LMFDB - Embedded newform 5290.2.a.bj.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 15x^{8} + 35x^{7} + 78x^{6} - 123x^{5} - 185x^{4} + 140x^{3} + 177x^{2} - 15x - 23 $ x^10 - 3x^9 - 15x^8 + 35x^7 + 78x^6 - 123x^5 - 185x^4 + 140x^3 + 177x^2 - 15*x - 23
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.92764$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.34421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34421 q^{6} +0.948752 q^{7} -1.00000 q^{8} -1.19309 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.34421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34421 q^{6} +0.948752 q^{7} -1.00000 q^{8} -1.19309 q^{9} -1.00000 q^{10} +2.71227 q^{11} +1.34421 q^{12} +2.35000 q^{13} -0.948752 q^{14} +1.34421 q^{15} +1.00000 q^{16} +0.966621 q^{17} +1.19309 q^{18} +7.96281 q^{19} +1.00000 q^{20} +1.27532 q^{21} -2.71227 q^{22} -1.34421 q^{24} +1.00000 q^{25} -2.35000 q^{26} -5.63641 q^{27} +0.948752 q^{28} +10.3443 q^{29} -1.34421 q^{30} +2.62327 q^{31} -1.00000 q^{32} +3.64587 q^{33} -0.966621 q^{34} +0.948752 q^{35} -1.19309 q^{36} +3.71211 q^{37} -7.96281 q^{38} +3.15890 q^{39} -1.00000 q^{40} -1.84968 q^{41} -1.27532 q^{42} -5.08172 q^{43} +2.71227 q^{44} -1.19309 q^{45} -1.77280 q^{47} +1.34421 q^{48} -6.09987 q^{49} -1.00000 q^{50} +1.29934 q^{51} +2.35000 q^{52} -0.594825 q^{53} +5.63641 q^{54} +2.71227 q^{55} -0.948752 q^{56} +10.7037 q^{57} -10.3443 q^{58} -1.24115 q^{59} +1.34421 q^{60} -12.1585 q^{61} -2.62327 q^{62} -1.13195 q^{63} +1.00000 q^{64} +2.35000 q^{65} -3.64587 q^{66} +1.91529 q^{67} +0.966621 q^{68} -0.948752 q^{70} +14.2696 q^{71} +1.19309 q^{72} -3.25495 q^{73} -3.71211 q^{74} +1.34421 q^{75} +7.96281 q^{76} +2.57327 q^{77} -3.15890 q^{78} -11.4402 q^{79} +1.00000 q^{80} -3.99724 q^{81} +1.84968 q^{82} -15.1276 q^{83} +1.27532 q^{84} +0.966621 q^{85} +5.08172 q^{86} +13.9050 q^{87} -2.71227 q^{88} -1.09983 q^{89} +1.19309 q^{90} +2.22957 q^{91} +3.52623 q^{93} +1.77280 q^{94} +7.96281 q^{95} -1.34421 q^{96} -0.767674 q^{97} +6.09987 q^{98} -3.23600 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.34421	0.776081	0.388041	−	0.921642i	$-0.373152\pi$
$3$	1.34421	0.776081	0.388041	+	0.921642i	$0.373152\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.34421	−0.548772
$7$	0.948752	0.358594	0.179297	−	0.983795i	$-0.442618\pi$
$7$	0.948752	0.358594	0.179297	+	0.983795i	$0.442618\pi$
$8$	−1.00000	−0.353553
$9$	−1.19309	−0.397698
$10$	−1.00000	−0.316228
$11$	2.71227	0.817781	0.408891	−	0.912583i	$-0.365916\pi$
$11$	2.71227	0.817781	0.408891	+	0.912583i	$0.365916\pi$
$12$	1.34421	0.388041
$13$	2.35000	0.651773	0.325887	−	0.945409i	$-0.394337\pi$
$13$	2.35000	0.651773	0.325887	+	0.945409i	$0.394337\pi$
$14$	−0.948752	−0.253565
$15$	1.34421	0.347074
$16$	1.00000	0.250000
$17$	0.966621	0.234440	0.117220	−	0.993106i	$-0.462602\pi$
$17$	0.966621	0.234440	0.117220	+	0.993106i	$0.462602\pi$
$18$	1.19309	0.281215
$19$	7.96281	1.82679	0.913397	−	0.407071i	$-0.133450\pi$
$19$	7.96281	1.82679	0.913397	+	0.407071i	$0.133450\pi$
$20$	1.00000	0.223607
$21$	1.27532	0.278298
$22$	−2.71227	−0.578259
$23$	0	0
$23$	0	0
$24$	−1.34421	−0.274386
$25$	1.00000	0.200000
$26$	−2.35000	−0.460873
$27$	−5.63641	−1.08473
$28$	0.948752	0.179297
$29$	10.3443	1.92089	0.960446	−	0.278467i	$-0.0898263\pi$
$29$	10.3443	1.92089	0.960446	+	0.278467i	$0.0898263\pi$
$30$	−1.34421	−0.245418
$31$	2.62327	0.471153	0.235577	−	0.971856i	$-0.424302\pi$
$31$	2.62327	0.471153	0.235577	+	0.971856i	$0.424302\pi$
$32$	−1.00000	−0.176777
$33$	3.64587	0.634664
$34$	−0.966621	−0.165774
$35$	0.948752	0.160368
$36$	−1.19309	−0.198849
$37$	3.71211	0.610268	0.305134	−	0.952309i	$-0.401299\pi$
$37$	3.71211	0.610268	0.305134	+	0.952309i	$0.401299\pi$
$38$	−7.96281	−1.29174
$39$	3.15890	0.505829
$40$	−1.00000	−0.158114
$41$	−1.84968	−0.288871	−0.144435	−	0.989514i	$-0.546137\pi$
$41$	−1.84968	−0.288871	−0.144435	+	0.989514i	$0.546137\pi$
$42$	−1.27532	−0.196787
$43$	−5.08172	−0.774954	−0.387477	−	0.921879i	$-0.626653\pi$
$43$	−5.08172	−0.774954	−0.387477	+	0.921879i	$0.626653\pi$
$44$	2.71227	0.408891
$45$	−1.19309	−0.177856
$46$	0	0
$47$	−1.77280	−0.258589	−0.129295	−	0.991606i	$-0.541271\pi$
$47$	−1.77280	−0.258589	−0.129295	+	0.991606i	$0.541271\pi$
$48$	1.34421	0.194020
$49$	−6.09987	−0.871410
$50$	−1.00000	−0.141421
$51$	1.29934	0.181944
$52$	2.35000	0.325887
$53$	−0.594825	−0.0817054	−0.0408527	−	0.999165i	$-0.513007\pi$
$53$	−0.594825	−0.0817054	−0.0408527	+	0.999165i	$0.513007\pi$
$54$	5.63641	0.767018
$55$	2.71227	0.365723
$56$	−0.948752	−0.126782
$57$	10.7037	1.41774
$58$	−10.3443	−1.35828
$59$	−1.24115	−0.161584	−0.0807918	−	0.996731i	$-0.525745\pi$
$59$	−1.24115	−0.161584	−0.0807918	+	0.996731i	$0.525745\pi$
$60$	1.34421	0.173537
$61$	−12.1585	−1.55673	−0.778367	−	0.627809i	$-0.783952\pi$
$61$	−12.1585	−1.55673	−0.778367	+	0.627809i	$0.783952\pi$
$62$	−2.62327	−0.333156
$63$	−1.13195	−0.142612
$64$	1.00000	0.125000
$65$	2.35000	0.291482
$66$	−3.64587	−0.448775
$67$	1.91529	0.233990	0.116995	−	0.993132i	$-0.462674\pi$
$67$	1.91529	0.233990	0.116995	+	0.993132i	$0.462674\pi$
$68$	0.966621	0.117220
$69$	0	0
$70$	−0.948752	−0.113398
$71$	14.2696	1.69349	0.846743	−	0.532002i	$-0.178560\pi$
$71$	14.2696	1.69349	0.846743	+	0.532002i	$0.178560\pi$
$72$	1.19309	0.140608
$73$	−3.25495	−0.380963	−0.190482	−	0.981691i	$-0.561005\pi$
$73$	−3.25495	−0.380963	−0.190482	+	0.981691i	$0.561005\pi$
$74$	−3.71211	−0.431524
$75$	1.34421	0.155216
$76$	7.96281	0.913397
$77$	2.57327	0.293252
$78$	−3.15890	−0.357675
$79$	−11.4402	−1.28712	−0.643562	−	0.765394i	$-0.722544\pi$
$79$	−11.4402	−1.28712	−0.643562	+	0.765394i	$0.722544\pi$
$80$	1.00000	0.111803
$81$	−3.99724	−0.444138
$82$	1.84968	0.204262
$83$	−15.1276	−1.66047	−0.830233	−	0.557417i	$-0.811792\pi$
$83$	−15.1276	−1.66047	−0.830233	+	0.557417i	$0.811792\pi$
$84$	1.27532	0.139149
$85$	0.966621	0.104845
$86$	5.08172	0.547975
$87$	13.9050	1.49077
$88$	−2.71227	−0.289129
$89$	−1.09983	−0.116581	−0.0582907	−	0.998300i	$-0.518565\pi$
$89$	−1.09983	−0.116581	−0.0582907	+	0.998300i	$0.518565\pi$
$90$	1.19309	0.125763
$91$	2.22957	0.233722
$92$	0	0
$93$	3.52623	0.365653
$94$	1.77280	0.182850
$95$	7.96281	0.816967
$96$	−1.34421	−0.137193
$97$	−0.767674	−0.0779455	−0.0389728	−	0.999240i	$-0.512409\pi$
$97$	−0.767674	−0.0779455	−0.0389728	+	0.999240i	$0.512409\pi$
$98$	6.09987	0.616180
$99$	−3.23600	−0.325230
$100$	1.00000	0.100000
$101$	0.544671	0.0541967	0.0270984	−	0.999633i	$-0.491373\pi$
$101$	0.544671	0.0541967	0.0270984	+	0.999633i	$0.491373\pi$
$102$	−1.29934	−0.128654
$103$	−0.479174	−0.0472144	−0.0236072	−	0.999721i	$-0.507515\pi$
$103$	−0.479174	−0.0472144	−0.0236072	+	0.999721i	$0.507515\pi$
$104$	−2.35000	−0.230437
$105$	1.27532	0.124459
$106$	0.594825	0.0577745
$107$	4.86403	0.470224	0.235112	−	0.971968i	$-0.424454\pi$
$107$	4.86403	0.470224	0.235112	+	0.971968i	$0.424454\pi$
$108$	−5.63641	−0.542364
$109$	7.11502	0.681496	0.340748	−	0.940155i	$-0.389320\pi$
$109$	7.11502	0.681496	0.340748	+	0.940155i	$0.389320\pi$
$110$	−2.71227	−0.258605
$111$	4.98987	0.473617
$112$	0.948752	0.0896486
$113$	9.89282	0.930638	0.465319	−	0.885143i	$-0.345940\pi$
$113$	9.89282	0.930638	0.465319	+	0.885143i	$0.345940\pi$
$114$	−10.7037	−1.00249
$115$	0	0
$116$	10.3443	0.960446
$117$	−2.80377	−0.259209
$118$	1.24115	0.114257
$119$	0.917083	0.0840689
$120$	−1.34421	−0.122709
$121$	−3.64358	−0.331234
$122$	12.1585	1.10078
$123$	−2.48636	−0.224187
$124$	2.62327	0.235577
$125$	1.00000	0.0894427
$126$	1.13195	0.100842
$127$	−2.50768	−0.222521	−0.111260	−	0.993791i	$-0.535489\pi$
$127$	−2.50768	−0.222521	−0.111260	+	0.993791i	$0.535489\pi$
$128$	−1.00000	−0.0883883
$129$	−6.83090	−0.601427
$130$	−2.35000	−0.206109
$131$	10.1259	0.884705	0.442353	−	0.896841i	$-0.354144\pi$
$131$	10.1259	0.884705	0.442353	+	0.896841i	$0.354144\pi$
$132$	3.64587	0.317332
$133$	7.55473	0.655078
$134$	−1.91529	−0.165456
$135$	−5.63641	−0.485105
$136$	−0.966621	−0.0828870
$137$	−18.0249	−1.53997	−0.769985	−	0.638062i	$-0.779736\pi$
$137$	−18.0249	−1.53997	−0.769985	+	0.638062i	$0.779736\pi$
$138$	0	0
$139$	3.29781	0.279716	0.139858	−	0.990172i	$-0.455335\pi$
$139$	3.29781	0.279716	0.139858	+	0.990172i	$0.455335\pi$
$140$	0.948752	0.0801842
$141$	−2.38301	−0.200686
$142$	−14.2696	−1.19748
$143$	6.37385	0.533008
$144$	−1.19309	−0.0994246
$145$	10.3443	0.859049
$146$	3.25495	0.269382
$147$	−8.19952	−0.676285
$148$	3.71211	0.305134
$149$	15.0164	1.23019	0.615095	−	0.788453i	$-0.289118\pi$
$149$	15.0164	1.23019	0.615095	+	0.788453i	$0.289118\pi$
$150$	−1.34421	−0.109754
$151$	17.3196	1.40945	0.704723	−	0.709483i	$-0.251071\pi$
$151$	17.3196	1.40945	0.704723	+	0.709483i	$0.251071\pi$
$152$	−7.96281	−0.645869
$153$	−1.15327	−0.0932363
$154$	−2.57327	−0.207360
$155$	2.62327	0.210706
$156$	3.15890	0.252914
$157$	14.4913	1.15653	0.578264	−	0.815850i	$-0.303730\pi$
$157$	14.4913	1.15653	0.578264	+	0.815850i	$0.303730\pi$
$158$	11.4402	0.910134
$159$	−0.799570	−0.0634100
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	3.99724	0.314053
$163$	9.32430	0.730336	0.365168	−	0.930942i	$-0.381012\pi$
$163$	9.32430	0.730336	0.365168	+	0.930942i	$0.381012\pi$
$164$	−1.84968	−0.144435
$165$	3.64587	0.283831
$166$	15.1276	1.17413
$167$	18.9407	1.46568	0.732838	−	0.680403i	$-0.238195\pi$
$167$	18.9407	1.46568	0.732838	+	0.680403i	$0.238195\pi$
$168$	−1.27532	−0.0983933
$169$	−7.47749	−0.575192
$170$	−0.966621	−0.0741364
$171$	−9.50038	−0.726512
$172$	−5.08172	−0.387477
$173$	13.7002	1.04160	0.520802	−	0.853678i	$-0.325633\pi$
$173$	13.7002	1.04160	0.520802	+	0.853678i	$0.325633\pi$
$174$	−13.9050	−1.05413
$175$	0.948752	0.0717189
$176$	2.71227	0.204445
$177$	−1.66837	−0.125402
$178$	1.09983	0.0824355
$179$	7.85965	0.587458	0.293729	−	0.955889i	$-0.405104\pi$
$179$	7.85965	0.587458	0.293729	+	0.955889i	$0.405104\pi$
$180$	−1.19309	−0.0889280
$181$	−12.5282	−0.931211	−0.465606	−	0.884992i	$-0.654163\pi$
$181$	−12.5282	−0.931211	−0.465606	+	0.884992i	$0.654163\pi$
$182$	−2.22957	−0.165267
$183$	−16.3436	−1.20815
$184$	0	0
$185$	3.71211	0.272920
$186$	−3.52623	−0.258556
$187$	2.62174	0.191721
$188$	−1.77280	−0.129295
$189$	−5.34755	−0.388977
$190$	−7.96281	−0.577683
$191$	−16.6649	−1.20583	−0.602915	−	0.797806i	$-0.705994\pi$
$191$	−16.6649	−1.20583	−0.602915	+	0.797806i	$0.705994\pi$
$192$	1.34421	0.0970101
$193$	23.1060	1.66320	0.831602	−	0.555372i	$-0.187424\pi$
$193$	23.1060	1.66320	0.831602	+	0.555372i	$0.187424\pi$
$194$	0.767674	0.0551158
$195$	3.15890	0.226214
$196$	−6.09987	−0.435705
$197$	13.3764	0.953032	0.476516	−	0.879166i	$-0.341899\pi$
$197$	13.3764	0.953032	0.476516	+	0.879166i	$0.341899\pi$
$198$	3.23600	0.229972
$199$	−17.3195	−1.22775	−0.613874	−	0.789404i	$-0.710390\pi$
$199$	−17.3195	−1.22775	−0.613874	+	0.789404i	$0.710390\pi$
$200$	−1.00000	−0.0707107
$201$	2.57456	0.181595
$202$	−0.544671	−0.0383229
$203$	9.81419	0.688821
$204$	1.29934	0.0909722
$205$	−1.84968	−0.129187
$206$	0.479174	0.0333856
$207$	0	0
$208$	2.35000	0.162943
$209$	21.5973	1.49392
$210$	−1.27532	−0.0880057
$211$	−14.6301	−1.00718	−0.503589	−	0.863943i	$-0.667987\pi$
$211$	−14.6301	−1.00718	−0.503589	+	0.863943i	$0.667987\pi$
$212$	−0.594825	−0.0408527
$213$	19.1813	1.31428
$214$	−4.86403	−0.332498
$215$	−5.08172	−0.346570
$216$	5.63641	0.383509
$217$	2.48883	0.168953
$218$	−7.11502	−0.481890
$219$	−4.37534	−0.295658
$220$	2.71227	0.182861
$221$	2.27156	0.152802
$222$	−4.98987	−0.334898
$223$	−15.6112	−1.04540	−0.522702	−	0.852516i	$-0.675076\pi$
$223$	−15.6112	−1.04540	−0.522702	+	0.852516i	$0.675076\pi$
$224$	−0.948752	−0.0633911
$225$	−1.19309	−0.0795396
$226$	−9.89282	−0.658060
$227$	−6.23747	−0.413996	−0.206998	−	0.978341i	$-0.566369\pi$
$227$	−6.23747	−0.413996	−0.206998	+	0.978341i	$0.566369\pi$
$228$	10.7037	0.708870
$229$	9.80799	0.648130	0.324065	−	0.946035i	$-0.394950\pi$
$229$	9.80799	0.648130	0.324065	+	0.946035i	$0.394950\pi$
$230$	0	0
$231$	3.45902	0.227587
$232$	−10.3443	−0.679138
$233$	−1.34823	−0.0883253	−0.0441627	−	0.999024i	$-0.514062\pi$
$233$	−1.34823	−0.0883253	−0.0441627	+	0.999024i	$0.514062\pi$
$234$	2.80377	0.183288
$235$	−1.77280	−0.115645
$236$	−1.24115	−0.0807918
$237$	−15.3781	−0.998912
$238$	−0.917083	−0.0594457
$239$	19.5626	1.26540	0.632699	−	0.774398i	$-0.281947\pi$
$239$	19.5626	1.26540	0.632699	+	0.774398i	$0.281947\pi$
$240$	1.34421	0.0867685
$241$	29.0806	1.87325	0.936624	−	0.350336i	$-0.113933\pi$
$241$	29.0806	1.87325	0.936624	+	0.350336i	$0.113933\pi$
$242$	3.64358	0.234218
$243$	11.5361	0.740040
$244$	−12.1585	−0.778367
$245$	−6.09987	−0.389706
$246$	2.48636	0.158524
$247$	18.7126	1.19066
$248$	−2.62327	−0.166578
$249$	−20.3346	−1.28866
$250$	−1.00000	−0.0632456
$251$	19.4253	1.22611	0.613056	−	0.790039i	$-0.289940\pi$
$251$	19.4253	1.22611	0.613056	+	0.790039i	$0.289940\pi$
$252$	−1.13195	−0.0713062
$253$	0	0
$254$	2.50768	0.157346
$255$	1.29934	0.0813680
$256$	1.00000	0.0625000
$257$	7.69411	0.479946	0.239973	−	0.970780i	$-0.422861\pi$
$257$	7.69411	0.479946	0.239973	+	0.970780i	$0.422861\pi$
$258$	6.83090	0.425273
$259$	3.52187	0.218839
$260$	2.35000	0.145741
$261$	−12.3417	−0.763935
$262$	−10.1259	−0.625581
$263$	−15.9369	−0.982710	−0.491355	−	0.870959i	$-0.663498\pi$
$263$	−15.9369	−0.982710	−0.491355	+	0.870959i	$0.663498\pi$
$264$	−3.64587	−0.224388
$265$	−0.594825	−0.0365398
$266$	−7.55473	−0.463210
$267$	−1.47840	−0.0904766
$268$	1.91529	0.116995
$269$	−24.9326	−1.52017	−0.760085	−	0.649824i	$-0.774843\pi$
$269$	−24.9326	−1.52017	−0.760085	+	0.649824i	$0.774843\pi$
$270$	5.63641	0.343021
$271$	−4.09018	−0.248461	−0.124230	−	0.992253i	$-0.539646\pi$
$271$	−4.09018	−0.248461	−0.124230	+	0.992253i	$0.539646\pi$
$272$	0.966621	0.0586100
$273$	2.99701	0.181387
$274$	18.0249	1.08892
$275$	2.71227	0.163556
$276$	0	0
$277$	25.8748	1.55467	0.777334	−	0.629088i	$-0.216572\pi$
$277$	25.8748	1.55467	0.777334	+	0.629088i	$0.216572\pi$
$278$	−3.29781	−0.197789
$279$	−3.12981	−0.187377
$280$	−0.948752	−0.0566988
$281$	19.7273	1.17683	0.588417	−	0.808558i	$-0.299752\pi$
$281$	19.7273	1.17683	0.588417	+	0.808558i	$0.299752\pi$
$282$	2.38301	0.141906
$283$	−19.1382	−1.13765	−0.568824	−	0.822459i	$-0.692602\pi$
$283$	−19.1382	−1.13765	−0.568824	+	0.822459i	$0.692602\pi$
$284$	14.2696	0.846743
$285$	10.7037	0.634032
$286$	−6.37385	−0.376893
$287$	−1.75488	−0.103587
$288$	1.19309	0.0703038
$289$	−16.0656	−0.945038
$290$	−10.3443	−0.607439
$291$	−1.03192	−0.0604920
$292$	−3.25495	−0.190482
$293$	−17.8663	−1.04376	−0.521879	−	0.853019i	$-0.674769\pi$
$293$	−17.8663	−1.04376	−0.521879	+	0.853019i	$0.674769\pi$
$294$	8.19952	0.478206
$295$	−1.24115	−0.0722624
$296$	−3.71211	−0.215762
$297$	−15.2875	−0.887069
$298$	−15.0164	−0.869876
$299$	0	0
$300$	1.34421	0.0776081
$301$	−4.82129	−0.277894
$302$	−17.3196	−0.996629
$303$	0.732153	0.0420611
$304$	7.96281	0.456698
$305$	−12.1585	−0.696193
$306$	1.15327	0.0659281
$307$	−26.4739	−1.51094	−0.755472	−	0.655181i	$-0.772592\pi$
$307$	−26.4739	−1.51094	−0.755472	+	0.655181i	$0.772592\pi$
$308$	2.57327	0.146626
$309$	−0.644111	−0.0366422
$310$	−2.62327	−0.148992
$311$	−0.857519	−0.0486254	−0.0243127	−	0.999704i	$-0.507740\pi$
$311$	−0.857519	−0.0486254	−0.0243127	+	0.999704i	$0.507740\pi$
$312$	−3.15890	−0.178838
$313$	−12.9497	−0.731962	−0.365981	−	0.930622i	$-0.619266\pi$
$313$	−12.9497	−0.731962	−0.365981	+	0.930622i	$0.619266\pi$
$314$	−14.4913	−0.817789
$315$	−1.13195	−0.0637782
$316$	−11.4402	−0.643562
$317$	31.6205	1.77598	0.887991	−	0.459860i	$-0.152100\pi$
$317$	31.6205	1.77598	0.887991	+	0.459860i	$0.152100\pi$
$318$	0.799570	0.0448377
$319$	28.0566	1.57087
$320$	1.00000	0.0559017
$321$	6.53829	0.364932
$322$	0	0
$323$	7.69701	0.428273
$324$	−3.99724	−0.222069
$325$	2.35000	0.130355
$326$	−9.32430	−0.516425
$327$	9.56410	0.528896
$328$	1.84968	0.102131
$329$	−1.68194	−0.0927286
$330$	−3.64587	−0.200698
$331$	12.3757	0.680233	0.340116	−	0.940383i	$-0.389534\pi$
$331$	12.3757	0.680233	0.340116	+	0.940383i	$0.389534\pi$
$332$	−15.1276	−0.830233
$333$	−4.42890	−0.242702
$334$	−18.9407	−1.03639
$335$	1.91529	0.104644
$336$	1.27532	0.0695746
$337$	23.6651	1.28912	0.644561	−	0.764553i	$-0.277040\pi$
$337$	23.6651	1.28912	0.644561	+	0.764553i	$0.277040\pi$
$338$	7.47749	0.406722
$339$	13.2980	0.722250
$340$	0.966621	0.0524224
$341$	7.11502	0.385300
$342$	9.50038	0.513722
$343$	−12.4285	−0.671077
$344$	5.08172	0.273988
$345$	0	0
$346$	−13.7002	−0.736525
$347$	−36.0168	−1.93348	−0.966740	−	0.255760i	$-0.917674\pi$
$347$	−36.0168	−1.93348	−0.966740	+	0.255760i	$0.917674\pi$
$348$	13.9050	0.745384
$349$	−27.4819	−1.47107	−0.735536	−	0.677486i	$-0.763069\pi$
$349$	−27.4819	−1.47107	−0.735536	+	0.677486i	$0.763069\pi$
$350$	−0.948752	−0.0507129
$351$	−13.2456	−0.706996
$352$	−2.71227	−0.144565
$353$	−32.3382	−1.72119	−0.860595	−	0.509289i	$-0.829908\pi$
$353$	−32.3382	−1.72119	−0.860595	+	0.509289i	$0.829908\pi$
$354$	1.66837	0.0886726
$355$	14.2696	0.757350
$356$	−1.09983	−0.0582907
$357$	1.23275	0.0652443
$358$	−7.85965	−0.415395
$359$	8.17633	0.431530	0.215765	−	0.976445i	$-0.430775\pi$
$359$	8.17633	0.431530	0.215765	+	0.976445i	$0.430775\pi$
$360$	1.19309	0.0628816
$361$	44.4063	2.33717
$362$	12.5282	0.658466
$363$	−4.89774	−0.257065
$364$	2.22957	0.116861
$365$	−3.25495	−0.170372
$366$	16.3436	0.854293
$367$	−15.4442	−0.806182	−0.403091	−	0.915160i	$-0.632064\pi$
$367$	−15.4442	−0.806182	−0.403091	+	0.915160i	$0.632064\pi$
$368$	0	0
$369$	2.20684	0.114883
$370$	−3.71211	−0.192984
$371$	−0.564341	−0.0292991
$372$	3.52623	0.182826
$373$	−11.6412	−0.602759	−0.301380	−	0.953504i	$-0.597447\pi$
$373$	−11.6412	−0.602759	−0.301380	+	0.953504i	$0.597447\pi$
$374$	−2.62174	−0.135567
$375$	1.34421	0.0694148
$376$	1.77280	0.0914250
$377$	24.3092	1.25199
$378$	5.34755	0.275048
$379$	10.2900	0.528560	0.264280	−	0.964446i	$-0.414866\pi$
$379$	10.2900	0.528560	0.264280	+	0.964446i	$0.414866\pi$
$380$	7.96281	0.408483
$381$	−3.37085	−0.172694
$382$	16.6649	0.852650
$383$	−28.7032	−1.46666	−0.733332	−	0.679871i	$-0.762036\pi$
$383$	−28.7032	−1.46666	−0.733332	+	0.679871i	$0.762036\pi$
$384$	−1.34421	−0.0685965
$385$	2.57327	0.131146
$386$	−23.1060	−1.17606
$387$	6.06297	0.308198
$388$	−0.767674	−0.0389728
$389$	−33.9419	−1.72092	−0.860461	−	0.509516i	$-0.829824\pi$
$389$	−33.9419	−1.72092	−0.860461	+	0.509516i	$0.829824\pi$
$390$	−3.15890	−0.159957
$391$	0	0
$392$	6.09987	0.308090
$393$	13.6114	0.686603
$394$	−13.3764	−0.673895
$395$	−11.4402	−0.575619
$396$	−3.23600	−0.162615
$397$	−37.3865	−1.87637	−0.938186	−	0.346130i	$-0.887496\pi$
$397$	−37.3865	−1.87637	−0.938186	+	0.346130i	$0.887496\pi$
$398$	17.3195	0.868150
$399$	10.1552	0.508394
$400$	1.00000	0.0500000
$401$	−0.358667	−0.0179110	−0.00895550	−	0.999960i	$-0.502851\pi$
$401$	−0.358667	−0.0179110	−0.00895550	+	0.999960i	$0.502851\pi$
$402$	−2.57456	−0.128407
$403$	6.16469	0.307085
$404$	0.544671	0.0270984
$405$	−3.99724	−0.198625
$406$	−9.81419	−0.487070
$407$	10.0683	0.499065
$408$	−1.29934	−0.0643271
$409$	24.2366	1.19842	0.599210	−	0.800592i	$-0.295481\pi$
$409$	24.2366	1.19842	0.599210	+	0.800592i	$0.295481\pi$
$410$	1.84968	0.0913490
$411$	−24.2293	−1.19514
$412$	−0.479174	−0.0236072
$413$	−1.17754	−0.0579430
$414$	0	0
$415$	−15.1276	−0.742583
$416$	−2.35000	−0.115218
$417$	4.43295	0.217082
$418$	−21.5973	−1.05636
$419$	−3.33724	−0.163035	−0.0815174	−	0.996672i	$-0.525977\pi$
$419$	−3.33724	−0.163035	−0.0815174	+	0.996672i	$0.525977\pi$
$420$	1.27532	0.0622294
$421$	15.0403	0.733019	0.366509	−	0.930414i	$-0.380553\pi$
$421$	15.0403	0.733019	0.366509	+	0.930414i	$0.380553\pi$
$422$	14.6301	0.712182
$423$	2.11511	0.102840
$424$	0.594825	0.0288872
$425$	0.966621	0.0468880
$426$	−19.1813	−0.929338
$427$	−11.5354	−0.558236
$428$	4.86403	0.235112
$429$	8.56780	0.413657
$430$	5.08172	0.245062
$431$	24.8825	1.19855	0.599273	−	0.800544i	$-0.295456\pi$
$431$	24.8825	1.19855	0.599273	+	0.800544i	$0.295456\pi$
$432$	−5.63641	−0.271182
$433$	−26.8458	−1.29012	−0.645062	−	0.764130i	$-0.723169\pi$
$433$	−26.8458	−1.29012	−0.645062	+	0.764130i	$0.723169\pi$
$434$	−2.48883	−0.119468
$435$	13.9050	0.666692
$436$	7.11502	0.340748
$437$	0	0
$438$	4.37534	0.209062
$439$	5.45719	0.260457	0.130229	−	0.991484i	$-0.458429\pi$
$439$	5.45719	0.260457	0.130229	+	0.991484i	$0.458429\pi$
$440$	−2.71227	−0.129303
$441$	7.27772	0.346558
$442$	−2.27156	−0.108047
$443$	9.74011	0.462767	0.231383	−	0.972863i	$-0.425675\pi$
$443$	9.74011	0.462767	0.231383	+	0.972863i	$0.425675\pi$
$444$	4.98987	0.236809
$445$	−1.09983	−0.0521368
$446$	15.6112	0.739212
$447$	20.1852	0.954727
$448$	0.948752	0.0448243
$449$	20.1352	0.950237	0.475118	−	0.879922i	$-0.342405\pi$
$449$	20.1352	0.950237	0.475118	+	0.879922i	$0.342405\pi$
$450$	1.19309	0.0562430
$451$	−5.01682	−0.236233
$452$	9.89282	0.465319
$453$	23.2812	1.09384
$454$	6.23747	0.292739
$455$	2.22957	0.104524
$456$	−10.7037	−0.501247
$457$	36.8190	1.72232	0.861161	−	0.508332i	$-0.169738\pi$
$457$	36.8190	1.72232	0.861161	+	0.508332i	$0.169738\pi$
$458$	−9.80799	−0.458297
$459$	−5.44827	−0.254303
$460$	0	0
$461$	16.5267	0.769725	0.384863	−	0.922974i	$-0.374249\pi$
$461$	16.5267	0.769725	0.384863	+	0.922974i	$0.374249\pi$
$462$	−3.45902	−0.160928
$463$	−1.11585	−0.0518579	−0.0259290	−	0.999664i	$-0.508254\pi$
$463$	−1.11585	−0.0518579	−0.0259290	+	0.999664i	$0.508254\pi$
$464$	10.3443	0.480223
$465$	3.52623	0.163525
$466$	1.34823	0.0624554
$467$	−11.8153	−0.546745	−0.273373	−	0.961908i	$-0.588139\pi$
$467$	−11.8153	−0.546745	−0.273373	+	0.961908i	$0.588139\pi$
$468$	−2.80377	−0.129605
$469$	1.81714	0.0839076
$470$	1.77280	0.0817730
$471$	19.4793	0.897560
$472$	1.24115	0.0571285
$473$	−13.7830	−0.633743
$474$	15.3781	0.706338
$475$	7.96281	0.365359
$476$	0.917083	0.0420344
$477$	0.709682	0.0324941
$478$	−19.5626	−0.894771
$479$	25.8473	1.18099	0.590497	−	0.807040i	$-0.298932\pi$
$479$	25.8473	1.18099	0.590497	+	0.807040i	$0.298932\pi$
$480$	−1.34421	−0.0613546
$481$	8.72347	0.397756
$482$	−29.0806	−1.32459
$483$	0	0
$484$	−3.64358	−0.165617
$485$	−0.767674	−0.0348583
$486$	−11.5361	−0.523287
$487$	6.70229	0.303710	0.151855	−	0.988403i	$-0.451475\pi$
$487$	6.70229	0.303710	0.151855	+	0.988403i	$0.451475\pi$
$488$	12.1585	0.550389
$489$	12.5338	0.566800
$490$	6.09987	0.275564
$491$	33.0388	1.49102	0.745510	−	0.666494i	$-0.232206\pi$
$491$	33.0388	1.49102	0.745510	+	0.666494i	$0.232206\pi$
$492$	−2.48636	−0.112094
$493$	9.99903	0.450334
$494$	−18.7126	−0.841920
$495$	−3.23600	−0.145447
$496$	2.62327	0.117788
$497$	13.5383	0.607275
$498$	20.3346	0.911217
$499$	−28.9380	−1.29544	−0.647722	−	0.761876i	$-0.724278\pi$
$499$	−28.9380	−1.29544	−0.647722	+	0.761876i	$0.724278\pi$
$500$	1.00000	0.0447214
$501$	25.4603	1.13748
$502$	−19.4253	−0.866993
$503$	−8.36942	−0.373174	−0.186587	−	0.982438i	$-0.559743\pi$
$503$	−8.36942	−0.373174	−0.186587	+	0.982438i	$0.559743\pi$
$504$	1.13195	0.0504211
$505$	0.544671	0.0242375
$506$	0	0
$507$	−10.0513	−0.446395
$508$	−2.50768	−0.111260
$509$	−15.1661	−0.672227	−0.336113	−	0.941822i	$-0.609113\pi$
$509$	−15.1661	−0.672227	−0.336113	+	0.941822i	$0.609113\pi$
$510$	−1.29934	−0.0575359
$511$	−3.08814	−0.136611
$512$	−1.00000	−0.0441942
$513$	−44.8816	−1.98157
$514$	−7.69411	−0.339373
$515$	−0.479174	−0.0211149
$516$	−6.83090	−0.300714
$517$	−4.80831	−0.211469
$518$	−3.52187	−0.154742
$519$	18.4159	0.808369
$520$	−2.35000	−0.103054
$521$	24.1415	1.05766	0.528828	−	0.848729i	$-0.322632\pi$
$521$	24.1415	1.05766	0.528828	+	0.848729i	$0.322632\pi$
$522$	12.3417	0.540184
$523$	13.6431	0.596571	0.298285	−	0.954477i	$-0.403585\pi$
$523$	13.6431	0.596571	0.298285	+	0.954477i	$0.403585\pi$
$524$	10.1259	0.442353
$525$	1.27532	0.0556597
$526$	15.9369	0.694881
$527$	2.53571	0.110457
$528$	3.64587	0.158666
$529$	0	0
$530$	0.594825	0.0258375
$531$	1.48081	0.0642615
$532$	7.55473	0.327539
$533$	−4.34674	−0.188278
$534$	1.47840	0.0639766
$535$	4.86403	0.210290
$536$	−1.91529	−0.0827280
$537$	10.5650	0.455915
$538$	24.9326	1.07492
$539$	−16.5445	−0.712623
$540$	−5.63641	−0.242552
$541$	−6.35675	−0.273298	−0.136649	−	0.990620i	$-0.543633\pi$
$541$	−6.35675	−0.273298	−0.136649	+	0.990620i	$0.543633\pi$
$542$	4.09018	0.175688
$543$	−16.8405	−0.722695
$544$	−0.966621	−0.0414435
$545$	7.11502	0.304774
$546$	−2.99701	−0.128260
$547$	33.1488	1.41734	0.708669	−	0.705541i	$-0.249296\pi$
$547$	33.1488	1.41734	0.708669	+	0.705541i	$0.249296\pi$
$548$	−18.0249	−0.769985
$549$	14.5062	0.619111
$550$	−2.71227	−0.115652
$551$	82.3698	3.50907
$552$	0	0
$553$	−10.8539	−0.461555
$554$	−25.8748	−1.09932
$555$	4.98987	0.211808
$556$	3.29781	0.139858
$557$	−35.8902	−1.52071	−0.760357	−	0.649505i	$-0.774976\pi$
$557$	−35.8902	−1.52071	−0.760357	+	0.649505i	$0.774976\pi$
$558$	3.12981	0.132495
$559$	−11.9420	−0.505095
$560$	0.948752	0.0400921
$561$	3.52417	0.148791
$562$	−19.7273	−0.832147
$563$	−37.2747	−1.57094	−0.785472	−	0.618898i	$-0.787580\pi$
$563$	−37.2747	−1.57094	−0.785472	+	0.618898i	$0.787580\pi$
$564$	−2.38301	−0.100343
$565$	9.89282	0.416194
$566$	19.1382	0.804439
$567$	−3.79239	−0.159265
$568$	−14.2696	−0.598738
$569$	−15.1548	−0.635322	−0.317661	−	0.948204i	$-0.602897\pi$
$569$	−15.1548	−0.635322	−0.317661	+	0.948204i	$0.602897\pi$
$570$	−10.7037	−0.448329
$571$	−14.3479	−0.600441	−0.300221	−	0.953870i	$-0.597060\pi$
$571$	−14.3479	−0.600441	−0.300221	+	0.953870i	$0.597060\pi$
$572$	6.37385	0.266504
$573$	−22.4012	−0.935821
$574$	1.75488	0.0732474
$575$	0	0
$576$	−1.19309	−0.0497123
$577$	21.5062	0.895315	0.447657	−	0.894205i	$-0.352258\pi$
$577$	21.5062	0.895315	0.447657	+	0.894205i	$0.352258\pi$
$578$	16.0656	0.668243
$579$	31.0593	1.29078
$580$	10.3443	0.429524
$581$	−14.3523	−0.595434
$582$	1.03192	0.0427743
$583$	−1.61333	−0.0668172
$584$	3.25495	0.134691
$585$	−2.80377	−0.115922
$586$	17.8663	0.738049
$587$	42.5732	1.75719	0.878593	−	0.477572i	$-0.158483\pi$
$587$	42.5732	1.75719	0.878593	+	0.477572i	$0.158483\pi$
$588$	−8.19952	−0.338142
$589$	20.8886	0.860699
$590$	1.24115	0.0510972
$591$	17.9808	0.739630
$592$	3.71211	0.152567
$593$	0.108456	0.00445374	0.00222687	−	0.999998i	$-0.499291\pi$
$593$	0.108456	0.00445374	0.00222687	+	0.999998i	$0.499291\pi$
$594$	15.2875	0.627253
$595$	0.917083	0.0375967
$596$	15.0164	0.615095
$597$	−23.2811	−0.952833
$598$	0	0
$599$	20.9206	0.854794	0.427397	−	0.904064i	$-0.359431\pi$
$599$	20.9206	0.854794	0.427397	+	0.904064i	$0.359431\pi$
$600$	−1.34421	−0.0548772
$601$	−31.9134	−1.30178	−0.650888	−	0.759174i	$-0.725603\pi$
$601$	−31.9134	−1.30178	−0.650888	+	0.759174i	$0.725603\pi$
$602$	4.82129	0.196501
$603$	−2.28512	−0.0930575
$604$	17.3196	0.704723
$605$	−3.64358	−0.148132
$606$	−0.732153	−0.0297417
$607$	−28.9699	−1.17585	−0.587927	−	0.808914i	$-0.700056\pi$
$607$	−28.9699	−1.17585	−0.587927	+	0.808914i	$0.700056\pi$
$608$	−7.96281	−0.322934
$609$	13.1923	0.534581
$610$	12.1585	0.492283
$611$	−4.16608	−0.168541
$612$	−1.15327	−0.0466182
$613$	−46.0819	−1.86123	−0.930616	−	0.365998i	$-0.880728\pi$
$613$	−46.0819	−1.86123	−0.930616	+	0.365998i	$0.880728\pi$
$614$	26.4739	1.06840
$615$	−2.48636	−0.100260
$616$	−2.57327	−0.103680
$617$	−5.11350	−0.205862	−0.102931	−	0.994689i	$-0.532822\pi$
$617$	−5.11350	−0.205862	−0.102931	+	0.994689i	$0.532822\pi$
$618$	0.644111	0.0259099
$619$	−19.8493	−0.797812	−0.398906	−	0.916992i	$-0.630610\pi$
$619$	−19.8493	−0.797812	−0.398906	+	0.916992i	$0.630610\pi$
$620$	2.62327	0.105353
$621$	0	0
$622$	0.857519	0.0343834
$623$	−1.04346	−0.0418054
$624$	3.15890	0.126457
$625$	1.00000	0.0400000
$626$	12.9497	0.517575
$627$	29.0314	1.15940
$628$	14.4913	0.578264
$629$	3.58821	0.143071
$630$	1.13195	0.0450980
$631$	17.2340	0.686073	0.343037	−	0.939322i	$-0.388544\pi$
$631$	17.2340	0.686073	0.343037	+	0.939322i	$0.388544\pi$
$632$	11.4402	0.455067
$633$	−19.6660	−0.781652
$634$	−31.6205	−1.25581
$635$	−2.50768	−0.0995142
$636$	−0.799570	−0.0317050
$637$	−14.3347	−0.567962
$638$	−28.0566	−1.11077
$639$	−17.0249	−0.673496
$640$	−1.00000	−0.0395285
$641$	−30.2758	−1.19582	−0.597910	−	0.801563i	$-0.704002\pi$
$641$	−30.2758	−1.19582	−0.597910	+	0.801563i	$0.704002\pi$
$642$	−6.53829	−0.258046
$643$	−2.96160	−0.116794	−0.0583971	−	0.998293i	$-0.518599\pi$
$643$	−2.96160	−0.116794	−0.0583971	+	0.998293i	$0.518599\pi$
$644$	0	0
$645$	−6.83090	−0.268966
$646$	−7.69701	−0.302835
$647$	19.2412	0.756450	0.378225	−	0.925714i	$-0.376534\pi$
$647$	19.2412	0.756450	0.378225	+	0.925714i	$0.376534\pi$
$648$	3.99724	0.157026
$649$	−3.36633	−0.132140
$650$	−2.35000	−0.0921747
$651$	3.34552	0.131121
$652$	9.32430	0.365168
$653$	−7.88066	−0.308394	−0.154197	−	0.988040i	$-0.549279\pi$
$653$	−7.88066	−0.308394	−0.154197	+	0.988040i	$0.549279\pi$
$654$	−9.56410	−0.373986
$655$	10.1259	0.395652
$656$	−1.84968	−0.0722177
$657$	3.88346	0.151508
$658$	1.68194	0.0655690
$659$	−13.3346	−0.519443	−0.259721	−	0.965684i	$-0.583631\pi$
$659$	−13.3346	−0.519443	−0.259721	+	0.965684i	$0.583631\pi$
$660$	3.64587	0.141915
$661$	−17.2729	−0.671836	−0.335918	−	0.941891i	$-0.609047\pi$
$661$	−17.2729	−0.671836	−0.335918	+	0.941891i	$0.609047\pi$
$662$	−12.3757	−0.480997
$663$	3.05346	0.118586
$664$	15.1276	0.587063
$665$	7.55473	0.292960
$666$	4.42890	0.171617
$667$	0	0
$668$	18.9407	0.732838
$669$	−20.9848	−0.811318
$670$	−1.91529	−0.0739942
$671$	−32.9771	−1.27307
$672$	−1.27532	−0.0491967
$673$	−33.3324	−1.28487	−0.642434	−	0.766341i	$-0.722075\pi$
$673$	−33.3324	−1.28487	−0.642434	+	0.766341i	$0.722075\pi$
$674$	−23.6651	−0.911547
$675$	−5.63641	−0.216945
$676$	−7.47749	−0.287596
$677$	6.92500	0.266149	0.133075	−	0.991106i	$-0.457515\pi$
$677$	6.92500	0.266149	0.133075	+	0.991106i	$0.457515\pi$
$678$	−13.2980	−0.510708
$679$	−0.728332	−0.0279508
$680$	−0.966621	−0.0370682
$681$	−8.38448	−0.321294
$682$	−7.11502	−0.272448
$683$	−9.92815	−0.379890	−0.189945	−	0.981795i	$-0.560831\pi$
$683$	−9.92815	−0.379890	−0.189945	+	0.981795i	$0.560831\pi$
$684$	−9.50038	−0.363256
$685$	−18.0249	−0.688696
$686$	12.4285	0.474523
$687$	13.1840	0.503002
$688$	−5.08172	−0.193739
$689$	−1.39784	−0.0532534
$690$	0	0
$691$	−27.7379	−1.05520	−0.527599	−	0.849494i	$-0.676908\pi$
$691$	−27.7379	−1.05520	−0.527599	+	0.849494i	$0.676908\pi$
$692$	13.7002	0.520802
$693$	−3.07016	−0.116626
$694$	36.0168	1.36718
$695$	3.29781	0.125093
$696$	−13.9050	−0.527066
$697$	−1.78793	−0.0677228
$698$	27.4819	1.04020
$699$	−1.81230	−0.0685476
$700$	0.948752	0.0358594
$701$	−0.943093	−0.0356201	−0.0178101	−	0.999841i	$-0.505669\pi$
$701$	−0.943093	−0.0356201	−0.0178101	+	0.999841i	$0.505669\pi$
$702$	13.2456	0.499922
$703$	29.5588	1.11483
$704$	2.71227	0.102223
$705$	−2.38301	−0.0897495
$706$	32.3382	1.21707
$707$	0.516757	0.0194347
$708$	−1.66837	−0.0627010
$709$	−41.1445	−1.54521	−0.772607	−	0.634885i	$-0.781048\pi$
$709$	−41.1445	−1.54521	−0.772607	+	0.634885i	$0.781048\pi$
$710$	−14.2696	−0.535527
$711$	13.6492	0.511887
$712$	1.09983	0.0412177
$713$	0	0
$714$	−1.23275	−0.0461347
$715$	6.37385	0.238368
$716$	7.85965	0.293729
$717$	26.2962	0.982051
$718$	−8.17633	−0.305138
$719$	23.2098	0.865578	0.432789	−	0.901495i	$-0.357530\pi$
$719$	23.2098	0.865578	0.432789	+	0.901495i	$0.357530\pi$
$720$	−1.19309	−0.0444640
$721$	−0.454617	−0.0169308
$722$	−44.4063	−1.65263
$723$	39.0905	1.45379
$724$	−12.5282	−0.465606
$725$	10.3443	0.384178
$726$	4.89774	0.181772
$727$	7.06706	0.262103	0.131051	−	0.991376i	$-0.458165\pi$
$727$	7.06706	0.262103	0.131051	+	0.991376i	$0.458165\pi$
$728$	−2.22957	−0.0826333
$729$	27.4987	1.01847
$730$	3.25495	0.120471
$731$	−4.91209	−0.181680
$732$	−16.3436	−0.604076
$733$	24.3706	0.900149	0.450075	−	0.892991i	$-0.351397\pi$
$733$	24.3706	0.900149	0.450075	+	0.892991i	$0.351397\pi$
$734$	15.4442	0.570056
$735$	−8.19952	−0.302444
$736$	0	0
$737$	5.19480	0.191353
$738$	−2.20684	−0.0812348
$739$	22.6559	0.833410	0.416705	−	0.909042i	$-0.363185\pi$
$739$	22.6559	0.833410	0.416705	+	0.909042i	$0.363185\pi$
$740$	3.71211	0.136460
$741$	25.1537	0.924045
$742$	0.564341	0.0207176
$743$	42.3634	1.55416	0.777082	−	0.629400i	$-0.216699\pi$
$743$	42.3634	1.55416	0.777082	+	0.629400i	$0.216699\pi$
$744$	−3.52623	−0.129278
$745$	15.0164	0.550158
$746$	11.6412	0.426215
$747$	18.0486	0.660364
$748$	2.62174	0.0958603
$749$	4.61476	0.168620
$750$	−1.34421	−0.0490837
$751$	6.70568	0.244694	0.122347	−	0.992487i	$-0.460958\pi$
$751$	6.70568	0.244694	0.122347	+	0.992487i	$0.460958\pi$
$752$	−1.77280	−0.0646473
$753$	26.1117	0.951563
$754$	−24.3092	−0.885288
$755$	17.3196	0.630323
$756$	−5.34755	−0.194489
$757$	−21.8836	−0.795374	−0.397687	−	0.917521i	$-0.630187\pi$
$757$	−21.8836	−0.795374	−0.397687	+	0.917521i	$0.630187\pi$
$758$	−10.2900	−0.373748
$759$	0	0
$760$	−7.96281	−0.288841
$761$	3.95944	0.143529	0.0717647	−	0.997422i	$-0.477137\pi$
$761$	3.95944	0.143529	0.0717647	+	0.997422i	$0.477137\pi$
$762$	3.37085	0.122113
$763$	6.75039	0.244381
$764$	−16.6649	−0.602915
$765$	−1.15327	−0.0416966
$766$	28.7032	1.03709
$767$	−2.91670	−0.105316
$768$	1.34421	0.0485051
$769$	5.78251	0.208523	0.104261	−	0.994550i	$-0.466752\pi$
$769$	5.78251	0.208523	0.104261	+	0.994550i	$0.466752\pi$
$770$	−2.57327	−0.0927343
$771$	10.3425	0.372477
$772$	23.1060	0.831602
$773$	−5.31710	−0.191243	−0.0956214	−	0.995418i	$-0.530484\pi$
$773$	−5.31710	−0.191243	−0.0956214	+	0.995418i	$0.530484\pi$
$774$	−6.06297	−0.217929
$775$	2.62327	0.0942306
$776$	0.767674	0.0275579
$777$	4.73414	0.169837
$778$	33.9419	1.21688
$779$	−14.7286	−0.527707
$780$	3.15890	0.113107
$781$	38.7029	1.38490
$782$	0	0
$783$	−58.3048	−2.08364
$784$	−6.09987	−0.217853
$785$	14.4913	0.517215
$786$	−13.6114	−0.485502
$787$	−38.3181	−1.36589	−0.682946	−	0.730469i	$-0.739302\pi$
$787$	−38.3181	−1.36589	−0.682946	+	0.730469i	$0.739302\pi$
$788$	13.3764	0.476516
$789$	−21.4225	−0.762663
$790$	11.4402	0.407024
$791$	9.38583	0.333722
$792$	3.23600	0.114986
$793$	−28.5725	−1.01464
$794$	37.3865	1.32680
$795$	−0.799570	−0.0283578
$796$	−17.3195	−0.613874
$797$	34.0735	1.20695	0.603473	−	0.797383i	$-0.293783\pi$
$797$	34.0735	1.20695	0.603473	+	0.797383i	$0.293783\pi$
$798$	−10.1552	−0.359489
$799$	−1.71362	−0.0606236
$800$	−1.00000	−0.0353553
$801$	1.31220	0.0463642
$802$	0.358667	0.0126650
$803$	−8.82831	−0.311544
$804$	2.57456	0.0907977
$805$	0	0
$806$	−6.16469	−0.217142
$807$	−33.5147	−1.17978
$808$	−0.544671	−0.0191614
$809$	4.68151	0.164593	0.0822965	−	0.996608i	$-0.473775\pi$
$809$	4.68151	0.164593	0.0822965	+	0.996608i	$0.473775\pi$
$810$	3.99724	0.140449
$811$	−21.6526	−0.760324	−0.380162	−	0.924920i	$-0.624132\pi$
$811$	−21.6526	−0.760324	−0.380162	+	0.924920i	$0.624132\pi$
$812$	9.81419	0.344411
$813$	−5.49807	−0.192826
$814$	−10.0683	−0.352893
$815$	9.32430	0.326616
$816$	1.29934	0.0454861
$817$	−40.4647	−1.41568
$818$	−24.2366	−0.847411
$819$	−2.66009	−0.0929509
$820$	−1.84968	−0.0645935
$821$	−16.8867	−0.589351	−0.294675	−	0.955597i	$-0.595212\pi$
$821$	−16.8867	−0.589351	−0.294675	+	0.955597i	$0.595212\pi$
$822$	24.2293	0.845093
$823$	24.4456	0.852122	0.426061	−	0.904695i	$-0.359901\pi$
$823$	24.4456	0.852122	0.426061	+	0.904695i	$0.359901\pi$
$824$	0.479174	0.0166928
$825$	3.64587	0.126933
$826$	1.17754	0.0409719
$827$	33.2499	1.15621	0.578106	−	0.815961i	$-0.303792\pi$
$827$	33.2499	1.15621	0.578106	+	0.815961i	$0.303792\pi$
$828$	0	0
$829$	31.6911	1.10068	0.550338	−	0.834942i	$-0.314499\pi$
$829$	31.6911	1.10068	0.550338	+	0.834942i	$0.314499\pi$
$830$	15.1276	0.525085
$831$	34.7812	1.20655
$832$	2.35000	0.0814717
$833$	−5.89626	−0.204293
$834$	−4.43295	−0.153500
$835$	18.9407	0.655470
$836$	21.5973	0.746958
$837$	−14.7858	−0.511072
$838$	3.33724	0.115283
$839$	9.62440	0.332271	0.166136	−	0.986103i	$-0.446871\pi$
$839$	9.62440	0.332271	0.166136	+	0.986103i	$0.446871\pi$
$840$	−1.27532	−0.0440028
$841$	78.0049	2.68982
$842$	−15.0403	−0.518323
$843$	26.5177	0.913318
$844$	−14.6301	−0.503589
$845$	−7.47749	−0.257234
$846$	−2.11511	−0.0727191
$847$	−3.45685	−0.118779
$848$	−0.594825	−0.0204264
$849$	−25.7258	−0.882907
$850$	−0.966621	−0.0331548
$851$	0	0
$852$	19.1813	0.657141
$853$	−11.9844	−0.410339	−0.205170	−	0.978726i	$-0.565775\pi$
$853$	−11.9844	−0.410339	−0.205170	+	0.978726i	$0.565775\pi$
$854$	11.5354	0.394733
$855$	−9.50038	−0.324906
$856$	−4.86403	−0.166249
$857$	12.7084	0.434111	0.217055	−	0.976159i	$-0.430355\pi$
$857$	12.7084	0.434111	0.217055	+	0.976159i	$0.430355\pi$
$858$	−8.56780	−0.292500
$859$	19.9309	0.680034	0.340017	−	0.940419i	$-0.389567\pi$
$859$	19.9309	0.680034	0.340017	+	0.940419i	$0.389567\pi$
$860$	−5.08172	−0.173285
$861$	−2.35893	−0.0803923
$862$	−24.8825	−0.847501
$863$	33.5405	1.14173	0.570865	−	0.821044i	$-0.306608\pi$
$863$	33.5405	1.14173	0.570865	+	0.821044i	$0.306608\pi$
$864$	5.63641	0.191754
$865$	13.7002	0.465819
$866$	26.8458	0.912256
$867$	−21.5956	−0.733426
$868$	2.48883	0.0844764
$869$	−31.0290	−1.05259
$870$	−13.9050	−0.471422
$871$	4.50094	0.152509
$872$	−7.11502	−0.240945
$873$	0.915908	0.0309988
$874$	0	0
$875$	0.948752	0.0320737
$876$	−4.37534	−0.147829
$877$	−13.2545	−0.447571	−0.223786	−	0.974638i	$-0.571842\pi$
$877$	−13.2545	−0.447571	−0.223786	+	0.974638i	$0.571842\pi$
$878$	−5.45719	−0.184171
$879$	−24.0160	−0.810041
$880$	2.71227	0.0914307
$881$	37.1811	1.25266	0.626331	−	0.779557i	$-0.284556\pi$
$881$	37.1811	1.25266	0.626331	+	0.779557i	$0.284556\pi$
$882$	−7.27772	−0.245054
$883$	−36.4966	−1.22821	−0.614105	−	0.789224i	$-0.710483\pi$
$883$	−36.4966	−1.22821	−0.614105	+	0.789224i	$0.710483\pi$
$884$	2.27156	0.0764008
$885$	−1.66837	−0.0560815
$886$	−9.74011	−0.327226
$887$	−32.1056	−1.07800	−0.539001	−	0.842305i	$-0.681198\pi$
$887$	−32.1056	−1.07800	−0.539001	+	0.842305i	$0.681198\pi$
$888$	−4.98987	−0.167449
$889$	−2.37916	−0.0797946
$890$	1.09983	0.0368663
$891$	−10.8416	−0.363208
$892$	−15.6112	−0.522702
$893$	−14.1164	−0.472389
$894$	−20.1852	−0.675094
$895$	7.85965	0.262719
$896$	−0.948752	−0.0316956
$897$	0	0
$898$	−20.1352	−0.671919
$899$	27.1359	0.905034
$900$	−1.19309	−0.0397698
$901$	−0.574970	−0.0191550
$902$	5.01682	0.167042
$903$	−6.48083	−0.215669
$904$	−9.89282	−0.329030
$905$	−12.5282	−0.416450
$906$	−23.2812	−0.773465
$907$	−16.1477	−0.536174	−0.268087	−	0.963395i	$-0.586391\pi$
$907$	−16.1477	−0.536174	−0.268087	+	0.963395i	$0.586391\pi$
$908$	−6.23747	−0.206998
$909$	−0.649843	−0.0215539
$910$	−2.22957	−0.0739095
$911$	−18.1425	−0.601086	−0.300543	−	0.953768i	$-0.597168\pi$
$911$	−18.1425	−0.601086	−0.300543	+	0.953768i	$0.597168\pi$
$912$	10.7037	0.354435
$913$	−41.0301	−1.35790
$914$	−36.8190	−1.21787
$915$	−16.3436	−0.540302
$916$	9.80799	0.324065
$917$	9.60698	0.317250
$918$	5.44827	0.179820
$919$	−3.38889	−0.111789	−0.0558945	−	0.998437i	$-0.517801\pi$
$919$	−3.38889	−0.111789	−0.0558945	+	0.998437i	$0.517801\pi$
$920$	0	0
$921$	−35.5865	−1.17262
$922$	−16.5267	−0.544278
$923$	33.5335	1.10377
$924$	3.45902	0.113794
$925$	3.71211	0.122054
$926$	1.11585	0.0366691
$927$	0.571700	0.0187771
$928$	−10.3443	−0.339569
$929$	−32.6728	−1.07196	−0.535980	−	0.844231i	$-0.680058\pi$
$929$	−32.6728	−1.07196	−0.535980	+	0.844231i	$0.680058\pi$
$930$	−3.52623	−0.115630
$931$	−48.5721	−1.59189
$932$	−1.34823	−0.0441627
$933$	−1.15269	−0.0377373
$934$	11.8153	0.386607
$935$	2.62174	0.0857400
$936$	2.80377	0.0916442
$937$	−26.8810	−0.878165	−0.439082	−	0.898447i	$-0.644696\pi$
$937$	−26.8810	−0.878165	−0.439082	+	0.898447i	$0.644696\pi$
$938$	−1.81714	−0.0593316
$939$	−17.4072	−0.568062
$940$	−1.77280	−0.0578223
$941$	49.5304	1.61464	0.807322	−	0.590112i	$-0.200916\pi$
$941$	49.5304	1.61464	0.807322	+	0.590112i	$0.200916\pi$
$942$	−19.4793	−0.634671
$943$	0	0
$944$	−1.24115	−0.0403959
$945$	−5.34755	−0.173956
$946$	13.7830	0.448124
$947$	29.8622	0.970393	0.485196	−	0.874405i	$-0.338748\pi$
$947$	29.8622	0.970393	0.485196	+	0.874405i	$0.338748\pi$
$948$	−15.3781	−0.499456
$949$	−7.64914	−0.248302
$950$	−7.96281	−0.258348
$951$	42.5046	1.37831
$952$	−0.917083	−0.0297228
$953$	20.0213	0.648554	0.324277	−	0.945962i	$-0.394879\pi$
$953$	20.0213	0.648554	0.324277	+	0.945962i	$0.394879\pi$
$954$	−0.709682	−0.0229768
$955$	−16.6649	−0.539263
$956$	19.5626	0.632699
$957$	37.7140	1.21912
$958$	−25.8473	−0.835089
$959$	−17.1011	−0.552225
$960$	1.34421	0.0433842
$961$	−24.1185	−0.778015
$962$	−8.72347	−0.281256
$963$	−5.80325	−0.187007
$964$	29.0806	0.936624
$965$	23.1060	0.743808
$966$	0	0
$967$	11.9160	0.383194	0.191597	−	0.981474i	$-0.438633\pi$
$967$	11.9160	0.383194	0.191597	+	0.981474i	$0.438633\pi$
$968$	3.64358	0.117109
$969$	10.3464	0.332375
$970$	0.767674	0.0246485
$971$	12.1626	0.390317	0.195158	−	0.980772i	$-0.437478\pi$
$971$	12.1626	0.390317	0.195158	+	0.980772i	$0.437478\pi$
$972$	11.5361	0.370020
$973$	3.12880	0.100305
$974$	−6.70229	−0.214755
$975$	3.15890	0.101166
$976$	−12.1585	−0.389184
$977$	−38.4196	−1.22915	−0.614576	−	0.788858i	$-0.710673\pi$
$977$	−38.4196	−1.22915	−0.614576	+	0.788858i	$0.710673\pi$
$978$	−12.5338	−0.400788
$979$	−2.98303	−0.0953380
$980$	−6.09987	−0.194853
$981$	−8.48890	−0.271030
$982$	−33.0388	−1.05431
$983$	9.46732	0.301961	0.150980	−	0.988537i	$-0.451757\pi$
$983$	9.46732	0.301961	0.150980	+	0.988537i	$0.451757\pi$
$984$	2.48636	0.0792621
$985$	13.3764	0.426209
$986$	−9.99903	−0.318434
$987$	−2.26089	−0.0719649
$988$	18.7126	0.595328
$989$	0	0
$990$	3.23600	0.102847
$991$	40.8931	1.29901	0.649506	−	0.760357i	$-0.274976\pi$
$991$	40.8931	1.29901	0.649506	+	0.760357i	$0.274976\pi$
$992$	−2.62327	−0.0832889
$993$	16.6356	0.527916
$994$	−13.5383	−0.429408
$995$	−17.3195	−0.549066
$996$	−20.3346	−0.644328
$997$	−54.1952	−1.71638	−0.858190	−	0.513332i	$-0.828411\pi$
$997$	−54.1952	−1.71638	−0.858190	+	0.513332i	$0.828411\pi$
$998$	28.9380	0.916018
$999$	−20.9230	−0.661974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bj.1.6		10
23.3	even	11		230.2.g.b.101.1	yes	20
23.8	even	11		230.2.g.b.41.1	✓	20
23.22	odd	2		5290.2.a.bi.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.41.1	✓	20	23.8	even	11
230.2.g.b.101.1	yes	20	23.3	even	11
5290.2.a.bi.1.6		10	23.22	odd	2
5290.2.a.bj.1.6		10	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.34421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34421 q^{6} +0.948752 q^{7} -1.00000 q^{8} -1.19309 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.34421 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.34421 q^{6} +0.948752 q^{7} -1.00000 q^{8} -1.19309 q^{9} -1.00000 q^{10} +2.71227 q^{11} +1.34421 q^{12} +2.35000 q^{13} -0.948752 q^{14} +1.34421 q^{15} +1.00000 q^{16} +0.966621 q^{17} +1.19309 q^{18} +7.96281 q^{19} +1.00000 q^{20} +1.27532 q^{21} -2.71227 q^{22} -1.34421 q^{24} +1.00000 q^{25} -2.35000 q^{26} -5.63641 q^{27} +0.948752 q^{28} +10.3443 q^{29} -1.34421 q^{30} +2.62327 q^{31} -1.00000 q^{32} +3.64587 q^{33} -0.966621 q^{34} +0.948752 q^{35} -1.19309 q^{36} +3.71211 q^{37} -7.96281 q^{38} +3.15890 q^{39} -1.00000 q^{40} -1.84968 q^{41} -1.27532 q^{42} -5.08172 q^{43} +2.71227 q^{44} -1.19309 q^{45} -1.77280 q^{47} +1.34421 q^{48} -6.09987 q^{49} -1.00000 q^{50} +1.29934 q^{51} +2.35000 q^{52} -0.594825 q^{53} +5.63641 q^{54} +2.71227 q^{55} -0.948752 q^{56} +10.7037 q^{57} -10.3443 q^{58} -1.24115 q^{59} +1.34421 q^{60} -12.1585 q^{61} -2.62327 q^{62} -1.13195 q^{63} +1.00000 q^{64} +2.35000 q^{65} -3.64587 q^{66} +1.91529 q^{67} +0.966621 q^{68} -0.948752 q^{70} +14.2696 q^{71} +1.19309 q^{72} -3.25495 q^{73} -3.71211 q^{74} +1.34421 q^{75} +7.96281 q^{76} +2.57327 q^{77} -3.15890 q^{78} -11.4402 q^{79} +1.00000 q^{80} -3.99724 q^{81} +1.84968 q^{82} -15.1276 q^{83} +1.27532 q^{84} +0.966621 q^{85} +5.08172 q^{86} +13.9050 q^{87} -2.71227 q^{88} -1.09983 q^{89} +1.19309 q^{90} +2.22957 q^{91} +3.52623 q^{93} +1.77280 q^{94} +7.96281 q^{95} -1.34421 q^{96} -0.767674 q^{97} +6.09987 q^{98} -3.23600 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 7 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 9 q^{11} + 4 q^{12} - 7 q^{13} + 7 q^{14} + 4 q^{15} + 10 q^{16} - 18 q^{17} - 14 q^{18} + 16 q^{19} + 10 q^{20} + 12 q^{21} - 9 q^{22} - 4 q^{24} + 10 q^{25} + 7 q^{26} + 13 q^{27} - 7 q^{28} + 10 q^{29} - 4 q^{30} - 3 q^{31} - 10 q^{32} + 25 q^{33} + 18 q^{34} - 7 q^{35} + 14 q^{36} - 8 q^{37} - 16 q^{38} + 12 q^{39} - 10 q^{40} + 10 q^{41} - 12 q^{42} - 9 q^{43} + 9 q^{44} + 14 q^{45} + 21 q^{47} + 4 q^{48} + 7 q^{49} - 10 q^{50} - 9 q^{51} - 7 q^{52} - 40 q^{53} - 13 q^{54} + 9 q^{55} + 7 q^{56} + 9 q^{57} - 10 q^{58} + 29 q^{59} + 4 q^{60} + 25 q^{61} + 3 q^{62} + 6 q^{63} + 10 q^{64} - 7 q^{65} - 25 q^{66} - 7 q^{67} - 18 q^{68} + 7 q^{70} + 64 q^{71} - 14 q^{72} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 16 q^{76} + 57 q^{77} - 12 q^{78} + 44 q^{79} + 10 q^{80} + 14 q^{81} - 10 q^{82} - 26 q^{83} + 12 q^{84} - 18 q^{85} + 9 q^{86} + 25 q^{87} - 9 q^{88} + 11 q^{89} - 14 q^{90} + 5 q^{93} - 21 q^{94} + 16 q^{95} - 4 q^{96} - 10 q^{97} - 7 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 10 * q^5 - 4 * q^6 - 7 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 9 * q^11 + 4 * q^12 - 7 * q^13 + 7 * q^14 + 4 * q^15 + 10 * q^16 - 18 * q^17 - 14 * q^18 + 16 * q^19 + 10 * q^20 + 12 * q^21 - 9 * q^22 - 4 * q^24 + 10 * q^25 + 7 * q^26 + 13 * q^27 - 7 * q^28 + 10 * q^29 - 4 * q^30 - 3 * q^31 - 10 * q^32 + 25 * q^33 + 18 * q^34 - 7 * q^35 + 14 * q^36 - 8 * q^37 - 16 * q^38 + 12 * q^39 - 10 * q^40 + 10 * q^41 - 12 * q^42 - 9 * q^43 + 9 * q^44 + 14 * q^45 + 21 * q^47 + 4 * q^48 + 7 * q^49 - 10 * q^50 - 9 * q^51 - 7 * q^52 - 40 * q^53 - 13 * q^54 + 9 * q^55 + 7 * q^56 + 9 * q^57 - 10 * q^58 + 29 * q^59 + 4 * q^60 + 25 * q^61 + 3 * q^62 + 6 * q^63 + 10 * q^64 - 7 * q^65 - 25 * q^66 - 7 * q^67 - 18 * q^68 + 7 * q^70 + 64 * q^71 - 14 * q^72 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 16 * q^76 + 57 * q^77 - 12 * q^78 + 44 * q^79 + 10 * q^80 + 14 * q^81 - 10 * q^82 - 26 * q^83 + 12 * q^84 - 18 * q^85 + 9 * q^86 + 25 * q^87 - 9 * q^88 + 11 * q^89 - 14 * q^90 + 5 * q^93 - 21 * q^94 + 16 * q^95 - 4 * q^96 - 10 * q^97 - 7 * q^98 + 13 * q^99

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