LMFDB - Embedded newform 528.2.bn.d.17.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [528,2,Mod(17,528)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(528, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 5, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("528.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 528 = 2^{4} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	528.bn (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-1,0,0,0,0,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.21610122672$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} - 12 x^{13} + 23 x^{12} - 72 x^{11} + 146 x^{10} - 176 x^{9} + 223 x^{8} + \cdots + 6561 $ x^16 - 4x^15 + 8x^14 - 12x^13 + 23x^12 - 72x^11 + 146x^10 - 176x^9 + 223x^8 - 528x^7 + 1314x^6 - 1944x^5 + 1863x^4 - 2916x^3 + 5832x^2 - 8748*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 132)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.4
Root			$-1.53089 + 0.810175i$ of defining polynomial
Character	$\chi$	$=$	528.17
Dual form			528.2.bn.d.497.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71472 - 0.244388i) q^{3} +(-2.90910 - 0.945225i) q^{5} +(2.14565 + 2.95324i) q^{7} +(2.88055 - 0.838115i) q^{9} +(3.28976 - 0.421300i) q^{11} +(1.02762 - 0.333894i) q^{13} +(-5.21931 - 0.909850i) q^{15} +(-0.380654 + 1.17153i) q^{17} +(3.04469 - 4.19066i) q^{19} +(4.40094 + 4.53961i) q^{21} +6.43947i q^{23} +(3.52435 + 2.56059i) q^{25} +(4.73452 - 2.14111i) q^{27} +(6.00366 - 4.36191i) q^{29} +(-1.21108 - 3.72731i) q^{31} +(5.53806 - 1.52639i) q^{33} +(-3.45045 - 10.6194i) q^{35} +(-0.171284 + 0.124445i) q^{37} +(1.68048 - 0.823673i) q^{39} +(-5.20230 - 3.77969i) q^{41} +11.6128i q^{43} +(-9.17202 - 0.284604i) q^{45} +(-1.87249 + 2.57726i) q^{47} +(-1.95467 + 6.01586i) q^{49} +(-0.366408 + 2.10188i) q^{51} +(-7.80158 + 2.53489i) q^{53} +(-9.96847 - 1.88396i) q^{55} +(4.19665 - 7.92990i) q^{57} +(-3.66438 - 5.04359i) q^{59} +(-5.80774 - 1.88705i) q^{61} +(8.65581 + 6.70864i) q^{63} -3.30506 q^{65} +3.24458 q^{67} +(1.57373 + 11.0419i) q^{69} +(-0.315849 - 0.102625i) q^{71} +(-8.00563 - 11.0188i) q^{73} +(6.66906 + 3.52939i) q^{75} +(8.30288 + 8.81148i) q^{77} +(-1.26290 + 0.410340i) q^{79} +(7.59513 - 4.82846i) q^{81} +(-2.41384 + 7.42902i) q^{83} +(2.21472 - 3.04831i) q^{85} +(9.22861 - 8.94669i) q^{87} +10.3772i q^{89} +(3.19098 + 2.31838i) q^{91} +(-2.98757 - 6.09534i) q^{93} +(-12.8184 + 9.31313i) q^{95} +(1.96422 + 6.04523i) q^{97} +(9.12321 - 3.97077i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{3} + 5 q^{9} - 9 q^{15} + 30 q^{19} - 12 q^{25} - q^{27} + 10 q^{31} - 41 q^{33} - 24 q^{37} + 35 q^{39} + 2 q^{45} + 12 q^{49} + 15 q^{51} - 62 q^{55} + 35 q^{57} + 40 q^{61} - 55 q^{63} - 44 q^{67}+ \cdots + 101 q^{99}+O(q^{100}) $ 16 * q - q^3 + 5 * q^9 - 9 * q^15 + 30 * q^19 - 12 * q^25 - q^27 + 10 * q^31 - 41 * q^33 - 24 * q^37 + 35 * q^39 + 2 * q^45 + 12 * q^49 + 15 * q^51 - 62 * q^55 + 35 * q^57 + 40 * q^61 - 55 * q^63 - 44 * q^67 + 46 * q^69 + 10 * q^73 - 21 * q^75 - 20 * q^79 + 57 * q^81 - 60 * q^85 + 60 * q^91 + 7 * q^93 - 36 * q^97 + 101 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

$n$	$133$	$145$	$353$	$463$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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
$3$	1.71472	−	0.244388i	0.989996	−	0.141097i
$3$	1.71472	−	0.244388i	0.989996	−	0.141097i
$4$		0			0
$5$	−2.90910	−	0.945225i	−1.30099	−	0.422718i	−0.425065	−	0.905163i	$-0.639749\pi$
$5$	−2.90910	−	0.945225i	−1.30099	−	0.422718i	−0.875926	+	0.482445i	$0.839749\pi$
$6$		0			0
$7$	2.14565	+	2.95324i	0.810981	+	1.11622i	0.991171	+	0.132588i	$0.0423286\pi$
$7$	2.14565	+	2.95324i	0.810981	+	1.11622i	−0.180191	+	0.983632i	$0.557671\pi$
$8$		0			0
$9$	2.88055	−	0.838115i	0.960183	−	0.279372i
$10$		0			0
$11$	3.28976	−	0.421300i	0.991899	−	0.127027i
$11$	3.28976	−	0.421300i	0.991899	−	0.127027i
$12$		0			0
$13$	1.02762	−	0.333894i	0.285010	−	0.0926055i	−0.163023	−	0.986622i	$-0.552125\pi$
$13$	1.02762	−	0.333894i	0.285010	−	0.0926055i	0.448033	+	0.894017i	$0.352125\pi$
$14$		0			0
$15$	−5.21931	−	0.909850i	−1.34762	−	0.234922i
$16$		0			0
$17$	−0.380654	+	1.17153i	−0.0923222	+	0.284138i	−0.986547	−	0.163481i	$-0.947728\pi$
$17$	−0.380654	+	1.17153i	−0.0923222	+	0.284138i	0.894224	+	0.447619i	$0.147728\pi$
$18$		0			0
$19$	3.04469	−	4.19066i	0.698500	−	0.961402i	−0.301469	−	0.953476i	$-0.597477\pi$
$19$	3.04469	−	4.19066i	0.698500	−	0.961402i	0.999969	−	0.00792623i	$-0.00252302\pi$
$20$		0			0
$21$	4.40094	+	4.53961i	0.960363	+	0.990625i
$22$		0			0
$23$			6.43947i			1.34272i	0.741130	+	0.671361i	$0.234290\pi$
$23$			6.43947i			1.34272i	−0.741130	+	0.671361i	$0.765710\pi$
$24$		0			0
$25$	3.52435	+	2.56059i	0.704870	+	0.512118i
$26$		0			0
$27$	4.73452	−	2.14111i	0.911159	−	0.412056i
$28$		0			0
$29$	6.00366	−	4.36191i	1.11485	−	0.809987i	0.131430	−	0.991325i	$-0.458043\pi$
$29$	6.00366	−	4.36191i	1.11485	−	0.809987i	0.983421	+	0.181339i	$0.0580430\pi$
$30$		0			0
$31$	−1.21108	−	3.72731i	−0.217516	−	0.669446i	−0.998965	−	0.0454768i	$-0.985519\pi$
$31$	−1.21108	−	3.72731i	−0.217516	−	0.669446i	0.781449	−	0.623969i	$-0.214481\pi$
$32$		0			0
$33$	5.53806	−	1.52639i	0.964053	−	0.265710i
$34$		0			0
$35$	−3.45045	−	10.6194i	−0.583233	−	1.79501i
$36$		0			0
$37$	−0.171284	+	0.124445i	−0.0281589	+	0.0204586i	−0.601776	−	0.798665i	$-0.705540\pi$
$37$	−0.171284	+	0.124445i	−0.0281589	+	0.0204586i	0.573617	+	0.819124i	$0.305540\pi$
$38$		0			0
$39$	1.68048	−	0.823673i	0.269093	−	0.131893i
$40$		0			0
$41$	−5.20230	−	3.77969i	−0.812462	−	0.590288i	0.102081	−	0.994776i	$-0.467450\pi$
$41$	−5.20230	−	3.77969i	−0.812462	−	0.590288i	−0.914543	+	0.404488i	$0.867450\pi$
$42$		0			0
$43$			11.6128i			1.77094i	0.464699	+	0.885469i	$0.346163\pi$
$43$			11.6128i			1.77094i	−0.464699	+	0.885469i	$0.653837\pi$
$44$		0			0
$45$	−9.17202	−	0.284604i	−1.36728	−	0.0424263i
$46$		0			0
$47$	−1.87249	+	2.57726i	−0.273130	+	0.375932i	−0.923443	−	0.383735i	$-0.874638\pi$
$47$	−1.87249	+	2.57726i	−0.273130	+	0.375932i	0.650313	+	0.759666i	$0.274638\pi$
$48$		0			0
$49$	−1.95467	+	6.01586i	−0.279239	+	0.859408i
$50$		0			0
$51$	−0.366408	+	2.10188i	−0.0513074	+	0.294322i
$52$		0			0
$53$	−7.80158	+	2.53489i	−1.07163	+	0.348194i	−0.791122	−	0.611658i	$-0.790503\pi$
$53$	−7.80158	+	2.53489i	−1.07163	+	0.348194i	−0.280508	+	0.959852i	$0.590503\pi$
$54$		0			0
$55$	−9.96847	−	1.88396i	−1.34415	−	0.254033i
$56$		0			0
$57$	4.19665	−	7.92990i	0.555860	−	1.05034i
$58$		0			0
$59$	−3.66438	−	5.04359i	−0.477062	−	0.656619i	0.500875	−	0.865520i	$-0.333012\pi$
$59$	−3.66438	−	5.04359i	−0.477062	−	0.656619i	−0.977937	+	0.208900i	$0.933012\pi$
$60$		0			0
$61$	−5.80774	−	1.88705i	−0.743604	−	0.241612i	−0.0873774	−	0.996175i	$-0.527849\pi$
$61$	−5.80774	−	1.88705i	−0.743604	−	0.241612i	−0.656227	+	0.754564i	$0.727849\pi$
$62$		0			0
$63$	8.65581	+	6.70864i	1.09053	+	0.845210i
$64$		0			0
$65$	−3.30506			−0.409942
$66$		0			0
$67$	3.24458			0.396388			0.198194	−	0.980163i	$-0.436492\pi$
$67$	3.24458			0.396388			0.198194	+	0.980163i	$0.436492\pi$
$68$		0			0
$69$	1.57373	+	11.0419i	0.189455	+	1.32929i
$70$		0			0
$71$	−0.315849	−	0.102625i	−0.0374843	−	0.0121794i	0.290215	−	0.956962i	$-0.406273\pi$
$71$	−0.315849	−	0.102625i	−0.0374843	−	0.0121794i	−0.327699	+	0.944782i	$0.606273\pi$
$72$		0			0
$73$	−8.00563	−	11.0188i	−0.936989	−	1.28965i	−0.957070	−	0.289856i	$-0.906393\pi$
$73$	−8.00563	−	11.0188i	−0.936989	−	1.28965i	0.0200816	−	0.999798i	$-0.493607\pi$
$74$		0			0
$75$	6.66906	+	3.52939i	0.770077	+	0.407539i
$76$		0			0
$77$	8.30288	+	8.81148i	0.946201	+	1.00416i
$78$		0			0
$79$	−1.26290	+	0.410340i	−0.142087	+	0.0461668i	−0.379197	−	0.925316i	$-0.623800\pi$
$79$	−1.26290	+	0.410340i	−0.142087	+	0.0461668i	0.237110	+	0.971483i	$0.423800\pi$
$80$		0			0
$81$	7.59513	−	4.82846i	0.843903	−	0.536496i
$82$		0			0
$83$	−2.41384	+	7.42902i	−0.264953	+	0.815441i	0.726751	+	0.686901i	$0.241029\pi$
$83$	−2.41384	+	7.42902i	−0.264953	+	0.815441i	−0.991704	+	0.128541i	$0.958971\pi$
$84$		0			0
$85$	2.21472	−	3.04831i	0.240221	−	0.330635i
$86$		0			0
$87$	9.22861	−	8.94669i	0.989411	−	0.959186i
$88$		0			0
$89$			10.3772i			1.09998i	0.835172	+	0.549989i	$0.185368\pi$
$89$			10.3772i			1.09998i	−0.835172	+	0.549989i	$0.814632\pi$
$90$		0			0
$91$	3.19098	+	2.31838i	0.334506	+	0.243033i
$92$		0			0
$93$	−2.98757	−	6.09534i	−0.309797	−	0.632057i
$94$		0			0
$95$	−12.8184	+	9.31313i	−1.31514	+	0.955507i
$96$		0			0
$97$	1.96422	+	6.04523i	0.199436	+	0.613801i	0.999896	+	0.0144147i	$0.00458849\pi$
$97$	1.96422	+	6.04523i	0.199436	+	0.613801i	−0.800460	+	0.599386i	$0.795412\pi$
$98$		0			0
$99$	9.12321	−	3.97077i	0.916917	−	0.399077i
$100$		0			0
$101$	−2.41384	−	7.42902i	−0.240186	−	0.739215i	−0.996391	−	0.0848812i	$-0.972949\pi$
$101$	−2.41384	−	7.42902i	−0.240186	−	0.739215i	0.756205	−	0.654334i	$-0.227051\pi$
$102$		0			0
$103$	0.354742	−	0.257735i	0.0349538	−	0.0253954i	−0.570171	−	0.821526i	$-0.693123\pi$
$103$	0.354742	−	0.257735i	0.0349538	−	0.0253954i	0.605125	+	0.796130i	$0.293123\pi$
$104$		0			0
$105$	−8.51182	−	17.3661i	−0.830669	−	1.69476i
$106$		0			0
$107$	−8.42725	−	6.12275i	−0.814693	−	0.591909i	0.100494	−	0.994938i	$-0.467958\pi$
$107$	−8.42725	−	6.12275i	−0.814693	−	0.591909i	−0.915187	+	0.403029i	$0.867958\pi$
$108$		0			0
$109$			2.29088i			0.219427i	0.993963	+	0.109713i	$0.0349933\pi$
$109$			2.29088i			0.219427i	−0.993963	+	0.109713i	$0.965007\pi$
$110$		0			0
$111$	−0.263292	+	0.255248i	−0.0249905	+	0.0242271i
$112$		0			0
$113$	−7.04630	+	9.69840i	−0.662860	+	0.912349i	−0.999572	−	0.0292588i	$-0.990685\pi$
$113$	−7.04630	+	9.69840i	−0.662860	+	0.912349i	0.336711	+	0.941608i	$0.390685\pi$
$114$		0			0
$115$	6.08675	−	18.7331i	0.567592	−	1.74687i
$116$		0			0
$117$	2.68027	−	1.82306i	0.247791	−	0.168542i
$118$		0			0
$119$	−4.27657	+	1.38954i	−0.392032	+	0.127379i
$120$		0			0
$121$	10.6450	−	2.77195i	0.967728	−	0.251995i
$122$		0			0
$123$	−9.84421	−	5.20974i	−0.887622	−	0.469747i
$124$		0			0
$125$	1.15726	+	1.59283i	0.103509	+	0.142467i
$126$		0			0
$127$	−19.0155	−	6.17852i	−1.68736	−	0.548255i	−0.701041	−	0.713121i	$-0.747281\pi$
$127$	−19.0155	−	6.17852i	−1.68736	−	0.548255i	−0.986316	+	0.164866i	$0.947281\pi$
$128$		0			0
$129$	2.83803	+	19.9128i	0.249875	+	1.75322i
$130$		0			0
$131$	−6.04743			−0.528367			−0.264183	−	0.964472i	$-0.585102\pi$
$131$	−6.04743			−0.528367			−0.264183	+	0.964472i	$0.585102\pi$
$132$		0			0
$133$	18.9089			1.63961
$134$		0			0
$135$	−15.7970	+	1.75351i	−1.35959	+	0.150918i
$136$		0			0
$137$	3.40437	+	1.10615i	0.290855	+	0.0945045i	0.450810	−	0.892620i	$-0.351135\pi$
$137$	3.40437	+	1.10615i	0.290855	+	0.0945045i	−0.159955	+	0.987124i	$0.551135\pi$
$138$		0			0
$139$	3.89291	+	5.35813i	0.330192	+	0.454471i	0.941545	−	0.336888i	$-0.109374\pi$
$139$	3.89291	+	5.35813i	0.330192	+	0.454471i	−0.611352	+	0.791358i	$0.709374\pi$
$140$		0			0
$141$	−2.58095	+	4.87689i	−0.217355	+	0.410709i
$142$		0			0
$143$	3.23995	−	1.53137i	0.270938	−	0.128059i
$144$		0			0
$145$	−21.5882	+	7.01445i	−1.79281	+	0.582518i
$146$		0			0
$147$	−1.88152	+	10.7932i	−0.155185	+	0.890210i
$148$		0			0
$149$	4.77786	−	14.7048i	0.391418	−	1.20466i	−0.540298	−	0.841473i	$-0.681689\pi$
$149$	4.77786	−	14.7048i	0.391418	−	1.20466i	0.931716	−	0.363187i	$-0.118311\pi$
$150$		0			0
$151$	3.82609	−	5.26616i	0.311363	−	0.428554i	−0.624443	−	0.781070i	$-0.714674\pi$
$151$	3.82609	−	5.26616i	0.311363	−	0.428554i	0.935806	+	0.352517i	$0.114674\pi$
$152$		0			0
$153$	−0.114614	+	3.69369i	−0.00926597	+	0.298617i
$154$		0			0
$155$			11.9879i			0.962890i
$156$		0			0
$157$	−16.8906	−	12.2718i	−1.34802	−	0.979393i	−0.999108	−	0.0422371i	$-0.986552\pi$
$157$	−16.8906	−	12.2718i	−1.34802	−	0.979393i	−0.348911	−	0.937156i	$-0.613448\pi$
$158$		0			0
$159$	−12.7581	+	6.25324i	−1.01178	+	0.495914i
$160$		0			0
$161$	−19.0173	+	13.8169i	−1.49877	+	1.08892i
$162$		0			0
$163$	−0.506916	−	1.56013i	−0.0397047	−	0.122199i	0.929240	−	0.369478i	$-0.120463\pi$
$163$	−0.506916	−	1.56013i	−0.0397047	−	0.122199i	−0.968944	+	0.247279i	$0.920463\pi$
$164$		0			0
$165$	−17.5536	−	0.794291i	−1.36654	−	0.0618354i
$166$		0			0
$167$	1.53561	+	4.72613i	0.118829	+	0.365719i	0.992726	−	0.120392i	$-0.0384152\pi$
$167$	1.53561	+	4.72613i	0.118829	+	0.365719i	−0.873897	+	0.486111i	$0.838415\pi$
$168$		0			0
$169$	−9.57270	+	6.95498i	−0.736362	+	0.534998i
$170$		0			0
$171$	5.25813	−	14.6232i	0.402099	−	1.11826i
$172$		0			0
$173$	−5.89880	−	4.28573i	−0.448477	−	0.325838i	0.340517	−	0.940238i	$-0.389398\pi$
$173$	−5.89880	−	4.28573i	−0.448477	−	0.325838i	−0.788994	+	0.614400i	$0.789398\pi$
$174$		0			0
$175$			15.9024i			1.20211i
$176$		0			0
$177$	−7.51599	−	7.75283i	−0.564937	−	0.582738i
$178$		0			0
$179$	5.35142	−	7.36560i	0.399984	−	0.550531i	−0.560756	−	0.827981i	$-0.689489\pi$
$179$	5.35142	−	7.36560i	0.399984	−	0.550531i	0.960740	+	0.277450i	$0.0894894\pi$
$180$		0			0
$181$	6.81590	−	20.9772i	0.506622	−	1.55922i	−0.291405	−	0.956600i	$-0.594123\pi$
$181$	6.81590	−	20.9772i	0.506622	−	1.55922i	0.798027	−	0.602622i	$-0.205877\pi$
$182$		0			0
$183$	−10.4198	−	1.81642i	−0.770256	−	0.134274i
$184$		0			0
$185$	0.615911	−	0.200122i	0.0452827	−	0.0147132i
$186$		0			0
$187$	−0.758693	+	4.01443i	−0.0554811	+	0.293564i
$188$		0			0
$189$	16.4818	+	9.38809i	1.19888	+	0.682883i
$190$		0			0
$191$	5.67281	+	7.80795i	0.410470	+	0.564964i	0.963333	−	0.268309i	$-0.0864647\pi$
$191$	5.67281	+	7.80795i	0.410470	+	0.564964i	−0.552863	+	0.833272i	$0.686465\pi$
$192$		0			0
$193$	2.14654	+	0.697453i	0.154511	+	0.0502037i	0.385251	−	0.922812i	$-0.374115\pi$
$193$	2.14654	+	0.697453i	0.154511	+	0.0502037i	−0.230740	+	0.973015i	$0.574115\pi$
$194$		0			0
$195$	−5.66726	+	0.807716i	−0.405841	+	0.0578417i
$196$		0			0
$197$	−5.10641			−0.363816			−0.181908	−	0.983316i	$-0.558227\pi$
$197$	−5.10641			−0.363816			−0.181908	+	0.983316i	$0.558227\pi$
$198$		0			0
$199$	9.78375			0.693552			0.346776	−	0.937948i	$-0.387276\pi$
$199$	9.78375			0.693552			0.346776	+	0.937948i	$0.387276\pi$
$200$		0			0
$201$	5.56355	−	0.792935i	0.392423	−	0.0559293i
$202$		0			0
$203$	25.7635	+	8.37108i	1.80825	+	0.587535i
$204$		0			0
$205$	11.5614	+	15.9129i	0.807481	+	1.11140i
$206$		0			0
$207$	5.39702	+	18.5492i	0.375119	+	1.28926i
$208$		0			0
$209$	8.25077	−	15.0690i	0.570718	−	1.04234i
$210$		0			0
$211$	−6.99936	+	2.27423i	−0.481856	+	0.156564i	−0.539865	−	0.841752i	$-0.681525\pi$
$211$	−6.99936	+	2.27423i	−0.481856	+	0.156564i	0.0580092	+	0.998316i	$0.481525\pi$
$212$		0			0
$213$	−0.566673	−	0.0987846i	−0.0388278	−	0.00676861i
$214$		0			0
$215$	10.9767	−	33.7829i	0.748606	−	2.30397i
$216$		0			0
$217$	8.40910	−	11.5741i	0.570847	−	0.785703i
$218$		0			0
$219$	−16.4203	−	16.9377i	−1.10958	−	1.14455i
$220$		0			0
$221$			1.33099i			0.0895319i
$222$		0			0
$223$	3.18505	+	2.31408i	0.213287	+	0.154962i	0.689300	−	0.724476i	$-0.257918\pi$
$223$	3.18505	+	2.31408i	0.213287	+	0.154962i	−0.476013	+	0.879438i	$0.657918\pi$
$224$		0			0
$225$	12.2981	+	4.42209i	0.819875	+	0.294806i
$226$		0			0
$227$	23.2691	−	16.9060i	1.54442	−	1.12209i	0.596941	−	0.802285i	$-0.296382\pi$
$227$	23.2691	−	16.9060i	1.54442	−	1.12209i	0.947483	−	0.319805i	$-0.103618\pi$
$228$		0			0
$229$	3.93271	+	12.1036i	0.259881	+	0.799830i	0.992829	+	0.119546i	$0.0381437\pi$
$229$	3.93271	+	12.1036i	0.259881	+	0.799830i	−0.732948	+	0.680284i	$0.761856\pi$
$230$		0			0
$231$	16.3906	+	13.0801i	1.07842	+	0.860609i
$232$		0			0
$233$	−5.88532	−	18.1131i	−0.385560	−	1.18663i	−0.936073	−	0.351805i	$-0.885568\pi$
$233$	−5.88532	−	18.1131i	−0.385560	−	1.18663i	0.550513	−	0.834826i	$-0.314432\pi$
$234$		0			0
$235$	7.88335	−	5.72759i	0.514253	−	0.373627i
$236$		0			0
$237$	−2.06523	+	1.01226i	−0.134151	+	0.0657530i
$238$		0			0
$239$	16.5847	+	12.0495i	1.07278	+	0.779418i	0.976409	−	0.215928i	$-0.0692775\pi$
$239$	16.5847	+	12.0495i	1.07278	+	0.779418i	0.0963677	+	0.995346i	$0.469278\pi$
$240$		0			0
$241$		−	18.9036i		−	1.21769i	−0.793290	−	0.608845i	$-0.791633\pi$
$241$		−	18.9036i		−	1.21769i	0.793290	−	0.608845i	$-0.208367\pi$
$242$		0			0
$243$	11.8435	−	10.1356i	0.759762	−	0.650201i
$244$		0			0
$245$	11.3727	−	15.6531i	0.726574	−	1.00004i
$246$		0			0
$247$	1.72955	−	5.32300i	0.110048	−	0.338694i
$248$		0			0
$249$	−2.32350	+	13.3286i	−0.147246	+	0.844668i
$250$		0			0
$251$	−24.2657	+	7.88439i	−1.53164	+	0.497659i	−0.949054	−	0.315114i	$-0.897957\pi$
$251$	−24.2657	+	7.88439i	−1.53164	+	0.497659i	−0.582582	+	0.812772i	$0.697957\pi$
$252$		0			0
$253$	2.71295	+	21.1843i	0.170562	+	1.33185i
$254$		0			0
$255$	3.05267	−	5.76825i	0.191166	−	0.361222i
$256$		0			0
$257$	3.99783	+	5.50254i	0.249378	+	0.343239i	0.915293	−	0.402788i	$-0.131959\pi$
$257$	3.99783	+	5.50254i	0.249378	+	0.343239i	−0.665915	+	0.746027i	$0.731959\pi$
$258$		0			0
$259$	−0.735032	−	0.238826i	−0.0456726	−	0.0148399i
$260$		0			0
$261$	13.6380	−	17.5965i	0.844174	−	1.08919i
$262$		0			0
$263$	−17.9177			−1.10485			−0.552426	−	0.833562i	$-0.686298\pi$
$263$	−17.9177			−1.10485			−0.552426	+	0.833562i	$0.686298\pi$
$264$		0			0
$265$	25.0916			1.54137
$266$		0			0
$267$	2.53605	+	17.7940i	0.155204	+	1.08897i
$268$		0			0
$269$	27.2051	+	8.83946i	1.65872	+	0.538952i	0.980604	−	0.196001i	$-0.0627956\pi$
$269$	27.2051	+	8.83946i	1.65872	+	0.538952i	0.678119	+	0.734952i	$0.262796\pi$
$270$		0			0
$271$	1.87897	+	2.58618i	0.114139	+	0.157099i	0.862264	−	0.506458i	$-0.169046\pi$
$271$	1.87897	+	2.58618i	0.114139	+	0.157099i	−0.748125	+	0.663558i	$0.769046\pi$
$272$		0			0
$273$	6.03824	+	3.19555i	0.365451	+	0.193403i
$274$		0			0
$275$	12.6730	+	6.93891i	0.764213	+	0.418432i
$276$		0			0
$277$	−20.3821	+	6.62255i	−1.22464	+	0.397911i	−0.848771	−	0.528761i	$-0.822657\pi$
$277$	−20.3821	+	6.62255i	−1.22464	+	0.397911i	−0.375872	+	0.926672i	$0.622657\pi$
$278$		0			0
$279$	−6.61249	−	9.72169i	−0.395879	−	0.582022i
$280$		0			0
$281$	−3.19044	+	9.81917i	−0.190326	+	0.585763i	−0.999999	−	0.00111782i	$-0.999644\pi$
$281$	−3.19044	+	9.81917i	−0.190326	+	0.585763i	0.809674	+	0.586881i	$0.199644\pi$
$282$		0			0
$283$	−3.55539	+	4.89357i	−0.211346	+	0.290893i	−0.901508	−	0.432762i	$-0.857539\pi$
$283$	−3.55539	+	4.89357i	−0.211346	+	0.290893i	0.690162	+	0.723655i	$0.257539\pi$
$284$		0			0
$285$	−19.7040	+	19.1021i	−1.16717	+	1.13151i
$286$		0			0
$287$		−	23.4735i		−	1.38560i
$288$		0			0
$289$	12.5257	+	9.10045i	0.736806	+	0.535321i
$290$		0			0
$291$	4.84547	+	9.88587i	0.284046	+	0.579520i
$292$		0			0
$293$	22.6690	−	16.4700i	1.32434	−	0.962186i	0.324469	−	0.945896i	$-0.394815\pi$
$293$	22.6690	−	16.4700i	1.32434	−	0.962186i	0.999867	−	0.0162899i	$-0.00518546\pi$
$294$		0			0
$295$	5.89274	+	18.1360i	0.343089	+	1.05592i
$296$		0			0
$297$	14.6734	−	9.03837i	0.851435	−	0.524460i
$298$		0			0
$299$	2.15010	+	6.61732i	0.124343	+	0.382690i
$300$		0			0
$301$	−34.2954	+	24.9171i	−1.97675	+	1.43620i
$302$		0			0
$303$	−5.95462	−	12.1488i	−0.342084	−	0.697931i
$304$		0			0
$305$	15.1116	+	10.9792i	0.865289	+	0.628669i
$306$		0			0
$307$			7.37725i			0.421042i	0.977589	+	0.210521i	$0.0675160\pi$
$307$			7.37725i			0.421042i	−0.977589	+	0.210521i	$0.932484\pi$
$308$		0			0
$309$	0.545298	−	0.528640i	0.0310209	−	0.0300733i
$310$		0			0
$311$	−6.66335	+	9.17131i	−0.377844	+	0.520057i	−0.955012	−	0.296568i	$-0.904158\pi$
$311$	−6.66335	+	9.17131i	−0.377844	+	0.520057i	0.577168	+	0.816625i	$0.304158\pi$
$312$		0			0
$313$	0.518846	−	1.59684i	0.0293269	−	0.0902589i	−0.935322	−	0.353798i	$-0.884890\pi$
$313$	0.518846	−	1.59684i	0.0293269	−	0.0902589i	0.964649	+	0.263539i	$0.0848899\pi$
$314$		0			0
$315$	−18.8395	−	27.6978i	−1.06148	−	1.56060i
$316$		0			0
$317$	0.811116	−	0.263548i	0.0455568	−	0.0148023i	−0.286150	−	0.958185i	$-0.592376\pi$
$317$	0.811116	−	0.263548i	0.0455568	−	0.0148023i	0.331707	+	0.943383i	$0.392376\pi$
$318$		0			0
$319$	17.9129	−	16.8790i	1.00293	−	0.945041i
$320$		0			0
$321$	−15.9467	−	8.43931i	−0.890059	−	0.471036i
$322$		0			0
$323$	3.75052	+	5.16214i	0.208684	+	0.287229i
$324$		0			0
$325$	4.47665	+	1.45455i	0.248320	+	0.0806841i
$326$		0			0
$327$	0.559863	+	3.92822i	0.0309605	+	0.217231i
$328$		0			0
$329$	−11.6290			−0.641125
$330$		0			0
$331$	−21.1263			−1.16121			−0.580603	−	0.814187i	$-0.697183\pi$
$331$	−21.1263			−1.16121			−0.580603	+	0.814187i	$0.697183\pi$
$332$		0			0
$333$	−0.389092	+	0.502026i	−0.0213221	+	0.0275108i
$334$		0			0
$335$	−9.43881	−	3.06686i	−0.515697	−	0.167560i
$336$		0			0
$337$	7.08246	+	9.74817i	0.385806	+	0.531017i	0.957111	−	0.289721i	$-0.0935626\pi$
$337$	7.08246	+	9.74817i	0.385806	+	0.531017i	−0.571305	+	0.820738i	$0.693563\pi$
$338$		0			0
$339$	−9.71229	+	18.3521i	−0.527499	+	0.996750i
$340$		0			0
$341$	−5.55447	−	11.7517i	−0.300791	−	0.636392i
$342$		0			0
$343$	2.34188	−	0.760921i	0.126449	−	0.0410859i
$344$		0			0
$345$	5.85895	−	33.6096i	0.315435	−	1.80948i
$346$		0			0
$347$	−0.646694	+	1.99032i	−0.0347164	+	0.106846i	−0.966913	−	0.255106i	$-0.917890\pi$
$347$	−0.646694	+	1.99032i	−0.0347164	+	0.106846i	0.932197	+	0.361952i	$0.117890\pi$
$348$		0			0
$349$	7.38093	−	10.1590i	0.395092	−	0.543798i	−0.564412	−	0.825493i	$-0.690897\pi$
$349$	7.38093	−	10.1590i	0.395092	−	0.543798i	0.959504	+	0.281696i	$0.0908969\pi$
$350$		0			0
$351$	4.15038	−	3.78107i	0.221531	−	0.201818i
$352$		0			0
$353$			11.9737i			0.637296i	0.947873	+	0.318648i	$0.103229\pi$
$353$			11.9737i			0.637296i	−0.947873	+	0.318648i	$0.896771\pi$
$354$		0			0
$355$	0.821832	+	0.597096i	0.0436183	+	0.0316906i
$356$		0			0
$357$	−6.99354	+	3.42782i	−0.370137	+	0.181419i
$358$		0			0
$359$	22.8386	−	16.5932i	1.20538	−	0.875758i	0.210575	−	0.977578i	$-0.432467\pi$
$359$	22.8386	−	16.5932i	1.20538	−	0.875758i	0.994803	+	0.101820i	$0.0324665\pi$
$360$		0			0
$361$	−2.42014	−	7.44841i	−0.127376	−	0.392022i
$362$		0			0
$363$	17.5758	−	7.35464i	0.922491	−	0.386018i
$364$		0			0
$365$	12.8740	+	39.6220i	0.673854	+	2.07391i
$366$		0			0
$367$	−11.1605	+	8.10857i	−0.582573	+	0.423264i	−0.839651	−	0.543127i	$-0.817240\pi$
$367$	−11.1605	+	8.10857i	−0.582573	+	0.423264i	0.257078	+	0.966391i	$0.417240\pi$
$368$		0			0
$369$	−18.1533	−	6.52746i	−0.945022	−	0.339806i
$370$		0			0
$371$	−24.2256	−	17.6009i	−1.25773	−	0.913795i
$372$		0			0
$373$		−	4.34739i		−	0.225099i	−0.993646	−	0.112550i	$-0.964098\pi$
$373$		−	4.34739i		−	0.225099i	0.993646	−	0.112550i	$-0.0359017\pi$
$374$		0			0
$375$	2.37365	+	2.44845i	0.122575	+	0.126437i
$376$		0			0
$377$	4.71306	−	6.48697i	0.242735	−	0.334096i
$378$		0			0
$379$	−6.93091	+	21.3311i	−0.356017	+	1.09571i	0.599401	+	0.800449i	$0.295406\pi$
$379$	−6.93091	+	21.3311i	−0.356017	+	1.09571i	−0.955418	+	0.295258i	$0.904594\pi$
$380$		0			0
$381$	−34.1163	−	5.94729i	−1.74783	−	0.304689i
$382$		0			0
$383$	17.2752	−	5.61305i	0.882722	−	0.286814i	0.167635	−	0.985849i	$-0.446387\pi$
$383$	17.2752	−	5.61305i	0.882722	−	0.286814i	0.715087	+	0.699036i	$0.246387\pi$
$384$		0			0
$385$	−15.8251	−	33.4816i	−0.806522	−	1.70638i
$386$		0			0
$387$	9.73287	+	33.4513i	0.494750	+	1.70042i
$388$		0			0
$389$	−14.8824	−	20.4839i	−0.754567	−	1.03857i	−0.997647	−	0.0685664i	$-0.978157\pi$
$389$	−14.8824	−	20.4839i	−0.754567	−	1.03857i	0.243079	−	0.970006i	$-0.421843\pi$
$390$		0			0
$391$	−7.54405	−	2.45121i	−0.381519	−	0.123963i
$392$		0			0
$393$	−10.3697	+	1.47792i	−0.523081	+	0.0745512i
$394$		0			0
$395$	4.06176			0.204369
$396$		0			0
$397$	−1.96507			−0.0986240			−0.0493120	−	0.998783i	$-0.515703\pi$
$397$	−1.96507			−0.0986240			−0.0493120	+	0.998783i	$0.515703\pi$
$398$		0			0
$399$	32.4234	−	4.62109i	1.62320	−	0.231344i
$400$		0			0
$401$	17.6060	+	5.72055i	0.879204	+	0.285671i	0.713627	−	0.700526i	$-0.247051\pi$
$401$	17.6060	+	5.72055i	0.879204	+	0.285671i	0.165577	+	0.986197i	$0.447051\pi$
$402$		0			0
$403$	−2.48905	−	3.42589i	−0.123989	−	0.170656i
$404$		0			0
$405$	−26.6590	+	6.86739i	−1.32470	+	0.341244i
$406$		0			0
$407$	−0.511054	+	0.481556i	−0.0253320	+	0.0238698i
$408$		0			0
$409$	11.0518	−	3.59093i	0.546474	−	0.177560i	−0.0227521	−	0.999741i	$-0.507243\pi$
$409$	11.0518	−	3.59093i	0.546474	−	0.177560i	0.569226	+	0.822181i	$0.307243\pi$
$410$		0			0
$411$	6.10788	+	1.06475i	0.301280	+	0.0525202i
$412$		0			0
$413$	7.03243	−	21.6436i	0.346043	−	1.06501i
$414$		0			0
$415$	14.0442	−	19.3302i	0.689403	−	0.948881i
$416$		0			0
$417$	7.98473	+	8.23633i	0.391014	+	0.403335i
$418$		0			0
$419$			29.2430i			1.42861i	0.699833	+	0.714306i	$0.253258\pi$
$419$			29.2430i			1.42861i	−0.699833	+	0.714306i	$0.746742\pi$
$420$		0			0
$421$	−14.6602	−	10.6512i	−0.714493	−	0.519109i	0.170127	−	0.985422i	$-0.445582\pi$
$421$	−14.6602	−	10.6512i	−0.714493	−	0.519109i	−0.884620	+	0.466313i	$0.845582\pi$
$422$		0			0
$423$	−3.23375	+	8.99327i	−0.157230	+	0.437268i
$424$		0			0
$425$	−4.34137	+	3.15419i	−0.210587	+	0.153001i
$426$		0			0
$427$	−6.88849	−	21.2006i	−0.333357	−	1.02597i
$428$		0			0
$429$	5.18137	−	3.41767i	0.250159	−	0.165007i
$430$		0			0
$431$	4.44702	+	13.6865i	0.214205	+	0.659256i	0.999209	+	0.0397652i	$0.0126610\pi$
$431$	4.44702	+	13.6865i	0.214205	+	0.659256i	−0.785004	+	0.619491i	$0.787339\pi$
$432$		0			0
$433$	−16.4587	+	11.9579i	−0.790954	+	0.574661i	−0.908246	−	0.418436i	$-0.862578\pi$
$433$	−16.4587	+	11.9579i	−0.790954	+	0.574661i	0.117293	+	0.993097i	$0.462578\pi$
$434$		0			0
$435$	−35.3036	+	17.3037i	−1.69268	+	0.829651i
$436$		0			0
$437$	26.9856	+	19.6062i	1.29090	+	0.937891i
$438$		0			0
$439$			4.46676i			0.213187i	0.994303	+	0.106593i	$0.0339943\pi$
$439$			4.46676i			0.213187i	−0.994303	+	0.106593i	$0.966006\pi$
$440$		0			0
$441$	−0.588545	+	18.9672i	−0.0280259	+	0.903200i
$442$		0			0
$443$	7.33510	−	10.0959i	0.348501	−	0.479670i	−0.598399	−	0.801198i	$-0.704196\pi$
$443$	7.33510	−	10.0959i	0.348501	−	0.479670i	0.946900	+	0.321528i	$0.104196\pi$
$444$		0			0
$445$	9.80876	−	30.1883i	0.464980	−	1.43106i
$446$		0			0
$447$	4.59905	−	26.3822i	0.217528	−	1.24784i
$448$		0			0
$449$	−12.9949	+	4.22230i	−0.613268	+	0.199263i	−0.599149	−	0.800638i	$-0.704494\pi$
$449$	−12.9949	+	4.22230i	−0.613268	+	0.199263i	−0.0141188	+	0.999900i	$0.504494\pi$
$450$		0			0
$451$	−18.7067	−	10.2425i	−0.880863	−	0.482302i
$452$		0			0
$453$	5.27369	−	9.96505i	0.247780	−	0.468199i
$454$		0			0
$455$	−7.09151	−	9.76062i	−0.332455	−	0.457585i
$456$		0			0
$457$	8.47229	+	2.75281i	0.396317	+	0.128771i	0.500393	−	0.865798i	$-0.333189\pi$
$457$	8.47229	+	2.75281i	0.396317	+	0.128771i	−0.104077	+	0.994569i	$0.533189\pi$
$458$		0			0
$459$	0.706162	+	6.36166i	0.0329608	+	0.296937i
$460$		0			0
$461$	−12.5468			−0.584365			−0.292182	−	0.956363i	$-0.594381\pi$
$461$	−12.5468			−0.584365			−0.292182	+	0.956363i	$0.594381\pi$
$462$		0			0
$463$	5.12033			0.237962			0.118981	−	0.992897i	$-0.462037\pi$
$463$	5.12033			0.237962			0.118981	+	0.992897i	$0.462037\pi$
$464$		0			0
$465$	2.92969	+	20.5559i	0.135861	+	0.953257i
$466$		0			0
$467$	−20.4005	−	6.62854i	−0.944024	−	0.306732i	−0.203739	−	0.979025i	$-0.565309\pi$
$467$	−20.4005	−	6.62854i	−0.944024	−	0.306732i	−0.740285	+	0.672293i	$0.765309\pi$
$468$		0			0
$469$	6.96174	+	9.58201i	0.321463	+	0.442456i
$470$		0			0
$471$	−31.9618	−	16.9148i	−1.47272	−	0.779393i
$472$		0			0
$473$	4.89248	+	38.2034i	0.224956	+	1.75659i
$474$		0			0
$475$	21.4611	−	6.97313i	0.984703	−	0.319949i
$476$		0			0
$477$	−20.3483	+	13.8405i	−0.931685	+	0.633712i
$478$		0			0
$479$	−2.31222	+	7.11627i	−0.105648	+	0.325151i	−0.989882	−	0.141893i	$-0.954681\pi$
$479$	−2.31222	+	7.11627i	−0.105648	+	0.325151i	0.884234	+	0.467044i	$0.154681\pi$
$480$		0			0
$481$	−0.134463	+	0.185073i	−0.00613099	+	0.00843859i
$482$		0			0
$483$	−29.2327	+	28.3397i	−1.33013	+	1.28950i
$484$		0			0
$485$		−	19.4428i		−	0.882854i
$486$		0			0
$487$	9.11476	+	6.62226i	0.413029	+	0.300083i	0.774827	−	0.632173i	$-0.217837\pi$
$487$	9.11476	+	6.62226i	0.413029	+	0.300083i	−0.361798	+	0.932257i	$0.617837\pi$
$488$		0			0
$489$	−1.25050	−	2.55130i	−0.0565494	−	0.115374i
$490$		0			0
$491$	−11.1254	+	8.08305i	−0.502081	+	0.364783i	−0.809811	−	0.586691i	$-0.800430\pi$
$491$	−11.1254	+	8.08305i	−0.502081	+	0.364783i	0.307731	+	0.951474i	$0.400430\pi$
$492$		0			0
$493$	2.82481	+	8.69386i	0.127223	+	0.391552i
$494$		0			0
$495$	−30.2936	+	2.92789i	−1.36160	+	0.131599i
$496$		0			0
$497$	−0.374624	−	1.15297i	−0.0168042	−	0.0517180i
$498$		0			0
$499$	−21.2230	+	15.4194i	−0.950070	+	0.690266i	−0.950823	−	0.309733i	$-0.899760\pi$
$499$	−21.2230	+	15.4194i	−0.950070	+	0.690266i	0.000753422		1.00000i	$0.499760\pi$
$500$		0			0
$501$	3.78816	+	7.72871i	0.169242	+	0.345293i
$502$		0			0
$503$	15.8081	+	11.4853i	0.704849	+	0.512103i	0.881508	−	0.472169i	$-0.156529\pi$
$503$	15.8081	+	11.4853i	0.704849	+	0.512103i	−0.176659	+	0.984272i	$0.556529\pi$
$504$		0			0
$505$			23.8934i			1.06324i
$506$		0			0
$507$	−14.7148	+	14.2653i	−0.653508	+	0.633545i
$508$		0			0
$509$	−0.170150	+	0.234192i	−0.00754178	+	0.0103804i	−0.812771	−	0.582583i	$-0.802042\pi$
$509$	−0.170150	+	0.234192i	−0.00754178	+	0.0103804i	0.805229	+	0.592963i	$0.202042\pi$
$510$		0			0
$511$	15.3639	−	47.2851i	0.679657	−	2.09177i
$512$		0			0
$513$	5.44250	−	26.3597i	0.240292	−	1.16381i
$514$		0			0
$515$	−1.27560	+	0.414468i	−0.0562097	+	0.0182636i
$516$		0			0
$517$	−5.07423	+	9.26743i	−0.223164	+	0.407581i
$518$		0			0
$519$	−11.1622	−	5.90724i	−0.489966	−	0.259299i
$520$		0			0
$521$	−21.6263	−	29.7661i	−0.947467	−	1.30408i	−0.952643	−	0.304090i	$-0.901648\pi$
$521$	−21.6263	−	29.7661i	−0.947467	−	1.30408i	0.00517663	−	0.999987i	$-0.498352\pi$
$522$		0			0
$523$	4.82060	+	1.56631i	0.210790	+	0.0684899i	0.412509	−	0.910954i	$-0.364653\pi$
$523$	4.82060	+	1.56631i	0.210790	+	0.0684899i	−0.201719	+	0.979444i	$0.564653\pi$
$524$		0			0
$525$	3.88635	+	27.2682i	0.169614	+	1.19008i
$526$		0			0
$527$	4.82767			0.210297
$528$		0			0
$529$	−18.4668			−0.802903
$530$		0			0
$531$	−14.7825	−	11.4571i	−0.641508	−	0.497197i
$532$		0			0
$533$	−6.60800	−	2.14707i	−0.286224	−	0.0929998i
$534$		0			0
$535$	18.7284	+	25.7774i	0.809698	+	1.11445i
$536$		0			0
$537$	7.37614	−	13.9378i	0.318304	−	0.601460i
$538$		0			0
$539$	−3.89591	+	20.6142i	−0.167809	+	0.887917i
$540$		0			0
$541$	20.1681	−	6.55302i	0.867095	−	0.281736i	0.158506	−	0.987358i	$-0.449332\pi$
$541$	20.1681	−	6.55302i	0.867095	−	0.281736i	0.708589	+	0.705622i	$0.249332\pi$
$542$		0			0
$543$	6.56081	−	37.6358i	0.281551	−	1.61511i
$544$		0			0
$545$	2.16540	−	6.66441i	0.0927554	−	0.285472i
$546$		0			0
$547$	0.567465	−	0.781049i	0.0242631	−	0.0333952i	−0.796713	−	0.604358i	$-0.793430\pi$
$547$	0.567465	−	0.781049i	0.0242631	−	0.0333952i	0.820976	+	0.570962i	$0.193430\pi$
$548$		0			0
$549$	−18.3110	−	0.568184i	−0.781496	−	0.0242495i
$550$		0			0
$551$		−	38.4399i		−	1.63760i
$552$		0			0
$553$	−3.92157	−	2.84919i	−0.166762	−	0.121160i
$554$		0			0
$555$	1.00721	−	0.493674i	0.0427537	−	0.0209553i
$556$		0			0
$557$	11.4562	−	8.32342i	0.485415	−	0.352675i	−0.318003	−	0.948090i	$-0.603012\pi$
$557$	11.4562	−	8.32342i	0.485415	−	0.352675i	0.803418	+	0.595415i	$0.203012\pi$
$558$		0			0
$559$	3.87745	+	11.9336i	0.163999	+	0.504736i
$560$		0			0
$561$	−0.319871	+	7.06905i	−0.0135050	+	0.298455i
$562$		0			0
$563$	−3.20574	−	9.86626i	−0.135106	−	0.415813i	0.860501	−	0.509449i	$-0.170151\pi$
$563$	−3.20574	−	9.86626i	−0.135106	−	0.415813i	−0.995606	+	0.0936363i	$0.970151\pi$
$564$		0			0
$565$	29.6656	−	21.5533i	1.24804	−	0.906755i
$566$		0			0
$567$	30.5561	+	12.0700i	1.28324	+	0.506893i
$568$		0			0
$569$	−10.4409	−	7.58577i	−0.437706	−	0.318012i	0.347017	−	0.937859i	$-0.387195\pi$
$569$	−10.4409	−	7.58577i	−0.437706	−	0.318012i	−0.784723	+	0.619847i	$0.787195\pi$
$570$		0			0
$571$		−	29.4474i		−	1.23234i	−0.787614	−	0.616169i	$-0.788684\pi$
$571$		−	29.4474i		−	1.23234i	0.787614	−	0.616169i	$-0.211316\pi$
$572$		0			0
$573$	11.6355	+	12.0021i	0.486079	+	0.501395i
$574$		0			0
$575$	−16.4888	+	22.6949i	−0.687632	+	0.946445i
$576$		0			0
$577$	−1.24885	+	3.84357i	−0.0519904	+	0.160010i	−0.973681	−	0.227917i	$-0.926809\pi$
$577$	−1.24885	+	3.84357i	−0.0519904	+	0.160010i	0.921690	+	0.387927i	$0.126809\pi$
$578$		0			0
$579$	3.85117	+	0.671350i	0.160049	+	0.0279004i
$580$		0			0
$581$	−27.1189	+	8.81148i	−1.12508	+	0.365562i
$582$		0			0
$583$	−24.5974	+	11.6260i	−1.01872	+	0.481499i
$584$		0			0
$585$	−9.52038	+	2.77002i	−0.393619	+	0.114526i
$586$		0			0
$587$	−12.2449	−	16.8536i	−0.505400	−	0.695623i	0.477735	−	0.878504i	$-0.341458\pi$
$587$	−12.2449	−	16.8536i	−0.505400	−	0.695623i	−0.983135	+	0.182880i	$0.941458\pi$
$588$		0			0
$589$	−19.3072	−	6.27330i	−0.795541	−	0.258487i
$590$		0			0
$591$	−8.75607	+	1.24794i	−0.360177	+	0.0513335i
$592$		0			0
$593$	12.8061			0.525882			0.262941	−	0.964812i	$-0.415308\pi$
$593$	12.8061			0.525882			0.262941	+	0.964812i	$0.415308\pi$
$594$		0			0
$595$	13.7544			0.563876
$596$		0			0
$597$	16.7764	−	2.39103i	0.686613	−	0.0978583i
$598$		0			0
$599$	32.1018	+	10.4305i	1.31164	+	0.426178i	0.879617	−	0.475683i	$-0.157799\pi$
$599$	32.1018	+	10.4305i	1.31164	+	0.426178i	0.432026	+	0.901861i	$0.357799\pi$
$600$		0			0
$601$	23.7848	+	32.7370i	0.970202	+	1.33537i	0.941945	+	0.335767i	$0.108996\pi$
$601$	23.7848	+	32.7370i	0.970202	+	1.33537i	0.0282567	+	0.999601i	$0.491004\pi$
$602$		0			0
$603$	9.34616	−	2.71933i	0.380605	−	0.110740i
$604$		0			0
$605$	−33.5876	−	1.99805i	−1.36553	−	0.0812321i
$606$		0			0
$607$	−21.4525	+	6.97033i	−0.870729	+	0.282917i	−0.710102	−	0.704098i	$-0.751351\pi$
$607$	−21.4525	+	6.97033i	−0.870729	+	0.282917i	−0.160626	+	0.987015i	$0.551351\pi$
$608$		0			0
$609$	46.2231	+	8.05779i	1.87305	+	0.326518i
$610$		0			0
$611$	−1.06367	+	3.27365i	−0.0430316	+	0.132438i
$612$		0			0
$613$	16.0195	−	22.0489i	0.647020	−	0.890547i	−0.351945	−	0.936021i	$-0.614480\pi$
$613$	16.0195	−	22.0489i	0.647020	−	0.890547i	0.998966	+	0.0454737i	$0.0144797\pi$
$614$		0			0
$615$	23.7134	+	24.4607i	0.956218	+	0.986350i
$616$		0			0
$617$			6.44731i			0.259559i	0.991543	+	0.129779i	$0.0414269\pi$
$617$			6.44731i			0.259559i	−0.991543	+	0.129779i	$0.958573\pi$
$618$		0			0
$619$	−37.8534	−	27.5021i	−1.52146	−	1.10540i	−0.960760	−	0.277380i	$-0.910534\pi$
$619$	−37.8534	−	27.5021i	−1.52146	−	1.10540i	−0.560695	−	0.828022i	$-0.689466\pi$
$620$		0			0
$621$	13.7876	+	30.4878i	0.553277	+	1.22343i
$622$		0			0
$623$	−30.6463	+	22.2658i	−1.22782	+	0.892061i
$624$		0			0
$625$	−8.59191	−	26.4432i	−0.343677	−	1.05773i
$626$		0			0
$627$	10.4651	−	27.8555i	0.417936	−	1.11244i
$628$		0			0
$629$	−0.0805915	−	0.248035i	−0.00321339	−	0.00988981i
$630$		0			0
$631$	−9.89291	+	7.18762i	−0.393831	+	0.286135i	−0.767023	−	0.641619i	$-0.778263\pi$
$631$	−9.89291	+	7.18762i	−0.393831	+	0.286135i	0.373193	+	0.927754i	$0.378263\pi$
$632$		0			0
$633$	−11.4462	+	5.61023i	−0.454944	+	0.222987i
$634$		0			0
$635$	49.4781	+	35.9479i	1.96348	+	1.42655i
$636$		0			0
$637$			6.83466i			0.270799i
$638$		0			0
$639$	−0.995829	−	0.0309002i	−0.0393944	−	0.00122239i
$640$		0			0
$641$	−11.9388	+	16.4323i	−0.471553	+	0.649038i	−0.976854	−	0.213906i	$-0.931382\pi$
$641$	−11.9388	+	16.4323i	−0.471553	+	0.649038i	0.505301	+	0.862943i	$0.331382\pi$
$642$		0			0
$643$	7.34016	−	22.5907i	0.289468	−	0.890889i	−0.695556	−	0.718472i	$-0.744842\pi$
$643$	7.34016	−	22.5907i	0.289468	−	0.890889i	0.985024	−	0.172418i	$-0.0551580\pi$
$644$		0			0
$645$	10.5659	−	60.6109i	0.416033	−	2.38655i
$646$		0			0
$647$	−1.85376	+	0.602324i	−0.0728789	+	0.0236798i	−0.345230	−	0.938518i	$-0.612199\pi$
$647$	−1.85376	+	0.602324i	−0.0728789	+	0.0236798i	0.272351	+	0.962198i	$0.412199\pi$
$648$		0			0
$649$	−14.1798	−	15.0484i	−0.556606	−	0.590701i
$650$		0			0
$651$	11.5907	−	21.9015i	0.454275	−	0.858388i
$652$		0			0
$653$	13.5705	+	18.6781i	0.531053	+	0.730932i	0.987291	−	0.158926i	$-0.0508031\pi$
$653$	13.5705	+	18.6781i	0.531053	+	0.730932i	−0.456237	+	0.889858i	$0.650803\pi$
$654$		0			0
$655$	17.5926	+	5.71619i	0.687400	+	0.223350i
$656$		0			0
$657$	−32.2957	−	25.0306i	−1.25997	−	0.976536i
$658$		0			0
$659$	44.0671			1.71661			0.858305	−	0.513139i	$-0.171518\pi$
$659$	44.0671			1.71661			0.858305	+	0.513139i	$0.171518\pi$
$660$		0			0
$661$	−31.5126			−1.22570			−0.612848	−	0.790201i	$-0.709976\pi$
$661$	−31.5126			−1.22570			−0.612848	+	0.790201i	$0.709976\pi$
$662$		0			0
$663$	0.325277	+	2.28227i	0.0126327	+	0.0886362i
$664$		0			0
$665$	−55.0078	−	17.8731i	−2.13311	−	0.693090i
$666$		0			0
$667$	28.0884	+	38.6604i	1.08759	+	1.49694i
$668$		0			0
$669$	6.02701	+	3.18961i	0.233018	+	0.123317i
$670$		0			0
$671$	−19.9011	−	3.76113i	−0.768272	−	0.145197i
$672$		0			0
$673$	−37.8385	+	12.2945i	−1.45857	+	0.473918i	−0.927633	−	0.373494i	$-0.878160\pi$
$673$	−37.8385	+	12.2945i	−1.45857	+	0.473918i	−0.530936	+	0.847412i	$0.678160\pi$
$674$		0			0
$675$	22.1686	+	4.57715i	0.853269	+	0.176175i
$676$		0			0
$677$	−12.2831	+	37.8035i	−0.472078	+	1.45291i	0.377780	+	0.925896i	$0.376688\pi$
$677$	−12.2831	+	37.8035i	−0.472078	+	1.45291i	−0.849858	+	0.527012i	$0.823312\pi$
$678$		0			0
$679$	−13.6385	+	18.7718i	−0.523397	+	0.720395i
$680$		0			0
$681$	35.7684	−	34.6758i	1.37065	−	1.32878i
$682$		0			0
$683$			24.4150i			0.934216i	0.884200	+	0.467108i	$0.154704\pi$
$683$			24.4150i			0.934216i	−0.884200	+	0.467108i	$0.845296\pi$
$684$		0			0
$685$	−8.85811	−	6.43579i	−0.338451	−	0.245899i
$686$		0			0
$687$	9.70148	+	19.7933i	0.370135	+	0.755160i
$688$		0			0
$689$	−7.17067	+	5.20980i	−0.273181	+	0.198478i
$690$		0			0
$691$	9.30862	+	28.6490i	0.354117	+	1.08986i	0.956520	+	0.291667i	$0.0942099\pi$
$691$	9.30862	+	28.6490i	0.354117	+	1.08986i	−0.602403	+	0.798192i	$0.705790\pi$
$692$		0			0
$693$	31.3019	+	18.4231i	1.18906	+	0.699837i
$694$		0			0
$695$	−6.26024	−	19.2670i	−0.237465	−	0.730841i
$696$		0			0
$697$	6.40830	−	4.65591i	0.242732	−	0.176355i
$698$		0			0
$699$	−14.5183	−	29.6207i	−0.549133	−	1.12036i
$700$		0			0
$701$	−6.88933	−	5.00539i	−0.260207	−	0.189051i	0.450032	−	0.893013i	$-0.351413\pi$
$701$	−6.88933	−	5.00539i	−0.260207	−	0.189051i	−0.710238	+	0.703962i	$0.751413\pi$
$702$		0			0
$703$			1.09669i			0.0413624i
$704$		0			0
$705$	12.1180	−	11.7478i	0.456390	−	0.442448i
$706$		0			0
$707$	16.7604	−	23.0687i	0.630341	−	0.867589i
$708$		0			0
$709$	−0.381815	+	1.17511i	−0.0143394	+	0.0441320i	−0.957970	−	0.286868i	$-0.907386\pi$
$709$	−0.381815	+	1.17511i	−0.0143394	+	0.0441320i	0.943631	+	0.331000i	$0.107386\pi$
$710$		0			0
$711$	−3.29392	+	2.24046i	−0.123532	+	0.0840236i
$712$		0			0
$713$	24.0019	−	7.79870i	0.898879	−	0.292064i
$714$		0			0
$715$	−10.8728	+	1.39242i	−0.406621	+	0.0520735i
$716$		0			0
$717$	31.3830	+	16.6085i	1.17202	+	0.620255i
$718$		0			0
$719$	−12.2944	−	16.9218i	−0.458503	−	0.631075i	0.515694	−	0.856773i	$-0.327534\pi$
$719$	−12.2944	−	16.9218i	−0.458503	−	0.631075i	−0.974197	+	0.225697i	$0.927534\pi$
$720$		0			0
$721$	1.52231	+	0.494628i	0.0566937	+	0.0184209i
$722$		0			0
$723$	−4.61982	−	32.4145i	−0.171813	−	1.20551i
$724$		0			0
$725$	32.3281			1.20063
$726$		0			0
$727$	5.62159			0.208493			0.104247	−	0.994551i	$-0.466757\pi$
$727$	5.62159			0.208493			0.104247	+	0.994551i	$0.466757\pi$
$728$		0			0
$729$	17.8313	−	20.2742i	0.660420	−	0.750897i
$730$		0			0
$731$	−13.6048	−	4.42046i	−0.503191	−	0.163497i
$732$		0			0
$733$	−10.6432	−	14.6491i	−0.393115	−	0.541076i	0.565884	−	0.824485i	$-0.308535\pi$
$733$	−10.6432	−	14.6491i	−0.393115	−	0.541076i	−0.958999	+	0.283408i	$0.908535\pi$
$734$		0			0
$735$	15.6756	−	29.6202i	0.578201	−	1.09256i
$736$		0			0
$737$	10.6739	−	1.36694i	0.393177	−	0.0503519i
$738$		0			0
$739$	−47.2943	+	15.3668i	−1.73975	+	0.565279i	−0.994800	−	0.101844i	$-0.967526\pi$
$739$	−47.2943	+	15.3668i	−1.73975	+	0.565279i	−0.744948	+	0.667122i	$0.767526\pi$
$740$		0			0
$741$	1.66482	−	9.55015i	0.0611586	−	0.350834i
$742$		0			0
$743$	4.72836	−	14.5524i	0.173467	−	0.533875i	−0.826094	−	0.563533i	$-0.809442\pi$
$743$	4.72836	−	14.5524i	0.173467	−	0.533875i	0.999560	+	0.0296578i	$0.00944174\pi$
$744$		0			0
$745$	−27.7986	+	38.2615i	−1.01846	+	1.40179i
$746$		0			0
$747$	−0.726798	+	23.4227i	−0.0265922	+	0.856993i
$748$		0			0
$749$		−	38.0250i		−	1.38940i
$750$		0			0
$751$	0.955311	+	0.694074i	0.0348598	+	0.0253271i	0.605079	−	0.796166i	$-0.293142\pi$
$751$	0.955311	+	0.694074i	0.0348598	+	0.0253271i	−0.570219	+	0.821493i	$0.693142\pi$
$752$		0			0
$753$	−39.6820	+	19.4498i	−1.44609	+	0.708790i
$754$		0			0
$755$	−16.1082	+	11.7033i	−0.586237	+	0.425926i
$756$		0			0
$757$	16.9914	+	52.2942i	0.617563	+	1.90066i	0.345896	+	0.938273i	$0.387575\pi$
$757$	16.9914	+	52.2942i	0.617563	+	1.90066i	0.271667	+	0.962391i	$0.412425\pi$
$758$		0			0
$759$	9.82914	+	35.6622i	0.356775	+	1.29446i
$760$		0			0
$761$	−11.3528	−	34.9402i	−0.411538	−	1.26658i	−0.915311	−	0.402747i	$-0.868055\pi$
$761$	−11.3528	−	34.9402i	−0.411538	−	1.26658i	0.503774	−	0.863836i	$-0.331945\pi$
$762$		0			0
$763$	−6.76552	+	4.91543i	−0.244928	+	0.177951i
$764$		0			0
$765$	3.82479	−	10.6370i	0.138286	−	0.384581i
$766$		0			0
$767$	−5.44961	−	3.95938i	−0.196774	−	0.142965i
$768$		0			0
$769$			33.5717i			1.21063i	0.795988	+	0.605313i	$0.206952\pi$
$769$			33.5717i			1.21063i	−0.795988	+	0.605313i	$0.793048\pi$
$770$		0			0
$771$	8.19993	+	8.45832i	0.295313	+	0.304619i
$772$		0			0
$773$	4.68913	−	6.45403i	0.168656	−	0.232135i	−0.716320	−	0.697772i	$-0.754175\pi$
$773$	4.68913	−	6.45403i	0.168656	−	0.232135i	0.884976	+	0.465637i	$0.154175\pi$
$774$		0			0
$775$	5.27586	−	16.2374i	0.189515	−	0.583266i
$776$		0			0
$777$	−1.31874	−	0.229888i	−0.0473096	−	0.00824719i
$778$		0			0
$779$	−31.6788	+	10.2931i	−1.13501	+	0.368787i
$780$		0			0
$781$	−1.08230	−	0.204546i	−0.0387278	−	0.00731923i
$782$		0			0
$783$	19.0851	−	33.5060i	0.682046	−	1.19741i
$784$		0			0
$785$	37.5370	+	51.6653i	1.33975	+	1.84401i
$786$		0			0
$787$	22.2647	+	7.23422i	0.793649	+	0.257872i	0.677657	−	0.735378i	$-0.262995\pi$
$787$	22.2647	+	7.23422i	0.793649	+	0.257872i	0.115992	+	0.993250i	$0.462995\pi$
$788$		0			0
$789$	−30.7239	+	4.37886i	−1.09380	+	0.155892i
$790$		0			0
$791$	−43.7606			−1.55595
$792$		0			0
$793$	−6.59822			−0.234310
$794$		0			0
$795$	43.0252	−	6.13209i	1.52595	−	0.217483i
$796$		0			0
$797$	−10.1288	−	3.29105i	−0.358780	−	0.116575i	0.124080	−	0.992272i	$-0.460402\pi$
$797$	−10.1288	−	3.29105i	−0.358780	−	0.116575i	−0.482860	+	0.875697i	$0.660402\pi$
$798$		0			0
$799$	−2.30657	−	3.17472i	−0.0816006	−	0.112314i
$800$		0			0
$801$	8.69726	+	29.8919i	0.307303	+	1.05618i
$802$		0			0
$803$	−30.9788	−	32.8764i	−1.09322	−	1.16018i
$804$		0			0
$805$	68.3833	−	22.2191i	2.41020	−	0.783120i
$806$		0			0
$807$	48.8094	+	8.50864i	1.71817	+	0.299518i
$808$		0			0
$809$	12.2662	−	37.7515i	0.431257	−	1.32727i	−0.465618	−	0.884986i	$-0.654168\pi$
$809$	12.2662	−	37.7515i	0.431257	−	1.32727i	0.896874	−	0.442286i	$-0.145832\pi$
$810$		0			0
$811$	23.3622	−	32.1553i	0.820357	−	1.12912i	−0.169285	−	0.985567i	$-0.554146\pi$
$811$	23.3622	−	32.1553i	0.820357	−	1.12912i	0.989642	−	0.143558i	$-0.0458542\pi$
$812$		0			0
$813$	3.85395	+	3.97539i	0.135164	+	0.139423i
$814$		0			0
$815$			5.01772i			0.175763i
$816$		0			0
$817$	48.6653	+	35.3574i	1.70258	+	1.23700i
$818$		0			0
$819$	11.1349	+	4.00381i	0.389083	+	0.139904i
$820$		0			0
$821$	−29.4898	+	21.4256i	−1.02920	+	0.747758i	−0.968148	−	0.250377i	$-0.919446\pi$
$821$	−29.4898	+	21.4256i	−1.02920	+	0.747758i	−0.0610520	+	0.998135i	$0.519446\pi$
$822$		0			0
$823$	−12.3254	−	37.9338i	−0.429637	−	1.32229i	−0.898483	−	0.439008i	$-0.855330\pi$
$823$	−12.3254	−	37.9338i	−0.429637	−	1.32229i	0.468846	−	0.883280i	$-0.344670\pi$
$824$		0			0
$825$	23.4265	+	8.80118i	0.815607	+	0.306418i
$826$		0			0
$827$	−4.37961	−	13.4790i	−0.152294	−	0.468712i	0.845583	−	0.533844i	$-0.179253\pi$
$827$	−4.37961	−	13.4790i	−0.152294	−	0.468712i	−0.997877	+	0.0651319i	$0.979253\pi$
$828$		0			0
$829$	31.9573	−	23.2184i	1.10992	−	0.806407i	0.127273	−	0.991868i	$-0.459378\pi$
$829$	31.9573	−	23.2184i	1.10992	−	0.806407i	0.982652	+	0.185460i	$0.0593776\pi$
$830$		0			0
$831$	−33.3312	+	16.3370i	−1.15625	+	0.566724i
$832$		0			0
$833$	−6.30372	−	4.57992i	−0.218411	−	0.158685i
$834$		0			0
$835$		−	15.2003i		−	0.526028i
$836$		0			0
$837$	−13.7144	−	15.0540i	−0.474041	−	0.520342i
$838$		0			0
$839$	10.2091	−	14.0516i	0.352457	−	0.485115i	−0.595571	−	0.803303i	$-0.703074\pi$
$839$	10.2091	−	14.0516i	0.352457	−	0.485115i	0.948028	+	0.318187i	$0.103074\pi$
$840$		0			0
$841$	8.05612	−	24.7942i	0.277797	−	0.854972i
$842$		0			0
$843$	−3.07104	+	17.6169i	−0.105772	+	0.606757i
$844$		0			0
$845$	34.4220	−	11.1844i	1.18415	−	0.384755i
$846$		0			0
$847$	31.0267	+	25.4896i	1.06609	+	0.875834i
$848$		0			0
$849$	−4.90058	+	9.26002i	−0.168187	+	0.317803i
$850$		0			0
$851$	−0.801360	−	1.10298i	−0.0274703	−	0.0378096i
$852$		0			0
$853$	8.78978	+	2.85597i	0.300956	+	0.0977867i	0.455603	−	0.890183i	$-0.349424\pi$
$853$	8.78978	+	2.85597i	0.300956	+	0.0977867i	−0.154646	+	0.987970i	$0.549424\pi$
$854$		0			0
$855$	−29.1186	+	37.5703i	−0.995836	+	1.28488i
$856$		0			0
$857$	56.2505			1.92148			0.960740	−	0.277449i	$-0.0894889\pi$
$857$	56.2505			1.92148			0.960740	+	0.277449i	$0.0894889\pi$
$858$		0			0
$859$	38.7547			1.32229			0.661147	−	0.750257i	$-0.270070\pi$
$859$	38.7547			1.32229			0.661147	+	0.750257i	$0.270070\pi$
$860$		0			0
$861$	−5.73664	−	40.2506i	−0.195504	−	1.37174i
$862$		0			0
$863$	5.32524	+	1.73028i	0.181273	+	0.0588993i	0.398247	−	0.917278i	$-0.369619\pi$
$863$	5.32524	+	1.73028i	0.181273	+	0.0588993i	−0.216974	+	0.976177i	$0.569619\pi$
$864$		0			0
$865$	13.1092	+	18.0433i	0.445728	+	0.613491i
$866$		0			0
$867$	23.7021	+	12.5436i	0.804967	+	0.426004i
$868$		0			0
$869$	−3.98174	+	1.88198i	−0.135071	+	0.0638417i
$870$		0			0
$871$	3.33419	−	1.08334i	0.112975	−	0.0367077i
$872$		0			0
$873$	10.7246	+	15.7674i	0.362973	+	0.533644i
$874$		0			0
$875$	−2.22093	+	6.83533i	−0.0750813	+	0.231076i
$876$		0			0
$877$	−20.2476	+	27.8684i	−0.683712	+	0.941049i	−0.999971	−	0.00762378i	$-0.997573\pi$
$877$	−20.2476	+	27.8684i	−0.683712	+	0.941049i	0.316259	+	0.948673i	$0.397573\pi$
$878$		0			0
$879$	34.8460	−	33.7815i	1.17532	−	1.13942i
$880$		0			0
$881$		−	8.23935i		−	0.277591i	−0.990321	−	0.138795i	$-0.955677\pi$
$881$		−	8.23935i		−	0.277591i	0.990321	−	0.138795i	$-0.0443231\pi$
$882$		0			0
$883$	6.22787	+	4.52481i	0.209585	+	0.152272i	0.687626	−	0.726065i	$-0.258653\pi$
$883$	6.22787	+	4.52481i	0.209585	+	0.152272i	−0.478041	+	0.878337i	$0.658653\pi$
$884$		0			0
$885$	14.5366	+	29.6581i	0.488644	+	0.996946i
$886$		0			0
$887$	−10.2713	+	7.46250i	−0.344875	+	0.250566i	−0.746716	−	0.665143i	$-0.768371\pi$
$887$	−10.2713	+	7.46250i	−0.344875	+	0.250566i	0.401841	+	0.915710i	$0.368371\pi$
$888$		0			0
$889$	−22.5541	−	69.4144i	−0.756441	−	2.32808i
$890$		0			0
$891$	22.9519	−	19.0843i	0.768917	−	0.639348i
$892$		0			0
$893$	5.09925	+	15.6939i	0.170640	+	0.525176i
$894$		0			0
$895$	−22.5300	+	16.3690i	−0.753094	+	0.547155i
$896$		0			0
$897$	5.30402	+	10.8214i	0.177096	+	0.361317i
$898$		0			0
$899$	−23.5291	−	17.0949i	−0.784740	−	0.570147i
$900$		0			0
$901$		−	10.1047i		−	0.336637i
$902$		0			0
$903$	−52.7177	+	51.1073i	−1.75434	+	1.70074i
$904$		0			0
$905$	−39.6563	+	54.5823i	−1.31822	+	1.81438i
$906$		0			0
$907$	−13.7515	+	42.3228i	−0.456612	+	1.40531i	0.412621	+	0.910903i	$0.364613\pi$
$907$	−13.7515	+	42.3228i	−0.456612	+	1.40531i	−0.869233	+	0.494403i	$0.835387\pi$
$908$		0			0
$909$	−13.1795	−	19.3766i	−0.437138	−	0.642681i
$910$		0			0
$911$	49.5522	−	16.1005i	1.64174	−	0.533433i	0.664811	−	0.747012i	$-0.268512\pi$
$911$	49.5522	−	16.1005i	1.64174	−	0.533433i	0.976926	+	0.213579i	$0.0685121\pi$
$912$		0			0
$913$	−4.81109	+	25.4566i	−0.159224	+	0.842492i
$914$		0			0
$915$	28.5954	+	15.1333i	0.945336	+	0.500290i
$916$		0			0
$917$	−12.9757	−	17.8595i	−0.428495	−	0.589773i
$918$		0			0
$919$	43.5280	+	14.1431i	1.43586	+	0.466538i	0.920603	−	0.390500i	$-0.127698\pi$
$919$	43.5280	+	14.1431i	1.43586	+	0.466538i	0.515253	+	0.857038i	$0.327698\pi$
$920$		0			0
$921$	1.80291	+	12.6499i	0.0594079	+	0.416830i
$922$		0			0
$923$	−0.358838			−0.0118113
$924$		0			0
$925$	−0.922317			−0.0303256
$926$		0			0
$927$	0.805841	−	1.03973i	0.0264673	−	0.0341494i
$928$		0			0
$929$	−23.7662	−	7.72210i	−0.779743	−	0.253354i	−0.108013	−	0.994150i	$-0.534449\pi$
$929$	−23.7662	−	7.72210i	−0.779743	−	0.253354i	−0.671731	+	0.740796i	$0.734449\pi$
$930$		0			0
$931$	19.2590	+	26.5078i	0.631189	+	0.868757i
$932$		0			0
$933$	−9.18444	+	17.3547i	−0.300685	+	0.568167i
$934$		0			0
$935$	6.00165	−	10.9613i	0.196275	−	0.358471i
$936$		0			0
$937$	−6.47451	+	2.10370i	−0.211513	+	0.0687248i	−0.412857	−	0.910796i	$-0.635469\pi$
$937$	−6.47451	+	2.10370i	−0.211513	+	0.0687248i	0.201344	+	0.979521i	$0.435469\pi$
$938$		0			0
$939$	0.499428	−	2.86494i	0.0162982	−	0.0934939i
$940$		0			0
$941$	−0.0824070	+	0.253623i	−0.00268639	+	0.00826787i	−0.952391	−	0.304880i	$-0.901384\pi$
$941$	−0.0824070	+	0.253623i	−0.00268639	+	0.00826787i	0.949704	+	0.313148i	$0.101384\pi$
$942$		0			0
$943$	24.3392	−	33.5000i	0.792593	−	1.09091i
$944$		0			0
$945$	−39.0735	−	42.8900i	−1.27106	−	1.39521i
$946$		0			0
$947$		−	33.2727i		−	1.08122i	−0.841274	−	0.540609i	$-0.818194\pi$
$947$		−	33.2727i		−	1.08122i	0.841274	−	0.540609i	$-0.181806\pi$
$948$		0			0
$949$	−11.9059	−	8.65011i	−0.386481	−	0.280795i
$950$		0			0
$951$	1.32643	−	0.650138i	0.0430125	−	0.0210822i
$952$		0			0
$953$	28.2860	−	20.5509i	0.916272	−	0.665710i	−0.0263214	−	0.999654i	$-0.508379\pi$
$953$	28.2860	−	20.5509i	0.916272	−	0.665710i	0.942593	+	0.333943i	$0.108379\pi$
$954$		0			0
$955$	−9.12252	−	28.0762i	−0.295198	−	0.908526i
$956$		0			0
$957$	26.5906	−	33.3205i	0.859554	−	1.07710i
$958$		0			0
$959$	4.03788	+	12.4273i	0.130390	+	0.401299i
$960$		0			0
$961$	12.6534	−	9.19320i	0.408173	−	0.296555i
$962$		0			0
$963$	−29.4067	−	10.5739i	−0.947617	−	0.340739i
$964$		0			0
$965$	−5.58525	−	4.05792i	−0.179796	−	0.130629i
$966$		0			0
$967$		−	28.9143i		−	0.929821i	−0.885358	−	0.464910i	$-0.846087\pi$
$967$		−	28.9143i		−	0.929821i	0.885358	−	0.464910i	$-0.153913\pi$
$968$		0			0
$969$	7.69266	+	7.93506i	0.247124	+	0.254911i
$970$		0			0
$971$	−17.7091	+	24.3745i	−0.568312	+	0.782214i	−0.992353	−	0.123429i	$-0.960611\pi$
$971$	−17.7091	+	24.3745i	−0.568312	+	0.782214i	0.424042	+	0.905643i	$0.360611\pi$
$972$		0			0
$973$	−7.47101	+	22.9934i	−0.239509	+	0.737134i
$974$		0			0
$975$	8.03170	+	1.40012i	0.257220	+	0.0448396i
$976$		0			0
$977$	20.3315	−	6.60611i	0.650463	−	0.211348i	0.0348447	−	0.999393i	$-0.488906\pi$
$977$	20.3315	−	6.60611i	0.650463	−	0.211348i	0.615618	+	0.788045i	$0.288906\pi$
$978$		0			0
$979$	4.37190	+	34.1384i	0.139727	+	1.09107i
$980$		0			0
$981$	1.92002	+	6.59899i	0.0613015	+	0.210690i
$982$		0			0
$983$	29.5552	+	40.6793i	0.942665	+	1.29747i	0.954709	+	0.297540i	$0.0961661\pi$
$983$	29.5552	+	40.6793i	0.942665	+	1.29747i	−0.0120443	+	0.999927i	$0.503834\pi$
$984$		0			0
$985$	14.8551	+	4.82670i	0.473322	+	0.153792i
$986$		0			0
$987$	−19.9404	+	2.84198i	−0.634711	+	0.0904611i
$988$		0			0
$989$	−74.7804			−2.37788
$990$		0			0
$991$	−26.0847			−0.828609			−0.414305	−	0.910138i	$-0.635975\pi$
$991$	−26.0847			−0.828609			−0.414305	+	0.910138i	$0.635975\pi$
$992$		0			0
$993$	−36.2257	+	5.16301i	−1.14959	+	0.163843i
$994$		0			0
$995$	−28.4619	−	9.24785i	−0.902304	−	0.293176i
$996$		0			0
$997$	−13.2782	−	18.2759i	−0.420525	−	0.578803i	0.545221	−	0.838292i	$-0.316446\pi$
$997$	−13.2782	−	18.2759i	−0.420525	−	0.578803i	−0.965746	+	0.259490i	$0.916446\pi$
$998$		0			0
$999$	−0.544497	+	0.955924i	−0.0172271	+	0.0302441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.bn.d.17.4		16
3.2	odd	2	inner	528.2.bn.d.17.3		16
4.3	odd	2		132.2.p.a.17.1	✓	16
11.2	odd	10	inner	528.2.bn.d.497.3		16
12.11	even	2		132.2.p.a.17.2	yes	16
33.2	even	10	inner	528.2.bn.d.497.4		16
44.3	odd	10		1452.2.b.e.725.10		16
44.19	even	10		1452.2.b.e.725.9		16
44.35	even	10		132.2.p.a.101.2	yes	16
132.35	odd	10		132.2.p.a.101.1	yes	16
132.47	even	10		1452.2.b.e.725.12		16
132.107	odd	10		1452.2.b.e.725.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.p.a.17.1	✓	16	4.3	odd	2
132.2.p.a.17.2	yes	16	12.11	even	2
132.2.p.a.101.1	yes	16	132.35	odd	10
132.2.p.a.101.2	yes	16	44.35	even	10
528.2.bn.d.17.3		16	3.2	odd	2	inner
528.2.bn.d.17.4		16	1.1	even	1	trivial
528.2.bn.d.497.3		16	11.2	odd	10	inner
528.2.bn.d.497.4		16	33.2	even	10	inner
1452.2.b.e.725.9		16	44.19	even	10
1452.2.b.e.725.10		16	44.3	odd	10
1452.2.b.e.725.11		16	132.107	odd	10
1452.2.b.e.725.12		16	132.47	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 528 = 2^{4} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	528.bn (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.71472 - 0.244388i) q^{3} +(-2.90910 - 0.945225i) q^{5} +(2.14565 + 2.95324i) q^{7} +(2.88055 - 0.838115i) q^{9} +(3.28976 - 0.421300i) q^{11} +(1.02762 - 0.333894i) q^{13} +(-5.21931 - 0.909850i) q^{15} +(-0.380654 + 1.17153i) q^{17} +(3.04469 - 4.19066i) q^{19} +(4.40094 + 4.53961i) q^{21} +6.43947i q^{23} +(3.52435 + 2.56059i) q^{25} +(4.73452 - 2.14111i) q^{27} +(6.00366 - 4.36191i) q^{29} +(-1.21108 - 3.72731i) q^{31} +(5.53806 - 1.52639i) q^{33} +(-3.45045 - 10.6194i) q^{35} +(-0.171284 + 0.124445i) q^{37} +(1.68048 - 0.823673i) q^{39} +(-5.20230 - 3.77969i) q^{41} +11.6128i q^{43} +(-9.17202 - 0.284604i) q^{45} +(-1.87249 + 2.57726i) q^{47} +(-1.95467 + 6.01586i) q^{49} +(-0.366408 + 2.10188i) q^{51} +(-7.80158 + 2.53489i) q^{53} +(-9.96847 - 1.88396i) q^{55} +(4.19665 - 7.92990i) q^{57} +(-3.66438 - 5.04359i) q^{59} +(-5.80774 - 1.88705i) q^{61} +(8.65581 + 6.70864i) q^{63} -3.30506 q^{65} +3.24458 q^{67} +(1.57373 + 11.0419i) q^{69} +(-0.315849 - 0.102625i) q^{71} +(-8.00563 - 11.0188i) q^{73} +(6.66906 + 3.52939i) q^{75} +(8.30288 + 8.81148i) q^{77} +(-1.26290 + 0.410340i) q^{79} +(7.59513 - 4.82846i) q^{81} +(-2.41384 + 7.42902i) q^{83} +(2.21472 - 3.04831i) q^{85} +(9.22861 - 8.94669i) q^{87} +10.3772i q^{89} +(3.19098 + 2.31838i) q^{91} +(-2.98757 - 6.09534i) q^{93} +(-12.8184 + 9.31313i) q^{95} +(1.96422 + 6.04523i) q^{97} +(9.12321 - 3.97077i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 5 q^{9} - 9 q^{15} + 30 q^{19} - 12 q^{25} - q^{27} + 10 q^{31} - 41 q^{33} - 24 q^{37} + 35 q^{39} + 2 q^{45} + 12 q^{49} + 15 q^{51} - 62 q^{55} + 35 q^{57} + 40 q^{61} - 55 q^{63} - 44 q^{67}+ \cdots + 101 q^{99}+O(q^{100}) \) 16 * q - q^3 + 5 * q^9 - 9 * q^15 + 30 * q^19 - 12 * q^25 - q^27 + 10 * q^31 - 41 * q^33 - 24 * q^37 + 35 * q^39 + 2 * q^45 + 12 * q^49 + 15 * q^51 - 62 * q^55 + 35 * q^57 + 40 * q^61 - 55 * q^63 - 44 * q^67 + 46 * q^69 + 10 * q^73 - 21 * q^75 - 20 * q^79 + 57 * q^81 - 60 * q^85 + 60 * q^91 + 7 * q^93 - 36 * q^97 + 101 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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