LMFDB - Embedded newform 4017.2.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34842 q^{2} -1.00000 q^{3} -0.181762 q^{4} -1.77320 q^{5} -1.34842 q^{6} +1.31404 q^{7} -2.94193 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.34842 q^{2} -1.00000 q^{3} -0.181762 q^{4} -1.77320 q^{5} -1.34842 q^{6} +1.31404 q^{7} -2.94193 q^{8} +1.00000 q^{9} -2.39102 q^{10} -1.43681 q^{11} +0.181762 q^{12} +1.00000 q^{13} +1.77188 q^{14} +1.77320 q^{15} -3.60344 q^{16} -0.353504 q^{17} +1.34842 q^{18} +6.34324 q^{19} +0.322301 q^{20} -1.31404 q^{21} -1.93743 q^{22} +3.44161 q^{23} +2.94193 q^{24} -1.85576 q^{25} +1.34842 q^{26} -1.00000 q^{27} -0.238843 q^{28} +8.26096 q^{29} +2.39102 q^{30} +4.74752 q^{31} +1.02492 q^{32} +1.43681 q^{33} -0.476672 q^{34} -2.33006 q^{35} -0.181762 q^{36} -11.3111 q^{37} +8.55336 q^{38} -1.00000 q^{39} +5.21664 q^{40} +0.305020 q^{41} -1.77188 q^{42} -6.02412 q^{43} +0.261158 q^{44} -1.77320 q^{45} +4.64073 q^{46} -9.42424 q^{47} +3.60344 q^{48} -5.27330 q^{49} -2.50234 q^{50} +0.353504 q^{51} -0.181762 q^{52} +1.86199 q^{53} -1.34842 q^{54} +2.54775 q^{55} -3.86582 q^{56} -6.34324 q^{57} +11.1393 q^{58} -8.84735 q^{59} -0.322301 q^{60} +10.5977 q^{61} +6.40166 q^{62} +1.31404 q^{63} +8.58889 q^{64} -1.77320 q^{65} +1.93743 q^{66} -10.5644 q^{67} +0.0642537 q^{68} -3.44161 q^{69} -3.14190 q^{70} -6.44020 q^{71} -2.94193 q^{72} -9.96414 q^{73} -15.2521 q^{74} +1.85576 q^{75} -1.15296 q^{76} -1.88803 q^{77} -1.34842 q^{78} +16.5936 q^{79} +6.38962 q^{80} +1.00000 q^{81} +0.411296 q^{82} -9.14531 q^{83} +0.238843 q^{84} +0.626834 q^{85} -8.12304 q^{86} -8.26096 q^{87} +4.22700 q^{88} -9.98710 q^{89} -2.39102 q^{90} +1.31404 q^{91} -0.625554 q^{92} -4.74752 q^{93} -12.7078 q^{94} -11.2478 q^{95} -1.02492 q^{96} -15.2494 q^{97} -7.11062 q^{98} -1.43681 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * 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 $

$2$	1.34842	0.953477	0.476739	−	0.879045i	$-0.341819\pi$
$2$	1.34842	0.953477	0.476739	+	0.879045i	$0.341819\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.181762	−0.0908811
$5$	−1.77320	−0.793000	−0.396500	−	0.918035i	$-0.629775\pi$
$5$	−1.77320	−0.793000	−0.396500	+	0.918035i	$0.629775\pi$
$6$	−1.34842	−0.550490
$7$	1.31404	0.496660	0.248330	−	0.968675i	$-0.420118\pi$
$7$	1.31404	0.496660	0.248330	+	0.968675i	$0.420118\pi$
$8$	−2.94193	−1.04013
$9$	1.00000	0.333333
$10$	−2.39102	−0.756107
$11$	−1.43681	−0.433215	−0.216607	−	0.976259i	$-0.569499\pi$
$11$	−1.43681	−0.433215	−0.216607	+	0.976259i	$0.569499\pi$
$12$	0.181762	0.0524702
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.77188	0.473554
$15$	1.77320	0.457839
$16$	−3.60344	−0.900860
$17$	−0.353504	−0.0857373	−0.0428687	−	0.999081i	$-0.513650\pi$
$17$	−0.353504	−0.0857373	−0.0428687	+	0.999081i	$0.513650\pi$
$18$	1.34842	0.317826
$19$	6.34324	1.45524	0.727620	−	0.685980i	$-0.240626\pi$
$19$	6.34324	1.45524	0.727620	+	0.685980i	$0.240626\pi$
$20$	0.322301	0.0720687
$21$	−1.31404	−0.286747
$22$	−1.93743	−0.413061
$23$	3.44161	0.717624	0.358812	−	0.933410i	$-0.383182\pi$
$23$	3.44161	0.717624	0.358812	+	0.933410i	$0.383182\pi$
$24$	2.94193	0.600520
$25$	−1.85576	−0.371152
$26$	1.34842	0.264447
$27$	−1.00000	−0.192450
$28$	−0.238843	−0.0451370
$29$	8.26096	1.53402	0.767011	−	0.641634i	$-0.221743\pi$
$29$	8.26096	1.53402	0.767011	+	0.641634i	$0.221743\pi$
$30$	2.39102	0.436539
$31$	4.74752	0.852680	0.426340	−	0.904563i	$-0.359803\pi$
$31$	4.74752	0.852680	0.426340	+	0.904563i	$0.359803\pi$
$32$	1.02492	0.181181
$33$	1.43681	0.250117
$34$	−0.476672	−0.0817486
$35$	−2.33006	−0.393851
$36$	−0.181762	−0.0302937
$37$	−11.3111	−1.85954	−0.929768	−	0.368147i	$-0.879992\pi$
$37$	−11.3111	−1.85954	−0.929768	+	0.368147i	$0.879992\pi$
$38$	8.55336	1.38754
$39$	−1.00000	−0.160128
$40$	5.21664	0.824823
$41$	0.305020	0.0476362	0.0238181	−	0.999716i	$-0.492418\pi$
$41$	0.305020	0.0476362	0.0238181	+	0.999716i	$0.492418\pi$
$42$	−1.77188	−0.273407
$43$	−6.02412	−0.918669	−0.459335	−	0.888263i	$-0.651912\pi$
$43$	−6.02412	−0.918669	−0.459335	+	0.888263i	$0.651912\pi$
$44$	0.261158	0.0393710
$45$	−1.77320	−0.264333
$46$	4.64073	0.684238
$47$	−9.42424	−1.37467	−0.687333	−	0.726342i	$-0.741219\pi$
$47$	−9.42424	−1.37467	−0.687333	+	0.726342i	$0.741219\pi$
$48$	3.60344	0.520111
$49$	−5.27330	−0.753328
$50$	−2.50234	−0.353885
$51$	0.353504	0.0495005
$52$	−0.181762	−0.0252059
$53$	1.86199	0.255764	0.127882	−	0.991789i	$-0.459182\pi$
$53$	1.86199	0.255764	0.127882	+	0.991789i	$0.459182\pi$
$54$	−1.34842	−0.183497
$55$	2.54775	0.343539
$56$	−3.86582	−0.516592
$57$	−6.34324	−0.840183
$58$	11.1393	1.46266
$59$	−8.84735	−1.15183	−0.575913	−	0.817511i	$-0.695353\pi$
$59$	−8.84735	−1.15183	−0.575913	+	0.817511i	$0.695353\pi$
$60$	−0.322301	−0.0416089
$61$	10.5977	1.35690	0.678449	−	0.734648i	$-0.262653\pi$
$61$	10.5977	1.35690	0.678449	+	0.734648i	$0.262653\pi$
$62$	6.40166	0.813011
$63$	1.31404	0.165553
$64$	8.58889	1.07361
$65$	−1.77320	−0.219939
$66$	1.93743	0.238481
$67$	−10.5644	−1.29065	−0.645323	−	0.763910i	$-0.723277\pi$
$67$	−10.5644	−1.29065	−0.645323	+	0.763910i	$0.723277\pi$
$68$	0.0642537	0.00779190
$69$	−3.44161	−0.414321
$70$	−3.14190	−0.375528
$71$	−6.44020	−0.764311	−0.382155	−	0.924098i	$-0.624818\pi$
$71$	−6.44020	−0.764311	−0.382155	+	0.924098i	$0.624818\pi$
$72$	−2.94193	−0.346710
$73$	−9.96414	−1.16621	−0.583107	−	0.812395i	$-0.698163\pi$
$73$	−9.96414	−1.16621	−0.583107	+	0.812395i	$0.698163\pi$
$74$	−15.2521	−1.77302
$75$	1.85576	0.214285
$76$	−1.15296	−0.132254
$77$	−1.88803	−0.215161
$78$	−1.34842	−0.152679
$79$	16.5936	1.86692	0.933462	−	0.358676i	$-0.116772\pi$
$79$	16.5936	1.86692	0.933462	+	0.358676i	$0.116772\pi$
$80$	6.38962	0.714381
$81$	1.00000	0.111111
$82$	0.411296	0.0454200
$83$	−9.14531	−1.00383	−0.501914	−	0.864917i	$-0.667371\pi$
$83$	−9.14531	−1.00383	−0.501914	+	0.864917i	$0.667371\pi$
$84$	0.238843	0.0260599
$85$	0.626834	0.0679896
$86$	−8.12304	−0.875930
$87$	−8.26096	−0.885668
$88$	4.22700	0.450600
$89$	−9.98710	−1.05863	−0.529315	−	0.848425i	$-0.677551\pi$
$89$	−9.98710	−1.05863	−0.529315	+	0.848425i	$0.677551\pi$
$90$	−2.39102	−0.252036
$91$	1.31404	0.137749
$92$	−0.625554	−0.0652185
$93$	−4.74752	−0.492295
$94$	−12.7078	−1.31071
$95$	−11.2478	−1.15400
$96$	−1.02492	−0.104605
$97$	−15.2494	−1.54834	−0.774169	−	0.632979i	$-0.781832\pi$
$97$	−15.2494	−1.54834	−0.774169	+	0.632979i	$0.781832\pi$
$98$	−7.11062	−0.718282
$99$	−1.43681	−0.144405
$100$	0.337307	0.0337307
$101$	−9.89403	−0.984493	−0.492247	−	0.870456i	$-0.663824\pi$
$101$	−9.89403	−0.984493	−0.492247	+	0.870456i	$0.663824\pi$
$102$	0.476672	0.0471976
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.94193	−0.288480
$105$	2.33006	0.227390
$106$	2.51075	0.243865
$107$	3.38176	0.326927	0.163463	−	0.986549i	$-0.447733\pi$
$107$	3.38176	0.326927	0.163463	+	0.986549i	$0.447733\pi$
$108$	0.181762	0.0174901
$109$	12.3011	1.17823	0.589114	−	0.808050i	$-0.299477\pi$
$109$	12.3011	1.17823	0.589114	+	0.808050i	$0.299477\pi$
$110$	3.43544	0.327557
$111$	11.3111	1.07360
$112$	−4.73506	−0.447421
$113$	−6.68042	−0.628441	−0.314220	−	0.949350i	$-0.601743\pi$
$113$	−6.68042	−0.628441	−0.314220	+	0.949350i	$0.601743\pi$
$114$	−8.55336	−0.801096
$115$	−6.10266	−0.569076
$116$	−1.50153	−0.139414
$117$	1.00000	0.0924500
$118$	−11.9299	−1.09824
$119$	−0.464518	−0.0425823
$120$	−5.21664	−0.476212
$121$	−8.93557	−0.812325
$122$	14.2902	1.29377
$123$	−0.305020	−0.0275028
$124$	−0.862920	−0.0774925
$125$	12.1566	1.08732
$126$	1.77188	0.157851
$127$	9.99138	0.886591	0.443296	−	0.896375i	$-0.353809\pi$
$127$	9.99138	0.886591	0.443296	+	0.896375i	$0.353809\pi$
$128$	9.53161	0.842483
$129$	6.02412	0.530394
$130$	−2.39102	−0.209706
$131$	−16.6646	−1.45599	−0.727997	−	0.685580i	$-0.759549\pi$
$131$	−16.6646	−1.45599	−0.727997	+	0.685580i	$0.759549\pi$
$132$	−0.261158	−0.0227309
$133$	8.33528	0.722760
$134$	−14.2452	−1.23060
$135$	1.77320	0.152613
$136$	1.03998	0.0891780
$137$	−11.3796	−0.972225	−0.486113	−	0.873896i	$-0.661586\pi$
$137$	−11.3796	−0.972225	−0.486113	+	0.873896i	$0.661586\pi$
$138$	−4.64073	−0.395045
$139$	18.8994	1.60303	0.801514	−	0.597976i	$-0.204028\pi$
$139$	18.8994	1.60303	0.801514	+	0.597976i	$0.204028\pi$
$140$	0.423516	0.0357937
$141$	9.42424	0.793664
$142$	−8.68409	−0.728753
$143$	−1.43681	−0.120152
$144$	−3.60344	−0.300287
$145$	−14.6483	−1.21648
$146$	−13.4358	−1.11196
$147$	5.27330	0.434934
$148$	2.05593	0.168997
$149$	5.73376	0.469728	0.234864	−	0.972028i	$-0.424535\pi$
$149$	5.73376	0.469728	0.234864	+	0.972028i	$0.424535\pi$
$150$	2.50234	0.204315
$151$	13.5718	1.10446	0.552229	−	0.833692i	$-0.313777\pi$
$151$	13.5718	1.10446	0.552229	+	0.833692i	$0.313777\pi$
$152$	−18.6614	−1.51364
$153$	−0.353504	−0.0285791
$154$	−2.54585	−0.205151
$155$	−8.41831	−0.676175
$156$	0.181762	0.0145526
$157$	−14.3910	−1.14852	−0.574262	−	0.818671i	$-0.694711\pi$
$157$	−14.3910	−1.14852	−0.574262	+	0.818671i	$0.694711\pi$
$158$	22.3751	1.78007
$159$	−1.86199	−0.147666
$160$	−1.81738	−0.143677
$161$	4.52241	0.356416
$162$	1.34842	0.105942
$163$	−15.2265	−1.19263	−0.596317	−	0.802749i	$-0.703370\pi$
$163$	−15.2265	−1.19263	−0.596317	+	0.802749i	$0.703370\pi$
$164$	−0.0554412	−0.00432923
$165$	−2.54775	−0.198342
$166$	−12.3317	−0.957128
$167$	0.259202	0.0200576	0.0100288	−	0.999950i	$-0.496808\pi$
$167$	0.259202	0.0200576	0.0100288	+	0.999950i	$0.496808\pi$
$168$	3.86582	0.298254
$169$	1.00000	0.0769231
$170$	0.845235	0.0648266
$171$	6.34324	0.485080
$172$	1.09496	0.0834897
$173$	4.41019	0.335300	0.167650	−	0.985847i	$-0.446382\pi$
$173$	4.41019	0.335300	0.167650	+	0.985847i	$0.446382\pi$
$174$	−11.1393	−0.844464
$175$	−2.43854	−0.184336
$176$	5.17746	0.390266
$177$	8.84735	0.665008
$178$	−13.4668	−1.00938
$179$	−7.72137	−0.577122	−0.288561	−	0.957462i	$-0.593177\pi$
$179$	−7.72137	−0.577122	−0.288561	+	0.957462i	$0.593177\pi$
$180$	0.322301	0.0240229
$181$	2.33128	0.173283	0.0866413	−	0.996240i	$-0.472387\pi$
$181$	2.33128	0.173283	0.0866413	+	0.996240i	$0.472387\pi$
$182$	1.77188	0.131340
$183$	−10.5977	−0.783405
$184$	−10.1250	−0.746423
$185$	20.0569	1.47461
$186$	−6.40166	−0.469392
$187$	0.507918	0.0371427
$188$	1.71297	0.124931
$189$	−1.31404	−0.0955823
$190$	−15.1668	−1.10032
$191$	−1.18311	−0.0856068	−0.0428034	−	0.999084i	$-0.513629\pi$
$191$	−1.18311	−0.0856068	−0.0428034	+	0.999084i	$0.513629\pi$
$192$	−8.58889	−0.619850
$193$	−10.8098	−0.778105	−0.389052	−	0.921216i	$-0.627197\pi$
$193$	−10.8098	−0.778105	−0.389052	+	0.921216i	$0.627197\pi$
$194$	−20.5625	−1.47630
$195$	1.77320	0.126982
$196$	0.958486	0.0684633
$197$	−16.6180	−1.18398	−0.591990	−	0.805945i	$-0.701658\pi$
$197$	−16.6180	−1.18398	−0.591990	+	0.805945i	$0.701658\pi$
$198$	−1.93743	−0.137687
$199$	−6.93656	−0.491719	−0.245860	−	0.969305i	$-0.579070\pi$
$199$	−6.93656	−0.491719	−0.245860	+	0.969305i	$0.579070\pi$
$200$	5.45952	0.386046
$201$	10.5644	0.745154
$202$	−13.3413	−0.938692
$203$	10.8552	0.761888
$204$	−0.0642537	−0.00449866
$205$	−0.540863	−0.0377755
$206$	1.34842	0.0939489
$207$	3.44161	0.239208
$208$	−3.60344	−0.249853
$209$	−9.11404	−0.630432
$210$	3.14190	0.216811
$211$	5.71095	0.393158	0.196579	−	0.980488i	$-0.437017\pi$
$211$	5.71095	0.393158	0.196579	+	0.980488i	$0.437017\pi$
$212$	−0.338440	−0.0232441
$213$	6.44020	0.441275
$214$	4.56003	0.311717
$215$	10.6820	0.728504
$216$	2.94193	0.200173
$217$	6.23843	0.423493
$218$	16.5870	1.12341
$219$	9.96414	0.673314
$220$	−0.463086	−0.0312212
$221$	−0.353504	−0.0237792
$222$	15.2521	1.02366
$223$	−7.00934	−0.469380	−0.234690	−	0.972070i	$-0.575408\pi$
$223$	−7.00934	−0.469380	−0.234690	+	0.972070i	$0.575408\pi$
$224$	1.34678	0.0899856
$225$	−1.85576	−0.123717
$226$	−9.00801	−0.599204
$227$	−18.6169	−1.23565	−0.617823	−	0.786317i	$-0.711985\pi$
$227$	−18.6169	−1.23565	−0.617823	+	0.786317i	$0.711985\pi$
$228$	1.15296	0.0763568
$229$	5.28154	0.349014	0.174507	−	0.984656i	$-0.444167\pi$
$229$	5.28154	0.349014	0.174507	+	0.984656i	$0.444167\pi$
$230$	−8.22895	−0.542601
$231$	1.88803	0.124223
$232$	−24.3032	−1.59558
$233$	−17.9516	−1.17605	−0.588023	−	0.808844i	$-0.700094\pi$
$233$	−17.9516	−1.17605	−0.588023	+	0.808844i	$0.700094\pi$
$234$	1.34842	0.0881490
$235$	16.7111	1.09011
$236$	1.60811	0.104679
$237$	−16.5936	−1.07787
$238$	−0.626366	−0.0406013
$239$	14.9158	0.964825	0.482412	−	0.875944i	$-0.339761\pi$
$239$	14.9158	0.964825	0.482412	+	0.875944i	$0.339761\pi$
$240$	−6.38962	−0.412448
$241$	23.7612	1.53060	0.765298	−	0.643676i	$-0.222592\pi$
$241$	23.7612	1.53060	0.765298	+	0.643676i	$0.222592\pi$
$242$	−12.0489	−0.774533
$243$	−1.00000	−0.0641500
$244$	−1.92626	−0.123316
$245$	9.35062	0.597389
$246$	−0.411296	−0.0262233
$247$	6.34324	0.403611
$248$	−13.9669	−0.886899
$249$	9.14531	0.579561
$250$	16.3923	1.03674
$251$	−31.5128	−1.98907	−0.994536	−	0.104394i	$-0.966710\pi$
$251$	−31.5128	−1.98907	−0.994536	+	0.104394i	$0.966710\pi$
$252$	−0.238843	−0.0150457
$253$	−4.94494	−0.310886
$254$	13.4726	0.845345
$255$	−0.626834	−0.0392538
$256$	−4.32517	−0.270323
$257$	−2.46740	−0.153912	−0.0769562	−	0.997034i	$-0.524520\pi$
$257$	−2.46740	−0.153912	−0.0769562	+	0.997034i	$0.524520\pi$
$258$	8.12304	0.505719
$259$	−14.8633	−0.923557
$260$	0.322301	0.0199883
$261$	8.26096	0.511341
$262$	−22.4709	−1.38826
$263$	−17.3388	−1.06915	−0.534577	−	0.845120i	$-0.679529\pi$
$263$	−17.3388	−1.06915	−0.534577	+	0.845120i	$0.679529\pi$
$264$	−4.22700	−0.260154
$265$	−3.30169	−0.202821
$266$	11.2395	0.689135
$267$	9.98710	0.611201
$268$	1.92021	0.117295
$269$	−5.56357	−0.339217	−0.169608	−	0.985512i	$-0.554250\pi$
$269$	−5.56357	−0.339217	−0.169608	+	0.985512i	$0.554250\pi$
$270$	2.39102	0.145513
$271$	12.1362	0.737223	0.368611	−	0.929584i	$-0.379833\pi$
$271$	12.1362	0.737223	0.368611	+	0.929584i	$0.379833\pi$
$272$	1.27383	0.0772373
$273$	−1.31404	−0.0795293
$274$	−15.3445	−0.926995
$275$	2.66637	0.160788
$276$	0.625554	0.0376539
$277$	14.6007	0.877273	0.438636	−	0.898665i	$-0.355462\pi$
$277$	14.6007	0.877273	0.438636	+	0.898665i	$0.355462\pi$
$278$	25.4844	1.52845
$279$	4.74752	0.284227
$280$	6.85487	0.409657
$281$	−12.5784	−0.750362	−0.375181	−	0.926952i	$-0.622419\pi$
$281$	−12.5784	−0.750362	−0.375181	+	0.926952i	$0.622419\pi$
$282$	12.7078	0.756741
$283$	25.5906	1.52120	0.760601	−	0.649219i	$-0.224904\pi$
$283$	25.5906	1.52120	0.760601	+	0.649219i	$0.224904\pi$
$284$	1.17058	0.0694614
$285$	11.2478	0.666265
$286$	−1.93743	−0.114562
$287$	0.400809	0.0236590
$288$	1.02492	0.0603937
$289$	−16.8750	−0.992649
$290$	−19.7521	−1.15989
$291$	15.2494	0.893933
$292$	1.81110	0.105987
$293$	−2.42378	−0.141599	−0.0707994	−	0.997491i	$-0.522555\pi$
$293$	−2.42378	−0.141599	−0.0707994	+	0.997491i	$0.522555\pi$
$294$	7.11062	0.414700
$295$	15.6881	0.913398
$296$	33.2765	1.93416
$297$	1.43681	0.0833722
$298$	7.73152	0.447875
$299$	3.44161	0.199033
$300$	−0.337307	−0.0194744
$301$	−7.91593	−0.456267
$302$	18.3005	1.05308
$303$	9.89403	0.568397
$304$	−22.8575	−1.31097
$305$	−18.7919	−1.07602
$306$	−0.476672	−0.0272495
$307$	−16.8670	−0.962648	−0.481324	−	0.876543i	$-0.659844\pi$
$307$	−16.8670	−0.962648	−0.481324	+	0.876543i	$0.659844\pi$
$308$	0.343172	0.0195540
$309$	−1.00000	−0.0568880
$310$	−11.3514	−0.644718
$311$	17.9486	1.01777	0.508887	−	0.860833i	$-0.330057\pi$
$311$	17.9486	1.01777	0.508887	+	0.860833i	$0.330057\pi$
$312$	2.94193	0.166554
$313$	5.70949	0.322720	0.161360	−	0.986896i	$-0.448412\pi$
$313$	5.70949	0.322720	0.161360	+	0.986896i	$0.448412\pi$
$314$	−19.4051	−1.09509
$315$	−2.33006	−0.131284
$316$	−3.01609	−0.169668
$317$	21.3040	1.19655	0.598275	−	0.801291i	$-0.295853\pi$
$317$	21.3040	1.19655	0.598275	+	0.801291i	$0.295853\pi$
$318$	−2.51075	−0.140796
$319$	−11.8694	−0.664561
$320$	−15.2298	−0.851374
$321$	−3.38176	−0.188751
$322$	6.09811	0.339834
$323$	−2.24236	−0.124768
$324$	−0.181762	−0.0100979
$325$	−1.85576	−0.102939
$326$	−20.5318	−1.13715
$327$	−12.3011	−0.680250
$328$	−0.897350	−0.0495479
$329$	−12.3838	−0.682742
$330$	−3.43544	−0.189115
$331$	12.7165	0.698962	0.349481	−	0.936943i	$-0.386358\pi$
$331$	12.7165	0.698962	0.349481	+	0.936943i	$0.386358\pi$
$332$	1.66227	0.0912290
$333$	−11.3111	−0.619845
$334$	0.349513	0.0191245
$335$	18.7328	1.02348
$336$	4.73506	0.258319
$337$	−2.85191	−0.155354	−0.0776768	−	0.996979i	$-0.524750\pi$
$337$	−2.85191	−0.155354	−0.0776768	+	0.996979i	$0.524750\pi$
$338$	1.34842	0.0733444
$339$	6.68042	0.362830
$340$	−0.113935	−0.00617897
$341$	−6.82129	−0.369394
$342$	8.55336	0.462513
$343$	−16.1276	−0.870809
$344$	17.7225	0.955536
$345$	6.10266	0.328556
$346$	5.94678	0.319701
$347$	−1.96473	−0.105472	−0.0527362	−	0.998608i	$-0.516794\pi$
$347$	−1.96473	−0.105472	−0.0527362	+	0.998608i	$0.516794\pi$
$348$	1.50153	0.0804905
$349$	−21.7614	−1.16486	−0.582430	−	0.812881i	$-0.697898\pi$
$349$	−21.7614	−1.16486	−0.582430	+	0.812881i	$0.697898\pi$
$350$	−3.28818	−0.175761
$351$	−1.00000	−0.0533761
$352$	−1.47261	−0.0784904
$353$	−25.7299	−1.36947	−0.684733	−	0.728794i	$-0.740081\pi$
$353$	−25.7299	−1.36947	−0.684733	+	0.728794i	$0.740081\pi$
$354$	11.9299	0.634070
$355$	11.4198	0.606098
$356$	1.81528	0.0962095
$357$	0.464518	0.0245849
$358$	−10.4116	−0.550273
$359$	−17.6557	−0.931831	−0.465916	−	0.884829i	$-0.654275\pi$
$359$	−17.6557	−0.931831	−0.465916	+	0.884829i	$0.654275\pi$
$360$	5.21664	0.274941
$361$	21.2367	1.11772
$362$	3.14354	0.165221
$363$	8.93557	0.468996
$364$	−0.238843	−0.0125188
$365$	17.6684	0.924807
$366$	−14.2902	−0.746959
$367$	−6.64922	−0.347087	−0.173543	−	0.984826i	$-0.555522\pi$
$367$	−6.64922	−0.347087	−0.173543	+	0.984826i	$0.555522\pi$
$368$	−12.4016	−0.646479
$369$	0.305020	0.0158787
$370$	27.0451	1.40601
$371$	2.44673	0.127028
$372$	0.862920	0.0447403
$373$	−29.8702	−1.54662	−0.773310	−	0.634028i	$-0.781400\pi$
$373$	−29.8702	−1.54662	−0.773310	+	0.634028i	$0.781400\pi$
$374$	0.684888	0.0354147
$375$	−12.1566	−0.627766
$376$	27.7255	1.42983
$377$	8.26096	0.425461
$378$	−1.77188	−0.0911356
$379$	−11.5100	−0.591228	−0.295614	−	0.955307i	$-0.595524\pi$
$379$	−11.5100	−0.591228	−0.295614	+	0.955307i	$0.595524\pi$
$380$	2.04443	0.104877
$381$	−9.99138	−0.511874
$382$	−1.59533	−0.0816242
$383$	0.825078	0.0421595	0.0210798	−	0.999778i	$-0.493290\pi$
$383$	0.825078	0.0421595	0.0210798	+	0.999778i	$0.493290\pi$
$384$	−9.53161	−0.486408
$385$	3.34785	0.170622
$386$	−14.5761	−0.741905
$387$	−6.02412	−0.306223
$388$	2.77176	0.140715
$389$	−2.98428	−0.151309	−0.0756546	−	0.997134i	$-0.524105\pi$
$389$	−2.98428	−0.151309	−0.0756546	+	0.997134i	$0.524105\pi$
$390$	2.39102	0.121074
$391$	−1.21662	−0.0615272
$392$	15.5137	0.783560
$393$	16.6646	0.840619
$394$	−22.4080	−1.12890
$395$	−29.4238	−1.48047
$396$	0.261158	0.0131237
$397$	26.6402	1.33704	0.668518	−	0.743696i	$-0.266929\pi$
$397$	26.6402	1.33704	0.668518	+	0.743696i	$0.266929\pi$
$398$	−9.35340	−0.468843
$399$	−8.33528	−0.417286
$400$	6.68711	0.334356
$401$	31.7548	1.58576	0.792880	−	0.609377i	$-0.208580\pi$
$401$	31.7548	1.58576	0.792880	+	0.609377i	$0.208580\pi$
$402$	14.2452	0.710488
$403$	4.74752	0.236491
$404$	1.79836	0.0894718
$405$	−1.77320	−0.0881111
$406$	14.6374	0.726443
$407$	16.2519	0.805578
$408$	−1.03998	−0.0514869
$409$	−5.03897	−0.249161	−0.124581	−	0.992209i	$-0.539759\pi$
$409$	−5.03897	−0.249161	−0.124581	+	0.992209i	$0.539759\pi$
$410$	−0.729310	−0.0360181
$411$	11.3796	0.561314
$412$	−0.181762	−0.00895478
$413$	−11.6258	−0.572067
$414$	4.64073	0.228079
$415$	16.2165	0.796035
$416$	1.02492	0.0502506
$417$	−18.8994	−0.925509
$418$	−12.2896	−0.601102
$419$	0.565038	0.0276039	0.0138020	−	0.999905i	$-0.495607\pi$
$419$	0.565038	0.0276039	0.0138020	+	0.999905i	$0.495607\pi$
$420$	−0.423516	−0.0206655
$421$	9.09856	0.443437	0.221718	−	0.975111i	$-0.428833\pi$
$421$	9.09856	0.443437	0.221718	+	0.975111i	$0.428833\pi$
$422$	7.70076	0.374867
$423$	−9.42424	−0.458222
$424$	−5.47786	−0.266028
$425$	0.656018	0.0318215
$426$	8.68409	0.420746
$427$	13.9258	0.673917
$428$	−0.614675	−0.0297115
$429$	1.43681	0.0693699
$430$	14.4038	0.694612
$431$	−25.2842	−1.21790	−0.608950	−	0.793209i	$-0.708409\pi$
$431$	−25.2842	−1.21790	−0.608950	+	0.793209i	$0.708409\pi$
$432$	3.60344	0.173370
$433$	4.45306	0.214000	0.107000	−	0.994259i	$-0.465875\pi$
$433$	4.45306	0.214000	0.107000	+	0.994259i	$0.465875\pi$
$434$	8.41203	0.403791
$435$	14.6483	0.702334
$436$	−2.23587	−0.107079
$437$	21.8309	1.04432
$438$	13.4358	0.641990
$439$	−2.51681	−0.120121	−0.0600605	−	0.998195i	$-0.519129\pi$
$439$	−2.51681	−0.120121	−0.0600605	+	0.998195i	$0.519129\pi$
$440$	−7.49532	−0.357326
$441$	−5.27330	−0.251109
$442$	−0.476672	−0.0226730
$443$	−5.58524	−0.265363	−0.132681	−	0.991159i	$-0.542359\pi$
$443$	−5.58524	−0.265363	−0.132681	+	0.991159i	$0.542359\pi$
$444$	−2.05593	−0.0975702
$445$	17.7091	0.839494
$446$	−9.45154	−0.447543
$447$	−5.73376	−0.271198
$448$	11.2861	0.533220
$449$	11.3162	0.534045	0.267023	−	0.963690i	$-0.413960\pi$
$449$	11.3162	0.534045	0.267023	+	0.963690i	$0.413960\pi$
$450$	−2.50234	−0.117962
$451$	−0.438257	−0.0206367
$452$	1.21425	0.0571134
$453$	−13.5718	−0.637659
$454$	−25.1034	−1.17816
$455$	−2.33006	−0.109235
$456$	18.6614	0.873900
$457$	14.1443	0.661641	0.330820	−	0.943694i	$-0.392675\pi$
$457$	14.1443	0.661641	0.330820	+	0.943694i	$0.392675\pi$
$458$	7.12174	0.332777
$459$	0.353504	0.0165002
$460$	1.10923	0.0517182
$461$	40.8724	1.90362	0.951809	−	0.306690i	$-0.0992216\pi$
$461$	40.8724	1.90362	0.951809	+	0.306690i	$0.0992216\pi$
$462$	2.54585	0.118444
$463$	−14.3494	−0.666875	−0.333437	−	0.942772i	$-0.608209\pi$
$463$	−14.3494	−0.666875	−0.333437	+	0.942772i	$0.608209\pi$
$464$	−29.7679	−1.38194
$465$	8.41831	0.390390
$466$	−24.2063	−1.12133
$467$	31.3137	1.44902	0.724512	−	0.689262i	$-0.242065\pi$
$467$	31.3137	1.44902	0.724512	+	0.689262i	$0.242065\pi$
$468$	−0.181762	−0.00840196
$469$	−13.8820	−0.641012
$470$	22.5335	1.03940
$471$	14.3910	0.663101
$472$	26.0283	1.19805
$473$	8.65552	0.397981
$474$	−22.3751	−1.02772
$475$	−11.7715	−0.540115
$476$	0.0844319	0.00386993
$477$	1.86199	0.0852548
$478$	20.1128	0.919938
$479$	−20.3107	−0.928021	−0.464010	−	0.885830i	$-0.653590\pi$
$479$	−20.3107	−0.928021	−0.464010	+	0.885830i	$0.653590\pi$
$480$	1.81738	0.0829518
$481$	−11.3111	−0.515742
$482$	32.0401	1.45939
$483$	−4.52241	−0.205777
$484$	1.62415	0.0738250
$485$	27.0402	1.22783
$486$	−1.34842	−0.0611656
$487$	−35.9309	−1.62819	−0.814093	−	0.580734i	$-0.802766\pi$
$487$	−35.9309	−1.62819	−0.814093	+	0.580734i	$0.802766\pi$
$488$	−31.1777	−1.41135
$489$	15.2265	0.688567
$490$	12.6086	0.569597
$491$	29.6704	1.33901	0.669504	−	0.742809i	$-0.266507\pi$
$491$	29.6704	1.33901	0.669504	+	0.742809i	$0.266507\pi$
$492$	0.0554412	0.00249948
$493$	−2.92028	−0.131523
$494$	8.55336	0.384834
$495$	2.54775	0.114513
$496$	−17.1074	−0.768145
$497$	−8.46267	−0.379603
$498$	12.3317	0.552598
$499$	23.9104	1.07037	0.535187	−	0.844733i	$-0.320241\pi$
$499$	23.9104	1.07037	0.535187	+	0.844733i	$0.320241\pi$
$500$	−2.20962	−0.0988171
$501$	−0.259202	−0.0115803
$502$	−42.4925	−1.89653
$503$	0.217861	0.00971395	0.00485698	−	0.999988i	$-0.498454\pi$
$503$	0.217861	0.00971395	0.00485698	+	0.999988i	$0.498454\pi$
$504$	−3.86582	−0.172197
$505$	17.5441	0.780703
$506$	−6.66785	−0.296422
$507$	−1.00000	−0.0444116
$508$	−1.81605	−0.0805744
$509$	−33.0449	−1.46469	−0.732344	−	0.680934i	$-0.761574\pi$
$509$	−33.0449	−1.46469	−0.732344	+	0.680934i	$0.761574\pi$
$510$	−0.845235	−0.0374276
$511$	−13.0933	−0.579212
$512$	−24.8954	−1.10023
$513$	−6.34324	−0.280061
$514$	−3.32710	−0.146752
$515$	−1.77320	−0.0781366
$516$	−1.09496	−0.0482028
$517$	13.5409	0.595526
$518$	−20.0419	−0.880591
$519$	−4.41019	−0.193586
$520$	5.21664	0.228765
$521$	4.74664	0.207954	0.103977	−	0.994580i	$-0.466843\pi$
$521$	4.74664	0.207954	0.103977	+	0.994580i	$0.466843\pi$
$522$	11.1393	0.487552
$523$	18.1701	0.794521	0.397261	−	0.917706i	$-0.369961\pi$
$523$	18.1701	0.794521	0.397261	+	0.917706i	$0.369961\pi$
$524$	3.02900	0.132322
$525$	2.43854	0.106427
$526$	−23.3799	−1.01941
$527$	−1.67827	−0.0731065
$528$	−5.17746	−0.225320
$529$	−11.1554	−0.485015
$530$	−4.45206	−0.193385
$531$	−8.84735	−0.383942
$532$	−1.51504	−0.0656852
$533$	0.305020	0.0132119
$534$	13.4668	0.582766
$535$	−5.99653	−0.259253
$536$	31.0797	1.34244
$537$	7.72137	0.333202
$538$	−7.50203	−0.323435
$539$	7.57674	0.326353
$540$	−0.322301	−0.0138696
$541$	3.29177	0.141524	0.0707622	−	0.997493i	$-0.477457\pi$
$541$	3.29177	0.141524	0.0707622	+	0.997493i	$0.477457\pi$
$542$	16.3647	0.702925
$543$	−2.33128	−0.100045
$544$	−0.362312	−0.0155340
$545$	−21.8123	−0.934334
$546$	−1.77188	−0.0758294
$547$	−9.36019	−0.400213	−0.200106	−	0.979774i	$-0.564129\pi$
$547$	−9.36019	−0.400213	−0.200106	+	0.979774i	$0.564129\pi$
$548$	2.06838	0.0883569
$549$	10.5977	0.452299
$550$	3.59539	0.153308
$551$	52.4013	2.23237
$552$	10.1250	0.430947
$553$	21.8046	0.927227
$554$	19.6879	0.836460
$555$	−20.0569	−0.851367
$556$	−3.43520	−0.145685
$557$	41.6704	1.76563	0.882816	−	0.469720i	$-0.155645\pi$
$557$	41.6704	1.76563	0.882816	+	0.469720i	$0.155645\pi$
$558$	6.40166	0.271004
$559$	−6.02412	−0.254793
$560$	8.39622	0.354805
$561$	−0.507918	−0.0214443
$562$	−16.9609	−0.715453
$563$	−14.4041	−0.607059	−0.303529	−	0.952822i	$-0.598165\pi$
$563$	−14.4041	−0.607059	−0.303529	+	0.952822i	$0.598165\pi$
$564$	−1.71297	−0.0721291
$565$	11.8457	0.498353
$566$	34.5069	1.45043
$567$	1.31404	0.0551845
$568$	18.9466	0.794983
$569$	−37.5701	−1.57502	−0.787511	−	0.616301i	$-0.788631\pi$
$569$	−37.5701	−1.57502	−0.787511	+	0.616301i	$0.788631\pi$
$570$	15.1668	0.635268
$571$	−1.75827	−0.0735811	−0.0367906	−	0.999323i	$-0.511713\pi$
$571$	−1.75827	−0.0735811	−0.0367906	+	0.999323i	$0.511713\pi$
$572$	0.261158	0.0109196
$573$	1.18311	0.0494251
$574$	0.540459	0.0225583
$575$	−6.38679	−0.266347
$576$	8.58889	0.357871
$577$	37.1182	1.54525	0.772626	−	0.634861i	$-0.218943\pi$
$577$	37.1182	1.54525	0.772626	+	0.634861i	$0.218943\pi$
$578$	−22.7546	−0.946468
$579$	10.8098	0.449239
$580$	2.66252	0.110555
$581$	−12.0173	−0.498562
$582$	20.5625	0.852345
$583$	−2.67533	−0.110801
$584$	29.3138	1.21301
$585$	−1.77320	−0.0733128
$586$	−3.26827	−0.135011
$587$	18.6890	0.771378	0.385689	−	0.922629i	$-0.373964\pi$
$587$	18.6890	0.771378	0.385689	+	0.922629i	$0.373964\pi$
$588$	−0.958486	−0.0395273
$589$	30.1147	1.24085
$590$	21.1542	0.870904
$591$	16.6180	0.683572
$592$	40.7589	1.67518
$593$	18.5461	0.761597	0.380798	−	0.924658i	$-0.375649\pi$
$593$	18.5461	0.761597	0.380798	+	0.924658i	$0.375649\pi$
$594$	1.93743	0.0794935
$595$	0.823684	0.0337678
$596$	−1.04218	−0.0426894
$597$	6.93656	0.283894
$598$	4.64073	0.189774
$599$	−19.3460	−0.790457	−0.395228	−	0.918583i	$-0.629335\pi$
$599$	−19.3460	−0.790457	−0.395228	+	0.918583i	$0.629335\pi$
$600$	−5.45952	−0.222884
$601$	33.1614	1.35268	0.676340	−	0.736590i	$-0.263565\pi$
$601$	33.1614	1.35268	0.676340	+	0.736590i	$0.263565\pi$
$602$	−10.6740	−0.435040
$603$	−10.5644	−0.430215
$604$	−2.46684	−0.100374
$605$	15.8446	0.644173
$606$	13.3413	0.541954
$607$	−13.4535	−0.546061	−0.273030	−	0.962005i	$-0.588026\pi$
$607$	−13.4535	−0.546061	−0.273030	+	0.962005i	$0.588026\pi$
$608$	6.50129	0.263662
$609$	−10.8552	−0.439876
$610$	−25.3393	−1.02596
$611$	−9.42424	−0.381264
$612$	0.0642537	0.00259730
$613$	18.0184	0.727757	0.363878	−	0.931446i	$-0.381452\pi$
$613$	18.0184	0.727757	0.363878	+	0.931446i	$0.381452\pi$
$614$	−22.7438	−0.917863
$615$	0.540863	0.0218097
$616$	5.55445	0.223795
$617$	−1.45961	−0.0587618	−0.0293809	−	0.999568i	$-0.509354\pi$
$617$	−1.45961	−0.0587618	−0.0293809	+	0.999568i	$0.509354\pi$
$618$	−1.34842	−0.0542414
$619$	6.70749	0.269597	0.134798	−	0.990873i	$-0.456961\pi$
$619$	6.70749	0.269597	0.134798	+	0.990873i	$0.456961\pi$
$620$	1.53013	0.0614515
$621$	−3.44161	−0.138107
$622$	24.2023	0.970425
$623$	−13.1234	−0.525780
$624$	3.60344	0.144253
$625$	−12.2774	−0.491095
$626$	7.69880	0.307706
$627$	9.11404	0.363980
$628$	2.61573	0.104379
$629$	3.99852	0.159432
$630$	−3.14190	−0.125176
$631$	−3.18769	−0.126900	−0.0634499	−	0.997985i	$-0.520210\pi$
$631$	−3.18769	−0.126900	−0.0634499	+	0.997985i	$0.520210\pi$
$632$	−48.8172	−1.94184
$633$	−5.71095	−0.226990
$634$	28.7267	1.14088
$635$	−17.7167	−0.703067
$636$	0.338440	0.0134200
$637$	−5.27330	−0.208936
$638$	−16.0050	−0.633644
$639$	−6.44020	−0.254770
$640$	−16.9015	−0.668089
$641$	−6.11866	−0.241672	−0.120836	−	0.992672i	$-0.538558\pi$
$641$	−6.11866	−0.241672	−0.120836	+	0.992672i	$0.538558\pi$
$642$	−4.56003	−0.179970
$643$	24.8607	0.980409	0.490204	−	0.871608i	$-0.336922\pi$
$643$	24.8607	0.980409	0.490204	+	0.871608i	$0.336922\pi$
$644$	−0.822003	−0.0323914
$645$	−10.6820	−0.420602
$646$	−3.02365	−0.118964
$647$	−16.4576	−0.647015	−0.323508	−	0.946226i	$-0.604862\pi$
$647$	−16.4576	−0.647015	−0.323508	+	0.946226i	$0.604862\pi$
$648$	−2.94193	−0.115570
$649$	12.7120	0.498989
$650$	−2.50234	−0.0981500
$651$	−6.23843	−0.244504
$652$	2.76761	0.108388
$653$	−6.31354	−0.247068	−0.123534	−	0.992340i	$-0.539423\pi$
$653$	−6.31354	−0.247068	−0.123534	+	0.992340i	$0.539423\pi$
$654$	−16.5870	−0.648603
$655$	29.5497	1.15460
$656$	−1.09912	−0.0429135
$657$	−9.96414	−0.388738
$658$	−16.6986	−0.650979
$659$	−6.57158	−0.255993	−0.127996	−	0.991775i	$-0.540855\pi$
$659$	−6.57158	−0.255993	−0.127996	+	0.991775i	$0.540855\pi$
$660$	0.463086	0.0180256
$661$	−20.1062	−0.782039	−0.391020	−	0.920382i	$-0.627878\pi$
$661$	−20.1062	−0.782039	−0.391020	+	0.920382i	$0.627878\pi$
$662$	17.1472	0.666445
$663$	0.353504	0.0137290
$664$	26.9049	1.04411
$665$	−14.7801	−0.573148
$666$	−15.2521	−0.591008
$667$	28.4310	1.10085
$668$	−0.0471131	−0.00182286
$669$	7.00934	0.270997
$670$	25.2597	0.975866
$671$	−15.2269	−0.587828
$672$	−1.34678	−0.0519532
$673$	−31.7768	−1.22491	−0.612453	−	0.790507i	$-0.709817\pi$
$673$	−31.7768	−1.22491	−0.612453	+	0.790507i	$0.709817\pi$
$674$	−3.84558	−0.148126
$675$	1.85576	0.0714282
$676$	−0.181762	−0.00699085
$677$	−0.668684	−0.0256996	−0.0128498	−	0.999917i	$-0.504090\pi$
$677$	−0.668684	−0.0256996	−0.0128498	+	0.999917i	$0.504090\pi$
$678$	9.00801	0.345950
$679$	−20.0383	−0.768998
$680$	−1.84410	−0.0707181
$681$	18.6169	0.713401
$682$	−9.19797	−0.352209
$683$	−1.05659	−0.0404294	−0.0202147	−	0.999796i	$-0.506435\pi$
$683$	−1.05659	−0.0404294	−0.0202147	+	0.999796i	$0.506435\pi$
$684$	−1.15296	−0.0440846
$685$	20.1783	0.770974
$686$	−21.7468	−0.830296
$687$	−5.28154	−0.201503
$688$	21.7075	0.827592
$689$	1.86199	0.0709363
$690$	8.22895	0.313271
$691$	−13.3347	−0.507274	−0.253637	−	0.967299i	$-0.581627\pi$
$691$	−13.3347	−0.507274	−0.253637	+	0.967299i	$0.581627\pi$
$692$	−0.801605	−0.0304724
$693$	−1.88803	−0.0717202
$694$	−2.64929	−0.100566
$695$	−33.5125	−1.27120
$696$	24.3032	0.921210
$697$	−0.107826	−0.00408420
$698$	−29.3435	−1.11067
$699$	17.9516	0.678991
$700$	0.443235	0.0167527
$701$	1.20181	0.0453917	0.0226958	−	0.999742i	$-0.492775\pi$
$701$	1.20181	0.0453917	0.0226958	+	0.999742i	$0.492775\pi$
$702$	−1.34842	−0.0508929
$703$	−71.7491	−2.70607
$704$	−12.3406	−0.465105
$705$	−16.7111	−0.629375
$706$	−34.6948	−1.30576
$707$	−13.0012	−0.488959
$708$	−1.60811	−0.0604366
$709$	−47.2542	−1.77467	−0.887335	−	0.461125i	$-0.847446\pi$
$709$	−47.2542	−1.77467	−0.887335	+	0.461125i	$0.847446\pi$
$710$	15.3986	0.577901
$711$	16.5936	0.622308
$712$	29.3814	1.10111
$713$	16.3391	0.611904
$714$	0.626366	0.0234412
$715$	2.54775	0.0952806
$716$	1.40345	0.0524495
$717$	−14.9158	−0.557042
$718$	−23.8073	−0.888480
$719$	35.8071	1.33538	0.667690	−	0.744439i	$-0.267283\pi$
$719$	35.8071	1.33538	0.667690	+	0.744439i	$0.267283\pi$
$720$	6.38962	0.238127
$721$	1.31404	0.0489374
$722$	28.6361	1.06572
$723$	−23.7612	−0.883690
$724$	−0.423738	−0.0157481
$725$	−15.3304	−0.569355
$726$	12.0489	0.447177
$727$	49.9963	1.85426	0.927130	−	0.374741i	$-0.122268\pi$
$727$	49.9963	1.85426	0.927130	+	0.374741i	$0.122268\pi$
$728$	−3.86582	−0.143277
$729$	1.00000	0.0370370
$730$	23.8245	0.881783
$731$	2.12955	0.0787642
$732$	1.92626	0.0711967
$733$	13.2200	0.488290	0.244145	−	0.969739i	$-0.421493\pi$
$733$	13.2200	0.488290	0.244145	+	0.969739i	$0.421493\pi$
$734$	−8.96595	−0.330939
$735$	−9.35062	−0.344903
$736$	3.52736	0.130020
$737$	15.1790	0.559127
$738$	0.411296	0.0151400
$739$	−10.7562	−0.395674	−0.197837	−	0.980235i	$-0.563392\pi$
$739$	−10.7562	−0.395674	−0.197837	+	0.980235i	$0.563392\pi$
$740$	−3.64558	−0.134014
$741$	−6.34324	−0.233025
$742$	3.29922	0.121118
$743$	−10.3190	−0.378569	−0.189284	−	0.981922i	$-0.560617\pi$
$743$	−10.3190	−0.378569	−0.189284	+	0.981922i	$0.560617\pi$
$744$	13.9669	0.512051
$745$	−10.1671	−0.372494
$746$	−40.2776	−1.47467
$747$	−9.14531	−0.334609
$748$	−0.0923204	−0.00337557
$749$	4.44376	0.162372
$750$	−16.3923	−0.598561
$751$	1.24818	0.0455469	0.0227734	−	0.999741i	$-0.492750\pi$
$751$	1.24818	0.0455469	0.0227734	+	0.999741i	$0.492750\pi$
$752$	33.9597	1.23838
$753$	31.5128	1.14839
$754$	11.1393	0.405668
$755$	−24.0655	−0.875835
$756$	0.238843	0.00868663
$757$	48.6549	1.76839	0.884196	−	0.467116i	$-0.154707\pi$
$757$	48.6549	1.76839	0.884196	+	0.467116i	$0.154707\pi$
$758$	−15.5203	−0.563723
$759$	4.94494	0.179490
$760$	33.0904	1.20032
$761$	26.1629	0.948405	0.474203	−	0.880416i	$-0.342736\pi$
$761$	26.1629	0.948405	0.474203	+	0.880416i	$0.342736\pi$
$762$	−13.4726	−0.488060
$763$	16.1641	0.585179
$764$	0.215045	0.00778004
$765$	0.626834	0.0226632
$766$	1.11255	0.0401982
$767$	−8.84735	−0.319459
$768$	4.32517	0.156071
$769$	−11.1726	−0.402893	−0.201446	−	0.979500i	$-0.564564\pi$
$769$	−11.1726	−0.402893	−0.201446	+	0.979500i	$0.564564\pi$
$770$	4.51431	0.162684
$771$	2.46740	0.0888614
$772$	1.96481	0.0707150
$773$	31.2693	1.12468	0.562339	−	0.826907i	$-0.309902\pi$
$773$	31.2693	1.12468	0.562339	+	0.826907i	$0.309902\pi$
$774$	−8.12304	−0.291977
$775$	−8.81026	−0.316474
$776$	44.8626	1.61047
$777$	14.8633	0.533216
$778$	−4.02407	−0.144270
$779$	1.93482	0.0693221
$780$	−0.322301	−0.0115402
$781$	9.25334	0.331111
$782$	−1.64052	−0.0586648
$783$	−8.26096	−0.295223
$784$	19.0020	0.678643
$785$	25.5181	0.910779
$786$	22.4709	0.801511
$787$	32.6223	1.16286	0.581430	−	0.813597i	$-0.302493\pi$
$787$	32.6223	1.16286	0.581430	+	0.813597i	$0.302493\pi$
$788$	3.02052	0.107601
$789$	17.3388	0.617276
$790$	−39.6756	−1.41159
$791$	−8.77833	−0.312122
$792$	4.22700	0.150200
$793$	10.5977	0.376336
$794$	35.9223	1.27483
$795$	3.30169	0.117099
$796$	1.26080	0.0446880
$797$	20.3390	0.720443	0.360221	−	0.932867i	$-0.382701\pi$
$797$	20.3390	0.720443	0.360221	+	0.932867i	$0.382701\pi$
$798$	−11.2395	−0.397872
$799$	3.33151	0.117860
$800$	−1.90200	−0.0672457
$801$	−9.98710	−0.352877
$802$	42.8189	1.51199
$803$	14.3166	0.505221
$804$	−1.92021	−0.0677205
$805$	−8.01914	−0.282637
$806$	6.40166	0.225489
$807$	5.56357	0.195847
$808$	29.1076	1.02400
$809$	30.2112	1.06217	0.531084	−	0.847319i	$-0.321785\pi$
$809$	30.2112	1.06217	0.531084	+	0.847319i	$0.321785\pi$
$810$	−2.39102	−0.0840119
$811$	0.407187	0.0142983	0.00714913	−	0.999974i	$-0.497724\pi$
$811$	0.407187	0.0142983	0.00714913	+	0.999974i	$0.497724\pi$
$812$	−1.97307	−0.0692412
$813$	−12.1362	−0.425636
$814$	21.9144	0.768101
$815$	26.9997	0.945758
$816$	−1.27383	−0.0445930
$817$	−38.2124	−1.33688
$818$	−6.79465	−0.237569
$819$	1.31404	0.0459163
$820$	0.0983084	0.00343308
$821$	−48.9320	−1.70774	−0.853869	−	0.520489i	$-0.825750\pi$
$821$	−48.9320	−1.70774	−0.853869	+	0.520489i	$0.825750\pi$
$822$	15.3445	0.535201
$823$	−16.8822	−0.588477	−0.294239	−	0.955732i	$-0.595066\pi$
$823$	−16.8822	−0.588477	−0.294239	+	0.955732i	$0.595066\pi$
$824$	−2.94193	−0.102487
$825$	−2.66637	−0.0928313
$826$	−15.6764	−0.545453
$827$	−51.6212	−1.79504	−0.897522	−	0.440970i	$-0.854635\pi$
$827$	−51.6212	−1.79504	−0.897522	+	0.440970i	$0.854635\pi$
$828$	−0.625554	−0.0217395
$829$	15.6165	0.542384	0.271192	−	0.962525i	$-0.412582\pi$
$829$	15.6165	0.542384	0.271192	+	0.962525i	$0.412582\pi$
$830$	21.8666	0.759002
$831$	−14.6007	−0.506494
$832$	8.58889	0.297766
$833$	1.86413	0.0645883
$834$	−25.4844	−0.882452
$835$	−0.459617	−0.0159057
$836$	1.65659	0.0572943
$837$	−4.74752	−0.164098
$838$	0.761909	0.0263197
$839$	−46.8734	−1.61825	−0.809124	−	0.587638i	$-0.800058\pi$
$839$	−46.8734	−1.61825	−0.809124	+	0.587638i	$0.800058\pi$
$840$	−6.85487	−0.236515
$841$	39.2435	1.35322
$842$	12.2687	0.422807
$843$	12.5784	0.433222
$844$	−1.03803	−0.0357306
$845$	−1.77320	−0.0610000
$846$	−12.7078	−0.436904
$847$	−11.7417	−0.403450
$848$	−6.70957	−0.230408
$849$	−25.5906	−0.878267
$850$	0.884588	0.0303411
$851$	−38.9284	−1.33445
$852$	−1.17058	−0.0401035
$853$	−35.8127	−1.22620	−0.613102	−	0.790004i	$-0.710078\pi$
$853$	−35.8127	−1.22620	−0.613102	+	0.790004i	$0.710078\pi$
$854$	18.7778	0.642565
$855$	−11.2478	−0.384668
$856$	−9.94890	−0.340046
$857$	−13.4408	−0.459128	−0.229564	−	0.973294i	$-0.573730\pi$
$857$	−13.4408	−0.459128	−0.229564	+	0.973294i	$0.573730\pi$
$858$	1.93743	0.0661426
$859$	−3.72029	−0.126935	−0.0634674	−	0.997984i	$-0.520216\pi$
$859$	−3.72029	−0.126935	−0.0634674	+	0.997984i	$0.520216\pi$
$860$	−1.94158	−0.0662073
$861$	−0.400809	−0.0136595
$862$	−34.0938	−1.16124
$863$	−13.8630	−0.471901	−0.235950	−	0.971765i	$-0.575820\pi$
$863$	−13.8630	−0.471901	−0.235950	+	0.971765i	$0.575820\pi$
$864$	−1.02492	−0.0348683
$865$	−7.82014	−0.265893
$866$	6.00459	0.204044
$867$	16.8750	0.573106
$868$	−1.13391	−0.0384875
$869$	−23.8419	−0.808779
$870$	19.7521	0.669660
$871$	−10.5644	−0.357961
$872$	−36.1889	−1.22551
$873$	−15.2494	−0.516112
$874$	29.4373	0.995731
$875$	15.9743	0.540030
$876$	−1.81110	−0.0611915
$877$	49.0616	1.65669	0.828347	−	0.560216i	$-0.189282\pi$
$877$	49.0616	1.65669	0.828347	+	0.560216i	$0.189282\pi$
$878$	−3.39372	−0.114533
$879$	2.42378	0.0817521
$880$	−9.18068	−0.309481
$881$	8.49791	0.286302	0.143151	−	0.989701i	$-0.454277\pi$
$881$	8.49791	0.286302	0.143151	+	0.989701i	$0.454277\pi$
$882$	−7.11062	−0.239427
$883$	−17.6196	−0.592946	−0.296473	−	0.955041i	$-0.595810\pi$
$883$	−17.6196	−0.592946	−0.296473	+	0.955041i	$0.595810\pi$
$884$	0.0642537	0.00216108
$885$	−15.6881	−0.527351
$886$	−7.53125	−0.253017
$887$	−38.3575	−1.28792	−0.643960	−	0.765059i	$-0.722710\pi$
$887$	−38.3575	−1.28792	−0.643960	+	0.765059i	$0.722710\pi$
$888$	−33.2765	−1.11669
$889$	13.1291	0.440335
$890$	23.8794	0.800438
$891$	−1.43681	−0.0481350
$892$	1.27403	0.0426578
$893$	−59.7802	−2.00047
$894$	−7.73152	−0.258581
$895$	13.6915	0.457657
$896$	12.5249	0.418428
$897$	−3.44161	−0.114912
$898$	15.2590	0.509200
$899$	39.2191	1.30803
$900$	0.337307	0.0112436
$901$	−0.658222	−0.0219285
$902$	−0.590954	−0.0196766
$903$	7.91593	0.263426
$904$	19.6533	0.653660
$905$	−4.13383	−0.137413
$906$	−18.3005	−0.607994
$907$	−18.2145	−0.604803	−0.302401	−	0.953181i	$-0.597788\pi$
$907$	−18.2145	−0.604803	−0.302401	+	0.953181i	$0.597788\pi$
$908$	3.38385	0.112297
$909$	−9.89403	−0.328164
$910$	−3.14190	−0.104153
$911$	−24.0806	−0.797825	−0.398913	−	0.916989i	$-0.630612\pi$
$911$	−24.0806	−0.797825	−0.398913	+	0.916989i	$0.630612\pi$
$912$	22.8575	0.756887
$913$	13.1401	0.434873
$914$	19.0724	0.630860
$915$	18.7919	0.621240
$916$	−0.959984	−0.0317188
$917$	−21.8980	−0.723135
$918$	0.476672	0.0157325
$919$	23.7210	0.782482	0.391241	−	0.920288i	$-0.372046\pi$
$919$	23.7210	0.782482	0.391241	+	0.920288i	$0.372046\pi$
$920$	17.9536	0.591913
$921$	16.8670	0.555785
$922$	55.1132	1.81506
$923$	−6.44020	−0.211982
$924$	−0.343172	−0.0112895
$925$	20.9907	0.690170
$926$	−19.3491	−0.635850
$927$	1.00000	0.0328443
$928$	8.46679	0.277936
$929$	−10.8802	−0.356966	−0.178483	−	0.983943i	$-0.557119\pi$
$929$	−10.8802	−0.356966	−0.178483	+	0.983943i	$0.557119\pi$
$930$	11.3514	0.372228
$931$	−33.4498	−1.09627
$932$	3.26292	0.106880
$933$	−17.9486	−0.587612
$934$	42.2240	1.38161
$935$	−0.900641	−0.0294541
$936$	−2.94193	−0.0961601
$937$	−7.41462	−0.242225	−0.121113	−	0.992639i	$-0.538646\pi$
$937$	−7.41462	−0.242225	−0.121113	+	0.992639i	$0.538646\pi$
$938$	−18.7188	−0.611191
$939$	−5.70949	−0.186322
$940$	−3.03744	−0.0990704
$941$	−55.1308	−1.79721	−0.898607	−	0.438755i	$-0.855420\pi$
$941$	−55.1308	−1.79721	−0.898607	+	0.438755i	$0.855420\pi$
$942$	19.4051	0.632252
$943$	1.04976	0.0341849
$944$	31.8809	1.03763
$945$	2.33006	0.0757968
$946$	11.6713	0.379466
$947$	42.1126	1.36848	0.684238	−	0.729259i	$-0.260135\pi$
$947$	42.1126	1.36848	0.684238	+	0.729259i	$0.260135\pi$
$948$	3.01609	0.0979579
$949$	−9.96414	−0.323450
$950$	−15.8730	−0.514987
$951$	−21.3040	−0.690828
$952$	1.36658	0.0442912
$953$	−32.6027	−1.05611	−0.528053	−	0.849211i	$-0.677078\pi$
$953$	−32.6027	−1.05611	−0.528053	+	0.849211i	$0.677078\pi$
$954$	2.51075	0.0812885
$955$	2.09789	0.0678862
$956$	−2.71113	−0.0876843
$957$	11.8694	0.383685
$958$	−27.3874	−0.884847
$959$	−14.9533	−0.482866
$960$	15.2298	0.491541
$961$	−8.46102	−0.272936
$962$	−15.2521	−0.491749
$963$	3.38176	0.108976
$964$	−4.31889	−0.139102
$965$	19.1679	0.617037
$966$	−6.09811	−0.196203
$967$	−44.1023	−1.41824	−0.709118	−	0.705090i	$-0.750907\pi$
$967$	−44.1023	−1.41824	−0.709118	+	0.705090i	$0.750907\pi$
$968$	26.2879	0.844924
$969$	2.24236	0.0720350
$970$	36.4615	1.17071
$971$	−16.5951	−0.532562	−0.266281	−	0.963895i	$-0.585795\pi$
$971$	−16.5951	−0.532562	−0.266281	+	0.963895i	$0.585795\pi$
$972$	0.181762	0.00583003
$973$	24.8346	0.796161
$974$	−48.4500	−1.55244
$975$	1.85576	0.0594318
$976$	−38.1882	−1.22237
$977$	−32.9020	−1.05263	−0.526313	−	0.850291i	$-0.676426\pi$
$977$	−32.9020	−1.05263	−0.526313	+	0.850291i	$0.676426\pi$
$978$	20.5318	0.656533
$979$	14.3496	0.458615
$980$	−1.69959	−0.0542914
$981$	12.3011	0.392743
$982$	40.0082	1.27671
$983$	53.4386	1.70443	0.852214	−	0.523194i	$-0.175260\pi$
$983$	53.4386	1.70443	0.852214	+	0.523194i	$0.175260\pi$
$984$	0.897350	0.0286065
$985$	29.4670	0.938896
$986$	−3.93777	−0.125404
$987$	12.3838	0.394182
$988$	−1.15296	−0.0366806
$989$	−20.7326	−0.659259
$990$	3.43544	0.109186
$991$	−42.9357	−1.36390	−0.681948	−	0.731401i	$-0.738867\pi$
$991$	−42.9357	−1.36390	−0.681948	+	0.731401i	$0.738867\pi$
$992$	4.86581	0.154490
$993$	−12.7165	−0.403546
$994$	−11.4112	−0.361943
$995$	12.2999	0.389933
$996$	−1.66227	−0.0526711
$997$	13.8936	0.440016	0.220008	−	0.975498i	$-0.429392\pi$
$997$	13.8936	0.440016	0.220008	+	0.975498i	$0.429392\pi$
$998$	32.2412	1.02058
$999$	11.3111	0.357868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.18	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.18	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34842 q^{2} -1.00000 q^{3} -0.181762 q^{4} -1.77320 q^{5} -1.34842 q^{6} +1.31404 q^{7} -2.94193 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.34842 q^{2} -1.00000 q^{3} -0.181762 q^{4} -1.77320 q^{5} -1.34842 q^{6} +1.31404 q^{7} -2.94193 q^{8} +1.00000 q^{9} -2.39102 q^{10} -1.43681 q^{11} +0.181762 q^{12} +1.00000 q^{13} +1.77188 q^{14} +1.77320 q^{15} -3.60344 q^{16} -0.353504 q^{17} +1.34842 q^{18} +6.34324 q^{19} +0.322301 q^{20} -1.31404 q^{21} -1.93743 q^{22} +3.44161 q^{23} +2.94193 q^{24} -1.85576 q^{25} +1.34842 q^{26} -1.00000 q^{27} -0.238843 q^{28} +8.26096 q^{29} +2.39102 q^{30} +4.74752 q^{31} +1.02492 q^{32} +1.43681 q^{33} -0.476672 q^{34} -2.33006 q^{35} -0.181762 q^{36} -11.3111 q^{37} +8.55336 q^{38} -1.00000 q^{39} +5.21664 q^{40} +0.305020 q^{41} -1.77188 q^{42} -6.02412 q^{43} +0.261158 q^{44} -1.77320 q^{45} +4.64073 q^{46} -9.42424 q^{47} +3.60344 q^{48} -5.27330 q^{49} -2.50234 q^{50} +0.353504 q^{51} -0.181762 q^{52} +1.86199 q^{53} -1.34842 q^{54} +2.54775 q^{55} -3.86582 q^{56} -6.34324 q^{57} +11.1393 q^{58} -8.84735 q^{59} -0.322301 q^{60} +10.5977 q^{61} +6.40166 q^{62} +1.31404 q^{63} +8.58889 q^{64} -1.77320 q^{65} +1.93743 q^{66} -10.5644 q^{67} +0.0642537 q^{68} -3.44161 q^{69} -3.14190 q^{70} -6.44020 q^{71} -2.94193 q^{72} -9.96414 q^{73} -15.2521 q^{74} +1.85576 q^{75} -1.15296 q^{76} -1.88803 q^{77} -1.34842 q^{78} +16.5936 q^{79} +6.38962 q^{80} +1.00000 q^{81} +0.411296 q^{82} -9.14531 q^{83} +0.238843 q^{84} +0.626834 q^{85} -8.12304 q^{86} -8.26096 q^{87} +4.22700 q^{88} -9.98710 q^{89} -2.39102 q^{90} +1.31404 q^{91} -0.625554 q^{92} -4.74752 q^{93} -12.7078 q^{94} -11.2478 q^{95} -1.02492 q^{96} -15.2494 q^{97} -7.11062 q^{98} -1.43681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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