LMFDB - Embedded newform 429.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(1,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, 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("429.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} +2.21432 q^{5} +0.311108 q^{6} +1.52543 q^{7} -1.21432 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} +2.21432 q^{5} +0.311108 q^{6} +1.52543 q^{7} -1.21432 q^{8} +1.00000 q^{9} +0.688892 q^{10} +1.00000 q^{11} -1.90321 q^{12} +1.00000 q^{13} +0.474572 q^{14} +2.21432 q^{15} +3.42864 q^{16} -1.73975 q^{17} +0.311108 q^{18} +4.28100 q^{19} -4.21432 q^{20} +1.52543 q^{21} +0.311108 q^{22} +0.474572 q^{23} -1.21432 q^{24} -0.0967881 q^{25} +0.311108 q^{26} +1.00000 q^{27} -2.90321 q^{28} +5.11753 q^{29} +0.688892 q^{30} -4.21432 q^{31} +3.49532 q^{32} +1.00000 q^{33} -0.541249 q^{34} +3.37778 q^{35} -1.90321 q^{36} +0.428639 q^{37} +1.33185 q^{38} +1.00000 q^{39} -2.68889 q^{40} +6.28100 q^{41} +0.474572 q^{42} -8.16839 q^{43} -1.90321 q^{44} +2.21432 q^{45} +0.147643 q^{46} +5.05086 q^{47} +3.42864 q^{48} -4.67307 q^{49} -0.0301115 q^{50} -1.73975 q^{51} -1.90321 q^{52} -14.0415 q^{53} +0.311108 q^{54} +2.21432 q^{55} -1.85236 q^{56} +4.28100 q^{57} +1.59210 q^{58} -1.67307 q^{59} -4.21432 q^{60} -5.80642 q^{61} -1.31111 q^{62} +1.52543 q^{63} -5.76986 q^{64} +2.21432 q^{65} +0.311108 q^{66} -6.02074 q^{67} +3.31111 q^{68} +0.474572 q^{69} +1.05086 q^{70} +5.18421 q^{71} -1.21432 q^{72} -8.08742 q^{73} +0.133353 q^{74} -0.0967881 q^{75} -8.14764 q^{76} +1.52543 q^{77} +0.311108 q^{78} +0.260253 q^{79} +7.59210 q^{80} +1.00000 q^{81} +1.95407 q^{82} -1.37778 q^{83} -2.90321 q^{84} -3.85236 q^{85} -2.54125 q^{86} +5.11753 q^{87} -1.21432 q^{88} -10.1541 q^{89} +0.688892 q^{90} +1.52543 q^{91} -0.903212 q^{92} -4.21432 q^{93} +1.57136 q^{94} +9.47949 q^{95} +3.49532 q^{96} +0.428639 q^{97} -1.45383 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + q^{4} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + q^4 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + q^{4} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} + 3 q^{13} + 8 q^{14} - 3 q^{16} + 8 q^{17} + q^{18} + 6 q^{19} - 6 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 3 q^{24} - 7 q^{25} + q^{26} + 3 q^{27} - 2 q^{28} + 2 q^{29} + 2 q^{30} - 6 q^{31} - 3 q^{32} + 3 q^{33} - 8 q^{34} + 10 q^{35} + q^{36} - 12 q^{37} - 16 q^{38} + 3 q^{39} - 8 q^{40} + 12 q^{41} + 8 q^{42} + 2 q^{43} + q^{44} - 6 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 7 q^{50} + 8 q^{51} + q^{52} - 2 q^{53} + q^{54} - 12 q^{56} + 6 q^{57} - 2 q^{58} + 8 q^{59} - 6 q^{60} - 4 q^{61} - 4 q^{62} - 2 q^{63} - 11 q^{64} + q^{66} + 2 q^{67} + 10 q^{68} + 8 q^{69} - 10 q^{70} + 2 q^{71} + 3 q^{72} - 4 q^{73} - 7 q^{75} - 18 q^{76} - 2 q^{77} + q^{78} + 14 q^{79} + 16 q^{80} + 3 q^{81} - 14 q^{82} - 4 q^{83} - 2 q^{84} - 18 q^{85} - 14 q^{86} + 2 q^{87} + 3 q^{88} - 10 q^{89} + 2 q^{90} - 2 q^{91} + 4 q^{92} - 6 q^{93} + 18 q^{94} + 2 q^{95} - 3 q^{96} - 12 q^{97} - 31 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + q^4 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 + q^12 + 3 * q^13 + 8 * q^14 - 3 * q^16 + 8 * q^17 + q^18 + 6 * q^19 - 6 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 3 * q^24 - 7 * q^25 + q^26 + 3 * q^27 - 2 * q^28 + 2 * q^29 + 2 * q^30 - 6 * q^31 - 3 * q^32 + 3 * q^33 - 8 * q^34 + 10 * q^35 + q^36 - 12 * q^37 - 16 * q^38 + 3 * q^39 - 8 * q^40 + 12 * q^41 + 8 * q^42 + 2 * q^43 + q^44 - 6 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 7 * q^50 + 8 * q^51 + q^52 - 2 * q^53 + q^54 - 12 * q^56 + 6 * q^57 - 2 * q^58 + 8 * q^59 - 6 * q^60 - 4 * q^61 - 4 * q^62 - 2 * q^63 - 11 * q^64 + q^66 + 2 * q^67 + 10 * q^68 + 8 * q^69 - 10 * q^70 + 2 * q^71 + 3 * q^72 - 4 * q^73 - 7 * q^75 - 18 * q^76 - 2 * q^77 + q^78 + 14 * q^79 + 16 * q^80 + 3 * q^81 - 14 * q^82 - 4 * q^83 - 2 * q^84 - 18 * q^85 - 14 * q^86 + 2 * q^87 + 3 * q^88 - 10 * q^89 + 2 * q^90 - 2 * q^91 + 4 * q^92 - 6 * q^93 + 18 * q^94 + 2 * q^95 - 3 * q^96 - 12 * q^97 - 31 * 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 $

$2$	0.311108	0.219986	0.109993	−	0.993932i	$-0.464917\pi$
$2$	0.311108	0.219986	0.109993	+	0.993932i	$0.464917\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90321	−0.951606
$5$	2.21432	0.990274	0.495137	−	0.868815i	$-0.335118\pi$
$5$	2.21432	0.990274	0.495137	+	0.868815i	$0.335118\pi$
$6$	0.311108	0.127009
$7$	1.52543	0.576557	0.288279	−	0.957547i	$-0.406917\pi$
$7$	1.52543	0.576557	0.288279	+	0.957547i	$0.406917\pi$
$8$	−1.21432	−0.429327
$9$	1.00000	0.333333
$10$	0.688892	0.217847
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.90321	−0.549410
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.474572	0.126835
$15$	2.21432	0.571735
$16$	3.42864	0.857160
$17$	−1.73975	−0.421951	−0.210975	−	0.977491i	$-0.567664\pi$
$17$	−1.73975	−0.421951	−0.210975	+	0.977491i	$0.567664\pi$
$18$	0.311108	0.0733288
$19$	4.28100	0.982128	0.491064	−	0.871124i	$-0.336608\pi$
$19$	4.28100	0.982128	0.491064	+	0.871124i	$0.336608\pi$
$20$	−4.21432	−0.942351
$21$	1.52543	0.332876
$22$	0.311108	0.0663284
$23$	0.474572	0.0989552	0.0494776	−	0.998775i	$-0.484244\pi$
$23$	0.474572	0.0989552	0.0494776	+	0.998775i	$0.484244\pi$
$24$	−1.21432	−0.247872
$25$	−0.0967881	−0.0193576
$26$	0.311108	0.0610133
$27$	1.00000	0.192450
$28$	−2.90321	−0.548655
$29$	5.11753	0.950302	0.475151	−	0.879904i	$-0.342393\pi$
$29$	5.11753	0.950302	0.475151	+	0.879904i	$0.342393\pi$
$30$	0.688892	0.125774
$31$	−4.21432	−0.756914	−0.378457	−	0.925619i	$-0.623545\pi$
$31$	−4.21432	−0.756914	−0.378457	+	0.925619i	$0.623545\pi$
$32$	3.49532	0.617890
$33$	1.00000	0.174078
$34$	−0.541249	−0.0928234
$35$	3.37778	0.570950
$36$	−1.90321	−0.317202
$37$	0.428639	0.0704679	0.0352339	−	0.999379i	$-0.488782\pi$
$37$	0.428639	0.0704679	0.0352339	+	0.999379i	$0.488782\pi$
$38$	1.33185	0.216055
$39$	1.00000	0.160128
$40$	−2.68889	−0.425151
$41$	6.28100	0.980927	0.490463	−	0.871462i	$-0.336828\pi$
$41$	6.28100	0.980927	0.490463	+	0.871462i	$0.336828\pi$
$42$	0.474572	0.0732281
$43$	−8.16839	−1.24567	−0.622834	−	0.782354i	$-0.714019\pi$
$43$	−8.16839	−1.24567	−0.622834	+	0.782354i	$0.714019\pi$
$44$	−1.90321	−0.286920
$45$	2.21432	0.330091
$46$	0.147643	0.0217688
$47$	5.05086	0.736743	0.368371	−	0.929679i	$-0.379915\pi$
$47$	5.05086	0.736743	0.368371	+	0.929679i	$0.379915\pi$
$48$	3.42864	0.494881
$49$	−4.67307	−0.667582
$50$	−0.0301115	−0.00425841
$51$	−1.73975	−0.243613
$52$	−1.90321	−0.263928
$53$	−14.0415	−1.92875	−0.964373	−	0.264545i	$-0.914778\pi$
$53$	−14.0415	−1.92875	−0.964373	+	0.264545i	$0.914778\pi$
$54$	0.311108	0.0423364
$55$	2.21432	0.298579
$56$	−1.85236	−0.247532
$57$	4.28100	0.567032
$58$	1.59210	0.209054
$59$	−1.67307	−0.217815	−0.108908	−	0.994052i	$-0.534735\pi$
$59$	−1.67307	−0.217815	−0.108908	+	0.994052i	$0.534735\pi$
$60$	−4.21432	−0.544066
$61$	−5.80642	−0.743436	−0.371718	−	0.928346i	$-0.621231\pi$
$61$	−5.80642	−0.743436	−0.371718	+	0.928346i	$0.621231\pi$
$62$	−1.31111	−0.166511
$63$	1.52543	0.192186
$64$	−5.76986	−0.721232
$65$	2.21432	0.274653
$66$	0.311108	0.0382947
$67$	−6.02074	−0.735551	−0.367775	−	0.929915i	$-0.619880\pi$
$67$	−6.02074	−0.735551	−0.367775	+	0.929915i	$0.619880\pi$
$68$	3.31111	0.401531
$69$	0.474572	0.0571318
$70$	1.05086	0.125601
$71$	5.18421	0.615252	0.307626	−	0.951507i	$-0.400465\pi$
$71$	5.18421	0.615252	0.307626	+	0.951507i	$0.400465\pi$
$72$	−1.21432	−0.143109
$73$	−8.08742	−0.946561	−0.473280	−	0.880912i	$-0.656930\pi$
$73$	−8.08742	−0.946561	−0.473280	+	0.880912i	$0.656930\pi$
$74$	0.133353	0.0155020
$75$	−0.0967881	−0.0111761
$76$	−8.14764	−0.934599
$77$	1.52543	0.173839
$78$	0.311108	0.0352260
$79$	0.260253	0.0292807	0.0146404	−	0.999893i	$-0.495340\pi$
$79$	0.260253	0.0292807	0.0146404	+	0.999893i	$0.495340\pi$
$80$	7.59210	0.848823
$81$	1.00000	0.111111
$82$	1.95407	0.215791
$83$	−1.37778	−0.151231	−0.0756157	−	0.997137i	$-0.524092\pi$
$83$	−1.37778	−0.151231	−0.0756157	+	0.997137i	$0.524092\pi$
$84$	−2.90321	−0.316766
$85$	−3.85236	−0.417847
$86$	−2.54125	−0.274030
$87$	5.11753	0.548657
$88$	−1.21432	−0.129447
$89$	−10.1541	−1.07633	−0.538166	−	0.842839i	$-0.680883\pi$
$89$	−10.1541	−1.07633	−0.538166	+	0.842839i	$0.680883\pi$
$90$	0.688892	0.0726156
$91$	1.52543	0.159908
$92$	−0.903212	−0.0941664
$93$	−4.21432	−0.437005
$94$	1.57136	0.162073
$95$	9.47949	0.972576
$96$	3.49532	0.356739
$97$	0.428639	0.0435217	0.0217609	−	0.999763i	$-0.493073\pi$
$97$	0.428639	0.0435217	0.0217609	+	0.999763i	$0.493073\pi$
$98$	−1.45383	−0.146859
$99$	1.00000	0.100504
$100$	0.184208	0.0184208
$101$	3.93332	0.391380	0.195690	−	0.980666i	$-0.437305\pi$
$101$	3.93332	0.391380	0.195690	+	0.980666i	$0.437305\pi$
$102$	−0.541249	−0.0535916
$103$	−13.8064	−1.36039	−0.680194	−	0.733032i	$-0.738104\pi$
$103$	−13.8064	−1.36039	−0.680194	+	0.733032i	$0.738104\pi$
$104$	−1.21432	−0.119074
$105$	3.37778	0.329638
$106$	−4.36842	−0.424298
$107$	9.67307	0.935131	0.467566	−	0.883958i	$-0.345131\pi$
$107$	9.67307	0.935131	0.467566	+	0.883958i	$0.345131\pi$
$108$	−1.90321	−0.183137
$109$	−17.6271	−1.68837	−0.844187	−	0.536049i	$-0.819916\pi$
$109$	−17.6271	−1.68837	−0.844187	+	0.536049i	$0.819916\pi$
$110$	0.688892	0.0656833
$111$	0.428639	0.0406847
$112$	5.23014	0.494202
$113$	13.4795	1.26804	0.634022	−	0.773315i	$-0.281403\pi$
$113$	13.4795	1.26804	0.634022	+	0.773315i	$0.281403\pi$
$114$	1.33185	0.124739
$115$	1.05086	0.0979927
$116$	−9.73975	−0.904313
$117$	1.00000	0.0924500
$118$	−0.520505	−0.0479164
$119$	−2.65386	−0.243279
$120$	−2.68889	−0.245461
$121$	1.00000	0.0909091
$122$	−1.80642	−0.163546
$123$	6.28100	0.566338
$124$	8.02074	0.720284
$125$	−11.2859	−1.00944
$126$	0.474572	0.0422783
$127$	20.2415	1.79614	0.898072	−	0.439848i	$-0.144968\pi$
$127$	20.2415	1.79614	0.898072	+	0.439848i	$0.144968\pi$
$128$	−8.78568	−0.776552
$129$	−8.16839	−0.719186
$130$	0.688892	0.0604198
$131$	8.29529	0.724763	0.362381	−	0.932030i	$-0.381964\pi$
$131$	8.29529	0.724763	0.362381	+	0.932030i	$0.381964\pi$
$132$	−1.90321	−0.165653
$133$	6.53035	0.566253
$134$	−1.87310	−0.161811
$135$	2.21432	0.190578
$136$	2.11261	0.181155
$137$	−14.7447	−1.25972	−0.629861	−	0.776708i	$-0.716888\pi$
$137$	−14.7447	−1.25972	−0.629861	+	0.776708i	$0.716888\pi$
$138$	0.147643	0.0125682
$139$	−9.05731	−0.768231	−0.384115	−	0.923285i	$-0.625494\pi$
$139$	−9.05731	−0.768231	−0.384115	+	0.923285i	$0.625494\pi$
$140$	−6.42864	−0.543319
$141$	5.05086	0.425359
$142$	1.61285	0.135347
$143$	1.00000	0.0836242
$144$	3.42864	0.285720
$145$	11.3319	0.941059
$146$	−2.51606	−0.208231
$147$	−4.67307	−0.385428
$148$	−0.815792	−0.0670577
$149$	−2.01429	−0.165017	−0.0825085	−	0.996590i	$-0.526293\pi$
$149$	−2.01429	−0.165017	−0.0825085	+	0.996590i	$0.526293\pi$
$150$	−0.0301115	−0.00245860
$151$	0.668149	0.0543732	0.0271866	−	0.999630i	$-0.491345\pi$
$151$	0.668149	0.0543732	0.0271866	+	0.999630i	$0.491345\pi$
$152$	−5.19850	−0.421654
$153$	−1.73975	−0.140650
$154$	0.474572	0.0382421
$155$	−9.33185	−0.749552
$156$	−1.90321	−0.152379
$157$	4.70964	0.375870	0.187935	−	0.982181i	$-0.439821\pi$
$157$	4.70964	0.375870	0.187935	+	0.982181i	$0.439821\pi$
$158$	0.0809666	0.00644136
$159$	−14.0415	−1.11356
$160$	7.73975	0.611881
$161$	0.723926	0.0570534
$162$	0.311108	0.0244429
$163$	−2.73483	−0.214208	−0.107104	−	0.994248i	$-0.534158\pi$
$163$	−2.73483	−0.214208	−0.107104	+	0.994248i	$0.534158\pi$
$164$	−11.9541	−0.933456
$165$	2.21432	0.172385
$166$	−0.428639	−0.0332689
$167$	−0.561993	−0.0434883	−0.0217441	−	0.999764i	$-0.506922\pi$
$167$	−0.561993	−0.0434883	−0.0217441	+	0.999764i	$0.506922\pi$
$168$	−1.85236	−0.142912
$169$	1.00000	0.0769231
$170$	−1.19850	−0.0919206
$171$	4.28100	0.327376
$172$	15.5462	1.18538
$173$	8.88247	0.675322	0.337661	−	0.941268i	$-0.390364\pi$
$173$	8.88247	0.675322	0.337661	+	0.941268i	$0.390364\pi$
$174$	1.59210	0.120697
$175$	−0.147643	−0.0111608
$176$	3.42864	0.258443
$177$	−1.67307	−0.125756
$178$	−3.15902	−0.236778
$179$	−4.51606	−0.337546	−0.168773	−	0.985655i	$-0.553981\pi$
$179$	−4.51606	−0.337546	−0.168773	+	0.985655i	$0.553981\pi$
$180$	−4.21432	−0.314117
$181$	−24.7096	−1.83665	−0.918326	−	0.395824i	$-0.870459\pi$
$181$	−24.7096	−1.83665	−0.918326	+	0.395824i	$0.870459\pi$
$182$	0.474572	0.0351776
$183$	−5.80642	−0.429223
$184$	−0.576283	−0.0424841
$185$	0.949145	0.0697825
$186$	−1.31111	−0.0961351
$187$	−1.73975	−0.127223
$188$	−9.61285	−0.701089
$189$	1.52543	0.110959
$190$	2.94914	0.213953
$191$	12.9906	0.939969	0.469985	−	0.882675i	$-0.344259\pi$
$191$	12.9906	0.939969	0.469985	+	0.882675i	$0.344259\pi$
$192$	−5.76986	−0.416404
$193$	15.0464	1.08306	0.541532	−	0.840680i	$-0.317844\pi$
$193$	15.0464	1.08306	0.541532	+	0.840680i	$0.317844\pi$
$194$	0.133353	0.00957419
$195$	2.21432	0.158571
$196$	8.89384	0.635275
$197$	15.8622	1.13014	0.565068	−	0.825045i	$-0.308850\pi$
$197$	15.8622	1.13014	0.565068	+	0.825045i	$0.308850\pi$
$198$	0.311108	0.0221095
$199$	13.4193	0.951267	0.475633	−	0.879644i	$-0.342219\pi$
$199$	13.4193	0.951267	0.475633	+	0.879644i	$0.342219\pi$
$200$	0.117532	0.00831074
$201$	−6.02074	−0.424671
$202$	1.22369	0.0860984
$203$	7.80642	0.547904
$204$	3.31111	0.231824
$205$	13.9081	0.971386
$206$	−4.29529	−0.299267
$207$	0.474572	0.0329851
$208$	3.42864	0.237733
$209$	4.28100	0.296123
$210$	1.05086	0.0725159
$211$	24.1684	1.66382	0.831910	−	0.554910i	$-0.187247\pi$
$211$	24.1684	1.66382	0.831910	+	0.554910i	$0.187247\pi$
$212$	26.7239	1.83541
$213$	5.18421	0.355216
$214$	3.00937	0.205716
$215$	−18.0874	−1.23355
$216$	−1.21432	−0.0826240
$217$	−6.42864	−0.436404
$218$	−5.48394	−0.371419
$219$	−8.08742	−0.546497
$220$	−4.21432	−0.284129
$221$	−1.73975	−0.117028
$222$	0.133353	0.00895007
$223$	−9.50024	−0.636183	−0.318092	−	0.948060i	$-0.603042\pi$
$223$	−9.50024	−0.636183	−0.318092	+	0.948060i	$0.603042\pi$
$224$	5.33185	0.356249
$225$	−0.0967881	−0.00645254
$226$	4.19358	0.278953
$227$	8.41435	0.558480	0.279240	−	0.960221i	$-0.409917\pi$
$227$	8.41435	0.558480	0.279240	+	0.960221i	$0.409917\pi$
$228$	−8.14764	−0.539591
$229$	29.0321	1.91850	0.959248	−	0.282565i	$-0.0911852\pi$
$229$	29.0321	1.91850	0.959248	+	0.282565i	$0.0911852\pi$
$230$	0.326929	0.0215571
$231$	1.52543	0.100366
$232$	−6.21432	−0.407990
$233$	12.3017	0.805914	0.402957	−	0.915219i	$-0.367982\pi$
$233$	12.3017	0.805914	0.402957	+	0.915219i	$0.367982\pi$
$234$	0.311108	0.0203378
$235$	11.1842	0.729577
$236$	3.18421	0.207274
$237$	0.260253	0.0169052
$238$	−0.825636	−0.0535180
$239$	21.5669	1.39505	0.697524	−	0.716562i	$-0.254285\pi$
$239$	21.5669	1.39505	0.697524	+	0.716562i	$0.254285\pi$
$240$	7.59210	0.490068
$241$	−25.0005	−1.61042	−0.805211	−	0.592988i	$-0.797948\pi$
$241$	−25.0005	−1.61042	−0.805211	+	0.592988i	$0.797948\pi$
$242$	0.311108	0.0199988
$243$	1.00000	0.0641500
$244$	11.0509	0.707459
$245$	−10.3477	−0.661089
$246$	1.95407	0.124587
$247$	4.28100	0.272393
$248$	5.11753	0.324964
$249$	−1.37778	−0.0873135
$250$	−3.51114	−0.222064
$251$	11.4795	0.724579	0.362290	−	0.932066i	$-0.381995\pi$
$251$	11.4795	0.724579	0.362290	+	0.932066i	$0.381995\pi$
$252$	−2.90321	−0.182885
$253$	0.474572	0.0298361
$254$	6.29729	0.395127
$255$	−3.85236	−0.241244
$256$	8.80642	0.550401
$257$	12.1017	0.754884	0.377442	−	0.926033i	$-0.376804\pi$
$257$	12.1017	0.754884	0.377442	+	0.926033i	$0.376804\pi$
$258$	−2.54125	−0.158211
$259$	0.653858	0.0406288
$260$	−4.21432	−0.261361
$261$	5.11753	0.316767
$262$	2.58073	0.159438
$263$	−19.6543	−1.21194	−0.605969	−	0.795488i	$-0.707215\pi$
$263$	−19.6543	−1.21194	−0.605969	+	0.795488i	$0.707215\pi$
$264$	−1.21432	−0.0747362
$265$	−31.0923	−1.90999
$266$	2.03164	0.124568
$267$	−10.1541	−0.621421
$268$	11.4588	0.699955
$269$	−4.62222	−0.281821	−0.140911	−	0.990022i	$-0.545003\pi$
$269$	−4.62222	−0.281821	−0.140911	+	0.990022i	$0.545003\pi$
$270$	0.688892	0.0419246
$271$	−7.37334	−0.447898	−0.223949	−	0.974601i	$-0.571895\pi$
$271$	−7.37334	−0.447898	−0.223949	+	0.974601i	$0.571895\pi$
$272$	−5.96497	−0.361679
$273$	1.52543	0.0923231
$274$	−4.58718	−0.277122
$275$	−0.0967881	−0.00583654
$276$	−0.903212	−0.0543670
$277$	24.0098	1.44261	0.721306	−	0.692617i	$-0.243542\pi$
$277$	24.0098	1.44261	0.721306	+	0.692617i	$0.243542\pi$
$278$	−2.81780	−0.169000
$279$	−4.21432	−0.252305
$280$	−4.10171	−0.245124
$281$	10.6178	0.633403	0.316702	−	0.948525i	$-0.397425\pi$
$281$	10.6178	0.633403	0.316702	+	0.948525i	$0.397425\pi$
$282$	1.57136	0.0935732
$283$	8.88247	0.528008	0.264004	−	0.964522i	$-0.414957\pi$
$283$	8.88247	0.528008	0.264004	+	0.964522i	$0.414957\pi$
$284$	−9.86665	−0.585478
$285$	9.47949	0.561517
$286$	0.311108	0.0183962
$287$	9.58120	0.565561
$288$	3.49532	0.205963
$289$	−13.9733	−0.821958
$290$	3.52543	0.207020
$291$	0.428639	0.0251273
$292$	15.3921	0.900753
$293$	−21.1985	−1.23843	−0.619215	−	0.785222i	$-0.712549\pi$
$293$	−21.1985	−1.23843	−0.619215	+	0.785222i	$0.712549\pi$
$294$	−1.45383	−0.0847890
$295$	−3.70471	−0.215697
$296$	−0.520505	−0.0302538
$297$	1.00000	0.0580259
$298$	−0.626661	−0.0363015
$299$	0.474572	0.0274452
$300$	0.184208	0.0106353
$301$	−12.4603	−0.718199
$302$	0.207866	0.0119614
$303$	3.93332	0.225964
$304$	14.6780	0.841841
$305$	−12.8573	−0.736206
$306$	−0.541249	−0.0309411
$307$	10.0874	0.575719	0.287860	−	0.957673i	$-0.407056\pi$
$307$	10.0874	0.575719	0.287860	+	0.957673i	$0.407056\pi$
$308$	−2.90321	−0.165426
$309$	−13.8064	−0.785420
$310$	−2.90321	−0.164891
$311$	17.0366	0.966055	0.483027	−	0.875605i	$-0.339537\pi$
$311$	17.0366	0.966055	0.483027	+	0.875605i	$0.339537\pi$
$312$	−1.21432	−0.0687473
$313$	−19.5986	−1.10778	−0.553888	−	0.832591i	$-0.686856\pi$
$313$	−19.5986	−1.10778	−0.553888	+	0.832591i	$0.686856\pi$
$314$	1.46520	0.0826863
$315$	3.37778	0.190317
$316$	−0.495316	−0.0278637
$317$	−31.8687	−1.78992	−0.894961	−	0.446144i	$-0.852797\pi$
$317$	−31.8687	−1.78992	−0.894961	+	0.446144i	$0.852797\pi$
$318$	−4.36842	−0.244969
$319$	5.11753	0.286527
$320$	−12.7763	−0.714218
$321$	9.67307	0.539898
$322$	0.225219	0.0125510
$323$	−7.44785	−0.414410
$324$	−1.90321	−0.105734
$325$	−0.0967881	−0.00536884
$326$	−0.850825	−0.0471229
$327$	−17.6271	−0.974783
$328$	−7.62714	−0.421138
$329$	7.70471	0.424775
$330$	0.688892	0.0379223
$331$	1.09033	0.0599302	0.0299651	−	0.999551i	$-0.490460\pi$
$331$	1.09033	0.0599302	0.0299651	+	0.999551i	$0.490460\pi$
$332$	2.62222	0.143913
$333$	0.428639	0.0234893
$334$	−0.174840	−0.00956683
$335$	−13.3319	−0.728397
$336$	5.23014	0.285328
$337$	−11.0825	−0.603702	−0.301851	−	0.953355i	$-0.597605\pi$
$337$	−11.0825	−0.603702	−0.301851	+	0.953355i	$0.597605\pi$
$338$	0.311108	0.0169220
$339$	13.4795	0.732106
$340$	7.33185	0.397625
$341$	−4.21432	−0.228218
$342$	1.33185	0.0720183
$343$	−17.8064	−0.961457
$344$	9.91903	0.534798
$345$	1.05086	0.0565761
$346$	2.76341	0.148562
$347$	−0.326929	−0.0175505	−0.00877524	−	0.999961i	$-0.502793\pi$
$347$	−0.326929	−0.0175505	−0.00877524	+	0.999961i	$0.502793\pi$
$348$	−9.73975	−0.522105
$349$	−3.93978	−0.210891	−0.105446	−	0.994425i	$-0.533627\pi$
$349$	−3.93978	−0.210891	−0.105446	+	0.994425i	$0.533627\pi$
$350$	−0.0459330	−0.00245522
$351$	1.00000	0.0533761
$352$	3.49532	0.186301
$353$	−36.7862	−1.95793	−0.978965	−	0.204029i	$-0.934596\pi$
$353$	−36.7862	−1.95793	−0.978965	+	0.204029i	$0.934596\pi$
$354$	−0.520505	−0.0276645
$355$	11.4795	0.609268
$356$	19.3254	1.02424
$357$	−2.65386	−0.140457
$358$	−1.40498	−0.0742556
$359$	−5.48394	−0.289431	−0.144716	−	0.989473i	$-0.546227\pi$
$359$	−5.48394	−0.289431	−0.144716	+	0.989473i	$0.546227\pi$
$360$	−2.68889	−0.141717
$361$	−0.673071	−0.0354248
$362$	−7.68736	−0.404039
$363$	1.00000	0.0524864
$364$	−2.90321	−0.152170
$365$	−17.9081	−0.937355
$366$	−1.80642	−0.0944233
$367$	5.28592	0.275923	0.137961	−	0.990438i	$-0.455945\pi$
$367$	5.28592	0.275923	0.137961	+	0.990438i	$0.455945\pi$
$368$	1.62714	0.0848204
$369$	6.28100	0.326976
$370$	0.295286	0.0153512
$371$	−21.4193	−1.11203
$372$	8.02074	0.415856
$373$	−13.5714	−0.702698	−0.351349	−	0.936244i	$-0.614277\pi$
$373$	−13.5714	−0.702698	−0.351349	+	0.936244i	$0.614277\pi$
$374$	−0.541249	−0.0279873
$375$	−11.2859	−0.582802
$376$	−6.13335	−0.316304
$377$	5.11753	0.263566
$378$	0.474572	0.0244094
$379$	0.836535	0.0429699	0.0214850	−	0.999769i	$-0.493161\pi$
$379$	0.836535	0.0429699	0.0214850	+	0.999769i	$0.493161\pi$
$380$	−18.0415	−0.925509
$381$	20.2415	1.03700
$382$	4.04149	0.206780
$383$	−12.1334	−0.619985	−0.309993	−	0.950739i	$-0.600327\pi$
$383$	−12.1334	−0.619985	−0.309993	+	0.950739i	$0.600327\pi$
$384$	−8.78568	−0.448342
$385$	3.37778	0.172148
$386$	4.68106	0.238259
$387$	−8.16839	−0.415222
$388$	−0.815792	−0.0414156
$389$	−20.9175	−1.06056	−0.530280	−	0.847823i	$-0.677913\pi$
$389$	−20.9175	−1.06056	−0.530280	+	0.847823i	$0.677913\pi$
$390$	0.688892	0.0348834
$391$	−0.825636	−0.0417542
$392$	5.67460	0.286611
$393$	8.29529	0.418442
$394$	4.93485	0.248614
$395$	0.576283	0.0289959
$396$	−1.90321	−0.0956400
$397$	3.45091	0.173196	0.0865982	−	0.996243i	$-0.472400\pi$
$397$	3.45091	0.173196	0.0865982	+	0.996243i	$0.472400\pi$
$398$	4.17484	0.209266
$399$	6.53035	0.326926
$400$	−0.331851	−0.0165926
$401$	38.1639	1.90582	0.952908	−	0.303259i	$-0.0980748\pi$
$401$	38.1639	1.90582	0.952908	+	0.303259i	$0.0980748\pi$
$402$	−1.87310	−0.0934218
$403$	−4.21432	−0.209930
$404$	−7.48595	−0.372440
$405$	2.21432	0.110030
$406$	2.42864	0.120531
$407$	0.428639	0.0212469
$408$	2.11261	0.104590
$409$	38.0973	1.88379	0.941894	−	0.335910i	$-0.109044\pi$
$409$	38.0973	1.88379	0.941894	+	0.335910i	$0.109044\pi$
$410$	4.32693	0.213692
$411$	−14.7447	−0.727301
$412$	26.2766	1.29455
$413$	−2.55215	−0.125583
$414$	0.147643	0.00725627
$415$	−3.05086	−0.149761
$416$	3.49532	0.171372
$417$	−9.05731	−0.443538
$418$	1.33185	0.0651430
$419$	9.73191	0.475435	0.237717	−	0.971334i	$-0.423601\pi$
$419$	9.73191	0.475435	0.237717	+	0.971334i	$0.423601\pi$
$420$	−6.42864	−0.313685
$421$	−25.0509	−1.22090	−0.610452	−	0.792053i	$-0.709012\pi$
$421$	−25.0509	−1.22090	−0.610452	+	0.792053i	$0.709012\pi$
$422$	7.51897	0.366018
$423$	5.05086	0.245581
$424$	17.0509	0.828063
$425$	0.168387	0.00816796
$426$	1.61285	0.0781427
$427$	−8.85728	−0.428634
$428$	−18.4099	−0.889876
$429$	1.00000	0.0482805
$430$	−5.62714	−0.271365
$431$	−23.2543	−1.12012	−0.560060	−	0.828452i	$-0.689222\pi$
$431$	−23.2543	−1.12012	−0.560060	+	0.828452i	$0.689222\pi$
$432$	3.42864	0.164960
$433$	−20.1017	−0.966027	−0.483013	−	0.875613i	$-0.660458\pi$
$433$	−20.1017	−0.966027	−0.483013	+	0.875613i	$0.660458\pi$
$434$	−2.00000	−0.0960031
$435$	11.3319	0.543321
$436$	33.5482	1.60667
$437$	2.03164	0.0971867
$438$	−2.51606	−0.120222
$439$	32.1180	1.53291	0.766454	−	0.642299i	$-0.222019\pi$
$439$	32.1180	1.53291	0.766454	+	0.642299i	$0.222019\pi$
$440$	−2.68889	−0.128188
$441$	−4.67307	−0.222527
$442$	−0.541249	−0.0257446
$443$	30.8385	1.46518	0.732592	−	0.680668i	$-0.238311\pi$
$443$	30.8385	1.46518	0.732592	+	0.680668i	$0.238311\pi$
$444$	−0.815792	−0.0387158
$445$	−22.4844	−1.06586
$446$	−2.95560	−0.139952
$447$	−2.01429	−0.0952727
$448$	−8.80150	−0.415832
$449$	−19.3254	−0.912022	−0.456011	−	0.889974i	$-0.650722\pi$
$449$	−19.3254	−0.912022	−0.456011	+	0.889974i	$0.650722\pi$
$450$	−0.0301115	−0.00141947
$451$	6.28100	0.295761
$452$	−25.6543	−1.20668
$453$	0.668149	0.0313924
$454$	2.61777	0.122858
$455$	3.37778	0.158353
$456$	−5.19850	−0.243442
$457$	−8.58073	−0.401390	−0.200695	−	0.979654i	$-0.564320\pi$
$457$	−8.58073	−0.401390	−0.200695	+	0.979654i	$0.564320\pi$
$458$	9.03212	0.422043
$459$	−1.73975	−0.0812045
$460$	−2.00000	−0.0932505
$461$	−4.94470	−0.230298	−0.115149	−	0.993348i	$-0.536734\pi$
$461$	−4.94470	−0.230298	−0.115149	+	0.993348i	$0.536734\pi$
$462$	0.474572	0.0220791
$463$	19.9289	0.926173	0.463087	−	0.886313i	$-0.346742\pi$
$463$	19.9289	0.926173	0.463087	+	0.886313i	$0.346742\pi$
$464$	17.5462	0.814561
$465$	−9.33185	−0.432754
$466$	3.82717	0.177290
$467$	18.5763	0.859608	0.429804	−	0.902922i	$-0.358583\pi$
$467$	18.5763	0.859608	0.429804	+	0.902922i	$0.358583\pi$
$468$	−1.90321	−0.0879760
$469$	−9.18421	−0.424087
$470$	3.47949	0.160497
$471$	4.70964	0.217009
$472$	2.03164	0.0935139
$473$	−8.16839	−0.375583
$474$	0.0809666	0.00371892
$475$	−0.414349	−0.0190117
$476$	5.05086	0.231506
$477$	−14.0415	−0.642916
$478$	6.70964	0.306892
$479$	−1.09679	−0.0501135	−0.0250568	−	0.999686i	$-0.507977\pi$
$479$	−1.09679	−0.0501135	−0.0250568	+	0.999686i	$0.507977\pi$
$480$	7.73975	0.353270
$481$	0.428639	0.0195443
$482$	−7.77784	−0.354271
$483$	0.723926	0.0329398
$484$	−1.90321	−0.0865096
$485$	0.949145	0.0430984
$486$	0.311108	0.0141121
$487$	−28.6113	−1.29650	−0.648251	−	0.761427i	$-0.724499\pi$
$487$	−28.6113	−1.29650	−0.648251	+	0.761427i	$0.724499\pi$
$488$	7.05086	0.319177
$489$	−2.73483	−0.123673
$490$	−3.21924	−0.145431
$491$	−19.4608	−0.878252	−0.439126	−	0.898426i	$-0.644712\pi$
$491$	−19.4608	−0.878252	−0.439126	+	0.898426i	$0.644712\pi$
$492$	−11.9541	−0.538931
$493$	−8.90321	−0.400980
$494$	1.33185	0.0599228
$495$	2.21432	0.0995263
$496$	−14.4494	−0.648796
$497$	7.90813	0.354728
$498$	−0.428639	−0.0192078
$499$	−0.601472	−0.0269256	−0.0134628	−	0.999909i	$-0.504285\pi$
$499$	−0.601472	−0.0269256	−0.0134628	+	0.999909i	$0.504285\pi$
$500$	21.4795	0.960592
$501$	−0.561993	−0.0251080
$502$	3.57136	0.159398
$503$	8.69535	0.387706	0.193853	−	0.981031i	$-0.437901\pi$
$503$	8.69535	0.387706	0.193853	+	0.981031i	$0.437901\pi$
$504$	−1.85236	−0.0825105
$505$	8.70964	0.387574
$506$	0.147643	0.00656354
$507$	1.00000	0.0444116
$508$	−38.5239	−1.70922
$509$	−3.94761	−0.174975	−0.0874874	−	0.996166i	$-0.527884\pi$
$509$	−3.94761	−0.174975	−0.0874874	+	0.996166i	$0.527884\pi$
$510$	−1.19850	−0.0530704
$511$	−12.3368	−0.545747
$512$	20.3111	0.897633
$513$	4.28100	0.189011
$514$	3.76494	0.166064
$515$	−30.5718	−1.34716
$516$	15.5462	0.684382
$517$	5.05086	0.222136
$518$	0.203420	0.00893778
$519$	8.88247	0.389897
$520$	−2.68889	−0.117916
$521$	22.4701	0.984434	0.492217	−	0.870472i	$-0.336187\pi$
$521$	22.4701	0.984434	0.492217	+	0.870472i	$0.336187\pi$
$522$	1.59210	0.0696845
$523$	−21.4257	−0.936882	−0.468441	−	0.883495i	$-0.655184\pi$
$523$	−21.4257	−0.936882	−0.468441	+	0.883495i	$0.655184\pi$
$524$	−15.7877	−0.689688
$525$	−0.147643	−0.00644368
$526$	−6.11462	−0.266610
$527$	7.33185	0.319380
$528$	3.42864	0.149212
$529$	−22.7748	−0.990208
$530$	−9.67307	−0.420171
$531$	−1.67307	−0.0726051
$532$	−12.4286	−0.538850
$533$	6.28100	0.272060
$534$	−3.15902	−0.136704
$535$	21.4193	0.926036
$536$	7.31111	0.315792
$537$	−4.51606	−0.194882
$538$	−1.43801	−0.0619969
$539$	−4.67307	−0.201283
$540$	−4.21432	−0.181355
$541$	−26.6735	−1.14679	−0.573393	−	0.819281i	$-0.694373\pi$
$541$	−26.6735	−1.14679	−0.573393	+	0.819281i	$0.694373\pi$
$542$	−2.29390	−0.0985316
$543$	−24.7096	−1.06039
$544$	−6.08097	−0.260719
$545$	−39.0321	−1.67195
$546$	0.474572	0.0203098
$547$	−16.1497	−0.690509	−0.345255	−	0.938509i	$-0.612207\pi$
$547$	−16.1497	−0.690509	−0.345255	+	0.938509i	$0.612207\pi$
$548$	28.0622	1.19876
$549$	−5.80642	−0.247812
$550$	−0.0301115	−0.00128396
$551$	21.9081	0.933318
$552$	−0.576283	−0.0245282
$553$	0.396997	0.0168820
$554$	7.46965	0.317355
$555$	0.949145	0.0402890
$556$	17.2380	0.731053
$557$	−25.2400	−1.06945	−0.534726	−	0.845025i	$-0.679585\pi$
$557$	−25.2400	−1.06945	−0.534726	+	0.845025i	$0.679585\pi$
$558$	−1.31111	−0.0555036
$559$	−8.16839	−0.345486
$560$	11.5812	0.489395
$561$	−1.73975	−0.0734522
$562$	3.30327	0.139340
$563$	−8.37826	−0.353102	−0.176551	−	0.984292i	$-0.556494\pi$
$563$	−8.37826	−0.353102	−0.176551	+	0.984292i	$0.556494\pi$
$564$	−9.61285	−0.404774
$565$	29.8479	1.25571
$566$	2.76341	0.116155
$567$	1.52543	0.0640619
$568$	−6.29529	−0.264144
$569$	37.9432	1.59066	0.795330	−	0.606176i	$-0.207297\pi$
$569$	37.9432	1.59066	0.795330	+	0.606176i	$0.207297\pi$
$570$	2.94914	0.123526
$571$	30.1782	1.26292	0.631460	−	0.775409i	$-0.282456\pi$
$571$	30.1782	1.26292	0.631460	+	0.775409i	$0.282456\pi$
$572$	−1.90321	−0.0795773
$573$	12.9906	0.542691
$574$	2.98079	0.124416
$575$	−0.0459330	−0.00191554
$576$	−5.76986	−0.240411
$577$	−24.1936	−1.00719	−0.503596	−	0.863939i	$-0.667990\pi$
$577$	−24.1936	−1.00719	−0.503596	+	0.863939i	$0.667990\pi$
$578$	−4.34720	−0.180820
$579$	15.0464	0.625307
$580$	−21.5669	−0.895517
$581$	−2.10171	−0.0871936
$582$	0.133353	0.00552766
$583$	−14.0415	−0.581539
$584$	9.82071	0.406384
$585$	2.21432	0.0915509
$586$	−6.59502	−0.272438
$587$	−30.7971	−1.27113	−0.635565	−	0.772047i	$-0.719233\pi$
$587$	−30.7971	−1.27113	−0.635565	+	0.772047i	$0.719233\pi$
$588$	8.89384	0.366776
$589$	−18.0415	−0.743387
$590$	−1.15257	−0.0474504
$591$	15.8622	0.652484
$592$	1.46965	0.0604023
$593$	14.7382	0.605226	0.302613	−	0.953114i	$-0.402141\pi$
$593$	14.7382	0.605226	0.302613	+	0.953114i	$0.402141\pi$
$594$	0.311108	0.0127649
$595$	−5.87649	−0.240913
$596$	3.83362	0.157031
$597$	13.4193	0.549214
$598$	0.147643	0.00603758
$599$	11.5999	0.473961	0.236980	−	0.971514i	$-0.423842\pi$
$599$	11.5999	0.473961	0.236980	+	0.971514i	$0.423842\pi$
$600$	0.117532	0.00479821
$601$	27.3274	1.11471	0.557354	−	0.830275i	$-0.311817\pi$
$601$	27.3274	1.11471	0.557354	+	0.830275i	$0.311817\pi$
$602$	−3.87649	−0.157994
$603$	−6.02074	−0.245184
$604$	−1.27163	−0.0517418
$605$	2.21432	0.0900249
$606$	1.22369	0.0497089
$607$	0.0952567	0.00386635	0.00193318	−	0.999998i	$-0.499385\pi$
$607$	0.0952567	0.00386635	0.00193318	+	0.999998i	$0.499385\pi$
$608$	14.9634	0.606847
$609$	7.80642	0.316332
$610$	−4.00000	−0.161955
$611$	5.05086	0.204336
$612$	3.31111	0.133844
$613$	33.3230	1.34590	0.672951	−	0.739687i	$-0.265027\pi$
$613$	33.3230	1.34590	0.672951	+	0.739687i	$0.265027\pi$
$614$	3.13828	0.126650
$615$	13.9081	0.560830
$616$	−1.85236	−0.0746336
$617$	41.7353	1.68020	0.840100	−	0.542432i	$-0.182496\pi$
$617$	41.7353	1.68020	0.840100	+	0.542432i	$0.182496\pi$
$618$	−4.29529	−0.172782
$619$	29.8687	1.20052	0.600261	−	0.799804i	$-0.295063\pi$
$619$	29.8687	1.20052	0.600261	+	0.799804i	$0.295063\pi$
$620$	17.7605	0.713278
$621$	0.474572	0.0190439
$622$	5.30021	0.212519
$623$	−15.4893	−0.620567
$624$	3.42864	0.137255
$625$	−24.5067	−0.980268
$626$	−6.09726	−0.243696
$627$	4.28100	0.170967
$628$	−8.96343	−0.357680
$629$	−0.745724	−0.0297340
$630$	1.05086	0.0418671
$631$	12.3160	0.490293	0.245147	−	0.969486i	$-0.421164\pi$
$631$	12.3160	0.490293	0.245147	+	0.969486i	$0.421164\pi$
$632$	−0.316030	−0.0125710
$633$	24.1684	0.960607
$634$	−9.91459	−0.393759
$635$	44.8212	1.77867
$636$	26.7239	1.05967
$637$	−4.67307	−0.185154
$638$	1.59210	0.0630320
$639$	5.18421	0.205084
$640$	−19.4543	−0.768999
$641$	44.0928	1.74156	0.870781	−	0.491671i	$-0.163614\pi$
$641$	44.0928	1.74156	0.870781	+	0.491671i	$0.163614\pi$
$642$	3.00937	0.118770
$643$	32.1225	1.26679	0.633393	−	0.773830i	$-0.281662\pi$
$643$	32.1225	1.26679	0.633393	+	0.773830i	$0.281662\pi$
$644$	−1.37778	−0.0542923
$645$	−18.0874	−0.712191
$646$	−2.31708	−0.0911645
$647$	7.47949	0.294049	0.147025	−	0.989133i	$-0.453030\pi$
$647$	7.47949	0.294049	0.147025	+	0.989133i	$0.453030\pi$
$648$	−1.21432	−0.0477030
$649$	−1.67307	−0.0656738
$650$	−0.0301115	−0.00118107
$651$	−6.42864	−0.251958
$652$	5.20495	0.203842
$653$	41.3087	1.61653	0.808267	−	0.588817i	$-0.200406\pi$
$653$	41.3087	1.61653	0.808267	+	0.588817i	$0.200406\pi$
$654$	−5.48394	−0.214439
$655$	18.3684	0.717713
$656$	21.5353	0.840811
$657$	−8.08742	−0.315520
$658$	2.39700	0.0934447
$659$	−12.6637	−0.493308	−0.246654	−	0.969104i	$-0.579331\pi$
$659$	−12.6637	−0.493308	−0.246654	+	0.969104i	$0.579331\pi$
$660$	−4.21432	−0.164042
$661$	13.5999	0.528976	0.264488	−	0.964389i	$-0.414797\pi$
$661$	13.5999	0.528976	0.264488	+	0.964389i	$0.414797\pi$
$662$	0.339212	0.0131838
$663$	−1.73975	−0.0675662
$664$	1.67307	0.0649277
$665$	14.4603	0.560746
$666$	0.133353	0.00516733
$667$	2.42864	0.0940373
$668$	1.06959	0.0413837
$669$	−9.50024	−0.367300
$670$	−4.14764	−0.160237
$671$	−5.80642	−0.224155
$672$	5.33185	0.205681
$673$	−12.9621	−0.499650	−0.249825	−	0.968291i	$-0.580373\pi$
$673$	−12.9621	−0.499650	−0.249825	+	0.968291i	$0.580373\pi$
$674$	−3.44785	−0.132806
$675$	−0.0967881	−0.00372537
$676$	−1.90321	−0.0732005
$677$	−19.0988	−0.734026	−0.367013	−	0.930216i	$-0.619620\pi$
$677$	−19.0988	−0.734026	−0.367013	+	0.930216i	$0.619620\pi$
$678$	4.19358	0.161053
$679$	0.653858	0.0250928
$680$	4.67799	0.179393
$681$	8.41435	0.322439
$682$	−1.31111	−0.0502049
$683$	47.0450	1.80013	0.900064	−	0.435758i	$-0.143520\pi$
$683$	47.0450	1.80013	0.900064	+	0.435758i	$0.143520\pi$
$684$	−8.14764	−0.311533
$685$	−32.6494	−1.24747
$686$	−5.53972	−0.211507
$687$	29.0321	1.10764
$688$	−28.0065	−1.06774
$689$	−14.0415	−0.534938
$690$	0.326929	0.0124460
$691$	44.5827	1.69601	0.848004	−	0.529990i	$-0.177804\pi$
$691$	44.5827	1.69601	0.848004	+	0.529990i	$0.177804\pi$
$692$	−16.9052	−0.642640
$693$	1.52543	0.0579462
$694$	−0.101710	−0.00386087
$695$	−20.0558	−0.760759
$696$	−6.21432	−0.235553
$697$	−10.9273	−0.413903
$698$	−1.22570	−0.0463933
$699$	12.3017	0.465295
$700$	0.280996	0.0106207
$701$	43.3624	1.63778	0.818888	−	0.573953i	$-0.194591\pi$
$701$	43.3624	1.63778	0.818888	+	0.573953i	$0.194591\pi$
$702$	0.311108	0.0117420
$703$	1.83500	0.0692085
$704$	−5.76986	−0.217460
$705$	11.1842	0.421222
$706$	−11.4445	−0.430718
$707$	6.00000	0.225653
$708$	3.18421	0.119670
$709$	−3.34614	−0.125667	−0.0628335	−	0.998024i	$-0.520014\pi$
$709$	−3.34614	−0.125667	−0.0628335	+	0.998024i	$0.520014\pi$
$710$	3.57136	0.134031
$711$	0.260253	0.00976024
$712$	12.3303	0.462098
$713$	−2.00000	−0.0749006
$714$	−0.825636	−0.0308987
$715$	2.21432	0.0828109
$716$	8.59502	0.321211
$717$	21.5669	0.805431
$718$	−1.70610	−0.0636710
$719$	−45.3274	−1.69043	−0.845213	−	0.534429i	$-0.820527\pi$
$719$	−45.3274	−1.69043	−0.845213	+	0.534429i	$0.820527\pi$
$720$	7.59210	0.282941
$721$	−21.0607	−0.784341
$722$	−0.209398	−0.00779297
$723$	−25.0005	−0.929778
$724$	47.0277	1.74777
$725$	−0.495316	−0.0183956
$726$	0.311108	0.0115463
$727$	−24.2163	−0.898134	−0.449067	−	0.893498i	$-0.648244\pi$
$727$	−24.2163	−0.898134	−0.449067	+	0.893498i	$0.648244\pi$
$728$	−1.85236	−0.0686529
$729$	1.00000	0.0370370
$730$	−5.57136	−0.206205
$731$	14.2109	0.525610
$732$	11.0509	0.408451
$733$	−31.9037	−1.17839	−0.589195	−	0.807991i	$-0.700555\pi$
$733$	−31.9037	−1.17839	−0.589195	+	0.807991i	$0.700555\pi$
$734$	1.64449	0.0606993
$735$	−10.3477	−0.381680
$736$	1.65878	0.0611435
$737$	−6.02074	−0.221777
$738$	1.95407	0.0719302
$739$	44.3926	1.63301	0.816503	−	0.577341i	$-0.195910\pi$
$739$	44.3926	1.63301	0.816503	+	0.577341i	$0.195910\pi$
$740$	−1.80642	−0.0664055
$741$	4.28100	0.157266
$742$	−6.66370	−0.244632
$743$	−52.2449	−1.91668	−0.958340	−	0.285630i	$-0.907797\pi$
$743$	−52.2449	−1.91668	−0.958340	+	0.285630i	$0.907797\pi$
$744$	5.11753	0.187618
$745$	−4.46028	−0.163412
$746$	−4.22216	−0.154584
$747$	−1.37778	−0.0504105
$748$	3.31111	0.121066
$749$	14.7556	0.539157
$750$	−3.51114	−0.128209
$751$	−9.81933	−0.358312	−0.179156	−	0.983821i	$-0.557337\pi$
$751$	−9.81933	−0.358312	−0.179156	+	0.983821i	$0.557337\pi$
$752$	17.3176	0.631506
$753$	11.4795	0.418336
$754$	1.59210	0.0579810
$755$	1.47949	0.0538443
$756$	−2.90321	−0.105589
$757$	−22.5990	−0.821376	−0.410688	−	0.911776i	$-0.634711\pi$
$757$	−22.5990	−0.821376	−0.410688	+	0.911776i	$0.634711\pi$
$758$	0.260253	0.00945280
$759$	0.474572	0.0172259
$760$	−11.5111	−0.417553
$761$	0.0745132	0.00270110	0.00135055	−	0.999999i	$-0.499570\pi$
$761$	0.0745132	0.00270110	0.00135055	+	0.999999i	$0.499570\pi$
$762$	6.29729	0.228127
$763$	−26.8889	−0.973444
$764$	−24.7239	−0.894480
$765$	−3.85236	−0.139282
$766$	−3.77478	−0.136388
$767$	−1.67307	−0.0604111
$768$	8.80642	0.317774
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	1.05086	0.0378702
$771$	12.1017	0.435832
$772$	−28.6365	−1.03065
$773$	−2.66170	−0.0957345	−0.0478673	−	0.998854i	$-0.515242\pi$
$773$	−2.66170	−0.0957345	−0.0478673	+	0.998854i	$0.515242\pi$
$774$	−2.54125	−0.0913433
$775$	0.407896	0.0146521
$776$	−0.520505	−0.0186851
$777$	0.653858	0.0234570
$778$	−6.50760	−0.233309
$779$	26.8889	0.963396
$780$	−4.21432	−0.150897
$781$	5.18421	0.185506
$782$	−0.256862	−0.00918536
$783$	5.11753	0.182886
$784$	−16.0223	−0.572224
$785$	10.4286	0.372214
$786$	2.58073	0.0920515
$787$	28.5763	1.01863	0.509317	−	0.860579i	$-0.329898\pi$
$787$	28.5763	1.01863	0.509317	+	0.860579i	$0.329898\pi$
$788$	−30.1891	−1.07544
$789$	−19.6543	−0.699713
$790$	0.179286	0.00637871
$791$	20.5620	0.731100
$792$	−1.21432	−0.0431490
$793$	−5.80642	−0.206192
$794$	1.07361	0.0381009
$795$	−31.0923	−1.10273
$796$	−25.5397	−0.905231
$797$	−27.6860	−0.980688	−0.490344	−	0.871529i	$-0.663129\pi$
$797$	−27.6860	−0.980688	−0.490344	+	0.871529i	$0.663129\pi$
$798$	2.03164	0.0719194
$799$	−8.78721	−0.310869
$800$	−0.338305	−0.0119609
$801$	−10.1541	−0.358777
$802$	11.8731	0.419254
$803$	−8.08742	−0.285399
$804$	11.4588	0.404119
$805$	1.60300	0.0564984
$806$	−1.31111	−0.0461818
$807$	−4.62222	−0.162710
$808$	−4.77631	−0.168030
$809$	−43.7911	−1.53961	−0.769806	−	0.638278i	$-0.779647\pi$
$809$	−43.7911	−1.53961	−0.769806	+	0.638278i	$0.779647\pi$
$810$	0.688892	0.0242052
$811$	42.4371	1.49017	0.745084	−	0.666971i	$-0.232409\pi$
$811$	42.4371	1.49017	0.745084	+	0.666971i	$0.232409\pi$
$812$	−14.8573	−0.521388
$813$	−7.37334	−0.258594
$814$	0.133353	0.00467402
$815$	−6.05578	−0.212125
$816$	−5.96497	−0.208816
$817$	−34.9688	−1.22340
$818$	11.8524	0.414408
$819$	1.52543	0.0533028
$820$	−26.4701	−0.924377
$821$	−44.5705	−1.55552	−0.777760	−	0.628562i	$-0.783644\pi$
$821$	−44.5705	−1.55552	−0.777760	+	0.628562i	$0.783644\pi$
$822$	−4.58718	−0.159996
$823$	−19.8666	−0.692508	−0.346254	−	0.938141i	$-0.612546\pi$
$823$	−19.8666	−0.692508	−0.346254	+	0.938141i	$0.612546\pi$
$824$	16.7654	0.584051
$825$	−0.0967881	−0.00336973
$826$	−0.793993	−0.0276266
$827$	−23.3822	−0.813080	−0.406540	−	0.913633i	$-0.633265\pi$
$827$	−23.3822	−0.813080	−0.406540	+	0.913633i	$0.633265\pi$
$828$	−0.903212	−0.0313888
$829$	9.52987	0.330986	0.165493	−	0.986211i	$-0.447078\pi$
$829$	9.52987	0.330986	0.165493	+	0.986211i	$0.447078\pi$
$830$	−0.949145	−0.0329453
$831$	24.0098	0.832892
$832$	−5.76986	−0.200034
$833$	8.12996	0.281686
$834$	−2.81780	−0.0975724
$835$	−1.24443	−0.0430653
$836$	−8.14764	−0.281792
$837$	−4.21432	−0.145668
$838$	3.02767	0.104589
$839$	−6.58073	−0.227192	−0.113596	−	0.993527i	$-0.536237\pi$
$839$	−6.58073	−0.227192	−0.113596	+	0.993527i	$0.536237\pi$
$840$	−4.10171	−0.141522
$841$	−2.81087	−0.0969265
$842$	−7.79352	−0.268582
$843$	10.6178	0.365695
$844$	−45.9976	−1.58330
$845$	2.21432	0.0761749
$846$	1.57136	0.0540245
$847$	1.52543	0.0524143
$848$	−48.1432	−1.65324
$849$	8.88247	0.304846
$850$	0.0523864	0.00179684
$851$	0.203420	0.00697316
$852$	−9.86665	−0.338026
$853$	0.726989	0.0248916	0.0124458	−	0.999923i	$-0.496038\pi$
$853$	0.726989	0.0248916	0.0124458	+	0.999923i	$0.496038\pi$
$854$	−2.75557	−0.0942936
$855$	9.47949	0.324192
$856$	−11.7462	−0.401477
$857$	28.7304	0.981411	0.490706	−	0.871325i	$-0.336739\pi$
$857$	28.7304	0.981411	0.490706	+	0.871325i	$0.336739\pi$
$858$	0.311108	0.0106210
$859$	56.9273	1.94234	0.971168	−	0.238396i	$-0.0766217\pi$
$859$	56.9273	1.94234	0.971168	+	0.238396i	$0.0766217\pi$
$860$	34.4242	1.17386
$861$	9.58120	0.326527
$862$	−7.23459	−0.246411
$863$	7.86665	0.267784	0.133892	−	0.990996i	$-0.457253\pi$
$863$	7.86665	0.267784	0.133892	+	0.990996i	$0.457253\pi$
$864$	3.49532	0.118913
$865$	19.6686	0.668753
$866$	−6.25380	−0.212513
$867$	−13.9733	−0.474557
$868$	12.2351	0.415285
$869$	0.260253	0.00882847
$870$	3.52543	0.119523
$871$	−6.02074	−0.204005
$872$	21.4050	0.724864
$873$	0.428639	0.0145072
$874$	0.632060	0.0213797
$875$	−17.2159	−0.582002
$876$	15.3921	0.520050
$877$	−5.18421	−0.175058	−0.0875291	−	0.996162i	$-0.527897\pi$
$877$	−5.18421	−0.175058	−0.0875291	+	0.996162i	$0.527897\pi$
$878$	9.99216	0.337219
$879$	−21.1985	−0.715008
$880$	7.59210	0.255930
$881$	23.5111	0.792110	0.396055	−	0.918227i	$-0.370379\pi$
$881$	23.5111	0.792110	0.396055	+	0.918227i	$0.370379\pi$
$882$	−1.45383	−0.0489530
$883$	−6.07313	−0.204377	−0.102189	−	0.994765i	$-0.532585\pi$
$883$	−6.07313	−0.204377	−0.102189	+	0.994765i	$0.532585\pi$
$884$	3.31111	0.111365
$885$	−3.70471	−0.124533
$886$	9.59411	0.322320
$887$	46.4612	1.56002	0.780008	−	0.625770i	$-0.215215\pi$
$887$	46.4612	1.56002	0.780008	+	0.625770i	$0.215215\pi$
$888$	−0.520505	−0.0174670
$889$	30.8770	1.03558
$890$	−6.99508	−0.234476
$891$	1.00000	0.0335013
$892$	18.0810	0.605396
$893$	21.6227	0.723576
$894$	−0.626661	−0.0209587
$895$	−10.0000	−0.334263
$896$	−13.4019	−0.447727
$897$	0.474572	0.0158455
$898$	−6.01228	−0.200632
$899$	−21.5669	−0.719297
$900$	0.184208	0.00614027
$901$	24.4286	0.813836
$902$	1.95407	0.0650633
$903$	−12.4603	−0.414652
$904$	−16.3684	−0.544405
$905$	−54.7150	−1.81879
$906$	0.207866	0.00690589
$907$	44.3912	1.47398	0.736992	−	0.675901i	$-0.236245\pi$
$907$	44.3912	1.47398	0.736992	+	0.675901i	$0.236245\pi$
$908$	−16.0143	−0.531453
$909$	3.93332	0.130460
$910$	1.05086	0.0348355
$911$	10.4385	0.345842	0.172921	−	0.984936i	$-0.444679\pi$
$911$	10.4385	0.345842	0.172921	+	0.984936i	$0.444679\pi$
$912$	14.6780	0.486037
$913$	−1.37778	−0.0455980
$914$	−2.66953	−0.0883003
$915$	−12.8573	−0.425049
$916$	−55.2543	−1.82565
$917$	12.6539	0.417867
$918$	−0.541249	−0.0178639
$919$	−20.4953	−0.676078	−0.338039	−	0.941132i	$-0.609764\pi$
$919$	−20.4953	−0.676078	−0.338039	+	0.941132i	$0.609764\pi$
$920$	−1.27607	−0.0420709
$921$	10.0874	0.332392
$922$	−1.53833	−0.0506624
$923$	5.18421	0.170640
$924$	−2.90321	−0.0955087
$925$	−0.0414872	−0.00136409
$926$	6.20003	0.203746
$927$	−13.8064	−0.453462
$928$	17.8874	0.587182
$929$	−12.8178	−0.420538	−0.210269	−	0.977644i	$-0.567434\pi$
$929$	−12.8178	−0.420538	−0.210269	+	0.977644i	$0.567434\pi$
$930$	−2.90321	−0.0952001
$931$	−20.0054	−0.655650
$932$	−23.4128	−0.766912
$933$	17.0366	0.557752
$934$	5.77923	0.189102
$935$	−3.85236	−0.125986
$936$	−1.21432	−0.0396913
$937$	−33.3145	−1.08834	−0.544169	−	0.838976i	$-0.683155\pi$
$937$	−33.3145	−1.08834	−0.544169	+	0.838976i	$0.683155\pi$
$938$	−2.85728	−0.0932935
$939$	−19.5986	−0.639575
$940$	−21.2859	−0.694270
$941$	55.1008	1.79623	0.898117	−	0.439756i	$-0.144935\pi$
$941$	55.1008	1.79623	0.898117	+	0.439756i	$0.144935\pi$
$942$	1.46520	0.0477389
$943$	2.98079	0.0970678
$944$	−5.73636	−0.186703
$945$	3.37778	0.109879
$946$	−2.54125	−0.0826231
$947$	−13.6958	−0.445054	−0.222527	−	0.974926i	$-0.571431\pi$
$947$	−13.6958	−0.445054	−0.222527	+	0.974926i	$0.571431\pi$
$948$	−0.495316	−0.0160871
$949$	−8.08742	−0.262529
$950$	−0.128907	−0.00418231
$951$	−31.8687	−1.03341
$952$	3.22263	0.104446
$953$	−12.0350	−0.389853	−0.194926	−	0.980818i	$-0.562447\pi$
$953$	−12.0350	−0.389853	−0.194926	+	0.980818i	$0.562447\pi$
$954$	−4.36842	−0.141433
$955$	28.7654	0.930827
$956$	−41.0464	−1.32754
$957$	5.11753	0.165426
$958$	−0.341219	−0.0110243
$959$	−22.4919	−0.726302
$960$	−12.7763	−0.412354
$961$	−13.2395	−0.427081
$962$	0.133353	0.00429948
$963$	9.67307	0.311710
$964$	47.5812	1.53249
$965$	33.3176	1.07253
$966$	0.225219	0.00724630
$967$	−59.5768	−1.91586	−0.957930	−	0.287003i	$-0.907341\pi$
$967$	−59.5768	−1.91586	−0.957930	+	0.287003i	$0.907341\pi$
$968$	−1.21432	−0.0390297
$969$	−7.44785	−0.239259
$970$	0.295286	0.00948107
$971$	−53.2944	−1.71030	−0.855149	−	0.518382i	$-0.826534\pi$
$971$	−53.2944	−1.71030	−0.855149	+	0.518382i	$0.826534\pi$
$972$	−1.90321	−0.0610456
$973$	−13.8163	−0.442929
$974$	−8.90120	−0.285213
$975$	−0.0967881	−0.00309970
$976$	−19.9081	−0.637244
$977$	−0.481026	−0.0153894	−0.00769469	−	0.999970i	$-0.502449\pi$
$977$	−0.481026	−0.0153894	−0.00769469	+	0.999970i	$0.502449\pi$
$978$	−0.850825	−0.0272064
$979$	−10.1541	−0.324526
$980$	19.6938	0.629096
$981$	−17.6271	−0.562791
$982$	−6.05439	−0.193203
$983$	32.4612	1.03535	0.517676	−	0.855577i	$-0.326797\pi$
$983$	32.4612	1.03535	0.517676	+	0.855577i	$0.326797\pi$
$984$	−7.62714	−0.243144
$985$	35.1240	1.11914
$986$	−2.76986	−0.0882103
$987$	7.70471	0.245244
$988$	−8.14764	−0.259211
$989$	−3.87649	−0.123265
$990$	0.688892	0.0218944
$991$	61.3056	1.94744	0.973718	−	0.227755i	$-0.0731386\pi$
$991$	61.3056	1.94744	0.973718	+	0.227755i	$0.0731386\pi$
$992$	−14.7304	−0.467690
$993$	1.09033	0.0346007
$994$	2.46028	0.0780354
$995$	29.7146	0.942015
$996$	2.62222	0.0830881
$997$	−3.20294	−0.101438	−0.0507191	−	0.998713i	$-0.516151\pi$
$997$	−3.20294	−0.101438	−0.0507191	+	0.998713i	$0.516151\pi$
$998$	−0.187123	−0.00592326
$999$	0.428639	0.0135616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.a.f.1.2	✓	3
3.2	odd	2		1287.2.a.i.1.2		3
4.3	odd	2		6864.2.a.bp.1.3		3
11.10	odd	2		4719.2.a.t.1.2		3
13.12	even	2		5577.2.a.k.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.a.f.1.2	✓	3	1.1	even	1	trivial
1287.2.a.i.1.2		3	3.2	odd	2
4719.2.a.t.1.2		3	11.10	odd	2
5577.2.a.k.1.2		3	13.12	even	2
6864.2.a.bp.1.3		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.a (trivial)

\(f(q)\)	\(=\)	\(q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} +2.21432 q^{5} +0.311108 q^{6} +1.52543 q^{7} -1.21432 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} +2.21432 q^{5} +0.311108 q^{6} +1.52543 q^{7} -1.21432 q^{8} +1.00000 q^{9} +0.688892 q^{10} +1.00000 q^{11} -1.90321 q^{12} +1.00000 q^{13} +0.474572 q^{14} +2.21432 q^{15} +3.42864 q^{16} -1.73975 q^{17} +0.311108 q^{18} +4.28100 q^{19} -4.21432 q^{20} +1.52543 q^{21} +0.311108 q^{22} +0.474572 q^{23} -1.21432 q^{24} -0.0967881 q^{25} +0.311108 q^{26} +1.00000 q^{27} -2.90321 q^{28} +5.11753 q^{29} +0.688892 q^{30} -4.21432 q^{31} +3.49532 q^{32} +1.00000 q^{33} -0.541249 q^{34} +3.37778 q^{35} -1.90321 q^{36} +0.428639 q^{37} +1.33185 q^{38} +1.00000 q^{39} -2.68889 q^{40} +6.28100 q^{41} +0.474572 q^{42} -8.16839 q^{43} -1.90321 q^{44} +2.21432 q^{45} +0.147643 q^{46} +5.05086 q^{47} +3.42864 q^{48} -4.67307 q^{49} -0.0301115 q^{50} -1.73975 q^{51} -1.90321 q^{52} -14.0415 q^{53} +0.311108 q^{54} +2.21432 q^{55} -1.85236 q^{56} +4.28100 q^{57} +1.59210 q^{58} -1.67307 q^{59} -4.21432 q^{60} -5.80642 q^{61} -1.31111 q^{62} +1.52543 q^{63} -5.76986 q^{64} +2.21432 q^{65} +0.311108 q^{66} -6.02074 q^{67} +3.31111 q^{68} +0.474572 q^{69} +1.05086 q^{70} +5.18421 q^{71} -1.21432 q^{72} -8.08742 q^{73} +0.133353 q^{74} -0.0967881 q^{75} -8.14764 q^{76} +1.52543 q^{77} +0.311108 q^{78} +0.260253 q^{79} +7.59210 q^{80} +1.00000 q^{81} +1.95407 q^{82} -1.37778 q^{83} -2.90321 q^{84} -3.85236 q^{85} -2.54125 q^{86} +5.11753 q^{87} -1.21432 q^{88} -10.1541 q^{89} +0.688892 q^{90} +1.52543 q^{91} -0.903212 q^{92} -4.21432 q^{93} +1.57136 q^{94} +9.47949 q^{95} +3.49532 q^{96} +0.428639 q^{97} -1.45383 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + q^{4} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + q^4 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + q^{4} + q^{6} - 2 q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} + 3 q^{13} + 8 q^{14} - 3 q^{16} + 8 q^{17} + q^{18} + 6 q^{19} - 6 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 3 q^{24} - 7 q^{25} + q^{26} + 3 q^{27} - 2 q^{28} + 2 q^{29} + 2 q^{30} - 6 q^{31} - 3 q^{32} + 3 q^{33} - 8 q^{34} + 10 q^{35} + q^{36} - 12 q^{37} - 16 q^{38} + 3 q^{39} - 8 q^{40} + 12 q^{41} + 8 q^{42} + 2 q^{43} + q^{44} - 6 q^{46} + 2 q^{47} - 3 q^{48} - q^{49} - 7 q^{50} + 8 q^{51} + q^{52} - 2 q^{53} + q^{54} - 12 q^{56} + 6 q^{57} - 2 q^{58} + 8 q^{59} - 6 q^{60} - 4 q^{61} - 4 q^{62} - 2 q^{63} - 11 q^{64} + q^{66} + 2 q^{67} + 10 q^{68} + 8 q^{69} - 10 q^{70} + 2 q^{71} + 3 q^{72} - 4 q^{73} - 7 q^{75} - 18 q^{76} - 2 q^{77} + q^{78} + 14 q^{79} + 16 q^{80} + 3 q^{81} - 14 q^{82} - 4 q^{83} - 2 q^{84} - 18 q^{85} - 14 q^{86} + 2 q^{87} + 3 q^{88} - 10 q^{89} + 2 q^{90} - 2 q^{91} + 4 q^{92} - 6 q^{93} + 18 q^{94} + 2 q^{95} - 3 q^{96} - 12 q^{97} - 31 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + q^4 + q^6 - 2 * q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + 3 * q^11 + q^12 + 3 * q^13 + 8 * q^14 - 3 * q^16 + 8 * q^17 + q^18 + 6 * q^19 - 6 * q^20 - 2 * q^21 + q^22 + 8 * q^23 + 3 * q^24 - 7 * q^25 + q^26 + 3 * q^27 - 2 * q^28 + 2 * q^29 + 2 * q^30 - 6 * q^31 - 3 * q^32 + 3 * q^33 - 8 * q^34 + 10 * q^35 + q^36 - 12 * q^37 - 16 * q^38 + 3 * q^39 - 8 * q^40 + 12 * q^41 + 8 * q^42 + 2 * q^43 + q^44 - 6 * q^46 + 2 * q^47 - 3 * q^48 - q^49 - 7 * q^50 + 8 * q^51 + q^52 - 2 * q^53 + q^54 - 12 * q^56 + 6 * q^57 - 2 * q^58 + 8 * q^59 - 6 * q^60 - 4 * q^61 - 4 * q^62 - 2 * q^63 - 11 * q^64 + q^66 + 2 * q^67 + 10 * q^68 + 8 * q^69 - 10 * q^70 + 2 * q^71 + 3 * q^72 - 4 * q^73 - 7 * q^75 - 18 * q^76 - 2 * q^77 + q^78 + 14 * q^79 + 16 * q^80 + 3 * q^81 - 14 * q^82 - 4 * q^83 - 2 * q^84 - 18 * q^85 - 14 * q^86 + 2 * q^87 + 3 * q^88 - 10 * q^89 + 2 * q^90 - 2 * q^91 + 4 * q^92 - 6 * q^93 + 18 * q^94 + 2 * q^95 - 3 * q^96 - 12 * q^97 - 31 * q^98 + 3 * q^99

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