LMFDB - Embedded newform 381.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,2,Mod(1,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, 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("381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	381.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:	$3.04230031701$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.81509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 3x^{2} + 5x - 2 $ x^5 - x^4 - 5x^3 + 3x^2 + 5*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.14113$ of defining polynomial
Character	$\chi$	$=$	381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.14113 q^{2} -1.00000 q^{3} -0.697826 q^{4} +0.866045 q^{5} -1.14113 q^{6} -4.61870 q^{7} -3.07857 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.14113 q^{2} -1.00000 q^{3} -0.697826 q^{4} +0.866045 q^{5} -1.14113 q^{6} -4.61870 q^{7} -3.07857 q^{8} +1.00000 q^{9} +0.988269 q^{10} -2.50587 q^{11} +0.697826 q^{12} -0.0237406 q^{13} -5.27053 q^{14} -0.866045 q^{15} -2.11739 q^{16} +2.24679 q^{17} +1.14113 q^{18} -6.29427 q^{19} -0.604349 q^{20} +4.61870 q^{21} -2.85951 q^{22} +0.404481 q^{23} +3.07857 q^{24} -4.24997 q^{25} -0.0270911 q^{26} -1.00000 q^{27} +3.22304 q^{28} +2.03491 q^{29} -0.988269 q^{30} +2.82387 q^{31} +3.74092 q^{32} +2.50587 q^{33} +2.56387 q^{34} -4.00000 q^{35} -0.697826 q^{36} +4.22623 q^{37} -7.18257 q^{38} +0.0237406 q^{39} -2.66618 q^{40} -1.78309 q^{41} +5.27053 q^{42} +3.67791 q^{43} +1.74866 q^{44} +0.866045 q^{45} +0.461565 q^{46} -7.27371 q^{47} +2.11739 q^{48} +14.3324 q^{49} -4.84976 q^{50} -2.24679 q^{51} +0.0165668 q^{52} -11.9573 q^{53} -1.14113 q^{54} -2.17019 q^{55} +14.2190 q^{56} +6.29427 q^{57} +2.32209 q^{58} -11.5322 q^{59} +0.604349 q^{60} -5.99944 q^{61} +3.22240 q^{62} -4.61870 q^{63} +8.50365 q^{64} -0.0205604 q^{65} +2.85951 q^{66} +9.33906 q^{67} -1.56786 q^{68} -0.404481 q^{69} -4.56451 q^{70} +7.22538 q^{71} -3.07857 q^{72} +17.0109 q^{73} +4.82267 q^{74} +4.24997 q^{75} +4.39230 q^{76} +11.5738 q^{77} +0.0270911 q^{78} -9.72221 q^{79} -1.83375 q^{80} +1.00000 q^{81} -2.03474 q^{82} +14.6234 q^{83} -3.22304 q^{84} +1.94582 q^{85} +4.19697 q^{86} -2.03491 q^{87} +7.71447 q^{88} -14.3315 q^{89} +0.988269 q^{90} +0.109651 q^{91} -0.282257 q^{92} -2.82387 q^{93} -8.30023 q^{94} -5.45112 q^{95} -3.74092 q^{96} -7.63897 q^{97} +16.3551 q^{98} -2.50587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9} - 2 q^{10} - 16 q^{11} - q^{12} + 3 q^{13} - 6 q^{14} + 5 q^{15} - 7 q^{16} - 6 q^{17} - q^{18} - 8 q^{19} - 12 q^{20} - 8 q^{22} - 9 q^{23} + 3 q^{24} + 4 q^{25} - 2 q^{26} - 5 q^{27} + 2 q^{28} - 17 q^{29} + 2 q^{30} - 9 q^{31} - 2 q^{32} + 16 q^{33} - q^{34} - 20 q^{35} + q^{36} - q^{37} + q^{38} - 3 q^{39} + 16 q^{40} - 2 q^{41} + 6 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} + 4 q^{46} - 8 q^{47} + 7 q^{48} + 13 q^{49} + 15 q^{50} + 6 q^{51} + 13 q^{52} - 15 q^{53} + q^{54} + 20 q^{55} + 8 q^{56} + 8 q^{57} + 34 q^{58} - 19 q^{59} + 12 q^{60} + q^{61} + 15 q^{62} + q^{64} - 5 q^{65} + 8 q^{66} - 2 q^{67} + 14 q^{68} + 9 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 17 q^{74} - 4 q^{75} + 8 q^{76} + 2 q^{77} + 2 q^{78} - 28 q^{79} + 12 q^{80} + 5 q^{81} + 30 q^{82} - q^{83} - 2 q^{84} + 6 q^{85} + 32 q^{86} + 17 q^{87} + 3 q^{88} + q^{89} - 2 q^{90} - 18 q^{91} + 12 q^{92} + 9 q^{93} + 16 q^{94} + 4 q^{95} + 2 q^{96} + 28 q^{97} + 15 q^{98} - 16 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9 - 2 * q^10 - 16 * q^11 - q^12 + 3 * q^13 - 6 * q^14 + 5 * q^15 - 7 * q^16 - 6 * q^17 - q^18 - 8 * q^19 - 12 * q^20 - 8 * q^22 - 9 * q^23 + 3 * q^24 + 4 * q^25 - 2 * q^26 - 5 * q^27 + 2 * q^28 - 17 * q^29 + 2 * q^30 - 9 * q^31 - 2 * q^32 + 16 * q^33 - q^34 - 20 * q^35 + q^36 - q^37 + q^38 - 3 * q^39 + 16 * q^40 - 2 * q^41 + 6 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 + 4 * q^46 - 8 * q^47 + 7 * q^48 + 13 * q^49 + 15 * q^50 + 6 * q^51 + 13 * q^52 - 15 * q^53 + q^54 + 20 * q^55 + 8 * q^56 + 8 * q^57 + 34 * q^58 - 19 * q^59 + 12 * q^60 + q^61 + 15 * q^62 + q^64 - 5 * q^65 + 8 * q^66 - 2 * q^67 + 14 * q^68 + 9 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 17 * q^74 - 4 * q^75 + 8 * q^76 + 2 * q^77 + 2 * q^78 - 28 * q^79 + 12 * q^80 + 5 * q^81 + 30 * q^82 - q^83 - 2 * q^84 + 6 * q^85 + 32 * q^86 + 17 * q^87 + 3 * q^88 + q^89 - 2 * q^90 - 18 * q^91 + 12 * q^92 + 9 * q^93 + 16 * q^94 + 4 * q^95 + 2 * q^96 + 28 * q^97 + 15 * q^98 - 16 * 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 $

$2$	1.14113	0.806900	0.403450	−	0.915002i	$-0.367811\pi$
$2$	1.14113	0.806900	0.403450	+	0.915002i	$0.367811\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.697826	−0.348913
$5$	0.866045	0.387307	0.193654	−	0.981070i	$-0.437966\pi$
$5$	0.866045	0.387307	0.193654	+	0.981070i	$0.437966\pi$
$6$	−1.14113	−0.465864
$7$	−4.61870	−1.74570	−0.872852	−	0.487986i	$-0.837732\pi$
$7$	−4.61870	−1.74570	−0.872852	+	0.487986i	$0.837732\pi$
$8$	−3.07857	−1.08844
$9$	1.00000	0.333333
$10$	0.988269	0.312518
$11$	−2.50587	−0.755547	−0.377773	−	0.925898i	$-0.623310\pi$
$11$	−2.50587	−0.755547	−0.377773	+	0.925898i	$0.623310\pi$
$12$	0.697826	0.201445
$13$	−0.0237406	−0.00658445	−0.00329223	−	0.999995i	$-0.501048\pi$
$13$	−0.0237406	−0.00658445	−0.00329223	+	0.999995i	$0.501048\pi$
$14$	−5.27053	−1.40861
$15$	−0.866045	−0.223612
$16$	−2.11739	−0.529347
$17$	2.24679	0.544926	0.272463	−	0.962166i	$-0.412162\pi$
$17$	2.24679	0.544926	0.272463	+	0.962166i	$0.412162\pi$
$18$	1.14113	0.268967
$19$	−6.29427	−1.44400	−0.722002	−	0.691891i	$-0.756778\pi$
$19$	−6.29427	−1.44400	−0.722002	+	0.691891i	$0.756778\pi$
$20$	−0.604349	−0.135136
$21$	4.61870	1.00788
$22$	−2.85951	−0.609651
$23$	0.404481	0.0843401	0.0421700	−	0.999110i	$-0.486573\pi$
$23$	0.404481	0.0843401	0.0421700	+	0.999110i	$0.486573\pi$
$24$	3.07857	0.628410
$25$	−4.24997	−0.849993
$26$	−0.0270911	−0.00531299
$27$	−1.00000	−0.192450
$28$	3.22304	0.609098
$29$	2.03491	0.377873	0.188936	−	0.981989i	$-0.439496\pi$
$29$	2.03491	0.377873	0.188936	+	0.981989i	$0.439496\pi$
$30$	−0.988269	−0.180432
$31$	2.82387	0.507183	0.253591	−	0.967311i	$-0.418388\pi$
$31$	2.82387	0.507183	0.253591	+	0.967311i	$0.418388\pi$
$32$	3.74092	0.661307
$33$	2.50587	0.436215
$34$	2.56387	0.439700
$35$	−4.00000	−0.676123
$36$	−0.697826	−0.116304
$37$	4.22623	0.694787	0.347394	−	0.937719i	$-0.387067\pi$
$37$	4.22623	0.694787	0.347394	+	0.937719i	$0.387067\pi$
$38$	−7.18257	−1.16517
$39$	0.0237406	0.00380154
$40$	−2.66618	−0.421560
$41$	−1.78309	−0.278472	−0.139236	−	0.990259i	$-0.544465\pi$
$41$	−1.78309	−0.278472	−0.139236	+	0.990259i	$0.544465\pi$
$42$	5.27053	0.813260
$43$	3.67791	0.560876	0.280438	−	0.959872i	$-0.409520\pi$
$43$	3.67791	0.560876	0.280438	+	0.959872i	$0.409520\pi$
$44$	1.74866	0.263620
$45$	0.866045	0.129102
$46$	0.461565	0.0680540
$47$	−7.27371	−1.06098	−0.530490	−	0.847691i	$-0.677992\pi$
$47$	−7.27371	−1.06098	−0.530490	+	0.847691i	$0.677992\pi$
$48$	2.11739	0.305619
$49$	14.3324	2.04748
$50$	−4.84976	−0.685859
$51$	−2.24679	−0.314613
$52$	0.0165668	0.00229740
$53$	−11.9573	−1.64246	−0.821228	−	0.570600i	$-0.806711\pi$
$53$	−11.9573	−1.64246	−0.821228	+	0.570600i	$0.806711\pi$
$54$	−1.14113	−0.155288
$55$	−2.17019	−0.292629
$56$	14.2190	1.90009
$57$	6.29427	0.833696
$58$	2.32209	0.304906
$59$	−11.5322	−1.50137	−0.750684	−	0.660662i	$-0.770276\pi$
$59$	−11.5322	−1.50137	−0.750684	+	0.660662i	$0.770276\pi$
$60$	0.604349	0.0780211
$61$	−5.99944	−0.768149	−0.384075	−	0.923302i	$-0.625479\pi$
$61$	−5.99944	−0.768149	−0.384075	+	0.923302i	$0.625479\pi$
$62$	3.22240	0.409245
$63$	−4.61870	−0.581901
$64$	8.50365	1.06296
$65$	−0.0205604	−0.00255021
$66$	2.85951	0.351982
$67$	9.33906	1.14095	0.570474	−	0.821316i	$-0.306760\pi$
$67$	9.33906	1.14095	0.570474	+	0.821316i	$0.306760\pi$
$68$	−1.56786	−0.190132
$69$	−0.404481	−0.0486938
$70$	−4.56451	−0.545564
$71$	7.22538	0.857495	0.428748	−	0.903424i	$-0.358955\pi$
$71$	7.22538	0.857495	0.428748	+	0.903424i	$0.358955\pi$
$72$	−3.07857	−0.362812
$73$	17.0109	1.99097	0.995487	−	0.0949023i	$-0.0302539\pi$
$73$	17.0109	1.99097	0.995487	+	0.0949023i	$0.0302539\pi$
$74$	4.82267	0.560624
$75$	4.24997	0.490744
$76$	4.39230	0.503831
$77$	11.5738	1.31896
$78$	0.0270911	0.00306746
$79$	−9.72221	−1.09383	−0.546917	−	0.837187i	$-0.684199\pi$
$79$	−9.72221	−1.09383	−0.546917	+	0.837187i	$0.684199\pi$
$80$	−1.83375	−0.205020
$81$	1.00000	0.111111
$82$	−2.03474	−0.224699
$83$	14.6234	1.60513	0.802566	−	0.596564i	$-0.203468\pi$
$83$	14.6234	1.60513	0.802566	+	0.596564i	$0.203468\pi$
$84$	−3.22304	−0.351663
$85$	1.94582	0.211054
$86$	4.19697	0.452571
$87$	−2.03491	−0.218165
$88$	7.71447	0.822365
$89$	−14.3315	−1.51914	−0.759569	−	0.650427i	$-0.774590\pi$
$89$	−14.3315	−1.51914	−0.759569	+	0.650427i	$0.774590\pi$
$90$	0.988269	0.104173
$91$	0.109651	0.0114945
$92$	−0.282257	−0.0294273
$93$	−2.82387	−0.292822
$94$	−8.30023	−0.856104
$95$	−5.45112	−0.559273
$96$	−3.74092	−0.381806
$97$	−7.63897	−0.775620	−0.387810	−	0.921739i	$-0.626768\pi$
$97$	−7.63897	−0.775620	−0.387810	+	0.921739i	$0.626768\pi$
$98$	16.3551	1.65211
$99$	−2.50587	−0.251849
$100$	2.96574	0.296574
$101$	1.24361	0.123743	0.0618717	−	0.998084i	$-0.480293\pi$
$101$	1.24361	0.123743	0.0618717	+	0.998084i	$0.480293\pi$
$102$	−2.56387	−0.253861
$103$	5.92554	0.583860	0.291930	−	0.956440i	$-0.405703\pi$
$103$	5.92554	0.583860	0.291930	+	0.956440i	$0.405703\pi$
$104$	0.0730869	0.00716676
$105$	4.00000	0.390360
$106$	−13.6448	−1.32530
$107$	−9.55843	−0.924049	−0.462024	−	0.886867i	$-0.652877\pi$
$107$	−9.55843	−0.924049	−0.462024	+	0.886867i	$0.652877\pi$
$108$	0.697826	0.0671483
$109$	−7.08026	−0.678166	−0.339083	−	0.940756i	$-0.610117\pi$
$109$	−7.08026	−0.678166	−0.339083	+	0.940756i	$0.610117\pi$
$110$	−2.47647	−0.236122
$111$	−4.22623	−0.401136
$112$	9.77957	0.924083
$113$	−12.2158	−1.14916	−0.574582	−	0.818447i	$-0.694835\pi$
$113$	−12.2158	−1.14916	−0.574582	+	0.818447i	$0.694835\pi$
$114$	7.18257	0.672709
$115$	0.350299	0.0326655
$116$	−1.42001	−0.131845
$117$	−0.0237406	−0.00219482
$118$	−13.1597	−1.21145
$119$	−10.3772	−0.951278
$120$	2.66618	0.243388
$121$	−4.72064	−0.429149
$122$	−6.84613	−0.619819
$123$	1.78309	0.160776
$124$	−1.97057	−0.176962
$125$	−8.01089	−0.716516
$126$	−5.27053	−0.469536
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	2.22191	0.196391
$129$	−3.67791	−0.323822
$130$	−0.0234621	−0.00205776
$131$	0.0949623	0.00829690	0.00414845	−	0.999991i	$-0.498680\pi$
$131$	0.0949623	0.00829690	0.00414845	+	0.999991i	$0.498680\pi$
$132$	−1.74866	−0.152201
$133$	29.0713	2.52080
$134$	10.6571	0.920630
$135$	−0.866045	−0.0745373
$136$	−6.91688	−0.593117
$137$	−4.83291	−0.412904	−0.206452	−	0.978457i	$-0.566192\pi$
$137$	−4.83291	−0.412904	−0.206452	+	0.978457i	$0.566192\pi$
$138$	−0.461565	−0.0392910
$139$	1.20539	0.102240	0.0511198	−	0.998693i	$-0.483721\pi$
$139$	1.20539	0.102240	0.0511198	+	0.998693i	$0.483721\pi$
$140$	2.79130	0.235908
$141$	7.27371	0.612557
$142$	8.24509	0.691913
$143$	0.0594907	0.00497486
$144$	−2.11739	−0.176449
$145$	1.76232	0.146353
$146$	19.4116	1.60652
$147$	−14.3324	−1.18211
$148$	−2.94917	−0.242420
$149$	−14.6043	−1.19643	−0.598214	−	0.801336i	$-0.704123\pi$
$149$	−14.6043	−1.19643	−0.598214	+	0.801336i	$0.704123\pi$
$150$	4.84976	0.395981
$151$	−13.4066	−1.09101	−0.545507	−	0.838106i	$-0.683663\pi$
$151$	−13.4066	−1.09101	−0.545507	+	0.838106i	$0.683663\pi$
$152$	19.3773	1.57171
$153$	2.24679	0.181642
$154$	13.2072	1.06427
$155$	2.44560	0.196435
$156$	−0.0165668	−0.00132640
$157$	8.19047	0.653671	0.326836	−	0.945081i	$-0.394018\pi$
$157$	8.19047	0.653671	0.326836	+	0.945081i	$0.394018\pi$
$158$	−11.0943	−0.882614
$159$	11.9573	0.948273
$160$	3.23981	0.256129
$161$	−1.86817	−0.147233
$162$	1.14113	0.0896555
$163$	−7.49441	−0.587008	−0.293504	−	0.955958i	$-0.594821\pi$
$163$	−7.49441	−0.587008	−0.293504	+	0.955958i	$0.594821\pi$
$164$	1.24429	0.0971625
$165$	2.17019	0.168949
$166$	16.6872	1.29518
$167$	7.29399	0.564426	0.282213	−	0.959352i	$-0.408932\pi$
$167$	7.29399	0.564426	0.282213	+	0.959352i	$0.408932\pi$
$168$	−14.2190	−1.09702
$169$	−12.9994	−0.999957
$170$	2.22043	0.170299
$171$	−6.29427	−0.481335
$172$	−2.56654	−0.195697
$173$	−14.6272	−1.11209	−0.556044	−	0.831153i	$-0.687682\pi$
$173$	−14.6272	−1.11209	−0.556044	+	0.831153i	$0.687682\pi$
$174$	−2.32209	−0.176037
$175$	19.6293	1.48384
$176$	5.30589	0.399946
$177$	11.5322	0.866815
$178$	−16.3541	−1.22579
$179$	−12.6000	−0.941767	−0.470884	−	0.882195i	$-0.656065\pi$
$179$	−12.6000	−0.941767	−0.470884	+	0.882195i	$0.656065\pi$
$180$	−0.604349	−0.0450455
$181$	11.0678	0.822660	0.411330	−	0.911487i	$-0.365064\pi$
$181$	11.0678	0.822660	0.411330	+	0.911487i	$0.365064\pi$
$182$	0.125125	0.00927491
$183$	5.99944	0.443491
$184$	−1.24522	−0.0917989
$185$	3.66010	0.269096
$186$	−3.22240	−0.236278
$187$	−5.63014	−0.411717
$188$	5.07578	0.370189
$189$	4.61870	0.335961
$190$	−6.22043	−0.451277
$191$	11.3558	0.821678	0.410839	−	0.911708i	$-0.365236\pi$
$191$	11.3558	0.821678	0.410839	+	0.911708i	$0.365236\pi$
$192$	−8.50365	−0.613698
$193$	−2.44575	−0.176049	−0.0880244	−	0.996118i	$-0.528055\pi$
$193$	−2.44575	−0.176049	−0.0880244	+	0.996118i	$0.528055\pi$
$194$	−8.71705	−0.625848
$195$	0.0205604	0.00147236
$196$	−10.0015	−0.714392
$197$	7.94319	0.565929	0.282965	−	0.959130i	$-0.408682\pi$
$197$	7.94319	0.565929	0.282965	+	0.959130i	$0.408682\pi$
$198$	−2.85951	−0.203217
$199$	−24.8584	−1.76217	−0.881084	−	0.472961i	$-0.843185\pi$
$199$	−24.8584	−1.76217	−0.881084	+	0.472961i	$0.843185\pi$
$200$	13.0838	0.925164
$201$	−9.33906	−0.658726
$202$	1.41911	0.0998485
$203$	−9.39862	−0.659654
$204$	1.56786	0.109772
$205$	−1.54424	−0.107854
$206$	6.76180	0.471117
$207$	0.404481	0.0281134
$208$	0.0502680	0.00348546
$209$	15.7726	1.09101
$210$	4.56451	0.314981
$211$	−4.60407	−0.316957	−0.158479	−	0.987362i	$-0.550659\pi$
$211$	−4.60407	−0.316957	−0.158479	+	0.987362i	$0.550659\pi$
$212$	8.34409	0.573074
$213$	−7.22538	−0.495075
$214$	−10.9074	−0.745614
$215$	3.18524	0.217231
$216$	3.07857	0.209470
$217$	−13.0426	−0.885390
$218$	−8.07949	−0.547212
$219$	−17.0109	−1.14949
$220$	1.51442	0.102102
$221$	−0.0533400	−0.00358804
$222$	−4.82267	−0.323676
$223$	25.1188	1.68208	0.841039	−	0.540974i	$-0.181944\pi$
$223$	25.1188	1.68208	0.841039	+	0.540974i	$0.181944\pi$
$224$	−17.2782	−1.15445
$225$	−4.24997	−0.283331
$226$	−13.9398	−0.927260
$227$	−8.98714	−0.596498	−0.298249	−	0.954488i	$-0.596403\pi$
$227$	−8.98714	−0.596498	−0.298249	+	0.954488i	$0.596403\pi$
$228$	−4.39230	−0.290887
$229$	7.44347	0.491879	0.245939	−	0.969285i	$-0.420904\pi$
$229$	7.44347	0.491879	0.245939	+	0.969285i	$0.420904\pi$
$230$	0.399736	0.0263578
$231$	−11.5738	−0.761502
$232$	−6.26460	−0.411291
$233$	−28.2813	−1.85277	−0.926384	−	0.376580i	$-0.877100\pi$
$233$	−28.2813	−1.85277	−0.926384	+	0.376580i	$0.877100\pi$
$234$	−0.0270911	−0.00177100
$235$	−6.29936	−0.410925
$236$	8.04748	0.523846
$237$	9.72221	0.631525
$238$	−11.8417	−0.767586
$239$	18.8174	1.21720	0.608599	−	0.793478i	$-0.291732\pi$
$239$	18.8174	1.21720	0.608599	+	0.793478i	$0.291732\pi$
$240$	1.83375	0.118368
$241$	25.6768	1.65399	0.826993	−	0.562212i	$-0.190049\pi$
$241$	25.6768	1.65399	0.826993	+	0.562212i	$0.190049\pi$
$242$	−5.38685	−0.346280
$243$	−1.00000	−0.0641500
$244$	4.18656	0.268017
$245$	12.4125	0.793003
$246$	2.03474	0.129730
$247$	0.149430	0.00950797
$248$	−8.69348	−0.552036
$249$	−14.6234	−0.926723
$250$	−9.14145	−0.578156
$251$	0.815872	0.0514974	0.0257487	−	0.999668i	$-0.491803\pi$
$251$	0.815872	0.0514974	0.0257487	+	0.999668i	$0.491803\pi$
$252$	3.22304	0.203033
$253$	−1.01357	−0.0637229
$254$	−1.14113	−0.0716008
$255$	−1.94582	−0.121852
$256$	−14.4718	−0.904488
$257$	24.7849	1.54604	0.773019	−	0.634383i	$-0.218746\pi$
$257$	24.7849	1.54604	0.773019	+	0.634383i	$0.218746\pi$
$258$	−4.19697	−0.261292
$259$	−19.5196	−1.21289
$260$	0.0143476	0.000889800 0
$261$	2.03491	0.125958
$262$	0.108364	0.00669476
$263$	8.21365	0.506475	0.253238	−	0.967404i	$-0.418505\pi$
$263$	8.21365	0.506475	0.253238	+	0.967404i	$0.418505\pi$
$264$	−7.71447	−0.474793
$265$	−10.3555	−0.636135
$266$	33.1741	2.03403
$267$	14.3315	0.877074
$268$	−6.51703	−0.398091
$269$	−6.04346	−0.368476	−0.184238	−	0.982882i	$-0.558982\pi$
$269$	−6.04346	−0.368476	−0.184238	+	0.982882i	$0.558982\pi$
$270$	−0.988269	−0.0601441
$271$	21.2963	1.29366	0.646830	−	0.762635i	$-0.276094\pi$
$271$	21.2963	1.29366	0.646830	+	0.762635i	$0.276094\pi$
$272$	−4.75732	−0.288455
$273$	−0.109651	−0.00663635
$274$	−5.51497	−0.333172
$275$	10.6498	0.642210
$276$	0.282257	0.0169899
$277$	−2.26008	−0.135795	−0.0678976	−	0.997692i	$-0.521629\pi$
$277$	−2.26008	−0.135795	−0.0678976	+	0.997692i	$0.521629\pi$
$278$	1.37550	0.0824970
$279$	2.82387	0.169061
$280$	12.3143	0.735918
$281$	17.9505	1.07084	0.535418	−	0.844587i	$-0.320154\pi$
$281$	17.9505	1.07084	0.535418	+	0.844587i	$0.320154\pi$
$282$	8.30023	0.494272
$283$	11.3307	0.673538	0.336769	−	0.941587i	$-0.390666\pi$
$283$	11.3307	0.673538	0.336769	+	0.941587i	$0.390666\pi$
$284$	−5.04206	−0.299191
$285$	5.45112	0.322896
$286$	0.0678865	0.00401422
$287$	8.23556	0.486130
$288$	3.74092	0.220436
$289$	−11.9520	−0.703056
$290$	2.01104	0.118092
$291$	7.63897	0.447804
$292$	−11.8706	−0.694676
$293$	7.66695	0.447908	0.223954	−	0.974600i	$-0.428103\pi$
$293$	7.66695	0.447908	0.223954	+	0.974600i	$0.428103\pi$
$294$	−16.3551	−0.953846
$295$	−9.98743	−0.581490
$296$	−13.0107	−0.756232
$297$	2.50587	0.145405
$298$	−16.6654	−0.965398
$299$	−0.00960261	−0.000555333 0
$300$	−2.96574	−0.171227
$301$	−16.9871	−0.979123
$302$	−15.2987	−0.880339
$303$	−1.24361	−0.0714433
$304$	13.3274	0.764379
$305$	−5.19578	−0.297510
$306$	2.56387	0.146567
$307$	−22.1039	−1.26154	−0.630768	−	0.775972i	$-0.717260\pi$
$307$	−22.1039	−1.26154	−0.630768	+	0.775972i	$0.717260\pi$
$308$	−8.07652	−0.460202
$309$	−5.92554	−0.337092
$310$	2.79075	0.158504
$311$	−6.55234	−0.371549	−0.185775	−	0.982592i	$-0.559479\pi$
$311$	−6.55234	−0.371549	−0.185775	+	0.982592i	$0.559479\pi$
$312$	−0.0730869	−0.00413773
$313$	−16.9684	−0.959108	−0.479554	−	0.877512i	$-0.659202\pi$
$313$	−16.9684	−0.959108	−0.479554	+	0.877512i	$0.659202\pi$
$314$	9.34638	0.527447
$315$	−4.00000	−0.225374
$316$	6.78441	0.381653
$317$	8.67382	0.487170	0.243585	−	0.969879i	$-0.421676\pi$
$317$	8.67382	0.487170	0.243585	+	0.969879i	$0.421676\pi$
$318$	13.6448	0.765161
$319$	−5.09921	−0.285501
$320$	7.36454	0.411690
$321$	9.55843	0.533500
$322$	−2.13183	−0.118802
$323$	−14.1419	−0.786875
$324$	−0.697826	−0.0387681
$325$	0.100897	0.00559674
$326$	−8.55209	−0.473656
$327$	7.08026	0.391539
$328$	5.48937	0.303100
$329$	33.5950	1.85215
$330$	2.47647	0.136325
$331$	29.7375	1.63452	0.817260	−	0.576269i	$-0.195492\pi$
$331$	29.7375	1.63452	0.817260	+	0.576269i	$0.195492\pi$
$332$	−10.2046	−0.560051
$333$	4.22623	0.231596
$334$	8.32338	0.455435
$335$	8.08804	0.441897
$336$	−9.77957	−0.533519
$337$	15.0635	0.820561	0.410281	−	0.911959i	$-0.365431\pi$
$337$	15.0635	0.820561	0.410281	+	0.911959i	$0.365431\pi$
$338$	−14.8340	−0.806865
$339$	12.2158	0.663470
$340$	−1.35784	−0.0736393
$341$	−7.07625	−0.383200
$342$	−7.18257	−0.388389
$343$	−33.8659	−1.82859
$344$	−11.3227	−0.610478
$345$	−0.350299	−0.0188594
$346$	−16.6916	−0.897344
$347$	16.4285	0.881928	0.440964	−	0.897525i	$-0.354637\pi$
$347$	16.4285	0.881928	0.440964	+	0.897525i	$0.354637\pi$
$348$	1.42001	0.0761206
$349$	31.0968	1.66457	0.832287	−	0.554346i	$-0.187031\pi$
$349$	31.0968	1.66457	0.832287	+	0.554346i	$0.187031\pi$
$350$	22.3996	1.19731
$351$	0.0237406	0.00126718
$352$	−9.37424	−0.499649
$353$	−26.8102	−1.42696	−0.713481	−	0.700675i	$-0.752882\pi$
$353$	−26.8102	−1.42696	−0.713481	+	0.700675i	$0.752882\pi$
$354$	13.1597	0.699433
$355$	6.25751	0.332114
$356$	10.0009	0.530047
$357$	10.3772	0.549221
$358$	−14.3782	−0.759912
$359$	−2.78347	−0.146906	−0.0734531	−	0.997299i	$-0.523402\pi$
$359$	−2.78347	−0.146906	−0.0734531	+	0.997299i	$0.523402\pi$
$360$	−2.66618	−0.140520
$361$	20.6178	1.08515
$362$	12.6297	0.663804
$363$	4.72064	0.247769
$364$	−0.0765170	−0.00401058
$365$	14.7322	0.771118
$366$	6.84613	0.357853
$367$	6.34160	0.331029	0.165514	−	0.986207i	$-0.447072\pi$
$367$	6.34160	0.331029	0.165514	+	0.986207i	$0.447072\pi$
$368$	−0.856443	−0.0446452
$369$	−1.78309	−0.0928241
$370$	4.17665	0.217134
$371$	55.2270	2.86724
$372$	1.97057	0.102169
$373$	23.4764	1.21556	0.607782	−	0.794104i	$-0.292060\pi$
$373$	23.4764	1.21556	0.607782	+	0.794104i	$0.292060\pi$
$374$	−6.42472	−0.332214
$375$	8.01089	0.413681
$376$	22.3926	1.15481
$377$	−0.0483099	−0.00248809
$378$	5.27053	0.271087
$379$	−32.7965	−1.68464	−0.842322	−	0.538974i	$-0.818812\pi$
$379$	−32.7965	−1.68464	−0.842322	+	0.538974i	$0.818812\pi$
$380$	3.80393	0.195138
$381$	1.00000	0.0512316
$382$	12.9584	0.663012
$383$	36.3430	1.85704	0.928519	−	0.371284i	$-0.121082\pi$
$383$	36.3430	1.85704	0.928519	+	0.371284i	$0.121082\pi$
$384$	−2.22191	−0.113387
$385$	10.0235	0.510843
$386$	−2.79091	−0.142054
$387$	3.67791	0.186959
$388$	5.33067	0.270624
$389$	−22.1126	−1.12116	−0.560578	−	0.828102i	$-0.689421\pi$
$389$	−22.1126	−1.12116	−0.560578	+	0.828102i	$0.689421\pi$
$390$	0.0234621	0.00118805
$391$	0.908781	0.0459591
$392$	−44.1231	−2.22855
$393$	−0.0949623	−0.00479022
$394$	9.06421	0.456648
$395$	−8.41987	−0.423650
$396$	1.74866	0.0878733
$397$	−16.0345	−0.804748	−0.402374	−	0.915475i	$-0.631815\pi$
$397$	−16.0345	−0.804748	−0.402374	+	0.915475i	$0.631815\pi$
$398$	−28.3667	−1.42189
$399$	−29.0713	−1.45539
$400$	8.99883	0.449941
$401$	16.0545	0.801723	0.400861	−	0.916139i	$-0.368711\pi$
$401$	16.0545	0.801723	0.400861	+	0.916139i	$0.368711\pi$
$402$	−10.6571	−0.531526
$403$	−0.0670404	−0.00333952
$404$	−0.867820	−0.0431756
$405$	0.866045	0.0430341
$406$	−10.7250	−0.532275
$407$	−10.5904	−0.524944
$408$	6.91688	0.342436
$409$	32.6181	1.61286	0.806431	−	0.591328i	$-0.201396\pi$
$409$	32.6181	1.61286	0.806431	+	0.591328i	$0.201396\pi$
$410$	−1.76217	−0.0870276
$411$	4.83291	0.238390
$412$	−4.13499	−0.203716
$413$	53.2638	2.62094
$414$	0.461565	0.0226847
$415$	12.6646	0.621679
$416$	−0.0888116	−0.00435435
$417$	−1.20539	−0.0590280
$418$	17.9985	0.880338
$419$	−33.2248	−1.62314	−0.811569	−	0.584256i	$-0.801386\pi$
$419$	−33.2248	−1.62314	−0.811569	+	0.584256i	$0.801386\pi$
$420$	−2.79130	−0.136202
$421$	−29.0112	−1.41392	−0.706961	−	0.707253i	$-0.749934\pi$
$421$	−29.0112	−1.41392	−0.706961	+	0.707253i	$0.749934\pi$
$422$	−5.25384	−0.255753
$423$	−7.27371	−0.353660
$424$	36.8112	1.78771
$425$	−9.54876	−0.463183
$426$	−8.24509	−0.399476
$427$	27.7096	1.34096
$428$	6.67012	0.322412
$429$	−0.0594907	−0.00287224
$430$	3.63476	0.175284
$431$	−12.8436	−0.618654	−0.309327	−	0.950956i	$-0.600104\pi$
$431$	−12.8436	−0.618654	−0.309327	+	0.950956i	$0.600104\pi$
$432$	2.11739	0.101873
$433$	35.4242	1.70238	0.851190	−	0.524857i	$-0.175881\pi$
$433$	35.4242	1.70238	0.851190	+	0.524857i	$0.175881\pi$
$434$	−14.8833	−0.714421
$435$	−1.76232	−0.0844969
$436$	4.94079	0.236621
$437$	−2.54591	−0.121787
$438$	−19.4116	−0.927522
$439$	−7.86946	−0.375589	−0.187794	−	0.982208i	$-0.560134\pi$
$439$	−7.86946	−0.375589	−0.187794	+	0.982208i	$0.560134\pi$
$440$	6.68108	0.318508
$441$	14.3324	0.682493
$442$	−0.0608678	−0.00289519
$443$	−7.12574	−0.338554	−0.169277	−	0.985568i	$-0.554143\pi$
$443$	−7.12574	−0.338554	−0.169277	+	0.985568i	$0.554143\pi$
$444$	2.94917	0.139961
$445$	−12.4117	−0.588373
$446$	28.6638	1.35727
$447$	14.6043	0.690758
$448$	−39.2758	−1.85561
$449$	6.19812	0.292507	0.146254	−	0.989247i	$-0.453278\pi$
$449$	6.19812	0.292507	0.146254	+	0.989247i	$0.453278\pi$
$450$	−4.84976	−0.228620
$451$	4.46819	0.210399
$452$	8.52449	0.400958
$453$	13.4066	0.629897
$454$	−10.2555	−0.481314
$455$	0.0949623	0.00445190
$456$	−19.3773	−0.907426
$457$	5.11925	0.239468	0.119734	−	0.992806i	$-0.461796\pi$
$457$	5.11925	0.239468	0.119734	+	0.992806i	$0.461796\pi$
$458$	8.49396	0.396897
$459$	−2.24679	−0.104871
$460$	−0.244447	−0.0113974
$461$	39.0488	1.81868	0.909342	−	0.416050i	$-0.136586\pi$
$461$	39.0488	1.81868	0.909342	+	0.416050i	$0.136586\pi$
$462$	−13.2072	−0.614456
$463$	−16.4486	−0.764430	−0.382215	−	0.924073i	$-0.624839\pi$
$463$	−16.4486	−0.764430	−0.382215	+	0.924073i	$0.624839\pi$
$464$	−4.30869	−0.200026
$465$	−2.44560	−0.113412
$466$	−32.2726	−1.49500
$467$	−29.2325	−1.35272	−0.676359	−	0.736572i	$-0.736443\pi$
$467$	−29.2325	−1.35272	−0.676359	+	0.736572i	$0.736443\pi$
$468$	0.0165668	0.000765800 0
$469$	−43.1343	−1.99176
$470$	−7.18838	−0.331575
$471$	−8.19047	−0.377397
$472$	35.5027	1.63414
$473$	−9.21634	−0.423768
$474$	11.0943	0.509578
$475$	26.7504	1.22739
$476$	7.24149	0.331913
$477$	−11.9573	−0.547486
$478$	21.4731	0.982157
$479$	2.27538	0.103965	0.0519823	−	0.998648i	$-0.483446\pi$
$479$	2.27538	0.103965	0.0519823	+	0.998648i	$0.483446\pi$
$480$	−3.23981	−0.147876
$481$	−0.100333	−0.00457479
$482$	29.3005	1.33460
$483$	1.86817	0.0850048
$484$	3.29418	0.149736
$485$	−6.61570	−0.300403
$486$	−1.14113	−0.0517626
$487$	7.44329	0.337288	0.168644	−	0.985677i	$-0.446061\pi$
$487$	7.44329	0.337288	0.168644	+	0.985677i	$0.446061\pi$
$488$	18.4697	0.836082
$489$	7.49441	0.338909
$490$	14.1642	0.639874
$491$	−2.09530	−0.0945597	−0.0472798	−	0.998882i	$-0.515055\pi$
$491$	−2.09530	−0.0945597	−0.0472798	+	0.998882i	$0.515055\pi$
$492$	−1.24429	−0.0560968
$493$	4.57200	0.205913
$494$	0.170518	0.00767198
$495$	−2.17019	−0.0975429
$496$	−5.97923	−0.268476
$497$	−33.3718	−1.49693
$498$	−16.6872	−0.747772
$499$	−16.9842	−0.760316	−0.380158	−	0.924922i	$-0.624130\pi$
$499$	−16.9842	−0.760316	−0.380158	+	0.924922i	$0.624130\pi$
$500$	5.59020	0.250002
$501$	−7.29399	−0.325871
$502$	0.931015	0.0415532
$503$	−10.2426	−0.456696	−0.228348	−	0.973580i	$-0.573332\pi$
$503$	−10.2426	−0.456696	−0.228348	+	0.973580i	$0.573332\pi$
$504$	14.2190	0.633363
$505$	1.07702	0.0479267
$506$	−1.15662	−0.0514180
$507$	12.9994	0.577325
$508$	0.697826	0.0309610
$509$	−13.9145	−0.616751	−0.308375	−	0.951265i	$-0.599785\pi$
$509$	−13.9145	−0.616751	−0.308375	+	0.951265i	$0.599785\pi$
$510$	−2.22043	−0.0983222
$511$	−78.5681	−3.47565
$512$	−20.9580	−0.926222
$513$	6.29427	0.277899
$514$	28.2827	1.24750
$515$	5.13178	0.226133
$516$	2.56654	0.112986
$517$	18.2269	0.801619
$518$	−22.2744	−0.978682
$519$	14.6272	0.642065
$520$	0.0632966	0.00277574
$521$	−43.2226	−1.89362	−0.946809	−	0.321796i	$-0.895713\pi$
$521$	−43.2226	−1.89362	−0.946809	+	0.321796i	$0.895713\pi$
$522$	2.32209	0.101635
$523$	−9.32499	−0.407753	−0.203877	−	0.978997i	$-0.565354\pi$
$523$	−9.32499	−0.407753	−0.203877	+	0.978997i	$0.565354\pi$
$524$	−0.0662672	−0.00289489
$525$	−19.6293	−0.856693
$526$	9.37283	0.408675
$527$	6.34464	0.276377
$528$	−5.30589	−0.230909
$529$	−22.8364	−0.992887
$530$	−11.8170	−0.513297
$531$	−11.5322	−0.500456
$532$	−20.2867	−0.879540
$533$	0.0423317	0.00183359
$534$	16.3541	0.707711
$535$	−8.27804	−0.357891
$536$	−28.7509	−1.24185
$537$	12.6000	0.543730
$538$	−6.89636	−0.297323
$539$	−35.9150	−1.54697
$540$	0.604349	0.0260070
$541$	−16.5697	−0.712389	−0.356195	−	0.934412i	$-0.615926\pi$
$541$	−16.5697	−0.712389	−0.356195	+	0.934412i	$0.615926\pi$
$542$	24.3018	1.04385
$543$	−11.0678	−0.474963
$544$	8.40504	0.360363
$545$	−6.13183	−0.262659
$546$	−0.125125	−0.00535487
$547$	18.0367	0.771193	0.385596	−	0.922668i	$-0.373996\pi$
$547$	18.0367	0.771193	0.385596	+	0.922668i	$0.373996\pi$
$548$	3.37253	0.144067
$549$	−5.99944	−0.256050
$550$	12.1528	0.518199
$551$	−12.8083	−0.545650
$552$	1.24522	0.0530001
$553$	44.9039	1.90951
$554$	−2.57904	−0.109573
$555$	−3.66010	−0.155363
$556$	−0.841149	−0.0356727
$557$	25.7122	1.08946	0.544730	−	0.838612i	$-0.316632\pi$
$557$	25.7122	1.08946	0.544730	+	0.838612i	$0.316632\pi$
$558$	3.22240	0.136415
$559$	−0.0873157	−0.00369306
$560$	8.46955	0.357904
$561$	5.63014	0.237705
$562$	20.4838	0.864058
$563$	−36.4798	−1.53744	−0.768720	−	0.639585i	$-0.779106\pi$
$563$	−36.4798	−1.53744	−0.768720	+	0.639585i	$0.779106\pi$
$564$	−5.07578	−0.213729
$565$	−10.5794	−0.445079
$566$	12.9298	0.543478
$567$	−4.61870	−0.193967
$568$	−22.2438	−0.933330
$569$	−11.1266	−0.466453	−0.233226	−	0.972422i	$-0.574928\pi$
$569$	−11.1266	−0.466453	−0.233226	+	0.972422i	$0.574928\pi$
$570$	6.22043	0.260545
$571$	−38.1095	−1.59483	−0.797416	−	0.603430i	$-0.793800\pi$
$571$	−38.1095	−1.59483	−0.797416	+	0.603430i	$0.793800\pi$
$572$	−0.0415141	−0.00173579
$573$	−11.3558	−0.474396
$574$	9.39784	0.392258
$575$	−1.71903	−0.0716885
$576$	8.50365	0.354319
$577$	12.0047	0.499761	0.249880	−	0.968277i	$-0.419609\pi$
$577$	12.0047	0.499761	0.249880	+	0.968277i	$0.419609\pi$
$578$	−13.6387	−0.567296
$579$	2.44575	0.101642
$580$	−1.22979	−0.0510644
$581$	−67.5412	−2.80208
$582$	8.71705	0.361333
$583$	29.9633	1.24095
$584$	−52.3691	−2.16705
$585$	−0.0205604	−0.000850069 0
$586$	8.74898	0.361417
$587$	−26.4306	−1.09091	−0.545454	−	0.838141i	$-0.683643\pi$
$587$	−26.4306	−1.09091	−0.545454	+	0.838141i	$0.683643\pi$
$588$	10.0015	0.412454
$589$	−17.7742	−0.732373
$590$	−11.3969	−0.469204
$591$	−7.94319	−0.326739
$592$	−8.94856	−0.367783
$593$	41.2874	1.69547	0.847734	−	0.530421i	$-0.177966\pi$
$593$	41.2874	1.69547	0.847734	+	0.530421i	$0.177966\pi$
$594$	2.85951	0.117327
$595$	−8.98714	−0.368437
$596$	10.1912	0.417449
$597$	24.8584	1.01739
$598$	−0.0109578	−0.000448098 0
$599$	4.55814	0.186241	0.0931203	−	0.995655i	$-0.470316\pi$
$599$	4.55814	0.186241	0.0931203	+	0.995655i	$0.470316\pi$
$600$	−13.0838	−0.534144
$601$	−2.60232	−0.106151	−0.0530755	−	0.998591i	$-0.516902\pi$
$601$	−2.60232	−0.106151	−0.0530755	+	0.998591i	$0.516902\pi$
$602$	−19.3845	−0.790054
$603$	9.33906	0.380316
$604$	9.35548	0.380669
$605$	−4.08829	−0.166212
$606$	−1.41911	−0.0576475
$607$	9.08808	0.368874	0.184437	−	0.982844i	$-0.440954\pi$
$607$	9.08808	0.368874	0.184437	+	0.982844i	$0.440954\pi$
$608$	−23.5463	−0.954930
$609$	9.39862	0.380851
$610$	−5.92906	−0.240060
$611$	0.172682	0.00698597
$612$	−1.56786	−0.0633772
$613$	31.1842	1.25952	0.629758	−	0.776791i	$-0.283154\pi$
$613$	31.1842	1.25952	0.629758	+	0.776791i	$0.283154\pi$
$614$	−25.2234	−1.01793
$615$	1.54424	0.0622697
$616$	−35.6308	−1.43561
$617$	−35.5350	−1.43059	−0.715293	−	0.698824i	$-0.753707\pi$
$617$	−35.5350	−1.43059	−0.715293	+	0.698824i	$0.753707\pi$
$618$	−6.76180	−0.271999
$619$	20.2797	0.815108	0.407554	−	0.913181i	$-0.366382\pi$
$619$	20.2797	0.815108	0.407554	+	0.913181i	$0.366382\pi$
$620$	−1.70660	−0.0685388
$621$	−0.404481	−0.0162313
$622$	−7.47706	−0.299803
$623$	66.1929	2.65196
$624$	−0.0502680	−0.00201233
$625$	14.3120	0.572481
$626$	−19.3631	−0.773904
$627$	−15.7726	−0.629896
$628$	−5.71552	−0.228074
$629$	9.49542	0.378607
$630$	−4.56451	−0.181855
$631$	6.64773	0.264642	0.132321	−	0.991207i	$-0.457757\pi$
$631$	6.64773	0.264642	0.132321	+	0.991207i	$0.457757\pi$
$632$	29.9305	1.19057
$633$	4.60407	0.182995
$634$	9.89795	0.393098
$635$	−0.866045	−0.0343680
$636$	−8.34409	−0.330865
$637$	−0.340258	−0.0134815
$638$	−5.81885	−0.230370
$639$	7.22538	0.285832
$640$	1.92428	0.0760638
$641$	−31.4407	−1.24183	−0.620917	−	0.783876i	$-0.713240\pi$
$641$	−31.4407	−1.24183	−0.620917	+	0.783876i	$0.713240\pi$
$642$	10.9074	0.430481
$643$	−3.12125	−0.123090	−0.0615451	−	0.998104i	$-0.519603\pi$
$643$	−3.12125	−0.123090	−0.0615451	+	0.998104i	$0.519603\pi$
$644$	1.30366	0.0513714
$645$	−3.18524	−0.125419
$646$	−16.1377	−0.634929
$647$	42.8123	1.68313	0.841563	−	0.540159i	$-0.181636\pi$
$647$	42.8123	1.68313	0.841563	+	0.540159i	$0.181636\pi$
$648$	−3.07857	−0.120937
$649$	28.8982	1.13435
$650$	0.115136	0.00451601
$651$	13.0426	0.511180
$652$	5.22979	0.204815
$653$	−35.0488	−1.37156	−0.685782	−	0.727807i	$-0.740540\pi$
$653$	−35.0488	−1.37156	−0.685782	+	0.727807i	$0.740540\pi$
$654$	8.07949	0.315933
$655$	0.0822417	0.00321345
$656$	3.77550	0.147408
$657$	17.0109	0.663658
$658$	38.3363	1.49450
$659$	−21.8125	−0.849693	−0.424846	−	0.905265i	$-0.639672\pi$
$659$	−21.8125	−0.849693	−0.424846	+	0.905265i	$0.639672\pi$
$660$	−1.51442	−0.0589486
$661$	24.6367	0.958257	0.479129	−	0.877745i	$-0.340953\pi$
$661$	24.6367	0.958257	0.479129	+	0.877745i	$0.340953\pi$
$662$	33.9343	1.31889
$663$	0.0533400	0.00207155
$664$	−45.0192	−1.74708
$665$	25.1771	0.976325
$666$	4.82267	0.186875
$667$	0.823081	0.0318698
$668$	−5.08993	−0.196935
$669$	−25.1188	−0.971148
$670$	9.22950	0.356567
$671$	15.0338	0.580373
$672$	17.2782	0.666520
$673$	−15.1947	−0.585714	−0.292857	−	0.956156i	$-0.594606\pi$
$673$	−15.1947	−0.585714	−0.292857	+	0.956156i	$0.594606\pi$
$674$	17.1894	0.662111
$675$	4.24997	0.163581
$676$	9.07134	0.348898
$677$	−42.3018	−1.62579	−0.812896	−	0.582409i	$-0.802110\pi$
$677$	−42.3018	−1.62579	−0.812896	+	0.582409i	$0.802110\pi$
$678$	13.9398	0.535354
$679$	35.2821	1.35400
$680$	−5.99033	−0.229719
$681$	8.98714	0.344388
$682$	−8.07491	−0.309204
$683$	−5.89744	−0.225659	−0.112830	−	0.993614i	$-0.535991\pi$
$683$	−5.89744	−0.225659	−0.112830	+	0.993614i	$0.535991\pi$
$684$	4.39230	0.167944
$685$	−4.18552	−0.159921
$686$	−38.6454	−1.47549
$687$	−7.44347	−0.283986
$688$	−7.78756	−0.296898
$689$	0.283872	0.0108147
$690$	−0.399736	−0.0152177
$691$	12.9783	0.493716	0.246858	−	0.969052i	$-0.420602\pi$
$691$	12.9783	0.493716	0.246858	+	0.969052i	$0.420602\pi$
$692$	10.2073	0.388022
$693$	11.5738	0.439654
$694$	18.7470	0.711628
$695$	1.04392	0.0395981
$696$	6.26460	0.237459
$697$	−4.00623	−0.151747
$698$	35.4854	1.34314
$699$	28.2813	1.06970
$700$	−13.6978	−0.517729
$701$	−48.0815	−1.81601	−0.908007	−	0.418956i	$-0.862396\pi$
$701$	−48.0815	−1.81601	−0.908007	+	0.418956i	$0.862396\pi$
$702$	0.0270911	0.00102249
$703$	−26.6010	−1.00328
$704$	−21.3090	−0.803113
$705$	6.29936	0.237248
$706$	−30.5939	−1.15141
$707$	−5.74383	−0.216019
$708$	−8.04748	−0.302443
$709$	−37.0041	−1.38972	−0.694859	−	0.719146i	$-0.744533\pi$
$709$	−37.0041	−1.38972	−0.694859	+	0.719146i	$0.744533\pi$
$710$	7.14062	0.267983
$711$	−9.72221	−0.364611
$712$	44.1205	1.65349
$713$	1.14220	0.0427758
$714$	11.8417	0.443166
$715$	0.0515216	0.00192680
$716$	8.79259	0.328595
$717$	−18.8174	−0.702750
$718$	−3.17630	−0.118539
$719$	44.0197	1.64166	0.820828	−	0.571175i	$-0.193512\pi$
$719$	44.0197	1.64166	0.820828	+	0.571175i	$0.193512\pi$
$720$	−1.83375	−0.0683400
$721$	−27.3683	−1.01925
$722$	23.5276	0.875605
$723$	−25.6768	−0.954930
$724$	−7.72336	−0.287037
$725$	−8.64829	−0.321189
$726$	5.38685	0.199925
$727$	20.4134	0.757089	0.378545	−	0.925583i	$-0.376425\pi$
$727$	20.4134	0.757089	0.378545	+	0.925583i	$0.376425\pi$
$728$	−0.337566	−0.0125110
$729$	1.00000	0.0370370
$730$	16.8113	0.622215
$731$	8.26347	0.305636
$732$	−4.18656	−0.154740
$733$	−14.9377	−0.551737	−0.275868	−	0.961195i	$-0.588965\pi$
$733$	−14.9377	−0.551737	−0.275868	+	0.961195i	$0.588965\pi$
$734$	7.23658	0.267107
$735$	−12.4125	−0.457841
$736$	1.51313	0.0557747
$737$	−23.4024	−0.862039
$738$	−2.03474	−0.0748997
$739$	−15.9188	−0.585581	−0.292791	−	0.956177i	$-0.594584\pi$
$739$	−15.9188	−0.585581	−0.292791	+	0.956177i	$0.594584\pi$
$740$	−2.55411	−0.0938911
$741$	−0.149430	−0.00548943
$742$	63.0211	2.31358
$743$	25.1415	0.922350	0.461175	−	0.887309i	$-0.347428\pi$
$743$	25.1415	0.922350	0.461175	+	0.887309i	$0.347428\pi$
$744$	8.69348	0.318718
$745$	−12.6480	−0.463385
$746$	26.7896	0.980838
$747$	14.6234	0.535044
$748$	3.92886	0.143653
$749$	44.1475	1.61311
$750$	9.14145	0.333799
$751$	42.4219	1.54800	0.773998	−	0.633188i	$-0.218254\pi$
$751$	42.4219	1.54800	0.773998	+	0.633188i	$0.218254\pi$
$752$	15.4013	0.561626
$753$	−0.815872	−0.0297320
$754$	−0.0551278	−0.00200764
$755$	−11.6107	−0.422558
$756$	−3.22304	−0.117221
$757$	−21.9736	−0.798644	−0.399322	−	0.916811i	$-0.630755\pi$
$757$	−21.9736	−0.798644	−0.399322	+	0.916811i	$0.630755\pi$
$758$	−37.4251	−1.35934
$759$	1.01357	0.0367904
$760$	16.7816	0.608734
$761$	−0.519935	−0.0188476	−0.00942381	−	0.999956i	$-0.503000\pi$
$761$	−0.519935	−0.0188476	−0.00942381	+	0.999956i	$0.503000\pi$
$762$	1.14113	0.0413387
$763$	32.7016	1.18388
$764$	−7.92438	−0.286694
$765$	1.94582	0.0703512
$766$	41.4720	1.49844
$767$	0.273782	0.00988568
$768$	14.4718	0.522206
$769$	21.6785	0.781748	0.390874	−	0.920444i	$-0.372173\pi$
$769$	21.6785	0.781748	0.390874	+	0.920444i	$0.372173\pi$
$770$	11.4381	0.412199
$771$	−24.7849	−0.892605
$772$	1.70671	0.0614257
$773$	31.8512	1.14561	0.572803	−	0.819693i	$-0.305856\pi$
$773$	31.8512	1.14561	0.572803	+	0.819693i	$0.305856\pi$
$774$	4.19697	0.150857
$775$	−12.0014	−0.431102
$776$	23.5171	0.844214
$777$	19.5196	0.700264
$778$	−25.2334	−0.904660
$779$	11.2233	0.402115
$780$	−0.0143476	−0.000513726 0
$781$	−18.1058	−0.647878
$782$	1.03704	0.0370843
$783$	−2.03491	−0.0727217
$784$	−30.3472	−1.08383
$785$	7.09332	0.253172
$786$	−0.108364	−0.00386522
$787$	−11.6350	−0.414743	−0.207371	−	0.978262i	$-0.566491\pi$
$787$	−11.6350	−0.414743	−0.207371	+	0.978262i	$0.566491\pi$
$788$	−5.54297	−0.197460
$789$	−8.21365	−0.292414
$790$	−9.60816	−0.341843
$791$	56.4210	2.00610
$792$	7.71447	0.274122
$793$	0.142430	0.00505784
$794$	−18.2974	−0.649351
$795$	10.3555	0.367273
$796$	17.3468	0.614843
$797$	30.2884	1.07287	0.536436	−	0.843941i	$-0.319770\pi$
$797$	30.2884	1.07287	0.536436	+	0.843941i	$0.319770\pi$
$798$	−33.1741	−1.17435
$799$	−16.3425	−0.578155
$800$	−15.8988	−0.562107
$801$	−14.3315	−0.506379
$802$	18.3202	0.646910
$803$	−42.6270	−1.50427
$804$	6.51703	0.229838
$805$	−1.61792	−0.0570243
$806$	−0.0765017	−0.00269466
$807$	6.04346	0.212740
$808$	−3.82852	−0.134687
$809$	43.9163	1.54401	0.772007	−	0.635614i	$-0.219253\pi$
$809$	43.9163	1.54401	0.772007	+	0.635614i	$0.219253\pi$
$810$	0.988269	0.0347242
$811$	−30.9134	−1.08552	−0.542758	−	0.839889i	$-0.682620\pi$
$811$	−30.9134	−1.08552	−0.542758	+	0.839889i	$0.682620\pi$
$812$	6.55860	0.230162
$813$	−21.2963	−0.746895
$814$	−12.0850	−0.423577
$815$	−6.49050	−0.227352
$816$	4.75732	0.166539
$817$	−23.1497	−0.809907
$818$	37.2215	1.30142
$819$	0.109651	0.00383150
$820$	1.07761	0.0376318
$821$	11.2680	0.393255	0.196627	−	0.980478i	$-0.437001\pi$
$821$	11.2680	0.393255	0.196627	+	0.980478i	$0.437001\pi$
$822$	5.51497	0.192357
$823$	−31.6821	−1.10437	−0.552185	−	0.833722i	$-0.686206\pi$
$823$	−31.6821	−1.10437	−0.552185	+	0.833722i	$0.686206\pi$
$824$	−18.2422	−0.635496
$825$	−10.6498	−0.370780
$826$	60.7809	2.11484
$827$	1.14556	0.0398351	0.0199175	−	0.999802i	$-0.493660\pi$
$827$	1.14556	0.0398351	0.0199175	+	0.999802i	$0.493660\pi$
$828$	−0.282257	−0.00980911
$829$	−30.2590	−1.05094	−0.525469	−	0.850812i	$-0.676110\pi$
$829$	−30.2590	−1.05094	−0.525469	+	0.850812i	$0.676110\pi$
$830$	14.4519	0.501633
$831$	2.26008	0.0784014
$832$	−0.201882	−0.00699898
$833$	32.2017	1.11572
$834$	−1.37550	−0.0476297
$835$	6.31692	0.218606
$836$	−11.0065	−0.380668
$837$	−2.82387	−0.0976073
$838$	−37.9138	−1.30971
$839$	−25.7069	−0.887499	−0.443750	−	0.896151i	$-0.646352\pi$
$839$	−25.7069	−0.887499	−0.443750	+	0.896151i	$0.646352\pi$
$840$	−12.3143	−0.424882
$841$	−24.8591	−0.857212
$842$	−33.1056	−1.14089
$843$	−17.9505	−0.618248
$844$	3.21284	0.110590
$845$	−11.2581	−0.387290
$846$	−8.30023	−0.285368
$847$	21.8032	0.749167
$848$	25.3182	0.869429
$849$	−11.3307	−0.388868
$850$	−10.8964	−0.373742
$851$	1.70943	0.0585984
$852$	5.04206	0.172738
$853$	5.49690	0.188210	0.0941051	−	0.995562i	$-0.470001\pi$
$853$	5.49690	0.188210	0.0941051	+	0.995562i	$0.470001\pi$
$854$	31.6202	1.08202
$855$	−5.45112	−0.186424
$856$	29.4263	1.00577
$857$	−28.3413	−0.968122	−0.484061	−	0.875034i	$-0.660839\pi$
$857$	−28.3413	−0.968122	−0.484061	+	0.875034i	$0.660839\pi$
$858$	−0.0678865	−0.00231761
$859$	−34.3165	−1.17086	−0.585432	−	0.810722i	$-0.699075\pi$
$859$	−34.3165	−1.17086	−0.585432	+	0.810722i	$0.699075\pi$
$860$	−2.22274	−0.0757948
$861$	−8.23556	−0.280667
$862$	−14.6562	−0.499192
$863$	−35.1550	−1.19669	−0.598346	−	0.801238i	$-0.704175\pi$
$863$	−35.1550	−1.19669	−0.598346	+	0.801238i	$0.704175\pi$
$864$	−3.74092	−0.127269
$865$	−12.6679	−0.430720
$866$	40.4236	1.37365
$867$	11.9520	0.405910
$868$	9.10147	0.308924
$869$	24.3625	0.826443
$870$	−2.01104	−0.0681805
$871$	−0.221715	−0.00751251
$872$	21.7970	0.738141
$873$	−7.63897	−0.258540
$874$	−2.90521	−0.0982702
$875$	36.9999	1.25082
$876$	11.8706	0.401071
$877$	35.3841	1.19484	0.597418	−	0.801930i	$-0.296193\pi$
$877$	35.3841	1.19484	0.597418	+	0.801930i	$0.296193\pi$
$878$	−8.98007	−0.303063
$879$	−7.66695	−0.258600
$880$	4.59514	0.154902
$881$	−15.9379	−0.536961	−0.268480	−	0.963285i	$-0.586521\pi$
$881$	−15.9379	−0.536961	−0.268480	+	0.963285i	$0.586521\pi$
$882$	16.3551	0.550703
$883$	38.6747	1.30151	0.650754	−	0.759289i	$-0.274453\pi$
$883$	38.6747	1.30151	0.650754	+	0.759289i	$0.274453\pi$
$884$	0.0372220	0.00125191
$885$	9.98743	0.335724
$886$	−8.13139	−0.273179
$887$	−38.4009	−1.28938	−0.644689	−	0.764445i	$-0.723013\pi$
$887$	−38.4009	−1.28938	−0.644689	+	0.764445i	$0.723013\pi$
$888$	13.0107	0.436611
$889$	4.61870	0.154906
$890$	−14.1634	−0.474758
$891$	−2.50587	−0.0839497
$892$	−17.5285	−0.586899
$893$	45.7826	1.53206
$894$	16.6654	0.557373
$895$	−10.9122	−0.364753
$896$	−10.2623	−0.342841
$897$	0.00960261	0.000320622 0
$898$	7.07285	0.236024
$899$	5.74632	0.191651
$900$	2.96574	0.0988578
$901$	−26.8654	−0.895016
$902$	5.09878	0.169771
$903$	16.9871	0.565297
$904$	37.6071	1.25079
$905$	9.58518	0.318622
$906$	15.2987	0.508264
$907$	−20.7411	−0.688698	−0.344349	−	0.938842i	$-0.611900\pi$
$907$	−20.7411	−0.688698	−0.344349	+	0.938842i	$0.611900\pi$
$908$	6.27146	0.208126
$909$	1.24361	0.0412478
$910$	0.108364	0.00359224
$911$	20.9929	0.695527	0.347764	−	0.937582i	$-0.386941\pi$
$911$	20.9929	0.695527	0.347764	+	0.937582i	$0.386941\pi$
$912$	−13.3274	−0.441314
$913$	−36.6444	−1.21275
$914$	5.84172	0.193227
$915$	5.19578	0.171767
$916$	−5.19425	−0.171623
$917$	−0.438602	−0.0144839
$918$	−2.56387	−0.0846204
$919$	40.4100	1.33300	0.666502	−	0.745503i	$-0.267791\pi$
$919$	40.4100	1.33300	0.666502	+	0.745503i	$0.267791\pi$
$920$	−1.07842	−0.0355544
$921$	22.1039	0.728348
$922$	44.5597	1.46750
$923$	−0.171535	−0.00564614
$924$	8.07652	0.265698
$925$	−17.9613	−0.590564
$926$	−18.7699	−0.616818
$927$	5.92554	0.194620
$928$	7.61243	0.249890
$929$	29.2152	0.958520	0.479260	−	0.877673i	$-0.340905\pi$
$929$	29.2152	0.958520	0.479260	+	0.877673i	$0.340905\pi$
$930$	−2.79075	−0.0915122
$931$	−90.2117	−2.95657
$932$	19.7354	0.646455
$933$	6.55234	0.214514
$934$	−33.3580	−1.09151
$935$	−4.87596	−0.159461
$936$	0.0730869	0.00238892
$937$	11.0639	0.361441	0.180721	−	0.983534i	$-0.442157\pi$
$937$	11.0639	0.361441	0.180721	+	0.983534i	$0.442157\pi$
$938$	−49.2217	−1.60715
$939$	16.9684	0.553741
$940$	4.39585	0.143377
$941$	8.05100	0.262455	0.131228	−	0.991352i	$-0.458108\pi$
$941$	8.05100	0.262455	0.131228	+	0.991352i	$0.458108\pi$
$942$	−9.34638	−0.304522
$943$	−0.721227	−0.0234864
$944$	24.4182	0.794744
$945$	4.00000	0.130120
$946$	−10.5170	−0.341938
$947$	45.3498	1.47367	0.736836	−	0.676072i	$-0.236319\pi$
$947$	45.3498	1.47367	0.736836	+	0.676072i	$0.236319\pi$
$948$	−6.78441	−0.220347
$949$	−0.403848	−0.0131095
$950$	30.5257	0.990383
$951$	−8.67382	−0.281268
$952$	31.9470	1.03541
$953$	−53.1712	−1.72238	−0.861191	−	0.508281i	$-0.830281\pi$
$953$	−53.1712	−1.72238	−0.861191	+	0.508281i	$0.830281\pi$
$954$	−13.6448	−0.441766
$955$	9.83465	0.318242
$956$	−13.1313	−0.424696
$957$	5.09921	0.164834
$958$	2.59650	0.0838890
$959$	22.3218	0.720807
$960$	−7.36454	−0.237690
$961$	−23.0257	−0.742766
$962$	−0.114493	−0.00369140
$963$	−9.55843	−0.308016
$964$	−17.9179	−0.577097
$965$	−2.11813	−0.0681850
$966$	2.13183	0.0685904
$967$	−30.4078	−0.977848	−0.488924	−	0.872327i	$-0.662610\pi$
$967$	−30.4078	−0.977848	−0.488924	+	0.872327i	$0.662610\pi$
$968$	14.5328	0.467102
$969$	14.1419	0.454302
$970$	−7.54936	−0.242395
$971$	−21.5166	−0.690501	−0.345250	−	0.938511i	$-0.612206\pi$
$971$	−21.5166	−0.690501	−0.345250	+	0.938511i	$0.612206\pi$
$972$	0.697826	0.0223828
$973$	−5.56731	−0.178480
$974$	8.49375	0.272157
$975$	−0.100897	−0.00323128
$976$	12.7031	0.406617
$977$	−42.7977	−1.36922	−0.684610	−	0.728910i	$-0.740027\pi$
$977$	−42.7977	−1.36922	−0.684610	+	0.728910i	$0.740027\pi$
$978$	8.55209	0.273466
$979$	35.9128	1.14778
$980$	−8.66174	−0.276689
$981$	−7.08026	−0.226055
$982$	−2.39101	−0.0763002
$983$	3.67993	0.117371	0.0586857	−	0.998277i	$-0.481309\pi$
$983$	3.67993	0.117371	0.0586857	+	0.998277i	$0.481309\pi$
$984$	−5.48937	−0.174995
$985$	6.87917	0.219188
$986$	5.21724	0.166151
$987$	−33.5950	−1.06934
$988$	−0.104276	−0.00331745
$989$	1.48764	0.0473043
$990$	−2.47647	−0.0787074
$991$	−6.99941	−0.222344	−0.111172	−	0.993801i	$-0.535460\pi$
$991$	−6.99941	−0.222344	−0.111172	+	0.993801i	$0.535460\pi$
$992$	10.5639	0.335404
$993$	−29.7375	−0.943690
$994$	−38.0816	−1.20787
$995$	−21.5285	−0.682500
$996$	10.2046	0.323346
$997$	−17.1456	−0.543008	−0.271504	−	0.962437i	$-0.587521\pi$
$997$	−17.1456	−0.543008	−0.271504	+	0.962437i	$0.587521\pi$
$998$	−19.3811	−0.613499
$999$	−4.22623	−0.133712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.2.a.c.1.4	✓	5
3.2	odd	2		1143.2.a.h.1.2		5
4.3	odd	2		6096.2.a.be.1.4		5
5.4	even	2		9525.2.a.k.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.a.c.1.4	✓	5	1.1	even	1	trivial
1143.2.a.h.1.2		5	3.2	odd	2
6096.2.a.be.1.4		5	4.3	odd	2
9525.2.a.k.1.2		5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.a (trivial)

\(f(q)\)	\(=\)	\(q+1.14113 q^{2} -1.00000 q^{3} -0.697826 q^{4} +0.866045 q^{5} -1.14113 q^{6} -4.61870 q^{7} -3.07857 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.14113 q^{2} -1.00000 q^{3} -0.697826 q^{4} +0.866045 q^{5} -1.14113 q^{6} -4.61870 q^{7} -3.07857 q^{8} +1.00000 q^{9} +0.988269 q^{10} -2.50587 q^{11} +0.697826 q^{12} -0.0237406 q^{13} -5.27053 q^{14} -0.866045 q^{15} -2.11739 q^{16} +2.24679 q^{17} +1.14113 q^{18} -6.29427 q^{19} -0.604349 q^{20} +4.61870 q^{21} -2.85951 q^{22} +0.404481 q^{23} +3.07857 q^{24} -4.24997 q^{25} -0.0270911 q^{26} -1.00000 q^{27} +3.22304 q^{28} +2.03491 q^{29} -0.988269 q^{30} +2.82387 q^{31} +3.74092 q^{32} +2.50587 q^{33} +2.56387 q^{34} -4.00000 q^{35} -0.697826 q^{36} +4.22623 q^{37} -7.18257 q^{38} +0.0237406 q^{39} -2.66618 q^{40} -1.78309 q^{41} +5.27053 q^{42} +3.67791 q^{43} +1.74866 q^{44} +0.866045 q^{45} +0.461565 q^{46} -7.27371 q^{47} +2.11739 q^{48} +14.3324 q^{49} -4.84976 q^{50} -2.24679 q^{51} +0.0165668 q^{52} -11.9573 q^{53} -1.14113 q^{54} -2.17019 q^{55} +14.2190 q^{56} +6.29427 q^{57} +2.32209 q^{58} -11.5322 q^{59} +0.604349 q^{60} -5.99944 q^{61} +3.22240 q^{62} -4.61870 q^{63} +8.50365 q^{64} -0.0205604 q^{65} +2.85951 q^{66} +9.33906 q^{67} -1.56786 q^{68} -0.404481 q^{69} -4.56451 q^{70} +7.22538 q^{71} -3.07857 q^{72} +17.0109 q^{73} +4.82267 q^{74} +4.24997 q^{75} +4.39230 q^{76} +11.5738 q^{77} +0.0270911 q^{78} -9.72221 q^{79} -1.83375 q^{80} +1.00000 q^{81} -2.03474 q^{82} +14.6234 q^{83} -3.22304 q^{84} +1.94582 q^{85} +4.19697 q^{86} -2.03491 q^{87} +7.71447 q^{88} -14.3315 q^{89} +0.988269 q^{90} +0.109651 q^{91} -0.282257 q^{92} -2.82387 q^{93} -8.30023 q^{94} -5.45112 q^{95} -3.74092 q^{96} -7.63897 q^{97} +16.3551 q^{98} -2.50587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 5 q^{3} + q^{4} - 5 q^{5} + q^{6} - 3 q^{8} + 5 q^{9} - 2 q^{10} - 16 q^{11} - q^{12} + 3 q^{13} - 6 q^{14} + 5 q^{15} - 7 q^{16} - 6 q^{17} - q^{18} - 8 q^{19} - 12 q^{20} - 8 q^{22} - 9 q^{23} + 3 q^{24} + 4 q^{25} - 2 q^{26} - 5 q^{27} + 2 q^{28} - 17 q^{29} + 2 q^{30} - 9 q^{31} - 2 q^{32} + 16 q^{33} - q^{34} - 20 q^{35} + q^{36} - q^{37} + q^{38} - 3 q^{39} + 16 q^{40} - 2 q^{41} + 6 q^{42} - 4 q^{43} + 3 q^{44} - 5 q^{45} + 4 q^{46} - 8 q^{47} + 7 q^{48} + 13 q^{49} + 15 q^{50} + 6 q^{51} + 13 q^{52} - 15 q^{53} + q^{54} + 20 q^{55} + 8 q^{56} + 8 q^{57} + 34 q^{58} - 19 q^{59} + 12 q^{60} + q^{61} + 15 q^{62} + q^{64} - 5 q^{65} + 8 q^{66} - 2 q^{67} + 14 q^{68} + 9 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 17 q^{74} - 4 q^{75} + 8 q^{76} + 2 q^{77} + 2 q^{78} - 28 q^{79} + 12 q^{80} + 5 q^{81} + 30 q^{82} - q^{83} - 2 q^{84} + 6 q^{85} + 32 q^{86} + 17 q^{87} + 3 q^{88} + q^{89} - 2 q^{90} - 18 q^{91} + 12 q^{92} + 9 q^{93} + 16 q^{94} + 4 q^{95} + 2 q^{96} + 28 q^{97} + 15 q^{98} - 16 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + q^4 - 5 * q^5 + q^6 - 3 * q^8 + 5 * q^9 - 2 * q^10 - 16 * q^11 - q^12 + 3 * q^13 - 6 * q^14 + 5 * q^15 - 7 * q^16 - 6 * q^17 - q^18 - 8 * q^19 - 12 * q^20 - 8 * q^22 - 9 * q^23 + 3 * q^24 + 4 * q^25 - 2 * q^26 - 5 * q^27 + 2 * q^28 - 17 * q^29 + 2 * q^30 - 9 * q^31 - 2 * q^32 + 16 * q^33 - q^34 - 20 * q^35 + q^36 - q^37 + q^38 - 3 * q^39 + 16 * q^40 - 2 * q^41 + 6 * q^42 - 4 * q^43 + 3 * q^44 - 5 * q^45 + 4 * q^46 - 8 * q^47 + 7 * q^48 + 13 * q^49 + 15 * q^50 + 6 * q^51 + 13 * q^52 - 15 * q^53 + q^54 + 20 * q^55 + 8 * q^56 + 8 * q^57 + 34 * q^58 - 19 * q^59 + 12 * q^60 + q^61 + 15 * q^62 + q^64 - 5 * q^65 + 8 * q^66 - 2 * q^67 + 14 * q^68 + 9 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 17 * q^74 - 4 * q^75 + 8 * q^76 + 2 * q^77 + 2 * q^78 - 28 * q^79 + 12 * q^80 + 5 * q^81 + 30 * q^82 - q^83 - 2 * q^84 + 6 * q^85 + 32 * q^86 + 17 * q^87 + 3 * q^88 + q^89 - 2 * q^90 - 18 * q^91 + 12 * q^92 + 9 * q^93 + 16 * q^94 + 4 * q^95 + 2 * q^96 + 28 * q^97 + 15 * q^98 - 16 * q^99

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