LMFDB - Embedded newform 8018.2.a.d.1.13

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			1.13
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.894762 q^{3} +1.00000 q^{4} -0.0669598 q^{5} -0.894762 q^{6} +1.42997 q^{7} +1.00000 q^{8} -2.19940 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.894762 q^{3} +1.00000 q^{4} -0.0669598 q^{5} -0.894762 q^{6} +1.42997 q^{7} +1.00000 q^{8} -2.19940 q^{9} -0.0669598 q^{10} -3.23328 q^{11} -0.894762 q^{12} +4.17646 q^{13} +1.42997 q^{14} +0.0599131 q^{15} +1.00000 q^{16} -0.463825 q^{17} -2.19940 q^{18} +1.00000 q^{19} -0.0669598 q^{20} -1.27948 q^{21} -3.23328 q^{22} -2.96000 q^{23} -0.894762 q^{24} -4.99552 q^{25} +4.17646 q^{26} +4.65223 q^{27} +1.42997 q^{28} +5.89722 q^{29} +0.0599131 q^{30} -5.02580 q^{31} +1.00000 q^{32} +2.89302 q^{33} -0.463825 q^{34} -0.0957506 q^{35} -2.19940 q^{36} -5.53876 q^{37} +1.00000 q^{38} -3.73694 q^{39} -0.0669598 q^{40} +3.26660 q^{41} -1.27948 q^{42} +0.640662 q^{43} -3.23328 q^{44} +0.147271 q^{45} -2.96000 q^{46} +0.940223 q^{47} -0.894762 q^{48} -4.95518 q^{49} -4.99552 q^{50} +0.415013 q^{51} +4.17646 q^{52} -11.0185 q^{53} +4.65223 q^{54} +0.216500 q^{55} +1.42997 q^{56} -0.894762 q^{57} +5.89722 q^{58} +3.02758 q^{59} +0.0599131 q^{60} +11.8105 q^{61} -5.02580 q^{62} -3.14508 q^{63} +1.00000 q^{64} -0.279655 q^{65} +2.89302 q^{66} -7.46996 q^{67} -0.463825 q^{68} +2.64850 q^{69} -0.0957506 q^{70} -2.88742 q^{71} -2.19940 q^{72} -11.7213 q^{73} -5.53876 q^{74} +4.46980 q^{75} +1.00000 q^{76} -4.62350 q^{77} -3.73694 q^{78} +13.6699 q^{79} -0.0669598 q^{80} +2.43557 q^{81} +3.26660 q^{82} +1.25135 q^{83} -1.27948 q^{84} +0.0310576 q^{85} +0.640662 q^{86} -5.27661 q^{87} -3.23328 q^{88} -3.46503 q^{89} +0.147271 q^{90} +5.97222 q^{91} -2.96000 q^{92} +4.49690 q^{93} +0.940223 q^{94} -0.0669598 q^{95} -0.894762 q^{96} -16.2444 q^{97} -4.95518 q^{98} +7.11129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.894762	−0.516591	−0.258296	−	0.966066i	$-0.583161\pi$
$3$	−0.894762	−0.516591	−0.258296	+	0.966066i	$0.583161\pi$
$4$	1.00000	0.500000
$5$	−0.0669598	−0.0299453	−0.0149727	−	0.999888i	$-0.504766\pi$
$5$	−0.0669598	−0.0299453	−0.0149727	+	0.999888i	$0.504766\pi$
$6$	−0.894762	−0.365285
$7$	1.42997	0.540479	0.270239	−	0.962793i	$-0.412897\pi$
$7$	1.42997	0.540479	0.270239	+	0.962793i	$0.412897\pi$
$8$	1.00000	0.353553
$9$	−2.19940	−0.733134
$10$	−0.0669598	−0.0211745
$11$	−3.23328	−0.974872	−0.487436	−	0.873159i	$-0.662068\pi$
$11$	−3.23328	−0.974872	−0.487436	+	0.873159i	$0.662068\pi$
$12$	−0.894762	−0.258296
$13$	4.17646	1.15834	0.579171	−	0.815206i	$-0.303376\pi$
$13$	4.17646	1.15834	0.579171	+	0.815206i	$0.303376\pi$
$14$	1.42997	0.382176
$15$	0.0599131	0.0154695
$16$	1.00000	0.250000
$17$	−0.463825	−0.112494	−0.0562471	−	0.998417i	$-0.517913\pi$
$17$	−0.463825	−0.112494	−0.0562471	+	0.998417i	$0.517913\pi$
$18$	−2.19940	−0.518404
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.0669598	−0.0149727
$21$	−1.27948	−0.279206
$22$	−3.23328	−0.689338
$23$	−2.96000	−0.617203	−0.308602	−	0.951191i	$-0.599861\pi$
$23$	−2.96000	−0.617203	−0.308602	+	0.951191i	$0.599861\pi$
$24$	−0.894762	−0.182643
$25$	−4.99552	−0.999103
$26$	4.17646	0.819071
$27$	4.65223	0.895321
$28$	1.42997	0.270239
$29$	5.89722	1.09509	0.547543	−	0.836778i	$-0.315563\pi$
$29$	5.89722	1.09509	0.547543	+	0.836778i	$0.315563\pi$
$30$	0.0599131	0.0109386
$31$	−5.02580	−0.902660	−0.451330	−	0.892357i	$-0.649050\pi$
$31$	−5.02580	−0.902660	−0.451330	+	0.892357i	$0.649050\pi$
$32$	1.00000	0.176777
$33$	2.89302	0.503610
$34$	−0.463825	−0.0795454
$35$	−0.0957506	−0.0161848
$36$	−2.19940	−0.366567
$37$	−5.53876	−0.910566	−0.455283	−	0.890347i	$-0.650462\pi$
$37$	−5.53876	−0.910566	−0.455283	+	0.890347i	$0.650462\pi$
$38$	1.00000	0.162221
$39$	−3.73694	−0.598389
$40$	−0.0669598	−0.0105873
$41$	3.26660	0.510157	0.255079	−	0.966920i	$-0.417899\pi$
$41$	3.26660	0.510157	0.255079	+	0.966920i	$0.417899\pi$
$42$	−1.27948	−0.197429
$43$	0.640662	0.0977000	0.0488500	−	0.998806i	$-0.484444\pi$
$43$	0.640662	0.0977000	0.0488500	+	0.998806i	$0.484444\pi$
$44$	−3.23328	−0.487436
$45$	0.147271	0.0219539
$46$	−2.96000	−0.436428
$47$	0.940223	0.137146	0.0685728	−	0.997646i	$-0.478155\pi$
$47$	0.940223	0.137146	0.0685728	+	0.997646i	$0.478155\pi$
$48$	−0.894762	−0.129148
$49$	−4.95518	−0.707883
$50$	−4.99552	−0.706473
$51$	0.415013	0.0581135
$52$	4.17646	0.579171
$53$	−11.0185	−1.51351	−0.756756	−	0.653698i	$-0.773217\pi$
$53$	−11.0185	−1.51351	−0.756756	+	0.653698i	$0.773217\pi$
$54$	4.65223	0.633088
$55$	0.216500	0.0291928
$56$	1.42997	0.191088
$57$	−0.894762	−0.118514
$58$	5.89722	0.774343
$59$	3.02758	0.394157	0.197079	−	0.980388i	$-0.436855\pi$
$59$	3.02758	0.394157	0.197079	+	0.980388i	$0.436855\pi$
$60$	0.0599131	0.00773474
$61$	11.8105	1.51218	0.756092	−	0.654465i	$-0.227106\pi$
$61$	11.8105	1.51218	0.756092	+	0.654465i	$0.227106\pi$
$62$	−5.02580	−0.638277
$63$	−3.14508	−0.396243
$64$	1.00000	0.125000
$65$	−0.279655	−0.0346869
$66$	2.89302	0.356106
$67$	−7.46996	−0.912601	−0.456301	−	0.889826i	$-0.650826\pi$
$67$	−7.46996	−0.912601	−0.456301	+	0.889826i	$0.650826\pi$
$68$	−0.463825	−0.0562471
$69$	2.64850	0.318842
$70$	−0.0957506	−0.0114444
$71$	−2.88742	−0.342674	−0.171337	−	0.985212i	$-0.554809\pi$
$71$	−2.88742	−0.342674	−0.171337	+	0.985212i	$0.554809\pi$
$72$	−2.19940	−0.259202
$73$	−11.7213	−1.37188	−0.685938	−	0.727660i	$-0.740608\pi$
$73$	−11.7213	−1.37188	−0.685938	+	0.727660i	$0.740608\pi$
$74$	−5.53876	−0.643867
$75$	4.46980	0.516128
$76$	1.00000	0.114708
$77$	−4.62350	−0.526897
$78$	−3.73694	−0.423125
$79$	13.6699	1.53798	0.768990	−	0.639261i	$-0.220760\pi$
$79$	13.6699	1.53798	0.768990	+	0.639261i	$0.220760\pi$
$80$	−0.0669598	−0.00748633
$81$	2.43557	0.270618
$82$	3.26660	0.360736
$83$	1.25135	0.137354	0.0686768	−	0.997639i	$-0.478122\pi$
$83$	1.25135	0.137354	0.0686768	+	0.997639i	$0.478122\pi$
$84$	−1.27948	−0.139603
$85$	0.0310576	0.00336867
$86$	0.640662	0.0690844
$87$	−5.27661	−0.565712
$88$	−3.23328	−0.344669
$89$	−3.46503	−0.367292	−0.183646	−	0.982992i	$-0.558790\pi$
$89$	−3.46503	−0.367292	−0.183646	+	0.982992i	$0.558790\pi$
$90$	0.147271	0.0155238
$91$	5.97222	0.626059
$92$	−2.96000	−0.308602
$93$	4.49690	0.466306
$94$	0.940223	0.0969766
$95$	−0.0669598	−0.00686993
$96$	−0.894762	−0.0913213
$97$	−16.2444	−1.64937	−0.824684	−	0.565593i	$-0.808647\pi$
$97$	−16.2444	−1.64937	−0.824684	+	0.565593i	$0.808647\pi$
$98$	−4.95518	−0.500549
$99$	7.11129	0.714711
$100$	−4.99552	−0.499552
$101$	0.143986	0.0143271	0.00716355	−	0.999974i	$-0.497720\pi$
$101$	0.143986	0.0143271	0.00716355	+	0.999974i	$0.497720\pi$
$102$	0.415013	0.0410924
$103$	−17.1246	−1.68734	−0.843669	−	0.536864i	$-0.819609\pi$
$103$	−17.1246	−1.68734	−0.843669	+	0.536864i	$0.819609\pi$
$104$	4.17646	0.409536
$105$	0.0856740	0.00836092
$106$	−11.0185	−1.07021
$107$	3.36857	0.325652	0.162826	−	0.986655i	$-0.447939\pi$
$107$	3.36857	0.325652	0.162826	+	0.986655i	$0.447939\pi$
$108$	4.65223	0.447661
$109$	2.29513	0.219834	0.109917	−	0.993941i	$-0.464941\pi$
$109$	2.29513	0.219834	0.109917	+	0.993941i	$0.464941\pi$
$110$	0.216500	0.0206425
$111$	4.95587	0.470390
$112$	1.42997	0.135120
$113$	4.15323	0.390703	0.195352	−	0.980733i	$-0.437415\pi$
$113$	4.15323	0.390703	0.195352	+	0.980733i	$0.437415\pi$
$114$	−0.894762	−0.0838021
$115$	0.198201	0.0184823
$116$	5.89722	0.547543
$117$	−9.18571	−0.849219
$118$	3.02758	0.278711
$119$	−0.663257	−0.0608007
$120$	0.0599131	0.00546929
$121$	−0.545879	−0.0496254
$122$	11.8105	1.06928
$123$	−2.92283	−0.263543
$124$	−5.02580	−0.451330
$125$	0.669297	0.0598638
$126$	−3.14508	−0.280186
$127$	5.73201	0.508634	0.254317	−	0.967121i	$-0.418149\pi$
$127$	5.73201	0.508634	0.254317	+	0.967121i	$0.418149\pi$
$128$	1.00000	0.0883883
$129$	−0.573240	−0.0504710
$130$	−0.279655	−0.0245274
$131$	−21.0961	−1.84318	−0.921589	−	0.388167i	$-0.873108\pi$
$131$	−21.0961	−1.84318	−0.921589	+	0.388167i	$0.873108\pi$
$132$	2.89302	0.251805
$133$	1.42997	0.123994
$134$	−7.46996	−0.645306
$135$	−0.311512	−0.0268107
$136$	−0.463825	−0.0397727
$137$	10.7451	0.918019	0.459009	−	0.888431i	$-0.348204\pi$
$137$	10.7451	0.918019	0.459009	+	0.888431i	$0.348204\pi$
$138$	2.64850	0.225455
$139$	−2.46250	−0.208867	−0.104433	−	0.994532i	$-0.533303\pi$
$139$	−2.46250	−0.208867	−0.104433	+	0.994532i	$0.533303\pi$
$140$	−0.0957506	−0.00809240
$141$	−0.841276	−0.0708482
$142$	−2.88742	−0.242307
$143$	−13.5037	−1.12923
$144$	−2.19940	−0.183283
$145$	−0.394876	−0.0327927
$146$	−11.7213	−0.970063
$147$	4.43371	0.365686
$148$	−5.53876	−0.455283
$149$	9.41318	0.771157	0.385579	−	0.922675i	$-0.374002\pi$
$149$	9.41318	0.771157	0.385579	+	0.922675i	$0.374002\pi$
$150$	4.46980	0.364958
$151$	10.1727	0.827839	0.413920	−	0.910313i	$-0.364159\pi$
$151$	10.1727	0.827839	0.413920	+	0.910313i	$0.364159\pi$
$152$	1.00000	0.0811107
$153$	1.02014	0.0824732
$154$	−4.62350	−0.372573
$155$	0.336526	0.0270304
$156$	−3.73694	−0.299195
$157$	−17.5166	−1.39797	−0.698987	−	0.715135i	$-0.746365\pi$
$157$	−17.5166	−1.39797	−0.698987	+	0.715135i	$0.746365\pi$
$158$	13.6699	1.08752
$159$	9.85896	0.781867
$160$	−0.0669598	−0.00529363
$161$	−4.23272	−0.333585
$162$	2.43557	0.191356
$163$	4.95308	0.387955	0.193977	−	0.981006i	$-0.437861\pi$
$163$	4.95308	0.387955	0.193977	+	0.981006i	$0.437861\pi$
$164$	3.26660	0.255079
$165$	−0.193716	−0.0150808
$166$	1.25135	0.0971236
$167$	−19.9309	−1.54230	−0.771151	−	0.636652i	$-0.780319\pi$
$167$	−19.9309	−1.54230	−0.771151	+	0.636652i	$0.780319\pi$
$168$	−1.27948	−0.0987144
$169$	4.44283	0.341756
$170$	0.0310576	0.00238201
$171$	−2.19940	−0.168192
$172$	0.640662	0.0488500
$173$	−12.1777	−0.925851	−0.462926	−	0.886397i	$-0.653200\pi$
$173$	−12.1777	−0.925851	−0.462926	+	0.886397i	$0.653200\pi$
$174$	−5.27661	−0.400019
$175$	−7.14345	−0.539994
$176$	−3.23328	−0.243718
$177$	−2.70896	−0.203618
$178$	−3.46503	−0.259715
$179$	−18.0969	−1.35263	−0.676314	−	0.736614i	$-0.736424\pi$
$179$	−18.0969	−1.35263	−0.676314	+	0.736614i	$0.736424\pi$
$180$	0.147271	0.0109770
$181$	−8.35520	−0.621037	−0.310518	−	0.950567i	$-0.600503\pi$
$181$	−8.35520	−0.621037	−0.310518	+	0.950567i	$0.600503\pi$
$182$	5.97222	0.442691
$183$	−10.5676	−0.781181
$184$	−2.96000	−0.218214
$185$	0.370874	0.0272672
$186$	4.49690	0.329728
$187$	1.49968	0.109667
$188$	0.940223	0.0685728
$189$	6.65255	0.483902
$190$	−0.0669598	−0.00485777
$191$	3.42398	0.247750	0.123875	−	0.992298i	$-0.460468\pi$
$191$	3.42398	0.247750	0.123875	+	0.992298i	$0.460468\pi$
$192$	−0.894762	−0.0645739
$193$	−23.2628	−1.67449	−0.837247	−	0.546824i	$-0.815837\pi$
$193$	−23.2628	−1.67449	−0.837247	+	0.546824i	$0.815837\pi$
$194$	−16.2444	−1.16628
$195$	0.250225	0.0179190
$196$	−4.95518	−0.353941
$197$	8.23004	0.586366	0.293183	−	0.956056i	$-0.405285\pi$
$197$	8.23004	0.586366	0.293183	+	0.956056i	$0.405285\pi$
$198$	7.11129	0.505377
$199$	13.7781	0.976704	0.488352	−	0.872647i	$-0.337598\pi$
$199$	13.7781	0.976704	0.488352	+	0.872647i	$0.337598\pi$
$200$	−4.99552	−0.353236
$201$	6.68384	0.471442
$202$	0.143986	0.0101308
$203$	8.43286	0.591871
$204$	0.415013	0.0290567
$205$	−0.218731	−0.0152768
$206$	−17.1246	−1.19313
$207$	6.51023	0.452492
$208$	4.17646	0.289585
$209$	−3.23328	−0.223651
$210$	0.0856740	0.00591207
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−11.0185	−0.756756
$213$	2.58355	0.177022
$214$	3.36857	0.230271
$215$	−0.0428986	−0.00292566
$216$	4.65223	0.316544
$217$	−7.18675	−0.487869
$218$	2.29513	0.155446
$219$	10.4878	0.708699
$220$	0.216500	0.0145964
$221$	−1.93715	−0.130307
$222$	4.95587	0.332616
$223$	0.0330141	0.00221079	0.00110539	−	0.999999i	$-0.499648\pi$
$223$	0.0330141	0.00221079	0.00110539	+	0.999999i	$0.499648\pi$
$224$	1.42997	0.0955440
$225$	10.9871	0.732476
$226$	4.15323	0.276269
$227$	9.85789	0.654291	0.327146	−	0.944974i	$-0.393913\pi$
$227$	9.85789	0.654291	0.327146	+	0.944974i	$0.393913\pi$
$228$	−0.894762	−0.0592571
$229$	−26.1817	−1.73013	−0.865066	−	0.501657i	$-0.832724\pi$
$229$	−26.1817	−1.73013	−0.865066	+	0.501657i	$0.832724\pi$
$230$	0.198201	0.0130690
$231$	4.13694	0.272190
$232$	5.89722	0.387171
$233$	−18.5618	−1.21602	−0.608011	−	0.793929i	$-0.708032\pi$
$233$	−18.5618	−1.21602	−0.608011	+	0.793929i	$0.708032\pi$
$234$	−9.18571	−0.600489
$235$	−0.0629571	−0.00410687
$236$	3.02758	0.197079
$237$	−12.2313	−0.794507
$238$	−0.663257	−0.0429926
$239$	10.0354	0.649137	0.324568	−	0.945862i	$-0.394781\pi$
$239$	10.0354	0.649137	0.324568	+	0.945862i	$0.394781\pi$
$240$	0.0599131	0.00386737
$241$	9.53632	0.614289	0.307144	−	0.951663i	$-0.400627\pi$
$241$	9.53632	0.614289	0.307144	+	0.951663i	$0.400627\pi$
$242$	−0.545879	−0.0350904
$243$	−16.1359	−1.03512
$244$	11.8105	0.756092
$245$	0.331798	0.0211978
$246$	−2.92283	−0.186353
$247$	4.17646	0.265742
$248$	−5.02580	−0.319139
$249$	−1.11966	−0.0709556
$250$	0.669297	0.0423301
$251$	24.8990	1.57161	0.785807	−	0.618472i	$-0.212248\pi$
$251$	24.8990	1.57161	0.785807	+	0.618472i	$0.212248\pi$
$252$	−3.14508	−0.198121
$253$	9.57053	0.601694
$254$	5.73201	0.359658
$255$	−0.0277892	−0.00174023
$256$	1.00000	0.0625000
$257$	1.12662	0.0702763	0.0351382	−	0.999382i	$-0.488813\pi$
$257$	1.12662	0.0702763	0.0351382	+	0.999382i	$0.488813\pi$
$258$	−0.573240	−0.0356884
$259$	−7.92027	−0.492141
$260$	−0.279655	−0.0173435
$261$	−12.9703	−0.802844
$262$	−21.0961	−1.30332
$263$	−1.34463	−0.0829133	−0.0414567	−	0.999140i	$-0.513200\pi$
$263$	−1.34463	−0.0829133	−0.0414567	+	0.999140i	$0.513200\pi$
$264$	2.89302	0.178053
$265$	0.737798	0.0453226
$266$	1.42997	0.0876772
$267$	3.10037	0.189740
$268$	−7.46996	−0.456301
$269$	−16.7280	−1.01992	−0.509961	−	0.860197i	$-0.670340\pi$
$269$	−16.7280	−1.01992	−0.509961	+	0.860197i	$0.670340\pi$
$270$	−0.311512	−0.0189580
$271$	−17.8311	−1.08316	−0.541582	−	0.840648i	$-0.682174\pi$
$271$	−17.8311	−1.08316	−0.541582	+	0.840648i	$0.682174\pi$
$272$	−0.463825	−0.0281235
$273$	−5.34372	−0.323417
$274$	10.7451	0.649137
$275$	16.1519	0.973997
$276$	2.64850	0.159421
$277$	−2.04524	−0.122887	−0.0614434	−	0.998111i	$-0.519570\pi$
$277$	−2.04524	−0.122887	−0.0614434	+	0.998111i	$0.519570\pi$
$278$	−2.46250	−0.147691
$279$	11.0537	0.661771
$280$	−0.0957506	−0.00572219
$281$	−9.57838	−0.571398	−0.285699	−	0.958319i	$-0.592226\pi$
$281$	−9.57838	−0.571398	−0.285699	+	0.958319i	$0.592226\pi$
$282$	−0.841276	−0.0500972
$283$	13.8347	0.822386	0.411193	−	0.911548i	$-0.365112\pi$
$283$	13.8347	0.822386	0.411193	+	0.911548i	$0.365112\pi$
$284$	−2.88742	−0.171337
$285$	0.0599131	0.00354894
$286$	−13.5037	−0.798490
$287$	4.67115	0.275729
$288$	−2.19940	−0.129601
$289$	−16.7849	−0.987345
$290$	−0.394876	−0.0231879
$291$	14.5349	0.852049
$292$	−11.7213	−0.685938
$293$	28.0241	1.63718	0.818592	−	0.574376i	$-0.194755\pi$
$293$	28.0241	1.63718	0.818592	+	0.574376i	$0.194755\pi$
$294$	4.43371	0.258579
$295$	−0.202726	−0.0118032
$296$	−5.53876	−0.321934
$297$	−15.0420	−0.872823
$298$	9.41318	0.545291
$299$	−12.3623	−0.714932
$300$	4.46980	0.258064
$301$	0.916129	0.0528048
$302$	10.1727	0.585371
$303$	−0.128833	−0.00740126
$304$	1.00000	0.0573539
$305$	−0.790831	−0.0452828
$306$	1.02014	0.0583174
$307$	−0.669660	−0.0382195	−0.0191098	−	0.999817i	$-0.506083\pi$
$307$	−0.669660	−0.0382195	−0.0191098	+	0.999817i	$0.506083\pi$
$308$	−4.62350	−0.263449
$309$	15.3224	0.871664
$310$	0.336526	0.0191134
$311$	−26.6499	−1.51118	−0.755589	−	0.655046i	$-0.772649\pi$
$311$	−26.6499	−1.51118	−0.755589	+	0.655046i	$0.772649\pi$
$312$	−3.73694	−0.211563
$313$	13.8057	0.780347	0.390173	−	0.920741i	$-0.372415\pi$
$313$	13.8057	0.780347	0.390173	+	0.920741i	$0.372415\pi$
$314$	−17.5166	−0.988517
$315$	0.210594	0.0118656
$316$	13.6699	0.768990
$317$	−7.28445	−0.409135	−0.204568	−	0.978852i	$-0.565579\pi$
$317$	−7.28445	−0.409135	−0.204568	+	0.978852i	$0.565579\pi$
$318$	9.85896	0.552863
$319$	−19.0674	−1.06757
$320$	−0.0669598	−0.00374316
$321$	−3.01407	−0.168229
$322$	−4.23272	−0.235880
$323$	−0.463825	−0.0258079
$324$	2.43557	0.135309
$325$	−20.8636	−1.15730
$326$	4.95308	0.274325
$327$	−2.05360	−0.113564
$328$	3.26660	0.180368
$329$	1.34449	0.0741243
$330$	−0.193716	−0.0106637
$331$	20.6018	1.13238	0.566188	−	0.824276i	$-0.308417\pi$
$331$	20.6018	1.13238	0.566188	+	0.824276i	$0.308417\pi$
$332$	1.25135	0.0686768
$333$	12.1819	0.667566
$334$	−19.9309	−1.09057
$335$	0.500187	0.0273281
$336$	−1.27948	−0.0698016
$337$	−2.81924	−0.153574	−0.0767869	−	0.997048i	$-0.524466\pi$
$337$	−2.81924	−0.153574	−0.0767869	+	0.997048i	$0.524466\pi$
$338$	4.44283	0.241658
$339$	−3.71615	−0.201834
$340$	0.0310576	0.00168434
$341$	16.2498	0.879978
$342$	−2.19940	−0.118930
$343$	−17.0956	−0.923074
$344$	0.640662	0.0345422
$345$	−0.177343	−0.00954781
$346$	−12.1777	−0.654676
$347$	27.5593	1.47946	0.739730	−	0.672904i	$-0.234953\pi$
$347$	27.5593	1.47946	0.739730	+	0.672904i	$0.234953\pi$
$348$	−5.27661	−0.282856
$349$	15.7773	0.844537	0.422269	−	0.906471i	$-0.361234\pi$
$349$	15.7773	0.844537	0.422269	+	0.906471i	$0.361234\pi$
$350$	−7.14345	−0.381833
$351$	19.4298	1.03709
$352$	−3.23328	−0.172335
$353$	−21.9369	−1.16758	−0.583790	−	0.811904i	$-0.698431\pi$
$353$	−21.9369	−1.16758	−0.583790	+	0.811904i	$0.698431\pi$
$354$	−2.70896	−0.143980
$355$	0.193341	0.0102615
$356$	−3.46503	−0.183646
$357$	0.593457	0.0314091
$358$	−18.0969	−0.956452
$359$	−22.8882	−1.20799	−0.603996	−	0.796987i	$-0.706426\pi$
$359$	−22.8882	−1.20799	−0.603996	+	0.796987i	$0.706426\pi$
$360$	0.147271	0.00776188
$361$	1.00000	0.0526316
$362$	−8.35520	−0.439139
$363$	0.488432	0.0256360
$364$	5.97222	0.313030
$365$	0.784856	0.0410812
$366$	−10.5676	−0.552378
$367$	−27.0452	−1.41175	−0.705874	−	0.708337i	$-0.749446\pi$
$367$	−27.0452	−1.41175	−0.705874	+	0.708337i	$0.749446\pi$
$368$	−2.96000	−0.154301
$369$	−7.18456	−0.374013
$370$	0.370874	0.0192808
$371$	−15.7562	−0.818020
$372$	4.49690	0.233153
$373$	14.7445	0.763443	0.381722	−	0.924277i	$-0.375331\pi$
$373$	14.7445	0.763443	0.381722	+	0.924277i	$0.375331\pi$
$374$	1.49968	0.0775465
$375$	−0.598862	−0.0309251
$376$	0.940223	0.0484883
$377$	24.6295	1.26848
$378$	6.65255	0.342170
$379$	−17.3322	−0.890298	−0.445149	−	0.895457i	$-0.646849\pi$
$379$	−17.3322	−0.890298	−0.445149	+	0.895457i	$0.646849\pi$
$380$	−0.0669598	−0.00343496
$381$	−5.12878	−0.262756
$382$	3.42398	0.175186
$383$	−31.3055	−1.59964	−0.799818	−	0.600243i	$-0.795071\pi$
$383$	−31.3055	−1.59964	−0.799818	+	0.600243i	$0.795071\pi$
$384$	−0.894762	−0.0456606
$385$	0.309589	0.0157781
$386$	−23.2628	−1.18405
$387$	−1.40907	−0.0716272
$388$	−16.2444	−0.824684
$389$	−19.1839	−0.972663	−0.486332	−	0.873774i	$-0.661665\pi$
$389$	−19.1839	−0.972663	−0.486332	+	0.873774i	$0.661665\pi$
$390$	0.250225	0.0126706
$391$	1.37292	0.0694317
$392$	−4.95518	−0.250274
$393$	18.8760	0.952169
$394$	8.23004	0.414624
$395$	−0.915331	−0.0460553
$396$	7.11129	0.357356
$397$	24.9671	1.25306	0.626531	−	0.779396i	$-0.284474\pi$
$397$	24.9671	1.25306	0.626531	+	0.779396i	$0.284474\pi$
$398$	13.7781	0.690634
$399$	−1.27948	−0.0640543
$400$	−4.99552	−0.249776
$401$	16.2670	0.812336	0.406168	−	0.913798i	$-0.366865\pi$
$401$	16.2670	0.812336	0.406168	+	0.913798i	$0.366865\pi$
$402$	6.68384	0.333360
$403$	−20.9901	−1.04559
$404$	0.143986	0.00716355
$405$	−0.163085	−0.00810376
$406$	8.43286	0.418516
$407$	17.9084	0.887685
$408$	0.415013	0.0205462
$409$	−16.4952	−0.815635	−0.407817	−	0.913064i	$-0.633710\pi$
$409$	−16.4952	−0.815635	−0.407817	+	0.913064i	$0.633710\pi$
$410$	−0.218731	−0.0108023
$411$	−9.61434	−0.474240
$412$	−17.1246	−0.843669
$413$	4.32936	0.213034
$414$	6.51023	0.319960
$415$	−0.0837901	−0.00411310
$416$	4.17646	0.204768
$417$	2.20335	0.107899
$418$	−3.23328	−0.158145
$419$	−18.5736	−0.907380	−0.453690	−	0.891159i	$-0.649893\pi$
$419$	−18.5736	−0.907380	−0.453690	+	0.891159i	$0.649893\pi$
$420$	0.0856740	0.00418046
$421$	−27.7847	−1.35414	−0.677072	−	0.735917i	$-0.736751\pi$
$421$	−27.7847	−1.35414	−0.677072	+	0.735917i	$0.736751\pi$
$422$	−1.00000	−0.0486792
$423$	−2.06793	−0.100546
$424$	−11.0185	−0.535107
$425$	2.31705	0.112393
$426$	2.58355	0.125174
$427$	16.8887	0.817303
$428$	3.36857	0.162826
$429$	12.0826	0.583353
$430$	−0.0428986	−0.00206875
$431$	−34.7106	−1.67195	−0.835977	−	0.548765i	$-0.815098\pi$
$431$	−34.7106	−1.67195	−0.835977	+	0.548765i	$0.815098\pi$
$432$	4.65223	0.223830
$433$	−23.7888	−1.14322	−0.571609	−	0.820526i	$-0.693681\pi$
$433$	−23.7888	−1.14322	−0.571609	+	0.820526i	$0.693681\pi$
$434$	−7.18675	−0.344975
$435$	0.353320	0.0169404
$436$	2.29513	0.109917
$437$	−2.96000	−0.141596
$438$	10.4878	0.501126
$439$	36.8791	1.76014	0.880072	−	0.474840i	$-0.157494\pi$
$439$	36.8791	1.76014	0.880072	+	0.474840i	$0.157494\pi$
$440$	0.216500	0.0103212
$441$	10.8984	0.518973
$442$	−1.93715	−0.0921408
$443$	18.7710	0.891837	0.445918	−	0.895074i	$-0.352877\pi$
$443$	18.7710	0.891837	0.445918	+	0.895074i	$0.352877\pi$
$444$	4.95587	0.235195
$445$	0.232017	0.0109987
$446$	0.0330141	0.00156326
$447$	−8.42255	−0.398373
$448$	1.42997	0.0675598
$449$	7.66794	0.361873	0.180936	−	0.983495i	$-0.442087\pi$
$449$	7.66794	0.361873	0.180936	+	0.983495i	$0.442087\pi$
$450$	10.9871	0.517939
$451$	−10.5618	−0.497338
$452$	4.15323	0.195352
$453$	−9.10211	−0.427654
$454$	9.85789	0.462654
$455$	−0.399899	−0.0187475
$456$	−0.894762	−0.0419011
$457$	−13.5028	−0.631636	−0.315818	−	0.948820i	$-0.602279\pi$
$457$	−13.5028	−0.631636	−0.315818	+	0.948820i	$0.602279\pi$
$458$	−26.1817	−1.22339
$459$	−2.15782	−0.100718
$460$	0.198201	0.00924117
$461$	11.3288	0.527634	0.263817	−	0.964573i	$-0.415018\pi$
$461$	11.3288	0.527634	0.263817	+	0.964573i	$0.415018\pi$
$462$	4.13694	0.192468
$463$	−2.50054	−0.116210	−0.0581049	−	0.998310i	$-0.518506\pi$
$463$	−2.50054	−0.116210	−0.0581049	+	0.998310i	$0.518506\pi$
$464$	5.89722	0.273772
$465$	−0.301111	−0.0139637
$466$	−18.5618	−0.859857
$467$	−9.47731	−0.438557	−0.219279	−	0.975662i	$-0.570370\pi$
$467$	−9.47731	−0.438557	−0.219279	+	0.975662i	$0.570370\pi$
$468$	−9.18571	−0.424610
$469$	−10.6818	−0.493241
$470$	−0.0629571	−0.00290399
$471$	15.6732	0.722181
$472$	3.02758	0.139356
$473$	−2.07144	−0.0952450
$474$	−12.2313	−0.561801
$475$	−4.99552	−0.229210
$476$	−0.663257	−0.0304003
$477$	24.2342	1.10961
$478$	10.0354	0.459009
$479$	25.1951	1.15119	0.575597	−	0.817734i	$-0.304770\pi$
$479$	25.1951	1.15119	0.575597	+	0.817734i	$0.304770\pi$
$480$	0.0599131	0.00273464
$481$	−23.1324	−1.05475
$482$	9.53632	0.434368
$483$	3.78728	0.172327
$484$	−0.545879	−0.0248127
$485$	1.08772	0.0493909
$486$	−16.1359	−0.731941
$487$	−10.4758	−0.474706	−0.237353	−	0.971423i	$-0.576280\pi$
$487$	−10.4758	−0.474706	−0.237353	+	0.971423i	$0.576280\pi$
$488$	11.8105	0.534638
$489$	−4.43182	−0.200414
$490$	0.331798	0.0149891
$491$	39.2210	1.77002	0.885010	−	0.465572i	$-0.154151\pi$
$491$	39.2210	1.77002	0.885010	+	0.465572i	$0.154151\pi$
$492$	−2.92283	−0.131771
$493$	−2.73528	−0.123191
$494$	4.17646	0.187908
$495$	−0.476170	−0.0214022
$496$	−5.02580	−0.225665
$497$	−4.12893	−0.185208
$498$	−1.11966	−0.0501732
$499$	−7.95532	−0.356129	−0.178065	−	0.984019i	$-0.556984\pi$
$499$	−7.95532	−0.356129	−0.178065	+	0.984019i	$0.556984\pi$
$500$	0.669297	0.0299319
$501$	17.8335	0.796740
$502$	24.8990	1.11130
$503$	34.2518	1.52721	0.763605	−	0.645683i	$-0.223427\pi$
$503$	34.2518	1.52721	0.763605	+	0.645683i	$0.223427\pi$
$504$	−3.14508	−0.140093
$505$	−0.00964125	−0.000429030 0
$506$	9.57053	0.425462
$507$	−3.97528	−0.176548
$508$	5.73201	0.254317
$509$	5.15090	0.228310	0.114155	−	0.993463i	$-0.463584\pi$
$509$	5.15090	0.228310	0.114155	+	0.993463i	$0.463584\pi$
$510$	−0.0277892	−0.00123053
$511$	−16.7611	−0.741469
$512$	1.00000	0.0441942
$513$	4.65223	0.205401
$514$	1.12662	0.0496929
$515$	1.14666	0.0505279
$516$	−0.573240	−0.0252355
$517$	−3.04001	−0.133699
$518$	−7.92027	−0.347996
$519$	10.8961	0.478287
$520$	−0.279655	−0.0122637
$521$	−16.5531	−0.725202	−0.362601	−	0.931944i	$-0.618111\pi$
$521$	−16.5531	−0.725202	−0.362601	+	0.931944i	$0.618111\pi$
$522$	−12.9703	−0.567697
$523$	−32.7917	−1.43388	−0.716939	−	0.697135i	$-0.754458\pi$
$523$	−32.7917	−1.43388	−0.716939	+	0.697135i	$0.754458\pi$
$524$	−21.0961	−0.921589
$525$	6.39169	0.278956
$526$	−1.34463	−0.0586286
$527$	2.33109	0.101544
$528$	2.89302	0.125903
$529$	−14.2384	−0.619060
$530$	0.737798	0.0320479
$531$	−6.65886	−0.288970
$532$	1.42997	0.0619971
$533$	13.6428	0.590937
$534$	3.10037	0.134166
$535$	−0.225558	−0.00975174
$536$	−7.46996	−0.322653
$537$	16.1924	0.698755
$538$	−16.7280	−0.721194
$539$	16.0215	0.690095
$540$	−0.311512	−0.0134053
$541$	−30.1889	−1.29792	−0.648961	−	0.760822i	$-0.724796\pi$
$541$	−30.1889	−1.29792	−0.648961	+	0.760822i	$0.724796\pi$
$542$	−17.8311	−0.765912
$543$	7.47591	0.320822
$544$	−0.463825	−0.0198863
$545$	−0.153682	−0.00658300
$546$	−5.34372	−0.228690
$547$	10.2456	0.438068	0.219034	−	0.975717i	$-0.429709\pi$
$547$	10.2456	0.438068	0.219034	+	0.975717i	$0.429709\pi$
$548$	10.7451	0.459009
$549$	−25.9761	−1.10863
$550$	16.1519	0.688720
$551$	5.89722	0.251230
$552$	2.64850	0.112728
$553$	19.5475	0.831245
$554$	−2.04524	−0.0868940
$555$	−0.331844	−0.0140860
$556$	−2.46250	−0.104433
$557$	34.9497	1.48087	0.740433	−	0.672130i	$-0.234620\pi$
$557$	34.9497	1.48087	0.740433	+	0.672130i	$0.234620\pi$
$558$	11.0537	0.467943
$559$	2.67570	0.113170
$560$	−0.0957506	−0.00404620
$561$	−1.34186	−0.0566532
$562$	−9.57838	−0.404039
$563$	34.9170	1.47157	0.735787	−	0.677213i	$-0.236812\pi$
$563$	34.9170	1.47157	0.735787	+	0.677213i	$0.236812\pi$
$564$	−0.841276	−0.0354241
$565$	−0.278099	−0.0116997
$566$	13.8347	0.581515
$567$	3.48279	0.146263
$568$	−2.88742	−0.121153
$569$	33.2616	1.39440	0.697199	−	0.716878i	$-0.254429\pi$
$569$	33.2616	1.39440	0.697199	+	0.716878i	$0.254429\pi$
$570$	0.0599131	0.00250948
$571$	−32.2694	−1.35043	−0.675217	−	0.737619i	$-0.735950\pi$
$571$	−32.2694	−1.35043	−0.675217	+	0.737619i	$0.735950\pi$
$572$	−13.5037	−0.564617
$573$	−3.06365	−0.127986
$574$	4.67115	0.194970
$575$	14.7867	0.616650
$576$	−2.19940	−0.0916417
$577$	−24.6167	−1.02481	−0.512403	−	0.858745i	$-0.671245\pi$
$577$	−24.6167	−1.02481	−0.512403	+	0.858745i	$0.671245\pi$
$578$	−16.7849	−0.698158
$579$	20.8147	0.865029
$580$	−0.394876	−0.0163963
$581$	1.78940	0.0742367
$582$	14.5349	0.602490
$583$	35.6260	1.47548
$584$	−11.7213	−0.485031
$585$	0.615073	0.0254301
$586$	28.0241	1.15766
$587$	32.2113	1.32950	0.664752	−	0.747064i	$-0.268537\pi$
$587$	32.2113	1.32950	0.664752	+	0.747064i	$0.268537\pi$
$588$	4.43371	0.182843
$589$	−5.02580	−0.207085
$590$	−0.202726	−0.00834610
$591$	−7.36393	−0.302912
$592$	−5.53876	−0.227641
$593$	32.0403	1.31574	0.657869	−	0.753132i	$-0.271458\pi$
$593$	32.0403	1.31574	0.657869	+	0.753132i	$0.271458\pi$
$594$	−15.0420	−0.617179
$595$	0.0444115	0.00182070
$596$	9.41318	0.385579
$597$	−12.3281	−0.504557
$598$	−12.3623	−0.505533
$599$	19.9390	0.814687	0.407343	−	0.913275i	$-0.366455\pi$
$599$	19.9390	0.814687	0.407343	+	0.913275i	$0.366455\pi$
$600$	4.46980	0.182479
$601$	−8.82658	−0.360044	−0.180022	−	0.983663i	$-0.557617\pi$
$601$	−8.82658	−0.360044	−0.180022	+	0.983663i	$0.557617\pi$
$602$	0.916129	0.0373386
$603$	16.4294	0.669059
$604$	10.1727	0.413920
$605$	0.0365519	0.00148605
$606$	−0.128833	−0.00523348
$607$	−6.03639	−0.245009	−0.122505	−	0.992468i	$-0.539093\pi$
$607$	−6.03639	−0.245009	−0.122505	+	0.992468i	$0.539093\pi$
$608$	1.00000	0.0405554
$609$	−7.54540	−0.305755
$610$	−0.790831	−0.0320198
$611$	3.92680	0.158862
$612$	1.02014	0.0412366
$613$	15.5906	0.629699	0.314850	−	0.949142i	$-0.398046\pi$
$613$	15.5906	0.629699	0.314850	+	0.949142i	$0.398046\pi$
$614$	−0.669660	−0.0270253
$615$	0.195712	0.00789187
$616$	−4.62350	−0.186286
$617$	−9.28165	−0.373665	−0.186833	−	0.982392i	$-0.559822\pi$
$617$	−9.28165	−0.373665	−0.186833	+	0.982392i	$0.559822\pi$
$618$	15.3224	0.616359
$619$	5.34460	0.214817	0.107409	−	0.994215i	$-0.465745\pi$
$619$	5.34460	0.214817	0.107409	+	0.994215i	$0.465745\pi$
$620$	0.336526	0.0135152
$621$	−13.7706	−0.552595
$622$	−26.6499	−1.06856
$623$	−4.95489	−0.198514
$624$	−3.73694	−0.149597
$625$	24.9328	0.997311
$626$	13.8057	0.551788
$627$	2.89302	0.115536
$628$	−17.5166	−0.698987
$629$	2.56902	0.102433
$630$	0.210594	0.00839026
$631$	−21.5798	−0.859079	−0.429540	−	0.903048i	$-0.641324\pi$
$631$	−21.5798	−0.859079	−0.429540	+	0.903048i	$0.641324\pi$
$632$	13.6699	0.543758
$633$	0.894762	0.0355636
$634$	−7.28445	−0.289302
$635$	−0.383814	−0.0152312
$636$	9.85896	0.390933
$637$	−20.6951	−0.819971
$638$	−19.0674	−0.754885
$639$	6.35060	0.251226
$640$	−0.0669598	−0.00264682
$641$	24.7578	0.977874	0.488937	−	0.872319i	$-0.337385\pi$
$641$	24.7578	0.977874	0.488937	+	0.872319i	$0.337385\pi$
$642$	−3.01407	−0.118956
$643$	1.69702	0.0669241	0.0334621	−	0.999440i	$-0.489347\pi$
$643$	1.69702	0.0669241	0.0334621	+	0.999440i	$0.489347\pi$
$644$	−4.23272	−0.166793
$645$	0.0383840	0.00151137
$646$	−0.463825	−0.0182490
$647$	15.4827	0.608686	0.304343	−	0.952562i	$-0.401563\pi$
$647$	15.4827	0.608686	0.304343	+	0.952562i	$0.401563\pi$
$648$	2.43557	0.0956781
$649$	−9.78903	−0.384253
$650$	−20.8636	−0.818337
$651$	6.43043	0.252029
$652$	4.95308	0.193977
$653$	3.27690	0.128235	0.0641175	−	0.997942i	$-0.479577\pi$
$653$	3.27690	0.128235	0.0641175	+	0.997942i	$0.479577\pi$
$654$	−2.05360	−0.0803021
$655$	1.41259	0.0551945
$656$	3.26660	0.127539
$657$	25.7799	1.00577
$658$	1.34449	0.0524138
$659$	−10.5496	−0.410954	−0.205477	−	0.978662i	$-0.565875\pi$
$659$	−10.5496	−0.410954	−0.205477	+	0.978662i	$0.565875\pi$
$660$	−0.193716	−0.00754038
$661$	−26.4876	−1.03025	−0.515125	−	0.857115i	$-0.672255\pi$
$661$	−26.4876	−1.03025	−0.515125	+	0.857115i	$0.672255\pi$
$662$	20.6018	0.800711
$663$	1.73329	0.0673153
$664$	1.25135	0.0485618
$665$	−0.0957506	−0.00371305
$666$	12.1819	0.472041
$667$	−17.4558	−0.675890
$668$	−19.9309	−0.771151
$669$	−0.0295398	−0.00114207
$670$	0.500187	0.0193239
$671$	−38.1868	−1.47419
$672$	−1.27948	−0.0493572
$673$	−4.62534	−0.178294	−0.0891468	−	0.996018i	$-0.528414\pi$
$673$	−4.62534	−0.178294	−0.0891468	+	0.996018i	$0.528414\pi$
$674$	−2.81924	−0.108593
$675$	−23.2403	−0.894519
$676$	4.44283	0.170878
$677$	26.1516	1.00509	0.502543	−	0.864552i	$-0.332398\pi$
$677$	26.1516	1.00509	0.502543	+	0.864552i	$0.332398\pi$
$678$	−3.71615	−0.142718
$679$	−23.2290	−0.891448
$680$	0.0310576	0.00119101
$681$	−8.82047	−0.338001
$682$	16.2498	0.622238
$683$	−30.8227	−1.17940	−0.589699	−	0.807623i	$-0.700754\pi$
$683$	−30.8227	−1.17940	−0.589699	+	0.807623i	$0.700754\pi$
$684$	−2.19940	−0.0840962
$685$	−0.719492	−0.0274904
$686$	−17.0956	−0.652712
$687$	23.4264	0.893771
$688$	0.640662	0.0244250
$689$	−46.0185	−1.75316
$690$	−0.177343	−0.00675132
$691$	11.0033	0.418586	0.209293	−	0.977853i	$-0.432884\pi$
$691$	11.0033	0.418586	0.209293	+	0.977853i	$0.432884\pi$
$692$	−12.1777	−0.462926
$693$	10.1689	0.386286
$694$	27.5593	1.04614
$695$	0.164888	0.00625458
$696$	−5.27661	−0.200009
$697$	−1.51513	−0.0573897
$698$	15.7773	0.597178
$699$	16.6084	0.628186
$700$	−7.14345	−0.269997
$701$	−32.5727	−1.23025	−0.615126	−	0.788429i	$-0.710895\pi$
$701$	−32.5727	−1.23025	−0.615126	+	0.788429i	$0.710895\pi$
$702$	19.4298	0.733332
$703$	−5.53876	−0.208898
$704$	−3.23328	−0.121859
$705$	0.0563316	0.00212157
$706$	−21.9369	−0.825604
$707$	0.205895	0.00774350
$708$	−2.70896	−0.101809
$709$	−10.8216	−0.406415	−0.203208	−	0.979136i	$-0.565137\pi$
$709$	−10.8216	−0.406415	−0.203208	+	0.979136i	$0.565137\pi$
$710$	0.193341	0.00725596
$711$	−30.0655	−1.12754
$712$	−3.46503	−0.129857
$713$	14.8764	0.557125
$714$	0.593457	0.0222096
$715$	0.904203	0.0338153
$716$	−18.0969	−0.676314
$717$	−8.97931	−0.335338
$718$	−22.8882	−0.854180
$719$	12.0564	0.449626	0.224813	−	0.974402i	$-0.427823\pi$
$719$	12.0564	0.449626	0.224813	+	0.974402i	$0.427823\pi$
$720$	0.147271	0.00548848
$721$	−24.4877	−0.911970
$722$	1.00000	0.0372161
$723$	−8.53274	−0.317336
$724$	−8.35520	−0.310518
$725$	−29.4597	−1.09410
$726$	0.488432	0.0181274
$727$	6.97553	0.258708	0.129354	−	0.991598i	$-0.458710\pi$
$727$	6.97553	0.258708	0.129354	+	0.991598i	$0.458710\pi$
$728$	5.97222	0.221345
$729$	7.13112	0.264116
$730$	0.784856	0.0290488
$731$	−0.297155	−0.0109907
$732$	−10.5676	−0.390591
$733$	−23.8008	−0.879102	−0.439551	−	0.898218i	$-0.644862\pi$
$733$	−23.8008	−0.879102	−0.439551	+	0.898218i	$0.644862\pi$
$734$	−27.0452	−0.998256
$735$	−0.296880	−0.0109506
$736$	−2.96000	−0.109107
$737$	24.1525	0.889669
$738$	−7.18456	−0.264467
$739$	14.6454	0.538741	0.269371	−	0.963037i	$-0.413184\pi$
$739$	14.6454	0.538741	0.269371	+	0.963037i	$0.413184\pi$
$740$	0.370874	0.0136336
$741$	−3.73694	−0.137280
$742$	−15.7562	−0.578428
$743$	−12.5843	−0.461672	−0.230836	−	0.972993i	$-0.574146\pi$
$743$	−12.5843	−0.461672	−0.230836	+	0.972993i	$0.574146\pi$
$744$	4.49690	0.164864
$745$	−0.630304	−0.0230925
$746$	14.7445	0.539836
$747$	−2.75222	−0.100699
$748$	1.49968	0.0548337
$749$	4.81696	0.176008
$750$	−0.598862	−0.0218673
$751$	−8.54675	−0.311875	−0.155938	−	0.987767i	$-0.549840\pi$
$751$	−8.54675	−0.311875	−0.155938	+	0.987767i	$0.549840\pi$
$752$	0.940223	0.0342864
$753$	−22.2787	−0.811882
$754$	24.6295	0.896954
$755$	−0.681159	−0.0247899
$756$	6.65255	0.241951
$757$	1.53898	0.0559351	0.0279675	−	0.999609i	$-0.491096\pi$
$757$	1.53898	0.0559351	0.0279675	+	0.999609i	$0.491096\pi$
$758$	−17.3322	−0.629535
$759$	−8.56334	−0.310830
$760$	−0.0669598	−0.00242889
$761$	5.68064	0.205923	0.102961	−	0.994685i	$-0.467168\pi$
$761$	5.68064	0.205923	0.102961	+	0.994685i	$0.467168\pi$
$762$	−5.12878	−0.185796
$763$	3.28198	0.118816
$764$	3.42398	0.123875
$765$	−0.0683082	−0.00246969
$766$	−31.3055	−1.13111
$767$	12.6446	0.456569
$768$	−0.894762	−0.0322869
$769$	−25.4526	−0.917843	−0.458922	−	0.888477i	$-0.651764\pi$
$769$	−25.4526	−0.917843	−0.458922	+	0.888477i	$0.651764\pi$
$770$	0.309589	0.0111568
$771$	−1.00805	−0.0363041
$772$	−23.2628	−0.837247
$773$	−1.87884	−0.0675772	−0.0337886	−	0.999429i	$-0.510757\pi$
$773$	−1.87884	−0.0675772	−0.0337886	+	0.999429i	$0.510757\pi$
$774$	−1.40907	−0.0506481
$775$	25.1065	0.901851
$776$	−16.2444	−0.583140
$777$	7.08675	0.254236
$778$	−19.1839	−0.687777
$779$	3.26660	0.117038
$780$	0.250225	0.00895948
$781$	9.33585	0.334063
$782$	1.37292	0.0490957
$783$	27.4352	0.980454
$784$	−4.95518	−0.176971
$785$	1.17290	0.0418628
$786$	18.8760	0.673285
$787$	−22.6411	−0.807068	−0.403534	−	0.914965i	$-0.632218\pi$
$787$	−22.6411	−0.807068	−0.403534	+	0.914965i	$0.632218\pi$
$788$	8.23004	0.293183
$789$	1.20312	0.0428323
$790$	−0.915331	−0.0325660
$791$	5.93900	0.211167
$792$	7.11129	0.252689
$793$	49.3263	1.75163
$794$	24.9671	0.886049
$795$	−0.660154	−0.0234132
$796$	13.7781	0.488352
$797$	−49.2885	−1.74589	−0.872945	−	0.487819i	$-0.837793\pi$
$797$	−49.2885	−1.74589	−0.872945	+	0.487819i	$0.837793\pi$
$798$	−1.27948	−0.0452933
$799$	−0.436099	−0.0154281
$800$	−4.99552	−0.176618
$801$	7.62098	0.269274
$802$	16.2670	0.574408
$803$	37.8983	1.33740
$804$	6.68384	0.235721
$805$	0.283422	0.00998931
$806$	−20.9901	−0.739343
$807$	14.9676	0.526883
$808$	0.143986	0.00506540
$809$	46.0017	1.61733	0.808667	−	0.588267i	$-0.200189\pi$
$809$	46.0017	1.61733	0.808667	+	0.588267i	$0.200189\pi$
$810$	−0.163085	−0.00573022
$811$	−10.0420	−0.352624	−0.176312	−	0.984334i	$-0.556417\pi$
$811$	−10.0420	−0.352624	−0.176312	+	0.984334i	$0.556417\pi$
$812$	8.43286	0.295935
$813$	15.9546	0.559552
$814$	17.9084	0.627688
$815$	−0.331657	−0.0116174
$816$	0.415013	0.0145284
$817$	0.640662	0.0224139
$818$	−16.4952	−0.576741
$819$	−13.1353	−0.458985
$820$	−0.218731	−0.00763841
$821$	−18.0128	−0.628650	−0.314325	−	0.949315i	$-0.601778\pi$
$821$	−18.0128	−0.628650	−0.314325	+	0.949315i	$0.601778\pi$
$822$	−9.61434	−0.335339
$823$	9.25191	0.322501	0.161251	−	0.986913i	$-0.448447\pi$
$823$	9.25191	0.322501	0.161251	+	0.986913i	$0.448447\pi$
$824$	−17.1246	−0.596564
$825$	−14.4521	−0.503158
$826$	4.32936	0.150638
$827$	29.7423	1.03424	0.517121	−	0.855913i	$-0.327004\pi$
$827$	29.7423	1.03424	0.517121	+	0.855913i	$0.327004\pi$
$828$	6.51023	0.226246
$829$	−7.63241	−0.265085	−0.132542	−	0.991177i	$-0.542314\pi$
$829$	−7.63241	−0.265085	−0.132542	+	0.991177i	$0.542314\pi$
$830$	−0.0837901	−0.00290840
$831$	1.83001	0.0634822
$832$	4.17646	0.144793
$833$	2.29834	0.0796327
$834$	2.20335	0.0762959
$835$	1.33457	0.0461847
$836$	−3.23328	−0.111825
$837$	−23.3812	−0.808171
$838$	−18.5736	−0.641615
$839$	21.6760	0.748337	0.374169	−	0.927361i	$-0.377928\pi$
$839$	21.6760	0.748337	0.374169	+	0.927361i	$0.377928\pi$
$840$	0.0856740	0.00295603
$841$	5.77719	0.199213
$842$	−27.7847	−0.957524
$843$	8.57037	0.295179
$844$	−1.00000	−0.0344214
$845$	−0.297491	−0.0102340
$846$	−2.06793	−0.0710968
$847$	−0.780591	−0.0268214
$848$	−11.0185	−0.378378
$849$	−12.3787	−0.424837
$850$	2.31705	0.0794740
$851$	16.3947	0.562004
$852$	2.58355	0.0885111
$853$	44.7515	1.53226	0.766132	−	0.642683i	$-0.222179\pi$
$853$	44.7515	1.53226	0.766132	+	0.642683i	$0.222179\pi$
$854$	16.8887	0.577921
$855$	0.147271	0.00503657
$856$	3.36857	0.115135
$857$	−10.1111	−0.345390	−0.172695	−	0.984975i	$-0.555247\pi$
$857$	−10.1111	−0.345390	−0.172695	+	0.984975i	$0.555247\pi$
$858$	12.0826	0.412493
$859$	49.2301	1.67971	0.839854	−	0.542812i	$-0.182640\pi$
$859$	49.2301	1.67971	0.839854	+	0.542812i	$0.182640\pi$
$860$	−0.0428986	−0.00146283
$861$	−4.17956	−0.142439
$862$	−34.7106	−1.18225
$863$	−14.1606	−0.482033	−0.241016	−	0.970521i	$-0.577481\pi$
$863$	−14.1606	−0.482033	−0.241016	+	0.970521i	$0.577481\pi$
$864$	4.65223	0.158272
$865$	0.815414	0.0277249
$866$	−23.7888	−0.808377
$867$	15.0185	0.510054
$868$	−7.18675	−0.243934
$869$	−44.1985	−1.49933
$870$	0.353320	0.0119787
$871$	−31.1980	−1.05710
$872$	2.29513	0.0777231
$873$	35.7279	1.20921
$874$	−2.96000	−0.100124
$875$	0.957076	0.0323551
$876$	10.4878	0.354349
$877$	8.88043	0.299871	0.149935	−	0.988696i	$-0.452093\pi$
$877$	8.88043	0.299871	0.149935	+	0.988696i	$0.452093\pi$
$878$	36.8791	1.24461
$879$	−25.0749	−0.845755
$880$	0.216500	0.00729821
$881$	20.7540	0.699219	0.349609	−	0.936896i	$-0.386314\pi$
$881$	20.7540	0.699219	0.349609	+	0.936896i	$0.386314\pi$
$882$	10.8984	0.366969
$883$	−45.9956	−1.54788	−0.773938	−	0.633262i	$-0.781716\pi$
$883$	−45.9956	−1.54788	−0.773938	+	0.633262i	$0.781716\pi$
$884$	−1.93715	−0.0651534
$885$	0.181392	0.00609741
$886$	18.7710	0.630624
$887$	−22.3918	−0.751844	−0.375922	−	0.926651i	$-0.622674\pi$
$887$	−22.3918	−0.751844	−0.375922	+	0.926651i	$0.622674\pi$
$888$	4.95587	0.166308
$889$	8.19661	0.274906
$890$	0.232017	0.00777724
$891$	−7.87488	−0.263818
$892$	0.0330141	0.00110539
$893$	0.940223	0.0314634
$894$	−8.42255	−0.281692
$895$	1.21177	0.0405048
$896$	1.42997	0.0477720
$897$	11.0613	0.369328
$898$	7.66794	0.255883
$899$	−29.6382	−0.988491
$900$	10.9871	0.366238
$901$	5.11067	0.170261
$902$	−10.5618	−0.351671
$903$	−0.819717	−0.0272785
$904$	4.15323	0.138134
$905$	0.559462	0.0185971
$906$	−9.10211	−0.302397
$907$	−11.2584	−0.373830	−0.186915	−	0.982376i	$-0.559849\pi$
$907$	−11.2584	−0.373830	−0.186915	+	0.982376i	$0.559849\pi$
$908$	9.85789	0.327146
$909$	−0.316682	−0.0105037
$910$	−0.399899	−0.0132565
$911$	15.0265	0.497849	0.248925	−	0.968523i	$-0.419923\pi$
$911$	15.0265	0.497849	0.248925	+	0.968523i	$0.419923\pi$
$912$	−0.894762	−0.0296285
$913$	−4.04597	−0.133902
$914$	−13.5028	−0.446634
$915$	0.707605	0.0233927
$916$	−26.1817	−0.865066
$917$	−30.1669	−0.996198
$918$	−2.15782	−0.0712187
$919$	−31.0414	−1.02396	−0.511981	−	0.858997i	$-0.671088\pi$
$919$	−31.0414	−1.02396	−0.511981	+	0.858997i	$0.671088\pi$
$920$	0.198201	0.00653449
$921$	0.599186	0.0197439
$922$	11.3288	0.373094
$923$	−12.0592	−0.396933
$924$	4.13694	0.136095
$925$	27.6689	0.909749
$926$	−2.50054	−0.0821727
$927$	37.6639	1.23704
$928$	5.89722	0.193586
$929$	−31.9212	−1.04730	−0.523650	−	0.851934i	$-0.675430\pi$
$929$	−31.9212	−1.04730	−0.523650	+	0.851934i	$0.675430\pi$
$930$	−0.301111	−0.00987382
$931$	−4.95518	−0.162399
$932$	−18.5618	−0.608011
$933$	23.8453	0.780661
$934$	−9.47731	−0.310107
$935$	−0.100418	−0.00328402
$936$	−9.18571	−0.300244
$937$	35.5515	1.16142	0.580709	−	0.814111i	$-0.302775\pi$
$937$	35.5515	1.16142	0.580709	+	0.814111i	$0.302775\pi$
$938$	−10.6818	−0.348774
$939$	−12.3529	−0.403120
$940$	−0.0629571	−0.00205343
$941$	−51.0565	−1.66439	−0.832196	−	0.554481i	$-0.812917\pi$
$941$	−51.0565	−1.66439	−0.832196	+	0.554481i	$0.812917\pi$
$942$	15.6732	0.510659
$943$	−9.66914	−0.314871
$944$	3.02758	0.0985394
$945$	−0.445453	−0.0144906
$946$	−2.07144	−0.0673484
$947$	−22.4032	−0.728006	−0.364003	−	0.931398i	$-0.618590\pi$
$947$	−22.4032	−0.728006	−0.364003	+	0.931398i	$0.618590\pi$
$948$	−12.2313	−0.397253
$949$	−48.9536	−1.58910
$950$	−4.99552	−0.162076
$951$	6.51785	0.211356
$952$	−0.663257	−0.0214963
$953$	−16.4898	−0.534157	−0.267079	−	0.963675i	$-0.586058\pi$
$953$	−16.4898	−0.534157	−0.267079	+	0.963675i	$0.586058\pi$
$954$	24.2342	0.784610
$955$	−0.229269	−0.00741897
$956$	10.0354	0.324568
$957$	17.0608	0.551496
$958$	25.1951	0.814017
$959$	15.3652	0.496169
$960$	0.0599131	0.00193369
$961$	−5.74133	−0.185204
$962$	−23.1324	−0.745819
$963$	−7.40883	−0.238746
$964$	9.53632	0.307144
$965$	1.55767	0.0501433
$966$	3.78728	0.121854
$967$	44.2347	1.42249	0.711246	−	0.702943i	$-0.248131\pi$
$967$	44.2347	1.42249	0.711246	+	0.702943i	$0.248131\pi$
$968$	−0.545879	−0.0175452
$969$	0.415013	0.0133321
$970$	1.08772	0.0349246
$971$	−8.90513	−0.285779	−0.142890	−	0.989739i	$-0.545639\pi$
$971$	−8.90513	−0.285779	−0.142890	+	0.989739i	$0.545639\pi$
$972$	−16.1359	−0.517560
$973$	−3.52131	−0.112888
$974$	−10.4758	−0.335668
$975$	18.6679	0.597853
$976$	11.8105	0.378046
$977$	5.69080	0.182065	0.0910325	−	0.995848i	$-0.470983\pi$
$977$	5.69080	0.182065	0.0910325	+	0.995848i	$0.470983\pi$
$978$	−4.43182	−0.141714
$979$	11.2034	0.358063
$980$	0.331798	0.0105989
$981$	−5.04792	−0.161168
$982$	39.2210	1.25159
$983$	1.30631	0.0416648	0.0208324	−	0.999783i	$-0.493368\pi$
$983$	1.30631	0.0416648	0.0208324	+	0.999783i	$0.493368\pi$
$984$	−2.92283	−0.0931764
$985$	−0.551082	−0.0175589
$986$	−2.73528	−0.0871090
$987$	−1.20300	−0.0382919
$988$	4.17646	0.132871
$989$	−1.89636	−0.0603008
$990$	−0.476170	−0.0151337
$991$	47.8763	1.52084	0.760421	−	0.649430i	$-0.224993\pi$
$991$	47.8763	1.52084	0.760421	+	0.649430i	$0.224993\pi$
$992$	−5.02580	−0.159569
$993$	−18.4337	−0.584976
$994$	−4.12893	−0.130962
$995$	−0.922579	−0.0292477
$996$	−1.11966	−0.0354778
$997$	−16.9545	−0.536953	−0.268477	−	0.963286i	$-0.586520\pi$
$997$	−16.9545	−0.536953	−0.268477	+	0.963286i	$0.586520\pi$
$998$	−7.95532	−0.251821
$999$	−25.7675	−0.815249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.13	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.894762 q^{3} +1.00000 q^{4} -0.0669598 q^{5} -0.894762 q^{6} +1.42997 q^{7} +1.00000 q^{8} -2.19940 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.894762 q^{3} +1.00000 q^{4} -0.0669598 q^{5} -0.894762 q^{6} +1.42997 q^{7} +1.00000 q^{8} -2.19940 q^{9} -0.0669598 q^{10} -3.23328 q^{11} -0.894762 q^{12} +4.17646 q^{13} +1.42997 q^{14} +0.0599131 q^{15} +1.00000 q^{16} -0.463825 q^{17} -2.19940 q^{18} +1.00000 q^{19} -0.0669598 q^{20} -1.27948 q^{21} -3.23328 q^{22} -2.96000 q^{23} -0.894762 q^{24} -4.99552 q^{25} +4.17646 q^{26} +4.65223 q^{27} +1.42997 q^{28} +5.89722 q^{29} +0.0599131 q^{30} -5.02580 q^{31} +1.00000 q^{32} +2.89302 q^{33} -0.463825 q^{34} -0.0957506 q^{35} -2.19940 q^{36} -5.53876 q^{37} +1.00000 q^{38} -3.73694 q^{39} -0.0669598 q^{40} +3.26660 q^{41} -1.27948 q^{42} +0.640662 q^{43} -3.23328 q^{44} +0.147271 q^{45} -2.96000 q^{46} +0.940223 q^{47} -0.894762 q^{48} -4.95518 q^{49} -4.99552 q^{50} +0.415013 q^{51} +4.17646 q^{52} -11.0185 q^{53} +4.65223 q^{54} +0.216500 q^{55} +1.42997 q^{56} -0.894762 q^{57} +5.89722 q^{58} +3.02758 q^{59} +0.0599131 q^{60} +11.8105 q^{61} -5.02580 q^{62} -3.14508 q^{63} +1.00000 q^{64} -0.279655 q^{65} +2.89302 q^{66} -7.46996 q^{67} -0.463825 q^{68} +2.64850 q^{69} -0.0957506 q^{70} -2.88742 q^{71} -2.19940 q^{72} -11.7213 q^{73} -5.53876 q^{74} +4.46980 q^{75} +1.00000 q^{76} -4.62350 q^{77} -3.73694 q^{78} +13.6699 q^{79} -0.0669598 q^{80} +2.43557 q^{81} +3.26660 q^{82} +1.25135 q^{83} -1.27948 q^{84} +0.0310576 q^{85} +0.640662 q^{86} -5.27661 q^{87} -3.23328 q^{88} -3.46503 q^{89} +0.147271 q^{90} +5.97222 q^{91} -2.96000 q^{92} +4.49690 q^{93} +0.940223 q^{94} -0.0669598 q^{95} -0.894762 q^{96} -16.2444 q^{97} -4.95518 q^{98} +7.11129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 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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