LMFDB - Embedded newform 816.2.bf.d.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(47,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 2, 1]))

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

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

chi := DirichletCharacter("816.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.bf (of order $4$, degree $2$, 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:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	816.47
Dual form			816.2.bf.d.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71292 + 0.256691i) q^{3} +(-1.13275 + 1.13275i) q^{5} +(-2.41609 - 2.41609i) q^{7} +(2.86822 - 0.879385i) q^{9} +(1.45623 - 1.45623i) q^{11} +4.45336 q^{13} +(1.64955 - 2.23108i) q^{15} +(-4.00097 + 0.996122i) q^{17} +3.93923 q^{19} +(4.75877 + 3.51839i) q^{21} +(-3.68731 + 3.68731i) q^{23} +2.43376i q^{25} +(-4.68731 + 2.24257i) q^{27} +(-6.86919 + 6.86919i) q^{29} +(-2.89122 + 2.89122i) q^{31} +(-2.12061 + 2.86822i) q^{33} +5.47365 q^{35} +(1.53209 + 1.53209i) q^{37} +(-7.62827 + 1.14314i) q^{39} +(3.00485 + 3.00485i) q^{41} +0.475129 q^{43} +(-2.25285 + 4.24509i) q^{45} -11.8368 q^{47} +4.67499i q^{49} +(6.59766 - 2.73329i) q^{51} +8.51548 q^{53} +3.29909i q^{55} +(-6.74760 + 1.01117i) q^{57} +1.90098i q^{59} +(3.29086 - 3.29086i) q^{61} +(-9.05455 - 4.80520i) q^{63} +(-5.04454 + 5.04454i) q^{65} +7.87846i q^{67} +(5.36959 - 7.26259i) q^{69} +(6.24849 + 6.24849i) q^{71} +(-8.75877 - 8.75877i) q^{73} +(-0.624726 - 4.16885i) q^{75} -7.03678 q^{77} +(9.65441 + 9.65441i) q^{79} +(7.45336 - 5.04454i) q^{81} +7.02334i q^{83} +(3.40373 - 5.66044i) q^{85} +(10.0031 - 13.5297i) q^{87} -2.26550i q^{89} +(-10.7597 - 10.7597i) q^{91} +(4.21029 - 5.69459i) q^{93} +(-4.46216 + 4.46216i) q^{95} +(9.90673 + 9.90673i) q^{97} +(2.89621 - 5.45739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{21} - 96 q^{33} + 24 q^{45} - 48 q^{57} - 48 q^{61} + 72 q^{69} - 120 q^{73} + 72 q^{81} + 192 q^{85} + 24 q^{97}+O(q^{100}) $ 24 * q + 24 * q^21 - 96 * q^33 + 24 * q^45 - 48 * q^57 - 48 * q^61 + 72 * q^69 - 120 * q^73 + 72 * q^81 + 192 * q^85 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.71292	+	0.256691i	−0.988957	+	0.148201i
$3$	−1.71292	+	0.256691i	−0.988957	+	0.148201i
$4$		0			0
$5$	−1.13275	+	1.13275i	−0.506580	+	0.506580i	−0.913475	−	0.406895i	$-0.866612\pi$
$5$	−1.13275	+	1.13275i	−0.506580	+	0.506580i	0.406895	+	0.913475i	$0.366612\pi$
$6$		0			0
$7$	−2.41609	−	2.41609i	−0.913197	−	0.913197i	0.0833258	−	0.996522i	$-0.473446\pi$
$7$	−2.41609	−	2.41609i	−0.913197	−	0.913197i	−0.996522	+	0.0833258i	$0.973446\pi$
$8$		0			0
$9$	2.86822	−	0.879385i	0.956073	−	0.293128i
$10$		0			0
$11$	1.45623	−	1.45623i	0.439071	−	0.439071i	−0.452628	−	0.891699i	$-0.649514\pi$
$11$	1.45623	−	1.45623i	0.439071	−	0.439071i	0.891699	+	0.452628i	$0.149514\pi$
$12$		0			0
$13$	4.45336			1.23514			0.617570	−	0.786516i	$-0.288117\pi$
$13$	4.45336			1.23514			0.617570	+	0.786516i	$0.288117\pi$
$14$		0			0
$15$	1.64955	−	2.23108i	0.425911	−	0.576062i
$16$		0			0
$17$	−4.00097	+	0.996122i	−0.970377	+	0.241595i
$17$	−4.00097	+	0.996122i	−0.970377	+	0.241595i
$18$		0			0
$19$	3.93923			0.903722			0.451861	−	0.892088i	$-0.350760\pi$
$19$	3.93923			0.903722			0.451861	+	0.892088i	$0.350760\pi$
$20$		0			0
$21$	4.75877	+	3.51839i	1.03845	+	0.767776i
$22$		0			0
$23$	−3.68731	+	3.68731i	−0.768858	+	0.768858i	−0.977905	−	0.209048i	$-0.932964\pi$
$23$	−3.68731	+	3.68731i	−0.768858	+	0.768858i	0.209048	+	0.977905i	$0.432964\pi$
$24$		0			0
$25$			2.43376i			0.486753i
$26$		0			0
$27$	−4.68731	+	2.24257i	−0.902074	+	0.431582i
$28$		0			0
$29$	−6.86919	+	6.86919i	−1.27558	+	1.27558i	−0.332458	+	0.943118i	$0.607878\pi$
$29$	−6.86919	+	6.86919i	−1.27558	+	1.27558i	−0.943118	+	0.332458i	$0.892122\pi$
$30$		0			0
$31$	−2.89122	+	2.89122i	−0.519279	+	0.519279i	−0.917353	−	0.398075i	$-0.869679\pi$
$31$	−2.89122	+	2.89122i	−0.519279	+	0.519279i	0.398075	+	0.917353i	$0.369679\pi$
$32$		0			0
$33$	−2.12061	+	2.86822i	−0.369152	+	0.499293i
$34$		0			0
$35$	5.47365			0.925215
$36$		0			0
$37$	1.53209	+	1.53209i	0.251874	+	0.251874i	0.821739	−	0.569865i	$-0.193004\pi$
$37$	1.53209	+	1.53209i	0.251874	+	0.251874i	−0.569865	+	0.821739i	$0.693004\pi$
$38$		0			0
$39$	−7.62827	+	1.14314i	−1.22150	+	0.183049i
$40$		0			0
$41$	3.00485	+	3.00485i	0.469278	+	0.469278i	0.901681	−	0.432403i	$-0.142334\pi$
$41$	3.00485	+	3.00485i	0.469278	+	0.469278i	−0.432403	+	0.901681i	$0.642334\pi$
$42$		0			0
$43$	0.475129			0.0724566			0.0362283	−	0.999344i	$-0.488466\pi$
$43$	0.475129			0.0724566			0.0362283	+	0.999344i	$0.488466\pi$
$44$		0			0
$45$	−2.25285	+	4.24509i	−0.335835	+	0.632821i
$46$		0			0
$47$	−11.8368			−1.72657			−0.863286	−	0.504715i	$-0.831598\pi$
$47$	−11.8368			−1.72657			−0.863286	+	0.504715i	$0.831598\pi$
$48$		0			0
$49$			4.67499i			0.667856i
$50$		0			0
$51$	6.59766	−	2.73329i	0.923857	−	0.382738i
$52$		0			0
$53$	8.51548			1.16969			0.584846	−	0.811145i	$-0.301155\pi$
$53$	8.51548			1.16969			0.584846	+	0.811145i	$0.301155\pi$
$54$		0			0
$55$			3.29909i			0.444849i
$56$		0			0
$57$	−6.74760	+	1.01117i	−0.893742	+	0.133932i
$58$		0			0
$59$			1.90098i			0.247486i	0.992314	+	0.123743i	$0.0394899\pi$
$59$			1.90098i			0.247486i	−0.992314	+	0.123743i	$0.960510\pi$
$60$		0			0
$61$	3.29086	−	3.29086i	0.421351	−	0.421351i	−0.464317	−	0.885669i	$-0.653700\pi$
$61$	3.29086	−	3.29086i	0.421351	−	0.421351i	0.885669	+	0.464317i	$0.153700\pi$
$62$		0			0
$63$	−9.05455	−	4.80520i	−1.14077	−	0.605399i
$64$		0			0
$65$	−5.04454	+	5.04454i	−0.625698	+	0.625698i
$66$		0			0
$67$			7.87846i			0.962507i	0.876581	+	0.481254i	$0.159818\pi$
$67$			7.87846i			0.962507i	−0.876581	+	0.481254i	$0.840182\pi$
$68$		0			0
$69$	5.36959	−	7.26259i	0.646422	−	0.874313i
$70$		0			0
$71$	6.24849	+	6.24849i	0.741559	+	0.741559i	0.972878	−	0.231319i	$-0.0743040\pi$
$71$	6.24849	+	6.24849i	0.741559	+	0.741559i	−0.231319	+	0.972878i	$0.574304\pi$
$72$		0			0
$73$	−8.75877	−	8.75877i	−1.02514	−	1.02514i	−0.999676	−	0.0254607i	$-0.991895\pi$
$73$	−8.75877	−	8.75877i	−1.02514	−	1.02514i	−0.0254607	−	0.999676i	$-0.508105\pi$
$74$		0			0
$75$	−0.624726	−	4.16885i	−0.0721371	−	0.481378i
$76$		0			0
$77$	−7.03678			−0.801916
$78$		0			0
$79$	9.65441	+	9.65441i	1.08621	+	1.08621i	0.995915	+	0.0902909i	$0.0287797\pi$
$79$	9.65441	+	9.65441i	1.08621	+	1.08621i	0.0902909	+	0.995915i	$0.471220\pi$
$80$		0			0
$81$	7.45336	−	5.04454i	0.828151	−	0.560504i
$82$		0			0
$83$			7.02334i			0.770911i	0.922726	+	0.385456i	$0.125956\pi$
$83$			7.02334i			0.770911i	−0.922726	+	0.385456i	$0.874044\pi$
$84$		0			0
$85$	3.40373	−	5.66044i	0.369187	−	0.613961i
$86$		0			0
$87$	10.0031	−	13.5297i	1.07245	−	1.45053i
$88$		0			0
$89$		−	2.26550i		−	0.240142i	−0.992765	−	0.120071i	$-0.961688\pi$
$89$		−	2.26550i		−	0.240142i	0.992765	−	0.120071i	$-0.0383122\pi$
$90$		0			0
$91$	−10.7597	−	10.7597i	−1.12793	−	1.12793i
$92$		0			0
$93$	4.21029	−	5.69459i	0.436587	−	0.590502i
$94$		0			0
$95$	−4.46216	+	4.46216i	−0.457808	+	0.457808i
$96$		0			0
$97$	9.90673	+	9.90673i	1.00588	+	1.00588i	0.999983	+	0.00589303i	$0.00187582\pi$
$97$	9.90673	+	9.90673i	1.00588	+	1.00588i	0.00589303	+	0.999983i	$0.498124\pi$
$98$		0			0
$99$	2.89621	−	5.45739i	0.291080	−	0.548488i
$100$		0			0
$101$			6.00969i			0.597987i	0.954255	+	0.298993i	$0.0966508\pi$
$101$			6.00969i			0.597987i	−0.954255	+	0.298993i	$0.903349\pi$
$102$		0			0
$103$			3.21129i			0.316418i	0.987406	+	0.158209i	$0.0505720\pi$
$103$			3.21129i			0.316418i	−0.987406	+	0.158209i	$0.949428\pi$
$104$		0			0
$105$	−9.37594	+	1.40504i	−0.914998	+	0.137118i
$106$		0			0
$107$	12.7548	+	12.7548i	1.23305	+	1.23305i	0.962785	+	0.270269i	$0.0871128\pi$
$107$	12.7548	+	12.7548i	1.23305	+	1.23305i	0.270269	+	0.962785i	$0.412887\pi$
$108$		0			0
$109$	−9.61587	+	9.61587i	−0.921033	+	0.921033i	−0.997103	−	0.0760695i	$-0.975763\pi$
$109$	−9.61587	+	9.61587i	−0.921033	+	0.921033i	0.0760695	+	0.997103i	$0.475763\pi$
$110$		0			0
$111$	−3.01763	−	2.23108i	−0.286420	−	0.211765i
$112$		0			0
$113$	−0.739349	−	0.739349i	−0.0695521	−	0.0695521i	0.671475	−	0.741027i	$-0.265661\pi$
$113$	−0.739349	−	0.739349i	−0.0695521	−	0.0695521i	−0.741027	+	0.671475i	$0.765661\pi$
$114$		0			0
$115$		−	8.35359i		−	0.778976i
$116$		0			0
$117$	12.7732	−	3.91622i	1.18088	−	0.362055i
$118$		0			0
$119$	12.0734	+	7.25998i	1.10677	+	0.665521i
$120$		0			0
$121$			6.75877i			0.614434i
$122$		0			0
$123$	−5.91839	−	4.37576i	−0.533643	−	0.394549i
$124$		0			0
$125$	−8.42058	−	8.42058i	−0.753160	−	0.753160i
$126$		0			0
$127$	−9.82938			−0.872216			−0.436108	−	0.899894i	$-0.643643\pi$
$127$	−9.82938			−0.872216			−0.436108	+	0.899894i	$0.643643\pi$
$128$		0			0
$129$	−0.813861	+	0.121962i	−0.0716564	+	0.0107381i
$130$		0			0
$131$	5.38019	+	5.38019i	0.470069	+	0.470069i	0.901937	−	0.431868i	$-0.142145\pi$
$131$	5.38019	+	5.38019i	0.470069	+	0.470069i	−0.431868	+	0.901937i	$0.642145\pi$
$132$		0			0
$133$	−9.51754	−	9.51754i	−0.825275	−	0.825275i
$134$		0			0
$135$	2.76928	−	7.84981i	0.238342	−	0.675604i
$136$		0			0
$137$		−	14.3468i		−	1.22573i	−0.790187	−	0.612866i	$-0.790017\pi$
$137$		−	14.3468i		−	1.22573i	0.790187	−	0.612866i	$-0.209983\pi$
$138$		0			0
$139$	14.9331	−	14.9331i	1.26661	−	1.26661i	0.318777	−	0.947830i	$-0.396728\pi$
$139$	14.9331	−	14.9331i	1.26661	−	1.26661i	0.947830	−	0.318777i	$-0.103272\pi$
$140$		0			0
$141$	20.2755	−	3.03840i	1.70751	−	0.255879i
$142$		0			0
$143$	6.48513	−	6.48513i	0.542314	−	0.542314i
$144$		0			0
$145$		−	15.5621i		−	1.29236i
$146$		0			0
$147$	−1.20003	−	8.00791i	−0.0989768	−	0.660481i
$148$		0			0
$149$			0.691899i			0.0566826i	0.999598	+	0.0283413i	$0.00902252\pi$
$149$			0.691899i			0.0566826i	−0.999598	+	0.0283413i	$0.990977\pi$
$150$		0			0
$151$	−7.71345			−0.627712			−0.313856	−	0.949471i	$-0.601621\pi$
$151$	−7.71345			−0.627712			−0.313856	+	0.949471i	$0.601621\pi$
$152$		0			0
$153$	−10.5997	+	6.37549i	−0.856933	+	0.515428i
$154$		0			0
$155$		−	6.55005i		−	0.526113i
$156$		0			0
$157$	−21.7743			−1.73777			−0.868887	−	0.495010i	$-0.835164\pi$
$157$	−21.7743			−1.73777			−0.868887	+	0.495010i	$0.835164\pi$
$158$		0			0
$159$	−14.5864	+	2.18585i	−1.15677	+	0.173349i
$160$		0			0
$161$	17.8178			1.40424
$162$		0			0
$163$	−4.06564	−	4.06564i	−0.318445	−	0.318445i	0.529725	−	0.848170i	$-0.322295\pi$
$163$	−4.06564	−	4.06564i	−0.318445	−	0.318445i	−0.848170	+	0.529725i	$0.822295\pi$
$164$		0			0
$165$	−0.846848	−	5.65109i	−0.0659270	−	0.439937i
$166$		0			0
$167$	−7.61127	−	7.61127i	−0.588977	−	0.588977i	0.348377	−	0.937355i	$-0.386733\pi$
$167$	−7.61127	−	7.61127i	−0.588977	−	0.588977i	−0.937355	+	0.348377i	$0.886733\pi$
$168$		0			0
$169$	6.83244			0.525573
$170$		0			0
$171$	11.2986	−	3.46410i	0.864024	−	0.264906i
$172$		0			0
$173$	−2.61145	+	2.61145i	−0.198545	+	0.198545i	−0.799376	−	0.600831i	$-0.794836\pi$
$173$	−2.61145	+	2.61145i	−0.198545	+	0.198545i	0.600831	+	0.799376i	$0.294836\pi$
$174$		0			0
$175$	5.88019	−	5.88019i	0.444501	−	0.444501i
$176$		0			0
$177$	−0.487964	−	3.25623i	−0.0366776	−	0.244753i
$178$		0			0
$179$		−	1.36278i		−	0.101859i	−0.998702	−	0.0509293i	$-0.983782\pi$
$179$		−	1.36278i		−	0.101859i	0.998702	−	0.0509293i	$-0.0162183\pi$
$180$		0			0
$181$	6.83750	−	6.83750i	0.508227	−	0.508227i	−0.405755	−	0.913982i	$-0.632991\pi$
$181$	6.83750	−	6.83750i	0.508227	−	0.508227i	0.913982	+	0.405755i	$0.132991\pi$
$182$		0			0
$183$	−4.79226	+	6.48173i	−0.354254	+	0.479143i
$184$		0			0
$185$	−3.47094			−0.255189
$186$		0			0
$187$	−4.37576	+	7.27693i	−0.319987	+	0.532142i
$188$		0			0
$189$	16.7432	+	5.90673i	1.21789	+	0.429651i
$190$		0			0
$191$	−13.8598			−1.00286			−0.501428	−	0.865199i	$-0.667192\pi$
$191$	−13.8598			−1.00286			−0.501428	+	0.865199i	$0.667192\pi$
$192$		0			0
$193$	−1.08378	+	1.08378i	−0.0780121	+	0.0780121i	−0.745036	−	0.667024i	$-0.767568\pi$
$193$	−1.08378	+	1.08378i	−0.0780121	+	0.0780121i	0.667024	+	0.745036i	$0.267568\pi$
$194$		0			0
$195$	7.34603	−	9.93580i	0.526060	−	0.711518i
$196$		0			0
$197$	−13.9060	−	13.9060i	−0.990759	−	0.990759i	0.00919834	−	0.999958i	$-0.497072\pi$
$197$	−13.9060	−	13.9060i	−0.990759	−	0.990759i	−0.999958	+	0.00919834i	$0.997072\pi$
$198$		0			0
$199$	−1.46583	+	1.46583i	−0.103910	+	0.103910i	−0.757151	−	0.653240i	$-0.773409\pi$
$199$	−1.46583	+	1.46583i	−0.103910	+	0.103910i	0.653240	+	0.757151i	$0.273409\pi$
$200$		0			0
$201$	−2.02233	−	13.4952i	−0.142644	−	0.951879i
$202$		0			0
$203$	33.1932			2.32970
$204$		0			0
$205$	−6.80747			−0.475454
$206$		0			0
$207$	−7.33345	+	13.8186i	−0.509710	+	0.960458i
$208$		0			0
$209$	5.73644	−	5.73644i	0.396798	−	0.396798i
$210$		0			0
$211$	6.07386	+	6.07386i	0.418142	+	0.418142i	0.884563	−	0.466421i	$-0.154457\pi$
$211$	6.07386	+	6.07386i	0.418142	+	0.418142i	−0.466421	+	0.884563i	$0.654457\pi$
$212$		0			0
$213$	−12.3071	−	9.09926i	−0.843270	−	0.623471i
$214$		0			0
$215$	−0.538202	+	0.538202i	−0.0367051	+	0.0367051i
$216$		0			0
$217$	13.9709			0.948407
$218$		0			0
$219$	17.2514	+	12.7548i	1.16574	+	0.861890i
$220$		0			0
$221$	−17.8178	+	4.43609i	−1.19855	+	0.298404i
$222$		0			0
$223$	−3.15398			−0.211206			−0.105603	−	0.994408i	$-0.533677\pi$
$223$	−3.15398			−0.211206			−0.105603	+	0.994408i	$0.533677\pi$
$224$		0			0
$225$	2.14022	+	6.98057i	0.142681	+	0.465371i
$226$		0			0
$227$	−17.2170	+	17.2170i	−1.14273	+	1.14273i	−0.154782	+	0.987949i	$0.549467\pi$
$227$	−17.2170	+	17.2170i	−1.14273	+	1.14273i	−0.987949	+	0.154782i	$0.950533\pi$
$228$		0			0
$229$			6.12836i			0.404973i	0.979285	+	0.202487i	$0.0649022\pi$
$229$			6.12836i			0.404973i	−0.979285	+	0.202487i	$0.935098\pi$
$230$		0			0
$231$	12.0535	−	1.80628i	0.793061	−	0.118845i
$232$		0			0
$233$	19.5223	−	19.5223i	1.27895	−	1.27895i	0.337688	−	0.941258i	$-0.390355\pi$
$233$	19.5223	−	19.5223i	1.27895	−	1.27895i	0.941258	−	0.337688i	$-0.109645\pi$
$234$		0			0
$235$	13.4081	−	13.4081i	0.874647	−	0.874647i
$236$		0			0
$237$	−19.0155	−	14.0591i	−1.23519	−	0.913235i
$238$		0			0
$239$	9.81380			0.634802			0.317401	−	0.948291i	$-0.397190\pi$
$239$	9.81380			0.634802			0.317401	+	0.948291i	$0.397190\pi$
$240$		0			0
$241$	−18.7743	−	18.7743i	−1.20936	−	1.20936i	−0.971236	−	0.238120i	$-0.923469\pi$
$241$	−18.7743	−	18.7743i	−1.20936	−	1.20936i	−0.238120	−	0.971236i	$-0.576531\pi$
$242$		0			0
$243$	−11.4722	+	10.5541i	−0.735939	+	0.677048i
$244$		0			0
$245$	−5.29559	−	5.29559i	−0.338323	−	0.338323i
$246$		0			0
$247$	17.5428			1.11622
$248$		0			0
$249$	−1.80283	−	12.0304i	−0.114250	−	0.762398i
$250$		0			0
$251$	13.1996			0.833149			0.416574	−	0.909102i	$-0.363231\pi$
$251$	13.1996			0.833149			0.416574	+	0.909102i	$0.363231\pi$
$252$		0			0
$253$			10.7392i			0.675166i
$254$		0			0
$255$	−4.37735	+	10.5696i	−0.274120	+	0.661895i
$256$		0			0
$257$	5.73644			0.357829			0.178915	−	0.983865i	$-0.442741\pi$
$257$	5.73644			0.357829			0.178915	+	0.983865i	$0.442741\pi$
$258$		0			0
$259$		−	7.40333i		−	0.460021i
$260$		0			0
$261$	−13.6617	+	25.7430i	−0.845636	+	1.59345i
$262$		0			0
$263$			15.2225i			0.938662i	0.883022	+	0.469331i	$0.155505\pi$
$263$			15.2225i			0.938662i	−0.883022	+	0.469331i	$0.844495\pi$
$264$		0			0
$265$	−9.64590	+	9.64590i	−0.592543	+	0.592543i
$266$		0			0
$267$	0.581533	+	3.88062i	0.0355892	+	0.237490i
$268$		0			0
$269$	−3.21989	+	3.21989i	−0.196320	+	0.196320i	−0.798421	−	0.602100i	$-0.794331\pi$
$269$	−3.21989	+	3.21989i	−0.196320	+	0.196320i	0.602100	+	0.798421i	$0.294331\pi$
$270$		0			0
$271$			5.36462i			0.325877i	0.986636	+	0.162939i	$0.0520973\pi$
$271$			5.36462i			0.325877i	−0.986636	+	0.162939i	$0.947903\pi$
$272$		0			0
$273$	21.1925	+	15.6687i	1.28263	+	0.948311i
$274$		0			0
$275$	3.54413	+	3.54413i	0.213719	+	0.213719i
$276$		0			0
$277$	17.2618	+	17.2618i	1.03716	+	1.03716i	0.999282	+	0.0378764i	$0.0120593\pi$
$277$	17.2618	+	17.2618i	1.03716	+	1.03716i	0.0378764	+	0.999282i	$0.487941\pi$
$278$		0			0
$279$	−5.75016	+	10.8352i	−0.344253	+	0.648684i
$280$		0			0
$281$	−9.57553			−0.571228			−0.285614	−	0.958345i	$-0.592198\pi$
$281$	−9.57553			−0.571228			−0.285614	+	0.958345i	$0.592198\pi$
$282$		0			0
$283$	−1.32948	−	1.32948i	−0.0790291	−	0.0790291i	0.666487	−	0.745516i	$-0.267797\pi$
$283$	−1.32948	−	1.32948i	−0.0790291	−	0.0790291i	−0.745516	+	0.666487i	$0.767797\pi$
$284$		0			0
$285$	6.49794	−	8.78873i	0.384905	−	0.520600i
$286$		0			0
$287$		−	14.5200i		−	0.857086i
$288$		0			0
$289$	15.0155	−	7.97090i	0.883264	−	0.468877i
$290$		0			0
$291$	−19.5124	−	14.4265i	−1.14384	−	0.845697i
$292$		0			0
$293$			10.7810i			0.629831i	0.949120	+	0.314916i	$0.101976\pi$
$293$			10.7810i			0.629831i	−0.949120	+	0.314916i	$0.898024\pi$
$294$		0			0
$295$	−2.15333	−	2.15333i	−0.125372	−	0.125372i
$296$		0			0
$297$	−3.56012	+	10.0915i	−0.206579	+	0.585569i
$298$		0			0
$299$	−16.4209	+	16.4209i	−0.949647	+	0.949647i
$300$		0			0
$301$	−1.14796	−	1.14796i	−0.0661671	−	0.0661671i
$302$		0			0
$303$	−1.54263	−	10.2941i	−0.0886221	−	0.591383i
$304$		0			0
$305$			7.45543i			0.426897i
$306$		0			0
$307$			23.0830i			1.31742i	0.752397	+	0.658710i	$0.228897\pi$
$307$			23.0830i			1.31742i	−0.752397	+	0.658710i	$0.771103\pi$
$308$		0			0
$309$	−0.824310	−	5.50070i	−0.0468934	−	0.312924i
$310$		0			0
$311$	−15.5241	−	15.5241i	−0.880290	−	0.880290i	0.113273	−	0.993564i	$-0.463866\pi$
$311$	−15.5241	−	15.5241i	−0.880290	−	0.880290i	−0.993564	+	0.113273i	$0.963866\pi$
$312$		0			0
$313$	−10.5621	+	10.5621i	−0.597006	+	0.597006i	−0.939515	−	0.342509i	$-0.888723\pi$
$313$	−10.5621	+	10.5621i	−0.597006	+	0.597006i	0.342509	+	0.939515i	$0.388723\pi$
$314$		0			0
$315$	15.6996	−	4.81344i	0.884573	−	0.271207i
$316$		0			0
$317$	8.34788	+	8.34788i	0.468864	+	0.468864i	0.901546	−	0.432682i	$-0.142433\pi$
$317$	8.34788	+	8.34788i	0.468864	+	0.468864i	−0.432682	+	0.901546i	$0.642433\pi$
$318$		0			0
$319$			20.0063i			1.12014i
$320$		0			0
$321$	−25.1221	−	18.5740i	−1.40218	−	1.03670i
$322$		0			0
$323$	−15.7607	+	3.92396i	−0.876951	+	0.218335i
$324$		0			0
$325$			10.8384i			0.601208i
$326$		0			0
$327$	14.0029	−	18.9396i	0.774365	−	1.04736i
$328$		0			0
$329$	28.5987	+	28.5987i	1.57670	+	1.57670i
$330$		0			0
$331$	−6.45307			−0.354693			−0.177347	−	0.984148i	$-0.556751\pi$
$331$	−6.45307			−0.354693			−0.177347	+	0.984148i	$0.556751\pi$
$332$		0			0
$333$	5.74166	+	3.04707i	0.314641	+	0.166978i
$334$		0			0
$335$	−8.92431	−	8.92431i	−0.487587	−	0.487587i
$336$		0			0
$337$	−10.1925	−	10.1925i	−0.555223	−	0.555223i	0.372721	−	0.927944i	$-0.378425\pi$
$337$	−10.1925	−	10.1925i	−0.555223	−	0.555223i	−0.927944	+	0.372721i	$0.878425\pi$
$338$		0			0
$339$	1.45623	+	1.07666i	0.0790917	+	0.0584764i
$340$		0			0
$341$			8.42058i			0.456000i
$342$		0			0
$343$	−5.61743	+	5.61743i	−0.303313	+	0.303313i
$344$		0			0
$345$	2.14429	+	14.3091i	0.115445	+	0.770374i
$346$		0			0
$347$	21.1409	−	21.1409i	1.13490	−	1.13490i	0.145554	−	0.989350i	$-0.453504\pi$
$347$	21.1409	−	21.1409i	1.13490	−	1.13490i	0.989350	−	0.145554i	$-0.0464964\pi$
$348$		0			0
$349$		−	20.5817i		−	1.10171i	−0.834600	−	0.550857i	$-0.814301\pi$
$349$		−	20.5817i		−	1.10171i	0.834600	−	0.550857i	$-0.185699\pi$
$350$		0			0
$351$	−20.8743	+	9.98697i	−1.11419	+	0.533065i
$352$		0			0
$353$		−	31.0426i		−	1.65223i	−0.563501	−	0.826115i	$-0.690546\pi$
$353$		−	31.0426i		−	1.65223i	0.563501	−	0.826115i	$-0.309454\pi$
$354$		0			0
$355$	−14.1559			−0.751319
$356$		0			0
$357$	−22.5444	−	9.33665i	−1.19318	−	0.494148i
$358$		0			0
$359$			7.18771i			0.379353i	0.981847	+	0.189676i	$0.0607439\pi$
$359$			7.18771i			0.379353i	−0.981847	+	0.189676i	$0.939256\pi$
$360$		0			0
$361$	−3.48246			−0.183287
$362$		0			0
$363$	−1.73492	−	11.5773i	−0.0910595	−	0.607649i
$364$		0			0
$365$	19.8430			1.03863
$366$		0			0
$367$	−19.0660	−	19.0660i	−0.995235	−	0.995235i	0.00475336	−	0.999989i	$-0.498487\pi$
$367$	−19.0660	−	19.0660i	−0.995235	−	0.995235i	−0.999989	+	0.00475336i	$0.998487\pi$
$368$		0			0
$369$	11.2610	+	5.97614i	0.586223	+	0.311105i
$370$		0			0
$371$	−20.5742	−	20.5742i	−1.06816	−	1.06816i
$372$		0			0
$373$	30.0993			1.55848			0.779240	−	0.626725i	$-0.215605\pi$
$373$	30.0993			1.55848			0.779240	+	0.626725i	$0.215605\pi$
$374$		0			0
$375$	16.5853	+	12.2623i	0.856462	+	0.633224i
$376$		0			0
$377$	−30.5910	+	30.5910i	−1.57552	+	1.57552i
$378$		0			0
$379$	9.15063	−	9.15063i	0.470036	−	0.470036i	−0.431890	−	0.901926i	$-0.642153\pi$
$379$	9.15063	−	9.15063i	0.470036	−	0.470036i	0.901926	+	0.431890i	$0.142153\pi$
$380$		0			0
$381$	16.8370	−	2.52311i	0.862584	−	0.129263i
$382$		0			0
$383$		−	21.0475i		−	1.07548i	−0.843112	−	0.537738i	$-0.819279\pi$
$383$		−	21.0475i		−	1.07548i	0.843112	−	0.537738i	$-0.180721\pi$
$384$		0			0
$385$	7.97090	−	7.97090i	0.406235	−	0.406235i
$386$		0			0
$387$	1.36278	−	0.417822i	0.0692738	−	0.0212391i
$388$		0			0
$389$	17.8178			0.903396			0.451698	−	0.892171i	$-0.350818\pi$
$389$	17.8178			0.903396			0.451698	+	0.892171i	$0.350818\pi$
$390$		0			0
$391$	11.0798	−	18.4258i	0.560330	−	0.931834i
$392$		0			0
$393$	−10.5969	−	7.83481i	−0.534543	−	0.395214i
$394$		0			0
$395$	−21.8720			−1.10050
$396$		0			0
$397$	−7.33544	+	7.33544i	−0.368155	+	0.368155i	−0.866804	−	0.498649i	$-0.833830\pi$
$397$	−7.33544	+	7.33544i	−0.368155	+	0.368155i	0.498649	+	0.866804i	$0.333830\pi$
$398$		0			0
$399$	18.7459	+	13.8598i	0.938469	+	0.693856i
$400$		0			0
$401$	8.28968	+	8.28968i	0.413967	+	0.413967i	0.883118	−	0.469151i	$-0.155440\pi$
$401$	8.28968	+	8.28968i	0.413967	+	0.413967i	−0.469151	+	0.883118i	$0.655440\pi$
$402$		0			0
$403$	−12.8757	+	12.8757i	−0.641382	+	0.641382i
$404$		0			0
$405$	−2.72859	+	14.1570i	−0.135585	+	0.703466i
$406$		0			0
$407$	4.46216			0.221181
$408$		0			0
$409$	28.8931			1.42867			0.714336	−	0.699803i	$-0.246729\pi$
$409$	28.8931			1.42867			0.714336	+	0.699803i	$0.246729\pi$
$410$		0			0
$411$	3.68270	+	24.5750i	0.181654	+	1.21220i
$412$		0			0
$413$	4.59293	−	4.59293i	0.226004	−	0.226004i
$414$		0			0
$415$	−7.95567	−	7.95567i	−0.390529	−	0.390529i
$416$		0			0
$417$	−21.7460	+	29.4124i	−1.06491	+	1.44033i
$418$		0			0
$419$	0.0934578	−	0.0934578i	0.00456571	−	0.00456571i	−0.704820	−	0.709386i	$-0.748972\pi$
$419$	0.0934578	−	0.0934578i	0.00456571	−	0.00456571i	0.709386	+	0.704820i	$0.248972\pi$
$420$		0			0
$421$	−0.935822			−0.0456092			−0.0228046	−	0.999740i	$-0.507260\pi$
$421$	−0.935822			−0.0456092			−0.0228046	+	0.999740i	$0.507260\pi$
$422$		0			0
$423$	−33.9505	+	10.4091i	−1.65073	+	0.506107i
$424$		0			0
$425$	−2.42432	−	9.73741i	−0.117597	−	0.472334i
$426$		0			0
$427$	−15.9020			−0.769553
$428$		0			0
$429$	−9.44387	+	12.7732i	−0.455954	+	0.616697i
$430$		0			0
$431$	−10.1724	+	10.1724i	−0.489989	+	0.489989i	−0.908303	−	0.418313i	$-0.862621\pi$
$431$	−10.1724	+	10.1724i	−0.489989	+	0.489989i	0.418313	+	0.908303i	$0.362621\pi$
$432$		0			0
$433$			32.7101i			1.57195i	0.618261	+	0.785973i	$0.287838\pi$
$433$			32.7101i			1.57195i	−0.618261	+	0.785973i	$0.712162\pi$
$434$		0			0
$435$	3.99466	+	26.6567i	0.191529	+	1.27809i
$436$		0			0
$437$	−14.5252	+	14.5252i	−0.694833	+	0.694833i
$438$		0			0
$439$	16.8927	−	16.8927i	0.806246	−	0.806246i	−0.177817	−	0.984064i	$-0.556904\pi$
$439$	16.8927	−	16.8927i	0.806246	−	0.806246i	0.984064	+	0.177817i	$0.0569036\pi$
$440$		0			0
$441$	4.11112	+	13.4089i	0.195768	+	0.638519i
$442$		0			0
$443$	−23.4443			−1.11387			−0.556936	−	0.830556i	$-0.688023\pi$
$443$	−23.4443			−1.11387			−0.556936	+	0.830556i	$0.688023\pi$
$444$		0			0
$445$	2.56624	+	2.56624i	0.121651	+	0.121651i
$446$		0			0
$447$	−0.177604	−	1.18517i	−0.00840040	−	0.0560567i
$448$		0			0
$449$	28.7296	+	28.7296i	1.35584	+	1.35584i	0.878984	+	0.476852i	$0.158222\pi$
$449$	28.7296	+	28.7296i	1.35584	+	1.35584i	0.476852	+	0.878984i	$0.341778\pi$
$450$		0			0
$451$	8.75151			0.412093
$452$		0			0
$453$	13.2126	−	1.97998i	0.620780	−	0.0930274i
$454$		0			0
$455$	24.3761			1.14277
$456$		0			0
$457$			22.3250i			1.04432i	0.852848	+	0.522160i	$0.174874\pi$
$457$			22.3250i			1.04432i	−0.852848	+	0.522160i	$0.825126\pi$
$458$		0			0
$459$	16.5199	−	13.6416i	0.771083	−	0.636734i
$460$		0			0
$461$	−33.5813			−1.56404			−0.782019	−	0.623254i	$-0.785810\pi$
$461$	−33.5813			−1.56404			−0.782019	+	0.623254i	$0.785810\pi$
$462$		0			0
$463$			10.9751i			0.510058i	0.966933	+	0.255029i	$0.0820850\pi$
$463$			10.9751i			0.510058i	−0.966933	+	0.255029i	$0.917915\pi$
$464$		0			0
$465$	1.68134	+	11.2197i	0.0779703	+	0.520303i
$466$		0			0
$467$		−	38.0066i		−	1.75874i	−0.476143	−	0.879368i	$-0.657965\pi$
$467$		−	38.0066i		−	1.75874i	0.476143	−	0.879368i	$-0.342035\pi$
$468$		0			0
$469$	19.0351	−	19.0351i	0.878958	−	0.878958i
$470$		0			0
$471$	37.2976	−	5.58926i	1.71858	−	0.257539i
$472$		0			0
$473$	0.691899	−	0.691899i	0.0318136	−	0.0318136i
$474$		0			0
$475$			9.58715i			0.439889i
$476$		0			0
$477$	24.4243	−	7.48839i	1.11831	−	0.342870i
$478$		0			0
$479$	−16.5356	−	16.5356i	−0.755530	−	0.755530i	0.219975	−	0.975505i	$-0.429402\pi$
$479$	−16.5356	−	16.5356i	−0.755530	−	0.755530i	−0.975505	+	0.219975i	$0.929402\pi$
$480$		0			0
$481$	6.82295	+	6.82295i	0.311100	+	0.311100i
$482$		0			0
$483$	−30.5205	+	4.57366i	−1.38873	+	0.208109i
$484$		0			0
$485$	−22.4437			−1.01911
$486$		0			0
$487$	−0.465178	−	0.465178i	−0.0210792	−	0.0210792i	0.696489	−	0.717568i	$-0.254745\pi$
$487$	−0.465178	−	0.465178i	−0.0210792	−	0.0210792i	−0.717568	+	0.696489i	$0.754745\pi$
$488$		0			0
$489$	8.00774	+	5.92051i	0.362123	+	0.267735i
$490$		0			0
$491$		−	3.38575i		−	0.152797i	−0.997077	−	0.0763984i	$-0.975658\pi$
$491$		−	3.38575i		−	0.152797i	0.997077	−	0.0763984i	$-0.0243421\pi$
$492$		0			0
$493$	20.6408	−	34.3259i	0.929617	−	1.54596i
$494$		0			0
$495$	2.90117	+	9.46252i	0.130398	+	0.425308i
$496$		0			0
$497$		−	30.1938i		−	1.35438i
$498$		0			0
$499$	16.7564	+	16.7564i	0.750119	+	0.750119i	0.974501	−	0.224383i	$-0.0720365\pi$
$499$	16.7564	+	16.7564i	0.750119	+	0.750119i	−0.224383	+	0.974501i	$0.572037\pi$
$500$		0			0
$501$	14.9913	+	11.0838i	0.669760	+	0.495187i
$502$		0			0
$503$	22.5474	−	22.5474i	1.00534	−	1.00534i	0.00535448	−	0.999986i	$-0.498296\pi$
$503$	22.5474	−	22.5474i	1.00534	−	1.00534i	0.999986	−	0.00535448i	$-0.00170439\pi$
$504$		0			0
$505$	−6.80747	−	6.80747i	−0.302928	−	0.302928i
$506$		0			0
$507$	−11.7035	+	1.75383i	−0.519769	+	0.0778902i
$508$		0			0
$509$			2.81200i			0.124640i	0.998056	+	0.0623199i	$0.0198499\pi$
$509$			2.81200i			0.124640i	−0.998056	+	0.0623199i	$0.980150\pi$
$510$		0			0
$511$			42.3240i			1.87230i
$512$		0			0
$513$	−18.4644	+	8.83399i	−0.815223	+	0.390030i
$514$		0			0
$515$	−3.63758	−	3.63758i	−0.160291	−	0.160291i
$516$		0			0
$517$	−17.2371	+	17.2371i	−0.758087	+	0.758087i
$518$		0			0
$519$	3.80287	−	5.14354i	0.166928	−	0.225777i
$520$		0			0
$521$	−11.7606	−	11.7606i	−0.515242	−	0.515242i	0.400886	−	0.916128i	$-0.368702\pi$
$521$	−11.7606	−	11.7606i	−0.515242	−	0.515242i	−0.916128	+	0.400886i	$0.868702\pi$
$522$		0			0
$523$			36.3659i			1.59017i	0.606497	+	0.795086i	$0.292574\pi$
$523$			36.3659i			1.59017i	−0.606497	+	0.795086i	$0.707426\pi$
$524$		0			0
$525$	−8.56293	+	11.5817i	−0.373717	+	0.505468i
$526$		0			0
$527$	8.68767	−	14.4477i	0.378441	−	0.629351i
$528$		0			0
$529$		−	4.19253i		−	0.182284i
$530$		0			0
$531$	1.67169	+	5.45242i	0.0725452	+	0.236615i
$532$		0			0
$533$	13.3817	+	13.3817i	0.579624	+	0.579624i
$534$		0			0
$535$	−28.8960			−1.24928
$536$		0			0
$537$	0.349812	+	2.33433i	0.0150955	+	0.100734i
$538$		0			0
$539$	6.80788	+	6.80788i	0.293236	+	0.293236i
$540$		0			0
$541$	−6.80840	−	6.80840i	−0.292716	−	0.292716i	0.545436	−	0.838152i	$-0.316364\pi$
$541$	−6.80840	−	6.80840i	−0.292716	−	0.292716i	−0.838152	+	0.545436i	$0.816364\pi$
$542$		0			0
$543$	−9.95699	+	13.4672i	−0.427295	+	0.577935i
$544$		0			0
$545$		−	21.7847i		−	0.933155i
$546$		0			0
$547$	16.8840	−	16.8840i	0.721907	−	0.721907i	−0.247086	−	0.968993i	$-0.579473\pi$
$547$	16.8840	−	16.8840i	0.721907	−	0.721907i	0.968993	+	0.247086i	$0.0794732\pi$
$548$		0			0
$549$	6.54497	−	12.3328i	0.279333	−	0.526353i
$550$		0			0
$551$	−27.0593	+	27.0593i	−1.15277	+	1.15277i
$552$		0			0
$553$		−	46.6519i		−	1.98384i
$554$		0			0
$555$	5.94546	−	0.890960i	0.252371	−	0.0378192i
$556$		0			0
$557$			2.86250i			0.121288i	0.998159	+	0.0606439i	$0.0193154\pi$
$557$			2.86250i			0.121288i	−0.998159	+	0.0606439i	$0.980685\pi$
$558$		0			0
$559$	2.11592			0.0894940
$560$		0			0
$561$	5.62741	−	13.5880i	0.237590	−	0.573688i
$562$		0			0
$563$			5.70293i			0.240350i	0.992753	+	0.120175i	$0.0383456\pi$
$563$			5.70293i			0.240350i	−0.992753	+	0.120175i	$0.961654\pi$
$564$		0			0
$565$	1.67499			0.0704675
$566$		0			0
$567$	−30.1961	−	5.81994i	−1.26812	−	0.244414i
$568$		0			0
$569$	−18.8664			−0.790919			−0.395460	−	0.918483i	$-0.629415\pi$
$569$	−18.8664			−0.790919			−0.395460	+	0.918483i	$0.629415\pi$
$570$		0			0
$571$	−5.28861	−	5.28861i	−0.221321	−	0.221321i	0.587733	−	0.809055i	$-0.300020\pi$
$571$	−5.28861	−	5.28861i	−0.221321	−	0.221321i	−0.809055	+	0.587733i	$0.800020\pi$
$572$		0			0
$573$	23.7407	−	3.55768i	0.991783	−	0.148624i
$574$		0			0
$575$	−8.97404	−	8.97404i	−0.374243	−	0.374243i
$576$		0			0
$577$	−34.4005			−1.43211			−0.716057	−	0.698042i	$-0.754055\pi$
$577$	−34.4005			−1.43211			−0.716057	+	0.698042i	$0.754055\pi$
$578$		0			0
$579$	1.57823	−	2.13463i	0.0655891	−	0.0887120i
$580$		0			0
$581$	16.9690	−	16.9690i	0.703994	−	0.703994i
$582$		0			0
$583$	12.4005	−	12.4005i	0.513577	−	0.513577i
$584$		0			0
$585$	−10.0328	+	18.9049i	−0.414803	+	0.781623i
$586$		0			0
$587$		−	25.0363i		−	1.03336i	−0.856179	−	0.516680i	$-0.827168\pi$
$587$		−	25.0363i		−	1.03336i	0.856179	−	0.516680i	$-0.172832\pi$
$588$		0			0
$589$	−11.3892	+	11.3892i	−0.469283	+	0.469283i
$590$		0			0
$591$	27.3894	+	20.2503i	1.12665	+	0.832987i
$592$		0			0
$593$	26.5446			1.09005			0.545027	−	0.838418i	$-0.316519\pi$
$593$	26.5446			1.09005			0.545027	+	0.838418i	$0.316519\pi$
$594$		0			0
$595$	−21.8999	+	5.45242i	−0.897808	+	0.223527i
$596$		0			0
$597$	2.13459	−	2.88713i	0.0873631	−	0.118162i
$598$		0			0
$599$	8.92431			0.364638			0.182319	−	0.983239i	$-0.441640\pi$
$599$	8.92431			0.364638			0.182319	+	0.983239i	$0.441640\pi$
$600$		0			0
$601$	−32.1789	+	32.1789i	−1.31261	+	1.31261i	−0.393117	+	0.919488i	$0.628603\pi$
$601$	−32.1789	+	32.1789i	−1.31261	+	1.31261i	−0.919488	+	0.393117i	$0.871397\pi$
$602$		0			0
$603$	6.92820	+	22.5972i	0.282138	+	0.920227i
$604$		0			0
$605$	−7.65599	−	7.65599i	−0.311260	−	0.311260i
$606$		0			0
$607$	−9.23659	+	9.23659i	−0.374902	+	0.374902i	−0.869259	−	0.494357i	$-0.835403\pi$
$607$	−9.23659	+	9.23659i	−0.374902	+	0.374902i	0.494357	+	0.869259i	$0.335403\pi$
$608$		0			0
$609$	−56.8574	+	8.52039i	−2.30398	+	0.345264i
$610$		0			0
$611$	−52.7135			−2.13256
$612$		0			0
$613$	5.51754			0.222851			0.111426	−	0.993773i	$-0.464458\pi$
$613$	5.51754			0.222851			0.111426	+	0.993773i	$0.464458\pi$
$614$		0			0
$615$	11.6607	−	1.74742i	0.470204	−	0.0704627i
$616$		0			0
$617$	−5.41574	+	5.41574i	−0.218029	+	0.218029i	−0.807668	−	0.589638i	$-0.799270\pi$
$617$	−5.41574	+	5.41574i	−0.218029	+	0.218029i	0.589638	+	0.807668i	$0.299270\pi$
$618$		0			0
$619$	19.5124	+	19.5124i	0.784271	+	0.784271i	0.980548	−	0.196277i	$-0.0628852\pi$
$619$	19.5124	+	19.5124i	0.784271	+	0.784271i	−0.196277	+	0.980548i	$0.562885\pi$
$620$		0			0
$621$	9.01454	−	25.5526i	0.361741	−	1.02539i
$622$		0			0
$623$	−5.47365	+	5.47365i	−0.219297	+	0.219297i
$624$		0			0
$625$	6.90798			0.276319
$626$		0			0
$627$	−8.35359	+	11.2986i	−0.333610	+	0.451222i
$628$		0			0
$629$	−7.65599	−	4.60369i	−0.305264	−	0.183561i
$630$		0			0
$631$	33.3876			1.32914			0.664569	−	0.747227i	$-0.268615\pi$
$631$	33.3876			1.32914			0.664569	+	0.747227i	$0.268615\pi$
$632$		0			0
$633$	−11.9632	−	8.84495i	−0.475493	−	0.351555i
$634$		0			0
$635$	11.1342	−	11.1342i	0.441848	−	0.441848i
$636$		0			0
$637$			20.8194i			0.824896i
$638$		0			0
$639$	23.4169	+	12.4272i	0.926357	+	0.491613i
$640$		0			0
$641$	26.2858	−	26.2858i	1.03823	−	1.03823i	0.0389867	−	0.999240i	$-0.487587\pi$
$641$	26.2858	−	26.2858i	1.03823	−	1.03823i	0.999240	−	0.0389867i	$-0.0124130\pi$
$642$		0			0
$643$	3.75552	−	3.75552i	0.148103	−	0.148103i	−0.629167	−	0.777270i	$-0.716604\pi$
$643$	3.75552	−	3.75552i	0.148103	−	0.148103i	0.777270	+	0.629167i	$0.216604\pi$
$644$		0			0
$645$	0.783748	−	1.06005i	0.0308600	−	0.0417395i
$646$		0			0
$647$	40.2589			1.58274			0.791370	−	0.611338i	$-0.209368\pi$
$647$	40.2589			1.58274			0.791370	+	0.611338i	$0.209368\pi$
$648$		0			0
$649$	2.76827	+	2.76827i	0.108664	+	0.108664i
$650$		0			0
$651$	−23.9311	+	3.58621i	−0.937934	+	0.140555i
$652$		0			0
$653$	15.7528	+	15.7528i	0.616455	+	0.616455i	0.944620	−	0.328165i	$-0.106430\pi$
$653$	15.7528	+	15.7528i	0.616455	+	0.616455i	−0.328165	+	0.944620i	$0.606430\pi$
$654$		0			0
$655$	−12.1888			−0.476256
$656$		0			0
$657$	−32.8244	−	17.4197i	−1.28060	−	0.679609i
$658$		0			0
$659$	−11.9588			−0.465848			−0.232924	−	0.972495i	$-0.574829\pi$
$659$	−11.9588			−0.465848			−0.232924	+	0.972495i	$0.574829\pi$
$660$		0			0
$661$			29.9127i			1.16347i	0.813378	+	0.581735i	$0.197626\pi$
$661$			29.9127i			1.16347i	−0.813378	+	0.581735i	$0.802374\pi$
$662$		0			0
$663$	29.3818	−	12.1724i	1.14109	−	0.472735i
$664$		0			0
$665$	21.5620			0.836137
$666$		0			0
$667$		−	50.6577i		−	1.96147i
$668$		0			0
$669$	5.40253	−	0.809600i	0.208874	−	0.0313009i
$670$		0			0
$671$		−	9.58452i		−	0.370006i
$672$		0			0
$673$	−7.21213	+	7.21213i	−0.278007	+	0.278007i	−0.832313	−	0.554306i	$-0.812984\pi$
$673$	−7.21213	+	7.21213i	−0.278007	+	0.278007i	0.554306	+	0.832313i	$0.312984\pi$
$674$		0			0
$675$	−5.45788	−	11.4078i	−0.210074	−	0.439087i
$676$		0			0
$677$	−8.86143	+	8.86143i	−0.340572	+	0.340572i	−0.856583	−	0.516010i	$-0.827417\pi$
$677$	−8.86143	+	8.86143i	−0.340572	+	0.340572i	0.516010	+	0.856583i	$0.327417\pi$
$678$		0			0
$679$		−	47.8711i		−	1.83712i
$680$		0			0
$681$	25.0719	−	33.9108i	0.960758	−	1.29946i
$682$		0			0
$683$	−20.1294	−	20.1294i	−0.770231	−	0.770231i	0.207915	−	0.978147i	$-0.433332\pi$
$683$	−20.1294	−	20.1294i	−0.770231	−	0.770231i	−0.978147	+	0.207915i	$0.933332\pi$
$684$		0			0
$685$	16.2513	+	16.2513i	0.620932	+	0.620932i
$686$		0			0
$687$	−1.57310	−	10.4974i	−0.0600173	−	0.400501i
$688$		0			0
$689$	37.9225			1.44473
$690$		0			0
$691$	−9.20794	−	9.20794i	−0.350286	−	0.350286i	0.509930	−	0.860216i	$-0.329671\pi$
$691$	−9.20794	−	9.20794i	−0.350286	−	0.350286i	−0.860216	+	0.509930i	$0.829671\pi$
$692$		0			0
$693$	−20.1830	+	6.18804i	−0.766690	+	0.235064i
$694$		0			0
$695$			33.8308i			1.28328i
$696$		0			0
$697$	−15.0155	−	9.02910i	−0.568752	−	0.342001i
$698$		0			0
$699$	−28.4290	+	38.4513i	−1.07528	+	1.45436i
$700$		0			0
$701$			47.7498i			1.80349i	0.432273	+	0.901743i	$0.357712\pi$
$701$			47.7498i			1.80349i	−0.432273	+	0.901743i	$0.642288\pi$
$702$		0			0
$703$	6.03525	+	6.03525i	0.227624	+	0.227624i
$704$		0			0
$705$	−19.5253	+	26.4088i	−0.735366	+	0.994612i
$706$		0			0
$707$	14.5200	−	14.5200i	0.546079	−	0.546079i
$708$		0			0
$709$	−16.6064	−	16.6064i	−0.623665	−	0.623665i	0.322801	−	0.946467i	$-0.395375\pi$
$709$	−16.6064	−	16.6064i	−0.623665	−	0.623665i	−0.946467	+	0.322801i	$0.895375\pi$
$710$		0			0
$711$	36.1809	+	19.2010i	1.35689	+	0.720095i
$712$		0			0
$713$		−	21.3217i		−	0.798503i
$714$		0			0
$715$			14.6921i			0.549452i
$716$		0			0
$717$	−16.8103	+	2.51912i	−0.627792	+	0.0940781i
$718$		0			0
$719$	26.4714	+	26.4714i	0.987216	+	0.987216i	0.999919	−	0.0127033i	$-0.00404369\pi$
$719$	26.4714	+	26.4714i	0.987216	+	0.987216i	−0.0127033	+	0.999919i	$0.504044\pi$
$720$		0			0
$721$	7.75877	−	7.75877i	0.288952	−	0.288952i
$722$		0			0
$723$	36.9781	+	27.3397i	1.37523	+	1.01677i
$724$		0			0
$725$	−16.7180	−	16.7180i	−0.620890	−	0.620890i
$726$		0			0
$727$		−	25.5290i		−	0.946818i	−0.880843	−	0.473409i	$-0.843023\pi$
$727$		−	25.5290i		−	0.946818i	0.880843	−	0.473409i	$-0.156977\pi$
$728$		0			0
$729$	16.9418	−	21.0232i	0.627474	−	0.778638i
$730$		0			0
$731$	−1.90098	+	0.473287i	−0.0703102	+	0.0175051i
$732$		0			0
$733$		−	17.2627i		−	0.637612i	−0.947820	−	0.318806i	$-0.896718\pi$
$733$		−	17.2627i		−	0.637612i	0.947820	−	0.318806i	$-0.103282\pi$
$734$		0			0
$735$	10.4303	+	7.71161i	0.384726	+	0.284447i
$736$		0			0
$737$	11.4729	+	11.4729i	0.422609	+	0.422609i
$738$		0			0
$739$	−53.8315			−1.98023			−0.990113	−	0.140274i	$-0.955202\pi$
$739$	−53.8315			−1.98023			−0.990113	+	0.140274i	$0.955202\pi$
$740$		0			0
$741$	−30.0495	+	4.50309i	−1.10390	+	0.165425i
$742$		0			0
$743$	15.6461	+	15.6461i	0.573999	+	0.573999i	0.933244	−	0.359244i	$-0.116965\pi$
$743$	15.6461	+	15.6461i	0.573999	+	0.573999i	−0.359244	+	0.933244i	$0.616965\pi$
$744$		0			0
$745$	−0.783748	−	0.783748i	−0.0287143	−	0.0287143i
$746$		0			0
$747$	6.17622	+	20.1445i	0.225976	+	0.737048i
$748$		0			0
$749$		−	61.6336i		−	2.25204i
$750$		0			0
$751$	22.4224	−	22.4224i	0.818204	−	0.818204i	−0.167644	−	0.985848i	$-0.553616\pi$
$751$	22.4224	−	22.4224i	0.818204	−	0.818204i	0.985848	+	0.167644i	$0.0536159\pi$
$752$		0			0
$753$	−22.6098	+	3.38821i	−0.823948	+	0.123473i
$754$		0			0
$755$	8.73740	−	8.73740i	0.317986	−	0.317986i
$756$		0			0
$757$		−	44.2877i		−	1.60966i	−0.593503	−	0.804831i	$-0.702256\pi$
$757$		−	44.2877i		−	1.60966i	0.593503	−	0.804831i	$-0.297744\pi$
$758$		0			0
$759$	−2.75665	−	18.3954i	−0.100060	−	0.667710i
$760$		0			0
$761$		−	42.8507i		−	1.55334i	−0.629911	−	0.776668i	$-0.716909\pi$
$761$		−	42.8507i		−	1.55334i	0.629911	−	0.776668i	$-0.283091\pi$
$762$		0			0
$763$	46.4656			1.68217
$764$		0			0
$765$	4.78494	−	19.2286i	0.173000	−	0.695211i
$766$		0			0
$767$			8.46574i			0.305680i
$768$		0			0
$769$	−14.7939			−0.533480			−0.266740	−	0.963769i	$-0.585946\pi$
$769$	−14.7939			−0.533480			−0.266740	+	0.963769i	$0.585946\pi$
$770$		0			0
$771$	−9.82608	+	1.47249i	−0.353878	+	0.0530306i
$772$		0			0
$773$	7.24809			0.260696			0.130348	−	0.991468i	$-0.458391\pi$
$773$	7.24809			0.260696			0.130348	+	0.991468i	$0.458391\pi$
$774$		0			0
$775$	−7.03654	−	7.03654i	−0.252760	−	0.252760i
$776$		0			0
$777$	1.90037	+	12.6813i	0.0681754	+	0.454941i
$778$		0			0
$779$	11.8368	+	11.8368i	0.424097	+	0.424097i
$780$		0			0
$781$	18.1985			0.651194
$782$		0			0
$783$	16.7934	−	47.6026i	0.600147	−	1.70118i
$784$		0			0
$785$	24.6647	−	24.6647i	0.880323	−	0.880323i
$786$		0			0
$787$	−25.6928	+	25.6928i	−0.915849	+	0.915849i	−0.996724	−	0.0808748i	$-0.974229\pi$
$787$	−25.6928	+	25.6928i	−0.915849	+	0.915849i	0.0808748	+	0.996724i	$0.474229\pi$
$788$		0			0
$789$	−3.90749	−	26.0750i	−0.139110	−	0.928296i
$790$		0			0
$791$			3.57267i			0.127029i
$792$		0			0
$793$	14.6554	−	14.6554i	0.520428	−	0.520428i
$794$		0			0
$795$	14.0467	−	18.9987i	0.498184	−	0.673815i
$796$		0			0
$797$	−22.3992			−0.793422			−0.396711	−	0.917944i	$-0.629849\pi$
$797$	−22.3992			−0.793422			−0.396711	+	0.917944i	$0.629849\pi$
$798$		0			0
$799$	47.3586	−	11.7909i	1.67543	−	0.417131i
$800$		0			0
$801$	−1.99224	−	6.49794i	−0.0703925	−	0.229593i
$802$		0			0
$803$	−25.5096			−0.900215
$804$		0			0
$805$	−20.1830	+	20.1830i	−0.711359	+	0.711359i
$806$		0			0
$807$	4.68891	−	6.34195i	0.165058	−	0.223247i
$808$		0			0
$809$	24.0533	+	24.0533i	0.845667	+	0.845667i	0.989589	−	0.143922i	$-0.0459713\pi$
$809$	24.0533	+	24.0533i	0.845667	+	0.845667i	−0.143922	+	0.989589i	$0.545971\pi$
$810$		0			0
$811$	0.146308	−	0.146308i	0.00513758	−	0.00513758i	−0.704533	−	0.709671i	$-0.748844\pi$
$811$	0.146308	−	0.146308i	0.00513758	−	0.00513758i	0.709671	+	0.704533i	$0.248844\pi$
$812$		0			0
$813$	−1.37705	−	9.18919i	−0.0482953	−	0.322279i
$814$		0			0
$815$	9.21069			0.322636
$816$		0			0
$817$	1.87164			0.0654806
$818$		0			0
$819$	−40.3232	−	21.3993i	−1.40901	−	0.747753i
$820$		0			0
$821$	24.0785	−	24.0785i	0.840346	−	0.840346i	−0.148558	−	0.988904i	$-0.547463\pi$
$821$	24.0785	−	24.0785i	0.840346	−	0.840346i	0.988904	+	0.148558i	$0.0474632\pi$
$822$		0			0
$823$	−29.8830	−	29.8830i	−1.04166	−	1.04166i	−0.999094	−	0.0425623i	$-0.986448\pi$
$823$	−29.8830	−	29.8830i	−1.04166	−	1.04166i	−0.0425623	−	0.999094i	$-0.513552\pi$
$824$		0			0
$825$	−6.98057	−	5.16107i	−0.243032	−	0.179686i
$826$		0			0
$827$	35.3520	−	35.3520i	1.22931	−	1.22931i	0.265083	−	0.964226i	$-0.414601\pi$
$827$	35.3520	−	35.3520i	1.22931	−	1.22931i	0.964226	−	0.265083i	$-0.0853993\pi$
$828$		0			0
$829$	31.4783			1.09329			0.546644	−	0.837365i	$-0.315905\pi$
$829$	31.4783			1.09329			0.546644	+	0.837365i	$0.315905\pi$
$830$		0			0
$831$	−33.9990	−	25.1372i	−1.17941	−	0.871998i
$832$		0			0
$833$	−4.65686	−	18.7045i	−0.161351	−	0.648072i
$834$		0			0
$835$	17.2433			0.596729
$836$		0			0
$837$	7.06830	−	20.0358i	0.244316	−	0.692539i
$838$		0			0
$839$	21.6579	−	21.6579i	0.747715	−	0.747715i	−0.226335	−	0.974050i	$-0.572674\pi$
$839$	21.6579	−	21.6579i	0.747715	−	0.747715i	0.974050	+	0.226335i	$0.0726742\pi$
$840$		0			0
$841$		−	65.3715i		−	2.25419i
$842$		0			0
$843$	16.4022	−	2.45796i	0.564920	−	0.0846565i
$844$		0			0
$845$	−7.73944	+	7.73944i	−0.266245	+	0.266245i
$846$		0			0
$847$	16.3298	−	16.3298i	0.561099	−	0.561099i
$848$		0			0
$849$	2.61856	+	1.93603i	0.0898686	+	0.0664442i
$850$		0			0
$851$	−11.2986			−0.387310
$852$		0			0
$853$	−3.20708	−	3.20708i	−0.109808	−	0.109808i	0.650068	−	0.759876i	$-0.274740\pi$
$853$	−3.20708	−	3.20708i	−0.109808	−	0.109808i	−0.759876	+	0.650068i	$0.774740\pi$
$854$		0			0
$855$	−8.87449	+	16.7224i	−0.303501	+	0.571894i
$856$		0			0
$857$	11.0687	+	11.0687i	0.378100	+	0.378100i	0.870416	−	0.492316i	$-0.163850\pi$
$857$	11.0687	+	11.0687i	0.378100	+	0.378100i	−0.492316	+	0.870416i	$0.663850\pi$
$858$		0			0
$859$	−16.6231			−0.567172			−0.283586	−	0.958947i	$-0.591524\pi$
$859$	−16.6231			−0.567172			−0.283586	+	0.958947i	$0.591524\pi$
$860$		0			0
$861$	3.72715	+	24.8716i	0.127021	+	0.847622i
$862$		0			0
$863$	5.12236			0.174367			0.0871836	−	0.996192i	$-0.472213\pi$
$863$	5.12236			0.174367			0.0871836	+	0.996192i	$0.472213\pi$
$864$		0			0
$865$		−	5.91622i		−	0.201158i
$866$		0			0
$867$	−23.6743	+	17.5079i	−0.804022	+	0.594599i
$868$		0			0
$869$	28.1182			0.953843
$870$		0			0
$871$			35.0857i			1.18883i
$872$		0			0
$873$	37.1265	+	19.7028i	1.25654	+	0.666840i
$874$		0			0
$875$			40.6898i			1.37557i
$876$		0			0
$877$	7.64496	−	7.64496i	0.258152	−	0.258152i	−0.566150	−	0.824302i	$-0.691568\pi$
$877$	7.64496	−	7.64496i	0.258152	−	0.258152i	0.824302	+	0.566150i	$0.191568\pi$
$878$		0			0
$879$	−2.76738	−	18.4670i	−0.0933415	−	0.622876i
$880$		0			0
$881$	−28.5513	+	28.5513i	−0.961917	+	0.961917i	−0.999301	−	0.0373836i	$-0.988098\pi$
$881$	−28.5513	+	28.5513i	−0.961917	+	0.961917i	0.0373836	+	0.999301i	$0.488098\pi$
$882$		0			0
$883$			2.01513i			0.0678146i	0.999425	+	0.0339073i	$0.0107951\pi$
$883$			2.01513i			0.0678146i	−0.999425	+	0.0339073i	$0.989205\pi$
$884$		0			0
$885$	4.24123	+	3.13575i	0.142567	+	0.105407i
$886$		0			0
$887$	−15.2948	−	15.2948i	−0.513549	−	0.513549i	0.402063	−	0.915612i	$-0.368293\pi$
$887$	−15.2948	−	15.2948i	−0.513549	−	0.513549i	−0.915612	+	0.402063i	$0.868293\pi$
$888$		0			0
$889$	23.7487	+	23.7487i	0.796505	+	0.796505i
$890$		0			0
$891$	3.50781	−	18.1999i	0.117516	−	0.609718i
$892$		0			0
$893$	−46.6278			−1.56034
$894$		0			0
$895$	1.54368	+	1.54368i	0.0515996	+	0.0515996i
$896$		0			0
$897$	23.9127	−	32.3429i	0.798422	−	1.07990i
$898$		0			0
$899$		−	39.7207i		−	1.32476i
$900$		0			0
$901$	−34.0702	+	8.48246i	−1.13504	+	0.282592i
$902$		0			0
$903$	2.26103	+	1.67169i	0.0752424	+	0.0556304i
$904$		0			0
$905$			15.4903i			0.514916i
$906$		0			0
$907$	−38.7335	−	38.7335i	−1.28612	−	1.28612i	−0.937122	−	0.349002i	$-0.886521\pi$
$907$	−38.7335	−	38.7335i	−1.28612	−	1.28612i	−0.349002	−	0.937122i	$-0.613479\pi$
$908$		0			0
$909$	5.28483	+	17.2371i	0.175287	+	0.571719i
$910$		0			0
$911$	−24.3835	+	24.3835i	−0.807861	+	0.807861i	−0.984310	−	0.176449i	$-0.943539\pi$
$911$	−24.3835	+	24.3835i	−0.807861	+	0.807861i	0.176449	+	0.984310i	$0.443539\pi$
$912$		0			0
$913$	10.2276	+	10.2276i	0.338485	+	0.338485i
$914$		0			0
$915$	−1.91374	−	12.7706i	−0.0632664	−	0.422183i
$916$		0			0
$917$		−	25.9980i		−	0.858531i
$918$		0			0
$919$			27.3149i			0.901035i	0.892768	+	0.450518i	$0.148761\pi$
$919$			27.3149i			0.901035i	−0.892768	+	0.450518i	$0.851239\pi$
$920$		0			0
$921$	−5.92522	−	39.5395i	−0.195242	−	1.30287i
$922$		0			0
$923$	27.8268	+	27.8268i	0.915930	+	0.915930i
$924$		0			0
$925$	−3.72874	+	3.72874i	−0.122600	+	0.122600i
$926$		0			0
$927$	2.82396	+	9.21069i	0.0927511	+	0.302519i
$928$		0			0
$929$	−0.644449	−	0.644449i	−0.0211437	−	0.0211437i	0.696456	−	0.717600i	$-0.254759\pi$
$929$	−0.644449	−	0.644449i	−0.0211437	−	0.0211437i	−0.717600	+	0.696456i	$0.754759\pi$
$930$		0			0
$931$			18.4159i			0.603556i
$932$		0			0
$933$	30.5765	+	22.6067i	1.00103	+	0.740110i
$934$		0			0
$935$	−3.28630	−	13.1996i	−0.107473	−	0.431672i
$936$		0			0
$937$			51.5431i			1.68384i	0.539602	+	0.841920i	$0.318575\pi$
$937$			51.5431i			1.68384i	−0.539602	+	0.841920i	$0.681425\pi$
$938$		0			0
$939$	15.3809	−	20.8033i	0.501937	−	0.678890i
$940$		0			0
$941$	8.62114	+	8.62114i	0.281041	+	0.281041i	0.833524	−	0.552483i	$-0.186320\pi$
$941$	8.62114	+	8.62114i	0.281041	+	0.281041i	−0.552483	+	0.833524i	$0.686320\pi$
$942$		0			0
$943$	−22.1596			−0.721616
$944$		0			0
$945$	−25.6567	+	12.2750i	−0.834612	+	0.399306i
$946$		0			0
$947$	14.3045	+	14.3045i	0.464834	+	0.464834i	0.900236	−	0.435402i	$-0.143394\pi$
$947$	14.3045	+	14.3045i	0.464834	+	0.464834i	−0.435402	+	0.900236i	$0.643394\pi$
$948$		0			0
$949$	−39.0060	−	39.0060i	−1.26619	−	1.26619i
$950$		0			0
$951$	−16.4421	−	12.1565i	−0.533172	−	0.394200i
$952$		0			0
$953$			5.76940i			0.186889i	0.995624	+	0.0934445i	$0.0297878\pi$
$953$			5.76940i			0.186889i	−0.995624	+	0.0934445i	$0.970212\pi$
$954$		0			0
$955$	15.6996	−	15.6996i	0.508028	−	0.508028i
$956$		0			0
$957$	−5.13543	−	34.2692i	−0.166005	−	1.10777i
$958$		0			0
$959$	−34.6632	+	34.6632i	−1.11933	+	1.11933i
$960$		0			0
$961$			14.2817i			0.460700i
$962$		0			0
$963$	47.8000	+	25.3672i	1.54033	+	0.817447i
$964$		0			0
$965$		−	2.45530i		−	0.0790388i
$966$		0			0
$967$	36.4537			1.17227			0.586137	−	0.810212i	$-0.300648\pi$
$967$	36.4537			1.17227			0.586137	+	0.810212i	$0.300648\pi$
$968$		0			0
$969$	25.9897	−	10.7671i	0.834909	−	0.345888i
$970$		0			0
$971$			48.4157i			1.55373i	0.629665	+	0.776867i	$0.283192\pi$
$971$			48.4157i			1.55373i	−0.629665	+	0.776867i	$0.716808\pi$
$972$		0			0
$973$	−72.1593			−2.31332
$974$		0			0
$975$	−2.78213	−	18.5654i	−0.0890995	−	0.594569i
$976$		0			0
$977$	−42.5484			−1.36124			−0.680622	−	0.732634i	$-0.738291\pi$
$977$	−42.5484			−1.36124			−0.680622	+	0.732634i	$0.738291\pi$
$978$		0			0
$979$	−3.29909	−	3.29909i	−0.105439	−	0.105439i
$980$		0			0
$981$	−19.1244	+	36.0365i	−0.610594	+	1.15056i
$982$		0			0
$983$	20.8108	+	20.8108i	0.663762	+	0.663762i	0.956265	−	0.292503i	$-0.0944880\pi$
$983$	20.8108	+	20.8108i	0.663762	+	0.663762i	−0.292503	+	0.956265i	$0.594488\pi$
$984$		0			0
$985$	31.5039			1.00380
$986$		0			0
$987$	−56.3285	−	41.6464i	−1.79296	−	1.32562i
$988$		0			0
$989$	−1.75195	+	1.75195i	−0.0557088	+	0.0557088i
$990$		0			0
$991$	5.55017	−	5.55017i	0.176307	−	0.176307i	−0.613437	−	0.789744i	$-0.710213\pi$
$991$	5.55017	−	5.55017i	0.176307	−	0.176307i	0.789744	+	0.613437i	$0.210213\pi$
$992$		0			0
$993$	11.0536	−	1.65645i	0.350776	−	0.0525658i
$994$		0			0
$995$		−	3.32084i		−	0.105278i
$996$		0			0
$997$	−19.3200	+	19.3200i	−0.611869	+	0.611869i	−0.943433	−	0.331564i	$-0.892424\pi$
$997$	−19.3200	+	19.3200i	−0.611869	+	0.611869i	0.331564	+	0.943433i	$0.392424\pi$
$998$		0			0
$999$	−10.6172	−	3.74557i	−0.335913	−	0.118504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.bf.d.47.1	✓	24
3.2	odd	2	inner	816.2.bf.d.47.6	yes	24
4.3	odd	2	inner	816.2.bf.d.47.12	yes	24
12.11	even	2	inner	816.2.bf.d.47.7	yes	24
17.4	even	4	inner	816.2.bf.d.191.7	yes	24
51.38	odd	4	inner	816.2.bf.d.191.12	yes	24
68.55	odd	4	inner	816.2.bf.d.191.6	yes	24
204.191	even	4	inner	816.2.bf.d.191.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
816.2.bf.d.47.1	✓	24	1.1	even	1	trivial
816.2.bf.d.47.6	yes	24	3.2	odd	2	inner
816.2.bf.d.47.7	yes	24	12.11	even	2	inner
816.2.bf.d.47.12	yes	24	4.3	odd	2	inner
816.2.bf.d.191.1	yes	24	204.191	even	4	inner
816.2.bf.d.191.6	yes	24	68.55	odd	4	inner
816.2.bf.d.191.7	yes	24	17.4	even	4	inner
816.2.bf.d.191.12	yes	24	51.38	odd	4	inner

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.bf (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71292 + 0.256691i) q^{3} +(-1.13275 + 1.13275i) q^{5} +(-2.41609 - 2.41609i) q^{7} +(2.86822 - 0.879385i) q^{9} +(1.45623 - 1.45623i) q^{11} +4.45336 q^{13} +(1.64955 - 2.23108i) q^{15} +(-4.00097 + 0.996122i) q^{17} +3.93923 q^{19} +(4.75877 + 3.51839i) q^{21} +(-3.68731 + 3.68731i) q^{23} +2.43376i q^{25} +(-4.68731 + 2.24257i) q^{27} +(-6.86919 + 6.86919i) q^{29} +(-2.89122 + 2.89122i) q^{31} +(-2.12061 + 2.86822i) q^{33} +5.47365 q^{35} +(1.53209 + 1.53209i) q^{37} +(-7.62827 + 1.14314i) q^{39} +(3.00485 + 3.00485i) q^{41} +0.475129 q^{43} +(-2.25285 + 4.24509i) q^{45} -11.8368 q^{47} +4.67499i q^{49} +(6.59766 - 2.73329i) q^{51} +8.51548 q^{53} +3.29909i q^{55} +(-6.74760 + 1.01117i) q^{57} +1.90098i q^{59} +(3.29086 - 3.29086i) q^{61} +(-9.05455 - 4.80520i) q^{63} +(-5.04454 + 5.04454i) q^{65} +7.87846i q^{67} +(5.36959 - 7.26259i) q^{69} +(6.24849 + 6.24849i) q^{71} +(-8.75877 - 8.75877i) q^{73} +(-0.624726 - 4.16885i) q^{75} -7.03678 q^{77} +(9.65441 + 9.65441i) q^{79} +(7.45336 - 5.04454i) q^{81} +7.02334i q^{83} +(3.40373 - 5.66044i) q^{85} +(10.0031 - 13.5297i) q^{87} -2.26550i q^{89} +(-10.7597 - 10.7597i) q^{91} +(4.21029 - 5.69459i) q^{93} +(-4.46216 + 4.46216i) q^{95} +(9.90673 + 9.90673i) q^{97} +(2.89621 - 5.45739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{21} - 96 q^{33} + 24 q^{45} - 48 q^{57} - 48 q^{61} + 72 q^{69} - 120 q^{73} + 72 q^{81} + 192 q^{85} + 24 q^{97}+O(q^{100}) \) 24 * q + 24 * q^21 - 96 * q^33 + 24 * q^45 - 48 * q^57 - 48 * q^61 + 72 * q^69 - 120 * q^73 + 72 * q^81 + 192 * q^85 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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