LMFDB - Embedded newform 819.2.dl.g.415.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(298,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("819.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.dl (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 11x^{14} + 85x^{12} - 310x^{10} + 807x^{8} - 1196x^{6} + 1273x^{4} - 688x^{2} + 256 $ x^16 - 11x^14 + 85x^12 - 310x^10 + 807x^8 - 1196x^6 + 1273x^4 - 688*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.2
Root			$1.02312 - 0.590698i$ of defining polynomial
Character	$\chi$	$=$	819.415
Dual form			819.2.dl.g.298.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69305 - 0.977485i) q^{2} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} +(-0.807080 + 2.51965i) q^{7} +0.348171i q^{8} +O(q^{10})$	\(q+(-1.69305 - 0.977485i) q^{2} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} +(-0.807080 + 2.51965i) q^{7} +0.348171i q^{8} +(-0.147356 - 0.255228i) q^{10} +(-0.669934 + 0.386787i) q^{11} +(3.25910 + 1.54216i) q^{13} +(3.82934 - 3.47699i) q^{14} +(2.16224 - 3.74510i) q^{16} +(-0.461444 - 0.799245i) q^{17} +(-6.54095 - 3.77642i) q^{19} +0.274652i q^{20} +1.51231 q^{22} +(-3.61624 + 6.26351i) q^{23} +(-2.48864 - 4.31045i) q^{25} +(-4.01039 - 5.79668i) q^{26} +(-4.71075 + 1.02186i) q^{28} -1.68142 q^{29} +(-0.532789 + 0.307606i) q^{31} +(-6.71851 + 3.87893i) q^{32} +1.80422i q^{34} +(-0.295285 + 0.268115i) q^{35} +(-3.09117 - 1.78469i) q^{37} +(7.38278 + 12.7874i) q^{38} +(-0.0262434 + 0.0454549i) q^{40} -10.5905i q^{41} -0.868503 q^{43} +(-1.22056 - 0.704688i) q^{44} +(12.2450 - 7.06964i) q^{46} +(4.89695 + 2.82725i) q^{47} +(-5.69725 - 4.06711i) q^{49} +9.73042i q^{50} +(0.535636 + 6.54710i) q^{52} +(-4.65125 - 8.05620i) q^{53} -0.116616 q^{55} +(-0.877269 - 0.281002i) q^{56} +(2.84673 + 1.64356i) q^{58} +(-7.07374 + 4.08402i) q^{59} +(-5.90253 + 10.2235i) q^{61} +1.20272 q^{62} +6.51745 q^{64} +(0.309246 + 0.446989i) q^{65} +(4.56962 - 2.63827i) q^{67} +(0.840708 - 1.45615i) q^{68} +(0.762012 - 0.165296i) q^{70} +9.73042i q^{71} +(-4.19319 + 2.42094i) q^{73} +(3.48901 + 6.04315i) q^{74} -13.7605i q^{76} +(-0.433876 - 2.00017i) q^{77} +(-6.82897 + 11.8281i) q^{79} +(0.564575 - 0.325957i) q^{80} +(-10.3520 + 17.9303i) q^{82} -3.57563i q^{83} -0.139126i q^{85} +(1.47042 + 0.848948i) q^{86} +(-0.134668 - 0.233252i) q^{88} +(-8.95299 - 5.16901i) q^{89} +(-6.51606 + 6.96714i) q^{91} -13.1769 q^{92} +(-5.52719 - 9.57338i) q^{94} +(-0.569295 - 0.986048i) q^{95} +4.78983i q^{97} +(5.67020 + 12.4548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} - 16 q^{10} + 6 q^{13} + 10 q^{14} - 28 q^{16} + 2 q^{17} + 60 q^{22} - 24 q^{23} + 10 q^{25} - 14 q^{26} - 24 q^{29} + 30 q^{35} + 26 q^{40} - 76 q^{43} + 2 q^{49} - 10 q^{53} - 16 q^{55} - 72 q^{56} + 26 q^{61} + 104 q^{62} - 84 q^{64} + 32 q^{65} + 12 q^{68} + 54 q^{74} + 10 q^{77} - 10 q^{79} - 48 q^{82} + 68 q^{88} - 57 q^{91} - 16 q^{92} - 48 q^{94} - 18 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 16 * q^10 + 6 * q^13 + 10 * q^14 - 28 * q^16 + 2 * q^17 + 60 * q^22 - 24 * q^23 + 10 * q^25 - 14 * q^26 - 24 * q^29 + 30 * q^35 + 26 * q^40 - 76 * q^43 + 2 * q^49 - 10 * q^53 - 16 * q^55 - 72 * q^56 + 26 * q^61 + 104 * q^62 - 84 * q^64 + 32 * q^65 + 12 * q^68 + 54 * q^74 + 10 * q^77 - 10 * q^79 - 48 * q^82 + 68 * q^88 - 57 * q^91 - 16 * q^92 - 48 * q^94 - 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.69305	−	0.977485i	−1.19717	−	0.691186i	−0.237246	−	0.971450i	$-0.576245\pi$
$2$	−1.69305	−	0.977485i	−1.19717	−	0.691186i	−0.959923	+	0.280264i	$0.909578\pi$
$3$		0			0
$3$		0			0
$4$	0.910952	+	1.57782i	0.455476	+	0.788908i
$5$	0.130553	+	0.0753750i	0.0583852	+	0.0337087i	0.528908	−	0.848679i	$-0.322601\pi$
$5$	0.130553	+	0.0753750i	0.0583852	+	0.0337087i	−0.470523	+	0.882388i	$0.655935\pi$
$6$		0			0
$7$	−0.807080	+	2.51965i	−0.305047	+	0.952337i
$7$	−0.807080	+	2.51965i	−0.305047	+	0.952337i
$8$			0.348171i			0.123097i
$9$		0			0
$10$	−0.147356	−	0.255228i	−0.0465980	−	0.0807101i
$11$	−0.669934	+	0.386787i	−0.201993	+	0.116621i	−0.597585	−	0.801806i	$-0.703873\pi$
$11$	−0.669934	+	0.386787i	−0.201993	+	0.116621i	0.395592	+	0.918426i	$0.370539\pi$
$12$		0			0
$13$	3.25910	+	1.54216i	0.903912	+	0.427719i
$13$	3.25910	+	1.54216i	0.903912	+	0.427719i
$14$	3.82934	−	3.47699i	1.02344	−	0.929264i
$15$		0			0
$16$	2.16224	−	3.74510i	0.540559	−	0.936276i
$17$	−0.461444	−	0.799245i	−0.111917	−	0.193845i	0.804626	−	0.593782i	$-0.202366\pi$
$17$	−0.461444	−	0.799245i	−0.111917	−	0.193845i	−0.916543	+	0.399936i	$0.869032\pi$
$18$		0			0
$19$	−6.54095	−	3.77642i	−1.50060	−	0.866370i	−1.00000		0.000689073i	$-0.999781\pi$
$19$	−6.54095	−	3.77642i	−1.50060	−	0.866370i	−0.500597	−	0.865681i	$-0.666886\pi$
$20$			0.274652i			0.0614141i
$21$		0			0
$22$	1.51231			0.322426
$23$	−3.61624	+	6.26351i	−0.754038	+	1.30603i	0.191813	+	0.981432i	$0.438563\pi$
$23$	−3.61624	+	6.26351i	−0.754038	+	1.30603i	−0.945851	+	0.324601i	$0.894770\pi$
$24$		0			0
$25$	−2.48864	−	4.31045i	−0.497727	−	0.862089i
$26$	−4.01039	−	5.79668i	−0.786502	−	1.13682i
$27$		0			0
$28$	−4.71075	+	1.02186i	−0.890248	+	0.193113i
$29$	−1.68142			−0.312231			−0.156115	−	0.987739i	$-0.549897\pi$
$29$	−1.68142			−0.312231			−0.156115	+	0.987739i	$0.549897\pi$
$30$		0			0
$31$	−0.532789	+	0.307606i	−0.0956917	+	0.0552476i	−0.547082	−	0.837079i	$-0.684261\pi$
$31$	−0.532789	+	0.307606i	−0.0956917	+	0.0552476i	0.451390	+	0.892327i	$0.350928\pi$
$32$	−6.71851	+	3.87893i	−1.18768	+	0.685705i
$33$		0			0
$34$			1.80422i			0.309421i
$35$	−0.295285	+	0.268115i	−0.0499123	+	0.0453197i
$36$		0			0
$37$	−3.09117	−	1.78469i	−0.508186	−	0.293401i	0.223902	−	0.974612i	$-0.428120\pi$
$37$	−3.09117	−	1.78469i	−0.508186	−	0.293401i	−0.732088	+	0.681211i	$0.761454\pi$
$38$	7.38278	+	12.7874i	1.19765	+	2.07438i
$39$		0			0
$40$	−0.0262434	+	0.0454549i	−0.00414945	+	0.00718705i
$41$		−	10.5905i		−	1.65396i	−0.562234	−	0.826978i	$-0.690058\pi$
$41$		−	10.5905i		−	1.65396i	0.562234	−	0.826978i	$-0.309942\pi$
$42$		0			0
$43$	−0.868503			−0.132445			−0.0662227	−	0.997805i	$-0.521095\pi$
$43$	−0.868503			−0.132445			−0.0662227	+	0.997805i	$0.521095\pi$
$44$	−1.22056	−	0.704688i	−0.184006	−	0.106236i
$45$		0			0
$46$	12.2450	−	7.06964i	1.80542	−	1.04236i
$47$	4.89695	+	2.82725i	0.714293	+	0.412397i	0.812649	−	0.582754i	$-0.198025\pi$
$47$	4.89695	+	2.82725i	0.714293	+	0.412397i	−0.0983556	+	0.995151i	$0.531358\pi$
$48$		0			0
$49$	−5.69725	−	4.06711i	−0.813892	−	0.581016i
$50$			9.73042i			1.37609i
$51$		0			0
$52$	0.535636	+	6.54710i	0.0742794	+	0.907919i
$53$	−4.65125	−	8.05620i	−0.638898	−	1.10660i	−0.985675	−	0.168656i	$-0.946057\pi$
$53$	−4.65125	−	8.05620i	−0.638898	−	1.10660i	0.346777	−	0.937948i	$-0.387276\pi$
$54$		0			0
$55$	−0.116616			−0.0157245
$56$	−0.877269	−	0.281002i	−0.117230	−	0.0375504i
$57$		0			0
$58$	2.84673	+	1.64356i	0.373793	+	0.215810i
$59$	−7.07374	+	4.08402i	−0.920922	+	0.531695i	−0.883929	−	0.467621i	$-0.845111\pi$
$59$	−7.07374	+	4.08402i	−0.920922	+	0.531695i	−0.0369930	+	0.999316i	$0.511778\pi$
$60$		0			0
$61$	−5.90253	+	10.2235i	−0.755742	+	1.30898i	0.189263	+	0.981927i	$0.439390\pi$
$61$	−5.90253	+	10.2235i	−0.755742	+	1.30898i	−0.945005	+	0.327057i	$0.893943\pi$
$62$	1.20272			0.152746
$63$		0			0
$64$	6.51745			0.814681
$65$	0.309246	+	0.446989i	0.0383572	+	0.0554422i
$66$		0			0
$67$	4.56962	−	2.63827i	0.558268	−	0.322316i	−0.194182	−	0.980966i	$-0.562205\pi$
$67$	4.56962	−	2.63827i	0.558268	−	0.322316i	0.752450	+	0.658649i	$0.228872\pi$
$68$	0.840708	−	1.45615i	0.101951	−	0.176584i
$69$		0			0
$70$	0.762012	−	0.165296i	0.0910779	−	0.0197566i
$71$			9.73042i			1.15479i	0.816466	+	0.577394i	$0.195930\pi$
$71$			9.73042i			1.15479i	−0.816466	+	0.577394i	$0.804070\pi$
$72$		0			0
$73$	−4.19319	+	2.42094i	−0.490775	+	0.283349i	−0.724896	−	0.688858i	$-0.758112\pi$
$73$	−4.19319	+	2.42094i	−0.490775	+	0.283349i	0.234121	+	0.972208i	$0.424779\pi$
$74$	3.48901	+	6.04315i	0.405590	+	0.702502i
$75$		0			0
$76$		−	13.7605i		−	1.57844i
$77$	−0.433876	−	2.00017i	−0.0494447	−	0.227940i
$78$		0			0
$79$	−6.82897	+	11.8281i	−0.768319	+	1.33077i	0.170155	+	0.985417i	$0.445573\pi$
$79$	−6.82897	+	11.8281i	−0.768319	+	1.33077i	−0.938474	+	0.345350i	$0.887760\pi$
$80$	0.564575	−	0.325957i	0.0631214	−	0.0364431i
$81$		0			0
$82$	−10.3520	+	17.9303i	−1.14319	+	1.98007i
$83$		−	3.57563i		−	0.392477i	−0.980556	−	0.196238i	$-0.937127\pi$
$83$		−	3.57563i		−	0.392477i	0.980556	−	0.196238i	$-0.0628727\pi$
$84$		0			0
$85$		−	0.139126i		−	0.0150903i
$86$	1.47042	+	0.848948i	0.158560	+	0.0915445i
$87$		0			0
$88$	−0.134668	−	0.233252i	−0.0143557	−	0.0248647i
$89$	−8.95299	−	5.16901i	−0.949015	−	0.547914i	−0.0562399	−	0.998417i	$-0.517911\pi$
$89$	−8.95299	−	5.16901i	−0.949015	−	0.547914i	−0.892775	+	0.450503i	$0.851245\pi$
$90$		0			0
$91$	−6.51606	+	6.96714i	−0.683069	+	0.730354i
$92$	−13.1769			−1.37379
$93$		0			0
$94$	−5.52719	−	9.57338i	−0.570086	−	0.987419i
$95$	−0.569295	−	0.986048i	−0.0584085	−	0.101166i
$96$		0			0
$97$			4.78983i			0.486334i	0.969984	+	0.243167i	$0.0781863\pi$
$97$			4.78983i			0.486334i	−0.969984	+	0.243167i	$0.921814\pi$
$98$	5.67020	+	12.4548i	0.572777	+	1.25813i
$99$		0			0
$100$	4.53406	−	7.85322i	0.453406	−	0.785322i
$101$	8.35948	+	14.4790i	0.831800	+	1.44072i	0.896610	+	0.442821i	$0.146022\pi$
$101$	8.35948	+	14.4790i	0.831800	+	1.44072i	−0.0648103	+	0.997898i	$0.520644\pi$
$102$		0			0
$103$	2.73248	−	4.73280i	0.269239	−	0.466336i	−0.699426	−	0.714705i	$-0.746561\pi$
$103$	2.73248	−	4.73280i	0.269239	−	0.466336i	0.968666	+	0.248369i	$0.0798944\pi$
$104$	−0.536937	+	1.13472i	−0.0526510	+	0.111269i
$105$		0			0
$106$			18.1861i			1.76639i
$107$	3.74774	−	6.49127i	0.362307	−	0.627535i	−0.626033	−	0.779797i	$-0.715322\pi$
$107$	3.74774	−	6.49127i	0.362307	−	0.627535i	0.988340	+	0.152262i	$0.0486557\pi$
$108$		0			0
$109$	3.77312	−	2.17841i	0.361399	−	0.208654i	−0.308295	−	0.951291i	$-0.599758\pi$
$109$	3.77312	−	2.17841i	0.361399	−	0.208654i	0.669694	+	0.742637i	$0.266425\pi$
$110$	0.197437	+	0.113991i	0.0188249	+	0.0108686i
$111$		0			0
$112$	7.69124	+	8.47067i	0.726754	+	0.800403i
$113$	−8.82854			−0.830520			−0.415260	−	0.909703i	$-0.636309\pi$
$113$	−8.82854			−0.830520			−0.415260	+	0.909703i	$0.636309\pi$
$114$		0			0
$115$	−0.944225	+	0.545148i	−0.0880494	+	0.0508354i
$116$	−1.53169	−	2.65296i	−0.142214	−	0.246321i
$117$		0			0
$118$	15.9683			1.47000
$119$	2.38624	−	0.517623i	0.218746	−	0.0474504i
$120$		0			0
$121$	−5.20079	+	9.00804i	−0.472799	+	0.818912i
$122$	19.9866	−	11.5393i	1.80950	−	1.04472i
$123$		0			0
$124$	−0.970691	−	0.560428i	−0.0871706	−	0.0503280i
$125$		−	1.50407i		−	0.134529i
$126$		0			0
$127$	−11.4035			−1.01190			−0.505948	−	0.862564i	$-0.668857\pi$
$127$	−11.4035			−1.01190			−0.505948	+	0.862564i	$0.668857\pi$
$128$	2.40264	+	1.38716i	0.212365	+	0.122609i
$129$		0			0
$130$	−0.0866447	−	1.05906i	−0.00759924	−	0.0928857i
$131$	2.98864	−	5.17647i	0.261118	−	0.452270i	−0.705421	−	0.708789i	$-0.749242\pi$
$131$	2.98864	−	5.17647i	0.261118	−	0.452270i	0.966539	+	0.256518i	$0.0825753\pi$
$132$		0			0
$133$	14.7943	−	13.4330i	1.28283	−	1.16479i
$134$	−10.3155			−0.891122
$135$		0			0
$136$	0.278274	−	0.160662i	0.0238618	−	0.0137766i
$137$	11.5074	−	6.64379i	0.983142	−	0.567618i	0.0799250	−	0.996801i	$-0.474532\pi$
$137$	11.5074	−	6.64379i	0.983142	−	0.567618i	0.903217	+	0.429183i	$0.141199\pi$
$138$		0			0
$139$	−14.0454			−1.19131			−0.595657	−	0.803239i	$-0.703108\pi$
$139$	−14.0454			−1.19131			−0.595657	+	0.803239i	$0.703108\pi$
$140$	−0.692027	−	0.221666i	−0.0584869	−	0.0187342i
$141$		0			0
$142$	9.51133	−	16.4741i	0.798173	−	1.38248i
$143$	−2.77987	+	0.227429i	−0.232464	+	0.0190186i
$144$		0			0
$145$	−0.219514	−	0.126737i	−0.0182297	−	0.0105249i
$146$	9.46571			0.783388
$147$		0			0
$148$		−	6.50307i		−	0.534549i
$149$	−9.79389	−	5.65451i	−0.802347	−	0.463235i	0.0419442	−	0.999120i	$-0.486645\pi$
$149$	−9.79389	−	5.65451i	−0.802347	−	0.463235i	−0.844291	+	0.535885i	$0.819978\pi$
$150$		0			0
$151$	−0.693185	+	0.400211i	−0.0564106	+	0.0325687i	−0.527940	−	0.849282i	$-0.677035\pi$
$151$	−0.693185	+	0.400211i	−0.0564106	+	0.0325687i	0.471529	+	0.881850i	$0.343702\pi$
$152$	1.31484	−	2.27737i	0.106648	−	0.184719i
$153$		0			0
$154$	−1.22056	+	3.81049i	−0.0983552	+	0.307058i
$155$	−0.0927432			−0.00744931
$156$		0			0
$157$	−0.0964880	−	0.167122i	−0.00770058	−	0.0133378i	0.862149	−	0.506654i	$-0.169118\pi$
$157$	−0.0964880	−	0.167122i	−0.00770058	−	0.0133378i	−0.869850	+	0.493316i	$0.835785\pi$
$158$	23.1236	−	13.3504i	1.83962	−	1.06210i
$159$		0			0
$160$	−1.16950			−0.0924570
$161$	−12.8632	−	14.1668i	−1.01377	−	1.11650i
$162$		0			0
$163$	−13.3834	−	7.72692i	−1.04827	−	0.605219i	−0.126106	−	0.992017i	$-0.540248\pi$
$163$	−13.3834	−	7.72692i	−1.04827	−	0.605219i	−0.922165	+	0.386798i	$0.873581\pi$
$164$	16.7098	−	9.64743i	1.30482	−	0.753338i
$165$		0			0
$166$	−3.49513	+	6.05374i	−0.271275	+	0.469861i
$167$			4.18223i			0.323631i	0.986821	+	0.161815i	$0.0517349\pi$
$167$			4.18223i			0.323631i	−0.986821	+	0.161815i	$0.948265\pi$
$168$		0			0
$169$	8.24347	+	10.0521i	0.634113	+	0.773240i
$170$	−0.135993	+	0.235547i	−0.0104302	+	0.0180656i
$171$		0			0
$172$	−0.791165	−	1.37034i	−0.0603258	−	0.104487i
$173$	−10.8135	+	18.7295i	−0.822134	+	1.42398i	0.0819559	+	0.996636i	$0.473883\pi$
$173$	−10.8135	+	18.7295i	−0.822134	+	1.42398i	−0.904090	+	0.427342i	$0.859450\pi$
$174$		0			0
$175$	12.8693	−	2.79162i	0.972830	−	0.211026i
$176$			3.34530i			0.252161i
$177$		0			0
$178$	10.1053	+	17.5028i	0.757421	+	1.31189i
$179$	−9.29373	−	16.0972i	−0.694646	−	1.20316i	−0.970300	−	0.241906i	$-0.922228\pi$
$179$	−9.29373	−	16.0972i	−0.694646	−	1.20316i	0.275654	−	0.961257i	$-0.411106\pi$
$180$		0			0
$181$	−2.54992			−0.189534			−0.0947670	−	0.995499i	$-0.530211\pi$
$181$	−2.54992			−0.189534			−0.0947670	+	0.995499i	$0.530211\pi$
$182$	17.8423	−	5.42638i	1.32256	−	0.402230i
$183$		0			0
$184$	−2.18077	−	1.25907i	−0.160769	−	0.0928199i
$185$	−0.269042	−	0.465994i	−0.0197804	−	0.0342606i
$186$		0			0
$187$	0.618275	+	0.356961i	0.0452127	+	0.0261036i
$188$			10.3020i			0.751348i
$189$		0			0
$190$			2.22591i			0.161484i
$191$	0.995504	−	1.72426i	0.0720321	−	0.124763i	−0.827760	−	0.561083i	$-0.810385\pi$
$191$	0.995504	−	1.72426i	0.0720321	−	0.124763i	0.899792	+	0.436320i	$0.143718\pi$
$192$		0			0
$193$	15.1267	−	8.73340i	1.08884	−	0.628644i	0.155575	−	0.987824i	$-0.450277\pi$
$193$	15.1267	−	8.73340i	1.08884	−	0.628644i	0.933268	+	0.359180i	$0.116944\pi$
$194$	4.68199	−	8.10944i	0.336147	−	0.582224i
$195$		0			0
$196$	1.22723	−	12.6941i	0.0876595	−	0.906725i
$197$		−	13.5807i		−	0.967585i	−0.875183	−	0.483793i	$-0.839259\pi$
$197$		−	13.5807i		−	0.967585i	0.875183	−	0.483793i	$-0.160741\pi$
$198$		0			0
$199$	0.751660	+	1.30191i	0.0532838	+	0.0922902i	0.891437	−	0.453145i	$-0.149698\pi$
$199$	0.751660	+	1.30191i	0.0532838	+	0.0922902i	−0.838153	+	0.545435i	$0.816365\pi$
$200$	1.50077	−	0.866472i	0.106121	−	0.0612688i
$201$		0			0
$202$		−	32.6851i		−	2.29971i
$203$	1.35704	−	4.23657i	0.0952452	−	0.297349i
$204$		0			0
$205$	0.798259	−	1.38262i	0.0557528	−	0.0965667i
$206$	−9.25247	+	5.34192i	−0.644650	+	0.372189i
$207$		0			0
$208$	12.8225	−	8.87115i	0.889081	−	0.615103i
$209$	5.84267			0.404146
$210$		0			0
$211$	24.0919			1.65856			0.829279	−	0.558835i	$-0.188752\pi$
$211$	24.0919			1.65856			0.829279	+	0.558835i	$0.188752\pi$
$212$	8.47413	−	14.6776i	0.582006	−	1.00806i
$213$		0			0
$214$	−12.6902	+	7.32671i	−0.867487	+	0.500844i
$215$	−0.113386	−	0.0654634i	−0.00773286	−	0.00446457i
$216$		0			0
$217$	−0.345055	−	1.59070i	−0.0234239	−	0.107984i
$218$	−8.51745			−0.576874
$219$		0			0
$220$	−0.106232	−	0.183999i	−0.00716215	−	0.0124052i
$221$	−0.271327	−	3.31644i	−0.0182515	−	0.223088i
$222$		0			0
$223$		−	11.1398i		−	0.745976i	−0.927836	−	0.372988i	$-0.878333\pi$
$223$		−	11.1398i		−	0.745976i	0.927836	−	0.372988i	$-0.121667\pi$
$224$	−4.35117	−	20.0589i	−0.290725	−	1.34024i
$225$		0			0
$226$	14.9472	+	8.62977i	0.994272	+	0.574043i
$227$	−2.21721	+	1.28011i	−0.147161	+	0.0849636i	−0.571773	−	0.820412i	$-0.693744\pi$
$227$	−2.21721	+	1.28011i	−0.147161	+	0.0849636i	0.424611	+	0.905376i	$0.360411\pi$
$228$		0			0
$229$	−2.08405	−	1.20323i	−0.137718	−	0.0795114i	0.429558	−	0.903039i	$-0.358669\pi$
$229$	−2.08405	−	1.20323i	−0.137718	−	0.0795114i	−0.567276	+	0.823528i	$0.692003\pi$
$230$	2.13150			0.140547
$231$		0			0
$232$		−	0.585420i		−	0.0384347i
$233$	9.28924	−	16.0894i	0.608558	−	1.05405i	−0.382920	−	0.923781i	$-0.625082\pi$
$233$	9.28924	−	16.0894i	0.608558	−	1.05405i	0.991478	−	0.130272i	$-0.0415851\pi$
$234$		0			0
$235$	0.426209	+	0.738215i	0.0278028	+	0.0481558i
$236$	−12.8877	−	7.44070i	−0.838916	−	0.484348i
$237$		0			0
$238$	−4.54600	−	1.45615i	−0.294673	−	0.0943881i
$239$			18.5657i			1.20092i	0.799656	+	0.600458i	$0.205015\pi$
$239$			18.5657i			1.20092i	−0.799656	+	0.600458i	$0.794985\pi$
$240$		0			0
$241$	22.1422	−	12.7838i	1.42630	−	0.823477i	0.429477	−	0.903078i	$-0.358698\pi$
$241$	22.1422	−	12.7838i	1.42630	−	0.823477i	0.996827	+	0.0796012i	$0.0253647\pi$
$242$	17.6104	−	10.1674i	1.13204	−	0.653584i
$243$		0			0
$244$	−21.5077			−1.37689
$245$	−0.437236	−	0.960405i	−0.0279340	−	0.0613580i
$246$		0			0
$247$	−15.4938	−	22.3949i	−0.985844	−	1.42496i
$248$	−0.107099	−	0.185502i	−0.00680082	−	0.0117794i
$249$		0			0
$250$	−1.47021	+	2.54648i	−0.0929842	+	0.161053i
$251$	−1.34056			−0.0846153			−0.0423077	−	0.999105i	$-0.513471\pi$
$251$	−1.34056			−0.0846153			−0.0423077	+	0.999105i	$0.513471\pi$
$252$		0			0
$253$		−	5.59486i		−	0.351746i
$254$	19.3067	+	11.1467i	1.21141	+	0.699408i
$255$		0			0
$256$	−9.22931	−	15.9856i	−0.576832	−	0.999102i
$257$	−10.0147	+	17.3459i	−0.624697	+	1.08201i	0.363902	+	0.931437i	$0.381444\pi$
$257$	−10.0147	+	17.3459i	−0.624697	+	1.08201i	−0.988599	+	0.150570i	$0.951889\pi$
$258$		0			0
$259$	6.99161	−	6.34828i	0.434438	−	0.394463i
$260$	−0.423558	+	0.895119i	−0.0262680	+	0.0555129i
$261$		0			0
$262$	−10.1198	+	5.84269i	−0.625206	+	0.360963i
$263$	10.8649	+	18.8186i	0.669960	+	1.16040i	0.977915	+	0.209004i	$0.0670222\pi$
$263$	10.8649	+	18.8186i	0.669960	+	1.16040i	−0.307955	+	0.951401i	$0.599645\pi$
$264$		0			0
$265$		−	1.40235i		−	0.0861458i
$266$	−38.1781	+	8.28159i	−2.34085	+	0.507777i
$267$		0			0
$268$	8.32541	+	4.80668i	0.508556	+	0.293615i
$269$	−0.783952	−	1.35784i	−0.0477984	−	0.0827892i	0.841136	−	0.540823i	$-0.181887\pi$
$269$	−0.783952	−	1.35784i	−0.0477984	−	0.0827892i	−0.888935	+	0.458034i	$0.848554\pi$
$270$		0			0
$271$	−3.15341	−	1.82062i	−0.191556	−	0.110595i	0.401155	−	0.916010i	$-0.368609\pi$
$271$	−3.15341	−	1.82062i	−0.191556	−	0.110595i	−0.592711	+	0.805415i	$0.701942\pi$
$272$	−3.99101			−0.241990
$273$		0			0
$274$	−25.9768			−1.56932
$275$	3.33445	+	1.92514i	0.201075	+	0.116091i
$276$		0			0
$277$	−4.03856	−	6.99498i	−0.242653	−	0.420288i	0.718816	−	0.695200i	$-0.244684\pi$
$277$	−4.03856	−	6.99498i	−0.242653	−	0.420288i	−0.961469	+	0.274913i	$0.911351\pi$
$278$	23.7796	+	13.7292i	1.42621	+	0.823420i
$279$		0			0
$280$	−0.0933498	−	0.102810i	−0.00557872	−	0.00614407i
$281$			0.685719i			0.0409065i	0.999791	+	0.0204533i	$0.00651093\pi$
$281$			0.685719i			0.0409065i	−0.999791	+	0.0204533i	$0.993489\pi$
$282$		0			0
$283$	7.69275	+	13.3242i	0.457286	+	0.792043i	0.998816	−	0.0486380i	$-0.0154881\pi$
$283$	7.69275	+	13.3242i	0.457286	+	0.792043i	−0.541530	+	0.840681i	$0.682155\pi$
$284$	−15.3528	+	8.86395i	−0.911021	+	0.525978i
$285$		0			0
$286$	4.92878	+	2.33223i	0.291445	+	0.137908i
$287$	26.6843	+	8.54737i	1.57512	+	0.504535i
$288$		0			0
$289$	8.07414	−	13.9848i	0.474949	−	0.822636i
$290$	0.247766	+	0.429144i	0.0145493	+	0.0252002i
$291$		0			0
$292$	−7.63958	−	4.41072i	−0.447073	−	0.258118i
$293$			12.1224i			0.708199i	0.935208	+	0.354099i	$0.115213\pi$
$293$			12.1224i			0.708199i	−0.935208	+	0.354099i	$0.884787\pi$
$294$		0			0
$295$	−1.23133			−0.0716910
$296$	0.621377	−	1.07626i	0.0361168	−	0.0625562i
$297$		0			0
$298$	11.0544	+	19.1468i	0.640363	+	1.10914i
$299$	−21.4450	+	14.8366i	−1.24020	+	0.858022i
$300$		0			0
$301$	0.700951	−	2.18832i	0.0404022	−	0.126133i
$302$	1.56480			0.0900441
$303$		0			0
$304$	−28.2862	+	16.3310i	−1.62232	+	0.936648i
$305$	−1.54119	+	0.889807i	−0.0882484	+	0.0509502i
$306$		0			0
$307$			19.3806i			1.10611i	0.833145	+	0.553054i	$0.186538\pi$
$307$			19.3806i			1.10611i	−0.833145	+	0.553054i	$0.813462\pi$
$308$	2.76065	−	2.50663i	0.157303	−	0.142829i
$309$		0			0
$310$	0.157019	+	0.0906550i	0.00891809	+	0.00514886i
$311$	5.03074	+	8.71350i	0.285267	+	0.494097i	0.972674	−	0.232176i	$-0.0745844\pi$
$311$	5.03074	+	8.71350i	0.285267	+	0.494097i	−0.687407	+	0.726273i	$0.741251\pi$
$312$		0			0
$313$	9.30155	−	16.1108i	0.525755	−	0.910634i	−0.473795	−	0.880635i	$-0.657116\pi$
$313$	9.30155	−	16.1108i	0.525755	−	0.910634i	0.999550	−	0.0299988i	$-0.00955033\pi$
$314$			0.377262i			0.0212901i
$315$		0			0
$316$	−24.8835			−1.39980
$317$	−2.96604	−	1.71244i	−0.166589	−	0.0961804i	0.414387	−	0.910101i	$-0.363996\pi$
$317$	−2.96604	−	1.71244i	−0.166589	−	0.0961804i	−0.580977	+	0.813920i	$0.697329\pi$
$318$		0			0
$319$	1.12644	−	0.650349i	0.0630684	−	0.0364126i
$320$	0.850875	+	0.491253i	0.0475654	+	0.0274619i
$321$		0			0
$322$	7.93033	+	36.5588i	0.441940	+	2.03734i
$323$			6.97043i			0.387845i
$324$		0			0
$325$	−1.46331	−	17.8861i	−0.0811698	−	0.992140i
$326$	15.1059	+	26.1642i	0.836638	+	1.44910i
$327$		0			0
$328$	3.68730			0.203597
$329$	−11.0759	+	10.0568i	−0.610634	+	0.554447i
$330$		0			0
$331$	−15.3310	−	8.85135i	−0.842667	−	0.486514i	0.0155026	−	0.999880i	$-0.495065\pi$
$331$	−15.3310	−	8.85135i	−0.842667	−	0.486514i	−0.858170	+	0.513366i	$0.828398\pi$
$332$	5.64169	−	3.25723i	0.309628	−	0.178764i
$333$		0			0
$334$	4.08807	−	7.08074i	0.223689	−	0.387441i
$335$	0.795439			0.0434595
$336$		0			0
$337$	−19.9495			−1.08672			−0.543361	−	0.839499i	$-0.682848\pi$
$337$	−19.9495			−1.08672			−0.543361	+	0.839499i	$0.682848\pi$
$338$	−4.13083	−	25.0766i	−0.224688	−	1.36399i
$339$		0			0
$340$	0.219514	−	0.126737i	0.0119048	−	0.00687326i
$341$	0.237956	−	0.412151i	0.0128860	−	0.0223192i
$342$		0			0
$343$	14.8458	−	11.0726i	0.801599	−	0.597862i
$344$		−	0.302388i		−	0.0163037i
$345$		0			0
$346$	36.6156	−	21.1400i	1.96847	−	1.13650i
$347$	1.59686	+	2.76585i	0.0857241	+	0.148479i	0.905700	−	0.423920i	$-0.139346\pi$
$347$	1.59686	+	2.76585i	0.0857241	+	0.148479i	−0.819975	+	0.572399i	$0.806013\pi$
$348$		0			0
$349$			21.4556i			1.14849i	0.818682	+	0.574247i	$0.194705\pi$
$349$			21.4556i			1.14849i	−0.818682	+	0.574247i	$0.805295\pi$
$350$	−24.5172	−	7.85322i	−1.31050	−	0.419772i
$351$		0			0
$352$	3.00064	−	5.19726i	0.159935	−	0.277015i
$353$	−23.3191	+	13.4633i	−1.24115	+	0.716579i	−0.969329	−	0.245769i	$-0.920960\pi$
$353$	−23.3191	+	13.4633i	−1.24115	+	0.716579i	−0.271822	+	0.962347i	$0.587626\pi$
$354$		0			0
$355$	−0.733431	+	1.27034i	−0.0389265	+	0.0674226i
$356$		−	18.8349i		−	0.998247i
$357$		0			0
$358$			36.3379i			1.92052i
$359$	−2.64852	−	1.52912i	−0.139783	−	0.0807040i	0.428477	−	0.903553i	$-0.359050\pi$
$359$	−2.64852	−	1.52912i	−0.139783	−	0.0807040i	−0.568261	+	0.822849i	$0.692384\pi$
$360$		0			0
$361$	19.0227	+	32.9482i	1.00119	+	1.73412i
$362$	4.31715	+	2.49251i	0.226904	+	0.131003i
$363$		0			0
$364$	−16.9287	−	3.93441i	−0.887304	−	0.206219i
$365$	−0.729913			−0.0382054
$366$		0			0
$367$	11.2300	+	19.4509i	0.586200	+	1.01533i	0.994725	+	0.102581i	$0.0327101\pi$
$367$	11.2300	+	19.4509i	0.586200	+	1.01533i	−0.408524	+	0.912747i	$0.633957\pi$
$368$	15.6383	+	27.0864i	0.815205	+	1.41198i
$369$		0			0
$370$			1.05194i			0.0546876i
$371$	24.0527	−	5.21751i	1.24875	−	0.270880i
$372$		0			0
$373$	−16.2812	+	28.1999i	−0.843008	+	1.46013i	0.0443314	+	0.999017i	$0.485884\pi$
$373$	−16.2812	+	28.1999i	−0.843008	+	1.46013i	−0.887340	+	0.461116i	$0.847449\pi$
$374$	−0.697848	−	1.20871i	−0.0360849	−	0.0625008i
$375$		0			0
$376$	−0.984368	+	1.70498i	−0.0507649	+	0.0879274i
$377$	−5.47990	−	2.59302i	−0.282229	−	0.133547i
$378$		0			0
$379$			30.6652i			1.57516i	0.616209	+	0.787582i	$0.288667\pi$
$379$			30.6652i			1.57516i	−0.616209	+	0.787582i	$0.711333\pi$
$380$	1.03720	−	1.79649i	0.0532073	−	0.0921578i
$381$		0			0
$382$	−3.37088	+	1.94618i	−0.172469	+	0.0995752i
$383$	23.6125	+	13.6327i	1.20654	+	0.696598i	0.962002	−	0.273041i	$-0.0880296\pi$
$383$	23.6125	+	13.6327i	1.20654	+	0.696598i	0.244541	+	0.969639i	$0.421363\pi$
$384$		0			0
$385$	0.0941186	−	0.293832i	0.00479673	−	0.0149751i
$386$	−34.1471			−1.73804
$387$		0			0
$388$	−7.55747	+	4.36331i	−0.383673	+	0.221514i
$389$	−15.2847	−	26.4739i	−0.774967	−	1.34228i	−0.934813	−	0.355140i	$-0.884433\pi$
$389$	−15.2847	−	26.4739i	−0.774967	−	1.34228i	0.159846	−	0.987142i	$-0.448900\pi$
$390$		0			0
$391$	6.67478			0.337558
$392$	1.41605	−	1.98362i	0.0715214	−	0.100188i
$393$		0			0
$394$	−13.2749	+	22.9929i	−0.668781	+	1.15836i
$395$	−1.78309	+	1.02947i	−0.0897170	+	0.0517981i
$396$		0			0
$397$	19.3546	+	11.1744i	0.971378	+	0.560826i	0.899656	−	0.436599i	$-0.143817\pi$
$397$	19.3546	+	11.1744i	0.971378	+	0.560826i	0.0717222	+	0.997425i	$0.477150\pi$
$398$		−	2.93894i		−	0.147316i
$399$		0			0
$400$	−21.5241			−1.07620
$401$	−24.6356	−	14.2234i	−1.23024	−	0.710282i	−0.263164	−	0.964751i	$-0.584766\pi$
$401$	−24.6356	−	14.2234i	−1.23024	−	0.710282i	−0.967081	+	0.254469i	$0.918099\pi$
$402$		0			0
$403$	−2.21079	+	0.180871i	−0.110127	+	0.00900983i
$404$	−15.2302	+	26.3794i	−0.757730	+	1.31243i
$405$		0			0
$406$	−6.43872	+	5.84626i	−0.319548	+	0.290145i
$407$	2.76118			0.136866
$408$		0			0
$409$	−13.0772	+	7.55015i	−0.646628	+	0.373331i	−0.787163	−	0.616745i	$-0.788451\pi$
$409$	−13.0772	+	7.55015i	−0.646628	+	0.373331i	0.140535	+	0.990076i	$0.455118\pi$
$410$	−2.70299	+	1.56057i	−0.133491	+	0.0770711i
$411$		0			0
$412$	9.95664			0.490528
$413$	−4.58123	−	21.1195i	−0.225428	−	1.03922i
$414$		0			0
$415$	0.269514	−	0.466811i	0.0132299	−	0.0229149i
$416$	−27.8783	+	2.28080i	−1.36684	+	0.111825i
$417$		0			0
$418$	−9.89196	−	5.71112i	−0.483831	−	0.279340i
$419$	8.52484			0.416466			0.208233	−	0.978079i	$-0.433229\pi$
$419$	8.52484			0.416466			0.208233	+	0.978079i	$0.433229\pi$
$420$		0			0
$421$		−	35.9003i		−	1.74967i	−0.484417	−	0.874837i	$-0.660968\pi$
$421$		−	35.9003i		−	1.74967i	0.484417	−	0.874837i	$-0.339032\pi$
$422$	−40.7889	−	23.5495i	−1.98557	−	1.14637i
$423$		0			0
$424$	2.80494	−	1.61943i	0.136220	−	0.0786465i
$425$	−2.29674	+	3.97806i	−0.111408	+	0.192964i
$426$		0			0
$427$	−20.9958	−	23.1235i	−1.01606	−	1.11902i
$428$	13.6560			0.660090
$429$		0			0
$430$	0.127979	+	0.221666i	0.00617170	+	0.0106897i
$431$	−34.9245	+	20.1637i	−1.68225	+	0.971250i	−0.722096	+	0.691793i	$0.756821\pi$
$431$	−34.9245	+	20.1637i	−1.68225	+	0.971250i	−0.960158	+	0.279456i	$0.909846\pi$
$432$		0			0
$433$	7.65839			0.368039			0.184019	−	0.982923i	$-0.441089\pi$
$433$	7.65839			0.368039			0.184019	+	0.982923i	$0.441089\pi$
$434$	−0.970691	+	3.03043i	−0.0465946	+	0.145465i
$435$		0			0
$436$	6.87426	+	3.96886i	0.329217	+	0.190074i
$437$	47.3073	−	27.3129i	2.26301	−	1.30655i
$438$		0			0
$439$	−9.44132	+	16.3528i	−0.450609	+	0.780478i	−0.998424	−	0.0561214i	$-0.982127\pi$
$439$	−9.44132	+	16.3528i	−0.450609	+	0.780478i	0.547815	+	0.836600i	$0.315460\pi$
$440$		−	0.0406024i		−	0.00193564i
$441$		0			0
$442$	−2.78240	+	5.88013i	−0.132345	+	0.279689i
$443$	7.89924	−	13.6819i	0.375304	−	0.650046i	−0.615068	−	0.788474i	$-0.710872\pi$
$443$	7.89924	−	13.6819i	0.375304	−	0.650046i	0.990373	+	0.138428i	$0.0442049\pi$
$444$		0			0
$445$	−0.779228	−	1.34966i	−0.0369390	−	0.0639802i
$446$	−10.8890	+	18.8603i	−0.515608	+	0.893059i
$447$		0			0
$448$	−5.26010	+	16.4217i	−0.248516	+	0.775851i
$449$		−	23.5766i		−	1.11265i	−0.830966	−	0.556324i	$-0.812211\pi$
$449$		−	23.5766i		−	1.11265i	0.830966	−	0.556324i	$-0.187789\pi$
$450$		0			0
$451$	4.09626	+	7.09493i	0.192885	+	0.334087i
$452$	−8.04238	−	13.9298i	−0.378282	−	0.655203i
$453$		0			0
$454$	5.00514			0.234903
$455$	−1.37584	+	0.418435i	−0.0645004	+	0.0196165i
$456$		0			0
$457$	22.1748	+	12.8026i	1.03730	+	0.598883i	0.919066	−	0.394104i	$-0.128945\pi$
$457$	22.1748	+	12.8026i	1.03730	+	0.598883i	0.118229	+	0.992986i	$0.462278\pi$
$458$	2.35227	+	4.07425i	0.109914	+	0.190377i
$459$		0			0
$460$	−1.72029	−	0.993208i	−0.0802088	−	0.0463086i
$461$		−	9.31900i		−	0.434029i	−0.976168	−	0.217014i	$-0.930368\pi$
$461$		−	9.31900i		−	0.434029i	0.976168	−	0.217014i	$-0.0696319\pi$
$462$		0			0
$463$		−	22.9646i		−	1.06726i	−0.845719	−	0.533628i	$-0.820828\pi$
$463$		−	22.9646i		−	1.06726i	0.845719	−	0.533628i	$-0.179172\pi$
$464$	−3.63562	+	6.29707i	−0.168779	+	0.292334i
$465$		0			0
$466$	−31.4543	+	18.1602i	−1.45709	+	0.841254i
$467$	9.64755	−	16.7101i	0.446436	−	0.773249i	−0.551715	−	0.834032i	$-0.686027\pi$
$467$	9.64755	−	16.7101i	0.446436	−	0.773249i	0.998151	+	0.0607834i	$0.0193599\pi$
$468$		0			0
$469$	2.95947	+	13.6431i	0.136655	+	0.629981i
$470$		−	1.66645i		−	0.0768676i
$471$		0			0
$472$	−1.42194	−	2.46287i	−0.0654501	−	0.113363i
$473$	0.581840	−	0.335925i	0.0267530	−	0.0154459i
$474$		0			0
$475$			37.5925i			1.72486i
$476$	2.99046	+	3.29351i	0.137068	+	0.150958i
$477$		0			0
$478$	18.1477	−	31.4327i	0.830057	−	1.43770i
$479$	−14.6709	+	8.47023i	−0.670329	+	0.387014i	−0.796201	−	0.605032i	$-0.793160\pi$
$479$	−14.6709	+	8.47023i	−0.670329	+	0.387014i	0.125872	+	0.992046i	$0.459827\pi$
$480$		0			0
$481$	−7.32216	−	10.5836i	−0.333862	−	0.482569i
$482$	−49.9839			−2.27670
$483$		0			0
$484$	−18.9507			−0.861395
$485$	−0.361034	+	0.625329i	−0.0163937	+	0.0283947i
$486$		0			0
$487$	−11.7638	+	6.79182i	−0.533068	+	0.307767i	−0.742265	−	0.670107i	$-0.766248\pi$
$487$	−11.7638	+	6.79182i	−0.533068	+	0.307767i	0.209197	+	0.977874i	$0.432915\pi$
$488$	−3.55952	−	2.05509i	−0.161132	−	0.0930296i
$489$		0			0
$490$	−0.198518	+	2.05341i	−0.00896811	+	0.0927635i
$491$	7.89307			0.356209			0.178105	−	0.984012i	$-0.443003\pi$
$491$	7.89307			0.356209			0.178105	+	0.984012i	$0.443003\pi$
$492$		0			0
$493$	0.775880	+	1.34386i	0.0349439	+	0.0605245i
$494$	4.34105	+	53.0607i	0.195313	+	2.38731i
$495$		0			0
$496$			2.66047i			0.119458i
$497$	−24.5172	−	7.85322i	−1.09975	−	0.352265i
$498$		0			0
$499$	29.5229	+	17.0450i	1.32162	+	0.763041i	0.983988	−	0.178236i	$-0.0570390\pi$
$499$	29.5229	+	17.0450i	1.32162	+	0.763041i	0.337637	+	0.941276i	$0.390372\pi$
$500$	2.37315	−	1.37014i	0.106131	−	0.0612745i
$501$		0			0
$502$	2.26964	+	1.31038i	0.101299	+	0.0584849i
$503$	30.0070			1.33795			0.668974	−	0.743286i	$-0.266734\pi$
$503$	30.0070			1.33795			0.668974	+	0.743286i	$0.266734\pi$
$504$		0			0
$505$			2.52038i			0.112156i
$506$	−5.46888	+	9.47239i	−0.243122	+	0.421099i
$507$		0			0
$508$	−10.3880	−	17.9926i	−0.460894	−	0.798292i
$509$	17.7454	+	10.2453i	0.786550	+	0.454115i	0.838747	−	0.544522i	$-0.183289\pi$
$509$	17.7454	+	10.2453i	0.786550	+	0.454115i	−0.0521966	+	0.998637i	$0.516622\pi$
$510$		0			0
$511$	−2.71567	−	12.5192i	−0.120134	−	0.553818i
$512$			30.5374i			1.34957i
$513$		0			0
$514$	33.9107	−	19.5783i	1.49574	−	0.863564i
$515$	0.713469	−	0.411922i	0.0314392	−	0.0181514i
$516$		0			0
$517$	−4.37418			−0.192376
$518$	−18.0425	+	3.91378i	−0.792742	+	0.171962i
$519$		0			0
$520$	−0.155629	+	0.107671i	−0.00682477	+	0.00472167i
$521$	20.6778	+	35.8151i	0.905913	+	1.56909i	0.819688	+	0.572811i	$0.194147\pi$
$521$	20.6778	+	35.8151i	0.905913	+	1.56909i	0.0862251	+	0.996276i	$0.472520\pi$
$522$		0			0
$523$	6.73305	−	11.6620i	0.294416	−	0.509943i	−0.680433	−	0.732810i	$-0.738208\pi$
$523$	6.73305	−	11.6620i	0.294416	−	0.509943i	0.974849	+	0.222867i	$0.0715416\pi$
$524$	10.8900			0.475733
$525$		0			0
$526$		−	42.4812i		−	1.85227i
$527$	0.491705	+	0.283886i	0.0214190	+	0.0123663i
$528$		0			0
$529$	−14.6544	−	25.3822i	−0.637147	−	1.10357i
$530$	−1.37078	+	2.37426i	−0.0595428	+	0.103131i
$531$		0			0
$532$	34.6717	+	11.1059i	1.50321	+	0.481500i
$533$	16.3323	−	34.5155i	0.707429	−	1.49503i
$534$		0			0
$535$	0.978560	−	0.564972i	0.0423068	−	0.0244259i
$536$	0.918570	+	1.59101i	0.0396762	+	0.0687212i
$537$		0			0
$538$			3.06520i			0.132150i
$539$	5.38988	+	0.521078i	0.232159	+	0.0224444i
$540$		0			0
$541$	−24.8152	−	14.3271i	−1.06689	−	0.615969i	−0.139560	−	0.990214i	$-0.544569\pi$
$541$	−24.8152	−	14.3271i	−1.06689	−	0.615969i	−0.927330	+	0.374244i	$0.877902\pi$
$542$	3.55926	+	6.16481i	0.152883	+	0.264801i
$543$		0			0
$544$	6.20044	+	3.57983i	0.265842	+	0.153484i
$545$	0.656791			0.0281338
$546$		0			0
$547$	14.1081			0.603218			0.301609	−	0.953432i	$-0.402476\pi$
$547$	14.1081			0.603218			0.301609	+	0.953432i	$0.402476\pi$
$548$	20.9654	+	12.1044i	0.895596	+	0.517072i
$549$		0			0
$550$	−3.76360	−	6.51874i	−0.160480	−	0.277960i
$551$	10.9980	+	6.34973i	0.468533	+	0.270507i
$552$		0			0
$553$	−24.2912	−	26.7528i	−1.03297	−	1.13765i
$554$			15.7905i			0.670874i
$555$		0			0
$556$	−12.7947	−	22.1610i	−0.542615	−	0.939837i
$557$	−1.09997	+	0.635069i	−0.0466073	+	0.0269087i	−0.523123	−	0.852257i	$-0.675233\pi$
$557$	−1.09997	+	0.635069i	−0.0466073	+	0.0269087i	0.476515	+	0.879166i	$0.341900\pi$
$558$		0			0
$559$	−2.83054	−	1.33937i	−0.119719	−	0.0566494i
$560$	0.365641	+	1.68560i	0.0154511	+	0.0712297i
$561$		0			0
$562$	0.670279	−	1.16096i	0.0282740	−	0.0489721i
$563$	−11.7278	−	20.3131i	−0.494267	−	0.856096i	0.505711	−	0.862703i	$-0.331230\pi$
$563$	−11.7278	−	20.3131i	−0.494267	−	0.856096i	−0.999978	+	0.00660697i	$0.997897\pi$
$564$		0			0
$565$	−1.15260	−	0.665452i	−0.0484901	−	0.0279958i
$566$		−	30.0782i		−	1.26428i
$567$		0			0
$568$	−3.38785			−0.142151
$569$	−0.0264704	+	0.0458481i	−0.00110970	+	0.00192205i	−0.866580	−	0.499039i	$-0.833687\pi$
$569$	−0.0264704	+	0.0458481i	−0.00110970	+	0.00192205i	0.865470	+	0.500961i	$0.167020\pi$
$570$		0			0
$571$	2.43580	+	4.21894i	0.101935	+	0.176557i	0.912482	−	0.409117i	$-0.134163\pi$
$571$	2.43580	+	4.21894i	0.101935	+	0.176557i	−0.810547	+	0.585674i	$0.800830\pi$
$572$	−2.89117	−	4.17895i	−0.120886	−	0.174731i
$573$		0			0
$574$	−36.8230	−	40.5546i	−1.53696	−	1.69272i
$575$	35.9980			1.50122
$576$		0			0
$577$	−38.0743	+	21.9822i	−1.58505	+	0.915131i	−0.590948	+	0.806710i	$0.701246\pi$
$577$	−38.0743	+	21.9822i	−1.58505	+	0.915131i	−0.994105	+	0.108421i	$0.965420\pi$
$578$	−27.3399	+	15.7847i	−1.13719	+	0.656557i
$579$		0			0
$580$		−	0.461804i		−	0.0191754i
$581$	9.00934	+	2.88582i	0.373770	+	0.119724i
$582$		0			0
$583$	6.23206	+	3.59808i	0.258106	+	0.149017i
$584$	−0.842900	−	1.45995i	−0.0348795	−	0.0604130i
$585$		0			0
$586$	11.8495	−	20.5239i	0.489497	−	0.847834i
$587$			27.3732i			1.12981i	0.825155	+	0.564906i	$0.191087\pi$
$587$			27.3732i			1.12981i	−0.825155	+	0.564906i	$0.808913\pi$
$588$		0			0
$589$	4.64659			0.191460
$590$	2.08471	+	1.20361i	0.0858263	+	0.0495518i
$591$		0			0
$592$	−13.3677	+	7.71784i	−0.549409	+	0.317201i
$593$	35.6228	+	20.5669i	1.46285	+	0.844580i	0.999142	−	0.0414062i	$-0.0131838\pi$
$593$	35.6228	+	20.5669i	1.46285	+	0.844580i	0.463712	+	0.885986i	$0.346517\pi$
$594$		0			0
$595$	0.350547	+	0.112285i	0.0143710	+	0.00460325i
$596$		−	20.6039i		−	0.843970i
$597$		0			0
$598$	50.8101	−	4.15692i	2.07778	−	0.169989i
$599$	−8.87901	−	15.3789i	−0.362786	−	0.628364i	0.625632	−	0.780118i	$-0.284841\pi$
$599$	−8.87901	−	15.3789i	−0.362786	−	0.628364i	−0.988418	+	0.151754i	$0.951508\pi$
$600$		0			0
$601$	11.7901			0.480929			0.240465	−	0.970658i	$-0.422700\pi$
$601$	11.7901			0.480929			0.240465	+	0.970658i	$0.422700\pi$
$602$	−3.32580	+	3.01978i	−0.135549	+	0.123077i
$603$		0			0
$604$	−1.26292	−	0.729146i	−0.0513874	−	0.0296685i
$605$	−1.35796	+	0.784020i	−0.0552090	+	0.0318749i
$606$		0			0
$607$	8.03071	−	13.9096i	0.325956	−	0.564573i	−0.655749	−	0.754979i	$-0.727647\pi$
$607$	8.03071	−	13.9096i	0.325956	−	0.564573i	0.981705	+	0.190406i	$0.0609804\pi$
$608$	58.5939			2.37630
$609$		0			0
$610$	3.47909			0.140864
$611$	11.5996	+	16.7662i	0.469268	+	0.678287i
$612$		0			0
$613$	16.7067	−	9.64563i	0.674778	−	0.389583i	−0.123106	−	0.992393i	$-0.539286\pi$
$613$	16.7067	−	9.64563i	0.674778	−	0.389583i	0.797885	+	0.602810i	$0.205952\pi$
$614$	18.9442	−	32.8124i	0.764527	−	1.32420i
$615$		0			0
$616$	0.696400	−	0.151063i	0.0280588	−	0.00608650i
$617$			34.6180i			1.39367i	0.717233	+	0.696833i	$0.245408\pi$
$617$			34.6180i			1.39367i	−0.717233	+	0.696833i	$0.754592\pi$
$618$		0			0
$619$	13.7392	−	7.93230i	0.552223	−	0.318826i	−0.197795	−	0.980243i	$-0.563378\pi$
$619$	13.7392	−	7.93230i	0.552223	−	0.318826i	0.750018	+	0.661417i	$0.230045\pi$
$620$	−0.0844846	−	0.146332i	−0.00339298	−	0.00587682i
$621$		0			0
$622$		−	19.6699i		−	0.788690i
$623$	20.2499	−	18.3866i	0.811293	−	0.736642i
$624$		0			0
$625$	−12.3298	+	21.3559i	−0.493193	+	0.854235i
$626$	−31.4960	+	18.1842i	−1.25883	+	0.726788i
$627$		0			0
$628$	0.175792	−	0.304481i	0.00701486	−	0.0121501i
$629$			3.29414i			0.131346i
$630$		0			0
$631$			5.72803i			0.228029i	0.993479	+	0.114015i	$0.0363710\pi$
$631$			5.72803i			0.228029i	−0.993479	+	0.114015i	$0.963629\pi$
$632$	−4.11821	−	2.37765i	−0.163814	−	0.0945778i
$633$		0			0
$634$	3.34777	+	5.79851i	0.132957	+	0.230288i
$635$	−1.48876	−	0.859538i	−0.0590798	−	0.0341097i
$636$		0			0
$637$	−12.2957	−	22.0412i	−0.487175	−	0.873304i
$638$	−2.54282			−0.100671
$639$		0			0
$640$	0.209115	+	0.362198i	0.00826599	+	0.0143171i
$641$	−9.27361	−	16.0624i	−0.366285	−	0.634425i	0.622696	−	0.782464i	$-0.286037\pi$
$641$	−9.27361	−	16.0624i	−0.366285	−	0.634425i	−0.988982	+	0.148039i	$0.952704\pi$
$642$		0			0
$643$			43.4949i			1.71527i	0.514257	+	0.857636i	$0.328068\pi$
$643$			43.4949i			1.71527i	−0.514257	+	0.857636i	$0.671932\pi$
$644$	10.6348	−	33.2011i	0.419070	−	1.30831i
$645$		0			0
$646$	6.81349	−	11.8013i	0.268073	−	0.464316i
$647$	−7.97924	−	13.8204i	−0.313696	−	0.543338i	0.665463	−	0.746431i	$-0.268234\pi$
$647$	−7.97924	−	13.8204i	−0.313696	−	0.543338i	−0.979160	+	0.203093i	$0.934901\pi$
$648$		0			0
$649$	3.15929	−	5.47205i	0.124013	−	0.214797i
$650$	−15.0059	+	31.7124i	−0.588579	+	1.24386i
$651$		0			0
$652$		−	28.1554i		−	1.10265i
$653$	−11.4443	+	19.8220i	−0.447849	+	0.775696i	−0.998246	−	0.0592065i	$-0.981143\pi$
$653$	−11.4443	+	19.8220i	−0.447849	+	0.775696i	0.550397	+	0.834903i	$0.314476\pi$
$654$		0			0
$655$	0.780353	−	0.450537i	0.0304909	−	0.0176039i
$656$	−39.6625	−	22.8991i	−1.54856	−	0.894061i
$657$		0			0
$658$	28.5824	−	6.20010i	1.11426	−	0.241705i
$659$	−19.2602			−0.750269			−0.375134	−	0.926970i	$-0.622403\pi$
$659$	−19.2602			−0.750269			−0.375134	+	0.926970i	$0.622403\pi$
$660$		0			0
$661$	−2.86323	+	1.65308i	−0.111367	+	0.0642975i	−0.554649	−	0.832085i	$-0.687147\pi$
$661$	−2.86323	+	1.65308i	−0.111367	+	0.0642975i	0.443282	+	0.896382i	$0.353814\pi$
$662$	17.3041	+	29.9716i	0.672544	+	1.16488i
$663$		0			0
$664$	1.24493			0.0483128
$665$	2.94396	−	0.638604i	0.114162	−	0.0247640i
$666$		0			0
$667$	6.08040	−	10.5316i	0.235434	−	0.407784i
$668$	−6.59879	+	3.80982i	−0.255315	+	0.147406i
$669$		0			0
$670$	−1.34672	−	0.777530i	−0.0520284	−	0.0300386i
$671$		−	9.13209i		−	0.352540i
$672$		0			0
$673$	20.7526			0.799953			0.399977	−	0.916525i	$-0.369018\pi$
$673$	20.7526			0.799953			0.399977	+	0.916525i	$0.369018\pi$
$674$	33.7756	+	19.5004i	1.30099	+	0.751126i
$675$		0			0
$676$	−8.35099	+	22.1637i	−0.321192	+	0.852449i
$677$	20.4176	−	35.3643i	0.784711	−	1.35916i	−0.144461	−	0.989510i	$-0.546145\pi$
$677$	20.4176	−	35.3643i	0.784711	−	1.35916i	0.929172	−	0.369648i	$-0.120522\pi$
$678$		0			0
$679$	−12.0687	−	3.86578i	−0.463154	−	0.148355i
$680$	0.0484395			0.00185757
$681$		0			0
$682$	−0.805743	+	0.465196i	−0.0308535	+	0.0178133i
$683$	13.7114	−	7.91625i	0.524650	−	0.302907i	−0.214185	−	0.976793i	$-0.568710\pi$
$683$	13.7114	−	7.91625i	0.524650	−	0.302907i	0.738835	+	0.673886i	$0.235376\pi$
$684$		0			0
$685$	2.00310			0.0765347
$686$	−35.9580	+	4.23488i	−1.37288	+	0.161689i
$687$		0			0
$688$	−1.87791	+	3.25263i	−0.0715946	+	0.124006i
$689$	−2.73492	−	33.4289i	−0.104192	−	1.27354i
$690$		0			0
$691$	34.5351	+	19.9389i	1.31378	+	0.758510i	0.982720	−	0.185100i	$-0.0592608\pi$
$691$	34.5351	+	19.9389i	1.31378	+	0.758510i	0.331059	+	0.943610i	$0.392594\pi$
$692$	−39.4023			−1.49785
$693$		0			0
$694$		−	6.24364i		−	0.237005i
$695$	−1.83367	−	1.05867i	−0.0695552	−	0.0401577i
$696$		0			0
$697$	−8.46440	+	4.88692i	−0.320612	+	0.185105i
$698$	20.9726	−	36.3255i	0.793823	−	1.37494i
$699$		0			0
$700$	16.1280	+	17.7624i	0.609581	+	0.671356i
$701$	−25.8419			−0.976034			−0.488017	−	0.872834i	$-0.662280\pi$
$701$	−25.8419			−0.976034			−0.488017	+	0.872834i	$0.662280\pi$
$702$		0			0
$703$	13.4795	+	23.3471i	0.508388	+	0.880553i
$704$	−4.36626	+	2.52086i	−0.164560	+	0.0950086i
$705$		0			0
$706$	52.6406			1.98116
$707$	−43.2289	+	9.37720i	−1.62579	+	0.352666i
$708$		0			0
$709$	−9.94974	−	5.74448i	−0.373670	−	0.215739i	0.301390	−	0.953501i	$-0.402549\pi$
$709$	−9.94974	−	5.74448i	−0.373670	−	0.215739i	−0.675061	+	0.737762i	$0.735883\pi$
$710$	2.48347	−	1.43383i	0.0932031	−	0.0538108i
$711$		0			0
$712$	1.79970	−	3.11717i	0.0674466	−	0.116821i
$713$		−	4.44951i		−	0.166635i
$714$		0			0
$715$	−0.380064	−	0.179841i	−0.0142136	−	0.00672568i
$716$	16.9323	−	29.3276i	0.632790	−	1.09602i
$717$		0			0
$718$	2.98939	+	5.17777i	0.111563	+	0.193233i
$719$	−12.4830	+	21.6211i	−0.465536	+	0.806332i	−0.999226	−	0.0393484i	$-0.987472\pi$
$719$	−12.4830	+	21.6211i	−0.465536	+	0.806332i	0.533690	+	0.845680i	$0.320805\pi$
$720$		0			0
$721$	9.71965	+	10.7046i	0.361979	+	0.398661i
$722$		−	74.3775i		−	2.76804i
$723$		0			0
$724$	−2.32285	−	4.02330i	−0.0863282	−	0.149525i
$725$	4.18443	+	7.24765i	0.155406	+	0.269171i
$726$		0			0
$727$	−37.9518			−1.40756			−0.703778	−	0.710420i	$-0.748505\pi$
$727$	−37.9518			−1.40756			−0.703778	+	0.710420i	$0.748505\pi$
$728$	−2.42576	−	2.26870i	−0.0899045	−	0.0840838i
$729$		0			0
$730$	1.23578	+	0.713478i	0.0457383	+	0.0264070i
$731$	0.400766	+	0.694147i	0.0148229	+	0.0256740i
$732$		0			0
$733$	26.8008	+	15.4734i	0.989909	+	0.571524i	0.905247	−	0.424886i	$-0.139686\pi$
$733$	26.8008	+	15.4734i	0.989909	+	0.571524i	0.0846618	+	0.996410i	$0.473019\pi$
$734$		−	43.9085i		−	1.62069i
$735$		0			0
$736$		−	56.1086i		−	2.06819i
$737$	−2.04090	+	3.53494i	−0.0751774	+	0.130211i
$738$		0			0
$739$	−16.9505	+	9.78635i	−0.623533	+	0.359997i	−0.778243	−	0.627963i	$-0.783889\pi$
$739$	−16.9505	+	9.78635i	−0.623533	+	0.359997i	0.154710	+	0.987960i	$0.450556\pi$
$740$	0.490169	−	0.848997i	0.0180190	−	0.0312098i
$741$		0			0
$742$	−45.8226	−	14.6776i	−1.68220	−	0.538833i
$743$			34.0186i			1.24802i	0.781416	+	0.624010i	$0.214498\pi$
$743$			34.0186i			1.24802i	−0.781416	+	0.624010i	$0.785502\pi$
$744$		0			0
$745$	−0.852417	−	1.47643i	−0.0312301	−	0.0540922i
$746$	55.1298	−	31.8292i	2.01845	−	1.16535i
$747$		0			0
$748$			1.30070i			0.0475582i
$749$	13.3310	+	14.6819i	0.487104	+	0.536467i
$750$		0			0
$751$	20.6159	−	35.7077i	0.752284	−	1.30299i	−0.194430	−	0.980916i	$-0.562286\pi$
$751$	20.6159	−	35.7077i	0.752284	−	1.30299i	0.946713	−	0.322077i	$-0.104381\pi$
$752$	21.1767	−	12.2264i	0.772235	−	0.445850i
$753$		0			0
$754$	6.74313	+	9.74663i	0.245570	+	0.354951i
$755$	−0.120664			−0.00439140
$756$		0			0
$757$	4.10877			0.149336			0.0746679	−	0.997208i	$-0.476210\pi$
$757$	4.10877			0.149336			0.0746679	+	0.997208i	$0.476210\pi$
$758$	29.9747	−	51.9178i	1.08873	−	1.88574i
$759$		0			0
$760$	0.343314	−	0.198212i	0.0124533	−	0.00718991i
$761$	18.2651	+	10.5454i	0.662111	+	0.382270i	0.793081	−	0.609116i	$-0.208476\pi$
$761$	18.2651	+	10.5454i	0.662111	+	0.382270i	−0.130970	+	0.991386i	$0.541809\pi$
$762$		0			0
$763$	2.44362	+	11.2651i	0.0884650	+	0.407823i
$764$	3.62743			0.131236
$765$		0			0
$766$	−26.6515	−	46.1617i	−0.962957	−	1.66789i
$767$	−29.3522	+	2.40139i	−1.05985	+	0.0867092i
$768$		0			0
$769$		−	31.6857i		−	1.14262i	−0.820735	−	0.571309i	$-0.806436\pi$
$769$		−	31.6857i		−	1.14262i	0.820735	−	0.571309i	$-0.193564\pi$
$770$	−0.446564	+	0.405473i	−0.0160930	+	0.0146122i
$771$		0			0
$772$	27.5594	+	15.9114i	0.991885	+	0.572665i
$773$	45.2445	−	26.1219i	1.62733	−	0.939540i	0.642446	−	0.766331i	$-0.277920\pi$
$773$	45.2445	−	26.1219i	1.62733	−	0.939540i	0.984885	−	0.173209i	$-0.0554137\pi$
$774$		0			0
$775$	2.65184	+	1.53104i	0.0952568	+	0.0549965i
$776$	−1.66768			−0.0598663
$777$		0			0
$778$			59.7624i			2.14259i
$779$	−39.9941	+	69.2718i	−1.43294	+	2.48192i
$780$		0			0
$781$	−3.76360	−	6.51874i	−0.134672	−	0.233259i
$782$	−11.3007	−	6.52449i	−0.404114	−	0.233315i
$783$		0			0
$784$	−27.5505	+	12.5427i	−0.983948	+	0.447954i
$785$		−	0.0290912i		−	0.00103831i
$786$		0			0
$787$	−19.5495	+	11.2869i	−0.696863	+	0.402334i	−0.806178	−	0.591673i	$-0.798468\pi$
$787$	−19.5495	+	11.2869i	−0.696863	+	0.402334i	0.109315	+	0.994007i	$0.465134\pi$
$788$	21.4278	−	12.3714i	0.763336	−	0.440712i
$789$		0			0
$790$	4.02515			0.143209
$791$	7.12534	−	22.2448i	0.253348	−	0.790935i
$792$		0			0
$793$	−35.0032	+	24.2167i	−1.24300	+	0.859960i
$794$	−21.8456	−	37.8376i	−0.775270	−	1.34281i
$795$		0			0
$796$	−1.36945	+	2.37196i	−0.0485390	+	0.0840719i
$797$	11.0947			0.392996			0.196498	−	0.980504i	$-0.437043\pi$
$797$	11.0947			0.392996			0.196498	+	0.980504i	$0.437043\pi$
$798$		0			0
$799$		−	5.21848i		−	0.184617i
$800$	33.4399	+	19.3065i	1.18228	+	0.682589i
$801$		0			0
$802$	27.8063	+	48.1619i	0.981874	+	1.70066i
$803$	1.87277	−	3.24374i	0.0660887	−	0.114469i
$804$		0			0
$805$	−0.611517	−	2.81909i	−0.0215532	−	0.0993599i
$806$	3.91978	+	1.85479i	0.138069	+	0.0653322i
$807$		0			0
$808$	−5.04119	+	2.91053i	−0.177348	+	0.102392i
$809$	−12.6465	−	21.9044i	−0.444628	−	0.770119i	0.553398	−	0.832917i	$-0.313331\pi$
$809$	−12.6465	−	21.9044i	−0.444628	−	0.770119i	−0.998026	+	0.0627983i	$0.979998\pi$
$810$		0			0
$811$		−	14.1042i		−	0.495267i	−0.968854	−	0.247633i	$-0.920347\pi$
$811$		−	14.1042i		−	0.495267i	0.968854	−	0.247633i	$-0.0796528\pi$
$812$	7.92073	−	1.71816i	0.277963	−	0.0602957i
$813$		0			0
$814$	−4.67482	−	2.69901i	−0.163852	−	0.0946002i
$815$	−1.16483	−	2.01755i	−0.0408024	−	0.0706717i
$816$		0			0
$817$	5.68083	+	3.27983i	0.198747	+	0.114747i
$818$	29.5206			1.03216
$819$		0			0
$820$	2.90870			0.101576
$821$	47.5632	+	27.4606i	1.65997	+	0.958383i	0.972727	+	0.231954i	$0.0745119\pi$
$821$	47.5632	+	27.4606i	1.65997	+	0.958383i	0.687242	+	0.726429i	$0.258821\pi$
$822$		0			0
$823$	−5.48342	−	9.49756i	−0.191140	−	0.331064i	0.754488	−	0.656313i	$-0.227885\pi$
$823$	−5.48342	−	9.49756i	−0.191140	−	0.331064i	−0.945628	+	0.325249i	$0.894552\pi$
$824$	1.64782	+	0.951371i	0.0574046	+	0.0331426i
$825$		0			0
$826$	−12.8877	+	40.2344i	−0.448420	+	1.39994i
$827$		−	47.0639i		−	1.63657i	−0.574810	−	0.818287i	$-0.694924\pi$
$827$		−	47.0639i		−	1.63657i	0.574810	−	0.818287i	$-0.305076\pi$
$828$		0			0
$829$	−13.4513	−	23.2983i	−0.467182	−	0.809183i	0.532115	−	0.846672i	$-0.321397\pi$
$829$	−13.4513	−	23.2983i	−0.467182	−	0.809183i	−0.999297	+	0.0374890i	$0.988064\pi$
$830$	−0.912602	+	0.526891i	−0.0316769	+	0.0182886i
$831$		0			0
$832$	21.2410	+	10.0510i	0.736400	+	0.348455i
$833$	−0.621657	+	6.43024i	−0.0215391	+	0.222795i
$834$		0			0
$835$	−0.315236	+	0.546005i	−0.0109092	+	0.0188953i
$836$	5.32240	+	9.21866i	0.184079	+	0.318834i
$837$		0			0
$838$	−14.4330	−	8.33290i	−0.498580	−	0.287855i
$839$			35.4835i			1.22503i	0.790460	+	0.612514i	$0.209842\pi$
$839$			35.4835i			1.22503i	−0.790460	+	0.612514i	$0.790158\pi$
$840$		0			0
$841$	−26.1728			−0.902512
$842$	−35.0920	+	60.7811i	−1.20935	+	2.09466i
$843$		0			0
$844$	21.9466	+	38.0126i	0.755433	+	1.30845i
$845$	0.318533	+	1.93369i	0.0109579	+	0.0665210i
$846$		0			0
$847$	−18.4996	−	20.3744i	−0.635655	−	0.700071i
$848$	−40.2284			−1.38145
$849$		0			0
$850$	7.77699	−	4.49005i	0.266749	−	0.154007i
$851$	22.3568	−	12.9077i	0.766383	−	0.442471i
$852$		0			0
$853$		−	3.39402i		−	0.116209i	−0.998311	−	0.0581046i	$-0.981494\pi$
$853$		−	3.39402i		−	0.116209i	0.998311	−	0.0581046i	$-0.0185057\pi$
$854$	12.9441	+	59.6723i	0.442938	+	2.04194i
$855$		0			0
$856$	2.26007	+	1.30485i	0.0772477	+	0.0445990i
$857$	18.3203	+	31.7317i	0.625810	+	1.08394i	0.988384	+	0.151980i	$0.0485649\pi$
$857$	18.3203	+	31.7317i	0.625810	+	1.08394i	−0.362573	+	0.931955i	$0.618102\pi$
$858$		0			0
$859$	4.69785	−	8.13691i	0.160289	−	0.277628i	−0.774684	−	0.632349i	$-0.782091\pi$
$859$	4.69785	−	8.13691i	0.160289	−	0.277628i	0.934972	+	0.354721i	$0.115424\pi$
$860$		−	0.238536i		−	0.00813402i
$861$		0			0
$862$	78.8387			2.68526
$863$	−22.8030	−	13.1653i	−0.776222	−	0.448152i	0.0588674	−	0.998266i	$-0.481251\pi$
$863$	−22.8030	−	13.1653i	−0.776222	−	0.448152i	−0.835090	+	0.550114i	$0.814584\pi$
$864$		0			0
$865$	−2.82347	+	1.63013i	−0.0960010	+	0.0554262i
$866$	−12.9661	−	7.48596i	−0.440605	−	0.254383i
$867$		0			0
$868$	2.19551	−	1.99349i	0.0745203	−	0.0676634i
$869$		−	10.5654i		−	0.358407i
$870$		0			0
$871$	18.9615	−	1.55129i	0.642486	−	0.0525636i
$872$	0.758460	+	1.31369i	0.0256847	+	0.0444872i
$873$		0			0
$874$	−106.792			−3.61228
$875$	3.78974	+	1.21391i	0.128117	+	0.0410376i
$876$		0			0
$877$	31.8523	+	18.3900i	1.07558	+	0.620985i	0.929700	−	0.368318i	$-0.120066\pi$
$877$	31.8523	+	18.3900i	1.07558	+	0.620985i	0.145877	+	0.989303i	$0.453400\pi$
$878$	31.9693	−	18.4575i	1.07891	−	0.622910i
$879$		0			0
$880$	−0.252152	+	0.436740i	−0.00850004	+	0.0147225i
$881$	31.1520			1.04954			0.524768	−	0.851245i	$-0.324152\pi$
$881$	31.1520			1.04954			0.524768	+	0.851245i	$0.324152\pi$
$882$		0			0
$883$	−35.2516			−1.18631			−0.593155	−	0.805089i	$-0.702118\pi$
$883$	−35.2516			−1.18631			−0.593155	+	0.805089i	$0.702118\pi$
$884$	4.98557	−	3.44923i	0.167683	−	0.116010i
$885$		0			0
$886$	−26.7477	+	15.4428i	−0.898606	+	0.518810i
$887$	−16.2604	+	28.1638i	−0.545971	+	0.945649i	0.452574	+	0.891727i	$0.350506\pi$
$887$	−16.2604	+	28.1638i	−0.545971	+	0.945649i	−0.998545	+	0.0539223i	$0.982828\pi$
$888$		0			0
$889$	9.20352	−	28.7328i	0.308676	−	0.963666i
$890$			3.04673i			0.102127i
$891$		0			0
$892$	17.5765	−	10.1478i	0.588506	−	0.339774i
$893$	−21.3538	−	36.9858i	−0.714577	−	1.23768i
$894$		0			0
$895$		−	2.80206i		−	0.0936626i
$896$	−5.43428	+	4.93425i	−0.181547	+	0.164842i
$897$		0			0
$898$	−23.0457	+	39.9164i	−0.769046	+	1.33203i
$899$	0.895839	−	0.517213i	0.0298779	−	0.0172500i
$900$		0			0
$901$	−4.29259	+	7.43498i	−0.143007	+	0.247695i
$902$		−	16.0161i		−	0.533279i
$903$		0			0
$904$		−	3.07384i		−	0.102235i
$905$	−0.332900	−	0.192200i	−0.0110660	−	0.00638895i
$906$		0			0
$907$	−25.7504	−	44.6010i	−0.855029	−	1.48095i	−0.876618	−	0.481186i	$-0.840206\pi$
$907$	−25.7504	−	44.6010i	−0.855029	−	1.48095i	0.0215894	−	0.999767i	$-0.493127\pi$
$908$	−4.03954	−	2.33223i	−0.134057	−	0.0773978i
$909$		0			0
$910$	2.73839	+	0.636431i	0.0907766	+	0.0210975i
$911$	−45.9134			−1.52118			−0.760589	−	0.649234i	$-0.775090\pi$
$911$	−45.9134			−1.52118			−0.760589	+	0.649234i	$0.775090\pi$
$912$		0			0
$913$	1.38301	+	2.39544i	0.0457709	+	0.0792775i
$914$	−25.0288	−	43.3511i	−0.827879	−	1.43393i
$915$		0			0
$916$		−	4.38432i		−	0.144862i
$917$	10.6308	+	11.7081i	0.351060	+	0.386637i
$918$		0			0
$919$	12.5947	−	21.8147i	0.415461	−	0.719600i	−0.580016	−	0.814605i	$-0.696954\pi$
$919$	12.5947	−	21.8147i	0.415461	−	0.719600i	0.995477	+	0.0950056i	$0.0302869\pi$
$920$	−0.189805	−	0.328752i	−0.00625768	−	0.0108386i
$921$		0			0
$922$	−9.10918	+	15.7776i	−0.299995	+	0.519606i
$923$	−15.0059	+	31.7124i	−0.493925	+	1.04383i
$924$		0			0
$925$			17.7658i			0.584135i
$926$	−22.4476	+	38.8803i	−0.737672	+	1.27769i
$927$		0			0
$928$	11.2966	−	6.52210i	0.370829	−	0.214098i
$929$	−32.2348	−	18.6108i	−1.05759	−	0.610599i	−0.132825	−	0.991140i	$-0.542405\pi$
$929$	−32.2348	−	18.6108i	−1.05759	−	0.610599i	−0.924764	+	0.380540i	$0.875738\pi$
$930$		0			0
$931$	21.9063	+	48.1179i	0.717949	+	1.57700i
$932$	33.8482			1.10873
$933$		0			0
$934$	−32.6676	+	18.8607i	−1.06892	+	0.617140i
$935$	0.0538119	+	0.0932050i	0.00175984	+	0.00304813i
$936$		0			0
$937$	7.76176			0.253566			0.126783	−	0.991930i	$-0.459535\pi$
$937$	7.76176			0.253566			0.126783	+	0.991930i	$0.459535\pi$
$938$	8.32541	−	25.9914i	0.271834	−	0.848648i
$939$		0			0
$940$	−0.776511	+	1.34496i	−0.0253270	+	0.0438677i
$941$	21.1138	−	12.1901i	0.688291	−	0.397385i	−0.114681	−	0.993402i	$-0.536585\pi$
$941$	21.1138	−	12.1901i	0.688291	−	0.397385i	0.802971	+	0.596018i	$0.203251\pi$
$942$		0			0
$943$	66.3337	+	38.2978i	2.16012	+	1.24715i
$944$			35.3225i			1.14965i
$945$		0			0
$946$	−1.31345			−0.0427039
$947$	−8.89648	−	5.13638i	−0.289097	−	0.166910i	0.348438	−	0.937332i	$-0.386712\pi$
$947$	−8.89648	−	5.13638i	−0.289097	−	0.166910i	−0.637534	+	0.770422i	$0.720046\pi$
$948$		0			0
$949$	−17.3995	+	1.42350i	−0.564811	+	0.0462088i
$950$	36.7461	−	63.6462i	1.19220	−	2.06495i
$951$		0			0
$952$	0.180221	+	0.830819i	0.00584101	+	0.0269270i
$953$	45.5757			1.47634			0.738170	−	0.674614i	$-0.235690\pi$
$953$	45.5757			1.47634			0.738170	+	0.674614i	$0.235690\pi$
$954$		0			0
$955$	0.259933	−	0.150072i	0.00841123	−	0.00485622i
$956$	−29.2933	+	16.9125i	−0.947412	+	0.546989i
$957$		0			0
$958$	33.1181			1.07000
$959$	7.45264	+	34.3566i	0.240658	+	1.10943i
$960$		0			0
$961$	−15.3108	+	26.5190i	−0.493895	+	0.855452i
$962$	2.05153	+	25.0758i	0.0661438	+	0.808478i
$963$		0			0
$964$	40.3409	+	23.2909i	1.29929	+	0.750148i
$965$	2.63312			0.0847632
$966$		0			0
$967$			44.8970i			1.44379i	0.692003	+	0.721895i	$0.256729\pi$
$967$			44.8970i			1.44379i	−0.692003	+	0.721895i	$0.743271\pi$
$968$	−3.13634	−	1.81077i	−0.100806	−	0.0582002i
$969$		0			0
$970$	1.22250	−	0.705810i	0.0392521	−	0.0226622i
$971$	0.842100	−	1.45856i	0.0270243	−	0.0468074i	−0.852197	−	0.523221i	$-0.824730\pi$
$971$	0.842100	−	1.45856i	0.0270243	−	0.0468074i	0.879221	+	0.476414i	$0.158064\pi$
$972$		0			0
$973$	11.3357	−	35.3894i	0.363407	−	1.13453i
$974$	26.5556			0.850897
$975$		0			0
$976$	25.5253	+	44.2112i	0.817046	+	1.41517i
$977$	−34.2101	+	19.7512i	−1.09448	+	0.631897i	−0.934765	−	0.355266i	$-0.884390\pi$
$977$	−34.2101	+	19.7512i	−1.09448	+	0.631897i	−0.159713	+	0.987163i	$0.551057\pi$
$978$		0			0
$979$	7.99722			0.255592
$980$	1.11704	−	1.56476i	0.0356826	−	0.0499845i
$981$		0			0
$982$	−13.3634	−	7.71535i	−0.426443	−	0.246207i
$983$	−10.9155	+	6.30206i	−0.348150	+	0.201004i	−0.663870	−	0.747848i	$-0.731087\pi$
$983$	−10.9155	+	6.30206i	−0.348150	+	0.201004i	0.315720	+	0.948852i	$0.397754\pi$
$984$		0			0
$985$	1.02365	−	1.77301i	0.0326161	−	0.0564927i
$986$		−	3.03364i		−	0.0966108i
$987$		0			0
$988$	21.2210	−	44.8470i	0.675130	−	1.42677i
$989$	3.14072	−	5.43988i	0.0998690	−	0.172978i
$990$		0			0
$991$	22.1789	+	38.4150i	0.704535	+	1.22029i	0.966859	+	0.255311i	$0.0821779\pi$
$991$	22.1789	+	38.4150i	0.704535	+	1.22029i	−0.262323	+	0.964980i	$0.584489\pi$
$992$	2.38637	−	4.13331i	0.0757672	−	0.131233i
$993$		0			0
$994$	33.8326	+	37.2611i	1.07310	+	1.18185i
$995$			0.226626i			0.00718451i
$996$		0			0
$997$	−15.0675	−	26.0977i	−0.477193	−	0.826523i	0.522465	−	0.852661i	$-0.325012\pi$
$997$	−15.0675	−	26.0977i	−0.477193	−	0.826523i	−0.999658	+	0.0261380i	$0.991679\pi$
$998$	−33.3225	−	57.7163i	−1.05481	−	1.82698i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.dl.g.415.2		16
3.2	odd	2		273.2.bj.d.142.7	yes	16
7.4	even	3	inner	819.2.dl.g.298.7		16
13.12	even	2	inner	819.2.dl.g.415.7		16
21.2	odd	6		1911.2.c.j.883.2		8
21.5	even	6		1911.2.c.m.883.2		8
21.11	odd	6		273.2.bj.d.25.2	✓	16
39.38	odd	2		273.2.bj.d.142.2	yes	16
91.25	even	6	inner	819.2.dl.g.298.2		16
273.116	odd	6		273.2.bj.d.25.7	yes	16
273.194	even	6		1911.2.c.m.883.7		8
273.233	odd	6		1911.2.c.j.883.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.d.25.2	✓	16	21.11	odd	6
273.2.bj.d.25.7	yes	16	273.116	odd	6
273.2.bj.d.142.2	yes	16	39.38	odd	2
273.2.bj.d.142.7	yes	16	3.2	odd	2
819.2.dl.g.298.2		16	91.25	even	6	inner
819.2.dl.g.298.7		16	7.4	even	3	inner
819.2.dl.g.415.2		16	1.1	even	1	trivial
819.2.dl.g.415.7		16	13.12	even	2	inner
1911.2.c.j.883.2		8	21.2	odd	6
1911.2.c.j.883.7		8	273.233	odd	6
1911.2.c.m.883.2		8	21.5	even	6
1911.2.c.m.883.7		8	273.194	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.dl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69305 - 0.977485i) q^{2} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} +(-0.807080 + 2.51965i) q^{7} +0.348171i q^{8} +O(q^{10})\)	\(q+(-1.69305 - 0.977485i) q^{2} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} +(-0.807080 + 2.51965i) q^{7} +0.348171i q^{8} +(-0.147356 - 0.255228i) q^{10} +(-0.669934 + 0.386787i) q^{11} +(3.25910 + 1.54216i) q^{13} +(3.82934 - 3.47699i) q^{14} +(2.16224 - 3.74510i) q^{16} +(-0.461444 - 0.799245i) q^{17} +(-6.54095 - 3.77642i) q^{19} +0.274652i q^{20} +1.51231 q^{22} +(-3.61624 + 6.26351i) q^{23} +(-2.48864 - 4.31045i) q^{25} +(-4.01039 - 5.79668i) q^{26} +(-4.71075 + 1.02186i) q^{28} -1.68142 q^{29} +(-0.532789 + 0.307606i) q^{31} +(-6.71851 + 3.87893i) q^{32} +1.80422i q^{34} +(-0.295285 + 0.268115i) q^{35} +(-3.09117 - 1.78469i) q^{37} +(7.38278 + 12.7874i) q^{38} +(-0.0262434 + 0.0454549i) q^{40} -10.5905i q^{41} -0.868503 q^{43} +(-1.22056 - 0.704688i) q^{44} +(12.2450 - 7.06964i) q^{46} +(4.89695 + 2.82725i) q^{47} +(-5.69725 - 4.06711i) q^{49} +9.73042i q^{50} +(0.535636 + 6.54710i) q^{52} +(-4.65125 - 8.05620i) q^{53} -0.116616 q^{55} +(-0.877269 - 0.281002i) q^{56} +(2.84673 + 1.64356i) q^{58} +(-7.07374 + 4.08402i) q^{59} +(-5.90253 + 10.2235i) q^{61} +1.20272 q^{62} +6.51745 q^{64} +(0.309246 + 0.446989i) q^{65} +(4.56962 - 2.63827i) q^{67} +(0.840708 - 1.45615i) q^{68} +(0.762012 - 0.165296i) q^{70} +9.73042i q^{71} +(-4.19319 + 2.42094i) q^{73} +(3.48901 + 6.04315i) q^{74} -13.7605i q^{76} +(-0.433876 - 2.00017i) q^{77} +(-6.82897 + 11.8281i) q^{79} +(0.564575 - 0.325957i) q^{80} +(-10.3520 + 17.9303i) q^{82} -3.57563i q^{83} -0.139126i q^{85} +(1.47042 + 0.848948i) q^{86} +(-0.134668 - 0.233252i) q^{88} +(-8.95299 - 5.16901i) q^{89} +(-6.51606 + 6.96714i) q^{91} -13.1769 q^{92} +(-5.52719 - 9.57338i) q^{94} +(-0.569295 - 0.986048i) q^{95} +4.78983i q^{97} +(5.67020 + 12.4548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} - 16 q^{10} + 6 q^{13} + 10 q^{14} - 28 q^{16} + 2 q^{17} + 60 q^{22} - 24 q^{23} + 10 q^{25} - 14 q^{26} - 24 q^{29} + 30 q^{35} + 26 q^{40} - 76 q^{43} + 2 q^{49} - 10 q^{53} - 16 q^{55} - 72 q^{56} + 26 q^{61} + 104 q^{62} - 84 q^{64} + 32 q^{65} + 12 q^{68} + 54 q^{74} + 10 q^{77} - 10 q^{79} - 48 q^{82} + 68 q^{88} - 57 q^{91} - 16 q^{92} - 48 q^{94} - 18 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 16 * q^10 + 6 * q^13 + 10 * q^14 - 28 * q^16 + 2 * q^17 + 60 * q^22 - 24 * q^23 + 10 * q^25 - 14 * q^26 - 24 * q^29 + 30 * q^35 + 26 * q^40 - 76 * q^43 + 2 * q^49 - 10 * q^53 - 16 * q^55 - 72 * q^56 + 26 * q^61 + 104 * q^62 - 84 * q^64 + 32 * q^65 + 12 * q^68 + 54 * q^74 + 10 * q^77 - 10 * q^79 - 48 * q^82 + 68 * q^88 - 57 * q^91 - 16 * q^92 - 48 * q^94 - 18 * q^95

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