LMFDB - Embedded newform 2001.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.77164$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.77164 q^{2} +1.00000 q^{3} +5.68196 q^{4} +2.29773 q^{5} -2.77164 q^{6} -5.27354 q^{7} -10.2051 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.77164 q^{2} +1.00000 q^{3} +5.68196 q^{4} +2.29773 q^{5} -2.77164 q^{6} -5.27354 q^{7} -10.2051 q^{8} +1.00000 q^{9} -6.36848 q^{10} +1.67873 q^{11} +5.68196 q^{12} +3.70083 q^{13} +14.6163 q^{14} +2.29773 q^{15} +16.9208 q^{16} -2.24661 q^{17} -2.77164 q^{18} +3.22268 q^{19} +13.0556 q^{20} -5.27354 q^{21} -4.65284 q^{22} -1.00000 q^{23} -10.2051 q^{24} +0.279573 q^{25} -10.2573 q^{26} +1.00000 q^{27} -29.9640 q^{28} -1.00000 q^{29} -6.36848 q^{30} +5.83534 q^{31} -26.4881 q^{32} +1.67873 q^{33} +6.22679 q^{34} -12.1172 q^{35} +5.68196 q^{36} -1.40968 q^{37} -8.93210 q^{38} +3.70083 q^{39} -23.4485 q^{40} -7.14568 q^{41} +14.6163 q^{42} +8.82562 q^{43} +9.53851 q^{44} +2.29773 q^{45} +2.77164 q^{46} +10.7579 q^{47} +16.9208 q^{48} +20.8102 q^{49} -0.774875 q^{50} -2.24661 q^{51} +21.0280 q^{52} -10.6567 q^{53} -2.77164 q^{54} +3.85728 q^{55} +53.8167 q^{56} +3.22268 q^{57} +2.77164 q^{58} -5.86788 q^{59} +13.0556 q^{60} +4.02077 q^{61} -16.1734 q^{62} -5.27354 q^{63} +39.5738 q^{64} +8.50351 q^{65} -4.65284 q^{66} -4.06540 q^{67} -12.7652 q^{68} -1.00000 q^{69} +33.5844 q^{70} +8.18183 q^{71} -10.2051 q^{72} -1.30400 q^{73} +3.90713 q^{74} +0.279573 q^{75} +18.3112 q^{76} -8.85287 q^{77} -10.2573 q^{78} +9.03636 q^{79} +38.8794 q^{80} +1.00000 q^{81} +19.8052 q^{82} -1.52544 q^{83} -29.9640 q^{84} -5.16211 q^{85} -24.4614 q^{86} -1.00000 q^{87} -17.1316 q^{88} +14.5519 q^{89} -6.36848 q^{90} -19.5164 q^{91} -5.68196 q^{92} +5.83534 q^{93} -29.8170 q^{94} +7.40486 q^{95} -26.4881 q^{96} +8.58188 q^{97} -57.6782 q^{98} +1.67873 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * 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 $

$2$	−2.77164	−1.95984	−0.979921	−	0.199386i	$-0.936105\pi$
$2$	−2.77164	−1.95984	−0.979921	+	0.199386i	$0.936105\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.68196	2.84098
$5$	2.29773	1.02758	0.513789	−	0.857917i	$-0.328242\pi$
$5$	2.29773	1.02758	0.513789	+	0.857917i	$0.328242\pi$
$6$	−2.77164	−1.13152
$7$	−5.27354	−1.99321	−0.996605	−	0.0823371i	$-0.973762\pi$
$7$	−5.27354	−1.99321	−0.996605	+	0.0823371i	$0.973762\pi$
$8$	−10.2051	−3.60803
$9$	1.00000	0.333333
$10$	−6.36848	−2.01389
$11$	1.67873	0.506157	0.253079	−	0.967446i	$-0.418557\pi$
$11$	1.67873	0.506157	0.253079	+	0.967446i	$0.418557\pi$
$12$	5.68196	1.64024
$13$	3.70083	1.02642	0.513212	−	0.858262i	$-0.328455\pi$
$13$	3.70083	1.02642	0.513212	+	0.858262i	$0.328455\pi$
$14$	14.6163	3.90638
$15$	2.29773	0.593272
$16$	16.9208	4.23019
$17$	−2.24661	−0.544883	−0.272442	−	0.962172i	$-0.587831\pi$
$17$	−2.24661	−0.544883	−0.272442	+	0.962172i	$0.587831\pi$
$18$	−2.77164	−0.653281
$19$	3.22268	0.739334	0.369667	−	0.929164i	$-0.379472\pi$
$19$	3.22268	0.739334	0.369667	+	0.929164i	$0.379472\pi$
$20$	13.0556	2.91933
$21$	−5.27354	−1.15078
$22$	−4.65284	−0.991989
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−10.2051	−2.08310
$25$	0.279573	0.0559147
$26$	−10.2573	−2.01163
$27$	1.00000	0.192450
$28$	−29.9640	−5.66267
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−6.36848	−1.16272
$31$	5.83534	1.04806	0.524029	−	0.851700i	$-0.324428\pi$
$31$	5.83534	1.04806	0.524029	+	0.851700i	$0.324428\pi$
$32$	−26.4881	−4.68248
$33$	1.67873	0.292230
$34$	6.22679	1.06789
$35$	−12.1172	−2.04818
$36$	5.68196	0.946994
$37$	−1.40968	−0.231750	−0.115875	−	0.993264i	$-0.536967\pi$
$37$	−1.40968	−0.231750	−0.115875	+	0.993264i	$0.536967\pi$
$38$	−8.93210	−1.44898
$39$	3.70083	0.592607
$40$	−23.4485	−3.70753
$41$	−7.14568	−1.11597	−0.557984	−	0.829852i	$-0.688425\pi$
$41$	−7.14568	−1.11597	−0.557984	+	0.829852i	$0.688425\pi$
$42$	14.6163	2.25535
$43$	8.82562	1.34589	0.672947	−	0.739690i	$-0.265028\pi$
$43$	8.82562	1.34589	0.672947	+	0.739690i	$0.265028\pi$
$44$	9.53851	1.43798
$45$	2.29773	0.342526
$46$	2.77164	0.408655
$47$	10.7579	1.56920	0.784600	−	0.620002i	$-0.212868\pi$
$47$	10.7579	1.56920	0.784600	+	0.620002i	$0.212868\pi$
$48$	16.9208	2.44230
$49$	20.8102	2.97288
$50$	−0.774875	−0.109584
$51$	−2.24661	−0.314589
$52$	21.0280	2.91605
$53$	−10.6567	−1.46382	−0.731908	−	0.681403i	$-0.761370\pi$
$53$	−10.6567	−1.46382	−0.731908	+	0.681403i	$0.761370\pi$
$54$	−2.77164	−0.377172
$55$	3.85728	0.520116
$56$	53.8167	7.19156
$57$	3.22268	0.426855
$58$	2.77164	0.363934
$59$	−5.86788	−0.763933	−0.381967	−	0.924176i	$-0.624753\pi$
$59$	−5.86788	−0.763933	−0.381967	+	0.924176i	$0.624753\pi$
$60$	13.0556	1.68547
$61$	4.02077	0.514807	0.257404	−	0.966304i	$-0.417133\pi$
$61$	4.02077	0.514807	0.257404	+	0.966304i	$0.417133\pi$
$62$	−16.1734	−2.05403
$63$	−5.27354	−0.664403
$64$	39.5738	4.94672
$65$	8.50351	1.05473
$66$	−4.65284	−0.572725
$67$	−4.06540	−0.496667	−0.248334	−	0.968675i	$-0.579883\pi$
$67$	−4.06540	−0.496667	−0.248334	+	0.968675i	$0.579883\pi$
$68$	−12.7652	−1.54800
$69$	−1.00000	−0.120386
$70$	33.5844	4.01410
$71$	8.18183	0.971005	0.485503	−	0.874235i	$-0.338637\pi$
$71$	8.18183	0.971005	0.485503	+	0.874235i	$0.338637\pi$
$72$	−10.2051	−1.20268
$73$	−1.30400	−0.152622	−0.0763109	−	0.997084i	$-0.524314\pi$
$73$	−1.30400	−0.152622	−0.0763109	+	0.997084i	$0.524314\pi$
$74$	3.90713	0.454194
$75$	0.279573	0.0322824
$76$	18.3112	2.10043
$77$	−8.85287	−1.00888
$78$	−10.2573	−1.16142
$79$	9.03636	1.01667	0.508335	−	0.861159i	$-0.330261\pi$
$79$	9.03636	1.01667	0.508335	+	0.861159i	$0.330261\pi$
$80$	38.8794	4.34685
$81$	1.00000	0.111111
$82$	19.8052	2.18712
$83$	−1.52544	−0.167438	−0.0837191	−	0.996489i	$-0.526680\pi$
$83$	−1.52544	−0.167438	−0.0837191	+	0.996489i	$0.526680\pi$
$84$	−29.9640	−3.26934
$85$	−5.16211	−0.559910
$86$	−24.4614	−2.63774
$87$	−1.00000	−0.107211
$88$	−17.1316	−1.82623
$89$	14.5519	1.54249	0.771247	−	0.636535i	$-0.219633\pi$
$89$	14.5519	1.54249	0.771247	+	0.636535i	$0.219633\pi$
$90$	−6.36848	−0.671296
$91$	−19.5164	−2.04588
$92$	−5.68196	−0.592385
$93$	5.83534	0.605097
$94$	−29.8170	−3.07538
$95$	7.40486	0.759723
$96$	−26.4881	−2.70343
$97$	8.58188	0.871358	0.435679	−	0.900102i	$-0.356508\pi$
$97$	8.58188	0.871358	0.435679	+	0.900102i	$0.356508\pi$
$98$	−57.6782	−5.82638
$99$	1.67873	0.168719
$100$	1.58853	0.158853
$101$	−16.9500	−1.68659	−0.843295	−	0.537451i	$-0.819387\pi$
$101$	−16.9500	−1.68659	−0.843295	+	0.537451i	$0.819387\pi$
$102$	6.22679	0.616544
$103$	11.1996	1.10353	0.551766	−	0.833999i	$-0.313954\pi$
$103$	11.1996	1.10353	0.551766	+	0.833999i	$0.313954\pi$
$104$	−37.7671	−3.70337
$105$	−12.1172	−1.18251
$106$	29.5366	2.86885
$107$	10.1710	0.983268	0.491634	−	0.870802i	$-0.336400\pi$
$107$	10.1710	0.983268	0.491634	+	0.870802i	$0.336400\pi$
$108$	5.68196	0.546747
$109$	2.78611	0.266861	0.133431	−	0.991058i	$-0.457401\pi$
$109$	2.78611	0.266861	0.133431	+	0.991058i	$0.457401\pi$
$110$	−10.6910	−1.01934
$111$	−1.40968	−0.133801
$112$	−89.2323	−8.43166
$113$	14.9996	1.41104	0.705522	−	0.708688i	$-0.250713\pi$
$113$	14.9996	1.41104	0.705522	+	0.708688i	$0.250713\pi$
$114$	−8.93210	−0.836568
$115$	−2.29773	−0.214265
$116$	−5.68196	−0.527557
$117$	3.70083	0.342142
$118$	16.2636	1.49719
$119$	11.8476	1.08607
$120$	−23.4485	−2.14054
$121$	−8.18185	−0.743805
$122$	−11.1441	−1.00894
$123$	−7.14568	−0.644304
$124$	33.1562	2.97751
$125$	−10.8463	−0.970120
$126$	14.6163	1.30213
$127$	9.47544	0.840809	0.420405	−	0.907337i	$-0.361888\pi$
$127$	9.47544	0.840809	0.420405	+	0.907337i	$0.361888\pi$
$128$	−56.7079	−5.01232
$129$	8.82562	0.777053
$130$	−23.5686	−2.06711
$131$	10.2890	0.898951	0.449475	−	0.893293i	$-0.351611\pi$
$131$	10.2890	0.898951	0.449475	+	0.893293i	$0.351611\pi$
$132$	9.53851	0.830220
$133$	−16.9949	−1.47365
$134$	11.2678	0.973389
$135$	2.29773	0.197757
$136$	22.9268	1.96596
$137$	−9.72484	−0.830849	−0.415425	−	0.909628i	$-0.636367\pi$
$137$	−9.72484	−0.830849	−0.415425	+	0.909628i	$0.636367\pi$
$138$	2.77164	0.235937
$139$	−9.72154	−0.824570	−0.412285	−	0.911055i	$-0.635269\pi$
$139$	−9.72154	−0.824570	−0.412285	+	0.911055i	$0.635269\pi$
$140$	−68.8493	−5.81883
$141$	10.7579	0.905978
$142$	−22.6771	−1.90302
$143$	6.21271	0.519533
$144$	16.9208	1.41006
$145$	−2.29773	−0.190816
$146$	3.61421	0.299115
$147$	20.8102	1.71639
$148$	−8.00977	−0.658399
$149$	14.5112	1.18880	0.594400	−	0.804169i	$-0.297389\pi$
$149$	14.5112	1.18880	0.594400	+	0.804169i	$0.297389\pi$
$150$	−0.774875	−0.0632683
$151$	3.76576	0.306453	0.153226	−	0.988191i	$-0.451034\pi$
$151$	3.76576	0.306453	0.153226	+	0.988191i	$0.451034\pi$
$152$	−32.8877	−2.66754
$153$	−2.24661	−0.181628
$154$	24.5369	1.97724
$155$	13.4081	1.07696
$156$	21.0280	1.68358
$157$	17.5108	1.39752	0.698758	−	0.715358i	$-0.253737\pi$
$157$	17.5108	1.39752	0.698758	+	0.715358i	$0.253737\pi$
$158$	−25.0455	−1.99251
$159$	−10.6567	−0.845135
$160$	−60.8625	−4.81161
$161$	5.27354	0.415613
$162$	−2.77164	−0.217760
$163$	−17.2023	−1.34738	−0.673692	−	0.739012i	$-0.735293\pi$
$163$	−17.2023	−1.34738	−0.673692	+	0.739012i	$0.735293\pi$
$164$	−40.6015	−3.17044
$165$	3.85728	0.300289
$166$	4.22795	0.328153
$167$	−9.74013	−0.753714	−0.376857	−	0.926271i	$-0.622995\pi$
$167$	−9.74013	−0.753714	−0.376857	+	0.926271i	$0.622995\pi$
$168$	53.8167	4.15205
$169$	0.696119	0.0535476
$170$	14.3075	1.09733
$171$	3.22268	0.246445
$172$	50.1468	3.82366
$173$	20.1382	1.53108	0.765541	−	0.643387i	$-0.222471\pi$
$173$	20.1382	1.53108	0.765541	+	0.643387i	$0.222471\pi$
$174$	2.77164	0.210117
$175$	−1.47434	−0.111450
$176$	28.4055	2.14114
$177$	−5.86788	−0.441057
$178$	−40.3325	−3.02305
$179$	10.6994	0.799714	0.399857	−	0.916578i	$-0.369060\pi$
$179$	10.6994	0.799714	0.399857	+	0.916578i	$0.369060\pi$
$180$	13.0556	0.973109
$181$	−20.1216	−1.49563	−0.747814	−	0.663908i	$-0.768896\pi$
$181$	−20.1216	−1.49563	−0.747814	+	0.663908i	$0.768896\pi$
$182$	54.0925	4.00960
$183$	4.02077	0.297224
$184$	10.2051	0.752327
$185$	−3.23907	−0.238141
$186$	−16.1734	−1.18589
$187$	−3.77146	−0.275797
$188$	61.1260	4.45807
$189$	−5.27354	−0.383593
$190$	−20.5236	−1.48894
$191$	16.9007	1.22289	0.611446	−	0.791286i	$-0.290588\pi$
$191$	16.9007	1.22289	0.611446	+	0.791286i	$0.290588\pi$
$192$	39.5738	2.85599
$193$	−2.84220	−0.204586	−0.102293	−	0.994754i	$-0.532618\pi$
$193$	−2.84220	−0.204586	−0.102293	+	0.994754i	$0.532618\pi$
$194$	−23.7859	−1.70772
$195$	8.50351	0.608949
$196$	118.243	8.44590
$197$	−1.41372	−0.100723	−0.0503616	−	0.998731i	$-0.516037\pi$
$197$	−1.41372	−0.100723	−0.0503616	+	0.998731i	$0.516037\pi$
$198$	−4.65284	−0.330663
$199$	19.5480	1.38572	0.692860	−	0.721072i	$-0.256350\pi$
$199$	19.5480	1.38572	0.692860	+	0.721072i	$0.256350\pi$
$200$	−2.85306	−0.201742
$201$	−4.06540	−0.286751
$202$	46.9793	3.30545
$203$	5.27354	0.370130
$204$	−12.7652	−0.893740
$205$	−16.4189	−1.14674
$206$	−31.0413	−2.16275
$207$	−1.00000	−0.0695048
$208$	62.6208	4.34197
$209$	5.41003	0.374220
$210$	33.5844	2.31754
$211$	15.2346	1.04879	0.524397	−	0.851474i	$-0.324291\pi$
$211$	15.2346	1.04879	0.524397	+	0.851474i	$0.324291\pi$
$212$	−60.5512	−4.15867
$213$	8.18183	0.560610
$214$	−28.1903	−1.92705
$215$	20.2789	1.38301
$216$	−10.2051	−0.694366
$217$	−30.7729	−2.08900
$218$	−7.72208	−0.523006
$219$	−1.30400	−0.0881162
$220$	21.9169	1.47764
$221$	−8.31432	−0.559282
$222$	3.90713	0.262229
$223$	−3.31580	−0.222042	−0.111021	−	0.993818i	$-0.535412\pi$
$223$	−3.31580	−0.222042	−0.111021	+	0.993818i	$0.535412\pi$
$224$	139.686	9.33316
$225$	0.279573	0.0186382
$226$	−41.5734	−2.76542
$227$	−6.38701	−0.423921	−0.211960	−	0.977278i	$-0.567985\pi$
$227$	−6.38701	−0.423921	−0.211960	+	0.977278i	$0.567985\pi$
$228$	18.3112	1.21269
$229$	−1.71280	−0.113185	−0.0565926	−	0.998397i	$-0.518024\pi$
$229$	−1.71280	−0.113185	−0.0565926	+	0.998397i	$0.518024\pi$
$230$	6.36848	0.419925
$231$	−8.85287	−0.582476
$232$	10.2051	0.669995
$233$	−10.2185	−0.669434	−0.334717	−	0.942319i	$-0.608641\pi$
$233$	−10.2185	−0.669434	−0.334717	+	0.942319i	$0.608641\pi$
$234$	−10.2573	−0.670543
$235$	24.7188	1.61247
$236$	−33.3411	−2.17032
$237$	9.03636	0.586975
$238$	−32.8372	−2.12852
$239$	−18.5912	−1.20256	−0.601282	−	0.799037i	$-0.705343\pi$
$239$	−18.5912	−1.20256	−0.601282	+	0.799037i	$0.705343\pi$
$240$	38.8794	2.50965
$241$	22.8983	1.47501	0.737504	−	0.675343i	$-0.236004\pi$
$241$	22.8983	1.47501	0.737504	+	0.675343i	$0.236004\pi$
$242$	22.6771	1.45774
$243$	1.00000	0.0641500
$244$	22.8459	1.46256
$245$	47.8162	3.05487
$246$	19.8052	1.26273
$247$	11.9266	0.758871
$248$	−59.5500	−3.78143
$249$	−1.52544	−0.0966705
$250$	30.0619	1.90128
$251$	18.8395	1.18914	0.594568	−	0.804045i	$-0.297323\pi$
$251$	18.8395	1.18914	0.594568	+	0.804045i	$0.297323\pi$
$252$	−29.9640	−1.88756
$253$	−1.67873	−0.105541
$254$	−26.2625	−1.64785
$255$	−5.16211	−0.323264
$256$	78.0261	4.87663
$257$	−14.3969	−0.898054	−0.449027	−	0.893518i	$-0.648229\pi$
$257$	−14.3969	−0.898054	−0.449027	+	0.893518i	$0.648229\pi$
$258$	−24.4614	−1.52290
$259$	7.43401	0.461927
$260$	48.3166	2.99647
$261$	−1.00000	−0.0618984
$262$	−28.5173	−1.76180
$263$	1.78382	0.109995	0.0549976	−	0.998486i	$-0.482485\pi$
$263$	1.78382	0.109995	0.0549976	+	0.998486i	$0.482485\pi$
$264$	−17.1316	−1.05438
$265$	−24.4863	−1.50418
$266$	47.1038	2.88812
$267$	14.5519	0.890560
$268$	−23.0994	−1.41102
$269$	−2.57069	−0.156738	−0.0783689	−	0.996924i	$-0.524971\pi$
$269$	−2.57069	−0.156738	−0.0783689	+	0.996924i	$0.524971\pi$
$270$	−6.36848	−0.387573
$271$	−5.38793	−0.327293	−0.163647	−	0.986519i	$-0.552326\pi$
$271$	−5.38793	−0.327293	−0.163647	+	0.986519i	$0.552326\pi$
$272$	−38.0144	−2.30496
$273$	−19.5164	−1.18119
$274$	26.9537	1.62833
$275$	0.469329	0.0283016
$276$	−5.68196	−0.342014
$277$	25.2470	1.51694	0.758472	−	0.651705i	$-0.225946\pi$
$277$	25.2470	1.51694	0.758472	+	0.651705i	$0.225946\pi$
$278$	26.9446	1.61603
$279$	5.83534	0.349353
$280$	123.656	7.38988
$281$	−12.6699	−0.755823	−0.377912	−	0.925842i	$-0.623358\pi$
$281$	−12.6699	−0.755823	−0.377912	+	0.925842i	$0.623358\pi$
$282$	−29.8170	−1.77557
$283$	22.1074	1.31415	0.657073	−	0.753827i	$-0.271794\pi$
$283$	22.1074	1.31415	0.657073	+	0.753827i	$0.271794\pi$
$284$	46.4889	2.75861
$285$	7.40486	0.438626
$286$	−17.2194	−1.01820
$287$	37.6830	2.22436
$288$	−26.4881	−1.56083
$289$	−11.9527	−0.703102
$290$	6.36848	0.373970
$291$	8.58188	0.503079
$292$	−7.40928	−0.433595
$293$	−22.1453	−1.29374	−0.646870	−	0.762600i	$-0.723922\pi$
$293$	−22.1453	−1.29374	−0.646870	+	0.762600i	$0.723922\pi$
$294$	−57.6782	−3.36386
$295$	−13.4828	−0.785000
$296$	14.3859	0.836163
$297$	1.67873	0.0974101
$298$	−40.2197	−2.32986
$299$	−3.70083	−0.214024
$300$	1.58853	0.0917136
$301$	−46.5422	−2.68265
$302$	−10.4373	−0.600599
$303$	−16.9500	−0.973753
$304$	54.5303	3.12753
$305$	9.23866	0.529004
$306$	6.22679	0.355962
$307$	13.9191	0.794406	0.397203	−	0.917731i	$-0.369981\pi$
$307$	13.9191	0.794406	0.397203	+	0.917731i	$0.369981\pi$
$308$	−50.3016	−2.86620
$309$	11.1996	0.637125
$310$	−37.1622	−2.11067
$311$	−5.38930	−0.305599	−0.152799	−	0.988257i	$-0.548829\pi$
$311$	−5.38930	−0.305599	−0.152799	+	0.988257i	$0.548829\pi$
$312$	−37.7671	−2.13814
$313$	−22.3895	−1.26553	−0.632764	−	0.774345i	$-0.718080\pi$
$313$	−22.3895	−1.26553	−0.632764	+	0.774345i	$0.718080\pi$
$314$	−48.5336	−2.73891
$315$	−12.1172	−0.682725
$316$	51.3443	2.88834
$317$	3.60388	0.202414	0.101207	−	0.994865i	$-0.467730\pi$
$317$	3.60388	0.202414	0.101207	+	0.994865i	$0.467730\pi$
$318$	29.5366	1.65633
$319$	−1.67873	−0.0939911
$320$	90.9300	5.08314
$321$	10.1710	0.567690
$322$	−14.6163	−0.814536
$323$	−7.24012	−0.402851
$324$	5.68196	0.315665
$325$	1.03465	0.0573922
$326$	47.6784	2.64066
$327$	2.78611	0.154072
$328$	72.9221	4.02645
$329$	−56.7321	−3.12774
$330$	−10.6910	−0.588519
$331$	−28.4927	−1.56610	−0.783051	−	0.621958i	$-0.786338\pi$
$331$	−28.4927	−1.56610	−0.783051	+	0.621958i	$0.786338\pi$
$332$	−8.66747	−0.475689
$333$	−1.40968	−0.0772502
$334$	26.9961	1.47716
$335$	−9.34119	−0.510364
$336$	−89.2323	−4.86802
$337$	24.0084	1.30782	0.653911	−	0.756572i	$-0.273127\pi$
$337$	24.0084	1.30782	0.653911	+	0.756572i	$0.273127\pi$
$338$	−1.92939	−0.104945
$339$	14.9996	0.814666
$340$	−29.3309	−1.59069
$341$	9.79599	0.530483
$342$	−8.93210	−0.482993
$343$	−72.8285	−3.93237
$344$	−90.0660	−4.85603
$345$	−2.29773	−0.123706
$346$	−55.8159	−3.00068
$347$	30.5553	1.64029	0.820146	−	0.572154i	$-0.193892\pi$
$347$	30.5553	1.64029	0.820146	+	0.572154i	$0.193892\pi$
$348$	−5.68196	−0.304585
$349$	−10.0999	−0.540635	−0.270317	−	0.962771i	$-0.587129\pi$
$349$	−10.0999	−0.540635	−0.270317	+	0.962771i	$0.587129\pi$
$350$	4.08633	0.218424
$351$	3.70083	0.197536
$352$	−44.4665	−2.37007
$353$	19.2053	1.02220	0.511098	−	0.859522i	$-0.329239\pi$
$353$	19.2053	1.02220	0.511098	+	0.859522i	$0.329239\pi$
$354$	16.2636	0.864402
$355$	18.7997	0.997783
$356$	82.6832	4.38220
$357$	11.8476	0.627041
$358$	−29.6550	−1.56731
$359$	22.4237	1.18348	0.591740	−	0.806129i	$-0.298441\pi$
$359$	22.4237	1.18348	0.591740	+	0.806129i	$0.298441\pi$
$360$	−23.4485	−1.23584
$361$	−8.61432	−0.453385
$362$	55.7698	2.93119
$363$	−8.18185	−0.429436
$364$	−110.892	−5.81230
$365$	−2.99624	−0.156831
$366$	−11.1441	−0.582512
$367$	22.1059	1.15392	0.576960	−	0.816772i	$-0.304239\pi$
$367$	22.1059	1.15392	0.576960	+	0.816772i	$0.304239\pi$
$368$	−16.9208	−0.882056
$369$	−7.14568	−0.371989
$370$	8.97753	0.466720
$371$	56.1987	2.91769
$372$	33.1562	1.71907
$373$	−14.0351	−0.726709	−0.363354	−	0.931651i	$-0.618369\pi$
$373$	−14.0351	−0.726709	−0.363354	+	0.931651i	$0.618369\pi$
$374$	10.4531	0.540518
$375$	−10.8463	−0.560099
$376$	−109.785	−5.66173
$377$	−3.70083	−0.190602
$378$	14.6163	0.751782
$379$	−21.1240	−1.08507	−0.542534	−	0.840034i	$-0.682535\pi$
$379$	−21.1240	−1.08507	−0.542534	+	0.840034i	$0.682535\pi$
$380$	42.0741	2.15836
$381$	9.47544	0.485441
$382$	−46.8426	−2.39668
$383$	16.0170	0.818431	0.409216	−	0.912438i	$-0.365802\pi$
$383$	16.0170	0.818431	0.409216	+	0.912438i	$0.365802\pi$
$384$	−56.7079	−2.89386
$385$	−20.3415	−1.03670
$386$	7.87754	0.400956
$387$	8.82562	0.448632
$388$	48.7619	2.47551
$389$	9.48004	0.480657	0.240329	−	0.970692i	$-0.422745\pi$
$389$	9.48004	0.480657	0.240329	+	0.970692i	$0.422745\pi$
$390$	−23.5686	−1.19344
$391$	2.24661	0.113616
$392$	−212.369	−10.7263
$393$	10.2890	0.519009
$394$	3.91831	0.197402
$395$	20.7631	1.04471
$396$	9.53851	0.479328
$397$	10.8768	0.545892	0.272946	−	0.962029i	$-0.412002\pi$
$397$	10.8768	0.545892	0.272946	+	0.962029i	$0.412002\pi$
$398$	−54.1799	−2.71579
$399$	−16.9949	−0.850811
$400$	4.73060	0.236530
$401$	−17.0386	−0.850869	−0.425435	−	0.904989i	$-0.639879\pi$
$401$	−17.0386	−0.850869	−0.425435	+	0.904989i	$0.639879\pi$
$402$	11.2678	0.561987
$403$	21.5956	1.07575
$404$	−96.3094	−4.79157
$405$	2.29773	0.114175
$406$	−14.6163	−0.725396
$407$	−2.36648	−0.117302
$408$	22.9268	1.13505
$409$	7.07988	0.350077	0.175039	−	0.984562i	$-0.443995\pi$
$409$	7.07988	0.350077	0.175039	+	0.984562i	$0.443995\pi$
$410$	45.5071	2.24743
$411$	−9.72484	−0.479691
$412$	63.6359	3.13512
$413$	30.9445	1.52268
$414$	2.77164	0.136218
$415$	−3.50504	−0.172056
$416$	−98.0278	−4.80621
$417$	−9.72154	−0.476066
$418$	−14.9946	−0.733411
$419$	16.0016	0.781730	0.390865	−	0.920448i	$-0.372176\pi$
$419$	16.0016	0.781730	0.390865	+	0.920448i	$0.372176\pi$
$420$	−68.8493	−3.35950
$421$	12.4817	0.608322	0.304161	−	0.952621i	$-0.401624\pi$
$421$	12.4817	0.608322	0.304161	+	0.952621i	$0.401624\pi$
$422$	−42.2248	−2.05547
$423$	10.7579	0.523067
$424$	108.753	5.28150
$425$	−0.628093	−0.0304670
$426$	−22.6771	−1.09871
$427$	−21.2037	−1.02612
$428$	57.7912	2.79344
$429$	6.21271	0.299952
$430$	−56.2058	−2.71048
$431$	6.72467	0.323916	0.161958	−	0.986798i	$-0.448219\pi$
$431$	6.72467	0.323916	0.161958	+	0.986798i	$0.448219\pi$
$432$	16.9208	0.814101
$433$	8.87260	0.426390	0.213195	−	0.977010i	$-0.431613\pi$
$433$	8.87260	0.426390	0.213195	+	0.977010i	$0.431613\pi$
$434$	85.2912	4.09411
$435$	−2.29773	−0.110168
$436$	15.8306	0.758147
$437$	−3.22268	−0.154162
$438$	3.61421	0.172694
$439$	28.8671	1.37775	0.688877	−	0.724878i	$-0.258104\pi$
$439$	28.8671	1.37775	0.688877	+	0.724878i	$0.258104\pi$
$440$	−39.3638	−1.87659
$441$	20.8102	0.990961
$442$	23.0443	1.09610
$443$	−2.97745	−0.141463	−0.0707314	−	0.997495i	$-0.522533\pi$
$443$	−2.97745	−0.141463	−0.0707314	+	0.997495i	$0.522533\pi$
$444$	−8.00977	−0.380127
$445$	33.4363	1.58503
$446$	9.19018	0.435168
$447$	14.5112	0.686354
$448$	−208.694	−9.85985
$449$	6.31768	0.298150	0.149075	−	0.988826i	$-0.452370\pi$
$449$	6.31768	0.298150	0.149075	+	0.988826i	$0.452370\pi$
$450$	−0.774875	−0.0365280
$451$	−11.9957	−0.564855
$452$	85.2271	4.00875
$453$	3.76576	0.176931
$454$	17.7025	0.830818
$455$	−44.8436	−2.10230
$456$	−32.8877	−1.54011
$457$	7.06653	0.330558	0.165279	−	0.986247i	$-0.447148\pi$
$457$	7.06653	0.330558	0.165279	+	0.986247i	$0.447148\pi$
$458$	4.74726	0.221825
$459$	−2.24661	−0.104863
$460$	−13.0556	−0.608722
$461$	12.9326	0.602332	0.301166	−	0.953572i	$-0.402624\pi$
$461$	12.9326	0.602332	0.301166	+	0.953572i	$0.402624\pi$
$462$	24.5369	1.14156
$463$	−42.0848	−1.95585	−0.977924	−	0.208963i	$-0.932991\pi$
$463$	−42.0848	−1.95585	−0.977924	+	0.208963i	$0.932991\pi$
$464$	−16.9208	−0.785527
$465$	13.4081	0.621784
$466$	28.3219	1.31198
$467$	5.03119	0.232816	0.116408	−	0.993202i	$-0.462862\pi$
$467$	5.03119	0.232816	0.116408	+	0.993202i	$0.462862\pi$
$468$	21.0280	0.972018
$469$	21.4390	0.989961
$470$	−68.5114	−3.16019
$471$	17.5108	0.806856
$472$	59.8821	2.75630
$473$	14.8159	0.681235
$474$	−25.0455	−1.15038
$475$	0.900976	0.0413396
$476$	67.3175	3.08549
$477$	−10.6567	−0.487939
$478$	51.5280	2.35684
$479$	11.6047	0.530231	0.265115	−	0.964217i	$-0.414590\pi$
$479$	11.6047	0.530231	0.265115	+	0.964217i	$0.414590\pi$
$480$	−60.8625	−2.77798
$481$	−5.21699	−0.237874
$482$	−63.4656	−2.89078
$483$	5.27354	0.239954
$484$	−46.4890	−2.11313
$485$	19.7189	0.895388
$486$	−2.77164	−0.125724
$487$	8.92181	0.404286	0.202143	−	0.979356i	$-0.435209\pi$
$487$	8.92181	0.404286	0.202143	+	0.979356i	$0.435209\pi$
$488$	−41.0322	−1.85744
$489$	−17.2023	−0.777913
$490$	−132.529	−5.98705
$491$	12.3990	0.559558	0.279779	−	0.960064i	$-0.409739\pi$
$491$	12.3990	0.559558	0.279779	+	0.960064i	$0.409739\pi$
$492$	−40.6015	−1.83046
$493$	2.24661	0.101182
$494$	−33.0562	−1.48727
$495$	3.85728	0.173372
$496$	98.7385	4.43349
$497$	−43.1472	−1.93542
$498$	4.22795	0.189459
$499$	−35.9590	−1.60974	−0.804872	−	0.593448i	$-0.797766\pi$
$499$	−35.9590	−1.60974	−0.804872	+	0.593448i	$0.797766\pi$
$500$	−61.6281	−2.75609
$501$	−9.74013	−0.435157
$502$	−52.2161	−2.33052
$503$	−24.7041	−1.10150	−0.550751	−	0.834669i	$-0.685659\pi$
$503$	−24.7041	−1.10150	−0.550751	+	0.834669i	$0.685659\pi$
$504$	53.8167	2.39719
$505$	−38.9466	−1.73310
$506$	4.65284	0.206844
$507$	0.696119	0.0309157
$508$	53.8391	2.38872
$509$	−33.8638	−1.50099	−0.750494	−	0.660877i	$-0.770184\pi$
$509$	−33.8638	−1.50099	−0.750494	+	0.660877i	$0.770184\pi$
$510$	14.3075	0.633546
$511$	6.87669	0.304207
$512$	−102.844	−4.54511
$513$	3.22268	0.142285
$514$	39.9030	1.76004
$515$	25.7338	1.13397
$516$	50.1468	2.20759
$517$	18.0596	0.794262
$518$	−20.6044	−0.905304
$519$	20.1382	0.883971
$520$	−86.7788	−3.80550
$521$	13.8126	0.605140	0.302570	−	0.953127i	$-0.402155\pi$
$521$	13.8126	0.605140	0.302570	+	0.953127i	$0.402155\pi$
$522$	2.77164	0.121311
$523$	4.38916	0.191925	0.0959624	−	0.995385i	$-0.469407\pi$
$523$	4.38916	0.191925	0.0959624	+	0.995385i	$0.469407\pi$
$524$	58.4615	2.55390
$525$	−1.47434	−0.0643455
$526$	−4.94410	−0.215573
$527$	−13.1097	−0.571070
$528$	28.4055	1.23619
$529$	1.00000	0.0434783
$530$	67.8672	2.94796
$531$	−5.86788	−0.254644
$532$	−96.5646	−4.18660
$533$	−26.4449	−1.14546
$534$	−40.3325	−1.74536
$535$	23.3702	1.01038
$536$	41.4876	1.79199
$537$	10.6994	0.461715
$538$	7.12502	0.307181
$539$	34.9348	1.50475
$540$	13.0556	0.561825
$541$	−30.7399	−1.32161	−0.660806	−	0.750556i	$-0.729786\pi$
$541$	−30.7399	−1.32161	−0.660806	+	0.750556i	$0.729786\pi$
$542$	14.9334	0.641443
$543$	−20.1216	−0.863501
$544$	59.5084	2.55140
$545$	6.40174	0.274220
$546$	54.0925	2.31494
$547$	−7.41249	−0.316935	−0.158468	−	0.987364i	$-0.550655\pi$
$547$	−7.41249	−0.316935	−0.158468	+	0.987364i	$0.550655\pi$
$548$	−55.2562	−2.36043
$549$	4.02077	0.171602
$550$	−1.30081	−0.0554667
$551$	−3.22268	−0.137291
$552$	10.2051	0.434356
$553$	−47.6536	−2.02644
$554$	−69.9755	−2.97297
$555$	−3.23907	−0.137491
$556$	−55.2374	−2.34259
$557$	−5.78672	−0.245191	−0.122596	−	0.992457i	$-0.539122\pi$
$557$	−5.78672	−0.245191	−0.122596	+	0.992457i	$0.539122\pi$
$558$	−16.1734	−0.684677
$559$	32.6621	1.38146
$560$	−205.032	−8.66418
$561$	−3.77146	−0.159231
$562$	35.1164	1.48129
$563$	−22.3792	−0.943170	−0.471585	−	0.881821i	$-0.656318\pi$
$563$	−22.3792	−0.943170	−0.471585	+	0.881821i	$0.656318\pi$
$564$	61.1260	2.57387
$565$	34.4651	1.44996
$566$	−61.2735	−2.57552
$567$	−5.27354	−0.221468
$568$	−83.4961	−3.50342
$569$	17.3697	0.728175	0.364088	−	0.931365i	$-0.381381\pi$
$569$	17.3697	0.728175	0.364088	+	0.931365i	$0.381381\pi$
$570$	−20.5236	−0.859638
$571$	−30.1747	−1.26277	−0.631386	−	0.775469i	$-0.717514\pi$
$571$	−30.1747	−1.26277	−0.631386	+	0.775469i	$0.717514\pi$
$572$	35.3004	1.47598
$573$	16.9007	0.706037
$574$	−104.444	−4.35939
$575$	−0.279573	−0.0116590
$576$	39.5738	1.64891
$577$	7.97999	0.332212	0.166106	−	0.986108i	$-0.446881\pi$
$577$	7.97999	0.332212	0.166106	+	0.986108i	$0.446881\pi$
$578$	33.1286	1.37797
$579$	−2.84220	−0.118118
$580$	−13.0556	−0.542105
$581$	8.04444	0.333739
$582$	−23.7859	−0.985955
$583$	−17.8898	−0.740921
$584$	13.3074	0.550664
$585$	8.50351	0.351577
$586$	61.3786	2.53553
$587$	19.7257	0.814169	0.407084	−	0.913391i	$-0.366546\pi$
$587$	19.7257	0.814169	0.407084	+	0.913391i	$0.366546\pi$
$588$	118.243	4.87624
$589$	18.8055	0.774866
$590$	37.3695	1.53848
$591$	−1.41372	−0.0581526
$592$	−23.8529	−0.980349
$593$	−37.3676	−1.53450	−0.767252	−	0.641345i	$-0.778377\pi$
$593$	−37.3676	−1.53450	−0.767252	+	0.641345i	$0.778377\pi$
$594$	−4.65284	−0.190908
$595$	27.2226	1.11602
$596$	82.4519	3.37736
$597$	19.5480	0.800046
$598$	10.2573	0.419454
$599$	−16.4020	−0.670167	−0.335083	−	0.942189i	$-0.608764\pi$
$599$	−16.4020	−0.670167	−0.335083	+	0.942189i	$0.608764\pi$
$600$	−2.85306	−0.116476
$601$	−38.6689	−1.57734	−0.788668	−	0.614819i	$-0.789229\pi$
$601$	−38.6689	−1.57734	−0.788668	+	0.614819i	$0.789229\pi$
$602$	128.998	5.25757
$603$	−4.06540	−0.165556
$604$	21.3969	0.870627
$605$	−18.7997	−0.764317
$606$	46.9793	1.90840
$607$	25.8529	1.04934	0.524669	−	0.851307i	$-0.324189\pi$
$607$	25.8529	1.04934	0.524669	+	0.851307i	$0.324189\pi$
$608$	−85.3627	−3.46191
$609$	5.27354	0.213694
$610$	−25.6062	−1.03676
$611$	39.8131	1.61067
$612$	−12.7652	−0.516001
$613$	−12.9124	−0.521527	−0.260764	−	0.965403i	$-0.583974\pi$
$613$	−12.9124	−0.521527	−0.260764	+	0.965403i	$0.583974\pi$
$614$	−38.5787	−1.55691
$615$	−16.4189	−0.662072
$616$	90.3440	3.64006
$617$	−26.7525	−1.07701	−0.538507	−	0.842621i	$-0.681012\pi$
$617$	−26.7525	−1.07701	−0.538507	+	0.842621i	$0.681012\pi$
$618$	−31.0413	−1.24866
$619$	−30.7646	−1.23653	−0.618266	−	0.785969i	$-0.712165\pi$
$619$	−30.7646	−1.23653	−0.618266	+	0.785969i	$0.712165\pi$
$620$	76.1841	3.05963
$621$	−1.00000	−0.0401286
$622$	14.9372	0.598926
$623$	−76.7398	−3.07451
$624$	62.6208	2.50684
$625$	−26.3197	−1.05279
$626$	62.0554	2.48023
$627$	5.41003	0.216056
$628$	99.4958	3.97031
$629$	3.16701	0.126277
$630$	33.5844	1.33803
$631$	11.5124	0.458302	0.229151	−	0.973391i	$-0.426405\pi$
$631$	11.5124	0.458302	0.229151	+	0.973391i	$0.426405\pi$
$632$	−92.2166	−3.66818
$633$	15.2346	0.605521
$634$	−9.98863	−0.396699
$635$	21.7720	0.863996
$636$	−60.5512	−2.40101
$637$	77.0149	3.05144
$638$	4.65284	0.184208
$639$	8.18183	0.323668
$640$	−130.300	−5.15054
$641$	30.2176	1.19353	0.596763	−	0.802418i	$-0.296453\pi$
$641$	30.2176	1.19353	0.596763	+	0.802418i	$0.296453\pi$
$642$	−28.1903	−1.11258
$643$	0.0750745	0.00296065	0.00148033	−	0.999999i	$-0.499529\pi$
$643$	0.0750745	0.00296065	0.00148033	+	0.999999i	$0.499529\pi$
$644$	29.9640	1.18075
$645$	20.2789	0.798481
$646$	20.0670	0.789524
$647$	28.4909	1.12009	0.560045	−	0.828462i	$-0.310784\pi$
$647$	28.4909	1.12009	0.560045	+	0.828462i	$0.310784\pi$
$648$	−10.2051	−0.400892
$649$	−9.85062	−0.386670
$650$	−2.86768	−0.112480
$651$	−30.7729	−1.20608
$652$	−97.7426	−3.82789
$653$	−20.8705	−0.816726	−0.408363	−	0.912820i	$-0.633900\pi$
$653$	−20.8705	−0.816726	−0.408363	+	0.912820i	$0.633900\pi$
$654$	−7.72208	−0.301957
$655$	23.6413	0.923741
$656$	−120.910	−4.72076
$657$	−1.30400	−0.0508739
$658$	157.241	6.12988
$659$	−50.7944	−1.97867	−0.989334	−	0.145664i	$-0.953468\pi$
$659$	−50.7944	−1.97867	−0.989334	+	0.145664i	$0.953468\pi$
$660$	21.9169	0.853115
$661$	−3.65855	−0.142301	−0.0711505	−	0.997466i	$-0.522667\pi$
$661$	−3.65855	−0.142301	−0.0711505	+	0.997466i	$0.522667\pi$
$662$	78.9714	3.06931
$663$	−8.31432	−0.322901
$664$	15.5672	0.604123
$665$	−39.0498	−1.51429
$666$	3.90713	0.151398
$667$	1.00000	0.0387202
$668$	−55.3431	−2.14129
$669$	−3.31580	−0.128196
$670$	25.8904	1.00023
$671$	6.74981	0.260573
$672$	139.686	5.38850
$673$	−14.6688	−0.565440	−0.282720	−	0.959202i	$-0.591237\pi$
$673$	−14.6688	−0.565440	−0.282720	+	0.959202i	$0.591237\pi$
$674$	−66.5426	−2.56312
$675$	0.279573	0.0107608
$676$	3.95532	0.152128
$677$	−35.1696	−1.35168	−0.675839	−	0.737050i	$-0.736218\pi$
$677$	−35.1696	−1.35168	−0.675839	+	0.737050i	$0.736218\pi$
$678$	−41.5734	−1.59662
$679$	−45.2569	−1.73680
$680$	52.6796	2.02017
$681$	−6.38701	−0.244751
$682$	−27.1509	−1.03966
$683$	−44.8115	−1.71466	−0.857332	−	0.514763i	$-0.827880\pi$
$683$	−44.8115	−1.71466	−0.857332	+	0.514763i	$0.827880\pi$
$684$	18.3112	0.700145
$685$	−22.3451	−0.853761
$686$	201.854	7.70682
$687$	−1.71280	−0.0653475
$688$	149.336	5.69339
$689$	−39.4388	−1.50250
$690$	6.36848	0.242444
$691$	−3.58113	−0.136233	−0.0681163	−	0.997677i	$-0.521699\pi$
$691$	−3.58113	−0.136233	−0.0681163	+	0.997677i	$0.521699\pi$
$692$	114.425	4.34978
$693$	−8.85287	−0.336293
$694$	−84.6881	−3.21471
$695$	−22.3375	−0.847310
$696$	10.2051	0.386822
$697$	16.0536	0.608072
$698$	27.9932	1.05956
$699$	−10.2185	−0.386498
$700$	−8.37714	−0.316626
$701$	17.0168	0.642714	0.321357	−	0.946958i	$-0.395861\pi$
$701$	17.0168	0.642714	0.321357	+	0.946958i	$0.395861\pi$
$702$	−10.2573	−0.387138
$703$	−4.54296	−0.171341
$704$	66.4339	2.50382
$705$	24.7188	0.930962
$706$	−53.2302	−2.00334
$707$	89.3865	3.36173
$708$	−33.3411	−1.25303
$709$	21.7959	0.818561	0.409281	−	0.912409i	$-0.365780\pi$
$709$	21.7959	0.818561	0.409281	+	0.912409i	$0.365780\pi$
$710$	−52.1058	−1.95550
$711$	9.03636	0.338890
$712$	−148.503	−5.56537
$713$	−5.83534	−0.218535
$714$	−32.8372	−1.22890
$715$	14.2751	0.533860
$716$	60.7938	2.27197
$717$	−18.5912	−0.694301
$718$	−62.1504	−2.31943
$719$	−50.2327	−1.87336	−0.936682	−	0.350182i	$-0.886120\pi$
$719$	−50.2327	−1.87336	−0.936682	+	0.350182i	$0.886120\pi$
$720$	38.8794	1.44895
$721$	−59.0617	−2.19957
$722$	23.8757	0.888563
$723$	22.8983	0.851596
$724$	−114.330	−4.24905
$725$	−0.279573	−0.0103831
$726$	22.6771	0.841626
$727$	−25.4213	−0.942823	−0.471411	−	0.881913i	$-0.656255\pi$
$727$	−25.4213	−0.942823	−0.471411	+	0.881913i	$0.656255\pi$
$728$	199.166	7.38160
$729$	1.00000	0.0370370
$730$	8.30450	0.307363
$731$	−19.8277	−0.733355
$732$	22.8459	0.844408
$733$	27.3676	1.01085	0.505423	−	0.862872i	$-0.331336\pi$
$733$	27.3676	1.01085	0.505423	+	0.862872i	$0.331336\pi$
$734$	−61.2696	−2.26150
$735$	47.8162	1.76373
$736$	26.4881	0.976364
$737$	−6.82472	−0.251392
$738$	19.8052	0.729040
$739$	−10.5300	−0.387351	−0.193675	−	0.981066i	$-0.562041\pi$
$739$	−10.5300	−0.387351	−0.193675	+	0.981066i	$0.562041\pi$
$740$	−18.4043	−0.676555
$741$	11.9266	0.438134
$742$	−155.762	−5.71821
$743$	37.2813	1.36772	0.683860	−	0.729613i	$-0.260300\pi$
$743$	37.2813	1.36772	0.683860	+	0.729613i	$0.260300\pi$
$744$	−59.5500	−2.18321
$745$	33.3428	1.22158
$746$	38.9001	1.42423
$747$	−1.52544	−0.0558128
$748$	−21.4293	−0.783533
$749$	−53.6371	−1.95986
$750$	30.0619	1.09771
$751$	24.2787	0.885943	0.442972	−	0.896536i	$-0.353924\pi$
$751$	24.2787	0.885943	0.442972	+	0.896536i	$0.353924\pi$
$752$	182.032	6.63802
$753$	18.8395	0.686548
$754$	10.2573	0.373550
$755$	8.65270	0.314904
$756$	−29.9640	−1.08978
$757$	−22.0047	−0.799773	−0.399887	−	0.916565i	$-0.630951\pi$
$757$	−22.0047	−0.799773	−0.399887	+	0.916565i	$0.630951\pi$
$758$	58.5481	2.12656
$759$	−1.67873	−0.0609342
$760$	−75.5670	−2.74110
$761$	15.8149	0.573291	0.286646	−	0.958037i	$-0.407460\pi$
$761$	15.8149	0.573291	0.286646	+	0.958037i	$0.407460\pi$
$762$	−26.2625	−0.951388
$763$	−14.6927	−0.531910
$764$	96.0292	3.47422
$765$	−5.16211	−0.186637
$766$	−44.3933	−1.60400
$767$	−21.7160	−0.784120
$768$	78.0261	2.81552
$769$	−7.73217	−0.278829	−0.139415	−	0.990234i	$-0.544522\pi$
$769$	−7.73217	−0.278829	−0.139415	+	0.990234i	$0.544522\pi$
$770$	56.3793	2.03177
$771$	−14.3969	−0.518492
$772$	−16.1493	−0.581225
$773$	−1.43601	−0.0516496	−0.0258248	−	0.999666i	$-0.508221\pi$
$773$	−1.43601	−0.0516496	−0.0258248	+	0.999666i	$0.508221\pi$
$774$	−24.4614	−0.879247
$775$	1.63141	0.0586019
$776$	−87.5786	−3.14389
$777$	7.43401	0.266694
$778$	−26.2752	−0.942012
$779$	−23.0283	−0.825073
$780$	48.3166	1.73001
$781$	13.7351	0.491482
$782$	−6.22679	−0.222669
$783$	−1.00000	−0.0357371
$784$	352.124	12.5759
$785$	40.2352	1.43605
$786$	−28.5173	−1.01718
$787$	−26.9478	−0.960586	−0.480293	−	0.877108i	$-0.659470\pi$
$787$	−26.9478	−0.960586	−0.480293	+	0.877108i	$0.659470\pi$
$788$	−8.03269	−0.286153
$789$	1.78382	0.0635057
$790$	−57.5478	−2.04746
$791$	−79.1009	−2.81250
$792$	−17.1316	−0.608744
$793$	14.8802	0.528411
$794$	−30.1466	−1.06986
$795$	−24.4863	−0.868441
$796$	111.071	3.93681
$797$	25.1365	0.890380	0.445190	−	0.895436i	$-0.353136\pi$
$797$	25.1365	0.890380	0.445190	+	0.895436i	$0.353136\pi$
$798$	47.1038	1.66745
$799$	−24.1688	−0.855031
$800$	−7.40536	−0.261819
$801$	14.5519	0.514165
$802$	47.2249	1.66757
$803$	−2.18907	−0.0772506
$804$	−23.0994	−0.814654
$805$	12.1172	0.427074
$806$	−59.8551	−2.10831
$807$	−2.57069	−0.0904927
$808$	172.976	6.08527
$809$	6.20511	0.218160	0.109080	−	0.994033i	$-0.465210\pi$
$809$	6.20511	0.218160	0.109080	+	0.994033i	$0.465210\pi$
$810$	−6.36848	−0.223765
$811$	−53.5107	−1.87901	−0.939507	−	0.342529i	$-0.888716\pi$
$811$	−53.5107	−1.87901	−0.939507	+	0.342529i	$0.888716\pi$
$812$	29.9640	1.05153
$813$	−5.38793	−0.188963
$814$	6.55903	0.229894
$815$	−39.5262	−1.38454
$816$	−38.0144	−1.33077
$817$	28.4422	0.995066
$818$	−19.6228	−0.686096
$819$	−19.5164	−0.681960
$820$	−93.2913	−3.25787
$821$	−43.8028	−1.52873	−0.764364	−	0.644785i	$-0.776947\pi$
$821$	−43.8028	−1.52873	−0.764364	+	0.644785i	$0.776947\pi$
$822$	26.9537	0.940118
$823$	9.16598	0.319506	0.159753	−	0.987157i	$-0.448930\pi$
$823$	9.16598	0.319506	0.159753	+	0.987157i	$0.448930\pi$
$824$	−114.293	−3.98158
$825$	0.469329	0.0163400
$826$	−85.7668	−2.98421
$827$	−7.52174	−0.261557	−0.130778	−	0.991412i	$-0.541748\pi$
$827$	−7.52174	−0.261557	−0.130778	+	0.991412i	$0.541748\pi$
$828$	−5.68196	−0.197462
$829$	15.6528	0.543644	0.271822	−	0.962348i	$-0.412374\pi$
$829$	15.6528	0.543644	0.271822	+	0.962348i	$0.412374\pi$
$830$	9.71470	0.337202
$831$	25.2470	0.875808
$832$	146.456	5.07744
$833$	−46.7524	−1.61987
$834$	26.9446	0.933014
$835$	−22.3802	−0.774499
$836$	30.7396	1.06315
$837$	5.83534	0.201699
$838$	−44.3507	−1.53207
$839$	35.7749	1.23509	0.617544	−	0.786536i	$-0.288128\pi$
$839$	35.7749	1.23509	0.617544	+	0.786536i	$0.288128\pi$
$840$	123.656	4.26655
$841$	1.00000	0.0344828
$842$	−34.5948	−1.19221
$843$	−12.6699	−0.436375
$844$	86.5624	2.97960
$845$	1.59949	0.0550243
$846$	−29.8170	−1.02513
$847$	43.1473	1.48256
$848$	−180.320	−6.19222
$849$	22.1074	0.758722
$850$	1.74084	0.0597105
$851$	1.40968	0.0483233
$852$	46.4889	1.59268
$853$	40.3320	1.38094	0.690471	−	0.723360i	$-0.257403\pi$
$853$	40.3320	1.38094	0.690471	+	0.723360i	$0.257403\pi$
$854$	58.7689	2.01103
$855$	7.40486	0.253241
$856$	−103.796	−3.54766
$857$	12.9572	0.442609	0.221305	−	0.975205i	$-0.428968\pi$
$857$	12.9572	0.442609	0.221305	+	0.975205i	$0.428968\pi$
$858$	−17.2194	−0.587859
$859$	−34.2116	−1.16728	−0.583642	−	0.812011i	$-0.698373\pi$
$859$	−34.2116	−1.16728	−0.583642	+	0.812011i	$0.698373\pi$
$860$	115.224	3.92911
$861$	37.6830	1.28423
$862$	−18.6383	−0.634824
$863$	46.0580	1.56783	0.783916	−	0.620867i	$-0.213219\pi$
$863$	46.0580	1.56783	0.783916	+	0.620867i	$0.213219\pi$
$864$	−26.4881	−0.901143
$865$	46.2723	1.57331
$866$	−24.5916	−0.835657
$867$	−11.9527	−0.405936
$868$	−174.850	−5.93481
$869$	15.1697	0.514595
$870$	6.36848	0.215912
$871$	−15.0453	−0.509791
$872$	−28.4324	−0.962843
$873$	8.58188	0.290453
$874$	8.93210	0.302133
$875$	57.1982	1.93365
$876$	−7.40928	−0.250336
$877$	55.0308	1.85826	0.929129	−	0.369756i	$-0.120559\pi$
$877$	55.0308	1.85826	0.929129	+	0.369756i	$0.120559\pi$
$878$	−80.0092	−2.70018
$879$	−22.1453	−0.746941
$880$	65.2682	2.20019
$881$	−34.6195	−1.16636	−0.583180	−	0.812343i	$-0.698192\pi$
$881$	−34.6195	−1.16636	−0.583180	+	0.812343i	$0.698192\pi$
$882$	−57.6782	−1.94213
$883$	25.0742	0.843814	0.421907	−	0.906639i	$-0.361361\pi$
$883$	25.0742	0.843814	0.421907	+	0.906639i	$0.361361\pi$
$884$	−47.2416	−1.58891
$885$	−13.4828	−0.453220
$886$	8.25240	0.277245
$887$	−30.2600	−1.01603	−0.508015	−	0.861348i	$-0.669621\pi$
$887$	−30.2600	−1.01603	−0.508015	+	0.861348i	$0.669621\pi$
$888$	14.3859	0.482759
$889$	−49.9691	−1.67591
$890$	−92.6732	−3.10641
$891$	1.67873	0.0562397
$892$	−18.8402	−0.630818
$893$	34.6693	1.16016
$894$	−40.2197	−1.34515
$895$	24.5845	0.821768
$896$	299.051	9.99060
$897$	−3.70083	−0.123567
$898$	−17.5103	−0.584327
$899$	−5.83534	−0.194620
$900$	1.58853	0.0529508
$901$	23.9416	0.797609
$902$	33.2477	1.10703
$903$	−46.5422	−1.54883
$904$	−153.072	−5.09109
$905$	−46.2341	−1.53687
$906$	−10.4373	−0.346756
$907$	−36.3480	−1.20691	−0.603457	−	0.797395i	$-0.706211\pi$
$907$	−36.3480	−1.20691	−0.603457	+	0.797395i	$0.706211\pi$
$908$	−36.2907	−1.20435
$909$	−16.9500	−0.562197
$910$	124.290	4.12017
$911$	−24.5626	−0.813796	−0.406898	−	0.913474i	$-0.633390\pi$
$911$	−24.5626	−0.813796	−0.406898	+	0.913474i	$0.633390\pi$
$912$	54.5303	1.80568
$913$	−2.56080	−0.0847501
$914$	−19.5858	−0.647842
$915$	9.23866	0.305421
$916$	−9.73207	−0.321557
$917$	−54.2592	−1.79180
$918$	6.22679	0.205515
$919$	0.797896	0.0263202	0.0131601	−	0.999913i	$-0.495811\pi$
$919$	0.797896	0.0263202	0.0131601	+	0.999913i	$0.495811\pi$
$920$	23.4485	0.773074
$921$	13.9191	0.458651
$922$	−35.8445	−1.18048
$923$	30.2796	0.996664
$924$	−50.3016	−1.65480
$925$	−0.394110	−0.0129583
$926$	116.644	3.83315
$927$	11.1996	0.367844
$928$	26.4881	0.869514
$929$	8.85813	0.290626	0.145313	−	0.989386i	$-0.453581\pi$
$929$	8.85813	0.290626	0.145313	+	0.989386i	$0.453581\pi$
$930$	−37.1622	−1.21860
$931$	67.0646	2.19795
$932$	−58.0609	−1.90185
$933$	−5.38930	−0.176438
$934$	−13.9446	−0.456282
$935$	−8.66581	−0.283402
$936$	−37.7671	−1.23446
$937$	14.0445	0.458814	0.229407	−	0.973331i	$-0.426321\pi$
$937$	14.0445	0.458814	0.229407	+	0.973331i	$0.426321\pi$
$938$	−59.4211	−1.94017
$939$	−22.3895	−0.730653
$940$	140.451	4.58101
$941$	−8.17124	−0.266375	−0.133187	−	0.991091i	$-0.542521\pi$
$941$	−8.17124	−0.266375	−0.133187	+	0.991091i	$0.542521\pi$
$942$	−48.5336	−1.58131
$943$	7.14568	0.232695
$944$	−99.2891	−3.23158
$945$	−12.1172	−0.394172
$946$	−41.0642	−1.33511
$947$	−42.8749	−1.39325	−0.696623	−	0.717437i	$-0.745315\pi$
$947$	−42.8749	−1.39325	−0.696623	+	0.717437i	$0.745315\pi$
$948$	51.3443	1.66758
$949$	−4.82588	−0.156655
$950$	−2.49718	−0.0810191
$951$	3.60388	0.116864
$952$	−120.905	−3.91856
$953$	−20.8388	−0.675034	−0.337517	−	0.941319i	$-0.609587\pi$
$953$	−20.8388	−0.675034	−0.337517	+	0.941319i	$0.609587\pi$
$954$	29.5366	0.956283
$955$	38.8333	1.25662
$956$	−105.634	−3.41646
$957$	−1.67873	−0.0542658
$958$	−32.1639	−1.03917
$959$	51.2843	1.65606
$960$	90.9300	2.93475
$961$	3.05124	0.0984270
$962$	14.4596	0.466196
$963$	10.1710	0.327756
$964$	130.107	4.19047
$965$	−6.53061	−0.210228
$966$	−14.6163	−0.470272
$967$	46.9763	1.51066	0.755328	−	0.655347i	$-0.227477\pi$
$967$	46.9763	1.51066	0.755328	+	0.655347i	$0.227477\pi$
$968$	83.4962	2.68367
$969$	−7.24012	−0.232586
$970$	−54.6535	−1.75482
$971$	5.28608	0.169638	0.0848192	−	0.996396i	$-0.472969\pi$
$971$	5.28608	0.169638	0.0848192	+	0.996396i	$0.472969\pi$
$972$	5.68196	0.182249
$973$	51.2669	1.64354
$974$	−24.7280	−0.792336
$975$	1.03465	0.0331354
$976$	68.0345	2.17773
$977$	−10.4569	−0.334547	−0.167274	−	0.985911i	$-0.553496\pi$
$977$	−10.4569	−0.334547	−0.167274	+	0.985911i	$0.553496\pi$
$978$	47.6784	1.52459
$979$	24.4287	0.780745
$980$	271.690	8.67882
$981$	2.78611	0.0889537
$982$	−34.3655	−1.09665
$983$	27.7660	0.885597	0.442798	−	0.896621i	$-0.353986\pi$
$983$	27.7660	0.885597	0.442798	+	0.896621i	$0.353986\pi$
$984$	72.9221	2.32467
$985$	−3.24834	−0.103501
$986$	−6.22679	−0.198301
$987$	−56.7321	−1.80580
$988$	67.7664	2.15594
$989$	−8.82562	−0.280638
$990$	−10.6910	−0.339782
$991$	−12.8880	−0.409400	−0.204700	−	0.978825i	$-0.565622\pi$
$991$	−12.8880	−0.409400	−0.204700	+	0.978825i	$0.565622\pi$
$992$	−154.567	−4.90751
$993$	−28.4927	−0.904189
$994$	119.588	3.79311
$995$	44.9161	1.42394
$996$	−8.66747	−0.274639
$997$	−12.5755	−0.398271	−0.199135	−	0.979972i	$-0.563813\pi$
$997$	−12.5755	−0.398271	−0.199135	+	0.979972i	$0.563813\pi$
$998$	99.6651	3.15484
$999$	−1.40968	−0.0446004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.1	✓	16
3.2	odd	2		6003.2.a.r.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.1	✓	16	1.1	even	1	trivial
6003.2.a.r.1.16		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.77164 q^{2} +1.00000 q^{3} +5.68196 q^{4} +2.29773 q^{5} -2.77164 q^{6} -5.27354 q^{7} -10.2051 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.77164 q^{2} +1.00000 q^{3} +5.68196 q^{4} +2.29773 q^{5} -2.77164 q^{6} -5.27354 q^{7} -10.2051 q^{8} +1.00000 q^{9} -6.36848 q^{10} +1.67873 q^{11} +5.68196 q^{12} +3.70083 q^{13} +14.6163 q^{14} +2.29773 q^{15} +16.9208 q^{16} -2.24661 q^{17} -2.77164 q^{18} +3.22268 q^{19} +13.0556 q^{20} -5.27354 q^{21} -4.65284 q^{22} -1.00000 q^{23} -10.2051 q^{24} +0.279573 q^{25} -10.2573 q^{26} +1.00000 q^{27} -29.9640 q^{28} -1.00000 q^{29} -6.36848 q^{30} +5.83534 q^{31} -26.4881 q^{32} +1.67873 q^{33} +6.22679 q^{34} -12.1172 q^{35} +5.68196 q^{36} -1.40968 q^{37} -8.93210 q^{38} +3.70083 q^{39} -23.4485 q^{40} -7.14568 q^{41} +14.6163 q^{42} +8.82562 q^{43} +9.53851 q^{44} +2.29773 q^{45} +2.77164 q^{46} +10.7579 q^{47} +16.9208 q^{48} +20.8102 q^{49} -0.774875 q^{50} -2.24661 q^{51} +21.0280 q^{52} -10.6567 q^{53} -2.77164 q^{54} +3.85728 q^{55} +53.8167 q^{56} +3.22268 q^{57} +2.77164 q^{58} -5.86788 q^{59} +13.0556 q^{60} +4.02077 q^{61} -16.1734 q^{62} -5.27354 q^{63} +39.5738 q^{64} +8.50351 q^{65} -4.65284 q^{66} -4.06540 q^{67} -12.7652 q^{68} -1.00000 q^{69} +33.5844 q^{70} +8.18183 q^{71} -10.2051 q^{72} -1.30400 q^{73} +3.90713 q^{74} +0.279573 q^{75} +18.3112 q^{76} -8.85287 q^{77} -10.2573 q^{78} +9.03636 q^{79} +38.8794 q^{80} +1.00000 q^{81} +19.8052 q^{82} -1.52544 q^{83} -29.9640 q^{84} -5.16211 q^{85} -24.4614 q^{86} -1.00000 q^{87} -17.1316 q^{88} +14.5519 q^{89} -6.36848 q^{90} -19.5164 q^{91} -5.68196 q^{92} +5.83534 q^{93} -29.8170 q^{94} +7.40486 q^{95} -26.4881 q^{96} +8.58188 q^{97} -57.6782 q^{98} +1.67873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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