LMFDB - Embedded newform 8018.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.180143 q^{3} +1.00000 q^{4} +0.229721 q^{5} +0.180143 q^{6} -1.11361 q^{7} +1.00000 q^{8} -2.96755 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.180143 q^{3} +1.00000 q^{4} +0.229721 q^{5} +0.180143 q^{6} -1.11361 q^{7} +1.00000 q^{8} -2.96755 q^{9} +0.229721 q^{10} -4.26991 q^{11} +0.180143 q^{12} +5.52427 q^{13} -1.11361 q^{14} +0.0413825 q^{15} +1.00000 q^{16} +3.05989 q^{17} -2.96755 q^{18} +1.00000 q^{19} +0.229721 q^{20} -0.200608 q^{21} -4.26991 q^{22} -0.559549 q^{23} +0.180143 q^{24} -4.94723 q^{25} +5.52427 q^{26} -1.07501 q^{27} -1.11361 q^{28} -4.00049 q^{29} +0.0413825 q^{30} +9.37372 q^{31} +1.00000 q^{32} -0.769192 q^{33} +3.05989 q^{34} -0.255818 q^{35} -2.96755 q^{36} +4.95059 q^{37} +1.00000 q^{38} +0.995156 q^{39} +0.229721 q^{40} -10.1260 q^{41} -0.200608 q^{42} -12.2198 q^{43} -4.26991 q^{44} -0.681707 q^{45} -0.559549 q^{46} -6.32808 q^{47} +0.180143 q^{48} -5.75988 q^{49} -4.94723 q^{50} +0.551216 q^{51} +5.52427 q^{52} -0.623348 q^{53} -1.07501 q^{54} -0.980886 q^{55} -1.11361 q^{56} +0.180143 q^{57} -4.00049 q^{58} +2.85480 q^{59} +0.0413825 q^{60} -12.0077 q^{61} +9.37372 q^{62} +3.30468 q^{63} +1.00000 q^{64} +1.26904 q^{65} -0.769192 q^{66} -9.26742 q^{67} +3.05989 q^{68} -0.100799 q^{69} -0.255818 q^{70} +8.20192 q^{71} -2.96755 q^{72} +15.2736 q^{73} +4.95059 q^{74} -0.891207 q^{75} +1.00000 q^{76} +4.75499 q^{77} +0.995156 q^{78} -4.06243 q^{79} +0.229721 q^{80} +8.70899 q^{81} -10.1260 q^{82} +4.31169 q^{83} -0.200608 q^{84} +0.702920 q^{85} -12.2198 q^{86} -0.720658 q^{87} -4.26991 q^{88} -2.30328 q^{89} -0.681707 q^{90} -6.15185 q^{91} -0.559549 q^{92} +1.68861 q^{93} -6.32808 q^{94} +0.229721 q^{95} +0.180143 q^{96} -2.67655 q^{97} -5.75988 q^{98} +12.6712 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	0.180143	0.104005	0.0520027	−	0.998647i	$-0.483440\pi$
$3$	0.180143	0.104005	0.0520027	+	0.998647i	$0.483440\pi$
$4$	1.00000	0.500000
$5$	0.229721	0.102734	0.0513671	−	0.998680i	$-0.483642\pi$
$5$	0.229721	0.102734	0.0513671	+	0.998680i	$0.483642\pi$
$6$	0.180143	0.0735429
$7$	−1.11361	−0.420903	−0.210452	−	0.977604i	$-0.567493\pi$
$7$	−1.11361	−0.420903	−0.210452	+	0.977604i	$0.567493\pi$
$8$	1.00000	0.353553
$9$	−2.96755	−0.989183
$10$	0.229721	0.0726440
$11$	−4.26991	−1.28743	−0.643713	−	0.765267i	$-0.722607\pi$
$11$	−4.26991	−1.28743	−0.643713	+	0.765267i	$0.722607\pi$
$12$	0.180143	0.0520027
$13$	5.52427	1.53216	0.766078	−	0.642748i	$-0.222206\pi$
$13$	5.52427	1.53216	0.766078	+	0.642748i	$0.222206\pi$
$14$	−1.11361	−0.297624
$15$	0.0413825	0.0106849
$16$	1.00000	0.250000
$17$	3.05989	0.742132	0.371066	−	0.928607i	$-0.378992\pi$
$17$	3.05989	0.742132	0.371066	+	0.928607i	$0.378992\pi$
$18$	−2.96755	−0.699458
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.229721	0.0513671
$21$	−0.200608	−0.0437762
$22$	−4.26991	−0.910347
$23$	−0.559549	−0.116674	−0.0583370	−	0.998297i	$-0.518580\pi$
$23$	−0.559549	−0.116674	−0.0583370	+	0.998297i	$0.518580\pi$
$24$	0.180143	0.0367715
$25$	−4.94723	−0.989446
$26$	5.52427	1.08340
$27$	−1.07501	−0.206886
$28$	−1.11361	−0.210452
$29$	−4.00049	−0.742872	−0.371436	−	0.928459i	$-0.621134\pi$
$29$	−4.00049	−0.742872	−0.371436	+	0.928459i	$0.621134\pi$
$30$	0.0413825	0.00755537
$31$	9.37372	1.68357	0.841785	−	0.539813i	$-0.181505\pi$
$31$	9.37372	1.68357	0.841785	+	0.539813i	$0.181505\pi$
$32$	1.00000	0.176777
$33$	−0.769192	−0.133899
$34$	3.05989	0.524767
$35$	−0.255818	−0.0432412
$36$	−2.96755	−0.494591
$37$	4.95059	0.813871	0.406936	−	0.913457i	$-0.366597\pi$
$37$	4.95059	0.813871	0.406936	+	0.913457i	$0.366597\pi$
$38$	1.00000	0.162221
$39$	0.995156	0.159352
$40$	0.229721	0.0363220
$41$	−10.1260	−1.58142	−0.790710	−	0.612190i	$-0.790289\pi$
$41$	−10.1260	−1.58142	−0.790710	+	0.612190i	$0.790289\pi$
$42$	−0.200608	−0.0309545
$43$	−12.2198	−1.86351	−0.931753	−	0.363094i	$-0.881721\pi$
$43$	−12.2198	−1.86351	−0.931753	+	0.363094i	$0.881721\pi$
$44$	−4.26991	−0.643713
$45$	−0.681707	−0.101623
$46$	−0.559549	−0.0825010
$47$	−6.32808	−0.923046	−0.461523	−	0.887128i	$-0.652697\pi$
$47$	−6.32808	−0.923046	−0.461523	+	0.887128i	$0.652697\pi$
$48$	0.180143	0.0260013
$49$	−5.75988	−0.822840
$50$	−4.94723	−0.699644
$51$	0.551216	0.0771857
$52$	5.52427	0.766078
$53$	−0.623348	−0.0856234	−0.0428117	−	0.999083i	$-0.513632\pi$
$53$	−0.623348	−0.0856234	−0.0428117	+	0.999083i	$0.513632\pi$
$54$	−1.07501	−0.146290
$55$	−0.980886	−0.132263
$56$	−1.11361	−0.148812
$57$	0.180143	0.0238605
$58$	−4.00049	−0.525290
$59$	2.85480	0.371663	0.185832	−	0.982582i	$-0.440502\pi$
$59$	2.85480	0.371663	0.185832	+	0.982582i	$0.440502\pi$
$60$	0.0413825	0.00534245
$61$	−12.0077	−1.53743	−0.768716	−	0.639590i	$-0.779104\pi$
$61$	−12.0077	−1.53743	−0.768716	+	0.639590i	$0.779104\pi$
$62$	9.37372	1.19046
$63$	3.30468	0.416350
$64$	1.00000	0.125000
$65$	1.26904	0.157405
$66$	−0.769192	−0.0946810
$67$	−9.26742	−1.13220	−0.566098	−	0.824338i	$-0.691547\pi$
$67$	−9.26742	−1.13220	−0.566098	+	0.824338i	$0.691547\pi$
$68$	3.05989	0.371066
$69$	−0.100799	−0.0121347
$70$	−0.255818	−0.0305761
$71$	8.20192	0.973389	0.486694	−	0.873572i	$-0.338202\pi$
$71$	8.20192	0.973389	0.486694	+	0.873572i	$0.338202\pi$
$72$	−2.96755	−0.349729
$73$	15.2736	1.78765	0.893823	−	0.448421i	$-0.148013\pi$
$73$	15.2736	1.78765	0.893823	+	0.448421i	$0.148013\pi$
$74$	4.95059	0.575494
$75$	−0.891207	−0.102908
$76$	1.00000	0.114708
$77$	4.75499	0.541882
$78$	0.995156	0.112679
$79$	−4.06243	−0.457059	−0.228529	−	0.973537i	$-0.573392\pi$
$79$	−4.06243	−0.457059	−0.228529	+	0.973537i	$0.573392\pi$
$80$	0.229721	0.0256835
$81$	8.70899	0.967666
$82$	−10.1260	−1.11823
$83$	4.31169	0.473269	0.236635	−	0.971599i	$-0.423956\pi$
$83$	4.31169	0.473269	0.236635	+	0.971599i	$0.423956\pi$
$84$	−0.200608	−0.0218881
$85$	0.702920	0.0762423
$86$	−12.2198	−1.31770
$87$	−0.720658	−0.0772627
$88$	−4.26991	−0.455174
$89$	−2.30328	−0.244148	−0.122074	−	0.992521i	$-0.538954\pi$
$89$	−2.30328	−0.244148	−0.122074	+	0.992521i	$0.538954\pi$
$90$	−0.681707	−0.0718582
$91$	−6.15185	−0.644889
$92$	−0.559549	−0.0583370
$93$	1.68861	0.175100
$94$	−6.32808	−0.652692
$95$	0.229721	0.0235688
$96$	0.180143	0.0183857
$97$	−2.67655	−0.271762	−0.135881	−	0.990725i	$-0.543387\pi$
$97$	−2.67655	−0.271762	−0.135881	+	0.990725i	$0.543387\pi$
$98$	−5.75988	−0.581836
$99$	12.6712	1.27350
$100$	−4.94723	−0.494723
$101$	−1.51488	−0.150736	−0.0753679	−	0.997156i	$-0.524013\pi$
$101$	−1.51488	−0.150736	−0.0753679	+	0.997156i	$0.524013\pi$
$102$	0.551216	0.0545785
$103$	6.71149	0.661302	0.330651	−	0.943753i	$-0.392732\pi$
$103$	6.71149	0.661302	0.330651	+	0.943753i	$0.392732\pi$
$104$	5.52427	0.541699
$105$	−0.0460838	−0.00449731
$106$	−0.623348	−0.0605449
$107$	18.0314	1.74316	0.871578	−	0.490256i	$-0.163097\pi$
$107$	18.0314	1.74316	0.871578	+	0.490256i	$0.163097\pi$
$108$	−1.07501	−0.103443
$109$	−3.09897	−0.296828	−0.148414	−	0.988925i	$-0.547417\pi$
$109$	−3.09897	−0.296828	−0.148414	+	0.988925i	$0.547417\pi$
$110$	−0.980886	−0.0935238
$111$	0.891811	0.0846470
$112$	−1.11361	−0.105226
$113$	−5.13579	−0.483134	−0.241567	−	0.970384i	$-0.577661\pi$
$113$	−5.13579	−0.483134	−0.241567	+	0.970384i	$0.577661\pi$
$114$	0.180143	0.0168719
$115$	−0.128540	−0.0119864
$116$	−4.00049	−0.371436
$117$	−16.3935	−1.51558
$118$	2.85480	0.262806
$119$	−3.40751	−0.312366
$120$	0.0413825	0.00377769
$121$	7.23210	0.657464
$122$	−12.0077	−1.08713
$123$	−1.82413	−0.164476
$124$	9.37372	0.841785
$125$	−2.28508	−0.204384
$126$	3.30468	0.294404
$127$	−12.5240	−1.11133	−0.555664	−	0.831407i	$-0.687536\pi$
$127$	−12.5240	−1.11133	−0.555664	+	0.831407i	$0.687536\pi$
$128$	1.00000	0.0883883
$129$	−2.20131	−0.193815
$130$	1.26904	0.111302
$131$	−2.57515	−0.224992	−0.112496	−	0.993652i	$-0.535885\pi$
$131$	−2.57515	−0.224992	−0.112496	+	0.993652i	$0.535885\pi$
$132$	−0.769192	−0.0669496
$133$	−1.11361	−0.0965619
$134$	−9.26742	−0.800583
$135$	−0.246952	−0.0212542
$136$	3.05989	0.262383
$137$	−4.92632	−0.420884	−0.210442	−	0.977606i	$-0.567490\pi$
$137$	−4.92632	−0.420884	−0.210442	+	0.977606i	$0.567490\pi$
$138$	−0.100799	−0.00858055
$139$	−16.8290	−1.42741	−0.713707	−	0.700444i	$-0.752985\pi$
$139$	−16.8290	−1.42741	−0.713707	+	0.700444i	$0.752985\pi$
$140$	−0.255818	−0.0216206
$141$	−1.13996	−0.0960017
$142$	8.20192	0.688290
$143$	−23.5881	−1.97254
$144$	−2.96755	−0.247296
$145$	−0.918994	−0.0763183
$146$	15.2736	1.26406
$147$	−1.03760	−0.0855798
$148$	4.95059	0.406936
$149$	−19.6430	−1.60922	−0.804609	−	0.593805i	$-0.797625\pi$
$149$	−19.6430	−1.60922	−0.804609	+	0.593805i	$0.797625\pi$
$150$	−0.891207	−0.0727667
$151$	−8.52109	−0.693437	−0.346718	−	0.937969i	$-0.612704\pi$
$151$	−8.52109	−0.693437	−0.346718	+	0.937969i	$0.612704\pi$
$152$	1.00000	0.0811107
$153$	−9.08037	−0.734104
$154$	4.75499	0.383168
$155$	2.15334	0.172960
$156$	0.995156	0.0796762
$157$	−8.73492	−0.697123	−0.348561	−	0.937286i	$-0.613330\pi$
$157$	−8.73492	−0.697123	−0.348561	+	0.937286i	$0.613330\pi$
$158$	−4.06243	−0.323189
$159$	−0.112292	−0.00890530
$160$	0.229721	0.0181610
$161$	0.623117	0.0491085
$162$	8.70899	0.684243
$163$	−5.89902	−0.462047	−0.231024	−	0.972948i	$-0.574207\pi$
$163$	−5.89902	−0.462047	−0.231024	+	0.972948i	$0.574207\pi$
$164$	−10.1260	−0.790710
$165$	−0.176699	−0.0137560
$166$	4.31169	0.334652
$167$	4.96906	0.384518	0.192259	−	0.981344i	$-0.438419\pi$
$167$	4.96906	0.384518	0.192259	+	0.981344i	$0.438419\pi$
$168$	−0.200608	−0.0154772
$169$	17.5175	1.34750
$170$	0.702920	0.0539115
$171$	−2.96755	−0.226934
$172$	−12.2198	−0.931753
$173$	−16.4703	−1.25222	−0.626108	−	0.779736i	$-0.715353\pi$
$173$	−16.4703	−1.25222	−0.626108	+	0.779736i	$0.715353\pi$
$174$	−0.720658	−0.0546330
$175$	5.50926	0.416461
$176$	−4.26991	−0.321856
$177$	0.514271	0.0386550
$178$	−2.30328	−0.172638
$179$	0.150726	0.0112658	0.00563289	−	0.999984i	$-0.498207\pi$
$179$	0.150726	0.0112658	0.00563289	+	0.999984i	$0.498207\pi$
$180$	−0.681707	−0.0508115
$181$	−26.2189	−1.94884	−0.974418	−	0.224744i	$-0.927845\pi$
$181$	−26.2189	−1.94884	−0.974418	+	0.224744i	$0.927845\pi$
$182$	−6.15185	−0.456006
$183$	−2.16310	−0.159901
$184$	−0.559549	−0.0412505
$185$	1.13725	0.0836124
$186$	1.68861	0.123815
$187$	−13.0654	−0.955439
$188$	−6.32808	−0.461523
$189$	1.19714	0.0870789
$190$	0.229721	0.0166657
$191$	3.97821	0.287853	0.143927	−	0.989588i	$-0.454027\pi$
$191$	3.97821	0.287853	0.143927	+	0.989588i	$0.454027\pi$
$192$	0.180143	0.0130007
$193$	−19.4922	−1.40308	−0.701540	−	0.712630i	$-0.747504\pi$
$193$	−19.4922	−1.40308	−0.701540	+	0.712630i	$0.747504\pi$
$194$	−2.67655	−0.192165
$195$	0.228608	0.0163709
$196$	−5.75988	−0.411420
$197$	0.443923	0.0316282	0.0158141	−	0.999875i	$-0.494966\pi$
$197$	0.443923	0.0316282	0.0158141	+	0.999875i	$0.494966\pi$
$198$	12.6712	0.900500
$199$	−1.10002	−0.0779783	−0.0389892	−	0.999240i	$-0.512414\pi$
$199$	−1.10002	−0.0779783	−0.0389892	+	0.999240i	$0.512414\pi$
$200$	−4.94723	−0.349822
$201$	−1.66946	−0.117754
$202$	−1.51488	−0.106586
$203$	4.45496	0.312677
$204$	0.551216	0.0385929
$205$	−2.32616	−0.162466
$206$	6.71149	0.467611
$207$	1.66049	0.115412
$208$	5.52427	0.383039
$209$	−4.26991	−0.295356
$210$	−0.0460838	−0.00318008
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−0.623348	−0.0428117
$213$	1.47752	0.101238
$214$	18.0314	1.23260
$215$	−2.80715	−0.191446
$216$	−1.07501	−0.0731452
$217$	−10.4386	−0.708620
$218$	−3.09897	−0.209889
$219$	2.75144	0.185925
$220$	−0.980886	−0.0661313
$221$	16.9036	1.13706
$222$	0.891811	0.0598545
$223$	−20.3912	−1.36550	−0.682748	−	0.730654i	$-0.739215\pi$
$223$	−20.3912	−1.36550	−0.682748	+	0.730654i	$0.739215\pi$
$224$	−1.11361	−0.0744059
$225$	14.6811	0.978743
$226$	−5.13579	−0.341628
$227$	15.0417	0.998356	0.499178	−	0.866500i	$-0.333635\pi$
$227$	15.0417	0.998356	0.499178	+	0.866500i	$0.333635\pi$
$228$	0.180143	0.0119302
$229$	−14.5838	−0.963725	−0.481862	−	0.876247i	$-0.660039\pi$
$229$	−14.5838	−0.963725	−0.481862	+	0.876247i	$0.660039\pi$
$230$	−0.128540	−0.00847568
$231$	0.856577	0.0563586
$232$	−4.00049	−0.262645
$233$	17.6557	1.15667	0.578333	−	0.815801i	$-0.303703\pi$
$233$	17.6557	1.15667	0.578333	+	0.815801i	$0.303703\pi$
$234$	−16.3935	−1.07168
$235$	−1.45369	−0.0948284
$236$	2.85480	0.185832
$237$	−0.731816	−0.0475366
$238$	−3.40751	−0.220876
$239$	4.26804	0.276077	0.138038	−	0.990427i	$-0.455920\pi$
$239$	4.26804	0.276077	0.138038	+	0.990427i	$0.455920\pi$
$240$	0.0413825	0.00267123
$241$	−19.2029	−1.23697	−0.618483	−	0.785798i	$-0.712253\pi$
$241$	−19.2029	−1.23697	−0.618483	+	0.785798i	$0.712253\pi$
$242$	7.23210	0.464897
$243$	4.79389	0.307528
$244$	−12.0077	−0.768716
$245$	−1.32316	−0.0845338
$246$	−1.82413	−0.116302
$247$	5.52427	0.351501
$248$	9.37372	0.595232
$249$	0.776719	0.0492226
$250$	−2.28508	−0.144521
$251$	1.45843	0.0920550	0.0460275	−	0.998940i	$-0.485344\pi$
$251$	1.45843	0.0920550	0.0460275	+	0.998940i	$0.485344\pi$
$252$	3.30468	0.208175
$253$	2.38922	0.150209
$254$	−12.5240	−0.785828
$255$	0.126626	0.00792961
$256$	1.00000	0.0625000
$257$	12.5816	0.784820	0.392410	−	0.919790i	$-0.371641\pi$
$257$	12.5816	0.784820	0.392410	+	0.919790i	$0.371641\pi$
$258$	−2.20131	−0.137048
$259$	−5.51300	−0.342561
$260$	1.26904	0.0787024
$261$	11.8716	0.734836
$262$	−2.57515	−0.159094
$263$	27.4585	1.69316	0.846582	−	0.532259i	$-0.178657\pi$
$263$	27.4585	1.69316	0.846582	+	0.532259i	$0.178657\pi$
$264$	−0.769192	−0.0473405
$265$	−0.143196	−0.00879645
$266$	−1.11361	−0.0682795
$267$	−0.414920	−0.0253927
$268$	−9.26742	−0.566098
$269$	−0.813377	−0.0495924	−0.0247962	−	0.999693i	$-0.507894\pi$
$269$	−0.813377	−0.0495924	−0.0247962	+	0.999693i	$0.507894\pi$
$270$	−0.246952	−0.0150290
$271$	−0.269699	−0.0163830	−0.00819152	−	0.999966i	$-0.502607\pi$
$271$	−0.269699	−0.0163830	−0.00819152	+	0.999966i	$0.502607\pi$
$272$	3.05989	0.185533
$273$	−1.10821	−0.0670720
$274$	−4.92632	−0.297610
$275$	21.1242	1.27384
$276$	−0.100799	−0.00606737
$277$	6.75257	0.405723	0.202861	−	0.979207i	$-0.434976\pi$
$277$	6.75257	0.405723	0.202861	+	0.979207i	$0.434976\pi$
$278$	−16.8290	−1.00933
$279$	−27.8170	−1.66536
$280$	−0.255818	−0.0152881
$281$	−12.3044	−0.734017	−0.367009	−	0.930218i	$-0.619618\pi$
$281$	−12.3044	−0.734017	−0.367009	+	0.930218i	$0.619618\pi$
$282$	−1.13996	−0.0678835
$283$	21.2192	1.26135	0.630674	−	0.776047i	$-0.282778\pi$
$283$	21.2192	1.26135	0.630674	+	0.776047i	$0.282778\pi$
$284$	8.20192	0.486694
$285$	0.0413825	0.00245129
$286$	−23.5881	−1.39479
$287$	11.2764	0.665625
$288$	−2.96755	−0.174864
$289$	−7.63708	−0.449240
$290$	−0.918994	−0.0539652
$291$	−0.482160	−0.0282647
$292$	15.2736	0.893823
$293$	−4.08543	−0.238673	−0.119337	−	0.992854i	$-0.538077\pi$
$293$	−4.08543	−0.238673	−0.119337	+	0.992854i	$0.538077\pi$
$294$	−1.03760	−0.0605141
$295$	0.655807	0.0381825
$296$	4.95059	0.287747
$297$	4.59019	0.266350
$298$	−19.6430	−1.13789
$299$	−3.09110	−0.178763
$300$	−0.891207	−0.0514538
$301$	13.6081	0.784356
$302$	−8.52109	−0.490334
$303$	−0.272894	−0.0156773
$304$	1.00000	0.0573539
$305$	−2.75842	−0.157947
$306$	−9.08037	−0.519090
$307$	−2.86108	−0.163290	−0.0816452	−	0.996661i	$-0.526017\pi$
$307$	−2.86108	−0.163290	−0.0816452	+	0.996661i	$0.526017\pi$
$308$	4.75499	0.270941
$309$	1.20902	0.0687790
$310$	2.15334	0.122301
$311$	−7.66583	−0.434690	−0.217345	−	0.976095i	$-0.569740\pi$
$311$	−7.66583	−0.434690	−0.217345	+	0.976095i	$0.569740\pi$
$312$	0.995156	0.0563396
$313$	−4.17760	−0.236132	−0.118066	−	0.993006i	$-0.537669\pi$
$313$	−4.17760	−0.236132	−0.118066	+	0.993006i	$0.537669\pi$
$314$	−8.73492	−0.492940
$315$	0.759153	0.0427734
$316$	−4.06243	−0.228529
$317$	28.2365	1.58592	0.792961	−	0.609272i	$-0.208538\pi$
$317$	28.2365	1.58592	0.792961	+	0.609272i	$0.208538\pi$
$318$	−0.112292	−0.00629700
$319$	17.0817	0.956392
$320$	0.229721	0.0128418
$321$	3.24822	0.181298
$322$	0.623117	0.0347250
$323$	3.05989	0.170257
$324$	8.70899	0.483833
$325$	−27.3298	−1.51598
$326$	−5.89902	−0.326717
$327$	−0.558257	−0.0308717
$328$	−10.1260	−0.559117
$329$	7.04699	0.388513
$330$	−0.176699	−0.00972698
$331$	−20.2332	−1.11212	−0.556058	−	0.831144i	$-0.687687\pi$
$331$	−20.2332	−1.11212	−0.556058	+	0.831144i	$0.687687\pi$
$332$	4.31169	0.236635
$333$	−14.6911	−0.805068
$334$	4.96906	0.271895
$335$	−2.12892	−0.116315
$336$	−0.200608	−0.0109441
$337$	−26.6353	−1.45092	−0.725459	−	0.688265i	$-0.758372\pi$
$337$	−26.6353	−1.45092	−0.725459	+	0.688265i	$0.758372\pi$
$338$	17.5175	0.952827
$339$	−0.925175	−0.0502486
$340$	0.702920	0.0381212
$341$	−40.0249	−2.16747
$342$	−2.96755	−0.160467
$343$	14.2095	0.767240
$344$	−12.2198	−0.658849
$345$	−0.0231555	−0.00124665
$346$	−16.4703	−0.885451
$347$	−6.57563	−0.352999	−0.176499	−	0.984301i	$-0.556477\pi$
$347$	−6.57563	−0.352999	−0.176499	+	0.984301i	$0.556477\pi$
$348$	−0.720658	−0.0386313
$349$	−13.3044	−0.712168	−0.356084	−	0.934454i	$-0.615888\pi$
$349$	−13.3044	−0.712168	−0.356084	+	0.934454i	$0.615888\pi$
$350$	5.50926	0.294482
$351$	−5.93864	−0.316981
$352$	−4.26991	−0.227587
$353$	−8.67801	−0.461884	−0.230942	−	0.972968i	$-0.574181\pi$
$353$	−8.67801	−0.461884	−0.230942	+	0.972968i	$0.574181\pi$
$354$	0.514271	0.0273332
$355$	1.88415	0.100000
$356$	−2.30328	−0.122074
$357$	−0.613838	−0.0324877
$358$	0.150726	0.00796610
$359$	7.49472	0.395556	0.197778	−	0.980247i	$-0.436627\pi$
$359$	7.49472	0.395556	0.197778	+	0.980247i	$0.436627\pi$
$360$	−0.681707	−0.0359291
$361$	1.00000	0.0526316
$362$	−26.2189	−1.37803
$363$	1.30281	0.0683798
$364$	−6.15185	−0.322445
$365$	3.50867	0.183652
$366$	−2.16310	−0.113067
$367$	−11.4329	−0.596793	−0.298397	−	0.954442i	$-0.596452\pi$
$367$	−11.4329	−0.596793	−0.298397	+	0.954442i	$0.596452\pi$
$368$	−0.559549	−0.0291685
$369$	30.0495	1.56431
$370$	1.13725	0.0591229
$371$	0.694164	0.0360392
$372$	1.68861	0.0875501
$373$	22.2220	1.15061	0.575306	−	0.817938i	$-0.304883\pi$
$373$	22.2220	1.15061	0.575306	+	0.817938i	$0.304883\pi$
$374$	−13.0654	−0.675598
$375$	−0.411641	−0.0212570
$376$	−6.32808	−0.326346
$377$	−22.0998	−1.13820
$378$	1.19714	0.0615741
$379$	−12.2328	−0.628357	−0.314179	−	0.949364i	$-0.601729\pi$
$379$	−12.2328	−0.628357	−0.314179	+	0.949364i	$0.601729\pi$
$380$	0.229721	0.0117844
$381$	−2.25611	−0.115584
$382$	3.97821	0.203543
$383$	−31.6357	−1.61651	−0.808254	−	0.588833i	$-0.799587\pi$
$383$	−31.6357	−1.61651	−0.808254	+	0.588833i	$0.799587\pi$
$384$	0.180143	0.00919286
$385$	1.09232	0.0556698
$386$	−19.4922	−0.992128
$387$	36.2629	1.84335
$388$	−2.67655	−0.135881
$389$	−33.3039	−1.68857	−0.844287	−	0.535892i	$-0.819975\pi$
$389$	−33.3039	−1.68857	−0.844287	+	0.535892i	$0.819975\pi$
$390$	0.228608	0.0115760
$391$	−1.71216	−0.0865876
$392$	−5.75988	−0.290918
$393$	−0.463895	−0.0234004
$394$	0.443923	0.0223645
$395$	−0.933223	−0.0469556
$396$	12.6712	0.636749
$397$	−17.2426	−0.865379	−0.432690	−	0.901543i	$-0.642435\pi$
$397$	−17.2426	−0.865379	−0.432690	+	0.901543i	$0.642435\pi$
$398$	−1.10002	−0.0551390
$399$	−0.200608	−0.0100430
$400$	−4.94723	−0.247361
$401$	3.51519	0.175540	0.0877701	−	0.996141i	$-0.472026\pi$
$401$	3.51519	0.175540	0.0877701	+	0.996141i	$0.472026\pi$
$402$	−1.66946	−0.0832649
$403$	51.7829	2.57949
$404$	−1.51488	−0.0753679
$405$	2.00064	0.0994124
$406$	4.45496	0.221096
$407$	−21.1385	−1.04780
$408$	0.551216	0.0272893
$409$	3.69626	0.182768	0.0913841	−	0.995816i	$-0.470871\pi$
$409$	3.69626	0.182768	0.0913841	+	0.995816i	$0.470871\pi$
$410$	−2.32616	−0.114881
$411$	−0.887440	−0.0437742
$412$	6.71149	0.330651
$413$	−3.17912	−0.156434
$414$	1.66049	0.0816086
$415$	0.990484	0.0486210
$416$	5.52427	0.270849
$417$	−3.03161	−0.148459
$418$	−4.26991	−0.208848
$419$	6.28854	0.307215	0.153608	−	0.988132i	$-0.450911\pi$
$419$	6.28854	0.307215	0.153608	+	0.988132i	$0.450911\pi$
$420$	−0.0460838	−0.00224866
$421$	30.0515	1.46462	0.732310	−	0.680971i	$-0.238442\pi$
$421$	30.0515	1.46462	0.732310	+	0.680971i	$0.238442\pi$
$422$	−1.00000	−0.0486792
$423$	18.7789	0.913061
$424$	−0.623348	−0.0302724
$425$	−15.1380	−0.734299
$426$	1.47752	0.0715859
$427$	13.3719	0.647111
$428$	18.0314	0.871578
$429$	−4.24922	−0.205154
$430$	−2.80715	−0.135373
$431$	−2.18952	−0.105466	−0.0527328	−	0.998609i	$-0.516793\pi$
$431$	−2.18952	−0.105466	−0.0527328	+	0.998609i	$0.516793\pi$
$432$	−1.07501	−0.0517214
$433$	18.0306	0.866496	0.433248	−	0.901275i	$-0.357367\pi$
$433$	18.0306	0.866496	0.433248	+	0.901275i	$0.357367\pi$
$434$	−10.4386	−0.501070
$435$	−0.165550	−0.00793752
$436$	−3.09897	−0.148414
$437$	−0.559549	−0.0267669
$438$	2.75144	0.131469
$439$	−28.5483	−1.36254	−0.681268	−	0.732034i	$-0.738571\pi$
$439$	−28.5483	−1.36254	−0.681268	+	0.732034i	$0.738571\pi$
$440$	−0.980886	−0.0467619
$441$	17.0927	0.813940
$442$	16.9036	0.804024
$443$	21.4218	1.01778	0.508889	−	0.860832i	$-0.330056\pi$
$443$	21.4218	1.01778	0.508889	+	0.860832i	$0.330056\pi$
$444$	0.891811	0.0423235
$445$	−0.529112	−0.0250823
$446$	−20.3912	−0.965551
$447$	−3.53854	−0.167367
$448$	−1.11361	−0.0526129
$449$	18.6241	0.878925	0.439463	−	0.898261i	$-0.355169\pi$
$449$	18.6241	0.878925	0.439463	+	0.898261i	$0.355169\pi$
$450$	14.6811	0.692076
$451$	43.2372	2.03596
$452$	−5.13579	−0.241567
$453$	−1.53501	−0.0721211
$454$	15.0417	0.705944
$455$	−1.41321	−0.0662522
$456$	0.180143	0.00843595
$457$	−10.6850	−0.499826	−0.249913	−	0.968268i	$-0.580402\pi$
$457$	−10.6850	−0.499826	−0.249913	+	0.968268i	$0.580402\pi$
$458$	−14.5838	−0.681456
$459$	−3.28941	−0.153537
$460$	−0.128540	−0.00599321
$461$	−17.8639	−0.832003	−0.416001	−	0.909364i	$-0.636569\pi$
$461$	−17.8639	−0.832003	−0.416001	+	0.909364i	$0.636569\pi$
$462$	0.856577	0.0398516
$463$	34.8728	1.62068	0.810338	−	0.585962i	$-0.199283\pi$
$463$	34.8728	1.62068	0.810338	+	0.585962i	$0.199283\pi$
$464$	−4.00049	−0.185718
$465$	0.387908	0.0179888
$466$	17.6557	0.817887
$467$	27.8937	1.29077	0.645384	−	0.763858i	$-0.276697\pi$
$467$	27.8937	1.29077	0.645384	+	0.763858i	$0.276697\pi$
$468$	−16.3935	−0.757791
$469$	10.3202	0.476545
$470$	−1.45369	−0.0670538
$471$	−1.57353	−0.0725045
$472$	2.85480	0.131403
$473$	52.1775	2.39912
$474$	−0.731816	−0.0336134
$475$	−4.94723	−0.226994
$476$	−3.40751	−0.156183
$477$	1.84982	0.0846972
$478$	4.26804	0.195216
$479$	32.8962	1.50306	0.751532	−	0.659696i	$-0.229315\pi$
$479$	32.8962	1.50306	0.751532	+	0.659696i	$0.229315\pi$
$480$	0.0413825	0.00188884
$481$	27.3484	1.24698
$482$	−19.2029	−0.874668
$483$	0.112250	0.00510755
$484$	7.23210	0.328732
$485$	−0.614858	−0.0279193
$486$	4.79389	0.217455
$487$	−40.1341	−1.81865	−0.909326	−	0.416085i	$-0.863402\pi$
$487$	−40.1341	−1.81865	−0.909326	+	0.416085i	$0.863402\pi$
$488$	−12.0077	−0.543565
$489$	−1.06267	−0.0480554
$490$	−1.32316	−0.0597745
$491$	22.5398	1.01721	0.508603	−	0.861001i	$-0.330162\pi$
$491$	22.5398	1.01721	0.508603	+	0.861001i	$0.330162\pi$
$492$	−1.82413	−0.0822381
$493$	−12.2410	−0.551309
$494$	5.52427	0.248548
$495$	2.91083	0.130832
$496$	9.37372	0.420892
$497$	−9.13371	−0.409703
$498$	0.776719	0.0348056
$499$	3.63815	0.162866	0.0814330	−	0.996679i	$-0.474050\pi$
$499$	3.63815	0.162866	0.0814330	+	0.996679i	$0.474050\pi$
$500$	−2.28508	−0.102192
$501$	0.895140	0.0399919
$502$	1.45843	0.0650927
$503$	20.2758	0.904052	0.452026	−	0.892005i	$-0.350701\pi$
$503$	20.2758	0.904052	0.452026	+	0.892005i	$0.350701\pi$
$504$	3.30468	0.147202
$505$	−0.347998	−0.0154857
$506$	2.38922	0.106214
$507$	3.15565	0.140147
$508$	−12.5240	−0.555664
$509$	−38.9237	−1.72526	−0.862632	−	0.505832i	$-0.831186\pi$
$509$	−38.9237	−1.72526	−0.862632	+	0.505832i	$0.831186\pi$
$510$	0.126626	0.00560708
$511$	−17.0088	−0.752426
$512$	1.00000	0.0441942
$513$	−1.07501	−0.0474628
$514$	12.5816	0.554951
$515$	1.54177	0.0679384
$516$	−2.20131	−0.0969073
$517$	27.0203	1.18835
$518$	−5.51300	−0.242227
$519$	−2.96701	−0.130237
$520$	1.26904	0.0556510
$521$	25.0557	1.09771	0.548854	−	0.835918i	$-0.315064\pi$
$521$	25.0557	1.09771	0.548854	+	0.835918i	$0.315064\pi$
$522$	11.8716	0.519608
$523$	−0.879046	−0.0384380	−0.0192190	−	0.999815i	$-0.506118\pi$
$523$	−0.879046	−0.0384380	−0.0192190	+	0.999815i	$0.506118\pi$
$524$	−2.57515	−0.112496
$525$	0.992453	0.0433142
$526$	27.4585	1.19725
$527$	28.6825	1.24943
$528$	−0.769192	−0.0334748
$529$	−22.6869	−0.986387
$530$	−0.143196	−0.00622003
$531$	−8.47176	−0.367643
$532$	−1.11361	−0.0482809
$533$	−55.9389	−2.42298
$534$	−0.414920	−0.0179553
$535$	4.14217	0.179082
$536$	−9.26742	−0.400291
$537$	0.0271521	0.00117170
$538$	−0.813377	−0.0350672
$539$	24.5942	1.05935
$540$	−0.246952	−0.0106271
$541$	11.7477	0.505072	0.252536	−	0.967588i	$-0.418735\pi$
$541$	11.7477	0.505072	0.252536	+	0.967588i	$0.418735\pi$
$542$	−0.269699	−0.0115846
$543$	−4.72314	−0.202689
$544$	3.05989	0.131192
$545$	−0.711898	−0.0304944
$546$	−1.10821	−0.0474270
$547$	25.4968	1.09017	0.545083	−	0.838382i	$-0.316498\pi$
$547$	25.4968	1.09017	0.545083	+	0.838382i	$0.316498\pi$
$548$	−4.92632	−0.210442
$549$	35.6335	1.52080
$550$	21.1242	0.900739
$551$	−4.00049	−0.170426
$552$	−0.100799	−0.00429028
$553$	4.52394	0.192378
$554$	6.75257	0.286889
$555$	0.204868	0.00869614
$556$	−16.8290	−0.713707
$557$	−17.3617	−0.735641	−0.367820	−	0.929897i	$-0.619896\pi$
$557$	−17.3617	−0.735641	−0.367820	+	0.929897i	$0.619896\pi$
$558$	−27.8170	−1.17759
$559$	−67.5055	−2.85518
$560$	−0.255818	−0.0108103
$561$	−2.35364	−0.0993708
$562$	−12.3044	−0.519029
$563$	15.6627	0.660105	0.330053	−	0.943963i	$-0.392933\pi$
$563$	15.6627	0.660105	0.330053	+	0.943963i	$0.392933\pi$
$564$	−1.13996	−0.0480009
$565$	−1.17980	−0.0496344
$566$	21.2192	0.891908
$567$	−9.69838	−0.407294
$568$	8.20192	0.344145
$569$	33.3860	1.39962	0.699808	−	0.714331i	$-0.253269\pi$
$569$	33.3860	1.39962	0.699808	+	0.714331i	$0.253269\pi$
$570$	0.0413825	0.00173332
$571$	7.59220	0.317724	0.158862	−	0.987301i	$-0.449218\pi$
$571$	7.59220	0.317724	0.158862	+	0.987301i	$0.449218\pi$
$572$	−23.5881	−0.986268
$573$	0.716646	0.0299383
$574$	11.2764	0.470668
$575$	2.76822	0.115443
$576$	−2.96755	−0.123648
$577$	−21.1446	−0.880262	−0.440131	−	0.897934i	$-0.645068\pi$
$577$	−21.1446	−0.880262	−0.440131	+	0.897934i	$0.645068\pi$
$578$	−7.63708	−0.317661
$579$	−3.51138	−0.145928
$580$	−0.918994	−0.0381592
$581$	−4.80152	−0.199201
$582$	−0.482160	−0.0199862
$583$	2.66164	0.110234
$584$	15.2736	0.632028
$585$	−3.76593	−0.155702
$586$	−4.08543	−0.168768
$587$	34.8324	1.43769	0.718844	−	0.695172i	$-0.244672\pi$
$587$	34.8324	1.43769	0.718844	+	0.695172i	$0.244672\pi$
$588$	−1.03760	−0.0427899
$589$	9.37372	0.386237
$590$	0.655807	0.0269991
$591$	0.0799695	0.00328951
$592$	4.95059	0.203468
$593$	9.49659	0.389978	0.194989	−	0.980805i	$-0.437533\pi$
$593$	9.49659	0.389978	0.194989	+	0.980805i	$0.437533\pi$
$594$	4.59019	0.188338
$595$	−0.782775	−0.0320907
$596$	−19.6430	−0.804609
$597$	−0.198160	−0.00811016
$598$	−3.09110	−0.126404
$599$	2.83024	0.115641	0.0578203	−	0.998327i	$-0.481585\pi$
$599$	2.83024	0.115641	0.0578203	+	0.998327i	$0.481585\pi$
$600$	−0.891207	−0.0363834
$601$	15.2341	0.621411	0.310705	−	0.950506i	$-0.399435\pi$
$601$	15.2341	0.621411	0.310705	+	0.950506i	$0.399435\pi$
$602$	13.6081	0.554623
$603$	27.5015	1.11995
$604$	−8.52109	−0.346718
$605$	1.66136	0.0675440
$606$	−0.272894	−0.0110855
$607$	7.71824	0.313274	0.156637	−	0.987656i	$-0.449935\pi$
$607$	7.71824	0.313274	0.156637	+	0.987656i	$0.449935\pi$
$608$	1.00000	0.0405554
$609$	0.802529	0.0325201
$610$	−2.75842	−0.111685
$611$	−34.9580	−1.41425
$612$	−9.08037	−0.367052
$613$	−14.0496	−0.567458	−0.283729	−	0.958904i	$-0.591572\pi$
$613$	−14.0496	−0.567458	−0.283729	+	0.958904i	$0.591572\pi$
$614$	−2.86108	−0.115464
$615$	−0.419040	−0.0168973
$616$	4.75499	0.191584
$617$	24.6093	0.990732	0.495366	−	0.868684i	$-0.335034\pi$
$617$	24.6093	0.990732	0.495366	+	0.868684i	$0.335034\pi$
$618$	1.20902	0.0486341
$619$	25.3138	1.01745	0.508723	−	0.860930i	$-0.330118\pi$
$619$	25.3138	1.01745	0.508723	+	0.860930i	$0.330118\pi$
$620$	2.15334	0.0864801
$621$	0.601521	0.0241382
$622$	−7.66583	−0.307372
$623$	2.56495	0.102763
$624$	0.995156	0.0398381
$625$	24.2112	0.968448
$626$	−4.17760	−0.166970
$627$	−0.769192	−0.0307186
$628$	−8.73492	−0.348561
$629$	15.1482	0.604000
$630$	0.759153	0.0302454
$631$	47.2848	1.88238	0.941190	−	0.337878i	$-0.109709\pi$
$631$	47.2848	1.88238	0.941190	+	0.337878i	$0.109709\pi$
$632$	−4.06243	−0.161595
$633$	−0.180143	−0.00716003
$634$	28.2365	1.12142
$635$	−2.87703	−0.114171
$636$	−0.112292	−0.00445265
$637$	−31.8191	−1.26072
$638$	17.0817	0.676271
$639$	−24.3396	−0.962860
$640$	0.229721	0.00908051
$641$	0.909587	0.0359265	0.0179633	−	0.999839i	$-0.494282\pi$
$641$	0.909587	0.0359265	0.0179633	+	0.999839i	$0.494282\pi$
$642$	3.24822	0.128197
$643$	−34.6847	−1.36783	−0.683915	−	0.729562i	$-0.739724\pi$
$643$	−34.6847	−1.36783	−0.683915	+	0.729562i	$0.739724\pi$
$644$	0.623117	0.0245543
$645$	−0.505686	−0.0199114
$646$	3.05989	0.120390
$647$	0.935069	0.0367614	0.0183807	−	0.999831i	$-0.494149\pi$
$647$	0.935069	0.0367614	0.0183807	+	0.999831i	$0.494149\pi$
$648$	8.70899	0.342121
$649$	−12.1897	−0.478489
$650$	−27.3298	−1.07196
$651$	−1.88044	−0.0737003
$652$	−5.89902	−0.231024
$653$	−12.8674	−0.503540	−0.251770	−	0.967787i	$-0.581013\pi$
$653$	−12.8674	−0.503540	−0.251770	+	0.967787i	$0.581013\pi$
$654$	−0.558257	−0.0218296
$655$	−0.591566	−0.0231144
$656$	−10.1260	−0.395355
$657$	−45.3253	−1.76831
$658$	7.04699	0.274720
$659$	−3.02116	−0.117688	−0.0588439	−	0.998267i	$-0.518741\pi$
$659$	−3.02116	−0.117688	−0.0588439	+	0.998267i	$0.518741\pi$
$660$	−0.176699	−0.00687801
$661$	34.2100	1.33061	0.665307	−	0.746570i	$-0.268301\pi$
$661$	34.2100	1.33061	0.665307	+	0.746570i	$0.268301\pi$
$662$	−20.2332	−0.786385
$663$	3.04507	0.118261
$664$	4.31169	0.167326
$665$	−0.255818	−0.00992020
$666$	−14.6911	−0.569269
$667$	2.23847	0.0866739
$668$	4.96906	0.192259
$669$	−3.67332	−0.142019
$670$	−2.12892	−0.0822472
$671$	51.2719	1.97933
$672$	−0.200608	−0.00773862
$673$	−4.36989	−0.168447	−0.0842234	−	0.996447i	$-0.526841\pi$
$673$	−4.36989	−0.168447	−0.0842234	+	0.996447i	$0.526841\pi$
$674$	−26.6353	−1.02595
$675$	5.31832	0.204702
$676$	17.5175	0.673750
$677$	27.0152	1.03828	0.519140	−	0.854689i	$-0.326252\pi$
$677$	27.0152	1.03828	0.519140	+	0.854689i	$0.326252\pi$
$678$	−0.925175	−0.0355311
$679$	2.98062	0.114386
$680$	0.702920	0.0269557
$681$	2.70966	0.103834
$682$	−40.0249	−1.53263
$683$	17.6562	0.675595	0.337797	−	0.941219i	$-0.390318\pi$
$683$	17.6562	0.675595	0.337797	+	0.941219i	$0.390318\pi$
$684$	−2.96755	−0.113467
$685$	−1.13168	−0.0432392
$686$	14.2095	0.542520
$687$	−2.62716	−0.100233
$688$	−12.2198	−0.465876
$689$	−3.44354	−0.131188
$690$	−0.0231555	−0.000881516 0
$691$	−20.7315	−0.788664	−0.394332	−	0.918968i	$-0.629024\pi$
$691$	−20.7315	−0.788664	−0.394332	+	0.918968i	$0.629024\pi$
$692$	−16.4703	−0.626108
$693$	−14.1107	−0.536020
$694$	−6.57563	−0.249608
$695$	−3.86596	−0.146644
$696$	−0.720658	−0.0273165
$697$	−30.9845	−1.17362
$698$	−13.3044	−0.503579
$699$	3.18055	0.120300
$700$	5.50926	0.208231
$701$	−17.2579	−0.651820	−0.325910	−	0.945401i	$-0.605671\pi$
$701$	−17.2579	−0.651820	−0.325910	+	0.945401i	$0.605671\pi$
$702$	−5.93864	−0.224140
$703$	4.95059	0.186715
$704$	−4.26991	−0.160928
$705$	−0.261872	−0.00986266
$706$	−8.67801	−0.326601
$707$	1.68697	0.0634452
$708$	0.514271	0.0193275
$709$	−38.7954	−1.45699	−0.728497	−	0.685049i	$-0.759781\pi$
$709$	−38.7954	−1.45699	−0.728497	+	0.685049i	$0.759781\pi$
$710$	1.88415	0.0707109
$711$	12.0554	0.452115
$712$	−2.30328	−0.0863192
$713$	−5.24506	−0.196429
$714$	−0.613838	−0.0229723
$715$	−5.41867	−0.202647
$716$	0.150726	0.00563289
$717$	0.768856	0.0287135
$718$	7.49472	0.279701
$719$	−18.4676	−0.688727	−0.344364	−	0.938836i	$-0.611905\pi$
$719$	−18.4676	−0.688727	−0.344364	+	0.938836i	$0.611905\pi$
$720$	−0.681707	−0.0254057
$721$	−7.47395	−0.278344
$722$	1.00000	0.0372161
$723$	−3.45926	−0.128651
$724$	−26.2189	−0.974418
$725$	19.7913	0.735031
$726$	1.30281	0.0483518
$727$	−3.11969	−0.115703	−0.0578514	−	0.998325i	$-0.518425\pi$
$727$	−3.11969	−0.115703	−0.0578514	+	0.998325i	$0.518425\pi$
$728$	−6.15185	−0.228003
$729$	−25.2634	−0.935681
$730$	3.50867	0.129862
$731$	−37.3913	−1.38297
$732$	−2.16310	−0.0799506
$733$	52.9978	1.95752	0.978759	−	0.205012i	$-0.0657233\pi$
$733$	52.9978	1.95752	0.978759	+	0.205012i	$0.0657233\pi$
$734$	−11.4329	−0.421997
$735$	−0.238358	−0.00879197
$736$	−0.559549	−0.0206253
$737$	39.5710	1.45762
$738$	30.0495	1.10614
$739$	7.47621	0.275017	0.137508	−	0.990501i	$-0.456091\pi$
$739$	7.47621	0.275017	0.137508	+	0.990501i	$0.456091\pi$
$740$	1.13725	0.0418062
$741$	0.995156	0.0365580
$742$	0.694164	0.0254836
$743$	−46.1925	−1.69464	−0.847318	−	0.531085i	$-0.821784\pi$
$743$	−46.1925	−1.69464	−0.847318	+	0.531085i	$0.821784\pi$
$744$	1.68861	0.0619073
$745$	−4.51240	−0.165322
$746$	22.2220	0.813606
$747$	−12.7952	−0.468150
$748$	−13.0654	−0.477720
$749$	−20.0798	−0.733701
$750$	−0.411641	−0.0150310
$751$	16.1242	0.588380	0.294190	−	0.955747i	$-0.404950\pi$
$751$	16.1242	0.588380	0.294190	+	0.955747i	$0.404950\pi$
$752$	−6.32808	−0.230761
$753$	0.262725	0.00957422
$754$	−22.0998	−0.804825
$755$	−1.95747	−0.0712397
$756$	1.19714	0.0435395
$757$	31.3916	1.14095	0.570474	−	0.821316i	$-0.306760\pi$
$757$	31.3916	1.14095	0.570474	+	0.821316i	$0.306760\pi$
$758$	−12.2328	−0.444316
$759$	0.430401	0.0156226
$760$	0.229721	0.00833284
$761$	12.4286	0.450537	0.225268	−	0.974297i	$-0.427674\pi$
$761$	12.4286	0.450537	0.225268	+	0.974297i	$0.427674\pi$
$762$	−2.25611	−0.0817303
$763$	3.45103	0.124936
$764$	3.97821	0.143927
$765$	−2.08595	−0.0754176
$766$	−31.6357	−1.14304
$767$	15.7707	0.569446
$768$	0.180143	0.00650034
$769$	23.4742	0.846500	0.423250	−	0.906013i	$-0.360889\pi$
$769$	23.4742	0.846500	0.423250	+	0.906013i	$0.360889\pi$
$770$	1.09232	0.0393645
$771$	2.26649	0.0816255
$772$	−19.4922	−0.701540
$773$	49.3268	1.77416	0.887082	−	0.461613i	$-0.152729\pi$
$773$	49.3268	1.77416	0.887082	+	0.461613i	$0.152729\pi$
$774$	36.2629	1.30344
$775$	−46.3739	−1.66580
$776$	−2.67655	−0.0960825
$777$	−0.993126	−0.0356282
$778$	−33.3039	−1.19400
$779$	−10.1260	−0.362803
$780$	0.228608	0.00818547
$781$	−35.0214	−1.25317
$782$	−1.71216	−0.0612266
$783$	4.30056	0.153690
$784$	−5.75988	−0.205710
$785$	−2.00659	−0.0716183
$786$	−0.463895	−0.0165466
$787$	10.4308	0.371818	0.185909	−	0.982567i	$-0.440477\pi$
$787$	10.4308	0.371818	0.185909	+	0.982567i	$0.440477\pi$
$788$	0.443923	0.0158141
$789$	4.94645	0.176098
$790$	−0.933223	−0.0332026
$791$	5.71924	0.203353
$792$	12.6712	0.450250
$793$	−66.3339	−2.35559
$794$	−17.2426	−0.611916
$795$	−0.0257957	−0.000914878 0
$796$	−1.10002	−0.0389892
$797$	8.25571	0.292432	0.146216	−	0.989253i	$-0.453291\pi$
$797$	8.25571	0.292432	0.146216	+	0.989253i	$0.453291\pi$
$798$	−0.200608	−0.00710144
$799$	−19.3632	−0.685022
$800$	−4.94723	−0.174911
$801$	6.83511	0.241507
$802$	3.51519	0.124126
$803$	−65.2171	−2.30146
$804$	−1.66946	−0.0588772
$805$	0.143143	0.00504512
$806$	51.7829	1.82397
$807$	−0.146524	−0.00515788
$808$	−1.51488	−0.0532932
$809$	−4.02957	−0.141672	−0.0708361	−	0.997488i	$-0.522567\pi$
$809$	−4.02957	−0.141672	−0.0708361	+	0.997488i	$0.522567\pi$
$810$	2.00064	0.0702951
$811$	−7.86026	−0.276011	−0.138006	−	0.990431i	$-0.544069\pi$
$811$	−7.86026	−0.276011	−0.138006	+	0.990431i	$0.544069\pi$
$812$	4.45496	0.156339
$813$	−0.0485843	−0.00170392
$814$	−21.1385	−0.740905
$815$	−1.35513	−0.0474680
$816$	0.551216	0.0192964
$817$	−12.2198	−0.427517
$818$	3.69626	0.129237
$819$	18.2559	0.637914
$820$	−2.32616	−0.0812330
$821$	−28.1334	−0.981864	−0.490932	−	0.871198i	$-0.663344\pi$
$821$	−28.1334	−0.981864	−0.490932	+	0.871198i	$0.663344\pi$
$822$	−0.887440	−0.0309530
$823$	14.5052	0.505621	0.252810	−	0.967516i	$-0.418645\pi$
$823$	14.5052	0.505621	0.252810	+	0.967516i	$0.418645\pi$
$824$	6.71149	0.233806
$825$	3.80537	0.132486
$826$	−3.17912	−0.110616
$827$	1.43755	0.0499886	0.0249943	−	0.999688i	$-0.492043\pi$
$827$	1.43755	0.0499886	0.0249943	+	0.999688i	$0.492043\pi$
$828$	1.66049	0.0577060
$829$	−3.82894	−0.132984	−0.0664922	−	0.997787i	$-0.521181\pi$
$829$	−3.82894	−0.132984	−0.0664922	+	0.997787i	$0.521181\pi$
$830$	0.990484	0.0343802
$831$	1.21643	0.0421974
$832$	5.52427	0.191519
$833$	−17.6246	−0.610656
$834$	−3.03161	−0.104976
$835$	1.14150	0.0395031
$836$	−4.26991	−0.147678
$837$	−10.0768	−0.348306
$838$	6.28854	0.217234
$839$	−5.82105	−0.200965	−0.100482	−	0.994939i	$-0.532039\pi$
$839$	−5.82105	−0.200965	−0.100482	+	0.994939i	$0.532039\pi$
$840$	−0.0460838	−0.00159004
$841$	−12.9961	−0.448142
$842$	30.0515	1.03564
$843$	−2.21654	−0.0763418
$844$	−1.00000	−0.0344214
$845$	4.02413	0.138434
$846$	18.7789	0.645632
$847$	−8.05371	−0.276729
$848$	−0.623348	−0.0214059
$849$	3.82248	0.131187
$850$	−15.1380	−0.519228
$851$	−2.77010	−0.0949577
$852$	1.47752	0.0506188
$853$	−14.0942	−0.482576	−0.241288	−	0.970454i	$-0.577570\pi$
$853$	−14.0942	−0.482576	−0.241288	+	0.970454i	$0.577570\pi$
$854$	13.3719	0.457576
$855$	−0.681707	−0.0233139
$856$	18.0314	0.616299
$857$	−2.59336	−0.0885875	−0.0442938	−	0.999019i	$-0.514104\pi$
$857$	−2.59336	−0.0885875	−0.0442938	+	0.999019i	$0.514104\pi$
$858$	−4.24922	−0.145066
$859$	−48.2396	−1.64592	−0.822958	−	0.568103i	$-0.807678\pi$
$859$	−48.2396	−1.64592	−0.822958	+	0.568103i	$0.807678\pi$
$860$	−2.80715	−0.0957229
$861$	2.03136	0.0692286
$862$	−2.18952	−0.0745755
$863$	−27.8447	−0.947845	−0.473922	−	0.880567i	$-0.657162\pi$
$863$	−27.8447	−0.947845	−0.473922	+	0.880567i	$0.657162\pi$
$864$	−1.07501	−0.0365726
$865$	−3.78358	−0.128645
$866$	18.0306	0.612705
$867$	−1.37576	−0.0467234
$868$	−10.4386	−0.354310
$869$	17.3462	0.588429
$870$	−0.165550	−0.00561267
$871$	−51.1957	−1.73470
$872$	−3.09897	−0.104944
$873$	7.94279	0.268823
$874$	−0.559549	−0.0189270
$875$	2.54468	0.0860260
$876$	2.75144	0.0929624
$877$	29.6613	1.00159	0.500795	−	0.865566i	$-0.333041\pi$
$877$	29.6613	1.00159	0.500795	+	0.865566i	$0.333041\pi$
$878$	−28.5483	−0.963458
$879$	−0.735960	−0.0248233
$880$	−0.980886	−0.0330656
$881$	−0.579311	−0.0195175	−0.00975874	−	0.999952i	$-0.503106\pi$
$881$	−0.579311	−0.0195175	−0.00975874	+	0.999952i	$0.503106\pi$
$882$	17.0927	0.575542
$883$	46.2508	1.55646	0.778232	−	0.627977i	$-0.216117\pi$
$883$	46.2508	1.55646	0.778232	+	0.627977i	$0.216117\pi$
$884$	16.9036	0.568531
$885$	0.118139	0.00397119
$886$	21.4218	0.719678
$887$	58.8398	1.97565	0.987824	−	0.155575i	$-0.0497229\pi$
$887$	58.8398	1.97565	0.987824	+	0.155575i	$0.0497229\pi$
$888$	0.891811	0.0299272
$889$	13.9468	0.467762
$890$	−0.529112	−0.0177359
$891$	−37.1866	−1.24580
$892$	−20.3912	−0.682748
$893$	−6.32808	−0.211761
$894$	−3.53854	−0.118347
$895$	0.0346248	0.00115738
$896$	−1.11361	−0.0372030
$897$	−0.556838	−0.0185923
$898$	18.6241	0.621494
$899$	−37.4994	−1.25068
$900$	14.6811	0.489371
$901$	−1.90737	−0.0635439
$902$	43.2372	1.43964
$903$	2.45139	0.0815772
$904$	−5.13579	−0.170814
$905$	−6.02302	−0.200212
$906$	−1.53501	−0.0509973
$907$	39.6193	1.31554	0.657768	−	0.753221i	$-0.271501\pi$
$907$	39.6193	1.31554	0.657768	+	0.753221i	$0.271501\pi$
$908$	15.0417	0.499178
$909$	4.49547	0.149105
$910$	−1.41321	−0.0468474
$911$	17.3758	0.575687	0.287843	−	0.957677i	$-0.407062\pi$
$911$	17.3758	0.575687	0.287843	+	0.957677i	$0.407062\pi$
$912$	0.180143	0.00596512
$913$	−18.4105	−0.609299
$914$	−10.6850	−0.353430
$915$	−0.496910	−0.0164273
$916$	−14.5838	−0.481862
$917$	2.86771	0.0947000
$918$	−3.28941	−0.108567
$919$	52.2347	1.72306	0.861532	−	0.507703i	$-0.169505\pi$
$919$	52.2347	1.72306	0.861532	+	0.507703i	$0.169505\pi$
$920$	−0.128540	−0.00423784
$921$	−0.515402	−0.0169831
$922$	−17.8639	−0.588315
$923$	45.3096	1.49138
$924$	0.856577	0.0281793
$925$	−24.4917	−0.805281
$926$	34.8728	1.14599
$927$	−19.9167	−0.654149
$928$	−4.00049	−0.131322
$929$	3.72749	0.122295	0.0611474	−	0.998129i	$-0.480524\pi$
$929$	3.72749	0.122295	0.0611474	+	0.998129i	$0.480524\pi$
$930$	0.387908	0.0127200
$931$	−5.75988	−0.188773
$932$	17.6557	0.578333
$933$	−1.38094	−0.0452101
$934$	27.8937	0.912711
$935$	−3.00140	−0.0981563
$936$	−16.3935	−0.535839
$937$	8.87541	0.289947	0.144974	−	0.989436i	$-0.453690\pi$
$937$	8.87541	0.289947	0.144974	+	0.989436i	$0.453690\pi$
$938$	10.3202	0.336968
$939$	−0.752563	−0.0245590
$940$	−1.45369	−0.0474142
$941$	49.6865	1.61973	0.809867	−	0.586614i	$-0.199539\pi$
$941$	49.6865	1.61973	0.809867	+	0.586614i	$0.199539\pi$
$942$	−1.57353	−0.0512684
$943$	5.66601	0.184511
$944$	2.85480	0.0929159
$945$	0.275007	0.00894598
$946$	52.1775	1.69644
$947$	21.3104	0.692495	0.346248	−	0.938143i	$-0.387456\pi$
$947$	21.3104	0.692495	0.346248	+	0.938143i	$0.387456\pi$
$948$	−0.731816	−0.0237683
$949$	84.3757	2.73895
$950$	−4.94723	−0.160509
$951$	5.08660	0.164944
$952$	−3.40751	−0.110438
$953$	25.2963	0.819429	0.409715	−	0.912214i	$-0.365628\pi$
$953$	25.2963	0.819429	0.409715	+	0.912214i	$0.365628\pi$
$954$	1.84982	0.0598900
$955$	0.913878	0.0295724
$956$	4.26804	0.138038
$957$	3.07714	0.0994699
$958$	32.8962	1.06283
$959$	5.48598	0.177152
$960$	0.0413825	0.00133561
$961$	56.8666	1.83441
$962$	27.3484	0.881746
$963$	−53.5089	−1.72430
$964$	−19.2029	−0.618483
$965$	−4.47777	−0.144144
$966$	0.112250	0.00361158
$967$	26.3850	0.848483	0.424241	−	0.905549i	$-0.360541\pi$
$967$	26.3850	0.848483	0.424241	+	0.905549i	$0.360541\pi$
$968$	7.23210	0.232449
$969$	0.551216	0.0177076
$970$	−0.614858	−0.0197419
$971$	−36.0319	−1.15632	−0.578160	−	0.815924i	$-0.696229\pi$
$971$	−36.0319	−1.15632	−0.578160	+	0.815924i	$0.696229\pi$
$972$	4.79389	0.153764
$973$	18.7408	0.600804
$974$	−40.1341	−1.28598
$975$	−4.92326	−0.157671
$976$	−12.0077	−0.384358
$977$	−10.8656	−0.347620	−0.173810	−	0.984779i	$-0.555608\pi$
$977$	−10.8656	−0.347620	−0.173810	+	0.984779i	$0.555608\pi$
$978$	−1.06267	−0.0339803
$979$	9.83481	0.314322
$980$	−1.32316	−0.0422669
$981$	9.19635	0.293617
$982$	22.5398	0.719273
$983$	−40.6673	−1.29708	−0.648542	−	0.761179i	$-0.724621\pi$
$983$	−40.6673	−1.29708	−0.648542	+	0.761179i	$0.724621\pi$
$984$	−1.82413	−0.0581512
$985$	0.101978	0.00324930
$986$	−12.2410	−0.389834
$987$	1.26946	0.0404075
$988$	5.52427	0.175750
$989$	6.83759	0.217423
$990$	2.91083	0.0925121
$991$	−6.98112	−0.221763	−0.110881	−	0.993834i	$-0.535367\pi$
$991$	−6.98112	−0.221763	−0.110881	+	0.993834i	$0.535367\pi$
$992$	9.37372	0.297616
$993$	−3.64486	−0.115666
$994$	−9.13371	−0.289704
$995$	−0.252697	−0.00801104
$996$	0.776719	0.0246113
$997$	−4.59083	−0.145393	−0.0726966	−	0.997354i	$-0.523160\pi$
$997$	−4.59083	−0.145393	−0.0726966	+	0.997354i	$0.523160\pi$
$998$	3.63815	0.115164
$999$	−5.32193	−0.168378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.17	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.17	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.180143 q^{3} +1.00000 q^{4} +0.229721 q^{5} +0.180143 q^{6} -1.11361 q^{7} +1.00000 q^{8} -2.96755 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.180143 q^{3} +1.00000 q^{4} +0.229721 q^{5} +0.180143 q^{6} -1.11361 q^{7} +1.00000 q^{8} -2.96755 q^{9} +0.229721 q^{10} -4.26991 q^{11} +0.180143 q^{12} +5.52427 q^{13} -1.11361 q^{14} +0.0413825 q^{15} +1.00000 q^{16} +3.05989 q^{17} -2.96755 q^{18} +1.00000 q^{19} +0.229721 q^{20} -0.200608 q^{21} -4.26991 q^{22} -0.559549 q^{23} +0.180143 q^{24} -4.94723 q^{25} +5.52427 q^{26} -1.07501 q^{27} -1.11361 q^{28} -4.00049 q^{29} +0.0413825 q^{30} +9.37372 q^{31} +1.00000 q^{32} -0.769192 q^{33} +3.05989 q^{34} -0.255818 q^{35} -2.96755 q^{36} +4.95059 q^{37} +1.00000 q^{38} +0.995156 q^{39} +0.229721 q^{40} -10.1260 q^{41} -0.200608 q^{42} -12.2198 q^{43} -4.26991 q^{44} -0.681707 q^{45} -0.559549 q^{46} -6.32808 q^{47} +0.180143 q^{48} -5.75988 q^{49} -4.94723 q^{50} +0.551216 q^{51} +5.52427 q^{52} -0.623348 q^{53} -1.07501 q^{54} -0.980886 q^{55} -1.11361 q^{56} +0.180143 q^{57} -4.00049 q^{58} +2.85480 q^{59} +0.0413825 q^{60} -12.0077 q^{61} +9.37372 q^{62} +3.30468 q^{63} +1.00000 q^{64} +1.26904 q^{65} -0.769192 q^{66} -9.26742 q^{67} +3.05989 q^{68} -0.100799 q^{69} -0.255818 q^{70} +8.20192 q^{71} -2.96755 q^{72} +15.2736 q^{73} +4.95059 q^{74} -0.891207 q^{75} +1.00000 q^{76} +4.75499 q^{77} +0.995156 q^{78} -4.06243 q^{79} +0.229721 q^{80} +8.70899 q^{81} -10.1260 q^{82} +4.31169 q^{83} -0.200608 q^{84} +0.702920 q^{85} -12.2198 q^{86} -0.720658 q^{87} -4.26991 q^{88} -2.30328 q^{89} -0.681707 q^{90} -6.15185 q^{91} -0.559549 q^{92} +1.68861 q^{93} -6.32808 q^{94} +0.229721 q^{95} +0.180143 q^{96} -2.67655 q^{97} -5.75988 q^{98} +12.6712 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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