LMFDB - Embedded newform 6015.2.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.403903 q^{2} +1.00000 q^{3} -1.83686 q^{4} -1.00000 q^{5} +0.403903 q^{6} +0.330671 q^{7} -1.54972 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.403903 q^{2} +1.00000 q^{3} -1.83686 q^{4} -1.00000 q^{5} +0.403903 q^{6} +0.330671 q^{7} -1.54972 q^{8} +1.00000 q^{9} -0.403903 q^{10} +0.933448 q^{11} -1.83686 q^{12} -4.15432 q^{13} +0.133559 q^{14} -1.00000 q^{15} +3.04779 q^{16} -0.316975 q^{17} +0.403903 q^{18} +2.03547 q^{19} +1.83686 q^{20} +0.330671 q^{21} +0.377023 q^{22} +1.34990 q^{23} -1.54972 q^{24} +1.00000 q^{25} -1.67794 q^{26} +1.00000 q^{27} -0.607397 q^{28} +0.499857 q^{29} -0.403903 q^{30} +2.54548 q^{31} +4.33045 q^{32} +0.933448 q^{33} -0.128027 q^{34} -0.330671 q^{35} -1.83686 q^{36} -6.91988 q^{37} +0.822135 q^{38} -4.15432 q^{39} +1.54972 q^{40} +6.76056 q^{41} +0.133559 q^{42} +10.2322 q^{43} -1.71462 q^{44} -1.00000 q^{45} +0.545229 q^{46} -12.3033 q^{47} +3.04779 q^{48} -6.89066 q^{49} +0.403903 q^{50} -0.316975 q^{51} +7.63092 q^{52} +0.790332 q^{53} +0.403903 q^{54} -0.933448 q^{55} -0.512447 q^{56} +2.03547 q^{57} +0.201894 q^{58} -8.46192 q^{59} +1.83686 q^{60} +3.59102 q^{61} +1.02813 q^{62} +0.330671 q^{63} -4.34649 q^{64} +4.15432 q^{65} +0.377023 q^{66} -5.69675 q^{67} +0.582239 q^{68} +1.34990 q^{69} -0.133559 q^{70} +10.3801 q^{71} -1.54972 q^{72} -8.44298 q^{73} -2.79496 q^{74} +1.00000 q^{75} -3.73889 q^{76} +0.308664 q^{77} -1.67794 q^{78} +7.10902 q^{79} -3.04779 q^{80} +1.00000 q^{81} +2.73061 q^{82} -8.85599 q^{83} -0.607397 q^{84} +0.316975 q^{85} +4.13283 q^{86} +0.499857 q^{87} -1.44658 q^{88} +2.47224 q^{89} -0.403903 q^{90} -1.37371 q^{91} -2.47958 q^{92} +2.54548 q^{93} -4.96934 q^{94} -2.03547 q^{95} +4.33045 q^{96} -8.94115 q^{97} -2.78316 q^{98} +0.933448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - 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 $

$2$	0.403903	0.285603	0.142801	−	0.989751i	$-0.454389\pi$
$2$	0.403903	0.285603	0.142801	+	0.989751i	$0.454389\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.83686	−0.918431
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.403903	0.164893
$7$	0.330671	0.124982	0.0624909	−	0.998046i	$-0.480096\pi$
$7$	0.330671	0.124982	0.0624909	+	0.998046i	$0.480096\pi$
$8$	−1.54972	−0.547909
$9$	1.00000	0.333333
$10$	−0.403903	−0.127725
$11$	0.933448	0.281445	0.140723	−	0.990049i	$-0.455057\pi$
$11$	0.933448	0.281445	0.140723	+	0.990049i	$0.455057\pi$
$12$	−1.83686	−0.530256
$13$	−4.15432	−1.15220	−0.576101	−	0.817379i	$-0.695426\pi$
$13$	−4.15432	−1.15220	−0.576101	+	0.817379i	$0.695426\pi$
$14$	0.133559	0.0356951
$15$	−1.00000	−0.258199
$16$	3.04779	0.761947
$17$	−0.316975	−0.0768776	−0.0384388	−	0.999261i	$-0.512238\pi$
$17$	−0.316975	−0.0768776	−0.0384388	+	0.999261i	$0.512238\pi$
$18$	0.403903	0.0952009
$19$	2.03547	0.466970	0.233485	−	0.972360i	$-0.424987\pi$
$19$	2.03547	0.466970	0.233485	+	0.972360i	$0.424987\pi$
$20$	1.83686	0.410735
$21$	0.330671	0.0721583
$22$	0.377023	0.0803815
$23$	1.34990	0.281473	0.140737	−	0.990047i	$-0.455053\pi$
$23$	1.34990	0.281473	0.140737	+	0.990047i	$0.455053\pi$
$24$	−1.54972	−0.316336
$25$	1.00000	0.200000
$26$	−1.67794	−0.329072
$27$	1.00000	0.192450
$28$	−0.607397	−0.114787
$29$	0.499857	0.0928212	0.0464106	−	0.998922i	$-0.485222\pi$
$29$	0.499857	0.0928212	0.0464106	+	0.998922i	$0.485222\pi$
$30$	−0.403903	−0.0737423
$31$	2.54548	0.457182	0.228591	−	0.973523i	$-0.426588\pi$
$31$	2.54548	0.457182	0.228591	+	0.973523i	$0.426588\pi$
$32$	4.33045	0.765523
$33$	0.933448	0.162492
$34$	−0.128027	−0.0219565
$35$	−0.330671	−0.0558936
$36$	−1.83686	−0.306144
$37$	−6.91988	−1.13762	−0.568810	−	0.822469i	$-0.692596\pi$
$37$	−6.91988	−1.13762	−0.568810	+	0.822469i	$0.692596\pi$
$38$	0.822135	0.133368
$39$	−4.15432	−0.665224
$40$	1.54972	0.245032
$41$	6.76056	1.05582	0.527911	−	0.849300i	$-0.322975\pi$
$41$	6.76056	1.05582	0.527911	+	0.849300i	$0.322975\pi$
$42$	0.133559	0.0206086
$43$	10.2322	1.56040	0.780200	−	0.625530i	$-0.215117\pi$
$43$	10.2322	1.56040	0.780200	+	0.625530i	$0.215117\pi$
$44$	−1.71462	−0.258488
$45$	−1.00000	−0.149071
$46$	0.545229	0.0803896
$47$	−12.3033	−1.79462	−0.897310	−	0.441402i	$-0.854481\pi$
$47$	−12.3033	−1.79462	−0.897310	+	0.441402i	$0.854481\pi$
$48$	3.04779	0.439910
$49$	−6.89066	−0.984380
$50$	0.403903	0.0571205
$51$	−0.316975	−0.0443853
$52$	7.63092	1.05822
$53$	0.790332	0.108561	0.0542803	−	0.998526i	$-0.482714\pi$
$53$	0.790332	0.108561	0.0542803	+	0.998526i	$0.482714\pi$
$54$	0.403903	0.0549643
$55$	−0.933448	−0.125866
$56$	−0.512447	−0.0684787
$57$	2.03547	0.269605
$58$	0.201894	0.0265100
$59$	−8.46192	−1.10165	−0.550824	−	0.834621i	$-0.685687\pi$
$59$	−8.46192	−1.10165	−0.550824	+	0.834621i	$0.685687\pi$
$60$	1.83686	0.237138
$61$	3.59102	0.459783	0.229892	−	0.973216i	$-0.426163\pi$
$61$	3.59102	0.459783	0.229892	+	0.973216i	$0.426163\pi$
$62$	1.02813	0.130572
$63$	0.330671	0.0416606
$64$	−4.34649	−0.543311
$65$	4.15432	0.515280
$66$	0.377023	0.0464083
$67$	−5.69675	−0.695969	−0.347985	−	0.937500i	$-0.613134\pi$
$67$	−5.69675	−0.695969	−0.347985	+	0.937500i	$0.613134\pi$
$68$	0.582239	0.0706068
$69$	1.34990	0.162509
$70$	−0.133559	−0.0159634
$71$	10.3801	1.23189	0.615944	−	0.787790i	$-0.288775\pi$
$71$	10.3801	1.23189	0.615944	+	0.787790i	$0.288775\pi$
$72$	−1.54972	−0.182636
$73$	−8.44298	−0.988176	−0.494088	−	0.869412i	$-0.664498\pi$
$73$	−8.44298	−0.988176	−0.494088	+	0.869412i	$0.664498\pi$
$74$	−2.79496	−0.324908
$75$	1.00000	0.115470
$76$	−3.73889	−0.428880
$77$	0.308664	0.0351755
$78$	−1.67794	−0.189990
$79$	7.10902	0.799827	0.399914	−	0.916553i	$-0.369040\pi$
$79$	7.10902	0.799827	0.399914	+	0.916553i	$0.369040\pi$
$80$	−3.04779	−0.340753
$81$	1.00000	0.111111
$82$	2.73061	0.301546
$83$	−8.85599	−0.972071	−0.486035	−	0.873939i	$-0.661557\pi$
$83$	−8.85599	−0.972071	−0.486035	+	0.873939i	$0.661557\pi$
$84$	−0.607397	−0.0662724
$85$	0.316975	0.0343807
$86$	4.13283	0.445655
$87$	0.499857	0.0535903
$88$	−1.44658	−0.154206
$89$	2.47224	0.262057	0.131028	−	0.991379i	$-0.458172\pi$
$89$	2.47224	0.262057	0.131028	+	0.991379i	$0.458172\pi$
$90$	−0.403903	−0.0425751
$91$	−1.37371	−0.144004
$92$	−2.47958	−0.258514
$93$	2.54548	0.263954
$94$	−4.96934	−0.512548
$95$	−2.03547	−0.208835
$96$	4.33045	0.441975
$97$	−8.94115	−0.907836	−0.453918	−	0.891043i	$-0.649974\pi$
$97$	−8.94115	−0.907836	−0.453918	+	0.891043i	$0.649974\pi$
$98$	−2.78316	−0.281142
$99$	0.933448	0.0938150
$100$	−1.83686	−0.183686
$101$	−11.0920	−1.10369	−0.551845	−	0.833946i	$-0.686076\pi$
$101$	−11.0920	−1.10369	−0.551845	+	0.833946i	$0.686076\pi$
$102$	−0.128027	−0.0126766
$103$	−8.64664	−0.851979	−0.425989	−	0.904728i	$-0.640074\pi$
$103$	−8.64664	−0.851979	−0.425989	+	0.904728i	$0.640074\pi$
$104$	6.43804	0.631302
$105$	−0.330671	−0.0322702
$106$	0.319218	0.0310052
$107$	−6.68773	−0.646527	−0.323264	−	0.946309i	$-0.604780\pi$
$107$	−6.68773	−0.646527	−0.323264	+	0.946309i	$0.604780\pi$
$108$	−1.83686	−0.176752
$109$	12.7586	1.22205	0.611026	−	0.791611i	$-0.290757\pi$
$109$	12.7586	1.22205	0.611026	+	0.791611i	$0.290757\pi$
$110$	−0.377023	−0.0359477
$111$	−6.91988	−0.656806
$112$	1.00781	0.0952295
$113$	0.944576	0.0888583	0.0444291	−	0.999013i	$-0.485853\pi$
$113$	0.944576	0.0888583	0.0444291	+	0.999013i	$0.485853\pi$
$114$	0.822135	0.0770000
$115$	−1.34990	−0.125879
$116$	−0.918169	−0.0852499
$117$	−4.15432	−0.384067
$118$	−3.41780	−0.314634
$119$	−0.104814	−0.00960830
$120$	1.54972	0.141470
$121$	−10.1287	−0.920789
$122$	1.45042	0.131315
$123$	6.76056	0.609579
$124$	−4.67570	−0.419890
$125$	−1.00000	−0.0894427
$126$	0.133559	0.0118984
$127$	4.26170	0.378165	0.189083	−	0.981961i	$-0.439449\pi$
$127$	4.26170	0.378165	0.189083	+	0.981961i	$0.439449\pi$
$128$	−10.4165	−0.920694
$129$	10.2322	0.900898
$130$	1.67794	0.147165
$131$	−18.6679	−1.63102	−0.815511	−	0.578741i	$-0.803544\pi$
$131$	−18.6679	−1.63102	−0.815511	+	0.578741i	$0.803544\pi$
$132$	−1.71462	−0.149238
$133$	0.673072	0.0583627
$134$	−2.30094	−0.198771
$135$	−1.00000	−0.0860663
$136$	0.491222	0.0421220
$137$	−2.83289	−0.242030	−0.121015	−	0.992651i	$-0.538615\pi$
$137$	−2.83289	−0.242030	−0.121015	+	0.992651i	$0.538615\pi$
$138$	0.545229	0.0464129
$139$	−6.98847	−0.592755	−0.296377	−	0.955071i	$-0.595779\pi$
$139$	−6.98847	−0.592755	−0.296377	+	0.955071i	$0.595779\pi$
$140$	0.607397	0.0513344
$141$	−12.3033	−1.03612
$142$	4.19255	0.351831
$143$	−3.87784	−0.324282
$144$	3.04779	0.253982
$145$	−0.499857	−0.0415109
$146$	−3.41015	−0.282226
$147$	−6.89066	−0.568332
$148$	12.7109	1.04483
$149$	13.4371	1.10081	0.550406	−	0.834897i	$-0.314473\pi$
$149$	13.4371	1.10081	0.550406	+	0.834897i	$0.314473\pi$
$150$	0.403903	0.0329786
$151$	−2.19844	−0.178907	−0.0894534	−	0.995991i	$-0.528512\pi$
$151$	−2.19844	−0.178907	−0.0894534	+	0.995991i	$0.528512\pi$
$152$	−3.15442	−0.255857
$153$	−0.316975	−0.0256259
$154$	0.124670	0.0100462
$155$	−2.54548	−0.204458
$156$	7.63092	0.610962
$157$	−22.0677	−1.76120	−0.880598	−	0.473864i	$-0.842859\pi$
$157$	−22.0677	−1.76120	−0.880598	+	0.473864i	$0.842859\pi$
$158$	2.87136	0.228433
$159$	0.790332	0.0626774
$160$	−4.33045	−0.342352
$161$	0.446372	0.0351790
$162$	0.403903	0.0317336
$163$	−3.96065	−0.310222	−0.155111	−	0.987897i	$-0.549573\pi$
$163$	−3.96065	−0.310222	−0.155111	+	0.987897i	$0.549573\pi$
$164$	−12.4182	−0.969700
$165$	−0.933448	−0.0726688
$166$	−3.57696	−0.277626
$167$	−11.9907	−0.927865	−0.463933	−	0.885871i	$-0.653562\pi$
$167$	−11.9907	−0.927865	−0.463933	+	0.885871i	$0.653562\pi$
$168$	−0.512447	−0.0395362
$169$	4.25839	0.327569
$170$	0.128027	0.00981923
$171$	2.03547	0.155657
$172$	−18.7952	−1.43312
$173$	−6.91630	−0.525837	−0.262918	−	0.964818i	$-0.584685\pi$
$173$	−6.91630	−0.525837	−0.262918	+	0.964818i	$0.584685\pi$
$174$	0.201894	0.0153055
$175$	0.330671	0.0249964
$176$	2.84495	0.214446
$177$	−8.46192	−0.636037
$178$	0.998545	0.0748441
$179$	3.84583	0.287451	0.143725	−	0.989618i	$-0.454092\pi$
$179$	3.84583	0.287451	0.143725	+	0.989618i	$0.454092\pi$
$180$	1.83686	0.136912
$181$	14.1111	1.04887	0.524434	−	0.851451i	$-0.324277\pi$
$181$	14.1111	1.04887	0.524434	+	0.851451i	$0.324277\pi$
$182$	−0.554847	−0.0411280
$183$	3.59102	0.265456
$184$	−2.09197	−0.154222
$185$	6.91988	0.508759
$186$	1.02813	0.0753861
$187$	−0.295879	−0.0216368
$188$	22.5994	1.64823
$189$	0.330671	0.0240528
$190$	−0.822135	−0.0596439
$191$	6.60370	0.477827	0.238913	−	0.971041i	$-0.423209\pi$
$191$	6.60370	0.477827	0.238913	+	0.971041i	$0.423209\pi$
$192$	−4.34649	−0.313681
$193$	−13.1900	−0.949436	−0.474718	−	0.880138i	$-0.657450\pi$
$193$	−13.1900	−0.949436	−0.474718	+	0.880138i	$0.657450\pi$
$194$	−3.61136	−0.259281
$195$	4.15432	0.297497
$196$	12.6572	0.904085
$197$	8.48030	0.604196	0.302098	−	0.953277i	$-0.402313\pi$
$197$	8.48030	0.604196	0.302098	+	0.953277i	$0.402313\pi$
$198$	0.377023	0.0267938
$199$	−13.2256	−0.937536	−0.468768	−	0.883321i	$-0.655302\pi$
$199$	−13.2256	−0.937536	−0.468768	+	0.883321i	$0.655302\pi$
$200$	−1.54972	−0.109582
$201$	−5.69675	−0.401818
$202$	−4.48008	−0.315217
$203$	0.165288	0.0116010
$204$	0.582239	0.0407649
$205$	−6.76056	−0.472178
$206$	−3.49241	−0.243327
$207$	1.34990	0.0938245
$208$	−12.6615	−0.877916
$209$	1.90001	0.131426
$210$	−0.133559	−0.00921645
$211$	0.408234	0.0281040	0.0140520	−	0.999901i	$-0.495527\pi$
$211$	0.408234	0.0281040	0.0140520	+	0.999901i	$0.495527\pi$
$212$	−1.45173	−0.0997053
$213$	10.3801	0.711231
$214$	−2.70120	−0.184650
$215$	−10.2322	−0.697832
$216$	−1.54972	−0.105445
$217$	0.841717	0.0571394
$218$	5.15324	0.349021
$219$	−8.44298	−0.570524
$220$	1.71462	0.115599
$221$	1.31681	0.0885785
$222$	−2.79496	−0.187585
$223$	−14.0551	−0.941202	−0.470601	−	0.882346i	$-0.655963\pi$
$223$	−14.0551	−0.941202	−0.470601	+	0.882346i	$0.655963\pi$
$224$	1.43195	0.0956765
$225$	1.00000	0.0666667
$226$	0.381517	0.0253782
$227$	−3.75510	−0.249235	−0.124617	−	0.992205i	$-0.539770\pi$
$227$	−3.75510	−0.249235	−0.124617	+	0.992205i	$0.539770\pi$
$228$	−3.73889	−0.247614
$229$	−9.26609	−0.612321	−0.306160	−	0.951980i	$-0.599044\pi$
$229$	−9.26609	−0.612321	−0.306160	+	0.951980i	$0.599044\pi$
$230$	−0.545229	−0.0359513
$231$	0.308664	0.0203086
$232$	−0.774640	−0.0508576
$233$	4.02541	0.263714	0.131857	−	0.991269i	$-0.457906\pi$
$233$	4.02541	0.263714	0.131857	+	0.991269i	$0.457906\pi$
$234$	−1.67794	−0.109691
$235$	12.3033	0.802578
$236$	15.5434	1.01179
$237$	7.10902	0.461781
$238$	−0.0423348	−0.00274416
$239$	−28.9780	−1.87443	−0.937215	−	0.348753i	$-0.886605\pi$
$239$	−28.9780	−1.87443	−0.937215	+	0.348753i	$0.886605\pi$
$240$	−3.04779	−0.196734
$241$	8.43323	0.543232	0.271616	−	0.962406i	$-0.412442\pi$
$241$	8.43323	0.543232	0.271616	+	0.962406i	$0.412442\pi$
$242$	−4.09100	−0.262980
$243$	1.00000	0.0641500
$244$	−6.59621	−0.422279
$245$	6.89066	0.440228
$246$	2.73061	0.174097
$247$	−8.45601	−0.538043
$248$	−3.94479	−0.250494
$249$	−8.85599	−0.561225
$250$	−0.403903	−0.0255451
$251$	−2.36679	−0.149391	−0.0746954	−	0.997206i	$-0.523798\pi$
$251$	−2.36679	−0.149391	−0.0746954	+	0.997206i	$0.523798\pi$
$252$	−0.607397	−0.0382624
$253$	1.26006	0.0792193
$254$	1.72132	0.108005
$255$	0.316975	0.0198497
$256$	4.48573	0.280358
$257$	−19.4506	−1.21329	−0.606647	−	0.794971i	$-0.707486\pi$
$257$	−19.4506	−1.21329	−0.606647	+	0.794971i	$0.707486\pi$
$258$	4.13283	0.257299
$259$	−2.28820	−0.142182
$260$	−7.63092	−0.473249
$261$	0.499857	0.0309404
$262$	−7.54003	−0.465824
$263$	21.8791	1.34912	0.674561	−	0.738219i	$-0.264333\pi$
$263$	21.8791	1.34912	0.674561	+	0.738219i	$0.264333\pi$
$264$	−1.44658	−0.0890311
$265$	−0.790332	−0.0485497
$266$	0.271856	0.0166686
$267$	2.47224	0.151298
$268$	10.4641	0.639200
$269$	12.9664	0.790576	0.395288	−	0.918557i	$-0.370645\pi$
$269$	12.9664	0.790576	0.395288	+	0.918557i	$0.370645\pi$
$270$	−0.403903	−0.0245808
$271$	16.0703	0.976204	0.488102	−	0.872787i	$-0.337689\pi$
$271$	16.0703	0.976204	0.488102	+	0.872787i	$0.337689\pi$
$272$	−0.966071	−0.0585766
$273$	−1.37371	−0.0831409
$274$	−1.14421	−0.0691245
$275$	0.933448	0.0562890
$276$	−2.47958	−0.149253
$277$	17.2107	1.03409	0.517046	−	0.855958i	$-0.327032\pi$
$277$	17.2107	1.03409	0.517046	+	0.855958i	$0.327032\pi$
$278$	−2.82267	−0.169292
$279$	2.54548	0.152394
$280$	0.512447	0.0306246
$281$	−2.91569	−0.173936	−0.0869678	−	0.996211i	$-0.527718\pi$
$281$	−2.91569	−0.173936	−0.0869678	+	0.996211i	$0.527718\pi$
$282$	−4.96934	−0.295920
$283$	−24.9906	−1.48554	−0.742769	−	0.669548i	$-0.766488\pi$
$283$	−24.9906	−1.48554	−0.742769	+	0.669548i	$0.766488\pi$
$284$	−19.0668	−1.13140
$285$	−2.03547	−0.120571
$286$	−1.56627	−0.0926157
$287$	2.23552	0.131959
$288$	4.33045	0.255174
$289$	−16.8995	−0.994090
$290$	−0.201894	−0.0118556
$291$	−8.94115	−0.524139
$292$	15.5086	0.907571
$293$	6.22609	0.363732	0.181866	−	0.983323i	$-0.441786\pi$
$293$	6.22609	0.363732	0.181866	+	0.983323i	$0.441786\pi$
$294$	−2.78316	−0.162317
$295$	8.46192	0.492672
$296$	10.7239	0.623313
$297$	0.933448	0.0541641
$298$	5.42729	0.314395
$299$	−5.60792	−0.324314
$300$	−1.83686	−0.106051
$301$	3.38350	0.195022
$302$	−0.887959	−0.0510963
$303$	−11.0920	−0.637216
$304$	6.20369	0.355806
$305$	−3.59102	−0.205621
$306$	−0.128027	−0.00731882
$307$	18.7982	1.07287	0.536436	−	0.843941i	$-0.319770\pi$
$307$	18.7982	1.07287	0.536436	+	0.843941i	$0.319770\pi$
$308$	−0.566973	−0.0323063
$309$	−8.64664	−0.491890
$310$	−1.02813	−0.0583938
$311$	−10.8948	−0.617790	−0.308895	−	0.951096i	$-0.599959\pi$
$311$	−10.8948	−0.617790	−0.308895	+	0.951096i	$0.599959\pi$
$312$	6.43804	0.364482
$313$	−0.161776	−0.00914411	−0.00457206	−	0.999990i	$-0.501455\pi$
$313$	−0.161776	−0.00914411	−0.00457206	+	0.999990i	$0.501455\pi$
$314$	−8.91323	−0.503002
$315$	−0.330671	−0.0186312
$316$	−13.0583	−0.734586
$317$	4.14838	0.232996	0.116498	−	0.993191i	$-0.462833\pi$
$317$	4.14838	0.232996	0.116498	+	0.993191i	$0.462833\pi$
$318$	0.319218	0.0179008
$319$	0.466591	0.0261241
$320$	4.34649	0.242976
$321$	−6.68773	−0.373273
$322$	0.180291	0.0100472
$323$	−0.645193	−0.0358995
$324$	−1.83686	−0.102048
$325$	−4.15432	−0.230440
$326$	−1.59972	−0.0886002
$327$	12.7586	0.705552
$328$	−10.4770	−0.578495
$329$	−4.06834	−0.224295
$330$	−0.377023	−0.0207544
$331$	7.92714	0.435715	0.217857	−	0.975981i	$-0.430093\pi$
$331$	7.92714	0.435715	0.217857	+	0.975981i	$0.430093\pi$
$332$	16.2672	0.892780
$333$	−6.91988	−0.379207
$334$	−4.84307	−0.265001
$335$	5.69675	0.311247
$336$	1.00781	0.0549808
$337$	−4.06564	−0.221469	−0.110735	−	0.993850i	$-0.535320\pi$
$337$	−4.06564	−0.221469	−0.110735	+	0.993850i	$0.535320\pi$
$338$	1.71998	0.0935545
$339$	0.944576	0.0513023
$340$	−0.582239	−0.0315763
$341$	2.37608	0.128672
$342$	0.822135	0.0444559
$343$	−4.59323	−0.248011
$344$	−15.8571	−0.854958
$345$	−1.34990	−0.0726761
$346$	−2.79352	−0.150180
$347$	−10.9278	−0.586638	−0.293319	−	0.956015i	$-0.594760\pi$
$347$	−10.9278	−0.586638	−0.293319	+	0.956015i	$0.594760\pi$
$348$	−0.918169	−0.0492190
$349$	−13.6521	−0.730779	−0.365390	−	0.930855i	$-0.619064\pi$
$349$	−13.6521	−0.730779	−0.365390	+	0.930855i	$0.619064\pi$
$350$	0.133559	0.00713903
$351$	−4.15432	−0.221741
$352$	4.04225	0.215453
$353$	16.5687	0.881864	0.440932	−	0.897541i	$-0.354648\pi$
$353$	16.5687	0.881864	0.440932	+	0.897541i	$0.354648\pi$
$354$	−3.41780	−0.181654
$355$	−10.3801	−0.550917
$356$	−4.54116	−0.240681
$357$	−0.104814	−0.00554736
$358$	1.55334	0.0820968
$359$	−24.3082	−1.28294	−0.641470	−	0.767148i	$-0.721675\pi$
$359$	−24.3082	−1.28294	−0.641470	+	0.767148i	$0.721675\pi$
$360$	1.54972	0.0816775
$361$	−14.8568	−0.781939
$362$	5.69951	0.299559
$363$	−10.1287	−0.531618
$364$	2.52332	0.132258
$365$	8.44298	0.441926
$366$	1.45042	0.0758149
$367$	−0.684512	−0.0357312	−0.0178656	−	0.999840i	$-0.505687\pi$
$367$	−0.684512	−0.0357312	−0.0178656	+	0.999840i	$0.505687\pi$
$368$	4.11420	0.214468
$369$	6.76056	0.351941
$370$	2.79496	0.145303
$371$	0.261340	0.0135681
$372$	−4.67570	−0.242424
$373$	18.7124	0.968891	0.484445	−	0.874822i	$-0.339021\pi$
$373$	18.7124	0.968891	0.484445	+	0.874822i	$0.339021\pi$
$374$	−0.119507	−0.00617954
$375$	−1.00000	−0.0516398
$376$	19.0667	0.983288
$377$	−2.07657	−0.106949
$378$	0.133559	0.00686953
$379$	−10.4497	−0.536763	−0.268382	−	0.963313i	$-0.586489\pi$
$379$	−10.4497	−0.536763	−0.268382	+	0.963313i	$0.586489\pi$
$380$	3.73889	0.191801
$381$	4.26170	0.218334
$382$	2.66726	0.136469
$383$	5.18988	0.265191	0.132595	−	0.991170i	$-0.457669\pi$
$383$	5.18988	0.265191	0.132595	+	0.991170i	$0.457669\pi$
$384$	−10.4165	−0.531563
$385$	−0.308664	−0.0157310
$386$	−5.32748	−0.271161
$387$	10.2322	0.520134
$388$	16.4237	0.833785
$389$	9.51203	0.482279	0.241140	−	0.970490i	$-0.422479\pi$
$389$	9.51203	0.482279	0.241140	+	0.970490i	$0.422479\pi$
$390$	1.67794	0.0849660
$391$	−0.427884	−0.0216390
$392$	10.6786	0.539351
$393$	−18.6679	−0.941671
$394$	3.42522	0.172560
$395$	−7.10902	−0.357694
$396$	−1.71462	−0.0861627
$397$	−7.84009	−0.393483	−0.196741	−	0.980455i	$-0.563036\pi$
$397$	−7.84009	−0.393483	−0.196741	+	0.980455i	$0.563036\pi$
$398$	−5.34185	−0.267763
$399$	0.673072	0.0336957
$400$	3.04779	0.152389
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−2.30094	−0.114760
$403$	−10.5748	−0.526766
$404$	20.3744	1.01366
$405$	−1.00000	−0.0496904
$406$	0.0667604	0.00331327
$407$	−6.45934	−0.320178
$408$	0.491222	0.0243191
$409$	−29.7989	−1.47346	−0.736731	−	0.676186i	$-0.763632\pi$
$409$	−29.7989	−1.47346	−0.736731	+	0.676186i	$0.763632\pi$
$410$	−2.73061	−0.134855
$411$	−2.83289	−0.139736
$412$	15.8827	0.782484
$413$	−2.79811	−0.137686
$414$	0.545229	0.0267965
$415$	8.85599	0.434723
$416$	−17.9901	−0.882037
$417$	−6.98847	−0.342227
$418$	0.767420	0.0375357
$419$	−26.2994	−1.28481	−0.642405	−	0.766365i	$-0.722063\pi$
$419$	−26.2994	−1.28481	−0.642405	+	0.766365i	$0.722063\pi$
$420$	0.607397	0.0296379
$421$	−6.91544	−0.337038	−0.168519	−	0.985698i	$-0.553898\pi$
$421$	−6.91544	−0.337038	−0.168519	+	0.985698i	$0.553898\pi$
$422$	0.164887	0.00802657
$423$	−12.3033	−0.598206
$424$	−1.22479	−0.0594813
$425$	−0.316975	−0.0153755
$426$	4.19255	0.203130
$427$	1.18745	0.0574645
$428$	12.2844	0.593791
$429$	−3.87784	−0.187224
$430$	−4.13283	−0.199303
$431$	9.04812	0.435833	0.217916	−	0.975967i	$-0.430074\pi$
$431$	9.04812	0.435833	0.217916	+	0.975967i	$0.430074\pi$
$432$	3.04779	0.146637
$433$	2.09925	0.100883	0.0504417	−	0.998727i	$-0.483937\pi$
$433$	2.09925	0.100883	0.0504417	+	0.998727i	$0.483937\pi$
$434$	0.339972	0.0163192
$435$	−0.499857	−0.0239663
$436$	−23.4358	−1.12237
$437$	2.74768	0.131440
$438$	−3.41015	−0.162943
$439$	−24.1314	−1.15173	−0.575866	−	0.817544i	$-0.695335\pi$
$439$	−24.1314	−1.15173	−0.575866	+	0.817544i	$0.695335\pi$
$440$	1.44658	0.0689632
$441$	−6.89066	−0.328127
$442$	0.531866	0.0252983
$443$	0.701008	0.0333059	0.0166529	−	0.999861i	$-0.494699\pi$
$443$	0.701008	0.0333059	0.0166529	+	0.999861i	$0.494699\pi$
$444$	12.7109	0.603231
$445$	−2.47224	−0.117195
$446$	−5.67692	−0.268810
$447$	13.4371	0.635554
$448$	−1.43726	−0.0679040
$449$	−4.65263	−0.219571	−0.109786	−	0.993955i	$-0.535016\pi$
$449$	−4.65263	−0.219571	−0.109786	+	0.993955i	$0.535016\pi$
$450$	0.403903	0.0190402
$451$	6.31063	0.297156
$452$	−1.73506	−0.0816102
$453$	−2.19844	−0.103292
$454$	−1.51670	−0.0711822
$455$	1.37371	0.0644006
$456$	−3.15442	−0.147719
$457$	−16.9130	−0.791159	−0.395580	−	0.918432i	$-0.629456\pi$
$457$	−16.9130	−0.791159	−0.395580	+	0.918432i	$0.629456\pi$
$458$	−3.74261	−0.174880
$459$	−0.316975	−0.0147951
$460$	2.47958	0.115611
$461$	42.0340	1.95772	0.978859	−	0.204534i	$-0.0655678\pi$
$461$	42.0340	1.95772	0.978859	+	0.204534i	$0.0655678\pi$
$462$	0.124670	0.00580019
$463$	8.67156	0.403002	0.201501	−	0.979488i	$-0.435418\pi$
$463$	8.67156	0.403002	0.201501	+	0.979488i	$0.435418\pi$
$464$	1.52346	0.0707248
$465$	−2.54548	−0.118044
$466$	1.62588	0.0753173
$467$	−28.5073	−1.31916	−0.659579	−	0.751635i	$-0.729266\pi$
$467$	−28.5073	−1.31916	−0.659579	+	0.751635i	$0.729266\pi$
$468$	7.63092	0.352739
$469$	−1.88375	−0.0869835
$470$	4.96934	0.229219
$471$	−22.0677	−1.01683
$472$	13.1136	0.603603
$473$	9.55126	0.439167
$474$	2.87136	0.131886
$475$	2.03547	0.0933940
$476$	0.192529	0.00882456
$477$	0.790332	0.0361868
$478$	−11.7043	−0.535342
$479$	10.7616	0.491708	0.245854	−	0.969307i	$-0.420932\pi$
$479$	10.7616	0.491708	0.245854	+	0.969307i	$0.420932\pi$
$480$	−4.33045	−0.197657
$481$	28.7474	1.31077
$482$	3.40621	0.155149
$483$	0.446372	0.0203106
$484$	18.6050	0.845681
$485$	8.94115	0.405997
$486$	0.403903	0.0183214
$487$	−24.2752	−1.10001	−0.550007	−	0.835160i	$-0.685375\pi$
$487$	−24.2752	−1.10001	−0.550007	+	0.835160i	$0.685375\pi$
$488$	−5.56508	−0.251919
$489$	−3.96065	−0.179107
$490$	2.78316	0.125730
$491$	−19.4660	−0.878488	−0.439244	−	0.898368i	$-0.644754\pi$
$491$	−19.4660	−0.878488	−0.439244	+	0.898368i	$0.644754\pi$
$492$	−12.4182	−0.559856
$493$	−0.158442	−0.00713587
$494$	−3.41541	−0.153667
$495$	−0.933448	−0.0419554
$496$	7.75809	0.348348
$497$	3.43239	0.153964
$498$	−3.57696	−0.160288
$499$	1.16044	0.0519484	0.0259742	−	0.999663i	$-0.491731\pi$
$499$	1.16044	0.0519484	0.0259742	+	0.999663i	$0.491731\pi$
$500$	1.83686	0.0821470
$501$	−11.9907	−0.535703
$502$	−0.955956	−0.0426664
$503$	26.4515	1.17942	0.589708	−	0.807617i	$-0.299243\pi$
$503$	26.4515	1.17942	0.589708	+	0.807617i	$0.299243\pi$
$504$	−0.512447	−0.0228262
$505$	11.0920	0.493586
$506$	0.508943	0.0226253
$507$	4.25839	0.189122
$508$	−7.82816	−0.347319
$509$	−20.6199	−0.913963	−0.456981	−	0.889476i	$-0.651069\pi$
$509$	−20.6199	−0.913963	−0.456981	+	0.889476i	$0.651069\pi$
$510$	0.128027	0.00566913
$511$	−2.79185	−0.123504
$512$	22.6447	1.00077
$513$	2.03547	0.0898684
$514$	−7.85615	−0.346520
$515$	8.64664	0.381017
$516$	−18.7952	−0.827413
$517$	−11.4845	−0.505087
$518$	−0.924212	−0.0406075
$519$	−6.91630	−0.303592
$520$	−6.43804	−0.282327
$521$	28.5143	1.24923	0.624616	−	0.780932i	$-0.285255\pi$
$521$	28.5143	1.24923	0.624616	+	0.780932i	$0.285255\pi$
$522$	0.201894	0.00883666
$523$	−26.0902	−1.14084	−0.570422	−	0.821352i	$-0.693220\pi$
$523$	−26.0902	−1.14084	−0.570422	+	0.821352i	$0.693220\pi$
$524$	34.2904	1.49798
$525$	0.330671	0.0144317
$526$	8.83704	0.385313
$527$	−0.806853	−0.0351471
$528$	2.84495	0.123811
$529$	−21.1778	−0.920773
$530$	−0.319218	−0.0138659
$531$	−8.46192	−0.367216
$532$	−1.23634	−0.0536021
$533$	−28.0855	−1.21652
$534$	0.998545	0.0432113
$535$	6.68773	0.289136
$536$	8.82838	0.381328
$537$	3.84583	0.165960
$538$	5.23717	0.225791
$539$	−6.43207	−0.277049
$540$	1.83686	0.0790460
$541$	12.3415	0.530601	0.265300	−	0.964166i	$-0.414529\pi$
$541$	12.3415	0.530601	0.265300	+	0.964166i	$0.414529\pi$
$542$	6.49087	0.278807
$543$	14.1111	0.605564
$544$	−1.37264	−0.0588516
$545$	−12.7586	−0.546518
$546$	−0.554847	−0.0237453
$547$	4.68679	0.200393	0.100196	−	0.994968i	$-0.468053\pi$
$547$	4.68679	0.200393	0.100196	+	0.994968i	$0.468053\pi$
$548$	5.20363	0.222288
$549$	3.59102	0.153261
$550$	0.377023	0.0160763
$551$	1.01745	0.0433447
$552$	−2.09197	−0.0890400
$553$	2.35075	0.0999639
$554$	6.95147	0.295340
$555$	6.91988	0.293732
$556$	12.8369	0.544404
$557$	−0.664352	−0.0281495	−0.0140748	−	0.999901i	$-0.504480\pi$
$557$	−0.664352	−0.0281495	−0.0140748	+	0.999901i	$0.504480\pi$
$558$	1.02813	0.0435242
$559$	−42.5080	−1.79790
$560$	−1.00781	−0.0425879
$561$	−0.295879	−0.0124920
$562$	−1.17766	−0.0496765
$563$	0.807495	0.0340319	0.0170159	−	0.999855i	$-0.494583\pi$
$563$	0.807495	0.0340319	0.0170159	+	0.999855i	$0.494583\pi$
$564$	22.5994	0.951608
$565$	−0.944576	−0.0397386
$566$	−10.0938	−0.424274
$567$	0.330671	0.0138869
$568$	−16.0862	−0.674963
$569$	−4.49182	−0.188307	−0.0941534	−	0.995558i	$-0.530014\pi$
$569$	−4.49182	−0.188307	−0.0941534	+	0.995558i	$0.530014\pi$
$570$	−0.822135	−0.0344354
$571$	34.9627	1.46315	0.731573	−	0.681764i	$-0.238787\pi$
$571$	34.9627	1.46315	0.731573	+	0.681764i	$0.238787\pi$
$572$	7.12306	0.297830
$573$	6.60370	0.275874
$574$	0.902933	0.0376877
$575$	1.34990	0.0562947
$576$	−4.34649	−0.181104
$577$	−27.1953	−1.13216	−0.566078	−	0.824352i	$-0.691540\pi$
$577$	−27.1953	−1.13216	−0.566078	+	0.824352i	$0.691540\pi$
$578$	−6.82577	−0.283915
$579$	−13.1900	−0.548157
$580$	0.918169	0.0381249
$581$	−2.92842	−0.121491
$582$	−3.61136	−0.149696
$583$	0.737734	0.0305538
$584$	13.0843	0.541431
$585$	4.15432	0.171760
$586$	2.51474	0.103883
$587$	1.28361	0.0529804	0.0264902	−	0.999649i	$-0.491567\pi$
$587$	1.28361	0.0529804	0.0264902	+	0.999649i	$0.491567\pi$
$588$	12.6572	0.521974
$589$	5.18126	0.213490
$590$	3.41780	0.140709
$591$	8.48030	0.348833
$592$	−21.0903	−0.866806
$593$	8.01492	0.329133	0.164567	−	0.986366i	$-0.447377\pi$
$593$	8.01492	0.329133	0.164567	+	0.986366i	$0.447377\pi$
$594$	0.377023	0.0154694
$595$	0.104814	0.00429696
$596$	−24.6821	−1.01102
$597$	−13.2256	−0.541287
$598$	−2.26506	−0.0926250
$599$	2.37215	0.0969235	0.0484617	−	0.998825i	$-0.484568\pi$
$599$	2.37215	0.0969235	0.0484617	+	0.998825i	$0.484568\pi$
$600$	−1.54972	−0.0632671
$601$	−10.7388	−0.438044	−0.219022	−	0.975720i	$-0.570287\pi$
$601$	−10.7388	−0.438044	−0.219022	+	0.975720i	$0.570287\pi$
$602$	1.36661	0.0556987
$603$	−5.69675	−0.231990
$604$	4.03824	0.164314
$605$	10.1287	0.411789
$606$	−4.48008	−0.181991
$607$	42.4024	1.72106	0.860531	−	0.509398i	$-0.170132\pi$
$607$	42.4024	1.72106	0.860531	+	0.509398i	$0.170132\pi$
$608$	8.81453	0.357476
$609$	0.165288	0.00669782
$610$	−1.45042	−0.0587260
$611$	51.1118	2.06776
$612$	0.582239	0.0235356
$613$	−0.395651	−0.0159802	−0.00799010	−	0.999968i	$-0.502543\pi$
$613$	−0.395651	−0.0159802	−0.00799010	+	0.999968i	$0.502543\pi$
$614$	7.59267	0.306415
$615$	−6.76056	−0.272612
$616$	−0.478343	−0.0192730
$617$	10.4590	0.421064	0.210532	−	0.977587i	$-0.432480\pi$
$617$	10.4590	0.421064	0.210532	+	0.977587i	$0.432480\pi$
$618$	−3.49241	−0.140485
$619$	−1.00571	−0.0404228	−0.0202114	−	0.999796i	$-0.506434\pi$
$619$	−1.00571	−0.0404228	−0.0202114	+	0.999796i	$0.506434\pi$
$620$	4.67570	0.187781
$621$	1.34990	0.0541696
$622$	−4.40046	−0.176442
$623$	0.817497	0.0327523
$624$	−12.6615	−0.506865
$625$	1.00000	0.0400000
$626$	−0.0653418	−0.00261158
$627$	1.90001	0.0758791
$628$	40.5354	1.61754
$629$	2.19342	0.0874576
$630$	−0.133559	−0.00532112
$631$	−14.2967	−0.569141	−0.284570	−	0.958655i	$-0.591851\pi$
$631$	−14.2967	−0.569141	−0.284570	+	0.958655i	$0.591851\pi$
$632$	−11.0170	−0.438233
$633$	0.408234	0.0162258
$634$	1.67554	0.0665444
$635$	−4.26170	−0.169121
$636$	−1.45173	−0.0575649
$637$	28.6260	1.13420
$638$	0.188458	0.00746111
$639$	10.3801	0.410630
$640$	10.4165	0.411747
$641$	10.3054	0.407039	0.203519	−	0.979071i	$-0.434762\pi$
$641$	10.3054	0.407039	0.203519	+	0.979071i	$0.434762\pi$
$642$	−2.70120	−0.106608
$643$	−2.09045	−0.0824391	−0.0412196	−	0.999150i	$-0.513124\pi$
$643$	−2.09045	−0.0824391	−0.0412196	+	0.999150i	$0.513124\pi$
$644$	−0.819924	−0.0323095
$645$	−10.2322	−0.402894
$646$	−0.260596	−0.0102530
$647$	34.3501	1.35044	0.675221	−	0.737616i	$-0.264048\pi$
$647$	34.3501	1.35044	0.675221	+	0.737616i	$0.264048\pi$
$648$	−1.54972	−0.0608788
$649$	−7.89877	−0.310054
$650$	−1.67794	−0.0658144
$651$	0.841717	0.0329895
$652$	7.27516	0.284917
$653$	38.6161	1.51116	0.755582	−	0.655054i	$-0.227354\pi$
$653$	38.6161	1.51116	0.755582	+	0.655054i	$0.227354\pi$
$654$	5.15324	0.201507
$655$	18.6679	0.729415
$656$	20.6047	0.804480
$657$	−8.44298	−0.329392
$658$	−1.64321	−0.0640592
$659$	14.4464	0.562753	0.281376	−	0.959597i	$-0.409209\pi$
$659$	14.4464	0.562753	0.281376	+	0.959597i	$0.409209\pi$
$660$	1.71462	0.0667413
$661$	5.32853	0.207256	0.103628	−	0.994616i	$-0.466955\pi$
$661$	5.32853	0.207256	0.103628	+	0.994616i	$0.466955\pi$
$662$	3.20180	0.124441
$663$	1.31681	0.0511408
$664$	13.7243	0.532607
$665$	−0.673072	−0.0261006
$666$	−2.79496	−0.108303
$667$	0.674757	0.0261267
$668$	22.0252	0.852180
$669$	−14.0551	−0.543403
$670$	2.30094	0.0888930
$671$	3.35203	0.129404
$672$	1.43195	0.0552388
$673$	42.3219	1.63139	0.815695	−	0.578482i	$-0.196355\pi$
$673$	42.3219	1.63139	0.815695	+	0.578482i	$0.196355\pi$
$674$	−1.64212	−0.0632523
$675$	1.00000	0.0384900
$676$	−7.82208	−0.300849
$677$	−12.6603	−0.486575	−0.243288	−	0.969954i	$-0.578226\pi$
$677$	−12.6603	−0.486575	−0.243288	+	0.969954i	$0.578226\pi$
$678$	0.381517	0.0146521
$679$	−2.95658	−0.113463
$680$	−0.491222	−0.0188375
$681$	−3.75510	−0.143896
$682$	0.959705	0.0367490
$683$	−13.6963	−0.524074	−0.262037	−	0.965058i	$-0.584394\pi$
$683$	−13.6963	−0.524074	−0.262037	+	0.965058i	$0.584394\pi$
$684$	−3.73889	−0.142960
$685$	2.83289	0.108239
$686$	−1.85522	−0.0708327
$687$	−9.26609	−0.353524
$688$	31.1857	1.18894
$689$	−3.28330	−0.125084
$690$	−0.545229	−0.0207565
$691$	−42.5251	−1.61773	−0.808865	−	0.587994i	$-0.799918\pi$
$691$	−42.5251	−1.61773	−0.808865	+	0.587994i	$0.799918\pi$
$692$	12.7043	0.482945
$693$	0.308664	0.0117252
$694$	−4.41379	−0.167545
$695$	6.98847	0.265088
$696$	−0.774640	−0.0293626
$697$	−2.14293	−0.0811691
$698$	−5.51412	−0.208713
$699$	4.02541	0.152255
$700$	−0.607397	−0.0229574
$701$	−23.9574	−0.904860	−0.452430	−	0.891800i	$-0.649443\pi$
$701$	−23.9574	−0.904860	−0.452430	+	0.891800i	$0.649443\pi$
$702$	−1.67794	−0.0633299
$703$	−14.0852	−0.531234
$704$	−4.05722	−0.152912
$705$	12.3033	0.463369
$706$	6.69216	0.251863
$707$	−3.66778	−0.137941
$708$	15.5434	0.584156
$709$	21.6775	0.814115	0.407057	−	0.913403i	$-0.366555\pi$
$709$	21.6775	0.814115	0.407057	+	0.913403i	$0.366555\pi$
$710$	−4.19255	−0.157344
$711$	7.10902	0.266609
$712$	−3.83128	−0.143583
$713$	3.43614	0.128685
$714$	−0.0423348	−0.00158434
$715$	3.87784	0.145023
$716$	−7.06426	−0.264004
$717$	−28.9780	−1.08220
$718$	−9.81817	−0.366411
$719$	−10.0900	−0.376293	−0.188146	−	0.982141i	$-0.560248\pi$
$719$	−10.0900	−0.376293	−0.188146	+	0.982141i	$0.560248\pi$
$720$	−3.04779	−0.113584
$721$	−2.85919	−0.106482
$722$	−6.00073	−0.223324
$723$	8.43323	0.313635
$724$	−25.9201	−0.963313
$725$	0.499857	0.0185642
$726$	−4.09100	−0.151831
$727$	13.5163	0.501292	0.250646	−	0.968079i	$-0.419357\pi$
$727$	13.5163	0.501292	0.250646	+	0.968079i	$0.419357\pi$
$728$	2.12887	0.0789012
$729$	1.00000	0.0370370
$730$	3.41015	0.126215
$731$	−3.24336	−0.119960
$732$	−6.59621	−0.243803
$733$	13.7605	0.508256	0.254128	−	0.967171i	$-0.418212\pi$
$733$	13.7605	0.508256	0.254128	+	0.967171i	$0.418212\pi$
$734$	−0.276476	−0.0102049
$735$	6.89066	0.254166
$736$	5.84567	0.215474
$737$	−5.31762	−0.195877
$738$	2.73061	0.100515
$739$	19.4034	0.713767	0.356883	−	0.934149i	$-0.383839\pi$
$739$	19.4034	0.713767	0.356883	+	0.934149i	$0.383839\pi$
$740$	−12.7109	−0.467260
$741$	−8.45601	−0.310639
$742$	0.105556	0.00387508
$743$	22.5951	0.828935	0.414468	−	0.910064i	$-0.363968\pi$
$743$	22.5951	0.828935	0.414468	+	0.910064i	$0.363968\pi$
$744$	−3.94479	−0.144623
$745$	−13.4371	−0.492298
$746$	7.55799	0.276718
$747$	−8.85599	−0.324024
$748$	0.543489	0.0198719
$749$	−2.21144	−0.0808041
$750$	−0.403903	−0.0147485
$751$	8.57010	0.312727	0.156364	−	0.987700i	$-0.450023\pi$
$751$	8.57010	0.312727	0.156364	+	0.987700i	$0.450023\pi$
$752$	−37.4978	−1.36740
$753$	−2.36679	−0.0862508
$754$	−0.838733	−0.0305448
$755$	2.19844	0.0800096
$756$	−0.607397	−0.0220908
$757$	20.3805	0.740742	0.370371	−	0.928884i	$-0.379231\pi$
$757$	20.3805	0.740742	0.370371	+	0.928884i	$0.379231\pi$
$758$	−4.22066	−0.153301
$759$	1.26006	0.0457373
$760$	3.15442	0.114423
$761$	2.87214	0.104115	0.0520576	−	0.998644i	$-0.483422\pi$
$761$	2.87214	0.104115	0.0520576	+	0.998644i	$0.483422\pi$
$762$	1.72132	0.0623567
$763$	4.21889	0.152734
$764$	−12.1301	−0.438851
$765$	0.316975	0.0114602
$766$	2.09621	0.0757392
$767$	35.1536	1.26932
$768$	4.48573	0.161865
$769$	46.1525	1.66430	0.832152	−	0.554548i	$-0.187109\pi$
$769$	46.1525	1.66430	0.832152	+	0.554548i	$0.187109\pi$
$770$	−0.124670	−0.00449281
$771$	−19.4506	−0.700495
$772$	24.2282	0.871991
$773$	30.5835	1.10001	0.550007	−	0.835160i	$-0.314625\pi$
$773$	30.5835	1.10001	0.550007	+	0.835160i	$0.314625\pi$
$774$	4.13283	0.148552
$775$	2.54548	0.0914364
$776$	13.8563	0.497412
$777$	−2.28820	−0.0820887
$778$	3.84194	0.137740
$779$	13.7609	0.493037
$780$	−7.63092	−0.273231
$781$	9.68926	0.346709
$782$	−0.172824	−0.00618016
$783$	0.499857	0.0178634
$784$	−21.0013	−0.750045
$785$	22.0677	0.787631
$786$	−7.54003	−0.268944
$787$	−8.83095	−0.314789	−0.157395	−	0.987536i	$-0.550309\pi$
$787$	−8.83095	−0.314789	−0.157395	+	0.987536i	$0.550309\pi$
$788$	−15.5771	−0.554913
$789$	21.8791	0.778916
$790$	−2.87136	−0.102158
$791$	0.312344	0.0111057
$792$	−1.44658	−0.0514021
$793$	−14.9183	−0.529763
$794$	−3.16664	−0.112380
$795$	−0.790332	−0.0280302
$796$	24.2936	0.861063
$797$	10.6084	0.375770	0.187885	−	0.982191i	$-0.439837\pi$
$797$	10.6084	0.375770	0.187885	+	0.982191i	$0.439837\pi$
$798$	0.271856	0.00962359
$799$	3.89983	0.137966
$800$	4.33045	0.153105
$801$	2.47224	0.0873522
$802$	0.403903	0.0142623
$803$	−7.88108	−0.278117
$804$	10.4641	0.369042
$805$	−0.446372	−0.0157325
$806$	−4.27118	−0.150446
$807$	12.9664	0.456439
$808$	17.1894	0.604722
$809$	−34.9098	−1.22736	−0.613682	−	0.789553i	$-0.710312\pi$
$809$	−34.9098	−1.22736	−0.613682	+	0.789553i	$0.710312\pi$
$810$	−0.403903	−0.0141917
$811$	49.5018	1.73824	0.869122	−	0.494597i	$-0.164684\pi$
$811$	49.5018	1.73824	0.869122	+	0.494597i	$0.164684\pi$
$812$	−0.303612	−0.0106547
$813$	16.0703	0.563612
$814$	−2.60895	−0.0914437
$815$	3.96065	0.138735
$816$	−0.966071	−0.0338192
$817$	20.8274	0.728660
$818$	−12.0359	−0.420825
$819$	−1.37371	−0.0480014
$820$	12.4182	0.433663
$821$	46.2753	1.61502	0.807510	−	0.589855i	$-0.200815\pi$
$821$	46.2753	1.61502	0.807510	+	0.589855i	$0.200815\pi$
$822$	−1.14421	−0.0399090
$823$	1.72272	0.0600503	0.0300251	−	0.999549i	$-0.490441\pi$
$823$	1.72272	0.0600503	0.0300251	+	0.999549i	$0.490441\pi$
$824$	13.3999	0.466807
$825$	0.933448	0.0324985
$826$	−1.13017	−0.0393235
$827$	22.6063	0.786097	0.393048	−	0.919518i	$-0.371420\pi$
$827$	22.6063	0.786097	0.393048	+	0.919518i	$0.371420\pi$
$828$	−2.47958	−0.0861713
$829$	−38.7242	−1.34495	−0.672473	−	0.740122i	$-0.734768\pi$
$829$	−38.7242	−1.34495	−0.672473	+	0.740122i	$0.734768\pi$
$830$	3.57696	0.124158
$831$	17.2107	0.597033
$832$	18.0567	0.626004
$833$	2.18416	0.0756768
$834$	−2.82267	−0.0977410
$835$	11.9907	0.414954
$836$	−3.49005	−0.120706
$837$	2.54548	0.0879847
$838$	−10.6224	−0.366945
$839$	14.5321	0.501704	0.250852	−	0.968025i	$-0.419289\pi$
$839$	14.5321	0.501704	0.250852	+	0.968025i	$0.419289\pi$
$840$	0.512447	0.0176811
$841$	−28.7501	−0.991384
$842$	−2.79317	−0.0962589
$843$	−2.91569	−0.100422
$844$	−0.749869	−0.0258116
$845$	−4.25839	−0.146493
$846$	−4.96934	−0.170849
$847$	−3.34926	−0.115082
$848$	2.40876	0.0827173
$849$	−24.9906	−0.857676
$850$	−0.128027	−0.00439129
$851$	−9.34113	−0.320210
$852$	−19.0668	−0.653217
$853$	−31.8196	−1.08948	−0.544742	−	0.838604i	$-0.683372\pi$
$853$	−31.8196	−1.08948	−0.544742	+	0.838604i	$0.683372\pi$
$854$	0.479613	0.0164120
$855$	−2.03547	−0.0696117
$856$	10.3641	0.354238
$857$	−27.9407	−0.954436	−0.477218	−	0.878785i	$-0.658355\pi$
$857$	−27.9407	−0.954436	−0.477218	+	0.878785i	$0.658355\pi$
$858$	−1.56627	−0.0534717
$859$	−22.1398	−0.755401	−0.377700	−	0.925928i	$-0.623285\pi$
$859$	−22.1398	−0.755401	−0.377700	+	0.925928i	$0.623285\pi$
$860$	18.7952	0.640911
$861$	2.23552	0.0761863
$862$	3.65457	0.124475
$863$	−9.42254	−0.320747	−0.160373	−	0.987056i	$-0.551270\pi$
$863$	−9.42254	−0.320747	−0.160373	+	0.987056i	$0.551270\pi$
$864$	4.33045	0.147325
$865$	6.91630	0.235161
$866$	0.847892	0.0288126
$867$	−16.8995	−0.573938
$868$	−1.54612	−0.0524786
$869$	6.63590	0.225108
$870$	−0.201894	−0.00684485
$871$	23.6661	0.801897
$872$	−19.7723	−0.669573
$873$	−8.94115	−0.302612
$874$	1.10980	0.0375395
$875$	−0.330671	−0.0111787
$876$	15.5086	0.523987
$877$	48.7699	1.64684	0.823422	−	0.567430i	$-0.192062\pi$
$877$	48.7699	1.64684	0.823422	+	0.567430i	$0.192062\pi$
$878$	−9.74677	−0.328938
$879$	6.22609	0.210001
$880$	−2.84495	−0.0959033
$881$	50.5805	1.70410	0.852051	−	0.523459i	$-0.175359\pi$
$881$	50.5805	1.70410	0.852051	+	0.523459i	$0.175359\pi$
$882$	−2.78316	−0.0937138
$883$	−53.4677	−1.79933	−0.899666	−	0.436578i	$-0.856190\pi$
$883$	−53.4677	−1.79933	−0.899666	+	0.436578i	$0.856190\pi$
$884$	−2.41881	−0.0813533
$885$	8.46192	0.284444
$886$	0.283139	0.00951226
$887$	−10.4708	−0.351575	−0.175787	−	0.984428i	$-0.556247\pi$
$887$	−10.4708	−0.351575	−0.175787	+	0.984428i	$0.556247\pi$
$888$	10.7239	0.359870
$889$	1.40922	0.0472638
$890$	−0.998545	−0.0334713
$891$	0.933448	0.0312717
$892$	25.8174	0.864430
$893$	−25.0430	−0.838033
$894$	5.42729	0.181516
$895$	−3.84583	−0.128552
$896$	−3.44442	−0.115070
$897$	−5.60792	−0.187243
$898$	−1.87921	−0.0627102
$899$	1.27238	0.0424362
$900$	−1.83686	−0.0612287
$901$	−0.250515	−0.00834587
$902$	2.54888	0.0848686
$903$	3.38350	0.112596
$904$	−1.46383	−0.0486863
$905$	−14.1111	−0.469068
$906$	−0.887959	−0.0295004
$907$	−32.3757	−1.07502	−0.537509	−	0.843258i	$-0.680635\pi$
$907$	−32.3757	−1.07502	−0.537509	+	0.843258i	$0.680635\pi$
$908$	6.89760	0.228905
$909$	−11.0920	−0.367897
$910$	0.554847	0.0183930
$911$	10.4183	0.345174	0.172587	−	0.984994i	$-0.444787\pi$
$911$	10.4183	0.345174	0.172587	+	0.984994i	$0.444787\pi$
$912$	6.20369	0.205425
$913$	−8.26660	−0.273585
$914$	−6.83124	−0.225957
$915$	−3.59102	−0.118715
$916$	17.0205	0.562374
$917$	−6.17293	−0.203848
$918$	−0.128027	−0.00422552
$919$	−5.41010	−0.178463	−0.0892313	−	0.996011i	$-0.528441\pi$
$919$	−5.41010	−0.178463	−0.0892313	+	0.996011i	$0.528441\pi$
$920$	2.09197	0.0689701
$921$	18.7982	0.619423
$922$	16.9777	0.559130
$923$	−43.1222	−1.41938
$924$	−0.566973	−0.0186520
$925$	−6.91988	−0.227524
$926$	3.50247	0.115098
$927$	−8.64664	−0.283993
$928$	2.16461	0.0710568
$929$	11.7135	0.384307	0.192154	−	0.981365i	$-0.438453\pi$
$929$	11.7135	0.384307	0.192154	+	0.981365i	$0.438453\pi$
$930$	−1.02813	−0.0337137
$931$	−14.0258	−0.459675
$932$	−7.39413	−0.242203
$933$	−10.8948	−0.356681
$934$	−11.5142	−0.376755
$935$	0.295879	0.00967629
$936$	6.43804	0.210434
$937$	−21.2578	−0.694464	−0.347232	−	0.937779i	$-0.612878\pi$
$937$	−21.2578	−0.694464	−0.347232	+	0.937779i	$0.612878\pi$
$938$	−0.760852	−0.0248427
$939$	−0.161776	−0.00527936
$940$	−22.5994	−0.737113
$941$	14.7211	0.479895	0.239948	−	0.970786i	$-0.422870\pi$
$941$	14.7211	0.479895	0.239948	+	0.970786i	$0.422870\pi$
$942$	−8.91323	−0.290409
$943$	9.12607	0.297186
$944$	−25.7901	−0.839398
$945$	−0.330671	−0.0107567
$946$	3.85778	0.125427
$947$	30.4228	0.988608	0.494304	−	0.869289i	$-0.335423\pi$
$947$	30.4228	0.988608	0.494304	+	0.869289i	$0.335423\pi$
$948$	−13.0583	−0.424114
$949$	35.0748	1.13858
$950$	0.822135	0.0266736
$951$	4.14838	0.134520
$952$	0.162433	0.00526448
$953$	−36.0024	−1.16623	−0.583117	−	0.812388i	$-0.698167\pi$
$953$	−36.0024	−1.16623	−0.583117	+	0.812388i	$0.698167\pi$
$954$	0.319218	0.0103351
$955$	−6.60370	−0.213691
$956$	53.2285	1.72153
$957$	0.466591	0.0150827
$958$	4.34663	0.140433
$959$	−0.936754	−0.0302494
$960$	4.34649	0.140282
$961$	−24.5205	−0.790984
$962$	11.6112	0.374359
$963$	−6.68773	−0.215509
$964$	−15.4907	−0.498921
$965$	13.1900	0.424601
$966$	0.180291	0.00580077
$967$	25.9074	0.833126	0.416563	−	0.909107i	$-0.363235\pi$
$967$	25.9074	0.833126	0.416563	+	0.909107i	$0.363235\pi$
$968$	15.6966	0.504509
$969$	−0.645193	−0.0207266
$970$	3.61136	0.115954
$971$	−20.8881	−0.670330	−0.335165	−	0.942159i	$-0.608792\pi$
$971$	−20.8881	−0.670330	−0.335165	+	0.942159i	$0.608792\pi$
$972$	−1.83686	−0.0589174
$973$	−2.31088	−0.0740835
$974$	−9.80482	−0.314167
$975$	−4.15432	−0.133045
$976$	10.9447	0.350330
$977$	−31.9603	−1.02250	−0.511251	−	0.859432i	$-0.670818\pi$
$977$	−31.9603	−1.02250	−0.511251	+	0.859432i	$0.670818\pi$
$978$	−1.59972	−0.0511533
$979$	2.30771	0.0737546
$980$	−12.6572	−0.404319
$981$	12.7586	0.407350
$982$	−7.86238	−0.250899
$983$	55.0022	1.75430	0.877149	−	0.480219i	$-0.159443\pi$
$983$	55.0022	1.75430	0.877149	+	0.480219i	$0.159443\pi$
$984$	−10.4770	−0.333994
$985$	−8.48030	−0.270205
$986$	−0.0639953	−0.00203802
$987$	−4.06834	−0.129497
$988$	15.5325	0.494156
$989$	13.8125	0.439211
$990$	−0.377023	−0.0119826
$991$	−37.5660	−1.19332	−0.596661	−	0.802493i	$-0.703506\pi$
$991$	−37.5660	−1.19332	−0.596661	+	0.802493i	$0.703506\pi$
$992$	11.0231	0.349984
$993$	7.92714	0.251560
$994$	1.38635	0.0439724
$995$	13.2256	0.419279
$996$	16.2672	0.515447
$997$	−15.1765	−0.480646	−0.240323	−	0.970693i	$-0.577253\pi$
$997$	−15.1765	−0.480646	−0.240323	+	0.970693i	$0.577253\pi$
$998$	0.468705	0.0148366
$999$	−6.91988	−0.218935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.17	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.17	✓	28	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.403903 q^{2} +1.00000 q^{3} -1.83686 q^{4} -1.00000 q^{5} +0.403903 q^{6} +0.330671 q^{7} -1.54972 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.403903 q^{2} +1.00000 q^{3} -1.83686 q^{4} -1.00000 q^{5} +0.403903 q^{6} +0.330671 q^{7} -1.54972 q^{8} +1.00000 q^{9} -0.403903 q^{10} +0.933448 q^{11} -1.83686 q^{12} -4.15432 q^{13} +0.133559 q^{14} -1.00000 q^{15} +3.04779 q^{16} -0.316975 q^{17} +0.403903 q^{18} +2.03547 q^{19} +1.83686 q^{20} +0.330671 q^{21} +0.377023 q^{22} +1.34990 q^{23} -1.54972 q^{24} +1.00000 q^{25} -1.67794 q^{26} +1.00000 q^{27} -0.607397 q^{28} +0.499857 q^{29} -0.403903 q^{30} +2.54548 q^{31} +4.33045 q^{32} +0.933448 q^{33} -0.128027 q^{34} -0.330671 q^{35} -1.83686 q^{36} -6.91988 q^{37} +0.822135 q^{38} -4.15432 q^{39} +1.54972 q^{40} +6.76056 q^{41} +0.133559 q^{42} +10.2322 q^{43} -1.71462 q^{44} -1.00000 q^{45} +0.545229 q^{46} -12.3033 q^{47} +3.04779 q^{48} -6.89066 q^{49} +0.403903 q^{50} -0.316975 q^{51} +7.63092 q^{52} +0.790332 q^{53} +0.403903 q^{54} -0.933448 q^{55} -0.512447 q^{56} +2.03547 q^{57} +0.201894 q^{58} -8.46192 q^{59} +1.83686 q^{60} +3.59102 q^{61} +1.02813 q^{62} +0.330671 q^{63} -4.34649 q^{64} +4.15432 q^{65} +0.377023 q^{66} -5.69675 q^{67} +0.582239 q^{68} +1.34990 q^{69} -0.133559 q^{70} +10.3801 q^{71} -1.54972 q^{72} -8.44298 q^{73} -2.79496 q^{74} +1.00000 q^{75} -3.73889 q^{76} +0.308664 q^{77} -1.67794 q^{78} +7.10902 q^{79} -3.04779 q^{80} +1.00000 q^{81} +2.73061 q^{82} -8.85599 q^{83} -0.607397 q^{84} +0.316975 q^{85} +4.13283 q^{86} +0.499857 q^{87} -1.44658 q^{88} +2.47224 q^{89} -0.403903 q^{90} -1.37371 q^{91} -2.47958 q^{92} +2.54548 q^{93} -4.96934 q^{94} -2.03547 q^{95} +4.33045 q^{96} -8.94115 q^{97} -2.78316 q^{98} +0.933448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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