$	41.2966	1.31716	0.658579	−	0.752511i	$-0.271158\pi$
$983$	41.2966	1.31716	0.658579	+	0.752511i	$0.271158\pi$
$984$	4.11234	0.131097
$985$	−19.5000	−0.621320
$986$	−25.8016	−0.821692
$987$	6.41547	0.204207
$988$	3.12618	0.0994572
$989$	3.69234	0.117410
$990$	0.327207	0.0103993
$991$	6.48023	0.205851	0.102926	−	0.994689i	$-0.467180\pi$
$991$	6.48023	0.205851	0.102926	+	0.994689i	$0.467180\pi$
$992$	−2.92415	−0.0928419
$993$	−29.6929	−0.942275
$994$	7.87036	0.249633
$995$	−13.1615	−0.417248
$996$	18.1462	0.574985
$997$	−3.89933	−0.123493	−0.0617465	−	0.998092i	$-0.519667\pi$
$997$	−3.89933	−0.123493	−0.0617465	+	0.998092i	$0.519667\pi$
$998$	8.03382	0.254306
$999$	21.4067	0.677279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.u.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.u.1.2	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.63487 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.63487 q^{6} +1.96207 q^{7} +1.00000 q^{8} -0.327207 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.63487 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.63487 q^{6} +1.96207 q^{7} +1.00000 q^{8} -0.327207 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.63487 q^{12} -4.51539 q^{13} +1.96207 q^{14} -1.63487 q^{15} +1.00000 q^{16} +3.62773 q^{17} -0.327207 q^{18} -0.692339 q^{19} +1.00000 q^{20} -3.20773 q^{21} -1.00000 q^{22} -3.69234 q^{23} -1.63487 q^{24} +1.00000 q^{25} -4.51539 q^{26} +5.43954 q^{27} +1.96207 q^{28} -7.11234 q^{29} -1.63487 q^{30} -2.92415 q^{31} +1.00000 q^{32} +1.63487 q^{33} +3.62773 q^{34} +1.96207 q^{35} -0.327207 q^{36} +3.93539 q^{37} -0.692339 q^{38} +7.38207 q^{39} +1.00000 q^{40} -2.51539 q^{41} -3.20773 q^{42} -1.00000 q^{43} -1.00000 q^{44} -0.327207 q^{45} -3.69234 q^{46} -2.00000 q^{47} -1.63487 q^{48} -3.15026 q^{49} +1.00000 q^{50} -5.93086 q^{51} -4.51539 q^{52} -5.09279 q^{53} +5.43954 q^{54} -1.00000 q^{55} +1.96207 q^{56} +1.13188 q^{57} -7.11234 q^{58} -7.91701 q^{59} -1.63487 q^{60} +0.949239 q^{61} -2.92415 q^{62} -0.642005 q^{63} +1.00000 q^{64} -4.51539 q^{65} +1.63487 q^{66} +5.28215 q^{67} +3.62773 q^{68} +6.03649 q^{69} +1.96207 q^{70} +4.01124 q^{71} -0.327207 q^{72} -9.47747 q^{73} +3.93539 q^{74} -1.63487 q^{75} -0.692339 q^{76} -1.96207 q^{77} +7.38207 q^{78} -15.3554 q^{79} +1.00000 q^{80} -7.91131 q^{81} -2.51539 q^{82} -11.0995 q^{83} -3.20773 q^{84} +3.62773 q^{85} -1.00000 q^{86} +11.6277 q^{87} -1.00000 q^{88} +9.93086 q^{89} -0.327207 q^{90} -8.85954 q^{91} -3.69234 q^{92} +4.78060 q^{93} -2.00000 q^{94} -0.692339 q^{95} -1.63487 q^{96} -0.791840 q^{97} -3.15026 q^{98} +0.327207 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} - 3 q^{12} - 9 q^{13} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 3 q^{21} - 4 q^{22} - 14 q^{23} - 3 q^{24} + 4 q^{25} - 9 q^{26} - 3 q^{27} - 8 q^{29} - 3 q^{30} + 4 q^{31} + 4 q^{32} + 3 q^{33} - 15 q^{34} + 3 q^{36} - 13 q^{37} - 2 q^{38} + 2 q^{39} + 4 q^{40} - q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} + 3 q^{45} - 14 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{50} + 5 q^{51} - 9 q^{52} - 5 q^{53} - 3 q^{54} - 4 q^{55} - 21 q^{57} - 8 q^{58} + 10 q^{59} - 3 q^{60} - 12 q^{61} + 4 q^{62} - 25 q^{63} + 4 q^{64} - 9 q^{65} + 3 q^{66} - 17 q^{67} - 15 q^{68} - 12 q^{69} + 3 q^{71} + 3 q^{72} - 21 q^{73} - 13 q^{74} - 3 q^{75} - 2 q^{76} + 2 q^{78} - 13 q^{79} + 4 q^{80} - 8 q^{81} - q^{82} - 16 q^{83} - 3 q^{84} - 15 q^{85} - 4 q^{86} + 17 q^{87} - 4 q^{88} + 11 q^{89} + 3 q^{90} + 9 q^{91} - 14 q^{92} + 3 q^{93} - 8 q^{94} - 2 q^{95} - 3 q^{96} + 26 q^{97} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 - 3 * q^12 - 9 * q^13 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 3 * q^21 - 4 * q^22 - 14 * q^23 - 3 * q^24 + 4 * q^25 - 9 * q^26 - 3 * q^27 - 8 * q^29 - 3 * q^30 + 4 * q^31 + 4 * q^32 + 3 * q^33 - 15 * q^34 + 3 * q^36 - 13 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - q^41 - 3 * q^42 - 4 * q^43 - 4 * q^44 + 3 * q^45 - 14 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^50 + 5 * q^51 - 9 * q^52 - 5 * q^53 - 3 * q^54 - 4 * q^55 - 21 * q^57 - 8 * q^58 + 10 * q^59 - 3 * q^60 - 12 * q^61 + 4 * q^62 - 25 * q^63 + 4 * q^64 - 9 * q^65 + 3 * q^66 - 17 * q^67 - 15 * q^68 - 12 * q^69 + 3 * q^71 + 3 * q^72 - 21 * q^73 - 13 * q^74 - 3 * q^75 - 2 * q^76 + 2 * q^78 - 13 * q^79 + 4 * q^80 - 8 * q^81 - q^82 - 16 * q^83 - 3 * q^84 - 15 * q^85 - 4 * q^86 + 17 * q^87 - 4 * q^88 + 11 * q^89 + 3 * q^90 + 9 * q^91 - 14 * q^92 + 3 * q^93 - 8 * q^94 - 2 * q^95 - 3 * q^96 + 26 * q^97 - 3 * q^99

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