LMFDB - Embedded newform 1338.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1338,2,Mod(1,1338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1338, 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("1338.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.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:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.356173.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 9x^{2} + 14x - 4 $ x^5 - 2x^4 - 7x^3 + 9x^2 + 14x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.75496$ of defining polynomial
Character	$\chi$	$=$	1338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.54501 q^{5} -1.00000 q^{6} -1.28984 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.54501 q^{5} -1.00000 q^{6} -1.28984 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.54501 q^{10} -2.49412 q^{11} +1.00000 q^{12} -2.65927 q^{13} +1.28984 q^{14} +1.54501 q^{15} +1.00000 q^{16} +1.92011 q^{17} -1.00000 q^{18} +4.69562 q^{19} +1.54501 q^{20} -1.28984 q^{21} +2.49412 q^{22} +3.63334 q^{23} -1.00000 q^{24} -2.61296 q^{25} +2.65927 q^{26} +1.00000 q^{27} -1.28984 q^{28} +9.08085 q^{29} -1.54501 q^{30} +5.96966 q^{31} -1.00000 q^{32} -2.49412 q^{33} -1.92011 q^{34} -1.99281 q^{35} +1.00000 q^{36} +5.70604 q^{37} -4.69562 q^{38} -2.65927 q^{39} -1.54501 q^{40} +6.53614 q^{41} +1.28984 q^{42} +6.44584 q^{43} -2.49412 q^{44} +1.54501 q^{45} -3.63334 q^{46} +12.1071 q^{47} +1.00000 q^{48} -5.33631 q^{49} +2.61296 q^{50} +1.92011 q^{51} -2.65927 q^{52} +2.97407 q^{53} -1.00000 q^{54} -3.85342 q^{55} +1.28984 q^{56} +4.69562 q^{57} -9.08085 q^{58} -12.6372 q^{59} +1.54501 q^{60} -10.5220 q^{61} -5.96966 q^{62} -1.28984 q^{63} +1.00000 q^{64} -4.10859 q^{65} +2.49412 q^{66} +4.51299 q^{67} +1.92011 q^{68} +3.63334 q^{69} +1.99281 q^{70} +6.01319 q^{71} -1.00000 q^{72} -9.46377 q^{73} -5.70604 q^{74} -2.61296 q^{75} +4.69562 q^{76} +3.21701 q^{77} +2.65927 q^{78} -9.23357 q^{79} +1.54501 q^{80} +1.00000 q^{81} -6.53614 q^{82} +12.9523 q^{83} -1.28984 q^{84} +2.96659 q^{85} -6.44584 q^{86} +9.08085 q^{87} +2.49412 q^{88} -0.168223 q^{89} -1.54501 q^{90} +3.43004 q^{91} +3.63334 q^{92} +5.96966 q^{93} -12.1071 q^{94} +7.25476 q^{95} -1.00000 q^{96} +1.05018 q^{97} +5.33631 q^{98} -2.49412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} - 5 q^{10} + 9 q^{11} + 5 q^{12} + q^{14} + 5 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - 4 q^{19} + 5 q^{20} - q^{21} - 9 q^{22} + 16 q^{23} - 5 q^{24} + 8 q^{25} + 5 q^{27} - q^{28} + 8 q^{29} - 5 q^{30} - q^{31} - 5 q^{32} + 9 q^{33} - 6 q^{34} + 22 q^{35} + 5 q^{36} - 2 q^{37} + 4 q^{38} - 5 q^{40} + 4 q^{41} + q^{42} + 3 q^{43} + 9 q^{44} + 5 q^{45} - 16 q^{46} + 18 q^{47} + 5 q^{48} + 2 q^{49} - 8 q^{50} + 6 q^{51} + 26 q^{53} - 5 q^{54} + q^{55} + q^{56} - 4 q^{57} - 8 q^{58} + 21 q^{59} + 5 q^{60} - 20 q^{61} + q^{62} - q^{63} + 5 q^{64} - 3 q^{65} - 9 q^{66} - 5 q^{67} + 6 q^{68} + 16 q^{69} - 22 q^{70} + 17 q^{71} - 5 q^{72} + 5 q^{73} + 2 q^{74} + 8 q^{75} - 4 q^{76} + 2 q^{77} - 21 q^{79} + 5 q^{80} + 5 q^{81} - 4 q^{82} + 11 q^{83} - q^{84} - 12 q^{85} - 3 q^{86} + 8 q^{87} - 9 q^{88} - 5 q^{89} - 5 q^{90} - 10 q^{91} + 16 q^{92} - q^{93} - 18 q^{94} + 10 q^{95} - 5 q^{96} - 11 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 - 5 * q^10 + 9 * q^11 + 5 * q^12 + q^14 + 5 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - 4 * q^19 + 5 * q^20 - q^21 - 9 * q^22 + 16 * q^23 - 5 * q^24 + 8 * q^25 + 5 * q^27 - q^28 + 8 * q^29 - 5 * q^30 - q^31 - 5 * q^32 + 9 * q^33 - 6 * q^34 + 22 * q^35 + 5 * q^36 - 2 * q^37 + 4 * q^38 - 5 * q^40 + 4 * q^41 + q^42 + 3 * q^43 + 9 * q^44 + 5 * q^45 - 16 * q^46 + 18 * q^47 + 5 * q^48 + 2 * q^49 - 8 * q^50 + 6 * q^51 + 26 * q^53 - 5 * q^54 + q^55 + q^56 - 4 * q^57 - 8 * q^58 + 21 * q^59 + 5 * q^60 - 20 * q^61 + q^62 - q^63 + 5 * q^64 - 3 * q^65 - 9 * q^66 - 5 * q^67 + 6 * q^68 + 16 * q^69 - 22 * q^70 + 17 * q^71 - 5 * q^72 + 5 * q^73 + 2 * q^74 + 8 * q^75 - 4 * q^76 + 2 * q^77 - 21 * q^79 + 5 * q^80 + 5 * q^81 - 4 * q^82 + 11 * q^83 - q^84 - 12 * q^85 - 3 * q^86 + 8 * q^87 - 9 * q^88 - 5 * q^89 - 5 * q^90 - 10 * q^91 + 16 * q^92 - q^93 - 18 * q^94 + 10 * q^95 - 5 * q^96 - 11 * q^97 - 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.54501	0.690947	0.345474	−	0.938428i	$-0.387718\pi$
$5$	1.54501	0.690947	0.345474	+	0.938428i	$0.387718\pi$
$6$	−1.00000	−0.408248
$7$	−1.28984	−0.487514	−0.243757	−	0.969836i	$-0.578380\pi$
$7$	−1.28984	−0.487514	−0.243757	+	0.969836i	$0.578380\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.54501	−0.488574
$11$	−2.49412	−0.752005	−0.376002	−	0.926619i	$-0.622702\pi$
$11$	−2.49412	−0.752005	−0.376002	+	0.926619i	$0.622702\pi$
$12$	1.00000	0.288675
$13$	−2.65927	−0.737549	−0.368775	−	0.929519i	$-0.620223\pi$
$13$	−2.65927	−0.737549	−0.368775	+	0.929519i	$0.620223\pi$
$14$	1.28984	0.344724
$15$	1.54501	0.398919
$16$	1.00000	0.250000
$17$	1.92011	0.465696	0.232848	−	0.972513i	$-0.425195\pi$
$17$	1.92011	0.465696	0.232848	+	0.972513i	$0.425195\pi$
$18$	−1.00000	−0.235702
$19$	4.69562	1.07725	0.538624	−	0.842546i	$-0.318944\pi$
$19$	4.69562	1.07725	0.538624	+	0.842546i	$0.318944\pi$
$20$	1.54501	0.345474
$21$	−1.28984	−0.281466
$22$	2.49412	0.531747
$23$	3.63334	0.757604	0.378802	−	0.925478i	$-0.376336\pi$
$23$	3.63334	0.757604	0.378802	+	0.925478i	$0.376336\pi$
$24$	−1.00000	−0.204124
$25$	−2.61296	−0.522592
$26$	2.65927	0.521526
$27$	1.00000	0.192450
$28$	−1.28984	−0.243757
$29$	9.08085	1.68627	0.843136	−	0.537700i	$-0.180707\pi$
$29$	9.08085	1.68627	0.843136	+	0.537700i	$0.180707\pi$
$30$	−1.54501	−0.282078
$31$	5.96966	1.07218	0.536091	−	0.844160i	$-0.319900\pi$
$31$	5.96966	1.07218	0.536091	+	0.844160i	$0.319900\pi$
$32$	−1.00000	−0.176777
$33$	−2.49412	−0.434170
$34$	−1.92011	−0.329297
$35$	−1.99281	−0.336846
$36$	1.00000	0.166667
$37$	5.70604	0.938067	0.469033	−	0.883180i	$-0.344602\pi$
$37$	5.70604	0.938067	0.469033	+	0.883180i	$0.344602\pi$
$38$	−4.69562	−0.761730
$39$	−2.65927	−0.425824
$40$	−1.54501	−0.244287
$41$	6.53614	1.02077	0.510387	−	0.859945i	$-0.329502\pi$
$41$	6.53614	1.02077	0.510387	+	0.859945i	$0.329502\pi$
$42$	1.28984	0.199027
$43$	6.44584	0.982981	0.491491	−	0.870883i	$-0.336452\pi$
$43$	6.44584	0.982981	0.491491	+	0.870883i	$0.336452\pi$
$44$	−2.49412	−0.376002
$45$	1.54501	0.230316
$46$	−3.63334	−0.535707
$47$	12.1071	1.76600	0.882999	−	0.469374i	$-0.155521\pi$
$47$	12.1071	1.76600	0.882999	+	0.469374i	$0.155521\pi$
$48$	1.00000	0.144338
$49$	−5.33631	−0.762330
$50$	2.61296	0.369528
$51$	1.92011	0.268870
$52$	−2.65927	−0.368775
$53$	2.97407	0.408520	0.204260	−	0.978917i	$-0.434521\pi$
$53$	2.97407	0.408520	0.204260	+	0.978917i	$0.434521\pi$
$54$	−1.00000	−0.136083
$55$	−3.85342	−0.519595
$56$	1.28984	0.172362
$57$	4.69562	0.621950
$58$	−9.08085	−1.19237
$59$	−12.6372	−1.64523	−0.822615	−	0.568599i	$-0.807486\pi$
$59$	−12.6372	−1.64523	−0.822615	+	0.568599i	$0.807486\pi$
$60$	1.54501	0.199459
$61$	−10.5220	−1.34721	−0.673603	−	0.739094i	$-0.735254\pi$
$61$	−10.5220	−1.34721	−0.673603	+	0.739094i	$0.735254\pi$
$62$	−5.96966	−0.758147
$63$	−1.28984	−0.162505
$64$	1.00000	0.125000
$65$	−4.10859	−0.509608
$66$	2.49412	0.307005
$67$	4.51299	0.551349	0.275675	−	0.961251i	$-0.411099\pi$
$67$	4.51299	0.551349	0.275675	+	0.961251i	$0.411099\pi$
$68$	1.92011	0.232848
$69$	3.63334	0.437403
$70$	1.99281	0.238186
$71$	6.01319	0.713635	0.356817	−	0.934174i	$-0.383862\pi$
$71$	6.01319	0.713635	0.356817	+	0.934174i	$0.383862\pi$
$72$	−1.00000	−0.117851
$73$	−9.46377	−1.10765	−0.553825	−	0.832633i	$-0.686832\pi$
$73$	−9.46377	−1.10765	−0.553825	+	0.832633i	$0.686832\pi$
$74$	−5.70604	−0.663313
$75$	−2.61296	−0.301719
$76$	4.69562	0.538624
$77$	3.21701	0.366613
$78$	2.65927	0.301103
$79$	−9.23357	−1.03886	−0.519429	−	0.854514i	$-0.673855\pi$
$79$	−9.23357	−1.03886	−0.519429	+	0.854514i	$0.673855\pi$
$80$	1.54501	0.172737
$81$	1.00000	0.111111
$82$	−6.53614	−0.721796
$83$	12.9523	1.42170	0.710852	−	0.703342i	$-0.248310\pi$
$83$	12.9523	1.42170	0.710852	+	0.703342i	$0.248310\pi$
$84$	−1.28984	−0.140733
$85$	2.96659	0.321772
$86$	−6.44584	−0.695073
$87$	9.08085	0.973570
$88$	2.49412	0.265874
$89$	−0.168223	−0.0178316	−0.00891580	−	0.999960i	$-0.502838\pi$
$89$	−0.168223	−0.0178316	−0.00891580	+	0.999960i	$0.502838\pi$
$90$	−1.54501	−0.162858
$91$	3.43004	0.359565
$92$	3.63334	0.378802
$93$	5.96966	0.619024
$94$	−12.1071	−1.24875
$95$	7.25476	0.744322
$96$	−1.00000	−0.102062
$97$	1.05018	0.106630	0.0533151	−	0.998578i	$-0.483021\pi$
$97$	1.05018	0.106630	0.0533151	+	0.998578i	$0.483021\pi$
$98$	5.33631	0.539049
$99$	−2.49412	−0.250668
$100$	−2.61296	−0.261296
$101$	−4.99849	−0.497368	−0.248684	−	0.968585i	$-0.579998\pi$
$101$	−4.99849	−0.497368	−0.248684	+	0.968585i	$0.579998\pi$
$102$	−1.92011	−0.190120
$103$	15.2450	1.50213	0.751065	−	0.660228i	$-0.229540\pi$
$103$	15.2450	1.50213	0.751065	+	0.660228i	$0.229540\pi$
$104$	2.65927	0.260763
$105$	−1.99281	−0.194478
$106$	−2.97407	−0.288867
$107$	−11.7155	−1.13258	−0.566288	−	0.824207i	$-0.691621\pi$
$107$	−11.7155	−1.13258	−0.566288	+	0.824207i	$0.691621\pi$
$108$	1.00000	0.0962250
$109$	−16.5487	−1.58508	−0.792541	−	0.609818i	$-0.791242\pi$
$109$	−16.5487	−1.58508	−0.792541	+	0.609818i	$0.791242\pi$
$110$	3.85342	0.367409
$111$	5.70604	0.541593
$112$	−1.28984	−0.121878
$113$	2.38720	0.224569	0.112284	−	0.993676i	$-0.464183\pi$
$113$	2.38720	0.224569	0.112284	+	0.993676i	$0.464183\pi$
$114$	−4.69562	−0.439785
$115$	5.61353	0.523465
$116$	9.08085	0.843136
$117$	−2.65927	−0.245850
$118$	12.6372	1.16335
$119$	−2.47664	−0.227033
$120$	−1.54501	−0.141039
$121$	−4.77938	−0.434489
$122$	10.5220	0.952618
$123$	6.53614	0.589344
$124$	5.96966	0.536091
$125$	−11.7621	−1.05203
$126$	1.28984	0.114908
$127$	−14.2746	−1.26667	−0.633333	−	0.773880i	$-0.718314\pi$
$127$	−14.2746	−1.26667	−0.633333	+	0.773880i	$0.718314\pi$
$128$	−1.00000	−0.0883883
$129$	6.44584	0.567524
$130$	4.10859	0.360347
$131$	19.9949	1.74696	0.873480	−	0.486859i	$-0.161858\pi$
$131$	19.9949	1.74696	0.873480	+	0.486859i	$0.161858\pi$
$132$	−2.49412	−0.217085
$133$	−6.05660	−0.525174
$134$	−4.51299	−0.389863
$135$	1.54501	0.132973
$136$	−1.92011	−0.164648
$137$	10.4458	0.892448	0.446224	−	0.894921i	$-0.352768\pi$
$137$	10.4458	0.892448	0.446224	+	0.894921i	$0.352768\pi$
$138$	−3.63334	−0.309291
$139$	12.4043	1.05212	0.526058	−	0.850449i	$-0.323669\pi$
$139$	12.4043	1.05212	0.526058	+	0.850449i	$0.323669\pi$
$140$	−1.99281	−0.168423
$141$	12.1071	1.01960
$142$	−6.01319	−0.504616
$143$	6.63253	0.554640
$144$	1.00000	0.0833333
$145$	14.0300	1.16513
$146$	9.46377	0.783227
$147$	−5.33631	−0.440132
$148$	5.70604	0.469033
$149$	2.70297	0.221436	0.110718	−	0.993852i	$-0.464685\pi$
$149$	2.70297	0.221436	0.110718	+	0.993852i	$0.464685\pi$
$150$	2.61296	0.213347
$151$	−22.0553	−1.79483	−0.897415	−	0.441187i	$-0.854558\pi$
$151$	−22.0553	−1.79483	−0.897415	+	0.441187i	$0.854558\pi$
$152$	−4.69562	−0.380865
$153$	1.92011	0.155232
$154$	−3.21701	−0.259234
$155$	9.22315	0.740821
$156$	−2.65927	−0.212912
$157$	7.38327	0.589249	0.294625	−	0.955613i	$-0.404805\pi$
$157$	7.38327	0.589249	0.294625	+	0.955613i	$0.404805\pi$
$158$	9.23357	0.734583
$159$	2.97407	0.235859
$160$	−1.54501	−0.122143
$161$	−4.68643	−0.369343
$162$	−1.00000	−0.0785674
$163$	−4.26962	−0.334423	−0.167211	−	0.985921i	$-0.553476\pi$
$163$	−4.26962	−0.334423	−0.167211	+	0.985921i	$0.553476\pi$
$164$	6.53614	0.510387
$165$	−3.85342	−0.299989
$166$	−12.9523	−1.00530
$167$	−8.38192	−0.648613	−0.324306	−	0.945952i	$-0.605131\pi$
$167$	−8.38192	−0.648613	−0.324306	+	0.945952i	$0.605131\pi$
$168$	1.28984	0.0995133
$169$	−5.92827	−0.456021
$170$	−2.96659	−0.227527
$171$	4.69562	0.359083
$172$	6.44584	0.491491
$173$	−6.01306	−0.457164	−0.228582	−	0.973525i	$-0.573409\pi$
$173$	−6.01306	−0.457164	−0.228582	+	0.973525i	$0.573409\pi$
$174$	−9.08085	−0.688418
$175$	3.37030	0.254771
$176$	−2.49412	−0.188001
$177$	−12.6372	−0.949874
$178$	0.168223	0.0126089
$179$	23.1043	1.72690	0.863449	−	0.504435i	$-0.168299\pi$
$179$	23.1043	1.72690	0.863449	+	0.504435i	$0.168299\pi$
$180$	1.54501	0.115158
$181$	−20.2695	−1.50662	−0.753310	−	0.657666i	$-0.771544\pi$
$181$	−20.2695	−1.50662	−0.753310	+	0.657666i	$0.771544\pi$
$182$	−3.43004	−0.254251
$183$	−10.5220	−0.777809
$184$	−3.63334	−0.267854
$185$	8.81586	0.648155
$186$	−5.96966	−0.437716
$187$	−4.78899	−0.350206
$188$	12.1071	0.882999
$189$	−1.28984	−0.0938221
$190$	−7.25476	−0.526315
$191$	5.79518	0.419325	0.209662	−	0.977774i	$-0.432764\pi$
$191$	5.79518	0.419325	0.209662	+	0.977774i	$0.432764\pi$
$192$	1.00000	0.0721688
$193$	12.3097	0.886070	0.443035	−	0.896504i	$-0.353902\pi$
$193$	12.3097	0.886070	0.443035	+	0.896504i	$0.353902\pi$
$194$	−1.05018	−0.0753989
$195$	−4.10859	−0.294222
$196$	−5.33631	−0.381165
$197$	18.7257	1.33415	0.667077	−	0.744989i	$-0.267545\pi$
$197$	18.7257	1.33415	0.667077	+	0.744989i	$0.267545\pi$
$198$	2.49412	0.177249
$199$	3.65510	0.259103	0.129552	−	0.991573i	$-0.458646\pi$
$199$	3.65510	0.259103	0.129552	+	0.991573i	$0.458646\pi$
$200$	2.61296	0.184764
$201$	4.51299	0.318322
$202$	4.99849	0.351692
$203$	−11.7128	−0.822081
$204$	1.92011	0.134435
$205$	10.0984	0.705301
$206$	−15.2450	−1.06217
$207$	3.63334	0.252535
$208$	−2.65927	−0.184387
$209$	−11.7114	−0.810096
$210$	1.99281	0.137517
$211$	26.2300	1.80575	0.902873	−	0.429907i	$-0.141454\pi$
$211$	26.2300	1.80575	0.902873	+	0.429907i	$0.141454\pi$
$212$	2.97407	0.204260
$213$	6.01319	0.412017
$214$	11.7155	0.800852
$215$	9.95885	0.679188
$216$	−1.00000	−0.0680414
$217$	−7.69990	−0.522703
$218$	16.5487	1.12082
$219$	−9.46377	−0.639502
$220$	−3.85342	−0.259798
$221$	−5.10611	−0.343474
$222$	−5.70604	−0.382964
$223$	−1.00000	−0.0669650
$223$	−1.00000	−0.0669650
$224$	1.28984	0.0861811
$225$	−2.61296	−0.174197
$226$	−2.38720	−0.158794
$227$	−27.2280	−1.80718	−0.903592	−	0.428395i	$-0.859079\pi$
$227$	−27.2280	−1.80718	−0.903592	+	0.428395i	$0.859079\pi$
$228$	4.69562	0.310975
$229$	−2.43949	−0.161206	−0.0806029	−	0.996746i	$-0.525685\pi$
$229$	−2.43949	−0.161206	−0.0806029	+	0.996746i	$0.525685\pi$
$230$	−5.61353	−0.370145
$231$	3.21701	0.211664
$232$	−9.08085	−0.596187
$233$	−11.3011	−0.740358	−0.370179	−	0.928961i	$-0.620704\pi$
$233$	−11.3011	−0.740358	−0.370179	+	0.928961i	$0.620704\pi$
$234$	2.65927	0.173842
$235$	18.7055	1.22021
$236$	−12.6372	−0.822615
$237$	−9.23357	−0.599785
$238$	2.47664	0.160537
$239$	−8.55819	−0.553584	−0.276792	−	0.960930i	$-0.589271\pi$
$239$	−8.55819	−0.553584	−0.276792	+	0.960930i	$0.589271\pi$
$240$	1.54501	0.0997297
$241$	17.4393	1.12336	0.561681	−	0.827354i	$-0.310155\pi$
$241$	17.4393	1.12336	0.561681	+	0.827354i	$0.310155\pi$
$242$	4.77938	0.307230
$243$	1.00000	0.0641500
$244$	−10.5220	−0.673603
$245$	−8.24463	−0.526730
$246$	−6.53614	−0.416729
$247$	−12.4869	−0.794524
$248$	−5.96966	−0.379074
$249$	12.9523	0.820821
$250$	11.7621	0.743898
$251$	0.239068	0.0150898	0.00754492	−	0.999972i	$-0.497598\pi$
$251$	0.239068	0.0150898	0.00754492	+	0.999972i	$0.497598\pi$
$252$	−1.28984	−0.0812523
$253$	−9.06198	−0.569722
$254$	14.2746	0.895668
$255$	2.96659	0.185775
$256$	1.00000	0.0625000
$257$	0.145523	0.00907746	0.00453873	−	0.999990i	$-0.498555\pi$
$257$	0.145523	0.00907746	0.00453873	+	0.999990i	$0.498555\pi$
$258$	−6.44584	−0.401300
$259$	−7.35988	−0.457320
$260$	−4.10859	−0.254804
$261$	9.08085	0.562091
$262$	−19.9949	−1.23529
$263$	−8.17409	−0.504036	−0.252018	−	0.967723i	$-0.581094\pi$
$263$	−8.17409	−0.504036	−0.252018	+	0.967723i	$0.581094\pi$
$264$	2.49412	0.153502
$265$	4.59496	0.282266
$266$	6.05660	0.371354
$267$	−0.168223	−0.0102951
$268$	4.51299	0.275675
$269$	−21.6988	−1.32300	−0.661501	−	0.749944i	$-0.730080\pi$
$269$	−21.6988	−1.32300	−0.661501	+	0.749944i	$0.730080\pi$
$270$	−1.54501	−0.0940260
$271$	−31.1848	−1.89434	−0.947170	−	0.320732i	$-0.896071\pi$
$271$	−31.1848	−1.89434	−0.947170	+	0.320732i	$0.896071\pi$
$272$	1.92011	0.116424
$273$	3.43004	0.207595
$274$	−10.4458	−0.631056
$275$	6.51703	0.392991
$276$	3.63334	0.218702
$277$	19.0999	1.14760	0.573802	−	0.818994i	$-0.305468\pi$
$277$	19.0999	1.14760	0.573802	+	0.818994i	$0.305468\pi$
$278$	−12.4043	−0.743959
$279$	5.96966	0.357394
$280$	1.99281	0.119093
$281$	7.56711	0.451416	0.225708	−	0.974195i	$-0.427531\pi$
$281$	7.56711	0.451416	0.225708	+	0.974195i	$0.427531\pi$
$282$	−12.1071	−0.720966
$283$	−5.87036	−0.348956	−0.174478	−	0.984661i	$-0.555824\pi$
$283$	−5.87036	−0.348956	−0.174478	+	0.984661i	$0.555824\pi$
$284$	6.01319	0.356817
$285$	7.25476	0.429735
$286$	−6.63253	−0.392190
$287$	−8.43058	−0.497641
$288$	−1.00000	−0.0589256
$289$	−13.3132	−0.783127
$290$	−14.0300	−0.823868
$291$	1.05018	0.0615629
$292$	−9.46377	−0.553825
$293$	−16.2606	−0.949954	−0.474977	−	0.879998i	$-0.657544\pi$
$293$	−16.2606	−0.949954	−0.474977	+	0.879998i	$0.657544\pi$
$294$	5.33631	0.311220
$295$	−19.5246	−1.13677
$296$	−5.70604	−0.331657
$297$	−2.49412	−0.144723
$298$	−2.70297	−0.156579
$299$	−9.66205	−0.558771
$300$	−2.61296	−0.150859
$301$	−8.31410	−0.479217
$302$	22.0553	1.26914
$303$	−4.99849	−0.287156
$304$	4.69562	0.269312
$305$	−16.2566	−0.930848
$306$	−1.92011	−0.109766
$307$	−7.70583	−0.439795	−0.219897	−	0.975523i	$-0.570572\pi$
$307$	−7.70583	−0.439795	−0.219897	+	0.975523i	$0.570572\pi$
$308$	3.21701	0.183306
$309$	15.2450	0.867255
$310$	−9.22315	−0.523840
$311$	8.35322	0.473668	0.236834	−	0.971550i	$-0.423890\pi$
$311$	8.35322	0.473668	0.236834	+	0.971550i	$0.423890\pi$
$312$	2.65927	0.150552
$313$	−12.8779	−0.727900	−0.363950	−	0.931418i	$-0.618572\pi$
$313$	−12.8779	−0.727900	−0.363950	+	0.931418i	$0.618572\pi$
$314$	−7.38327	−0.416662
$315$	−1.99281	−0.112282
$316$	−9.23357	−0.519429
$317$	17.0655	0.958493	0.479246	−	0.877680i	$-0.340910\pi$
$317$	17.0655	0.958493	0.479246	+	0.877680i	$0.340910\pi$
$318$	−2.97407	−0.166778
$319$	−22.6487	−1.26808
$320$	1.54501	0.0863684
$321$	−11.7155	−0.653893
$322$	4.68643	0.261165
$323$	9.01613	0.501671
$324$	1.00000	0.0555556
$325$	6.94857	0.385437
$326$	4.26962	0.236472
$327$	−16.5487	−0.915148
$328$	−6.53614	−0.360898
$329$	−15.6162	−0.860949
$330$	3.85342	0.212124
$331$	−19.9208	−1.09495	−0.547473	−	0.836823i	$-0.684410\pi$
$331$	−19.9208	−1.09495	−0.547473	+	0.836823i	$0.684410\pi$
$332$	12.9523	0.710852
$333$	5.70604	0.312689
$334$	8.38192	0.458638
$335$	6.97259	0.380953
$336$	−1.28984	−0.0703665
$337$	4.53383	0.246973	0.123487	−	0.992346i	$-0.460592\pi$
$337$	4.53383	0.246973	0.123487	+	0.992346i	$0.460592\pi$
$338$	5.92827	0.322456
$339$	2.38720	0.129655
$340$	2.96659	0.160886
$341$	−14.8890	−0.806286
$342$	−4.69562	−0.253910
$343$	15.9119	0.859160
$344$	−6.44584	−0.347536
$345$	5.61353	0.302222
$346$	6.01306	0.323264
$347$	−34.7965	−1.86797	−0.933986	−	0.357309i	$-0.883694\pi$
$347$	−34.7965	−1.86797	−0.933986	+	0.357309i	$0.883694\pi$
$348$	9.08085	0.486785
$349$	−21.9889	−1.17704	−0.588518	−	0.808484i	$-0.700288\pi$
$349$	−21.9889	−1.17704	−0.588518	+	0.808484i	$0.700288\pi$
$350$	−3.37030	−0.180150
$351$	−2.65927	−0.141941
$352$	2.49412	0.132937
$353$	−5.13896	−0.273519	−0.136760	−	0.990604i	$-0.543669\pi$
$353$	−5.13896	−0.273519	−0.136760	+	0.990604i	$0.543669\pi$
$354$	12.6372	0.671662
$355$	9.29041	0.493084
$356$	−0.168223	−0.00891580
$357$	−2.47664	−0.131078
$358$	−23.1043	−1.22110
$359$	11.4094	0.602163	0.301081	−	0.953598i	$-0.402652\pi$
$359$	11.4094	0.602163	0.301081	+	0.953598i	$0.402652\pi$
$360$	−1.54501	−0.0814289
$361$	3.04884	0.160465
$362$	20.2695	1.06534
$363$	−4.77938	−0.250852
$364$	3.43004	0.179783
$365$	−14.6216	−0.765328
$366$	10.5220	0.549994
$367$	23.4709	1.22517	0.612585	−	0.790405i	$-0.290130\pi$
$367$	23.4709	1.22517	0.612585	+	0.790405i	$0.290130\pi$
$368$	3.63334	0.189401
$369$	6.53614	0.340258
$370$	−8.81586	−0.458315
$371$	−3.83608	−0.199159
$372$	5.96966	0.309512
$373$	14.7702	0.764773	0.382387	−	0.924002i	$-0.375102\pi$
$373$	14.7702	0.764773	0.382387	+	0.924002i	$0.375102\pi$
$374$	4.78899	0.247633
$375$	−11.7621	−0.607390
$376$	−12.1071	−0.624375
$377$	−24.1485	−1.24371
$378$	1.28984	0.0663422
$379$	9.14574	0.469785	0.234893	−	0.972021i	$-0.424526\pi$
$379$	9.14574	0.469785	0.234893	+	0.972021i	$0.424526\pi$
$380$	7.25476	0.372161
$381$	−14.2746	−0.731310
$382$	−5.79518	−0.296507
$383$	−15.2947	−0.781520	−0.390760	−	0.920493i	$-0.627788\pi$
$383$	−15.2947	−0.781520	−0.390760	+	0.920493i	$0.627788\pi$
$384$	−1.00000	−0.0510310
$385$	4.97030	0.253310
$386$	−12.3097	−0.626546
$387$	6.44584	0.327660
$388$	1.05018	0.0533151
$389$	−37.7337	−1.91317	−0.956586	−	0.291449i	$-0.905862\pi$
$389$	−37.7337	−1.91317	−0.956586	+	0.291449i	$0.905862\pi$
$390$	4.10859	0.208046
$391$	6.97644	0.352814
$392$	5.33631	0.269524
$393$	19.9949	1.00861
$394$	−18.7257	−0.943390
$395$	−14.2659	−0.717796
$396$	−2.49412	−0.125334
$397$	−26.6903	−1.33955	−0.669774	−	0.742565i	$-0.733609\pi$
$397$	−26.6903	−1.33955	−0.669774	+	0.742565i	$0.733609\pi$
$398$	−3.65510	−0.183214
$399$	−6.05660	−0.303209
$400$	−2.61296	−0.130648
$401$	−31.3412	−1.56510	−0.782552	−	0.622585i	$-0.786082\pi$
$401$	−31.3412	−1.56510	−0.782552	+	0.622585i	$0.786082\pi$
$402$	−4.51299	−0.225087
$403$	−15.8749	−0.790787
$404$	−4.99849	−0.248684
$405$	1.54501	0.0767719
$406$	11.7128	0.581299
$407$	−14.2315	−0.705430
$408$	−1.92011	−0.0950599
$409$	38.0880	1.88333	0.941666	−	0.336550i	$-0.109260\pi$
$409$	38.0880	1.88333	0.941666	+	0.336550i	$0.109260\pi$
$410$	−10.0984	−0.498723
$411$	10.4458	0.515255
$412$	15.2450	0.751065
$413$	16.3000	0.802072
$414$	−3.63334	−0.178569
$415$	20.0114	0.982323
$416$	2.65927	0.130382
$417$	12.4043	0.607440
$418$	11.7114	0.572824
$419$	22.7446	1.11115	0.555574	−	0.831467i	$-0.312499\pi$
$419$	22.7446	1.11115	0.555574	+	0.831467i	$0.312499\pi$
$420$	−1.99281	−0.0972391
$421$	−21.6762	−1.05643	−0.528217	−	0.849109i	$-0.677139\pi$
$421$	−21.6762	−1.05643	−0.528217	+	0.849109i	$0.677139\pi$
$422$	−26.2300	−1.27686
$423$	12.1071	0.588666
$424$	−2.97407	−0.144434
$425$	−5.01718	−0.243369
$426$	−6.01319	−0.291340
$427$	13.5717	0.656781
$428$	−11.7155	−0.566288
$429$	6.63253	0.320222
$430$	−9.95885	−0.480259
$431$	−24.7372	−1.19155	−0.595775	−	0.803151i	$-0.703155\pi$
$431$	−24.7372	−1.19155	−0.595775	+	0.803151i	$0.703155\pi$
$432$	1.00000	0.0481125
$433$	29.6583	1.42529	0.712645	−	0.701525i	$-0.247497\pi$
$433$	29.6583	1.42529	0.712645	+	0.701525i	$0.247497\pi$
$434$	7.69990	0.369607
$435$	14.0300	0.672685
$436$	−16.5487	−0.792541
$437$	17.0608	0.816128
$438$	9.46377	0.452197
$439$	27.9533	1.33414	0.667069	−	0.744996i	$-0.267548\pi$
$439$	27.9533	1.33414	0.667069	+	0.744996i	$0.267548\pi$
$440$	3.85342	0.183705
$441$	−5.33631	−0.254110
$442$	5.10611	0.242873
$443$	21.5451	1.02364	0.511819	−	0.859093i	$-0.328972\pi$
$443$	21.5451	1.02364	0.511819	+	0.859093i	$0.328972\pi$
$444$	5.70604	0.270797
$445$	−0.259905	−0.0123207
$446$	1.00000	0.0473514
$447$	2.70297	0.127846
$448$	−1.28984	−0.0609392
$449$	38.3133	1.80812	0.904059	−	0.427407i	$-0.140573\pi$
$449$	38.3133	1.80812	0.904059	+	0.427407i	$0.140573\pi$
$450$	2.61296	0.123176
$451$	−16.3019	−0.767627
$452$	2.38720	0.112284
$453$	−22.0553	−1.03625
$454$	27.2280	1.27787
$455$	5.29942	0.248441
$456$	−4.69562	−0.219893
$457$	−8.77811	−0.410623	−0.205311	−	0.978697i	$-0.565821\pi$
$457$	−8.77811	−0.410623	−0.205311	+	0.978697i	$0.565821\pi$
$458$	2.43949	0.113990
$459$	1.92011	0.0896233
$460$	5.61353	0.261732
$461$	−14.4028	−0.670807	−0.335404	−	0.942075i	$-0.608873\pi$
$461$	−14.4028	−0.670807	−0.335404	+	0.942075i	$0.608873\pi$
$462$	−3.21701	−0.149669
$463$	13.6803	0.635779	0.317889	−	0.948128i	$-0.397026\pi$
$463$	13.6803	0.635779	0.317889	+	0.948128i	$0.397026\pi$
$464$	9.08085	0.421568
$465$	9.22315	0.427713
$466$	11.3011	0.523512
$467$	8.37193	0.387407	0.193703	−	0.981060i	$-0.437950\pi$
$467$	8.37193	0.387407	0.193703	+	0.981060i	$0.437950\pi$
$468$	−2.65927	−0.122925
$469$	−5.82103	−0.268790
$470$	−18.7055	−0.862820
$471$	7.38327	0.340203
$472$	12.6372	0.581676
$473$	−16.0767	−0.739206
$474$	9.23357	0.424112
$475$	−12.2695	−0.562961
$476$	−2.47664	−0.113517
$477$	2.97407	0.136173
$478$	8.55819	0.391443
$479$	−21.7260	−0.992688	−0.496344	−	0.868126i	$-0.665325\pi$
$479$	−21.7260	−0.992688	−0.496344	+	0.868126i	$0.665325\pi$
$480$	−1.54501	−0.0705195
$481$	−15.1739	−0.691870
$482$	−17.4393	−0.794337
$483$	−4.68643	−0.213240
$484$	−4.77938	−0.217245
$485$	1.62254	0.0736758
$486$	−1.00000	−0.0453609
$487$	2.38053	0.107872	0.0539360	−	0.998544i	$-0.482823\pi$
$487$	2.38053	0.107872	0.0539360	+	0.998544i	$0.482823\pi$
$488$	10.5220	0.476309
$489$	−4.26962	−0.193079
$490$	8.24463	0.372454
$491$	20.8266	0.939890	0.469945	−	0.882696i	$-0.344274\pi$
$491$	20.8266	0.939890	0.469945	+	0.882696i	$0.344274\pi$
$492$	6.53614	0.294672
$493$	17.4363	0.785291
$494$	12.4869	0.561813
$495$	−3.85342	−0.173198
$496$	5.96966	0.268045
$497$	−7.75606	−0.347907
$498$	−12.9523	−0.580408
$499$	18.7813	0.840765	0.420382	−	0.907347i	$-0.361896\pi$
$499$	18.7813	0.840765	0.420382	+	0.907347i	$0.361896\pi$
$500$	−11.7621	−0.526015
$501$	−8.38192	−0.374477
$502$	−0.239068	−0.0106701
$503$	−11.5451	−0.514771	−0.257385	−	0.966309i	$-0.582861\pi$
$503$	−11.5451	−0.514771	−0.257385	+	0.966309i	$0.582861\pi$
$504$	1.28984	0.0574540
$505$	−7.72269	−0.343655
$506$	9.06198	0.402854
$507$	−5.92827	−0.263284
$508$	−14.2746	−0.633333
$509$	21.8205	0.967177	0.483589	−	0.875295i	$-0.339333\pi$
$509$	21.8205	0.967177	0.483589	+	0.875295i	$0.339333\pi$
$510$	−2.96659	−0.131363
$511$	12.2068	0.539995
$512$	−1.00000	−0.0441942
$513$	4.69562	0.207317
$514$	−0.145523	−0.00641873
$515$	23.5535	1.03789
$516$	6.44584	0.283762
$517$	−30.1965	−1.32804
$518$	7.35988	0.323374
$519$	−6.01306	−0.263944
$520$	4.10859	0.180174
$521$	−5.31636	−0.232914	−0.116457	−	0.993196i	$-0.537154\pi$
$521$	−5.31636	−0.232914	−0.116457	+	0.993196i	$0.537154\pi$
$522$	−9.08085	−0.397458
$523$	31.5525	1.37969	0.689847	−	0.723955i	$-0.257678\pi$
$523$	31.5525	1.37969	0.689847	+	0.723955i	$0.257678\pi$
$524$	19.9949	0.873480
$525$	3.37030	0.147092
$526$	8.17409	0.356407
$527$	11.4624	0.499311
$528$	−2.49412	−0.108543
$529$	−9.79882	−0.426036
$530$	−4.59496	−0.199592
$531$	−12.6372	−0.548410
$532$	−6.05660	−0.262587
$533$	−17.3814	−0.752871
$534$	0.168223	0.00727972
$535$	−18.1004	−0.782550
$536$	−4.51299	−0.194931
$537$	23.1043	0.997026
$538$	21.6988	0.935504
$539$	13.3094	0.573276
$540$	1.54501	0.0664864
$541$	−10.2150	−0.439179	−0.219590	−	0.975592i	$-0.570472\pi$
$541$	−10.2150	−0.439179	−0.219590	+	0.975592i	$0.570472\pi$
$542$	31.1848	1.33950
$543$	−20.2695	−0.869847
$544$	−1.92011	−0.0823242
$545$	−25.5679	−1.09521
$546$	−3.43004	−0.146792
$547$	6.88780	0.294501	0.147251	−	0.989099i	$-0.452958\pi$
$547$	6.88780	0.294501	0.147251	+	0.989099i	$0.452958\pi$
$548$	10.4458	0.446224
$549$	−10.5220	−0.449068
$550$	−6.51703	−0.277887
$551$	42.6402	1.81653
$552$	−3.63334	−0.154645
$553$	11.9098	0.506457
$554$	−19.0999	−0.811478
$555$	8.81586	0.374212
$556$	12.4043	0.526058
$557$	−25.1326	−1.06490	−0.532451	−	0.846461i	$-0.678729\pi$
$557$	−25.1326	−1.06490	−0.532451	+	0.846461i	$0.678729\pi$
$558$	−5.96966	−0.252716
$559$	−17.1412	−0.724997
$560$	−1.99281	−0.0842116
$561$	−4.78899	−0.202191
$562$	−7.56711	−0.319199
$563$	36.3836	1.53339	0.766693	−	0.642013i	$-0.221901\pi$
$563$	36.3836	1.53339	0.766693	+	0.642013i	$0.221901\pi$
$564$	12.1071	0.509800
$565$	3.68824	0.155165
$566$	5.87036	0.246749
$567$	−1.28984	−0.0541682
$568$	−6.01319	−0.252308
$569$	−40.7614	−1.70881	−0.854404	−	0.519610i	$-0.826077\pi$
$569$	−40.7614	−1.70881	−0.854404	+	0.519610i	$0.826077\pi$
$570$	−7.25476	−0.303868
$571$	−12.3995	−0.518903	−0.259451	−	0.965756i	$-0.583542\pi$
$571$	−12.3995	−0.518903	−0.259451	+	0.965756i	$0.583542\pi$
$572$	6.63253	0.277320
$573$	5.79518	0.242097
$574$	8.43058	0.351886
$575$	−9.49378	−0.395918
$576$	1.00000	0.0416667
$577$	−9.50735	−0.395796	−0.197898	−	0.980223i	$-0.563412\pi$
$577$	−9.50735	−0.395796	−0.197898	+	0.980223i	$0.563412\pi$
$578$	13.3132	0.553754
$579$	12.3097	0.511573
$580$	14.0300	0.582563
$581$	−16.7064	−0.693100
$582$	−1.05018	−0.0435316
$583$	−7.41768	−0.307209
$584$	9.46377	0.391614
$585$	−4.10859	−0.169869
$586$	16.2606	0.671719
$587$	−28.0628	−1.15827	−0.579137	−	0.815230i	$-0.696610\pi$
$587$	−28.0628	−1.15827	−0.579137	+	0.815230i	$0.696610\pi$
$588$	−5.33631	−0.220066
$589$	28.0312	1.15501
$590$	19.5246	0.803815
$591$	18.7257	0.770274
$592$	5.70604	0.234517
$593$	−38.8259	−1.59439	−0.797194	−	0.603723i	$-0.793683\pi$
$593$	−38.8259	−1.59439	−0.797194	+	0.603723i	$0.793683\pi$
$594$	2.49412	0.102335
$595$	−3.82642	−0.156868
$596$	2.70297	0.110718
$597$	3.65510	0.149593
$598$	9.66205	0.395110
$599$	40.9391	1.67273	0.836363	−	0.548176i	$-0.184678\pi$
$599$	40.9391	1.67273	0.836363	+	0.548176i	$0.184678\pi$
$600$	2.61296	0.106674
$601$	−20.9510	−0.854608	−0.427304	−	0.904108i	$-0.640537\pi$
$601$	−20.9510	−0.854608	−0.427304	+	0.904108i	$0.640537\pi$
$602$	8.31410	0.338857
$603$	4.51299	0.183783
$604$	−22.0553	−0.897415
$605$	−7.38417	−0.300209
$606$	4.99849	0.203050
$607$	18.1587	0.737039	0.368519	−	0.929620i	$-0.379865\pi$
$607$	18.1587	0.737039	0.368519	+	0.929620i	$0.379865\pi$
$608$	−4.69562	−0.190432
$609$	−11.7128	−0.474629
$610$	16.2566	0.658209
$611$	−32.1960	−1.30251
$612$	1.92011	0.0776160
$613$	33.1238	1.33786	0.668928	−	0.743327i	$-0.266753\pi$
$613$	33.1238	1.33786	0.668928	+	0.743327i	$0.266753\pi$
$614$	7.70583	0.310982
$615$	10.0984	0.407206
$616$	−3.21701	−0.129617
$617$	20.7781	0.836493	0.418247	−	0.908333i	$-0.362645\pi$
$617$	20.7781	0.836493	0.418247	+	0.908333i	$0.362645\pi$
$618$	−15.2450	−0.613242
$619$	−44.0401	−1.77012	−0.885060	−	0.465476i	$-0.845883\pi$
$619$	−44.0401	−1.77012	−0.885060	+	0.465476i	$0.845883\pi$
$620$	9.22315	0.370411
$621$	3.63334	0.145801
$622$	−8.35322	−0.334934
$623$	0.216981	0.00869315
$624$	−2.65927	−0.106456
$625$	−5.10765	−0.204306
$626$	12.8779	0.514703
$627$	−11.7114	−0.467709
$628$	7.38327	0.294625
$629$	10.9562	0.436854
$630$	1.99281	0.0793954
$631$	−42.0837	−1.67533	−0.837664	−	0.546186i	$-0.816079\pi$
$631$	−42.0837	−1.67533	−0.837664	+	0.546186i	$0.816079\pi$
$632$	9.23357	0.367292
$633$	26.2300	1.04255
$634$	−17.0655	−0.677757
$635$	−22.0543	−0.875199
$636$	2.97407	0.117930
$637$	14.1907	0.562256
$638$	22.6487	0.896671
$639$	6.01319	0.237878
$640$	−1.54501	−0.0610717
$641$	25.3047	0.999475	0.499738	−	0.866177i	$-0.333430\pi$
$641$	25.3047	0.999475	0.499738	+	0.866177i	$0.333430\pi$
$642$	11.7155	0.462372
$643$	33.5383	1.32262	0.661310	−	0.750113i	$-0.270001\pi$
$643$	33.5383	1.32262	0.661310	+	0.750113i	$0.270001\pi$
$644$	−4.68643	−0.184671
$645$	9.95885	0.392129
$646$	−9.01613	−0.354735
$647$	26.8197	1.05439	0.527195	−	0.849744i	$-0.323244\pi$
$647$	26.8197	1.05439	0.527195	+	0.849744i	$0.323244\pi$
$648$	−1.00000	−0.0392837
$649$	31.5188	1.23722
$650$	−6.94857	−0.272545
$651$	−7.69990	−0.301783
$652$	−4.26962	−0.167211
$653$	33.5965	1.31473	0.657366	−	0.753571i	$-0.271671\pi$
$653$	33.5965	1.31473	0.657366	+	0.753571i	$0.271671\pi$
$654$	16.5487	0.647107
$655$	30.8922	1.20706
$656$	6.53614	0.255193
$657$	−9.46377	−0.369217
$658$	15.6162	0.608783
$659$	7.35401	0.286471	0.143236	−	0.989689i	$-0.454249\pi$
$659$	7.35401	0.286471	0.143236	+	0.989689i	$0.454249\pi$
$660$	−3.85342	−0.149994
$661$	−25.7191	−1.00036	−0.500179	−	0.865922i	$-0.666732\pi$
$661$	−25.7191	−1.00036	−0.500179	+	0.865922i	$0.666732\pi$
$662$	19.9208	0.774243
$663$	−5.10611	−0.198305
$664$	−12.9523	−0.502648
$665$	−9.35747	−0.362867
$666$	−5.70604	−0.221104
$667$	32.9939	1.27753
$668$	−8.38192	−0.324306
$669$	−1.00000	−0.0386622
$670$	−6.97259	−0.269375
$671$	26.2431	1.01310
$672$	1.28984	0.0497567
$673$	18.1684	0.700340	0.350170	−	0.936686i	$-0.386124\pi$
$673$	18.1684	0.700340	0.350170	+	0.936686i	$0.386124\pi$
$674$	−4.53383	−0.174636
$675$	−2.61296	−0.100573
$676$	−5.92827	−0.228011
$677$	−13.2991	−0.511125	−0.255563	−	0.966793i	$-0.582261\pi$
$677$	−13.2991	−0.511125	−0.255563	+	0.966793i	$0.582261\pi$
$678$	−2.38720	−0.0916799
$679$	−1.35457	−0.0519836
$680$	−2.96659	−0.113763
$681$	−27.2280	−1.04338
$682$	14.8890	0.570130
$683$	−25.8252	−0.988175	−0.494087	−	0.869412i	$-0.664498\pi$
$683$	−25.8252	−0.988175	−0.494087	+	0.869412i	$0.664498\pi$
$684$	4.69562	0.179541
$685$	16.1389	0.616635
$686$	−15.9119	−0.607518
$687$	−2.43949	−0.0930722
$688$	6.44584	0.245745
$689$	−7.90886	−0.301304
$690$	−5.61353	−0.213704
$691$	−30.4652	−1.15895	−0.579476	−	0.814989i	$-0.696743\pi$
$691$	−30.4652	−1.15895	−0.579476	+	0.814989i	$0.696743\pi$
$692$	−6.01306	−0.228582
$693$	3.21701	0.122204
$694$	34.7965	1.32086
$695$	19.1647	0.726957
$696$	−9.08085	−0.344209
$697$	12.5501	0.475371
$698$	21.9889	0.832290
$699$	−11.3011	−0.427446
$700$	3.37030	0.127385
$701$	−5.22755	−0.197442	−0.0987209	−	0.995115i	$-0.531475\pi$
$701$	−5.22755	−0.197442	−0.0987209	+	0.995115i	$0.531475\pi$
$702$	2.65927	0.100368
$703$	26.7934	1.01053
$704$	−2.49412	−0.0940006
$705$	18.7055	0.704490
$706$	5.13896	0.193407
$707$	6.44725	0.242474
$708$	−12.6372	−0.474937
$709$	30.7149	1.15352	0.576760	−	0.816913i	$-0.304317\pi$
$709$	30.7149	1.15352	0.576760	+	0.816913i	$0.304317\pi$
$710$	−9.29041	−0.348663
$711$	−9.23357	−0.346286
$712$	0.168223	0.00630443
$713$	21.6898	0.812290
$714$	2.47664	0.0926860
$715$	10.2473	0.383227
$716$	23.1043	0.863449
$717$	−8.55819	−0.319612
$718$	−11.4094	−0.425793
$719$	−19.0574	−0.710722	−0.355361	−	0.934729i	$-0.615642\pi$
$719$	−19.0574	−0.710722	−0.355361	+	0.934729i	$0.615642\pi$
$720$	1.54501	0.0575789
$721$	−19.6636	−0.732309
$722$	−3.04884	−0.113466
$723$	17.4393	0.648573
$724$	−20.2695	−0.753310
$725$	−23.7279	−0.881232
$726$	4.77938	0.177379
$727$	39.1391	1.45159	0.725794	−	0.687913i	$-0.241473\pi$
$727$	39.1391	1.45159	0.725794	+	0.687913i	$0.241473\pi$
$728$	−3.43004	−0.127126
$729$	1.00000	0.0370370
$730$	14.6216	0.541169
$731$	12.3768	0.457771
$732$	−10.5220	−0.388905
$733$	−18.2484	−0.674020	−0.337010	−	0.941501i	$-0.609416\pi$
$733$	−18.2484	−0.674020	−0.337010	+	0.941501i	$0.609416\pi$
$734$	−23.4709	−0.866326
$735$	−8.24463	−0.304108
$736$	−3.63334	−0.133927
$737$	−11.2559	−0.414617
$738$	−6.53614	−0.240599
$739$	−20.2613	−0.745323	−0.372661	−	0.927967i	$-0.621555\pi$
$739$	−20.2613	−0.745323	−0.372661	+	0.927967i	$0.621555\pi$
$740$	8.81586	0.324077
$741$	−12.4869	−0.458719
$742$	3.83608	0.140827
$743$	6.60499	0.242314	0.121157	−	0.992633i	$-0.461340\pi$
$743$	6.60499	0.242314	0.121157	+	0.992633i	$0.461340\pi$
$744$	−5.96966	−0.218858
$745$	4.17610	0.153001
$746$	−14.7702	−0.540776
$747$	12.9523	0.473901
$748$	−4.78899	−0.175103
$749$	15.1111	0.552146
$750$	11.7621	0.429490
$751$	29.0359	1.05953	0.529767	−	0.848143i	$-0.322279\pi$
$751$	29.0359	1.05953	0.529767	+	0.848143i	$0.322279\pi$
$752$	12.1071	0.441500
$753$	0.239068	0.00871212
$754$	24.1485	0.879435
$755$	−34.0755	−1.24013
$756$	−1.28984	−0.0469110
$757$	−27.4584	−0.997993	−0.498997	−	0.866604i	$-0.666298\pi$
$757$	−27.4584	−0.997993	−0.498997	+	0.866604i	$0.666298\pi$
$758$	−9.14574	−0.332188
$759$	−9.06198	−0.328929
$760$	−7.25476	−0.263158
$761$	6.91985	0.250844	0.125422	−	0.992103i	$-0.459971\pi$
$761$	6.91985	0.250844	0.125422	+	0.992103i	$0.459971\pi$
$762$	14.2746	0.517114
$763$	21.3452	0.772750
$764$	5.79518	0.209662
$765$	2.96659	0.107257
$766$	15.2947	0.552618
$767$	33.6059	1.21344
$768$	1.00000	0.0360844
$769$	−11.4749	−0.413796	−0.206898	−	0.978362i	$-0.566337\pi$
$769$	−11.4749	−0.413796	−0.206898	+	0.978362i	$0.566337\pi$
$770$	−4.97030	−0.179117
$771$	0.145523	0.00524087
$772$	12.3097	0.443035
$773$	21.8130	0.784559	0.392279	−	0.919846i	$-0.371687\pi$
$773$	21.8130	0.784559	0.392279	+	0.919846i	$0.371687\pi$
$774$	−6.44584	−0.231691
$775$	−15.5985	−0.560313
$776$	−1.05018	−0.0376994
$777$	−7.35988	−0.264034
$778$	37.7337	1.35282
$779$	30.6912	1.09963
$780$	−4.10859	−0.147111
$781$	−14.9976	−0.536657
$782$	−6.97644	−0.249477
$783$	9.08085	0.324523
$784$	−5.33631	−0.190583
$785$	11.4072	0.407140
$786$	−19.9949	−0.713194
$787$	14.3504	0.511538	0.255769	−	0.966738i	$-0.417671\pi$
$787$	14.3504	0.511538	0.255769	+	0.966738i	$0.417671\pi$
$788$	18.7257	0.667077
$789$	−8.17409	−0.291005
$790$	14.2659	0.507558
$791$	−3.07911	−0.109480
$792$	2.49412	0.0886246
$793$	27.9809	0.993630
$794$	26.6903	0.947204
$795$	4.59496	0.162966
$796$	3.65510	0.129552
$797$	−2.16335	−0.0766298	−0.0383149	−	0.999266i	$-0.512199\pi$
$797$	−2.16335	−0.0766298	−0.0383149	+	0.999266i	$0.512199\pi$
$798$	6.05660	0.214401
$799$	23.2470	0.822419
$800$	2.61296	0.0923821
$801$	−0.168223	−0.00594387
$802$	31.3412	1.10670
$803$	23.6038	0.832958
$804$	4.51299	0.159161
$805$	−7.24056	−0.255196
$806$	15.8749	0.559171
$807$	−21.6988	−0.763836
$808$	4.99849	0.175846
$809$	7.90979	0.278093	0.139047	−	0.990286i	$-0.455596\pi$
$809$	7.90979	0.278093	0.139047	+	0.990286i	$0.455596\pi$
$810$	−1.54501	−0.0542859
$811$	−23.1783	−0.813900	−0.406950	−	0.913450i	$-0.633408\pi$
$811$	−23.1783	−0.813900	−0.406950	+	0.913450i	$0.633408\pi$
$812$	−11.7128	−0.411040
$813$	−31.1848	−1.09370
$814$	14.2315	0.498815
$815$	−6.59659	−0.231068
$816$	1.92011	0.0672175
$817$	30.2672	1.05892
$818$	−38.0880	−1.33172
$819$	3.43004	0.119855
$820$	10.0984	0.352650
$821$	−13.0185	−0.454347	−0.227174	−	0.973854i	$-0.572949\pi$
$821$	−13.0185	−0.454347	−0.227174	+	0.973854i	$0.572949\pi$
$822$	−10.4458	−0.364340
$823$	−23.0296	−0.802762	−0.401381	−	0.915911i	$-0.631470\pi$
$823$	−23.0296	−0.802762	−0.401381	+	0.915911i	$0.631470\pi$
$824$	−15.2450	−0.531083
$825$	6.51703	0.226894
$826$	−16.3000	−0.567150
$827$	−48.7420	−1.69492	−0.847462	−	0.530856i	$-0.821871\pi$
$827$	−48.7420	−1.69492	−0.847462	+	0.530856i	$0.821871\pi$
$828$	3.63334	0.126267
$829$	−3.02728	−0.105142	−0.0525709	−	0.998617i	$-0.516742\pi$
$829$	−3.02728	−0.105142	−0.0525709	+	0.998617i	$0.516742\pi$
$830$	−20.0114	−0.694607
$831$	19.0999	0.662569
$832$	−2.65927	−0.0921937
$833$	−10.2463	−0.355014
$834$	−12.4043	−0.429525
$835$	−12.9501	−0.448157
$836$	−11.7114	−0.405048
$837$	5.96966	0.206341
$838$	−22.7446	−0.785700
$839$	−21.2196	−0.732583	−0.366292	−	0.930500i	$-0.619373\pi$
$839$	−21.2196	−0.732583	−0.366292	+	0.930500i	$0.619373\pi$
$840$	1.99281	0.0687585
$841$	53.4619	1.84351
$842$	21.6762	0.747012
$843$	7.56711	0.260625
$844$	26.2300	0.902873
$845$	−9.15921	−0.315087
$846$	−12.1071	−0.416250
$847$	6.16464	0.211819
$848$	2.97407	0.102130
$849$	−5.87036	−0.201470
$850$	5.01718	0.172088
$851$	20.7320	0.710684
$852$	6.01319	0.206009
$853$	−23.0700	−0.789901	−0.394950	−	0.918703i	$-0.629238\pi$
$853$	−23.0700	−0.789901	−0.394950	+	0.918703i	$0.629238\pi$
$854$	−13.5717	−0.464414
$855$	7.25476	0.248107
$856$	11.7155	0.400426
$857$	2.90304	0.0991661	0.0495831	−	0.998770i	$-0.484211\pi$
$857$	2.90304	0.0991661	0.0495831	+	0.998770i	$0.484211\pi$
$858$	−6.63253	−0.226431
$859$	30.4007	1.03726	0.518629	−	0.854999i	$-0.326443\pi$
$859$	30.4007	1.03726	0.518629	+	0.854999i	$0.326443\pi$
$860$	9.95885	0.339594
$861$	−8.43058	−0.287313
$862$	24.7372	0.842553
$863$	38.0933	1.29671	0.648356	−	0.761337i	$-0.275457\pi$
$863$	38.0933	1.29671	0.648356	+	0.761337i	$0.275457\pi$
$864$	−1.00000	−0.0340207
$865$	−9.29021	−0.315877
$866$	−29.6583	−1.00783
$867$	−13.3132	−0.452139
$868$	−7.69990	−0.261352
$869$	23.0296	0.781226
$870$	−14.0300	−0.475660
$871$	−12.0013	−0.406647
$872$	16.5487	0.560411
$873$	1.05018	0.0355434
$874$	−17.0608	−0.577090
$875$	15.1712	0.512879
$876$	−9.46377	−0.319751
$877$	−45.3907	−1.53274	−0.766368	−	0.642402i	$-0.777938\pi$
$877$	−45.3907	−1.53274	−0.766368	+	0.642402i	$0.777938\pi$
$878$	−27.9533	−0.943379
$879$	−16.2606	−0.548456
$880$	−3.85342	−0.129899
$881$	17.8676	0.601976	0.300988	−	0.953628i	$-0.402684\pi$
$881$	17.8676	0.601976	0.300988	+	0.953628i	$0.402684\pi$
$882$	5.33631	0.179683
$883$	25.3660	0.853634	0.426817	−	0.904338i	$-0.359635\pi$
$883$	25.3660	0.853634	0.426817	+	0.904338i	$0.359635\pi$
$884$	−5.10611	−0.171737
$885$	−19.5246	−0.656313
$886$	−21.5451	−0.723822
$887$	−31.6442	−1.06251	−0.531255	−	0.847212i	$-0.678279\pi$
$887$	−31.6442	−1.06251	−0.531255	+	0.847212i	$0.678279\pi$
$888$	−5.70604	−0.191482
$889$	18.4119	0.617517
$890$	0.259905	0.00871205
$891$	−2.49412	−0.0835561
$892$	−1.00000	−0.0334825
$893$	56.8502	1.90242
$894$	−2.70297	−0.0904008
$895$	35.6963	1.19320
$896$	1.28984	0.0430905
$897$	−9.66205	−0.322606
$898$	−38.3133	−1.27853
$899$	54.2096	1.80799
$900$	−2.61296	−0.0870986
$901$	5.71056	0.190246
$902$	16.3019	0.542794
$903$	−8.31410	−0.276676
$904$	−2.38720	−0.0793971
$905$	−31.3165	−1.04099
$906$	22.0553	0.732737
$907$	27.9750	0.928894	0.464447	−	0.885601i	$-0.346253\pi$
$907$	27.9750	0.928894	0.464447	+	0.885601i	$0.346253\pi$
$908$	−27.2280	−0.903592
$909$	−4.99849	−0.165789
$910$	−5.29942	−0.175674
$911$	8.88228	0.294283	0.147142	−	0.989115i	$-0.452993\pi$
$911$	8.88228	0.294283	0.147142	+	0.989115i	$0.452993\pi$
$912$	4.69562	0.155487
$913$	−32.3046	−1.06913
$914$	8.77811	0.290354
$915$	−16.2566	−0.537425
$916$	−2.43949	−0.0806029
$917$	−25.7902	−0.851667
$918$	−1.92011	−0.0633732
$919$	−38.5695	−1.27229	−0.636146	−	0.771569i	$-0.719472\pi$
$919$	−38.5695	−1.27229	−0.636146	+	0.771569i	$0.719472\pi$
$920$	−5.61353	−0.185073
$921$	−7.70583	−0.253916
$922$	14.4028	0.474332
$923$	−15.9907	−0.526341
$924$	3.21701	0.105832
$925$	−14.9096	−0.490226
$926$	−13.6803	−0.449563
$927$	15.2450	0.500710
$928$	−9.08085	−0.298094
$929$	−16.4905	−0.541037	−0.270518	−	0.962715i	$-0.587195\pi$
$929$	−16.4905	−0.541037	−0.270518	+	0.962715i	$0.587195\pi$
$930$	−9.22315	−0.302439
$931$	−25.0573	−0.821220
$932$	−11.3011	−0.370179
$933$	8.35322	0.273472
$934$	−8.37193	−0.273938
$935$	−7.39902	−0.241974
$936$	2.65927	0.0869210
$937$	−19.5436	−0.638462	−0.319231	−	0.947677i	$-0.603425\pi$
$937$	−19.5436	−0.638462	−0.319231	+	0.947677i	$0.603425\pi$
$938$	5.82103	0.190063
$939$	−12.8779	−0.420253
$940$	18.7055	0.610106
$941$	−58.8382	−1.91807	−0.959035	−	0.283287i	$-0.908575\pi$
$941$	−58.8382	−1.91807	−0.959035	+	0.283287i	$0.908575\pi$
$942$	−7.38327	−0.240560
$943$	23.7480	0.773343
$944$	−12.6372	−0.411307
$945$	−1.99281	−0.0648261
$946$	16.0767	0.522698
$947$	−19.1164	−0.621199	−0.310600	−	0.950541i	$-0.600530\pi$
$947$	−19.1164	−0.621199	−0.310600	+	0.950541i	$0.600530\pi$
$948$	−9.23357	−0.299892
$949$	25.1667	0.816947
$950$	12.2695	0.398074
$951$	17.0655	0.553386
$952$	2.47664	0.0802684
$953$	−8.48256	−0.274777	−0.137389	−	0.990517i	$-0.543871\pi$
$953$	−8.48256	−0.274777	−0.137389	+	0.990517i	$0.543871\pi$
$954$	−2.97407	−0.0962891
$955$	8.95359	0.289731
$956$	−8.55819	−0.276792
$957$	−22.6487	−0.732129
$958$	21.7260	0.701936
$959$	−13.4735	−0.435081
$960$	1.54501	0.0498648
$961$	4.63679	0.149574
$962$	15.1739	0.489226
$963$	−11.7155	−0.377525
$964$	17.4393	0.561681
$965$	19.0185	0.612228
$966$	4.68643	0.150783
$967$	−6.04992	−0.194552	−0.0972762	−	0.995257i	$-0.531013\pi$
$967$	−6.04992	−0.194552	−0.0972762	+	0.995257i	$0.531013\pi$
$968$	4.77938	0.153615
$969$	9.01613	0.289640
$970$	−1.62254	−0.0520967
$971$	8.71377	0.279638	0.139819	−	0.990177i	$-0.455348\pi$
$971$	8.71377	0.279638	0.139819	+	0.990177i	$0.455348\pi$
$972$	1.00000	0.0320750
$973$	−15.9995	−0.512921
$974$	−2.38053	−0.0762770
$975$	6.94857	0.222532
$976$	−10.5220	−0.336801
$977$	−59.1766	−1.89323	−0.946614	−	0.322370i	$-0.895521\pi$
$977$	−59.1766	−1.89323	−0.946614	+	0.322370i	$0.895521\pi$
$978$	4.26962	0.136527
$979$	0.419568	0.0134095
$980$	−8.24463	−0.263365
$981$	−16.5487	−0.528361
$982$	−20.8266	−0.664603
$983$	28.0539	0.894780	0.447390	−	0.894339i	$-0.352354\pi$
$983$	28.0539	0.894780	0.447390	+	0.894339i	$0.352354\pi$
$984$	−6.53614	−0.208365
$985$	28.9314	0.921830
$986$	−17.4363	−0.555284
$987$	−15.6162	−0.497069
$988$	−12.4869	−0.397262
$989$	23.4199	0.744711
$990$	3.85342	0.122470
$991$	5.76653	0.183180	0.0915899	−	0.995797i	$-0.470805\pi$
$991$	5.76653	0.183180	0.0915899	+	0.995797i	$0.470805\pi$
$992$	−5.96966	−0.189537
$993$	−19.9208	−0.632167
$994$	7.75606	0.246007
$995$	5.64715	0.179027
$996$	12.9523	0.410411
$997$	−27.9499	−0.885183	−0.442592	−	0.896723i	$-0.645941\pi$
$997$	−27.9499	−0.885183	−0.442592	+	0.896723i	$0.645941\pi$
$998$	−18.7813	−0.594511
$999$	5.70604	0.180531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.a.h.1.4	✓	5
3.2	odd	2		4014.2.a.r.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.a.h.1.4	✓	5	1.1	even	1	trivial
4014.2.a.r.1.2		5	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:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.54501 q^{5} -1.00000 q^{6} -1.28984 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.54501 q^{5} -1.00000 q^{6} -1.28984 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.54501 q^{10} -2.49412 q^{11} +1.00000 q^{12} -2.65927 q^{13} +1.28984 q^{14} +1.54501 q^{15} +1.00000 q^{16} +1.92011 q^{17} -1.00000 q^{18} +4.69562 q^{19} +1.54501 q^{20} -1.28984 q^{21} +2.49412 q^{22} +3.63334 q^{23} -1.00000 q^{24} -2.61296 q^{25} +2.65927 q^{26} +1.00000 q^{27} -1.28984 q^{28} +9.08085 q^{29} -1.54501 q^{30} +5.96966 q^{31} -1.00000 q^{32} -2.49412 q^{33} -1.92011 q^{34} -1.99281 q^{35} +1.00000 q^{36} +5.70604 q^{37} -4.69562 q^{38} -2.65927 q^{39} -1.54501 q^{40} +6.53614 q^{41} +1.28984 q^{42} +6.44584 q^{43} -2.49412 q^{44} +1.54501 q^{45} -3.63334 q^{46} +12.1071 q^{47} +1.00000 q^{48} -5.33631 q^{49} +2.61296 q^{50} +1.92011 q^{51} -2.65927 q^{52} +2.97407 q^{53} -1.00000 q^{54} -3.85342 q^{55} +1.28984 q^{56} +4.69562 q^{57} -9.08085 q^{58} -12.6372 q^{59} +1.54501 q^{60} -10.5220 q^{61} -5.96966 q^{62} -1.28984 q^{63} +1.00000 q^{64} -4.10859 q^{65} +2.49412 q^{66} +4.51299 q^{67} +1.92011 q^{68} +3.63334 q^{69} +1.99281 q^{70} +6.01319 q^{71} -1.00000 q^{72} -9.46377 q^{73} -5.70604 q^{74} -2.61296 q^{75} +4.69562 q^{76} +3.21701 q^{77} +2.65927 q^{78} -9.23357 q^{79} +1.54501 q^{80} +1.00000 q^{81} -6.53614 q^{82} +12.9523 q^{83} -1.28984 q^{84} +2.96659 q^{85} -6.44584 q^{86} +9.08085 q^{87} +2.49412 q^{88} -0.168223 q^{89} -1.54501 q^{90} +3.43004 q^{91} +3.63334 q^{92} +5.96966 q^{93} -12.1071 q^{94} +7.25476 q^{95} -1.00000 q^{96} +1.05018 q^{97} +5.33631 q^{98} -2.49412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - q^{7} - 5 q^{8} + 5 q^{9} - 5 q^{10} + 9 q^{11} + 5 q^{12} + q^{14} + 5 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - 4 q^{19} + 5 q^{20} - q^{21} - 9 q^{22} + 16 q^{23} - 5 q^{24} + 8 q^{25} + 5 q^{27} - q^{28} + 8 q^{29} - 5 q^{30} - q^{31} - 5 q^{32} + 9 q^{33} - 6 q^{34} + 22 q^{35} + 5 q^{36} - 2 q^{37} + 4 q^{38} - 5 q^{40} + 4 q^{41} + q^{42} + 3 q^{43} + 9 q^{44} + 5 q^{45} - 16 q^{46} + 18 q^{47} + 5 q^{48} + 2 q^{49} - 8 q^{50} + 6 q^{51} + 26 q^{53} - 5 q^{54} + q^{55} + q^{56} - 4 q^{57} - 8 q^{58} + 21 q^{59} + 5 q^{60} - 20 q^{61} + q^{62} - q^{63} + 5 q^{64} - 3 q^{65} - 9 q^{66} - 5 q^{67} + 6 q^{68} + 16 q^{69} - 22 q^{70} + 17 q^{71} - 5 q^{72} + 5 q^{73} + 2 q^{74} + 8 q^{75} - 4 q^{76} + 2 q^{77} - 21 q^{79} + 5 q^{80} + 5 q^{81} - 4 q^{82} + 11 q^{83} - q^{84} - 12 q^{85} - 3 q^{86} + 8 q^{87} - 9 q^{88} - 5 q^{89} - 5 q^{90} - 10 q^{91} + 16 q^{92} - q^{93} - 18 q^{94} + 10 q^{95} - 5 q^{96} - 11 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - q^7 - 5 * q^8 + 5 * q^9 - 5 * q^10 + 9 * q^11 + 5 * q^12 + q^14 + 5 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - 4 * q^19 + 5 * q^20 - q^21 - 9 * q^22 + 16 * q^23 - 5 * q^24 + 8 * q^25 + 5 * q^27 - q^28 + 8 * q^29 - 5 * q^30 - q^31 - 5 * q^32 + 9 * q^33 - 6 * q^34 + 22 * q^35 + 5 * q^36 - 2 * q^37 + 4 * q^38 - 5 * q^40 + 4 * q^41 + q^42 + 3 * q^43 + 9 * q^44 + 5 * q^45 - 16 * q^46 + 18 * q^47 + 5 * q^48 + 2 * q^49 - 8 * q^50 + 6 * q^51 + 26 * q^53 - 5 * q^54 + q^55 + q^56 - 4 * q^57 - 8 * q^58 + 21 * q^59 + 5 * q^60 - 20 * q^61 + q^62 - q^63 + 5 * q^64 - 3 * q^65 - 9 * q^66 - 5 * q^67 + 6 * q^68 + 16 * q^69 - 22 * q^70 + 17 * q^71 - 5 * q^72 + 5 * q^73 + 2 * q^74 + 8 * q^75 - 4 * q^76 + 2 * q^77 - 21 * q^79 + 5 * q^80 + 5 * q^81 - 4 * q^82 + 11 * q^83 - q^84 - 12 * q^85 - 3 * q^86 + 8 * q^87 - 9 * q^88 - 5 * q^89 - 5 * q^90 - 10 * q^91 + 16 * q^92 - q^93 - 18 * q^94 + 10 * q^95 - 5 * q^96 - 11 * q^97 - 2 * q^98 + 9 * q^99

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