LMFDB - Embedded newform 6042.2.a.z.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 $ x^9 - 4x^8 - 11x^7 + 51x^6 + 25x^5 - 180x^4 + 29x^3 + 119x^2 - 8x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.37216$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.912007 q^{5} +1.00000 q^{6} +3.48340 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.912007 q^{5} +1.00000 q^{6} +3.48340 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.912007 q^{10} -0.480498 q^{11} -1.00000 q^{12} +5.22319 q^{13} -3.48340 q^{14} -0.912007 q^{15} +1.00000 q^{16} +6.25232 q^{17} -1.00000 q^{18} -1.00000 q^{19} +0.912007 q^{20} -3.48340 q^{21} +0.480498 q^{22} +7.18776 q^{23} +1.00000 q^{24} -4.16824 q^{25} -5.22319 q^{26} -1.00000 q^{27} +3.48340 q^{28} +2.36574 q^{29} +0.912007 q^{30} +2.59294 q^{31} -1.00000 q^{32} +0.480498 q^{33} -6.25232 q^{34} +3.17689 q^{35} +1.00000 q^{36} -3.99773 q^{37} +1.00000 q^{38} -5.22319 q^{39} -0.912007 q^{40} +5.30220 q^{41} +3.48340 q^{42} +5.88658 q^{43} -0.480498 q^{44} +0.912007 q^{45} -7.18776 q^{46} +1.45172 q^{47} -1.00000 q^{48} +5.13408 q^{49} +4.16824 q^{50} -6.25232 q^{51} +5.22319 q^{52} +1.00000 q^{53} +1.00000 q^{54} -0.438218 q^{55} -3.48340 q^{56} +1.00000 q^{57} -2.36574 q^{58} +12.9354 q^{59} -0.912007 q^{60} +11.8597 q^{61} -2.59294 q^{62} +3.48340 q^{63} +1.00000 q^{64} +4.76358 q^{65} -0.480498 q^{66} -10.5160 q^{67} +6.25232 q^{68} -7.18776 q^{69} -3.17689 q^{70} +12.3755 q^{71} -1.00000 q^{72} -10.7021 q^{73} +3.99773 q^{74} +4.16824 q^{75} -1.00000 q^{76} -1.67377 q^{77} +5.22319 q^{78} -15.0539 q^{79} +0.912007 q^{80} +1.00000 q^{81} -5.30220 q^{82} -7.68354 q^{83} -3.48340 q^{84} +5.70217 q^{85} -5.88658 q^{86} -2.36574 q^{87} +0.480498 q^{88} +4.29778 q^{89} -0.912007 q^{90} +18.1945 q^{91} +7.18776 q^{92} -2.59294 q^{93} -1.45172 q^{94} -0.912007 q^{95} +1.00000 q^{96} -12.8959 q^{97} -5.13408 q^{98} -0.480498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9} + q^{10} + 12 q^{11} - 9 q^{12} - q^{13} - 4 q^{14} + q^{15} + 9 q^{16} + 12 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} - 4 q^{21} - 12 q^{22} + 11 q^{23} + 9 q^{24} + 10 q^{25} + q^{26} - 9 q^{27} + 4 q^{28} + 7 q^{29} - q^{30} - 12 q^{31} - 9 q^{32} - 12 q^{33} - 12 q^{34} + 15 q^{35} + 9 q^{36} - 9 q^{37} + 9 q^{38} + q^{39} + q^{40} - 4 q^{41} + 4 q^{42} + 23 q^{43} + 12 q^{44} - q^{45} - 11 q^{46} + 35 q^{47} - 9 q^{48} + 3 q^{49} - 10 q^{50} - 12 q^{51} - q^{52} + 9 q^{53} + 9 q^{54} + 3 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} + 14 q^{59} + q^{60} + 14 q^{61} + 12 q^{62} + 4 q^{63} + 9 q^{64} + 13 q^{65} + 12 q^{66} - 10 q^{67} + 12 q^{68} - 11 q^{69} - 15 q^{70} + 4 q^{71} - 9 q^{72} - 5 q^{73} + 9 q^{74} - 10 q^{75} - 9 q^{76} + 17 q^{77} - q^{78} - 14 q^{79} - q^{80} + 9 q^{81} + 4 q^{82} + 37 q^{83} - 4 q^{84} - 31 q^{85} - 23 q^{86} - 7 q^{87} - 12 q^{88} - 20 q^{89} + q^{90} - 12 q^{91} + 11 q^{92} + 12 q^{93} - 35 q^{94} + q^{95} + 9 q^{96} - 2 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9 + q^10 + 12 * q^11 - 9 * q^12 - q^13 - 4 * q^14 + q^15 + 9 * q^16 + 12 * q^17 - 9 * q^18 - 9 * q^19 - q^20 - 4 * q^21 - 12 * q^22 + 11 * q^23 + 9 * q^24 + 10 * q^25 + q^26 - 9 * q^27 + 4 * q^28 + 7 * q^29 - q^30 - 12 * q^31 - 9 * q^32 - 12 * q^33 - 12 * q^34 + 15 * q^35 + 9 * q^36 - 9 * q^37 + 9 * q^38 + q^39 + q^40 - 4 * q^41 + 4 * q^42 + 23 * q^43 + 12 * q^44 - q^45 - 11 * q^46 + 35 * q^47 - 9 * q^48 + 3 * q^49 - 10 * q^50 - 12 * q^51 - q^52 + 9 * q^53 + 9 * q^54 + 3 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 + 14 * q^59 + q^60 + 14 * q^61 + 12 * q^62 + 4 * q^63 + 9 * q^64 + 13 * q^65 + 12 * q^66 - 10 * q^67 + 12 * q^68 - 11 * q^69 - 15 * q^70 + 4 * q^71 - 9 * q^72 - 5 * q^73 + 9 * q^74 - 10 * q^75 - 9 * q^76 + 17 * q^77 - q^78 - 14 * q^79 - q^80 + 9 * q^81 + 4 * q^82 + 37 * q^83 - 4 * q^84 - 31 * q^85 - 23 * q^86 - 7 * q^87 - 12 * q^88 - 20 * q^89 + q^90 - 12 * q^91 + 11 * q^92 + 12 * q^93 - 35 * q^94 + q^95 + 9 * q^96 - 2 * q^97 - 3 * q^98 + 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.912007	0.407862	0.203931	−	0.978985i	$-0.434628\pi$
$5$	0.912007	0.407862	0.203931	+	0.978985i	$0.434628\pi$
$6$	1.00000	0.408248
$7$	3.48340	1.31660	0.658301	−	0.752755i	$-0.271275\pi$
$7$	3.48340	1.31660	0.658301	+	0.752755i	$0.271275\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.912007	−0.288402
$11$	−0.480498	−0.144876	−0.0724378	−	0.997373i	$-0.523078\pi$
$11$	−0.480498	−0.144876	−0.0724378	+	0.997373i	$0.523078\pi$
$12$	−1.00000	−0.288675
$13$	5.22319	1.44865	0.724326	−	0.689458i	$-0.242151\pi$
$13$	5.22319	1.44865	0.724326	+	0.689458i	$0.242151\pi$
$14$	−3.48340	−0.930978
$15$	−0.912007	−0.235479
$16$	1.00000	0.250000
$17$	6.25232	1.51641	0.758206	−	0.652015i	$-0.226076\pi$
$17$	6.25232	1.51641	0.758206	+	0.652015i	$0.226076\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.912007	0.203931
$21$	−3.48340	−0.760140
$22$	0.480498	0.102442
$23$	7.18776	1.49875	0.749376	−	0.662145i	$-0.230354\pi$
$23$	7.18776	1.49875	0.749376	+	0.662145i	$0.230354\pi$
$24$	1.00000	0.204124
$25$	−4.16824	−0.833649
$26$	−5.22319	−1.02435
$27$	−1.00000	−0.192450
$28$	3.48340	0.658301
$29$	2.36574	0.439308	0.219654	−	0.975578i	$-0.429507\pi$
$29$	2.36574	0.439308	0.219654	+	0.975578i	$0.429507\pi$
$30$	0.912007	0.166509
$31$	2.59294	0.465706	0.232853	−	0.972512i	$-0.425194\pi$
$31$	2.59294	0.465706	0.232853	+	0.972512i	$0.425194\pi$
$32$	−1.00000	−0.176777
$33$	0.480498	0.0836439
$34$	−6.25232	−1.07226
$35$	3.17689	0.536992
$36$	1.00000	0.166667
$37$	−3.99773	−0.657222	−0.328611	−	0.944465i	$-0.606581\pi$
$37$	−3.99773	−0.657222	−0.328611	+	0.944465i	$0.606581\pi$
$38$	1.00000	0.162221
$39$	−5.22319	−0.836379
$40$	−0.912007	−0.144201
$41$	5.30220	0.828065	0.414032	−	0.910262i	$-0.364120\pi$
$41$	5.30220	0.828065	0.414032	+	0.910262i	$0.364120\pi$
$42$	3.48340	0.537500
$43$	5.88658	0.897695	0.448848	−	0.893608i	$-0.351835\pi$
$43$	5.88658	0.897695	0.448848	+	0.893608i	$0.351835\pi$
$44$	−0.480498	−0.0724378
$45$	0.912007	0.135954
$46$	−7.18776	−1.05978
$47$	1.45172	0.211756	0.105878	−	0.994379i	$-0.466235\pi$
$47$	1.45172	0.211756	0.105878	+	0.994379i	$0.466235\pi$
$48$	−1.00000	−0.144338
$49$	5.13408	0.733440
$50$	4.16824	0.589479
$51$	−6.25232	−0.875501
$52$	5.22319	0.724326
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−0.438218	−0.0590892
$56$	−3.48340	−0.465489
$57$	1.00000	0.132453
$58$	−2.36574	−0.310637
$59$	12.9354	1.68405	0.842024	−	0.539440i	$-0.181364\pi$
$59$	12.9354	1.68405	0.842024	+	0.539440i	$0.181364\pi$
$60$	−0.912007	−0.117740
$61$	11.8597	1.51848	0.759240	−	0.650810i	$-0.225571\pi$
$61$	11.8597	1.51848	0.759240	+	0.650810i	$0.225571\pi$
$62$	−2.59294	−0.329304
$63$	3.48340	0.438867
$64$	1.00000	0.125000
$65$	4.76358	0.590850
$66$	−0.480498	−0.0591452
$67$	−10.5160	−1.28474	−0.642369	−	0.766395i	$-0.722048\pi$
$67$	−10.5160	−1.28474	−0.642369	+	0.766395i	$0.722048\pi$
$68$	6.25232	0.758206
$69$	−7.18776	−0.865305
$70$	−3.17689	−0.379711
$71$	12.3755	1.46870	0.734352	−	0.678769i	$-0.237486\pi$
$71$	12.3755	1.46870	0.734352	+	0.678769i	$0.237486\pi$
$72$	−1.00000	−0.117851
$73$	−10.7021	−1.25258	−0.626291	−	0.779590i	$-0.715428\pi$
$73$	−10.7021	−1.25258	−0.626291	+	0.779590i	$0.715428\pi$
$74$	3.99773	0.464726
$75$	4.16824	0.481307
$76$	−1.00000	−0.114708
$77$	−1.67377	−0.190743
$78$	5.22319	0.591409
$79$	−15.0539	−1.69369	−0.846847	−	0.531837i	$-0.821502\pi$
$79$	−15.0539	−1.69369	−0.846847	+	0.531837i	$0.821502\pi$
$80$	0.912007	0.101966
$81$	1.00000	0.111111
$82$	−5.30220	−0.585530
$83$	−7.68354	−0.843378	−0.421689	−	0.906741i	$-0.638563\pi$
$83$	−7.68354	−0.843378	−0.421689	+	0.906741i	$0.638563\pi$
$84$	−3.48340	−0.380070
$85$	5.70217	0.618487
$86$	−5.88658	−0.634766
$87$	−2.36574	−0.253634
$88$	0.480498	0.0512212
$89$	4.29778	0.455564	0.227782	−	0.973712i	$-0.426853\pi$
$89$	4.29778	0.455564	0.227782	+	0.973712i	$0.426853\pi$
$90$	−0.912007	−0.0961340
$91$	18.1945	1.90730
$92$	7.18776	0.749376
$93$	−2.59294	−0.268875
$94$	−1.45172	−0.149734
$95$	−0.912007	−0.0935700
$96$	1.00000	0.102062
$97$	−12.8959	−1.30938	−0.654688	−	0.755900i	$-0.727200\pi$
$97$	−12.8959	−1.30938	−0.654688	+	0.755900i	$0.727200\pi$
$98$	−5.13408	−0.518620
$99$	−0.480498	−0.0482918
$100$	−4.16824	−0.416824
$101$	−8.44802	−0.840610	−0.420305	−	0.907383i	$-0.638077\pi$
$101$	−8.44802	−0.840610	−0.420305	+	0.907383i	$0.638077\pi$
$102$	6.25232	0.619072
$103$	−11.6808	−1.15094	−0.575471	−	0.817822i	$-0.695181\pi$
$103$	−11.6808	−1.15094	−0.575471	+	0.817822i	$0.695181\pi$
$104$	−5.22319	−0.512176
$105$	−3.17689	−0.310032
$106$	−1.00000	−0.0971286
$107$	10.0741	0.973902	0.486951	−	0.873429i	$-0.338109\pi$
$107$	10.0741	0.973902	0.486951	+	0.873429i	$0.338109\pi$
$108$	−1.00000	−0.0962250
$109$	−2.26079	−0.216545	−0.108272	−	0.994121i	$-0.534532\pi$
$109$	−2.26079	−0.216545	−0.108272	+	0.994121i	$0.534532\pi$
$110$	0.438218	0.0417824
$111$	3.99773	0.379448
$112$	3.48340	0.329150
$113$	−6.01163	−0.565526	−0.282763	−	0.959190i	$-0.591251\pi$
$113$	−6.01163	−0.565526	−0.282763	+	0.959190i	$0.591251\pi$
$114$	−1.00000	−0.0936586
$115$	6.55529	0.611284
$116$	2.36574	0.219654
$117$	5.22319	0.482884
$118$	−12.9354	−1.19080
$119$	21.7794	1.99651
$120$	0.912007	0.0832545
$121$	−10.7691	−0.979011
$122$	−11.8597	−1.07373
$123$	−5.30220	−0.478083
$124$	2.59294	0.232853
$125$	−8.36150	−0.747876
$126$	−3.48340	−0.310326
$127$	19.9474	1.77004	0.885022	−	0.465549i	$-0.154143\pi$
$127$	19.9474	1.77004	0.885022	+	0.465549i	$0.154143\pi$
$128$	−1.00000	−0.0883883
$129$	−5.88658	−0.518285
$130$	−4.76358	−0.417794
$131$	12.1849	1.06460	0.532298	−	0.846557i	$-0.321329\pi$
$131$	12.1849	1.06460	0.532298	+	0.846557i	$0.321329\pi$
$132$	0.480498	0.0418220
$133$	−3.48340	−0.302049
$134$	10.5160	0.908447
$135$	−0.912007	−0.0784931
$136$	−6.25232	−0.536132
$137$	2.38999	0.204191	0.102095	−	0.994775i	$-0.467445\pi$
$137$	2.38999	0.204191	0.102095	+	0.994775i	$0.467445\pi$
$138$	7.18776	0.611863
$139$	7.79093	0.660818	0.330409	−	0.943838i	$-0.392813\pi$
$139$	7.79093	0.660818	0.330409	+	0.943838i	$0.392813\pi$
$140$	3.17689	0.268496
$141$	−1.45172	−0.122257
$142$	−12.3755	−1.03853
$143$	−2.50973	−0.209874
$144$	1.00000	0.0833333
$145$	2.15758	0.179177
$146$	10.7021	0.885709
$147$	−5.13408	−0.423452
$148$	−3.99773	−0.328611
$149$	−4.36696	−0.357755	−0.178878	−	0.983871i	$-0.557247\pi$
$149$	−4.36696	−0.357755	−0.178878	+	0.983871i	$0.557247\pi$
$150$	−4.16824	−0.340336
$151$	−12.1432	−0.988202	−0.494101	−	0.869404i	$-0.664503\pi$
$151$	−12.1432	−0.988202	−0.494101	+	0.869404i	$0.664503\pi$
$152$	1.00000	0.0811107
$153$	6.25232	0.505470
$154$	1.67377	0.134876
$155$	2.36478	0.189944
$156$	−5.22319	−0.418190
$157$	−10.8697	−0.867499	−0.433750	−	0.901033i	$-0.642810\pi$
$157$	−10.8697	−0.867499	−0.433750	+	0.901033i	$0.642810\pi$
$158$	15.0539	1.19762
$159$	−1.00000	−0.0793052
$160$	−0.912007	−0.0721005
$161$	25.0378	1.97326
$162$	−1.00000	−0.0785674
$163$	18.7919	1.47190	0.735949	−	0.677037i	$-0.236736\pi$
$163$	18.7919	1.47190	0.735949	+	0.677037i	$0.236736\pi$
$164$	5.30220	0.414032
$165$	0.438218	0.0341152
$166$	7.68354	0.596358
$167$	−3.23137	−0.250051	−0.125025	−	0.992154i	$-0.539901\pi$
$167$	−3.23137	−0.250051	−0.125025	+	0.992154i	$0.539901\pi$
$168$	3.48340	0.268750
$169$	14.2817	1.09859
$170$	−5.70217	−0.437336
$171$	−1.00000	−0.0764719
$172$	5.88658	0.448848
$173$	−6.34356	−0.482292	−0.241146	−	0.970489i	$-0.577523\pi$
$173$	−6.34356	−0.482292	−0.241146	+	0.970489i	$0.577523\pi$
$174$	2.36574	0.179347
$175$	−14.5197	−1.09758
$176$	−0.480498	−0.0362189
$177$	−12.9354	−0.972285
$178$	−4.29778	−0.322132
$179$	−19.7974	−1.47973	−0.739863	−	0.672758i	$-0.765110\pi$
$179$	−19.7974	−1.47973	−0.739863	+	0.672758i	$0.765110\pi$
$180$	0.912007	0.0679770
$181$	2.58051	0.191808	0.0959039	−	0.995391i	$-0.469426\pi$
$181$	2.58051	0.191808	0.0959039	+	0.995391i	$0.469426\pi$
$182$	−18.1945	−1.34866
$183$	−11.8597	−0.876695
$184$	−7.18776	−0.529889
$185$	−3.64596	−0.268056
$186$	2.59294	0.190124
$187$	−3.00423	−0.219691
$188$	1.45172	0.105878
$189$	−3.48340	−0.253380
$190$	0.912007	0.0661640
$191$	−11.3588	−0.821897	−0.410949	−	0.911658i	$-0.634802\pi$
$191$	−11.3588	−0.821897	−0.410949	+	0.911658i	$0.634802\pi$
$192$	−1.00000	−0.0721688
$193$	−12.5809	−0.905590	−0.452795	−	0.891615i	$-0.649573\pi$
$193$	−12.5809	−0.905590	−0.452795	+	0.891615i	$0.649573\pi$
$194$	12.8959	0.925868
$195$	−4.76358	−0.341127
$196$	5.13408	0.366720
$197$	17.1083	1.21892	0.609459	−	0.792818i	$-0.291387\pi$
$197$	17.1083	1.21892	0.609459	+	0.792818i	$0.291387\pi$
$198$	0.480498	0.0341475
$199$	7.11536	0.504395	0.252197	−	0.967676i	$-0.418847\pi$
$199$	7.11536	0.504395	0.252197	+	0.967676i	$0.418847\pi$
$200$	4.16824	0.294739
$201$	10.5160	0.741744
$202$	8.44802	0.594401
$203$	8.24083	0.578393
$204$	−6.25232	−0.437750
$205$	4.83565	0.337736
$206$	11.6808	0.813839
$207$	7.18776	0.499584
$208$	5.22319	0.362163
$209$	0.480498	0.0332367
$210$	3.17689	0.219226
$211$	−17.7618	−1.22278	−0.611388	−	0.791331i	$-0.709389\pi$
$211$	−17.7618	−1.22278	−0.611388	+	0.791331i	$0.709389\pi$
$212$	1.00000	0.0686803
$213$	−12.3755	−0.847957
$214$	−10.0741	−0.688652
$215$	5.36860	0.366136
$216$	1.00000	0.0680414
$217$	9.03224	0.613149
$218$	2.26079	0.153120
$219$	10.7021	0.723178
$220$	−0.438218	−0.0295446
$221$	32.6571	2.19675
$222$	−3.99773	−0.268310
$223$	−23.1628	−1.55109	−0.775547	−	0.631290i	$-0.782526\pi$
$223$	−23.1628	−1.55109	−0.775547	+	0.631290i	$0.782526\pi$
$224$	−3.48340	−0.232744
$225$	−4.16824	−0.277883
$226$	6.01163	0.399888
$227$	−19.4761	−1.29267	−0.646337	−	0.763052i	$-0.723700\pi$
$227$	−19.4761	−1.29267	−0.646337	+	0.763052i	$0.723700\pi$
$228$	1.00000	0.0662266
$229$	1.82928	0.120882	0.0604412	−	0.998172i	$-0.480749\pi$
$229$	1.82928	0.120882	0.0604412	+	0.998172i	$0.480749\pi$
$230$	−6.55529	−0.432243
$231$	1.67377	0.110126
$232$	−2.36574	−0.155319
$233$	−11.8467	−0.776100	−0.388050	−	0.921638i	$-0.626851\pi$
$233$	−11.8467	−0.776100	−0.388050	+	0.921638i	$0.626851\pi$
$234$	−5.22319	−0.341450
$235$	1.32398	0.0863670
$236$	12.9354	0.842024
$237$	15.0539	0.977855
$238$	−21.7794	−1.41175
$239$	−9.02154	−0.583555	−0.291777	−	0.956486i	$-0.594247\pi$
$239$	−9.02154	−0.583555	−0.291777	+	0.956486i	$0.594247\pi$
$240$	−0.912007	−0.0588698
$241$	−28.6918	−1.84820	−0.924101	−	0.382149i	$-0.875184\pi$
$241$	−28.6918	−1.84820	−0.924101	+	0.382149i	$0.875184\pi$
$242$	10.7691	0.692265
$243$	−1.00000	−0.0641500
$244$	11.8597	0.759240
$245$	4.68232	0.299142
$246$	5.30220	0.338056
$247$	−5.22319	−0.332343
$248$	−2.59294	−0.164652
$249$	7.68354	0.486924
$250$	8.36150	0.528828
$251$	−17.0589	−1.07675	−0.538374	−	0.842706i	$-0.680961\pi$
$251$	−17.0589	−1.07675	−0.538374	+	0.842706i	$0.680961\pi$
$252$	3.48340	0.219434
$253$	−3.45370	−0.217132
$254$	−19.9474	−1.25161
$255$	−5.70217	−0.357083
$256$	1.00000	0.0625000
$257$	−14.7564	−0.920477	−0.460238	−	0.887795i	$-0.652236\pi$
$257$	−14.7564	−0.920477	−0.460238	+	0.887795i	$0.652236\pi$
$258$	5.88658	0.366482
$259$	−13.9257	−0.865300
$260$	4.76358	0.295425
$261$	2.36574	0.146436
$262$	−12.1849	−0.752783
$263$	16.7061	1.03014	0.515071	−	0.857148i	$-0.327766\pi$
$263$	16.7061	1.03014	0.515071	+	0.857148i	$0.327766\pi$
$264$	−0.480498	−0.0295726
$265$	0.912007	0.0560242
$266$	3.48340	0.213581
$267$	−4.29778	−0.263020
$268$	−10.5160	−0.642369
$269$	−13.4058	−0.817367	−0.408684	−	0.912676i	$-0.634012\pi$
$269$	−13.4058	−0.817367	−0.408684	+	0.912676i	$0.634012\pi$
$270$	0.912007	0.0555030
$271$	20.4557	1.24259	0.621297	−	0.783575i	$-0.286606\pi$
$271$	20.4557	1.24259	0.621297	+	0.783575i	$0.286606\pi$
$272$	6.25232	0.379103
$273$	−18.1945	−1.10118
$274$	−2.38999	−0.144385
$275$	2.00283	0.120775
$276$	−7.18776	−0.432652
$277$	28.9193	1.73759	0.868796	−	0.495170i	$-0.164894\pi$
$277$	28.9193	1.73759	0.868796	+	0.495170i	$0.164894\pi$
$278$	−7.79093	−0.467269
$279$	2.59294	0.155235
$280$	−3.17689	−0.189855
$281$	−18.7848	−1.12060	−0.560302	−	0.828288i	$-0.689315\pi$
$281$	−18.7848	−1.12060	−0.560302	+	0.828288i	$0.689315\pi$
$282$	1.45172	0.0864488
$283$	2.57262	0.152926	0.0764632	−	0.997072i	$-0.475637\pi$
$283$	2.57262	0.152926	0.0764632	+	0.997072i	$0.475637\pi$
$284$	12.3755	0.734352
$285$	0.912007	0.0540226
$286$	2.50973	0.148403
$287$	18.4697	1.09023
$288$	−1.00000	−0.0589256
$289$	22.0916	1.29950
$290$	−2.15758	−0.126697
$291$	12.8959	0.755968
$292$	−10.7021	−0.626291
$293$	4.96978	0.290338	0.145169	−	0.989407i	$-0.453627\pi$
$293$	4.96978	0.290338	0.145169	+	0.989407i	$0.453627\pi$
$294$	5.13408	0.299426
$295$	11.7972	0.686859
$296$	3.99773	0.232363
$297$	0.480498	0.0278813
$298$	4.36696	0.252971
$299$	37.5430	2.17117
$300$	4.16824	0.240654
$301$	20.5053	1.18191
$302$	12.1432	0.698764
$303$	8.44802	0.485326
$304$	−1.00000	−0.0573539
$305$	10.8161	0.619331
$306$	−6.25232	−0.357422
$307$	−4.91481	−0.280503	−0.140251	−	0.990116i	$-0.544791\pi$
$307$	−4.91481	−0.280503	−0.140251	+	0.990116i	$0.544791\pi$
$308$	−1.67377	−0.0953717
$309$	11.6808	0.664497
$310$	−2.36478	−0.134310
$311$	12.5066	0.709185	0.354592	−	0.935021i	$-0.384620\pi$
$311$	12.5066	0.709185	0.354592	+	0.935021i	$0.384620\pi$
$312$	5.22319	0.295705
$313$	−31.0011	−1.75229	−0.876144	−	0.482050i	$-0.839892\pi$
$313$	−31.0011	−1.75229	−0.876144	+	0.482050i	$0.839892\pi$
$314$	10.8697	0.613415
$315$	3.17689	0.178997
$316$	−15.0539	−0.846847
$317$	−30.0777	−1.68933	−0.844665	−	0.535295i	$-0.820200\pi$
$317$	−30.0777	−1.68933	−0.844665	+	0.535295i	$0.820200\pi$
$318$	1.00000	0.0560772
$319$	−1.13673	−0.0636449
$320$	0.912007	0.0509828
$321$	−10.0741	−0.562282
$322$	−25.0378	−1.39530
$323$	−6.25232	−0.347889
$324$	1.00000	0.0555556
$325$	−21.7715	−1.20767
$326$	−18.7919	−1.04079
$327$	2.26079	0.125022
$328$	−5.30220	−0.292765
$329$	5.05693	0.278798
$330$	−0.438218	−0.0241231
$331$	32.4227	1.78211	0.891057	−	0.453891i	$-0.149964\pi$
$331$	32.4227	1.78211	0.891057	+	0.453891i	$0.149964\pi$
$332$	−7.68354	−0.421689
$333$	−3.99773	−0.219074
$334$	3.23137	0.176813
$335$	−9.59070	−0.523996
$336$	−3.48340	−0.190035
$337$	−4.12467	−0.224685	−0.112343	−	0.993670i	$-0.535835\pi$
$337$	−4.12467	−0.224685	−0.112343	+	0.993670i	$0.535835\pi$
$338$	−14.2817	−0.776821
$339$	6.01163	0.326507
$340$	5.70217	0.309243
$341$	−1.24590	−0.0674693
$342$	1.00000	0.0540738
$343$	−6.49975	−0.350954
$344$	−5.88658	−0.317383
$345$	−6.55529	−0.352925
$346$	6.34356	0.341032
$347$	−10.3082	−0.553371	−0.276685	−	0.960961i	$-0.589236\pi$
$347$	−10.3082	−0.553371	−0.276685	+	0.960961i	$0.589236\pi$
$348$	−2.36574	−0.126817
$349$	−21.7868	−1.16622	−0.583112	−	0.812392i	$-0.698165\pi$
$349$	−21.7868	−1.16622	−0.583112	+	0.812392i	$0.698165\pi$
$350$	14.5197	0.776108
$351$	−5.22319	−0.278793
$352$	0.480498	0.0256106
$353$	33.2853	1.77160	0.885798	−	0.464070i	$-0.153612\pi$
$353$	33.2853	1.77160	0.885798	+	0.464070i	$0.153612\pi$
$354$	12.9354	0.687510
$355$	11.2866	0.599029
$356$	4.29778	0.227782
$357$	−21.7794	−1.15269
$358$	19.7974	1.04632
$359$	−4.75545	−0.250983	−0.125492	−	0.992095i	$-0.540051\pi$
$359$	−4.75545	−0.250983	−0.125492	+	0.992095i	$0.540051\pi$
$360$	−0.912007	−0.0480670
$361$	1.00000	0.0526316
$362$	−2.58051	−0.135629
$363$	10.7691	0.565232
$364$	18.1945	0.953648
$365$	−9.76036	−0.510880
$366$	11.8597	0.619917
$367$	4.58054	0.239102	0.119551	−	0.992828i	$-0.461854\pi$
$367$	4.58054	0.239102	0.119551	+	0.992828i	$0.461854\pi$
$368$	7.18776	0.374688
$369$	5.30220	0.276022
$370$	3.64596	0.189544
$371$	3.48340	0.180849
$372$	−2.59294	−0.134438
$373$	28.3019	1.46542	0.732709	−	0.680542i	$-0.238256\pi$
$373$	28.3019	1.46542	0.732709	+	0.680542i	$0.238256\pi$
$374$	3.00423	0.155345
$375$	8.36150	0.431786
$376$	−1.45172	−0.0748669
$377$	12.3567	0.636404
$378$	3.48340	0.179167
$379$	26.3112	1.35152	0.675758	−	0.737124i	$-0.263817\pi$
$379$	26.3112	1.35152	0.675758	+	0.737124i	$0.263817\pi$
$380$	−0.912007	−0.0467850
$381$	−19.9474	−1.02194
$382$	11.3588	0.581169
$383$	−5.20123	−0.265771	−0.132885	−	0.991131i	$-0.542424\pi$
$383$	−5.20123	−0.265771	−0.132885	+	0.991131i	$0.542424\pi$
$384$	1.00000	0.0510310
$385$	−1.52649	−0.0777970
$386$	12.5809	0.640349
$387$	5.88658	0.299232
$388$	−12.8959	−0.654688
$389$	−2.43930	−0.123678	−0.0618388	−	0.998086i	$-0.519696\pi$
$389$	−2.43930	−0.123678	−0.0618388	+	0.998086i	$0.519696\pi$
$390$	4.76358	0.241213
$391$	44.9402	2.27272
$392$	−5.13408	−0.259310
$393$	−12.1849	−0.614645
$394$	−17.1083	−0.861905
$395$	−13.7292	−0.690793
$396$	−0.480498	−0.0241459
$397$	17.1036	0.858405	0.429202	−	0.903208i	$-0.358795\pi$
$397$	17.1036	0.858405	0.429202	+	0.903208i	$0.358795\pi$
$398$	−7.11536	−0.356661
$399$	3.48340	0.174388
$400$	−4.16824	−0.208412
$401$	−31.7115	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$401$	−31.7115	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$402$	−10.5160	−0.524492
$403$	13.5434	0.674645
$404$	−8.44802	−0.420305
$405$	0.912007	0.0453180
$406$	−8.24083	−0.408986
$407$	1.92090	0.0952155
$408$	6.25232	0.309536
$409$	−35.9101	−1.77564	−0.887821	−	0.460189i	$-0.847782\pi$
$409$	−35.9101	−1.77564	−0.887821	+	0.460189i	$0.847782\pi$
$410$	−4.83565	−0.238816
$411$	−2.38999	−0.117890
$412$	−11.6808	−0.575471
$413$	45.0592	2.21722
$414$	−7.18776	−0.353259
$415$	−7.00744	−0.343982
$416$	−5.22319	−0.256088
$417$	−7.79093	−0.381523
$418$	−0.480498	−0.0235019
$419$	0.0354799	0.00173331	0.000866654	−	1.00000i	$-0.499724\pi$
$419$	0.0354799	0.00173331	0.000866654		1.00000i	$0.499724\pi$
$420$	−3.17689	−0.155016
$421$	31.3181	1.52635	0.763176	−	0.646191i	$-0.223639\pi$
$421$	31.3181	1.52635	0.763176	+	0.646191i	$0.223639\pi$
$422$	17.7618	0.864633
$423$	1.45172	0.0705852
$424$	−1.00000	−0.0485643
$425$	−26.0612	−1.26415
$426$	12.3755	0.599596
$427$	41.3121	1.99923
$428$	10.0741	0.486951
$429$	2.50973	0.121171
$430$	−5.36860	−0.258897
$431$	−23.1566	−1.11542	−0.557708	−	0.830037i	$-0.688319\pi$
$431$	−23.1566	−1.11542	−0.557708	+	0.830037i	$0.688319\pi$
$432$	−1.00000	−0.0481125
$433$	15.4160	0.740845	0.370423	−	0.928863i	$-0.379213\pi$
$433$	15.4160	0.740845	0.370423	+	0.928863i	$0.379213\pi$
$434$	−9.03224	−0.433562
$435$	−2.15758	−0.103448
$436$	−2.26079	−0.108272
$437$	−7.18776	−0.343837
$438$	−10.7021	−0.511364
$439$	32.2792	1.54060	0.770300	−	0.637681i	$-0.220106\pi$
$439$	32.2792	1.54060	0.770300	+	0.637681i	$0.220106\pi$
$440$	0.438218	0.0208912
$441$	5.13408	0.244480
$442$	−32.6571	−1.55334
$443$	8.53021	0.405283	0.202641	−	0.979253i	$-0.435047\pi$
$443$	8.53021	0.405283	0.202641	+	0.979253i	$0.435047\pi$
$444$	3.99773	0.189724
$445$	3.91961	0.185807
$446$	23.1628	1.09679
$447$	4.36696	0.206550
$448$	3.48340	0.164575
$449$	13.7894	0.650763	0.325382	−	0.945583i	$-0.394507\pi$
$449$	13.7894	0.650763	0.325382	+	0.945583i	$0.394507\pi$
$450$	4.16824	0.196493
$451$	−2.54770	−0.119966
$452$	−6.01163	−0.282763
$453$	12.1432	0.570539
$454$	19.4761	0.914059
$455$	16.5935	0.777914
$456$	−1.00000	−0.0468293
$457$	−0.348199	−0.0162880	−0.00814402	−	0.999967i	$-0.502592\pi$
$457$	−0.348199	−0.0162880	−0.00814402	+	0.999967i	$0.502592\pi$
$458$	−1.82928	−0.0854767
$459$	−6.25232	−0.291834
$460$	6.55529	0.305642
$461$	6.83494	0.318335	0.159167	−	0.987252i	$-0.449119\pi$
$461$	6.83494	0.318335	0.159167	+	0.987252i	$0.449119\pi$
$462$	−1.67377	−0.0778707
$463$	−16.5702	−0.770081	−0.385040	−	0.922900i	$-0.625812\pi$
$463$	−16.5702	−0.770081	−0.385040	+	0.922900i	$0.625812\pi$
$464$	2.36574	0.109827
$465$	−2.36478	−0.109664
$466$	11.8467	0.548786
$467$	−11.2120	−0.518828	−0.259414	−	0.965766i	$-0.583529\pi$
$467$	−11.2120	−0.518828	−0.259414	+	0.965766i	$0.583529\pi$
$468$	5.22319	0.241442
$469$	−36.6316	−1.69149
$470$	−1.32398	−0.0610707
$471$	10.8697	0.500851
$472$	−12.9354	−0.595401
$473$	−2.82849	−0.130054
$474$	−15.0539	−0.691448
$475$	4.16824	0.191252
$476$	21.7794	0.998255
$477$	1.00000	0.0457869
$478$	9.02154	0.412635
$479$	42.1527	1.92600	0.963002	−	0.269493i	$-0.0868563\pi$
$479$	42.1527	1.92600	0.963002	+	0.269493i	$0.0868563\pi$
$480$	0.912007	0.0416272
$481$	−20.8809	−0.952086
$482$	28.6918	1.30688
$483$	−25.0378	−1.13926
$484$	−10.7691	−0.489506
$485$	−11.7611	−0.534044
$486$	1.00000	0.0453609
$487$	23.7279	1.07521	0.537607	−	0.843195i	$-0.319328\pi$
$487$	23.7279	1.07521	0.537607	+	0.843195i	$0.319328\pi$
$488$	−11.8597	−0.536864
$489$	−18.7919	−0.849800
$490$	−4.68232	−0.211526
$491$	43.6165	1.96838	0.984192	−	0.177104i	$-0.0566730\pi$
$491$	43.6165	1.96838	0.984192	+	0.177104i	$0.0566730\pi$
$492$	−5.30220	−0.239042
$493$	14.7914	0.666171
$494$	5.22319	0.235002
$495$	−0.438218	−0.0196964
$496$	2.59294	0.116426
$497$	43.1089	1.93370
$498$	−7.68354	−0.344307
$499$	20.5229	0.918731	0.459366	−	0.888247i	$-0.348077\pi$
$499$	20.5229	0.918731	0.459366	+	0.888247i	$0.348077\pi$
$500$	−8.36150	−0.373938
$501$	3.23137	0.144367
$502$	17.0589	0.761376
$503$	−12.7586	−0.568878	−0.284439	−	0.958694i	$-0.591807\pi$
$503$	−12.7586	−0.568878	−0.284439	+	0.958694i	$0.591807\pi$
$504$	−3.48340	−0.155163
$505$	−7.70466	−0.342853
$506$	3.45370	0.153536
$507$	−14.2817	−0.634272
$508$	19.9474	0.885022
$509$	37.6784	1.67006	0.835032	−	0.550201i	$-0.185449\pi$
$509$	37.6784	1.67006	0.835032	+	0.550201i	$0.185449\pi$
$510$	5.70217	0.252496
$511$	−37.2796	−1.64915
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	14.7564	0.650875
$515$	−10.6530	−0.469426
$516$	−5.88658	−0.259142
$517$	−0.697550	−0.0306782
$518$	13.9257	0.611860
$519$	6.34356	0.278451
$520$	−4.76358	−0.208897
$521$	24.7864	1.08591	0.542956	−	0.839761i	$-0.317305\pi$
$521$	24.7864	1.08591	0.542956	+	0.839761i	$0.317305\pi$
$522$	−2.36574	−0.103546
$523$	−41.3797	−1.80941	−0.904704	−	0.426040i	$-0.859908\pi$
$523$	−41.3797	−1.80941	−0.904704	+	0.426040i	$0.859908\pi$
$524$	12.1849	0.532298
$525$	14.5197	0.633690
$526$	−16.7061	−0.728420
$527$	16.2119	0.706201
$528$	0.480498	0.0209110
$529$	28.6639	1.24626
$530$	−0.912007	−0.0396151
$531$	12.9354	0.561349
$532$	−3.48340	−0.151025
$533$	27.6944	1.19958
$534$	4.29778	0.185983
$535$	9.18767	0.397218
$536$	10.5160	0.454224
$537$	19.7974	0.854320
$538$	13.4058	0.577966
$539$	−2.46691	−0.106257
$540$	−0.912007	−0.0392465
$541$	42.1692	1.81299	0.906497	−	0.422212i	$-0.138746\pi$
$541$	42.1692	1.81299	0.906497	+	0.422212i	$0.138746\pi$
$542$	−20.4557	−0.878647
$543$	−2.58051	−0.110740
$544$	−6.25232	−0.268066
$545$	−2.06186	−0.0883203
$546$	18.1945	0.778651
$547$	2.40085	0.102653	0.0513264	−	0.998682i	$-0.483655\pi$
$547$	2.40085	0.102653	0.0513264	+	0.998682i	$0.483655\pi$
$548$	2.38999	0.102095
$549$	11.8597	0.506160
$550$	−2.00283	−0.0854010
$551$	−2.36574	−0.100784
$552$	7.18776	0.305931
$553$	−52.4387	−2.22992
$554$	−28.9193	−1.22866
$555$	3.64596	0.154762
$556$	7.79093	0.330409
$557$	5.78701	0.245204	0.122602	−	0.992456i	$-0.460876\pi$
$557$	5.78701	0.245204	0.122602	+	0.992456i	$0.460876\pi$
$558$	−2.59294	−0.109768
$559$	30.7467	1.30045
$560$	3.17689	0.134248
$561$	3.00423	0.126839
$562$	18.7848	0.792387
$563$	38.0104	1.60195	0.800975	−	0.598698i	$-0.204315\pi$
$563$	38.0104	1.60195	0.800975	+	0.598698i	$0.204315\pi$
$564$	−1.45172	−0.0611286
$565$	−5.48265	−0.230657
$566$	−2.57262	−0.108135
$567$	3.48340	0.146289
$568$	−12.3755	−0.519265
$569$	44.7962	1.87795	0.938977	−	0.343980i	$-0.111775\pi$
$569$	44.7962	1.87795	0.938977	+	0.343980i	$0.111775\pi$
$570$	−0.912007	−0.0381998
$571$	−30.7837	−1.28826	−0.644128	−	0.764918i	$-0.722780\pi$
$571$	−30.7837	−1.28826	−0.644128	+	0.764918i	$0.722780\pi$
$572$	−2.50973	−0.104937
$573$	11.3588	0.474523
$574$	−18.4697	−0.770910
$575$	−29.9603	−1.24943
$576$	1.00000	0.0416667
$577$	1.25967	0.0524407	0.0262203	−	0.999656i	$-0.491653\pi$
$577$	1.25967	0.0524407	0.0262203	+	0.999656i	$0.491653\pi$
$578$	−22.0916	−0.918888
$579$	12.5809	0.522843
$580$	2.15758	0.0895885
$581$	−26.7648	−1.11039
$582$	−12.8959	−0.534550
$583$	−0.480498	−0.0199002
$584$	10.7021	0.442854
$585$	4.76358	0.196950
$586$	−4.96978	−0.205300
$587$	−1.05690	−0.0436230	−0.0218115	−	0.999762i	$-0.506943\pi$
$587$	−1.05690	−0.0436230	−0.0218115	+	0.999762i	$0.506943\pi$
$588$	−5.13408	−0.211726
$589$	−2.59294	−0.106840
$590$	−11.7972	−0.485683
$591$	−17.1083	−0.703743
$592$	−3.99773	−0.164306
$593$	15.8258	0.649890	0.324945	−	0.945733i	$-0.394654\pi$
$593$	15.8258	0.649890	0.324945	+	0.945733i	$0.394654\pi$
$594$	−0.480498	−0.0197151
$595$	19.8629	0.814301
$596$	−4.36696	−0.178878
$597$	−7.11536	−0.291212
$598$	−37.5430	−1.53525
$599$	−31.8200	−1.30013	−0.650065	−	0.759878i	$-0.725258\pi$
$599$	−31.8200	−1.30013	−0.650065	+	0.759878i	$0.725258\pi$
$600$	−4.16824	−0.170168
$601$	−39.8945	−1.62733	−0.813665	−	0.581335i	$-0.802531\pi$
$601$	−39.8945	−1.62733	−0.813665	+	0.581335i	$0.802531\pi$
$602$	−20.5053	−0.835734
$603$	−10.5160	−0.428246
$604$	−12.1432	−0.494101
$605$	−9.82152	−0.399301
$606$	−8.44802	−0.343177
$607$	32.3605	1.31347	0.656735	−	0.754121i	$-0.271937\pi$
$607$	32.3605	1.31347	0.656735	+	0.754121i	$0.271937\pi$
$608$	1.00000	0.0405554
$609$	−8.24083	−0.333935
$610$	−10.8161	−0.437933
$611$	7.58262	0.306760
$612$	6.25232	0.252735
$613$	37.3375	1.50805	0.754024	−	0.656847i	$-0.228110\pi$
$613$	37.3375	1.50805	0.754024	+	0.656847i	$0.228110\pi$
$614$	4.91481	0.198345
$615$	−4.83565	−0.194992
$616$	1.67377	0.0674380
$617$	−39.3049	−1.58235	−0.791177	−	0.611587i	$-0.790532\pi$
$617$	−39.3049	−1.58235	−0.791177	+	0.611587i	$0.790532\pi$
$618$	−11.6808	−0.469870
$619$	−11.4384	−0.459747	−0.229874	−	0.973220i	$-0.573831\pi$
$619$	−11.4384	−0.459747	−0.229874	+	0.973220i	$0.573831\pi$
$620$	2.36478	0.0949718
$621$	−7.18776	−0.288435
$622$	−12.5066	−0.501469
$623$	14.9709	0.599796
$624$	−5.22319	−0.209095
$625$	13.2155	0.528618
$626$	31.0011	1.23905
$627$	−0.480498	−0.0191892
$628$	−10.8697	−0.433750
$629$	−24.9951	−0.996620
$630$	−3.17689	−0.126570
$631$	15.1388	0.602667	0.301333	−	0.953519i	$-0.402568\pi$
$631$	15.1388	0.602667	0.301333	+	0.953519i	$0.402568\pi$
$632$	15.0539	0.598811
$633$	17.7618	0.705970
$634$	30.0777	1.19454
$635$	18.1922	0.721934
$636$	−1.00000	−0.0396526
$637$	26.8163	1.06250
$638$	1.13673	0.0450038
$639$	12.3755	0.489568
$640$	−0.912007	−0.0360503
$641$	34.5112	1.36311	0.681556	−	0.731766i	$-0.261304\pi$
$641$	34.5112	1.36311	0.681556	+	0.731766i	$0.261304\pi$
$642$	10.0741	0.397594
$643$	22.6965	0.895063	0.447531	−	0.894268i	$-0.352303\pi$
$643$	22.6965	0.895063	0.447531	+	0.894268i	$0.352303\pi$
$644$	25.0378	0.986629
$645$	−5.36860	−0.211389
$646$	6.25232	0.245994
$647$	−8.53264	−0.335453	−0.167726	−	0.985834i	$-0.553642\pi$
$647$	−8.53264	−0.335453	−0.167726	+	0.985834i	$0.553642\pi$
$648$	−1.00000	−0.0392837
$649$	−6.21544	−0.243977
$650$	21.7715	0.853949
$651$	−9.03224	−0.354002
$652$	18.7919	0.735949
$653$	38.5360	1.50803	0.754015	−	0.656857i	$-0.228115\pi$
$653$	38.5360	1.50803	0.754015	+	0.656857i	$0.228115\pi$
$654$	−2.26079	−0.0884040
$655$	11.1127	0.434208
$656$	5.30220	0.207016
$657$	−10.7021	−0.417527
$658$	−5.05693	−0.197140
$659$	19.3802	0.754945	0.377472	−	0.926021i	$-0.376793\pi$
$659$	19.3802	0.754945	0.377472	+	0.926021i	$0.376793\pi$
$660$	0.438218	0.0170576
$661$	17.5358	0.682065	0.341033	−	0.940051i	$-0.389223\pi$
$661$	17.5358	0.682065	0.341033	+	0.940051i	$0.389223\pi$
$662$	−32.4227	−1.26015
$663$	−32.6571	−1.26830
$664$	7.68354	0.298179
$665$	−3.17689	−0.123194
$666$	3.99773	0.154909
$667$	17.0044	0.658413
$668$	−3.23137	−0.125025
$669$	23.1628	0.895525
$670$	9.59070	0.370521
$671$	−5.69857	−0.219991
$672$	3.48340	0.134375
$673$	−23.1102	−0.890832	−0.445416	−	0.895324i	$-0.646944\pi$
$673$	−23.1102	−0.890832	−0.445416	+	0.895324i	$0.646944\pi$
$674$	4.12467	0.158876
$675$	4.16824	0.160436
$676$	14.2817	0.549296
$677$	−44.3835	−1.70580	−0.852899	−	0.522076i	$-0.825158\pi$
$677$	−44.3835	−1.70580	−0.852899	+	0.522076i	$0.825158\pi$
$678$	−6.01163	−0.230875
$679$	−44.9214	−1.72393
$680$	−5.70217	−0.218668
$681$	19.4761	0.746326
$682$	1.24590	0.0477080
$683$	45.3915	1.73686	0.868428	−	0.495815i	$-0.165131\pi$
$683$	45.3915	1.73686	0.868428	+	0.495815i	$0.165131\pi$
$684$	−1.00000	−0.0382360
$685$	2.17969	0.0832817
$686$	6.49975	0.248162
$687$	−1.82928	−0.0697914
$688$	5.88658	0.224424
$689$	5.22319	0.198988
$690$	6.55529	0.249556
$691$	−12.2611	−0.466434	−0.233217	−	0.972425i	$-0.574925\pi$
$691$	−12.2611	−0.466434	−0.233217	+	0.972425i	$0.574925\pi$
$692$	−6.34356	−0.241146
$693$	−1.67377	−0.0635811
$694$	10.3082	0.391292
$695$	7.10538	0.269523
$696$	2.36574	0.0896733
$697$	33.1511	1.25569
$698$	21.7868	0.824644
$699$	11.8467	0.448082
$700$	−14.5197	−0.548792
$701$	38.6327	1.45914	0.729569	−	0.683907i	$-0.239721\pi$
$701$	38.6327	1.45914	0.729569	+	0.683907i	$0.239721\pi$
$702$	5.22319	0.197136
$703$	3.99773	0.150777
$704$	−0.480498	−0.0181094
$705$	−1.32398	−0.0498640
$706$	−33.2853	−1.25271
$707$	−29.4278	−1.10675
$708$	−12.9354	−0.486143
$709$	−46.5309	−1.74751	−0.873753	−	0.486370i	$-0.838321\pi$
$709$	−46.5309	−1.74751	−0.873753	+	0.486370i	$0.838321\pi$
$710$	−11.2866	−0.423577
$711$	−15.0539	−0.564565
$712$	−4.29778	−0.161066
$713$	18.6374	0.697977
$714$	21.7794	0.815072
$715$	−2.28889	−0.0855997
$716$	−19.7974	−0.739863
$717$	9.02154	0.336915
$718$	4.75545	0.177472
$719$	−35.7562	−1.33348	−0.666740	−	0.745290i	$-0.732311\pi$
$719$	−35.7562	−1.33348	−0.666740	+	0.745290i	$0.732311\pi$
$720$	0.912007	0.0339885
$721$	−40.6889	−1.51533
$722$	−1.00000	−0.0372161
$723$	28.6918	1.06706
$724$	2.58051	0.0959039
$725$	−9.86100	−0.366228
$726$	−10.7691	−0.399680
$727$	10.4659	0.388157	0.194079	−	0.980986i	$-0.437828\pi$
$727$	10.4659	0.388157	0.194079	+	0.980986i	$0.437828\pi$
$728$	−18.1945	−0.674331
$729$	1.00000	0.0370370
$730$	9.76036	0.361247
$731$	36.8048	1.36128
$732$	−11.8597	−0.438348
$733$	41.6782	1.53942	0.769709	−	0.638395i	$-0.220401\pi$
$733$	41.6782	1.53942	0.769709	+	0.638395i	$0.220401\pi$
$734$	−4.58054	−0.169071
$735$	−4.68232	−0.172710
$736$	−7.18776	−0.264944
$737$	5.05293	0.186127
$738$	−5.30220	−0.195177
$739$	−33.4510	−1.23052	−0.615258	−	0.788326i	$-0.710948\pi$
$739$	−33.4510	−1.23052	−0.615258	+	0.788326i	$0.710948\pi$
$740$	−3.64596	−0.134028
$741$	5.22319	0.191879
$742$	−3.48340	−0.127880
$743$	24.6384	0.903894	0.451947	−	0.892045i	$-0.350730\pi$
$743$	24.6384	0.903894	0.451947	+	0.892045i	$0.350730\pi$
$744$	2.59294	0.0950618
$745$	−3.98270	−0.145915
$746$	−28.3019	−1.03621
$747$	−7.68354	−0.281126
$748$	−3.00423	−0.109845
$749$	35.0922	1.28224
$750$	−8.36150	−0.305319
$751$	−41.9655	−1.53134	−0.765672	−	0.643232i	$-0.777593\pi$
$751$	−41.9655	−1.53134	−0.765672	+	0.643232i	$0.777593\pi$
$752$	1.45172	0.0529389
$753$	17.0589	0.621661
$754$	−12.3567	−0.450005
$755$	−11.0747	−0.403050
$756$	−3.48340	−0.126690
$757$	−42.2943	−1.53721	−0.768606	−	0.639723i	$-0.779049\pi$
$757$	−42.2943	−1.53721	−0.768606	+	0.639723i	$0.779049\pi$
$758$	−26.3112	−0.955666
$759$	3.45370	0.125361
$760$	0.912007	0.0330820
$761$	−37.0213	−1.34202	−0.671011	−	0.741447i	$-0.734140\pi$
$761$	−37.0213	−1.34202	−0.671011	+	0.741447i	$0.734140\pi$
$762$	19.9474	0.722617
$763$	−7.87525	−0.285103
$764$	−11.3588	−0.410949
$765$	5.70217	0.206162
$766$	5.20123	0.187928
$767$	67.5641	2.43960
$768$	−1.00000	−0.0360844
$769$	−43.6603	−1.57443	−0.787215	−	0.616679i	$-0.788478\pi$
$769$	−43.6603	−1.57443	−0.787215	+	0.616679i	$0.788478\pi$
$770$	1.52649	0.0550108
$771$	14.7564	0.531437
$772$	−12.5809	−0.452795
$773$	−39.0261	−1.40367	−0.701836	−	0.712339i	$-0.747636\pi$
$773$	−39.0261	−1.40367	−0.701836	+	0.712339i	$0.747636\pi$
$774$	−5.88658	−0.211589
$775$	−10.8080	−0.388235
$776$	12.8959	0.462934
$777$	13.9257	0.499581
$778$	2.43930	0.0874532
$779$	−5.30220	−0.189971
$780$	−4.76358	−0.170564
$781$	−5.94641	−0.212779
$782$	−44.9402	−1.60706
$783$	−2.36574	−0.0845448
$784$	5.13408	0.183360
$785$	−9.91328	−0.353820
$786$	12.1849	0.434619
$787$	−13.1006	−0.466987	−0.233494	−	0.972358i	$-0.575016\pi$
$787$	−13.1006	−0.466987	−0.233494	+	0.972358i	$0.575016\pi$
$788$	17.1083	0.609459
$789$	−16.7061	−0.594752
$790$	13.7292	0.488465
$791$	−20.9409	−0.744573
$792$	0.480498	0.0170737
$793$	61.9455	2.19975
$794$	−17.1036	−0.606984
$795$	−0.912007	−0.0323456
$796$	7.11536	0.252197
$797$	47.4376	1.68033	0.840163	−	0.542334i	$-0.182459\pi$
$797$	47.4376	1.68033	0.840163	+	0.542334i	$0.182459\pi$
$798$	−3.48340	−0.123311
$799$	9.07664	0.321109
$800$	4.16824	0.147370
$801$	4.29778	0.151855
$802$	31.7115	1.11977
$803$	5.14232	0.181468
$804$	10.5160	0.370872
$805$	22.8347	0.804817
$806$	−13.5434	−0.477046
$807$	13.4058	0.471907
$808$	8.44802	0.297200
$809$	−27.3181	−0.960452	−0.480226	−	0.877145i	$-0.659445\pi$
$809$	−27.3181	−0.960452	−0.480226	+	0.877145i	$0.659445\pi$
$810$	−0.912007	−0.0320447
$811$	−7.84492	−0.275472	−0.137736	−	0.990469i	$-0.543983\pi$
$811$	−7.84492	−0.275472	−0.137736	+	0.990469i	$0.543983\pi$
$812$	8.24083	0.289197
$813$	−20.4557	−0.717412
$814$	−1.92090	−0.0673275
$815$	17.1384	0.600331
$816$	−6.25232	−0.218875
$817$	−5.88658	−0.205945
$818$	35.9101	1.25557
$819$	18.1945	0.635766
$820$	4.83565	0.168868
$821$	−56.4612	−1.97051	−0.985255	−	0.171091i	$-0.945271\pi$
$821$	−56.4612	−1.97051	−0.985255	+	0.171091i	$0.945271\pi$
$822$	2.38999	0.0833606
$823$	−9.31412	−0.324670	−0.162335	−	0.986736i	$-0.551903\pi$
$823$	−9.31412	−0.324670	−0.162335	+	0.986736i	$0.551903\pi$
$824$	11.6808	0.406919
$825$	−2.00283	−0.0697296
$826$	−45.0592	−1.56781
$827$	−29.3600	−1.02095	−0.510473	−	0.859894i	$-0.670530\pi$
$827$	−29.3600	−1.02095	−0.510473	+	0.859894i	$0.670530\pi$
$828$	7.18776	0.249792
$829$	−21.2992	−0.739751	−0.369876	−	0.929081i	$-0.620600\pi$
$829$	−21.2992	−0.739751	−0.369876	+	0.929081i	$0.620600\pi$
$830$	7.00744	0.243232
$831$	−28.9193	−1.00320
$832$	5.22319	0.181081
$833$	32.0999	1.11220
$834$	7.79093	0.269778
$835$	−2.94703	−0.101986
$836$	0.480498	0.0166184
$837$	−2.59294	−0.0896251
$838$	−0.0354799	−0.00122563
$839$	22.8603	0.789227	0.394613	−	0.918847i	$-0.370879\pi$
$839$	22.8603	0.789227	0.394613	+	0.918847i	$0.370879\pi$
$840$	3.17689	0.109613
$841$	−23.4033	−0.807009
$842$	−31.3181	−1.07929
$843$	18.7848	0.646981
$844$	−17.7618	−0.611388
$845$	13.0250	0.448074
$846$	−1.45172	−0.0499113
$847$	−37.5132	−1.28897
$848$	1.00000	0.0343401
$849$	−2.57262	−0.0882921
$850$	26.0612	0.893892
$851$	−28.7347	−0.985013
$852$	−12.3755	−0.423978
$853$	27.9984	0.958646	0.479323	−	0.877639i	$-0.340882\pi$
$853$	27.9984	0.958646	0.479323	+	0.877639i	$0.340882\pi$
$854$	−41.3121	−1.41367
$855$	−0.912007	−0.0311900
$856$	−10.0741	−0.344326
$857$	−25.6434	−0.875961	−0.437980	−	0.898985i	$-0.644306\pi$
$857$	−25.6434	−0.875961	−0.437980	+	0.898985i	$0.644306\pi$
$858$	−2.50973	−0.0856808
$859$	1.11402	0.0380098	0.0190049	−	0.999819i	$-0.493950\pi$
$859$	1.11402	0.0380098	0.0190049	+	0.999819i	$0.493950\pi$
$860$	5.36860	0.183068
$861$	−18.4697	−0.629445
$862$	23.1566	0.788719
$863$	40.2489	1.37009	0.685045	−	0.728501i	$-0.259783\pi$
$863$	40.2489	1.37009	0.685045	+	0.728501i	$0.259783\pi$
$864$	1.00000	0.0340207
$865$	−5.78537	−0.196708
$866$	−15.4160	−0.523857
$867$	−22.0916	−0.750269
$868$	9.03224	0.306574
$869$	7.23336	0.245375
$870$	2.15758	0.0731487
$871$	−54.9272	−1.86114
$872$	2.26079	0.0765601
$873$	−12.8959	−0.436458
$874$	7.18776	0.243130
$875$	−29.1265	−0.984654
$876$	10.7021	0.361589
$877$	−36.6857	−1.23879	−0.619393	−	0.785081i	$-0.712621\pi$
$877$	−36.6857	−1.23879	−0.619393	+	0.785081i	$0.712621\pi$
$878$	−32.2792	−1.08937
$879$	−4.96978	−0.167627
$880$	−0.438218	−0.0147723
$881$	20.1959	0.680418	0.340209	−	0.940350i	$-0.389502\pi$
$881$	20.1959	0.680418	0.340209	+	0.940350i	$0.389502\pi$
$882$	−5.13408	−0.172873
$883$	−21.5334	−0.724655	−0.362328	−	0.932051i	$-0.618018\pi$
$883$	−21.5334	−0.724655	−0.362328	+	0.932051i	$0.618018\pi$
$884$	32.6571	1.09838
$885$	−11.7972	−0.396558
$886$	−8.53021	−0.286578
$887$	−25.4958	−0.856064	−0.428032	−	0.903763i	$-0.640793\pi$
$887$	−25.4958	−0.856064	−0.428032	+	0.903763i	$0.640793\pi$
$888$	−3.99773	−0.134155
$889$	69.4847	2.33044
$890$	−3.91961	−0.131386
$891$	−0.480498	−0.0160973
$892$	−23.1628	−0.775547
$893$	−1.45172	−0.0485801
$894$	−4.36696	−0.146053
$895$	−18.0554	−0.603524
$896$	−3.48340	−0.116372
$897$	−37.5430	−1.25352
$898$	−13.7894	−0.460159
$899$	6.13423	0.204588
$900$	−4.16824	−0.138941
$901$	6.25232	0.208295
$902$	2.54770	0.0848290
$903$	−20.5053	−0.682374
$904$	6.01163	0.199944
$905$	2.35344	0.0782311
$906$	−12.1432	−0.403432
$907$	−37.3643	−1.24066	−0.620331	−	0.784340i	$-0.713002\pi$
$907$	−37.3643	−1.24066	−0.620331	+	0.784340i	$0.713002\pi$
$908$	−19.4761	−0.646337
$909$	−8.44802	−0.280203
$910$	−16.5935	−0.550068
$911$	25.7233	0.852251	0.426126	−	0.904664i	$-0.359878\pi$
$911$	25.7233	0.852251	0.426126	+	0.904664i	$0.359878\pi$
$912$	1.00000	0.0331133
$913$	3.69192	0.122185
$914$	0.348199	0.0115174
$915$	−10.8161	−0.357571
$916$	1.82928	0.0604412
$917$	42.4447	1.40165
$918$	6.25232	0.206357
$919$	−6.50138	−0.214461	−0.107230	−	0.994234i	$-0.534198\pi$
$919$	−6.50138	−0.214461	−0.107230	+	0.994234i	$0.534198\pi$
$920$	−6.55529	−0.216121
$921$	4.91481	0.161948
$922$	−6.83494	−0.225097
$923$	64.6396	2.12764
$924$	1.67377	0.0550629
$925$	16.6635	0.547893
$926$	16.5702	0.544529
$927$	−11.6808	−0.383647
$928$	−2.36574	−0.0776594
$929$	−37.8168	−1.24073	−0.620364	−	0.784314i	$-0.713015\pi$
$929$	−37.8168	−1.24073	−0.620364	+	0.784314i	$0.713015\pi$
$930$	2.36478	0.0775442
$931$	−5.13408	−0.168263
$932$	−11.8467	−0.388050
$933$	−12.5066	−0.409448
$934$	11.2120	0.366867
$935$	−2.73988	−0.0896036
$936$	−5.22319	−0.170725
$937$	−11.1079	−0.362879	−0.181440	−	0.983402i	$-0.558076\pi$
$937$	−11.1079	−0.362879	−0.181440	+	0.983402i	$0.558076\pi$
$938$	36.6316	1.19606
$939$	31.0011	1.01168
$940$	1.32398	0.0431835
$941$	−38.8914	−1.26782	−0.633912	−	0.773405i	$-0.718552\pi$
$941$	−38.8914	−1.26782	−0.633912	+	0.773405i	$0.718552\pi$
$942$	−10.8697	−0.354155
$943$	38.1109	1.24106
$944$	12.9354	0.421012
$945$	−3.17689	−0.103344
$946$	2.82849	0.0919621
$947$	34.4141	1.11831	0.559153	−	0.829064i	$-0.311126\pi$
$947$	34.4141	1.11831	0.559153	+	0.829064i	$0.311126\pi$
$948$	15.0539	0.488927
$949$	−55.8989	−1.81455
$950$	−4.16824	−0.135236
$951$	30.0777	0.975335
$952$	−21.7794	−0.705873
$953$	−1.31393	−0.0425625	−0.0212812	−	0.999774i	$-0.506775\pi$
$953$	−1.31393	−0.0425625	−0.0212812	+	0.999774i	$0.506775\pi$
$954$	−1.00000	−0.0323762
$955$	−10.3594	−0.335221
$956$	−9.02154	−0.291777
$957$	1.13673	0.0367454
$958$	−42.1527	−1.36189
$959$	8.32530	0.268838
$960$	−0.912007	−0.0294349
$961$	−24.2767	−0.783118
$962$	20.8809	0.673227
$963$	10.0741	0.324634
$964$	−28.6918	−0.924101
$965$	−11.4738	−0.369356
$966$	25.0378	0.805579
$967$	1.48538	0.0477668	0.0238834	−	0.999715i	$-0.492397\pi$
$967$	1.48538	0.0477668	0.0238834	+	0.999715i	$0.492397\pi$
$968$	10.7691	0.346133
$969$	6.25232	0.200854
$970$	11.7611	0.377626
$971$	53.8651	1.72861	0.864306	−	0.502966i	$-0.167758\pi$
$971$	53.8651	1.72861	0.864306	+	0.502966i	$0.167758\pi$
$972$	−1.00000	−0.0320750
$973$	27.1389	0.870034
$974$	−23.7279	−0.760292
$975$	21.7715	0.697246
$976$	11.8597	0.379620
$977$	26.4315	0.845618	0.422809	−	0.906219i	$-0.361044\pi$
$977$	26.4315	0.845618	0.422809	+	0.906219i	$0.361044\pi$
$978$	18.7919	0.600900
$979$	−2.06507	−0.0660000
$980$	4.68232	0.149571
$981$	−2.26079	−0.0721815
$982$	−43.6165	−1.39186
$983$	−15.0022	−0.478496	−0.239248	−	0.970959i	$-0.576901\pi$
$983$	−15.0022	−0.478496	−0.239248	+	0.970959i	$0.576901\pi$
$984$	5.30220	0.169028
$985$	15.6029	0.497150
$986$	−14.7914	−0.471054
$987$	−5.05693	−0.160964
$988$	−5.22319	−0.166172
$989$	42.3113	1.34542
$990$	0.438218	0.0139275
$991$	54.9320	1.74497	0.872486	−	0.488639i	$-0.162506\pi$
$991$	54.9320	1.74497	0.872486	+	0.488639i	$0.162506\pi$
$992$	−2.59294	−0.0823259
$993$	−32.4227	−1.02890
$994$	−43.1089	−1.36733
$995$	6.48926	0.205723
$996$	7.68354	0.243462
$997$	−25.7525	−0.815589	−0.407794	−	0.913074i	$-0.633702\pi$
$997$	−25.7525	−0.815589	−0.407794	+	0.913074i	$0.633702\pi$
$998$	−20.5229	−0.649641
$999$	3.99773	0.126483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.z.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.z.1.7	✓	9	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.912007 q^{5} +1.00000 q^{6} +3.48340 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.912007 q^{5} +1.00000 q^{6} +3.48340 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.912007 q^{10} -0.480498 q^{11} -1.00000 q^{12} +5.22319 q^{13} -3.48340 q^{14} -0.912007 q^{15} +1.00000 q^{16} +6.25232 q^{17} -1.00000 q^{18} -1.00000 q^{19} +0.912007 q^{20} -3.48340 q^{21} +0.480498 q^{22} +7.18776 q^{23} +1.00000 q^{24} -4.16824 q^{25} -5.22319 q^{26} -1.00000 q^{27} +3.48340 q^{28} +2.36574 q^{29} +0.912007 q^{30} +2.59294 q^{31} -1.00000 q^{32} +0.480498 q^{33} -6.25232 q^{34} +3.17689 q^{35} +1.00000 q^{36} -3.99773 q^{37} +1.00000 q^{38} -5.22319 q^{39} -0.912007 q^{40} +5.30220 q^{41} +3.48340 q^{42} +5.88658 q^{43} -0.480498 q^{44} +0.912007 q^{45} -7.18776 q^{46} +1.45172 q^{47} -1.00000 q^{48} +5.13408 q^{49} +4.16824 q^{50} -6.25232 q^{51} +5.22319 q^{52} +1.00000 q^{53} +1.00000 q^{54} -0.438218 q^{55} -3.48340 q^{56} +1.00000 q^{57} -2.36574 q^{58} +12.9354 q^{59} -0.912007 q^{60} +11.8597 q^{61} -2.59294 q^{62} +3.48340 q^{63} +1.00000 q^{64} +4.76358 q^{65} -0.480498 q^{66} -10.5160 q^{67} +6.25232 q^{68} -7.18776 q^{69} -3.17689 q^{70} +12.3755 q^{71} -1.00000 q^{72} -10.7021 q^{73} +3.99773 q^{74} +4.16824 q^{75} -1.00000 q^{76} -1.67377 q^{77} +5.22319 q^{78} -15.0539 q^{79} +0.912007 q^{80} +1.00000 q^{81} -5.30220 q^{82} -7.68354 q^{83} -3.48340 q^{84} +5.70217 q^{85} -5.88658 q^{86} -2.36574 q^{87} +0.480498 q^{88} +4.29778 q^{89} -0.912007 q^{90} +18.1945 q^{91} +7.18776 q^{92} -2.59294 q^{93} -1.45172 q^{94} -0.912007 q^{95} +1.00000 q^{96} -12.8959 q^{97} -5.13408 q^{98} -0.480498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} - q^{5} + 9 q^{6} + 4 q^{7} - 9 q^{8} + 9 q^{9} + q^{10} + 12 q^{11} - 9 q^{12} - q^{13} - 4 q^{14} + q^{15} + 9 q^{16} + 12 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} - 4 q^{21} - 12 q^{22} + 11 q^{23} + 9 q^{24} + 10 q^{25} + q^{26} - 9 q^{27} + 4 q^{28} + 7 q^{29} - q^{30} - 12 q^{31} - 9 q^{32} - 12 q^{33} - 12 q^{34} + 15 q^{35} + 9 q^{36} - 9 q^{37} + 9 q^{38} + q^{39} + q^{40} - 4 q^{41} + 4 q^{42} + 23 q^{43} + 12 q^{44} - q^{45} - 11 q^{46} + 35 q^{47} - 9 q^{48} + 3 q^{49} - 10 q^{50} - 12 q^{51} - q^{52} + 9 q^{53} + 9 q^{54} + 3 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} + 14 q^{59} + q^{60} + 14 q^{61} + 12 q^{62} + 4 q^{63} + 9 q^{64} + 13 q^{65} + 12 q^{66} - 10 q^{67} + 12 q^{68} - 11 q^{69} - 15 q^{70} + 4 q^{71} - 9 q^{72} - 5 q^{73} + 9 q^{74} - 10 q^{75} - 9 q^{76} + 17 q^{77} - q^{78} - 14 q^{79} - q^{80} + 9 q^{81} + 4 q^{82} + 37 q^{83} - 4 q^{84} - 31 q^{85} - 23 q^{86} - 7 q^{87} - 12 q^{88} - 20 q^{89} + q^{90} - 12 q^{91} + 11 q^{92} + 12 q^{93} - 35 q^{94} + q^{95} + 9 q^{96} - 2 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 - q^5 + 9 * q^6 + 4 * q^7 - 9 * q^8 + 9 * q^9 + q^10 + 12 * q^11 - 9 * q^12 - q^13 - 4 * q^14 + q^15 + 9 * q^16 + 12 * q^17 - 9 * q^18 - 9 * q^19 - q^20 - 4 * q^21 - 12 * q^22 + 11 * q^23 + 9 * q^24 + 10 * q^25 + q^26 - 9 * q^27 + 4 * q^28 + 7 * q^29 - q^30 - 12 * q^31 - 9 * q^32 - 12 * q^33 - 12 * q^34 + 15 * q^35 + 9 * q^36 - 9 * q^37 + 9 * q^38 + q^39 + q^40 - 4 * q^41 + 4 * q^42 + 23 * q^43 + 12 * q^44 - q^45 - 11 * q^46 + 35 * q^47 - 9 * q^48 + 3 * q^49 - 10 * q^50 - 12 * q^51 - q^52 + 9 * q^53 + 9 * q^54 + 3 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 + 14 * q^59 + q^60 + 14 * q^61 + 12 * q^62 + 4 * q^63 + 9 * q^64 + 13 * q^65 + 12 * q^66 - 10 * q^67 + 12 * q^68 - 11 * q^69 - 15 * q^70 + 4 * q^71 - 9 * q^72 - 5 * q^73 + 9 * q^74 - 10 * q^75 - 9 * q^76 + 17 * q^77 - q^78 - 14 * q^79 - q^80 + 9 * q^81 + 4 * q^82 + 37 * q^83 - 4 * q^84 - 31 * q^85 - 23 * q^86 - 7 * q^87 - 12 * q^88 - 20 * q^89 + q^90 - 12 * q^91 + 11 * q^92 + 12 * q^93 - 35 * q^94 + q^95 + 9 * q^96 - 2 * q^97 - 3 * q^98 + 12 * q^99

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