LMFDB - Embedded newform 1734.2.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(1,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1734.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.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:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	1734.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.120615 q^{5} -1.00000 q^{6} +1.69459 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.120615 q^{5} -1.00000 q^{6} +1.69459 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.120615 q^{10} +6.10607 q^{11} +1.00000 q^{12} -1.75877 q^{13} -1.69459 q^{14} +0.120615 q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.82295 q^{19} +0.120615 q^{20} +1.69459 q^{21} -6.10607 q^{22} +6.00000 q^{23} -1.00000 q^{24} -4.98545 q^{25} +1.75877 q^{26} +1.00000 q^{27} +1.69459 q^{28} -3.90167 q^{29} -0.120615 q^{30} -7.29086 q^{31} -1.00000 q^{32} +6.10607 q^{33} +0.204393 q^{35} +1.00000 q^{36} +3.67499 q^{37} -4.82295 q^{38} -1.75877 q^{39} -0.120615 q^{40} -3.14796 q^{41} -1.69459 q^{42} +6.73917 q^{43} +6.10607 q^{44} +0.120615 q^{45} -6.00000 q^{46} +5.43376 q^{47} +1.00000 q^{48} -4.12836 q^{49} +4.98545 q^{50} -1.75877 q^{52} +4.71688 q^{53} -1.00000 q^{54} +0.736482 q^{55} -1.69459 q^{56} +4.82295 q^{57} +3.90167 q^{58} +2.12061 q^{59} +0.120615 q^{60} -10.6946 q^{61} +7.29086 q^{62} +1.69459 q^{63} +1.00000 q^{64} -0.212134 q^{65} -6.10607 q^{66} -5.88713 q^{67} +6.00000 q^{69} -0.204393 q^{70} +15.4047 q^{71} -1.00000 q^{72} -12.5963 q^{73} -3.67499 q^{74} -4.98545 q^{75} +4.82295 q^{76} +10.3473 q^{77} +1.75877 q^{78} +13.9932 q^{79} +0.120615 q^{80} +1.00000 q^{81} +3.14796 q^{82} -14.8871 q^{83} +1.69459 q^{84} -6.73917 q^{86} -3.90167 q^{87} -6.10607 q^{88} +16.4979 q^{89} -0.120615 q^{90} -2.98040 q^{91} +6.00000 q^{92} -7.29086 q^{93} -5.43376 q^{94} +0.581719 q^{95} -1.00000 q^{96} -9.08647 q^{97} +4.12836 q^{98} +6.10607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 6 q^{10} + 6 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} - 6 q^{22} + 18 q^{23} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} + 3 q^{28} - 6 q^{30} - 6 q^{31} - 3 q^{32} + 6 q^{33} + 3 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} - 6 q^{40} + 6 q^{41} - 3 q^{42} + 6 q^{43} + 6 q^{44} + 6 q^{45} - 18 q^{46} + 3 q^{48} + 6 q^{49} - 3 q^{50} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} - 6 q^{57} + 12 q^{59} + 6 q^{60} - 30 q^{61} + 6 q^{62} + 3 q^{63} + 3 q^{64} + 24 q^{65} - 6 q^{66} + 12 q^{67} + 18 q^{69} - 6 q^{71} - 3 q^{72} - 24 q^{73} - 6 q^{74} + 3 q^{75} - 6 q^{76} + 30 q^{77} - 6 q^{78} + 6 q^{80} + 3 q^{81} - 6 q^{82} - 15 q^{83} + 3 q^{84} - 6 q^{86} - 6 q^{88} + 24 q^{89} - 6 q^{90} - 6 q^{91} + 18 q^{92} - 6 q^{93} - 30 q^{95} - 3 q^{96} - 12 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 6 * q^10 + 6 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 - 6 * q^22 + 18 * q^23 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^30 - 6 * q^31 - 3 * q^32 + 6 * q^33 + 3 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 - 6 * q^40 + 6 * q^41 - 3 * q^42 + 6 * q^43 + 6 * q^44 + 6 * q^45 - 18 * q^46 + 3 * q^48 + 6 * q^49 - 3 * q^50 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 - 6 * q^57 + 12 * q^59 + 6 * q^60 - 30 * q^61 + 6 * q^62 + 3 * q^63 + 3 * q^64 + 24 * q^65 - 6 * q^66 + 12 * q^67 + 18 * q^69 - 6 * q^71 - 3 * q^72 - 24 * q^73 - 6 * q^74 + 3 * q^75 - 6 * q^76 + 30 * q^77 - 6 * q^78 + 6 * q^80 + 3 * q^81 - 6 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^86 - 6 * q^88 + 24 * q^89 - 6 * q^90 - 6 * q^91 + 18 * q^92 - 6 * q^93 - 30 * q^95 - 3 * q^96 - 12 * q^97 - 6 * q^98 + 6 * 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
$5$	0.120615	0.0539406	0.0269703	−	0.999636i	$-0.491414\pi$
$5$	0.120615	0.0539406	0.0269703	+	0.999636i	$0.491414\pi$
$6$	−1.00000	−0.408248
$7$	1.69459	0.640496	0.320248	−	0.947334i	$-0.396234\pi$
$7$	1.69459	0.640496	0.320248	+	0.947334i	$0.396234\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.120615	−0.0381417
$11$	6.10607	1.84105	0.920524	−	0.390686i	$-0.127762\pi$
$11$	6.10607	1.84105	0.920524	+	0.390686i	$0.127762\pi$
$12$	1.00000	0.288675
$13$	−1.75877	−0.487795	−0.243898	−	0.969801i	$-0.578426\pi$
$13$	−1.75877	−0.487795	−0.243898	+	0.969801i	$0.578426\pi$
$14$	−1.69459	−0.452899
$15$	0.120615	0.0311426
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	4.82295	1.10646	0.553230	−	0.833028i	$-0.313395\pi$
$19$	4.82295	1.10646	0.553230	+	0.833028i	$0.313395\pi$
$20$	0.120615	0.0269703
$21$	1.69459	0.369790
$22$	−6.10607	−1.30182
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	−4.98545	−0.997090
$26$	1.75877	0.344923
$27$	1.00000	0.192450
$28$	1.69459	0.320248
$29$	−3.90167	−0.724523	−0.362261	−	0.932077i	$-0.617995\pi$
$29$	−3.90167	−0.724523	−0.362261	+	0.932077i	$0.617995\pi$
$30$	−0.120615	−0.0220211
$31$	−7.29086	−1.30948	−0.654738	−	0.755855i	$-0.727221\pi$
$31$	−7.29086	−1.30948	−0.654738	+	0.755855i	$0.727221\pi$
$32$	−1.00000	−0.176777
$33$	6.10607	1.06293
$34$	0	0
$35$	0.204393	0.0345487
$36$	1.00000	0.166667
$37$	3.67499	0.604165	0.302083	−	0.953282i	$-0.402318\pi$
$37$	3.67499	0.604165	0.302083	+	0.953282i	$0.402318\pi$
$38$	−4.82295	−0.782386
$39$	−1.75877	−0.281629
$40$	−0.120615	−0.0190709
$41$	−3.14796	−0.491628	−0.245814	−	0.969317i	$-0.579055\pi$
$41$	−3.14796	−0.491628	−0.245814	+	0.969317i	$0.579055\pi$
$42$	−1.69459	−0.261481
$43$	6.73917	1.02771	0.513857	−	0.857876i	$-0.328216\pi$
$43$	6.73917	1.02771	0.513857	+	0.857876i	$0.328216\pi$
$44$	6.10607	0.920524
$45$	0.120615	0.0179802
$46$	−6.00000	−0.884652
$47$	5.43376	0.792596	0.396298	−	0.918122i	$-0.370295\pi$
$47$	5.43376	0.792596	0.396298	+	0.918122i	$0.370295\pi$
$48$	1.00000	0.144338
$49$	−4.12836	−0.589765
$50$	4.98545	0.705049
$51$	0	0
$52$	−1.75877	−0.243898
$53$	4.71688	0.647913	0.323957	−	0.946072i	$-0.394987\pi$
$53$	4.71688	0.647913	0.323957	+	0.946072i	$0.394987\pi$
$54$	−1.00000	−0.136083
$55$	0.736482	0.0993072
$56$	−1.69459	−0.226449
$57$	4.82295	0.638815
$58$	3.90167	0.512315
$59$	2.12061	0.276081	0.138040	−	0.990427i	$-0.455920\pi$
$59$	2.12061	0.276081	0.138040	+	0.990427i	$0.455920\pi$
$60$	0.120615	0.0155713
$61$	−10.6946	−1.36930	−0.684651	−	0.728871i	$-0.740045\pi$
$61$	−10.6946	−1.36930	−0.684651	+	0.728871i	$0.740045\pi$
$62$	7.29086	0.925940
$63$	1.69459	0.213499
$64$	1.00000	0.125000
$65$	−0.212134	−0.0263119
$66$	−6.10607	−0.751605
$67$	−5.88713	−0.719227	−0.359613	−	0.933101i	$-0.617091\pi$
$67$	−5.88713	−0.719227	−0.359613	+	0.933101i	$0.617091\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	−0.204393	−0.0244296
$71$	15.4047	1.82820	0.914099	−	0.405492i	$-0.132900\pi$
$71$	15.4047	1.82820	0.914099	+	0.405492i	$0.132900\pi$
$72$	−1.00000	−0.117851
$73$	−12.5963	−1.47428	−0.737141	−	0.675739i	$-0.763825\pi$
$73$	−12.5963	−1.47428	−0.737141	+	0.675739i	$0.763825\pi$
$74$	−3.67499	−0.427209
$75$	−4.98545	−0.575670
$76$	4.82295	0.553230
$77$	10.3473	1.17918
$78$	1.75877	0.199142
$79$	13.9932	1.57436	0.787179	−	0.616725i	$-0.211541\pi$
$79$	13.9932	1.57436	0.787179	+	0.616725i	$0.211541\pi$
$80$	0.120615	0.0134851
$81$	1.00000	0.111111
$82$	3.14796	0.347634
$83$	−14.8871	−1.63407	−0.817037	−	0.576585i	$-0.804385\pi$
$83$	−14.8871	−1.63407	−0.817037	+	0.576585i	$0.804385\pi$
$84$	1.69459	0.184895
$85$	0	0
$86$	−6.73917	−0.726703
$87$	−3.90167	−0.418303
$88$	−6.10607	−0.650909
$89$	16.4979	1.74878	0.874389	−	0.485225i	$-0.161262\pi$
$89$	16.4979	1.74878	0.874389	+	0.485225i	$0.161262\pi$
$90$	−0.120615	−0.0127139
$91$	−2.98040	−0.312431
$92$	6.00000	0.625543
$93$	−7.29086	−0.756027
$94$	−5.43376	−0.560450
$95$	0.581719	0.0596831
$96$	−1.00000	−0.102062
$97$	−9.08647	−0.922591	−0.461295	−	0.887247i	$-0.652615\pi$
$97$	−9.08647	−0.922591	−0.461295	+	0.887247i	$0.652615\pi$
$98$	4.12836	0.417027
$99$	6.10607	0.613683
$100$	−4.98545	−0.498545
$101$	2.24897	0.223781	0.111890	−	0.993721i	$-0.464309\pi$
$101$	2.24897	0.223781	0.111890	+	0.993721i	$0.464309\pi$
$102$	0	0
$103$	18.3259	1.80571	0.902854	−	0.429947i	$-0.141468\pi$
$103$	18.3259	1.80571	0.902854	+	0.429947i	$0.141468\pi$
$104$	1.75877	0.172462
$105$	0.204393	0.0199467
$106$	−4.71688	−0.458144
$107$	14.1138	1.36443	0.682217	−	0.731150i	$-0.261016\pi$
$107$	14.1138	1.36443	0.682217	+	0.731150i	$0.261016\pi$
$108$	1.00000	0.0962250
$109$	−6.69459	−0.641226	−0.320613	−	0.947210i	$-0.603889\pi$
$109$	−6.69459	−0.641226	−0.320613	+	0.947210i	$0.603889\pi$
$110$	−0.736482	−0.0702208
$111$	3.67499	0.348815
$112$	1.69459	0.160124
$113$	−4.58172	−0.431012	−0.215506	−	0.976503i	$-0.569140\pi$
$113$	−4.58172	−0.431012	−0.215506	+	0.976503i	$0.569140\pi$
$114$	−4.82295	−0.451710
$115$	0.723689	0.0674843
$116$	−3.90167	−0.362261
$117$	−1.75877	−0.162598
$118$	−2.12061	−0.195218
$119$	0	0
$120$	−0.120615	−0.0110106
$121$	26.2841	2.38946
$122$	10.6946	0.968243
$123$	−3.14796	−0.283842
$124$	−7.29086	−0.654738
$125$	−1.20439	−0.107724
$126$	−1.69459	−0.150966
$127$	−4.30541	−0.382043	−0.191022	−	0.981586i	$-0.561180\pi$
$127$	−4.30541	−0.382043	−0.191022	+	0.981586i	$0.561180\pi$
$128$	−1.00000	−0.0883883
$129$	6.73917	0.593351
$130$	0.212134	0.0186054
$131$	−15.0155	−1.31191	−0.655954	−	0.754801i	$-0.727734\pi$
$131$	−15.0155	−1.31191	−0.655954	+	0.754801i	$0.727734\pi$
$132$	6.10607	0.531465
$133$	8.17293	0.708683
$134$	5.88713	0.508570
$135$	0.120615	0.0103809
$136$	0	0
$137$	−6.82295	−0.582924	−0.291462	−	0.956582i	$-0.594142\pi$
$137$	−6.82295	−0.582924	−0.291462	+	0.956582i	$0.594142\pi$
$138$	−6.00000	−0.510754
$139$	−16.9067	−1.43401	−0.717005	−	0.697068i	$-0.754488\pi$
$139$	−16.9067	−1.43401	−0.717005	+	0.697068i	$0.754488\pi$
$140$	0.204393	0.0172744
$141$	5.43376	0.457605
$142$	−15.4047	−1.29273
$143$	−10.7392	−0.898055
$144$	1.00000	0.0833333
$145$	−0.470599	−0.0390812
$146$	12.5963	1.04247
$147$	−4.12836	−0.340501
$148$	3.67499	0.302083
$149$	11.2831	0.924349	0.462175	−	0.886789i	$-0.347069\pi$
$149$	11.2831	0.924349	0.462175	+	0.886789i	$0.347069\pi$
$150$	4.98545	0.407060
$151$	23.1702	1.88557	0.942784	−	0.333404i	$-0.108197\pi$
$151$	23.1702	1.88557	0.942784	+	0.333404i	$0.108197\pi$
$152$	−4.82295	−0.391193
$153$	0	0
$154$	−10.3473	−0.833809
$155$	−0.879385	−0.0706339
$156$	−1.75877	−0.140814
$157$	5.38919	0.430104	0.215052	−	0.976603i	$-0.431008\pi$
$157$	5.38919	0.430104	0.215052	+	0.976603i	$0.431008\pi$
$158$	−13.9932	−1.11324
$159$	4.71688	0.374073
$160$	−0.120615	−0.00953543
$161$	10.1676	0.801316
$162$	−1.00000	−0.0785674
$163$	−17.8871	−1.40103	−0.700514	−	0.713639i	$-0.747046\pi$
$163$	−17.8871	−1.40103	−0.700514	+	0.713639i	$0.747046\pi$
$164$	−3.14796	−0.245814
$165$	0.736482	0.0573350
$166$	14.8871	1.15547
$167$	5.84255	0.452110	0.226055	−	0.974115i	$-0.427417\pi$
$167$	5.84255	0.452110	0.226055	+	0.974115i	$0.427417\pi$
$168$	−1.69459	−0.130741
$169$	−9.90673	−0.762056
$170$	0	0
$171$	4.82295	0.368820
$172$	6.73917	0.513857
$173$	−5.41147	−0.411427	−0.205713	−	0.978612i	$-0.565951\pi$
$173$	−5.41147	−0.411427	−0.205713	+	0.978612i	$0.565951\pi$
$174$	3.90167	0.295785
$175$	−8.44831	−0.638632
$176$	6.10607	0.460262
$177$	2.12061	0.159395
$178$	−16.4979	−1.23657
$179$	7.24123	0.541235	0.270617	−	0.962687i	$-0.412772\pi$
$179$	7.24123	0.541235	0.270617	+	0.962687i	$0.412772\pi$
$180$	0.120615	0.00899009
$181$	−0.157451	−0.0117033	−0.00585163	−	0.999983i	$-0.501863\pi$
$181$	−0.157451	−0.0117033	−0.00585163	+	0.999983i	$0.501863\pi$
$182$	2.98040	0.220922
$183$	−10.6946	−0.790567
$184$	−6.00000	−0.442326
$185$	0.443258	0.0325890
$186$	7.29086	0.534592
$187$	0	0
$188$	5.43376	0.396298
$189$	1.69459	0.123263
$190$	−0.581719	−0.0422023
$191$	−6.90673	−0.499753	−0.249877	−	0.968278i	$-0.580390\pi$
$191$	−6.90673	−0.499753	−0.249877	+	0.968278i	$0.580390\pi$
$192$	1.00000	0.0721688
$193$	−11.5253	−0.829608	−0.414804	−	0.909911i	$-0.636150\pi$
$193$	−11.5253	−0.829608	−0.414804	+	0.909911i	$0.636150\pi$
$194$	9.08647	0.652370
$195$	−0.212134	−0.0151912
$196$	−4.12836	−0.294883
$197$	6.71419	0.478366	0.239183	−	0.970974i	$-0.423120\pi$
$197$	6.71419	0.478366	0.239183	+	0.970974i	$0.423120\pi$
$198$	−6.10607	−0.433939
$199$	7.22937	0.512476	0.256238	−	0.966614i	$-0.417517\pi$
$199$	7.22937	0.512476	0.256238	+	0.966614i	$0.417517\pi$
$200$	4.98545	0.352525
$201$	−5.88713	−0.415246
$202$	−2.24897	−0.158237
$203$	−6.61175	−0.464054
$204$	0	0
$205$	−0.379690	−0.0265187
$206$	−18.3259	−1.27683
$207$	6.00000	0.417029
$208$	−1.75877	−0.121949
$209$	29.4492	2.03705
$210$	−0.204393	−0.0141044
$211$	10.5371	0.725407	0.362703	−	0.931905i	$-0.381854\pi$
$211$	10.5371	0.725407	0.362703	+	0.931905i	$0.381854\pi$
$212$	4.71688	0.323957
$213$	15.4047	1.05551
$214$	−14.1138	−0.964800
$215$	0.812843	0.0554355
$216$	−1.00000	−0.0680414
$217$	−12.3550	−0.838715
$218$	6.69459	0.453415
$219$	−12.5963	−0.851177
$220$	0.736482	0.0496536
$221$	0	0
$222$	−3.67499	−0.246649
$223$	−11.0027	−0.736795	−0.368397	−	0.929668i	$-0.620093\pi$
$223$	−11.0027	−0.736795	−0.368397	+	0.929668i	$0.620093\pi$
$224$	−1.69459	−0.113225
$225$	−4.98545	−0.332363
$226$	4.58172	0.304771
$227$	0.758770	0.0503614	0.0251807	−	0.999683i	$-0.491984\pi$
$227$	0.758770	0.0503614	0.0251807	+	0.999683i	$0.491984\pi$
$228$	4.82295	0.319408
$229$	24.5817	1.62441	0.812203	−	0.583375i	$-0.198268\pi$
$229$	24.5817	1.62441	0.812203	+	0.583375i	$0.198268\pi$
$230$	−0.723689	−0.0477186
$231$	10.3473	0.680802
$232$	3.90167	0.256157
$233$	5.67499	0.371781	0.185891	−	0.982570i	$-0.440483\pi$
$233$	5.67499	0.371781	0.185891	+	0.982570i	$0.440483\pi$
$234$	1.75877	0.114974
$235$	0.655392	0.0427531
$236$	2.12061	0.138040
$237$	13.9932	0.908956
$238$	0	0
$239$	25.5175	1.65059	0.825296	−	0.564700i	$-0.191008\pi$
$239$	25.5175	1.65059	0.825296	+	0.564700i	$0.191008\pi$
$240$	0.120615	0.00778565
$241$	20.4320	1.31614	0.658071	−	0.752956i	$-0.271373\pi$
$241$	20.4320	1.31614	0.658071	+	0.752956i	$0.271373\pi$
$242$	−26.2841	−1.68960
$243$	1.00000	0.0641500
$244$	−10.6946	−0.684651
$245$	−0.497941	−0.0318123
$246$	3.14796	0.200706
$247$	−8.48246	−0.539726
$248$	7.29086	0.462970
$249$	−14.8871	−0.943433
$250$	1.20439	0.0761725
$251$	7.50299	0.473585	0.236792	−	0.971560i	$-0.423904\pi$
$251$	7.50299	0.473585	0.236792	+	0.971560i	$0.423904\pi$
$252$	1.69459	0.106749
$253$	36.6364	2.30331
$254$	4.30541	0.270145
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.3851	−1.14683	−0.573414	−	0.819265i	$-0.694382\pi$
$257$	−18.3851	−1.14683	−0.573414	+	0.819265i	$0.694382\pi$
$258$	−6.73917	−0.419562
$259$	6.22762	0.386965
$260$	−0.212134	−0.0131560
$261$	−3.90167	−0.241508
$262$	15.0155	0.927660
$263$	−3.01960	−0.186197	−0.0930983	−	0.995657i	$-0.529677\pi$
$263$	−3.01960	−0.186197	−0.0930983	+	0.995657i	$0.529677\pi$
$264$	−6.10607	−0.375802
$265$	0.568926	0.0349488
$266$	−8.17293	−0.501115
$267$	16.4979	1.00966
$268$	−5.88713	−0.359613
$269$	−10.8452	−0.661246	−0.330623	−	0.943763i	$-0.607259\pi$
$269$	−10.8452	−0.661246	−0.330623	+	0.943763i	$0.607259\pi$
$270$	−0.120615	−0.00734038
$271$	−17.6159	−1.07009	−0.535044	−	0.844824i	$-0.679705\pi$
$271$	−17.6159	−1.07009	−0.535044	+	0.844824i	$0.679705\pi$
$272$	0	0
$273$	−2.98040	−0.180382
$274$	6.82295	0.412189
$275$	−30.4415	−1.83569
$276$	6.00000	0.361158
$277$	1.10338	0.0662956	0.0331478	−	0.999450i	$-0.489447\pi$
$277$	1.10338	0.0662956	0.0331478	+	0.999450i	$0.489447\pi$
$278$	16.9067	1.01400
$279$	−7.29086	−0.436492
$280$	−0.204393	−0.0122148
$281$	6.28581	0.374980	0.187490	−	0.982267i	$-0.439965\pi$
$281$	6.28581	0.374980	0.187490	+	0.982267i	$0.439965\pi$
$282$	−5.43376	−0.323576
$283$	3.27631	0.194757	0.0973783	−	0.995247i	$-0.468954\pi$
$283$	3.27631	0.194757	0.0973783	+	0.995247i	$0.468954\pi$
$284$	15.4047	0.914099
$285$	0.581719	0.0344580
$286$	10.7392	0.635020
$287$	−5.33450	−0.314886
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	0.470599	0.0276346
$291$	−9.08647	−0.532658
$292$	−12.5963	−0.737141
$293$	5.76651	0.336883	0.168442	−	0.985712i	$-0.446127\pi$
$293$	5.76651	0.336883	0.168442	+	0.985712i	$0.446127\pi$
$294$	4.12836	0.240771
$295$	0.255777	0.0148919
$296$	−3.67499	−0.213605
$297$	6.10607	0.354310
$298$	−11.2831	−0.653614
$299$	−10.5526	−0.610274
$300$	−4.98545	−0.287835
$301$	11.4201	0.658246
$302$	−23.1702	−1.33330
$303$	2.24897	0.129200
$304$	4.82295	0.276615
$305$	−1.28993	−0.0738609
$306$	0	0
$307$	−1.26083	−0.0719594	−0.0359797	−	0.999353i	$-0.511455\pi$
$307$	−1.26083	−0.0719594	−0.0359797	+	0.999353i	$0.511455\pi$
$308$	10.3473	0.589592
$309$	18.3259	1.04253
$310$	0.879385	0.0499457
$311$	4.77837	0.270957	0.135478	−	0.990780i	$-0.456743\pi$
$311$	4.77837	0.270957	0.135478	+	0.990780i	$0.456743\pi$
$312$	1.75877	0.0995708
$313$	−6.25671	−0.353650	−0.176825	−	0.984242i	$-0.556583\pi$
$313$	−6.25671	−0.353650	−0.176825	+	0.984242i	$0.556583\pi$
$314$	−5.38919	−0.304129
$315$	0.204393	0.0115162
$316$	13.9932	0.787179
$317$	−26.1925	−1.47112	−0.735560	−	0.677460i	$-0.763081\pi$
$317$	−26.1925	−1.47112	−0.735560	+	0.677460i	$0.763081\pi$
$318$	−4.71688	−0.264510
$319$	−23.8239	−1.33388
$320$	0.120615	0.00674257
$321$	14.1138	0.787756
$322$	−10.1676	−0.566616
$323$	0	0
$324$	1.00000	0.0555556
$325$	8.76827	0.486376
$326$	17.8871	0.990676
$327$	−6.69459	−0.370212
$328$	3.14796	0.173817
$329$	9.20801	0.507654
$330$	−0.736482	−0.0405420
$331$	−12.5817	−0.691554	−0.345777	−	0.938317i	$-0.612385\pi$
$331$	−12.5817	−0.691554	−0.345777	+	0.938317i	$0.612385\pi$
$332$	−14.8871	−0.817037
$333$	3.67499	0.201388
$334$	−5.84255	−0.319690
$335$	−0.710074	−0.0387955
$336$	1.69459	0.0924476
$337$	−23.2175	−1.26474	−0.632369	−	0.774667i	$-0.717917\pi$
$337$	−23.2175	−1.26474	−0.632369	+	0.774667i	$0.717917\pi$
$338$	9.90673	0.538855
$339$	−4.58172	−0.248845
$340$	0	0
$341$	−44.5185	−2.41081
$342$	−4.82295	−0.260795
$343$	−18.8580	−1.01824
$344$	−6.73917	−0.363352
$345$	0.723689	0.0389621
$346$	5.41147	0.290923
$347$	−10.7706	−0.578198	−0.289099	−	0.957299i	$-0.593356\pi$
$347$	−10.7706	−0.578198	−0.289099	+	0.957299i	$0.593356\pi$
$348$	−3.90167	−0.209152
$349$	−29.9864	−1.60513	−0.802567	−	0.596562i	$-0.796533\pi$
$349$	−29.9864	−1.60513	−0.802567	+	0.596562i	$0.796533\pi$
$350$	8.44831	0.451581
$351$	−1.75877	−0.0938762
$352$	−6.10607	−0.325454
$353$	−29.6459	−1.57789	−0.788946	−	0.614463i	$-0.789373\pi$
$353$	−29.6459	−1.57789	−0.788946	+	0.614463i	$0.789373\pi$
$354$	−2.12061	−0.112709
$355$	1.85803	0.0986140
$356$	16.4979	0.874389
$357$	0	0
$358$	−7.24123	−0.382711
$359$	−18.7101	−0.987480	−0.493740	−	0.869610i	$-0.664371\pi$
$359$	−18.7101	−0.987480	−0.493740	+	0.869610i	$0.664371\pi$
$360$	−0.120615	−0.00635696
$361$	4.26083	0.224254
$362$	0.157451	0.00827546
$363$	26.2841	1.37955
$364$	−2.98040	−0.156215
$365$	−1.51930	−0.0795236
$366$	10.6946	0.559015
$367$	5.84018	0.304855	0.152428	−	0.988315i	$-0.451291\pi$
$367$	5.84018	0.304855	0.152428	+	0.988315i	$0.451291\pi$
$368$	6.00000	0.312772
$369$	−3.14796	−0.163876
$370$	−0.443258	−0.0230439
$371$	7.99319	0.414986
$372$	−7.29086	−0.378013
$373$	−10.6209	−0.549930	−0.274965	−	0.961454i	$-0.588666\pi$
$373$	−10.6209	−0.549930	−0.274965	+	0.961454i	$0.588666\pi$
$374$	0	0
$375$	−1.20439	−0.0621946
$376$	−5.43376	−0.280225
$377$	6.86215	0.353419
$378$	−1.69459	−0.0871604
$379$	−0.340489	−0.0174898	−0.00874488	−	0.999962i	$-0.502784\pi$
$379$	−0.340489	−0.0174898	−0.00874488	+	0.999962i	$0.502784\pi$
$380$	0.581719	0.0298415
$381$	−4.30541	−0.220573
$382$	6.90673	0.353379
$383$	−30.8776	−1.57777	−0.788887	−	0.614539i	$-0.789342\pi$
$383$	−30.8776	−1.57777	−0.788887	+	0.614539i	$0.789342\pi$
$384$	−1.00000	−0.0510310
$385$	1.24804	0.0636058
$386$	11.5253	0.586621
$387$	6.73917	0.342571
$388$	−9.08647	−0.461295
$389$	−3.25166	−0.164866	−0.0824328	−	0.996597i	$-0.526269\pi$
$389$	−3.25166	−0.164866	−0.0824328	+	0.996597i	$0.526269\pi$
$390$	0.212134	0.0107418
$391$	0	0
$392$	4.12836	0.208513
$393$	−15.0155	−0.757431
$394$	−6.71419	−0.338256
$395$	1.68779	0.0849217
$396$	6.10607	0.306841
$397$	−18.3405	−0.920483	−0.460241	−	0.887794i	$-0.652237\pi$
$397$	−18.3405	−0.920483	−0.460241	+	0.887794i	$0.652237\pi$
$398$	−7.22937	−0.362376
$399$	8.17293	0.409158
$400$	−4.98545	−0.249273
$401$	−18.7101	−0.934337	−0.467168	−	0.884168i	$-0.654726\pi$
$401$	−18.7101	−0.934337	−0.467168	+	0.884168i	$0.654726\pi$
$402$	5.88713	0.293623
$403$	12.8229	0.638757
$404$	2.24897	0.111890
$405$	0.120615	0.00599340
$406$	6.61175	0.328136
$407$	22.4397	1.11230
$408$	0	0
$409$	−5.94862	−0.294140	−0.147070	−	0.989126i	$-0.546984\pi$
$409$	−5.94862	−0.294140	−0.147070	+	0.989126i	$0.546984\pi$
$410$	0.379690	0.0187515
$411$	−6.82295	−0.336551
$412$	18.3259	0.902854
$413$	3.59358	0.176828
$414$	−6.00000	−0.294884
$415$	−1.79561	−0.0881429
$416$	1.75877	0.0862308
$417$	−16.9067	−0.827926
$418$	−29.4492	−1.44041
$419$	−12.8990	−0.630157	−0.315078	−	0.949066i	$-0.602031\pi$
$419$	−12.8990	−0.630157	−0.315078	+	0.949066i	$0.602031\pi$
$420$	0.204393	0.00997335
$421$	−27.2472	−1.32795	−0.663974	−	0.747756i	$-0.731131\pi$
$421$	−27.2472	−1.32795	−0.663974	+	0.747756i	$0.731131\pi$
$422$	−10.5371	−0.512940
$423$	5.43376	0.264199
$424$	−4.71688	−0.229072
$425$	0	0
$426$	−15.4047	−0.746359
$427$	−18.1230	−0.877032
$428$	14.1138	0.682217
$429$	−10.7392	−0.518492
$430$	−0.812843	−0.0391988
$431$	−12.0547	−0.580654	−0.290327	−	0.956928i	$-0.593764\pi$
$431$	−12.0547	−0.580654	−0.290327	+	0.956928i	$0.593764\pi$
$432$	1.00000	0.0481125
$433$	−10.6031	−0.509551	−0.254776	−	0.967000i	$-0.582002\pi$
$433$	−10.6031	−0.509551	−0.254776	+	0.967000i	$0.582002\pi$
$434$	12.3550	0.593061
$435$	−0.470599	−0.0225635
$436$	−6.69459	−0.320613
$437$	28.9377	1.38428
$438$	12.5963	0.601873
$439$	7.09327	0.338543	0.169272	−	0.985569i	$-0.445858\pi$
$439$	7.09327	0.338543	0.169272	+	0.985569i	$0.445858\pi$
$440$	−0.736482	−0.0351104
$441$	−4.12836	−0.196588
$442$	0	0
$443$	−0.206148	−0.00979437	−0.00489718	−	0.999988i	$-0.501559\pi$
$443$	−0.206148	−0.00979437	−0.00489718	+	0.999988i	$0.501559\pi$
$444$	3.67499	0.174407
$445$	1.98990	0.0943301
$446$	11.0027	0.520992
$447$	11.2831	0.533673
$448$	1.69459	0.0800620
$449$	33.1343	1.56371	0.781853	−	0.623463i	$-0.214275\pi$
$449$	33.1343	1.56371	0.781853	+	0.623463i	$0.214275\pi$
$450$	4.98545	0.235016
$451$	−19.2216	−0.905111
$452$	−4.58172	−0.215506
$453$	23.1702	1.08863
$454$	−0.758770	−0.0356109
$455$	−0.359480	−0.0168527
$456$	−4.82295	−0.225855
$457$	−11.9463	−0.558822	−0.279411	−	0.960172i	$-0.590139\pi$
$457$	−11.9463	−0.558822	−0.279411	+	0.960172i	$0.590139\pi$
$458$	−24.5817	−1.14863
$459$	0	0
$460$	0.723689	0.0337422
$461$	25.5185	1.18851	0.594257	−	0.804275i	$-0.297446\pi$
$461$	25.5185	1.18851	0.594257	+	0.804275i	$0.297446\pi$
$462$	−10.3473	−0.481400
$463$	−36.5449	−1.69838	−0.849192	−	0.528084i	$-0.822911\pi$
$463$	−36.5449	−1.69838	−0.849192	+	0.528084i	$0.822911\pi$
$464$	−3.90167	−0.181131
$465$	−0.879385	−0.0407805
$466$	−5.67499	−0.262889
$467$	20.7246	0.959021	0.479511	−	0.877536i	$-0.340814\pi$
$467$	20.7246	0.959021	0.479511	+	0.877536i	$0.340814\pi$
$468$	−1.75877	−0.0812992
$469$	−9.97628	−0.460662
$470$	−0.655392	−0.0302310
$471$	5.38919	0.248321
$472$	−2.12061	−0.0976092
$473$	41.1498	1.89207
$474$	−13.9932	−0.642729
$475$	−24.0446	−1.10324
$476$	0	0
$477$	4.71688	0.215971
$478$	−25.5175	−1.16715
$479$	−31.6168	−1.44461	−0.722304	−	0.691575i	$-0.756917\pi$
$479$	−31.6168	−1.44461	−0.722304	+	0.691575i	$0.756917\pi$
$480$	−0.120615	−0.00550529
$481$	−6.46347	−0.294709
$482$	−20.4320	−0.930652
$483$	10.1676	0.462640
$484$	26.2841	1.19473
$485$	−1.09596	−0.0497651
$486$	−1.00000	−0.0453609
$487$	21.2841	0.964472	0.482236	−	0.876041i	$-0.339825\pi$
$487$	21.2841	0.964472	0.482236	+	0.876041i	$0.339825\pi$
$488$	10.6946	0.484121
$489$	−17.8871	−0.808884
$490$	0.497941	0.0224947
$491$	−19.5253	−0.881164	−0.440582	−	0.897712i	$-0.645228\pi$
$491$	−19.5253	−0.881164	−0.440582	+	0.897712i	$0.645228\pi$
$492$	−3.14796	−0.141921
$493$	0	0
$494$	8.48246	0.381644
$495$	0.736482	0.0331024
$496$	−7.29086	−0.327369
$497$	26.1046	1.17095
$498$	14.8871	0.667108
$499$	22.5972	1.01159	0.505795	−	0.862654i	$-0.331199\pi$
$499$	22.5972	1.01159	0.505795	+	0.862654i	$0.331199\pi$
$500$	−1.20439	−0.0538621
$501$	5.84255	0.261026
$502$	−7.50299	−0.334875
$503$	−13.3054	−0.593259	−0.296629	−	0.954993i	$-0.595863\pi$
$503$	−13.3054	−0.593259	−0.296629	+	0.954993i	$0.595863\pi$
$504$	−1.69459	−0.0754832
$505$	0.271259	0.0120709
$506$	−36.6364	−1.62869
$507$	−9.90673	−0.439973
$508$	−4.30541	−0.191022
$509$	40.9760	1.81623	0.908114	−	0.418724i	$-0.137522\pi$
$509$	40.9760	1.81623	0.908114	+	0.418724i	$0.137522\pi$
$510$	0	0
$511$	−21.3455	−0.944271
$512$	−1.00000	−0.0441942
$513$	4.82295	0.212938
$514$	18.3851	0.810931
$515$	2.21038	0.0974009
$516$	6.73917	0.296675
$517$	33.1789	1.45921
$518$	−6.22762	−0.273626
$519$	−5.41147	−0.237537
$520$	0.212134	0.00930268
$521$	−39.0951	−1.71279	−0.856395	−	0.516322i	$-0.827301\pi$
$521$	−39.0951	−1.71279	−0.856395	+	0.516322i	$0.827301\pi$
$522$	3.90167	0.170772
$523$	18.0702	0.790153	0.395077	−	0.918648i	$-0.370718\pi$
$523$	18.0702	0.790153	0.395077	+	0.918648i	$0.370718\pi$
$524$	−15.0155	−0.655954
$525$	−8.44831	−0.368715
$526$	3.01960	0.131661
$527$	0	0
$528$	6.10607	0.265732
$529$	13.0000	0.565217
$530$	−0.568926	−0.0247125
$531$	2.12061	0.0920268
$532$	8.17293	0.354342
$533$	5.53653	0.239814
$534$	−16.4979	−0.713936
$535$	1.70233	0.0735983
$536$	5.88713	0.254285
$537$	7.24123	0.312482
$538$	10.8452	0.467571
$539$	−25.2080	−1.08579
$540$	0.120615	0.00519043
$541$	−22.5270	−0.968513	−0.484256	−	0.874926i	$-0.660910\pi$
$541$	−22.5270	−0.968513	−0.484256	+	0.874926i	$0.660910\pi$
$542$	17.6159	0.756666
$543$	−0.157451	−0.00675689
$544$	0	0
$545$	−0.807467	−0.0345881
$546$	2.98040	0.127549
$547$	2.53714	0.108480	0.0542402	−	0.998528i	$-0.482726\pi$
$547$	2.53714	0.108480	0.0542402	+	0.998528i	$0.482726\pi$
$548$	−6.82295	−0.291462
$549$	−10.6946	−0.456434
$550$	30.4415	1.29803
$551$	−18.8176	−0.801656
$552$	−6.00000	−0.255377
$553$	23.7128	1.00837
$554$	−1.10338	−0.0468781
$555$	0.443258	0.0188153
$556$	−16.9067	−0.717005
$557$	24.9317	1.05639	0.528195	−	0.849123i	$-0.322869\pi$
$557$	24.9317	1.05639	0.528195	+	0.849123i	$0.322869\pi$
$558$	7.29086	0.308647
$559$	−11.8527	−0.501314
$560$	0.204393	0.00863718
$561$	0	0
$562$	−6.28581	−0.265151
$563$	−31.3354	−1.32063	−0.660316	−	0.750988i	$-0.729577\pi$
$563$	−31.3354	−1.32063	−0.660316	+	0.750988i	$0.729577\pi$
$564$	5.43376	0.228803
$565$	−0.552623	−0.0232490
$566$	−3.27631	−0.137714
$567$	1.69459	0.0711662
$568$	−15.4047	−0.646365
$569$	−22.9121	−0.960525	−0.480263	−	0.877125i	$-0.659459\pi$
$569$	−22.9121	−0.960525	−0.480263	+	0.877125i	$0.659459\pi$
$570$	−0.581719	−0.0243655
$571$	−10.5425	−0.441191	−0.220595	−	0.975365i	$-0.570800\pi$
$571$	−10.5425	−0.441191	−0.220595	+	0.975365i	$0.570800\pi$
$572$	−10.7392	−0.449027
$573$	−6.90673	−0.288533
$574$	5.33450	0.222658
$575$	−29.9127	−1.24745
$576$	1.00000	0.0416667
$577$	30.9418	1.28812	0.644062	−	0.764973i	$-0.277248\pi$
$577$	30.9418	1.28812	0.644062	+	0.764973i	$0.277248\pi$
$578$	0	0
$579$	−11.5253	−0.478974
$580$	−0.470599	−0.0195406
$581$	−25.2276	−1.04662
$582$	9.08647	0.376646
$583$	28.8016	1.19284
$584$	12.5963	0.521237
$585$	−0.212134	−0.00877065
$586$	−5.76651	−0.238212
$587$	−18.7861	−0.775386	−0.387693	−	0.921789i	$-0.626728\pi$
$587$	−18.7861	−0.775386	−0.387693	+	0.921789i	$0.626728\pi$
$588$	−4.12836	−0.170251
$589$	−35.1634	−1.44888
$590$	−0.255777	−0.0105302
$591$	6.71419	0.276185
$592$	3.67499	0.151041
$593$	−15.8817	−0.652185	−0.326093	−	0.945338i	$-0.605732\pi$
$593$	−15.8817	−0.652185	−0.326093	+	0.945338i	$0.605732\pi$
$594$	−6.10607	−0.250535
$595$	0	0
$596$	11.2831	0.462175
$597$	7.22937	0.295878
$598$	10.5526	0.431529
$599$	2.86215	0.116944	0.0584721	−	0.998289i	$-0.481377\pi$
$599$	2.86215	0.116944	0.0584721	+	0.998289i	$0.481377\pi$
$600$	4.98545	0.203530
$601$	−16.7929	−0.684997	−0.342499	−	0.939518i	$-0.611273\pi$
$601$	−16.7929	−0.684997	−0.342499	+	0.939518i	$0.611273\pi$
$602$	−11.4201	−0.465451
$603$	−5.88713	−0.239742
$604$	23.1702	0.942784
$605$	3.17024	0.128889
$606$	−2.24897	−0.0913582
$607$	−11.7151	−0.475502	−0.237751	−	0.971326i	$-0.576410\pi$
$607$	−11.7151	−0.475502	−0.237751	+	0.971326i	$0.576410\pi$
$608$	−4.82295	−0.195596
$609$	−6.61175	−0.267922
$610$	1.28993	0.0522276
$611$	−9.55674	−0.386624
$612$	0	0
$613$	−14.8675	−0.600494	−0.300247	−	0.953862i	$-0.597069\pi$
$613$	−14.8675	−0.600494	−0.300247	+	0.953862i	$0.597069\pi$
$614$	1.26083	0.0508830
$615$	−0.379690	−0.0153106
$616$	−10.3473	−0.416904
$617$	−49.0607	−1.97511	−0.987554	−	0.157280i	$-0.949728\pi$
$617$	−49.0607	−1.97511	−0.987554	+	0.157280i	$0.949728\pi$
$618$	−18.3259	−0.737177
$619$	−4.17293	−0.167724	−0.0838622	−	0.996477i	$-0.526726\pi$
$619$	−4.17293	−0.167724	−0.0838622	+	0.996477i	$0.526726\pi$
$620$	−0.879385	−0.0353170
$621$	6.00000	0.240772
$622$	−4.77837	−0.191595
$623$	27.9573	1.12009
$624$	−1.75877	−0.0704072
$625$	24.7820	0.991280
$626$	6.25671	0.250068
$627$	29.4492	1.17609
$628$	5.38919	0.215052
$629$	0	0
$630$	−0.204393	−0.00814321
$631$	16.2267	0.645974	0.322987	−	0.946403i	$-0.395313\pi$
$631$	16.2267	0.645974	0.322987	+	0.946403i	$0.395313\pi$
$632$	−13.9932	−0.556619
$633$	10.5371	0.418814
$634$	26.1925	1.04024
$635$	−0.519296	−0.0206076
$636$	4.71688	0.187037
$637$	7.26083	0.287685
$638$	23.8239	0.943197
$639$	15.4047	0.609399
$640$	−0.120615	−0.00476772
$641$	−5.83244	−0.230368	−0.115184	−	0.993344i	$-0.536746\pi$
$641$	−5.83244	−0.230368	−0.115184	+	0.993344i	$0.536746\pi$
$642$	−14.1138	−0.557028
$643$	−5.14796	−0.203016	−0.101508	−	0.994835i	$-0.532367\pi$
$643$	−5.14796	−0.203016	−0.101508	+	0.994835i	$0.532367\pi$
$644$	10.1676	0.400658
$645$	0.812843	0.0320057
$646$	0	0
$647$	−5.59121	−0.219813	−0.109907	−	0.993942i	$-0.535055\pi$
$647$	−5.59121	−0.219813	−0.109907	+	0.993942i	$0.535055\pi$
$648$	−1.00000	−0.0392837
$649$	12.9486	0.508278
$650$	−8.76827	−0.343920
$651$	−12.3550	−0.484232
$652$	−17.8871	−0.700514
$653$	−15.8716	−0.621105	−0.310553	−	0.950556i	$-0.600514\pi$
$653$	−15.8716	−0.621105	−0.310553	+	0.950556i	$0.600514\pi$
$654$	6.69459	0.261779
$655$	−1.81109	−0.0707651
$656$	−3.14796	−0.122907
$657$	−12.5963	−0.491427
$658$	−9.20801	−0.358966
$659$	26.0033	1.01294	0.506472	−	0.862256i	$-0.330949\pi$
$659$	26.0033	1.01294	0.506472	+	0.862256i	$0.330949\pi$
$660$	0.736482	0.0286675
$661$	11.7980	0.458888	0.229444	−	0.973322i	$-0.426309\pi$
$661$	11.7980	0.458888	0.229444	+	0.973322i	$0.426309\pi$
$662$	12.5817	0.489002
$663$	0	0
$664$	14.8871	0.577733
$665$	0.985776	0.0382268
$666$	−3.67499	−0.142403
$667$	−23.4100	−0.906441
$668$	5.84255	0.226055
$669$	−11.0027	−0.425389
$670$	0.710074	0.0274326
$671$	−65.3019	−2.52095
$672$	−1.69459	−0.0653703
$673$	47.9026	1.84651	0.923255	−	0.384188i	$-0.125519\pi$
$673$	47.9026	1.84651	0.923255	+	0.384188i	$0.125519\pi$
$674$	23.2175	0.894305
$675$	−4.98545	−0.191890
$676$	−9.90673	−0.381028
$677$	40.4303	1.55386	0.776930	−	0.629586i	$-0.216776\pi$
$677$	40.4303	1.55386	0.776930	+	0.629586i	$0.216776\pi$
$678$	4.58172	0.175960
$679$	−15.3979	−0.590916
$680$	0	0
$681$	0.758770	0.0290761
$682$	44.5185	1.70470
$683$	8.08141	0.309227	0.154613	−	0.987975i	$-0.450587\pi$
$683$	8.08141	0.309227	0.154613	+	0.987975i	$0.450587\pi$
$684$	4.82295	0.184410
$685$	−0.822948	−0.0314432
$686$	18.8580	0.720003
$687$	24.5817	0.937851
$688$	6.73917	0.256928
$689$	−8.29591	−0.316049
$690$	−0.723689	−0.0275504
$691$	−2.34049	−0.0890364	−0.0445182	−	0.999009i	$-0.514175\pi$
$691$	−2.34049	−0.0890364	−0.0445182	+	0.999009i	$0.514175\pi$
$692$	−5.41147	−0.205713
$693$	10.3473	0.393061
$694$	10.7706	0.408848
$695$	−2.03920	−0.0773513
$696$	3.90167	0.147893
$697$	0	0
$698$	29.9864	1.13500
$699$	5.67499	0.214648
$700$	−8.44831	−0.319316
$701$	19.5534	0.738523	0.369262	−	0.929325i	$-0.379611\pi$
$701$	19.5534	0.738523	0.369262	+	0.929325i	$0.379611\pi$
$702$	1.75877	0.0663805
$703$	17.7243	0.668485
$704$	6.10607	0.230131
$705$	0.655392	0.0246835
$706$	29.6459	1.11574
$707$	3.81109	0.143331
$708$	2.12061	0.0796976
$709$	35.2472	1.32374	0.661868	−	0.749620i	$-0.269764\pi$
$709$	35.2472	1.32374	0.661868	+	0.749620i	$0.269764\pi$
$710$	−1.85803	−0.0697306
$711$	13.9932	0.524786
$712$	−16.4979	−0.618286
$713$	−43.7452	−1.63827
$714$	0	0
$715$	−1.29530	−0.0484416
$716$	7.24123	0.270617
$717$	25.5175	0.952970
$718$	18.7101	0.698254
$719$	11.6013	0.432656	0.216328	−	0.976321i	$-0.430592\pi$
$719$	11.6013	0.432656	0.216328	+	0.976321i	$0.430592\pi$
$720$	0.120615	0.00449505
$721$	31.0550	1.15655
$722$	−4.26083	−0.158572
$723$	20.4320	0.759875
$724$	−0.157451	−0.00585163
$725$	19.4516	0.722415
$726$	−26.2841	−0.975493
$727$	41.7083	1.54688	0.773438	−	0.633872i	$-0.218535\pi$
$727$	41.7083	1.54688	0.773438	+	0.633872i	$0.218535\pi$
$728$	2.98040	0.110461
$729$	1.00000	0.0370370
$730$	1.51930	0.0562317
$731$	0	0
$732$	−10.6946	−0.395284
$733$	−46.2877	−1.70967	−0.854837	−	0.518896i	$-0.826343\pi$
$733$	−46.2877	−1.70967	−0.854837	+	0.518896i	$0.826343\pi$
$734$	−5.84018	−0.215565
$735$	−0.497941	−0.0183668
$736$	−6.00000	−0.221163
$737$	−35.9472	−1.32413
$738$	3.14796	0.115878
$739$	31.2080	1.14801	0.574003	−	0.818853i	$-0.305390\pi$
$739$	31.2080	1.14801	0.574003	+	0.818853i	$0.305390\pi$
$740$	0.443258	0.0162945
$741$	−8.48246	−0.311611
$742$	−7.99319	−0.293439
$743$	−30.5134	−1.11943	−0.559714	−	0.828686i	$-0.689089\pi$
$743$	−30.5134	−1.11943	−0.559714	+	0.828686i	$0.689089\pi$
$744$	7.29086	0.267296
$745$	1.36091	0.0498599
$746$	10.6209	0.388859
$747$	−14.8871	−0.544691
$748$	0	0
$749$	23.9172	0.873914
$750$	1.20439	0.0439782
$751$	30.4320	1.11048	0.555240	−	0.831690i	$-0.312626\pi$
$751$	30.4320	1.11048	0.555240	+	0.831690i	$0.312626\pi$
$752$	5.43376	0.198149
$753$	7.50299	0.273424
$754$	−6.86215	−0.249905
$755$	2.79467	0.101709
$756$	1.69459	0.0616317
$757$	17.5567	0.638111	0.319055	−	0.947736i	$-0.396634\pi$
$757$	17.5567	0.638111	0.319055	+	0.947736i	$0.396634\pi$
$758$	0.340489	0.0123671
$759$	36.6364	1.32982
$760$	−0.581719	−0.0211012
$761$	−4.69459	−0.170179	−0.0850894	−	0.996373i	$-0.527118\pi$
$761$	−4.69459	−0.170179	−0.0850894	+	0.996373i	$0.527118\pi$
$762$	4.30541	0.155968
$763$	−11.3446	−0.410702
$764$	−6.90673	−0.249877
$765$	0	0
$766$	30.8776	1.11565
$767$	−3.72967	−0.134671
$768$	1.00000	0.0360844
$769$	2.36184	0.0851703	0.0425851	−	0.999093i	$-0.486441\pi$
$769$	2.36184	0.0851703	0.0425851	+	0.999093i	$0.486441\pi$
$770$	−1.24804	−0.0449761
$771$	−18.3851	−0.662122
$772$	−11.5253	−0.414804
$773$	29.4561	1.05946	0.529730	−	0.848166i	$-0.322293\pi$
$773$	29.4561	1.05946	0.529730	+	0.848166i	$0.322293\pi$
$774$	−6.73917	−0.242234
$775$	36.3482	1.30567
$776$	9.08647	0.326185
$777$	6.22762	0.223414
$778$	3.25166	0.116578
$779$	−15.1824	−0.543967
$780$	−0.212134	−0.00759560
$781$	94.0619	3.36580
$782$	0	0
$783$	−3.90167	−0.139434
$784$	−4.12836	−0.147441
$785$	0.650015	0.0232000
$786$	15.0155	0.535584
$787$	−55.6715	−1.98447	−0.992237	−	0.124361i	$-0.960312\pi$
$787$	−55.6715	−1.98447	−0.992237	+	0.124361i	$0.960312\pi$
$788$	6.71419	0.239183
$789$	−3.01960	−0.107501
$790$	−1.68779	−0.0600487
$791$	−7.76415	−0.276061
$792$	−6.10607	−0.216970
$793$	18.8093	0.667939
$794$	18.3405	0.650880
$795$	0.568926	0.0201777
$796$	7.22937	0.256238
$797$	−19.7802	−0.700652	−0.350326	−	0.936628i	$-0.613929\pi$
$797$	−19.7802	−0.700652	−0.350326	+	0.936628i	$0.613929\pi$
$798$	−8.17293	−0.289319
$799$	0	0
$800$	4.98545	0.176262
$801$	16.4979	0.582926
$802$	18.7101	0.660676
$803$	−76.9136	−2.71422
$804$	−5.88713	−0.207623
$805$	1.22636	0.0432234
$806$	−12.8229	−0.451669
$807$	−10.8452	−0.381770
$808$	−2.24897	−0.0791185
$809$	20.9222	0.735586	0.367793	−	0.929908i	$-0.380114\pi$
$809$	20.9222	0.735586	0.367793	+	0.929908i	$0.380114\pi$
$810$	−0.120615	−0.00423797
$811$	−0.896622	−0.0314846	−0.0157423	−	0.999876i	$-0.505011\pi$
$811$	−0.896622	−0.0314846	−0.0157423	+	0.999876i	$0.505011\pi$
$812$	−6.61175	−0.232027
$813$	−17.6159	−0.617815
$814$	−22.4397	−0.786513
$815$	−2.15745	−0.0755722
$816$	0	0
$817$	32.5027	1.13712
$818$	5.94862	0.207988
$819$	−2.98040	−0.104144
$820$	−0.379690	−0.0132593
$821$	−37.6851	−1.31522	−0.657609	−	0.753359i	$-0.728432\pi$
$821$	−37.6851	−1.31522	−0.657609	+	0.753359i	$0.728432\pi$
$822$	6.82295	0.237978
$823$	−22.1607	−0.772475	−0.386238	−	0.922399i	$-0.626226\pi$
$823$	−22.1607	−0.772475	−0.386238	+	0.922399i	$0.626226\pi$
$824$	−18.3259	−0.638414
$825$	−30.4415	−1.05984
$826$	−3.59358	−0.125037
$827$	30.8016	1.07108	0.535538	−	0.844511i	$-0.320109\pi$
$827$	30.8016	1.07108	0.535538	+	0.844511i	$0.320109\pi$
$828$	6.00000	0.208514
$829$	18.5716	0.645019	0.322509	−	0.946566i	$-0.395474\pi$
$829$	18.5716	0.645019	0.322509	+	0.946566i	$0.395474\pi$
$830$	1.79561	0.0623264
$831$	1.10338	0.0382758
$832$	−1.75877	−0.0609744
$833$	0	0
$834$	16.9067	0.585432
$835$	0.704698	0.0243871
$836$	29.4492	1.01852
$837$	−7.29086	−0.252009
$838$	12.8990	0.445588
$839$	−27.9763	−0.965848	−0.482924	−	0.875662i	$-0.660425\pi$
$839$	−27.9763	−0.965848	−0.482924	+	0.875662i	$0.660425\pi$
$840$	−0.204393	−0.00705222
$841$	−13.7769	−0.475067
$842$	27.2472	0.939001
$843$	6.28581	0.216495
$844$	10.5371	0.362703
$845$	−1.19490	−0.0411057
$846$	−5.43376	−0.186817
$847$	44.5408	1.53044
$848$	4.71688	0.161978
$849$	3.27631	0.112443
$850$	0	0
$851$	22.0500	0.755863
$852$	15.4047	0.527755
$853$	10.6500	0.364650	0.182325	−	0.983238i	$-0.441638\pi$
$853$	10.6500	0.364650	0.182325	+	0.983238i	$0.441638\pi$
$854$	18.1230	0.620156
$855$	0.581719	0.0198944
$856$	−14.1138	−0.482400
$857$	42.3560	1.44685	0.723426	−	0.690402i	$-0.242566\pi$
$857$	42.3560	1.44685	0.723426	+	0.690402i	$0.242566\pi$
$858$	10.7392	0.366629
$859$	52.2039	1.78117	0.890587	−	0.454813i	$-0.150294\pi$
$859$	52.2039	1.78117	0.890587	+	0.454813i	$0.150294\pi$
$860$	0.812843	0.0277177
$861$	−5.33450	−0.181799
$862$	12.0547	0.410584
$863$	48.2330	1.64187	0.820935	−	0.571022i	$-0.193453\pi$
$863$	48.2330	1.64187	0.820935	+	0.571022i	$0.193453\pi$
$864$	−1.00000	−0.0340207
$865$	−0.652704	−0.0221926
$866$	10.6031	0.360307
$867$	0	0
$868$	−12.3550	−0.419357
$869$	85.4434	2.89847
$870$	0.470599	0.0159548
$871$	10.3541	0.350835
$872$	6.69459	0.226708
$873$	−9.08647	−0.307530
$874$	−28.9377	−0.978832
$875$	−2.04096	−0.0689969
$876$	−12.5963	−0.425588
$877$	−29.4884	−0.995754	−0.497877	−	0.867248i	$-0.665887\pi$
$877$	−29.4884	−0.995754	−0.497877	+	0.867248i	$0.665887\pi$
$878$	−7.09327	−0.239386
$879$	5.76651	0.194500
$880$	0.736482	0.0248268
$881$	6.92034	0.233152	0.116576	−	0.993182i	$-0.462808\pi$
$881$	6.92034	0.233152	0.116576	+	0.993182i	$0.462808\pi$
$882$	4.12836	0.139009
$883$	−19.0405	−0.640762	−0.320381	−	0.947289i	$-0.603811\pi$
$883$	−19.0405	−0.640762	−0.320381	+	0.947289i	$0.603811\pi$
$884$	0	0
$885$	0.255777	0.00859786
$886$	0.206148	0.00692566
$887$	−7.36009	−0.247128	−0.123564	−	0.992337i	$-0.539432\pi$
$887$	−7.36009	−0.247128	−0.123564	+	0.992337i	$0.539432\pi$
$888$	−3.67499	−0.123325
$889$	−7.29591	−0.244697
$890$	−1.98990	−0.0667014
$891$	6.10607	0.204561
$892$	−11.0027	−0.368397
$893$	26.2068	0.876976
$894$	−11.2831	−0.377364
$895$	0.873399	0.0291945
$896$	−1.69459	−0.0566124
$897$	−10.5526	−0.352342
$898$	−33.1343	−1.10571
$899$	28.4466	0.948746
$900$	−4.98545	−0.166182
$901$	0	0
$902$	19.2216	0.640010
$903$	11.4201	0.380039
$904$	4.58172	0.152386
$905$	−0.0189910	−0.000631281 0
$906$	−23.1702	−0.769780
$907$	42.7837	1.42061	0.710306	−	0.703894i	$-0.248557\pi$
$907$	42.7837	1.42061	0.710306	+	0.703894i	$0.248557\pi$
$908$	0.758770	0.0251807
$909$	2.24897	0.0745936
$910$	0.359480	0.0119167
$911$	0.508045	0.0168323	0.00841615	−	0.999965i	$-0.497321\pi$
$911$	0.508045	0.0168323	0.00841615	+	0.999965i	$0.497321\pi$
$912$	4.82295	0.159704
$913$	−90.9018	−3.00841
$914$	11.9463	0.395147
$915$	−1.28993	−0.0426436
$916$	24.5817	0.812203
$917$	−25.4451	−0.840272
$918$	0	0
$919$	8.20801	0.270757	0.135379	−	0.990794i	$-0.456775\pi$
$919$	8.20801	0.270757	0.135379	+	0.990794i	$0.456775\pi$
$920$	−0.723689	−0.0238593
$921$	−1.26083	−0.0415458
$922$	−25.5185	−0.840406
$923$	−27.0933	−0.891786
$924$	10.3473	0.340401
$925$	−18.3215	−0.602407
$926$	36.5449	1.20094
$927$	18.3259	0.601903
$928$	3.90167	0.128079
$929$	1.85616	0.0608987	0.0304494	−	0.999536i	$-0.490306\pi$
$929$	1.85616	0.0608987	0.0304494	+	0.999536i	$0.490306\pi$
$930$	0.879385	0.0288362
$931$	−19.9108	−0.652552
$932$	5.67499	0.185891
$933$	4.77837	0.156437
$934$	−20.7246	−0.678130
$935$	0	0
$936$	1.75877	0.0574872
$937$	−8.40104	−0.274450	−0.137225	−	0.990540i	$-0.543818\pi$
$937$	−8.40104	−0.274450	−0.137225	+	0.990540i	$0.543818\pi$
$938$	9.97628	0.325737
$939$	−6.25671	−0.204180
$940$	0.655392	0.0213765
$941$	−32.9459	−1.07401	−0.537003	−	0.843580i	$-0.680444\pi$
$941$	−32.9459	−1.07401	−0.537003	+	0.843580i	$0.680444\pi$
$942$	−5.38919	−0.175589
$943$	−18.8877	−0.615069
$944$	2.12061	0.0690201
$945$	0.204393	0.00664890
$946$	−41.1498	−1.33790
$947$	−19.6182	−0.637507	−0.318753	−	0.947838i	$-0.603264\pi$
$947$	−19.6182	−0.637507	−0.318753	+	0.947838i	$0.603264\pi$
$948$	13.9932	0.454478
$949$	22.1539	0.719147
$950$	24.0446	0.780109
$951$	−26.1925	−0.849351
$952$	0	0
$953$	−51.5931	−1.67126	−0.835632	−	0.549290i	$-0.814898\pi$
$953$	−51.5931	−1.67126	−0.835632	+	0.549290i	$0.814898\pi$
$954$	−4.71688	−0.152715
$955$	−0.833053	−0.0269570
$956$	25.5175	0.825296
$957$	−23.8239	−0.770117
$958$	31.6168	1.02149
$959$	−11.5621	−0.373360
$960$	0.120615	0.00389282
$961$	22.1566	0.714730
$962$	6.46347	0.208391
$963$	14.1138	0.454811
$964$	20.4320	0.658071
$965$	−1.39012	−0.0447495
$966$	−10.1676	−0.327136
$967$	−39.7475	−1.27819	−0.639097	−	0.769126i	$-0.720692\pi$
$967$	−39.7475	−1.27819	−0.639097	+	0.769126i	$0.720692\pi$
$968$	−26.2841	−0.844801
$969$	0	0
$970$	1.09596	0.0351892
$971$	39.5398	1.26889	0.634447	−	0.772967i	$-0.281228\pi$
$971$	39.5398	1.26889	0.634447	+	0.772967i	$0.281228\pi$
$972$	1.00000	0.0320750
$973$	−28.6500	−0.918477
$974$	−21.2841	−0.681985
$975$	8.76827	0.280809
$976$	−10.6946	−0.342326
$977$	10.3696	0.331752	0.165876	−	0.986147i	$-0.446955\pi$
$977$	10.3696	0.331752	0.165876	+	0.986147i	$0.446955\pi$
$978$	17.8871	0.571967
$979$	100.738	3.21959
$980$	−0.497941	−0.0159061
$981$	−6.69459	−0.213742
$982$	19.5253	0.623077
$983$	3.18243	0.101504	0.0507519	−	0.998711i	$-0.483838\pi$
$983$	3.18243	0.101504	0.0507519	+	0.998711i	$0.483838\pi$
$984$	3.14796	0.100353
$985$	0.809831	0.0258034
$986$	0	0
$987$	9.20801	0.293094
$988$	−8.48246	−0.269863
$989$	40.4350	1.28576
$990$	−0.736482	−0.0234069
$991$	−13.6946	−0.435023	−0.217512	−	0.976058i	$-0.569794\pi$
$991$	−13.6946	−0.435023	−0.217512	+	0.976058i	$0.569794\pi$
$992$	7.29086	0.231485
$993$	−12.5817	−0.399269
$994$	−26.1046	−0.827989
$995$	0.871969	0.0276433
$996$	−14.8871	−0.471717
$997$	0.964918	0.0305593	0.0152796	−	0.999883i	$-0.495136\pi$
$997$	0.964918	0.0305593	0.0152796	+	0.999883i	$0.495136\pi$
$998$	−22.5972	−0.715302
$999$	3.67499	0.116272

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.a.q.1.1	yes	3
3.2	odd	2		5202.2.a.bm.1.3		3
17.2	even	8		1734.2.f.n.1483.6		12
17.4	even	4		1734.2.b.j.577.3		6
17.8	even	8		1734.2.f.n.829.1		12
17.9	even	8		1734.2.f.n.829.6		12
17.13	even	4		1734.2.b.j.577.4		6
17.15	even	8		1734.2.f.n.1483.1		12
17.16	even	2		1734.2.a.p.1.3	✓	3
51.50	odd	2		5202.2.a.bp.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.p.1.3	✓	3	17.16	even	2
1734.2.a.q.1.1	yes	3	1.1	even	1	trivial
1734.2.b.j.577.3		6	17.4	even	4
1734.2.b.j.577.4		6	17.13	even	4
1734.2.f.n.829.1		12	17.8	even	8
1734.2.f.n.829.6		12	17.9	even	8
1734.2.f.n.1483.1		12	17.15	even	8
1734.2.f.n.1483.6		12	17.2	even	8
5202.2.a.bm.1.3		3	3.2	odd	2
5202.2.a.bp.1.1		3	51.50	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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.120615 q^{5} -1.00000 q^{6} +1.69459 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.120615 q^{5} -1.00000 q^{6} +1.69459 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.120615 q^{10} +6.10607 q^{11} +1.00000 q^{12} -1.75877 q^{13} -1.69459 q^{14} +0.120615 q^{15} +1.00000 q^{16} -1.00000 q^{18} +4.82295 q^{19} +0.120615 q^{20} +1.69459 q^{21} -6.10607 q^{22} +6.00000 q^{23} -1.00000 q^{24} -4.98545 q^{25} +1.75877 q^{26} +1.00000 q^{27} +1.69459 q^{28} -3.90167 q^{29} -0.120615 q^{30} -7.29086 q^{31} -1.00000 q^{32} +6.10607 q^{33} +0.204393 q^{35} +1.00000 q^{36} +3.67499 q^{37} -4.82295 q^{38} -1.75877 q^{39} -0.120615 q^{40} -3.14796 q^{41} -1.69459 q^{42} +6.73917 q^{43} +6.10607 q^{44} +0.120615 q^{45} -6.00000 q^{46} +5.43376 q^{47} +1.00000 q^{48} -4.12836 q^{49} +4.98545 q^{50} -1.75877 q^{52} +4.71688 q^{53} -1.00000 q^{54} +0.736482 q^{55} -1.69459 q^{56} +4.82295 q^{57} +3.90167 q^{58} +2.12061 q^{59} +0.120615 q^{60} -10.6946 q^{61} +7.29086 q^{62} +1.69459 q^{63} +1.00000 q^{64} -0.212134 q^{65} -6.10607 q^{66} -5.88713 q^{67} +6.00000 q^{69} -0.204393 q^{70} +15.4047 q^{71} -1.00000 q^{72} -12.5963 q^{73} -3.67499 q^{74} -4.98545 q^{75} +4.82295 q^{76} +10.3473 q^{77} +1.75877 q^{78} +13.9932 q^{79} +0.120615 q^{80} +1.00000 q^{81} +3.14796 q^{82} -14.8871 q^{83} +1.69459 q^{84} -6.73917 q^{86} -3.90167 q^{87} -6.10607 q^{88} +16.4979 q^{89} -0.120615 q^{90} -2.98040 q^{91} +6.00000 q^{92} -7.29086 q^{93} -5.43376 q^{94} +0.581719 q^{95} -1.00000 q^{96} -9.08647 q^{97} +4.12836 q^{98} +6.10607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 6 q^{10} + 6 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} - 6 q^{22} + 18 q^{23} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} + 3 q^{28} - 6 q^{30} - 6 q^{31} - 3 q^{32} + 6 q^{33} + 3 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} - 6 q^{40} + 6 q^{41} - 3 q^{42} + 6 q^{43} + 6 q^{44} + 6 q^{45} - 18 q^{46} + 3 q^{48} + 6 q^{49} - 3 q^{50} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} - 6 q^{57} + 12 q^{59} + 6 q^{60} - 30 q^{61} + 6 q^{62} + 3 q^{63} + 3 q^{64} + 24 q^{65} - 6 q^{66} + 12 q^{67} + 18 q^{69} - 6 q^{71} - 3 q^{72} - 24 q^{73} - 6 q^{74} + 3 q^{75} - 6 q^{76} + 30 q^{77} - 6 q^{78} + 6 q^{80} + 3 q^{81} - 6 q^{82} - 15 q^{83} + 3 q^{84} - 6 q^{86} - 6 q^{88} + 24 q^{89} - 6 q^{90} - 6 q^{91} + 18 q^{92} - 6 q^{93} - 30 q^{95} - 3 q^{96} - 12 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 6 * q^10 + 6 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 - 6 * q^22 + 18 * q^23 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^30 - 6 * q^31 - 3 * q^32 + 6 * q^33 + 3 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 - 6 * q^40 + 6 * q^41 - 3 * q^42 + 6 * q^43 + 6 * q^44 + 6 * q^45 - 18 * q^46 + 3 * q^48 + 6 * q^49 - 3 * q^50 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 - 6 * q^57 + 12 * q^59 + 6 * q^60 - 30 * q^61 + 6 * q^62 + 3 * q^63 + 3 * q^64 + 24 * q^65 - 6 * q^66 + 12 * q^67 + 18 * q^69 - 6 * q^71 - 3 * q^72 - 24 * q^73 - 6 * q^74 + 3 * q^75 - 6 * q^76 + 30 * q^77 - 6 * q^78 + 6 * q^80 + 3 * q^81 - 6 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^86 - 6 * q^88 + 24 * q^89 - 6 * q^90 - 6 * q^91 + 18 * q^92 - 6 * q^93 - 30 * q^95 - 3 * q^96 - 12 * q^97 - 6 * q^98 + 6 * q^99

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