LMFDB - Embedded newform 867.2.e.h.616.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			616.2
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	867.616
Dual form			867.2.e.h.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.765367i q^{2} +(0.707107 - 0.707107i) q^{3} +1.41421 q^{4} +(1.47247 - 1.47247i) q^{5} +(-0.541196 - 0.541196i) q^{6} +(0.873017 + 0.873017i) q^{7} -2.61313i q^{8} -1.00000i q^{9} +(-1.12698 - 1.12698i) q^{10} +(1.05826 + 1.05826i) q^{11} +(1.00000 - 1.00000i) q^{12} -4.10973 q^{13} +(0.668179 - 0.668179i) q^{14} -2.08239i q^{15} +0.828427 q^{16} -0.765367 q^{18} -6.81204i q^{19} +(2.08239 - 2.08239i) q^{20} +1.23463 q^{21} +(0.809957 - 0.809957i) q^{22} +(2.33956 + 2.33956i) q^{23} +(-1.84776 - 1.84776i) q^{24} +0.663643i q^{25} +3.14545i q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.23463 + 1.23463i) q^{28} +(4.41421 - 4.41421i) q^{29} -1.59379 q^{30} +(-7.26197 + 7.26197i) q^{31} -5.86030i q^{32} +1.49661 q^{33} +2.57099 q^{35} -1.41421i q^{36} +(-2.78384 + 2.78384i) q^{37} -5.21371 q^{38} +(-2.90602 + 2.90602i) q^{39} +(-3.84776 - 3.84776i) q^{40} +(8.58221 + 8.58221i) q^{41} -0.944947i q^{42} +3.44609i q^{43} +(1.49661 + 1.49661i) q^{44} +(-1.47247 - 1.47247i) q^{45} +(1.79063 - 1.79063i) q^{46} -1.56940 q^{47} +(0.585786 - 0.585786i) q^{48} -5.47568i q^{49} +0.507930 q^{50} -5.81204 q^{52} +3.96134i q^{53} +(-0.541196 + 0.541196i) q^{54} +3.11652 q^{55} +(2.28130 - 2.28130i) q^{56} +(-4.81684 - 4.81684i) q^{57} +(-3.37849 - 3.37849i) q^{58} -8.06306i q^{59} -2.94495i q^{60} +(2.31457 + 2.31457i) q^{61} +(5.55807 + 5.55807i) q^{62} +(0.873017 - 0.873017i) q^{63} -2.82843 q^{64} +(-6.05147 + 6.05147i) q^{65} -1.14545i q^{66} +2.11652 q^{67} +3.30864 q^{69} -1.96775i q^{70} +(0.160248 - 0.160248i) q^{71} -2.61313 q^{72} +(-0.260380 + 0.260380i) q^{73} +(2.13066 + 2.13066i) q^{74} +(0.469266 + 0.469266i) q^{75} -9.63368i q^{76} +1.84776i q^{77} +(2.22417 + 2.22417i) q^{78} +(-1.91969 - 1.91969i) q^{79} +(1.21984 - 1.21984i) q^{80} -1.00000 q^{81} +(6.56854 - 6.56854i) q^{82} +14.4138i q^{83} +1.74603 q^{84} +2.63752 q^{86} -6.24264i q^{87} +(2.76537 - 2.76537i) q^{88} -13.6694 q^{89} +(-1.12698 + 1.12698i) q^{90} +(-3.58787 - 3.58787i) q^{91} +(3.30864 + 3.30864i) q^{92} +10.2700i q^{93} +1.20116i q^{94} +(-10.0305 - 10.0305i) q^{95} +(-4.14386 - 4.14386i) q^{96} +(-1.89828 + 1.89828i) q^{97} -4.19090 q^{98} +(1.05826 - 1.05826i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{13} + 8 q^{14} - 16 q^{16} + 8 q^{20} + 16 q^{21} + 16 q^{22} + 16 q^{28} + 24 q^{29} + 16 q^{30} - 32 q^{31} - 8 q^{33} + 32 q^{35} + 16 q^{37} - 32 q^{38}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 16 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^13 + 8 * q^14 - 16 * q^16 + 8 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^28 + 24 * q^29 + 16 * q^30 - 32 * q^31 - 8 * q^33 + 32 * q^35 + 16 * q^37 - 32 * q^38 - 8 * q^39 - 16 * q^40 + 16 * q^41 - 8 * q^44 + 16 * q^46 - 16 * q^47 + 16 * q^48 + 32 * q^50 - 16 * q^52 + 24 * q^55 + 8 * q^57 - 32 * q^61 - 8 * q^65 + 16 * q^67 - 24 * q^69 - 24 * q^71 + 32 * q^73 - 8 * q^74 + 16 * q^75 + 16 * q^78 + 16 * q^79 + 16 * q^80 - 8 * q^81 + 16 * q^82 - 32 * q^86 + 16 * q^88 - 32 * q^89 - 16 * q^90 - 24 * q^92 - 24 * q^95 - 16 * q^97 - 64 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.765367i		−	0.541196i	−0.962692	−	0.270598i	$-0.912779\pi$
$2$		−	0.765367i		−	0.541196i	0.962692	−	0.270598i	$-0.0872214\pi$
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.41421			0.707107
$5$	1.47247	−	1.47247i	0.658510	−	0.658510i	−0.296517	−	0.955027i	$-0.595825\pi$
$5$	1.47247	−	1.47247i	0.658510	−	0.658510i	0.955027	+	0.296517i	$0.0958252\pi$
$6$	−0.541196	−	0.541196i	−0.220942	−	0.220942i
$7$	0.873017	+	0.873017i	0.329970	+	0.329970i	0.852575	−	0.522605i	$-0.175040\pi$
$7$	0.873017	+	0.873017i	0.329970	+	0.329970i	−0.522605	+	0.852575i	$0.675040\pi$
$8$		−	2.61313i		−	0.923880i
$9$		−	1.00000i		−	0.333333i
$10$	−1.12698	−	1.12698i	−0.356383	−	0.356383i
$11$	1.05826	+	1.05826i	0.319077	+	0.319077i	0.848413	−	0.529335i	$-0.177559\pi$
$11$	1.05826	+	1.05826i	0.319077	+	0.319077i	−0.529335	+	0.848413i	$0.677559\pi$
$12$	1.00000	−	1.00000i	0.288675	−	0.288675i
$13$	−4.10973			−1.13983			−0.569917	−	0.821702i	$-0.693025\pi$
$13$	−4.10973			−1.13983			−0.569917	+	0.821702i	$0.693025\pi$
$14$	0.668179	−	0.668179i	0.178578	−	0.178578i
$15$		−	2.08239i		−	0.537671i
$16$	0.828427			0.207107
$17$		0			0
$17$		0			0
$18$	−0.765367			−0.180399
$19$		−	6.81204i		−	1.56279i	−0.624038	−	0.781394i	$-0.714509\pi$
$19$		−	6.81204i		−	1.56279i	0.624038	−	0.781394i	$-0.285491\pi$
$20$	2.08239	−	2.08239i	0.465637	−	0.465637i
$21$	1.23463			0.269419
$22$	0.809957	−	0.809957i	0.172683	−	0.172683i
$23$	2.33956	+	2.33956i	0.487833	+	0.487833i	0.907622	−	0.419789i	$-0.137896\pi$
$23$	2.33956	+	2.33956i	0.487833	+	0.487833i	−0.419789	+	0.907622i	$0.637896\pi$
$24$	−1.84776	−	1.84776i	−0.377172	−	0.377172i
$25$			0.663643i			0.132729i
$26$			3.14545i			0.616874i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.23463	+	1.23463i	0.233324	+	0.233324i
$29$	4.41421	−	4.41421i	0.819699	−	0.819699i	−0.166365	−	0.986064i	$-0.553203\pi$
$29$	4.41421	−	4.41421i	0.819699	−	0.819699i	0.986064	+	0.166365i	$0.0532031\pi$
$30$	−1.59379			−0.290986
$31$	−7.26197	+	7.26197i	−1.30429	+	1.30429i	−0.378817	+	0.925471i	$0.623669\pi$
$31$	−7.26197	+	7.26197i	−1.30429	+	1.30429i	−0.925471	+	0.378817i	$0.876331\pi$
$32$		−	5.86030i		−	1.03596i
$33$	1.49661			0.260526
$34$		0			0
$35$	2.57099			0.434577
$36$		−	1.41421i		−	0.235702i
$37$	−2.78384	+	2.78384i	−0.457660	+	0.457660i	−0.897887	−	0.440227i	$-0.854898\pi$
$37$	−2.78384	+	2.78384i	−0.457660	+	0.457660i	0.440227	+	0.897887i	$0.354898\pi$
$38$	−5.21371			−0.845775
$39$	−2.90602	+	2.90602i	−0.465335	+	0.465335i
$40$	−3.84776	−	3.84776i	−0.608384	−	0.608384i
$41$	8.58221	+	8.58221i	1.34032	+	1.34032i	0.895743	+	0.444572i	$0.146644\pi$
$41$	8.58221	+	8.58221i	1.34032	+	1.34032i	0.444572	+	0.895743i	$0.353356\pi$
$42$		−	0.944947i		−	0.145809i
$43$			3.44609i			0.525524i	0.964861	+	0.262762i	$0.0846333\pi$
$43$			3.44609i			0.525524i	−0.964861	+	0.262762i	$0.915367\pi$
$44$	1.49661	+	1.49661i	0.225622	+	0.225622i
$45$	−1.47247	−	1.47247i	−0.219503	−	0.219503i
$46$	1.79063	−	1.79063i	0.264013	−	0.264013i
$47$	−1.56940			−0.228920			−0.114460	−	0.993428i	$-0.536514\pi$
$47$	−1.56940			−0.228920			−0.114460	+	0.993428i	$0.536514\pi$
$48$	0.585786	−	0.585786i	0.0845510	−	0.0845510i
$49$		−	5.47568i		−	0.782240i
$50$	0.507930			0.0718322
$51$		0			0
$52$	−5.81204			−0.805985
$53$			3.96134i			0.544131i	0.962279	+	0.272066i	$0.0877068\pi$
$53$			3.96134i			0.544131i	−0.962279	+	0.272066i	$0.912293\pi$
$54$	−0.541196	+	0.541196i	−0.0736475	+	0.0736475i
$55$	3.11652			0.420231
$56$	2.28130	−	2.28130i	0.304852	−	0.304852i
$57$	−4.81684	−	4.81684i	−0.638006	−	0.638006i
$58$	−3.37849	−	3.37849i	−0.443618	−	0.443618i
$59$		−	8.06306i		−	1.04972i	−0.851188	−	0.524861i	$-0.824117\pi$
$59$		−	8.06306i		−	1.04972i	0.851188	−	0.524861i	$-0.175883\pi$
$60$		−	2.94495i		−	0.380191i
$61$	2.31457	+	2.31457i	0.296350	+	0.296350i	0.839583	−	0.543232i	$-0.182800\pi$
$61$	2.31457	+	2.31457i	0.296350	+	0.296350i	−0.543232	+	0.839583i	$0.682800\pi$
$62$	5.55807	+	5.55807i	0.705876	+	0.705876i
$63$	0.873017	−	0.873017i	0.109990	−	0.109990i
$64$	−2.82843			−0.353553
$65$	−6.05147	+	6.05147i	−0.750593	+	0.750593i
$66$		−	1.14545i		−	0.140995i
$67$	2.11652			0.258574			0.129287	−	0.991607i	$-0.458731\pi$
$67$	2.11652			0.258574			0.129287	+	0.991607i	$0.458731\pi$
$68$		0			0
$69$	3.30864			0.398314
$70$		−	1.96775i		−	0.235191i
$71$	0.160248	−	0.160248i	0.0190180	−	0.0190180i	−0.697534	−	0.716552i	$-0.745719\pi$
$71$	0.160248	−	0.160248i	0.0190180	−	0.0190180i	0.716552	+	0.697534i	$0.245719\pi$
$72$	−2.61313			−0.307960
$73$	−0.260380	+	0.260380i	−0.0304752	+	0.0304752i	−0.722180	−	0.691705i	$-0.756860\pi$
$73$	−0.260380	+	0.260380i	−0.0304752	+	0.0304752i	0.691705	+	0.722180i	$0.256860\pi$
$74$	2.13066	+	2.13066i	0.247684	+	0.247684i
$75$	0.469266	+	0.469266i	0.0541862	+	0.0541862i
$76$		−	9.63368i		−	1.10506i
$77$			1.84776i			0.210572i
$78$	2.22417	+	2.22417i	0.251838	+	0.251838i
$79$	−1.91969	−	1.91969i	−0.215982	−	0.215982i	0.590821	−	0.806803i	$-0.298804\pi$
$79$	−1.91969	−	1.91969i	−0.215982	−	0.215982i	−0.806803	+	0.590821i	$0.798804\pi$
$80$	1.21984	−	1.21984i	0.136382	−	0.136382i
$81$	−1.00000			−0.111111
$82$	6.56854	−	6.56854i	0.725373	−	0.725373i
$83$			14.4138i			1.58212i	0.611736	+	0.791062i	$0.290472\pi$
$83$			14.4138i			1.58212i	−0.611736	+	0.791062i	$0.709528\pi$
$84$	1.74603			0.190508
$85$		0			0
$86$	2.63752			0.284411
$87$		−	6.24264i		−	0.669281i
$88$	2.76537	−	2.76537i	0.294789	−	0.294789i
$89$	−13.6694			−1.44895			−0.724477	−	0.689299i	$-0.757918\pi$
$89$	−13.6694			−1.44895			−0.724477	+	0.689299i	$0.757918\pi$
$90$	−1.12698	+	1.12698i	−0.118794	+	0.118794i
$91$	−3.58787	−	3.58787i	−0.376111	−	0.376111i
$92$	3.30864	+	3.30864i	0.344950	+	0.344950i
$93$			10.2700i			1.06495i
$94$			1.20116i			0.123891i
$95$	−10.0305	−	10.0305i	−1.02911	−	1.02911i
$96$	−4.14386	−	4.14386i	−0.422931	−	0.422931i
$97$	−1.89828	+	1.89828i	−0.192741	+	0.192741i	−0.796879	−	0.604139i	$-0.793517\pi$
$97$	−1.89828	+	1.89828i	−0.192741	+	0.192741i	0.604139	+	0.796879i	$0.293517\pi$
$98$	−4.19090			−0.423345
$99$	1.05826	−	1.05826i	0.106359	−	0.106359i
$100$			0.938533i			0.0938533i
$101$	−2.38009			−0.236827			−0.118414	−	0.992964i	$-0.537781\pi$
$101$	−2.38009			−0.236827			−0.118414	+	0.992964i	$0.537781\pi$
$102$		0			0
$103$	−13.2909			−1.30959			−0.654796	−	0.755806i	$-0.727245\pi$
$103$	−13.2909			−1.30959			−0.654796	+	0.755806i	$0.727245\pi$
$104$			10.7392i			1.05307i
$105$	1.81796	−	1.81796i	0.177415	−	0.177415i
$106$	3.03188			0.294482
$107$	9.24360	−	9.24360i	0.893612	−	0.893612i	−0.101249	−	0.994861i	$-0.532284\pi$
$107$	9.24360	−	9.24360i	0.893612	−	0.893612i	0.994861	+	0.101249i	$0.0322839\pi$
$108$	−1.00000	−	1.00000i	−0.0962250	−	0.0962250i
$109$	0.676186	+	0.676186i	0.0647669	+	0.0647669i	0.738748	−	0.673981i	$-0.235417\pi$
$109$	0.676186	+	0.676186i	0.0647669	+	0.0647669i	−0.673981	+	0.738748i	$0.735417\pi$
$110$		−	2.38528i		−	0.227428i
$111$			3.93694i			0.373678i
$112$	0.723231	+	0.723231i	0.0683389	+	0.0683389i
$113$	−6.10199	−	6.10199i	−0.574027	−	0.574027i	0.359224	−	0.933251i	$-0.383041\pi$
$113$	−6.10199	−	6.10199i	−0.574027	−	0.574027i	−0.933251	+	0.359224i	$0.883041\pi$
$114$	−3.68665	+	3.68665i	−0.345286	+	0.345286i
$115$	6.88989			0.642486
$116$	6.24264	−	6.24264i	0.579615	−	0.579615i
$117$			4.10973i			0.379945i
$118$	−6.17120			−0.568105
$119$		0			0
$120$	−5.44155			−0.496744
$121$		−	8.76017i		−	0.796379i
$122$	1.77150	−	1.77150i	0.160384	−	0.160384i
$123$	12.1371			1.09436
$124$	−10.2700	+	10.2700i	−0.922271	+	0.922271i
$125$	8.33956	+	8.33956i	0.745913	+	0.745913i
$126$	−0.668179	−	0.668179i	−0.0595261	−	0.0595261i
$127$			14.1484i			1.25547i	0.778428	+	0.627734i	$0.216017\pi$
$127$			14.1484i			1.25547i	−0.778428	+	0.627734i	$0.783983\pi$
$128$		−	9.55582i		−	0.844623i
$129$	2.43675	+	2.43675i	0.214544	+	0.214544i
$130$	4.63160	+	4.63160i	0.406218	+	0.406218i
$131$	−1.83201	+	1.83201i	−0.160063	+	0.160063i	−0.782595	−	0.622531i	$-0.786104\pi$
$131$	−1.83201	+	1.83201i	−0.160063	+	0.160063i	0.622531	+	0.782595i	$0.286104\pi$
$132$	2.11652			0.184219
$133$	5.94703	−	5.94703i	0.515673	−	0.515673i
$134$		−	1.61991i		−	0.139939i
$135$	−2.08239			−0.179224
$136$		0			0
$137$	15.2684			1.30447			0.652233	−	0.758018i	$-0.273832\pi$
$137$	15.2684			1.30447			0.652233	+	0.758018i	$0.273832\pi$
$138$		−	2.53233i		−	0.215566i
$139$	−2.85822	+	2.85822i	−0.242431	+	0.242431i	−0.817855	−	0.575424i	$-0.804837\pi$
$139$	−2.85822	+	2.85822i	−0.242431	+	0.242431i	0.575424	+	0.817855i	$0.304837\pi$
$140$	3.63593			0.307292
$141$	−1.10973	+	1.10973i	−0.0934563	+	0.0934563i
$142$	−0.122649	−	0.122649i	−0.0102925	−	0.0102925i
$143$	−4.34917	−	4.34917i	−0.363695	−	0.363695i
$144$		−	0.828427i		−	0.0690356i
$145$		−	12.9996i		−	1.07956i
$146$	0.199286	+	0.199286i	0.0164930	+	0.0164930i
$147$	−3.87189	−	3.87189i	−0.319348	−	0.319348i
$148$	−3.93694	+	3.93694i	−0.323614	+	0.323614i
$149$	18.1219			1.48460			0.742302	−	0.670065i	$-0.233734\pi$
$149$	18.1219			1.48460			0.742302	+	0.670065i	$0.233734\pi$
$150$	0.359161	−	0.359161i	0.0293254	−	0.0293254i
$151$			5.27133i			0.428975i	0.976727	+	0.214487i	$0.0688081\pi$
$151$			5.27133i			0.428975i	−0.976727	+	0.214487i	$0.931192\pi$
$152$	−17.8007			−1.44383
$153$		0			0
$154$	1.41421			0.113961
$155$			21.3861i			1.71778i
$156$	−4.10973	+	4.10973i	−0.329042	+	0.329042i
$157$	3.80334			0.303540			0.151770	−	0.988416i	$-0.451503\pi$
$157$	3.80334			0.303540			0.151770	+	0.988416i	$0.451503\pi$
$158$	−1.46927	+	1.46927i	−0.116889	+	0.116889i
$159$	2.80109	+	2.80109i	0.222141	+	0.222141i
$160$	−8.62914	−	8.62914i	−0.682193	−	0.682193i
$161$			4.08496i			0.321940i
$162$			0.765367i			0.0601329i
$163$	6.41262	+	6.41262i	0.502275	+	0.502275i	0.912144	−	0.409869i	$-0.134426\pi$
$163$	6.41262	+	6.41262i	0.502275	+	0.502275i	−0.409869	+	0.912144i	$0.634426\pi$
$164$	12.1371	+	12.1371i	0.947746	+	0.947746i
$165$	2.20371	−	2.20371i	0.171559	−	0.171559i
$166$	11.0319			0.856240
$167$	−6.28451	+	6.28451i	−0.486310	+	0.486310i	−0.907140	−	0.420830i	$-0.861739\pi$
$167$	−6.28451	+	6.28451i	−0.486310	+	0.486310i	0.420830	+	0.907140i	$0.361739\pi$
$168$		−	3.22625i		−	0.248911i
$169$	3.88989			0.299223
$170$		0			0
$171$	−6.81204			−0.520930
$172$			4.87351i			0.371601i
$173$	−8.66006	+	8.66006i	−0.658412	+	0.658412i	−0.955004	−	0.296592i	$-0.904150\pi$
$173$	−8.66006	+	8.66006i	−0.658412	+	0.658412i	0.296592	+	0.955004i	$0.404150\pi$
$174$	−4.77791			−0.362212
$175$	−0.579372	+	0.579372i	−0.0437964	+	0.0437964i
$176$	0.876691	+	0.876691i	0.0660831	+	0.0660831i
$177$	−5.70144	−	5.70144i	−0.428547	−	0.428547i
$178$			10.4621i			0.784168i
$179$			10.6173i			0.793573i	0.917911	+	0.396787i	$0.129875\pi$
$179$			10.6173i			0.793573i	−0.917911	+	0.396787i	$0.870125\pi$
$180$	−2.08239	−	2.08239i	−0.155212	−	0.155212i
$181$	−11.6866	−	11.6866i	−0.868662	−	0.868662i	0.123663	−	0.992324i	$-0.460536\pi$
$181$	−11.6866	−	11.6866i	−0.868662	−	0.868662i	−0.992324	+	0.123663i	$0.960536\pi$
$182$	−2.74603	+	2.74603i	−0.203550	+	0.203550i
$183$	3.27330			0.241969
$184$	6.11358	−	6.11358i	0.450699	−	0.450699i
$185$			8.19825i			0.602748i
$186$	7.86030			0.576345
$187$		0			0
$188$	−2.21946			−0.161871
$189$		−	1.23463i		−	0.0898063i
$190$	−7.67705	+	7.67705i	−0.556952	+	0.556952i
$191$	12.0167			0.869498			0.434749	−	0.900552i	$-0.356837\pi$
$191$	12.0167			0.869498			0.434749	+	0.900552i	$0.356837\pi$
$192$	−2.00000	+	2.00000i	−0.144338	+	0.144338i
$193$	7.57900	+	7.57900i	0.545548	+	0.545548i	0.925150	−	0.379602i	$-0.123939\pi$
$193$	7.57900	+	7.57900i	0.545548	+	0.545548i	−0.379602	+	0.925150i	$0.623939\pi$
$194$	1.45288	+	1.45288i	0.104311	+	0.104311i
$195$			8.55807i			0.612856i
$196$		−	7.74378i		−	0.553127i
$197$	−2.24078	−	2.24078i	−0.159649	−	0.159649i	0.622762	−	0.782411i	$-0.286010\pi$
$197$	−2.24078	−	2.24078i	−0.159649	−	0.159649i	−0.782411	+	0.622762i	$0.786010\pi$
$198$	−0.809957	−	0.809957i	−0.0575612	−	0.0575612i
$199$	−9.66940	+	9.66940i	−0.685445	+	0.685445i	−0.961222	−	0.275776i	$-0.911065\pi$
$199$	−9.66940	+	9.66940i	−0.685445	+	0.685445i	0.275776	+	0.961222i	$0.411065\pi$
$200$	1.73418			0.122625
$201$	1.49661	−	1.49661i	0.105562	−	0.105562i
$202$			1.82164i			0.128170i
$203$	7.70737			0.540951
$204$		0			0
$205$	25.2741			1.76522
$206$			10.1724i			0.708746i
$207$	2.33956	−	2.33956i	0.162611	−	0.162611i
$208$	−3.40461			−0.236067
$209$	7.20891	−	7.20891i	0.498651	−	0.498651i
$210$	−1.39141	−	1.39141i	−0.0960164	−	0.0960164i
$211$	−4.19212	−	4.19212i	−0.288598	−	0.288598i	0.547928	−	0.836526i	$-0.315417\pi$
$211$	−4.19212	−	4.19212i	−0.288598	−	0.288598i	−0.836526	+	0.547928i	$0.815417\pi$
$212$			5.60218i			0.384759i
$213$		−	0.226626i		−	0.0155281i
$214$	−7.07474	−	7.07474i	−0.483619	−	0.483619i
$215$	5.07428	+	5.07428i	0.346063	+	0.346063i
$216$	−1.84776	+	1.84776i	−0.125724	+	0.125724i
$217$	−12.6797			−0.860751
$218$	0.517531	−	0.517531i	0.0350516	−	0.0350516i
$219$			0.368233i			0.0248829i
$220$	4.40743			0.297149
$221$		0			0
$222$	3.01320			0.202233
$223$			26.1476i			1.75098i	0.483240	+	0.875488i	$0.339460\pi$
$223$			26.1476i			1.75098i	−0.483240	+	0.875488i	$0.660540\pi$
$224$	5.11615	−	5.11615i	0.341837	−	0.341837i
$225$	0.663643			0.0442428
$226$	−4.67026	+	4.67026i	−0.310661	+	0.310661i
$227$	7.76019	+	7.76019i	0.515062	+	0.515062i	0.916073	−	0.401011i	$-0.131341\pi$
$227$	7.76019	+	7.76019i	0.515062	+	0.515062i	−0.401011	+	0.916073i	$0.631341\pi$
$228$	−6.81204	−	6.81204i	−0.451138	−	0.451138i
$229$			14.4872i			0.957341i	0.877995	+	0.478670i	$0.158881\pi$
$229$			14.4872i			0.957341i	−0.877995	+	0.478670i	$0.841119\pi$
$230$		−	5.27330i		−	0.347711i
$231$	1.30656	+	1.30656i	0.0859655	+	0.0859655i
$232$	−11.5349	−	11.5349i	−0.757303	−	0.757303i
$233$	−13.5043	+	13.5043i	−0.884699	+	0.884699i	−0.994008	−	0.109309i	$-0.965136\pi$
$233$	−13.5043	+	13.5043i	−0.884699	+	0.884699i	0.109309	+	0.994008i	$0.465136\pi$
$234$	3.14545			0.205625
$235$	−2.31090	+	2.31090i	−0.150746	+	0.150746i
$236$		−	11.4029i		−	0.742265i
$237$	−2.71485			−0.176348
$238$		0			0
$239$	0.740970			0.0479294			0.0239647	−	0.999713i	$-0.492371\pi$
$239$	0.740970			0.0479294			0.0239647	+	0.999713i	$0.492371\pi$
$240$		−	1.72511i		−	0.111355i
$241$	15.1050	−	15.1050i	0.973000	−	0.973000i	−0.0266448	−	0.999645i	$-0.508482\pi$
$241$	15.1050	−	15.1050i	0.973000	−	0.973000i	0.999645	+	0.0266448i	$0.00848231\pi$
$242$	−6.70474			−0.430997
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.27330	+	3.27330i	0.209551	+	0.209551i
$245$	−8.06280	−	8.06280i	−0.515113	−	0.515113i
$246$		−	9.28931i		−	0.592265i
$247$			27.9956i			1.78132i
$248$	18.9764	+	18.9764i	1.20501	+	1.20501i
$249$	10.1921	+	10.1921i	0.645900	+	0.645900i
$250$	6.38283	−	6.38283i	0.403685	−	0.403685i
$251$	0.938819			0.0592577			0.0296289	−	0.999561i	$-0.490567\pi$
$251$	0.938819			0.0592577			0.0296289	+	0.999561i	$0.490567\pi$
$252$	1.23463	−	1.23463i	0.0777746	−	0.0777746i
$253$			4.95174i			0.311313i
$254$	10.8287			0.679454
$255$		0			0
$256$	−12.9706			−0.810660
$257$		−	15.8293i		−	0.987403i	−0.869631	−	0.493701i	$-0.835644\pi$
$257$		−	15.8293i		−	0.987403i	0.869631	−	0.493701i	$-0.164356\pi$
$258$	1.86501	−	1.86501i	0.116110	−	0.116110i
$259$	−4.86068			−0.302028
$260$	−8.55807	+	8.55807i	−0.530749	+	0.530749i
$261$	−4.41421	−	4.41421i	−0.273233	−	0.273233i
$262$	1.40216	+	1.40216i	0.0866256	+	0.0866256i
$263$		−	11.4573i		−	0.706486i	−0.935532	−	0.353243i	$-0.885079\pi$
$263$		−	11.4573i		−	0.706486i	0.935532	−	0.353243i	$-0.114921\pi$
$264$		−	3.91082i		−	0.240694i
$265$	5.83296	+	5.83296i	0.358316	+	0.358316i
$266$	−4.55166	−	4.55166i	−0.279080	−	0.279080i
$267$	−9.66572	+	9.66572i	−0.591533	+	0.591533i
$268$	2.99321			0.182839
$269$	13.5545	−	13.5545i	0.826432	−	0.826432i	−0.160589	−	0.987021i	$-0.551339\pi$
$269$	13.5545	−	13.5545i	0.826432	−	0.826432i	0.987021	+	0.160589i	$0.0513395\pi$
$270$			1.59379i			0.0969952i
$271$	6.82805			0.414775			0.207387	−	0.978259i	$-0.433504\pi$
$271$	6.82805			0.414775			0.207387	+	0.978259i	$0.433504\pi$
$272$		0			0
$273$	−5.07401			−0.307093
$274$		−	11.6859i		−	0.705972i
$275$	−0.702307	+	0.702307i	−0.0423507	+	0.0423507i
$276$	4.67913			0.281650
$277$	5.74725	−	5.74725i	0.345319	−	0.345319i	−0.513044	−	0.858363i	$-0.671482\pi$
$277$	5.74725	−	5.74725i	0.345319	−	0.345319i	0.858363	+	0.513044i	$0.171482\pi$
$278$	2.18759	+	2.18759i	0.131203	+	0.131203i
$279$	7.26197	+	7.26197i	0.434763	+	0.434763i
$280$		−	6.71832i		−	0.401497i
$281$		−	11.6070i		−	0.692417i	−0.938158	−	0.346209i	$-0.887469\pi$
$281$		−	11.6070i		−	0.692417i	0.938158	−	0.346209i	$-0.112531\pi$
$282$	0.849352	+	0.849352i	0.0505782	+	0.0505782i
$283$	4.28792	+	4.28792i	0.254890	+	0.254890i	0.822972	−	0.568082i	$-0.192314\pi$
$283$	4.28792	+	4.28792i	0.254890	+	0.254890i	−0.568082	+	0.822972i	$0.692314\pi$
$284$	0.226626	−	0.226626i	0.0134478	−	0.0134478i
$285$	−14.1853			−0.840267
$286$	−3.32871	+	3.32871i	−0.196831	+	0.196831i
$287$			14.9848i			0.884527i
$288$	−5.86030			−0.345322
$289$		0			0
$290$	−9.94948			−0.584254
$291$			2.68457i			0.157372i
$292$	−0.368233	+	0.368233i	−0.0215492	+	0.0215492i
$293$	−6.87547			−0.401669			−0.200835	−	0.979625i	$-0.564365\pi$
$293$	−6.87547			−0.401669			−0.200835	+	0.979625i	$0.564365\pi$
$294$	−2.96342	+	2.96342i	−0.172830	+	0.172830i
$295$	−11.8726	−	11.8726i	−0.691252	−	0.691252i
$296$	7.27452	+	7.27452i	0.422823	+	0.422823i
$297$		−	1.49661i		−	0.0868419i
$298$		−	13.8699i		−	0.803462i
$299$	−9.61498	−	9.61498i	−0.556049	−	0.556049i
$300$	0.663643	+	0.663643i	0.0383154	+	0.0383154i
$301$	−3.00850	+	3.00850i	−0.173407	+	0.173407i
$302$	4.03450			0.232159
$303$	−1.68297	+	1.68297i	−0.0966844	+	0.0966844i
$304$		−	5.64328i		−	0.323664i
$305$	6.81629			0.390300
$306$		0			0
$307$	22.2451			1.26959			0.634797	−	0.772679i	$-0.281084\pi$
$307$	22.2451			1.26959			0.634797	+	0.772679i	$0.281084\pi$
$308$			2.61313i			0.148897i
$309$	−9.39809	+	9.39809i	−0.534639	+	0.534639i
$310$	16.3682			0.929653
$311$	−3.82843	+	3.82843i	−0.217090	+	0.217090i	−0.807271	−	0.590181i	$-0.799056\pi$
$311$	−3.82843	+	3.82843i	−0.217090	+	0.217090i	0.590181	+	0.807271i	$0.299056\pi$
$312$	7.59379	+	7.59379i	0.429914	+	0.429914i
$313$	7.98642	+	7.98642i	0.451419	+	0.451419i	0.895825	−	0.444406i	$-0.146585\pi$
$313$	7.98642	+	7.98642i	0.451419	+	0.451419i	−0.444406	+	0.895825i	$0.646585\pi$
$314$		−	2.91095i		−	0.164274i
$315$		−	2.57099i		−	0.144859i
$316$	−2.71485	−	2.71485i	−0.152722	−	0.152722i
$317$	−13.0475	−	13.0475i	−0.732822	−	0.732822i	0.238356	−	0.971178i	$-0.423391\pi$
$317$	−13.0475	−	13.0475i	−0.732822	−	0.732822i	−0.971178	+	0.238356i	$0.923391\pi$
$318$	2.14386	−	2.14386i	0.120222	−	0.120222i
$319$	9.34277			0.523095
$320$	−4.16478	+	4.16478i	−0.232819	+	0.232819i
$321$		−	13.0724i		−	0.729631i
$322$	3.12649			0.174233
$323$		0			0
$324$	−1.41421			−0.0785674
$325$		−	2.72739i		−	0.151289i
$326$	4.90801	−	4.90801i	0.271829	−	0.271829i
$327$	0.956272			0.0528819
$328$	22.4264	−	22.4264i	1.23829	−	1.23829i
$329$	−1.37011	−	1.37011i	−0.0755367	−	0.0755367i
$330$	−1.68665	−	1.68665i	−0.0928469	−	0.0928469i
$331$		−	5.76606i		−	0.316931i	−0.987365	−	0.158466i	$-0.949345\pi$
$331$		−	5.76606i		−	0.316931i	0.987365	−	0.158466i	$-0.0506547\pi$
$332$			20.3842i			1.11873i
$333$	2.78384	+	2.78384i	0.152553	+	0.152553i
$334$	4.80996	+	4.80996i	0.263189	+	0.263189i
$335$	3.11652	−	3.11652i	0.170274	−	0.170274i
$336$	1.02280			0.0557985
$337$	−11.5051	+	11.5051i	−0.626723	+	0.626723i	−0.947242	−	0.320519i	$-0.896143\pi$
$337$	−11.5051	+	11.5051i	−0.626723	+	0.626723i	0.320519	+	0.947242i	$0.396143\pi$
$338$		−	2.97720i		−	0.161938i
$339$	−8.62951			−0.468691
$340$		0			0
$341$	−15.3701			−0.832338
$342$			5.21371i			0.281925i
$343$	10.8915	−	10.8915i	0.588085	−	0.588085i
$344$	9.00506			0.485521
$345$	4.87189	−	4.87189i	0.262294	−	0.262294i
$346$	6.62812	+	6.62812i	0.356330	+	0.356330i
$347$	−3.03375	−	3.03375i	−0.162860	−	0.162860i	0.620972	−	0.783833i	$-0.286738\pi$
$347$	−3.03375	−	3.03375i	−0.162860	−	0.162860i	−0.783833	+	0.620972i	$0.786738\pi$
$348$		−	8.82843i		−	0.473253i
$349$		−	14.1553i		−	0.757718i	−0.925454	−	0.378859i	$-0.876317\pi$
$349$		−	14.1553i		−	0.757718i	0.925454	−	0.378859i	$-0.123683\pi$
$350$	0.443432	+	0.443432i	0.0237024	+	0.0237024i
$351$	2.90602	+	2.90602i	0.155112	+	0.155112i
$352$	6.20172	−	6.20172i	0.330553	−	0.330553i
$353$	−23.8142			−1.26750			−0.633752	−	0.773536i	$-0.718486\pi$
$353$	−23.8142			−1.26750			−0.633752	+	0.773536i	$0.718486\pi$
$354$	−4.36370	+	4.36370i	−0.231928	+	0.231928i
$355$		−	0.471923i		−	0.0250471i
$356$	−19.3314			−1.02456
$357$		0			0
$358$	8.12612			0.429479
$359$		−	35.2676i		−	1.86135i	−0.365841	−	0.930677i	$-0.619219\pi$
$359$		−	35.2676i		−	1.86135i	0.365841	−	0.930677i	$-0.380781\pi$
$360$	−3.84776	+	3.84776i	−0.202795	+	0.202795i
$361$	−27.4039			−1.44231
$362$	−8.94457	+	8.94457i	−0.470116	+	0.470116i
$363$	−6.19438	−	6.19438i	−0.325120	−	0.325120i
$364$	−5.07401	−	5.07401i	−0.265950	−	0.265950i
$365$			0.766805i			0.0401364i
$366$		−	2.50527i		−	0.130953i
$367$	−11.5408	−	11.5408i	−0.602426	−	0.602426i	0.338530	−	0.940956i	$-0.390070\pi$
$367$	−11.5408	−	11.5408i	−0.602426	−	0.602426i	−0.940956	+	0.338530i	$0.890070\pi$
$368$	1.93816	+	1.93816i	0.101034	+	0.101034i
$369$	8.58221	−	8.58221i	0.446772	−	0.446772i
$370$	6.27467			0.326205
$371$	−3.45832	+	3.45832i	−0.179547	+	0.179547i
$372$			14.5239i			0.753031i
$373$	−25.0156			−1.29526			−0.647630	−	0.761955i	$-0.724240\pi$
$373$	−25.0156			−1.29526			−0.647630	+	0.761955i	$0.724240\pi$
$374$		0			0
$375$	11.7939			0.609036
$376$			4.10103i			0.211495i
$377$	−18.1412	+	18.1412i	−0.934321	+	0.934321i
$378$	−0.944947			−0.0486028
$379$	−23.0716	+	23.0716i	−1.18511	+	1.18511i	−0.206702	+	0.978404i	$0.566273\pi$
$379$	−23.0716	+	23.0716i	−1.18511	+	1.18511i	−0.978404	+	0.206702i	$0.933727\pi$
$380$	−14.1853	−	14.1853i	−0.727692	−	0.727692i
$381$	10.0044	+	10.0044i	0.512542	+	0.512542i
$382$		−	9.19719i		−	0.470569i
$383$			0.585258i			0.0299053i	0.999888	+	0.0149526i	$0.00475975\pi$
$383$			0.585258i			0.0299053i	−0.999888	+	0.0149526i	$0.995240\pi$
$384$	−6.75699	−	6.75699i	−0.344816	−	0.344816i
$385$	2.72078	+	2.72078i	0.138664	+	0.138664i
$386$	5.80071	−	5.80071i	0.295249	−	0.295249i
$387$	3.44609			0.175175
$388$	−2.68457	+	2.68457i	−0.136288	+	0.136288i
$389$		−	22.1261i		−	1.12184i	−0.827871	−	0.560918i	$-0.810448\pi$
$389$		−	22.1261i		−	1.12184i	0.827871	−	0.560918i	$-0.189552\pi$
$390$	6.55007			0.331675
$391$		0			0
$392$	−14.3086			−0.722696
$393$			2.59085i			0.130691i
$394$	−1.71502	+	1.71502i	−0.0864015	+	0.0864015i
$395$	−5.65338			−0.284453
$396$	1.49661	−	1.49661i	0.0752073	−	0.0752073i
$397$	−4.12265	−	4.12265i	−0.206910	−	0.206910i	0.596043	−	0.802953i	$-0.296739\pi$
$397$	−4.12265	−	4.12265i	−0.206910	−	0.206910i	−0.802953	+	0.596043i	$0.796739\pi$
$398$	7.40064	+	7.40064i	0.370960	+	0.370960i
$399$		−	8.41037i		−	0.421045i
$400$			0.549780i			0.0274890i
$401$	3.67004	+	3.67004i	0.183273	+	0.183273i	0.792780	−	0.609507i	$-0.208633\pi$
$401$	3.67004	+	3.67004i	0.183273	+	0.183273i	−0.609507	+	0.792780i	$0.708633\pi$
$402$	−1.14545	−	1.14545i	−0.0571300	−	0.0571300i
$403$	29.8448	−	29.8448i	1.48667	−	1.48667i
$404$	−3.36595			−0.167462
$405$	−1.47247	+	1.47247i	−0.0731678	+	0.0731678i
$406$		−	5.89897i		−	0.292761i
$407$	−5.89205			−0.292058
$408$		0			0
$409$	−27.2400			−1.34693			−0.673465	−	0.739219i	$-0.735195\pi$
$409$	−27.2400			−1.34693			−0.673465	+	0.739219i	$0.735195\pi$
$410$		−	19.3440i		−	0.955332i
$411$	10.7964	−	10.7964i	0.532546	−	0.532546i
$412$	−18.7962			−0.926021
$413$	7.03919	−	7.03919i	0.346376	−	0.346376i
$414$	−1.79063	−	1.79063i	−0.0880044	−	0.0880044i
$415$	21.2240	+	21.2240i	1.04185	+	1.04185i
$416$			24.0843i			1.18083i
$417$			4.04214i			0.197944i
$418$	−5.51746	−	5.51746i	−0.269868	−	0.269868i
$419$	9.92079	+	9.92079i	0.484662	+	0.484662i	0.906617	−	0.421955i	$-0.138656\pi$
$419$	9.92079	+	9.92079i	0.484662	+	0.484662i	−0.421955	+	0.906617i	$0.638656\pi$
$420$	2.57099	−	2.57099i	0.125451	−	0.125451i
$421$	−15.3811			−0.749627			−0.374814	−	0.927100i	$-0.622293\pi$
$421$	−15.3811			−0.749627			−0.374814	+	0.927100i	$0.622293\pi$
$422$	−3.20851	+	3.20851i	−0.156188	+	0.156188i
$423$			1.56940i			0.0763067i
$424$	10.3515			0.502712
$425$		0			0
$426$	−0.173452			−0.00840376
$427$			4.04132i			0.195573i
$428$	13.0724	−	13.0724i	0.631879	−	0.631879i
$429$	−6.15065			−0.296956
$430$	3.88368	−	3.88368i	0.187288	−	0.187288i
$431$	−11.5899	−	11.5899i	−0.558268	−	0.558268i	0.370546	−	0.928814i	$-0.379171\pi$
$431$	−11.5899	−	11.5899i	−0.558268	−	0.558268i	−0.928814	+	0.370546i	$0.879171\pi$
$432$	−0.585786	−	0.585786i	−0.0281837	−	0.0281837i
$433$		−	21.7106i		−	1.04335i	−0.853145	−	0.521673i	$-0.825308\pi$
$433$		−	21.7106i		−	1.04335i	0.853145	−	0.521673i	$-0.174692\pi$
$434$			9.70459i			0.465835i
$435$	−9.19212	−	9.19212i	−0.440729	−	0.440729i
$436$	0.956272	+	0.956272i	0.0457971	+	0.0457971i
$437$	15.9372	−	15.9372i	0.762380	−	0.762380i
$438$	0.281833			0.0134665
$439$	16.6385	−	16.6385i	0.794112	−	0.794112i	−0.188048	−	0.982160i	$-0.560216\pi$
$439$	16.6385	−	16.6385i	0.794112	−	0.794112i	0.982160	+	0.188048i	$0.0602159\pi$
$440$		−	8.14386i		−	0.388243i
$441$	−5.47568			−0.260747
$442$		0			0
$443$	−15.4238			−0.732808			−0.366404	−	0.930456i	$-0.619411\pi$
$443$	−15.4238			−0.732808			−0.366404	+	0.930456i	$0.619411\pi$
$444$			5.56767i			0.264230i
$445$	−20.1278	+	20.1278i	−0.954151	+	0.954151i
$446$	20.0125			0.947621
$447$	12.8141	−	12.8141i	0.606087	−	0.606087i
$448$	−2.46927	−	2.46927i	−0.116662	−	0.116662i
$449$	−9.58091	−	9.58091i	−0.452151	−	0.452151i	0.443917	−	0.896068i	$-0.353589\pi$
$449$	−9.58091	−	9.58091i	−0.452151	−	0.452151i	−0.896068	+	0.443917i	$0.853589\pi$
$450$		−	0.507930i		−	0.0239441i
$451$			18.1644i			0.855329i
$452$	−8.62951	−	8.62951i	−0.405898	−	0.405898i
$453$	3.72739	+	3.72739i	0.175128	+	0.175128i
$454$	5.93939	−	5.93939i	0.278750	−	0.278750i
$455$	−10.5661			−0.495346
$456$	−12.5870	+	12.5870i	−0.589441	+	0.589441i
$457$		−	15.3875i		−	0.719796i	−0.932992	−	0.359898i	$-0.882812\pi$
$457$		−	15.3875i		−	0.719796i	0.932992	−	0.359898i	$-0.117188\pi$
$458$	11.0880			0.518109
$459$		0			0
$460$	9.74378			0.454306
$461$		−	20.8006i		−	0.968780i	−0.874852	−	0.484390i	$-0.839042\pi$
$461$		−	20.8006i		−	0.968780i	0.874852	−	0.484390i	$-0.160958\pi$
$462$	1.00000	−	1.00000i	0.0465242	−	0.0465242i
$463$	26.4325			1.22842			0.614212	−	0.789141i	$-0.289474\pi$
$463$	26.4325			1.22842			0.614212	+	0.789141i	$0.289474\pi$
$464$	3.65685	−	3.65685i	0.169765	−	0.169765i
$465$	15.1223	+	15.1223i	0.701279	+	0.701279i
$466$	10.3358	+	10.3358i	0.478796	+	0.478796i
$467$			7.17088i			0.331829i	0.986140	+	0.165914i	$0.0530576\pi$
$467$			7.17088i			0.331829i	−0.986140	+	0.165914i	$0.946942\pi$
$468$			5.81204i			0.268662i
$469$	1.84776	+	1.84776i	0.0853216	+	0.0853216i
$470$	1.76868	+	1.76868i	0.0815833	+	0.0815833i
$471$	2.68937	−	2.68937i	0.123920	−	0.123920i
$472$	−21.0698			−0.969816
$473$	−3.64686	+	3.64686i	−0.167683	+	0.167683i
$474$			2.07786i			0.0954391i
$475$	4.52076			0.207427
$476$		0			0
$477$	3.96134			0.181377
$478$		−	0.567114i		−	0.0259392i
$479$	2.07465	−	2.07465i	0.0947931	−	0.0947931i	−0.658120	−	0.752913i	$-0.728648\pi$
$479$	2.07465	−	2.07465i	0.0947931	−	0.0947931i	0.752913	+	0.658120i	$0.228648\pi$
$480$	−12.2034			−0.557009
$481$	11.4408	−	11.4408i	0.521657	−	0.521657i
$482$	−11.5609	−	11.5609i	−0.526584	−	0.526584i
$483$	2.88850	+	2.88850i	0.131431	+	0.131431i
$484$		−	12.3888i		−	0.563125i
$485$			5.59032i			0.253843i
$486$	0.541196	+	0.541196i	0.0245492	+	0.0245492i
$487$	16.4346	+	16.4346i	0.744721	+	0.744721i	0.973483	−	0.228761i	$-0.0734676\pi$
$487$	16.4346	+	16.4346i	0.744721	+	0.744721i	−0.228761	+	0.973483i	$0.573468\pi$
$488$	6.04826	−	6.04826i	0.273792	−	0.273792i
$489$	9.06882			0.410106
$490$	−6.17100	+	6.17100i	−0.278777	+	0.278777i
$491$			13.6586i			0.616403i	0.951321	+	0.308202i	$0.0997271\pi$
$491$			13.6586i			0.616403i	−0.951321	+	0.308202i	$0.900273\pi$
$492$	17.1644			0.773831
$493$		0			0
$494$	21.4269			0.964044
$495$		−	3.11652i		−	0.140077i
$496$	−6.01602	+	6.01602i	−0.270127	+	0.270127i
$497$	0.279799			0.0125507
$498$	7.80071	−	7.80071i	0.349558	−	0.349558i
$499$	−5.32607	−	5.32607i	−0.238427	−	0.238427i	0.577771	−	0.816199i	$-0.303923\pi$
$499$	−5.32607	−	5.32607i	−0.238427	−	0.238427i	−0.816199	+	0.577771i	$0.803923\pi$
$500$	11.7939	+	11.7939i	0.527440	+	0.527440i
$501$			8.88764i			0.397071i
$502$		−	0.718541i		−	0.0320700i
$503$	18.1840	+	18.1840i	0.810785	+	0.810785i	0.984752	−	0.173967i	$-0.0556585\pi$
$503$	18.1840	+	18.1840i	0.810785	+	0.810785i	−0.173967	+	0.984752i	$0.555659\pi$
$504$	−2.28130	−	2.28130i	−0.101617	−	0.101617i
$505$	−3.50461	+	3.50461i	−0.155953	+	0.155953i
$506$	3.78989			0.168481
$507$	2.75057	−	2.75057i	0.122157	−	0.122157i
$508$			20.0089i			0.887749i
$509$	34.7796			1.54158			0.770789	−	0.637090i	$-0.219862\pi$
$509$	34.7796			1.54158			0.770789	+	0.637090i	$0.219862\pi$
$510$		0			0
$511$	−0.454632			−0.0201117
$512$		−	9.18440i		−	0.405897i
$513$	−4.81684	+	4.81684i	−0.212669	+	0.212669i
$514$	−12.1152			−0.534379
$515$	−19.5705	+	19.5705i	−0.862380	+	0.862380i
$516$	3.44609	+	3.44609i	0.151706	+	0.151706i
$517$	−1.66083	−	1.66083i	−0.0730433	−	0.0730433i
$518$			3.72020i			0.163456i
$519$			12.2472i			0.537591i
$520$	15.8133	+	15.8133i	0.693457	+	0.693457i
$521$	−31.5217	−	31.5217i	−1.38099	−	1.38099i	−0.842863	−	0.538129i	$-0.819131\pi$
$521$	−31.5217	−	31.5217i	−1.38099	−	1.38099i	−0.538129	−	0.842863i	$-0.680869\pi$
$522$	−3.37849	+	3.37849i	−0.147873	+	0.147873i
$523$	−19.8918			−0.869808			−0.434904	−	0.900477i	$-0.643218\pi$
$523$	−19.8918			−0.869808			−0.434904	+	0.900477i	$0.643218\pi$
$524$	−2.59085	+	2.59085i	−0.113182	+	0.113182i
$525$			0.819355i			0.0357596i
$526$	−8.76902			−0.382348
$527$		0			0
$528$	1.23983			0.0539566
$529$		−	12.0529i		−	0.524038i
$530$	4.46436	−	4.46436i	0.193919	−	0.193919i
$531$	−8.06306			−0.349907
$532$	8.41037	−	8.41037i	0.364636	−	0.364636i
$533$	−35.2706	−	35.2706i	−1.52774	−	1.52774i
$534$	7.39782	+	7.39782i	0.320135	+	0.320135i
$535$		−	27.2219i		−	1.17691i
$536$		−	5.53073i		−	0.238891i
$537$	7.50756	+	7.50756i	0.323975	+	0.323975i
$538$	−10.3742	−	10.3742i	−0.447262	−	0.447262i
$539$	5.79469	−	5.79469i	0.249595	−	0.249595i
$540$	−2.94495			−0.126730
$541$	0.552520	−	0.552520i	0.0237547	−	0.0237547i	−0.695130	−	0.718884i	$-0.744653\pi$
$541$	0.552520	−	0.552520i	0.0237547	−	0.0237547i	0.718884	+	0.695130i	$0.244653\pi$
$542$		−	5.22597i		−	0.224474i
$543$	−16.5274			−0.709259
$544$		0			0
$545$	1.99133			0.0852993
$546$			3.88348i			0.166198i
$547$	27.6171	−	27.6171i	1.18082	−	1.18082i	0.201291	−	0.979531i	$-0.435486\pi$
$547$	27.6171	−	27.6171i	1.18082	−	1.18082i	0.979531	−	0.201291i	$-0.0645137\pi$
$548$	21.5928			0.922397
$549$	2.31457	−	2.31457i	0.0987835	−	0.0987835i
$550$	0.537522	+	0.537522i	0.0229200	+	0.0229200i
$551$	−30.0698	−	30.0698i	−1.28102	−	1.28102i
$552$		−	8.64590i		−	0.367994i
$553$		−	3.35184i		−	0.142535i
$554$	−4.39876	−	4.39876i	−0.186885	−	0.186885i
$555$	5.79704	+	5.79704i	0.246071	+	0.246071i
$556$	−4.04214	+	4.04214i	−0.171425	+	0.171425i
$557$	13.0371			0.552398			0.276199	−	0.961100i	$-0.410925\pi$
$557$	13.0371			0.552398			0.276199	+	0.961100i	$0.410925\pi$
$558$	5.55807	−	5.55807i	0.235292	−	0.235292i
$559$		−	14.1625i		−	0.599010i
$560$	2.12988			0.0900038
$561$		0			0
$562$	−8.88363			−0.374734
$563$			11.2168i			0.472733i	0.971664	+	0.236367i	$0.0759566\pi$
$563$			11.2168i			0.472733i	−0.971664	+	0.236367i	$0.924043\pi$
$564$	−1.56940	+	1.56940i	−0.0660836	+	0.0660836i
$565$	−17.9700			−0.756005
$566$	3.28183	−	3.28183i	0.137946	−	0.137946i
$567$	−0.873017	−	0.873017i	−0.0366633	−	0.0366633i
$568$	−0.418749	−	0.418749i	−0.0175703	−	0.0175703i
$569$		−	36.4695i		−	1.52888i	−0.644694	−	0.764440i	$-0.723015\pi$
$569$		−	36.4695i		−	1.52888i	0.644694	−	0.764440i	$-0.276985\pi$
$570$			10.8570i			0.454749i
$571$	−9.57778	−	9.57778i	−0.400818	−	0.400818i	0.477704	−	0.878521i	$-0.341469\pi$
$571$	−9.57778	−	9.57778i	−0.400818	−	0.400818i	−0.878521	+	0.477704i	$0.841469\pi$
$572$	−6.15065	−	6.15065i	−0.257172	−	0.257172i
$573$	8.49709	−	8.49709i	0.354971	−	0.354971i
$574$	11.4689			0.478702
$575$	−1.55264	+	1.55264i	−0.0647494	+	0.0647494i
$576$			2.82843i			0.117851i
$577$	−7.10617			−0.295834			−0.147917	−	0.989000i	$-0.547257\pi$
$577$	−7.10617			−0.295834			−0.147917	+	0.989000i	$0.547257\pi$
$578$		0			0
$579$	10.7183			0.445438
$580$		−	18.3842i		−	0.763364i
$581$	−12.5835	+	12.5835i	−0.522053	+	0.522053i
$582$	2.05468			0.0851692
$583$	−4.19212	+	4.19212i	−0.173620	+	0.173620i
$584$	0.680405	+	0.680405i	0.0281554	+	0.0281554i
$585$	6.05147	+	6.05147i	0.250198	+	0.250198i
$586$			5.26226i			0.217382i
$587$		−	40.2951i		−	1.66316i	−0.555408	−	0.831578i	$-0.687438\pi$
$587$		−	40.2951i		−	1.66316i	0.555408	−	0.831578i	$-0.312562\pi$
$588$	−5.47568	−	5.47568i	−0.225813	−	0.225813i
$589$	49.4688	+	49.4688i	2.03833	+	2.03833i
$590$	−9.08693	+	9.08693i	−0.374103	+	0.374103i
$591$	−3.16895			−0.130353
$592$	−2.30621	+	2.30621i	−0.0947845	+	0.0947845i
$593$		−	37.8418i		−	1.55398i	−0.629515	−	0.776989i	$-0.716746\pi$
$593$		−	37.8418i		−	1.55398i	0.629515	−	0.776989i	$-0.283254\pi$
$594$	−1.14545			−0.0469985
$595$		0			0
$596$	25.6282			1.04977
$597$			13.6746i			0.559664i
$598$	−7.35899	+	7.35899i	−0.300931	+	0.300931i
$599$	10.1505			0.414739			0.207369	−	0.978263i	$-0.433510\pi$
$599$	10.1505			0.414739			0.207369	+	0.978263i	$0.433510\pi$
$600$	1.22625	−	1.22625i	0.0500615	−	0.0500615i
$601$	24.9282	+	24.9282i	1.01684	+	1.01684i	0.999856	+	0.0169861i	$0.00540712\pi$
$601$	24.9282	+	24.9282i	1.01684	+	1.01684i	0.0169861	+	0.999856i	$0.494593\pi$
$602$	2.30260	+	2.30260i	0.0938471	+	0.0938471i
$603$		−	2.11652i		−	0.0861914i
$604$			7.45479i			0.303331i
$605$	−12.8991	−	12.8991i	−0.524424	−	0.524424i
$606$	1.28809	+	1.28809i	0.0523252	+	0.0523252i
$607$	−33.6497	+	33.6497i	−1.36580	+	1.36580i	−0.499461	+	0.866337i	$0.666468\pi$
$607$	−33.6497	+	33.6497i	−1.36580	+	1.36580i	−0.866337	+	0.499461i	$0.833532\pi$
$608$	−39.9206			−1.61899
$609$	5.44993	−	5.44993i	0.220842	−	0.220842i
$610$		−	5.21696i		−	0.211229i
$611$	6.44980			0.260931
$612$		0			0
$613$	−26.9812			−1.08976			−0.544880	−	0.838514i	$-0.683425\pi$
$613$	−26.9812			−1.08976			−0.544880	+	0.838514i	$0.683425\pi$
$614$		−	17.0256i		−	0.687099i
$615$	17.8715	−	17.8715i	0.720649	−	0.720649i
$616$	4.82843			0.194543
$617$	−10.6009	+	10.6009i	−0.426776	+	0.426776i	−0.887529	−	0.460753i	$-0.847580\pi$
$617$	−10.6009	+	10.6009i	−0.426776	+	0.426776i	0.460753	+	0.887529i	$0.347580\pi$
$618$	7.19299	+	7.19299i	0.289344	+	0.289344i
$619$	1.55734	+	1.55734i	0.0625949	+	0.0625949i	0.737711	−	0.675116i	$-0.235907\pi$
$619$	1.55734	+	1.55734i	0.0625949	+	0.0625949i	−0.675116	+	0.737711i	$0.735907\pi$
$620$			30.2446i			1.21465i
$621$		−	3.30864i		−	0.132771i
$622$	2.93015	+	2.93015i	0.117488	+	0.117488i
$623$	−11.9336	−	11.9336i	−0.478111	−	0.478111i
$624$	−2.40743	+	2.40743i	−0.0963741	+	0.0963741i
$625$	21.2414			0.849655
$626$	6.11254	−	6.11254i	0.244306	−	0.244306i
$627$		−	10.1949i		−	0.407147i
$628$	5.37874			0.214635
$629$		0			0
$630$	−1.96775			−0.0783971
$631$			34.7230i			1.38230i	0.722710	+	0.691151i	$0.242896\pi$
$631$			34.7230i			1.38230i	−0.722710	+	0.691151i	$0.757104\pi$
$632$	−5.01639	+	5.01639i	−0.199541	+	0.199541i
$633$	−5.92856			−0.235639
$634$	−9.98614	+	9.98614i	−0.396600	+	0.396600i
$635$	20.8331	+	20.8331i	0.826738	+	0.826738i
$636$	3.96134	+	3.96134i	0.157077	+	0.157077i
$637$			22.5036i			0.891624i
$638$		−	7.15065i		−	0.283097i
$639$	−0.160248	−	0.160248i	−0.00633933	−	0.00633933i
$640$	−14.0707	−	14.0707i	−0.556193	−	0.556193i
$641$	−17.6282	+	17.6282i	−0.696273	+	0.696273i	−0.963605	−	0.267332i	$-0.913858\pi$
$641$	−17.6282	+	17.6282i	−0.696273	+	0.696273i	0.267332	+	0.963605i	$0.413858\pi$
$642$	−10.0052			−0.394874
$643$	−24.8629	+	24.8629i	−0.980496	+	0.980496i	−0.999813	−	0.0193174i	$-0.993851\pi$
$643$	−24.8629	+	24.8629i	−0.980496	+	0.980496i	0.0193174	+	0.999813i	$0.493851\pi$
$644$			5.77701i			0.227646i
$645$	7.17611			0.282559
$646$		0			0
$647$	−28.0142			−1.10135			−0.550677	−	0.834719i	$-0.685630\pi$
$647$	−28.0142			−1.10135			−0.550677	+	0.834719i	$0.685630\pi$
$648$			2.61313i			0.102653i
$649$	8.53281	−	8.53281i	0.334942	−	0.334942i
$650$	−2.08746			−0.0818768
$651$	−8.96587	+	8.96587i	−0.351400	+	0.351400i
$652$	9.06882	+	9.06882i	0.355162	+	0.355162i
$653$	−26.6392	−	26.6392i	−1.04247	−	1.04247i	−0.999057	−	0.0434140i	$-0.986177\pi$
$653$	−26.6392	−	26.6392i	−1.04247	−	1.04247i	−0.0434140	−	0.999057i	$-0.513823\pi$
$654$		−	0.731899i		−	0.0286195i
$655$			5.39517i			0.210807i
$656$	7.10973	+	7.10973i	0.277588	+	0.277588i
$657$	0.260380	+	0.260380i	0.0101584	+	0.0101584i
$658$	−1.04864	+	1.04864i	−0.0408802	+	0.0408802i
$659$	13.5356			0.527272			0.263636	−	0.964622i	$-0.415078\pi$
$659$	13.5356			0.527272			0.263636	+	0.964622i	$0.415078\pi$
$660$	3.11652	−	3.11652i	0.121310	−	0.121310i
$661$		−	2.00626i		−	0.0780345i	−0.999239	−	0.0390172i	$-0.987577\pi$
$661$		−	2.00626i		−	0.0780345i	0.999239	−	0.0390172i	$-0.0124227\pi$
$662$	−4.41315			−0.171522
$663$		0			0
$664$	37.6652			1.46169
$665$		−	17.5137i		−	0.679152i
$666$	2.13066	−	2.13066i	0.0825613	−	0.0825613i
$667$	20.6547			0.799752
$668$	−8.88764	+	8.88764i	−0.343873	+	0.343873i
$669$	18.4892	+	18.4892i	0.714833	+	0.714833i
$670$	−2.38528	−	2.38528i	−0.0921515	−	0.0921515i
$671$			4.89884i			0.189117i
$672$		−	7.23532i		−	0.279109i
$673$	11.8535	+	11.8535i	0.456918	+	0.456918i	0.897643	−	0.440724i	$-0.145278\pi$
$673$	11.8535	+	11.8535i	0.456918	+	0.456918i	−0.440724	+	0.897643i	$0.645278\pi$
$674$	8.80562	+	8.80562i	0.339180	+	0.339180i
$675$	0.469266	−	0.469266i	0.0180621	−	0.0180621i
$676$	5.50114			0.211582
$677$	−16.3092	+	16.3092i	−0.626814	+	0.626814i	−0.947265	−	0.320451i	$-0.896166\pi$
$677$	−16.3092	+	16.3092i	−0.626814	+	0.626814i	0.320451	+	0.947265i	$0.396166\pi$
$678$			6.60474i			0.253654i
$679$	−3.31446			−0.127197
$680$		0			0
$681$	10.9746			0.420546
$682$			11.7638i			0.450458i
$683$	19.8116	−	19.8116i	0.758071	−	0.758071i	−0.217900	−	0.975971i	$-0.569921\pi$
$683$	19.8116	−	19.8116i	0.758071	−	0.758071i	0.975971	+	0.217900i	$0.0699206\pi$
$684$	−9.63368			−0.368353
$685$	22.4823	−	22.4823i	0.859004	−	0.859004i
$686$	−8.33598	−	8.33598i	−0.318269	−	0.318269i
$687$	10.2440	+	10.2440i	0.390833	+	0.390833i
$688$			2.85483i			0.108840i
$689$		−	16.2800i		−	0.620220i
$690$	−3.72878	−	3.72878i	−0.141952	−	0.141952i
$691$	−18.8629	−	18.8629i	−0.717577	−	0.717577i	0.250531	−	0.968109i	$-0.419395\pi$
$691$	−18.8629	−	18.8629i	−0.717577	−	0.717577i	−0.968109	+	0.250531i	$0.919395\pi$
$692$	−12.2472	+	12.2472i	−0.465568	+	0.465568i
$693$	1.84776			0.0701906
$694$	−2.32193	+	2.32193i	−0.0881394	+	0.0881394i
$695$			8.41731i			0.319287i
$696$	−16.3128			−0.618335
$697$		0			0
$698$	−10.8340			−0.410074
$699$			19.0980i			0.722354i
$700$	−0.819355	+	0.819355i	−0.0309687	+	0.0309687i
$701$	9.75054			0.368273			0.184136	−	0.982901i	$-0.441051\pi$
$701$	9.75054			0.368273			0.184136	+	0.982901i	$0.441051\pi$
$702$	2.22417	−	2.22417i	0.0839459	−	0.0839459i
$703$	18.9636	+	18.9636i	0.715226	+	0.715226i
$704$	−2.99321	−	2.99321i	−0.112811	−	0.112811i
$705$			3.26810i			0.123084i
$706$			18.2266i			0.685968i
$707$	−2.07786	−	2.07786i	−0.0781458	−	0.0781458i
$708$	−8.06306	−	8.06306i	−0.303028	−	0.303028i
$709$	20.3318	−	20.3318i	0.763575	−	0.763575i	−0.213391	−	0.976967i	$-0.568451\pi$
$709$	20.3318	−	20.3318i	0.763575	−	0.763575i	0.976967	+	0.213391i	$0.0684509\pi$
$710$	−0.361194			−0.0135554
$711$	−1.91969	+	1.91969i	−0.0719940	+	0.0719940i
$712$			35.7199i			1.33866i
$713$	−33.9797			−1.27255
$714$		0			0
$715$	−12.8081			−0.478994
$716$			15.0151i			0.561141i
$717$	0.523945	−	0.523945i	0.0195671	−	0.0195671i
$718$	−26.9927			−1.00736
$719$	−33.3929	+	33.3929i	−1.24534	+	1.24534i	−0.287592	+	0.957753i	$0.592855\pi$
$719$	−33.3929	+	33.3929i	−1.24534	+	1.24534i	−0.957753	+	0.287592i	$0.907145\pi$
$720$	−1.21984	−	1.21984i	−0.0454606	−	0.0454606i
$721$	−11.6032	−	11.6032i	−0.432125	−	0.432125i
$722$			20.9740i			0.780572i
$723$		−	21.3617i		−	0.794451i
$724$	−16.5274	−	16.5274i	−0.614237	−	0.614237i
$725$	2.92946	+	2.92946i	0.108797	+	0.108797i
$726$	−4.74097	+	4.74097i	−0.175954	+	0.175954i
$727$	27.7790			1.03027			0.515134	−	0.857110i	$-0.327742\pi$
$727$	27.7790			1.03027			0.515134	+	0.857110i	$0.327742\pi$
$728$	−9.37555	+	9.37555i	−0.347481	+	0.347481i
$729$			1.00000i			0.0370370i
$730$	0.586887			0.0217217
$731$		0			0
$732$	4.62914			0.171098
$733$		−	5.38987i		−	0.199080i	−0.995034	−	0.0995398i	$-0.968263\pi$
$733$		−	5.38987i		−	0.199080i	0.995034	−	0.0995398i	$-0.0317371\pi$
$734$	−8.83296	+	8.83296i	−0.326031	+	0.326031i
$735$	−11.4025			−0.420588
$736$	13.7106	−	13.7106i	0.505378	−	0.505378i
$737$	2.23983	+	2.23983i	0.0825052	+	0.0825052i
$738$	−6.56854	−	6.56854i	−0.241791	−	0.241791i
$739$			3.61782i			0.133084i	0.997784	+	0.0665418i	$0.0211966\pi$
$739$			3.61782i			0.133084i	−0.997784	+	0.0665418i	$0.978803\pi$
$740$			11.5941i			0.426207i
$741$	19.7959	+	19.7959i	0.727221	+	0.727221i
$742$	2.64688	+	2.64688i	0.0971700	+	0.0971700i
$743$	−4.37274	+	4.37274i	−0.160420	+	0.160420i	−0.782753	−	0.622333i	$-0.786185\pi$
$743$	−4.37274	+	4.37274i	−0.160420	+	0.160420i	0.622333	+	0.782753i	$0.286185\pi$
$744$	26.8368			0.983883
$745$	26.6840	−	26.6840i	0.977627	−	0.977627i
$746$			19.1461i			0.700990i
$747$	14.4138			0.527375
$748$		0			0
$749$	16.1396			0.589730
$750$		−	9.02668i		−	0.329608i
$751$	−36.2970	+	36.2970i	−1.32450	+	1.32450i	−0.414401	+	0.910094i	$0.636009\pi$
$751$	−36.2970	+	36.2970i	−1.32450	+	1.32450i	−0.910094	+	0.414401i	$0.863991\pi$
$752$	−1.30013			−0.0474109
$753$	0.663845	−	0.663845i	0.0241919	−	0.0241919i
$754$	13.8847	+	13.8847i	0.505651	+	0.505651i
$755$	7.76190	+	7.76190i	0.282484	+	0.282484i
$756$		−	1.74603i		−	0.0635027i
$757$		−	3.83750i		−	0.139476i	−0.997565	−	0.0697381i	$-0.977784\pi$
$757$		−	3.83750i		−	0.139476i	0.997565	−	0.0697381i	$-0.0222164\pi$
$758$	17.6582	+	17.6582i	0.641375	+	0.641375i
$759$	3.50141	+	3.50141i	0.127093	+	0.127093i
$760$	−26.2111	+	26.2111i	−0.950776	+	0.950776i
$761$	16.5850			0.601206			0.300603	−	0.953749i	$-0.402812\pi$
$761$	16.5850			0.601206			0.300603	+	0.953749i	$0.402812\pi$
$762$	7.65706	−	7.65706i	0.277386	−	0.277386i
$763$			1.18064i			0.0427422i
$764$	16.9942			0.614828
$765$		0			0
$766$	0.447937			0.0161846
$767$			33.1370i			1.19651i
$768$	−9.17157	+	9.17157i	−0.330951	+	0.330951i
$769$	27.7826			1.00187			0.500933	−	0.865486i	$-0.332990\pi$
$769$	27.7826			1.00187			0.500933	+	0.865486i	$0.332990\pi$
$770$	2.08239	−	2.08239i	0.0750442	−	0.0750442i
$771$	−11.1930	−	11.1930i	−0.403106	−	0.403106i
$772$	10.7183	+	10.7183i	0.385761	+	0.385761i
$773$			13.9509i			0.501778i	0.968016	+	0.250889i	$0.0807229\pi$
$773$			13.9509i			0.501778i	−0.968016	+	0.250889i	$0.919277\pi$
$774$		−	2.63752i		−	0.0948038i
$775$	−4.81936	−	4.81936i	−0.173116	−	0.173116i
$776$	4.96043	+	4.96043i	0.178069	+	0.178069i
$777$	−3.43702	+	3.43702i	−0.123302	+	0.123302i
$778$	−16.9346			−0.607133
$779$	58.4623	−	58.4623i	2.09463	−	2.09463i
$780$			12.1029i			0.433355i
$781$	0.339169			0.0121364
$782$		0			0
$783$	−6.24264			−0.223094
$784$		−	4.53620i		−	0.162007i
$785$	5.60032	−	5.60032i	0.199884	−	0.199884i
$786$	1.98295			0.0707295
$787$	−2.99252	+	2.99252i	−0.106672	+	0.106672i	−0.758428	−	0.651756i	$-0.774032\pi$
$787$	−2.99252	+	2.99252i	−0.106672	+	0.106672i	0.651756	+	0.758428i	$0.274032\pi$
$788$	−3.16895	−	3.16895i	−0.112889	−	0.112889i
$789$	−8.10152	−	8.10152i	−0.288422	−	0.288422i
$790$			4.32691i			0.153945i
$791$		−	10.6543i		−	0.378823i
$792$	−2.76537	−	2.76537i	−0.0982630	−	0.0982630i
$793$	−9.51226	−	9.51226i	−0.337790	−	0.337790i
$794$	−3.15534	+	3.15534i	−0.111979	+	0.111979i
$795$	8.24906			0.292564
$796$	−13.6746	+	13.6746i	−0.484683	+	0.484683i
$797$		−	27.7502i		−	0.982962i	−0.870888	−	0.491481i	$-0.836456\pi$
$797$		−	27.7502i		−	0.982962i	0.870888	−	0.491481i	$-0.163544\pi$
$798$	−6.43702			−0.227868
$799$		0			0
$800$	3.88915			0.137502
$801$			13.6694i			0.482984i
$802$	2.80892	−	2.80892i	0.0991865	−	0.0991865i
$803$	−0.551099			−0.0194479
$804$	2.11652	−	2.11652i	0.0746439	−	0.0746439i
$805$	6.01500	+	6.01500i	0.212001	+	0.212001i
$806$	−22.8422	−	22.8422i	−0.804582	−	0.804582i
$807$		−	19.1689i		−	0.674779i
$808$			6.21946i			0.218800i
$809$	−2.87990	−	2.87990i	−0.101252	−	0.101252i	0.654666	−	0.755918i	$-0.272809\pi$
$809$	−2.87990	−	2.87990i	−0.101252	−	0.101252i	−0.755918	+	0.654666i	$0.772809\pi$
$810$	1.12698	+	1.12698i	0.0395981	+	0.0395981i
$811$	−4.44540	+	4.44540i	−0.156099	+	0.156099i	−0.780836	−	0.624737i	$-0.785206\pi$
$811$	−4.44540	+	4.44540i	−0.156099	+	0.156099i	0.624737	+	0.780836i	$0.285206\pi$
$812$	10.8999			0.382510
$813$	4.82816	−	4.82816i	0.169331	−	0.169331i
$814$			4.50958i			0.158061i
$815$	18.8848			0.661507
$816$		0			0
$817$	23.4749			0.821282
$818$			20.8486i			0.728954i
$819$	−3.58787	+	3.58787i	−0.125370	+	0.125370i
$820$	35.7430			1.24820
$821$	14.0006	−	14.0006i	0.488624	−	0.488624i	−0.419248	−	0.907872i	$-0.637706\pi$
$821$	14.0006	−	14.0006i	0.488624	−	0.488624i	0.907872	+	0.419248i	$0.137706\pi$
$822$	−8.26319	−	8.26319i	−0.288212	−	0.288212i
$823$	−8.25470	−	8.25470i	−0.287741	−	0.287741i	0.548446	−	0.836186i	$-0.315220\pi$
$823$	−8.25470	−	8.25470i	−0.287741	−	0.287741i	−0.836186	+	0.548446i	$0.815220\pi$
$824$			34.7308i			1.20991i
$825$			0.993212i			0.0345792i
$826$	−5.38756	−	5.38756i	−0.187457	−	0.187457i
$827$	−9.82241	−	9.82241i	−0.341559	−	0.341559i	0.515394	−	0.856953i	$-0.327645\pi$
$827$	−9.82241	−	9.82241i	−0.341559	−	0.341559i	−0.856953	+	0.515394i	$0.827645\pi$
$828$	3.30864	−	3.30864i	0.114983	−	0.114983i
$829$	34.2670			1.19014			0.595071	−	0.803673i	$-0.297124\pi$
$829$	34.2670			1.19014			0.595071	+	0.803673i	$0.297124\pi$
$830$	16.2441	−	16.2441i	0.563843	−	0.563843i
$831$		−	8.12784i		−	0.281952i
$832$	11.6241			0.402992
$833$		0			0
$834$	3.09372			0.107127
$835$			18.5076i			0.640480i
$836$	10.1949	−	10.1949i	0.352599	−	0.352599i
$837$	10.2700			0.354982
$838$	7.59305	−	7.59305i	0.262297	−	0.262297i
$839$	−17.1452	−	17.1452i	−0.591918	−	0.591918i	0.346231	−	0.938149i	$-0.387461\pi$
$839$	−17.1452	−	17.1452i	−0.591918	−	0.591918i	−0.938149	+	0.346231i	$0.887461\pi$
$840$	−4.75057	−	4.75057i	−0.163910	−	0.163910i
$841$		−	9.97056i		−	0.343813i
$842$			11.7722i			0.405695i
$843$	−8.20741	−	8.20741i	−0.282678	−	0.282678i
$844$	−5.92856	−	5.92856i	−0.204069	−	0.204069i
$845$	5.72777	−	5.72777i	0.197041	−	0.197041i
$846$	1.20116			0.0412969
$847$	7.64778	−	7.64778i	0.262781	−	0.262781i
$848$			3.28168i			0.112693i
$849$	6.06404			0.208117
$850$		0			0
$851$	−13.0259			−0.446523
$852$		−	0.320497i		−	0.0109800i
$853$	−5.22507	+	5.22507i	−0.178903	+	0.178903i	−0.790878	−	0.611974i	$-0.790376\pi$
$853$	−5.22507	+	5.22507i	−0.178903	+	0.178903i	0.611974	+	0.790878i	$0.290376\pi$
$854$	3.09309			0.105843
$855$	−10.0305	+	10.0305i	−0.343037	+	0.343037i
$856$	−24.1547	−	24.1547i	−0.825590	−	0.825590i
$857$	−5.68041	−	5.68041i	−0.194039	−	0.194039i	0.603400	−	0.797439i	$-0.293812\pi$
$857$	−5.68041	−	5.68041i	−0.194039	−	0.194039i	−0.797439	+	0.603400i	$0.793812\pi$
$858$			4.70750i			0.160711i
$859$			7.66672i			0.261585i	0.991410	+	0.130793i	$0.0417522\pi$
$859$			7.66672i			0.261585i	−0.991410	+	0.130793i	$0.958248\pi$
$860$	7.17611	+	7.17611i	0.244703	+	0.244703i
$861$	10.5959	+	10.5959i	0.361106	+	0.361106i
$862$	−8.87056	+	8.87056i	−0.302133	+	0.302133i
$863$	14.4183			0.490804			0.245402	−	0.969421i	$-0.421080\pi$
$863$	14.4183			0.490804			0.245402	+	0.969421i	$0.421080\pi$
$864$	−4.14386	+	4.14386i	−0.140977	+	0.140977i
$865$			25.5034i			0.867142i
$866$	−16.6166			−0.564655
$867$		0			0
$868$	−17.9317			−0.608643
$869$		−	4.06306i		−	0.137830i
$870$	−7.03535	+	7.03535i	−0.238521	+	0.238521i
$871$	−8.69833			−0.294732
$872$	1.76696	−	1.76696i	0.0598368	−	0.0598368i
$873$	1.89828	+	1.89828i	0.0642469	+	0.0642469i
$874$	−12.1978	−	12.1978i	−0.412597	−	0.412597i
$875$			14.5612i			0.492257i
$876$			0.520760i			0.0175948i
$877$	38.0584	+	38.0584i	1.28514	+	1.28514i	0.937704	+	0.347435i	$0.112947\pi$
$877$	38.0584	+	38.0584i	1.28514	+	1.28514i	0.347435	+	0.937704i	$0.387053\pi$
$878$	−12.7346	−	12.7346i	−0.429770	−	0.429770i
$879$	−4.86169	+	4.86169i	−0.163981	+	0.163981i
$880$	2.58181			0.0870328
$881$	21.0679	−	21.0679i	0.709795	−	0.709795i	−0.256697	−	0.966492i	$-0.582634\pi$
$881$	21.0679	−	21.0679i	0.709795	−	0.709795i	0.966492	+	0.256697i	$0.0826342\pi$
$882$			4.19090i			0.141115i
$883$	−28.2666			−0.951247			−0.475624	−	0.879649i	$-0.657778\pi$
$883$	−28.2666			−0.951247			−0.475624	+	0.879649i	$0.657778\pi$
$884$		0			0
$885$	−16.7905			−0.564405
$886$			11.8049i			0.396593i
$887$	−17.7602	+	17.7602i	−0.596330	+	0.596330i	−0.939334	−	0.343004i	$-0.888556\pi$
$887$	−17.7602	+	17.7602i	−0.596330	+	0.596330i	0.343004	+	0.939334i	$0.388556\pi$
$888$	10.2877			0.345233
$889$	−12.3518	+	12.3518i	−0.414266	+	0.414266i
$890$	15.4052	+	15.4052i	0.516383	+	0.516383i
$891$	−1.05826	−	1.05826i	−0.0354530	−	0.0354530i
$892$			36.9784i			1.23813i
$893$			10.6908i			0.357754i
$894$	−9.80750	−	9.80750i	−0.328012	−	0.328012i
$895$	15.6337	+	15.6337i	0.522576	+	0.522576i
$896$	8.34240	−	8.34240i	0.278700	−	0.278700i
$897$	−13.5976			−0.454012
$898$	−7.33291	+	7.33291i	−0.244702	+	0.244702i
$899$			64.1118i			2.13825i
$900$	0.938533			0.0312844
$901$		0			0
$902$	13.9024			0.462901
$903$			4.25466i			0.141586i
$904$	−15.9453	+	15.9453i	−0.530332	+	0.530332i
$905$	−34.4166			−1.14405
$906$	2.85282	−	2.85282i	0.0947787	−	0.0947787i
$907$	−34.7185	−	34.7185i	−1.15281	−	1.15281i	−0.985987	−	0.166820i	$-0.946650\pi$
$907$	−34.7185	−	34.7185i	−1.15281	−	1.15281i	−0.166820	−	0.985987i	$-0.553350\pi$
$908$	10.9746	+	10.9746i	0.364204	+	0.364204i
$909$			2.38009i			0.0789425i
$910$			8.08693i			0.268079i
$911$	−5.64007	−	5.64007i	−0.186864	−	0.186864i	0.607475	−	0.794339i	$-0.292183\pi$
$911$	−5.64007	−	5.64007i	−0.186864	−	0.186864i	−0.794339	+	0.607475i	$0.792183\pi$
$912$	−3.99040	−	3.99040i	−0.132135	−	0.132135i
$913$	−15.2536	+	15.2536i	−0.504820	+	0.504820i
$914$	−11.7771			−0.389551
$915$	4.81984	−	4.81984i	0.159339	−	0.159339i
$916$			20.4880i			0.676942i
$917$	−3.19875			−0.105632
$918$		0			0
$919$	19.8027			0.653229			0.326615	−	0.945158i	$-0.394092\pi$
$919$	19.8027			0.653229			0.326615	+	0.945158i	$0.394092\pi$
$920$		−	18.0042i		−	0.593580i
$921$	15.7296	−	15.7296i	0.518309	−	0.518309i
$922$	−15.9201			−0.524300
$923$	−0.658578	+	0.658578i	−0.0216774	+	0.0216774i
$924$	1.84776	+	1.84776i	0.0607868	+	0.0607868i
$925$	−1.84747	−	1.84747i	−0.0607445	−	0.0607445i
$926$		−	20.2306i		−	0.664818i
$927$			13.2909i			0.436531i
$928$	−25.8686	−	25.8686i	−0.849179	−	0.849179i
$929$	−3.94177	−	3.94177i	−0.129325	−	0.129325i	0.639481	−	0.768807i	$-0.279149\pi$
$929$	−3.94177	−	3.94177i	−0.129325	−	0.129325i	−0.768807	+	0.639481i	$0.779149\pi$
$930$	11.5741	−	11.5741i	0.379529	−	0.379529i
$931$	−37.3005			−1.22248
$932$	−19.0980	+	19.0980i	−0.625577	+	0.625577i
$933$			5.41421i			0.177253i
$934$	5.48836			0.179584
$935$		0			0
$936$	10.7392			0.351023
$937$			0.398572i			0.0130208i	0.999979	+	0.00651039i	$0.00207234\pi$
$937$			0.398572i			0.0130208i	−0.999979	+	0.00651039i	$0.997928\pi$
$938$	1.41421	−	1.41421i	0.0461757	−	0.0461757i
$939$	11.2945			0.368582
$940$	−3.26810	+	3.26810i	−0.106594	+	0.106594i
$941$	3.04654	+	3.04654i	0.0993144	+	0.0993144i	0.755018	−	0.655704i	$-0.227628\pi$
$941$	3.04654	+	3.04654i	0.0993144	+	0.0993144i	−0.655704	+	0.755018i	$0.727628\pi$
$942$	−2.05835	−	2.05835i	−0.0670648	−	0.0670648i
$943$			40.1572i			1.30770i
$944$		−	6.67966i		−	0.217404i
$945$	−1.81796	−	1.81796i	−0.0591384	−	0.0591384i
$946$	2.79118	+	2.79118i	0.0907492	+	0.0907492i
$947$	8.07204	−	8.07204i	0.262306	−	0.262306i	−0.563684	−	0.825990i	$-0.690616\pi$
$947$	8.07204	−	8.07204i	0.262306	−	0.262306i	0.825990	+	0.563684i	$0.190616\pi$
$948$	−3.83938			−0.124697
$949$	1.07009	−	1.07009i	0.0347366	−	0.0347366i
$950$		−	3.46004i		−	0.112259i
$951$	−18.4520			−0.598346
$952$		0			0
$953$	−40.8932			−1.32466			−0.662330	−	0.749213i	$-0.730432\pi$
$953$	−40.8932			−1.32466			−0.662330	+	0.749213i	$0.730432\pi$
$954$		−	3.03188i		−	0.0981606i
$955$	17.6943	−	17.6943i	0.572574	−	0.572574i
$956$	1.04789			0.0338912
$957$	6.60634	−	6.60634i	0.213553	−	0.213553i
$958$	−1.58787	−	1.58787i	−0.0513017	−	0.0513017i
$959$	13.3296	+	13.3296i	0.430434	+	0.430434i
$960$			5.88989i			0.190096i
$961$		−	74.4725i		−	2.40234i
$962$	−8.75643	−	8.75643i	−0.282319	−	0.282319i
$963$	−9.24360	−	9.24360i	−0.297871	−	0.297871i
$964$	21.3617	−	21.3617i	0.688015	−	0.688015i
$965$	22.3197			0.718498
$966$	2.21077	−	2.21077i	0.0711302	−	0.0711302i
$967$			23.5335i			0.756788i	0.925645	+	0.378394i	$0.123524\pi$
$967$			23.5335i			0.756788i	−0.925645	+	0.378394i	$0.876476\pi$
$968$	−22.8914			−0.735758
$969$		0			0
$970$	4.27865			0.137379
$971$			6.44140i			0.206714i	0.994644	+	0.103357i	$0.0329585\pi$
$971$			6.44140i			0.206714i	−0.994644	+	0.103357i	$0.967042\pi$
$972$	−1.00000	+	1.00000i	−0.0320750	+	0.0320750i
$973$	−4.99055			−0.159990
$974$	12.5785	−	12.5785i	0.403040	−	0.403040i
$975$	−1.92856	−	1.92856i	−0.0617633	−	0.0617633i
$976$	1.91745	+	1.91745i	0.0613762	+	0.0613762i
$977$		−	17.8474i		−	0.570989i	−0.958380	−	0.285495i	$-0.907842\pi$
$977$		−	17.8474i		−	0.570989i	0.958380	−	0.285495i	$-0.0921579\pi$
$978$		−	6.94097i		−	0.221948i
$979$	−14.4658	−	14.4658i	−0.462328	−	0.462328i
$980$	−11.4025	−	11.4025i	−0.364240	−	0.364240i
$981$	0.676186	−	0.676186i	0.0215890	−	0.0215890i
$982$	10.4538			0.333595
$983$	−17.0537	+	17.0537i	−0.543929	+	0.543929i	−0.924678	−	0.380749i	$-0.875666\pi$
$983$	−17.0537	+	17.0537i	−0.543929	+	0.543929i	0.380749	+	0.924678i	$0.375666\pi$
$984$		−	31.7157i		−	1.01106i
$985$	−6.59899			−0.210261
$986$		0			0
$987$	−1.93763			−0.0616755
$988$			39.5918i			1.25958i
$989$	−8.06235	+	8.06235i	−0.256368	+	0.256368i
$990$	−2.38528			−0.0758092
$991$	−17.1161	+	17.1161i	−0.543712	+	0.543712i	−0.924615	−	0.380903i	$-0.875613\pi$
$991$	−17.1161	+	17.1161i	−0.543712	+	0.543712i	0.380903	+	0.924615i	$0.375613\pi$
$992$	42.5574	+	42.5574i	1.35120	+	1.35120i
$993$	−4.07722	−	4.07722i	−0.129387	−	0.129387i
$994$		−	0.214149i		−	0.00679240i
$995$			28.4759i			0.902746i
$996$	14.4138	+	14.4138i	0.456720	+	0.456720i
$997$	−26.1029	−	26.1029i	−0.826688	−	0.826688i	0.160369	−	0.987057i	$-0.448732\pi$
$997$	−26.1029	−	26.1029i	−0.826688	−	0.826688i	−0.987057	+	0.160369i	$0.948732\pi$
$998$	−4.07639	+	4.07639i	−0.129036	+	0.129036i
$999$	3.93694			0.124559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.h.616.2		8
17.2	even	8		867.2.d.e.577.5		8
17.3	odd	16		867.2.h.b.733.1		8
17.4	even	4		867.2.e.i.829.3		8
17.5	odd	16		51.2.h.a.49.2	yes	8
17.6	odd	16		51.2.h.a.25.2	✓	8
17.7	odd	16		867.2.h.f.757.1		8
17.8	even	8		867.2.a.m.1.2		4
17.9	even	8		867.2.a.n.1.2		4
17.10	odd	16		867.2.h.b.757.1		8
17.11	odd	16		867.2.h.g.688.2		8
17.12	odd	16		867.2.h.g.712.2		8
17.13	even	4	inner	867.2.e.h.829.3		8
17.14	odd	16		867.2.h.f.733.1		8
17.15	even	8		867.2.d.e.577.6		8
17.16	even	2		867.2.e.i.616.2		8
51.5	even	16		153.2.l.e.100.1		8
51.8	odd	8		2601.2.a.bc.1.3		4
51.23	even	16		153.2.l.e.127.1		8
51.26	odd	8		2601.2.a.bd.1.3		4
68.23	even	16		816.2.bq.a.433.1		8
68.39	even	16		816.2.bq.a.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.h.a.25.2	✓	8	17.6	odd	16
51.2.h.a.49.2	yes	8	17.5	odd	16
153.2.l.e.100.1		8	51.5	even	16
153.2.l.e.127.1		8	51.23	even	16
816.2.bq.a.49.1		8	68.39	even	16
816.2.bq.a.433.1		8	68.23	even	16
867.2.a.m.1.2		4	17.8	even	8
867.2.a.n.1.2		4	17.9	even	8
867.2.d.e.577.5		8	17.2	even	8
867.2.d.e.577.6		8	17.15	even	8
867.2.e.h.616.2		8	1.1	even	1	trivial
867.2.e.h.829.3		8	17.13	even	4	inner
867.2.e.i.616.2		8	17.16	even	2
867.2.e.i.829.3		8	17.4	even	4
867.2.h.b.733.1		8	17.3	odd	16
867.2.h.b.757.1		8	17.10	odd	16
867.2.h.f.733.1		8	17.14	odd	16
867.2.h.f.757.1		8	17.7	odd	16
867.2.h.g.688.2		8	17.11	odd	16
867.2.h.g.712.2		8	17.12	odd	16
2601.2.a.bc.1.3		4	51.8	odd	8
2601.2.a.bd.1.3		4	51.26	odd	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.765367i q^{2} +(0.707107 - 0.707107i) q^{3} +1.41421 q^{4} +(1.47247 - 1.47247i) q^{5} +(-0.541196 - 0.541196i) q^{6} +(0.873017 + 0.873017i) q^{7} -2.61313i q^{8} -1.00000i q^{9} +(-1.12698 - 1.12698i) q^{10} +(1.05826 + 1.05826i) q^{11} +(1.00000 - 1.00000i) q^{12} -4.10973 q^{13} +(0.668179 - 0.668179i) q^{14} -2.08239i q^{15} +0.828427 q^{16} -0.765367 q^{18} -6.81204i q^{19} +(2.08239 - 2.08239i) q^{20} +1.23463 q^{21} +(0.809957 - 0.809957i) q^{22} +(2.33956 + 2.33956i) q^{23} +(-1.84776 - 1.84776i) q^{24} +0.663643i q^{25} +3.14545i q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.23463 + 1.23463i) q^{28} +(4.41421 - 4.41421i) q^{29} -1.59379 q^{30} +(-7.26197 + 7.26197i) q^{31} -5.86030i q^{32} +1.49661 q^{33} +2.57099 q^{35} -1.41421i q^{36} +(-2.78384 + 2.78384i) q^{37} -5.21371 q^{38} +(-2.90602 + 2.90602i) q^{39} +(-3.84776 - 3.84776i) q^{40} +(8.58221 + 8.58221i) q^{41} -0.944947i q^{42} +3.44609i q^{43} +(1.49661 + 1.49661i) q^{44} +(-1.47247 - 1.47247i) q^{45} +(1.79063 - 1.79063i) q^{46} -1.56940 q^{47} +(0.585786 - 0.585786i) q^{48} -5.47568i q^{49} +0.507930 q^{50} -5.81204 q^{52} +3.96134i q^{53} +(-0.541196 + 0.541196i) q^{54} +3.11652 q^{55} +(2.28130 - 2.28130i) q^{56} +(-4.81684 - 4.81684i) q^{57} +(-3.37849 - 3.37849i) q^{58} -8.06306i q^{59} -2.94495i q^{60} +(2.31457 + 2.31457i) q^{61} +(5.55807 + 5.55807i) q^{62} +(0.873017 - 0.873017i) q^{63} -2.82843 q^{64} +(-6.05147 + 6.05147i) q^{65} -1.14545i q^{66} +2.11652 q^{67} +3.30864 q^{69} -1.96775i q^{70} +(0.160248 - 0.160248i) q^{71} -2.61313 q^{72} +(-0.260380 + 0.260380i) q^{73} +(2.13066 + 2.13066i) q^{74} +(0.469266 + 0.469266i) q^{75} -9.63368i q^{76} +1.84776i q^{77} +(2.22417 + 2.22417i) q^{78} +(-1.91969 - 1.91969i) q^{79} +(1.21984 - 1.21984i) q^{80} -1.00000 q^{81} +(6.56854 - 6.56854i) q^{82} +14.4138i q^{83} +1.74603 q^{84} +2.63752 q^{86} -6.24264i q^{87} +(2.76537 - 2.76537i) q^{88} -13.6694 q^{89} +(-1.12698 + 1.12698i) q^{90} +(-3.58787 - 3.58787i) q^{91} +(3.30864 + 3.30864i) q^{92} +10.2700i q^{93} +1.20116i q^{94} +(-10.0305 - 10.0305i) q^{95} +(-4.14386 - 4.14386i) q^{96} +(-1.89828 + 1.89828i) q^{97} -4.19090 q^{98} +(1.05826 - 1.05826i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{13} + 8 q^{14} - 16 q^{16} + 8 q^{20} + 16 q^{21} + 16 q^{22} + 16 q^{28} + 24 q^{29} + 16 q^{30} - 32 q^{31} - 8 q^{33} + 32 q^{35} + 16 q^{37} - 32 q^{38}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 16 * q^10 + 8 * q^11 + 8 * q^12 + 8 * q^13 + 8 * q^14 - 16 * q^16 + 8 * q^20 + 16 * q^21 + 16 * q^22 + 16 * q^28 + 24 * q^29 + 16 * q^30 - 32 * q^31 - 8 * q^33 + 32 * q^35 + 16 * q^37 - 32 * q^38 - 8 * q^39 - 16 * q^40 + 16 * q^41 - 8 * q^44 + 16 * q^46 - 16 * q^47 + 16 * q^48 + 32 * q^50 - 16 * q^52 + 24 * q^55 + 8 * q^57 - 32 * q^61 - 8 * q^65 + 16 * q^67 - 24 * q^69 - 24 * q^71 + 32 * q^73 - 8 * q^74 + 16 * q^75 + 16 * q^78 + 16 * q^79 + 16 * q^80 - 8 * q^81 + 16 * q^82 - 32 * q^86 + 16 * q^88 - 32 * q^89 - 16 * q^90 - 24 * q^92 - 24 * q^95 - 16 * q^97 - 64 * q^98 + 8 * q^99

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