LMFDB - Embedded newform 408.2.l.b.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [408,2,Mod(373,408)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(408, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 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("408.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 408 = 2^{3} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	408.l (of order $2$, degree $1$, 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:	$3.25789640247$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			373.2
Root			$1.40931 + 0.117654i$ of defining polynomial
Character	$\chi$	$=$	408.373
Dual form			408.2.l.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40931 + 0.117654i) q^{2} +1.00000 q^{3} +(1.97232 - 0.331622i) q^{4} +1.46472 q^{5} +(-1.40931 + 0.117654i) q^{6} +3.26018i q^{7} +(-2.74059 + 0.699408i) q^{8} +1.00000 q^{9} +(-2.06424 + 0.172330i) q^{10} +0.312167 q^{11} +(1.97232 - 0.331622i) q^{12} +6.39254i q^{13} +(-0.383572 - 4.59460i) q^{14} +1.46472 q^{15} +(3.78005 - 1.30812i) q^{16} +(-3.01195 + 2.81570i) q^{17} +(-1.40931 + 0.117654i) q^{18} -2.24353i q^{19} +(2.88888 - 0.485732i) q^{20} +3.26018i q^{21} +(-0.439940 + 0.0367276i) q^{22} -7.34630i q^{23} +(-2.74059 + 0.699408i) q^{24} -2.85460 q^{25} +(-0.752107 - 9.00908i) q^{26} +1.00000 q^{27} +(1.08115 + 6.43010i) q^{28} +5.39236 q^{29} +(-2.06424 + 0.172330i) q^{30} +0.606910i q^{31} +(-5.17337 + 2.28829i) q^{32} +0.312167 q^{33} +(3.91349 - 4.32257i) q^{34} +4.77524i q^{35} +(1.97232 - 0.331622i) q^{36} +11.2816 q^{37} +(0.263960 + 3.16184i) q^{38} +6.39254i q^{39} +(-4.01419 + 1.02444i) q^{40} -5.36742i q^{41} +(-0.383572 - 4.59460i) q^{42} +7.51199i q^{43} +(0.615692 - 0.103521i) q^{44} +1.46472 q^{45} +(0.864321 + 10.3532i) q^{46} -4.24122 q^{47} +(3.78005 - 1.30812i) q^{48} -3.62875 q^{49} +(4.02302 - 0.335855i) q^{50} +(-3.01195 + 2.81570i) q^{51} +(2.11991 + 12.6081i) q^{52} +8.91746i q^{53} +(-1.40931 + 0.117654i) q^{54} +0.457236 q^{55} +(-2.28019 - 8.93480i) q^{56} -2.24353i q^{57} +(-7.59952 + 0.634432i) q^{58} -5.15579i q^{59} +(2.88888 - 0.485732i) q^{60} +6.41607 q^{61} +(-0.0714053 - 0.855325i) q^{62} +3.26018i q^{63} +(7.02166 - 3.83358i) q^{64} +9.36327i q^{65} +(-0.439940 + 0.0367276i) q^{66} -11.8427i q^{67} +(-5.00676 + 6.55228i) q^{68} -7.34630i q^{69} +(-0.561825 - 6.72979i) q^{70} +6.62295i q^{71} +(-2.74059 + 0.699408i) q^{72} -4.81332i q^{73} +(-15.8993 + 1.32733i) q^{74} -2.85460 q^{75} +(-0.744004 - 4.42496i) q^{76} +1.01772i q^{77} +(-0.752107 - 9.00908i) q^{78} -11.5068i q^{79} +(5.53671 - 1.91603i) q^{80} +1.00000 q^{81} +(0.631497 + 7.56436i) q^{82} -13.3845i q^{83} +(1.08115 + 6.43010i) q^{84} +(-4.41165 + 4.12421i) q^{85} +(-0.883814 - 10.5867i) q^{86} +5.39236 q^{87} +(-0.855521 + 0.218332i) q^{88} +9.54739 q^{89} +(-2.06424 + 0.172330i) q^{90} -20.8408 q^{91} +(-2.43619 - 14.4892i) q^{92} +0.606910i q^{93} +(5.97720 - 0.498996i) q^{94} -3.28614i q^{95} +(-5.17337 + 2.28829i) q^{96} -13.0210i q^{97} +(5.11404 - 0.426936i) q^{98} +0.312167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{3} + 2 q^{4} - 4 q^{5} + 18 q^{9} - 8 q^{10} + 2 q^{12} - 6 q^{14} - 4 q^{15} + 10 q^{16} - 2 q^{17} - 2 q^{20} + 2 q^{22} + 22 q^{25} + 2 q^{26} + 18 q^{27} - 10 q^{28} + 12 q^{29} - 8 q^{30}+ \cdots - 60 q^{98}+O(q^{100}) $ 18 * q + 18 * q^3 + 2 * q^4 - 4 * q^5 + 18 * q^9 - 8 * q^10 + 2 * q^12 - 6 * q^14 - 4 * q^15 + 10 * q^16 - 2 * q^17 - 2 * q^20 + 2 * q^22 + 22 * q^25 + 2 * q^26 + 18 * q^27 - 10 * q^28 + 12 * q^29 - 8 * q^30 + 6 * q^34 + 2 * q^36 - 16 * q^37 - 34 * q^38 - 10 * q^40 - 6 * q^42 + 12 * q^44 - 4 * q^45 + 32 * q^46 + 10 * q^48 - 18 * q^49 - 14 * q^50 - 2 * q^51 + 8 * q^52 - 16 * q^55 - 14 * q^56 - 6 * q^58 - 2 * q^60 - 16 * q^61 - 6 * q^62 + 2 * q^64 + 2 * q^66 - 36 * q^68 - 32 * q^70 - 6 * q^74 + 22 * q^75 + 2 * q^78 - 62 * q^80 + 18 * q^81 + 34 * q^82 - 10 * q^84 + 16 * q^85 + 14 * q^86 + 12 * q^87 + 16 * q^88 + 20 * q^89 - 8 * q^90 - 2 * q^92 + 12 * q^94 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/408\mathbb{Z}\right)^\times$.

$n$	$103$	$137$	$205$	$241$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.40931	+	0.117654i	−0.996533	+	0.0831938i
$2$	−1.40931	+	0.117654i	−0.996533	+	0.0831938i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.97232	−	0.331622i	0.986158	−	0.165811i
$5$	1.46472			0.655041			0.327521	−	0.944844i	$-0.393787\pi$
$5$	1.46472			0.655041			0.327521	+	0.944844i	$0.393787\pi$
$6$	−1.40931	+	0.117654i	−0.575349	+	0.0480320i
$7$			3.26018i			1.23223i	0.787656	+	0.616115i	$0.211295\pi$
$7$			3.26018i			1.23223i	−0.787656	+	0.616115i	$0.788705\pi$
$8$	−2.74059	+	0.699408i	−0.968945	+	0.247278i
$9$	1.00000			0.333333
$10$	−2.06424	+	0.172330i	−0.652771	+	0.0544954i
$11$	0.312167			0.0941219			0.0470609	−	0.998892i	$-0.485015\pi$
$11$	0.312167			0.0941219			0.0470609	+	0.998892i	$0.485015\pi$
$12$	1.97232	−	0.331622i	0.569358	−	0.0957309i
$13$			6.39254i			1.77297i	0.462755	+	0.886486i	$0.346861\pi$
$13$			6.39254i			1.77297i	−0.462755	+	0.886486i	$0.653139\pi$
$14$	−0.383572	−	4.59460i	−0.102514	−	1.22796i
$15$	1.46472			0.378188
$16$	3.78005	−	1.30812i	0.945014	−	0.327031i
$17$	−3.01195	+	2.81570i	−0.730505	+	0.682908i
$17$	−3.01195	+	2.81570i	−0.730505	+	0.682908i
$18$	−1.40931	+	0.117654i	−0.332178	+	0.0277313i
$19$		−	2.24353i		−	0.514702i	−0.966318	−	0.257351i	$-0.917150\pi$
$19$		−	2.24353i		−	0.514702i	0.966318	−	0.257351i	$-0.0828496\pi$
$20$	2.88888	−	0.485732i	0.645974	−	0.108613i
$21$			3.26018i			0.711429i
$22$	−0.439940	+	0.0367276i	−0.0937956	+	0.00783036i
$23$		−	7.34630i		−	1.53181i	−0.642954	−	0.765905i	$-0.722291\pi$
$23$		−	7.34630i		−	1.53181i	0.642954	−	0.765905i	$-0.277709\pi$
$24$	−2.74059	+	0.699408i	−0.559420	+	0.142766i
$25$	−2.85460			−0.570921
$26$	−0.752107	−	9.00908i	−0.147500	−	1.76683i
$27$	1.00000			0.192450
$28$	1.08115	+	6.43010i	0.204317	+	1.21517i
$29$	5.39236			1.00134			0.500668	−	0.865639i	$-0.333088\pi$
$29$	5.39236			1.00134			0.500668	+	0.865639i	$0.333088\pi$
$30$	−2.06424	+	0.172330i	−0.376877	+	0.0314629i
$31$			0.606910i			0.109004i	0.998514	+	0.0545021i	$0.0173572\pi$
$31$			0.606910i			0.109004i	−0.998514	+	0.0545021i	$0.982643\pi$
$32$	−5.17337	+	2.28829i	−0.914531	+	0.404517i
$33$	0.312167			0.0543413
$34$	3.91349	−	4.32257i	0.671159	−	0.741314i
$35$			4.77524i			0.807162i
$36$	1.97232	−	0.331622i	0.328719	−	0.0552703i
$37$	11.2816			1.85469			0.927344	−	0.374211i	$-0.122086\pi$
$37$	11.2816			1.85469			0.927344	+	0.374211i	$0.122086\pi$
$38$	0.263960	+	3.16184i	0.0428200	+	0.512918i
$39$			6.39254i			1.02363i
$40$	−4.01419	+	1.02444i	−0.634699	+	0.161977i
$41$		−	5.36742i		−	0.838249i	−0.907929	−	0.419125i	$-0.862337\pi$
$41$		−	5.36742i		−	0.838249i	0.907929	−	0.419125i	$-0.137663\pi$
$42$	−0.383572	−	4.59460i	−0.0591865	−	0.708963i
$43$			7.51199i			1.14557i	0.819707	+	0.572784i	$0.194137\pi$
$43$			7.51199i			1.14557i	−0.819707	+	0.572784i	$0.805863\pi$
$44$	0.615692	−	0.103521i	0.0928190	−	0.0156064i
$45$	1.46472			0.218347
$46$	0.864321	+	10.3532i	0.127437	+	1.52650i
$47$	−4.24122			−0.618646			−0.309323	−	0.950957i	$-0.600102\pi$
$47$	−4.24122			−0.618646			−0.309323	+	0.950957i	$0.600102\pi$
$48$	3.78005	−	1.30812i	0.545604	−	0.188812i
$49$	−3.62875			−0.518393
$50$	4.02302	−	0.335855i	0.568942	−	0.0474971i
$51$	−3.01195	+	2.81570i	−0.421757	+	0.394277i
$52$	2.11991	+	12.6081i	0.293978	+	1.74843i
$53$			8.91746i			1.22491i	0.790507	+	0.612454i	$0.209817\pi$
$53$			8.91746i			1.22491i	−0.790507	+	0.612454i	$0.790183\pi$
$54$	−1.40931	+	0.117654i	−0.191783	+	0.0160107i
$55$	0.457236			0.0616537
$56$	−2.28019	−	8.93480i	−0.304704	−	1.19396i
$57$		−	2.24353i		−	0.297163i
$58$	−7.59952	+	0.634432i	−0.997865	+	0.0833050i
$59$		−	5.15579i		−	0.671226i	−0.942000	−	0.335613i	$-0.891057\pi$
$59$		−	5.15579i		−	0.671226i	0.942000	−	0.335613i	$-0.108943\pi$
$60$	2.88888	−	0.485732i	0.372953	−	0.0627077i
$61$	6.41607			0.821493			0.410747	−	0.911750i	$-0.365268\pi$
$61$	6.41607			0.821493			0.410747	+	0.911750i	$0.365268\pi$
$62$	−0.0714053	−	0.855325i	−0.00906848	−	0.108626i
$63$			3.26018i			0.410744i
$64$	7.02166	−	3.83358i	0.877707	−	0.479198i
$65$			9.36327i			1.16137i
$66$	−0.439940	+	0.0367276i	−0.0541529	+	0.00452086i
$67$		−	11.8427i		−	1.44682i	−0.690421	−	0.723408i	$-0.742575\pi$
$67$		−	11.8427i		−	1.44682i	0.690421	−	0.723408i	$-0.257425\pi$
$68$	−5.00676	+	6.55228i	−0.607159	+	0.794580i
$69$		−	7.34630i		−	0.884391i
$70$	−0.561825	−	6.72979i	−0.0671509	−	0.804364i
$71$			6.62295i			0.785999i	0.919539	+	0.393000i	$0.128563\pi$
$71$			6.62295i			0.785999i	−0.919539	+	0.393000i	$0.871437\pi$
$72$	−2.74059	+	0.699408i	−0.322982	+	0.0824261i
$73$		−	4.81332i		−	0.563356i	−0.959509	−	0.281678i	$-0.909109\pi$
$73$		−	4.81332i		−	0.563356i	0.959509	−	0.281678i	$-0.0908910\pi$
$74$	−15.8993	+	1.32733i	−1.84826	+	0.154299i
$75$	−2.85460			−0.329621
$76$	−0.744004	−	4.42496i	−0.0853432	−	0.507577i
$77$			1.01772i			0.115980i
$78$	−0.752107	−	9.00908i	−0.0851594	−	1.02008i
$79$		−	11.5068i		−	1.29461i	−0.762230	−	0.647306i	$-0.775896\pi$
$79$		−	11.5068i		−	1.29461i	0.762230	−	0.647306i	$-0.224104\pi$
$80$	5.53671	−	1.91603i	0.619023	−	0.214219i
$81$	1.00000			0.111111
$82$	0.631497	+	7.56436i	0.0697372	+	0.835344i
$83$		−	13.3845i		−	1.46914i	−0.678535	−	0.734568i	$-0.737385\pi$
$83$		−	13.3845i		−	1.46914i	0.678535	−	0.734568i	$-0.262615\pi$
$84$	1.08115	+	6.43010i	0.117963	+	0.701581i
$85$	−4.41165	+	4.12421i	−0.478511	+	0.447333i
$86$	−0.883814	−	10.5867i	−0.0953041	−	1.14160i
$87$	5.39236			0.578122
$88$	−0.855521	+	0.218332i	−0.0911989	+	0.0232743i
$89$	9.54739			1.01202			0.506011	−	0.862527i	$-0.331120\pi$
$89$	9.54739			1.01202			0.506011	+	0.862527i	$0.331120\pi$
$90$	−2.06424	+	0.172330i	−0.217590	+	0.0181651i
$91$	−20.8408			−2.18471
$92$	−2.43619	−	14.4892i	−0.253991	−	1.51061i
$93$			0.606910i			0.0629336i
$94$	5.97720	−	0.498996i	0.616501	−	0.0514675i
$95$		−	3.28614i		−	0.337151i
$96$	−5.17337	+	2.28829i	−0.528004	+	0.233548i
$97$		−	13.0210i		−	1.32208i	−0.750351	−	0.661040i	$-0.770115\pi$
$97$		−	13.0210i		−	1.32208i	0.750351	−	0.661040i	$-0.229885\pi$
$98$	5.11404	−	0.426936i	0.516596	−	0.0431271i
$99$	0.312167			0.0313740
$100$	−5.63018	+	0.946648i	−0.563018	+	0.0946648i
$101$		−	1.94347i		−	0.193383i	−0.995314	−	0.0966913i	$-0.969174\pi$
$101$		−	1.94347i		−	0.193383i	0.995314	−	0.0966913i	$-0.0308259\pi$
$102$	3.91349	−	4.32257i	0.387494	−	0.427998i
$103$	6.97083			0.686856			0.343428	−	0.939179i	$-0.388412\pi$
$103$	6.97083			0.686856			0.343428	+	0.939179i	$0.388412\pi$
$104$	−4.47100	−	17.5193i	−0.438418	−	1.71791i
$105$			4.77524i			0.466015i
$106$	−1.04917	−	12.5675i	−0.101905	−	1.22066i
$107$	−7.39946			−0.715333			−0.357667	−	0.933849i	$-0.616428\pi$
$107$	−7.39946			−0.715333			−0.357667	+	0.933849i	$0.616428\pi$
$108$	1.97232	−	0.331622i	0.189786	−	0.0319103i
$109$	−10.6455			−1.01966			−0.509828	−	0.860277i	$-0.670291\pi$
$109$	−10.6455			−1.01966			−0.509828	+	0.860277i	$0.670291\pi$
$110$	−0.644388	+	0.0537956i	−0.0614400	+	0.00512921i
$111$	11.2816			1.07080
$112$	4.26472	+	12.3236i	0.402978	+	1.16447i
$113$			11.0887i			1.04313i	0.853211	+	0.521567i	$0.174652\pi$
$113$			11.0887i			1.04313i	−0.853211	+	0.521567i	$0.825348\pi$
$114$	0.263960	+	3.16184i	0.0247221	+	0.296133i
$115$		−	10.7603i		−	1.00340i
$116$	10.6354	−	1.78822i	0.987476	−	0.166032i
$117$			6.39254i			0.590991i
$118$	0.606598	+	7.26611i	0.0558419	+	0.668899i
$119$	−9.17968	−	9.81948i	−0.841500	−	0.900150i
$120$	−4.01419	+	1.02444i	−0.366444	+	0.0935178i
$121$	−10.9026			−0.991141
$122$	−9.04224	+	0.754875i	−0.818646	+	0.0683432i
$123$		−	5.36742i		−	0.483964i
$124$	0.201265	+	1.19702i	0.0180741	+	0.107495i
$125$	−11.5048			−1.02902
$126$	−0.383572	−	4.59460i	−0.0341713	−	0.409320i
$127$	−16.9758			−1.50636			−0.753179	−	0.657816i	$-0.771480\pi$
$127$	−16.9758			−1.50636			−0.753179	+	0.657816i	$0.771480\pi$
$128$	−9.44466	+	6.22883i	−0.834798	+	0.550556i
$129$			7.51199i			0.661394i
$130$	−1.10162	−	13.1958i	−0.0966189	−	1.15734i
$131$	−0.168506			−0.0147225			−0.00736123	−	0.999973i	$-0.502343\pi$
$131$	−0.168506			−0.0147225			−0.00736123	+	0.999973i	$0.502343\pi$
$132$	0.615692	−	0.103521i	0.0535891	−	0.00901037i
$133$	7.31432			0.634232
$134$	1.39334	+	16.6900i	0.120366	+	1.44180i
$135$	1.46472			0.126063
$136$	6.28519	−	9.82326i	0.538950	−	0.842338i
$137$	6.02753			0.514966			0.257483	−	0.966283i	$-0.417107\pi$
$137$	6.02753			0.514966			0.257483	+	0.966283i	$0.417107\pi$
$138$	0.864321	+	10.3532i	0.0735759	+	0.881325i
$139$	3.56380			0.302278			0.151139	−	0.988513i	$-0.451706\pi$
$139$	3.56380			0.302278			0.151139	+	0.988513i	$0.451706\pi$
$140$	1.58357	+	9.41827i	0.133836	+	0.795989i
$141$	−4.24122			−0.357175
$142$	−0.779215	−	9.33379i	−0.0653903	−	0.783274i
$143$			1.99554i			0.166875i
$144$	3.78005	−	1.30812i	0.315005	−	0.109010i
$145$	7.89829			0.655917
$146$	0.566305	+	6.78346i	0.0468677	+	0.561403i
$147$	−3.62875			−0.299294
$148$	22.2509	−	3.74123i	1.82901	−	0.307527i
$149$			5.50380i			0.450889i	0.974256	+	0.225444i	$0.0723834\pi$
$149$			5.50380i			0.450889i	−0.974256	+	0.225444i	$0.927617\pi$
$150$	4.02302	−	0.335855i	0.328479	−	0.0274224i
$151$	0.619725			0.0504325			0.0252162	−	0.999682i	$-0.491973\pi$
$151$	0.619725			0.0504325			0.0252162	+	0.999682i	$0.491973\pi$
$152$	1.56915	+	6.14860i	0.127275	+	0.498718i
$153$	−3.01195	+	2.81570i	−0.243502	+	0.227636i
$154$	−0.119739	−	1.43428i	−0.00964881	−	0.115578i
$155$			0.888952i			0.0714023i
$156$	2.11991	+	12.6081i	0.169728	+	1.00946i
$157$		−	18.7631i		−	1.49746i	−0.662875	−	0.748730i	$-0.730664\pi$
$157$		−	18.7631i		−	1.49746i	0.662875	−	0.748730i	$-0.269336\pi$
$158$	1.35381	+	16.2166i	0.107704	+	1.29012i
$159$			8.91746i			0.707200i
$160$	−7.57752	+	3.35170i	−0.599055	+	0.264975i
$161$	23.9502			1.88754
$162$	−1.40931	+	0.117654i	−0.110726	+	0.00924376i
$163$	15.9222			1.24712			0.623561	−	0.781775i	$-0.285685\pi$
$163$	15.9222			1.24712			0.623561	+	0.781775i	$0.285685\pi$
$164$	−1.77995	−	10.5862i	−0.138991	−	0.826646i
$165$	0.457236			0.0355958
$166$	1.57473	+	18.8629i	0.122223	+	1.46404i
$167$		−	7.08898i		−	0.548561i	−0.961650	−	0.274281i	$-0.911560\pi$
$167$		−	7.08898i		−	0.548561i	0.961650	−	0.274281i	$-0.0884397\pi$
$168$	−2.28019	−	8.93480i	−0.175921	−	0.689335i
$169$	−27.8646			−2.14343
$170$	5.73216	−	6.33134i	0.439637	−	0.485591i
$171$		−	2.24353i		−	0.171567i
$172$	2.49114	+	14.8160i	0.189947	+	1.12971i
$173$	10.1123			0.768827			0.384414	−	0.923161i	$-0.374404\pi$
$173$	10.1123			0.768827			0.384414	+	0.923161i	$0.374404\pi$
$174$	−7.59952	+	0.634432i	−0.576118	+	0.0480962i
$175$		−	9.30651i		−	0.703506i
$176$	1.18001	−	0.408353i	0.0889464	−	0.0307808i
$177$		−	5.15579i		−	0.387533i
$178$	−13.4552	+	1.12329i	−1.00851	+	0.0841939i
$179$		−	2.38313i		−	0.178124i	−0.996026	−	0.0890618i	$-0.971613\pi$
$179$		−	2.38313i		−	0.178124i	0.996026	−	0.0890618i	$-0.0283869\pi$
$180$	2.88888	−	0.485732i	0.215325	−	0.0362043i
$181$	−10.5481			−0.784038			−0.392019	−	0.919957i	$-0.628223\pi$
$181$	−10.5481			−0.784038			−0.392019	+	0.919957i	$0.628223\pi$
$182$	29.3712	−	2.45200i	2.17714	−	0.181754i
$183$	6.41607			0.474289
$184$	5.13807	+	20.1332i	0.378783	+	1.48424i
$185$	16.5244			1.21490
$186$	−0.0714053	−	0.855325i	−0.00523569	−	0.0627155i
$187$	−0.940230	+	0.878969i	−0.0687565	+	0.0642765i
$188$	−8.36502	+	1.40648i	−0.610082	+	0.102578i
$189$			3.26018i			0.237143i
$190$	0.386627	+	4.63120i	0.0280489	+	0.335982i
$191$	−16.9179			−1.22414			−0.612069	−	0.790804i	$-0.709662\pi$
$191$	−16.9179			−1.22414			−0.612069	+	0.790804i	$0.709662\pi$
$192$	7.02166	−	3.83358i	0.506744	−	0.276665i
$193$			3.08185i			0.221836i	0.993830	+	0.110918i	$0.0353791\pi$
$193$			3.08185i			0.221836i	−0.993830	+	0.110918i	$0.964621\pi$
$194$	1.53197	+	18.3506i	0.109989	+	1.31750i
$195$			9.36327i			0.670518i
$196$	−7.15704	+	1.20337i	−0.511217	+	0.0859551i
$197$	22.7820			1.62315			0.811577	−	0.584246i	$-0.198610\pi$
$197$	22.7820			1.62315			0.811577	+	0.584246i	$0.198610\pi$
$198$	−0.439940	+	0.0367276i	−0.0312652	+	0.00261012i
$199$			14.9021i			1.05638i	0.849126	+	0.528190i	$0.177129\pi$
$199$			14.9021i			1.05638i	−0.849126	+	0.528190i	$0.822871\pi$
$200$	7.82329	−	1.99653i	0.553190	−	0.141176i
$201$		−	11.8427i		−	0.835319i
$202$	0.228657	+	2.73895i	0.0160882	+	0.192712i
$203$			17.5801i			1.23388i
$204$	−5.00676	+	6.55228i	−0.350544	+	0.458751i
$205$		−	7.86175i		−	0.549088i
$206$	−9.82407	+	0.820145i	−0.684475	+	0.0571422i
$207$		−	7.34630i		−	0.510603i
$208$	8.36225	+	24.1642i	0.579817	+	1.67548i
$209$		−	0.700357i		−	0.0484447i
$210$	−0.561825	−	6.72979i	−0.0387696	−	0.464400i
$211$	11.1308			0.766278			0.383139	−	0.923691i	$-0.374843\pi$
$211$	11.1308			0.766278			0.383139	+	0.923691i	$0.374843\pi$
$212$	2.95722	+	17.5880i	0.203103	+	1.20795i
$213$			6.62295i			0.453797i
$214$	10.4281	−	0.870575i	0.712853	−	0.0595113i
$215$			11.0029i			0.750394i
$216$	−2.74059	+	0.699408i	−0.186473	+	0.0475887i
$217$	−1.97863			−0.134318
$218$	15.0028	−	1.25249i	1.01612	−	0.0848290i
$219$		−	4.81332i		−	0.325254i
$220$	0.901814	−	0.151629i	0.0608003	−	0.0102229i
$221$	−17.9995	−	19.2540i	−1.21078	−	1.29516i
$222$	−15.8993	+	1.32733i	−1.06709	+	0.0890843i
$223$	−0.320676			−0.0214741			−0.0107370	−	0.999942i	$-0.503418\pi$
$223$	−0.320676			−0.0214741			−0.0107370	+	0.999942i	$0.503418\pi$
$224$	−7.46024	−	16.8661i	−0.498458	−	1.12691i
$225$	−2.85460			−0.190307
$226$	−1.30462	−	15.6274i	−0.0867822	−	1.03952i
$227$	−26.1137			−1.73323			−0.866613	−	0.498980i	$-0.833708\pi$
$227$	−26.1137			−1.73323			−0.866613	+	0.498980i	$0.833708\pi$
$228$	−0.744004	−	4.42496i	−0.0492729	−	0.293050i
$229$			14.6905i			0.970772i	0.874300	+	0.485386i	$0.161321\pi$
$229$			14.6905i			0.970772i	−0.874300	+	0.485386i	$0.838679\pi$
$230$	1.26599	+	15.1645i	0.0834766	+	0.999921i
$231$			1.01772i			0.0669610i
$232$	−14.7782	+	3.77146i	−0.970240	+	0.247609i
$233$			27.5228i			1.80308i	0.432694	+	0.901541i	$0.357563\pi$
$233$			27.5228i			1.80308i	−0.432694	+	0.901541i	$0.642437\pi$
$234$	−0.752107	−	9.00908i	−0.0491668	−	0.588942i
$235$	−6.21219			−0.405239
$236$	−1.70977	−	10.1688i	−0.111297	−	0.661935i
$237$		−	11.5068i		−	0.747445i
$238$	14.0923	+	12.7587i	0.913470	+	0.827022i
$239$	5.80155			0.375271			0.187636	−	0.982239i	$-0.439918\pi$
$239$	5.80155			0.375271			0.187636	+	0.982239i	$0.439918\pi$
$240$	5.53671	−	1.91603i	0.357393	−	0.123679i
$241$		−	17.1627i		−	1.10554i	−0.833333	−	0.552772i	$-0.813570\pi$
$241$		−	17.1627i		−	1.10554i	0.833333	−	0.552772i	$-0.186430\pi$
$242$	15.3651	−	1.28273i	0.987705	−	0.0824568i
$243$	1.00000			0.0641500
$244$	12.6545	−	2.12771i	0.810122	−	0.136212i
$245$	−5.31509			−0.339569
$246$	0.631497	+	7.56436i	0.0402628	+	0.482286i
$247$	14.3419			0.912552
$248$	−0.424478	−	1.66329i	−0.0269544	−	0.105619i
$249$		−	13.3845i		−	0.848206i
$250$	16.2138	−	1.35358i	1.02545	−	0.0856079i
$251$		−	6.91981i		−	0.436774i	−0.975862	−	0.218387i	$-0.929920\pi$
$251$		−	6.91981i		−	0.436774i	0.975862	−	0.218387i	$-0.0700796\pi$
$252$	1.08115	+	6.43010i	0.0681057	+	0.405058i
$253$		−	2.29327i		−	0.144177i
$254$	23.9242	−	1.99727i	1.50114	−	0.125320i
$255$	−4.41165	+	4.12421i	−0.276268	+	0.258268i
$256$	12.5776	−	9.88957i	0.786101	−	0.618098i
$257$	−0.288958			−0.0180247			−0.00901234	−	0.999959i	$-0.502869\pi$
$257$	−0.288958			−0.0180247			−0.00901234	+	0.999959i	$0.502869\pi$
$258$	−0.883814	−	10.5867i	−0.0550239	−	0.659101i
$259$			36.7801i			2.28540i
$260$	3.10506	+	18.4673i	0.192568	+	1.14529i
$261$	5.39236			0.333779
$262$	0.237478	−	0.0198254i	0.0146714	−	0.00122482i
$263$	−1.38062			−0.0851326			−0.0425663	−	0.999094i	$-0.513553\pi$
$263$	−1.38062			−0.0851326			−0.0425663	+	0.999094i	$0.513553\pi$
$264$	−0.855521	+	0.218332i	−0.0526537	+	0.0134374i
$265$			13.0616i			0.802365i
$266$	−10.3081	+	0.860557i	−0.632033	+	0.0527641i
$267$	9.54739			0.584291
$268$	−3.92729	−	23.3575i	−0.239898	−	1.42679i
$269$	−17.5243			−1.06847			−0.534237	−	0.845335i	$-0.679401\pi$
$269$	−17.5243			−1.06847			−0.534237	+	0.845335i	$0.679401\pi$
$270$	−2.06424	+	0.172330i	−0.125626	+	0.0104876i
$271$	0.927991			0.0563715			0.0281857	−	0.999603i	$-0.491027\pi$
$271$	0.927991			0.0563715			0.0281857	+	0.999603i	$0.491027\pi$
$272$	−7.70204	+	14.5835i	−0.467005	+	0.884255i
$273$	−20.8408			−1.26134
$274$	−8.49466	+	0.709161i	−0.513181	+	0.0428420i
$275$	−0.891113			−0.0537361
$276$	−2.43619	−	14.4892i	−0.146642	−	0.872149i
$277$	9.97435			0.599301			0.299650	−	0.954049i	$-0.403130\pi$
$277$	9.97435			0.599301			0.299650	+	0.954049i	$0.403130\pi$
$278$	−5.02251	+	0.419295i	−0.301230	+	0.0251476i
$279$			0.606910i			0.0363348i
$280$	−3.33984	−	13.0870i	−0.199594	−	0.782096i
$281$	−19.4670			−1.16131			−0.580653	−	0.814151i	$-0.697203\pi$
$281$	−19.4670			−1.16131			−0.580653	+	0.814151i	$0.697203\pi$
$282$	5.97720	−	0.498996i	0.355937	−	0.0297148i
$283$	2.02405			0.120317			0.0601587	−	0.998189i	$-0.480839\pi$
$283$	2.02405			0.120317			0.0601587	+	0.998189i	$0.480839\pi$
$284$	2.19631	+	13.0625i	0.130327	+	0.775119i
$285$		−	3.28614i		−	0.194654i
$286$	−0.234783	−	2.81234i	−0.0138830	−	0.166297i
$287$	17.4987			1.03292
$288$	−5.17337	+	2.28829i	−0.304844	+	0.134839i
$289$	1.14366	−	16.9615i	0.0672742	−	0.997735i
$290$	−11.1311	+	0.929264i	−0.653643	+	0.0545682i
$291$		−	13.0210i		−	0.763303i
$292$	−1.59620	−	9.49337i	−0.0934105	−	0.555558i
$293$		−	1.29056i		−	0.0753952i	−0.999289	−	0.0376976i	$-0.987998\pi$
$293$		−	1.29056i		−	0.0753952i	0.999289	−	0.0376976i	$-0.0120024\pi$
$294$	5.11404	−	0.426936i	0.298257	−	0.0248994i
$295$		−	7.55177i		−	0.439681i
$296$	−30.9183	+	7.89046i	−1.79709	+	0.458624i
$297$	0.312167			0.0181138
$298$	−0.647543	−	7.75657i	−0.0375112	−	0.449326i
$299$	46.9616			2.71586
$300$	−5.63018	+	0.946648i	−0.325058	+	0.0546548i
$301$	−24.4904			−1.41160
$302$	−0.873385	+	0.0729130i	−0.0502577	+	0.00419567i
$303$		−	1.94347i		−	0.111649i
$304$	−2.93482	−	8.48068i	−0.168324	−	0.486400i
$305$	9.39773			0.538112
$306$	3.91349	−	4.32257i	0.223720	−	0.247105i
$307$			7.42682i			0.423871i	0.977284	+	0.211936i	$0.0679767\pi$
$307$			7.42682i			0.423871i	−0.977284	+	0.211936i	$0.932023\pi$
$308$	0.337498	+	2.00726i	0.0192307	+	0.114374i
$309$	6.97083			0.396557
$310$	−0.104589	−	1.25281i	−0.00594023	−	0.0711548i
$311$		−	3.73279i		−	0.211667i	−0.994384	−	0.105834i	$-0.966249\pi$
$311$		−	3.73279i		−	0.211667i	0.994384	−	0.105834i	$-0.0337511\pi$
$312$	−4.47100	−	17.5193i	−0.253120	−	0.991837i
$313$			1.09676i			0.0619925i	0.999520	+	0.0309963i	$0.00986800\pi$
$313$			1.09676i			0.0619925i	−0.999520	+	0.0309963i	$0.990132\pi$
$314$	2.20755	+	26.4431i	0.124579	+	1.49227i
$315$			4.77524i			0.269054i
$316$	−3.81589	−	22.6950i	−0.214661	−	1.27669i
$317$	−19.9349			−1.11965			−0.559827	−	0.828610i	$-0.689132\pi$
$317$	−19.9349			−1.11965			−0.559827	+	0.828610i	$0.689132\pi$
$318$	−1.04917	−	12.5675i	−0.0588347	−	0.704749i
$319$	1.68332			0.0942477
$320$	10.2847	−	5.61511i	0.574934	−	0.313894i
$321$	−7.39946			−0.412998
$322$	−33.7533	+	2.81784i	−1.88100	+	0.157032i
$323$	6.31712	+	6.75741i	0.351494	+	0.375992i
$324$	1.97232	−	0.331622i	0.109573	−	0.0184234i
$325$		−	18.2482i		−	1.01223i
$326$	−22.4393	+	1.87331i	−1.24280	+	0.103753i
$327$	−10.6455			−0.588698
$328$	3.75402	+	14.7099i	0.207281	+	0.812217i
$329$		−	13.8271i		−	0.762314i
$330$	−0.644388	+	0.0537956i	−0.0354724	+	0.00296135i
$331$		−	26.9222i		−	1.47978i	−0.672728	−	0.739890i	$-0.734878\pi$
$331$		−	26.9222i		−	1.47978i	0.672728	−	0.739890i	$-0.265122\pi$
$332$	−4.43858	−	26.3984i	−0.243599	−	1.44880i
$333$	11.2816			0.618229
$334$	0.834045	+	9.99057i	0.0456369	+	0.546660i
$335$		−	17.3462i		−	0.947724i
$336$	4.26472	+	12.3236i	0.232659	+	0.672310i
$337$		−	12.2109i		−	0.665170i	−0.943073	−	0.332585i	$-0.892079\pi$
$337$		−	12.2109i		−	0.665170i	0.943073	−	0.332585i	$-0.107921\pi$
$338$	39.2699	−	3.27838i	2.13600	−	0.178320i
$339$			11.0887i			0.602253i
$340$	−7.33349	+	9.59723i	−0.397714	+	0.520483i
$341$			0.189457i			0.0102597i
$342$	0.263960	+	3.16184i	0.0142733	+	0.170973i
$343$			10.9909i			0.593451i
$344$	−5.25395	−	20.5873i	−0.283274	−	1.10999i
$345$		−	10.7603i		−	0.579313i
$346$	−14.2514	+	1.18976i	−0.766162	+	0.0639617i
$347$	14.2507			0.765018			0.382509	−	0.923952i	$-0.375060\pi$
$347$	14.2507			0.765018			0.382509	+	0.923952i	$0.375060\pi$
$348$	10.6354	−	1.78822i	0.570119	−	0.0958589i
$349$		−	18.5830i		−	0.994725i	−0.867543	−	0.497363i	$-0.834302\pi$
$349$		−	18.5830i		−	0.994725i	0.867543	−	0.497363i	$-0.165698\pi$
$350$	1.09495	+	13.1158i	0.0585274	+	0.701067i
$351$			6.39254i			0.341209i
$352$	−1.61495	+	0.714329i	−0.0860773	+	0.0380739i
$353$	−3.89576			−0.207350			−0.103675	−	0.994611i	$-0.533060\pi$
$353$	−3.89576			−0.207350			−0.103675	+	0.994611i	$0.533060\pi$
$354$	0.606598	+	7.26611i	0.0322403	+	0.386189i
$355$			9.70074i			0.514862i
$356$	18.8305	−	3.16612i	0.998012	−	0.167804i
$357$	−9.17968	−	9.81948i	−0.485840	−	0.519702i
$358$	0.280385	+	3.35857i	0.0148188	+	0.177506i
$359$	8.66787			0.457472			0.228736	−	0.973488i	$-0.426541\pi$
$359$	8.66787			0.457472			0.228736	+	0.973488i	$0.426541\pi$
$360$	−4.01419	+	1.02444i	−0.211566	+	0.0539925i
$361$	13.9666			0.735082
$362$	14.8656	−	1.24103i	0.781320	−	0.0652271i
$363$	−10.9026			−0.572236
$364$	−41.1047	+	6.91127i	−2.15447	+	0.362249i
$365$		−	7.05015i		−	0.369022i
$366$	−9.04224	+	0.754875i	−0.472645	+	0.0394579i
$367$			32.3753i			1.68998i	0.534785	+	0.844988i	$0.320392\pi$
$367$			32.3753i			1.68998i	−0.534785	+	0.844988i	$0.679608\pi$
$368$	−9.60988	−	27.7694i	−0.500950	−	1.44758i
$369$		−	5.36742i		−	0.279416i
$370$	−23.2880	+	1.94416i	−1.21069	+	0.101072i
$371$	−29.0725			−1.50937
$372$	0.201265	+	1.19702i	0.0104351	+	0.0620625i
$373$			11.7221i			0.606947i	0.952840	+	0.303473i	$0.0981464\pi$
$373$			11.7221i			0.606947i	−0.952840	+	0.303473i	$0.901854\pi$
$374$	1.22166	−	1.34936i	0.0631707	−	0.0697738i
$375$	−11.5048			−0.594104
$376$	11.6234	−	2.96635i	0.599433	−	0.152978i
$377$			34.4709i			1.77534i
$378$	−0.383572	−	4.59460i	−0.0197288	−	0.236321i
$379$	27.7442			1.42512			0.712562	−	0.701609i	$-0.247535\pi$
$379$	27.7442			1.42512			0.712562	+	0.701609i	$0.247535\pi$
$380$	−1.08976	−	6.48131i	−0.0559033	−	0.332484i
$381$	−16.9758			−0.869696
$382$	23.8426	−	1.99046i	1.21989	−	0.101841i
$383$	−25.2288			−1.28913			−0.644566	−	0.764549i	$-0.722962\pi$
$383$	−25.2288			−1.28913			−0.644566	+	0.764549i	$0.722962\pi$
$384$	−9.44466	+	6.22883i	−0.481971	+	0.317864i
$385$			1.49067i			0.0759716i
$386$	−0.362591	−	4.34328i	−0.0184554	−	0.221067i
$387$			7.51199i			0.381856i
$388$	−4.31804	−	25.6815i	−0.219215	−	1.30378i
$389$			26.3923i			1.33814i	0.743198	+	0.669072i	$0.233308\pi$
$389$			26.3923i			1.33814i	−0.743198	+	0.669072i	$0.766692\pi$
$390$	−1.10162	−	13.1958i	−0.0557829	−	0.668193i
$391$	20.6850	+	22.1267i	1.04608	+	1.11899i
$392$	9.94491	−	2.53798i	0.502294	−	0.128187i
$393$	−0.168506			−0.00850002
$394$	−32.1070	+	2.68039i	−1.61753	+	0.135036i
$395$		−	16.8542i		−	0.848025i
$396$	0.615692	−	0.103521i	0.0309397	−	0.00520214i
$397$	−21.2037			−1.06418			−0.532091	−	0.846687i	$-0.678594\pi$
$397$	−21.2037			−1.06418			−0.532091	+	0.846687i	$0.678594\pi$
$398$	−1.75329	−	21.0017i	−0.0878843	−	1.05272i
$399$	7.31432			0.366174
$400$	−10.7906	+	3.73418i	−0.539528	+	0.186709i
$401$		−	7.21971i		−	0.360535i	−0.983618	−	0.180268i	$-0.942304\pi$
$401$		−	7.21971i		−	0.360535i	0.983618	−	0.180268i	$-0.0576964\pi$
$402$	1.39334	+	16.6900i	0.0694934	+	0.832423i
$403$	−3.87970			−0.193262
$404$	−0.644497	−	3.83314i	−0.0320649	−	0.190706i
$405$	1.46472			0.0727824
$406$	−2.06836	−	24.7758i	−0.102651	−	1.22960i
$407$	3.52175			0.174567
$408$	6.28519	−	9.82326i	0.311163	−	0.486324i
$409$	24.5533			1.21408			0.607042	−	0.794670i	$-0.292356\pi$
$409$	24.5533			1.21408			0.607042	+	0.794670i	$0.292356\pi$
$410$	0.924964	+	11.0796i	0.0456807	+	0.547185i
$411$	6.02753			0.297316
$412$	13.7487	−	2.31168i	0.677349	−	0.113888i
$413$	16.8088			0.827106
$414$	0.864321	+	10.3532i	0.0424790	+	0.508833i
$415$		−	19.6045i		−	0.962345i
$416$	−14.6280	−	33.0710i	−0.717197	−	1.62144i
$417$	3.56380			0.174520
$418$	0.0823997	+	0.987021i	0.00403030	+	0.0482768i
$419$	39.0863			1.90949			0.954745	−	0.297426i	$-0.0961283\pi$
$419$	39.0863			1.90949			0.954745	+	0.297426i	$0.0961283\pi$
$420$	1.58357	+	9.41827i	0.0772704	+	0.459565i
$421$			9.66214i			0.470904i	0.971886	+	0.235452i	$0.0756570\pi$
$421$			9.66214i			0.470904i	−0.971886	+	0.235452i	$0.924343\pi$
$422$	−15.6868	+	1.30958i	−0.763621	+	0.0637496i
$423$	−4.24122			−0.206215
$424$	−6.23695	−	24.4391i	−0.302893	−	1.18687i
$425$	8.59792	−	8.03771i	0.417060	−	0.389886i
$426$	−0.779215	−	9.33379i	−0.0377531	−	0.452224i
$427$			20.9175i			1.01227i
$428$	−14.5941	+	2.45382i	−0.705431	+	0.118610i
$429$			1.99554i			0.0963456i
$430$	−1.29454	−	15.5066i	−0.0624282	−	0.747793i
$431$		−	6.07054i		−	0.292408i	−0.989254	−	0.146204i	$-0.953294\pi$
$431$		−	6.07054i		−	0.292408i	0.989254	−	0.146204i	$-0.0467055\pi$
$432$	3.78005	−	1.30812i	0.181868	−	0.0629372i
$433$	20.5097			0.985634			0.492817	−	0.870133i	$-0.335967\pi$
$433$	20.5097			0.985634			0.492817	+	0.870133i	$0.335967\pi$
$434$	2.78851	−	0.232794i	0.133853	−	0.0111745i
$435$	7.89829			0.378694
$436$	−20.9963	+	3.53028i	−1.00554	+	0.169070i
$437$	−16.4817			−0.788426
$438$	0.566305	+	6.78346i	0.0270591	+	0.324126i
$439$			7.36907i			0.351706i	0.984416	+	0.175853i	$0.0562684\pi$
$439$			7.36907i			0.351706i	−0.984416	+	0.175853i	$0.943732\pi$
$440$	−1.25310	+	0.319795i	−0.0597390	+	0.0152456i
$441$	−3.62875			−0.172798
$442$	27.6322	+	25.0172i	1.31433	+	1.18995i
$443$			18.9079i			0.898342i	0.893446	+	0.449171i	$0.148281\pi$
$443$			18.9079i			0.898342i	−0.893446	+	0.449171i	$0.851719\pi$
$444$	22.2509	−	3.74123i	1.05598	−	0.177551i
$445$	13.9842			0.662916
$446$	0.451933	−	0.0377288i	0.0213996	−	0.00178651i
$447$			5.50380i			0.260321i
$448$	12.4982	+	22.8918i	0.590482	+	1.08154i
$449$			19.0187i			0.897550i	0.893645	+	0.448775i	$0.148139\pi$
$449$			19.0187i			0.897550i	−0.893645	+	0.448775i	$0.851861\pi$
$450$	4.02302	−	0.335855i	0.189647	−	0.0158324i
$451$		−	1.67553i		−	0.0788976i
$452$	3.67724	+	21.8703i	0.172963	+	1.02869i
$453$	0.619725			0.0291172
$454$	36.8023	−	3.07238i	1.72722	−	0.144194i
$455$	−30.5259			−1.43108
$456$	1.56915	+	6.14860i	0.0734820	+	0.287935i
$457$	−20.5126			−0.959539			−0.479769	−	0.877395i	$-0.659280\pi$
$457$	−20.5126			−0.959539			−0.479769	+	0.877395i	$0.659280\pi$
$458$	−1.72839	−	20.7034i	−0.0807623	−	0.967407i
$459$	−3.01195	+	2.81570i	−0.140586	+	0.131426i
$460$	−3.56833	−	21.2226i	−0.166374	−	0.989510i
$461$		−	8.07937i		−	0.376294i	−0.982141	−	0.188147i	$-0.939752\pi$
$461$		−	8.07937i		−	0.376294i	0.982141	−	0.188147i	$-0.0602481\pi$
$462$	−0.119739	−	1.43428i	−0.00557074	−	0.0667289i
$463$	12.6813			0.589350			0.294675	−	0.955597i	$-0.404789\pi$
$463$	12.6813			0.589350			0.294675	+	0.955597i	$0.404789\pi$
$464$	20.3834	−	7.05388i	0.946277	−	0.327468i
$465$			0.888952i			0.0412241i
$466$	−3.23817	−	38.7883i	−0.150005	−	1.79683i
$467$			32.1472i			1.48760i	0.668405	+	0.743798i	$0.266977\pi$
$467$			32.1472i			1.48760i	−0.668405	+	0.743798i	$0.733023\pi$
$468$	2.11991	+	12.6081i	0.0979927	+	0.582810i
$469$	38.6093			1.78281
$470$	8.75491	−	0.730888i	0.403834	−	0.0337133i
$471$		−	18.7631i		−	0.864559i
$472$	3.60600	+	14.1299i	0.165980	+	0.650381i
$473$			2.34499i			0.107823i
$474$	1.35381	+	16.2166i	0.0621828	+	0.744854i
$475$			6.40440i			0.293854i
$476$	−21.3616	−	16.3229i	−0.979106	−	0.748160i
$477$			8.91746i			0.408302i
$478$	−8.17619	+	0.682574i	−0.373970	+	0.0312202i
$479$		−	25.4835i		−	1.16437i	−0.813056	−	0.582185i	$-0.802198\pi$
$479$		−	25.4835i		−	1.16437i	0.813056	−	0.582185i	$-0.197802\pi$
$480$	−7.57752	+	3.35170i	−0.345865	+	0.152984i
$481$			72.1183i			3.28831i
$482$	2.01925	+	24.1875i	0.0919744	+	1.10171i
$483$	23.9502			1.08977
$484$	−21.5033	+	3.61552i	−0.977421	+	0.164342i
$485$		−	19.0721i		−	0.866017i
$486$	−1.40931	+	0.117654i	−0.0639276	+	0.00533689i
$487$		−	3.09673i		−	0.140326i	−0.997536	−	0.0701630i	$-0.977648\pi$
$487$		−	3.09673i		−	0.140326i	0.997536	−	0.0701630i	$-0.0223520\pi$
$488$	−17.5838	+	4.48745i	−0.795982	+	0.203137i
$489$	15.9222			0.720026
$490$	7.49062	−	0.625341i	0.338392	−	0.0282500i
$491$			37.4349i			1.68941i	0.535231	+	0.844706i	$0.320225\pi$
$491$			37.4349i			1.68941i	−0.535231	+	0.844706i	$0.679775\pi$
$492$	−1.77995	−	10.5862i	−0.0802464	−	0.477264i
$493$	−16.2415	+	15.1833i	−0.731481	+	0.683820i
$494$	−20.2122	+	1.68738i	−0.909389	+	0.0759187i
$495$	0.457236			0.0205512
$496$	0.793914	+	2.29415i	0.0356478	+	0.103011i
$497$	−21.5920			−0.968532
$498$	1.57473	+	18.8629i	0.0705655	+	0.845266i
$499$	−19.7963			−0.886204			−0.443102	−	0.896471i	$-0.646122\pi$
$499$	−19.7963			−0.886204			−0.443102	+	0.896471i	$0.646122\pi$
$500$	−22.6910	+	3.81523i	−1.01477	+	0.170622i
$501$		−	7.08898i		−	0.316712i
$502$	0.814142	+	9.75216i	0.0363369	+	0.435260i
$503$		−	10.8162i		−	0.482268i	−0.970492	−	0.241134i	$-0.922481\pi$
$503$		−	10.8162i		−	0.482268i	0.970492	−	0.241134i	$-0.0775194\pi$
$504$	−2.28019	−	8.93480i	−0.101568	−	0.397988i
$505$		−	2.84663i		−	0.126674i
$506$	0.269812	+	3.23193i	0.0119946	+	0.143677i
$507$	−27.8646			−1.23751
$508$	−33.4816	+	5.62954i	−1.48551	+	0.249770i
$509$			2.63717i			0.116890i	0.998291	+	0.0584452i	$0.0186143\pi$
$509$			2.63717i			0.116890i	−0.998291	+	0.0584452i	$0.981386\pi$
$510$	5.73216	−	6.33134i	0.253824	−	0.280356i
$511$	15.6923			0.694185
$512$	−16.5622	+	15.4173i	−0.731954	+	0.681354i
$513$		−	2.24353i		−	0.0990544i
$514$	0.407231	−	0.0339970i	0.0179622	−	0.00149954i
$515$	10.2103			0.449919
$516$	2.49114	+	14.8160i	0.109666	+	0.652238i
$517$	−1.32397			−0.0582281
$518$	−4.32732	−	51.8346i	−0.190131	−	2.27748i
$519$	10.1123			0.443883
$520$	−6.54875	−	25.6609i	−0.287182	−	1.12530i
$521$		−	38.5194i		−	1.68757i	−0.536684	−	0.843783i	$-0.680323\pi$
$521$		−	38.5194i		−	1.68757i	0.536684	−	0.843783i	$-0.319677\pi$
$522$	−7.59952	+	0.634432i	−0.332622	+	0.0277683i
$523$			0.305975i			0.0133793i	0.999978	+	0.00668967i	$0.00212940\pi$
$523$			0.305975i			0.0133793i	−0.999978	+	0.00668967i	$0.997871\pi$
$524$	−0.332347	+	0.0558803i	−0.0145187	+	0.00244114i
$525$		−	9.30651i		−	0.406169i
$526$	1.94572	−	0.162435i	0.0848375	−	0.00708250i
$527$	−1.70888	−	1.82798i	−0.0744399	−	0.0796281i
$528$	1.18001	−	0.408353i	0.0513533	−	0.0177713i
$529$	−30.9682			−1.34644
$530$	−1.53674	−	18.4078i	−0.0667518	−	0.799584i
$531$		−	5.15579i		−	0.223742i
$532$	14.4261	−	2.42559i	0.625452	−	0.105162i
$533$	34.3114			1.48619
$534$	−13.4552	+	1.12329i	−0.582265	+	0.0486094i
$535$	−10.8381			−0.468573
$536$	8.28288	+	32.4560i	0.357766	+	1.40188i
$537$		−	2.38313i		−	0.102840i
$538$	24.6972	−	2.06180i	1.06477	−	0.0888905i
$539$	−1.13278			−0.0487921
$540$	2.88888	−	0.485732i	0.124318	−	0.0209026i
$541$	1.50556			0.0647292			0.0323646	−	0.999476i	$-0.489696\pi$
$541$	1.50556			0.0647292			0.0323646	+	0.999476i	$0.489696\pi$
$542$	−1.30783	+	0.109182i	−0.0561760	+	0.00468976i
$543$	−10.5481			−0.452664
$544$	9.13876	−	21.4589i	0.391821	−	0.920041i
$545$	−15.5927			−0.667916
$546$	29.3712	−	2.45200i	1.25697	−	0.104936i
$547$	−3.68763			−0.157672			−0.0788358	−	0.996888i	$-0.525120\pi$
$547$	−3.68763			−0.157672			−0.0788358	+	0.996888i	$0.525120\pi$
$548$	11.8882	−	1.99886i	0.507838	−	0.0853870i
$549$	6.41607			0.273831
$550$	1.25585	−	0.104843i	0.0535498	−	0.00447051i
$551$		−	12.0979i		−	0.515390i
$552$	5.13807	+	20.1332i	0.218691	+	0.856926i
$553$	37.5141			1.59526
$554$	−14.0570	+	1.17352i	−0.597223	+	0.0498581i
$555$	16.5244			0.701421
$556$	7.02894	−	1.18183i	0.298094	−	0.0501209i
$557$		−	29.3032i		−	1.24162i	−0.783962	−	0.620809i	$-0.786804\pi$
$557$		−	29.3032i		−	1.24162i	0.783962	−	0.620809i	$-0.213196\pi$
$558$	−0.0714053	−	0.855325i	−0.00302283	−	0.0362088i
$559$	−48.0207			−2.03106
$560$	6.24661	+	18.0507i	0.263967	+	0.762779i
$561$	−0.940230	+	0.878969i	−0.0396966	+	0.0371101i
$562$	27.4351	−	2.29037i	1.15728	−	0.0966135i
$563$		−	27.2285i		−	1.14754i	−0.819015	−	0.573772i	$-0.805480\pi$
$563$		−	27.2285i		−	1.14754i	0.819015	−	0.573772i	$-0.194520\pi$
$564$	−8.36502	+	1.40648i	−0.352231	+	0.0592235i
$565$			16.2417i			0.683296i
$566$	−2.85252	+	0.238138i	−0.119900	+	0.0100097i
$567$			3.26018i			0.136915i
$568$	−4.63214	−	18.1508i	−0.194360	−	0.761589i
$569$	8.50233			0.356436			0.178218	−	0.983991i	$-0.442967\pi$
$569$	8.50233			0.356436			0.178218	+	0.983991i	$0.442967\pi$
$570$	0.386627	+	4.63120i	0.0161940	+	0.193979i
$571$	3.89571			0.163030			0.0815151	−	0.996672i	$-0.474024\pi$
$571$	3.89571			0.163030			0.0815151	+	0.996672i	$0.474024\pi$
$572$	0.661764	+	3.93584i	0.0276698	+	0.164566i
$573$	−16.9179			−0.706756
$574$	−24.6611	+	2.05879i	−1.02934	+	0.0859323i
$575$			20.9708i			0.874542i
$576$	7.02166	−	3.83358i	0.292569	−	0.159733i
$577$	3.69131			0.153671			0.0768355	−	0.997044i	$-0.475518\pi$
$577$	3.69131			0.153671			0.0768355	+	0.997044i	$0.475518\pi$
$578$	0.383810	+	24.0386i	0.0159644	+	0.999873i
$579$			3.08185i			0.128077i
$580$	15.5779	−	2.61924i	0.646837	−	0.108758i
$581$	43.6357			1.81032
$582$	1.53197	+	18.3506i	0.0635021	+	0.760657i
$583$			2.78374i			0.115291i
$584$	3.36647	+	13.1913i	0.139306	+	0.545861i
$585$			9.36327i			0.387124i
$586$	0.151839	+	1.81880i	0.00627241	+	0.0751338i
$587$		−	18.6727i		−	0.770704i	−0.922770	−	0.385352i	$-0.874080\pi$
$587$		−	18.6727i		−	0.770704i	0.922770	−	0.385352i	$-0.125920\pi$
$588$	−7.15704	+	1.20337i	−0.295151	+	0.0496262i
$589$	1.36162			0.0561047
$590$	0.888495	+	10.6428i	0.0365787	+	0.438157i
$591$	22.7820			0.937128
$592$	42.6451	−	14.7578i	1.75270	−	0.606541i
$593$	18.0541			0.741393			0.370697	−	0.928754i	$-0.379119\pi$
$593$	18.0541			0.741393			0.370697	+	0.928754i	$0.379119\pi$
$594$	−0.439940	+	0.0367276i	−0.0180510	+	0.00150695i
$595$	−13.4456	−	14.3828i	−0.551217	−	0.589636i
$596$	1.82518	+	10.8552i	0.0747623	+	0.444648i
$597$			14.9021i			0.609901i
$598$	−66.1835	+	5.52521i	−2.70644	+	0.225943i
$599$	−43.6498			−1.78348			−0.891741	−	0.452546i	$-0.850516\pi$
$599$	−43.6498			−1.78348			−0.891741	+	0.452546i	$0.850516\pi$
$600$	7.82329	−	1.99653i	0.319385	−	0.0815081i
$601$			10.1680i			0.414760i	0.978260	+	0.207380i	$0.0664937\pi$
$601$			10.1680i			0.414760i	−0.978260	+	0.207380i	$0.933506\pi$
$602$	34.5146	−	2.88139i	1.40671	−	0.117437i
$603$		−	11.8427i		−	0.482272i
$604$	1.22229	−	0.205514i	0.0497344	−	0.00836225i
$605$	−15.9692			−0.649239
$606$	0.228657	+	2.73895i	0.00928854	+	0.111262i
$607$		−	10.9378i		−	0.443952i	−0.975052	−	0.221976i	$-0.928749\pi$
$607$		−	10.9378i		−	0.443952i	0.975052	−	0.221976i	$-0.0712506\pi$
$608$	5.13386	+	11.6066i	0.208206	+	0.470711i
$609$			17.5801i			0.712380i
$610$	−13.2443	+	1.10568i	−0.536247	+	0.0447676i
$611$		−	27.1122i		−	1.09684i
$612$	−5.00676	+	6.55228i	−0.202386	+	0.264860i
$613$			35.0085i			1.41398i	0.707224	+	0.706990i	$0.249947\pi$
$613$			35.0085i			1.41398i	−0.707224	+	0.706990i	$0.750053\pi$
$614$	−0.873794	−	10.4667i	−0.0352635	−	0.422402i
$615$		−	7.86175i		−	0.317016i
$616$	−0.711801	−	2.78915i	−0.0286793	−	0.112378i
$617$		−	24.5518i		−	0.988419i	−0.869343	−	0.494209i	$-0.835458\pi$
$617$		−	24.5518i		−	0.988419i	0.869343	−	0.494209i	$-0.164542\pi$
$618$	−9.82407	+	0.820145i	−0.395182	+	0.0329911i
$619$	37.2040			1.49536			0.747678	−	0.664061i	$-0.231168\pi$
$619$	37.2040			1.49536			0.747678	+	0.664061i	$0.231168\pi$
$620$	0.294796	+	1.75329i	0.0118393	+	0.0704139i
$621$		−	7.34630i		−	0.294797i
$622$	0.439177	+	5.26067i	0.0176094	+	0.210933i
$623$			31.1262i			1.24704i
$624$	8.36225	+	24.1642i	0.334758	+	0.967341i
$625$	−2.57822			−0.103129
$626$	−0.129038	−	1.54568i	−0.00515740	−	0.0617776i
$627$		−	0.700357i		−	0.0279696i
$628$	−6.22226	−	37.0068i	−0.248295	−	1.47673i
$629$	−33.9797	+	31.7657i	−1.35486	+	1.26658i
$630$	−0.561825	−	6.72979i	−0.0223836	−	0.268121i
$631$	12.3656			0.492266			0.246133	−	0.969236i	$-0.420840\pi$
$631$	12.3656			0.492266			0.246133	+	0.969236i	$0.420840\pi$
$632$	8.04793	+	31.5353i	0.320129	+	1.25441i
$633$	11.1308			0.442411
$634$	28.0944	−	2.34541i	1.11577	−	0.0931483i
$635$	−24.8647			−0.986726
$636$	2.95722	+	17.5880i	0.117261	+	0.697411i
$637$		−	23.1969i		−	0.919096i
$638$	−2.37232	+	0.198049i	−0.0939209	+	0.00784082i
$639$			6.62295i			0.262000i
$640$	−13.8338	+	9.12348i	−0.546827	+	0.360637i
$641$		−	37.6527i		−	1.48719i	−0.668629	−	0.743596i	$-0.733118\pi$
$641$		−	37.6527i		−	1.48719i	0.668629	−	0.743596i	$-0.266882\pi$
$642$	10.4281	−	0.870575i	0.411566	−	0.0343589i
$643$	−29.1814			−1.15080			−0.575400	−	0.817872i	$-0.695154\pi$
$643$	−29.1814			−1.15080			−0.575400	+	0.817872i	$0.695154\pi$
$644$	47.2374	−	7.94242i	1.86142	−	0.312975i
$645$			11.0029i			0.433240i
$646$	−9.69782	−	8.78005i	−0.381556	−	0.345447i
$647$	32.6928			1.28529			0.642643	−	0.766166i	$-0.277838\pi$
$647$	32.6928			1.28529			0.642643	+	0.766166i	$0.277838\pi$
$648$	−2.74059	+	0.699408i	−0.107661	+	0.0274754i
$649$		−	1.60947i		−	0.0631771i
$650$	2.14697	+	25.7174i	0.0842110	+	1.00872i
$651$	−1.97863			−0.0775488
$652$	31.4036	−	5.28014i	1.22986	−	0.206786i
$653$	−5.75472			−0.225200			−0.112600	−	0.993640i	$-0.535918\pi$
$653$	−5.75472			−0.225200			−0.112600	+	0.993640i	$0.535918\pi$
$654$	15.0028	−	1.25249i	0.586657	−	0.0489760i
$655$	−0.246814			−0.00964382
$656$	−7.02125	−	20.2891i	−0.274134	−	0.792157i
$657$		−	4.81332i		−	0.187785i
$658$	1.62681	+	19.4867i	0.0634198	+	0.759672i
$659$			16.3764i			0.637933i	0.947766	+	0.318966i	$0.103336\pi$
$659$			16.3764i			0.637933i	−0.947766	+	0.318966i	$0.896664\pi$
$660$	0.901814	−	0.151629i	0.0351031	−	0.00590217i
$661$		−	26.9352i		−	1.04766i	−0.851823	−	0.523829i	$-0.824503\pi$
$661$		−	26.9352i		−	1.04766i	0.851823	−	0.523829i	$-0.175497\pi$
$662$	3.16750	+	37.9418i	0.123108	+	1.47465i
$663$	−17.9995	−	19.2540i	−0.699042	−	0.747764i
$664$	9.36121	+	36.6813i	0.363285	+	1.42351i
$665$	10.7134			0.415448
$666$	−15.8993	+	1.32733i	−0.616086	+	0.0514328i
$667$		−	39.6139i		−	1.53386i
$668$	−2.35086	−	13.9817i	−0.0909574	−	0.540968i
$669$	−0.320676			−0.0123981
$670$	2.04085	+	24.4462i	0.0788448	+	0.944439i
$671$	2.00288			0.0773205
$672$	−7.46024	−	16.8661i	−0.287785	−	0.650623i
$673$		−	48.5604i		−	1.87187i	−0.352179	−	0.935933i	$-0.614559\pi$
$673$		−	48.5604i		−	1.87187i	0.352179	−	0.935933i	$-0.385441\pi$
$674$	1.43666	+	17.2089i	0.0553380	+	0.662864i
$675$	−2.85460			−0.109874
$676$	−54.9578	+	9.24051i	−2.11376	+	0.355404i
$677$	18.4217			0.708002			0.354001	−	0.935245i	$-0.384821\pi$
$677$	18.4217			0.708002			0.354001	+	0.935245i	$0.384821\pi$
$678$	−1.30462	−	15.6274i	−0.0501037	−	0.600165i
$679$	42.4507			1.62911
$680$	9.20602	−	14.3883i	0.353035	−	0.551766i
$681$	−26.1137			−1.00068
$682$	−0.0222904	−	0.267004i	−0.000853542	−	0.0102241i
$683$	−35.1819			−1.34620			−0.673099	−	0.739552i	$-0.735037\pi$
$683$	−35.1819			−1.34620			−0.673099	+	0.739552i	$0.735037\pi$
$684$	−0.744004	−	4.42496i	−0.0284477	−	0.169192i
$685$	8.82862			0.337324
$686$	−1.29312	−	15.4896i	−0.0493715	−	0.591394i
$687$			14.6905i			0.560476i
$688$	9.82662	+	28.3957i	0.374636	+	1.08258i
$689$	−57.0052			−2.17173
$690$	1.26599	+	15.1645i	0.0481952	+	0.577305i
$691$	16.9759			0.645792			0.322896	−	0.946434i	$-0.395344\pi$
$691$	16.9759			0.645792			0.322896	+	0.946434i	$0.395344\pi$
$692$	19.9447	−	3.35347i	0.758185	−	0.127480i
$693$			1.01772i			0.0386600i
$694$	−20.0837	+	1.67665i	−0.762366	+	0.0636447i
$695$	5.21996			0.198004
$696$	−14.7782	+	3.77146i	−0.560168	+	0.142957i
$697$	15.1130	+	16.1664i	0.572447	+	0.612345i
$698$	2.18636	+	26.1892i	0.0827550	+	0.991277i
$699$			27.5228i			1.04101i
$700$	−3.08624	−	18.3554i	−0.116649	−	0.693768i
$701$			25.1119i			0.948462i	0.880400	+	0.474231i	$0.157274\pi$
$701$			25.1119i			0.948462i	−0.880400	+	0.474231i	$0.842726\pi$
$702$	−0.752107	−	9.00908i	−0.0283865	−	0.340026i
$703$		−	25.3107i		−	0.954611i
$704$	2.19193	−	1.19672i	0.0826114	−	0.0451030i
$705$	−6.21219			−0.233965
$706$	5.49033	−	0.458351i	0.206631	−	0.0172503i
$707$	6.33606			0.238292
$708$	−1.70977	−	10.1688i	−0.0642571	−	0.382168i
$709$	−32.3694			−1.21566			−0.607830	−	0.794067i	$-0.707960\pi$
$709$	−32.3694			−1.21566			−0.607830	+	0.794067i	$0.707960\pi$
$710$	−1.14133	−	13.6714i	−0.0428333	−	0.513077i
$711$		−	11.5068i		−	0.431537i
$712$	−26.1655	+	6.67752i	−0.980592	+	0.250251i
$713$	4.45855			0.166974
$714$	14.0923	+	12.7587i	0.527392	+	0.477482i
$715$			2.92290i			0.109310i
$716$	−0.790298	−	4.70029i	−0.0295348	−	0.175658i
$717$	5.80155			0.216663
$718$	−12.2157	+	1.01981i	−0.455887	+	0.0380589i
$719$			14.6515i			0.546410i	0.961956	+	0.273205i	$0.0880838\pi$
$719$			14.6515i			0.546410i	−0.961956	+	0.273205i	$0.911916\pi$
$720$	5.53671	−	1.91603i	0.206341	−	0.0714063i
$721$			22.7261i			0.846366i
$722$	−19.6832	+	1.64322i	−0.732534	+	0.0611543i
$723$		−	17.1627i		−	0.638286i
$724$	−20.8043	+	3.49799i	−0.773185	+	0.130002i
$725$	−15.3931			−0.571684
$726$	15.3651	−	1.28273i	0.570252	−	0.0476065i
$727$	5.77315			0.214114			0.107057	−	0.994253i	$-0.465857\pi$
$727$	5.77315			0.214114			0.107057	+	0.994253i	$0.465857\pi$
$728$	57.1161	−	14.5762i	2.11686	−	0.540232i
$729$	1.00000			0.0370370
$730$	0.829477	+	9.93585i	0.0307003	+	0.367742i
$731$	−21.1515	−	22.6257i	−0.782317	−	0.836842i
$732$	12.6545	−	2.12771i	0.467724	−	0.0786423i
$733$		−	9.97415i		−	0.368403i	−0.982888	−	0.184202i	$-0.941030\pi$
$733$		−	9.97415i		−	0.368403i	0.982888	−	0.184202i	$-0.0589700\pi$
$734$	−3.80907	−	45.6268i	−0.140596	−	1.68412i
$735$	−5.31509			−0.196050
$736$	16.8105	+	38.0051i	0.619643	+	1.40089i
$737$		−	3.69690i		−	0.136177i
$738$	0.631497	+	7.56436i	0.0232457	+	0.278448i
$739$			31.2897i			1.15101i	0.817798	+	0.575506i	$0.195195\pi$
$739$			31.2897i			1.15101i	−0.817798	+	0.575506i	$0.804805\pi$
$740$	32.5913	−	5.47984i	1.19808	−	0.201443i
$741$	14.3419			0.526862
$742$	40.9722	−	3.42049i	1.50414	−	0.125570i
$743$		−	0.432434i		−	0.0158645i	−0.999969	−	0.00793223i	$-0.997475\pi$
$743$		−	0.432434i		−	0.0158645i	0.999969	−	0.00793223i	$-0.00252493\pi$
$744$	−0.424478	−	1.66329i	−0.0155621	−	0.0609792i
$745$			8.06151i			0.295351i
$746$	−1.37915	−	16.5201i	−0.0504942	−	0.604843i
$747$		−	13.3845i		−	0.489712i
$748$	−1.56295	+	2.04540i	−0.0571470	+	0.0747874i
$749$		−	24.1236i		−	0.881455i
$750$	16.2138	−	1.35358i	0.592044	−	0.0494258i
$751$			44.0064i			1.60582i	0.596103	+	0.802908i	$0.296715\pi$
$751$			44.0064i			1.60582i	−0.596103	+	0.802908i	$0.703285\pi$
$752$	−16.0320	+	5.54805i	−0.584628	+	0.202316i
$753$		−	6.91981i		−	0.252172i
$754$	−4.05563	−	48.5802i	−0.147697	−	1.76919i
$755$	0.907721			0.0330354
$756$	1.08115	+	6.43010i	0.0393209	+	0.233860i
$757$			48.4044i			1.75929i	0.475634	+	0.879643i	$0.342219\pi$
$757$			48.4044i			1.75929i	−0.475634	+	0.879643i	$0.657781\pi$
$758$	−39.1002	+	3.26421i	−1.42018	+	0.118562i
$759$		−	2.29327i		−	0.0832405i
$760$	2.29836	+	9.00597i	0.0833701	+	0.326681i
$761$	−37.9787			−1.37673			−0.688363	−	0.725366i	$-0.741671\pi$
$761$	−37.9787			−1.37673			−0.688363	+	0.725366i	$0.741671\pi$
$762$	23.9242	−	1.99727i	0.866681	−	0.0723533i
$763$		−	34.7062i		−	1.25645i
$764$	−33.3675	+	5.61035i	−1.20719	+	0.202975i
$765$	−4.41165	+	4.12421i	−0.159504	+	0.149111i
$766$	35.5552	−	2.96826i	1.28466	−	0.107248i
$767$	32.9586			1.19007
$768$	12.5776	−	9.88957i	0.453856	−	0.356859i
$769$	−3.04684			−0.109872			−0.0549358	−	0.998490i	$-0.517495\pi$
$769$	−3.04684			−0.109872			−0.0549358	+	0.998490i	$0.517495\pi$
$770$	−0.175383	−	2.10082i	−0.00632037	−	0.0757083i
$771$	−0.288958			−0.0104066
$772$	1.02201	+	6.07837i	0.0367828	+	0.218765i
$773$			21.3814i			0.769036i	0.923118	+	0.384518i	$0.125632\pi$
$773$			21.3814i			0.769036i	−0.923118	+	0.384518i	$0.874368\pi$
$774$	−0.883814	−	10.5867i	−0.0317680	−	0.380532i
$775$		−	1.73249i		−	0.0622328i
$776$	9.10698	+	35.6851i	0.326922	+	1.28102i
$777$			36.7801i			1.31948i
$778$	−3.10516	−	37.1950i	−0.111325	−	1.33351i
$779$	−12.0420			−0.431449
$780$	3.10506	+	18.4673i	0.111179	+	0.661236i
$781$			2.06746i			0.0739797i
$782$	−31.7549	−	28.7497i	−1.13555	−	1.02809i
$783$	5.39236			0.192707
$784$	−13.7169	+	4.74686i	−0.489888	+	0.169531i
$785$		−	27.4827i		−	0.980899i
$786$	0.237478	−	0.0198254i	0.00847055	−	0.000707149i
$787$	−38.9140			−1.38713			−0.693567	−	0.720392i	$-0.743962\pi$
$787$	−38.9140			−1.38713			−0.693567	+	0.720392i	$0.743962\pi$
$788$	44.9334	−	7.55502i	1.60069	−	0.269136i
$789$	−1.38062			−0.0491513
$790$	1.98296	+	23.7528i	0.0705504	+	0.845085i
$791$	−36.1510			−1.28538
$792$	−0.855521	+	0.218332i	−0.0303996	+	0.00775810i
$793$			41.0150i			1.45649i
$794$	29.8826	−	2.49469i	1.06049	−	0.0885334i
$795$			13.0616i			0.463246i
$796$	4.94185	+	29.3916i	0.175159	+	1.04176i
$797$		−	18.6530i		−	0.660722i	−0.943855	−	0.330361i	$-0.892829\pi$
$797$		−	18.6530i		−	0.660722i	0.943855	−	0.330361i	$-0.107171\pi$
$798$	−10.3081	+	0.860557i	−0.364904	+	0.0304634i
$799$	12.7743	−	11.9420i	0.451924	−	0.422478i
$800$	14.7679	−	6.53217i	0.522124	−	0.230947i
$801$	9.54739			0.337340
$802$	0.849427	+	10.1748i	0.0299943	+	0.359285i
$803$		−	1.50256i		−	0.0530241i
$804$	−3.92729	−	23.3575i	−0.138505	−	0.823756i
$805$	35.0803			1.23642
$806$	5.46770	−	0.456461i	0.192592	−	0.0160782i
$807$	−17.5243			−0.616884
$808$	1.35928	+	5.32625i	0.0478193	+	0.187377i
$809$			32.7083i			1.14996i	0.818166	+	0.574982i	$0.194991\pi$
$809$			32.7083i			1.14996i	−0.818166	+	0.574982i	$0.805009\pi$
$810$	−2.06424	+	0.172330i	−0.0725301	+	0.00605504i
$811$	−31.1576			−1.09409			−0.547045	−	0.837103i	$-0.684247\pi$
$811$	−31.1576			−1.09409			−0.547045	+	0.837103i	$0.684247\pi$
$812$	5.82993	+	34.6734i	0.204590	+	1.21680i
$813$	0.927991			0.0325461
$814$	−4.96324	+	0.414347i	−0.173961	+	0.0145229i
$815$	23.3215			0.816916
$816$	−7.70204	+	14.5835i	−0.269625	+	0.510525i
$817$	16.8534			0.589626
$818$	−34.6033	+	2.88879i	−1.20987	+	0.101004i
$819$	−20.8408			−0.728237
$820$	−2.60713	−	15.5058i	−0.0910448	−	0.541487i
$821$	28.5075			0.994917			0.497459	−	0.867488i	$-0.334267\pi$
$821$	28.5075			0.994917			0.497459	+	0.867488i	$0.334267\pi$
$822$	−8.49466	+	0.709161i	−0.296285	+	0.0247348i
$823$			23.6353i			0.823876i	0.911212	+	0.411938i	$0.135148\pi$
$823$			23.6353i			0.823876i	−0.911212	+	0.411938i	$0.864852\pi$
$824$	−19.1042	+	4.87546i	−0.665526	+	0.169845i
$825$	−0.891113			−0.0310246
$826$	−23.6888	+	1.97762i	−0.824239	+	0.0688101i
$827$	33.1756			1.15363			0.576814	−	0.816875i	$-0.304296\pi$
$827$	33.1756			1.15363			0.576814	+	0.816875i	$0.304296\pi$
$828$	−2.43619	−	14.4892i	−0.0846636	−	0.503535i
$829$		−	24.0031i		−	0.833662i	−0.908984	−	0.416831i	$-0.863141\pi$
$829$		−	24.0031i		−	0.833662i	0.908984	−	0.416831i	$-0.136859\pi$
$830$	2.30654	+	27.6288i	0.0800612	+	0.959009i
$831$	9.97435			0.346007
$832$	24.5063	+	44.8862i	0.849605	+	1.55615i
$833$	10.9296	−	10.2175i	0.378688	−	0.354014i
$834$	−5.02251	+	0.419295i	−0.173915	+	0.0145190i
$835$		−	10.3833i		−	0.359330i
$836$	−0.232254	−	1.38132i	−0.00803266	−	0.0477741i
$837$			0.606910i			0.0209779i
$838$	−55.0847	+	4.59865i	−1.90287	+	0.158858i
$839$			27.2563i			0.940993i	0.882402	+	0.470496i	$0.155925\pi$
$839$			27.2563i			0.940993i	−0.882402	+	0.470496i	$0.844075\pi$
$840$	−3.33984	−	13.0870i	−0.115235	−	0.451543i
$841$	0.0775701			0.00267483
$842$	−1.13679	−	13.6170i	−0.0391763	−	0.469271i
$843$	−19.4670			−0.670481
$844$	21.9535	−	3.69122i	0.755671	−	0.127057i
$845$	−40.8138			−1.40404
$846$	5.97720	−	0.498996i	0.205500	−	0.0171558i
$847$		−	35.5442i		−	1.22131i
$848$	11.6651	+	33.7085i	0.400583	+	1.15755i
$849$	2.02405			0.0694653
$850$	−11.1715	+	12.3392i	−0.383178	+	0.423231i
$851$		−	82.8782i		−	2.84103i
$852$	2.19631	+	13.0625i	0.0752444	+	0.447515i
$853$	35.1320			1.20290			0.601449	−	0.798911i	$-0.294590\pi$
$853$	35.1320			1.20290			0.601449	+	0.798911i	$0.294590\pi$
$854$	−2.46103	−	29.4793i	−0.0842146	−	1.00876i
$855$		−	3.28614i		−	0.112384i
$856$	20.2789	−	5.17525i	0.693118	−	0.176886i
$857$		−	27.2840i		−	0.932005i	−0.884783	−	0.466002i	$-0.845694\pi$
$857$		−	27.2840i		−	0.932005i	0.884783	−	0.466002i	$-0.154306\pi$
$858$	−0.234783	−	2.81234i	−0.00801536	−	0.0960116i
$859$			3.90819i			0.133346i	0.997775	+	0.0666728i	$0.0212384\pi$
$859$			3.90819i			0.133346i	−0.997775	+	0.0666728i	$0.978762\pi$
$860$	3.64881	+	21.7013i	0.124423	+	0.740007i
$861$	17.4987			0.596355
$862$	0.714222	+	8.55528i	0.0243265	+	0.291394i
$863$	30.8940			1.05164			0.525821	−	0.850595i	$-0.323758\pi$
$863$	30.8940			1.05164			0.525821	+	0.850595i	$0.323758\pi$
$864$	−5.17337	+	2.28829i	−0.176001	+	0.0778493i
$865$	14.8117			0.503614
$866$	−28.9046	+	2.41305i	−0.982217	+	0.0819986i
$867$	1.14366	−	16.9615i	0.0388408	−	0.576042i
$868$	−3.90249	+	0.656158i	−0.132459	+	0.0222714i
$869$		−	3.59203i		−	0.121851i
$870$	−11.1311	+	0.929264i	−0.377381	+	0.0315050i
$871$	75.7049			2.56516
$872$	29.1750	−	7.44556i	0.987989	−	0.252139i
$873$		−	13.0210i		−	0.440693i
$874$	23.2278	−	1.93913i	0.785692	−	0.0655921i
$875$		−	37.5076i		−	1.26799i
$876$	−1.59620	−	9.49337i	−0.0539306	−	0.320751i
$877$	−17.7726			−0.600137			−0.300068	−	0.953918i	$-0.597010\pi$
$877$	−17.7726			−0.600137			−0.300068	+	0.953918i	$0.597010\pi$
$878$	−0.866999	−	10.3853i	−0.0292598	−	0.350487i
$879$		−	1.29056i		−	0.0435294i
$880$	1.72838	−	0.598122i	0.0582636	−	0.0201627i
$881$		−	34.8223i		−	1.17319i	−0.809879	−	0.586597i	$-0.800467\pi$
$881$		−	34.8223i		−	1.17319i	0.809879	−	0.586597i	$-0.199533\pi$
$882$	5.11404	−	0.426936i	0.172199	−	0.0143757i
$883$		−	7.89791i		−	0.265786i	−0.991130	−	0.132893i	$-0.957573\pi$
$883$		−	7.89791i		−	0.265786i	0.991130	−	0.132893i	$-0.0424266\pi$
$884$	−41.8857	−	32.0060i	−1.40877	−	1.07648i
$885$		−	7.55177i		−	0.253850i
$886$	−2.22459	−	26.6471i	−0.0747365	−	0.895228i
$887$		−	21.4557i		−	0.720412i	−0.932873	−	0.360206i	$-0.882706\pi$
$887$		−	21.4557i		−	0.720412i	0.932873	−	0.360206i	$-0.117294\pi$
$888$	−30.9183	+	7.89046i	−1.03755	+	0.264787i
$889$		−	55.3440i		−	1.85618i
$890$	−19.7081	+	1.64530i	−0.660618	+	0.0551505i
$891$	0.312167			0.0104580
$892$	−0.632475	+	0.106343i	−0.0211768	+	0.00356063i
$893$			9.51532i			0.318418i
$894$	−0.647543	−	7.75657i	−0.0216571	−	0.259418i
$895$		−	3.49061i		−	0.116678i
$896$	−20.3071	−	30.7913i	−0.678413	−	1.02866i
$897$	46.9616			1.56800
$898$	−2.23763	−	26.8033i	−0.0746706	−	0.894438i
$899$			3.27268i			0.109150i
$900$	−5.63018	+	0.946648i	−0.187673	+	0.0315549i
$901$	−25.1089	−	26.8589i	−0.836499	−	0.894800i
$902$	0.197132	+	2.36134i	0.00656379	+	0.0786241i
$903$	−24.4904			−0.814990
$904$	−7.75550	−	30.3895i	−0.257944	−	1.01074i
$905$	−15.4501			−0.513577
$906$	−0.873385	+	0.0729130i	−0.0290163	+	0.00242237i
$907$	−46.9549			−1.55911			−0.779557	−	0.626332i	$-0.784556\pi$
$907$	−46.9549			−1.55911			−0.779557	+	0.626332i	$0.784556\pi$
$908$	−51.5044	+	8.65987i	−1.70923	+	0.287388i
$909$		−	1.94347i		−	0.0644608i
$910$	43.0205	−	3.59149i	1.42612	−	0.119057i
$911$			20.5297i			0.680181i	0.940393	+	0.340090i	$0.110458\pi$
$911$			20.5297i			0.680181i	−0.940393	+	0.340090i	$0.889542\pi$
$912$	−2.93482	−	8.48068i	−0.0971817	−	0.280823i
$913$		−	4.17819i		−	0.138278i
$914$	28.9086	−	2.41339i	0.956212	−	0.0798277i
$915$	9.39773			0.310679
$916$	4.87167	+	28.9742i	0.160965	+	0.957335i
$917$		−	0.549360i		−	0.0181415i
$918$	3.91349	−	4.32257i	0.129165	−	0.142666i
$919$	−53.2755			−1.75740			−0.878698	−	0.477379i	$-0.841587\pi$
$919$	−53.2755			−1.75740			−0.878698	+	0.477379i	$0.841587\pi$
$920$	7.52581	+	29.4894i	0.248119	+	0.972238i
$921$			7.42682i			0.244722i
$922$	0.950569	+	11.3863i	0.0313053	+	0.374989i
$923$	−42.3375			−1.39355
$924$	0.337498	+	2.00726i	0.0111029	+	0.0660341i
$925$	−32.2046			−1.05888
$926$	−17.8719	+	1.49200i	−0.587307	+	0.0490303i
$927$	6.97083			0.228952
$928$	−27.8967	+	12.3393i	−0.915753	+	0.405057i
$929$			40.7355i			1.33649i	0.743942	+	0.668244i	$0.232954\pi$
$929$			40.7355i			1.33649i	−0.743942	+	0.668244i	$0.767046\pi$
$930$	−0.104589	−	1.25281i	−0.00342959	−	0.0410812i
$931$			8.14122i			0.266818i
$932$	9.12717	+	54.2837i	0.298970	+	1.77812i
$933$		−	3.73279i		−	0.122206i
$934$	−3.78224	−	45.3054i	−0.123759	−	1.48244i
$935$	−1.37717	+	1.28744i	−0.0450383	+	0.0421038i
$936$	−4.47100	−	17.5193i	−0.146139	−	0.572637i
$937$	−21.3186			−0.696449			−0.348225	−	0.937411i	$-0.613215\pi$
$937$	−21.3186			−0.696449			−0.348225	+	0.937411i	$0.613215\pi$
$938$	−54.4125	+	4.54253i	−1.77663	+	0.148319i
$939$			1.09676i			0.0357914i
$940$	−12.2524	+	2.06010i	−0.399629	+	0.0671929i
$941$	27.9682			0.911738			0.455869	−	0.890047i	$-0.349329\pi$
$941$	27.9682			0.911738			0.455869	+	0.890047i	$0.349329\pi$
$942$	2.20755	+	26.4431i	0.0719260	+	0.861562i
$943$	−39.4307			−1.28404
$944$	−6.74441	−	19.4892i	−0.219512	−	0.634318i
$945$			4.77524i			0.155338i
$946$	−0.275898	−	3.30483i	−0.00897020	−	0.107449i
$947$	−50.2968			−1.63443			−0.817214	−	0.576335i	$-0.804482\pi$
$947$	−50.2968			−1.63443			−0.817214	+	0.576335i	$0.804482\pi$
$948$	−3.81589	−	22.6950i	−0.123934	−	0.737098i
$949$	30.7693			0.998815
$950$	−0.753502	−	9.02579i	−0.0244468	−	0.292835i
$951$	−19.9349			−0.646432
$952$	32.0256	+	20.4908i	1.03795	+	0.664111i
$953$	−15.4664			−0.501006			−0.250503	−	0.968116i	$-0.580596\pi$
$953$	−15.4664			−0.501006			−0.250503	+	0.968116i	$0.580596\pi$
$954$	−1.04917	−	12.5675i	−0.0339682	−	0.406887i
$955$	−24.7800			−0.801861
$956$	11.4425	−	1.92392i	0.370076	−	0.0622240i
$957$	1.68332			0.0544139
$958$	2.99823	+	35.9142i	0.0968684	+	1.16033i
$959$			19.6508i			0.634557i
$960$	10.2847	−	5.61511i	0.331939	−	0.181227i
$961$	30.6317			0.988118
$962$	−8.48499	−	101.637i	−0.273567	−	3.27691i
$963$	−7.39946			−0.238444
$964$	−5.69151	−	33.8502i	−0.183311	−	1.09024i
$965$			4.51403i			0.145312i
$966$	−33.7533	+	2.81784i	−1.08600	+	0.0906624i
$967$	−50.1822			−1.61375			−0.806876	−	0.590721i	$-0.798843\pi$
$967$	−50.1822			−1.61375			−0.806876	+	0.590721i	$0.798843\pi$
$968$	29.8794	−	7.62534i	0.960361	−	0.245088i
$969$	6.31712	+	6.75741i	0.202935	+	0.217079i
$970$	2.24390	+	26.8785i	0.0720473	+	0.863015i
$971$			30.8673i			0.990579i	0.868728	+	0.495290i	$0.164938\pi$
$971$			30.8673i			0.990579i	−0.868728	+	0.495290i	$0.835062\pi$
$972$	1.97232	−	0.331622i	0.0632620	−	0.0106368i
$973$			11.6186i			0.372476i
$974$	0.364342	+	4.36425i	0.0116743	+	0.139840i
$975$		−	18.2482i		−	0.584409i
$976$	24.2531	−	8.39302i	0.776322	−	0.268654i
$977$	−31.1825			−0.997617			−0.498809	−	0.866712i	$-0.666229\pi$
$977$	−31.1825			−0.997617			−0.498809	+	0.866712i	$0.666229\pi$
$978$	−22.4393	+	1.87331i	−0.717530	+	0.0599017i
$979$	2.98038			0.0952533
$980$	−10.4830	+	1.76260i	−0.334868	+	0.0563042i
$981$	−10.6455			−0.339885
$982$	−4.40435	−	52.7574i	−0.140549	−	1.68356i
$983$		−	2.61279i		−	0.0833350i	−0.999132	−	0.0416675i	$-0.986733\pi$
$983$		−	2.61279i		−	0.0833350i	0.999132	−	0.0416675i	$-0.0132670\pi$
$984$	3.75402	+	14.7099i	0.119674	+	0.468934i
$985$	33.3693			1.06323
$986$	21.1030	−	23.3088i	0.672056	−	0.742305i
$987$		−	13.8271i		−	0.440122i
$988$	28.2867	−	4.75608i	0.899921	−	0.151311i
$989$	55.1853			1.75479
$990$	−0.644388	+	0.0537956i	−0.0204800	+	0.00170974i
$991$		−	35.6087i		−	1.13115i	−0.824698	−	0.565573i	$-0.808655\pi$
$991$		−	35.6087i		−	1.13115i	0.824698	−	0.565573i	$-0.191345\pi$
$992$	−1.38879	−	3.13977i	−0.0440941	−	0.0996877i
$993$		−	26.9222i		−	0.854351i
$994$	30.4298	−	2.54038i	0.965175	−	0.0805759i
$995$			21.8273i			0.691973i
$996$	−4.43858	−	26.3984i	−0.140642	−	0.836465i
$997$	−4.13227			−0.130870			−0.0654351	−	0.997857i	$-0.520844\pi$
$997$	−4.13227			−0.130870			−0.0654351	+	0.997857i	$0.520844\pi$
$998$	27.8991	−	2.32911i	0.883132	−	0.0737267i
$999$	11.2816			0.356935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	408.2.l.b.373.2	yes	18
3.2	odd	2		1224.2.l.d.1189.17		18
4.3	odd	2		1632.2.l.a.1393.13		18
8.3	odd	2		1632.2.l.b.1393.5		18
8.5	even	2		408.2.l.a.373.1	✓	18
12.11	even	2		4896.2.l.d.3025.5		18
17.16	even	2		408.2.l.a.373.2	yes	18
24.5	odd	2		1224.2.l.c.1189.18		18
24.11	even	2		4896.2.l.c.3025.13		18
51.50	odd	2		1224.2.l.c.1189.17		18
68.67	odd	2		1632.2.l.b.1393.6		18
136.67	odd	2		1632.2.l.a.1393.14		18
136.101	even	2	inner	408.2.l.b.373.1	yes	18
204.203	even	2		4896.2.l.c.3025.14		18
408.101	odd	2		1224.2.l.d.1189.18		18
408.203	even	2		4896.2.l.d.3025.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.1	✓	18	8.5	even	2
408.2.l.a.373.2	yes	18	17.16	even	2
408.2.l.b.373.1	yes	18	136.101	even	2	inner
408.2.l.b.373.2	yes	18	1.1	even	1	trivial
1224.2.l.c.1189.17		18	51.50	odd	2
1224.2.l.c.1189.18		18	24.5	odd	2
1224.2.l.d.1189.17		18	3.2	odd	2
1224.2.l.d.1189.18		18	408.101	odd	2
1632.2.l.a.1393.13		18	4.3	odd	2
1632.2.l.a.1393.14		18	136.67	odd	2
1632.2.l.b.1393.5		18	8.3	odd	2
1632.2.l.b.1393.6		18	68.67	odd	2
4896.2.l.c.3025.13		18	24.11	even	2
4896.2.l.c.3025.14		18	204.203	even	2
4896.2.l.d.3025.5		18	12.11	even	2
4896.2.l.d.3025.6		18	408.203	even	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:	\( N \)	\(=\)	\( 408 = 2^{3} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	408.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40931 + 0.117654i) q^{2} +1.00000 q^{3} +(1.97232 - 0.331622i) q^{4} +1.46472 q^{5} +(-1.40931 + 0.117654i) q^{6} +3.26018i q^{7} +(-2.74059 + 0.699408i) q^{8} +1.00000 q^{9} +(-2.06424 + 0.172330i) q^{10} +0.312167 q^{11} +(1.97232 - 0.331622i) q^{12} +6.39254i q^{13} +(-0.383572 - 4.59460i) q^{14} +1.46472 q^{15} +(3.78005 - 1.30812i) q^{16} +(-3.01195 + 2.81570i) q^{17} +(-1.40931 + 0.117654i) q^{18} -2.24353i q^{19} +(2.88888 - 0.485732i) q^{20} +3.26018i q^{21} +(-0.439940 + 0.0367276i) q^{22} -7.34630i q^{23} +(-2.74059 + 0.699408i) q^{24} -2.85460 q^{25} +(-0.752107 - 9.00908i) q^{26} +1.00000 q^{27} +(1.08115 + 6.43010i) q^{28} +5.39236 q^{29} +(-2.06424 + 0.172330i) q^{30} +0.606910i q^{31} +(-5.17337 + 2.28829i) q^{32} +0.312167 q^{33} +(3.91349 - 4.32257i) q^{34} +4.77524i q^{35} +(1.97232 - 0.331622i) q^{36} +11.2816 q^{37} +(0.263960 + 3.16184i) q^{38} +6.39254i q^{39} +(-4.01419 + 1.02444i) q^{40} -5.36742i q^{41} +(-0.383572 - 4.59460i) q^{42} +7.51199i q^{43} +(0.615692 - 0.103521i) q^{44} +1.46472 q^{45} +(0.864321 + 10.3532i) q^{46} -4.24122 q^{47} +(3.78005 - 1.30812i) q^{48} -3.62875 q^{49} +(4.02302 - 0.335855i) q^{50} +(-3.01195 + 2.81570i) q^{51} +(2.11991 + 12.6081i) q^{52} +8.91746i q^{53} +(-1.40931 + 0.117654i) q^{54} +0.457236 q^{55} +(-2.28019 - 8.93480i) q^{56} -2.24353i q^{57} +(-7.59952 + 0.634432i) q^{58} -5.15579i q^{59} +(2.88888 - 0.485732i) q^{60} +6.41607 q^{61} +(-0.0714053 - 0.855325i) q^{62} +3.26018i q^{63} +(7.02166 - 3.83358i) q^{64} +9.36327i q^{65} +(-0.439940 + 0.0367276i) q^{66} -11.8427i q^{67} +(-5.00676 + 6.55228i) q^{68} -7.34630i q^{69} +(-0.561825 - 6.72979i) q^{70} +6.62295i q^{71} +(-2.74059 + 0.699408i) q^{72} -4.81332i q^{73} +(-15.8993 + 1.32733i) q^{74} -2.85460 q^{75} +(-0.744004 - 4.42496i) q^{76} +1.01772i q^{77} +(-0.752107 - 9.00908i) q^{78} -11.5068i q^{79} +(5.53671 - 1.91603i) q^{80} +1.00000 q^{81} +(0.631497 + 7.56436i) q^{82} -13.3845i q^{83} +(1.08115 + 6.43010i) q^{84} +(-4.41165 + 4.12421i) q^{85} +(-0.883814 - 10.5867i) q^{86} +5.39236 q^{87} +(-0.855521 + 0.218332i) q^{88} +9.54739 q^{89} +(-2.06424 + 0.172330i) q^{90} -20.8408 q^{91} +(-2.43619 - 14.4892i) q^{92} +0.606910i q^{93} +(5.97720 - 0.498996i) q^{94} -3.28614i q^{95} +(-5.17337 + 2.28829i) q^{96} -13.0210i q^{97} +(5.11404 - 0.426936i) q^{98} +0.312167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{3} + 2 q^{4} - 4 q^{5} + 18 q^{9} - 8 q^{10} + 2 q^{12} - 6 q^{14} - 4 q^{15} + 10 q^{16} - 2 q^{17} - 2 q^{20} + 2 q^{22} + 22 q^{25} + 2 q^{26} + 18 q^{27} - 10 q^{28} + 12 q^{29} - 8 q^{30}+ \cdots - 60 q^{98}+O(q^{100}) \) 18 * q + 18 * q^3 + 2 * q^4 - 4 * q^5 + 18 * q^9 - 8 * q^10 + 2 * q^12 - 6 * q^14 - 4 * q^15 + 10 * q^16 - 2 * q^17 - 2 * q^20 + 2 * q^22 + 22 * q^25 + 2 * q^26 + 18 * q^27 - 10 * q^28 + 12 * q^29 - 8 * q^30 + 6 * q^34 + 2 * q^36 - 16 * q^37 - 34 * q^38 - 10 * q^40 - 6 * q^42 + 12 * q^44 - 4 * q^45 + 32 * q^46 + 10 * q^48 - 18 * q^49 - 14 * q^50 - 2 * q^51 + 8 * q^52 - 16 * q^55 - 14 * q^56 - 6 * q^58 - 2 * q^60 - 16 * q^61 - 6 * q^62 + 2 * q^64 + 2 * q^66 - 36 * q^68 - 32 * q^70 - 6 * q^74 + 22 * q^75 + 2 * q^78 - 62 * q^80 + 18 * q^81 + 34 * q^82 - 10 * q^84 + 16 * q^85 + 14 * q^86 + 12 * q^87 + 16 * q^88 + 20 * q^89 - 8 * q^90 - 2 * q^92 + 12 * q^94 - 60 * q^98

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