LMFDB - Embedded newform 1734.2.b.j.577.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(577,1734)]

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, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1734.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.419904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 9x^{2} + 1 $ x^6 + 6x^4 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			577.3
Root			$1.87939i$ of defining polynomial
Character	$\chi$	$=$	1734.577
Dual form			1734.2.b.j.577.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1734\mathbb{Z}\right)^\times$.

$n$	$1157$	$1159$
$\chi(n)$	$1$	$-1$

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
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	1.00000	0.500000
$5$	− 0.120615i	− 0.0539406i	−0.999636	−	0.0269703i	$-0.991414\pi$
$5$	− 0.120615i	− 0.0539406i	0.999636	−	0.0269703i	$-0.00858595\pi$
$6$	− 1.00000i	− 0.408248i
$7$	1.69459i	0.640496i	0.947334	+	0.320248i	$0.103766\pi$
$7$	1.69459i	0.640496i	−0.947334	+	0.320248i	$0.896234\pi$
$8$	1.00000	0.353553
$9$	−1.00000	−0.333333
$10$	− 0.120615i	− 0.0381417i
$11$	6.10607i	1.84105i	0.390686	+	0.920524i	$0.372238\pi$
$11$	6.10607i	1.84105i	−0.390686	+	0.920524i	$0.627762\pi$
$12$	− 1.00000i	− 0.288675i
$13$	−1.75877	−0.487795	−0.243898	−	0.969801i	$-0.578426\pi$
$13$	−1.75877	−0.487795	−0.243898	+	0.969801i	$0.578426\pi$
$14$	1.69459i	0.452899i
$15$	−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	$-0.686605\pi$
$19$	−4.82295	−1.10646	−0.553230	+	0.833028i	$0.686605\pi$
$20$	− 0.120615i	− 0.0269703i
$21$	1.69459	0.369790
$22$	6.10607i	1.30182i
$23$	6.00000i	1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$	6.00000i	1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	− 1.00000i	− 0.204124i
$25$	4.98545	0.997090
$26$	−1.75877	−0.344923
$27$	1.00000i	0.192450i
$28$	1.69459i	0.320248i
$29$	3.90167i	0.724523i	0.932077	+	0.362261i	$0.117995\pi$
$29$	3.90167i	0.724523i	−0.932077	+	0.362261i	$0.882005\pi$
$30$	−0.120615	−0.0220211
$31$	7.29086i	1.30948i	0.755855	+	0.654738i	$0.227221\pi$
$31$	7.29086i	1.30948i	−0.755855	+	0.654738i	$0.772779\pi$
$32$	1.00000	0.176777
$33$	6.10607	1.06293
$34$	0	0
$35$	0.204393	0.0345487
$36$	−1.00000	−0.166667
$37$	− 3.67499i	− 0.604165i	−0.953282	−	0.302083i	$-0.902318\pi$
$37$	− 3.67499i	− 0.604165i	0.953282	−	0.302083i	$-0.0976818\pi$
$38$	−4.82295	−0.782386
$39$	1.75877i	0.281629i
$40$	− 0.120615i	− 0.0190709i
$41$	− 3.14796i	− 0.491628i	−0.969317	−	0.245814i	$-0.920945\pi$
$41$	− 3.14796i	− 0.491628i	0.969317	−	0.245814i	$-0.0790553\pi$
$42$	1.69459	0.261481
$43$	−6.73917	−1.02771	−0.513857	−	0.857876i	$-0.671784\pi$
$43$	−6.73917	−1.02771	−0.513857	+	0.857876i	$0.671784\pi$
$44$	6.10607i	0.920524i
$45$	0.120615i	0.0179802i
$46$	6.00000i	0.884652i
$47$	5.43376	0.792596	0.396298	−	0.918122i	$-0.370295\pi$
$47$	5.43376	0.792596	0.396298	+	0.918122i	$0.370295\pi$
$48$	− 1.00000i	− 0.144338i
$49$	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	$-0.605013\pi$
$53$	−4.71688	−0.647913	−0.323957	+	0.946072i	$0.605013\pi$
$54$	1.00000i	0.136083i
$55$	0.736482	0.0993072
$56$	1.69459i	0.226449i
$57$	4.82295i	0.638815i
$58$	3.90167i	0.512315i
$59$	−2.12061	−0.276081	−0.138040	−	0.990427i	$-0.544080\pi$
$59$	−2.12061	−0.276081	−0.138040	+	0.990427i	$0.544080\pi$
$60$	−0.120615	−0.0155713
$61$	− 10.6946i	− 1.36930i	−0.728871	−	0.684651i	$-0.759955\pi$
$61$	− 10.6946i	− 1.36930i	0.728871	−	0.684651i	$-0.240045\pi$
$62$	7.29086i	0.925940i
$63$	− 1.69459i	− 0.213499i
$64$	1.00000	0.125000
$65$	0.212134i	0.0263119i
$66$	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
$71$	− 15.4047i	− 1.82820i	−0.405492	−	0.914099i	$-0.632900\pi$
$71$	− 15.4047i	− 1.82820i	0.405492	−	0.914099i	$-0.367100\pi$
$72$	−1.00000	−0.117851
$73$	12.5963i	1.47428i	0.675739	+	0.737141i	$0.263825\pi$
$73$	12.5963i	1.47428i	−0.675739	+	0.737141i	$0.736175\pi$
$74$	− 3.67499i	− 0.427209i
$75$	− 4.98545i	− 0.575670i
$76$	−4.82295	−0.553230
$77$	−10.3473	−1.17918
$78$	1.75877i	0.199142i
$79$	13.9932i	1.57436i	0.616725	+	0.787179i	$0.288459\pi$
$79$	13.9932i	1.57436i	−0.616725	+	0.787179i	$0.711541\pi$
$80$	− 0.120615i	− 0.0134851i
$81$	1.00000	0.111111
$82$	− 3.14796i	− 0.347634i
$83$	14.8871	1.63407	0.817037	−	0.576585i	$-0.195615\pi$
$83$	14.8871	1.63407	0.817037	+	0.576585i	$0.195615\pi$
$84$	1.69459	0.184895
$85$	0	0
$86$	−6.73917	−0.726703
$87$	3.90167	0.418303
$88$	6.10607i	0.650909i
$89$	16.4979	1.74878	0.874389	−	0.485225i	$-0.161262\pi$
$89$	16.4979	1.74878	0.874389	+	0.485225i	$0.161262\pi$
$90$	0.120615i	0.0127139i
$91$	− 2.98040i	− 0.312431i
$92$	6.00000i	0.625543i
$93$	7.29086	0.756027
$94$	5.43376	0.560450
$95$	0.581719i	0.0596831i
$96$	− 1.00000i	− 0.102062i
$97$	9.08647i	0.922591i	0.887247	+	0.461295i	$0.152615\pi$
$97$	9.08647i	0.922591i	−0.887247	+	0.461295i	$0.847385\pi$
$98$	4.12836	0.417027
$99$	− 6.10607i	− 0.613683i
$100$	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
$105$	− 0.204393i	− 0.0199467i
$106$	−4.71688	−0.458144
$107$	− 14.1138i	− 1.36443i	−0.731150	−	0.682217i	$-0.761016\pi$
$107$	− 14.1138i	− 1.36443i	0.731150	−	0.682217i	$-0.238984\pi$
$108$	1.00000i	0.0962250i
$109$	− 6.69459i	− 0.641226i	−0.947210	−	0.320613i	$-0.896111\pi$
$109$	− 6.69459i	− 0.641226i	0.947210	−	0.320613i	$-0.103889\pi$
$110$	0.736482	0.0702208
$111$	−3.67499	−0.348815
$112$	1.69459i	0.160124i
$113$	− 4.58172i	− 0.431012i	−0.976503	−	0.215506i	$-0.930860\pi$
$113$	− 4.58172i	− 0.431012i	0.976503	−	0.215506i	$-0.0691401\pi$
$114$	4.82295i	0.451710i
$115$	0.723689	0.0674843
$116$	3.90167i	0.362261i
$117$	1.75877	0.162598
$118$	−2.12061	−0.195218
$119$	0	0
$120$	−0.120615	−0.0110106
$121$	−26.2841	−2.38946
$122$	− 10.6946i	− 0.968243i
$123$	−3.14796	−0.283842
$124$	7.29086i	0.654738i
$125$	− 1.20439i	− 0.107724i
$126$	− 1.69459i	− 0.150966i
$127$	4.30541	0.382043	0.191022	−	0.981586i	$-0.438820\pi$
$127$	4.30541	0.382043	0.191022	+	0.981586i	$0.438820\pi$
$128$	1.00000	0.0883883
$129$	6.73917i	0.593351i
$130$	0.212134i	0.0186054i
$131$	15.0155i	1.31191i	0.754801	+	0.655954i	$0.227734\pi$
$131$	15.0155i	1.31191i	−0.754801	+	0.655954i	$0.772266\pi$
$132$	6.10607	0.531465
$133$	− 8.17293i	− 0.708683i
$134$	−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
$139$	16.9067i	1.43401i	0.697068	+	0.717005i	$0.254488\pi$
$139$	16.9067i	1.43401i	−0.697068	+	0.717005i	$0.745512\pi$
$140$	0.204393	0.0172744
$141$	− 5.43376i	− 0.457605i
$142$	− 15.4047i	− 1.29273i
$143$	− 10.7392i	− 0.898055i
$144$	−1.00000	−0.0833333
$145$	0.470599	0.0390812
$146$	12.5963i	1.04247i
$147$	− 4.12836i	− 0.340501i
$148$	− 3.67499i	− 0.302083i
$149$	11.2831	0.924349	0.462175	−	0.886789i	$-0.347069\pi$
$149$	11.2831	0.924349	0.462175	+	0.886789i	$0.347069\pi$
$150$	− 4.98545i	− 0.407060i
$151$	−23.1702	−1.88557	−0.942784	−	0.333404i	$-0.891803\pi$
$151$	−23.1702	−1.88557	−0.942784	+	0.333404i	$0.891803\pi$
$152$	−4.82295	−0.391193
$153$	0	0
$154$	−10.3473	−0.833809
$155$	0.879385	0.0706339
$156$	1.75877i	0.140814i
$157$	5.38919	0.430104	0.215052	−	0.976603i	$-0.431008\pi$
$157$	5.38919	0.430104	0.215052	+	0.976603i	$0.431008\pi$
$158$	13.9932i	1.11324i
$159$	4.71688i	0.374073i
$160$	− 0.120615i	− 0.00953543i
$161$	−10.1676	−0.801316
$162$	1.00000	0.0785674
$163$	− 17.8871i	− 1.40103i	−0.713639	−	0.700514i	$-0.752954\pi$
$163$	− 17.8871i	− 1.40103i	0.713639	−	0.700514i	$-0.247046\pi$
$164$	− 3.14796i	− 0.245814i
$165$	− 0.736482i	− 0.0573350i
$166$	14.8871	1.15547
$167$	− 5.84255i	− 0.452110i	−0.974115	−	0.226055i	$-0.927417\pi$
$167$	− 5.84255i	− 0.452110i	0.974115	−	0.226055i	$-0.0725829\pi$
$168$	1.69459	0.130741
$169$	−9.90673	−0.762056
$170$	0	0
$171$	4.82295	0.368820
$172$	−6.73917	−0.513857
$173$	5.41147i	0.411427i	0.978612	+	0.205713i	$0.0659515\pi$
$173$	5.41147i	0.411427i	−0.978612	+	0.205713i	$0.934049\pi$
$174$	3.90167	0.295785
$175$	8.44831i	0.638632i
$176$	6.10607i	0.460262i
$177$	2.12061i	0.159395i
$178$	16.4979	1.23657
$179$	−7.24123	−0.541235	−0.270617	−	0.962687i	$-0.587228\pi$
$179$	−7.24123	−0.541235	−0.270617	+	0.962687i	$0.587228\pi$
$180$	0.120615i	0.00899009i
$181$	− 0.157451i	− 0.0117033i	−0.999983	−	0.00585163i	$-0.998137\pi$
$181$	− 0.157451i	− 0.0117033i	0.999983	−	0.00585163i	$-0.00186264\pi$
$182$	− 2.98040i	− 0.220922i
$183$	−10.6946	−0.790567
$184$	6.00000i	0.442326i
$185$	−0.443258	−0.0325890
$186$	7.29086	0.534592
$187$	0	0
$188$	5.43376	0.396298
$189$	−1.69459	−0.123263
$190$	0.581719i	0.0422023i
$191$	−6.90673	−0.499753	−0.249877	−	0.968278i	$-0.580390\pi$
$191$	−6.90673	−0.499753	−0.249877	+	0.968278i	$0.580390\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 11.5253i	− 0.829608i	−0.909911	−	0.414804i	$-0.863850\pi$
$193$	− 11.5253i	− 0.829608i	0.909911	−	0.414804i	$-0.136150\pi$
$194$	9.08647i	0.652370i
$195$	0.212134	0.0151912
$196$	4.12836	0.294883
$197$	6.71419i	0.478366i	0.970974	+	0.239183i	$0.0768797\pi$
$197$	6.71419i	0.478366i	−0.970974	+	0.239183i	$0.923120\pi$
$198$	− 6.10607i	− 0.433939i
$199$	− 7.22937i	− 0.512476i	−0.966614	−	0.256238i	$-0.917517\pi$
$199$	− 7.22937i	− 0.512476i	0.966614	−	0.256238i	$-0.0824832\pi$
$200$	4.98545	0.352525
$201$	5.88713i	0.415246i
$202$	2.24897	0.158237
$203$	−6.61175	−0.464054
$204$	0	0
$205$	−0.379690	−0.0265187
$206$	18.3259	1.27683
$207$	− 6.00000i	− 0.417029i
$208$	−1.75877	−0.121949
$209$	− 29.4492i	− 2.03705i
$210$	− 0.204393i	− 0.0141044i
$211$	10.5371i	0.725407i	0.931905	+	0.362703i	$0.118146\pi$
$211$	10.5371i	0.725407i	−0.931905	+	0.362703i	$0.881854\pi$
$212$	−4.71688	−0.323957
$213$	−15.4047	−1.05551
$214$	− 14.1138i	− 0.964800i
$215$	0.812843i	0.0554355i
$216$	1.00000i	0.0680414i
$217$	−12.3550	−0.838715
$218$	− 6.69459i	− 0.453415i
$219$	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	$-0.379907\pi$
$223$	11.0027	0.736795	0.368397	+	0.929668i	$0.379907\pi$
$224$	1.69459i	0.113225i
$225$	−4.98545	−0.332363
$226$	− 4.58172i	− 0.304771i
$227$	0.758770i	0.0503614i	0.999683	+	0.0251807i	$0.00801611\pi$
$227$	0.758770i	0.0503614i	−0.999683	+	0.0251807i	$0.991984\pi$
$228$	4.82295i	0.319408i
$229$	−24.5817	−1.62441	−0.812203	−	0.583375i	$-0.801732\pi$
$229$	−24.5817	−1.62441	−0.812203	+	0.583375i	$0.801732\pi$
$230$	0.723689	0.0477186
$231$	10.3473i	0.680802i
$232$	3.90167i	0.256157i
$233$	− 5.67499i	− 0.371781i	−0.982570	−	0.185891i	$-0.940483\pi$
$233$	− 5.67499i	− 0.371781i	0.982570	−	0.185891i	$-0.0595170\pi$
$234$	1.75877	0.114974
$235$	− 0.655392i	− 0.0427531i
$236$	−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
$241$	− 20.4320i	− 1.31614i	−0.752956	−	0.658071i	$-0.771373\pi$
$241$	− 20.4320i	− 1.31614i	0.752956	−	0.658071i	$-0.228627\pi$
$242$	−26.2841	−1.68960
$243$	− 1.00000i	− 0.0641500i
$244$	− 10.6946i	− 0.684651i
$245$	− 0.497941i	− 0.0318123i
$246$	−3.14796	−0.200706
$247$	8.48246	0.539726
$248$	7.29086i	0.462970i
$249$	− 14.8871i	− 0.943433i
$250$	− 1.20439i	− 0.0761725i
$251$	7.50299	0.473585	0.236792	−	0.971560i	$-0.423904\pi$
$251$	7.50299	0.473585	0.236792	+	0.971560i	$0.423904\pi$
$252$	− 1.69459i	− 0.106749i
$253$	−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	$-0.305618\pi$
$257$	18.3851	1.14683	0.573414	+	0.819265i	$0.305618\pi$
$258$	6.73917i	0.419562i
$259$	6.22762	0.386965
$260$	0.212134i	0.0131560i
$261$	− 3.90167i	− 0.241508i
$262$	15.0155i	0.927660i
$263$	3.01960	0.186197	0.0930983	−	0.995657i	$-0.470323\pi$
$263$	3.01960	0.186197	0.0930983	+	0.995657i	$0.470323\pi$
$264$	6.10607	0.375802
$265$	0.568926i	0.0349488i
$266$	− 8.17293i	− 0.501115i
$267$	− 16.4979i	− 1.00966i
$268$	−5.88713	−0.359613
$269$	10.8452i	0.661246i	0.943763	+	0.330623i	$0.107259\pi$
$269$	10.8452i	0.661246i	−0.943763	+	0.330623i	$0.892741\pi$
$270$	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
$275$	30.4415i	1.83569i
$276$	6.00000	0.361158
$277$	− 1.10338i	− 0.0662956i	−0.999450	−	0.0331478i	$-0.989447\pi$
$277$	− 1.10338i	− 0.0662956i	0.999450	−	0.0331478i	$-0.0105532\pi$
$278$	16.9067i	1.01400i
$279$	− 7.29086i	− 0.436492i
$280$	0.204393	0.0122148
$281$	−6.28581	−0.374980	−0.187490	−	0.982267i	$-0.560035\pi$
$281$	−6.28581	−0.374980	−0.187490	+	0.982267i	$0.560035\pi$
$282$	− 5.43376i	− 0.323576i
$283$	3.27631i	0.194757i	0.995247	+	0.0973783i	$0.0310457\pi$
$283$	3.27631i	0.194757i	−0.995247	+	0.0973783i	$0.968954\pi$
$284$	− 15.4047i	− 0.914099i
$285$	0.581719	0.0344580
$286$	− 10.7392i	− 0.635020i
$287$	5.33450	0.314886
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	0.470599	0.0276346
$291$	9.08647	0.532658
$292$	12.5963i	0.737141i
$293$	5.76651	0.336883	0.168442	−	0.985712i	$-0.446127\pi$
$293$	5.76651	0.336883	0.168442	+	0.985712i	$0.446127\pi$
$294$	− 4.12836i	− 0.240771i
$295$	0.255777i	0.0148919i
$296$	− 3.67499i	− 0.213605i
$297$	−6.10607	−0.354310
$298$	11.2831	0.653614
$299$	− 10.5526i	− 0.610274i
$300$	− 4.98545i	− 0.287835i
$301$	− 11.4201i	− 0.658246i
$302$	−23.1702	−1.33330
$303$	− 2.24897i	− 0.129200i
$304$	−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
$309$	− 18.3259i	− 1.04253i
$310$	0.879385	0.0499457
$311$	− 4.77837i	− 0.270957i	−0.990780	−	0.135478i	$-0.956743\pi$
$311$	− 4.77837i	− 0.270957i	0.990780	−	0.135478i	$-0.0432571\pi$
$312$	1.75877i	0.0995708i
$313$	− 6.25671i	− 0.353650i	−0.984242	−	0.176825i	$-0.943417\pi$
$313$	− 6.25671i	− 0.353650i	0.984242	−	0.176825i	$-0.0565827\pi$
$314$	5.38919	0.304129
$315$	−0.204393	−0.0115162
$316$	13.9932i	0.787179i
$317$	− 26.1925i	− 1.47112i	−0.677460	−	0.735560i	$-0.736919\pi$
$317$	− 26.1925i	− 1.47112i	0.677460	−	0.735560i	$-0.263081\pi$
$318$	4.71688i	0.264510i
$319$	−23.8239	−1.33388
$320$	− 0.120615i	− 0.00674257i
$321$	−14.1138	−0.787756
$322$	−10.1676	−0.566616
$323$	0	0
$324$	1.00000	0.0555556
$325$	−8.76827	−0.486376
$326$	− 17.8871i	− 0.990676i
$327$	−6.69459	−0.370212
$328$	− 3.14796i	− 0.173817i
$329$	9.20801i	0.507654i
$330$	− 0.736482i	− 0.0405420i
$331$	12.5817	0.691554	0.345777	−	0.938317i	$-0.387615\pi$
$331$	12.5817	0.691554	0.345777	+	0.938317i	$0.387615\pi$
$332$	14.8871	0.817037
$333$	3.67499i	0.201388i
$334$	− 5.84255i	− 0.319690i
$335$	0.710074i	0.0387955i
$336$	1.69459	0.0924476
$337$	23.2175i	1.26474i	0.774667	+	0.632369i	$0.217917\pi$
$337$	23.2175i	1.26474i	−0.774667	+	0.632369i	$0.782083\pi$
$338$	−9.90673	−0.538855
$339$	−4.58172	−0.248845
$340$	0	0
$341$	−44.5185	−2.41081
$342$	4.82295	0.260795
$343$	18.8580i	1.01824i
$344$	−6.73917	−0.363352
$345$	− 0.723689i	− 0.0389621i
$346$	5.41147i	0.290923i
$347$	− 10.7706i	− 0.578198i	−0.957299	−	0.289099i	$-0.906644\pi$
$347$	− 10.7706i	− 0.578198i	0.957299	−	0.289099i	$-0.0933556\pi$
$348$	3.90167	0.209152
$349$	29.9864	1.60513	0.802567	−	0.596562i	$-0.203467\pi$
$349$	29.9864	1.60513	0.802567	+	0.596562i	$0.203467\pi$
$350$	8.44831i	0.451581i
$351$	− 1.75877i	− 0.0938762i
$352$	6.10607i	0.325454i
$353$	−29.6459	−1.57789	−0.788946	−	0.614463i	$-0.789373\pi$
$353$	−29.6459	−1.57789	−0.788946	+	0.614463i	$0.789373\pi$
$354$	2.12061i	0.112709i
$355$	−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	$-0.335629\pi$
$359$	18.7101	0.987480	0.493740	+	0.869610i	$0.335629\pi$
$360$	0.120615i	0.00635696i
$361$	4.26083	0.224254
$362$	− 0.157451i	− 0.00827546i
$363$	26.2841i	1.37955i
$364$	− 2.98040i	− 0.156215i
$365$	1.51930	0.0795236
$366$	−10.6946	−0.559015
$367$	5.84018i	0.304855i	0.988315	+	0.152428i	$0.0487091\pi$
$367$	5.84018i	0.304855i	−0.988315	+	0.152428i	$0.951291\pi$
$368$	6.00000i	0.312772i
$369$	3.14796i	0.163876i
$370$	−0.443258	−0.0230439
$371$	− 7.99319i	− 0.414986i
$372$	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
$377$	− 6.86215i	− 0.353419i
$378$	−1.69459	−0.0871604
$379$	0.340489i	0.0174898i	0.999962	+	0.00874488i	$0.00278362\pi$
$379$	0.340489i	0.0174898i	−0.999962	+	0.00874488i	$0.997216\pi$
$380$	0.581719i	0.0298415i
$381$	− 4.30541i	− 0.220573i
$382$	−6.90673	−0.353379
$383$	30.8776	1.57777	0.788887	−	0.614539i	$-0.210658\pi$
$383$	30.8776	1.57777	0.788887	+	0.614539i	$0.210658\pi$
$384$	− 1.00000i	− 0.0510310i
$385$	1.24804i	0.0636058i
$386$	− 11.5253i	− 0.586621i
$387$	6.73917	0.342571
$388$	9.08647i	0.461295i
$389$	3.25166	0.164866	0.0824328	−	0.996597i	$-0.473731\pi$
$389$	3.25166	0.164866	0.0824328	+	0.996597i	$0.473731\pi$
$390$	0.212134	0.0107418
$391$	0	0
$392$	4.12836	0.208513
$393$	15.0155	0.757431
$394$	6.71419i	0.338256i
$395$	1.68779	0.0849217
$396$	− 6.10607i	− 0.306841i
$397$	− 18.3405i	− 0.920483i	−0.887794	−	0.460241i	$-0.847763\pi$
$397$	− 18.3405i	− 0.920483i	0.887794	−	0.460241i	$-0.152237\pi$
$398$	− 7.22937i	− 0.362376i
$399$	−8.17293	−0.409158
$400$	4.98545	0.249273
$401$	− 18.7101i	− 0.934337i	−0.884168	−	0.467168i	$-0.845274\pi$
$401$	− 18.7101i	− 0.934337i	0.884168	−	0.467168i	$-0.154726\pi$
$402$	5.88713i	0.293623i
$403$	− 12.8229i	− 0.638757i
$404$	2.24897	0.111890
$405$	− 0.120615i	− 0.00599340i
$406$	−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
$411$	6.82295i	0.336551i
$412$	18.3259	0.902854
$413$	− 3.59358i	− 0.176828i
$414$	− 6.00000i	− 0.294884i
$415$	− 1.79561i	− 0.0881429i
$416$	−1.75877	−0.0862308
$417$	16.9067	0.827926
$418$	− 29.4492i	− 1.44041i
$419$	− 12.8990i	− 0.630157i	−0.949066	−	0.315078i	$-0.897969\pi$
$419$	− 12.8990i	− 0.630157i	0.949066	−	0.315078i	$-0.102031\pi$
$420$	− 0.204393i	− 0.00997335i
$421$	−27.2472	−1.32795	−0.663974	−	0.747756i	$-0.731131\pi$
$421$	−27.2472	−1.32795	−0.663974	+	0.747756i	$0.731131\pi$
$422$	10.5371i	0.512940i
$423$	−5.43376	−0.264199
$424$	−4.71688	−0.229072
$425$	0	0
$426$	−15.4047	−0.746359
$427$	18.1230	0.877032
$428$	− 14.1138i	− 0.682217i
$429$	−10.7392	−0.518492
$430$	0.812843i	0.0391988i
$431$	− 12.0547i	− 0.580654i	−0.956928	−	0.290327i	$-0.906236\pi$
$431$	− 12.0547i	− 0.580654i	0.956928	−	0.290327i	$-0.0937640\pi$
$432$	1.00000i	0.0481125i
$433$	10.6031	0.509551	0.254776	−	0.967000i	$-0.417998\pi$
$433$	10.6031	0.509551	0.254776	+	0.967000i	$0.417998\pi$
$434$	−12.3550	−0.593061
$435$	− 0.470599i	− 0.0225635i
$436$	− 6.69459i	− 0.320613i
$437$	− 28.9377i	− 1.38428i
$438$	12.5963	0.601873
$439$	− 7.09327i	− 0.338543i	−0.985569	−	0.169272i	$-0.945858\pi$
$439$	− 7.09327i	− 0.338543i	0.985569	−	0.169272i	$-0.0541416\pi$
$440$	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
$445$	− 1.98990i	− 0.0943301i
$446$	11.0027	0.520992
$447$	− 11.2831i	− 0.533673i
$448$	1.69459i	0.0800620i
$449$	33.1343i	1.56371i	0.623463	+	0.781853i	$0.285725\pi$
$449$	33.1343i	1.56371i	−0.623463	+	0.781853i	$0.714275\pi$
$450$	−4.98545	−0.235016
$451$	19.2216	0.905111
$452$	− 4.58172i	− 0.215506i
$453$	23.1702i	1.08863i
$454$	0.758770i	0.0356109i
$455$	−0.359480	−0.0168527
$456$	4.82295i	0.225855i
$457$	11.9463	0.558822	0.279411	−	0.960172i	$-0.409861\pi$
$457$	11.9463	0.558822	0.279411	+	0.960172i	$0.409861\pi$
$458$	−24.5817	−1.14863
$459$	0	0
$460$	0.723689	0.0337422
$461$	−25.5185	−1.18851	−0.594257	−	0.804275i	$-0.702554\pi$
$461$	−25.5185	−1.18851	−0.594257	+	0.804275i	$0.702554\pi$
$462$	10.3473i	0.481400i
$463$	−36.5449	−1.69838	−0.849192	−	0.528084i	$-0.822911\pi$
$463$	−36.5449	−1.69838	−0.849192	+	0.528084i	$0.822911\pi$
$464$	3.90167i	0.181131i
$465$	− 0.879385i	− 0.0407805i
$466$	− 5.67499i	− 0.262889i
$467$	−20.7246	−0.959021	−0.479511	−	0.877536i	$-0.659186\pi$
$467$	−20.7246	−0.959021	−0.479511	+	0.877536i	$0.659186\pi$
$468$	1.75877	0.0812992
$469$	− 9.97628i	− 0.460662i
$470$	− 0.655392i	− 0.0302310i
$471$	− 5.38919i	− 0.248321i
$472$	−2.12061	−0.0976092
$473$	− 41.1498i	− 1.89207i
$474$	13.9932	0.642729
$475$	−24.0446	−1.10324
$476$	0	0
$477$	4.71688	0.215971
$478$	25.5175	1.16715
$479$	31.6168i	1.44461i	0.691575	+	0.722304i	$0.256917\pi$
$479$	31.6168i	1.44461i	−0.691575	+	0.722304i	$0.743083\pi$
$480$	−0.120615	−0.00550529
$481$	6.46347i	0.294709i
$482$	− 20.4320i	− 0.930652i
$483$	10.1676i	0.462640i
$484$	−26.2841	−1.19473
$485$	1.09596	0.0497651
$486$	− 1.00000i	− 0.0453609i
$487$	21.2841i	0.964472i	0.876041	+	0.482236i	$0.160175\pi$
$487$	21.2841i	0.964472i	−0.876041	+	0.482236i	$0.839825\pi$
$488$	− 10.6946i	− 0.484121i
$489$	−17.8871	−0.808884
$490$	− 0.497941i	− 0.0224947i
$491$	19.5253	0.881164	0.440582	−	0.897712i	$-0.354772\pi$
$491$	19.5253	0.881164	0.440582	+	0.897712i	$0.354772\pi$
$492$	−3.14796	−0.141921
$493$	0	0
$494$	8.48246	0.381644
$495$	−0.736482	−0.0331024
$496$	7.29086i	0.327369i
$497$	26.1046	1.17095
$498$	− 14.8871i	− 0.667108i
$499$	22.5972i	1.01159i	0.862654	+	0.505795i	$0.168801\pi$
$499$	22.5972i	1.01159i	−0.862654	+	0.505795i	$0.831199\pi$
$500$	− 1.20439i	− 0.0538621i
$501$	−5.84255	−0.261026
$502$	7.50299	0.334875
$503$	− 13.3054i	− 0.593259i	−0.954993	−	0.296629i	$-0.904137\pi$
$503$	− 13.3054i	− 0.593259i	0.954993	−	0.296629i	$-0.0958626\pi$
$504$	− 1.69459i	− 0.0754832i
$505$	− 0.271259i	− 0.0120709i
$506$	−36.6364	−1.62869
$507$	9.90673i	0.439973i
$508$	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
$513$	− 4.82295i	− 0.212938i
$514$	18.3851	0.810931
$515$	− 2.21038i	− 0.0974009i
$516$	6.73917i	0.296675i
$517$	33.1789i	1.45921i
$518$	6.22762	0.273626
$519$	5.41147	0.237537
$520$	0.212134i	0.00930268i
$521$	− 39.0951i	− 1.71279i	−0.516322	−	0.856395i	$-0.672699\pi$
$521$	− 39.0951i	− 1.71279i	0.516322	−	0.856395i	$-0.327301\pi$
$522$	− 3.90167i	− 0.170772i
$523$	18.0702	0.790153	0.395077	−	0.918648i	$-0.370718\pi$
$523$	18.0702	0.790153	0.395077	+	0.918648i	$0.370718\pi$
$524$	15.0155i	0.655954i
$525$	8.44831	0.368715
$526$	3.01960	0.131661
$527$	0	0
$528$	6.10607	0.265732
$529$	−13.0000	−0.565217
$530$	0.568926i	0.0247125i
$531$	2.12061	0.0920268
$532$	− 8.17293i	− 0.354342i
$533$	5.53653i	0.239814i
$534$	− 16.4979i	− 0.713936i
$535$	−1.70233	−0.0735983
$536$	−5.88713	−0.254285
$537$	7.24123i	0.312482i
$538$	10.8452i	0.467571i
$539$	25.2080i	1.08579i
$540$	0.120615	0.00519043
$541$	22.5270i	0.968513i	0.874926	+	0.484256i	$0.160910\pi$
$541$	22.5270i	0.968513i	−0.874926	+	0.484256i	$0.839090\pi$
$542$	−17.6159	−0.756666
$543$	−0.157451	−0.00675689
$544$	0	0
$545$	−0.807467	−0.0345881
$546$	−2.98040	−0.127549
$547$	− 2.53714i	− 0.108480i	−0.998528	−	0.0542402i	$-0.982726\pi$
$547$	− 2.53714i	− 0.108480i	0.998528	−	0.0542402i	$-0.0172737\pi$
$548$	−6.82295	−0.291462
$549$	10.6946i	0.456434i
$550$	30.4415i	1.29803i
$551$	− 18.8176i	− 0.801656i
$552$	6.00000	0.255377
$553$	−23.7128	−1.00837
$554$	− 1.10338i	− 0.0468781i
$555$	0.443258i	0.0188153i
$556$	16.9067i	0.717005i
$557$	24.9317	1.05639	0.528195	−	0.849123i	$-0.322869\pi$
$557$	24.9317	1.05639	0.528195	+	0.849123i	$0.322869\pi$
$558$	− 7.29086i	− 0.308647i
$559$	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	$-0.270423\pi$
$563$	31.3354	1.32063	0.660316	+	0.750988i	$0.270423\pi$
$564$	− 5.43376i	− 0.228803i
$565$	−0.552623	−0.0232490
$566$	3.27631i	0.137714i
$567$	1.69459i	0.0711662i
$568$	− 15.4047i	− 0.646365i
$569$	22.9121	0.960525	0.480263	−	0.877125i	$-0.340541\pi$
$569$	22.9121	0.960525	0.480263	+	0.877125i	$0.340541\pi$
$570$	0.581719	0.0243655
$571$	− 10.5425i	− 0.441191i	−0.975365	−	0.220595i	$-0.929200\pi$
$571$	− 10.5425i	− 0.441191i	0.975365	−	0.220595i	$-0.0708000\pi$
$572$	− 10.7392i	− 0.449027i
$573$	6.90673i	0.288533i
$574$	5.33450	0.222658
$575$	29.9127i	1.24745i
$576$	−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
$581$	25.2276i	1.04662i
$582$	9.08647	0.376646
$583$	− 28.8016i	− 1.19284i
$584$	12.5963i	0.521237i
$585$	− 0.212134i	− 0.00877065i
$586$	5.76651	0.238212
$587$	18.7861	0.775386	0.387693	−	0.921789i	$-0.373272\pi$
$587$	18.7861	0.775386	0.387693	+	0.921789i	$0.373272\pi$
$588$	− 4.12836i	− 0.170251i
$589$	− 35.1634i	− 1.44888i
$590$	0.255777i	0.0105302i
$591$	6.71419	0.276185
$592$	− 3.67499i	− 0.151041i
$593$	15.8817	0.652185	0.326093	−	0.945338i	$-0.394268\pi$
$593$	15.8817	0.652185	0.326093	+	0.945338i	$0.394268\pi$
$594$	−6.10607	−0.250535
$595$	0	0
$596$	11.2831	0.462175
$597$	−7.22937	−0.295878
$598$	− 10.5526i	− 0.431529i
$599$	2.86215	0.116944	0.0584721	−	0.998289i	$-0.481377\pi$
$599$	2.86215	0.116944	0.0584721	+	0.998289i	$0.481377\pi$
$600$	− 4.98545i	− 0.203530i
$601$	− 16.7929i	− 0.684997i	−0.939518	−	0.342499i	$-0.888727\pi$
$601$	− 16.7929i	− 0.684997i	0.939518	−	0.342499i	$-0.111273\pi$
$602$	− 11.4201i	− 0.465451i
$603$	5.88713	0.239742
$604$	−23.1702	−0.942784
$605$	3.17024i	0.128889i
$606$	− 2.24897i	− 0.0913582i
$607$	11.7151i	0.475502i	0.971326	+	0.237751i	$0.0764103\pi$
$607$	11.7151i	0.475502i	−0.971326	+	0.237751i	$0.923590\pi$
$608$	−4.82295	−0.195596
$609$	6.61175i	0.267922i
$610$	−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
$615$	0.379690i	0.0153106i
$616$	−10.3473	−0.416904
$617$	49.0607i	1.97511i	0.157280	+	0.987554i	$0.449728\pi$
$617$	49.0607i	1.97511i	−0.157280	+	0.987554i	$0.550272\pi$
$618$	− 18.3259i	− 0.737177i
$619$	− 4.17293i	− 0.167724i	−0.996477	−	0.0838622i	$-0.973274\pi$
$619$	− 4.17293i	− 0.167724i	0.996477	−	0.0838622i	$-0.0267255\pi$
$620$	0.879385	0.0353170
$621$	−6.00000	−0.240772
$622$	− 4.77837i	− 0.191595i
$623$	27.9573i	1.12009i
$624$	1.75877i	0.0704072i
$625$	24.7820	0.991280
$626$	− 6.25671i	− 0.250068i
$627$	−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	$-0.604687\pi$
$631$	−16.2267	−0.645974	−0.322987	+	0.946403i	$0.604687\pi$
$632$	13.9932i	0.556619i
$633$	10.5371	0.418814
$634$	− 26.1925i	− 1.04024i
$635$	− 0.519296i	− 0.0206076i
$636$	4.71688i	0.187037i
$637$	−7.26083	−0.287685
$638$	−23.8239	−0.943197
$639$	15.4047i	0.609399i
$640$	− 0.120615i	− 0.00476772i
$641$	5.83244i	0.230368i	0.993344	+	0.115184i	$0.0367457\pi$
$641$	5.83244i	0.230368i	−0.993344	+	0.115184i	$0.963254\pi$
$642$	−14.1138	−0.557028
$643$	5.14796i	0.203016i	0.994835	+	0.101508i	$0.0323667\pi$
$643$	5.14796i	0.203016i	−0.994835	+	0.101508i	$0.967633\pi$
$644$	−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
$649$	− 12.9486i	− 0.508278i
$650$	−8.76827	−0.343920
$651$	12.3550i	0.484232i
$652$	− 17.8871i	− 0.700514i
$653$	− 15.8716i	− 0.621105i	−0.950556	−	0.310553i	$-0.899486\pi$
$653$	− 15.8716i	− 0.621105i	0.950556	−	0.310553i	$-0.100514\pi$
$654$	−6.69459	−0.261779
$655$	1.81109	0.0707651
$656$	− 3.14796i	− 0.122907i
$657$	− 12.5963i	− 0.491427i
$658$	9.20801i	0.358966i
$659$	26.0033	1.01294	0.506472	−	0.862256i	$-0.330949\pi$
$659$	26.0033	1.01294	0.506472	+	0.862256i	$0.330949\pi$
$660$	− 0.736482i	− 0.0286675i
$661$	−11.7980	−0.458888	−0.229444	−	0.973322i	$-0.573691\pi$
$661$	−11.7980	−0.458888	−0.229444	+	0.973322i	$0.573691\pi$
$662$	12.5817	0.489002
$663$	0	0
$664$	14.8871	0.577733
$665$	−0.985776	−0.0382268
$666$	3.67499i	0.142403i
$667$	−23.4100	−0.906441
$668$	− 5.84255i	− 0.226055i
$669$	− 11.0027i	− 0.425389i
$670$	0.710074i	0.0274326i
$671$	65.3019	2.52095
$672$	1.69459	0.0653703
$673$	47.9026i	1.84651i	0.384188	+	0.923255i	$0.374481\pi$
$673$	47.9026i	1.84651i	−0.384188	+	0.923255i	$0.625519\pi$
$674$	23.2175i	0.894305i
$675$	4.98545i	0.191890i
$676$	−9.90673	−0.381028
$677$	− 40.4303i	− 1.55386i	−0.629586	−	0.776930i	$-0.716776\pi$
$677$	− 40.4303i	− 1.55386i	0.629586	−	0.776930i	$-0.283224\pi$
$678$	−4.58172	−0.175960
$679$	−15.3979	−0.590916
$680$	0	0
$681$	0.758770	0.0290761
$682$	−44.5185	−1.70470
$683$	− 8.08141i	− 0.309227i	−0.987975	−	0.154613i	$-0.950587\pi$
$683$	− 8.08141i	− 0.309227i	0.987975	−	0.154613i	$-0.0494132\pi$
$684$	4.82295	0.184410
$685$	0.822948i	0.0314432i
$686$	18.8580i	0.720003i
$687$	24.5817i	0.937851i
$688$	−6.73917	−0.256928
$689$	8.29591	0.316049
$690$	− 0.723689i	− 0.0275504i
$691$	− 2.34049i	− 0.0890364i	−0.999009	−	0.0445182i	$-0.985825\pi$
$691$	− 2.34049i	− 0.0890364i	0.999009	−	0.0445182i	$-0.0141753\pi$
$692$	5.41147i	0.205713i
$693$	10.3473	0.393061
$694$	− 10.7706i	− 0.408848i
$695$	2.03920	0.0773513
$696$	3.90167	0.147893
$697$	0	0
$698$	29.9864	1.13500
$699$	−5.67499	−0.214648
$700$	8.44831i	0.319316i
$701$	19.5534	0.738523	0.369262	−	0.929325i	$-0.379611\pi$
$701$	19.5534	0.738523	0.369262	+	0.929325i	$0.379611\pi$
$702$	− 1.75877i	− 0.0663805i
$703$	17.7243i	0.668485i
$704$	6.10607i	0.230131i
$705$	−0.655392	−0.0246835
$706$	−29.6459	−1.11574
$707$	3.81109i	0.143331i
$708$	2.12061i	0.0796976i
$709$	− 35.2472i	− 1.32374i	−0.749620	−	0.661868i	$-0.769764\pi$
$709$	− 35.2472i	− 1.32374i	0.749620	−	0.661868i	$-0.230236\pi$
$710$	−1.85803	−0.0697306
$711$	− 13.9932i	− 0.524786i
$712$	16.4979	0.618286
$713$	−43.7452	−1.63827
$714$	0	0
$715$	−1.29530	−0.0484416
$716$	−7.24123	−0.270617
$717$	− 25.5175i	− 0.952970i
$718$	18.7101	0.698254
$719$	− 11.6013i	− 0.432656i	−0.976321	−	0.216328i	$-0.930592\pi$
$719$	− 11.6013i	− 0.432656i	0.976321	−	0.216328i	$-0.0694081\pi$
$720$	0.120615i	0.00449505i
$721$	31.0550i	1.15655i
$722$	4.26083	0.158572
$723$	−20.4320	−0.759875
$724$	− 0.157451i	− 0.00585163i
$725$	19.4516i	0.722415i
$726$	26.2841i	0.975493i
$727$	41.7083	1.54688	0.773438	−	0.633872i	$-0.218535\pi$
$727$	41.7083	1.54688	0.773438	+	0.633872i	$0.218535\pi$
$728$	− 2.98040i	− 0.110461i
$729$	−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	$-0.173657\pi$
$733$	46.2877	1.70967	0.854837	+	0.518896i	$0.173657\pi$
$734$	5.84018i	0.215565i
$735$	−0.497941	−0.0183668
$736$	6.00000i	0.221163i
$737$	− 35.9472i	− 1.32413i
$738$	3.14796i	0.115878i
$739$	−31.2080	−1.14801	−0.574003	−	0.818853i	$-0.694610\pi$
$739$	−31.2080	−1.14801	−0.574003	+	0.818853i	$0.694610\pi$
$740$	−0.443258	−0.0162945
$741$	− 8.48246i	− 0.311611i
$742$	− 7.99319i	− 0.293439i
$743$	30.5134i	1.11943i	0.828686	+	0.559714i	$0.189089\pi$
$743$	30.5134i	1.11943i	−0.828686	+	0.559714i	$0.810911\pi$
$744$	7.29086	0.267296
$745$	− 1.36091i	− 0.0498599i
$746$	−10.6209	−0.388859
$747$	−14.8871	−0.544691
$748$	0	0
$749$	23.9172	0.873914
$750$	−1.20439	−0.0439782
$751$	− 30.4320i	− 1.11048i	−0.831690	−	0.555240i	$-0.812626\pi$
$751$	− 30.4320i	− 1.11048i	0.831690	−	0.555240i	$-0.187374\pi$
$752$	5.43376	0.198149
$753$	− 7.50299i	− 0.273424i
$754$	− 6.86215i	− 0.249905i
$755$	2.79467i	0.101709i
$756$	−1.69459	−0.0616317
$757$	−17.5567	−0.638111	−0.319055	−	0.947736i	$-0.603366\pi$
$757$	−17.5567	−0.638111	−0.319055	+	0.947736i	$0.603366\pi$
$758$	0.340489i	0.0123671i
$759$	36.6364i	1.32982i
$760$	0.581719i	0.0211012i
$761$	−4.69459	−0.170179	−0.0850894	−	0.996373i	$-0.527118\pi$
$761$	−4.69459	−0.170179	−0.0850894	+	0.996373i	$0.527118\pi$
$762$	− 4.30541i	− 0.155968i
$763$	11.3446	0.410702
$764$	−6.90673	−0.249877
$765$	0	0
$766$	30.8776	1.11565
$767$	3.72967	0.134671
$768$	− 1.00000i	− 0.0360844i
$769$	2.36184	0.0851703	0.0425851	−	0.999093i	$-0.486441\pi$
$769$	2.36184	0.0851703	0.0425851	+	0.999093i	$0.486441\pi$
$770$	1.24804i	0.0449761i
$771$	− 18.3851i	− 0.662122i
$772$	− 11.5253i	− 0.414804i
$773$	−29.4561	−1.05946	−0.529730	−	0.848166i	$-0.677707\pi$
$773$	−29.4561	−1.05946	−0.529730	+	0.848166i	$0.677707\pi$
$774$	6.73917	0.242234
$775$	36.3482i	1.30567i
$776$	9.08647i	0.326185i
$777$	− 6.22762i	− 0.223414i
$778$	3.25166	0.116578
$779$	15.1824i	0.543967i
$780$	0.212134	0.00759560
$781$	94.0619	3.36580
$782$	0	0
$783$	−3.90167	−0.139434
$784$	4.12836	0.147441
$785$	− 0.650015i	− 0.0232000i
$786$	15.0155	0.535584
$787$	55.6715i	1.98447i	0.124361	+	0.992237i	$0.460312\pi$
$787$	55.6715i	1.98447i	−0.124361	+	0.992237i	$0.539688\pi$
$788$	6.71419i	0.239183i
$789$	− 3.01960i	− 0.107501i
$790$	1.68779	0.0600487
$791$	7.76415	0.276061
$792$	− 6.10607i	− 0.216970i
$793$	18.8093i	0.667939i
$794$	− 18.3405i	− 0.650880i
$795$	0.568926	0.0201777
$796$	− 7.22937i	− 0.256238i
$797$	19.7802	0.700652	0.350326	−	0.936628i	$-0.386071\pi$
$797$	19.7802	0.700652	0.350326	+	0.936628i	$0.386071\pi$
$798$	−8.17293	−0.289319
$799$	0	0
$800$	4.98545	0.176262
$801$	−16.4979	−0.582926
$802$	− 18.7101i	− 0.660676i
$803$	−76.9136	−2.71422
$804$	5.88713i	0.207623i
$805$	1.22636i	0.0432234i
$806$	− 12.8229i	− 0.451669i
$807$	10.8452	0.381770
$808$	2.24897	0.0791185
$809$	20.9222i	0.735586i	0.929908	+	0.367793i	$0.119886\pi$
$809$	20.9222i	0.735586i	−0.929908	+	0.367793i	$0.880114\pi$
$810$	− 0.120615i	− 0.00423797i
$811$	0.896622i	0.0314846i	0.999876	+	0.0157423i	$0.00501114\pi$
$811$	0.896622i	0.0314846i	−0.999876	+	0.0157423i	$0.994989\pi$
$812$	−6.61175	−0.232027
$813$	17.6159i	0.617815i
$814$	22.4397	0.786513
$815$	−2.15745	−0.0755722
$816$	0	0
$817$	32.5027	1.13712
$818$	−5.94862	−0.207988
$819$	2.98040i	0.104144i
$820$	−0.379690	−0.0132593
$821$	37.6851i	1.31522i	0.753359	+	0.657609i	$0.228432\pi$
$821$	37.6851i	1.31522i	−0.753359	+	0.657609i	$0.771568\pi$
$822$	6.82295i	0.237978i
$823$	− 22.1607i	− 0.772475i	−0.922399	−	0.386238i	$-0.873774\pi$
$823$	− 22.1607i	− 0.772475i	0.922399	−	0.386238i	$-0.126226\pi$
$824$	18.3259	0.638414
$825$	30.4415	1.05984
$826$	− 3.59358i	− 0.125037i
$827$	30.8016i	1.07108i	0.844511	+	0.535538i	$0.179891\pi$
$827$	30.8016i	1.07108i	−0.844511	+	0.535538i	$0.820109\pi$
$828$	− 6.00000i	− 0.208514i
$829$	18.5716	0.645019	0.322509	−	0.946566i	$-0.395474\pi$
$829$	18.5716	0.645019	0.322509	+	0.946566i	$0.395474\pi$
$830$	− 1.79561i	− 0.0623264i
$831$	−1.10338	−0.0382758
$832$	−1.75877	−0.0609744
$833$	0	0
$834$	16.9067	0.585432
$835$	−0.704698	−0.0243871
$836$	− 29.4492i	− 1.01852i
$837$	−7.29086	−0.252009
$838$	− 12.8990i	− 0.445588i
$839$	− 27.9763i	− 0.965848i	−0.875662	−	0.482924i	$-0.839575\pi$
$839$	− 27.9763i	− 0.965848i	0.875662	−	0.482924i	$-0.160425\pi$
$840$	− 0.204393i	− 0.00705222i
$841$	13.7769	0.475067
$842$	−27.2472	−0.939001
$843$	6.28581i	0.216495i
$844$	10.5371i	0.362703i
$845$	1.19490i	0.0411057i
$846$	−5.43376	−0.186817
$847$	− 44.5408i	− 1.53044i
$848$	−4.71688	−0.161978
$849$	3.27631	0.112443
$850$	0	0
$851$	22.0500	0.755863
$852$	−15.4047	−0.527755
$853$	− 10.6500i	− 0.364650i	−0.983238	−	0.182325i	$-0.941638\pi$
$853$	− 10.6500i	− 0.364650i	0.983238	−	0.182325i	$-0.0583622\pi$
$854$	18.1230	0.620156
$855$	− 0.581719i	− 0.0198944i
$856$	− 14.1138i	− 0.482400i
$857$	42.3560i	1.44685i	0.690402	+	0.723426i	$0.257434\pi$
$857$	42.3560i	1.44685i	−0.690402	+	0.723426i	$0.742566\pi$
$858$	−10.7392	−0.366629
$859$	−52.2039	−1.78117	−0.890587	−	0.454813i	$-0.849706\pi$
$859$	−52.2039	−1.78117	−0.890587	+	0.454813i	$0.849706\pi$
$860$	0.812843i	0.0277177i
$861$	− 5.33450i	− 0.181799i
$862$	− 12.0547i	− 0.410584i
$863$	48.2330	1.64187	0.820935	−	0.571022i	$-0.193453\pi$
$863$	48.2330	1.64187	0.820935	+	0.571022i	$0.193453\pi$
$864$	1.00000i	0.0340207i
$865$	0.652704	0.0221926
$866$	10.6031	0.360307
$867$	0	0
$868$	−12.3550	−0.419357
$869$	−85.4434	−2.89847
$870$	− 0.470599i	− 0.0159548i
$871$	10.3541	0.350835
$872$	− 6.69459i	− 0.226708i
$873$	− 9.08647i	− 0.307530i
$874$	− 28.9377i	− 0.978832i
$875$	2.04096	0.0689969
$876$	12.5963	0.425588
$877$	− 29.4884i	− 0.995754i	−0.867248	−	0.497877i	$-0.834113\pi$
$877$	− 29.4884i	− 0.995754i	0.867248	−	0.497877i	$-0.165887\pi$
$878$	− 7.09327i	− 0.239386i
$879$	− 5.76651i	− 0.194500i
$880$	0.736482	0.0248268
$881$	− 6.92034i	− 0.233152i	−0.993182	−	0.116576i	$-0.962808\pi$
$881$	− 6.92034i	− 0.233152i	0.993182	−	0.116576i	$-0.0371919\pi$
$882$	−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
$887$	7.36009i	0.247128i	0.992337	+	0.123564i	$0.0394324\pi$
$887$	7.36009i	0.247128i	−0.992337	+	0.123564i	$0.960568\pi$
$888$	−3.67499	−0.123325
$889$	7.29591i	0.244697i
$890$	− 1.98990i	− 0.0667014i
$891$	6.10607i	0.204561i
$892$	11.0027	0.368397
$893$	−26.2068	−0.876976
$894$	− 11.2831i	− 0.377364i
$895$	0.873399i	0.0291945i
$896$	1.69459i	0.0566124i
$897$	−10.5526	−0.352342
$898$	33.1343i	1.10571i
$899$	−28.4466	−0.948746
$900$	−4.98545	−0.166182
$901$	0	0
$902$	19.2216	0.640010
$903$	−11.4201	−0.380039
$904$	− 4.58172i	− 0.152386i
$905$	−0.0189910	−0.000631281 0
$906$	23.1702i	0.769780i
$907$	42.7837i	1.42061i	0.703894	+	0.710306i	$0.251443\pi$
$907$	42.7837i	1.42061i	−0.703894	+	0.710306i	$0.748557\pi$
$908$	0.758770i	0.0251807i
$909$	−2.24897	−0.0745936
$910$	−0.359480	−0.0119167
$911$	0.508045i	0.0168323i	0.999965	+	0.00841615i	$0.00267898\pi$
$911$	0.508045i	0.0168323i	−0.999965	+	0.00841615i	$0.997321\pi$
$912$	4.82295i	0.159704i
$913$	90.9018i	3.00841i
$914$	11.9463	0.395147
$915$	1.28993i	0.0426436i
$916$	−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
$921$	1.26083i	0.0415458i
$922$	−25.5185	−0.840406
$923$	27.0933i	0.891786i
$924$	10.3473i	0.340401i
$925$	− 18.3215i	− 0.602407i
$926$	−36.5449	−1.20094
$927$	−18.3259	−0.601903
$928$	3.90167i	0.128079i
$929$	1.85616i	0.0608987i	0.999536	+	0.0304494i	$0.00969383\pi$
$929$	1.85616i	0.0608987i	−0.999536	+	0.0304494i	$0.990306\pi$
$930$	− 0.879385i	− 0.0288362i
$931$	−19.9108	−0.652552
$932$	− 5.67499i	− 0.185891i
$933$	−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	$-0.456182\pi$
$937$	8.40104	0.274450	0.137225	+	0.990540i	$0.456182\pi$
$938$	− 9.97628i	− 0.325737i
$939$	−6.25671	−0.204180
$940$	− 0.655392i	− 0.0213765i
$941$	− 32.9459i	− 1.07401i	−0.843580	−	0.537003i	$-0.819556\pi$
$941$	− 32.9459i	− 1.07401i	0.843580	−	0.537003i	$-0.180444\pi$
$942$	− 5.38919i	− 0.175589i
$943$	18.8877	0.615069
$944$	−2.12061	−0.0690201
$945$	0.204393i	0.00664890i
$946$	− 41.1498i	− 1.33790i
$947$	19.6182i	0.637507i	0.947838	+	0.318753i	$0.103264\pi$
$947$	19.6182i	0.637507i	−0.947838	+	0.318753i	$0.896736\pi$
$948$	13.9932	0.454478
$949$	− 22.1539i	− 0.719147i
$950$	−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
$955$	0.833053i	0.0269570i
$956$	25.5175	0.825296
$957$	23.8239i	0.770117i
$958$	31.6168i	1.02149i
$959$	− 11.5621i	− 0.373360i
$960$	−0.120615	−0.00389282
$961$	−22.1566	−0.714730
$962$	6.46347i	0.208391i
$963$	14.1138i	0.454811i
$964$	− 20.4320i	− 0.658071i
$965$	−1.39012	−0.0447495
$966$	10.1676i	0.327136i
$967$	39.7475	1.27819	0.639097	−	0.769126i	$-0.279308\pi$
$967$	39.7475	1.27819	0.639097	+	0.769126i	$0.279308\pi$
$968$	−26.2841	−0.844801
$969$	0	0
$970$	1.09596	0.0351892
$971$	−39.5398	−1.26889	−0.634447	−	0.772967i	$-0.718772\pi$
$971$	−39.5398	−1.26889	−0.634447	+	0.772967i	$0.718772\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	−28.6500	−0.918477
$974$	21.2841i	0.681985i
$975$	8.76827i	0.280809i
$976$	− 10.6946i	− 0.342326i
$977$	−10.3696	−0.331752	−0.165876	−	0.986147i	$-0.553045\pi$
$977$	−10.3696	−0.331752	−0.165876	+	0.986147i	$0.553045\pi$
$978$	−17.8871	−0.571967
$979$	100.738i	3.21959i
$980$	− 0.497941i	− 0.0159061i
$981$	6.69459i	0.213742i
$982$	19.5253	0.623077
$983$	− 3.18243i	− 0.101504i	−0.998711	−	0.0507519i	$-0.983838\pi$
$983$	− 3.18243i	− 0.101504i	0.998711	−	0.0507519i	$-0.0161618\pi$
$984$	−3.14796	−0.100353
$985$	0.809831	0.0258034
$986$	0	0
$987$	9.20801	0.293094
$988$	8.48246	0.269863
$989$	− 40.4350i	− 1.28576i
$990$	−0.736482	−0.0234069
$991$	13.6946i	0.435023i	0.976058	+	0.217512i	$0.0697940\pi$
$991$	13.6946i	0.435023i	−0.976058	+	0.217512i	$0.930206\pi$
$992$	7.29086i	0.231485i
$993$	− 12.5817i	− 0.399269i
$994$	26.1046	0.827989
$995$	−0.871969	−0.0276433
$996$	− 14.8871i	− 0.471717i
$997$	0.964918i	0.0305593i	0.999883	+	0.0152796i	$0.00486385\pi$
$997$	0.964918i	0.0305593i	−0.999883	+	0.0152796i	$0.995136\pi$
$998$	22.5972i	0.715302i
$999$	3.67499	0.116272

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.p.1.3	✓	3	17.4	even	4
1734.2.a.q.1.1	yes	3	17.13	even	4
1734.2.b.j.577.3		6	1.1	even	1	trivial
1734.2.b.j.577.4		6	17.16	even	2	inner
1734.2.f.n.829.1		12	17.2	even	8
1734.2.f.n.829.6		12	17.15	even	8
1734.2.f.n.1483.1		12	17.8	even	8
1734.2.f.n.1483.6		12	17.9	even	8
5202.2.a.bm.1.3		3	51.47	odd	4
5202.2.a.bp.1.1		3	51.38	odd	4

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.b (of order \(2\), degree \(1\), not minimal)

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

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