LMFDB - Embedded newform 352.2.u.a.95.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(63,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.u (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			95.3
Character	$\chi$	$=$	352.95
Dual form			352.2.u.a.63.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.26076 - 0.734564i) q^{3} +(0.0210968 - 0.0153277i) q^{5} +(-0.140366 - 0.432001i) q^{7} +(2.14438 + 1.55799i) q^{9} +(-3.11868 + 1.12864i) q^{11} +(-1.27904 + 1.76045i) q^{13} +(-0.0589538 + 0.0191553i) q^{15} +(1.94076 + 2.67122i) q^{17} +(-0.802698 + 2.47045i) q^{19} +1.07976i q^{21} +3.69681i q^{23} +(-1.54487 + 4.75464i) q^{25} +(0.488184 + 0.671927i) q^{27} +(-9.31791 + 3.02757i) q^{29} +(-1.81250 + 2.49470i) q^{31} +(7.87964 - 0.260699i) q^{33} +(-0.00958284 - 0.00696234i) q^{35} +(-2.27701 - 7.00791i) q^{37} +(4.18475 - 3.04040i) q^{39} +(-3.59088 - 1.16675i) q^{41} +10.2735 q^{43} +0.0691199 q^{45} +(-10.7024 - 3.47742i) q^{47} +(5.49620 - 3.99322i) q^{49} +(-2.42539 - 7.46459i) q^{51} +(7.06555 + 5.13342i) q^{53} +(-0.0484947 + 0.0716128i) q^{55} +(3.62941 - 4.99545i) q^{57} +(6.16979 - 2.00468i) q^{59} +(-7.78761 - 10.7187i) q^{61} +(0.372054 - 1.14506i) q^{63} +0.0567444i q^{65} +8.31591i q^{67} +(2.71555 - 8.35759i) q^{69} +(-2.37385 - 3.26733i) q^{71} +(-3.48170 + 1.13127i) q^{73} +(6.98517 - 9.61426i) q^{75} +(0.925328 + 1.18885i) q^{77} +(-2.29058 - 1.66420i) q^{79} +(-3.06734 - 9.44029i) q^{81} +(-1.28563 + 0.934066i) q^{83} +(0.0818874 + 0.0266068i) q^{85} +23.2895 q^{87} -11.9991 q^{89} +(0.940047 + 0.305440i) q^{91} +(5.93015 - 4.30850i) q^{93} +(0.0209320 + 0.0644220i) q^{95} +(0.120561 + 0.0875928i) q^{97} +(-8.44605 - 2.43863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97}+O(q^{100}) $ 48 * q + 4 * q^9 + 4 * q^25 + 36 * q^33 + 40 * q^41 - 96 * q^45 - 4 * q^49 - 8 * q^53 + 20 * q^57 - 8 * q^69 - 40 * q^73 - 72 * q^77 - 72 * q^81 - 80 * q^85 - 40 * q^89 + 8 * q^93 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.26076	−	0.734564i	−1.30525	−	0.424101i	−0.427844	−	0.903853i	$-0.640727\pi$
$3$	−2.26076	−	0.734564i	−1.30525	−	0.424101i	−0.877404	+	0.479752i	$0.840727\pi$
$4$		0			0
$5$	0.0210968	−	0.0153277i	0.00943476	−	0.00685476i	−0.583058	−	0.812431i	$-0.698144\pi$
$5$	0.0210968	−	0.0153277i	0.00943476	−	0.00685476i	0.592493	+	0.805576i	$0.298144\pi$
$6$		0			0
$7$	−0.140366	−	0.432001i	−0.0530532	−	0.163281i	0.921019	−	0.389517i	$-0.127358\pi$
$7$	−0.140366	−	0.432001i	−0.0530532	−	0.163281i	−0.974073	+	0.226236i	$0.927358\pi$
$8$		0			0
$9$	2.14438	+	1.55799i	0.714795	+	0.519329i
$10$		0			0
$11$	−3.11868	+	1.12864i	−0.940318	+	0.340297i
$11$	−3.11868	+	1.12864i	−0.940318	+	0.340297i
$12$		0			0
$13$	−1.27904	+	1.76045i	−0.354741	+	0.488260i	−0.948674	−	0.316255i	$-0.897574\pi$
$13$	−1.27904	+	1.76045i	−0.354741	+	0.488260i	0.593933	+	0.804515i	$0.297574\pi$
$14$		0			0
$15$	−0.0589538	+	0.0191553i	−0.0152218	+	0.00494587i
$16$		0			0
$17$	1.94076	+	2.67122i	0.470703	+	0.647867i	0.976685	−	0.214677i	$-0.0688700\pi$
$17$	1.94076	+	2.67122i	0.470703	+	0.647867i	−0.505982	+	0.862544i	$0.668870\pi$
$18$		0			0
$19$	−0.802698	+	2.47045i	−0.184152	+	0.566760i	−0.999933	−	0.0116005i	$-0.996307\pi$
$19$	−0.802698	+	2.47045i	−0.184152	+	0.566760i	0.815781	+	0.578361i	$0.196307\pi$
$20$		0			0
$21$			1.07976i			0.235622i
$22$		0			0
$23$			3.69681i			0.770838i	0.922742	+	0.385419i	$0.125943\pi$
$23$			3.69681i			0.770838i	−0.922742	+	0.385419i	$0.874057\pi$
$24$		0			0
$25$	−1.54487	+	4.75464i	−0.308975	+	0.950927i
$26$		0			0
$27$	0.488184	+	0.671927i	0.0939510	+	0.129312i
$28$		0			0
$29$	−9.31791	+	3.02757i	−1.73029	+	0.562206i	−0.993492	−	0.113903i	$-0.963665\pi$
$29$	−9.31791	+	3.02757i	−1.73029	+	0.562206i	−0.736801	+	0.676110i	$0.763665\pi$
$30$		0			0
$31$	−1.81250	+	2.49470i	−0.325535	+	0.448061i	−0.940147	−	0.340769i	$-0.889313\pi$
$31$	−1.81250	+	2.49470i	−0.325535	+	0.448061i	0.614612	+	0.788830i	$0.289313\pi$
$32$		0			0
$33$	7.87964	−	0.260699i	1.37167	−	0.0453819i
$34$		0			0
$35$	−0.00958284	−	0.00696234i	−0.00161980	−	0.00117685i
$36$		0			0
$37$	−2.27701	−	7.00791i	−0.374338	−	1.15209i	−0.943924	−	0.330162i	$-0.892896\pi$
$37$	−2.27701	−	7.00791i	−0.374338	−	1.15209i	0.569586	−	0.821932i	$-0.307104\pi$
$38$		0			0
$39$	4.18475	−	3.04040i	0.670097	−	0.486854i
$40$		0			0
$41$	−3.59088	−	1.16675i	−0.560801	−	0.182215i	0.0148804	−	0.999889i	$-0.495263\pi$
$41$	−3.59088	−	1.16675i	−0.560801	−	0.182215i	−0.575682	+	0.817674i	$0.695263\pi$
$42$		0			0
$43$	10.2735			1.56669			0.783345	−	0.621588i	$-0.213512\pi$
$43$	10.2735			1.56669			0.783345	+	0.621588i	$0.213512\pi$
$44$		0			0
$45$	0.0691199			0.0103038
$46$		0			0
$47$	−10.7024	−	3.47742i	−1.56111	−	0.507234i	−0.604002	−	0.796983i	$-0.706428\pi$
$47$	−10.7024	−	3.47742i	−1.56111	−	0.507234i	−0.957103	+	0.289749i	$0.906428\pi$
$48$		0			0
$49$	5.49620	−	3.99322i	0.785171	−	0.570460i
$50$		0			0
$51$	−2.42539	−	7.46459i	−0.339623	−	1.04525i
$52$		0			0
$53$	7.06555	+	5.13342i	0.970527	+	0.705129i	0.955572	−	0.294759i	$-0.0952393\pi$
$53$	7.06555	+	5.13342i	0.970527	+	0.705129i	0.0149557	+	0.999888i	$0.495239\pi$
$54$		0			0
$55$	−0.0484947	+	0.0716128i	−0.00653903	+	0.00965627i
$56$		0			0
$57$	3.62941	−	4.99545i	0.480727	−	0.661664i
$58$		0			0
$59$	6.16979	−	2.00468i	0.803238	−	0.260988i	0.121507	−	0.992591i	$-0.461227\pi$
$59$	6.16979	−	2.00468i	0.803238	−	0.260988i	0.681731	+	0.731603i	$0.261227\pi$
$60$		0			0
$61$	−7.78761	−	10.7187i	−0.997102	−	1.37239i	−0.927087	−	0.374847i	$-0.877695\pi$
$61$	−7.78761	−	10.7187i	−0.997102	−	1.37239i	−0.0700146	−	0.997546i	$-0.522305\pi$
$62$		0			0
$63$	0.372054	−	1.14506i	0.0468744	−	0.144264i
$64$		0			0
$65$			0.0567444i			0.00703828i
$66$		0			0
$67$			8.31591i			1.01595i	0.861372	+	0.507975i	$0.169606\pi$
$67$			8.31591i			1.01595i	−0.861372	+	0.507975i	$0.830394\pi$
$68$		0			0
$69$	2.71555	−	8.35759i	0.326913	−	1.00614i
$70$		0			0
$71$	−2.37385	−	3.26733i	−0.281724	−	0.387761i	0.644580	−	0.764537i	$-0.277032\pi$
$71$	−2.37385	−	3.26733i	−0.281724	−	0.387761i	−0.926304	+	0.376777i	$0.877032\pi$
$72$		0			0
$73$	−3.48170	+	1.13127i	−0.407503	+	0.132406i	−0.505594	−	0.862772i	$-0.668726\pi$
$73$	−3.48170	+	1.13127i	−0.407503	+	0.132406i	0.0980908	+	0.995177i	$0.468726\pi$
$74$		0			0
$75$	6.98517	−	9.61426i	0.806578	−	1.11016i
$76$		0			0
$77$	0.925328	+	1.18885i	0.105451	+	0.135482i
$78$		0			0
$79$	−2.29058	−	1.66420i	−0.257710	−	0.187238i	0.451427	−	0.892308i	$-0.350915\pi$
$79$	−2.29058	−	1.66420i	−0.257710	−	0.187238i	−0.709137	+	0.705071i	$0.750915\pi$
$80$		0			0
$81$	−3.06734	−	9.44029i	−0.340815	−	1.04892i
$82$		0			0
$83$	−1.28563	+	0.934066i	−0.141116	+	0.102527i	−0.656104	−	0.754671i	$-0.727797\pi$
$83$	−1.28563	+	0.934066i	−0.141116	+	0.102527i	0.514987	+	0.857198i	$0.327797\pi$
$84$		0			0
$85$	0.0818874	+	0.0266068i	0.00888193	+	0.00288592i
$86$		0			0
$87$	23.2895			2.49689
$88$		0			0
$89$	−11.9991			−1.27191			−0.635954	−	0.771727i	$-0.719393\pi$
$89$	−11.9991			−1.27191			−0.635954	+	0.771727i	$0.719393\pi$
$90$		0			0
$91$	0.940047	+	0.305440i	0.0985437	+	0.0320188i
$92$		0			0
$93$	5.93015	−	4.30850i	0.614927	−	0.446771i
$94$		0			0
$95$	0.0209320	+	0.0644220i	0.00214758	+	0.00660956i
$96$		0			0
$97$	0.120561	+	0.0875928i	0.0122411	+	0.00889370i	0.593889	−	0.804547i	$-0.297592\pi$
$97$	0.120561	+	0.0875928i	0.0122411	+	0.00889370i	−0.581648	+	0.813441i	$0.697592\pi$
$98$		0			0
$99$	−8.44605	−	2.43863i	−0.848860	−	0.245092i
$100$		0			0
$101$	−3.09844	+	4.26463i	−0.308306	+	0.424347i	−0.934852	−	0.355038i	$-0.884468\pi$
$101$	−3.09844	+	4.26463i	−0.308306	+	0.424347i	0.626546	+	0.779384i	$0.284468\pi$
$102$		0			0
$103$	8.37049	−	2.71974i	0.824769	−	0.267984i	0.133928	−	0.990991i	$-0.457241\pi$
$103$	8.37049	−	2.71974i	0.824769	−	0.267984i	0.690840	+	0.723007i	$0.257241\pi$
$104$		0			0
$105$	0.0165502	+	0.0227794i	0.00161513	+	0.00222304i
$106$		0			0
$107$	−2.67977	+	8.24748i	−0.259063	+	0.797314i	0.733939	+	0.679215i	$0.237680\pi$
$107$	−2.67977	+	8.24748i	−0.259063	+	0.797314i	−0.993002	+	0.118098i	$0.962320\pi$
$108$		0			0
$109$			9.64326i			0.923657i	0.886969	+	0.461829i	$0.152806\pi$
$109$			9.64326i			0.923657i	−0.886969	+	0.461829i	$0.847194\pi$
$110$		0			0
$111$			17.5158i			1.66253i
$112$		0			0
$113$	−4.29726	+	13.2256i	−0.404252	+	1.24416i	0.517265	+	0.855825i	$0.326950\pi$
$113$	−4.29726	+	13.2256i	−0.404252	+	1.24416i	−0.921518	+	0.388336i	$0.873050\pi$
$114$		0			0
$115$	0.0566636	+	0.0779908i	0.00528391	+	0.00727268i
$116$		0			0
$117$	−5.48550	+	1.78235i	−0.507135	+	0.164778i
$118$		0			0
$119$	0.881555	−	1.21336i	0.0808120	−	0.111228i
$120$		0			0
$121$	8.45236	−	7.03972i	0.768396	−	0.639974i
$122$		0			0
$123$	7.26105	+	5.27546i	0.654707	+	0.475673i
$124$		0			0
$125$	0.0805770	+	0.247991i	0.00720703	+	0.0221809i
$126$		0			0
$127$	3.15194	−	2.29002i	0.279690	−	0.203207i	−0.439092	−	0.898442i	$-0.644700\pi$
$127$	3.15194	−	2.29002i	0.279690	−	0.203207i	0.718782	+	0.695235i	$0.244700\pi$
$128$		0			0
$129$	−23.2258	−	7.54652i	−2.04492	−	0.664434i
$130$		0			0
$131$	−10.5865			−0.924951			−0.462475	−	0.886632i	$-0.653039\pi$
$131$	−10.5865			−0.924951			−0.462475	+	0.886632i	$0.653039\pi$
$132$		0			0
$133$	1.17991			0.102311
$134$		0			0
$135$	0.0205982	+	0.00669276i	0.00177281	+	0.000576021i
$136$		0			0
$137$	2.45172	−	1.78128i	0.209465	−	0.152185i	−0.478107	−	0.878302i	$-0.658677\pi$
$137$	2.45172	−	1.78128i	0.209465	−	0.152185i	0.687571	+	0.726117i	$0.258677\pi$
$138$		0			0
$139$	−0.579834	−	1.78454i	−0.0491808	−	0.151363i	0.923450	−	0.383719i	$-0.125357\pi$
$139$	−0.579834	−	1.78454i	−0.0491808	−	0.151363i	−0.972631	+	0.232356i	$0.925357\pi$
$140$		0			0
$141$	21.6411	+	15.7232i	1.82251	+	1.32413i
$142$		0			0
$143$	2.00201	−	6.93384i	0.167417	−	0.579837i
$144$		0			0
$145$	−0.150172	+	0.206694i	−0.0124711	+	0.0171650i
$146$		0			0
$147$	−15.3588	+	4.99039i	−1.26678	+	0.411600i
$148$		0			0
$149$	3.20353	+	4.40929i	0.262444	+	0.361223i	0.919821	−	0.392339i	$-0.128334\pi$
$149$	3.20353	+	4.40929i	0.262444	+	0.361223i	−0.657377	+	0.753562i	$0.728334\pi$
$150$		0			0
$151$	−3.93782	+	12.1194i	−0.320455	+	0.986261i	0.652995	+	0.757362i	$0.273512\pi$
$151$	−3.93782	+	12.1194i	−0.320455	+	0.986261i	−0.973450	+	0.228898i	$0.926488\pi$
$152$		0			0
$153$			8.75180i			0.707541i
$154$		0			0
$155$			0.0804116i			0.00645881i
$156$		0			0
$157$	5.97380	−	18.3855i	0.476761	−	1.46732i	−0.366807	−	0.930297i	$-0.619549\pi$
$157$	5.97380	−	18.3855i	0.476761	−	1.46732i	0.843568	−	0.537022i	$-0.180451\pi$
$158$		0			0
$159$	−12.2027	−	16.7955i	−0.967733	−	1.33197i
$160$		0			0
$161$	1.59703	−	0.518905i	0.125863	−	0.0408955i
$162$		0			0
$163$	9.42304	−	12.9697i	0.738069	−	1.01587i	−0.260658	−	0.965431i	$-0.583940\pi$
$163$	9.42304	−	12.9697i	0.738069	−	1.01587i	0.998727	−	0.0504339i	$-0.0160604\pi$
$164$		0			0
$165$	0.162239	−	0.126277i	0.0126303	−	0.00983062i
$166$		0			0
$167$	−17.5676	−	12.7636i	−1.35942	−	0.987679i	−0.998481	−	0.0550907i	$-0.982455\pi$
$167$	−17.5676	−	12.7636i	−1.35942	−	0.987679i	−0.360942	−	0.932588i	$-0.617545\pi$
$168$		0			0
$169$	2.55399	+	7.86038i	0.196461	+	0.604645i
$170$		0			0
$171$	−5.57022	+	4.04700i	−0.425965	+	0.309482i
$172$		0			0
$173$	18.8643	+	6.12938i	1.43422	+	0.466008i	0.920092	−	0.391703i	$-0.128114\pi$
$173$	18.8643	+	6.12938i	1.43422	+	0.466008i	0.514133	+	0.857711i	$0.328114\pi$
$174$		0			0
$175$	2.27085			0.171660
$176$		0			0
$177$	−15.4210			−1.15911
$178$		0			0
$179$	−12.0833	−	3.92610i	−0.903147	−	0.293450i	−0.179612	−	0.983738i	$-0.557484\pi$
$179$	−12.0833	−	3.92610i	−0.903147	−	0.293450i	−0.723535	+	0.690287i	$0.757484\pi$
$180$		0			0
$181$	7.44220	−	5.40708i	0.553175	−	0.401905i	−0.275780	−	0.961221i	$-0.588936\pi$
$181$	7.44220	−	5.40708i	0.553175	−	0.401905i	0.828955	+	0.559316i	$0.188936\pi$
$182$		0			0
$183$	9.73230	+	29.9529i	0.719432	+	2.21418i
$184$		0			0
$185$	−0.155453	−	0.112943i	−0.0114291	−	0.00830374i
$186$		0			0
$187$	−9.06744	−	6.14029i	−0.663077	−	0.449022i
$188$		0			0
$189$	0.221749	−	0.305211i	0.0161299	−	0.0222009i
$190$		0			0
$191$	−22.3800	+	7.27171i	−1.61936	+	0.526162i	−0.971791	−	0.235844i	$-0.924215\pi$
$191$	−22.3800	+	7.27171i	−1.61936	+	0.526162i	−0.647570	+	0.762006i	$0.724215\pi$
$192$		0			0
$193$	10.7186	+	14.7528i	0.771539	+	1.06193i	0.996166	+	0.0874879i	$0.0278839\pi$
$193$	10.7186	+	14.7528i	0.771539	+	1.06193i	−0.224626	+	0.974445i	$0.572116\pi$
$194$		0			0
$195$	0.0416824	−	0.128285i	0.00298494	−	0.00918670i
$196$		0			0
$197$			26.2279i			1.86866i	0.356411	+	0.934329i	$0.384000\pi$
$197$			26.2279i			1.86866i	−0.356411	+	0.934329i	$0.616000\pi$
$198$		0			0
$199$		−	16.4890i		−	1.16887i	−0.811440	−	0.584436i	$-0.801316\pi$
$199$		−	16.4890i		−	1.16887i	0.811440	−	0.584436i	$-0.198684\pi$
$200$		0			0
$201$	6.10857	−	18.8002i	0.430865	−	1.32607i
$202$		0			0
$203$	2.61583	+	3.60038i	0.183595	+	0.252697i
$204$		0			0
$205$	−0.0936395	+	0.0304253i	−0.00654007	+	0.00212500i
$206$		0			0
$207$	−5.75958	+	7.92738i	−0.400319	+	0.550991i
$208$		0			0
$209$	−0.284880	−	8.61050i	−0.0197056	−	0.595601i
$210$		0			0
$211$	17.3680	+	12.6186i	1.19566	+	0.868699i	0.993851	−	0.110726i	$-0.0353175\pi$
$211$	17.3680	+	12.6186i	1.19566	+	0.868699i	0.201810	+	0.979425i	$0.435318\pi$
$212$		0			0
$213$	2.96664	+	9.13038i	0.203271	+	0.625603i
$214$		0			0
$215$	0.216737	−	0.157469i	0.0147813	−	0.0107393i
$216$		0			0
$217$	1.33212	+	0.432834i	0.0904305	+	0.0293827i
$218$		0			0
$219$	8.70228			0.588046
$220$		0			0
$221$	−7.18484			−0.483305
$222$		0			0
$223$	−11.9679	−	3.88861i	−0.801430	−	0.260401i	−0.120466	−	0.992717i	$-0.538439\pi$
$223$	−11.9679	−	3.88861i	−0.801430	−	0.260401i	−0.680964	+	0.732317i	$0.738439\pi$
$224$		0			0
$225$	−10.7205	+	7.78887i	−0.714697	+	0.519258i
$226$		0			0
$227$	−0.326578	−	1.00510i	−0.0216757	−	0.0667110i	0.939634	−	0.342182i	$-0.111166\pi$
$227$	−0.326578	−	1.00510i	−0.0216757	−	0.0667110i	−0.961309	+	0.275471i	$0.911166\pi$
$228$		0			0
$229$	−11.1768	−	8.12040i	−0.738581	−	0.536611i	0.153685	−	0.988120i	$-0.450886\pi$
$229$	−11.1768	−	8.12040i	−0.738581	−	0.536611i	−0.892267	+	0.451509i	$0.850886\pi$
$230$		0			0
$231$	−1.21865	−	3.36742i	−0.0801814	−	0.221560i
$232$		0			0
$233$	−1.90729	+	2.62516i	−0.124951	+	0.171980i	−0.866910	−	0.498466i	$-0.833897\pi$
$233$	−1.90729	+	2.62516i	−0.124951	+	0.171980i	0.741959	+	0.670446i	$0.233897\pi$
$234$		0			0
$235$	−0.279087	+	0.0906808i	−0.0182056	+	0.00591536i
$236$		0			0
$237$	3.95598	+	5.44494i	0.256968	+	0.353687i
$238$		0			0
$239$	0.582703	−	1.79337i	0.0376919	−	0.116004i	−0.930440	−	0.366444i	$-0.880575\pi$
$239$	0.582703	−	1.79337i	0.0376919	−	0.116004i	0.968132	+	0.250440i	$0.0805753\pi$
$240$		0			0
$241$			15.6282i			1.00670i	0.864082	+	0.503352i	$0.167900\pi$
$241$			15.6282i			1.00670i	−0.864082	+	0.503352i	$0.832100\pi$
$242$		0			0
$243$			21.1037i			1.35380i
$244$		0			0
$245$	0.0547451	−	0.168488i	0.00349754	−	0.0107643i
$246$		0			0
$247$	−3.32241	−	4.57291i	−0.211400	−	0.290967i
$248$		0			0
$249$	3.59263	−	1.16732i	0.227674	−	0.0739757i
$250$		0			0
$251$	15.1689	−	20.8782i	0.957453	−	1.31782i	0.00931622	−	0.999957i	$-0.497035\pi$
$251$	15.1689	−	20.8782i	0.957453	−	1.31782i	0.948136	−	0.317864i	$-0.102965\pi$
$252$		0			0
$253$	−4.17236	−	11.5292i	−0.262314	−	0.724833i
$254$		0			0
$255$	−0.165583	−	0.120303i	−0.0103692	−	0.00753367i
$256$		0			0
$257$	−0.226461	−	0.696974i	−0.0141262	−	0.0434760i	0.943745	−	0.330674i	$-0.107276\pi$
$257$	−0.226461	−	0.696974i	−0.0141262	−	0.0434760i	−0.957871	+	0.287198i	$0.907276\pi$
$258$		0			0
$259$	−2.70781	+	1.96734i	−0.168255	+	0.122245i
$260$		0			0
$261$	−24.6981	−	8.02490i	−1.52877	−	0.496729i
$262$		0			0
$263$	16.9497			1.04516			0.522581	−	0.852590i	$-0.324969\pi$
$263$	16.9497			1.04516			0.522581	+	0.852590i	$0.324969\pi$
$264$		0			0
$265$	0.227744			0.0139902
$266$		0			0
$267$	27.1272	+	8.81415i	1.66015	+	0.539417i
$268$		0			0
$269$	−8.18909	+	5.94972i	−0.499297	+	0.362761i	−0.808749	−	0.588155i	$-0.799855\pi$
$269$	−8.18909	+	5.94972i	−0.499297	+	0.362761i	0.309451	+	0.950915i	$0.399855\pi$
$270$		0			0
$271$	8.40216	+	25.8592i	0.510395	+	1.57083i	0.791507	+	0.611160i	$0.209297\pi$
$271$	8.40216	+	25.8592i	0.510395	+	1.57083i	−0.281112	+	0.959675i	$0.590703\pi$
$272$		0			0
$273$	−1.90085	−	1.38105i	−0.115045	−	0.0835849i
$274$		0			0
$275$	−0.548281	−	16.5718i	−0.0330626	−	0.999317i
$276$		0			0
$277$	−0.213858	+	0.294351i	−0.0128495	+	0.0176858i	−0.815393	−	0.578907i	$-0.803479\pi$
$277$	−0.213858	+	0.294351i	−0.0128495	+	0.0176858i	0.802544	+	0.596593i	$0.203479\pi$
$278$		0			0
$279$	−7.77341	+	2.52573i	−0.465382	+	0.151212i
$280$		0			0
$281$	0.274764	+	0.378180i	0.0163910	+	0.0225603i	0.817134	−	0.576448i	$-0.195562\pi$
$281$	0.274764	+	0.378180i	0.0163910	+	0.0225603i	−0.800743	+	0.599008i	$0.795562\pi$
$282$		0			0
$283$	−5.94504	+	18.2969i	−0.353396	+	1.08764i	0.603538	+	0.797334i	$0.293757\pi$
$283$	−5.94504	+	18.2969i	−0.353396	+	1.08764i	−0.956934	+	0.290306i	$0.906243\pi$
$284$		0			0
$285$		−	0.161018i		−	0.00953791i
$286$		0			0
$287$			1.71503i			0.101235i
$288$		0			0
$289$	1.88440	−	5.79958i	0.110847	−	0.341152i
$290$		0			0
$291$	−0.208217	−	0.286586i	−0.0122059	−	0.0168000i
$292$		0			0
$293$	21.4865	−	6.98138i	1.25525	−	0.407857i	0.395453	−	0.918486i	$-0.370588\pi$
$293$	21.4865	−	6.98138i	1.25525	−	0.407857i	0.859801	+	0.510630i	$0.170588\pi$
$294$		0			0
$295$	0.0994353	−	0.136861i	0.00578935	−	0.00796835i
$296$		0			0
$297$	−2.28085	−	1.54455i	−0.132348	−	0.0896237i
$298$		0			0
$299$	−6.50803	−	4.72836i	−0.376369	−	0.273448i
$300$		0			0
$301$	−1.44204	−	4.43815i	−0.0831179	−	0.255811i
$302$		0			0
$303$	10.1375	−	7.36529i	0.582382	−	0.423125i
$304$		0			0
$305$	−0.328587	−	0.106764i	−0.0188148	−	0.00611331i
$306$		0			0
$307$	−15.2212			−0.868718			−0.434359	−	0.900740i	$-0.643025\pi$
$307$	−15.2212			−0.868718			−0.434359	+	0.900740i	$0.643025\pi$
$308$		0			0
$309$	−20.9215			−1.19018
$310$		0			0
$311$	15.7690	+	5.12365i	0.894177	+	0.290536i	0.719831	−	0.694149i	$-0.244219\pi$
$311$	15.7690	+	5.12365i	0.894177	+	0.290536i	0.174345	+	0.984685i	$0.444219\pi$
$312$		0			0
$313$	10.4941	−	7.62441i	0.593161	−	0.430957i	−0.250284	−	0.968173i	$-0.580524\pi$
$313$	10.4941	−	7.62441i	0.593161	−	0.430957i	0.843445	+	0.537216i	$0.180524\pi$
$314$		0			0
$315$	−0.00970206	−	0.0298599i	−0.000546649	−	0.00168241i
$316$		0			0
$317$	−7.08461	−	5.14727i	−0.397912	−	0.289100i	0.370778	−	0.928721i	$-0.379091\pi$
$317$	−7.08461	−	5.14727i	−0.397912	−	0.289100i	−0.768690	+	0.639622i	$0.779091\pi$
$318$		0			0
$319$	25.6426	−	19.9586i	1.43571	−	1.11747i
$320$		0			0
$321$	12.1166	−	16.6771i	0.676283	−	0.930824i
$322$		0			0
$323$	−8.15696	+	2.65036i	−0.453866	+	0.147470i
$324$		0			0
$325$	−6.39432	−	8.80103i	−0.354693	−	0.488193i
$326$		0			0
$327$	7.08360	−	21.8011i	0.391724	−	1.20560i
$328$		0			0
$329$			5.11156i			0.281809i
$330$		0			0
$331$		−	30.3796i		−	1.66981i	−0.550391	−	0.834907i	$-0.685521\pi$
$331$		−	30.3796i		−	1.66981i	0.550391	−	0.834907i	$-0.314479\pi$
$332$		0			0
$333$	6.03545	−	18.5752i	0.330741	−	1.01792i
$334$		0			0
$335$	0.127464	+	0.175439i	0.00696409	+	0.00958525i
$336$		0			0
$337$	19.6412	−	6.38181i	1.06992	−	0.347640i	0.279466	−	0.960155i	$-0.409842\pi$
$337$	19.6412	−	6.38181i	1.06992	−	0.347640i	0.790458	+	0.612516i	$0.209842\pi$
$338$		0			0
$339$	19.4301	−	26.7433i	1.05530	−	1.45250i
$340$		0			0
$341$	2.83702	−	9.82583i	0.153633	−	0.532098i
$342$		0			0
$343$	−5.06892	−	3.68279i	−0.273696	−	0.198852i
$344$		0			0
$345$	−0.0708134	−	0.217941i	−0.00381247	−	0.0117336i
$346$		0			0
$347$	−14.9003	+	10.8257i	−0.799889	+	0.581153i	−0.910881	−	0.412668i	$-0.864597\pi$
$347$	−14.9003	+	10.8257i	−0.799889	+	0.581153i	0.110993	+	0.993821i	$0.464597\pi$
$348$		0			0
$349$	−12.9963	−	4.22276i	−0.695678	−	0.226039i	−0.0602314	−	0.998184i	$-0.519184\pi$
$349$	−12.9963	−	4.22276i	−0.695678	−	0.226039i	−0.635446	+	0.772145i	$0.719184\pi$
$350$		0			0
$351$	−1.80730			−0.0964664
$352$		0			0
$353$	−1.30748			−0.0695901			−0.0347951	−	0.999394i	$-0.511078\pi$
$353$	−1.30748			−0.0695901			−0.0347951	+	0.999394i	$0.511078\pi$
$354$		0			0
$355$	−0.100161	−	0.0325444i	−0.00531601	−	0.00172728i
$356$		0			0
$357$	−2.88427	+	2.09554i	−0.152652	+	0.110908i
$358$		0			0
$359$	1.30471	+	4.01549i	0.0688600	+	0.211929i	0.979565	−	0.201128i	$-0.0644608\pi$
$359$	1.30471	+	4.01549i	0.0688600	+	0.211929i	−0.910705	+	0.413058i	$0.864461\pi$
$360$		0			0
$361$	9.91252	+	7.20187i	0.521712	+	0.379046i
$362$		0			0
$363$	−24.2799	+	9.70628i	−1.27436	+	0.509448i
$364$		0			0
$365$	−0.0561129	+	0.0772328i	−0.00293708	+	0.00404255i
$366$		0			0
$367$	19.0582	−	6.19238i	0.994829	−	0.323240i	0.234032	−	0.972229i	$-0.424808\pi$
$367$	19.0582	−	6.19238i	0.994829	−	0.323240i	0.760797	+	0.648989i	$0.224808\pi$
$368$		0			0
$369$	−5.88245	−	8.09650i	−0.306228	−	0.421487i
$370$		0			0
$371$	1.22588	−	3.77288i	0.0636446	−	0.195878i
$372$		0			0
$373$		−	17.2680i		−	0.894104i	−0.894508	−	0.447052i	$-0.852474\pi$
$373$		−	17.2680i		−	0.894104i	0.894508	−	0.447052i	$-0.147526\pi$
$374$		0			0
$375$		−	0.619835i		−	0.0320082i
$376$		0			0
$377$	6.58809	−	20.2761i	0.339304	−	1.04427i
$378$		0			0
$379$	−0.110439	−	0.152006i	−0.00567287	−	0.00780804i	0.806171	−	0.591682i	$-0.201536\pi$
$379$	−0.110439	−	0.152006i	−0.00567287	−	0.00780804i	−0.811844	+	0.583874i	$0.801536\pi$
$380$		0			0
$381$	−8.80795	+	2.86188i	−0.451245	+	0.146618i
$382$		0			0
$383$	0.573439	−	0.789271i	0.0293014	−	0.0403299i	−0.794115	−	0.607768i	$-0.792065\pi$
$383$	0.573439	−	0.789271i	0.0293014	−	0.0403299i	0.823416	+	0.567438i	$0.192065\pi$
$384$		0			0
$385$	0.0377438	+	0.0108978i	0.00192360	+	0.000555403i
$386$		0			0
$387$	22.0303	+	16.0059i	1.11986	+	0.813627i
$388$		0			0
$389$	−2.22294	−	6.84150i	−0.112707	−	0.346878i	0.878755	−	0.477274i	$-0.158375\pi$
$389$	−2.22294	−	6.84150i	−0.112707	−	0.346878i	−0.991462	+	0.130396i	$0.958375\pi$
$390$		0			0
$391$	−9.87500	+	7.17461i	−0.499400	+	0.362836i
$392$		0			0
$393$	23.9336	+	7.77650i	1.20729	+	0.392272i
$394$		0			0
$395$	−0.0738323			−0.00371490
$396$		0			0
$397$	−15.9017			−0.798082			−0.399041	−	0.916933i	$-0.630657\pi$
$397$	−15.9017			−0.798082			−0.399041	+	0.916933i	$0.630657\pi$
$398$		0			0
$399$	−2.66748	−	0.866718i	−0.133541	−	0.0433902i
$400$		0			0
$401$	20.0698	−	14.5815i	1.00224	−	0.728167i	0.0396692	−	0.999213i	$-0.487370\pi$
$401$	20.0698	−	14.5815i	1.00224	−	0.728167i	0.962566	+	0.271046i	$0.0873696\pi$
$402$		0			0
$403$	−2.07352	−	6.38163i	−0.103289	−	0.317891i
$404$		0			0
$405$	−0.209409	−	0.152144i	−0.0104056	−	0.00756012i
$406$		0			0
$407$	15.0107	+	19.2855i	0.744051	+	0.955949i
$408$		0			0
$409$	−18.0584	+	24.8553i	−0.892932	+	1.22902i	0.0797365	+	0.996816i	$0.474592\pi$
$409$	−18.0584	+	24.8553i	−0.892932	+	1.22902i	−0.972668	+	0.232199i	$0.925408\pi$
$410$		0			0
$411$	−6.85121	+	2.22609i	−0.337945	+	0.109805i
$412$		0			0
$413$	−1.73205	−	2.38396i	−0.0852287	−	0.117307i
$414$		0			0
$415$	−0.0128056	+	0.0394116i	−0.000628602	+	0.00193464i
$416$		0			0
$417$			4.46034i			0.218424i
$418$		0			0
$419$			8.56570i			0.418462i	0.977866	+	0.209231i	$0.0670960\pi$
$419$			8.56570i			0.418462i	−0.977866	+	0.209231i	$0.932904\pi$
$420$		0			0
$421$	−11.7911	+	36.2891i	−0.574661	+	1.76862i	0.0626702	+	0.998034i	$0.480038\pi$
$421$	−11.7911	+	36.2891i	−0.574661	+	1.76862i	−0.637331	+	0.770590i	$0.719962\pi$
$422$		0			0
$423$	−17.5323	−	24.1311i	−0.852449	−	1.17329i
$424$		0			0
$425$	−15.6989	+	5.10089i	−0.761509	+	0.247429i
$426$		0			0
$427$	−3.53739	+	4.86880i	−0.171186	+	0.235618i
$428$		0			0
$429$	−9.61941	+	14.2051i	−0.464430	+	0.685829i
$430$		0			0
$431$	3.82179	+	2.77670i	0.184089	+	0.133749i	0.676013	−	0.736889i	$-0.263706\pi$
$431$	3.82179	+	2.77670i	0.184089	+	0.133749i	−0.491924	+	0.870638i	$0.663706\pi$
$432$		0			0
$433$	8.55863	+	26.3407i	0.411301	+	1.26586i	0.915518	+	0.402278i	$0.131781\pi$
$433$	8.55863	+	26.3407i	0.411301	+	1.26586i	−0.504216	+	0.863577i	$0.668219\pi$
$434$		0			0
$435$	0.491333	−	0.356974i	0.0235576	−	0.0171156i
$436$		0			0
$437$	−9.13279	−	2.96742i	−0.436881	−	0.141951i
$438$		0			0
$439$	−0.334645			−0.0159717			−0.00798587	−	0.999968i	$-0.502542\pi$
$439$	−0.334645			−0.0159717			−0.00798587	+	0.999968i	$0.502542\pi$
$440$		0			0
$441$	18.0073			0.857492
$442$		0			0
$443$	9.35307	+	3.03900i	0.444378	+	0.144387i	0.522655	−	0.852545i	$-0.324942\pi$
$443$	9.35307	+	3.03900i	0.444378	+	0.144387i	−0.0782767	+	0.996932i	$0.524942\pi$
$444$		0			0
$445$	−0.253143	+	0.183919i	−0.0120001	+	0.00871861i
$446$		0			0
$447$	−4.00351	−	12.3215i	−0.189359	−	0.582788i
$448$		0			0
$449$	3.92694	+	2.85309i	0.185324	+	0.134645i	0.676579	−	0.736370i	$-0.263462\pi$
$449$	3.92694	+	2.85309i	0.185324	+	0.134645i	−0.491255	+	0.871016i	$0.663462\pi$
$450$		0			0
$451$	12.5156	−	0.414082i	0.589339	−	0.0194984i
$452$		0			0
$453$	17.8049	−	24.5064i	0.836548	−	1.15141i
$454$		0			0
$455$	0.0245136	−	0.00796496i	0.00114922	−	0.000373403i
$456$		0			0
$457$	−10.0834	−	13.8787i	−0.471684	−	0.649217i	0.505197	−	0.863004i	$-0.331420\pi$
$457$	−10.0834	−	13.8787i	−0.471684	−	0.649217i	−0.976880	+	0.213787i	$0.931420\pi$
$458$		0			0
$459$	−0.847421	+	2.60809i	−0.0395542	+	0.121735i
$460$		0			0
$461$			6.38213i			0.297245i	0.988894	+	0.148623i	$0.0474840\pi$
$461$			6.38213i			0.297245i	−0.988894	+	0.148623i	$0.952516\pi$
$462$		0			0
$463$			41.4936i			1.92837i	0.265229	+	0.964185i	$0.414552\pi$
$463$			41.4936i			1.92837i	−0.265229	+	0.964185i	$0.585448\pi$
$464$		0			0
$465$	0.0590675	−	0.181791i	0.00273919	−	0.00843036i
$466$		0			0
$467$	12.7223	+	17.5107i	0.588718	+	0.810301i	0.994617	−	0.103617i	$-0.0330416\pi$
$467$	12.7223	+	17.5107i	0.588718	+	0.810301i	−0.405899	+	0.913918i	$0.633042\pi$
$468$		0			0
$469$	3.59248	−	1.16727i	0.165885	−	0.0538994i
$470$		0			0
$471$	−27.0106	+	37.1769i	−1.24458	+	1.71302i
$472$		0			0
$473$	−32.0397	+	11.5950i	−1.47319	+	0.533139i
$474$		0			0
$475$	−10.5060	−	7.63307i	−0.482049	−	0.350229i
$476$		0			0
$477$	7.15345	+	22.0160i	0.327534	+	1.00805i
$478$		0			0
$479$	29.5001	−	21.4331i	1.34789	−	0.979303i	0.348781	−	0.937204i	$-0.386596\pi$
$479$	29.5001	−	21.4331i	1.34789	−	0.979303i	0.999113	−	0.0420987i	$-0.0134044\pi$
$480$		0			0
$481$	15.2494	+	4.95484i	0.695314	+	0.225921i
$482$		0			0
$483$	−3.99166			−0.181627
$484$		0			0
$485$	0.00388605			0.000176456
$486$		0			0
$487$	−26.4619	−	8.59799i	−1.19910	−	0.389612i	−0.359672	−	0.933079i	$-0.617111\pi$
$487$	−26.4619	−	8.59799i	−1.19910	−	0.389612i	−0.839431	+	0.543467i	$0.817111\pi$
$488$		0			0
$489$	−30.8303	+	22.3995i	−1.39419	+	1.01294i
$490$		0			0
$491$	−0.713608	−	2.19626i	−0.0322047	−	0.0991158i	0.933662	−	0.358155i	$-0.116594\pi$
$491$	−0.713608	−	2.19626i	−0.0322047	−	0.0991158i	−0.965867	+	0.259039i	$0.916594\pi$
$492$		0			0
$493$	−26.1711	−	19.0144i	−1.17869	−	0.856367i
$494$		0			0
$495$	−0.215563	+	0.0780113i	−0.00968884	+	0.00350635i
$496$		0			0
$497$	−1.07828	+	1.48413i	−0.0483675	+	0.0665722i
$498$		0			0
$499$	19.0713	−	6.19664i	0.853748	−	0.277399i	0.150733	−	0.988575i	$-0.451837\pi$
$499$	19.0713	−	6.19664i	0.853748	−	0.277399i	0.703015	+	0.711175i	$0.251837\pi$
$500$		0			0
$501$	30.3404	+	41.7600i	1.35551	+	1.86570i
$502$		0			0
$503$	−10.6752	+	32.8548i	−0.475982	+	1.46492i	0.368647	+	0.929570i	$0.379821\pi$
$503$	−10.6752	+	32.8548i	−0.475982	+	1.46492i	−0.844629	+	0.535352i	$0.820179\pi$
$504$		0			0
$505$			0.137462i			0.00611697i
$506$		0			0
$507$		−	19.6465i		−	0.872531i
$508$		0			0
$509$	−6.82588	+	21.0079i	−0.302552	+	0.931159i	0.678028	+	0.735037i	$0.262835\pi$
$509$	−6.82588	+	21.0079i	−0.302552	+	0.931159i	−0.980579	+	0.196122i	$0.937165\pi$
$510$		0			0
$511$	0.977423	+	1.34531i	0.0432387	+	0.0595129i
$512$		0			0
$513$	−2.05183	+	0.666679i	−0.0905904	+	0.0294346i
$514$		0			0
$515$	0.134903	−	0.185678i	0.00594453	−	0.00818195i
$516$		0			0
$517$	37.3021	−	1.23415i	1.64055	−	0.0542777i
$518$		0			0
$519$	−38.1451	−	27.7141i	−1.67439	−	1.21651i
$520$		0			0
$521$	−8.49819	−	26.1547i	−0.372312	−	1.14586i	−0.945274	−	0.326277i	$-0.894206\pi$
$521$	−8.49819	−	26.1547i	−0.372312	−	1.14586i	0.572962	−	0.819582i	$-0.305794\pi$
$522$		0			0
$523$	−24.0690	+	17.4872i	−1.05246	+	0.764660i	−0.972679	−	0.232152i	$-0.925423\pi$
$523$	−24.0690	+	17.4872i	−1.05246	+	0.764660i	−0.0797845	+	0.996812i	$0.525423\pi$
$524$		0			0
$525$	−5.13385	−	1.66809i	−0.224059	−	0.0728013i
$526$		0			0
$527$	−10.1815			−0.443514
$528$		0			0
$529$	9.33359			0.405808
$530$		0			0
$531$	16.3537	+	5.31363i	0.709688	+	0.230592i
$532$		0			0
$533$	6.64687	−	4.82923i	0.287908	−	0.209177i
$534$		0			0
$535$	0.0698804	+	0.215070i	0.00302119	+	0.00929828i
$536$		0			0
$537$	24.4334	+	17.7519i	1.05438	+	0.766051i
$538$		0			0
$539$	−12.6340	+	18.6568i	−0.544185	+	0.803605i
$540$		0			0
$541$	−14.5819	+	20.0703i	−0.626926	+	0.862889i	−0.997834	−	0.0657801i	$-0.979046\pi$
$541$	−14.5819	+	20.0703i	−0.626926	+	0.862889i	0.370908	+	0.928670i	$0.379046\pi$
$542$		0			0
$543$	−20.7969	+	6.75731i	−0.892478	+	0.289984i
$544$		0			0
$545$	0.147809	+	0.203442i	0.00633144	+	0.00871449i
$546$		0			0
$547$	−0.873324	+	2.68782i	−0.0373406	+	0.114923i	−0.967989	−	0.250991i	$-0.919244\pi$
$547$	−0.873324	+	2.68782i	−0.0373406	+	0.114923i	0.930649	+	0.365914i	$0.119244\pi$
$548$		0			0
$549$		−	35.1181i		−	1.49880i
$550$		0			0
$551$		−	25.4497i		−	1.08419i
$552$		0			0
$553$	−0.397419	+	1.22313i	−0.0169000	+	0.0520128i
$554$		0			0
$555$	0.268477	+	0.369527i	0.0113962	+	0.0156855i
$556$		0			0
$557$	6.25436	−	2.03216i	0.265006	−	0.0861055i	−0.173500	−	0.984834i	$-0.555508\pi$
$557$	6.25436	−	2.03216i	0.265006	−	0.0861055i	0.438506	+	0.898728i	$0.355508\pi$
$558$		0			0
$559$	−13.1402	+	18.0859i	−0.555770	+	0.764951i
$560$		0			0
$561$	15.9888	+	20.5423i	0.675049	+	0.867297i
$562$		0			0
$563$	3.90810	+	2.83940i	0.164707	+	0.119667i	0.667085	−	0.744981i	$-0.267542\pi$
$563$	3.90810	+	2.83940i	0.164707	+	0.119667i	−0.502378	+	0.864648i	$0.667542\pi$
$564$		0			0
$565$	0.112060	+	0.344885i	0.00471440	+	0.0145094i
$566$		0			0
$567$	−3.64767	+	2.65018i	−0.153188	+	0.111297i
$568$		0			0
$569$	15.0706	+	4.89673i	0.631792	+	0.205282i	0.607369	−	0.794420i	$-0.292225\pi$
$569$	15.0706	+	4.89673i	0.631792	+	0.205282i	0.0244232	+	0.999702i	$0.492225\pi$
$570$		0			0
$571$	−21.0144			−0.879426			−0.439713	−	0.898138i	$-0.644920\pi$
$571$	−21.0144			−0.879426			−0.439713	+	0.898138i	$0.644920\pi$
$572$		0			0
$573$	55.9373			2.33681
$574$		0			0
$575$	−17.5770	−	5.71111i	−0.733011	−	0.238170i
$576$		0			0
$577$	6.39254	−	4.64445i	0.266125	−	0.193351i	−0.446718	−	0.894675i	$-0.647407\pi$
$577$	6.39254	−	4.64445i	0.266125	−	0.193351i	0.712843	+	0.701324i	$0.247407\pi$
$578$		0			0
$579$	−13.3952	−	41.2261i	−0.556684	−	1.71330i
$580$		0			0
$581$	0.583976	+	0.424283i	0.0242274	+	0.0176022i
$582$		0			0
$583$	−27.8290	−	8.03507i	−1.15256	−	0.332779i
$584$		0			0
$585$	−0.0884070	+	0.121682i	−0.00365518	+	0.00503093i
$586$		0			0
$587$	22.8359	−	7.41983i	0.942538	−	0.306249i	0.202858	−	0.979208i	$-0.434977\pi$
$587$	22.8359	−	7.41983i	0.942538	−	0.306249i	0.739680	+	0.672959i	$0.234977\pi$
$588$		0			0
$589$	−4.70813	−	6.48019i	−0.193995	−	0.267012i
$590$		0			0
$591$	19.2661	−	59.2948i	0.792500	−	2.43906i
$592$		0			0
$593$		−	39.4055i		−	1.61819i	−0.587677	−	0.809096i	$-0.699957\pi$
$593$		−	39.4055i		−	1.61819i	0.587677	−	0.809096i	$-0.300043\pi$
$594$		0			0
$595$		−	0.0391101i		−	0.00160336i
$596$		0			0
$597$	−12.1122	+	37.2775i	−0.495719	+	1.52567i
$598$		0			0
$599$	15.6818	+	21.5842i	0.640743	+	0.881907i	0.998655	−	0.0518485i	$-0.0165113\pi$
$599$	15.6818	+	21.5842i	0.640743	+	0.881907i	−0.357912	+	0.933755i	$0.616511\pi$
$600$		0			0
$601$	−41.3114	+	13.4229i	−1.68513	+	0.547531i	−0.985895	−	0.167365i	$-0.946474\pi$
$601$	−41.3114	+	13.4229i	−1.68513	+	0.547531i	−0.699231	+	0.714896i	$0.746474\pi$
$602$		0			0
$603$	−12.9561	+	17.8325i	−0.527612	+	0.726196i
$604$		0			0
$605$	0.0704148	−	0.278071i	0.00286277	−	0.0113052i
$606$		0			0
$607$	26.1695	+	19.0132i	1.06219	+	0.771723i	0.974492	−	0.224424i	$-0.0720502\pi$
$607$	26.1695	+	19.0132i	1.06219	+	0.771723i	0.0876942	+	0.996147i	$0.472050\pi$
$608$		0			0
$609$	−3.26904	−	10.0611i	−0.132468	−	0.407695i
$610$		0			0
$611$	19.8106	−	14.3932i	0.801450	−	0.582288i
$612$		0			0
$613$	24.5952	+	7.99146i	0.993391	+	0.322772i	0.760221	−	0.649664i	$-0.225090\pi$
$613$	24.5952	+	7.99146i	0.993391	+	0.322772i	0.233169	+	0.972436i	$0.425090\pi$
$614$		0			0
$615$	0.234046			0.00943763
$616$		0			0
$617$	24.7346			0.995777			0.497889	−	0.867241i	$-0.334109\pi$
$617$	24.7346			0.995777			0.497889	+	0.867241i	$0.334109\pi$
$618$		0			0
$619$	−28.2236	−	9.17040i	−1.13440	−	0.368589i	−0.319154	−	0.947703i	$-0.603399\pi$
$619$	−28.2236	−	9.17040i	−1.13440	−	0.368589i	−0.815247	+	0.579113i	$0.803399\pi$
$620$		0			0
$621$	−2.48399	+	1.80472i	−0.0996790	+	0.0724211i
$622$		0			0
$623$	1.68427	+	5.18364i	0.0674788	+	0.207678i
$624$		0			0
$625$	−20.2172	−	14.6886i	−0.808687	−	0.587545i
$626$		0			0
$627$	−5.68092	+	19.6755i	−0.226874	+	0.785764i
$628$		0			0
$629$	14.3006	−	19.6831i	0.570201	−	0.784815i
$630$		0			0
$631$	14.0650	−	4.56999i	0.559919	−	0.181929i	−0.0153660	−	0.999882i	$-0.504891\pi$
$631$	14.0650	−	4.56999i	0.559919	−	0.181929i	0.575285	+	0.817953i	$0.304891\pi$
$632$		0			0
$633$	−29.9956	−	41.2854i	−1.19222	−	1.64095i
$634$		0			0
$635$	0.0313951	−	0.0966241i	0.00124588	−	0.00383441i
$636$		0			0
$637$			14.7832i			0.585733i
$638$		0			0
$639$		−	10.7048i		−	0.423477i
$640$		0			0
$641$	−3.69099	+	11.3597i	−0.145785	+	0.448681i	−0.997111	−	0.0759564i	$-0.975799\pi$
$641$	−3.69099	+	11.3597i	−0.145785	+	0.448681i	0.851326	+	0.524637i	$0.175799\pi$
$642$		0			0
$643$	10.8775	+	14.9717i	0.428968	+	0.590424i	0.967716	−	0.252043i	$-0.0811024\pi$
$643$	10.8775	+	14.9717i	0.428968	+	0.590424i	−0.538748	+	0.842467i	$0.681102\pi$
$644$		0			0
$645$	−0.605660	+	0.196791i	−0.0238479	+	0.00774864i
$646$		0			0
$647$	−0.716412	+	0.986057i	−0.0281651	+	0.0387659i	−0.822867	−	0.568234i	$-0.807627\pi$
$647$	−0.716412	+	0.986057i	−0.0281651	+	0.0387659i	0.794702	+	0.606999i	$0.207627\pi$
$648$		0			0
$649$	−16.9790	+	13.2154i	−0.666486	+	0.518751i
$650$		0			0
$651$	−2.69367	−	1.95706i	−0.105573	−	0.0767033i
$652$		0			0
$653$	−13.6367	−	41.9693i	−0.533643	−	1.64239i	−0.746562	−	0.665316i	$-0.768297\pi$
$653$	−13.6367	−	41.9693i	−0.533643	−	1.64239i	0.212919	−	0.977070i	$-0.431703\pi$
$654$		0			0
$655$	−0.223342	+	0.162267i	−0.00872669	+	0.00634031i
$656$		0			0
$657$	−9.22862	−	2.99856i	−0.360043	−	0.116985i
$658$		0			0
$659$	−13.9014			−0.541521			−0.270761	−	0.962647i	$-0.587275\pi$
$659$	−13.9014			−0.541521			−0.270761	+	0.962647i	$0.587275\pi$
$660$		0			0
$661$	5.86221			0.228013			0.114007	−	0.993480i	$-0.463631\pi$
$661$	5.86221			0.228013			0.114007	+	0.993480i	$0.463631\pi$
$662$		0			0
$663$	16.2432	+	5.27773i	0.630833	+	0.204970i
$664$		0			0
$665$	0.0248922	−	0.0180853i	0.000965280	−	0.000701317i
$666$		0			0
$667$	−11.1924	−	34.4466i	−0.433370	−	1.33378i
$668$		0			0
$669$	24.2001	+	17.5824i	0.935630	+	0.679775i
$670$		0			0
$671$	36.3846	+	24.6389i	1.40461	+	0.951175i
$672$		0			0
$673$	−21.2516	+	29.2503i	−0.819189	+	1.12752i	0.170651	+	0.985332i	$0.445413\pi$
$673$	−21.2516	+	29.2503i	−0.819189	+	1.12752i	−0.989840	+	0.142186i	$0.954587\pi$
$674$		0			0
$675$	−3.94895	+	1.28309i	−0.151995	+	0.0493863i
$676$		0			0
$677$	6.10898	+	8.40828i	0.234787	+	0.323157i	0.910111	−	0.414365i	$-0.135996\pi$
$677$	6.10898	+	8.40828i	0.234787	+	0.323157i	−0.675324	+	0.737521i	$0.735996\pi$
$678$		0			0
$679$	0.0209175	−	0.0643776i	0.000802741	−	0.00247058i
$680$		0			0
$681$			2.51219i			0.0962672i
$682$		0			0
$683$			10.2692i			0.392939i	0.980510	+	0.196469i	$0.0629477\pi$
$683$			10.2692i			0.392939i	−0.980510	+	0.196469i	$0.937052\pi$
$684$		0			0
$685$	0.0244205	−	0.0751585i	0.000933059	−	0.00287166i
$686$		0			0
$687$	19.3030	+	26.5683i	0.736455	+	1.01364i
$688$		0			0
$689$	−18.0742	+	5.87267i	−0.688573	+	0.223731i
$690$		0			0
$691$	−19.2824	+	26.5400i	−0.733539	+	1.00963i	0.265426	+	0.964131i	$0.414487\pi$
$691$	−19.2824	+	26.5400i	−0.733539	+	1.00963i	−0.998964	+	0.0454981i	$0.985513\pi$
$692$		0			0
$693$	0.132043	+	3.99100i	0.00501590	+	0.151606i
$694$		0			0
$695$	−0.0395856	−	0.0287606i	−0.00150157	−	0.00109095i
$696$		0			0
$697$	−3.85238	−	11.8564i	−0.145919	−	0.449094i
$698$		0			0
$699$	6.24027	−	4.53382i	0.236029	−	0.171485i
$700$		0			0
$701$	17.0153	+	5.52861i	0.642660	+	0.208813i	0.612175	−	0.790722i	$-0.290295\pi$
$701$	17.0153	+	5.52861i	0.642660	+	0.208813i	0.0304849	+	0.999535i	$0.490295\pi$
$702$		0			0
$703$	19.1405			0.721896
$704$		0			0
$705$	0.697558			0.0262716
$706$		0			0
$707$	2.27724	+	0.739920i	0.0856444	+	0.0278275i
$708$		0			0
$709$	−17.7529	+	12.8983i	−0.666725	+	0.484404i	−0.868927	−	0.494940i	$-0.835190\pi$
$709$	−17.7529	+	12.8983i	−0.666725	+	0.484404i	0.202202	+	0.979344i	$0.435190\pi$
$710$		0			0
$711$	−2.31908	−	7.13738i	−0.0869722	−	0.267673i
$712$		0			0
$713$	−9.22243	−	6.70048i	−0.345383	−	0.250935i
$714$		0			0
$715$	−0.0640438	−	0.176968i	−0.00239510	−	0.00661822i
$716$		0			0
$717$	−2.63470	+	3.62635i	−0.0983946	+	0.135429i
$718$		0			0
$719$	40.2576	−	13.0805i	1.50136	−	0.487820i	0.560943	−	0.827855i	$-0.310439\pi$
$719$	40.2576	−	13.0805i	1.50136	−	0.487820i	0.940413	+	0.340035i	$0.110439\pi$
$720$		0			0
$721$	−2.34986	−	3.23430i	−0.0875132	−	0.120452i
$722$		0			0
$723$	11.4799	−	35.3316i	0.426944	−	1.31400i
$724$		0			0
$725$		−	48.9805i		−	1.81909i
$726$		0			0
$727$		−	30.3596i		−	1.12597i	−0.826466	−	0.562987i	$-0.809652\pi$
$727$		−	30.3596i		−	1.12597i	0.826466	−	0.562987i	$-0.190348\pi$
$728$		0			0
$729$	6.30002	−	19.3895i	0.233334	−	0.718129i
$730$		0			0
$731$	19.9383	+	27.4427i	0.737445	+	1.01501i
$732$		0			0
$733$	13.5042	−	4.38777i	0.498788	−	0.162066i	−0.0488094	−	0.998808i	$-0.515543\pi$
$733$	13.5042	−	4.38777i	0.498788	−	0.162066i	0.547597	+	0.836742i	$0.315543\pi$
$734$		0			0
$735$	−0.247531	+	0.340697i	−0.00913031	+	0.0125668i
$736$		0			0
$737$	−9.38564	−	25.9347i	−0.345724	−	0.955316i
$738$		0			0
$739$	31.1374	+	22.6226i	1.14541	+	0.832188i	0.987864	−	0.155324i	$-0.0496423\pi$
$739$	31.1374	+	22.6226i	1.14541	+	0.832188i	0.157544	+	0.987512i	$0.449642\pi$
$740$		0			0
$741$	4.15207	+	12.7788i	0.152530	+	0.469439i
$742$		0			0
$743$	4.50373	−	3.27215i	0.165226	−	0.120043i	−0.502100	−	0.864810i	$-0.667439\pi$
$743$	4.50373	−	3.27215i	0.165226	−	0.120043i	0.667325	+	0.744766i	$0.267439\pi$
$744$		0			0
$745$	0.135168	+	0.0439189i	0.00495219	+	0.00160906i
$746$		0			0
$747$	−4.21215			−0.154115
$748$		0			0
$749$	3.93906			0.143930
$750$		0			0
$751$	16.4146	+	5.33343i	0.598977	+	0.194620i	0.592784	−	0.805361i	$-0.298029\pi$
$751$	16.4146	+	5.33343i	0.598977	+	0.194620i	0.00619302	+	0.999981i	$0.498029\pi$
$752$		0			0
$753$	−49.6296	+	36.0580i	−1.80860	+	1.31403i
$754$		0			0
$755$	0.102687	+	0.316037i	0.00373715	+	0.0115018i
$756$		0			0
$757$	−34.0204	−	24.7173i	−1.23649	−	0.898364i	−0.239132	−	0.970987i	$-0.576863\pi$
$757$	−34.0204	−	24.7173i	−1.23649	−	0.898364i	−0.997359	+	0.0726230i	$0.976863\pi$
$758$		0			0
$759$	0.963755	+	29.1295i	0.0349821	+	1.05734i
$760$		0			0
$761$	6.87810	−	9.46689i	0.249331	−	0.343175i	−0.665946	−	0.746000i	$-0.731972\pi$
$761$	6.87810	−	9.46689i	0.249331	−	0.343175i	0.915277	+	0.402826i	$0.131972\pi$
$762$		0			0
$763$	4.16590	−	1.35358i	0.150816	−	0.0490030i
$764$		0			0
$765$	0.134145	+	0.184635i	0.00485002	+	0.00667548i
$766$		0			0
$767$	−4.36225	+	13.4256i	−0.157512	+	0.484772i
$768$		0			0
$769$		−	35.9081i		−	1.29488i	−0.762117	−	0.647439i	$-0.775840\pi$
$769$		−	35.9081i		−	1.29488i	0.762117	−	0.647439i	$-0.224160\pi$
$770$		0			0
$771$			1.74204i			0.0627380i
$772$		0			0
$773$	−11.9293	+	36.7145i	−0.429066	+	1.32053i	0.469981	+	0.882676i	$0.344261\pi$
$773$	−11.9293	+	36.7145i	−0.429066	+	1.32053i	−0.899047	+	0.437852i	$0.855739\pi$
$774$		0			0
$775$	−9.06129	−	12.4718i	−0.325491	−	0.448000i
$776$		0			0
$777$	7.56684	−	2.45862i	0.271459	−	0.0882023i
$778$		0			0
$779$	5.76478	−	7.93454i	0.206545	−	0.284285i
$780$		0			0
$781$	11.0909	+	7.51054i	0.396864	+	0.268748i
$782$		0			0
$783$	−6.58316	−	4.78295i	−0.235263	−	0.170929i
$784$		0			0
$785$	−0.155779	−	0.479438i	−0.00555999	−	0.0171119i
$786$		0			0
$787$	22.9481	−	16.6727i	0.818010	−	0.594319i	−0.0981316	−	0.995173i	$-0.531287\pi$
$787$	22.9481	−	16.6727i	0.818010	−	0.594319i	0.916142	+	0.400854i	$0.131287\pi$
$788$		0			0
$789$	−38.3191	−	12.4506i	−1.36420	−	0.443254i
$790$		0			0
$791$	6.31666			0.224595
$792$		0			0
$793$	28.8304			1.02380
$794$		0			0
$795$	−0.514873	−	0.167292i	−0.0182607	−	0.00593325i
$796$		0			0
$797$	10.0116	−	7.27382i	0.354628	−	0.257652i	−0.396180	−	0.918173i	$-0.629664\pi$
$797$	10.0116	−	7.27382i	0.354628	−	0.257652i	0.750808	+	0.660521i	$0.229664\pi$
$798$		0			0
$799$	−11.4818	−	35.3373i	−0.406196	−	1.25014i
$800$		0			0
$801$	−25.7308	−	18.6945i	−0.909153	−	0.660538i
$802$		0			0
$803$	9.58153	−	7.45766i	0.338125	−	0.263175i
$804$		0			0
$805$	0.0257385	−	0.0354260i	0.000907162	−	0.00124860i
$806$		0			0
$807$	22.8840	−	7.43546i	0.805554	−	0.261740i
$808$		0			0
$809$	−3.13608	−	4.31645i	−0.110259	−	0.151758i	0.750321	−	0.661073i	$-0.229899\pi$
$809$	−3.13608	−	4.31645i	−0.110259	−	0.151758i	−0.860580	+	0.509315i	$0.829899\pi$
$810$		0			0
$811$	−2.69151	+	8.28363i	−0.0945118	+	0.290878i	−0.987126	−	0.159944i	$-0.948869\pi$
$811$	−2.69151	+	8.28363i	−0.0945118	+	0.290878i	0.892614	+	0.450821i	$0.148869\pi$
$812$		0			0
$813$		−	64.6333i		−	2.26679i
$814$		0			0
$815$		−	0.418052i		−	0.0146437i
$816$		0			0
$817$	−8.24649	+	25.3801i	−0.288508	+	0.887937i
$818$		0			0
$819$	1.53995	+	2.11956i	0.0538102	+	0.0740634i
$820$		0			0
$821$	4.38902	−	1.42608i	0.153178	−	0.0497705i	−0.231425	−	0.972853i	$-0.574339\pi$
$821$	4.38902	−	1.42608i	0.153178	−	0.0497705i	0.384602	+	0.923082i	$0.374339\pi$
$822$		0			0
$823$	−14.2497	+	19.6130i	−0.496712	+	0.683665i	−0.981608	−	0.190906i	$-0.938857\pi$
$823$	−14.2497	+	19.6130i	−0.496712	+	0.683665i	0.484896	+	0.874572i	$0.338857\pi$
$824$		0			0
$825$	−10.9335	+	37.8676i	−0.380656	+	1.31838i
$826$		0			0
$827$	−21.5050	−	15.6243i	−0.747801	−	0.543310i	0.147343	−	0.989085i	$-0.452928\pi$
$827$	−21.5050	−	15.6243i	−0.747801	−	0.543310i	−0.895145	+	0.445776i	$0.852928\pi$
$828$		0			0
$829$	6.18680	+	19.0410i	0.214876	+	0.661322i	0.999162	+	0.0409220i	$0.0130295\pi$
$829$	6.18680	+	19.0410i	0.214876	+	0.661322i	−0.784286	+	0.620400i	$0.786970\pi$
$830$		0			0
$831$	0.699701	−	0.508362i	0.0242724	−	0.0176349i
$832$		0			0
$833$	21.3336	+	6.93169i	0.739164	+	0.240169i
$834$		0			0
$835$	−0.566257			−0.0195961
$836$		0			0
$837$	−2.56109			−0.0885242
$838$		0			0
$839$	6.67097	+	2.16753i	0.230308	+	0.0748315i	0.421897	−	0.906644i	$-0.361364\pi$
$839$	6.67097	+	2.16753i	0.230308	+	0.0748315i	−0.191590	+	0.981475i	$0.561364\pi$
$840$		0			0
$841$	54.1958	−	39.3756i	1.86882	−	1.35778i
$842$		0			0
$843$	−0.343377	−	1.05680i	−0.0118265	−	0.0363983i
$844$		0			0
$845$	0.174363	+	0.126682i	0.00599825	+	0.00435799i
$846$		0			0
$847$	−4.22758	−	2.66329i	−0.145262	−	0.0915118i
$848$		0			0
$849$	26.8806	−	36.9979i	0.922538	−	1.26977i
$850$		0			0
$851$	25.9069	−	8.41767i	0.888078	−	0.288554i
$852$		0			0
$853$	−1.82137	−	2.50690i	−0.0623624	−	0.0858345i	0.776697	−	0.629875i	$-0.216894\pi$
$853$	−1.82137	−	2.50690i	−0.0623624	−	0.0858345i	−0.839059	+	0.544040i	$0.816894\pi$
$854$		0			0
$855$	−0.0554824	+	0.170757i	−0.00189746	+	0.00583978i
$856$		0			0
$857$		−	15.5346i		−	0.530653i	−0.964159	−	0.265327i	$-0.914520\pi$
$857$		−	15.5346i		−	0.530653i	0.964159	−	0.265327i	$-0.0854798\pi$
$858$		0			0
$859$		−	25.5857i		−	0.872973i	−0.899711	−	0.436487i	$-0.856223\pi$
$859$		−	25.5857i		−	0.872973i	0.899711	−	0.436487i	$-0.143777\pi$
$860$		0			0
$861$	1.25980	−	3.87728i	0.0429340	−	0.132137i
$862$		0			0
$863$	−14.3530	−	19.7551i	−0.488580	−	0.672473i	0.491545	−	0.870852i	$-0.336432\pi$
$863$	−14.3530	−	19.7551i	−0.488580	−	0.672473i	−0.980125	+	0.198379i	$0.936432\pi$
$864$		0			0
$865$	0.491925	−	0.159836i	0.0167259	−	0.00543459i
$866$		0			0
$867$	−8.52032	+	11.7272i	−0.289365	+	0.398277i
$868$		0			0
$869$	9.02187	+	2.60489i	0.306046	+	0.0883649i
$870$		0			0
$871$	−14.6397	−	10.6364i	−0.496047	−	0.360400i
$872$		0			0
$873$	0.122061	+	0.375665i	0.00413114	+	0.0127143i
$874$		0			0
$875$	0.0958219	−	0.0696187i	0.00323937	−	0.00235354i
$876$		0			0
$877$	25.8588	+	8.40205i	0.873191	+	0.283717i	0.711127	−	0.703063i	$-0.248185\pi$
$877$	25.8588	+	8.40205i	0.873191	+	0.283717i	0.162064	+	0.986780i	$0.448185\pi$
$878$		0			0
$879$	−53.7040			−1.81139
$880$		0			0
$881$	−17.5760			−0.592152			−0.296076	−	0.955164i	$-0.595678\pi$
$881$	−17.5760			−0.592152			−0.296076	+	0.955164i	$0.595678\pi$
$882$		0			0
$883$	−9.05437	−	2.94194i	−0.304704	−	0.0990042i	0.152674	−	0.988277i	$-0.451211\pi$
$883$	−9.05437	−	2.94194i	−0.304704	−	0.0990042i	−0.457378	+	0.889272i	$0.651211\pi$
$884$		0			0
$885$	−0.325332	+	0.236368i	−0.0109359	+	0.00794541i
$886$		0			0
$887$	−6.86672	−	21.1336i	−0.230562	−	0.709597i	−0.997679	−	0.0680897i	$-0.978310\pi$
$887$	−6.86672	−	21.1336i	−0.230562	−	0.709597i	0.767117	−	0.641507i	$-0.221690\pi$
$888$		0			0
$889$	−1.43172	−	1.04020i	−0.0480182	−	0.0348873i
$890$		0			0
$891$	20.2207	+	25.9794i	0.677419	+	0.870341i
$892$		0			0
$893$	17.1816	−	23.6484i	0.574960	−	0.791364i
$894$		0			0
$895$	−0.315096	+	0.102381i	−0.0105325	+	0.00342222i
$896$		0			0
$897$	11.2398	+	15.4702i	0.375286	+	0.516537i
$898$		0			0
$899$	9.33587	−	28.7329i	0.311369	−	0.958295i
$900$		0			0
$901$			28.8364i			0.960679i
$902$		0			0
$903$			11.0928i			0.369147i
$904$		0			0
$905$	0.0741284	−	0.228144i	0.00246411	−	0.00758375i
$906$		0			0
$907$	−17.0954	−	23.5298i	−0.567644	−	0.781295i	0.424629	−	0.905367i	$-0.360405\pi$
$907$	−17.0954	−	23.5298i	−0.567644	−	0.781295i	−0.992273	+	0.124072i	$0.960405\pi$
$908$		0			0
$909$	−13.2885	+	4.31769i	−0.440751	+	0.143209i
$910$		0			0
$911$	−6.30695	+	8.68078i	−0.208959	+	0.287607i	−0.900613	−	0.434622i	$-0.856882\pi$
$911$	−6.30695	+	8.68078i	−0.208959	+	0.287607i	0.691654	+	0.722229i	$0.256882\pi$
$912$		0			0
$913$	2.95526	−	4.36407i	0.0978047	−	0.144430i
$914$		0			0
$915$	0.664430	+	0.482736i	0.0219654	+	0.0159588i
$916$		0			0
$917$	1.48599	+	4.57340i	0.0490716	+	0.151027i
$918$		0			0
$919$	−22.4291	+	16.2957i	−0.739867	+	0.537545i	−0.892669	−	0.450712i	$-0.851170\pi$
$919$	−22.4291	+	16.2957i	−0.739867	+	0.537545i	0.152802	+	0.988257i	$0.451170\pi$
$920$		0			0
$921$	34.4114	+	11.1809i	1.13389	+	0.368424i
$922$		0			0
$923$	8.78820			0.289267
$924$		0			0
$925$	36.8378			1.21122
$926$		0			0
$927$	22.1869	+	7.20895i	0.728712	+	0.236773i
$928$		0			0
$929$	0.154656	−	0.112364i	0.00507411	−	0.00368655i	−0.585245	−	0.810856i	$-0.699002\pi$
$929$	0.154656	−	0.112364i	0.00507411	−	0.00368655i	0.590319	+	0.807170i	$0.299002\pi$
$930$		0			0
$931$	5.45327	+	16.7834i	0.178724	+	0.550055i
$932$		0			0
$933$	−31.8862	−	23.1667i	−1.04391	−	0.758442i
$934$		0			0
$935$	−0.285410	+	0.00944284i	−0.00933391	+	0.000308814i
$936$		0			0
$937$	−26.1150	+	35.9442i	−0.853140	+	1.17425i	0.130022	+	0.991511i	$0.458495\pi$
$937$	−26.1150	+	35.9442i	−0.853140	+	1.17425i	−0.983162	+	0.182736i	$0.941505\pi$
$938$		0			0
$939$	−29.3252	+	9.52834i	−0.956992	+	0.310946i
$940$		0			0
$941$	−26.7236	−	36.7818i	−0.871163	−	1.19905i	−0.978791	−	0.204862i	$-0.934326\pi$
$941$	−26.7236	−	36.7818i	−0.871163	−	1.19905i	0.107628	−	0.994191i	$-0.465674\pi$
$942$		0			0
$943$	4.31325	−	13.2748i	0.140459	−	0.432287i
$944$		0			0
$945$		−	0.00983788i		−	0.000320026i
$946$		0			0
$947$			11.1236i			0.361468i	0.983532	+	0.180734i	$0.0578474\pi$
$947$			11.1236i			0.361468i	−0.983532	+	0.180734i	$0.942153\pi$
$948$		0			0
$949$	2.46169	−	7.57629i	0.0799097	−	0.245937i
$950$		0			0
$951$	12.2356	+	16.8408i	0.396766	+	0.546102i
$952$		0			0
$953$	36.7246	−	11.9326i	1.18963	−	0.386533i	0.353692	−	0.935362i	$-0.384926\pi$
$953$	36.7246	−	11.9326i	1.18963	−	0.386533i	0.835935	+	0.548829i	$0.184926\pi$
$954$		0			0
$955$	−0.360687	+	0.496444i	−0.0116716	+	0.0160645i
$956$		0			0
$957$	−72.6325	+	26.2854i	−2.34787	+	0.849685i
$958$		0			0
$959$	−1.11365	−	0.809116i	−0.0359617	−	0.0261277i
$960$		0			0
$961$	6.64118	+	20.4395i	0.214232	+	0.659337i
$962$		0			0
$963$	−18.5959	+	13.5107i	−0.599245	+	0.435377i
$964$		0			0
$965$	0.452254	+	0.146946i	0.0145586	+	0.00473037i
$966$		0			0
$967$	−47.6382			−1.53194			−0.765971	−	0.642875i	$-0.777741\pi$
$967$	−47.6382			−1.53194			−0.765971	+	0.642875i	$0.777741\pi$
$968$		0			0
$969$	20.3878			0.654949
$970$		0			0
$971$	29.0018	+	9.42327i	0.930713	+	0.302407i	0.734854	−	0.678225i	$-0.237251\pi$
$971$	29.0018	+	9.42327i	0.930713	+	0.302407i	0.195859	+	0.980632i	$0.437251\pi$
$972$		0			0
$973$	−0.689536	+	0.500977i	−0.0221055	+	0.0160606i
$974$		0			0
$975$	7.99108	+	24.5940i	0.255919	+	0.787639i
$976$		0			0
$977$	22.2206	+	16.1442i	0.710898	+	0.516498i	0.883463	−	0.468500i	$-0.155205\pi$
$977$	22.2206	+	16.1442i	0.710898	+	0.516498i	−0.172565	+	0.984998i	$0.555205\pi$
$978$		0			0
$979$	37.4215	−	13.5427i	1.19600	−	0.432826i
$980$		0			0
$981$	−15.0241	+	20.6789i	−0.479682	+	0.660225i
$982$		0			0
$983$	−43.0942	+	14.0022i	−1.37449	+	0.446600i	−0.900855	−	0.434120i	$-0.857059\pi$
$983$	−43.0942	+	14.0022i	−1.37449	+	0.446600i	−0.473637	+	0.880720i	$0.657059\pi$
$984$		0			0
$985$	0.402013	+	0.553323i	0.0128092	+	0.0176303i
$986$		0			0
$987$	3.75477	−	11.5560i	0.119516	−	0.367831i
$988$		0			0
$989$			37.9791i			1.20766i
$990$		0			0
$991$		−	49.4577i		−	1.57108i	−0.618813	−	0.785539i	$-0.712386\pi$
$991$		−	49.4577i		−	1.57108i	0.618813	−	0.785539i	$-0.287614\pi$
$992$		0			0
$993$	−22.3158	+	68.6809i	−0.708170	+	2.17952i
$994$		0			0
$995$	−0.252738	−	0.347864i	−0.00801233	−	0.0110280i
$996$		0			0
$997$	−2.11122	+	0.685977i	−0.0668631	+	0.0217251i	−0.342258	−	0.939606i	$-0.611192\pi$
$997$	−2.11122	+	0.685977i	−0.0668631	+	0.0217251i	0.275394	+	0.961331i	$0.411192\pi$
$998$		0			0
$999$	3.59721	−	4.95114i	0.113811	−	0.156647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.u.a.95.3	yes	48
4.3	odd	2	inner	352.2.u.a.95.10	yes	48
8.3	odd	2		704.2.u.d.447.3		48
8.5	even	2		704.2.u.d.447.10		48
11.8	odd	10	inner	352.2.u.a.63.10	yes	48
44.19	even	10	inner	352.2.u.a.63.3	✓	48
88.19	even	10		704.2.u.d.63.10		48
88.85	odd	10		704.2.u.d.63.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.u.a.63.3	✓	48	44.19	even	10	inner
352.2.u.a.63.10	yes	48	11.8	odd	10	inner
352.2.u.a.95.3	yes	48	1.1	even	1	trivial
352.2.u.a.95.10	yes	48	4.3	odd	2	inner
704.2.u.d.63.3		48	88.85	odd	10
704.2.u.d.63.10		48	88.19	even	10
704.2.u.d.447.3		48	8.3	odd	2
704.2.u.d.447.10		48	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.26076 - 0.734564i) q^{3} +(0.0210968 - 0.0153277i) q^{5} +(-0.140366 - 0.432001i) q^{7} +(2.14438 + 1.55799i) q^{9} +(-3.11868 + 1.12864i) q^{11} +(-1.27904 + 1.76045i) q^{13} +(-0.0589538 + 0.0191553i) q^{15} +(1.94076 + 2.67122i) q^{17} +(-0.802698 + 2.47045i) q^{19} +1.07976i q^{21} +3.69681i q^{23} +(-1.54487 + 4.75464i) q^{25} +(0.488184 + 0.671927i) q^{27} +(-9.31791 + 3.02757i) q^{29} +(-1.81250 + 2.49470i) q^{31} +(7.87964 - 0.260699i) q^{33} +(-0.00958284 - 0.00696234i) q^{35} +(-2.27701 - 7.00791i) q^{37} +(4.18475 - 3.04040i) q^{39} +(-3.59088 - 1.16675i) q^{41} +10.2735 q^{43} +0.0691199 q^{45} +(-10.7024 - 3.47742i) q^{47} +(5.49620 - 3.99322i) q^{49} +(-2.42539 - 7.46459i) q^{51} +(7.06555 + 5.13342i) q^{53} +(-0.0484947 + 0.0716128i) q^{55} +(3.62941 - 4.99545i) q^{57} +(6.16979 - 2.00468i) q^{59} +(-7.78761 - 10.7187i) q^{61} +(0.372054 - 1.14506i) q^{63} +0.0567444i q^{65} +8.31591i q^{67} +(2.71555 - 8.35759i) q^{69} +(-2.37385 - 3.26733i) q^{71} +(-3.48170 + 1.13127i) q^{73} +(6.98517 - 9.61426i) q^{75} +(0.925328 + 1.18885i) q^{77} +(-2.29058 - 1.66420i) q^{79} +(-3.06734 - 9.44029i) q^{81} +(-1.28563 + 0.934066i) q^{83} +(0.0818874 + 0.0266068i) q^{85} +23.2895 q^{87} -11.9991 q^{89} +(0.940047 + 0.305440i) q^{91} +(5.93015 - 4.30850i) q^{93} +(0.0209320 + 0.0644220i) q^{95} +(0.120561 + 0.0875928i) q^{97} +(-8.44605 - 2.43863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{9} + 4 q^{25} + 36 q^{33} + 40 q^{41} - 96 q^{45} - 4 q^{49} - 8 q^{53} + 20 q^{57} - 8 q^{69} - 40 q^{73} - 72 q^{77} - 72 q^{81} - 80 q^{85} - 40 q^{89} + 8 q^{93} + 4 q^{97}+O(q^{100}) \) 48 * q + 4 * q^9 + 4 * q^25 + 36 * q^33 + 40 * q^41 - 96 * q^45 - 4 * q^49 - 8 * q^53 + 20 * q^57 - 8 * q^69 - 40 * q^73 - 72 * q^77 - 72 * q^81 - 80 * q^85 - 40 * q^89 + 8 * q^93 + 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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