LMFDB - Embedded newform 528.2.bn.d.497.3

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			497.3
Root			$0.762305 - 1.55528i$ of defining polynomial
Character	$\chi$	$=$	528.497
Dual form			528.2.bn.d.17.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.297452 - 1.70632i) q^{3} +(2.90910 - 0.945225i) q^{5} +(2.14565 - 2.95324i) q^{7} +(-2.82304 - 1.01510i) q^{9} +(-3.28976 - 0.421300i) q^{11} +(1.02762 + 0.333894i) q^{13} +(-0.747537 - 5.24502i) q^{15} +(0.380654 + 1.17153i) q^{17} +(3.04469 + 4.19066i) q^{19} +(-4.40094 - 4.53961i) q^{21} +6.43947i q^{23} +(3.52435 - 2.56059i) q^{25} +(-2.57180 + 4.51507i) q^{27} +(-6.00366 - 4.36191i) q^{29} +(-1.21108 + 3.72731i) q^{31} +(-1.69742 + 5.48806i) q^{33} +(3.45045 - 10.6194i) q^{35} +(-0.171284 - 0.124445i) q^{37} +(0.875396 - 1.65413i) q^{39} +(5.20230 - 3.77969i) q^{41} -11.6128i q^{43} +(-9.17202 - 0.284604i) q^{45} +(1.87249 + 2.57726i) q^{47} +(-1.95467 - 6.01586i) q^{49} +(2.11223 - 0.301042i) q^{51} +(7.80158 + 2.53489i) q^{53} +(-9.96847 + 1.88396i) q^{55} +(8.05624 - 3.94869i) q^{57} +(3.66438 - 5.04359i) q^{59} +(-5.80774 + 1.88705i) q^{61} +(-9.05509 + 6.15908i) q^{63} +3.30506 q^{65} +3.24458 q^{67} +(10.9878 + 1.91543i) q^{69} +(0.315849 - 0.102625i) q^{71} +(-8.00563 + 11.0188i) q^{73} +(-3.32086 - 6.77531i) q^{75} +(-8.30288 + 8.81148i) q^{77} +(-1.26290 - 0.410340i) q^{79} +(6.93916 + 5.73132i) q^{81} +(2.41384 + 7.42902i) q^{83} +(2.21472 + 3.04831i) q^{85} +(-9.22861 + 8.94669i) q^{87} +10.3772i q^{89} +(3.19098 - 2.31838i) q^{91} +(5.99975 + 3.17518i) q^{93} +(12.8184 + 9.31313i) q^{95} +(1.96422 - 6.04523i) q^{97} +(8.85947 + 4.52877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/528\mathbb{Z}\right)^\times$.

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

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
$3$	0.297452	−	1.70632i	0.171734	−	0.985143i
$3$	0.297452	−	1.70632i	0.171734	−	0.985143i
$4$		0			0
$5$	2.90910	−	0.945225i	1.30099	−	0.422718i	0.425065	−	0.905163i	$-0.360251\pi$
$5$	2.90910	−	0.945225i	1.30099	−	0.422718i	0.875926	+	0.482445i	$0.160251\pi$
$6$		0			0
$7$	2.14565	−	2.95324i	0.810981	−	1.11622i	−0.180191	−	0.983632i	$-0.557671\pi$
$7$	2.14565	−	2.95324i	0.810981	−	1.11622i	0.991171	−	0.132588i	$-0.0423286\pi$
$8$		0			0
$9$	−2.82304	−	1.01510i	−0.941015	−	0.338365i
$10$		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	0.448033	−	0.894017i	$-0.352125\pi$
$13$	1.02762	+	0.333894i	0.285010	+	0.0926055i	−0.163023	+	0.986622i	$0.552125\pi$
$14$		0			0
$15$	−0.747537	−	5.24502i	−0.193013	−	1.35426i
$16$		0			0
$17$	0.380654	+	1.17153i	0.0923222	+	0.284138i	0.986547	−	0.163481i	$-0.0522721\pi$
$17$	0.380654	+	1.17153i	0.0923222	+	0.284138i	−0.894224	+	0.447619i	$0.852272\pi$
$18$		0			0
$19$	3.04469	+	4.19066i	0.698500	+	0.961402i	0.999969	+	0.00792623i	$0.00252302\pi$
$19$	3.04469	+	4.19066i	0.698500	+	0.961402i	−0.301469	+	0.953476i	$0.597477\pi$
$20$		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
$27$	−2.57180	+	4.51507i	−0.494942	+	0.868926i
$28$		0			0
$29$	−6.00366	−	4.36191i	−1.11485	−	0.809987i	−0.131430	−	0.991325i	$-0.541957\pi$
$29$	−6.00366	−	4.36191i	−1.11485	−	0.809987i	−0.983421	+	0.181339i	$0.941957\pi$
$30$		0			0
$31$	−1.21108	+	3.72731i	−0.217516	+	0.669446i	0.781449	+	0.623969i	$0.214481\pi$
$31$	−1.21108	+	3.72731i	−0.217516	+	0.669446i	−0.998965	+	0.0454768i	$0.985519\pi$
$32$		0			0
$33$	−1.69742	+	5.48806i	−0.295482	+	0.955348i
$34$		0			0
$35$	3.45045	−	10.6194i	0.583233	−	1.79501i
$36$		0			0
$37$	−0.171284	−	0.124445i	−0.0281589	−	0.0204586i	0.573617	−	0.819124i	$-0.305540\pi$
$37$	−0.171284	−	0.124445i	−0.0281589	−	0.0204586i	−0.601776	+	0.798665i	$0.705540\pi$
$38$		0			0
$39$	0.875396	−	1.65413i	0.140176	−	0.264873i
$40$		0			0
$41$	5.20230	−	3.77969i	0.812462	−	0.590288i	−0.102081	−	0.994776i	$-0.532550\pi$
$41$	5.20230	−	3.77969i	0.812462	−	0.590288i	0.914543	+	0.404488i	$0.132550\pi$
$42$		0			0
$43$		−	11.6128i		−	1.77094i	−0.464699	−	0.885469i	$-0.653837\pi$
$43$		−	11.6128i		−	1.77094i	0.464699	−	0.885469i	$-0.346163\pi$
$44$		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	$-0.125362\pi$
$47$	1.87249	+	2.57726i	0.273130	+	0.375932i	−0.650313	+	0.759666i	$0.725362\pi$
$48$		0			0
$49$	−1.95467	−	6.01586i	−0.279239	−	0.859408i
$50$		0			0
$51$	2.11223	−	0.301042i	0.295772	−	0.0421544i
$52$		0			0
$53$	7.80158	+	2.53489i	1.07163	+	0.348194i	0.791122	−	0.611658i	$-0.209497\pi$
$53$	7.80158	+	2.53489i	1.07163	+	0.348194i	0.280508	+	0.959852i	$0.409497\pi$
$54$		0			0
$55$	−9.96847	+	1.88396i	−1.34415	+	0.254033i
$56$		0			0
$57$	8.05624	−	3.94869i	1.06708	−	0.523017i
$58$		0			0
$59$	3.66438	−	5.04359i	0.477062	−	0.656619i	−0.500875	−	0.865520i	$-0.666988\pi$
$59$	3.66438	−	5.04359i	0.477062	−	0.656619i	0.977937	+	0.208900i	$0.0669884\pi$
$60$		0			0
$61$	−5.80774	+	1.88705i	−0.743604	+	0.241612i	−0.656227	−	0.754564i	$-0.727849\pi$
$61$	−5.80774	+	1.88705i	−0.743604	+	0.241612i	−0.0873774	+	0.996175i	$0.527849\pi$
$62$		0			0
$63$	−9.05509	+	6.15908i	−1.14083	+	0.775971i
$64$		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
$69$	10.9878	+	1.91543i	1.32277	+	0.230591i
$70$		0			0
$71$	0.315849	−	0.102625i	0.0374843	−	0.0121794i	−0.290215	−	0.956962i	$-0.593727\pi$
$71$	0.315849	−	0.102625i	0.0374843	−	0.0121794i	0.327699	+	0.944782i	$0.393727\pi$
$72$		0			0
$73$	−8.00563	+	11.0188i	−0.936989	+	1.28965i	0.0200816	+	0.999798i	$0.493607\pi$
$73$	−8.00563	+	11.0188i	−0.936989	+	1.28965i	−0.957070	+	0.289856i	$0.906393\pi$
$74$		0			0
$75$	−3.32086	−	6.77531i	−0.383460	−	0.782346i
$76$		0			0
$77$	−8.30288	+	8.81148i	−0.946201	+	1.00416i
$78$		0			0
$79$	−1.26290	−	0.410340i	−0.142087	−	0.0461668i	0.237110	−	0.971483i	$-0.423800\pi$
$79$	−1.26290	−	0.410340i	−0.142087	−	0.0461668i	−0.379197	+	0.925316i	$0.623800\pi$
$80$		0			0
$81$	6.93916	+	5.73132i	0.771018	+	0.636813i
$82$		0			0
$83$	2.41384	+	7.42902i	0.264953	+	0.815441i	0.991704	+	0.128541i	$0.0410293\pi$
$83$	2.41384	+	7.42902i	0.264953	+	0.815441i	−0.726751	+	0.686901i	$0.758971\pi$
$84$		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
$93$	5.99975	+	3.17518i	0.622145	+	0.329251i
$94$		0			0
$95$	12.8184	+	9.31313i	1.31514	+	0.955507i
$96$		0			0
$97$	1.96422	−	6.04523i	0.199436	−	0.613801i	−0.800460	−	0.599386i	$-0.795412\pi$
$97$	1.96422	−	6.04523i	0.199436	−	0.613801i	0.999896	−	0.0144147i	$-0.00458849\pi$
$98$		0			0
$99$	8.85947	+	4.52877i	0.890411	+	0.455158i
$100$		0			0
$101$	2.41384	−	7.42902i	0.240186	−	0.739215i	−0.756205	−	0.654334i	$-0.772949\pi$
$101$	2.41384	−	7.42902i	0.240186	−	0.739215i	0.996391	−	0.0848812i	$-0.0270511\pi$
$102$		0			0
$103$	0.354742	+	0.257735i	0.0349538	+	0.0253954i	0.605125	−	0.796130i	$-0.293123\pi$
$103$	0.354742	+	0.257735i	0.0349538	+	0.0253954i	−0.570171	+	0.821526i	$0.693123\pi$
$104$		0			0
$105$	−17.0937	−	9.04633i	−1.66818	−	0.882832i
$106$		0			0
$107$	8.42725	−	6.12275i	0.814693	−	0.591909i	−0.100494	−	0.994938i	$-0.532042\pi$
$107$	8.42725	−	6.12275i	0.814693	−	0.591909i	0.915187	+	0.403029i	$0.132042\pi$
$108$		0			0
$109$		−	2.29088i		−	0.219427i	−0.993963	−	0.109713i	$-0.965007\pi$
$109$		−	2.29088i		−	0.219427i	0.993963	−	0.109713i	$-0.0349933\pi$
$110$		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	$-0.00931468\pi$
$113$	7.04630	+	9.69840i	0.662860	+	0.912349i	−0.336711	+	0.941608i	$0.609315\pi$
$114$		0			0
$115$	6.08675	+	18.7331i	0.567592	+	1.74687i
$116$		0			0
$117$	−2.56208	−	1.98573i	−0.236865	−	0.183581i
$118$		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
$123$	−4.90192	−	10.0010i	−0.441991	−	0.901764i
$124$		0			0
$125$	−1.15726	+	1.59283i	−0.103509	+	0.142467i
$126$		0			0
$127$	−19.0155	+	6.17852i	−1.68736	+	0.548255i	−0.986316	−	0.164866i	$-0.947281\pi$
$127$	−19.0155	+	6.17852i	−1.68736	+	0.548255i	−0.701041	+	0.713121i	$0.747281\pi$
$128$		0			0
$129$	−19.8152	−	3.45425i	−1.74463	−	0.304130i
$130$		0			0
$131$	6.04743			0.528367			0.264183	−	0.964472i	$-0.414898\pi$
$131$	6.04743			0.528367			0.264183	+	0.964472i	$0.414898\pi$
$132$		0			0
$133$	18.9089			1.63961
$134$		0			0
$135$	−3.21386	+	15.5657i	−0.276605	+	1.33969i
$136$		0			0
$137$	−3.40437	+	1.10615i	−0.290855	+	0.0945045i	−0.450810	−	0.892620i	$-0.648865\pi$
$137$	−3.40437	+	1.10615i	−0.290855	+	0.0945045i	0.159955	+	0.987124i	$0.448865\pi$
$138$		0			0
$139$	3.89291	−	5.35813i	0.330192	−	0.454471i	−0.611352	−	0.791358i	$-0.709374\pi$
$139$	3.89291	−	5.35813i	0.330192	−	0.454471i	0.941545	+	0.336888i	$0.109374\pi$
$140$		0			0
$141$	4.95460	−	2.42845i	0.417252	−	0.204512i
$142$		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
$147$	−10.8464	+	1.54586i	−0.894595	+	0.127501i
$148$		0			0
$149$	−4.77786	−	14.7048i	−0.391418	−	1.20466i	−0.931716	−	0.363187i	$-0.881689\pi$
$149$	−4.77786	−	14.7048i	−0.391418	−	1.20466i	0.540298	−	0.841473i	$-0.318311\pi$
$150$		0			0
$151$	3.82609	+	5.26616i	0.311363	+	0.428554i	0.935806	−	0.352517i	$-0.114674\pi$
$151$	3.82609	+	5.26616i	0.311363	+	0.428554i	−0.624443	+	0.781070i	$0.714674\pi$
$152$		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	−0.348911	+	0.937156i	$0.613448\pi$
$157$	−16.8906	+	12.2718i	−1.34802	+	0.979393i	−0.999108	+	0.0422371i	$0.986552\pi$
$158$		0			0
$159$	6.64592	−	12.5580i	0.527056	−	0.995912i
$160$		0			0
$161$	19.0173	+	13.8169i	1.49877	+	1.08892i
$162$		0			0
$163$	−0.506916	+	1.56013i	−0.0397047	+	0.122199i	−0.968944	−	0.247279i	$-0.920463\pi$
$163$	−0.506916	+	1.56013i	−0.0397047	+	0.122199i	0.929240	+	0.369478i	$0.120463\pi$
$164$		0			0
$165$	0.249490	+	17.5698i	0.0194228	+	1.36780i
$166$		0			0
$167$	−1.53561	+	4.72613i	−0.118829	+	0.365719i	−0.992726	−	0.120392i	$-0.961585\pi$
$167$	−1.53561	+	4.72613i	−0.118829	+	0.365719i	0.873897	+	0.486111i	$0.161585\pi$
$168$		0			0
$169$	−9.57270	−	6.95498i	−0.736362	−	0.534998i
$170$		0			0
$171$	−4.34138	−	14.9211i	−0.331994	−	1.14104i
$172$		0			0
$173$	5.89880	−	4.28573i	0.448477	−	0.325838i	−0.340517	−	0.940238i	$-0.610602\pi$
$173$	5.89880	−	4.28573i	0.448477	−	0.325838i	0.788994	+	0.614400i	$0.210602\pi$
$174$		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	$-0.310511\pi$
$179$	−5.35142	−	7.36560i	−0.399984	−	0.550531i	−0.960740	+	0.277450i	$0.910511\pi$
$180$		0			0
$181$	6.81590	+	20.9772i	0.506622	+	1.55922i	0.798027	+	0.602622i	$0.205877\pi$
$181$	6.81590	+	20.9772i	0.506622	+	1.55922i	−0.291405	+	0.956600i	$0.594123\pi$
$182$		0			0
$183$	1.49238	+	10.4712i	0.110320	+	0.774050i
$184$		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
$189$	7.81590	+	17.2829i	0.568523	+	1.25715i
$190$		0			0
$191$	−5.67281	+	7.80795i	−0.410470	+	0.564964i	−0.963333	−	0.268309i	$-0.913535\pi$
$191$	−5.67281	+	7.80795i	−0.410470	+	0.564964i	0.552863	+	0.833272i	$0.313535\pi$
$192$		0			0
$193$	2.14654	−	0.697453i	0.154511	−	0.0502037i	−0.230740	−	0.973015i	$-0.574115\pi$
$193$	2.14654	−	0.697453i	0.154511	−	0.0502037i	0.385251	+	0.922812i	$0.374115\pi$
$194$		0			0
$195$	0.983095	−	5.63948i	0.0704009	−	0.403851i
$196$		0			0
$197$	5.10641			0.363816			0.181908	−	0.983316i	$-0.441773\pi$
$197$	5.10641			0.363816			0.181908	+	0.983316i	$0.441773\pi$
$198$		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
$201$	0.965105	−	5.53628i	0.0680733	−	0.390499i
$202$		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
$207$	6.53667	−	18.1789i	0.454330	−	1.26352i
$208$		0			0
$209$	−8.25077	−	15.0690i	−0.570718	−	1.04234i
$210$		0			0
$211$	−6.99936	−	2.27423i	−0.481856	−	0.156564i	0.0580092	−	0.998316i	$-0.481525\pi$
$211$	−6.99936	−	2.27423i	−0.481856	−	0.156564i	−0.539865	+	0.841752i	$0.681525\pi$
$212$		0			0
$213$	−0.0811619	−	0.569464i	−0.00556112	−	0.0390191i
$214$		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	−0.476013	−	0.879438i	$-0.657918\pi$
$223$	3.18505	−	2.31408i	0.213287	−	0.154962i	0.689300	+	0.724476i	$0.257918\pi$
$224$		0			0
$225$	−12.5486	+	3.65111i	−0.836576	+	0.243407i
$226$		0			0
$227$	−23.2691	−	16.9060i	−1.54442	−	1.12209i	−0.947483	−	0.319805i	$-0.896382\pi$
$227$	−23.2691	−	16.9060i	−1.54442	−	1.12209i	−0.596941	−	0.802285i	$-0.703618\pi$
$228$		0			0
$229$	3.93271	−	12.1036i	0.259881	−	0.799830i	−0.732948	−	0.680284i	$-0.761856\pi$
$229$	3.93271	−	12.1036i	0.259881	−	0.799830i	0.992829	−	0.119546i	$-0.0381437\pi$
$230$		0			0
$231$	12.5655	+	16.7883i	0.826748	+	1.10459i
$232$		0			0
$233$	5.88532	−	18.1131i	0.385560	−	1.18663i	−0.550513	−	0.834826i	$-0.685568\pi$
$233$	5.88532	−	18.1131i	0.385560	−	1.18663i	0.936073	−	0.351805i	$-0.114432\pi$
$234$		0			0
$235$	7.88335	+	5.72759i	0.514253	+	0.373627i
$236$		0			0
$237$	−1.07582	+	2.03285i	−0.0698821	+	0.132048i
$238$		0			0
$239$	−16.5847	+	12.0495i	−1.07278	+	0.779418i	−0.976409	−	0.215928i	$-0.930722\pi$
$239$	−16.5847	+	12.0495i	−1.07278	+	0.779418i	−0.0963677	+	0.995346i	$0.530722\pi$
$240$		0			0
$241$			18.9036i			1.21769i	0.793290	+	0.608845i	$0.208367\pi$
$241$			18.9036i			1.21769i	−0.793290	+	0.608845i	$0.791633\pi$
$242$		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
$249$	13.3943	−	1.90900i	0.848828	−	0.120978i
$250$		0			0
$251$	24.2657	+	7.88439i	1.53164	+	0.497659i	0.949054	−	0.315114i	$-0.102043\pi$
$251$	24.2657	+	7.88439i	1.53164	+	0.497659i	0.582582	+	0.812772i	$0.302043\pi$
$252$		0			0
$253$	2.71295	−	21.1843i	0.170562	−	1.33185i
$254$		0			0
$255$	5.86015	−	2.87230i	0.366977	−	0.179870i
$256$		0			0
$257$	−3.99783	+	5.50254i	−0.249378	+	0.343239i	−0.915293	−	0.402788i	$-0.868041\pi$
$257$	−3.99783	+	5.50254i	−0.249378	+	0.343239i	0.665915	+	0.746027i	$0.268041\pi$
$258$		0			0
$259$	−0.735032	+	0.238826i	−0.0456726	+	0.0148399i
$260$		0			0
$261$	12.5208	+	18.4082i	0.775020	+	1.13944i
$262$		0			0
$263$	17.9177			1.10485			0.552426	−	0.833562i	$-0.313702\pi$
$263$	17.9177			1.10485			0.552426	+	0.833562i	$0.313702\pi$
$264$		0			0
$265$	25.0916			1.54137
$266$		0			0
$267$	17.7068	+	3.08671i	1.08364	+	0.188903i
$268$		0			0
$269$	−27.2051	+	8.83946i	−1.65872	+	0.538952i	−0.980604	−	0.196001i	$-0.937204\pi$
$269$	−27.2051	+	8.83946i	−1.65872	+	0.538952i	−0.678119	+	0.734952i	$0.737204\pi$
$270$		0			0
$271$	1.87897	−	2.58618i	0.114139	−	0.157099i	−0.748125	−	0.663558i	$-0.769046\pi$
$271$	1.87897	−	2.58618i	0.114139	−	0.157099i	0.862264	+	0.506458i	$0.169046\pi$
$272$		0			0
$273$	−3.00674	−	6.13444i	−0.181976	−	0.371273i
$274$		0			0
$275$	−12.6730	+	6.93891i	−0.764213	+	0.418432i
$276$		0			0
$277$	−20.3821	−	6.62255i	−1.22464	−	0.397911i	−0.375872	−	0.926672i	$-0.622657\pi$
$277$	−20.3821	−	6.62255i	−1.22464	−	0.397911i	−0.848771	+	0.528761i	$0.822657\pi$
$278$		0			0
$279$	7.20251	−	9.29302i	0.431203	−	0.556358i
$280$		0			0
$281$	3.19044	+	9.81917i	0.190326	+	0.585763i	0.999999	−	0.00111782i	$-0.000355813\pi$
$281$	3.19044	+	9.81917i	0.190326	+	0.585763i	−0.809674	+	0.586881i	$0.800356\pi$
$282$		0			0
$283$	−3.55539	−	4.89357i	−0.211346	−	0.290893i	0.690162	−	0.723655i	$-0.257539\pi$
$283$	−3.55539	−	4.89357i	−0.211346	−	0.290893i	−0.901508	+	0.432762i	$0.857539\pi$
$284$		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
$291$	−9.73083	−	5.14974i	−0.570432	−	0.301883i
$292$		0			0
$293$	−22.6690	−	16.4700i	−1.32434	−	0.962186i	−0.999867	−	0.0162899i	$-0.994815\pi$
$293$	−22.6690	−	16.4700i	−1.32434	−	0.962186i	−0.324469	−	0.945896i	$-0.605185\pi$
$294$		0			0
$295$	5.89274	−	18.1360i	0.343089	−	1.05592i
$296$		0			0
$297$	10.3628	−	13.7700i	0.601310	−	0.799016i
$298$		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
$303$	−11.9583	−	6.32855i	−0.686985	−	0.363566i
$304$		0			0
$305$	−15.1116	+	10.9792i	−0.865289	+	0.628669i
$306$		0			0
$307$		−	7.37725i		−	0.421042i	−0.977589	−	0.210521i	$-0.932484\pi$
$307$		−	7.37725i		−	0.421042i	0.977589	−	0.210521i	$-0.0675160\pi$
$308$		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	$-0.0958422\pi$
$311$	6.66335	+	9.17131i	0.377844	+	0.520057i	−0.577168	+	0.816625i	$0.695842\pi$
$312$		0			0
$313$	0.518846	+	1.59684i	0.0293269	+	0.0902589i	0.964649	−	0.263539i	$-0.0848899\pi$
$313$	0.518846	+	1.59684i	0.0293269	+	0.0902589i	−0.935322	+	0.353798i	$0.884890\pi$
$314$		0			0
$315$	−20.5205	+	26.4765i	−1.15620	+	1.49178i
$316$		0			0
$317$	−0.811116	−	0.263548i	−0.0455568	−	0.0148023i	0.286150	−	0.958185i	$-0.407624\pi$
$317$	−0.811116	−	0.263548i	−0.0455568	−	0.0148023i	−0.331707	+	0.943383i	$0.607624\pi$
$318$		0			0
$319$	17.9129	+	16.8790i	1.00293	+	0.945041i
$320$		0			0
$321$	−7.94067	−	16.2008i	−0.443205	−	0.904240i
$322$		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
$327$	−3.90897	−	0.681427i	−0.216167	−	0.0376830i
$328$		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
$333$	0.357219	+	0.525183i	0.0195755	+	0.0287799i
$334$		0			0
$335$	9.43881	−	3.06686i	0.515697	−	0.167560i
$336$		0			0
$337$	7.08246	−	9.74817i	0.385806	−	0.531017i	−0.571305	−	0.820738i	$-0.693563\pi$
$337$	7.08246	−	9.74817i	0.385806	−	0.531017i	0.957111	+	0.289721i	$0.0935626\pi$
$338$		0			0
$339$	18.6445	−	9.13843i	1.01263	−	0.496331i
$340$		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
$345$	33.7751	−	4.81374i	1.81839	−	0.259163i
$346$		0			0
$347$	0.646694	+	1.99032i	0.0347164	+	0.106846i	0.966913	−	0.255106i	$-0.0821104\pi$
$347$	0.646694	+	1.99032i	0.0347164	+	0.106846i	−0.932197	+	0.361952i	$0.882110\pi$
$348$		0			0
$349$	7.38093	+	10.1590i	0.395092	+	0.543798i	0.959504	−	0.281696i	$-0.0908969\pi$
$349$	7.38093	+	10.1590i	0.395092	+	0.543798i	−0.564412	+	0.825493i	$0.690897\pi$
$350$		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
$357$	3.64307	−	6.88386i	0.192812	−	0.364333i
$358$		0			0
$359$	−22.8386	−	16.5932i	−1.20538	−	0.875758i	−0.210575	−	0.977578i	$-0.567533\pi$
$359$	−22.8386	−	16.5932i	−1.20538	−	0.875758i	−0.994803	+	0.101820i	$0.967533\pi$
$360$		0			0
$361$	−2.42014	+	7.44841i	−0.127376	+	0.392022i
$362$		0			0
$363$	7.89621	−	17.3393i	0.414443	−	0.910075i
$364$		0			0
$365$	−12.8740	+	39.6220i	−0.673854	+	2.07391i
$366$		0			0
$367$	−11.1605	−	8.10857i	−0.582573	−	0.423264i	0.257078	−	0.966391i	$-0.417240\pi$
$367$	−11.1605	−	8.10857i	−0.582573	−	0.423264i	−0.839651	+	0.543127i	$0.817240\pi$
$368$		0			0
$369$	−18.5231	+	5.38941i	−0.964272	+	0.280561i
$370$		0			0
$371$	24.2256	−	17.6009i	1.25773	−	0.913795i
$372$		0			0
$373$			4.34739i			0.225099i	0.993646	+	0.112550i	$0.0359017\pi$
$373$			4.34739i			0.225099i	−0.993646	+	0.112550i	$0.964098\pi$
$374$		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	−0.955418	−	0.295258i	$-0.904594\pi$
$379$	−6.93091	−	21.3311i	−0.356017	−	1.09571i	0.599401	−	0.800449i	$-0.295406\pi$
$380$		0			0
$381$	4.88632	+	34.2844i	0.250334	+	1.75644i
$382$		0			0
$383$	−17.2752	−	5.61305i	−0.882722	−	0.286814i	−0.167635	−	0.985849i	$-0.553613\pi$
$383$	−17.2752	−	5.61305i	−0.882722	−	0.286814i	−0.715087	+	0.699036i	$0.753613\pi$
$384$		0			0
$385$	−15.8251	+	33.4816i	−0.806522	+	1.70638i
$386$		0			0
$387$	−11.7881	+	32.7835i	−0.599223	+	1.66648i
$388$		0			0
$389$	14.8824	−	20.4839i	0.754567	−	1.03857i	−0.243079	−	0.970006i	$-0.578157\pi$
$389$	14.8824	−	20.4839i	0.754567	−	1.03857i	0.997647	−	0.0685664i	$-0.0218425\pi$
$390$		0			0
$391$	−7.54405	+	2.45121i	−0.381519	+	0.123963i
$392$		0			0
$393$	1.79882	−	10.3188i	0.0907385	−	0.520517i
$394$		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
$399$	5.62447	−	32.2645i	0.281576	−	1.61525i
$400$		0			0
$401$	−17.6060	+	5.72055i	−0.879204	+	0.285671i	−0.713627	−	0.700526i	$-0.752949\pi$
$401$	−17.6060	+	5.72055i	−0.879204	+	0.285671i	−0.165577	+	0.986197i	$0.552949\pi$
$402$		0			0
$403$	−2.48905	+	3.42589i	−0.123989	+	0.170656i
$404$		0			0
$405$	25.6041	+	10.1139i	1.27228	+	0.502565i
$406$		0			0
$407$	0.511054	+	0.481556i	0.0253320	+	0.0238698i
$408$		0			0
$409$	11.0518	+	3.59093i	0.546474	+	0.177560i	0.569226	−	0.822181i	$-0.307243\pi$
$409$	11.0518	+	3.59093i	0.546474	+	0.177560i	−0.0227521	+	0.999741i	$0.507243\pi$
$410$		0			0
$411$	0.874803	+	6.13797i	0.0431508	+	0.302764i
$412$		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	−0.884620	−	0.466313i	$-0.845582\pi$
$421$	−14.6602	+	10.6512i	−0.714493	+	0.519109i	0.170127	+	0.985422i	$0.445582\pi$
$422$		0			0
$423$	−2.66995	−	9.17646i	−0.129818	−	0.446175i
$424$		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
$429$	−3.57673	+	5.07288i	−0.172686	+	0.244921i
$430$		0			0
$431$	−4.44702	+	13.6865i	−0.214205	+	0.659256i	0.785004	+	0.619491i	$0.212661\pi$
$431$	−4.44702	+	13.6865i	−0.214205	+	0.659256i	−0.999209	+	0.0397652i	$0.987339\pi$
$432$		0			0
$433$	−16.4587	−	11.9579i	−0.790954	−	0.574661i	0.117293	−	0.993097i	$-0.462578\pi$
$433$	−16.4587	−	11.9579i	−0.790954	−	0.574661i	−0.908246	+	0.418436i	$0.862578\pi$
$434$		0			0
$435$	−18.3903	+	34.7500i	−0.881750	+	1.66613i
$436$		0			0
$437$	−26.9856	+	19.6062i	−1.29090	+	0.937891i
$438$		0			0
$439$		−	4.46676i		−	0.213187i	−0.994303	−	0.106593i	$-0.966006\pi$
$439$		−	4.46676i		−	0.213187i	0.994303	−	0.106593i	$-0.0339943\pi$
$440$		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	$-0.295804\pi$
$443$	−7.33510	−	10.0959i	−0.348501	−	0.479670i	−0.946900	+	0.321528i	$0.895804\pi$
$444$		0			0
$445$	9.80876	+	30.1883i	0.464980	+	1.43106i
$446$		0			0
$447$	−26.5122	+	3.77860i	−1.25398	+	0.178722i
$448$		0			0
$449$	12.9949	+	4.22230i	0.613268	+	0.199263i	0.599149	−	0.800638i	$-0.295506\pi$
$449$	12.9949	+	4.22230i	0.613268	+	0.199263i	0.0141188	+	0.999900i	$0.495506\pi$
$450$		0			0
$451$	−18.7067	+	10.2425i	−0.880863	+	0.482302i
$452$		0			0
$453$	10.1238	−	4.96209i	0.475658	−	0.233140i
$454$		0			0
$455$	7.09151	−	9.76062i	0.332455	−	0.457585i
$456$		0			0
$457$	8.47229	−	2.75281i	0.396317	−	0.128771i	−0.104077	−	0.994569i	$-0.533189\pi$
$457$	8.47229	−	2.75281i	0.396317	−	0.128771i	0.500393	+	0.865798i	$0.333189\pi$
$458$		0			0
$459$	−6.26852	−	1.29426i	−0.292589	−	0.0604110i
$460$		0			0
$461$	12.5468			0.584365			0.292182	−	0.956363i	$-0.405619\pi$
$461$	12.5468			0.584365			0.292182	+	0.956363i	$0.405619\pi$
$462$		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
$465$	20.4552	+	3.56582i	0.948585	+	0.165361i
$466$		0			0
$467$	20.4005	−	6.62854i	0.944024	−	0.306732i	0.203739	−	0.979025i	$-0.434691\pi$
$467$	20.4005	−	6.62854i	0.944024	−	0.306732i	0.740285	+	0.672293i	$0.234691\pi$
$468$		0			0
$469$	6.96174	−	9.58201i	0.321463	−	0.442456i
$470$		0			0
$471$	15.9154	+	32.4710i	0.733342	+	1.49619i
$472$		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
$477$	−19.4511	−	15.0754i	−0.890603	−	0.690257i
$478$		0			0
$479$	2.31222	+	7.11627i	0.105648	+	0.325151i	0.989882	−	0.141893i	$-0.0453189\pi$
$479$	2.31222	+	7.11627i	0.105648	+	0.325151i	−0.884234	+	0.467044i	$0.845319\pi$
$480$		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	−0.361798	−	0.932257i	$-0.617837\pi$
$487$	9.11476	−	6.62226i	0.413029	−	0.300083i	0.774827	+	0.632173i	$0.217837\pi$
$488$		0			0
$489$	2.51129	+	1.32902i	0.113564	+	0.0601005i
$490$		0			0
$491$	11.1254	+	8.08305i	0.502081	+	0.364783i	0.809811	−	0.586691i	$-0.199570\pi$
$491$	11.1254	+	8.08305i	0.502081	+	0.364783i	−0.307731	+	0.951474i	$0.599570\pi$
$492$		0			0
$493$	2.82481	−	8.69386i	0.127223	−	0.391552i
$494$		0			0
$495$	30.0538	+	4.80045i	1.35082	+	0.215764i
$496$		0			0
$497$	0.374624	−	1.15297i	0.0168042	−	0.0517180i
$498$		0			0
$499$	−21.2230	−	15.4194i	−0.950070	−	0.690266i	0.000753422	−	1.00000i	$-0.499760\pi$
$499$	−21.2230	−	15.4194i	−0.950070	−	0.690266i	−0.950823	+	0.309733i	$0.899760\pi$
$500$		0			0
$501$	7.60750	+	4.02604i	0.339878	+	0.179870i
$502$		0			0
$503$	−15.8081	+	11.4853i	−0.704849	+	0.512103i	−0.881508	−	0.472169i	$-0.843471\pi$
$503$	−15.8081	+	11.4853i	−0.704849	+	0.512103i	0.176659	+	0.984272i	$0.443471\pi$
$504$		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	$-0.197958\pi$
$509$	0.170150	+	0.234192i	0.00754178	+	0.0103804i	−0.805229	+	0.592963i	$0.797958\pi$
$510$		0			0
$511$	15.3639	+	47.2851i	0.679657	+	2.09177i
$512$		0			0
$513$	−26.7514	+	2.96948i	−1.18110	+	0.131106i
$514$		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
$519$	−5.55821	−	11.3400i	−0.243978	−	0.497772i
$520$		0			0
$521$	21.6263	−	29.7661i	0.947467	−	1.30408i	−0.00517663	−	0.999987i	$-0.501648\pi$
$521$	21.6263	−	29.7661i	0.947467	−	1.30408i	0.952643	−	0.304090i	$-0.0983522\pi$
$522$		0			0
$523$	4.82060	−	1.56631i	0.210790	−	0.0684899i	−0.201719	−	0.979444i	$-0.564653\pi$
$523$	4.82060	−	1.56631i	0.210790	−	0.0684899i	0.412509	+	0.910954i	$0.364653\pi$
$524$		0			0
$525$	−27.1345	−	4.73019i	−1.18425	−	0.206443i
$526$		0			0
$527$	−4.82767			−0.210297
$528$		0			0
$529$	−18.4668			−0.802903
$530$		0			0
$531$	−15.4644	+	10.5186i	−0.671099	+	0.456468i
$532$		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
$537$	−14.1598	+	6.94032i	−0.611042	+	0.299497i
$538$		0			0
$539$	3.89591	+	20.6142i	0.167809	+	0.887917i
$540$		0			0
$541$	20.1681	+	6.55302i	0.867095	+	0.281736i	0.708589	−	0.705622i	$-0.249332\pi$
$541$	20.1681	+	6.55302i	0.867095	+	0.281736i	0.158506	+	0.987358i	$0.449332\pi$
$542$		0			0
$543$	37.8212	−	5.39039i	1.62306	−	0.231324i
$544$		0			0
$545$	−2.16540	−	6.66441i	−0.0927554	−	0.285472i
$546$		0			0
$547$	0.567465	+	0.781049i	0.0242631	+	0.0333952i	0.820976	−	0.570962i	$-0.193430\pi$
$547$	0.567465	+	0.781049i	0.0242631	+	0.0333952i	−0.796713	+	0.604358i	$0.793430\pi$
$548$		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
$555$	−0.524675	+	0.991414i	−0.0222712	+	0.0420832i
$556$		0			0
$557$	−11.4562	−	8.32342i	−0.485415	−	0.352675i	0.318003	−	0.948090i	$-0.396988\pi$
$557$	−11.4562	−	8.32342i	−0.485415	−	0.352675i	−0.803418	+	0.595415i	$0.796988\pi$
$558$		0			0
$559$	3.87745	−	11.9336i	0.163999	−	0.504736i
$560$		0			0
$561$	−7.07557	+	0.100473i	−0.298731	+	0.00424196i
$562$		0			0
$563$	3.20574	−	9.86626i	0.135106	−	0.415813i	−0.860501	−	0.509449i	$-0.829849\pi$
$563$	3.20574	−	9.86626i	0.135106	−	0.415813i	0.995606	+	0.0936363i	$0.0298491\pi$
$564$		0			0
$565$	29.6656	+	21.5533i	1.24804	+	0.906755i
$566$		0			0
$567$	31.8150	−	8.19558i	1.33610	−	0.344182i
$568$		0			0
$569$	10.4409	−	7.58577i	0.437706	−	0.318012i	−0.347017	−	0.937859i	$-0.612805\pi$
$569$	10.4409	−	7.58577i	0.437706	−	0.318012i	0.784723	+	0.619847i	$0.212805\pi$
$570$		0			0
$571$			29.4474i			1.23234i	0.787614	+	0.616169i	$0.211316\pi$
$571$			29.4474i			1.23234i	−0.787614	+	0.616169i	$0.788684\pi$
$572$		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	0.921690	−	0.387927i	$-0.126809\pi$
$577$	−1.24885	−	3.84357i	−0.0519904	−	0.160010i	−0.973681	+	0.227917i	$0.926809\pi$
$578$		0			0
$579$	−0.551584	−	3.87014i	−0.0229231	−	0.160837i
$580$		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
$585$	−9.33032	−	3.35495i	−0.385761	−	0.138710i
$586$		0			0
$587$	12.2449	−	16.8536i	0.505400	−	0.695623i	−0.477735	−	0.878504i	$-0.658542\pi$
$587$	12.2449	−	16.8536i	0.505400	−	0.695623i	0.983135	+	0.182880i	$0.0585421\pi$
$588$		0			0
$589$	−19.3072	+	6.27330i	−0.795541	+	0.258487i
$590$		0			0
$591$	1.51891	−	8.71316i	0.0624796	−	0.358411i
$592$		0			0
$593$	−12.8061			−0.525882			−0.262941	−	0.964812i	$-0.584692\pi$
$593$	−12.8061			−0.525882			−0.262941	+	0.964812i	$0.584692\pi$
$594$		0			0
$595$	13.7544			0.563876
$596$		0			0
$597$	2.91019	−	16.6942i	0.119106	−	0.683248i
$598$		0			0
$599$	−32.1018	+	10.4305i	−1.31164	+	0.426178i	−0.879617	−	0.475683i	$-0.842201\pi$
$599$	−32.1018	+	10.4305i	−1.31164	+	0.426178i	−0.432026	+	0.901861i	$0.642201\pi$
$600$		0			0
$601$	23.7848	−	32.7370i	0.970202	−	1.33537i	0.0282567	−	0.999601i	$-0.491004\pi$
$601$	23.7848	−	32.7370i	0.970202	−	1.33537i	0.941945	−	0.335767i	$-0.108996\pi$
$602$		0			0
$603$	−9.15959	−	3.29355i	−0.373007	−	0.134124i
$604$		0			0
$605$	33.5876	−	1.99805i	1.36553	−	0.0812321i
$606$		0			0
$607$	−21.4525	−	6.97033i	−0.870729	−	0.282917i	−0.160626	−	0.987015i	$-0.551351\pi$
$607$	−21.4525	−	6.97033i	−0.870729	−	0.282917i	−0.710102	+	0.704098i	$0.751351\pi$
$608$		0			0
$609$	6.62032	+	46.4508i	0.268269	+	1.88228i
$610$		0			0
$611$	1.06367	+	3.27365i	0.0430316	+	0.132438i
$612$		0			0
$613$	16.0195	+	22.0489i	0.647020	+	0.890547i	0.998966	−	0.0454737i	$-0.0144797\pi$
$613$	16.0195	+	22.0489i	0.647020	+	0.890547i	−0.351945	+	0.936021i	$0.614480\pi$
$614$		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	−0.560695	+	0.828022i	$0.689466\pi$
$619$	−37.8534	+	27.5021i	−1.52146	+	1.10540i	−0.960760	+	0.277380i	$0.910534\pi$
$620$		0			0
$621$	−29.0747	−	16.5610i	−1.16673	−	0.664570i
$622$		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
$627$	−28.1667	+	9.59614i	−1.12487	+	0.383233i
$628$		0			0
$629$	0.0805915	−	0.248035i	0.00321339	−	0.00988981i
$630$		0			0
$631$	−9.89291	−	7.18762i	−0.393831	−	0.286135i	0.373193	−	0.927754i	$-0.378263\pi$
$631$	−9.89291	−	7.18762i	−0.393831	−	0.286135i	−0.767023	+	0.641619i	$0.778263\pi$
$632$		0			0
$633$	−5.96253	+	11.2667i	−0.236989	+	0.447810i
$634$		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	$-0.0686185\pi$
$641$	11.9388	+	16.4323i	0.471553	+	0.649038i	−0.505301	+	0.862943i	$0.668618\pi$
$642$		0			0
$643$	7.34016	+	22.5907i	0.289468	+	0.890889i	0.985024	+	0.172418i	$0.0551580\pi$
$643$	7.34016	+	22.5907i	0.289468	+	0.890889i	−0.695556	+	0.718472i	$0.744842\pi$
$644$		0			0
$645$	−60.9094	+	8.68101i	−2.39831	+	0.341814i
$646$		0			0
$647$	1.85376	+	0.602324i	0.0728789	+	0.0236798i	0.345230	−	0.938518i	$-0.387801\pi$
$647$	1.85376	+	0.602324i	0.0728789	+	0.0236798i	−0.272351	+	0.962198i	$0.587801\pi$
$648$		0			0
$649$	−14.1798	+	15.0484i	−0.556606	+	0.590701i
$650$		0			0
$651$	22.2504	−	10.9058i	0.872064	−	0.427434i
$652$		0			0
$653$	−13.5705	+	18.6781i	−0.531053	+	0.730932i	−0.987291	−	0.158926i	$-0.949197\pi$
$653$	−13.5705	+	18.6781i	−0.531053	+	0.730932i	0.456237	+	0.889858i	$0.349197\pi$
$654$		0			0
$655$	17.5926	−	5.71619i	0.687400	−	0.223350i
$656$		0			0
$657$	33.7854	−	22.9801i	1.31809	−	0.896540i
$658$		0			0
$659$	−44.0671			−1.71661			−0.858305	−	0.513139i	$-0.828482\pi$
$659$	−44.0671			−1.71661			−0.858305	+	0.513139i	$0.828482\pi$
$660$		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
$663$	2.27109	+	0.395905i	0.0882018	+	0.0153757i
$664$		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
$669$	−3.00115	−	6.12304i	−0.116031	−	0.236730i
$670$		0			0
$671$	19.9011	−	3.76113i	0.768272	−	0.145197i
$672$		0			0
$673$	−37.8385	−	12.2945i	−1.45857	−	0.473918i	−0.530936	−	0.847412i	$-0.678160\pi$
$673$	−37.8385	−	12.2945i	−1.45857	−	0.473918i	−0.927633	+	0.373494i	$0.878160\pi$
$674$		0			0
$675$	2.49734	+	22.4980i	0.0961227	+	0.865948i
$676$		0			0
$677$	12.2831	+	37.8035i	0.472078	+	1.45291i	0.849858	+	0.527012i	$0.176688\pi$
$677$	12.2831	+	37.8035i	0.472078	+	1.45291i	−0.377780	+	0.925896i	$0.623312\pi$
$678$		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
$687$	−19.4828	−	10.3107i	−0.743317	−	0.393377i
$688$		0			0
$689$	7.17067	+	5.20980i	0.273181	+	0.198478i
$690$		0			0
$691$	9.30862	−	28.6490i	0.354117	−	1.08986i	−0.602403	−	0.798192i	$-0.705790\pi$
$691$	9.30862	−	28.6490i	0.354117	−	1.08986i	0.956520	−	0.291667i	$-0.0942099\pi$
$692$		0			0
$693$	32.3839	−	16.4470i	1.23016	−	0.624769i
$694$		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
$699$	−29.1562	−	15.4300i	−1.10279	−	0.583617i
$700$		0			0
$701$	6.88933	−	5.00539i	0.260207	−	0.189051i	−0.450032	−	0.893013i	$-0.648587\pi$
$701$	6.88933	−	5.00539i	0.260207	−	0.189051i	0.710238	+	0.703962i	$0.248587\pi$
$702$		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	0.943631	−	0.331000i	$-0.107386\pi$
$709$	−0.381815	−	1.17511i	−0.0143394	−	0.0441320i	−0.957970	+	0.286868i	$0.907386\pi$
$710$		0			0
$711$	3.14868	+	2.44037i	0.118085	+	0.0915209i
$712$		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
$717$	15.6271	+	31.8830i	0.583606	+	1.19069i
$718$		0			0
$719$	12.2944	−	16.9218i	0.458503	−	0.631075i	−0.515694	−	0.856773i	$-0.672466\pi$
$719$	12.2944	−	16.9218i	0.458503	−	0.631075i	0.974197	+	0.225697i	$0.0724660\pi$
$720$		0			0
$721$	1.52231	−	0.494628i	0.0566937	−	0.0184209i
$722$		0			0
$723$	32.2556	+	5.62292i	1.19960	+	0.209119i
$724$		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
$729$	−13.7717	−	23.2237i	−0.510064	−	0.860136i
$730$		0			0
$731$	13.6048	−	4.42046i	0.503191	−	0.163497i
$732$		0			0
$733$	−10.6432	+	14.6491i	−0.393115	+	0.541076i	−0.958999	−	0.283408i	$-0.908535\pi$
$733$	−10.6432	+	14.6491i	−0.393115	+	0.541076i	0.565884	+	0.824485i	$0.308535\pi$
$734$		0			0
$735$	−30.0921	+	14.7494i	−1.10996	+	0.544038i
$736$		0			0
$737$	−10.6739	−	1.36694i	−0.393177	−	0.0503519i
$738$		0			0
$739$	−47.2943	−	15.3668i	−1.73975	−	0.565279i	−0.744948	−	0.667122i	$-0.767526\pi$
$739$	−47.2943	−	15.3668i	−1.73975	−	0.565279i	−0.994800	+	0.101844i	$0.967526\pi$
$740$		0			0
$741$	9.59719	−	1.36782i	0.352562	−	0.0502482i
$742$		0			0
$743$	−4.72836	−	14.5524i	−0.173467	−	0.533875i	0.826094	−	0.563533i	$-0.190558\pi$
$743$	−4.72836	−	14.5524i	−0.173467	−	0.533875i	−0.999560	+	0.0296578i	$0.990558\pi$
$744$		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	−0.570219	−	0.821493i	$-0.693142\pi$
$751$	0.955311	−	0.694074i	0.0348598	−	0.0253271i	0.605079	+	0.796166i	$0.293142\pi$
$752$		0			0
$753$	20.6712	−	39.0597i	0.753299	−	1.42342i
$754$		0			0
$755$	16.1082	+	11.7033i	0.586237	+	0.425926i
$756$		0			0
$757$	16.9914	−	52.2942i	0.617563	−	1.90066i	0.271667	−	0.962391i	$-0.412425\pi$
$757$	16.9914	−	52.2942i	0.617563	−	1.90066i	0.345896	−	0.938273i	$-0.387575\pi$
$758$		0			0
$759$	−35.3402	−	10.9305i	−1.28277	−	0.396751i
$760$		0			0
$761$	11.3528	−	34.9402i	0.411538	−	1.26658i	−0.503774	−	0.863836i	$-0.668055\pi$
$761$	11.3528	−	34.9402i	0.411538	−	1.26658i	0.915311	−	0.402747i	$-0.131945\pi$
$762$		0			0
$763$	−6.76552	−	4.91543i	−0.244928	−	0.177951i
$764$		0			0
$765$	−3.15794	−	10.8537i	−0.114176	−	0.392415i
$766$		0			0
$767$	5.44961	−	3.95938i	0.196774	−	0.142965i
$768$		0			0
$769$		−	33.5717i		−	1.21063i	−0.795988	−	0.605313i	$-0.793048\pi$
$769$		−	33.5717i		−	1.21063i	0.795988	−	0.605313i	$-0.206952\pi$
$770$		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	$-0.245825\pi$
$773$	−4.68913	−	6.45403i	−0.168656	−	0.232135i	−0.884976	+	0.465637i	$0.845825\pi$
$774$		0			0
$775$	5.27586	+	16.2374i	0.189515	+	0.583266i
$776$		0			0
$777$	0.188877	+	1.32524i	0.00677593	+	0.0475426i
$778$		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
$783$	35.1345	−	15.8890i	1.25561	−	0.567826i
$784$		0			0
$785$	−37.5370	+	51.6653i	−1.33975	+	1.84401i
$786$		0			0
$787$	22.2647	−	7.23422i	0.793649	−	0.257872i	0.115992	−	0.993250i	$-0.462995\pi$
$787$	22.2647	−	7.23422i	0.793649	−	0.257872i	0.677657	+	0.735378i	$0.262995\pi$
$788$		0			0
$789$	5.32965	−	30.5733i	0.189741	−	1.08844i
$790$		0			0
$791$	43.7606			1.55595
$792$		0			0
$793$	−6.59822			−0.234310
$794$		0			0
$795$	7.46356	−	42.8143i	0.264705	−	1.51847i
$796$		0			0
$797$	10.1288	−	3.29105i	0.358780	−	0.116575i	−0.124080	−	0.992272i	$-0.539598\pi$
$797$	10.1288	−	3.29105i	0.358780	−	0.116575i	0.482860	+	0.875697i	$0.339598\pi$
$798$		0			0
$799$	−2.30657	+	3.17472i	−0.0816006	+	0.112314i
$800$		0			0
$801$	10.5338	−	29.2952i	0.372194	−	1.03510i
$802$		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
$807$	6.99074	+	49.0498i	0.246086	+	1.72664i
$808$		0			0
$809$	−12.2662	−	37.7515i	−0.431257	−	1.32727i	−0.896874	−	0.442286i	$-0.854168\pi$
$809$	−12.2662	−	37.7515i	−0.431257	−	1.32727i	0.465618	−	0.884986i	$-0.345832\pi$
$810$		0			0
$811$	23.3622	+	32.1553i	0.820357	+	1.12912i	0.989642	+	0.143558i	$0.0458542\pi$
$811$	23.3622	+	32.1553i	0.820357	+	1.12912i	−0.169285	+	0.985567i	$0.554146\pi$
$812$		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
$819$	−11.3617	+	3.30575i	−0.397009	+	0.115512i
$820$		0			0
$821$	29.4898	+	21.4256i	1.02920	+	0.747758i	0.968148	−	0.250377i	$-0.0805545\pi$
$821$	29.4898	+	21.4256i	1.02920	+	0.747758i	0.0610520	+	0.998135i	$0.480554\pi$
$822$		0			0
$823$	−12.3254	+	37.9338i	−0.429637	+	1.32229i	0.468846	+	0.883280i	$0.344670\pi$
$823$	−12.3254	+	37.9338i	−0.429637	+	1.32229i	−0.898483	+	0.439008i	$0.855330\pi$
$824$		0			0
$825$	8.07038	+	23.6882i	0.280974	+	0.824718i
$826$		0			0
$827$	4.37961	−	13.4790i	0.152294	−	0.468712i	−0.845583	−	0.533844i	$-0.820747\pi$
$827$	4.37961	−	13.4790i	0.152294	−	0.468712i	0.997877	+	0.0651319i	$0.0207468\pi$
$828$		0			0
$829$	31.9573	+	23.2184i	1.10992	+	0.806407i	0.982652	−	0.185460i	$-0.0593776\pi$
$829$	31.9573	+	23.2184i	1.10992	+	0.806407i	0.127273	+	0.991868i	$0.459378\pi$
$830$		0			0
$831$	−17.3629	+	32.8085i	−0.602312	+	1.13811i
$832$		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	$-0.296926\pi$
$839$	−10.2091	−	14.0516i	−0.352457	−	0.485115i	−0.948028	+	0.318187i	$0.896926\pi$
$840$		0			0
$841$	8.05612	+	24.7942i	0.277797	+	0.854972i
$842$		0			0
$843$	17.7036	−	2.52318i	0.609746	−	0.0869029i
$844$		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
$849$	−9.40755	+	4.61102i	−0.322866	+	0.158250i
$850$		0			0
$851$	0.801360	−	1.10298i	0.0274703	−	0.0378096i
$852$		0			0
$853$	8.78978	−	2.85597i	0.300956	−	0.0977867i	−0.154646	−	0.987970i	$-0.549424\pi$
$853$	8.78978	−	2.85597i	0.300956	−	0.0977867i	0.455603	+	0.890183i	$0.349424\pi$
$854$		0			0
$855$	−26.7333	−	39.3033i	−0.914259	−	1.34415i
$856$		0			0
$857$	−56.2505			−1.92148			−0.960740	−	0.277449i	$-0.910511\pi$
$857$	−56.2505			−1.92148			−0.960740	+	0.277449i	$0.910511\pi$
$858$		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
$861$	−40.0533	−	6.98224i	−1.36501	−	0.237954i
$862$		0			0
$863$	−5.32524	+	1.73028i	−0.181273	+	0.0588993i	−0.398247	−	0.917278i	$-0.630381\pi$
$863$	−5.32524	+	1.73028i	−0.181273	+	0.0588993i	0.216974	+	0.976177i	$0.430381\pi$
$864$		0			0
$865$	13.1092	−	18.0433i	0.445728	−	0.613491i
$866$		0			0
$867$	−11.8025	−	24.0798i	−0.400833	−	0.817792i
$868$		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
$873$	−11.6816	+	15.0721i	−0.395361	+	0.510113i
$874$		0			0
$875$	2.22093	+	6.83533i	0.0750813	+	0.231076i
$876$		0			0
$877$	−20.2476	−	27.8684i	−0.683712	−	0.941049i	0.316259	−	0.948673i	$-0.397573\pi$
$877$	−20.2476	−	27.8684i	−0.683712	−	0.941049i	−0.999971	+	0.00762378i	$0.997573\pi$
$878$		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	−0.478041	−	0.878337i	$-0.658653\pi$
$883$	6.22787	−	4.52481i	0.209585	−	0.152272i	0.687626	+	0.726065i	$0.258653\pi$
$884$		0			0
$885$	−29.1930	−	15.4495i	−0.981311	−	0.519328i
$886$		0			0
$887$	10.2713	+	7.46250i	0.344875	+	0.250566i	0.746716	−	0.665143i	$-0.231629\pi$
$887$	10.2713	+	7.46250i	0.344875	+	0.250566i	−0.401841	+	0.915710i	$0.631629\pi$
$888$		0			0
$889$	−22.5541	+	69.4144i	−0.756441	+	2.32808i
$890$		0			0
$891$	−20.4136	−	21.7781i	−0.683880	−	0.729594i
$892$		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
$897$	10.6517	+	5.63709i	0.355650	+	0.188217i
$898$		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	−0.869233	−	0.494403i	$-0.835387\pi$
$907$	−13.7515	−	42.3228i	−0.456612	−	1.40531i	0.412621	−	0.910903i	$-0.364613\pi$
$908$		0			0
$909$	−14.3555	+	18.5222i	−0.476143	+	0.614342i
$910$		0			0
$911$	−49.5522	−	16.1005i	−1.64174	−	0.533433i	−0.664811	−	0.747012i	$-0.731488\pi$
$911$	−49.5522	−	16.1005i	−1.64174	−	0.533433i	−0.976926	+	0.213579i	$0.931488\pi$
$912$		0			0
$913$	−4.81109	−	25.4566i	−0.159224	−	0.842492i
$914$		0			0
$915$	14.2391	+	29.0510i	0.470730	+	0.960397i
$916$		0			0
$917$	12.9757	−	17.8595i	0.428495	−	0.589773i
$918$		0			0
$919$	43.5280	−	14.1431i	1.43586	−	0.466538i	0.515253	−	0.857038i	$-0.327698\pi$
$919$	43.5280	−	14.1431i	1.43586	−	0.466538i	0.920603	+	0.390500i	$0.127698\pi$
$920$		0			0
$921$	−12.5879	−	2.19438i	−0.414787	−	0.0723072i
$922$		0			0
$923$	0.358838			0.0118113
$924$		0			0
$925$	−0.922317			−0.0303256
$926$		0			0
$927$	−0.739828	−	1.08770i	−0.0242991	−	0.0357246i
$928$		0			0
$929$	23.7662	−	7.72210i	0.779743	−	0.253354i	0.108013	−	0.994150i	$-0.465551\pi$
$929$	23.7662	−	7.72210i	0.779743	−	0.253354i	0.671731	+	0.740796i	$0.265551\pi$
$930$		0			0
$931$	19.2590	−	26.5078i	0.631189	−	0.868757i
$932$		0			0
$933$	17.6312	−	8.64177i	0.577220	−	0.282919i
$934$		0			0
$935$	−6.00165	−	10.9613i	−0.196275	−	0.358471i
$936$		0			0
$937$	−6.47451	−	2.10370i	−0.211513	−	0.0687248i	0.201344	−	0.979521i	$-0.435469\pi$
$937$	−6.47451	−	2.10370i	−0.211513	−	0.0687248i	−0.412857	+	0.910796i	$0.635469\pi$
$938$		0			0
$939$	2.87906	−	0.410332i	0.0939544	−	0.0133907i
$940$		0			0
$941$	0.0824070	+	0.253623i	0.00268639	+	0.00826787i	0.952391	−	0.304880i	$-0.0986164\pi$
$941$	0.0824070	+	0.253623i	0.00268639	+	0.00826787i	−0.949704	+	0.313148i	$0.898616\pi$
$942$		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
$951$	−0.690964	+	1.30563i	−0.0224061	+	0.0423379i
$952$		0			0
$953$	−28.2860	−	20.5509i	−0.916272	−	0.665710i	0.0263214	−	0.999654i	$-0.491621\pi$
$953$	−28.2860	−	20.5509i	−0.916272	−	0.665710i	−0.942593	+	0.333943i	$0.891621\pi$
$954$		0			0
$955$	−9.12252	+	28.0762i	−0.295198	+	0.908526i
$956$		0			0
$957$	34.1291	−	25.5444i	1.10324	−	0.825734i
$958$		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
$963$	−30.0057	+	8.73035i	−0.966920	+	0.281332i
$964$		0			0
$965$	5.58525	−	4.05792i	0.179796	−	0.130629i
$966$		0			0
$967$			28.9143i			0.929821i	0.885358	+	0.464910i	$0.153913\pi$
$967$			28.9143i			0.929821i	−0.885358	+	0.464910i	$0.846087\pi$
$968$		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	$-0.0393890\pi$
$971$	17.7091	+	24.3745i	0.568312	+	0.782214i	−0.424042	+	0.905643i	$0.639389\pi$
$972$		0			0
$973$	−7.47101	−	22.9934i	−0.239509	−	0.737134i
$974$		0			0
$975$	−1.15034	−	8.07126i	−0.0368404	−	0.258487i
$976$		0			0
$977$	−20.3315	−	6.60611i	−0.650463	−	0.211348i	−0.0348447	−	0.999393i	$-0.511094\pi$
$977$	−20.3315	−	6.60611i	−0.650463	−	0.211348i	−0.615618	+	0.788045i	$0.711094\pi$
$978$		0			0
$979$	4.37190	−	34.1384i	0.139727	−	1.09107i
$980$		0			0
$981$	−2.32546	+	6.46726i	−0.0742463	+	0.206484i
$982$		0			0
$983$	−29.5552	+	40.6793i	−0.942665	+	1.29747i	0.0120443	+	0.999927i	$0.496166\pi$
$983$	−29.5552	+	40.6793i	−0.942665	+	1.29747i	−0.954709	+	0.297540i	$0.903834\pi$
$984$		0			0
$985$	14.8551	−	4.82670i	0.473322	−	0.153792i
$986$		0			0
$987$	3.45906	−	19.8427i	0.110103	−	0.631600i
$988$		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
$993$	−6.28405	+	36.0482i	−0.199418	+	1.14395i
$994$		0			0
$995$	28.4619	−	9.24785i	0.902304	−	0.293176i
$996$		0			0
$997$	−13.2782	+	18.2759i	−0.420525	+	0.578803i	−0.965746	−	0.259490i	$-0.916446\pi$
$997$	−13.2782	+	18.2759i	−0.420525	+	0.578803i	0.545221	+	0.838292i	$0.316446\pi$
$998$		0			0
$999$	1.00239	−	0.453312i	0.0317141	−	0.0143421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	528.2.bn.d.497.3		16
3.2	odd	2	inner	528.2.bn.d.497.4		16
4.3	odd	2		132.2.p.a.101.2	yes	16
11.6	odd	10	inner	528.2.bn.d.17.4		16
12.11	even	2		132.2.p.a.101.1	yes	16
33.17	even	10	inner	528.2.bn.d.17.3		16
44.7	even	10		1452.2.b.e.725.10		16
44.15	odd	10		1452.2.b.e.725.9		16
44.39	even	10		132.2.p.a.17.1	✓	16
132.59	even	10		1452.2.b.e.725.11		16
132.83	odd	10		132.2.p.a.17.2	yes	16
132.95	odd	10		1452.2.b.e.725.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.p.a.17.1	✓	16	44.39	even	10
132.2.p.a.17.2	yes	16	132.83	odd	10
132.2.p.a.101.1	yes	16	12.11	even	2
132.2.p.a.101.2	yes	16	4.3	odd	2
528.2.bn.d.17.3		16	33.17	even	10	inner
528.2.bn.d.17.4		16	11.6	odd	10	inner
528.2.bn.d.497.3		16	1.1	even	1	trivial
528.2.bn.d.497.4		16	3.2	odd	2	inner
1452.2.b.e.725.9		16	44.15	odd	10
1452.2.b.e.725.10		16	44.7	even	10
1452.2.b.e.725.11		16	132.59	even	10
1452.2.b.e.725.12		16	132.95	odd	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)

\(f(q)\)	\(=\)	\(q+(0.297452 - 1.70632i) q^{3} +(2.90910 - 0.945225i) q^{5} +(2.14565 - 2.95324i) q^{7} +(-2.82304 - 1.01510i) q^{9} +(-3.28976 - 0.421300i) q^{11} +(1.02762 + 0.333894i) q^{13} +(-0.747537 - 5.24502i) q^{15} +(0.380654 + 1.17153i) q^{17} +(3.04469 + 4.19066i) q^{19} +(-4.40094 - 4.53961i) q^{21} +6.43947i q^{23} +(3.52435 - 2.56059i) q^{25} +(-2.57180 + 4.51507i) q^{27} +(-6.00366 - 4.36191i) q^{29} +(-1.21108 + 3.72731i) q^{31} +(-1.69742 + 5.48806i) q^{33} +(3.45045 - 10.6194i) q^{35} +(-0.171284 - 0.124445i) q^{37} +(0.875396 - 1.65413i) q^{39} +(5.20230 - 3.77969i) q^{41} -11.6128i q^{43} +(-9.17202 - 0.284604i) q^{45} +(1.87249 + 2.57726i) q^{47} +(-1.95467 - 6.01586i) q^{49} +(2.11223 - 0.301042i) q^{51} +(7.80158 + 2.53489i) q^{53} +(-9.96847 + 1.88396i) q^{55} +(8.05624 - 3.94869i) q^{57} +(3.66438 - 5.04359i) q^{59} +(-5.80774 + 1.88705i) q^{61} +(-9.05509 + 6.15908i) q^{63} +3.30506 q^{65} +3.24458 q^{67} +(10.9878 + 1.91543i) q^{69} +(0.315849 - 0.102625i) q^{71} +(-8.00563 + 11.0188i) q^{73} +(-3.32086 - 6.77531i) q^{75} +(-8.30288 + 8.81148i) q^{77} +(-1.26290 - 0.410340i) q^{79} +(6.93916 + 5.73132i) q^{81} +(2.41384 + 7.42902i) q^{83} +(2.21472 + 3.04831i) q^{85} +(-9.22861 + 8.94669i) q^{87} +10.3772i q^{89} +(3.19098 - 2.31838i) q^{91} +(5.99975 + 3.17518i) q^{93} +(12.8184 + 9.31313i) q^{95} +(1.96422 - 6.04523i) q^{97} +(8.85947 + 4.52877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{3} + 5 q^{9} - 9 q^{15} + 30 q^{19} - 12 q^{25} - q^{27} + 10 q^{31} - 41 q^{33} - 24 q^{37} + 35 q^{39} + 2 q^{45} + 12 q^{49} + 15 q^{51} - 62 q^{55} + 35 q^{57} + 40 q^{61} - 55 q^{63} - 44 q^{67}+ \cdots + 101 q^{99}+O(q^{100}) \) 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

Fields

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Database

Properties

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