LMFDB - Embedded newform 8043.2.a.s.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62429 q^{2} -1.00000 q^{3} +4.88687 q^{4} -1.77661 q^{5} +2.62429 q^{6} -1.00000 q^{7} -7.57598 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62429 q^{2} -1.00000 q^{3} +4.88687 q^{4} -1.77661 q^{5} +2.62429 q^{6} -1.00000 q^{7} -7.57598 q^{8} +1.00000 q^{9} +4.66233 q^{10} -0.992937 q^{11} -4.88687 q^{12} +0.501623 q^{13} +2.62429 q^{14} +1.77661 q^{15} +10.1078 q^{16} -4.64450 q^{17} -2.62429 q^{18} +0.340784 q^{19} -8.68206 q^{20} +1.00000 q^{21} +2.60575 q^{22} +1.71356 q^{23} +7.57598 q^{24} -1.84366 q^{25} -1.31640 q^{26} -1.00000 q^{27} -4.88687 q^{28} -9.58297 q^{29} -4.66233 q^{30} -9.30586 q^{31} -11.3738 q^{32} +0.992937 q^{33} +12.1885 q^{34} +1.77661 q^{35} +4.88687 q^{36} -3.76751 q^{37} -0.894315 q^{38} -0.501623 q^{39} +13.4596 q^{40} +0.0486713 q^{41} -2.62429 q^{42} +1.77848 q^{43} -4.85236 q^{44} -1.77661 q^{45} -4.49688 q^{46} -5.26953 q^{47} -10.1078 q^{48} +1.00000 q^{49} +4.83830 q^{50} +4.64450 q^{51} +2.45137 q^{52} +1.88628 q^{53} +2.62429 q^{54} +1.76406 q^{55} +7.57598 q^{56} -0.340784 q^{57} +25.1485 q^{58} -7.26559 q^{59} +8.68206 q^{60} -1.78277 q^{61} +24.4212 q^{62} -1.00000 q^{63} +9.63241 q^{64} -0.891188 q^{65} -2.60575 q^{66} +14.0606 q^{67} -22.6971 q^{68} -1.71356 q^{69} -4.66233 q^{70} -8.17787 q^{71} -7.57598 q^{72} +6.13488 q^{73} +9.88701 q^{74} +1.84366 q^{75} +1.66537 q^{76} +0.992937 q^{77} +1.31640 q^{78} -16.6448 q^{79} -17.9576 q^{80} +1.00000 q^{81} -0.127727 q^{82} -14.1533 q^{83} +4.88687 q^{84} +8.25146 q^{85} -4.66723 q^{86} +9.58297 q^{87} +7.52247 q^{88} +5.45871 q^{89} +4.66233 q^{90} -0.501623 q^{91} +8.37397 q^{92} +9.30586 q^{93} +13.8287 q^{94} -0.605440 q^{95} +11.3738 q^{96} +7.64090 q^{97} -2.62429 q^{98} -0.992937 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * 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 $

$2$	−2.62429	−1.85565	−0.927825	−	0.373016i	$-0.878324\pi$
$2$	−2.62429	−1.85565	−0.927825	+	0.373016i	$0.878324\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.88687	2.44344
$5$	−1.77661	−0.794523	−0.397262	−	0.917705i	$-0.630039\pi$
$5$	−1.77661	−0.794523	−0.397262	+	0.917705i	$0.630039\pi$
$6$	2.62429	1.07136
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.57598	−2.67851
$9$	1.00000	0.333333
$10$	4.66233	1.47436
$11$	−0.992937	−0.299382	−0.149691	−	0.988733i	$-0.547828\pi$
$11$	−0.992937	−0.299382	−0.149691	+	0.988733i	$0.547828\pi$
$12$	−4.88687	−1.41072
$13$	0.501623	0.139125	0.0695626	−	0.997578i	$-0.477840\pi$
$13$	0.501623	0.139125	0.0695626	+	0.997578i	$0.477840\pi$
$14$	2.62429	0.701370
$15$	1.77661	0.458718
$16$	10.1078	2.52695
$17$	−4.64450	−1.12646	−0.563229	−	0.826301i	$-0.690441\pi$
$17$	−4.64450	−1.12646	−0.563229	+	0.826301i	$0.690441\pi$
$18$	−2.62429	−0.618550
$19$	0.340784	0.0781813	0.0390906	−	0.999236i	$-0.487554\pi$
$19$	0.340784	0.0781813	0.0390906	+	0.999236i	$0.487554\pi$
$20$	−8.68206	−1.94137
$21$	1.00000	0.218218
$22$	2.60575	0.555548
$23$	1.71356	0.357303	0.178651	−	0.983912i	$-0.442827\pi$
$23$	1.71356	0.357303	0.178651	+	0.983912i	$0.442827\pi$
$24$	7.57598	1.54644
$25$	−1.84366	−0.368732
$26$	−1.31640	−0.258168
$27$	−1.00000	−0.192450
$28$	−4.88687	−0.923532
$29$	−9.58297	−1.77951	−0.889757	−	0.456435i	$-0.849126\pi$
$29$	−9.58297	−1.77951	−0.889757	+	0.456435i	$0.849126\pi$
$30$	−4.66233	−0.851221
$31$	−9.30586	−1.67138	−0.835691	−	0.549200i	$-0.814933\pi$
$31$	−9.30586	−1.67138	−0.835691	+	0.549200i	$0.814933\pi$
$32$	−11.3738	−2.01062
$33$	0.992937	0.172848
$34$	12.1885	2.09031
$35$	1.77661	0.300302
$36$	4.88687	0.814479
$37$	−3.76751	−0.619374	−0.309687	−	0.950839i	$-0.600224\pi$
$37$	−3.76751	−0.619374	−0.309687	+	0.950839i	$0.600224\pi$
$38$	−0.894315	−0.145077
$39$	−0.501623	−0.0803240
$40$	13.4596	2.12814
$41$	0.0486713	0.00760117	0.00380059	−	0.999993i	$-0.498790\pi$
$41$	0.0486713	0.00760117	0.00380059	+	0.999993i	$0.498790\pi$
$42$	−2.62429	−0.404936
$43$	1.77848	0.271215	0.135608	−	0.990763i	$-0.456701\pi$
$43$	1.77848	0.271215	0.135608	+	0.990763i	$0.456701\pi$
$44$	−4.85236	−0.731520
$45$	−1.77661	−0.264841
$46$	−4.49688	−0.663029
$47$	−5.26953	−0.768639	−0.384320	−	0.923200i	$-0.625564\pi$
$47$	−5.26953	−0.768639	−0.384320	+	0.923200i	$0.625564\pi$
$48$	−10.1078	−1.45893
$49$	1.00000	0.142857
$50$	4.83830	0.684238
$51$	4.64450	0.650360
$52$	2.45137	0.339944
$53$	1.88628	0.259100	0.129550	−	0.991573i	$-0.458647\pi$
$53$	1.88628	0.259100	0.129550	+	0.991573i	$0.458647\pi$
$54$	2.62429	0.357120
$55$	1.76406	0.237866
$56$	7.57598	1.01238
$57$	−0.340784	−0.0451380
$58$	25.1485	3.30215
$59$	−7.26559	−0.945899	−0.472950	−	0.881089i	$-0.656811\pi$
$59$	−7.26559	−0.945899	−0.472950	+	0.881089i	$0.656811\pi$
$60$	8.68206	1.12085
$61$	−1.78277	−0.228260	−0.114130	−	0.993466i	$-0.536408\pi$
$61$	−1.78277	−0.228260	−0.114130	+	0.993466i	$0.536408\pi$
$62$	24.4212	3.10150
$63$	−1.00000	−0.125988
$64$	9.63241	1.20405
$65$	−0.891188	−0.110538
$66$	−2.60575	−0.320746
$67$	14.0606	1.71777	0.858886	−	0.512166i	$-0.171157\pi$
$67$	14.0606	1.71777	0.858886	+	0.512166i	$0.171157\pi$
$68$	−22.6971	−2.75243
$69$	−1.71356	−0.206289
$70$	−4.66233	−0.557255
$71$	−8.17787	−0.970534	−0.485267	−	0.874366i	$-0.661278\pi$
$71$	−8.17787	−0.970534	−0.485267	+	0.874366i	$0.661278\pi$
$72$	−7.57598	−0.892838
$73$	6.13488	0.718033	0.359017	−	0.933331i	$-0.383112\pi$
$73$	6.13488	0.718033	0.359017	+	0.933331i	$0.383112\pi$
$74$	9.88701	1.14934
$75$	1.84366	0.212888
$76$	1.66537	0.191031
$77$	0.992937	0.113156
$78$	1.31640	0.149053
$79$	−16.6448	−1.87269	−0.936344	−	0.351085i	$-0.885813\pi$
$79$	−16.6448	−1.87269	−0.936344	+	0.351085i	$0.885813\pi$
$80$	−17.9576	−2.00772
$81$	1.00000	0.111111
$82$	−0.127727	−0.0141051
$83$	−14.1533	−1.55353	−0.776764	−	0.629792i	$-0.783140\pi$
$83$	−14.1533	−1.55353	−0.776764	+	0.629792i	$0.783140\pi$
$84$	4.88687	0.533202
$85$	8.25146	0.894997
$86$	−4.66723	−0.503281
$87$	9.58297	1.02740
$88$	7.52247	0.801898
$89$	5.45871	0.578623	0.289311	−	0.957235i	$-0.406574\pi$
$89$	5.45871	0.578623	0.289311	+	0.957235i	$0.406574\pi$
$90$	4.66233	0.491452
$91$	−0.501623	−0.0525844
$92$	8.37397	0.873047
$93$	9.30586	0.964973
$94$	13.8287	1.42633
$95$	−0.605440	−0.0621169
$96$	11.3738	1.16083
$97$	7.64090	0.775816	0.387908	−	0.921698i	$-0.373198\pi$
$97$	7.64090	0.775816	0.387908	+	0.921698i	$0.373198\pi$
$98$	−2.62429	−0.265093
$99$	−0.992937	−0.0997939
$100$	−9.00975	−0.900975
$101$	−4.25601	−0.423489	−0.211744	−	0.977325i	$-0.567914\pi$
$101$	−4.25601	−0.423489	−0.211744	+	0.977325i	$0.567914\pi$
$102$	−12.1885	−1.20684
$103$	15.6206	1.53915	0.769573	−	0.638558i	$-0.220469\pi$
$103$	15.6206	1.53915	0.769573	+	0.638558i	$0.220469\pi$
$104$	−3.80029	−0.372649
$105$	−1.77661	−0.173379
$106$	−4.95013	−0.480799
$107$	−15.2885	−1.47800	−0.739000	−	0.673706i	$-0.764701\pi$
$107$	−15.2885	−1.47800	−0.739000	+	0.673706i	$0.764701\pi$
$108$	−4.88687	−0.470240
$109$	−2.51864	−0.241242	−0.120621	−	0.992699i	$-0.538489\pi$
$109$	−2.51864	−0.241242	−0.120621	+	0.992699i	$0.538489\pi$
$110$	−4.62940	−0.441396
$111$	3.76751	0.357596
$112$	−10.1078	−0.955096
$113$	−18.0760	−1.70045	−0.850223	−	0.526423i	$-0.823533\pi$
$113$	−18.0760	−1.70045	−0.850223	+	0.526423i	$0.823533\pi$
$114$	0.894315	0.0837603
$115$	−3.04433	−0.283885
$116$	−46.8308	−4.34813
$117$	0.501623	0.0463751
$118$	19.0670	1.75526
$119$	4.64450	0.425761
$120$	−13.4596	−1.22868
$121$	−10.0141	−0.910371
$122$	4.67849	0.423571
$123$	−0.0486713	−0.00438854
$124$	−45.4766	−4.08392
$125$	12.1585	1.08749
$126$	2.62429	0.233790
$127$	−4.45709	−0.395503	−0.197752	−	0.980252i	$-0.563364\pi$
$127$	−4.45709	−0.395503	−0.197752	+	0.980252i	$0.563364\pi$
$128$	−2.53068	−0.223683
$129$	−1.77848	−0.156586
$130$	2.33873	0.205120
$131$	−4.99986	−0.436840	−0.218420	−	0.975855i	$-0.570090\pi$
$131$	−4.99986	−0.436840	−0.218420	+	0.975855i	$0.570090\pi$
$132$	4.85236	0.422344
$133$	−0.340784	−0.0295498
$134$	−36.8990	−3.18759
$135$	1.77661	0.152906
$136$	35.1867	3.01723
$137$	−8.44788	−0.721751	−0.360875	−	0.932614i	$-0.617522\pi$
$137$	−8.44788	−0.721751	−0.360875	+	0.932614i	$0.617522\pi$
$138$	4.49688	0.382800
$139$	−9.63840	−0.817518	−0.408759	−	0.912642i	$-0.634038\pi$
$139$	−9.63840	−0.817518	−0.408759	+	0.912642i	$0.634038\pi$
$140$	8.68206	0.733768
$141$	5.26953	0.443774
$142$	21.4611	1.80097
$143$	−0.498080	−0.0416516
$144$	10.1078	0.842316
$145$	17.0252	1.41387
$146$	−16.0997	−1.33242
$147$	−1.00000	−0.0824786
$148$	−18.4113	−1.51340
$149$	−3.00263	−0.245985	−0.122992	−	0.992408i	$-0.539249\pi$
$149$	−3.00263	−0.245985	−0.122992	+	0.992408i	$0.539249\pi$
$150$	−4.83830	−0.395045
$151$	18.4976	1.50531	0.752655	−	0.658415i	$-0.228773\pi$
$151$	18.4976	1.50531	0.752655	+	0.658415i	$0.228773\pi$
$152$	−2.58178	−0.209410
$153$	−4.64450	−0.375486
$154$	−2.60575	−0.209977
$155$	16.5329	1.32795
$156$	−2.45137	−0.196267
$157$	10.7811	0.860429	0.430215	−	0.902727i	$-0.358438\pi$
$157$	10.7811	0.860429	0.430215	+	0.902727i	$0.358438\pi$
$158$	43.6807	3.47505
$159$	−1.88628	−0.149591
$160$	20.2067	1.59748
$161$	−1.71356	−0.135048
$162$	−2.62429	−0.206183
$163$	14.6436	1.14698	0.573489	−	0.819213i	$-0.305590\pi$
$163$	14.6436	1.14698	0.573489	+	0.819213i	$0.305590\pi$
$164$	0.237850	0.0185730
$165$	−1.76406	−0.137332
$166$	37.1423	2.88280
$167$	9.42831	0.729585	0.364792	−	0.931089i	$-0.381140\pi$
$167$	9.42831	0.729585	0.364792	+	0.931089i	$0.381140\pi$
$168$	−7.57598	−0.584500
$169$	−12.7484	−0.980644
$170$	−21.6542	−1.66080
$171$	0.340784	0.0260604
$172$	8.69119	0.662697
$173$	11.6110	0.882767	0.441383	−	0.897319i	$-0.354488\pi$
$173$	11.6110	0.882767	0.441383	+	0.897319i	$0.354488\pi$
$174$	−25.1485	−1.90650
$175$	1.84366	0.139368
$176$	−10.0364	−0.756522
$177$	7.26559	0.546115
$178$	−14.3252	−1.07372
$179$	3.95451	0.295574	0.147787	−	0.989019i	$-0.452785\pi$
$179$	3.95451	0.295574	0.147787	+	0.989019i	$0.452785\pi$
$180$	−8.68206	−0.647123
$181$	−17.8366	−1.32579	−0.662893	−	0.748714i	$-0.730671\pi$
$181$	−17.8366	−1.32579	−0.662893	+	0.748714i	$0.730671\pi$
$182$	1.31640	0.0975782
$183$	1.78277	0.131786
$184$	−12.9819	−0.957040
$185$	6.69338	0.492107
$186$	−24.4212	−1.79065
$187$	4.61170	0.337241
$188$	−25.7515	−1.87812
$189$	1.00000	0.0727393
$190$	1.58885	0.115267
$191$	17.3276	1.25378	0.626890	−	0.779108i	$-0.284327\pi$
$191$	17.3276	1.25378	0.626890	+	0.779108i	$0.284327\pi$
$192$	−9.63241	−0.695159
$193$	−6.12468	−0.440864	−0.220432	−	0.975402i	$-0.570747\pi$
$193$	−6.12468	−0.440864	−0.220432	+	0.975402i	$0.570747\pi$
$194$	−20.0519	−1.43964
$195$	0.891188	0.0638193
$196$	4.88687	0.349062
$197$	−24.0107	−1.71069	−0.855347	−	0.518056i	$-0.826656\pi$
$197$	−24.0107	−1.71069	−0.855347	+	0.518056i	$0.826656\pi$
$198$	2.60575	0.185183
$199$	−12.8479	−0.910760	−0.455380	−	0.890297i	$-0.650497\pi$
$199$	−12.8479	−0.910760	−0.455380	+	0.890297i	$0.650497\pi$
$200$	13.9676	0.987655
$201$	−14.0606	−0.991757
$202$	11.1690	0.785847
$203$	9.58297	0.672593
$204$	22.6971	1.58911
$205$	−0.0864698	−0.00603931
$206$	−40.9930	−2.85612
$207$	1.71356	0.119101
$208$	5.07030	0.351562
$209$	−0.338377	−0.0234061
$210$	4.66233	0.321731
$211$	−26.2150	−1.80471	−0.902357	−	0.430988i	$-0.858165\pi$
$211$	−26.2150	−1.80471	−0.902357	+	0.430988i	$0.858165\pi$
$212$	9.21799	0.633094
$213$	8.17787	0.560338
$214$	40.1215	2.74265
$215$	−3.15966	−0.215487
$216$	7.57598	0.515480
$217$	9.30586	0.631723
$218$	6.60964	0.447661
$219$	−6.13488	−0.414557
$220$	8.62074	0.581210
$221$	−2.32979	−0.156719
$222$	−9.88701	−0.663573
$223$	−16.9507	−1.13510	−0.567551	−	0.823338i	$-0.692109\pi$
$223$	−16.9507	−1.13510	−0.567551	+	0.823338i	$0.692109\pi$
$224$	11.3738	0.759941
$225$	−1.84366	−0.122911
$226$	47.4365	3.15543
$227$	−7.97495	−0.529316	−0.264658	−	0.964342i	$-0.585259\pi$
$227$	−7.97495	−0.529316	−0.264658	+	0.964342i	$0.585259\pi$
$228$	−1.66537	−0.110292
$229$	−25.7010	−1.69837	−0.849185	−	0.528096i	$-0.822906\pi$
$229$	−25.7010	−1.69837	−0.849185	+	0.528096i	$0.822906\pi$
$230$	7.98920	0.526792
$231$	−0.992937	−0.0653305
$232$	72.6004	4.76645
$233$	−5.85268	−0.383422	−0.191711	−	0.981451i	$-0.561404\pi$
$233$	−5.85268	−0.383422	−0.191711	+	0.981451i	$0.561404\pi$
$234$	−1.31640	−0.0860559
$235$	9.36189	0.610702
$236$	−35.5060	−2.31125
$237$	16.6448	1.08120
$238$	−12.1885	−0.790063
$239$	−15.0793	−0.975400	−0.487700	−	0.873011i	$-0.662164\pi$
$239$	−15.0793	−0.975400	−0.487700	+	0.873011i	$0.662164\pi$
$240$	17.9576	1.15916
$241$	−2.07380	−0.133586	−0.0667928	−	0.997767i	$-0.521277\pi$
$241$	−2.07380	−0.133586	−0.0667928	+	0.997767i	$0.521277\pi$
$242$	26.2798	1.68933
$243$	−1.00000	−0.0641500
$244$	−8.71216	−0.557739
$245$	−1.77661	−0.113503
$246$	0.127727	0.00814359
$247$	0.170945	0.0108770
$248$	70.5010	4.47682
$249$	14.1533	0.896929
$250$	−31.9074	−2.01800
$251$	14.4959	0.914974	0.457487	−	0.889216i	$-0.348750\pi$
$251$	14.4959	0.914974	0.457487	+	0.889216i	$0.348750\pi$
$252$	−4.88687	−0.307844
$253$	−1.70146	−0.106970
$254$	11.6967	0.733915
$255$	−8.25146	−0.516727
$256$	−12.6236	−0.788975
$257$	31.5705	1.96931	0.984656	−	0.174504i	$-0.0558323\pi$
$257$	31.5705	1.96931	0.984656	+	0.174504i	$0.0558323\pi$
$258$	4.66723	0.290569
$259$	3.76751	0.234101
$260$	−4.35512	−0.270093
$261$	−9.58297	−0.593171
$262$	13.1211	0.810621
$263$	−4.77522	−0.294453	−0.147226	−	0.989103i	$-0.547035\pi$
$263$	−4.77522	−0.294453	−0.147226	+	0.989103i	$0.547035\pi$
$264$	−7.52247	−0.462976
$265$	−3.35117	−0.205861
$266$	0.894315	0.0548340
$267$	−5.45871	−0.334068
$268$	68.7123	4.19727
$269$	22.3214	1.36096	0.680479	−	0.732767i	$-0.261772\pi$
$269$	22.3214	1.36096	0.680479	+	0.732767i	$0.261772\pi$
$270$	−4.66233	−0.283740
$271$	13.2707	0.806140	0.403070	−	0.915169i	$-0.367943\pi$
$271$	13.2707	0.806140	0.403070	+	0.915169i	$0.367943\pi$
$272$	−46.9456	−2.84650
$273$	0.501623	0.0303596
$274$	22.1696	1.33932
$275$	1.83064	0.110392
$276$	−8.37397	−0.504054
$277$	8.75389	0.525970	0.262985	−	0.964800i	$-0.415293\pi$
$277$	8.75389	0.525970	0.262985	+	0.964800i	$0.415293\pi$
$278$	25.2939	1.51703
$279$	−9.30586	−0.557127
$280$	−13.4596	−0.804362
$281$	−1.63759	−0.0976905	−0.0488453	−	0.998806i	$-0.515554\pi$
$281$	−1.63759	−0.0976905	−0.0488453	+	0.998806i	$0.515554\pi$
$282$	−13.8287	−0.823490
$283$	11.7581	0.698947	0.349474	−	0.936946i	$-0.386360\pi$
$283$	11.7581	0.698947	0.349474	+	0.936946i	$0.386360\pi$
$284$	−39.9642	−2.37144
$285$	0.605440	0.0358632
$286$	1.30710	0.0772907
$287$	−0.0486713	−0.00287297
$288$	−11.3738	−0.670205
$289$	4.57140	0.268906
$290$	−44.6790	−2.62364
$291$	−7.64090	−0.447918
$292$	29.9804	1.75447
$293$	25.8966	1.51289	0.756447	−	0.654055i	$-0.226933\pi$
$293$	25.8966	1.51289	0.756447	+	0.654055i	$0.226933\pi$
$294$	2.62429	0.153051
$295$	12.9081	0.751539
$296$	28.5426	1.65900
$297$	0.992937	0.0576161
$298$	7.87976	0.456462
$299$	0.859563	0.0497098
$300$	9.00975	0.520178
$301$	−1.77848	−0.102510
$302$	−48.5429	−2.79333
$303$	4.25601	0.244501
$304$	3.44458	0.197560
$305$	3.16728	0.181358
$306$	12.1885	0.696770
$307$	−7.94691	−0.453554	−0.226777	−	0.973947i	$-0.572819\pi$
$307$	−7.94691	−0.453554	−0.226777	+	0.973947i	$0.572819\pi$
$308$	4.85236	0.276489
$309$	−15.6206	−0.888627
$310$	−43.3870	−2.46422
$311$	15.8925	0.901182	0.450591	−	0.892731i	$-0.351213\pi$
$311$	15.8925	0.901182	0.450591	+	0.892731i	$0.351213\pi$
$312$	3.80029	0.215149
$313$	−13.8906	−0.785144	−0.392572	−	0.919721i	$-0.628415\pi$
$313$	−13.8906	−0.785144	−0.392572	+	0.919721i	$0.628415\pi$
$314$	−28.2928	−1.59666
$315$	1.77661	0.100101
$316$	−81.3411	−4.57579
$317$	−20.3898	−1.14520	−0.572602	−	0.819833i	$-0.694066\pi$
$317$	−20.3898	−1.14520	−0.572602	+	0.819833i	$0.694066\pi$
$318$	4.95013	0.277589
$319$	9.51529	0.532754
$320$	−17.1130	−0.956647
$321$	15.2885	0.853323
$322$	4.49688	0.250601
$323$	−1.58277	−0.0880679
$324$	4.88687	0.271493
$325$	−0.924824	−0.0513000
$326$	−38.4291	−2.12839
$327$	2.51864	0.139281
$328$	−0.368732	−0.0203598
$329$	5.26953	0.290518
$330$	4.62940	0.254840
$331$	−23.2121	−1.27585	−0.637927	−	0.770097i	$-0.720208\pi$
$331$	−23.2121	−1.27585	−0.637927	+	0.770097i	$0.720208\pi$
$332$	−69.1654	−3.79595
$333$	−3.76751	−0.206458
$334$	−24.7426	−1.35385
$335$	−24.9801	−1.36481
$336$	10.1078	0.551425
$337$	−22.5229	−1.22690	−0.613451	−	0.789733i	$-0.710219\pi$
$337$	−22.5229	−1.22690	−0.613451	+	0.789733i	$0.710219\pi$
$338$	33.4554	1.81973
$339$	18.0760	0.981753
$340$	40.3239	2.18687
$341$	9.24014	0.500381
$342$	−0.894315	−0.0483590
$343$	−1.00000	−0.0539949
$344$	−13.4737	−0.726454
$345$	3.04433	0.163901
$346$	−30.4705	−1.63811
$347$	−26.4144	−1.41800	−0.709001	−	0.705208i	$-0.750854\pi$
$347$	−26.4144	−1.41800	−0.709001	+	0.705208i	$0.750854\pi$
$348$	46.8308	2.51039
$349$	−23.1478	−1.23907	−0.619537	−	0.784968i	$-0.712680\pi$
$349$	−23.1478	−1.23907	−0.619537	+	0.784968i	$0.712680\pi$
$350$	−4.83830	−0.258618
$351$	−0.501623	−0.0267747
$352$	11.2934	0.601942
$353$	−30.4222	−1.61921	−0.809605	−	0.586976i	$-0.800318\pi$
$353$	−30.4222	−1.61921	−0.809605	+	0.586976i	$0.800318\pi$
$354$	−19.0670	−1.01340
$355$	14.5289	0.771112
$356$	26.6760	1.41383
$357$	−4.64450	−0.245813
$358$	−10.3778	−0.548482
$359$	7.78570	0.410914	0.205457	−	0.978666i	$-0.434132\pi$
$359$	7.78570	0.410914	0.205457	+	0.978666i	$0.434132\pi$
$360$	13.4596	0.709381
$361$	−18.8839	−0.993888
$362$	46.8084	2.46019
$363$	10.0141	0.525603
$364$	−2.45137	−0.128487
$365$	−10.8993	−0.570494
$366$	−4.67849	−0.244549
$367$	1.50946	0.0787934	0.0393967	−	0.999224i	$-0.487456\pi$
$367$	1.50946	0.0787934	0.0393967	+	0.999224i	$0.487456\pi$
$368$	17.3203	0.902885
$369$	0.0486713	0.00253372
$370$	−17.5654	−0.913179
$371$	−1.88628	−0.0979306
$372$	45.4766	2.35785
$373$	18.0600	0.935113	0.467557	−	0.883963i	$-0.345134\pi$
$373$	18.0600	0.935113	0.467557	+	0.883963i	$0.345134\pi$
$374$	−12.1024	−0.625801
$375$	−12.1585	−0.627863
$376$	39.9218	2.05881
$377$	−4.80704	−0.247575
$378$	−2.62429	−0.134979
$379$	11.9539	0.614032	0.307016	−	0.951704i	$-0.400670\pi$
$379$	11.9539	0.614032	0.307016	+	0.951704i	$0.400670\pi$
$380$	−2.95871	−0.151779
$381$	4.45709	0.228344
$382$	−45.4725	−2.32658
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	2.53068	0.129143
$385$	−1.76406	−0.0899048
$386$	16.0729	0.818089
$387$	1.77848	0.0904051
$388$	37.3401	1.89566
$389$	−36.1589	−1.83333	−0.916664	−	0.399659i	$-0.869128\pi$
$389$	−36.1589	−1.83333	−0.916664	+	0.399659i	$0.869128\pi$
$390$	−2.33873	−0.118426
$391$	−7.95865	−0.402486
$392$	−7.57598	−0.382645
$393$	4.99986	0.252209
$394$	63.0110	3.17445
$395$	29.5713	1.48789
$396$	−4.85236	−0.243840
$397$	6.11176	0.306740	0.153370	−	0.988169i	$-0.450987\pi$
$397$	6.11176	0.306740	0.153370	+	0.988169i	$0.450987\pi$
$398$	33.7164	1.69005
$399$	0.340784	0.0170606
$400$	−18.6353	−0.931767
$401$	7.05255	0.352188	0.176094	−	0.984373i	$-0.443654\pi$
$401$	7.05255	0.352188	0.176094	+	0.984373i	$0.443654\pi$
$402$	36.8990	1.84035
$403$	−4.66804	−0.232531
$404$	−20.7986	−1.03477
$405$	−1.77661	−0.0882804
$406$	−25.1485	−1.24810
$407$	3.74090	0.185429
$408$	−35.1867	−1.74200
$409$	21.5473	1.06545	0.532724	−	0.846289i	$-0.321169\pi$
$409$	21.5473	1.06545	0.532724	+	0.846289i	$0.321169\pi$
$410$	0.226921	0.0112068
$411$	8.44788	0.416703
$412$	76.3361	3.76081
$413$	7.26559	0.357516
$414$	−4.49688	−0.221010
$415$	25.1449	1.23431
$416$	−5.70534	−0.279727
$417$	9.63840	0.471994
$418$	0.887999	0.0434334
$419$	−4.16363	−0.203407	−0.101703	−	0.994815i	$-0.532429\pi$
$419$	−4.16363	−0.203407	−0.101703	+	0.994815i	$0.532429\pi$
$420$	−8.68206	−0.423641
$421$	−12.6669	−0.617349	−0.308674	−	0.951168i	$-0.599885\pi$
$421$	−12.6669	−0.617349	−0.308674	+	0.951168i	$0.599885\pi$
$422$	68.7956	3.34892
$423$	−5.26953	−0.256213
$424$	−14.2904	−0.694003
$425$	8.56289	0.415361
$426$	−21.4611	−1.03979
$427$	1.78277	0.0862742
$428$	−74.7132	−3.61140
$429$	0.498080	0.0240475
$430$	8.29184	0.399868
$431$	−29.3403	−1.41327	−0.706635	−	0.707578i	$-0.749788\pi$
$431$	−29.3403	−1.41327	−0.706635	+	0.707578i	$0.749788\pi$
$432$	−10.1078	−0.486311
$433$	−32.0134	−1.53846	−0.769232	−	0.638970i	$-0.779361\pi$
$433$	−32.0134	−1.53846	−0.769232	+	0.638970i	$0.779361\pi$
$434$	−24.4212	−1.17226
$435$	−17.0252	−0.816296
$436$	−12.3083	−0.589460
$437$	0.583956	0.0279344
$438$	16.0997	0.769272
$439$	6.83315	0.326128	0.163064	−	0.986615i	$-0.447862\pi$
$439$	6.83315	0.326128	0.163064	+	0.986615i	$0.447862\pi$
$440$	−13.3645	−0.637127
$441$	1.00000	0.0476190
$442$	6.11403	0.290815
$443$	40.8917	1.94282	0.971411	−	0.237404i	$-0.0762964\pi$
$443$	40.8917	1.94282	0.971411	+	0.237404i	$0.0762964\pi$
$444$	18.4113	0.873763
$445$	−9.69800	−0.459729
$446$	44.4834	2.10635
$447$	3.00263	0.142019
$448$	−9.63241	−0.455089
$449$	−14.6174	−0.689837	−0.344919	−	0.938633i	$-0.612094\pi$
$449$	−14.6174	−0.689837	−0.344919	+	0.938633i	$0.612094\pi$
$450$	4.83830	0.228079
$451$	−0.0483275	−0.00227565
$452$	−88.3350	−4.15493
$453$	−18.4976	−0.869091
$454$	20.9285	0.982225
$455$	0.891188	0.0417795
$456$	2.58178	0.120903
$457$	−22.2410	−1.04039	−0.520195	−	0.854048i	$-0.674141\pi$
$457$	−22.2410	−1.04039	−0.520195	+	0.854048i	$0.674141\pi$
$458$	67.4467	3.15158
$459$	4.64450	0.216787
$460$	−14.8773	−0.693656
$461$	−4.80576	−0.223826	−0.111913	−	0.993718i	$-0.535698\pi$
$461$	−4.80576	−0.223826	−0.111913	+	0.993718i	$0.535698\pi$
$462$	2.60575	0.121230
$463$	33.5759	1.56040	0.780202	−	0.625528i	$-0.215116\pi$
$463$	33.5759	1.56040	0.780202	+	0.625528i	$0.215116\pi$
$464$	−96.8627	−4.49674
$465$	−16.5329	−0.766694
$466$	15.3591	0.711496
$467$	−11.8626	−0.548934	−0.274467	−	0.961596i	$-0.588501\pi$
$467$	−11.8626	−0.548934	−0.274467	+	0.961596i	$0.588501\pi$
$468$	2.45137	0.113315
$469$	−14.0606	−0.649257
$470$	−24.5683	−1.13325
$471$	−10.7811	−0.496769
$472$	55.0440	2.53360
$473$	−1.76592	−0.0811969
$474$	−43.6807	−2.00632
$475$	−0.628291	−0.0288280
$476$	22.6971	1.04032
$477$	1.88628	0.0863666
$478$	39.5724	1.81000
$479$	−23.1695	−1.05864	−0.529321	−	0.848422i	$-0.677553\pi$
$479$	−23.1695	−1.05864	−0.529321	+	0.848422i	$0.677553\pi$
$480$	−20.2067	−0.922306
$481$	−1.88987	−0.0861706
$482$	5.44226	0.247888
$483$	1.71356	0.0779699
$484$	−48.9375	−2.22443
$485$	−13.5749	−0.616404
$486$	2.62429	0.119040
$487$	−2.54028	−0.115111	−0.0575555	−	0.998342i	$-0.518331\pi$
$487$	−2.54028	−0.115111	−0.0575555	+	0.998342i	$0.518331\pi$
$488$	13.5062	0.611398
$489$	−14.6436	−0.662208
$490$	4.66233	0.210622
$491$	37.6823	1.70058	0.850289	−	0.526317i	$-0.176427\pi$
$491$	37.6823	1.70058	0.850289	+	0.526317i	$0.176427\pi$
$492$	−0.237850	−0.0107231
$493$	44.5081	2.00455
$494$	−0.448609	−0.0201839
$495$	1.76406	0.0792886
$496$	−94.0617	−4.22349
$497$	8.17787	0.366828
$498$	−37.1423	−1.66439
$499$	−14.8685	−0.665603	−0.332802	−	0.942997i	$-0.607994\pi$
$499$	−14.8685	−0.665603	−0.332802	+	0.942997i	$0.607994\pi$
$500$	59.4171	2.65721
$501$	−9.42831	−0.421226
$502$	−38.0414	−1.69787
$503$	−9.70834	−0.432873	−0.216437	−	0.976297i	$-0.569444\pi$
$503$	−9.70834	−0.432873	−0.216437	+	0.976297i	$0.569444\pi$
$504$	7.57598	0.337461
$505$	7.56126	0.336472
$506$	4.46512	0.198499
$507$	12.7484	0.566175
$508$	−21.7812	−0.966387
$509$	−19.8834	−0.881316	−0.440658	−	0.897675i	$-0.645255\pi$
$509$	−19.8834	−0.881316	−0.440658	+	0.897675i	$0.645255\pi$
$510$	21.6542	0.958864
$511$	−6.13488	−0.271391
$512$	38.1893	1.68774
$513$	−0.340784	−0.0150460
$514$	−82.8500	−3.65436
$515$	−27.7517	−1.22289
$516$	−8.69119	−0.382608
$517$	5.23231	0.230117
$518$	−9.88701	−0.434410
$519$	−11.6110	−0.509666
$520$	6.75162	0.296078
$521$	34.5840	1.51515	0.757576	−	0.652747i	$-0.226384\pi$
$521$	34.5840	1.51515	0.757576	+	0.652747i	$0.226384\pi$
$522$	25.1485	1.10072
$523$	−18.3170	−0.800945	−0.400472	−	0.916309i	$-0.631154\pi$
$523$	−18.3170	−0.800945	−0.400472	+	0.916309i	$0.631154\pi$
$524$	−24.4337	−1.06739
$525$	−1.84366	−0.0804640
$526$	12.5315	0.546401
$527$	43.2211	1.88274
$528$	10.0364	0.436778
$529$	−20.0637	−0.872335
$530$	8.79444	0.382006
$531$	−7.26559	−0.315300
$532$	−1.66537	−0.0722029
$533$	0.0244146	0.00105751
$534$	14.3252	0.619913
$535$	27.1618	1.17430
$536$	−106.523	−4.60108
$537$	−3.95451	−0.170650
$538$	−58.5777	−2.52546
$539$	−0.992937	−0.0427688
$540$	8.68206	0.373616
$541$	43.6325	1.87591	0.937953	−	0.346763i	$-0.112719\pi$
$541$	43.6325	1.87591	0.937953	+	0.346763i	$0.112719\pi$
$542$	−34.8262	−1.49591
$543$	17.8366	0.765443
$544$	52.8254	2.26487
$545$	4.47464	0.191673
$546$	−1.31640	−0.0563368
$547$	−19.0031	−0.812515	−0.406258	−	0.913759i	$-0.633166\pi$
$547$	−19.0031	−0.812515	−0.406258	+	0.913759i	$0.633166\pi$
$548$	−41.2837	−1.76355
$549$	−1.78277	−0.0760867
$550$	−4.80412	−0.204849
$551$	−3.26573	−0.139125
$552$	12.9819	0.552547
$553$	16.6448	0.707809
$554$	−22.9727	−0.976017
$555$	−6.69338	−0.284118
$556$	−47.1016	−1.99755
$557$	−9.35733	−0.396483	−0.198241	−	0.980153i	$-0.563523\pi$
$557$	−9.35733	−0.396483	−0.198241	+	0.980153i	$0.563523\pi$
$558$	24.4212	1.03383
$559$	0.892125	0.0377329
$560$	17.9576	0.758846
$561$	−4.61170	−0.194706
$562$	4.29751	0.181279
$563$	−9.50393	−0.400543	−0.200271	−	0.979740i	$-0.564182\pi$
$563$	−9.50393	−0.400543	−0.200271	+	0.979740i	$0.564182\pi$
$564$	25.7515	1.08433
$565$	32.1139	1.35104
$566$	−30.8566	−1.29700
$567$	−1.00000	−0.0419961
$568$	61.9554	2.59959
$569$	32.3332	1.35548	0.677739	−	0.735303i	$-0.262960\pi$
$569$	32.3332	1.35548	0.677739	+	0.735303i	$0.262960\pi$
$570$	−1.58885	−0.0665495
$571$	35.8581	1.50061	0.750307	−	0.661090i	$-0.229906\pi$
$571$	35.8581	1.50061	0.750307	+	0.661090i	$0.229906\pi$
$572$	−2.43405	−0.101773
$573$	−17.3276	−0.723870
$574$	0.127727	0.00533123
$575$	−3.15923	−0.131749
$576$	9.63241	0.401350
$577$	14.1228	0.587939	0.293970	−	0.955815i	$-0.405024\pi$
$577$	14.1228	0.587939	0.293970	+	0.955815i	$0.405024\pi$
$578$	−11.9967	−0.498995
$579$	6.12468	0.254533
$580$	83.2000	3.45469
$581$	14.1533	0.587178
$582$	20.0519	0.831178
$583$	−1.87295	−0.0775698
$584$	−46.4777	−1.92326
$585$	−0.891188	−0.0368461
$586$	−67.9600	−2.80740
$587$	−41.2899	−1.70421	−0.852107	−	0.523367i	$-0.824676\pi$
$587$	−41.2899	−1.70421	−0.852107	+	0.523367i	$0.824676\pi$
$588$	−4.88687	−0.201531
$589$	−3.17129	−0.130671
$590$	−33.8746	−1.39459
$591$	24.0107	0.987669
$592$	−38.0812	−1.56513
$593$	−27.2943	−1.12084	−0.560421	−	0.828208i	$-0.689360\pi$
$593$	−27.2943	−1.12084	−0.560421	+	0.828208i	$0.689360\pi$
$594$	−2.60575	−0.106915
$595$	−8.25146	−0.338277
$596$	−14.6735	−0.601049
$597$	12.8479	0.525828
$598$	−2.25574	−0.0922440
$599$	24.5137	1.00160	0.500801	−	0.865562i	$-0.333039\pi$
$599$	24.5137	1.00160	0.500801	+	0.865562i	$0.333039\pi$
$600$	−13.9676	−0.570223
$601$	8.31234	0.339067	0.169534	−	0.985524i	$-0.445774\pi$
$601$	8.31234	0.339067	0.169534	+	0.985524i	$0.445774\pi$
$602$	4.66723	0.190222
$603$	14.0606	0.572591
$604$	90.3953	3.67813
$605$	17.7911	0.723311
$606$	−11.1690	−0.453709
$607$	21.8557	0.887097	0.443548	−	0.896250i	$-0.353719\pi$
$607$	21.8557	0.887097	0.443548	+	0.896250i	$0.353719\pi$
$608$	−3.87600	−0.157193
$609$	−9.58297	−0.388322
$610$	−8.31185	−0.336537
$611$	−2.64332	−0.106937
$612$	−22.6971	−0.917476
$613$	29.5801	1.19473	0.597364	−	0.801970i	$-0.296215\pi$
$613$	29.5801	1.19473	0.597364	+	0.801970i	$0.296215\pi$
$614$	20.8550	0.841637
$615$	0.0864698	0.00348680
$616$	−7.52247	−0.303089
$617$	9.93558	0.399991	0.199996	−	0.979797i	$-0.435907\pi$
$617$	9.93558	0.399991	0.199996	+	0.979797i	$0.435907\pi$
$618$	40.9930	1.64898
$619$	10.2123	0.410465	0.205233	−	0.978713i	$-0.434205\pi$
$619$	10.2123	0.410465	0.205233	+	0.978713i	$0.434205\pi$
$620$	80.7941	3.24477
$621$	−1.71356	−0.0687629
$622$	−41.7065	−1.67228
$623$	−5.45871	−0.218699
$624$	−5.07030	−0.202974
$625$	−12.3826	−0.495304
$626$	36.4529	1.45695
$627$	0.338377	0.0135135
$628$	52.6861	2.10240
$629$	17.4982	0.697699
$630$	−4.66233	−0.185752
$631$	−48.0232	−1.91177	−0.955886	−	0.293737i	$-0.905101\pi$
$631$	−48.0232	−1.91177	−0.955886	+	0.293737i	$0.905101\pi$
$632$	126.101	5.01602
$633$	26.2150	1.04195
$634$	53.5086	2.12510
$635$	7.91851	0.314236
$636$	−9.21799	−0.365517
$637$	0.501623	0.0198750
$638$	−24.9708	−0.988605
$639$	−8.17787	−0.323511
$640$	4.49603	0.177721
$641$	41.6119	1.64357	0.821786	−	0.569796i	$-0.192978\pi$
$641$	41.6119	1.64357	0.821786	+	0.569796i	$0.192978\pi$
$642$	−40.1215	−1.58347
$643$	−34.6713	−1.36730	−0.683652	−	0.729808i	$-0.739609\pi$
$643$	−34.6713	−1.36730	−0.683652	+	0.729808i	$0.739609\pi$
$644$	−8.37397	−0.329981
$645$	3.15966	0.124411
$646$	4.15365	0.163423
$647$	11.9719	0.470665	0.235333	−	0.971915i	$-0.424382\pi$
$647$	11.9719	0.470665	0.235333	+	0.971915i	$0.424382\pi$
$648$	−7.57598	−0.297613
$649$	7.21428	0.283185
$650$	2.42700	0.0951948
$651$	−9.30586	−0.364726
$652$	71.5616	2.80257
$653$	3.11125	0.121753	0.0608764	−	0.998145i	$-0.480610\pi$
$653$	3.11125	0.121753	0.0608764	+	0.998145i	$0.480610\pi$
$654$	−6.60964	−0.258457
$655$	8.88279	0.347079
$656$	0.491959	0.0192078
$657$	6.13488	0.239344
$658$	−13.8287	−0.539101
$659$	2.56283	0.0998337	0.0499168	−	0.998753i	$-0.484104\pi$
$659$	2.56283	0.0998337	0.0499168	+	0.998753i	$0.484104\pi$
$660$	−8.62074	−0.335562
$661$	−15.9289	−0.619563	−0.309781	−	0.950808i	$-0.600256\pi$
$661$	−15.9289	−0.619563	−0.309781	+	0.950808i	$0.600256\pi$
$662$	60.9153	2.36754
$663$	2.32979	0.0904815
$664$	107.225	4.16114
$665$	0.605440	0.0234780
$666$	9.88701	0.383114
$667$	−16.4210	−0.635825
$668$	46.0750	1.78269
$669$	16.9507	0.655352
$670$	65.5550	2.53261
$671$	1.77018	0.0683369
$672$	−11.3738	−0.438752
$673$	−30.5952	−1.17936	−0.589678	−	0.807638i	$-0.700745\pi$
$673$	−30.5952	−1.17936	−0.589678	+	0.807638i	$0.700745\pi$
$674$	59.1066	2.27670
$675$	1.84366	0.0709626
$676$	−62.2997	−2.39614
$677$	−6.49576	−0.249653	−0.124826	−	0.992179i	$-0.539837\pi$
$677$	−6.49576	−0.249653	−0.124826	+	0.992179i	$0.539837\pi$
$678$	−47.4365	−1.82179
$679$	−7.64090	−0.293231
$680$	−62.5129	−2.39726
$681$	7.97495	0.305601
$682$	−24.2488	−0.928533
$683$	−33.4022	−1.27810	−0.639051	−	0.769165i	$-0.720673\pi$
$683$	−33.4022	−1.27810	−0.639051	+	0.769165i	$0.720673\pi$
$684$	1.66537	0.0636770
$685$	15.0086	0.573448
$686$	2.62429	0.100196
$687$	25.7010	0.980554
$688$	17.9765	0.685346
$689$	0.946200	0.0360473
$690$	−7.98920	−0.304144
$691$	−0.759384	−0.0288883	−0.0144442	−	0.999896i	$-0.504598\pi$
$691$	−0.759384	−0.0288883	−0.0144442	+	0.999896i	$0.504598\pi$
$692$	56.7414	2.15698
$693$	0.992937	0.0377186
$694$	69.3190	2.63131
$695$	17.1237	0.649538
$696$	−72.6004	−2.75191
$697$	−0.226054	−0.00856240
$698$	60.7465	2.29929
$699$	5.85268	0.221369
$700$	9.00975	0.340536
$701$	22.1960	0.838333	0.419167	−	0.907909i	$-0.362322\pi$
$701$	22.1960	0.838333	0.419167	+	0.907909i	$0.362322\pi$
$702$	1.31640	0.0496844
$703$	−1.28391	−0.0484235
$704$	−9.56438	−0.360471
$705$	−9.36189	−0.352589
$706$	79.8365	3.00469
$707$	4.25601	0.160064
$708$	35.5060	1.33440
$709$	17.2755	0.648793	0.324397	−	0.945921i	$-0.394839\pi$
$709$	17.2755	0.648793	0.324397	+	0.945921i	$0.394839\pi$
$710$	−38.1279	−1.43091
$711$	−16.6448	−0.624229
$712$	−41.3551	−1.54985
$713$	−15.9462	−0.597190
$714$	12.1885	0.456143
$715$	0.884893	0.0330931
$716$	19.3252	0.722217
$717$	15.0793	0.563147
$718$	−20.4319	−0.762512
$719$	−19.7401	−0.736182	−0.368091	−	0.929790i	$-0.619989\pi$
$719$	−19.7401	−0.736182	−0.368091	+	0.929790i	$0.619989\pi$
$720$	−17.9576	−0.669240
$721$	−15.6206	−0.581743
$722$	49.5567	1.84431
$723$	2.07380	0.0771256
$724$	−87.1653	−3.23947
$725$	17.6678	0.656165
$726$	−26.2798	−0.975335
$727$	37.0101	1.37263	0.686314	−	0.727305i	$-0.259228\pi$
$727$	37.0101	1.37263	0.686314	+	0.727305i	$0.259228\pi$
$728$	3.80029	0.140848
$729$	1.00000	0.0370370
$730$	28.6028	1.05864
$731$	−8.26014	−0.305512
$732$	8.71216	0.322011
$733$	23.7613	0.877644	0.438822	−	0.898574i	$-0.355396\pi$
$733$	23.7613	0.877644	0.438822	+	0.898574i	$0.355396\pi$
$734$	−3.96127	−0.146213
$735$	1.77661	0.0655312
$736$	−19.4897	−0.718398
$737$	−13.9613	−0.514270
$738$	−0.127727	−0.00470171
$739$	−43.0792	−1.58469	−0.792347	−	0.610071i	$-0.791141\pi$
$739$	−43.0792	−1.58469	−0.792347	+	0.610071i	$0.791141\pi$
$740$	32.7097	1.20243
$741$	−0.170945	−0.00627983
$742$	4.95013	0.181725
$743$	−30.0448	−1.10224	−0.551118	−	0.834427i	$-0.685799\pi$
$743$	−30.0448	−1.10224	−0.551118	+	0.834427i	$0.685799\pi$
$744$	−70.5010	−2.58469
$745$	5.33450	0.195441
$746$	−47.3947	−1.73524
$747$	−14.1533	−0.517842
$748$	22.5368	0.824027
$749$	15.2885	0.558631
$750$	31.9074	1.16509
$751$	−10.9565	−0.399807	−0.199903	−	0.979816i	$-0.564063\pi$
$751$	−10.9565	−0.399807	−0.199903	+	0.979816i	$0.564063\pi$
$752$	−53.2633	−1.94231
$753$	−14.4959	−0.528261
$754$	12.6150	0.459413
$755$	−32.8629	−1.19600
$756$	4.88687	0.177734
$757$	37.5835	1.36600	0.682998	−	0.730420i	$-0.260676\pi$
$757$	37.5835	1.36600	0.682998	+	0.730420i	$0.260676\pi$
$758$	−31.3705	−1.13943
$759$	1.70146	0.0617591
$760$	4.58680	0.166381
$761$	13.6516	0.494870	0.247435	−	0.968905i	$-0.420412\pi$
$761$	13.6516	0.494870	0.247435	+	0.968905i	$0.420412\pi$
$762$	−11.6967	−0.423726
$763$	2.51864	0.0911810
$764$	84.6777	3.06353
$765$	8.25146	0.298332
$766$	−2.62429	−0.0948193
$767$	−3.64459	−0.131598
$768$	12.6236	0.455515
$769$	−34.8895	−1.25815	−0.629073	−	0.777346i	$-0.716566\pi$
$769$	−34.8895	−1.25815	−0.629073	+	0.777346i	$0.716566\pi$
$770$	4.62940	0.166832
$771$	−31.5705	−1.13698
$772$	−29.9305	−1.07722
$773$	41.2632	1.48413	0.742067	−	0.670326i	$-0.233846\pi$
$773$	41.2632	1.48413	0.742067	+	0.670326i	$0.233846\pi$
$774$	−4.66723	−0.167760
$775$	17.1569	0.616293
$776$	−57.8873	−2.07803
$777$	−3.76751	−0.135159
$778$	94.8912	3.40201
$779$	0.0165864	0.000594269 0
$780$	4.35512	0.155938
$781$	8.12011	0.290560
$782$	20.8858	0.746874
$783$	9.58297	0.342468
$784$	10.1078	0.360992
$785$	−19.1539	−0.683631
$786$	−13.1211	−0.468012
$787$	18.4112	0.656289	0.328145	−	0.944627i	$-0.393577\pi$
$787$	18.4112	0.656289	0.328145	+	0.944627i	$0.393577\pi$
$788$	−117.337	−4.17997
$789$	4.77522	0.170002
$790$	−77.6035	−2.76101
$791$	18.0760	0.642708
$792$	7.52247	0.267299
$793$	−0.894278	−0.0317567
$794$	−16.0390	−0.569203
$795$	3.35117	0.118854
$796$	−62.7858	−2.22539
$797$	19.8860	0.704397	0.352199	−	0.935925i	$-0.385434\pi$
$797$	19.8860	0.704397	0.352199	+	0.935925i	$0.385434\pi$
$798$	−0.894315	−0.0316584
$799$	24.4743	0.865840
$800$	20.9694	0.741379
$801$	5.45871	0.192874
$802$	−18.5079	−0.653537
$803$	−6.09155	−0.214966
$804$	−68.7123	−2.42329
$805$	3.04433	0.107299
$806$	12.2503	0.431497
$807$	−22.3214	−0.785750
$808$	32.2434	1.13432
$809$	32.1615	1.13074	0.565369	−	0.824838i	$-0.308734\pi$
$809$	32.1615	1.13074	0.565369	+	0.824838i	$0.308734\pi$
$810$	4.66233	0.163817
$811$	−2.23982	−0.0786508	−0.0393254	−	0.999226i	$-0.512521\pi$
$811$	−2.23982	−0.0786508	−0.0393254	+	0.999226i	$0.512521\pi$
$812$	46.8308	1.64344
$813$	−13.2707	−0.465425
$814$	−9.81718	−0.344092
$815$	−26.0160	−0.911301
$816$	46.9456	1.64343
$817$	0.606077	0.0212040
$818$	−56.5464	−1.97710
$819$	−0.501623	−0.0175281
$820$	−0.422567	−0.0147567
$821$	−8.01520	−0.279732	−0.139866	−	0.990170i	$-0.544667\pi$
$821$	−8.01520	−0.279732	−0.139866	+	0.990170i	$0.544667\pi$
$822$	−22.1696	−0.773255
$823$	44.1756	1.53987	0.769933	−	0.638125i	$-0.220290\pi$
$823$	44.1756	1.53987	0.769933	+	0.638125i	$0.220290\pi$
$824$	−118.342	−4.12263
$825$	−1.83064	−0.0637347
$826$	−19.0670	−0.663425
$827$	13.6086	0.473216	0.236608	−	0.971605i	$-0.423964\pi$
$827$	13.6086	0.473216	0.236608	+	0.971605i	$0.423964\pi$
$828$	8.37397	0.291016
$829$	1.85310	0.0643608	0.0321804	−	0.999482i	$-0.489755\pi$
$829$	1.85310	0.0643608	0.0321804	+	0.999482i	$0.489755\pi$
$830$	−65.9874	−2.29045
$831$	−8.75389	−0.303669
$832$	4.83184	0.167514
$833$	−4.64450	−0.160922
$834$	−25.2939	−0.875857
$835$	−16.7504	−0.579672
$836$	−1.65361	−0.0571912
$837$	9.30586	0.321658
$838$	10.9266	0.377452
$839$	−5.65578	−0.195259	−0.0976296	−	0.995223i	$-0.531126\pi$
$839$	−5.65578	−0.195259	−0.0976296	+	0.995223i	$0.531126\pi$
$840$	13.4596	0.464399
$841$	62.8334	2.16667
$842$	33.2417	1.14558
$843$	1.63759	0.0564016
$844$	−128.109	−4.40971
$845$	22.6489	0.779145
$846$	13.8287	0.475442
$847$	10.0141	0.344088
$848$	19.0661	0.654732
$849$	−11.7581	−0.403537
$850$	−22.4715	−0.770765
$851$	−6.45586	−0.221304
$852$	39.9642	1.36915
$853$	44.3752	1.51938	0.759689	−	0.650286i	$-0.225351\pi$
$853$	44.3752	1.51938	0.759689	+	0.650286i	$0.225351\pi$
$854$	−4.67849	−0.160095
$855$	−0.605440	−0.0207056
$856$	115.826	3.95884
$857$	53.5917	1.83066	0.915328	−	0.402709i	$-0.131931\pi$
$857$	53.5917	1.83066	0.915328	+	0.402709i	$0.131931\pi$
$858$	−1.30710	−0.0446238
$859$	−8.35020	−0.284905	−0.142453	−	0.989802i	$-0.545499\pi$
$859$	−8.35020	−0.284905	−0.142453	+	0.989802i	$0.545499\pi$
$860$	−15.4408	−0.526529
$861$	0.0486713	0.00165871
$862$	76.9972	2.62254
$863$	9.01108	0.306741	0.153370	−	0.988169i	$-0.450987\pi$
$863$	9.01108	0.306741	0.153370	+	0.988169i	$0.450987\pi$
$864$	11.3738	0.386943
$865$	−20.6282	−0.701379
$866$	84.0122	2.85485
$867$	−4.57140	−0.155253
$868$	45.4766	1.54358
$869$	16.5272	0.560648
$870$	44.6790	1.51476
$871$	7.05311	0.238986
$872$	19.0812	0.646171
$873$	7.64090	0.258605
$874$	−1.53247	−0.0518365
$875$	−12.1585	−0.411033
$876$	−29.9804	−1.01294
$877$	19.1418	0.646373	0.323187	−	0.946335i	$-0.395246\pi$
$877$	19.1418	0.646373	0.323187	+	0.946335i	$0.395246\pi$
$878$	−17.9321	−0.605180
$879$	−25.8966	−0.873470
$880$	17.8307	0.601074
$881$	40.6293	1.36884	0.684418	−	0.729090i	$-0.260057\pi$
$881$	40.6293	1.36884	0.684418	+	0.729090i	$0.260057\pi$
$882$	−2.62429	−0.0883643
$883$	29.2322	0.983741	0.491871	−	0.870668i	$-0.336313\pi$
$883$	29.2322	0.983741	0.491871	+	0.870668i	$0.336313\pi$
$884$	−11.3854	−0.382932
$885$	−12.9081	−0.433901
$886$	−107.311	−3.60520
$887$	32.2131	1.08161	0.540804	−	0.841149i	$-0.318120\pi$
$887$	32.2131	1.08161	0.540804	+	0.841149i	$0.318120\pi$
$888$	−28.5426	−0.957826
$889$	4.45709	0.149486
$890$	25.4503	0.853097
$891$	−0.992937	−0.0332646
$892$	−82.8359	−2.77355
$893$	−1.79577	−0.0600932
$894$	−7.87976	−0.263538
$895$	−7.02562	−0.234841
$896$	2.53068	0.0845441
$897$	−0.859563	−0.0287000
$898$	38.3602	1.28010
$899$	89.1779	2.97425
$900$	−9.00975	−0.300325
$901$	−8.76081	−0.291865
$902$	0.126825	0.00422281
$903$	1.77848	0.0591840
$904$	136.943	4.55467
$905$	31.6887	1.05337
$906$	48.5429	1.61273
$907$	42.7239	1.41862	0.709312	−	0.704895i	$-0.249006\pi$
$907$	42.7239	1.41862	0.709312	+	0.704895i	$0.249006\pi$
$908$	−38.9726	−1.29335
$909$	−4.25601	−0.141163
$910$	−2.33873	−0.0775282
$911$	2.67636	0.0886719	0.0443360	−	0.999017i	$-0.485883\pi$
$911$	2.67636	0.0886719	0.0443360	+	0.999017i	$0.485883\pi$
$912$	−3.44458	−0.114061
$913$	14.0533	0.465098
$914$	58.3667	1.93060
$915$	−3.16728	−0.104707
$916$	−125.598	−4.14986
$917$	4.99986	0.165110
$918$	−12.1885	−0.402280
$919$	11.1615	0.368185	0.184093	−	0.982909i	$-0.441065\pi$
$919$	11.1615	0.368185	0.184093	+	0.982909i	$0.441065\pi$
$920$	23.0638	0.760391
$921$	7.94691	0.261860
$922$	12.6117	0.415343
$923$	−4.10221	−0.135026
$924$	−4.85236	−0.159631
$925$	6.94601	0.228383
$926$	−88.1127	−2.89556
$927$	15.6206	0.513049
$928$	108.994	3.57792
$929$	−32.0442	−1.05134	−0.525668	−	0.850690i	$-0.676185\pi$
$929$	−32.0442	−1.05134	−0.525668	+	0.850690i	$0.676185\pi$
$930$	43.3870	1.42272
$931$	0.340784	0.0111688
$932$	−28.6013	−0.936867
$933$	−15.8925	−0.520297
$934$	31.1308	1.01863
$935$	−8.19318	−0.267946
$936$	−3.80029	−0.124216
$937$	−54.4300	−1.77815	−0.889076	−	0.457760i	$-0.848652\pi$
$937$	−54.4300	−1.77815	−0.889076	+	0.457760i	$0.848652\pi$
$938$	36.8990	1.20479
$939$	13.8906	0.453303
$940$	45.7504	1.49221
$941$	11.1920	0.364848	0.182424	−	0.983220i	$-0.441606\pi$
$941$	11.1920	0.364848	0.182424	+	0.983220i	$0.441606\pi$
$942$	28.2928	0.921829
$943$	0.0834013	0.00271592
$944$	−73.4391	−2.39024
$945$	−1.77661	−0.0577931
$946$	4.63427	0.150673
$947$	−37.6222	−1.22256	−0.611279	−	0.791415i	$-0.709345\pi$
$947$	−37.6222	−1.22256	−0.611279	+	0.791415i	$0.709345\pi$
$948$	81.3411	2.64184
$949$	3.07740	0.0998966
$950$	1.64882	0.0534946
$951$	20.3898	0.661184
$952$	−35.1867	−1.14041
$953$	39.7502	1.28764	0.643818	−	0.765179i	$-0.277349\pi$
$953$	39.7502	1.28764	0.643818	+	0.765179i	$0.277349\pi$
$954$	−4.95013	−0.160266
$955$	−30.7843	−0.996158
$956$	−73.6907	−2.38333
$957$	−9.51529	−0.307586
$958$	60.8034	1.96447
$959$	8.44788	0.272796
$960$	17.1130	0.552320
$961$	55.5991	1.79352
$962$	4.95955	0.159902
$963$	−15.2885	−0.492666
$964$	−10.1344	−0.326408
$965$	10.8812	0.350277
$966$	−4.49688	−0.144685
$967$	21.0681	0.677504	0.338752	−	0.940876i	$-0.389995\pi$
$967$	21.0681	0.677504	0.338752	+	0.940876i	$0.389995\pi$
$968$	75.8664	2.43844
$969$	1.58277	0.0508460
$970$	35.6244	1.14383
$971$	4.42267	0.141930	0.0709651	−	0.997479i	$-0.477392\pi$
$971$	4.42267	0.141930	0.0709651	+	0.997479i	$0.477392\pi$
$972$	−4.88687	−0.156747
$973$	9.63840	0.308993
$974$	6.66642	0.213606
$975$	0.924824	0.0296181
$976$	−18.0198	−0.576801
$977$	−40.9429	−1.30988	−0.654939	−	0.755681i	$-0.727306\pi$
$977$	−40.9429	−1.30988	−0.654939	+	0.755681i	$0.727306\pi$
$978$	38.4291	1.22883
$979$	−5.42016	−0.173229
$980$	−8.68206	−0.277338
$981$	−2.51864	−0.0804141
$982$	−98.8890	−3.15568
$983$	7.27209	0.231944	0.115972	−	0.993253i	$-0.463002\pi$
$983$	7.27209	0.231944	0.115972	+	0.993253i	$0.463002\pi$
$984$	0.368732	0.0117548
$985$	42.6577	1.35919
$986$	−116.802	−3.71974
$987$	−5.26953	−0.167731
$988$	0.835388	0.0265772
$989$	3.04753	0.0969059
$990$	−4.62940	−0.147132
$991$	51.8119	1.64586	0.822930	−	0.568142i	$-0.192338\pi$
$991$	51.8119	1.64586	0.822930	+	0.568142i	$0.192338\pi$
$992$	105.843	3.36051
$993$	23.2121	0.736615
$994$	−21.4611	−0.680704
$995$	22.8256	0.723620
$996$	69.1654	2.19159
$997$	17.9549	0.568636	0.284318	−	0.958730i	$-0.408233\pi$
$997$	17.9549	0.568636	0.284318	+	0.958730i	$0.408233\pi$
$998$	39.0191	1.23513
$999$	3.76751	0.119199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.4	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.4	✓	50	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.62429 q^{2} -1.00000 q^{3} +4.88687 q^{4} -1.77661 q^{5} +2.62429 q^{6} -1.00000 q^{7} -7.57598 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62429 q^{2} -1.00000 q^{3} +4.88687 q^{4} -1.77661 q^{5} +2.62429 q^{6} -1.00000 q^{7} -7.57598 q^{8} +1.00000 q^{9} +4.66233 q^{10} -0.992937 q^{11} -4.88687 q^{12} +0.501623 q^{13} +2.62429 q^{14} +1.77661 q^{15} +10.1078 q^{16} -4.64450 q^{17} -2.62429 q^{18} +0.340784 q^{19} -8.68206 q^{20} +1.00000 q^{21} +2.60575 q^{22} +1.71356 q^{23} +7.57598 q^{24} -1.84366 q^{25} -1.31640 q^{26} -1.00000 q^{27} -4.88687 q^{28} -9.58297 q^{29} -4.66233 q^{30} -9.30586 q^{31} -11.3738 q^{32} +0.992937 q^{33} +12.1885 q^{34} +1.77661 q^{35} +4.88687 q^{36} -3.76751 q^{37} -0.894315 q^{38} -0.501623 q^{39} +13.4596 q^{40} +0.0486713 q^{41} -2.62429 q^{42} +1.77848 q^{43} -4.85236 q^{44} -1.77661 q^{45} -4.49688 q^{46} -5.26953 q^{47} -10.1078 q^{48} +1.00000 q^{49} +4.83830 q^{50} +4.64450 q^{51} +2.45137 q^{52} +1.88628 q^{53} +2.62429 q^{54} +1.76406 q^{55} +7.57598 q^{56} -0.340784 q^{57} +25.1485 q^{58} -7.26559 q^{59} +8.68206 q^{60} -1.78277 q^{61} +24.4212 q^{62} -1.00000 q^{63} +9.63241 q^{64} -0.891188 q^{65} -2.60575 q^{66} +14.0606 q^{67} -22.6971 q^{68} -1.71356 q^{69} -4.66233 q^{70} -8.17787 q^{71} -7.57598 q^{72} +6.13488 q^{73} +9.88701 q^{74} +1.84366 q^{75} +1.66537 q^{76} +0.992937 q^{77} +1.31640 q^{78} -16.6448 q^{79} -17.9576 q^{80} +1.00000 q^{81} -0.127727 q^{82} -14.1533 q^{83} +4.88687 q^{84} +8.25146 q^{85} -4.66723 q^{86} +9.58297 q^{87} +7.52247 q^{88} +5.45871 q^{89} +4.66233 q^{90} -0.501623 q^{91} +8.37397 q^{92} +9.30586 q^{93} +13.8287 q^{94} -0.605440 q^{95} +11.3738 q^{96} +7.64090 q^{97} -2.62429 q^{98} -0.992937 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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