LMFDB - Embedded newform 4017.2.a.e.1.16

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} + \cdots + 7 $ x^16 - 21x^14 - 3x^13 + 177x^12 + 45x^11 - 763x^10 - 251x^9 + 1771x^8 + 639x^7 - 2118x^6 - 710x^5 + 1113x^4 + 243x^3 - 183x^2 - 10x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.28950$ of defining polynomial
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)

$f(q)$	$=$	$q+2.28950 q^{2} +1.00000 q^{3} +3.24180 q^{4} -3.89554 q^{5} +2.28950 q^{6} -1.35384 q^{7} +2.84309 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.28950 q^{2} +1.00000 q^{3} +3.24180 q^{4} -3.89554 q^{5} +2.28950 q^{6} -1.35384 q^{7} +2.84309 q^{8} +1.00000 q^{9} -8.91883 q^{10} +1.39025 q^{11} +3.24180 q^{12} -1.00000 q^{13} -3.09961 q^{14} -3.89554 q^{15} +0.0256562 q^{16} -0.168025 q^{17} +2.28950 q^{18} +3.52548 q^{19} -12.6285 q^{20} -1.35384 q^{21} +3.18296 q^{22} -4.03057 q^{23} +2.84309 q^{24} +10.1752 q^{25} -2.28950 q^{26} +1.00000 q^{27} -4.38888 q^{28} -6.37851 q^{29} -8.91883 q^{30} -6.92339 q^{31} -5.62744 q^{32} +1.39025 q^{33} -0.384692 q^{34} +5.27394 q^{35} +3.24180 q^{36} -2.60869 q^{37} +8.07157 q^{38} -1.00000 q^{39} -11.0754 q^{40} +2.45187 q^{41} -3.09961 q^{42} -9.77422 q^{43} +4.50689 q^{44} -3.89554 q^{45} -9.22797 q^{46} -6.47991 q^{47} +0.0256562 q^{48} -5.16712 q^{49} +23.2961 q^{50} -0.168025 q^{51} -3.24180 q^{52} +6.21910 q^{53} +2.28950 q^{54} -5.41575 q^{55} -3.84909 q^{56} +3.52548 q^{57} -14.6036 q^{58} +4.97378 q^{59} -12.6285 q^{60} -8.58385 q^{61} -15.8511 q^{62} -1.35384 q^{63} -12.9353 q^{64} +3.89554 q^{65} +3.18296 q^{66} -10.6249 q^{67} -0.544702 q^{68} -4.03057 q^{69} +12.0747 q^{70} -5.83696 q^{71} +2.84309 q^{72} -6.33308 q^{73} -5.97260 q^{74} +10.1752 q^{75} +11.4289 q^{76} -1.88217 q^{77} -2.28950 q^{78} -0.208422 q^{79} -0.0999448 q^{80} +1.00000 q^{81} +5.61356 q^{82} +3.54486 q^{83} -4.38888 q^{84} +0.654546 q^{85} -22.3781 q^{86} -6.37851 q^{87} +3.95260 q^{88} +8.49679 q^{89} -8.91883 q^{90} +1.35384 q^{91} -13.0663 q^{92} -6.92339 q^{93} -14.8357 q^{94} -13.7336 q^{95} -5.62744 q^{96} +2.54514 q^{97} -11.8301 q^{98} +1.39025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * 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 $

$2$	2.28950	1.61892	0.809460	−	0.587176i	$-0.199760\pi$
$2$	2.28950	1.61892	0.809460	+	0.587176i	$0.199760\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.24180	1.62090
$5$	−3.89554	−1.74214	−0.871069	−	0.491161i	$-0.836573\pi$
$5$	−3.89554	−1.74214	−0.871069	+	0.491161i	$0.836573\pi$
$6$	2.28950	0.934683
$7$	−1.35384	−0.511704	−0.255852	−	0.966716i	$-0.582356\pi$
$7$	−1.35384	−0.511704	−0.255852	+	0.966716i	$0.582356\pi$
$8$	2.84309	1.00518
$9$	1.00000	0.333333
$10$	−8.91883	−2.82038
$11$	1.39025	0.419175	0.209587	−	0.977790i	$-0.432788\pi$
$11$	1.39025	0.419175	0.209587	+	0.977790i	$0.432788\pi$
$12$	3.24180	0.935826
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.09961	−0.828407
$15$	−3.89554	−1.00582
$16$	0.0256562	0.00641406
$17$	−0.168025	−0.0407519	−0.0203760	−	0.999792i	$-0.506486\pi$
$17$	−0.168025	−0.0407519	−0.0203760	+	0.999792i	$0.506486\pi$
$18$	2.28950	0.539640
$19$	3.52548	0.808800	0.404400	−	0.914582i	$-0.367480\pi$
$19$	3.52548	0.808800	0.404400	+	0.914582i	$0.367480\pi$
$20$	−12.6285	−2.82383
$21$	−1.35384	−0.295432
$22$	3.18296	0.678610
$23$	−4.03057	−0.840431	−0.420216	−	0.907424i	$-0.638046\pi$
$23$	−4.03057	−0.840431	−0.420216	+	0.907424i	$0.638046\pi$
$24$	2.84309	0.580344
$25$	10.1752	2.03504
$26$	−2.28950	−0.449007
$27$	1.00000	0.192450
$28$	−4.38888	−0.829420
$29$	−6.37851	−1.18446	−0.592230	−	0.805769i	$-0.701752\pi$
$29$	−6.37851	−1.18446	−0.592230	+	0.805769i	$0.701752\pi$
$30$	−8.91883	−1.62835
$31$	−6.92339	−1.24348	−0.621739	−	0.783225i	$-0.713573\pi$
$31$	−6.92339	−1.24348	−0.621739	+	0.783225i	$0.713573\pi$
$32$	−5.62744	−0.994801
$33$	1.39025	0.242011
$34$	−0.384692	−0.0659741
$35$	5.27394	0.891458
$36$	3.24180	0.540300
$37$	−2.60869	−0.428867	−0.214433	−	0.976739i	$-0.568790\pi$
$37$	−2.60869	−0.428867	−0.214433	+	0.976739i	$0.568790\pi$
$38$	8.07157	1.30938
$39$	−1.00000	−0.160128
$40$	−11.0754	−1.75117
$41$	2.45187	0.382918	0.191459	−	0.981501i	$-0.438678\pi$
$41$	2.45187	0.382918	0.191459	+	0.981501i	$0.438678\pi$
$42$	−3.09961	−0.478281
$43$	−9.77422	−1.49056	−0.745278	−	0.666754i	$-0.767683\pi$
$43$	−9.77422	−1.49056	−0.745278	+	0.666754i	$0.767683\pi$
$44$	4.50689	0.679440
$45$	−3.89554	−0.580713
$46$	−9.22797	−1.36059
$47$	−6.47991	−0.945192	−0.472596	−	0.881279i	$-0.656683\pi$
$47$	−6.47991	−0.945192	−0.472596	+	0.881279i	$0.656683\pi$
$48$	0.0256562	0.00370316
$49$	−5.16712	−0.738159
$50$	23.2961	3.29457
$51$	−0.168025	−0.0235281
$52$	−3.24180	−0.449556
$53$	6.21910	0.854258	0.427129	−	0.904191i	$-0.359525\pi$
$53$	6.21910	0.854258	0.427129	+	0.904191i	$0.359525\pi$
$54$	2.28950	0.311561
$55$	−5.41575	−0.730260
$56$	−3.84909	−0.514357
$57$	3.52548	0.466961
$58$	−14.6036	−1.91754
$59$	4.97378	0.647531	0.323765	−	0.946137i	$-0.395051\pi$
$59$	4.97378	0.647531	0.323765	+	0.946137i	$0.395051\pi$
$60$	−12.6285	−1.63034
$61$	−8.58385	−1.09905	−0.549525	−	0.835477i	$-0.685191\pi$
$61$	−8.58385	−1.09905	−0.549525	+	0.835477i	$0.685191\pi$
$62$	−15.8511	−2.01309
$63$	−1.35384	−0.170568
$64$	−12.9353	−1.61692
$65$	3.89554	0.483182
$66$	3.18296	0.391796
$67$	−10.6249	−1.29803	−0.649017	−	0.760774i	$-0.724819\pi$
$67$	−10.6249	−1.29803	−0.649017	+	0.760774i	$0.724819\pi$
$68$	−0.544702	−0.0660548
$69$	−4.03057	−0.485223
$70$	12.0747	1.44320
$71$	−5.83696	−0.692720	−0.346360	−	0.938102i	$-0.612582\pi$
$71$	−5.83696	−0.692720	−0.346360	+	0.938102i	$0.612582\pi$
$72$	2.84309	0.335062
$73$	−6.33308	−0.741231	−0.370615	−	0.928786i	$-0.620853\pi$
$73$	−6.33308	−0.741231	−0.370615	+	0.928786i	$0.620853\pi$
$74$	−5.97260	−0.694300
$75$	10.1752	1.17493
$76$	11.4289	1.31098
$77$	−1.88217	−0.214493
$78$	−2.28950	−0.259235
$79$	−0.208422	−0.0234493	−0.0117247	−	0.999931i	$-0.503732\pi$
$79$	−0.208422	−0.0234493	−0.0117247	+	0.999931i	$0.503732\pi$
$80$	−0.0999448	−0.0111742
$81$	1.00000	0.111111
$82$	5.61356	0.619914
$83$	3.54486	0.389099	0.194550	−	0.980893i	$-0.437675\pi$
$83$	3.54486	0.389099	0.194550	+	0.980893i	$0.437675\pi$
$84$	−4.38888	−0.478866
$85$	0.654546	0.0709955
$86$	−22.3781	−2.41309
$87$	−6.37851	−0.683848
$88$	3.95260	0.421348
$89$	8.49679	0.900658	0.450329	−	0.892863i	$-0.351307\pi$
$89$	8.49679	0.900658	0.450329	+	0.892863i	$0.351307\pi$
$90$	−8.91883	−0.940127
$91$	1.35384	0.141921
$92$	−13.0663	−1.36225
$93$	−6.92339	−0.717922
$94$	−14.8357	−1.53019
$95$	−13.7336	−1.40904
$96$	−5.62744	−0.574349
$97$	2.54514	0.258420	0.129210	−	0.991617i	$-0.458756\pi$
$97$	2.54514	0.258420	0.129210	+	0.991617i	$0.458756\pi$
$98$	−11.8301	−1.19502
$99$	1.39025	0.139725
$100$	32.9860	3.29860
$101$	18.0121	1.79227	0.896137	−	0.443777i	$-0.146362\pi$
$101$	18.0121	1.79227	0.896137	+	0.443777i	$0.146362\pi$
$102$	−0.384692	−0.0380902
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.84309	−0.278788
$105$	5.27394	0.514684
$106$	14.2386	1.38298
$107$	−16.6483	−1.60945	−0.804724	−	0.593649i	$-0.797687\pi$
$107$	−16.6483	−1.60945	−0.804724	+	0.593649i	$0.797687\pi$
$108$	3.24180	0.311942
$109$	7.59984	0.727933	0.363966	−	0.931412i	$-0.381422\pi$
$109$	7.59984	0.727933	0.363966	+	0.931412i	$0.381422\pi$
$110$	−12.3994	−1.18223
$111$	−2.60869	−0.247606
$112$	−0.0347344	−0.00328210
$113$	12.9190	1.21532	0.607660	−	0.794197i	$-0.292108\pi$
$113$	12.9190	1.21532	0.607660	+	0.794197i	$0.292108\pi$
$114$	8.07157	0.755972
$115$	15.7012	1.46415
$116$	−20.6778	−1.91989
$117$	−1.00000	−0.0924500
$118$	11.3875	1.04830
$119$	0.227478	0.0208529
$120$	−11.0754	−1.01104
$121$	−9.06722	−0.824293
$122$	−19.6527	−1.77927
$123$	2.45187	0.221078
$124$	−22.4442	−2.01555
$125$	−20.1603	−1.80319
$126$	−3.09961	−0.276136
$127$	3.30511	0.293281	0.146641	−	0.989190i	$-0.453154\pi$
$127$	3.30511	0.293281	0.146641	+	0.989190i	$0.453154\pi$
$128$	−18.3605	−1.62286
$129$	−9.77422	−0.860572
$130$	8.91883	0.782233
$131$	4.50310	0.393438	0.196719	−	0.980460i	$-0.436971\pi$
$131$	4.50310	0.393438	0.196719	+	0.980460i	$0.436971\pi$
$132$	4.50689	0.392275
$133$	−4.77294	−0.413866
$134$	−24.3256	−2.10141
$135$	−3.89554	−0.335275
$136$	−0.477709	−0.0409632
$137$	5.10771	0.436381	0.218191	−	0.975906i	$-0.429985\pi$
$137$	5.10771	0.436381	0.218191	+	0.975906i	$0.429985\pi$
$138$	−9.22797	−0.785537
$139$	−0.619365	−0.0525339	−0.0262669	−	0.999655i	$-0.508362\pi$
$139$	−0.619365	−0.0525339	−0.0262669	+	0.999655i	$0.508362\pi$
$140$	17.0970	1.44496
$141$	−6.47991	−0.545707
$142$	−13.3637	−1.12146
$143$	−1.39025	−0.116258
$144$	0.0256562	0.00213802
$145$	24.8477	2.06349
$146$	−14.4996	−1.19999
$147$	−5.16712	−0.426177
$148$	−8.45686	−0.695149
$149$	8.66677	0.710010	0.355005	−	0.934864i	$-0.384479\pi$
$149$	8.66677	0.710010	0.355005	+	0.934864i	$0.384479\pi$
$150$	23.2961	1.90212
$151$	17.3829	1.41460	0.707301	−	0.706913i	$-0.249913\pi$
$151$	17.3829	1.41460	0.707301	+	0.706913i	$0.249913\pi$
$152$	10.0233	0.812994
$153$	−0.168025	−0.0135840
$154$	−4.30922	−0.347247
$155$	26.9703	2.16631
$156$	−3.24180	−0.259552
$157$	−18.3101	−1.46131	−0.730653	−	0.682749i	$-0.760784\pi$
$157$	−18.3101	−1.46131	−0.730653	+	0.682749i	$0.760784\pi$
$158$	−0.477182	−0.0379625
$159$	6.21910	0.493206
$160$	21.9219	1.73308
$161$	5.45674	0.430052
$162$	2.28950	0.179880
$163$	9.43679	0.739146	0.369573	−	0.929202i	$-0.379504\pi$
$163$	9.43679	0.739146	0.369573	+	0.929202i	$0.379504\pi$
$164$	7.94847	0.620672
$165$	−5.41575	−0.421616
$166$	8.11595	0.629920
$167$	19.4144	1.50233	0.751166	−	0.660113i	$-0.229492\pi$
$167$	19.4144	1.50233	0.751166	+	0.660113i	$0.229492\pi$
$168$	−3.84909	−0.296964
$169$	1.00000	0.0769231
$170$	1.49858	0.114936
$171$	3.52548	0.269600
$172$	−31.6861	−2.41604
$173$	−18.5077	−1.40711	−0.703556	−	0.710640i	$-0.748406\pi$
$173$	−18.5077	−1.40711	−0.703556	+	0.710640i	$0.748406\pi$
$174$	−14.6036	−1.10709
$175$	−13.7756	−1.04134
$176$	0.0356684	0.00268861
$177$	4.97378	0.373852
$178$	19.4534	1.45809
$179$	18.3104	1.36858	0.684292	−	0.729209i	$-0.260112\pi$
$179$	18.3104	1.36858	0.684292	+	0.729209i	$0.260112\pi$
$180$	−12.6285	−0.941276
$181$	8.58296	0.637966	0.318983	−	0.947760i	$-0.396659\pi$
$181$	8.58296	0.637966	0.318983	+	0.947760i	$0.396659\pi$
$182$	3.09961	0.229759
$183$	−8.58385	−0.634537
$184$	−11.4593	−0.844789
$185$	10.1623	0.747145
$186$	−15.8511	−1.16226
$187$	−0.233595	−0.0170822
$188$	−21.0066	−1.53206
$189$	−1.35384	−0.0984774
$190$	−31.4431	−2.28112
$191$	−16.3780	−1.18507	−0.592536	−	0.805544i	$-0.701873\pi$
$191$	−16.3780	−1.18507	−0.592536	+	0.805544i	$0.701873\pi$
$192$	−12.9353	−0.933527
$193$	4.16051	0.299480	0.149740	−	0.988725i	$-0.452156\pi$
$193$	4.16051	0.299480	0.149740	+	0.988725i	$0.452156\pi$
$194$	5.82709	0.418360
$195$	3.89554	0.278965
$196$	−16.7507	−1.19648
$197$	12.0779	0.860518	0.430259	−	0.902706i	$-0.358422\pi$
$197$	12.0779	0.860518	0.430259	+	0.902706i	$0.358422\pi$
$198$	3.18296	0.226203
$199$	−6.79605	−0.481759	−0.240880	−	0.970555i	$-0.577436\pi$
$199$	−6.79605	−0.481759	−0.240880	+	0.970555i	$0.577436\pi$
$200$	28.9291	2.04560
$201$	−10.6249	−0.749420
$202$	41.2387	2.90155
$203$	8.63549	0.606092
$204$	−0.544702	−0.0381367
$205$	−9.55137	−0.667096
$206$	2.28950	0.159517
$207$	−4.03057	−0.280144
$208$	−0.0256562	−0.00177894
$209$	4.90128	0.339029
$210$	12.0747	0.833231
$211$	4.41575	0.303993	0.151996	−	0.988381i	$-0.451430\pi$
$211$	4.41575	0.303993	0.151996	+	0.988381i	$0.451430\pi$
$212$	20.1610	1.38467
$213$	−5.83696	−0.399942
$214$	−38.1161	−2.60557
$215$	38.0759	2.59675
$216$	2.84309	0.193448
$217$	9.37316	0.636292
$218$	17.3998	1.17846
$219$	−6.33308	−0.427950
$220$	−17.5568	−1.18368
$221$	0.168025	0.0113026
$222$	−5.97260	−0.400854
$223$	−5.80596	−0.388796	−0.194398	−	0.980923i	$-0.562275\pi$
$223$	−5.80596	−0.388796	−0.194398	+	0.980923i	$0.562275\pi$
$224$	7.61866	0.509043
$225$	10.1752	0.678348
$226$	29.5781	1.96750
$227$	19.0013	1.26116	0.630582	−	0.776123i	$-0.282816\pi$
$227$	19.0013	1.26116	0.630582	+	0.776123i	$0.282816\pi$
$228$	11.4289	0.756897
$229$	−2.53131	−0.167274	−0.0836369	−	0.996496i	$-0.526654\pi$
$229$	−2.53131	−0.167274	−0.0836369	+	0.996496i	$0.526654\pi$
$230$	35.9479	2.37034
$231$	−1.88217	−0.123838
$232$	−18.1347	−1.19060
$233$	−19.2662	−1.26217	−0.631085	−	0.775713i	$-0.717390\pi$
$233$	−19.2662	−1.26217	−0.631085	+	0.775713i	$0.717390\pi$
$234$	−2.28950	−0.149669
$235$	25.2427	1.64666
$236$	16.1240	1.04958
$237$	−0.208422	−0.0135385
$238$	0.520811	0.0337592
$239$	−8.17745	−0.528956	−0.264478	−	0.964392i	$-0.585200\pi$
$239$	−8.17745	−0.528956	−0.264478	+	0.964392i	$0.585200\pi$
$240$	−0.0999448	−0.00645141
$241$	8.21852	0.529402	0.264701	−	0.964331i	$-0.414727\pi$
$241$	8.21852	0.529402	0.264701	+	0.964331i	$0.414727\pi$
$242$	−20.7594	−1.33446
$243$	1.00000	0.0641500
$244$	−27.8271	−1.78145
$245$	20.1287	1.28598
$246$	5.61356	0.357907
$247$	−3.52548	−0.224321
$248$	−19.6838	−1.24992
$249$	3.54486	0.224647
$250$	−46.1569	−2.91922
$251$	−19.1247	−1.20714	−0.603569	−	0.797311i	$-0.706255\pi$
$251$	−19.1247	−1.20714	−0.603569	+	0.797311i	$0.706255\pi$
$252$	−4.38888	−0.276473
$253$	−5.60348	−0.352288
$254$	7.56704	0.474798
$255$	0.654546	0.0409893
$256$	−16.1657	−1.01036
$257$	7.68330	0.479271	0.239635	−	0.970863i	$-0.422972\pi$
$257$	7.68330	0.479271	0.239635	+	0.970863i	$0.422972\pi$
$258$	−22.3781	−1.39320
$259$	3.53175	0.219453
$260$	12.6285	0.783189
$261$	−6.37851	−0.394820
$262$	10.3098	0.636944
$263$	−12.5884	−0.776234	−0.388117	−	0.921610i	$-0.626874\pi$
$263$	−12.5884	−0.776234	−0.388117	+	0.921610i	$0.626874\pi$
$264$	3.95260	0.243265
$265$	−24.2267	−1.48824
$266$	−10.9276	−0.670016
$267$	8.49679	0.519995
$268$	−34.4436	−2.10398
$269$	24.4450	1.49044	0.745220	−	0.666819i	$-0.232345\pi$
$269$	24.4450	1.49044	0.745220	+	0.666819i	$0.232345\pi$
$270$	−8.91883	−0.542782
$271$	5.48429	0.333147	0.166574	−	0.986029i	$-0.446730\pi$
$271$	5.48429	0.333147	0.166574	+	0.986029i	$0.446730\pi$
$272$	−0.00431088	−0.000261385 0
$273$	1.35384	0.0819382
$274$	11.6941	0.706466
$275$	14.1461	0.853039
$276$	−13.0663	−0.786498
$277$	−12.7955	−0.768809	−0.384405	−	0.923165i	$-0.625593\pi$
$277$	−12.7955	−0.768809	−0.384405	+	0.923165i	$0.625593\pi$
$278$	−1.41803	−0.0850481
$279$	−6.92339	−0.414492
$280$	14.9943	0.896080
$281$	8.70060	0.519034	0.259517	−	0.965739i	$-0.416437\pi$
$281$	8.70060	0.519034	0.259517	+	0.965739i	$0.416437\pi$
$282$	−14.8357	−0.883455
$283$	−26.9345	−1.60109	−0.800545	−	0.599273i	$-0.795456\pi$
$283$	−26.9345	−1.60109	−0.800545	+	0.599273i	$0.795456\pi$
$284$	−18.9222	−1.12283
$285$	−13.7336	−0.813511
$286$	−3.18296	−0.188213
$287$	−3.31944	−0.195941
$288$	−5.62744	−0.331600
$289$	−16.9718	−0.998339
$290$	56.8888	3.34063
$291$	2.54514	0.149199
$292$	−20.5306	−1.20146
$293$	1.49464	0.0873179	0.0436590	−	0.999046i	$-0.486098\pi$
$293$	1.49464	0.0873179	0.0436590	+	0.999046i	$0.486098\pi$
$294$	−11.8301	−0.689945
$295$	−19.3756	−1.12809
$296$	−7.41676	−0.431090
$297$	1.39025	0.0806702
$298$	19.8426	1.14945
$299$	4.03057	0.233094
$300$	32.9860	1.90445
$301$	13.2327	0.762722
$302$	39.7981	2.29013
$303$	18.0121	1.03477
$304$	0.0904505	0.00518769
$305$	33.4387	1.91470
$306$	−0.384692	−0.0219914
$307$	6.92236	0.395080	0.197540	−	0.980295i	$-0.436705\pi$
$307$	6.92236	0.395080	0.197540	+	0.980295i	$0.436705\pi$
$308$	−6.10161	−0.347672
$309$	1.00000	0.0568880
$310$	61.7485	3.50708
$311$	−0.873028	−0.0495049	−0.0247524	−	0.999694i	$-0.507880\pi$
$311$	−0.873028	−0.0495049	−0.0247524	+	0.999694i	$0.507880\pi$
$312$	−2.84309	−0.160958
$313$	0.986900	0.0557829	0.0278914	−	0.999611i	$-0.491121\pi$
$313$	0.986900	0.0557829	0.0278914	+	0.999611i	$0.491121\pi$
$314$	−41.9209	−2.36574
$315$	5.27394	0.297153
$316$	−0.675662	−0.0380089
$317$	−19.8424	−1.11446	−0.557229	−	0.830359i	$-0.688136\pi$
$317$	−19.8424	−1.11446	−0.557229	+	0.830359i	$0.688136\pi$
$318$	14.2386	0.798461
$319$	−8.86769	−0.496496
$320$	50.3901	2.81689
$321$	−16.6483	−0.929215
$322$	12.4932	0.696219
$323$	−0.592367	−0.0329602
$324$	3.24180	0.180100
$325$	−10.1752	−0.564420
$326$	21.6055	1.19662
$327$	7.59984	0.420272
$328$	6.97090	0.384904
$329$	8.77277	0.483658
$330$	−12.3994	−0.682562
$331$	0.296681	0.0163070	0.00815352	−	0.999967i	$-0.497405\pi$
$331$	0.296681	0.0163070	0.00815352	+	0.999967i	$0.497405\pi$
$332$	11.4917	0.630691
$333$	−2.60869	−0.142956
$334$	44.4492	2.43215
$335$	41.3896	2.26135
$336$	−0.0347344	−0.00189492
$337$	−9.44867	−0.514702	−0.257351	−	0.966318i	$-0.582850\pi$
$337$	−9.44867	−0.514702	−0.257351	+	0.966318i	$0.582850\pi$
$338$	2.28950	0.124532
$339$	12.9190	0.701665
$340$	2.12191	0.115077
$341$	−9.62521	−0.521234
$342$	8.07157	0.436461
$343$	16.4723	0.889422
$344$	−27.7890	−1.49828
$345$	15.7012	0.845326
$346$	−42.3733	−2.27800
$347$	−30.7192	−1.64909	−0.824546	−	0.565794i	$-0.808570\pi$
$347$	−30.7192	−1.64909	−0.824546	+	0.565794i	$0.808570\pi$
$348$	−20.6778	−1.10845
$349$	−28.4968	−1.52540	−0.762699	−	0.646753i	$-0.776126\pi$
$349$	−28.4968	−1.52540	−0.762699	+	0.646753i	$0.776126\pi$
$350$	−31.5393	−1.68584
$351$	−1.00000	−0.0533761
$352$	−7.82353	−0.416995
$353$	24.5328	1.30575	0.652875	−	0.757465i	$-0.273563\pi$
$353$	24.5328	1.30575	0.652875	+	0.757465i	$0.273563\pi$
$354$	11.3875	0.605236
$355$	22.7381	1.20681
$356$	27.5449	1.45987
$357$	0.227478	0.0120394
$358$	41.9216	2.21563
$359$	−19.9402	−1.05240	−0.526201	−	0.850360i	$-0.676384\pi$
$359$	−19.9402	−1.05240	−0.526201	+	0.850360i	$0.676384\pi$
$360$	−11.0754	−0.583724
$361$	−6.57100	−0.345842
$362$	19.6507	1.03282
$363$	−9.06722	−0.475906
$364$	4.38888	0.230040
$365$	24.6707	1.29133
$366$	−19.6527	−1.02726
$367$	34.9545	1.82461	0.912305	−	0.409512i	$-0.134301\pi$
$367$	34.9545	1.82461	0.912305	+	0.409512i	$0.134301\pi$
$368$	−0.103409	−0.00539057
$369$	2.45187	0.127639
$370$	23.2665	1.20957
$371$	−8.41966	−0.437127
$372$	−22.4442	−1.16368
$373$	−2.75857	−0.142833	−0.0714167	−	0.997447i	$-0.522752\pi$
$373$	−2.75857	−0.142833	−0.0714167	+	0.997447i	$0.522752\pi$
$374$	−0.534816	−0.0276547
$375$	−20.1603	−1.04107
$376$	−18.4230	−0.950093
$377$	6.37851	0.328510
$378$	−3.09961	−0.159427
$379$	−10.7461	−0.551992	−0.275996	−	0.961159i	$-0.589008\pi$
$379$	−10.7461	−0.551992	−0.275996	+	0.961159i	$0.589008\pi$
$380$	−44.5217	−2.28391
$381$	3.30511	0.169326
$382$	−37.4974	−1.91853
$383$	−19.2341	−0.982816	−0.491408	−	0.870930i	$-0.663518\pi$
$383$	−19.2341	−0.982816	−0.491408	+	0.870930i	$0.663518\pi$
$384$	−18.3605	−0.936956
$385$	7.33207	0.373677
$386$	9.52547	0.484834
$387$	−9.77422	−0.496852
$388$	8.25082	0.418872
$389$	−1.45721	−0.0738833	−0.0369417	−	0.999317i	$-0.511762\pi$
$389$	−1.45721	−0.0738833	−0.0369417	+	0.999317i	$0.511762\pi$
$390$	8.91883	0.451622
$391$	0.677234	0.0342492
$392$	−14.6906	−0.741987
$393$	4.50310	0.227151
$394$	27.6524	1.39311
$395$	0.811916	0.0408519
$396$	4.50689	0.226480
$397$	−7.92414	−0.397701	−0.198851	−	0.980030i	$-0.563721\pi$
$397$	−7.92414	−0.397701	−0.198851	+	0.980030i	$0.563721\pi$
$398$	−15.5595	−0.779929
$399$	−4.77294	−0.238946
$400$	0.261058	0.0130529
$401$	7.99609	0.399306	0.199653	−	0.979867i	$-0.436019\pi$
$401$	7.99609	0.399306	0.199653	+	0.979867i	$0.436019\pi$
$402$	−24.3256	−1.21325
$403$	6.92339	0.344878
$404$	58.3917	2.90510
$405$	−3.89554	−0.193571
$406$	19.7709	0.981214
$407$	−3.62672	−0.179770
$408$	−0.477709	−0.0236501
$409$	−9.65119	−0.477221	−0.238610	−	0.971115i	$-0.576692\pi$
$409$	−9.65119	−0.477221	−0.238610	+	0.971115i	$0.576692\pi$
$410$	−21.8678	−1.07997
$411$	5.10771	0.251945
$412$	3.24180	0.159712
$413$	−6.73370	−0.331344
$414$	−9.22797	−0.453530
$415$	−13.8092	−0.677865
$416$	5.62744	0.275908
$417$	−0.619365	−0.0303304
$418$	11.2215	0.548860
$419$	23.9955	1.17226	0.586129	−	0.810218i	$-0.300651\pi$
$419$	23.9955	1.17226	0.586129	+	0.810218i	$0.300651\pi$
$420$	17.0970	0.834250
$421$	20.1686	0.982958	0.491479	−	0.870889i	$-0.336456\pi$
$421$	20.1686	0.982958	0.491479	+	0.870889i	$0.336456\pi$
$422$	10.1098	0.492139
$423$	−6.47991	−0.315064
$424$	17.6815	0.858688
$425$	−1.70969	−0.0829320
$426$	−13.3637	−0.647473
$427$	11.6212	0.562388
$428$	−53.9703	−2.60875
$429$	−1.39025	−0.0671217
$430$	87.1746	4.20393
$431$	−17.6788	−0.851557	−0.425779	−	0.904827i	$-0.640000\pi$
$431$	−17.6788	−0.851557	−0.425779	+	0.904827i	$0.640000\pi$
$432$	0.0256562	0.00123439
$433$	35.3058	1.69669	0.848344	−	0.529446i	$-0.177600\pi$
$433$	35.3058	1.69669	0.848344	+	0.529446i	$0.177600\pi$
$434$	21.4598	1.03010
$435$	24.8477	1.19136
$436$	24.6372	1.17991
$437$	−14.2097	−0.679741
$438$	−14.4996	−0.692816
$439$	−19.8628	−0.948000	−0.474000	−	0.880525i	$-0.657190\pi$
$439$	−19.8628	−0.948000	−0.474000	+	0.880525i	$0.657190\pi$
$440$	−15.3975	−0.734046
$441$	−5.16712	−0.246053
$442$	0.384692	0.0182979
$443$	−32.6406	−1.55080	−0.775400	−	0.631470i	$-0.782452\pi$
$443$	−32.6406	−1.55080	−0.775400	+	0.631470i	$0.782452\pi$
$444$	−8.45686	−0.401345
$445$	−33.0996	−1.56907
$446$	−13.2927	−0.629429
$447$	8.66677	0.409924
$448$	17.5124	0.827382
$449$	−22.4004	−1.05714	−0.528570	−	0.848890i	$-0.677271\pi$
$449$	−22.4004	−1.05714	−0.528570	+	0.848890i	$0.677271\pi$
$450$	23.2961	1.09819
$451$	3.40870	0.160510
$452$	41.8809	1.96991
$453$	17.3829	0.816721
$454$	43.5035	2.04172
$455$	−5.27394	−0.247246
$456$	10.0233	0.469382
$457$	−15.6463	−0.731903	−0.365952	−	0.930634i	$-0.619256\pi$
$457$	−15.6463	−0.731903	−0.365952	+	0.930634i	$0.619256\pi$
$458$	−5.79543	−0.270803
$459$	−0.168025	−0.00784272
$460$	50.9002	2.37323
$461$	21.4154	0.997415	0.498708	−	0.866770i	$-0.333808\pi$
$461$	21.4154	0.997415	0.498708	+	0.866770i	$0.333808\pi$
$462$	−4.30922	−0.200483
$463$	27.4274	1.27466	0.637331	−	0.770590i	$-0.280039\pi$
$463$	27.4274	1.27466	0.637331	+	0.770590i	$0.280039\pi$
$464$	−0.163649	−0.00759719
$465$	26.9703	1.25072
$466$	−44.1099	−2.04335
$467$	13.5016	0.624778	0.312389	−	0.949954i	$-0.398871\pi$
$467$	13.5016	0.624778	0.312389	+	0.949954i	$0.398871\pi$
$468$	−3.24180	−0.149852
$469$	14.3844	0.664208
$470$	57.7932	2.66580
$471$	−18.3101	−0.843685
$472$	14.1409	0.650888
$473$	−13.5886	−0.624803
$474$	−0.477182	−0.0219177
$475$	35.8725	1.64594
$476$	0.737439	0.0338005
$477$	6.21910	0.284753
$478$	−18.7223	−0.856336
$479$	1.41149	0.0644928	0.0322464	−	0.999480i	$-0.489734\pi$
$479$	1.41149	0.0644928	0.0322464	+	0.999480i	$0.489734\pi$
$480$	21.9219	1.00059
$481$	2.60869	0.118946
$482$	18.8163	0.857058
$483$	5.45674	0.248290
$484$	−29.3941	−1.33609
$485$	−9.91468	−0.450203
$486$	2.28950	0.103854
$487$	−21.5656	−0.977229	−0.488614	−	0.872500i	$-0.662497\pi$
$487$	−21.5656	−0.977229	−0.488614	+	0.872500i	$0.662497\pi$
$488$	−24.4047	−1.10475
$489$	9.43679	0.426746
$490$	46.0846	2.08189
$491$	30.5160	1.37717	0.688584	−	0.725156i	$-0.258233\pi$
$491$	30.5160	1.37717	0.688584	+	0.725156i	$0.258233\pi$
$492$	7.94847	0.358345
$493$	1.07175	0.0482690
$494$	−8.07157	−0.363157
$495$	−5.41575	−0.243420
$496$	−0.177628	−0.00797573
$497$	7.90231	0.354467
$498$	8.11595	0.363685
$499$	−15.8283	−0.708571	−0.354286	−	0.935137i	$-0.615276\pi$
$499$	−15.8283	−0.708571	−0.354286	+	0.935137i	$0.615276\pi$
$500$	−65.3556	−2.92279
$501$	19.4144	0.867372
$502$	−43.7859	−1.95426
$503$	−16.5618	−0.738452	−0.369226	−	0.929340i	$-0.620377\pi$
$503$	−16.5618	−0.738452	−0.369226	+	0.929340i	$0.620377\pi$
$504$	−3.84909	−0.171452
$505$	−70.1670	−3.12239
$506$	−12.8291	−0.570325
$507$	1.00000	0.0444116
$508$	10.7145	0.475379
$509$	−5.94298	−0.263418	−0.131709	−	0.991288i	$-0.542046\pi$
$509$	−5.94298	−0.263418	−0.131709	+	0.991288i	$0.542046\pi$
$510$	1.49858	0.0663583
$511$	8.57398	0.379290
$512$	−0.290265	−0.0128280
$513$	3.52548	0.155654
$514$	17.5909	0.775901
$515$	−3.89554	−0.171658
$516$	−31.6861	−1.39490
$517$	−9.00867	−0.396201
$518$	8.08594	0.355276
$519$	−18.5077	−0.812396
$520$	11.0754	0.485687
$521$	7.86107	0.344400	0.172200	−	0.985062i	$-0.444913\pi$
$521$	7.86107	0.344400	0.172200	+	0.985062i	$0.444913\pi$
$522$	−14.6036	−0.639182
$523$	5.42602	0.237263	0.118632	−	0.992938i	$-0.462149\pi$
$523$	5.42602	0.237263	0.118632	+	0.992938i	$0.462149\pi$
$524$	14.5981	0.637723
$525$	−13.7756	−0.601218
$526$	−28.8211	−1.25666
$527$	1.16330	0.0506741
$528$	0.0356684	0.00155227
$529$	−6.75453	−0.293675
$530$	−55.4670	−2.40933
$531$	4.97378	0.215844
$532$	−15.4729	−0.670835
$533$	−2.45187	−0.106202
$534$	19.4534	0.841830
$535$	64.8539	2.80388
$536$	−30.2075	−1.30476
$537$	18.3104	0.790152
$538$	55.9668	2.41290
$539$	−7.18356	−0.309418
$540$	−12.6285	−0.543446
$541$	2.34605	0.100865	0.0504324	−	0.998727i	$-0.483940\pi$
$541$	2.34605	0.100865	0.0504324	+	0.998727i	$0.483940\pi$
$542$	12.5563	0.539338
$543$	8.58296	0.368330
$544$	0.945549	0.0405401
$545$	−29.6055	−1.26816
$546$	3.09961	0.132651
$547$	−16.8833	−0.721879	−0.360939	−	0.932589i	$-0.617544\pi$
$547$	−16.8833	−0.721879	−0.360939	+	0.932589i	$0.617544\pi$
$548$	16.5582	0.707330
$549$	−8.58385	−0.366350
$550$	32.3874	1.38100
$551$	−22.4873	−0.957991
$552$	−11.4593	−0.487739
$553$	0.282170	0.0119991
$554$	−29.2953	−1.24464
$555$	10.1623	0.431364
$556$	−2.00786	−0.0851521
$557$	−8.66492	−0.367144	−0.183572	−	0.983006i	$-0.558766\pi$
$557$	−8.66492	−0.367144	−0.183572	+	0.983006i	$0.558766\pi$
$558$	−15.8511	−0.671030
$559$	9.77422	0.413406
$560$	0.135309	0.00571786
$561$	−0.233595	−0.00986240
$562$	19.9200	0.840274
$563$	27.7805	1.17081	0.585403	−	0.810742i	$-0.300936\pi$
$563$	27.7805	1.17081	0.585403	+	0.810742i	$0.300936\pi$
$564$	−21.0066	−0.884536
$565$	−50.3266	−2.11726
$566$	−61.6664	−2.59203
$567$	−1.35384	−0.0568560
$568$	−16.5950	−0.696311
$569$	31.6348	1.32620	0.663100	−	0.748531i	$-0.269241\pi$
$569$	31.6348	1.32620	0.663100	+	0.748531i	$0.269241\pi$
$570$	−31.4431	−1.31701
$571$	1.91627	0.0801933	0.0400966	−	0.999196i	$-0.487233\pi$
$571$	1.91627	0.0801933	0.0400966	+	0.999196i	$0.487233\pi$
$572$	−4.50689	−0.188443
$573$	−16.3780	−0.684201
$574$	−7.59986	−0.317212
$575$	−41.0119	−1.71032
$576$	−12.9353	−0.538972
$577$	−7.66448	−0.319076	−0.159538	−	0.987192i	$-0.551000\pi$
$577$	−7.66448	−0.319076	−0.159538	+	0.987192i	$0.551000\pi$
$578$	−38.8568	−1.61623
$579$	4.16051	0.172905
$580$	80.5513	3.34471
$581$	−4.79918	−0.199104
$582$	5.82709	0.241540
$583$	8.64607	0.358084
$584$	−18.0055	−0.745074
$585$	3.89554	0.161061
$586$	3.42198	0.141361
$587$	38.6492	1.59522	0.797611	−	0.603172i	$-0.206097\pi$
$587$	38.6492	1.59522	0.797611	+	0.603172i	$0.206097\pi$
$588$	−16.7507	−0.690789
$589$	−24.4083	−1.00572
$590$	−44.3603	−1.82628
$591$	12.0779	0.496820
$592$	−0.0669292	−0.00275077
$593$	5.33027	0.218888	0.109444	−	0.993993i	$-0.465093\pi$
$593$	5.33027	0.218888	0.109444	+	0.993993i	$0.465093\pi$
$594$	3.18296	0.130599
$595$	−0.886151	−0.0363287
$596$	28.0959	1.15085
$597$	−6.79605	−0.278144
$598$	9.22797	0.377360
$599$	−24.9994	−1.02145	−0.510723	−	0.859745i	$-0.670622\pi$
$599$	−24.9994	−1.02145	−0.510723	+	0.859745i	$0.670622\pi$
$600$	28.9291	1.18103
$601$	−25.5873	−1.04373	−0.521863	−	0.853029i	$-0.674763\pi$
$601$	−25.5873	−1.04373	−0.521863	+	0.853029i	$0.674763\pi$
$602$	30.2963	1.23479
$603$	−10.6249	−0.432678
$604$	56.3519	2.29293
$605$	35.3217	1.43603
$606$	41.2387	1.67521
$607$	37.6552	1.52838	0.764189	−	0.644992i	$-0.223139\pi$
$607$	37.6552	1.52838	0.764189	+	0.644992i	$0.223139\pi$
$608$	−19.8394	−0.804595
$609$	8.63549	0.349928
$610$	76.5579	3.09974
$611$	6.47991	0.262149
$612$	−0.544702	−0.0220183
$613$	−15.2573	−0.616237	−0.308119	−	0.951348i	$-0.599699\pi$
$613$	−15.2573	−0.616237	−0.308119	+	0.951348i	$0.599699\pi$
$614$	15.8487	0.639602
$615$	−9.55137	−0.385148
$616$	−5.35118	−0.215605
$617$	−13.9440	−0.561365	−0.280682	−	0.959801i	$-0.590561\pi$
$617$	−13.9440	−0.561365	−0.280682	+	0.959801i	$0.590561\pi$
$618$	2.28950	0.0920971
$619$	3.12649	0.125664	0.0628321	−	0.998024i	$-0.479987\pi$
$619$	3.12649	0.125664	0.0628321	+	0.998024i	$0.479987\pi$
$620$	87.4323	3.51137
$621$	−4.03057	−0.161741
$622$	−1.99880	−0.0801444
$623$	−11.5033	−0.460870
$624$	−0.0256562	−0.00102707
$625$	27.6591	1.10636
$626$	2.25950	0.0903079
$627$	4.90128	0.195738
$628$	−59.3577	−2.36863
$629$	0.438325	0.0174771
$630$	12.0747	0.481066
$631$	39.3329	1.56582	0.782909	−	0.622137i	$-0.213735\pi$
$631$	39.3329	1.56582	0.782909	+	0.622137i	$0.213735\pi$
$632$	−0.592563	−0.0235709
$633$	4.41575	0.175510
$634$	−45.4291	−1.80422
$635$	−12.8752	−0.510936
$636$	20.1610	0.799438
$637$	5.16712	0.204729
$638$	−20.3026	−0.803786
$639$	−5.83696	−0.230907
$640$	71.5241	2.82724
$641$	−16.3150	−0.644405	−0.322202	−	0.946671i	$-0.604423\pi$
$641$	−16.3150	−0.644405	−0.322202	+	0.946671i	$0.604423\pi$
$642$	−38.1161	−1.50432
$643$	−12.6175	−0.497587	−0.248793	−	0.968557i	$-0.580034\pi$
$643$	−12.6175	−0.497587	−0.248793	+	0.968557i	$0.580034\pi$
$644$	17.6897	0.697070
$645$	38.0759	1.49924
$646$	−1.35622	−0.0533599
$647$	−25.0787	−0.985946	−0.492973	−	0.870045i	$-0.664090\pi$
$647$	−25.0787	−0.985946	−0.492973	+	0.870045i	$0.664090\pi$
$648$	2.84309	0.111687
$649$	6.91477	0.271429
$650$	−23.2961	−0.913750
$651$	9.37316	0.367363
$652$	30.5921	1.19808
$653$	−38.3177	−1.49949	−0.749744	−	0.661728i	$-0.769824\pi$
$653$	−38.3177	−1.49949	−0.749744	+	0.661728i	$0.769824\pi$
$654$	17.3998	0.680387
$655$	−17.5420	−0.685423
$656$	0.0629058	0.00245606
$657$	−6.33308	−0.247077
$658$	20.0852	0.783004
$659$	37.9878	1.47980	0.739898	−	0.672719i	$-0.234874\pi$
$659$	37.9878	1.47980	0.739898	+	0.672719i	$0.234874\pi$
$660$	−17.5568	−0.683397
$661$	−46.8779	−1.82334	−0.911669	−	0.410925i	$-0.865206\pi$
$661$	−46.8779	−1.82334	−0.911669	+	0.410925i	$0.865206\pi$
$662$	0.679249	0.0263998
$663$	0.168025	0.00652553
$664$	10.0784	0.391117
$665$	18.5932	0.721012
$666$	−5.97260	−0.231433
$667$	25.7090	0.995457
$668$	62.9376	2.43513
$669$	−5.80596	−0.224472
$670$	94.7613	3.66095
$671$	−11.9337	−0.460694
$672$	7.61866	0.293896
$673$	−0.871443	−0.0335916	−0.0167958	−	0.999859i	$-0.505347\pi$
$673$	−0.871443	−0.0335916	−0.0167958	+	0.999859i	$0.505347\pi$
$674$	−21.6327	−0.833261
$675$	10.1752	0.391645
$676$	3.24180	0.124685
$677$	5.43824	0.209009	0.104504	−	0.994524i	$-0.466674\pi$
$677$	5.43824	0.209009	0.104504	+	0.994524i	$0.466674\pi$
$678$	29.5781	1.13594
$679$	−3.44571	−0.132234
$680$	1.86094	0.0713636
$681$	19.0013	0.728133
$682$	−22.0369	−0.843836
$683$	8.17866	0.312948	0.156474	−	0.987682i	$-0.449987\pi$
$683$	8.17866	0.312948	0.156474	+	0.987682i	$0.449987\pi$
$684$	11.4289	0.436994
$685$	−19.8973	−0.760236
$686$	37.7134	1.43990
$687$	−2.53131	−0.0965756
$688$	−0.250770	−0.00956050
$689$	−6.21910	−0.236929
$690$	35.9479	1.36851
$691$	−19.4072	−0.738284	−0.369142	−	0.929373i	$-0.620348\pi$
$691$	−19.4072	−0.738284	−0.369142	+	0.929373i	$0.620348\pi$
$692$	−59.9981	−2.28079
$693$	−1.88217	−0.0714977
$694$	−70.3315	−2.66975
$695$	2.41276	0.0915213
$696$	−18.1347	−0.687394
$697$	−0.411975	−0.0156047
$698$	−65.2434	−2.46950
$699$	−19.2662	−0.728715
$700$	−44.6578	−1.68791
$701$	13.3478	0.504141	0.252071	−	0.967709i	$-0.418888\pi$
$701$	13.3478	0.504141	0.252071	+	0.967709i	$0.418888\pi$
$702$	−2.28950	−0.0864115
$703$	−9.19689	−0.346867
$704$	−17.9833	−0.677770
$705$	25.2427	0.950697
$706$	56.1678	2.11390
$707$	−24.3856	−0.917113
$708$	16.1240	0.605977
$709$	4.37630	0.164355	0.0821777	−	0.996618i	$-0.473812\pi$
$709$	4.37630	0.164355	0.0821777	+	0.996618i	$0.473812\pi$
$710$	52.0588	1.95373
$711$	−0.208422	−0.00781643
$712$	24.1571	0.905327
$713$	27.9052	1.04506
$714$	0.520811	0.0194909
$715$	5.41575	0.202538
$716$	59.3586	2.21833
$717$	−8.17745	−0.305393
$718$	−45.6530	−1.70375
$719$	49.1852	1.83430	0.917149	−	0.398545i	$-0.130485\pi$
$719$	49.1852	1.83430	0.917149	+	0.398545i	$0.130485\pi$
$720$	−0.0999448	−0.00372472
$721$	−1.35384	−0.0504197
$722$	−15.0443	−0.559890
$723$	8.21852	0.305650
$724$	27.8242	1.03408
$725$	−64.9028	−2.41043
$726$	−20.7594	−0.770453
$727$	2.73524	0.101445	0.0507223	−	0.998713i	$-0.483848\pi$
$727$	2.73524	0.101445	0.0507223	+	0.998713i	$0.483848\pi$
$728$	3.84909	0.142657
$729$	1.00000	0.0370370
$730$	56.4836	2.09055
$731$	1.64231	0.0607430
$732$	−27.8271	−1.02852
$733$	−24.1259	−0.891111	−0.445555	−	0.895254i	$-0.646994\pi$
$733$	−24.1259	−0.891111	−0.445555	+	0.895254i	$0.646994\pi$
$734$	80.0282	2.95389
$735$	20.1287	0.742458
$736$	22.6818	0.836062
$737$	−14.7712	−0.544103
$738$	5.61356	0.206638
$739$	40.3408	1.48396	0.741980	−	0.670422i	$-0.233887\pi$
$739$	40.3408	1.48396	0.741980	+	0.670422i	$0.233887\pi$
$740$	32.9440	1.21105
$741$	−3.52548	−0.129512
$742$	−19.2768	−0.707673
$743$	−23.3382	−0.856196	−0.428098	−	0.903732i	$-0.640816\pi$
$743$	−23.3382	−0.856196	−0.428098	+	0.903732i	$0.640816\pi$
$744$	−19.6838	−0.721644
$745$	−33.7618	−1.23694
$746$	−6.31574	−0.231236
$747$	3.54486	0.129700
$748$	−0.757269	−0.0276885
$749$	22.5391	0.823560
$750$	−46.1569	−1.68541
$751$	−46.4453	−1.69481	−0.847407	−	0.530943i	$-0.821838\pi$
$751$	−46.4453	−1.69481	−0.847407	+	0.530943i	$0.821838\pi$
$752$	−0.166250	−0.00606252
$753$	−19.1247	−0.696942
$754$	14.6036	0.531831
$755$	−67.7158	−2.46443
$756$	−4.38888	−0.159622
$757$	22.0652	0.801972	0.400986	−	0.916084i	$-0.368668\pi$
$757$	22.0652	0.801972	0.400986	+	0.916084i	$0.368668\pi$
$758$	−24.6032	−0.893630
$759$	−5.60348	−0.203393
$760$	−39.0460	−1.41635
$761$	−40.0449	−1.45163	−0.725813	−	0.687892i	$-0.758536\pi$
$761$	−40.0449	−1.45163	−0.725813	+	0.687892i	$0.758536\pi$
$762$	7.56704	0.274125
$763$	−10.2890	−0.372486
$764$	−53.0942	−1.92088
$765$	0.654546	0.0236652
$766$	−44.0364	−1.59110
$767$	−4.97378	−0.179593
$768$	−16.1657	−0.583329
$769$	−10.7183	−0.386513	−0.193256	−	0.981148i	$-0.561905\pi$
$769$	−10.7183	−0.386513	−0.193256	+	0.981148i	$0.561905\pi$
$770$	16.7867	0.604952
$771$	7.68330	0.276707
$772$	13.4875	0.485427
$773$	−16.8324	−0.605421	−0.302711	−	0.953083i	$-0.597892\pi$
$773$	−16.8324	−0.605421	−0.302711	+	0.953083i	$0.597892\pi$
$774$	−22.3781	−0.804363
$775$	−70.4470	−2.53053
$776$	7.23606	0.259759
$777$	3.53175	0.126701
$778$	−3.33627	−0.119611
$779$	8.64402	0.309704
$780$	12.6285	0.452175
$781$	−8.11480	−0.290371
$782$	1.55053	0.0554467
$783$	−6.37851	−0.227949
$784$	−0.132569	−0.00473460
$785$	71.3277	2.54580
$786$	10.3098	0.367740
$787$	15.4605	0.551109	0.275554	−	0.961285i	$-0.411139\pi$
$787$	15.4605	0.551109	0.275554	+	0.961285i	$0.411139\pi$
$788$	39.1542	1.39481
$789$	−12.5884	−0.448159
$790$	1.85888	0.0661360
$791$	−17.4903	−0.621884
$792$	3.95260	0.140449
$793$	8.58385	0.304822
$794$	−18.1423	−0.643846
$795$	−24.2267	−0.859234
$796$	−22.0314	−0.780883
$797$	−24.2805	−0.860061	−0.430031	−	0.902814i	$-0.641497\pi$
$797$	−24.2805	−0.860061	−0.430031	+	0.902814i	$0.641497\pi$
$798$	−10.9276	−0.386834
$799$	1.08878	0.0385184
$800$	−57.2605	−2.02446
$801$	8.49679	0.300219
$802$	18.3070	0.646444
$803$	−8.80453	−0.310705
$804$	−34.4436	−1.21473
$805$	−21.2570	−0.749209
$806$	15.8511	0.558330
$807$	24.4450	0.860506
$808$	51.2102	1.80157
$809$	−46.8094	−1.64573	−0.822865	−	0.568237i	$-0.807626\pi$
$809$	−46.8094	−1.64573	−0.822865	+	0.568237i	$0.807626\pi$
$810$	−8.91883	−0.313376
$811$	−15.6238	−0.548626	−0.274313	−	0.961640i	$-0.588450\pi$
$811$	−15.6238	−0.548626	−0.274313	+	0.961640i	$0.588450\pi$
$812$	27.9945	0.982414
$813$	5.48429	0.192343
$814$	−8.30337	−0.291033
$815$	−36.7614	−1.28769
$816$	−0.00431088	−0.000150911 0
$817$	−34.4588	−1.20556
$818$	−22.0964	−0.772582
$819$	1.35384	0.0473070
$820$	−30.9636	−1.08130
$821$	−31.2646	−1.09114	−0.545570	−	0.838065i	$-0.683687\pi$
$821$	−31.2646	−1.09114	−0.545570	+	0.838065i	$0.683687\pi$
$822$	11.6941	0.407878
$823$	−50.4110	−1.75722	−0.878609	−	0.477542i	$-0.841528\pi$
$823$	−50.4110	−1.75722	−0.878609	+	0.477542i	$0.841528\pi$
$824$	2.84309	0.0990438
$825$	14.1461	0.492502
$826$	−15.4168	−0.536419
$827$	−27.5030	−0.956374	−0.478187	−	0.878258i	$-0.658706\pi$
$827$	−27.5030	−0.956374	−0.478187	+	0.878258i	$0.658706\pi$
$828$	−13.0663	−0.454085
$829$	3.04752	0.105845	0.0529224	−	0.998599i	$-0.483146\pi$
$829$	3.04752	0.105845	0.0529224	+	0.998599i	$0.483146\pi$
$830$	−31.6160	−1.09741
$831$	−12.7955	−0.443872
$832$	12.9353	0.448452
$833$	0.868203	0.0300814
$834$	−1.41803	−0.0491025
$835$	−75.6296	−2.61727
$836$	15.8890	0.549531
$837$	−6.92339	−0.239307
$838$	54.9377	1.89779
$839$	−32.2323	−1.11278	−0.556392	−	0.830920i	$-0.687815\pi$
$839$	−32.2323	−1.11278	−0.556392	+	0.830920i	$0.687815\pi$
$840$	14.9943	0.517352
$841$	11.6854	0.402945
$842$	46.1760	1.59133
$843$	8.70060	0.299664
$844$	14.3150	0.492741
$845$	−3.89554	−0.134011
$846$	−14.8357	−0.510063
$847$	12.2756	0.421793
$848$	0.159559	0.00547926
$849$	−26.9345	−0.924389
$850$	−3.91433	−0.134260
$851$	10.5145	0.360433
$852$	−18.9222	−0.648265
$853$	30.0130	1.02763	0.513813	−	0.857902i	$-0.328233\pi$
$853$	30.0130	1.02763	0.513813	+	0.857902i	$0.328233\pi$
$854$	26.6066	0.910460
$855$	−13.7336	−0.469681
$856$	−47.3325	−1.61779
$857$	−37.6306	−1.28544	−0.642718	−	0.766103i	$-0.722193\pi$
$857$	−37.6306	−1.28544	−0.642718	+	0.766103i	$0.722193\pi$
$858$	−3.18296	−0.108665
$859$	−53.0493	−1.81002	−0.905010	−	0.425390i	$-0.860137\pi$
$859$	−53.0493	−1.81002	−0.905010	+	0.425390i	$0.860137\pi$
$860$	123.434	4.20907
$861$	−3.31944	−0.113126
$862$	−40.4755	−1.37860
$863$	10.9893	0.374079	0.187039	−	0.982352i	$-0.440111\pi$
$863$	10.9893	0.374079	0.187039	+	0.982352i	$0.440111\pi$
$864$	−5.62744	−0.191450
$865$	72.0973	2.45138
$866$	80.8325	2.74680
$867$	−16.9718	−0.576391
$868$	30.3859	1.03136
$869$	−0.289758	−0.00982936
$870$	56.8888	1.92871
$871$	10.6249	0.360010
$872$	21.6071	0.731707
$873$	2.54514	0.0861399
$874$	−32.5330	−1.10045
$875$	27.2938	0.922699
$876$	−20.5306	−0.693663
$877$	−42.3654	−1.43058	−0.715289	−	0.698828i	$-0.753705\pi$
$877$	−42.3654	−1.43058	−0.715289	+	0.698828i	$0.753705\pi$
$878$	−45.4758	−1.53473
$879$	1.49464	0.0504130
$880$	−0.138948	−0.00468393
$881$	21.7504	0.732790	0.366395	−	0.930459i	$-0.380592\pi$
$881$	21.7504	0.732790	0.366395	+	0.930459i	$0.380592\pi$
$882$	−11.8301	−0.398340
$883$	21.4723	0.722599	0.361299	−	0.932450i	$-0.382333\pi$
$883$	21.4723	0.722599	0.361299	+	0.932450i	$0.382333\pi$
$884$	0.544702	0.0183203
$885$	−19.3756	−0.651302
$886$	−74.7305	−2.51062
$887$	−32.9935	−1.10781	−0.553906	−	0.832579i	$-0.686863\pi$
$887$	−32.9935	−1.10781	−0.553906	+	0.832579i	$0.686863\pi$
$888$	−7.41676	−0.248890
$889$	−4.47459	−0.150073
$890$	−75.7814	−2.54020
$891$	1.39025	0.0465750
$892$	−18.8218	−0.630199
$893$	−22.8448	−0.764472
$894$	19.8426	0.663634
$895$	−71.3289	−2.38426
$896$	24.8572	0.830421
$897$	4.03057	0.134577
$898$	−51.2856	−1.71142
$899$	44.1609	1.47285
$900$	32.9860	1.09953
$901$	−1.04496	−0.0348127
$902$	7.80422	0.259852
$903$	13.2327	0.440358
$904$	36.7300	1.22162
$905$	−33.4352	−1.11143
$906$	39.7981	1.32220
$907$	−14.8094	−0.491737	−0.245869	−	0.969303i	$-0.579073\pi$
$907$	−14.8094	−0.491737	−0.245869	+	0.969303i	$0.579073\pi$
$908$	61.5985	2.04422
$909$	18.0121	0.597425
$910$	−12.0747	−0.400271
$911$	−8.04622	−0.266583	−0.133292	−	0.991077i	$-0.542555\pi$
$911$	−8.04622	−0.266583	−0.133292	+	0.991077i	$0.542555\pi$
$912$	0.0904505	0.00299511
$913$	4.92823	0.163101
$914$	−35.8222	−1.18489
$915$	33.4387	1.10545
$916$	−8.20600	−0.271134
$917$	−6.09648	−0.201323
$918$	−0.384692	−0.0126967
$919$	47.8792	1.57939	0.789694	−	0.613501i	$-0.210239\pi$
$919$	47.8792	1.57939	0.789694	+	0.613501i	$0.210239\pi$
$920$	44.6400	1.47174
$921$	6.92236	0.228099
$922$	49.0305	1.61473
$923$	5.83696	0.192126
$924$	−6.10161	−0.200728
$925$	−26.5440	−0.872763
$926$	62.7951	2.06357
$927$	1.00000	0.0328443
$928$	35.8947	1.17830
$929$	−15.5327	−0.509612	−0.254806	−	0.966992i	$-0.582012\pi$
$929$	−15.5327	−0.509612	−0.254806	+	0.966992i	$0.582012\pi$
$930$	61.7485	2.02481
$931$	−18.2166	−0.597024
$932$	−62.4571	−2.04585
$933$	−0.873028	−0.0285817
$934$	30.9118	1.01146
$935$	0.909980	0.0297595
$936$	−2.84309	−0.0929294
$937$	−26.4933	−0.865500	−0.432750	−	0.901514i	$-0.642457\pi$
$937$	−26.4933	−0.865500	−0.432750	+	0.901514i	$0.642457\pi$
$938$	32.9330	1.07530
$939$	0.986900	0.0322063
$940$	81.8319	2.66906
$941$	4.65439	0.151729	0.0758643	−	0.997118i	$-0.475828\pi$
$941$	4.65439	0.151729	0.0758643	+	0.997118i	$0.475828\pi$
$942$	−41.9209	−1.36586
$943$	−9.88244	−0.321816
$944$	0.127608	0.00415330
$945$	5.27394	0.171561
$946$	−31.1110	−1.01151
$947$	15.9614	0.518677	0.259339	−	0.965786i	$-0.416495\pi$
$947$	15.9614	0.518677	0.259339	+	0.965786i	$0.416495\pi$
$948$	−0.675662	−0.0219445
$949$	6.33308	0.205580
$950$	82.1301	2.66465
$951$	−19.8424	−0.643433
$952$	0.646742	0.0209610
$953$	44.2575	1.43364	0.716821	−	0.697257i	$-0.245596\pi$
$953$	44.2575	1.43364	0.716821	+	0.697257i	$0.245596\pi$
$954$	14.2386	0.460992
$955$	63.8012	2.06456
$956$	−26.5097	−0.857383
$957$	−8.86769	−0.286652
$958$	3.23161	0.104409
$959$	−6.91503	−0.223298
$960$	50.3901	1.62633
$961$	16.9333	0.546235
$962$	5.97260	0.192564
$963$	−16.6483	−0.536483
$964$	26.6428	0.858107
$965$	−16.2074	−0.521736
$966$	12.4932	0.401962
$967$	24.6206	0.791744	0.395872	−	0.918306i	$-0.370442\pi$
$967$	24.6206	0.791744	0.395872	+	0.918306i	$0.370442\pi$
$968$	−25.7789	−0.828566
$969$	−0.592367	−0.0190296
$970$	−22.6996	−0.728842
$971$	43.5016	1.39603	0.698017	−	0.716081i	$-0.254066\pi$
$971$	43.5016	1.39603	0.698017	+	0.716081i	$0.254066\pi$
$972$	3.24180	0.103981
$973$	0.838522	0.0268818
$974$	−49.3743	−1.58205
$975$	−10.1752	−0.325868
$976$	−0.220229	−0.00704937
$977$	34.4275	1.10143	0.550717	−	0.834692i	$-0.314354\pi$
$977$	34.4275	1.10143	0.550717	+	0.834692i	$0.314354\pi$
$978$	21.6055	0.690868
$979$	11.8126	0.377533
$980$	65.2532	2.08444
$981$	7.59984	0.242644
$982$	69.8663	2.22952
$983$	55.7416	1.77788	0.888940	−	0.458023i	$-0.151442\pi$
$983$	55.7416	1.77788	0.888940	+	0.458023i	$0.151442\pi$
$984$	6.97090	0.222224
$985$	−47.0501	−1.49914
$986$	2.45376	0.0781437
$987$	8.77277	0.279240
$988$	−11.4289	−0.363601
$989$	39.3957	1.25271
$990$	−12.3994	−0.394077
$991$	−45.6559	−1.45031	−0.725153	−	0.688587i	$-0.758231\pi$
$991$	−45.6559	−1.45031	−0.725153	+	0.688587i	$0.758231\pi$
$992$	38.9610	1.23701
$993$	0.296681	0.00941487
$994$	18.0923	0.573854
$995$	26.4743	0.839291
$996$	11.4917	0.364129
$997$	60.7698	1.92460	0.962299	−	0.271993i	$-0.0876828\pi$
$997$	60.7698	1.92460	0.962299	+	0.271993i	$0.0876828\pi$
$998$	−36.2388	−1.14712
$999$	−2.60869	−0.0825354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.16	✓	16	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)

\(f(q)\)	\(=\)	\(q+2.28950 q^{2} +1.00000 q^{3} +3.24180 q^{4} -3.89554 q^{5} +2.28950 q^{6} -1.35384 q^{7} +2.84309 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.28950 q^{2} +1.00000 q^{3} +3.24180 q^{4} -3.89554 q^{5} +2.28950 q^{6} -1.35384 q^{7} +2.84309 q^{8} +1.00000 q^{9} -8.91883 q^{10} +1.39025 q^{11} +3.24180 q^{12} -1.00000 q^{13} -3.09961 q^{14} -3.89554 q^{15} +0.0256562 q^{16} -0.168025 q^{17} +2.28950 q^{18} +3.52548 q^{19} -12.6285 q^{20} -1.35384 q^{21} +3.18296 q^{22} -4.03057 q^{23} +2.84309 q^{24} +10.1752 q^{25} -2.28950 q^{26} +1.00000 q^{27} -4.38888 q^{28} -6.37851 q^{29} -8.91883 q^{30} -6.92339 q^{31} -5.62744 q^{32} +1.39025 q^{33} -0.384692 q^{34} +5.27394 q^{35} +3.24180 q^{36} -2.60869 q^{37} +8.07157 q^{38} -1.00000 q^{39} -11.0754 q^{40} +2.45187 q^{41} -3.09961 q^{42} -9.77422 q^{43} +4.50689 q^{44} -3.89554 q^{45} -9.22797 q^{46} -6.47991 q^{47} +0.0256562 q^{48} -5.16712 q^{49} +23.2961 q^{50} -0.168025 q^{51} -3.24180 q^{52} +6.21910 q^{53} +2.28950 q^{54} -5.41575 q^{55} -3.84909 q^{56} +3.52548 q^{57} -14.6036 q^{58} +4.97378 q^{59} -12.6285 q^{60} -8.58385 q^{61} -15.8511 q^{62} -1.35384 q^{63} -12.9353 q^{64} +3.89554 q^{65} +3.18296 q^{66} -10.6249 q^{67} -0.544702 q^{68} -4.03057 q^{69} +12.0747 q^{70} -5.83696 q^{71} +2.84309 q^{72} -6.33308 q^{73} -5.97260 q^{74} +10.1752 q^{75} +11.4289 q^{76} -1.88217 q^{77} -2.28950 q^{78} -0.208422 q^{79} -0.0999448 q^{80} +1.00000 q^{81} +5.61356 q^{82} +3.54486 q^{83} -4.38888 q^{84} +0.654546 q^{85} -22.3781 q^{86} -6.37851 q^{87} +3.95260 q^{88} +8.49679 q^{89} -8.91883 q^{90} +1.35384 q^{91} -13.0663 q^{92} -6.92339 q^{93} -14.8357 q^{94} -13.7336 q^{95} -5.62744 q^{96} +2.54514 q^{97} -11.8301 q^{98} +1.39025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * q^99

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