LMFDB - Embedded newform 6045.2.a.bh.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$1.42963$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.42963 q^{2} -1.00000 q^{3} +0.0438374 q^{4} +1.00000 q^{5} -1.42963 q^{6} -4.47441 q^{7} -2.79659 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.42963 q^{2} -1.00000 q^{3} +0.0438374 q^{4} +1.00000 q^{5} -1.42963 q^{6} -4.47441 q^{7} -2.79659 q^{8} +1.00000 q^{9} +1.42963 q^{10} -2.86949 q^{11} -0.0438374 q^{12} +1.00000 q^{13} -6.39675 q^{14} -1.00000 q^{15} -4.08575 q^{16} -6.35442 q^{17} +1.42963 q^{18} +2.17027 q^{19} +0.0438374 q^{20} +4.47441 q^{21} -4.10231 q^{22} +1.22473 q^{23} +2.79659 q^{24} +1.00000 q^{25} +1.42963 q^{26} -1.00000 q^{27} -0.196146 q^{28} -3.42572 q^{29} -1.42963 q^{30} +1.00000 q^{31} -0.247937 q^{32} +2.86949 q^{33} -9.08446 q^{34} -4.47441 q^{35} +0.0438374 q^{36} -1.26022 q^{37} +3.10268 q^{38} -1.00000 q^{39} -2.79659 q^{40} -8.39821 q^{41} +6.39675 q^{42} +6.39998 q^{43} -0.125791 q^{44} +1.00000 q^{45} +1.75091 q^{46} -4.53772 q^{47} +4.08575 q^{48} +13.0204 q^{49} +1.42963 q^{50} +6.35442 q^{51} +0.0438374 q^{52} -9.61892 q^{53} -1.42963 q^{54} -2.86949 q^{55} +12.5131 q^{56} -2.17027 q^{57} -4.89751 q^{58} -6.33107 q^{59} -0.0438374 q^{60} +1.51919 q^{61} +1.42963 q^{62} -4.47441 q^{63} +7.81705 q^{64} +1.00000 q^{65} +4.10231 q^{66} +13.7987 q^{67} -0.278561 q^{68} -1.22473 q^{69} -6.39675 q^{70} +7.05201 q^{71} -2.79659 q^{72} +11.0374 q^{73} -1.80165 q^{74} -1.00000 q^{75} +0.0951390 q^{76} +12.8393 q^{77} -1.42963 q^{78} -9.26634 q^{79} -4.08575 q^{80} +1.00000 q^{81} -12.0063 q^{82} +15.6062 q^{83} +0.196146 q^{84} -6.35442 q^{85} +9.14959 q^{86} +3.42572 q^{87} +8.02478 q^{88} -9.24557 q^{89} +1.42963 q^{90} -4.47441 q^{91} +0.0536890 q^{92} -1.00000 q^{93} -6.48725 q^{94} +2.17027 q^{95} +0.247937 q^{96} +17.8425 q^{97} +18.6143 q^{98} -2.86949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * 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 $

$2$	1.42963	1.01090	0.505450	−	0.862856i	$-0.331327\pi$
$2$	1.42963	1.01090	0.505450	+	0.862856i	$0.331327\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.0438374	0.0219187
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.42963	−0.583643
$7$	−4.47441	−1.69117	−0.845584	−	0.533842i	$-0.820748\pi$
$7$	−4.47441	−1.69117	−0.845584	+	0.533842i	$0.820748\pi$
$8$	−2.79659	−0.988742
$9$	1.00000	0.333333
$10$	1.42963	0.452088
$11$	−2.86949	−0.865185	−0.432592	−	0.901590i	$-0.642401\pi$
$11$	−2.86949	−0.865185	−0.432592	+	0.901590i	$0.642401\pi$
$12$	−0.0438374	−0.0126548
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−6.39675	−1.70960
$15$	−1.00000	−0.258199
$16$	−4.08575	−1.02144
$17$	−6.35442	−1.54117	−0.770587	−	0.637335i	$-0.780037\pi$
$17$	−6.35442	−1.54117	−0.770587	+	0.637335i	$0.780037\pi$
$18$	1.42963	0.336967
$19$	2.17027	0.497895	0.248947	−	0.968517i	$-0.419915\pi$
$19$	2.17027	0.497895	0.248947	+	0.968517i	$0.419915\pi$
$20$	0.0438374	0.00980233
$21$	4.47441	0.976397
$22$	−4.10231	−0.874615
$23$	1.22473	0.255374	0.127687	−	0.991815i	$-0.459245\pi$
$23$	1.22473	0.255374	0.127687	+	0.991815i	$0.459245\pi$
$24$	2.79659	0.570851
$25$	1.00000	0.200000
$26$	1.42963	0.280373
$27$	−1.00000	−0.192450
$28$	−0.196146	−0.0370682
$29$	−3.42572	−0.636141	−0.318070	−	0.948067i	$-0.603035\pi$
$29$	−3.42572	−0.636141	−0.318070	+	0.948067i	$0.603035\pi$
$30$	−1.42963	−0.261013
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−0.247937	−0.0438295
$33$	2.86949	0.499515
$34$	−9.08446	−1.55797
$35$	−4.47441	−0.756314
$36$	0.0438374	0.00730623
$37$	−1.26022	−0.207179	−0.103589	−	0.994620i	$-0.533033\pi$
$37$	−1.26022	−0.207179	−0.103589	+	0.994620i	$0.533033\pi$
$38$	3.10268	0.503322
$39$	−1.00000	−0.160128
$40$	−2.79659	−0.442179
$41$	−8.39821	−1.31158	−0.655790	−	0.754943i	$-0.727664\pi$
$41$	−8.39821	−1.31158	−0.655790	+	0.754943i	$0.727664\pi$
$42$	6.39675	0.987039
$43$	6.39998	0.975987	0.487994	−	0.872847i	$-0.337729\pi$
$43$	6.39998	0.975987	0.487994	+	0.872847i	$0.337729\pi$
$44$	−0.125791	−0.0189637
$45$	1.00000	0.149071
$46$	1.75091	0.258158
$47$	−4.53772	−0.661894	−0.330947	−	0.943649i	$-0.607368\pi$
$47$	−4.53772	−0.661894	−0.330947	+	0.943649i	$0.607368\pi$
$48$	4.08575	0.589728
$49$	13.0204	1.86005
$50$	1.42963	0.202180
$51$	6.35442	0.889797
$52$	0.0438374	0.00607915
$53$	−9.61892	−1.32126	−0.660630	−	0.750711i	$-0.729711\pi$
$53$	−9.61892	−1.32126	−0.660630	+	0.750711i	$0.729711\pi$
$54$	−1.42963	−0.194548
$55$	−2.86949	−0.386922
$56$	12.5131	1.67213
$57$	−2.17027	−0.287460
$58$	−4.89751	−0.643075
$59$	−6.33107	−0.824235	−0.412118	−	0.911131i	$-0.635211\pi$
$59$	−6.33107	−0.824235	−0.412118	+	0.911131i	$0.635211\pi$
$60$	−0.0438374	−0.00565938
$61$	1.51919	0.194513	0.0972564	−	0.995259i	$-0.468993\pi$
$61$	1.51919	0.194513	0.0972564	+	0.995259i	$0.468993\pi$
$62$	1.42963	0.181563
$63$	−4.47441	−0.563723
$64$	7.81705	0.977131
$65$	1.00000	0.124035
$66$	4.10231	0.504959
$67$	13.7987	1.68578	0.842889	−	0.538087i	$-0.180853\pi$
$67$	13.7987	1.68578	0.842889	+	0.538087i	$0.180853\pi$
$68$	−0.278561	−0.0337805
$69$	−1.22473	−0.147440
$70$	−6.39675	−0.764557
$71$	7.05201	0.836919	0.418460	−	0.908235i	$-0.362570\pi$
$71$	7.05201	0.836919	0.418460	+	0.908235i	$0.362570\pi$
$72$	−2.79659	−0.329581
$73$	11.0374	1.29183	0.645917	−	0.763407i	$-0.276475\pi$
$73$	11.0374	1.29183	0.645917	+	0.763407i	$0.276475\pi$
$74$	−1.80165	−0.209437
$75$	−1.00000	−0.115470
$76$	0.0951390	0.0109132
$77$	12.8393	1.46317
$78$	−1.42963	−0.161874
$79$	−9.26634	−1.04254	−0.521272	−	0.853390i	$-0.674542\pi$
$79$	−9.26634	−1.04254	−0.521272	+	0.853390i	$0.674542\pi$
$80$	−4.08575	−0.456801
$81$	1.00000	0.111111
$82$	−12.0063	−1.32588
$83$	15.6062	1.71300	0.856501	−	0.516145i	$-0.172633\pi$
$83$	15.6062	1.71300	0.856501	+	0.516145i	$0.172633\pi$
$84$	0.196146	0.0214013
$85$	−6.35442	−0.689234
$86$	9.14959	0.986625
$87$	3.42572	0.367276
$88$	8.02478	0.855445
$89$	−9.24557	−0.980029	−0.490014	−	0.871714i	$-0.663008\pi$
$89$	−9.24557	−0.980029	−0.490014	+	0.871714i	$0.663008\pi$
$90$	1.42963	0.150696
$91$	−4.47441	−0.469046
$92$	0.0536890	0.00559746
$93$	−1.00000	−0.103695
$94$	−6.48725	−0.669109
$95$	2.17027	0.222665
$96$	0.247937	0.0253050
$97$	17.8425	1.81163	0.905816	−	0.423671i	$-0.139259\pi$
$97$	17.8425	1.81163	0.905816	+	0.423671i	$0.139259\pi$
$98$	18.6143	1.88033
$99$	−2.86949	−0.288395
$100$	0.0438374	0.00438374
$101$	−9.77269	−0.972419	−0.486210	−	0.873842i	$-0.661621\pi$
$101$	−9.77269	−0.972419	−0.486210	+	0.873842i	$0.661621\pi$
$102$	9.08446	0.899495
$103$	−1.18727	−0.116985	−0.0584925	−	0.998288i	$-0.518629\pi$
$103$	−1.18727	−0.116985	−0.0584925	+	0.998288i	$0.518629\pi$
$104$	−2.79659	−0.274228
$105$	4.47441	0.436658
$106$	−13.7515	−1.33566
$107$	−4.53205	−0.438130	−0.219065	−	0.975710i	$-0.570301\pi$
$107$	−4.53205	−0.438130	−0.219065	+	0.975710i	$0.570301\pi$
$108$	−0.0438374	−0.00421825
$109$	−3.16623	−0.303270	−0.151635	−	0.988437i	$-0.548454\pi$
$109$	−3.16623	−0.303270	−0.151635	+	0.988437i	$0.548454\pi$
$110$	−4.10231	−0.391140
$111$	1.26022	0.119615
$112$	18.2813	1.72742
$113$	1.99869	0.188021	0.0940105	−	0.995571i	$-0.470031\pi$
$113$	1.99869	0.188021	0.0940105	+	0.995571i	$0.470031\pi$
$114$	−3.10268	−0.290593
$115$	1.22473	0.114207
$116$	−0.150175	−0.0139434
$117$	1.00000	0.0924500
$118$	−9.05108	−0.833219
$119$	28.4323	2.60638
$120$	2.79659	0.255292
$121$	−2.76601	−0.251455
$122$	2.17188	0.196633
$123$	8.39821	0.757241
$124$	0.0438374	0.00393671
$125$	1.00000	0.0894427
$126$	−6.39675	−0.569867
$127$	12.0482	1.06910	0.534552	−	0.845135i	$-0.320480\pi$
$127$	12.0482	1.06910	0.534552	+	0.845135i	$0.320480\pi$
$128$	11.6713	1.03161
$129$	−6.39998	−0.563486
$130$	1.42963	0.125387
$131$	12.8368	1.12156	0.560780	−	0.827965i	$-0.310501\pi$
$131$	12.8368	1.12156	0.560780	+	0.827965i	$0.310501\pi$
$132$	0.125791	0.0109487
$133$	−9.71069	−0.842024
$134$	19.7270	1.70415
$135$	−1.00000	−0.0860663
$136$	17.7707	1.52382
$137$	−10.4020	−0.888701	−0.444350	−	0.895853i	$-0.646565\pi$
$137$	−10.4020	−0.888701	−0.444350	+	0.895853i	$0.646565\pi$
$138$	−1.75091	−0.149047
$139$	9.07898	0.770069	0.385034	−	0.922902i	$-0.374190\pi$
$139$	9.07898	0.770069	0.385034	+	0.922902i	$0.374190\pi$
$140$	−0.196146	−0.0165774
$141$	4.53772	0.382145
$142$	10.0817	0.846041
$143$	−2.86949	−0.239959
$144$	−4.08575	−0.340479
$145$	−3.42572	−0.284491
$146$	15.7794	1.30592
$147$	−13.0204	−1.07390
$148$	−0.0552448	−0.00454109
$149$	−6.37098	−0.521931	−0.260966	−	0.965348i	$-0.584041\pi$
$149$	−6.37098	−0.521931	−0.260966	+	0.965348i	$0.584041\pi$
$150$	−1.42963	−0.116729
$151$	2.49069	0.202689	0.101345	−	0.994851i	$-0.467686\pi$
$151$	2.49069	0.202689	0.101345	+	0.994851i	$0.467686\pi$
$152$	−6.06935	−0.492290
$153$	−6.35442	−0.513724
$154$	18.3554	1.47912
$155$	1.00000	0.0803219
$156$	−0.0438374	−0.00350980
$157$	18.1588	1.44923	0.724615	−	0.689154i	$-0.242018\pi$
$157$	18.1588	1.44923	0.724615	+	0.689154i	$0.242018\pi$
$158$	−13.2474	−1.05391
$159$	9.61892	0.762830
$160$	−0.247937	−0.0196012
$161$	−5.47995	−0.431881
$162$	1.42963	0.112322
$163$	−2.14427	−0.167952	−0.0839762	−	0.996468i	$-0.526762\pi$
$163$	−2.14427	−0.167952	−0.0839762	+	0.996468i	$0.526762\pi$
$164$	−0.368156	−0.0287481
$165$	2.86949	0.223390
$166$	22.3111	1.73167
$167$	−2.50366	−0.193739	−0.0968696	−	0.995297i	$-0.530883\pi$
$167$	−2.50366	−0.193739	−0.0968696	+	0.995297i	$0.530883\pi$
$168$	−12.5131	−0.965405
$169$	1.00000	0.0769231
$170$	−9.08446	−0.696746
$171$	2.17027	0.165965
$172$	0.280558	0.0213924
$173$	19.5084	1.48319	0.741597	−	0.670845i	$-0.234068\pi$
$173$	19.5084	1.48319	0.741597	+	0.670845i	$0.234068\pi$
$174$	4.89751	0.371279
$175$	−4.47441	−0.338234
$176$	11.7240	0.883733
$177$	6.33107	0.475872
$178$	−13.2177	−0.990711
$179$	17.3760	1.29875	0.649373	−	0.760470i	$-0.275032\pi$
$179$	17.3760	1.29875	0.649373	+	0.760470i	$0.275032\pi$
$180$	0.0438374	0.00326744
$181$	14.1087	1.04869	0.524346	−	0.851505i	$-0.324310\pi$
$181$	14.1087	1.04869	0.524346	+	0.851505i	$0.324310\pi$
$182$	−6.39675	−0.474158
$183$	−1.51919	−0.112302
$184$	−3.42506	−0.252499
$185$	−1.26022	−0.0926533
$186$	−1.42963	−0.104825
$187$	18.2340	1.33340
$188$	−0.198922	−0.0145079
$189$	4.47441	0.325466
$190$	3.10268	0.225092
$191$	−0.672943	−0.0486924	−0.0243462	−	0.999704i	$-0.507750\pi$
$191$	−0.672943	−0.0486924	−0.0243462	+	0.999704i	$0.507750\pi$
$192$	−7.81705	−0.564147
$193$	11.1627	0.803507	0.401754	−	0.915748i	$-0.368401\pi$
$193$	11.1627	0.803507	0.401754	+	0.915748i	$0.368401\pi$
$194$	25.5082	1.83138
$195$	−1.00000	−0.0716115
$196$	0.570779	0.0407699
$197$	−16.7711	−1.19489	−0.597446	−	0.801909i	$-0.703818\pi$
$197$	−16.7711	−1.19489	−0.597446	+	0.801909i	$0.703818\pi$
$198$	−4.10231	−0.291538
$199$	1.29278	0.0916425	0.0458212	−	0.998950i	$-0.485410\pi$
$199$	1.29278	0.0916425	0.0458212	+	0.998950i	$0.485410\pi$
$200$	−2.79659	−0.197748
$201$	−13.7987	−0.973284
$202$	−13.9713	−0.983019
$203$	15.3281	1.07582
$204$	0.278561	0.0195032
$205$	−8.39821	−0.586557
$206$	−1.69735	−0.118260
$207$	1.22473	0.0851247
$208$	−4.08575	−0.283296
$209$	−6.22758	−0.430771
$210$	6.39675	0.441417
$211$	−15.3133	−1.05421	−0.527106	−	0.849800i	$-0.676723\pi$
$211$	−15.3133	−1.05421	−0.527106	+	0.849800i	$0.676723\pi$
$212$	−0.421668	−0.0289603
$213$	−7.05201	−0.483195
$214$	−6.47915	−0.442906
$215$	6.39998	0.436475
$216$	2.79659	0.190284
$217$	−4.47441	−0.303743
$218$	−4.52653	−0.306576
$219$	−11.0374	−0.745841
$220$	−0.125791	−0.00848083
$221$	−6.35442	−0.427444
$222$	1.80165	0.120919
$223$	16.5103	1.10561	0.552806	−	0.833310i	$-0.313557\pi$
$223$	16.5103	1.10561	0.552806	+	0.833310i	$0.313557\pi$
$224$	1.10937	0.0741231
$225$	1.00000	0.0666667
$226$	2.85739	0.190070
$227$	14.6303	0.971045	0.485522	−	0.874224i	$-0.338629\pi$
$227$	14.6303	0.971045	0.485522	+	0.874224i	$0.338629\pi$
$228$	−0.0951390	−0.00630074
$229$	−16.1703	−1.06856	−0.534280	−	0.845307i	$-0.679417\pi$
$229$	−16.1703	−1.06856	−0.534280	+	0.845307i	$0.679417\pi$
$230$	1.75091	0.115452
$231$	−12.8393	−0.844764
$232$	9.58033	0.628979
$233$	16.8377	1.10307	0.551537	−	0.834150i	$-0.314041\pi$
$233$	16.8377	1.10307	0.551537	+	0.834150i	$0.314041\pi$
$234$	1.42963	0.0934577
$235$	−4.53772	−0.296008
$236$	−0.277537	−0.0180661
$237$	9.26634	0.601913
$238$	40.6476	2.63479
$239$	1.02344	0.0662007	0.0331003	−	0.999452i	$-0.489462\pi$
$239$	1.02344	0.0662007	0.0331003	+	0.999452i	$0.489462\pi$
$240$	4.08575	0.263734
$241$	−21.4332	−1.38063	−0.690317	−	0.723507i	$-0.742529\pi$
$241$	−21.4332	−1.38063	−0.690317	+	0.723507i	$0.742529\pi$
$242$	−3.95437	−0.254196
$243$	−1.00000	−0.0641500
$244$	0.0665974	0.00426346
$245$	13.0204	0.831841
$246$	12.0063	0.765495
$247$	2.17027	0.138091
$248$	−2.79659	−0.177583
$249$	−15.6062	−0.989003
$250$	1.42963	0.0904176
$251$	−21.2923	−1.34396	−0.671980	−	0.740570i	$-0.734556\pi$
$251$	−21.2923	−1.34396	−0.671980	+	0.740570i	$0.734556\pi$
$252$	−0.196146	−0.0123561
$253$	−3.51436	−0.220946
$254$	17.2244	1.08076
$255$	6.35442	0.397929
$256$	1.05160	0.0657247
$257$	0.0868775	0.00541927	0.00270964	−	0.999996i	$-0.499137\pi$
$257$	0.0868775	0.00541927	0.00270964	+	0.999996i	$0.499137\pi$
$258$	−9.14959	−0.569628
$259$	5.63875	0.350375
$260$	0.0438374	0.00271868
$261$	−3.42572	−0.212047
$262$	18.3519	1.13379
$263$	11.6286	0.717050	0.358525	−	0.933520i	$-0.383280\pi$
$263$	11.6286	0.717050	0.358525	+	0.933520i	$0.383280\pi$
$264$	−8.02478	−0.493891
$265$	−9.61892	−0.590886
$266$	−13.8827	−0.851202
$267$	9.24557	0.565820
$268$	0.604898	0.0369500
$269$	2.49992	0.152423	0.0762114	−	0.997092i	$-0.475718\pi$
$269$	2.49992	0.152423	0.0762114	+	0.997092i	$0.475718\pi$
$270$	−1.42963	−0.0870044
$271$	−24.5200	−1.48949	−0.744743	−	0.667351i	$-0.767428\pi$
$271$	−24.5200	−1.48949	−0.744743	+	0.667351i	$0.767428\pi$
$272$	25.9626	1.57421
$273$	4.47441	0.270804
$274$	−14.8710	−0.898387
$275$	−2.86949	−0.173037
$276$	−0.0536890	−0.00323170
$277$	−32.3790	−1.94547	−0.972734	−	0.231925i	$-0.925497\pi$
$277$	−32.3790	−1.94547	−0.972734	+	0.231925i	$0.925497\pi$
$278$	12.9796	0.778463
$279$	1.00000	0.0598684
$280$	12.5131	0.747799
$281$	2.24157	0.133721	0.0668604	−	0.997762i	$-0.478702\pi$
$281$	2.24157	0.133721	0.0668604	+	0.997762i	$0.478702\pi$
$282$	6.48725	0.386310
$283$	−31.3068	−1.86100	−0.930499	−	0.366295i	$-0.880626\pi$
$283$	−31.3068	−1.86100	−0.930499	+	0.366295i	$0.880626\pi$
$284$	0.309141	0.0183442
$285$	−2.17027	−0.128556
$286$	−4.10231	−0.242575
$287$	37.5771	2.21810
$288$	−0.247937	−0.0146098
$289$	23.3786	1.37521
$290$	−4.89751	−0.287592
$291$	−17.8425	−1.04595
$292$	0.483852	0.0283153
$293$	−33.1790	−1.93834	−0.969168	−	0.246402i	$-0.920752\pi$
$293$	−33.1790	−1.93834	−0.969168	+	0.246402i	$0.920752\pi$
$294$	−18.6143	−1.08561
$295$	−6.33107	−0.368609
$296$	3.52431	0.204847
$297$	2.86949	0.166505
$298$	−9.10814	−0.527620
$299$	1.22473	0.0708280
$300$	−0.0438374	−0.00253095
$301$	−28.6361	−1.65056
$302$	3.56076	0.204899
$303$	9.77269	0.561427
$304$	−8.86720	−0.508569
$305$	1.51919	0.0869887
$306$	−9.08446	−0.519324
$307$	−3.40426	−0.194291	−0.0971457	−	0.995270i	$-0.530971\pi$
$307$	−3.40426	−0.194291	−0.0971457	+	0.995270i	$0.530971\pi$
$308$	0.562841	0.0320708
$309$	1.18727	0.0675414
$310$	1.42963	0.0811974
$311$	−19.1888	−1.08810	−0.544048	−	0.839054i	$-0.683109\pi$
$311$	−19.1888	−1.08810	−0.544048	+	0.839054i	$0.683109\pi$
$312$	2.79659	0.158325
$313$	20.4573	1.15632	0.578158	−	0.815925i	$-0.303772\pi$
$313$	20.4573	1.15632	0.578158	+	0.815925i	$0.303772\pi$
$314$	25.9603	1.46503
$315$	−4.47441	−0.252105
$316$	−0.406212	−0.0228512
$317$	12.9611	0.727968	0.363984	−	0.931405i	$-0.381416\pi$
$317$	12.9611	0.727968	0.363984	+	0.931405i	$0.381416\pi$
$318$	13.7515	0.771145
$319$	9.83009	0.550379
$320$	7.81705	0.436986
$321$	4.53205	0.252954
$322$	−7.83429	−0.436588
$323$	−13.7908	−0.767342
$324$	0.0438374	0.00243541
$325$	1.00000	0.0554700
$326$	−3.06551	−0.169783
$327$	3.16623	0.175093
$328$	23.4863	1.29682
$329$	20.3036	1.11937
$330$	4.10231	0.225825
$331$	−6.79424	−0.373445	−0.186723	−	0.982413i	$-0.559787\pi$
$331$	−6.79424	−0.373445	−0.186723	+	0.982413i	$0.559787\pi$
$332$	0.684135	0.0375468
$333$	−1.26022	−0.0690597
$334$	−3.57931	−0.195851
$335$	13.7987	0.753903
$336$	−18.2813	−0.997329
$337$	32.0169	1.74407	0.872036	−	0.489442i	$-0.162799\pi$
$337$	32.0169	1.74407	0.872036	+	0.489442i	$0.162799\pi$
$338$	1.42963	0.0777615
$339$	−1.99869	−0.108554
$340$	−0.278561	−0.0151071
$341$	−2.86949	−0.155392
$342$	3.10268	0.167774
$343$	−26.9376	−1.45449
$344$	−17.8981	−0.965000
$345$	−1.22473	−0.0659373
$346$	27.8897	1.49936
$347$	30.1269	1.61730	0.808648	−	0.588293i	$-0.200200\pi$
$347$	30.1269	1.61730	0.808648	+	0.588293i	$0.200200\pi$
$348$	0.150175	0.00805021
$349$	14.2671	0.763703	0.381852	−	0.924224i	$-0.375287\pi$
$349$	14.2671	0.763703	0.381852	+	0.924224i	$0.375287\pi$
$350$	−6.39675	−0.341920
$351$	−1.00000	−0.0533761
$352$	0.711454	0.0379206
$353$	16.9210	0.900614	0.450307	−	0.892874i	$-0.351315\pi$
$353$	16.9210	0.900614	0.450307	+	0.892874i	$0.351315\pi$
$354$	9.05108	0.481059
$355$	7.05201	0.374282
$356$	−0.405302	−0.0214809
$357$	−28.4323	−1.50480
$358$	24.8413	1.31290
$359$	5.63749	0.297535	0.148768	−	0.988872i	$-0.452469\pi$
$359$	5.63749	0.297535	0.148768	+	0.988872i	$0.452469\pi$
$360$	−2.79659	−0.147393
$361$	−14.2899	−0.752101
$362$	20.1702	1.06012
$363$	2.76601	0.145178
$364$	−0.196146	−0.0102809
$365$	11.0374	0.577726
$366$	−2.17188	−0.113526
$367$	−2.66057	−0.138880	−0.0694402	−	0.997586i	$-0.522121\pi$
$367$	−2.66057	−0.138880	−0.0694402	+	0.997586i	$0.522121\pi$
$368$	−5.00395	−0.260849
$369$	−8.39821	−0.437193
$370$	−1.80165	−0.0936632
$371$	43.0390	2.23447
$372$	−0.0438374	−0.00227286
$373$	−19.4992	−1.00963	−0.504816	−	0.863227i	$-0.668440\pi$
$373$	−19.4992	−1.00963	−0.504816	+	0.863227i	$0.668440\pi$
$374$	26.0678	1.34793
$375$	−1.00000	−0.0516398
$376$	12.6901	0.654443
$377$	−3.42572	−0.176434
$378$	6.39675	0.329013
$379$	22.0893	1.13465	0.567327	−	0.823493i	$-0.307978\pi$
$379$	22.0893	1.13465	0.567327	+	0.823493i	$0.307978\pi$
$380$	0.0951390	0.00488053
$381$	−12.0482	−0.617248
$382$	−0.962058	−0.0492232
$383$	−23.5864	−1.20521	−0.602603	−	0.798041i	$-0.705870\pi$
$383$	−23.5864	−1.20521	−0.602603	+	0.798041i	$0.705870\pi$
$384$	−11.6713	−0.595601
$385$	12.8393	0.654351
$386$	15.9585	0.812265
$387$	6.39998	0.325329
$388$	0.782169	0.0397086
$389$	9.84561	0.499192	0.249596	−	0.968350i	$-0.419702\pi$
$389$	9.84561	0.499192	0.249596	+	0.968350i	$0.419702\pi$
$390$	−1.42963	−0.0723920
$391$	−7.78245	−0.393576
$392$	−36.4126	−1.83911
$393$	−12.8368	−0.647533
$394$	−23.9764	−1.20792
$395$	−9.26634	−0.466240
$396$	−0.125791	−0.00632124
$397$	20.2353	1.01558	0.507791	−	0.861480i	$-0.330462\pi$
$397$	20.2353	1.01558	0.507791	+	0.861480i	$0.330462\pi$
$398$	1.84819	0.0926414
$399$	9.71069	0.486143
$400$	−4.08575	−0.204288
$401$	23.5324	1.17515	0.587575	−	0.809170i	$-0.300083\pi$
$401$	23.5324	1.17515	0.587575	+	0.809170i	$0.300083\pi$
$402$	−19.7270	−0.983893
$403$	1.00000	0.0498135
$404$	−0.428409	−0.0213142
$405$	1.00000	0.0496904
$406$	21.9135	1.08755
$407$	3.61619	0.179248
$408$	−17.7707	−0.879780
$409$	0.0984305	0.00486707	0.00243354	−	0.999997i	$-0.499225\pi$
$409$	0.0984305	0.00486707	0.00243354	+	0.999997i	$0.499225\pi$
$410$	−12.0063	−0.592950
$411$	10.4020	0.513092
$412$	−0.0520467	−0.00256416
$413$	28.3278	1.39392
$414$	1.75091	0.0860525
$415$	15.6062	0.766078
$416$	−0.247937	−0.0121561
$417$	−9.07898	−0.444599
$418$	−8.90313	−0.435466
$419$	3.69507	0.180516	0.0902580	−	0.995918i	$-0.471231\pi$
$419$	3.69507	0.180516	0.0902580	+	0.995918i	$0.471231\pi$
$420$	0.196146	0.00957097
$421$	−29.0769	−1.41712	−0.708561	−	0.705649i	$-0.750655\pi$
$421$	−29.0769	−1.41712	−0.708561	+	0.705649i	$0.750655\pi$
$422$	−21.8924	−1.06570
$423$	−4.53772	−0.220631
$424$	26.9001	1.30639
$425$	−6.35442	−0.308235
$426$	−10.0817	−0.488462
$427$	−6.79750	−0.328954
$428$	−0.198673	−0.00960323
$429$	2.86949	0.138540
$430$	9.14959	0.441232
$431$	5.34712	0.257562	0.128781	−	0.991673i	$-0.458894\pi$
$431$	5.34712	0.257562	0.128781	+	0.991673i	$0.458894\pi$
$432$	4.08575	0.196576
$433$	−19.1267	−0.919171	−0.459585	−	0.888134i	$-0.652002\pi$
$433$	−19.1267	−0.919171	−0.459585	+	0.888134i	$0.652002\pi$
$434$	−6.39675	−0.307054
$435$	3.42572	0.164251
$436$	−0.138799	−0.00664728
$437$	2.65800	0.127149
$438$	−15.7794	−0.753971
$439$	22.6415	1.08062	0.540309	−	0.841466i	$-0.318307\pi$
$439$	22.6415	1.08062	0.540309	+	0.841466i	$0.318307\pi$
$440$	8.02478	0.382567
$441$	13.0204	0.620017
$442$	−9.08446	−0.432104
$443$	40.0442	1.90256	0.951279	−	0.308332i	$-0.0997707\pi$
$443$	40.0442	1.90256	0.951279	+	0.308332i	$0.0997707\pi$
$444$	0.0552448	0.00262180
$445$	−9.24557	−0.438282
$446$	23.6036	1.11766
$447$	6.37098	0.301337
$448$	−34.9767	−1.65249
$449$	−8.19922	−0.386945	−0.193473	−	0.981106i	$-0.561975\pi$
$449$	−8.19922	−0.386945	−0.193473	+	0.981106i	$0.561975\pi$
$450$	1.42963	0.0673933
$451$	24.0986	1.13476
$452$	0.0876173	0.00412117
$453$	−2.49069	−0.117023
$454$	20.9158	0.981629
$455$	−4.47441	−0.209764
$456$	6.06935	0.284224
$457$	7.05261	0.329907	0.164954	−	0.986301i	$-0.447253\pi$
$457$	7.05261	0.329907	0.164954	+	0.986301i	$0.447253\pi$
$458$	−23.1175	−1.08021
$459$	6.35442	0.296599
$460$	0.0536890	0.00250326
$461$	−25.3718	−1.18168	−0.590842	−	0.806787i	$-0.701204\pi$
$461$	−25.3718	−1.18168	−0.590842	+	0.806787i	$0.701204\pi$
$462$	−18.3554	−0.853971
$463$	10.6373	0.494356	0.247178	−	0.968970i	$-0.420497\pi$
$463$	10.6373	0.494356	0.247178	+	0.968970i	$0.420497\pi$
$464$	13.9967	0.649778
$465$	−1.00000	−0.0463739
$466$	24.0717	1.11510
$467$	−8.19953	−0.379429	−0.189714	−	0.981839i	$-0.560756\pi$
$467$	−8.19953	−0.379429	−0.189714	+	0.981839i	$0.560756\pi$
$468$	0.0438374	0.00202638
$469$	−61.7410	−2.85094
$470$	−6.48725	−0.299235
$471$	−18.1588	−0.836713
$472$	17.7054	0.814956
$473$	−18.3647	−0.844409
$474$	13.2474	0.608474
$475$	2.17027	0.0995789
$476$	1.24640	0.0571285
$477$	−9.61892	−0.440420
$478$	1.46314	0.0669223
$479$	20.8450	0.952433	0.476216	−	0.879328i	$-0.342008\pi$
$479$	20.8450	0.952433	0.476216	+	0.879328i	$0.342008\pi$
$480$	0.247937	0.0113167
$481$	−1.26022	−0.0574611
$482$	−30.6415	−1.39568
$483$	5.47995	0.249346
$484$	−0.121255	−0.00551157
$485$	17.8425	0.810186
$486$	−1.42963	−0.0648493
$487$	26.4623	1.19912	0.599561	−	0.800329i	$-0.295342\pi$
$487$	26.4623	1.19912	0.599561	+	0.800329i	$0.295342\pi$
$488$	−4.24855	−0.192323
$489$	2.14427	0.0969674
$490$	18.6143	0.840908
$491$	−28.2812	−1.27631	−0.638156	−	0.769907i	$-0.720303\pi$
$491$	−28.2812	−1.27631	−0.638156	+	0.769907i	$0.720303\pi$
$492$	0.368156	0.0165977
$493$	21.7685	0.980403
$494$	3.10268	0.139596
$495$	−2.86949	−0.128974
$496$	−4.08575	−0.183456
$497$	−31.5536	−1.41537
$498$	−22.3111	−0.999783
$499$	−30.8430	−1.38072	−0.690360	−	0.723466i	$-0.742548\pi$
$499$	−30.8430	−1.38072	−0.690360	+	0.723466i	$0.742548\pi$
$500$	0.0438374	0.00196047
$501$	2.50366	0.111855
$502$	−30.4401	−1.35861
$503$	8.18657	0.365021	0.182511	−	0.983204i	$-0.441578\pi$
$503$	8.18657	0.365021	0.182511	+	0.983204i	$0.441578\pi$
$504$	12.5131	0.557377
$505$	−9.77269	−0.434879
$506$	−5.02422	−0.223354
$507$	−1.00000	−0.0444116
$508$	0.528161	0.0234334
$509$	29.7467	1.31850	0.659250	−	0.751924i	$-0.270874\pi$
$509$	29.7467	1.31850	0.659250	+	0.751924i	$0.270874\pi$
$510$	9.08446	0.402267
$511$	−49.3861	−2.18471
$512$	−21.8393	−0.965170
$513$	−2.17027	−0.0958199
$514$	0.124203	0.00547834
$515$	−1.18727	−0.0523173
$516$	−0.280558	−0.0123509
$517$	13.0210	0.572661
$518$	8.06131	0.354194
$519$	−19.5084	−0.856323
$520$	−2.79659	−0.122638
$521$	−5.45918	−0.239171	−0.119586	−	0.992824i	$-0.538157\pi$
$521$	−5.45918	−0.239171	−0.119586	+	0.992824i	$0.538157\pi$
$522$	−4.89751	−0.214358
$523$	−8.19069	−0.358154	−0.179077	−	0.983835i	$-0.557311\pi$
$523$	−8.19069	−0.358154	−0.179077	+	0.983835i	$0.557311\pi$
$524$	0.562733	0.0245831
$525$	4.47441	0.195279
$526$	16.6246	0.724866
$527$	−6.35442	−0.276803
$528$	−11.7240	−0.510223
$529$	−21.5000	−0.934784
$530$	−13.7515	−0.597326
$531$	−6.33107	−0.274745
$532$	−0.425691	−0.0184561
$533$	−8.39821	−0.363767
$534$	13.2177	0.571987
$535$	−4.53205	−0.195938
$536$	−38.5892	−1.66680
$537$	−17.3760	−0.749831
$538$	3.57396	0.154084
$539$	−37.3618	−1.60929
$540$	−0.0438374	−0.00188646
$541$	8.91629	0.383341	0.191671	−	0.981459i	$-0.438609\pi$
$541$	8.91629	0.383341	0.191671	+	0.981459i	$0.438609\pi$
$542$	−35.0545	−1.50572
$543$	−14.1087	−0.605462
$544$	1.57550	0.0675489
$545$	−3.16623	−0.135626
$546$	6.39675	0.273755
$547$	18.1506	0.776066	0.388033	−	0.921646i	$-0.373155\pi$
$547$	18.1506	0.776066	0.388033	+	0.921646i	$0.373155\pi$
$548$	−0.455995	−0.0194791
$549$	1.51919	0.0648376
$550$	−4.10231	−0.174923
$551$	−7.43475	−0.316731
$552$	3.42506	0.145780
$553$	41.4614	1.76312
$554$	−46.2900	−1.96667
$555$	1.26022	0.0534934
$556$	0.397999	0.0168789
$557$	−18.8315	−0.797916	−0.398958	−	0.916969i	$-0.630628\pi$
$557$	−18.8315	−0.797916	−0.398958	+	0.916969i	$0.630628\pi$
$558$	1.42963	0.0605210
$559$	6.39998	0.270690
$560$	18.2813	0.772528
$561$	−18.2340	−0.769838
$562$	3.20461	0.135178
$563$	−30.7279	−1.29503	−0.647514	−	0.762053i	$-0.724191\pi$
$563$	−30.7279	−1.29503	−0.647514	+	0.762053i	$0.724191\pi$
$564$	0.198922	0.00837611
$565$	1.99869	0.0840856
$566$	−44.7571	−1.88128
$567$	−4.47441	−0.187908
$568$	−19.7215	−0.827497
$569$	21.3290	0.894160	0.447080	−	0.894494i	$-0.352464\pi$
$569$	21.3290	0.894160	0.447080	+	0.894494i	$0.352464\pi$
$570$	−3.10268	−0.129957
$571$	40.2346	1.68376	0.841882	−	0.539661i	$-0.181448\pi$
$571$	40.2346	1.68376	0.841882	+	0.539661i	$0.181448\pi$
$572$	−0.125791	−0.00525959
$573$	0.672943	0.0281126
$574$	53.7212	2.24228
$575$	1.22473	0.0510748
$576$	7.81705	0.325710
$577$	5.41816	0.225561	0.112781	−	0.993620i	$-0.464024\pi$
$577$	5.41816	0.225561	0.112781	+	0.993620i	$0.464024\pi$
$578$	33.4228	1.39020
$579$	−11.1627	−0.463905
$580$	−0.150175	−0.00623566
$581$	−69.8286	−2.89698
$582$	−25.5082	−1.05735
$583$	27.6014	1.14313
$584$	−30.8671	−1.27729
$585$	1.00000	0.0413449
$586$	−47.4336	−1.95946
$587$	29.0990	1.20104	0.600521	−	0.799609i	$-0.294960\pi$
$587$	29.0990	1.20104	0.600521	+	0.799609i	$0.294960\pi$
$588$	−0.570779	−0.0235385
$589$	2.17027	0.0894245
$590$	−9.05108	−0.372627
$591$	16.7711	0.689871
$592$	5.14895	0.211621
$593$	−6.09138	−0.250143	−0.125072	−	0.992148i	$-0.539916\pi$
$593$	−6.09138	−0.250143	−0.125072	+	0.992148i	$0.539916\pi$
$594$	4.10231	0.168320
$595$	28.4323	1.16561
$596$	−0.279287	−0.0114400
$597$	−1.29278	−0.0529098
$598$	1.75091	0.0716000
$599$	29.5761	1.20845	0.604223	−	0.796816i	$-0.293484\pi$
$599$	29.5761	1.20845	0.604223	+	0.796816i	$0.293484\pi$
$600$	2.79659	0.114170
$601$	−24.5755	−1.00246	−0.501228	−	0.865315i	$-0.667118\pi$
$601$	−24.5755	−1.00246	−0.501228	+	0.865315i	$0.667118\pi$
$602$	−40.9390	−1.66855
$603$	13.7987	0.561926
$604$	0.109185	0.00444268
$605$	−2.76601	−0.112454
$606$	13.9713	0.567546
$607$	−11.1444	−0.452338	−0.226169	−	0.974088i	$-0.572620\pi$
$607$	−11.1444	−0.452338	−0.226169	+	0.974088i	$0.572620\pi$
$608$	−0.538091	−0.0218225
$609$	−15.3281	−0.621126
$610$	2.17188	0.0879369
$611$	−4.53772	−0.183576
$612$	−0.278561	−0.0112602
$613$	1.41311	0.0570748	0.0285374	−	0.999593i	$-0.490915\pi$
$613$	1.41311	0.0570748	0.0285374	+	0.999593i	$0.490915\pi$
$614$	−4.86683	−0.196409
$615$	8.39821	0.338649
$616$	−35.9062	−1.44670
$617$	−40.9484	−1.64852	−0.824261	−	0.566211i	$-0.808409\pi$
$617$	−40.9484	−1.64852	−0.824261	+	0.566211i	$0.808409\pi$
$618$	1.69735	0.0682776
$619$	21.2520	0.854190	0.427095	−	0.904207i	$-0.359537\pi$
$619$	21.2520	0.854190	0.427095	+	0.904207i	$0.359537\pi$
$620$	0.0438374	0.00176055
$621$	−1.22473	−0.0491468
$622$	−27.4328	−1.09996
$623$	41.3685	1.65739
$624$	4.08575	0.163561
$625$	1.00000	0.0400000
$626$	29.2463	1.16892
$627$	6.22758	0.248706
$628$	0.796034	0.0317652
$629$	8.00797	0.319299
$630$	−6.39675	−0.254852
$631$	0.769178	0.0306205	0.0153102	−	0.999883i	$-0.495126\pi$
$631$	0.769178	0.0306205	0.0153102	+	0.999883i	$0.495126\pi$
$632$	25.9141	1.03081
$633$	15.3133	0.608650
$634$	18.5296	0.735903
$635$	12.0482	0.478118
$636$	0.421668	0.0167202
$637$	13.0204	0.515886
$638$	14.0534	0.556378
$639$	7.05201	0.278973
$640$	11.6713	0.461351
$641$	−11.3508	−0.448328	−0.224164	−	0.974551i	$-0.571965\pi$
$641$	−11.3508	−0.448328	−0.224164	+	0.974551i	$0.571965\pi$
$642$	6.47915	0.255712
$643$	13.3069	0.524772	0.262386	−	0.964963i	$-0.415491\pi$
$643$	13.3069	0.524772	0.262386	+	0.964963i	$0.415491\pi$
$644$	−0.240227	−0.00946625
$645$	−6.39998	−0.251999
$646$	−19.7158	−0.775706
$647$	−28.5035	−1.12059	−0.560295	−	0.828293i	$-0.689312\pi$
$647$	−28.5035	−1.12059	−0.560295	+	0.828293i	$0.689312\pi$
$648$	−2.79659	−0.109860
$649$	18.1670	0.713116
$650$	1.42963	0.0560746
$651$	4.47441	0.175366
$652$	−0.0939993	−0.00368130
$653$	5.82199	0.227832	0.113916	−	0.993490i	$-0.463661\pi$
$653$	5.82199	0.227832	0.113916	+	0.993490i	$0.463661\pi$
$654$	4.52653	0.177001
$655$	12.8368	0.501577
$656$	34.3130	1.33970
$657$	11.0374	0.430612
$658$	29.0266	1.13158
$659$	−24.2352	−0.944068	−0.472034	−	0.881580i	$-0.656480\pi$
$659$	−24.2352	−0.944068	−0.472034	+	0.881580i	$0.656480\pi$
$660$	0.125791	0.00489641
$661$	−10.8467	−0.421888	−0.210944	−	0.977498i	$-0.567654\pi$
$661$	−10.8467	−0.421888	−0.210944	+	0.977498i	$0.567654\pi$
$662$	−9.71324	−0.377516
$663$	6.35442	0.246785
$664$	−43.6441	−1.69372
$665$	−9.71069	−0.376565
$666$	−1.80165	−0.0698124
$667$	−4.19559	−0.162454
$668$	−0.109754	−0.00424651
$669$	−16.5103	−0.638325
$670$	19.7270	0.762120
$671$	−4.35931	−0.168289
$672$	−1.10937	−0.0427950
$673$	−26.1167	−1.00672	−0.503362	−	0.864076i	$-0.667904\pi$
$673$	−26.1167	−1.00672	−0.503362	+	0.864076i	$0.667904\pi$
$674$	45.7723	1.76308
$675$	−1.00000	−0.0384900
$676$	0.0438374	0.00168605
$677$	−3.93495	−0.151232	−0.0756161	−	0.997137i	$-0.524092\pi$
$677$	−3.93495	−0.151232	−0.0756161	+	0.997137i	$0.524092\pi$
$678$	−2.85739	−0.109737
$679$	−79.8347	−3.06378
$680$	17.7707	0.681474
$681$	−14.6303	−0.560633
$682$	−4.10231	−0.157086
$683$	8.94105	0.342120	0.171060	−	0.985261i	$-0.445281\pi$
$683$	8.94105	0.342120	0.171060	+	0.985261i	$0.445281\pi$
$684$	0.0951390	0.00363773
$685$	−10.4020	−0.397439
$686$	−38.5107	−1.47035
$687$	16.1703	0.616934
$688$	−26.1487	−0.996911
$689$	−9.61892	−0.366452
$690$	−1.75091	−0.0666560
$691$	21.1885	0.806048	0.403024	−	0.915189i	$-0.367959\pi$
$691$	21.1885	0.806048	0.403024	+	0.915189i	$0.367959\pi$
$692$	0.855196	0.0325097
$693$	12.8393	0.487724
$694$	43.0703	1.63492
$695$	9.07898	0.344385
$696$	−9.58033	−0.363141
$697$	53.3658	2.02137
$698$	20.3967	0.772027
$699$	−16.8377	−0.636860
$700$	−0.196146	−0.00741364
$701$	16.9080	0.638607	0.319303	−	0.947653i	$-0.396551\pi$
$701$	16.9080	0.638607	0.319303	+	0.947653i	$0.396551\pi$
$702$	−1.42963	−0.0539578
$703$	−2.73502	−0.103153
$704$	−22.4310	−0.845399
$705$	4.53772	0.170900
$706$	24.1907	0.910431
$707$	43.7271	1.64453
$708$	0.277537	0.0104305
$709$	35.8118	1.34494	0.672470	−	0.740125i	$-0.265233\pi$
$709$	35.8118	1.34494	0.672470	+	0.740125i	$0.265233\pi$
$710$	10.0817	0.378361
$711$	−9.26634	−0.347515
$712$	25.8560	0.968996
$713$	1.22473	0.0458665
$714$	−40.6476	−1.52120
$715$	−2.86949	−0.107313
$716$	0.761719	0.0284668
$717$	−1.02344	−0.0382210
$718$	8.05951	0.300778
$719$	50.8109	1.89493	0.947464	−	0.319862i	$-0.103637\pi$
$719$	50.8109	1.89493	0.947464	+	0.319862i	$0.103637\pi$
$720$	−4.08575	−0.152267
$721$	5.31233	0.197841
$722$	−20.4293	−0.760299
$723$	21.4332	0.797109
$724$	0.618488	0.0229859
$725$	−3.42572	−0.127228
$726$	3.95437	0.146760
$727$	11.1760	0.414496	0.207248	−	0.978288i	$-0.433549\pi$
$727$	11.1760	0.414496	0.207248	+	0.978288i	$0.433549\pi$
$728$	12.5131	0.463765
$729$	1.00000	0.0370370
$730$	15.7794	0.584023
$731$	−40.6681	−1.50417
$732$	−0.0665974	−0.00246151
$733$	−34.4498	−1.27243	−0.636217	−	0.771510i	$-0.719502\pi$
$733$	−34.4498	−1.27243	−0.636217	+	0.771510i	$0.719502\pi$
$734$	−3.80362	−0.140394
$735$	−13.0204	−0.480263
$736$	−0.303656	−0.0111929
$737$	−39.5952	−1.45851
$738$	−12.0063	−0.441959
$739$	12.8309	0.471994	0.235997	−	0.971754i	$-0.424164\pi$
$739$	12.8309	0.471994	0.235997	+	0.971754i	$0.424164\pi$
$740$	−0.0552448	−0.00203084
$741$	−2.17027	−0.0797270
$742$	61.5298	2.25883
$743$	−46.6391	−1.71102	−0.855512	−	0.517783i	$-0.826757\pi$
$743$	−46.6391	−1.71102	−0.855512	+	0.517783i	$0.826757\pi$
$744$	2.79659	0.102528
$745$	−6.37098	−0.233415
$746$	−27.8767	−1.02064
$747$	15.6062	0.571001
$748$	0.799329	0.0292264
$749$	20.2783	0.740952
$750$	−1.42963	−0.0522026
$751$	−44.3609	−1.61875	−0.809376	−	0.587291i	$-0.800194\pi$
$751$	−44.3609	−1.61875	−0.809376	+	0.587291i	$0.800194\pi$
$752$	18.5400	0.676084
$753$	21.2923	0.775935
$754$	−4.89751	−0.178357
$755$	2.49069	0.0906454
$756$	0.196146	0.00713378
$757$	−25.2583	−0.918028	−0.459014	−	0.888429i	$-0.651797\pi$
$757$	−25.2583	−0.918028	−0.459014	+	0.888429i	$0.651797\pi$
$758$	31.5795	1.14702
$759$	3.51436	0.127563
$760$	−6.06935	−0.220159
$761$	28.2240	1.02312	0.511560	−	0.859247i	$-0.329068\pi$
$761$	28.2240	1.02312	0.511560	+	0.859247i	$0.329068\pi$
$762$	−17.2244	−0.623976
$763$	14.1670	0.512881
$764$	−0.0295000	−0.00106727
$765$	−6.35442	−0.229745
$766$	−33.7197	−1.21834
$767$	−6.33107	−0.228602
$768$	−1.05160	−0.0379462
$769$	−14.7443	−0.531692	−0.265846	−	0.964016i	$-0.585651\pi$
$769$	−14.7443	−0.531692	−0.265846	+	0.964016i	$0.585651\pi$
$770$	18.3554	0.661483
$771$	−0.0868775	−0.00312882
$772$	0.489342	0.0176118
$773$	−37.3466	−1.34326	−0.671632	−	0.740885i	$-0.734407\pi$
$773$	−37.3466	−1.34326	−0.671632	+	0.740885i	$0.734407\pi$
$774$	9.14959	0.328875
$775$	1.00000	0.0359211
$776$	−49.8981	−1.79124
$777$	−5.63875	−0.202289
$778$	14.0756	0.504633
$779$	−18.2264	−0.653029
$780$	−0.0438374	−0.00156963
$781$	−20.2357	−0.724090
$782$	−11.1260	−0.397865
$783$	3.42572	0.122425
$784$	−53.1980	−1.89993
$785$	18.1588	0.648115
$786$	−18.3519	−0.654591
$787$	46.1830	1.64625	0.823123	−	0.567863i	$-0.192230\pi$
$787$	46.1830	1.64625	0.823123	+	0.567863i	$0.192230\pi$
$788$	−0.735201	−0.0261904
$789$	−11.6286	−0.413989
$790$	−13.2474	−0.471322
$791$	−8.94297	−0.317975
$792$	8.02478	0.285148
$793$	1.51919	0.0539481
$794$	28.9290	1.02665
$795$	9.61892	0.341148
$796$	0.0566719	0.00200868
$797$	−49.0737	−1.73828	−0.869139	−	0.494567i	$-0.835327\pi$
$797$	−49.0737	−1.73828	−0.869139	+	0.494567i	$0.835327\pi$
$798$	13.8827	0.491442
$799$	28.8346	1.02009
$800$	−0.247937	−0.00876591
$801$	−9.24557	−0.326676
$802$	33.6425	1.18796
$803$	−31.6719	−1.11768
$804$	−0.604898	−0.0213331
$805$	−5.47995	−0.193143
$806$	1.42963	0.0503565
$807$	−2.49992	−0.0880014
$808$	27.3302	0.961472
$809$	−27.4385	−0.964686	−0.482343	−	0.875982i	$-0.660214\pi$
$809$	−27.4385	−0.964686	−0.482343	+	0.875982i	$0.660214\pi$
$810$	1.42963	0.0502320
$811$	2.50285	0.0878868	0.0439434	−	0.999034i	$-0.486008\pi$
$811$	2.50285	0.0878868	0.0439434	+	0.999034i	$0.486008\pi$
$812$	0.671943	0.0235806
$813$	24.5200	0.859955
$814$	5.16981	0.181202
$815$	−2.14427	−0.0751106
$816$	−25.9626	−0.908872
$817$	13.8897	0.485939
$818$	0.140719	0.00492013
$819$	−4.47441	−0.156349
$820$	−0.368156	−0.0128565
$821$	38.6751	1.34977	0.674886	−	0.737922i	$-0.264193\pi$
$821$	38.6751	1.34977	0.674886	+	0.737922i	$0.264193\pi$
$822$	14.8710	0.518684
$823$	21.7932	0.759663	0.379832	−	0.925056i	$-0.375982\pi$
$823$	21.7932	0.759663	0.379832	+	0.925056i	$0.375982\pi$
$824$	3.32030	0.115668
$825$	2.86949	0.0999029
$826$	40.4982	1.40911
$827$	2.81434	0.0978642	0.0489321	−	0.998802i	$-0.484418\pi$
$827$	2.81434	0.0978642	0.0489321	+	0.998802i	$0.484418\pi$
$828$	0.0536890	0.00186582
$829$	12.5417	0.435592	0.217796	−	0.975994i	$-0.430113\pi$
$829$	12.5417	0.435592	0.217796	+	0.975994i	$0.430113\pi$
$830$	22.3111	0.774428
$831$	32.3790	1.12322
$832$	7.81705	0.271007
$833$	−82.7369	−2.86666
$834$	−12.9796	−0.449446
$835$	−2.50366	−0.0866428
$836$	−0.273001	−0.00944193
$837$	−1.00000	−0.0345651
$838$	5.28258	0.182484
$839$	7.22990	0.249604	0.124802	−	0.992182i	$-0.460170\pi$
$839$	7.22990	0.249604	0.124802	+	0.992182i	$0.460170\pi$
$840$	−12.5131	−0.431742
$841$	−17.2644	−0.595325
$842$	−41.5692	−1.43257
$843$	−2.24157	−0.0772038
$844$	−0.671295	−0.0231069
$845$	1.00000	0.0344010
$846$	−6.48725	−0.223036
$847$	12.3763	0.425253
$848$	39.3005	1.34959
$849$	31.3068	1.07445
$850$	−9.08446	−0.311594
$851$	−1.54343	−0.0529081
$852$	−0.309141	−0.0105910
$853$	−54.6938	−1.87268	−0.936340	−	0.351093i	$-0.885810\pi$
$853$	−54.6938	−1.87268	−0.936340	+	0.351093i	$0.885810\pi$
$854$	−9.71789	−0.332539
$855$	2.17027	0.0742218
$856$	12.6743	0.433198
$857$	28.4315	0.971201	0.485601	−	0.874181i	$-0.338601\pi$
$857$	28.4315	0.971201	0.485601	+	0.874181i	$0.338601\pi$
$858$	4.10231	0.140051
$859$	38.3246	1.30762	0.653810	−	0.756659i	$-0.273170\pi$
$859$	38.3246	1.30762	0.653810	+	0.756659i	$0.273170\pi$
$860$	0.280558	0.00956695
$861$	−37.5771	−1.28062
$862$	7.64440	0.260369
$863$	50.7220	1.72660	0.863298	−	0.504694i	$-0.168395\pi$
$863$	50.7220	1.72660	0.863298	+	0.504694i	$0.168395\pi$
$864$	0.247937	0.00843500
$865$	19.5084	0.663305
$866$	−27.3441	−0.929190
$867$	−23.3786	−0.793980
$868$	−0.196146	−0.00665764
$869$	26.5897	0.901994
$870$	4.89751	0.166041
$871$	13.7987	0.467551
$872$	8.85464	0.299856
$873$	17.8425	0.603877
$874$	3.79995	0.128535
$875$	−4.47441	−0.151263
$876$	−0.483852	−0.0163479
$877$	19.7064	0.665438	0.332719	−	0.943026i	$-0.392034\pi$
$877$	19.7064	0.665438	0.332719	+	0.943026i	$0.392034\pi$
$878$	32.3689	1.09240
$879$	33.1790	1.11910
$880$	11.7240	0.395217
$881$	−42.1093	−1.41870	−0.709349	−	0.704857i	$-0.751011\pi$
$881$	−42.1093	−1.41870	−0.709349	+	0.704857i	$0.751011\pi$
$882$	18.6143	0.626775
$883$	8.01981	0.269888	0.134944	−	0.990853i	$-0.456915\pi$
$883$	8.01981	0.269888	0.134944	+	0.990853i	$0.456915\pi$
$884$	−0.278561	−0.00936902
$885$	6.33107	0.212817
$886$	57.2483	1.92330
$887$	−7.04175	−0.236439	−0.118219	−	0.992988i	$-0.537719\pi$
$887$	−7.04175	−0.236439	−0.118219	+	0.992988i	$0.537719\pi$
$888$	−3.52431	−0.118268
$889$	−53.9086	−1.80804
$890$	−13.2177	−0.443059
$891$	−2.86949	−0.0961316
$892$	0.723769	0.0242336
$893$	−9.84809	−0.329554
$894$	9.10814	0.304622
$895$	17.3760	0.580816
$896$	−52.2224	−1.74463
$897$	−1.22473	−0.0408926
$898$	−11.7218	−0.391163
$899$	−3.42572	−0.114254
$900$	0.0438374	0.00146125
$901$	61.1227	2.03629
$902$	34.4521	1.14713
$903$	28.6361	0.952951
$904$	−5.58951	−0.185904
$905$	14.1087	0.468989
$906$	−3.56076	−0.118298
$907$	−5.01811	−0.166624	−0.0833118	−	0.996524i	$-0.526550\pi$
$907$	−5.01811	−0.166624	−0.0833118	+	0.996524i	$0.526550\pi$
$908$	0.641352	0.0212840
$909$	−9.77269	−0.324140
$910$	−6.39675	−0.212050
$911$	16.3645	0.542180	0.271090	−	0.962554i	$-0.412616\pi$
$911$	16.3645	0.542180	0.271090	+	0.962554i	$0.412616\pi$
$912$	8.86720	0.293622
$913$	−44.7819	−1.48206
$914$	10.0826	0.333503
$915$	−1.51919	−0.0502230
$916$	−0.708861	−0.0234214
$917$	−57.4373	−1.89675
$918$	9.08446	0.299832
$919$	24.2024	0.798362	0.399181	−	0.916872i	$-0.369294\pi$
$919$	24.2024	0.798362	0.399181	+	0.916872i	$0.369294\pi$
$920$	−3.42506	−0.112921
$921$	3.40426	0.112174
$922$	−36.2723	−1.19456
$923$	7.05201	0.232120
$924$	−0.562841	−0.0185161
$925$	−1.26022	−0.0414358
$926$	15.2073	0.499744
$927$	−1.18727	−0.0389950
$928$	0.849364	0.0278817
$929$	−3.59466	−0.117937	−0.0589685	−	0.998260i	$-0.518781\pi$
$929$	−3.59466	−0.117937	−0.0589685	+	0.998260i	$0.518781\pi$
$930$	−1.42963	−0.0468794
$931$	28.2577	0.926110
$932$	0.738120	0.0241779
$933$	19.1888	0.628212
$934$	−11.7223	−0.383565
$935$	18.2340	0.596314
$936$	−2.79659	−0.0914093
$937$	48.1916	1.57435	0.787175	−	0.616730i	$-0.211543\pi$
$937$	48.1916	1.57435	0.787175	+	0.616730i	$0.211543\pi$
$938$	−88.2667	−2.88201
$939$	−20.4573	−0.667599
$940$	−0.198922	−0.00648811
$941$	9.75622	0.318044	0.159022	−	0.987275i	$-0.449166\pi$
$941$	9.75622	0.318044	0.159022	+	0.987275i	$0.449166\pi$
$942$	−25.9603	−0.845833
$943$	−10.2855	−0.334944
$944$	25.8672	0.841905
$945$	4.47441	0.145553
$946$	−26.2547	−0.853613
$947$	−0.0463227	−0.00150529	−0.000752643	−	1.00000i	$-0.500240\pi$
$947$	−0.0463227	−0.00150529	−0.000752643		1.00000i	$0.500240\pi$
$948$	0.406212	0.0131932
$949$	11.0374	0.358290
$950$	3.10268	0.100664
$951$	−12.9611	−0.420292
$952$	−79.5133	−2.57704
$953$	−29.3351	−0.950257	−0.475129	−	0.879916i	$-0.657598\pi$
$953$	−29.3351	−0.950257	−0.475129	+	0.879916i	$0.657598\pi$
$954$	−13.7515	−0.445221
$955$	−0.672943	−0.0217759
$956$	0.0448648	0.00145103
$957$	−9.83009	−0.317762
$958$	29.8006	0.962814
$959$	46.5427	1.50294
$960$	−7.81705	−0.252294
$961$	1.00000	0.0322581
$962$	−1.80165	−0.0580874
$963$	−4.53205	−0.146043
$964$	−0.939575	−0.0302617
$965$	11.1627	0.359339
$966$	7.83429	0.252064
$967$	0.665964	0.0214160	0.0107080	−	0.999943i	$-0.496591\pi$
$967$	0.665964	0.0214160	0.0107080	+	0.999943i	$0.496591\pi$
$968$	7.73538	0.248625
$969$	13.7908	0.443025
$970$	25.5082	0.819017
$971$	14.2368	0.456882	0.228441	−	0.973558i	$-0.426637\pi$
$971$	14.2368	0.456882	0.228441	+	0.973558i	$0.426637\pi$
$972$	−0.0438374	−0.00140608
$973$	−40.6231	−1.30232
$974$	37.8313	1.21219
$975$	−1.00000	−0.0320256
$976$	−6.20705	−0.198683
$977$	7.56467	0.242015	0.121008	−	0.992652i	$-0.461387\pi$
$977$	7.56467	0.242015	0.121008	+	0.992652i	$0.461387\pi$
$978$	3.06551	0.0980243
$979$	26.5301	0.847906
$980$	0.570779	0.0182329
$981$	−3.16623	−0.101090
$982$	−40.4316	−1.29022
$983$	21.2236	0.676929	0.338465	−	0.940979i	$-0.390092\pi$
$983$	21.2236	0.676929	0.338465	+	0.940979i	$0.390092\pi$
$984$	−23.4863	−0.748717
$985$	−16.7711	−0.534372
$986$	31.1208	0.991089
$987$	−20.3036	−0.646271
$988$	0.0951390	0.00302678
$989$	7.83825	0.249242
$990$	−4.10231	−0.130380
$991$	25.2831	0.803145	0.401572	−	0.915827i	$-0.368464\pi$
$991$	25.2831	0.803145	0.401572	+	0.915827i	$0.368464\pi$
$992$	−0.247937	−0.00787202
$993$	6.79424	0.215609
$994$	−45.1099	−1.43080
$995$	1.29278	0.0409838
$996$	−0.684135	−0.0216776
$997$	9.55424	0.302586	0.151293	−	0.988489i	$-0.451656\pi$
$997$	9.55424	0.302586	0.151293	+	0.988489i	$0.451656\pi$
$998$	−44.0940	−1.39577
$999$	1.26022	0.0398716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.13	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.13	✓	17	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+1.42963 q^{2} -1.00000 q^{3} +0.0438374 q^{4} +1.00000 q^{5} -1.42963 q^{6} -4.47441 q^{7} -2.79659 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.42963 q^{2} -1.00000 q^{3} +0.0438374 q^{4} +1.00000 q^{5} -1.42963 q^{6} -4.47441 q^{7} -2.79659 q^{8} +1.00000 q^{9} +1.42963 q^{10} -2.86949 q^{11} -0.0438374 q^{12} +1.00000 q^{13} -6.39675 q^{14} -1.00000 q^{15} -4.08575 q^{16} -6.35442 q^{17} +1.42963 q^{18} +2.17027 q^{19} +0.0438374 q^{20} +4.47441 q^{21} -4.10231 q^{22} +1.22473 q^{23} +2.79659 q^{24} +1.00000 q^{25} +1.42963 q^{26} -1.00000 q^{27} -0.196146 q^{28} -3.42572 q^{29} -1.42963 q^{30} +1.00000 q^{31} -0.247937 q^{32} +2.86949 q^{33} -9.08446 q^{34} -4.47441 q^{35} +0.0438374 q^{36} -1.26022 q^{37} +3.10268 q^{38} -1.00000 q^{39} -2.79659 q^{40} -8.39821 q^{41} +6.39675 q^{42} +6.39998 q^{43} -0.125791 q^{44} +1.00000 q^{45} +1.75091 q^{46} -4.53772 q^{47} +4.08575 q^{48} +13.0204 q^{49} +1.42963 q^{50} +6.35442 q^{51} +0.0438374 q^{52} -9.61892 q^{53} -1.42963 q^{54} -2.86949 q^{55} +12.5131 q^{56} -2.17027 q^{57} -4.89751 q^{58} -6.33107 q^{59} -0.0438374 q^{60} +1.51919 q^{61} +1.42963 q^{62} -4.47441 q^{63} +7.81705 q^{64} +1.00000 q^{65} +4.10231 q^{66} +13.7987 q^{67} -0.278561 q^{68} -1.22473 q^{69} -6.39675 q^{70} +7.05201 q^{71} -2.79659 q^{72} +11.0374 q^{73} -1.80165 q^{74} -1.00000 q^{75} +0.0951390 q^{76} +12.8393 q^{77} -1.42963 q^{78} -9.26634 q^{79} -4.08575 q^{80} +1.00000 q^{81} -12.0063 q^{82} +15.6062 q^{83} +0.196146 q^{84} -6.35442 q^{85} +9.14959 q^{86} +3.42572 q^{87} +8.02478 q^{88} -9.24557 q^{89} +1.42963 q^{90} -4.47441 q^{91} +0.0536890 q^{92} -1.00000 q^{93} -6.48725 q^{94} +2.17027 q^{95} +0.247937 q^{96} +17.8425 q^{97} +18.6143 q^{98} -2.86949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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