LMFDB - Embedded newform 819.2.bm.d.550.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.d.478.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18890i q^{2} -2.79129 q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +1.73205i q^{8} +O(q^{10})$	\(q-2.18890i q^{2} -2.79129 q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +1.73205i q^{8} +(1.89564 + 3.28335i) q^{10} +(-3.00000 + 1.73205i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(2.89564 - 5.01540i) q^{14} -1.79129 q^{16} -1.00000 q^{17} +(4.58258 + 2.64575i) q^{19} +(4.18693 - 2.41733i) q^{20} +(3.79129 + 6.56670i) q^{22} +8.58258 q^{23} +(-1.00000 + 1.73205i) q^{25} +(7.58258 + 2.18890i) q^{26} +(-6.39564 - 3.69253i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(5.29129 + 3.05493i) q^{31} +7.38505i q^{32} +2.18890i q^{34} -4.58258 q^{35} -7.02355i q^{37} +(5.79129 - 10.0308i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(3.08258 + 1.77973i) q^{41} +(-2.29129 - 3.96863i) q^{43} +(8.37386 - 4.83465i) q^{44} -18.7864i q^{46} +(0.708712 - 0.409175i) q^{47} +(3.50000 + 6.06218i) q^{49} +(3.79129 + 2.18890i) q^{50} +(2.79129 - 9.66930i) q^{52} +(-3.08258 + 5.33918i) q^{53} +(3.00000 - 5.19615i) q^{55} +(-2.29129 + 3.96863i) q^{56} +(13.2695 + 7.66115i) q^{58} -4.28245i q^{59} +(2.58258 - 4.47315i) q^{61} +(6.68693 - 11.5821i) q^{62} +12.5826 q^{64} +(-1.50000 - 6.06218i) q^{65} +(-12.1652 + 7.02355i) q^{67} +2.79129 q^{68} +10.0308i q^{70} +(3.87386 - 2.23658i) q^{71} +(-7.50000 - 4.33013i) q^{73} -15.3739 q^{74} +(-12.7913 - 7.38505i) q^{76} -9.16515 q^{77} +(0.708712 + 1.22753i) q^{79} +(2.68693 - 1.55130i) q^{80} +(3.89564 - 6.74745i) q^{82} +3.46410i q^{83} +(1.50000 - 0.866025i) q^{85} +(-8.68693 + 5.01540i) q^{86} +(-3.00000 - 5.19615i) q^{88} +15.5885i q^{89} +(-6.87386 + 6.61438i) q^{91} -23.9564 q^{92} +(-0.895644 - 1.55130i) q^{94} -9.16515 q^{95} +(9.08258 - 5.24383i) q^{97} +(13.2695 - 7.66115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} - 6 q^{5}+O(q^{10}) $ 4 * q - 2 * q^4 - 6 * q^5	$ 4 q - 2 q^{4} - 6 q^{5} + 3 q^{10} - 12 q^{11} - 4 q^{13} + 7 q^{14} + 2 q^{16} - 4 q^{17} + 3 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 12 q^{26} - 21 q^{28} - 14 q^{29} + 12 q^{31} + 14 q^{38} - 6 q^{40} - 6 q^{41} + 6 q^{44} + 12 q^{47} + 14 q^{49} + 6 q^{50} + 2 q^{52} + 6 q^{53} + 12 q^{55} + 21 q^{58} - 8 q^{61} + 13 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 2 q^{68} - 12 q^{71} - 30 q^{73} - 34 q^{74} - 42 q^{76} + 12 q^{79} - 3 q^{80} + 11 q^{82} + 6 q^{85} - 21 q^{86} - 12 q^{88} - 50 q^{92} + q^{94} + 18 q^{97} + 21 q^{98}+O(q^{100}) $ 4 * q - 2 * q^4 - 6 * q^5 + 3 * q^10 - 12 * q^11 - 4 * q^13 + 7 * q^14 + 2 * q^16 - 4 * q^17 + 3 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 12 * q^26 - 21 * q^28 - 14 * q^29 + 12 * q^31 + 14 * q^38 - 6 * q^40 - 6 * q^41 + 6 * q^44 + 12 * q^47 + 14 * q^49 + 6 * q^50 + 2 * q^52 + 6 * q^53 + 12 * q^55 + 21 * q^58 - 8 * q^61 + 13 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 2 * q^68 - 12 * q^71 - 30 * q^73 - 34 * q^74 - 42 * q^76 + 12 * q^79 - 3 * q^80 + 11 * q^82 + 6 * q^85 - 21 * q^86 - 12 * q^88 - 50 * q^92 + q^94 + 18 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	2.18890i		−	1.54779i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$		−	2.18890i		−	1.54779i	0.633316	−	0.773893i	$-0.281693\pi$
$3$		0			0
$3$		0			0
$4$	−2.79129			−1.39564
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i
$7$	2.29129	+	1.32288i	0.866025	+	0.500000i
$8$			1.73205i			0.612372i
$9$		0			0
$10$	1.89564	+	3.28335i	0.599455	+	1.03829i
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$		0			0
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	2.89564	−	5.01540i	0.773893	−	1.34042i
$15$		0			0
$16$	−1.79129			−0.447822
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		0			0
$19$	4.58258	+	2.64575i	1.05131	+	0.606977i	0.923017	−	0.384759i	$-0.125715\pi$
$19$	4.58258	+	2.64575i	1.05131	+	0.606977i	0.128298	+	0.991736i	$0.459049\pi$
$20$	4.18693	−	2.41733i	0.936226	−	0.540531i
$21$		0			0
$22$	3.79129	+	6.56670i	0.808305	+	1.40003i
$23$	8.58258			1.78959			0.894795	−	0.446476i	$-0.147321\pi$
$23$	8.58258			1.78959			0.894795	+	0.446476i	$0.147321\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	7.58258	+	2.18890i	1.48707	+	0.429279i
$27$		0			0
$28$	−6.39564	−	3.69253i	−1.20866	−	0.697822i
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$		0			0
$31$	5.29129	+	3.05493i	0.950343	+	0.548681i	0.893188	−	0.449684i	$-0.148463\pi$
$31$	5.29129	+	3.05493i	0.950343	+	0.548681i	0.0571558	+	0.998365i	$0.481797\pi$
$32$			7.38505i			1.30551i
$33$		0			0
$34$			2.18890i			0.375393i
$35$	−4.58258			−0.774597
$36$		0			0
$37$		−	7.02355i		−	1.15467i	−0.816509	−	0.577333i	$-0.804094\pi$
$37$		−	7.02355i		−	1.15467i	0.816509	−	0.577333i	$-0.195906\pi$
$38$	5.79129	−	10.0308i	0.939471	−	1.62721i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	3.08258	+	1.77973i	0.481417	+	0.277946i	0.721007	−	0.692928i	$-0.243680\pi$
$41$	3.08258	+	1.77973i	0.481417	+	0.277946i	−0.239590	+	0.970874i	$0.577013\pi$
$42$		0			0
$43$	−2.29129	−	3.96863i	−0.349418	−	0.605210i	0.636728	−	0.771088i	$-0.280287\pi$
$43$	−2.29129	−	3.96863i	−0.349418	−	0.605210i	−0.986146	+	0.165878i	$0.946954\pi$
$44$	8.37386	−	4.83465i	1.26241	−	0.728851i
$45$		0			0
$46$		−	18.7864i		−	2.76990i
$47$	0.708712	−	0.409175i	0.103376	−	0.0596843i	−0.447421	−	0.894324i	$-0.647657\pi$
$47$	0.708712	−	0.409175i	0.103376	−	0.0596843i	0.550797	+	0.834639i	$0.314324\pi$
$48$		0			0
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	3.79129	+	2.18890i	0.536169	+	0.309557i
$51$		0			0
$52$	2.79129	−	9.66930i	0.387082	−	1.34089i
$53$	−3.08258	+	5.33918i	−0.423424	+	0.733392i	−0.996272	−	0.0862695i	$-0.972505\pi$
$53$	−3.08258	+	5.33918i	−0.423424	+	0.733392i	0.572848	+	0.819662i	$0.305839\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$	−2.29129	+	3.96863i	−0.306186	+	0.530330i
$57$		0			0
$58$	13.2695	+	7.66115i	1.74237	+	1.00596i
$59$		−	4.28245i		−	0.557528i	−0.960360	−	0.278764i	$-0.910075\pi$
$59$		−	4.28245i		−	0.557528i	0.960360	−	0.278764i	$-0.0899247\pi$
$60$		0			0
$61$	2.58258	−	4.47315i	0.330665	−	0.572728i	−0.651977	−	0.758238i	$-0.726060\pi$
$61$	2.58258	−	4.47315i	0.330665	−	0.572728i	0.982642	+	0.185510i	$0.0593937\pi$
$62$	6.68693	−	11.5821i	0.849241	−	1.47093i
$63$		0			0
$64$	12.5826			1.57282
$65$	−1.50000	−	6.06218i	−0.186052	−	0.751921i
$66$		0			0
$67$	−12.1652	+	7.02355i	−1.48621	+	0.858064i	−0.999877	−	0.0157098i	$-0.994999\pi$
$67$	−12.1652	+	7.02355i	−1.48621	+	0.858064i	−0.486333	+	0.873773i	$0.661666\pi$
$68$	2.79129			0.338493
$69$		0			0
$70$			10.0308i			1.19891i
$71$	3.87386	−	2.23658i	0.459743	−	0.265433i	−0.252193	−	0.967677i	$-0.581152\pi$
$71$	3.87386	−	2.23658i	0.459743	−	0.265433i	0.711936	+	0.702244i	$0.247819\pi$
$72$		0			0
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$	−15.3739			−1.78718
$75$		0			0
$76$	−12.7913	−	7.38505i	−1.46726	−	0.847124i
$77$	−9.16515			−1.04447
$78$		0			0
$79$	0.708712	+	1.22753i	0.0797363	+	0.138107i	0.903136	−	0.429354i	$-0.141259\pi$
$79$	0.708712	+	1.22753i	0.0797363	+	0.138107i	−0.823400	+	0.567462i	$0.807925\pi$
$80$	2.68693	−	1.55130i	0.300408	−	0.173441i
$81$		0			0
$82$	3.89564	−	6.74745i	0.430202	−	0.745132i
$83$			3.46410i			0.380235i	0.981761	+	0.190117i	$0.0608868\pi$
$83$			3.46410i			0.380235i	−0.981761	+	0.190117i	$0.939113\pi$
$84$		0			0
$85$	1.50000	−	0.866025i	0.162698	−	0.0939336i
$86$	−8.68693	+	5.01540i	−0.936736	+	0.540825i
$87$		0			0
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$			15.5885i			1.65237i	0.563397	+	0.826187i	$0.309494\pi$
$89$			15.5885i			1.65237i	−0.563397	+	0.826187i	$0.690506\pi$
$90$		0			0
$91$	−6.87386	+	6.61438i	−0.720577	+	0.693375i
$92$	−23.9564			−2.49763
$93$		0			0
$94$	−0.895644	−	1.55130i	−0.0923786	−	0.160004i
$95$	−9.16515			−0.940325
$96$		0			0
$97$	9.08258	−	5.24383i	0.922196	−	0.532430i	0.0378609	−	0.999283i	$-0.487946\pi$
$97$	9.08258	−	5.24383i	0.922196	−	0.532430i	0.884335	+	0.466853i	$0.154612\pi$
$98$	13.2695	−	7.66115i	1.34042	−	0.773893i
$99$		0			0
$100$	2.79129	−	4.83465i	0.279129	−	0.483465i
$101$	6.58258	+	11.4014i	0.654991	+	1.13448i	0.981896	+	0.189420i	$0.0606608\pi$
$101$	6.58258	+	11.4014i	0.654991	+	1.13448i	−0.326905	+	0.945057i	$0.606006\pi$
$102$		0			0
$103$	−1.70871	−	2.95958i	−0.168364	−	0.291616i	0.769481	−	0.638670i	$-0.220515\pi$
$103$	−1.70871	−	2.95958i	−0.168364	−	0.291616i	−0.937845	+	0.347055i	$0.887182\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$		0			0
$106$	11.6869	+	6.74745i	1.13514	+	0.655371i
$107$	1.41742			0.137028			0.0685138	−	0.997650i	$-0.478174\pi$
$107$	1.41742			0.137028			0.0685138	+	0.997650i	$0.478174\pi$
$108$		0			0
$109$	−16.6652	−	9.62163i	−1.59623	−	0.921585i	−0.992204	−	0.124622i	$-0.960228\pi$
$109$	−16.6652	−	9.62163i	−1.59623	−	0.921585i	−0.604028	−	0.796963i	$-0.706438\pi$
$110$	−11.3739	−	6.56670i	−1.08446	−	0.626111i
$111$		0			0
$112$	−4.10436	−	2.36965i	−0.387825	−	0.223911i
$113$	6.08258	+	10.5353i	0.572201	+	0.991080i	0.996340	+	0.0854834i	$0.0272435\pi$
$113$	6.08258	+	10.5353i	0.572201	+	0.991080i	−0.424139	+	0.905597i	$0.639423\pi$
$114$		0			0
$115$	−12.8739	+	7.43273i	−1.20049	+	0.693106i
$116$	9.76951	−	16.9213i	0.907076	−	1.57110i
$117$		0			0
$118$	−9.37386			−0.862934
$119$	−2.29129	−	1.32288i	−0.210042	−	0.121268i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	−9.79129	−	5.65300i	−0.886462	−	0.511799i
$123$		0			0
$124$	−14.7695	−	8.52718i	−1.32634	−	0.765763i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	−3.29129	+	5.70068i	−0.292055	+	0.505853i	−0.974295	−	0.225274i	$-0.927672\pi$
$127$	−3.29129	+	5.70068i	−0.292055	+	0.505853i	0.682241	+	0.731128i	$0.261006\pi$
$128$		−	12.7719i		−	1.12889i
$129$		0			0
$130$	−13.2695	+	3.28335i	−1.16381	+	0.287969i
$131$	0.708712	+	1.22753i	0.0619205	+	0.107249i	0.895324	−	0.445416i	$-0.146944\pi$
$131$	0.708712	+	1.22753i	0.0619205	+	0.107249i	−0.833403	+	0.552665i	$0.813611\pi$
$132$		0			0
$133$	7.00000	+	12.1244i	0.606977	+	1.05131i
$134$	15.3739	+	26.6283i	1.32810	+	2.30034i
$135$		0			0
$136$		−	1.73205i		−	0.148522i
$137$		−	8.66025i		−	0.739895i	−0.929053	−	0.369948i	$-0.879376\pi$
$137$		−	8.66025i		−	0.739895i	0.929053	−	0.369948i	$-0.120624\pi$
$138$		0			0
$139$	3.29129	+	5.70068i	0.279163	+	0.483525i	0.971177	−	0.238359i	$-0.0766096\pi$
$139$	3.29129	+	5.70068i	0.279163	+	0.483525i	−0.692014	+	0.721884i	$0.743276\pi$
$140$	12.7913			1.08106
$141$		0			0
$142$	−4.89564	−	8.47950i	−0.410833	−	0.711584i
$143$	−3.00000	−	12.1244i	−0.250873	−	1.01389i
$144$		0			0
$145$		−	12.1244i		−	1.00687i
$146$	−9.47822	+	16.4168i	−0.784423	+	1.35866i
$147$		0			0
$148$			19.6048i			1.61150i
$149$	−3.16515	−	1.82740i	−0.259299	−	0.149707i	0.364716	−	0.931119i	$-0.381166\pi$
$149$	−3.16515	−	1.82740i	−0.259299	−	0.149707i	−0.624015	+	0.781412i	$0.714500\pi$
$150$		0			0
$151$	14.4564	+	8.34643i	1.17645	+	0.679223i	0.955190	−	0.295993i	$-0.0956503\pi$
$151$	14.4564	+	8.34643i	1.17645	+	0.679223i	0.221258	+	0.975215i	$0.428984\pi$
$152$	−4.58258	+	7.93725i	−0.371696	+	0.643796i
$153$		0			0
$154$			20.0616i			1.61661i
$155$	−10.5826			−0.850013
$156$		0			0
$157$	−5.08258	+	8.80328i	−0.405634	+	0.702578i	−0.994395	−	0.105729i	$-0.966282\pi$
$157$	−5.08258	+	8.80328i	−0.405634	+	0.702578i	0.588761	+	0.808307i	$0.299616\pi$
$158$	2.68693	−	1.55130i	0.213761	−	0.123415i
$159$		0			0
$160$	−6.39564	−	11.0776i	−0.505620	−	0.875760i
$161$	19.6652	+	11.3537i	1.54983	+	0.894795i
$162$		0			0
$163$	3.00000	+	1.73205i	0.234978	+	0.135665i	0.612866	−	0.790186i	$-0.290016\pi$
$163$	3.00000	+	1.73205i	0.234978	+	0.135665i	−0.377888	+	0.925851i	$0.623350\pi$
$164$	−8.60436	−	4.96773i	−0.671887	−	0.387914i
$165$		0			0
$166$	7.58258			0.588522
$167$	−3.87386	−	2.23658i	−0.299769	−	0.173071i	0.342570	−	0.939492i	$-0.388702\pi$
$167$	−3.87386	−	2.23658i	−0.299769	−	0.173071i	−0.642339	+	0.766421i	$0.722036\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	−1.89564	−	3.28335i	−0.145389	−	0.251822i
$171$		0			0
$172$	6.39564	+	11.0776i	0.487663	+	0.844658i
$173$	12.1652	−	21.0707i	0.924899	−	1.60197i	0.133176	−	0.991092i	$-0.457482\pi$
$173$	12.1652	−	21.0707i	0.924899	−	1.60197i	0.791723	−	0.610880i	$-0.209184\pi$
$174$		0			0
$175$	−4.58258	+	2.64575i	−0.346410	+	0.200000i
$176$	5.37386	−	3.10260i	0.405070	−	0.233867i
$177$		0			0
$178$	34.1216			2.55752
$179$	0.417424	+	0.723000i	0.0311998	+	0.0540396i	0.881204	−	0.472737i	$-0.156734\pi$
$179$	0.417424	+	0.723000i	0.0311998	+	0.0540396i	−0.850004	+	0.526776i	$0.823401\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	14.4782	+	15.0462i	1.07320	+	1.11530i
$183$		0			0
$184$			14.8655i			1.09590i
$185$	6.08258	+	10.5353i	0.447200	+	0.774573i
$186$		0			0
$187$	3.00000	−	1.73205i	0.219382	−	0.126660i
$188$	−1.97822	+	1.14213i	−0.144276	+	0.0832981i
$189$		0			0
$190$			20.0616i			1.45542i
$191$	−7.16515	+	12.4104i	−0.518452	+	0.897985i	0.481318	+	0.876546i	$0.340158\pi$
$191$	−7.16515	+	12.4104i	−0.518452	+	0.897985i	−0.999770	+	0.0214394i	$0.993175\pi$
$192$		0			0
$193$	−3.16515	+	1.82740i	−0.227833	+	0.131539i	−0.609572	−	0.792731i	$-0.708659\pi$
$193$	−3.16515	+	1.82740i	−0.227833	+	0.131539i	0.381739	+	0.924270i	$0.375325\pi$
$194$	−11.4782	−	19.8809i	−0.824088	−	1.42736i
$195$		0			0
$196$	−9.76951	−	16.9213i	−0.697822	−	1.20866i
$197$	−15.2477	−	8.80328i	−1.08636	−	0.627208i	−0.153752	−	0.988110i	$-0.549136\pi$
$197$	−15.2477	−	8.80328i	−1.08636	−	0.627208i	−0.932604	+	0.360902i	$0.882469\pi$
$198$		0			0
$199$	2.58258			0.183074			0.0915370	−	0.995802i	$-0.470822\pi$
$199$	2.58258			0.183074			0.0915370	+	0.995802i	$0.470822\pi$
$200$	−3.00000	−	1.73205i	−0.212132	−	0.122474i
$201$		0			0
$202$	24.9564	−	14.4086i	1.75593	−	1.01379i
$203$	−16.0390	+	9.26013i	−1.12572	+	0.649934i
$204$		0			0
$205$	−6.16515			−0.430593
$206$	−6.47822	+	3.74020i	−0.451359	+	0.260592i
$207$		0			0
$208$	1.79129	−	6.20520i	0.124203	−	0.430253i
$209$	−18.3303			−1.26793
$210$		0			0
$211$	−3.29129	+	5.70068i	−0.226582	+	0.392451i	−0.956793	−	0.290771i	$-0.906088\pi$
$211$	−3.29129	+	5.70068i	−0.226582	+	0.392451i	0.730211	+	0.683222i	$0.239422\pi$
$212$	8.60436	−	14.9032i	0.590950	−	1.02355i
$213$		0			0
$214$		−	3.10260i		−	0.212089i
$215$	6.87386	+	3.96863i	0.468794	+	0.270658i
$216$		0			0
$217$	8.08258	+	13.9994i	0.548681	+	0.950343i
$218$	−21.0608	+	36.4784i	−1.42642	+	2.47063i
$219$		0			0
$220$	−8.37386	+	14.5040i	−0.564566	+	0.977857i
$221$	1.00000	−	3.46410i	0.0672673	−	0.233021i
$222$		0			0
$223$	−2.29129	−	1.32288i	−0.153436	−	0.0885863i	0.421316	−	0.906914i	$-0.361568\pi$
$223$	−2.29129	−	1.32288i	−0.153436	−	0.0885863i	−0.574752	+	0.818327i	$0.694902\pi$
$224$	−9.76951	+	16.9213i	−0.652753	+	1.13060i
$225$		0			0
$226$	23.0608	−	13.3142i	1.53398	−	0.885645i
$227$		−	27.2759i		−	1.81036i	−0.425026	−	0.905181i	$-0.639735\pi$
$227$		−	27.2759i		−	1.81036i	0.425026	−	0.905181i	$-0.360265\pi$
$228$		0			0
$229$	−9.08258	+	5.24383i	−0.600193	+	0.346522i	−0.769118	−	0.639107i	$-0.779304\pi$
$229$	−9.08258	+	5.24383i	−0.600193	+	0.346522i	0.168924	+	0.985629i	$0.445971\pi$
$230$	16.2695	+	28.1796i	1.07278	+	1.85811i
$231$		0			0
$232$	−10.5000	−	6.06218i	−0.689359	−	0.398001i
$233$	10.0826	+	17.4635i	0.660531	+	1.14407i	0.980476	+	0.196638i	$0.0630023\pi$
$233$	10.0826	+	17.4635i	0.660531	+	1.14407i	−0.319945	+	0.947436i	$0.603664\pi$
$234$		0			0
$235$	−0.708712	+	1.22753i	−0.0462313	+	0.0800749i
$236$			11.9536i			0.778110i
$237$		0			0
$238$	−2.89564	+	5.01540i	−0.187697	+	0.325100i
$239$		−	2.01810i		−	0.130540i	−0.997868	−	0.0652701i	$-0.979209\pi$
$239$		−	2.01810i		−	0.130540i	0.997868	−	0.0652701i	$-0.0207909\pi$
$240$		0			0
$241$		−	14.1425i		−	0.910996i	−0.890237	−	0.455498i	$-0.849461\pi$
$241$		−	14.1425i		−	0.910996i	0.890237	−	0.455498i	$-0.150539\pi$
$242$	−1.89564	−	1.09445i	−0.121857	−	0.0703539i
$243$		0			0
$244$	−7.20871	+	12.4859i	−0.461491	+	0.799325i
$245$	−10.5000	−	6.06218i	−0.670820	−	0.387298i
$246$		0			0
$247$	−13.7477	+	13.2288i	−0.874747	+	0.841726i
$248$	−5.29129	+	9.16478i	−0.335997	+	0.581964i
$249$		0			0
$250$	−26.5390			−1.67847
$251$	−10.2913	−	17.8250i	−0.649580	−	1.12511i	−0.983223	−	0.182407i	$-0.941611\pi$
$251$	−10.2913	−	17.8250i	−0.649580	−	1.12511i	0.333643	−	0.942700i	$-0.391722\pi$
$252$		0			0
$253$	−25.7477	+	14.8655i	−1.61875	+	0.934583i
$254$	12.4782	+	7.20430i	0.782953	+	0.452038i
$255$		0			0
$256$	−2.79129			−0.174455
$257$	9.33030			0.582008			0.291004	−	0.956722i	$-0.406011\pi$
$257$	9.33030			0.582008			0.291004	+	0.956722i	$0.406011\pi$
$258$		0			0
$259$	9.29129	−	16.0930i	0.577333	−	0.999969i
$260$	4.18693	+	16.9213i	0.259662	+	1.04941i
$261$		0			0
$262$	2.68693	−	1.55130i	0.165999	−	0.0958397i
$263$	−2.41742	−	4.18710i	−0.149065	−	0.258188i	0.781817	−	0.623508i	$-0.214293\pi$
$263$	−2.41742	−	4.18710i	−0.149065	−	0.258188i	−0.930882	+	0.365320i	$0.880960\pi$
$264$		0			0
$265$		−	10.6784i		−	0.655966i
$266$	26.5390	−	15.3223i	1.62721	−	0.939471i
$267$		0			0
$268$	33.9564	−	19.6048i	2.07422	−	1.19755i
$269$	−16.1652			−0.985607			−0.492803	−	0.870141i	$-0.664028\pi$
$269$	−16.1652			−0.985607			−0.492803	+	0.870141i	$0.664028\pi$
$270$		0			0
$271$		−	11.5921i		−	0.704167i	−0.935969	−	0.352084i	$-0.885473\pi$
$271$		−	11.5921i		−	0.704167i	0.935969	−	0.352084i	$-0.114527\pi$
$272$	1.79129			0.108613
$273$		0			0
$274$	−18.9564			−1.14520
$275$		−	6.92820i		−	0.417786i
$276$		0			0
$277$	9.33030			0.560604			0.280302	−	0.959912i	$-0.409565\pi$
$277$	9.33030			0.560604			0.280302	+	0.959912i	$0.409565\pi$
$278$	12.4782	−	7.20430i	0.748394	−	0.432085i
$279$		0			0
$280$		−	7.93725i		−	0.474342i
$281$		−	3.65480i		−	0.218027i	−0.994040	−	0.109014i	$-0.965231\pi$
$281$		−	3.65480i		−	0.218027i	0.994040	−	0.109014i	$-0.0347692\pi$
$282$		0			0
$283$	15.1652	+	26.2668i	0.901475	+	1.56140i	0.825581	+	0.564284i	$0.190848\pi$
$283$	15.1652	+	26.2668i	0.901475	+	1.56140i	0.0758940	+	0.997116i	$0.475819\pi$
$284$	−10.8131	+	6.24293i	−0.641638	+	0.370450i
$285$		0			0
$286$	−26.5390	+	6.56670i	−1.56928	+	0.388297i
$287$	4.70871	+	8.15573i	0.277946	+	0.481417i
$288$		0			0
$289$	−16.0000			−0.941176
$290$	−26.5390			−1.55842
$291$		0			0
$292$	20.9347	+	12.0866i	1.22511	+	0.707317i
$293$	−16.8303	+	9.71698i	−0.983237	+	0.567672i	−0.903246	−	0.429124i	$-0.858822\pi$
$293$	−16.8303	+	9.71698i	−0.983237	+	0.567672i	−0.0799910	+	0.996796i	$0.525489\pi$
$294$		0			0
$295$	3.70871	+	6.42368i	0.215930	+	0.374001i
$296$	12.1652			0.707085
$297$		0			0
$298$	−4.00000	+	6.92820i	−0.231714	+	0.401340i
$299$	−8.58258	+	29.7309i	−0.496343	+	1.71938i
$300$		0			0
$301$		−	12.1244i		−	0.698836i
$302$	18.2695	−	31.6437i	1.05129	−	1.82089i
$303$		0			0
$304$	−8.20871	−	4.73930i	−0.470802	−	0.271818i
$305$			8.94630i			0.512264i
$306$		0			0
$307$		−	20.9753i		−	1.19712i	−0.801076	−	0.598562i	$-0.795739\pi$
$307$		−	20.9753i		−	1.19712i	0.801076	−	0.598562i	$-0.204261\pi$
$308$	25.5826			1.45770
$309$		0			0
$310$			23.1642i			1.31564i
$311$	−4.29129	+	7.43273i	−0.243337	+	0.421471i	−0.961663	−	0.274235i	$-0.911575\pi$
$311$	−4.29129	+	7.43273i	−0.243337	+	0.421471i	0.718326	+	0.695707i	$0.244909\pi$
$312$		0			0
$313$	6.91742	+	11.9813i	0.390996	+	0.677225i	0.992581	−	0.121584i	$-0.0387973\pi$
$313$	6.91742	+	11.9813i	0.390996	+	0.677225i	−0.601585	+	0.798809i	$0.705464\pi$
$314$	19.2695	+	11.1253i	1.08744	+	0.627834i
$315$		0			0
$316$	−1.97822	−	3.42638i	−0.111284	−	0.192749i
$317$	1.66515	−	0.961376i	0.0935242	−	0.0539962i	−0.452508	−	0.891760i	$-0.649471\pi$
$317$	1.66515	−	0.961376i	0.0935242	−	0.0539962i	0.546033	+	0.837764i	$0.316137\pi$
$318$		0			0
$319$		−	24.2487i		−	1.35767i
$320$	−18.8739	+	10.8968i	−1.05508	+	0.609151i
$321$		0			0
$322$	24.8521	−	43.0451i	1.38495	−	2.39881i
$323$	−4.58258	−	2.64575i	−0.254981	−	0.147214i
$324$		0			0
$325$	−5.00000	−	5.19615i	−0.277350	−	0.288231i
$326$	3.79129	−	6.56670i	0.209980	−	0.363696i
$327$		0			0
$328$	−3.08258	+	5.33918i	−0.170207	+	0.294807i
$329$	2.16515			0.119369
$330$		0			0
$331$	−22.5826	−	13.0381i	−1.24125	−	0.716636i	−0.271902	−	0.962325i	$-0.587653\pi$
$331$	−22.5826	−	13.0381i	−1.24125	−	0.716636i	−0.969349	+	0.245689i	$0.920986\pi$
$332$		−	9.66930i		−	0.530672i
$333$		0			0
$334$	−4.89564	+	8.47950i	−0.267878	+	0.463978i
$335$	12.1652	−	21.0707i	0.664653	−	1.15121i
$336$		0			0
$337$	23.4955			1.27988			0.639939	−	0.768425i	$-0.278959\pi$
$337$	23.4955			1.27988			0.639939	+	0.768425i	$0.278959\pi$
$338$	−15.1652	+	24.0779i	−0.824875	+	1.30967i
$339$		0			0
$340$	−4.18693	+	2.41733i	−0.227068	+	0.131098i
$341$	−21.1652			−1.14616
$342$		0			0
$343$			18.5203i			1.00000i
$344$	6.87386	−	3.96863i	0.370614	−	0.213974i
$345$		0			0
$346$	−46.1216	−	26.6283i	−2.47951	−	1.43155i
$347$	25.7477			1.38221			0.691105	−	0.722754i	$-0.257124\pi$
$347$	25.7477			1.38221			0.691105	+	0.722754i	$0.257124\pi$
$348$		0			0
$349$	9.08258	+	5.24383i	0.486179	+	0.280696i	0.722988	−	0.690861i	$-0.242768\pi$
$349$	9.08258	+	5.24383i	0.486179	+	0.280696i	−0.236809	+	0.971556i	$0.576102\pi$
$350$	5.79129	+	10.0308i	0.309557	+	0.536169i
$351$		0			0
$352$	−12.7913	−	22.1552i	−0.681778	−	1.18087i
$353$	16.7477	−	9.66930i	0.891392	−	0.514645i	0.0169942	−	0.999856i	$-0.494590\pi$
$353$	16.7477	−	9.66930i	0.891392	−	0.514645i	0.874397	+	0.485210i	$0.161257\pi$
$354$		0			0
$355$	−3.87386	+	6.70973i	−0.205603	+	0.356115i
$356$		−	43.5119i		−	2.30612i
$357$		0			0
$358$	1.58258	−	0.913701i	0.0836417	−	0.0482906i
$359$	−16.0390	+	9.26013i	−0.846507	+	0.488731i	−0.859471	−	0.511185i	$-0.829207\pi$
$359$	−16.0390	+	9.26013i	−0.846507	+	0.488731i	0.0129639	+	0.999916i	$0.495873\pi$
$360$		0			0
$361$	4.50000	+	7.79423i	0.236842	+	0.410223i
$362$		−	48.1558i		−	2.53101i
$363$		0			0
$364$	19.1869	−	18.4626i	1.00567	−	0.967705i
$365$	15.0000			0.785136
$366$		0			0
$367$	−7.58258	−	13.1334i	−0.395807	−	0.685558i	0.597397	−	0.801946i	$-0.296202\pi$
$367$	−7.58258	−	13.1334i	−0.395807	−	0.685558i	−0.993204	+	0.116388i	$0.962868\pi$
$368$	−15.3739			−0.801418
$369$		0			0
$370$	23.0608	−	13.3142i	1.19887	−	0.692170i
$371$	−14.1261	+	8.15573i	−0.733392	+	0.423424i
$372$		0			0
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	−3.79129	−	6.56670i	−0.196043	−	0.339556i
$375$		0			0
$376$	0.708712	+	1.22753i	0.0365490	+	0.0633048i
$377$	−17.5000	−	18.1865i	−0.901296	−	0.936654i
$378$		0			0
$379$	16.0390	+	9.26013i	0.823869	+	0.475661i	0.851749	−	0.523950i	$-0.175542\pi$
$379$	16.0390	+	9.26013i	0.823869	+	0.475661i	−0.0278799	+	0.999611i	$0.508876\pi$
$380$	25.5826			1.31236
$381$		0			0
$382$	27.1652	+	15.6838i	1.38989	+	0.802453i
$383$	15.3303	+	8.85095i	0.783342	+	0.452263i	0.837613	−	0.546264i	$-0.183950\pi$
$383$	15.3303	+	8.85095i	0.783342	+	0.452263i	−0.0542715	+	0.998526i	$0.517284\pi$
$384$		0			0
$385$	13.7477	−	7.93725i	0.700649	−	0.404520i
$386$	4.00000	+	6.92820i	0.203595	+	0.352636i
$387$		0			0
$388$	−25.3521	+	14.6370i	−1.28706	+	0.743083i
$389$	13.6652	−	23.6687i	0.692851	−	1.20005i	−0.278049	−	0.960567i	$-0.589688\pi$
$389$	13.6652	−	23.6687i	0.692851	−	1.20005i	0.970900	−	0.239486i	$-0.0769788\pi$
$390$		0			0
$391$	−8.58258			−0.434040
$392$	−10.5000	+	6.06218i	−0.530330	+	0.306186i
$393$		0			0
$394$	−19.2695	+	33.3758i	−0.970784	+	1.68145i
$395$	−2.12614	−	1.22753i	−0.106978	−	0.0617635i
$396$		0			0
$397$	31.9129	+	18.4249i	1.60166	+	0.924720i	0.991155	+	0.132708i	$0.0423673\pi$
$397$	31.9129	+	18.4249i	1.60166	+	0.924720i	0.610506	+	0.792011i	$0.290966\pi$
$398$		−	5.65300i		−	0.283359i
$399$		0			0
$400$	1.79129	−	3.10260i	0.0895644	−	0.155130i
$401$		−	34.7364i		−	1.73465i	−0.497741	−	0.867326i	$-0.665837\pi$
$401$		−	34.7364i		−	1.73465i	0.497741	−	0.867326i	$-0.334163\pi$
$402$		0			0
$403$	−15.8739	+	15.2746i	−0.790733	+	0.760884i
$404$	−18.3739	−	31.8245i	−0.914134	−	1.58333i
$405$		0			0
$406$	20.2695	+	35.1078i	1.00596	+	1.74237i
$407$	12.1652	+	21.0707i	0.603004	+	1.04443i
$408$		0			0
$409$		−	31.2723i		−	1.54631i	−0.634215	−	0.773157i	$-0.718676\pi$
$409$		−	31.2723i		−	1.54631i	0.634215	−	0.773157i	$-0.281324\pi$
$410$			13.4949i			0.666466i
$411$		0			0
$412$	4.76951	+	8.26103i	0.234977	+	0.406992i
$413$	5.66515	−	9.81233i	0.278764	−	0.482833i
$414$		0			0
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	−25.5826	−	7.38505i	−1.25429	−	0.362082i
$417$		0			0
$418$			40.1232i			1.96249i
$419$	5.87386	−	10.1738i	0.286957	−	0.497024i	−0.686125	−	0.727484i	$-0.740690\pi$
$419$	5.87386	−	10.1738i	0.286957	−	0.497024i	0.973082	+	0.230460i	$0.0740230\pi$
$420$		0			0
$421$		−	40.5046i		−	1.97407i	−0.160492	−	0.987037i	$-0.551308\pi$
$421$		−	40.5046i		−	1.97407i	0.160492	−	0.987037i	$-0.448692\pi$
$422$	12.4782	+	7.20430i	0.607430	+	0.350700i
$423$		0			0
$424$	−9.24773	−	5.33918i	−0.449109	−	0.259293i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$	11.8348	−	6.83285i	0.572728	−	0.330665i
$428$	−3.95644			−0.191242
$429$		0			0
$430$	8.68693	−	15.0462i	0.418921	−	0.725593i
$431$	7.41742	−	4.28245i	0.357285	−	0.206278i	−0.310604	−	0.950539i	$-0.600531\pi$
$431$	7.41742	−	4.28245i	0.357285	−	0.206278i	0.667889	+	0.744261i	$0.267198\pi$
$432$		0			0
$433$	7.66515	+	13.2764i	0.368364	+	0.638025i	0.989310	−	0.145829i	$-0.0465848\pi$
$433$	7.66515	+	13.2764i	0.368364	+	0.638025i	−0.620946	+	0.783853i	$0.713251\pi$
$434$	30.6434	−	17.6920i	1.47093	−	0.849241i
$435$		0			0
$436$	46.5172	+	26.8567i	2.22777	+	1.28620i
$437$	39.3303	+	22.7074i	1.88142	+	1.08624i
$438$		0			0
$439$	−10.5826			−0.505079			−0.252539	−	0.967587i	$-0.581266\pi$
$439$	−10.5826			−0.505079			−0.252539	+	0.967587i	$0.581266\pi$
$440$	9.00000	+	5.19615i	0.429058	+	0.247717i
$441$		0			0
$442$	−7.58258	−	2.18890i	−0.360666	−	0.104115i
$443$	−2.87386	−	4.97768i	−0.136541	−	0.236497i	0.789644	−	0.613565i	$-0.210265\pi$
$443$	−2.87386	−	4.97768i	−0.136541	−	0.236497i	−0.926185	+	0.377069i	$0.876932\pi$
$444$		0			0
$445$	−13.5000	−	23.3827i	−0.639961	−	1.10845i
$446$	−2.89564	+	5.01540i	−0.137113	+	0.237486i
$447$		0			0
$448$	28.8303	+	16.6452i	1.36210	+	0.786411i
$449$	10.6652	−	6.15753i	0.503320	−	0.290592i	−0.226764	−	0.973950i	$-0.572815\pi$
$449$	10.6652	−	6.15753i	0.503320	−	0.290592i	0.730083	+	0.683358i	$0.239481\pi$
$450$		0			0
$451$	−12.3303			−0.580611
$452$	−16.9782	−	29.4071i	−0.798588	−	1.38320i
$453$		0			0
$454$	−59.7042			−2.80206
$455$	4.58258	−	15.8745i	0.214834	−	0.744208i
$456$		0			0
$457$		−	3.75015i		−	0.175425i	−0.996146	−	0.0877124i	$-0.972044\pi$
$457$		−	3.75015i		−	0.175425i	0.996146	−	0.0877124i	$-0.0279556\pi$
$458$	11.4782	+	19.8809i	0.536342	+	0.928972i
$459$		0			0
$460$	35.9347	−	20.7469i	1.67546	−	0.967328i
$461$	27.4129	−	15.8268i	1.27675	−	0.737129i	0.300497	−	0.953783i	$-0.402848\pi$
$461$	27.4129	−	15.8268i	1.27675	−	0.737129i	0.976248	+	0.216654i	$0.0695143\pi$
$462$		0			0
$463$		−	38.4865i		−	1.78862i	−0.447448	−	0.894310i	$-0.647667\pi$
$463$		−	38.4865i		−	1.78862i	0.447448	−	0.894310i	$-0.352333\pi$
$464$	6.26951	−	10.8591i	0.291055	−	0.504121i
$465$		0			0
$466$	38.2259	−	22.0698i	1.77078	−	1.02236i
$467$	−14.4564	−	25.0393i	−0.668964	−	1.15868i	−0.978194	−	0.207693i	$-0.933405\pi$
$467$	−14.4564	−	25.0393i	−0.668964	−	1.15868i	0.309230	−	0.950987i	$-0.399929\pi$
$468$		0			0
$469$	−37.1652			−1.71613
$470$	2.68693	+	1.55130i	0.123939	+	0.0715562i
$471$		0			0
$472$	7.41742			0.341415
$473$	13.7477	+	7.93725i	0.632121	+	0.364955i
$474$		0			0
$475$	−9.16515	+	5.29150i	−0.420526	+	0.242791i
$476$	6.39564	+	3.69253i	0.293144	+	0.169247i
$477$		0			0
$478$	−4.41742			−0.202048
$479$	−24.4955	+	14.1425i	−1.11923	+	0.646185i	−0.941203	−	0.337841i	$-0.890303\pi$
$479$	−24.4955	+	14.1425i	−1.11923	+	0.646185i	−0.178023	+	0.984026i	$0.556970\pi$
$480$		0			0
$481$	24.3303	+	7.02355i	1.10937	+	0.320246i
$482$	−30.9564			−1.41003
$483$		0			0
$484$	−1.39564	+	2.41733i	−0.0634384	+	0.109878i
$485$	−9.08258	+	15.7315i	−0.412419	+	0.714330i
$486$		0			0
$487$			11.0200i			0.499362i	0.968328	+	0.249681i	$0.0803257\pi$
$487$			11.0200i			0.499362i	−0.968328	+	0.249681i	$0.919674\pi$
$488$	7.74773	+	4.47315i	0.350723	+	0.202490i
$489$		0			0
$490$	−13.2695	+	22.9835i	−0.599455	+	1.03829i
$491$	1.87386	−	3.24563i	0.0845663	−	0.146473i	−0.820640	−	0.571445i	$-0.806383\pi$
$491$	1.87386	−	3.24563i	0.0845663	−	0.146473i	0.905206	+	0.424972i	$0.139716\pi$
$492$		0			0
$493$	3.50000	−	6.06218i	0.157632	−	0.273027i
$494$	28.9564	+	30.0924i	1.30281	+	1.35392i
$495$		0			0
$496$	−9.47822	−	5.47225i	−0.425585	−	0.245711i
$497$	11.8348			0.530866
$498$		0			0
$499$	−21.7087	+	12.5335i	−0.971815	+	0.561078i	−0.899789	−	0.436325i	$-0.856280\pi$
$499$	−21.7087	+	12.5335i	−0.971815	+	0.561078i	−0.0720262	+	0.997403i	$0.522947\pi$
$500$			33.8426i			1.51349i
$501$		0			0
$502$	−39.0172	+	22.5266i	−1.74142	+	1.00541i
$503$	0.873864	+	1.51358i	0.0389636	+	0.0674870i	0.884850	−	0.465877i	$-0.154261\pi$
$503$	0.873864	+	1.51358i	0.0389636	+	0.0674870i	−0.845886	+	0.533364i	$0.820928\pi$
$504$		0			0
$505$	−19.7477	−	11.4014i	−0.878762	−	0.507354i
$506$	32.5390	+	56.3592i	1.44654	+	2.50547i
$507$		0			0
$508$	9.18693	−	15.9122i	0.407604	−	0.705991i
$509$			27.9989i			1.24103i	0.784195	+	0.620514i	$0.213076\pi$
$509$			27.9989i			1.24103i	−0.784195	+	0.620514i	$0.786924\pi$
$510$		0			0
$511$	−11.4564	−	19.8431i	−0.506803	−	0.877809i
$512$		−	19.4340i		−	0.858868i
$513$		0			0
$514$		−	20.4231i		−	0.900825i
$515$	5.12614	+	2.95958i	0.225885	+	0.130415i
$516$		0			0
$517$	−1.41742	+	2.45505i	−0.0623382	+	0.107973i
$518$	−35.2259	−	20.3377i	−1.54774	−	0.893588i
$519$		0			0
$520$	10.5000	−	2.59808i	0.460455	−	0.113933i
$521$	1.66515	−	2.88413i	0.0729516	−	0.126356i	−0.827242	−	0.561846i	$-0.810091\pi$
$521$	1.66515	−	2.88413i	0.0729516	−	0.126356i	0.900194	+	0.435490i	$0.143425\pi$
$522$		0			0
$523$	−9.74773			−0.426238			−0.213119	−	0.977026i	$-0.568362\pi$
$523$	−9.74773			−0.426238			−0.213119	+	0.977026i	$0.568362\pi$
$524$	−1.97822	−	3.42638i	−0.0864189	−	0.149682i
$525$		0			0
$526$	−9.16515	+	5.29150i	−0.399620	+	0.230720i
$527$	−5.29129	−	3.05493i	−0.230492	−	0.133075i
$528$		0			0
$529$	50.6606			2.20264
$530$	−23.3739			−1.01530
$531$		0			0
$532$	−19.5390	−	33.8426i	−0.847124	−	1.46726i
$533$	−9.24773	+	8.89863i	−0.400564	+	0.385442i
$534$		0			0
$535$	−2.12614	+	1.22753i	−0.0919209	+	0.0530706i
$536$	−12.1652	−	21.0707i	−0.525455	−	0.910114i
$537$		0			0
$538$			35.3839i			1.52551i
$539$	−21.0000	−	12.1244i	−0.904534	−	0.522233i
$540$		0			0
$541$	7.33485	−	4.23478i	0.315350	−	0.182067i	−0.333968	−	0.942584i	$-0.608388\pi$
$541$	7.33485	−	4.23478i	0.315350	−	0.182067i	0.649318	+	0.760517i	$0.275054\pi$
$542$	−25.3739			−1.08990
$543$		0			0
$544$		−	7.38505i		−	0.316632i
$545$	33.3303			1.42771
$546$		0			0
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$			24.1733i			1.03263i
$549$		0			0
$550$	−15.1652			−0.646644
$551$	−32.0780	+	18.5203i	−1.36657	+	0.788990i
$552$		0			0
$553$			3.75015i			0.159473i
$554$		−	20.4231i		−	0.867695i
$555$		0			0
$556$	−9.18693	−	15.9122i	−0.389613	−	0.674829i
$557$	21.1652	−	12.2197i	0.896796	−	0.517766i	0.0206368	−	0.999787i	$-0.493431\pi$
$557$	21.1652	−	12.2197i	0.896796	−	0.517766i	0.876159	+	0.482021i	$0.160097\pi$
$558$		0			0
$559$	16.0390	−	3.96863i	0.678378	−	0.167855i
$560$	8.20871			0.346881
$561$		0			0
$562$	−8.00000			−0.337460
$563$	−5.41742			−0.228317			−0.114159	−	0.993463i	$-0.536417\pi$
$563$	−5.41742			−0.228317			−0.114159	+	0.993463i	$0.536417\pi$
$564$		0			0
$565$	−18.2477	−	10.5353i	−0.767688	−	0.443225i
$566$	57.4955	−	33.1950i	2.41671	−	1.39529i
$567$		0			0
$568$	3.87386	+	6.70973i	0.162544	+	0.281534i
$569$	5.33030			0.223458			0.111729	−	0.993739i	$-0.464361\pi$
$569$	5.33030			0.223458			0.111729	+	0.993739i	$0.464361\pi$
$570$		0			0
$571$	−23.8739	+	41.3507i	−0.999090	+	1.73047i	−0.462609	+	0.886562i	$0.653087\pi$
$571$	−23.8739	+	41.3507i	−0.999090	+	1.73047i	−0.536481	+	0.843913i	$0.680247\pi$
$572$	8.37386	+	33.8426i	0.350129	+	1.41503i
$573$		0			0
$574$	17.8521	−	10.3069i	0.745132	−	0.430202i
$575$	−8.58258	+	14.8655i	−0.357918	+	0.619932i
$576$		0			0
$577$	12.0826	+	6.97588i	0.503004	+	0.290410i	0.729953	−	0.683497i	$-0.239542\pi$
$577$	12.0826	+	6.97588i	0.503004	+	0.290410i	−0.226949	+	0.973907i	$0.572875\pi$
$578$			35.0224i			1.45674i
$579$		0			0
$580$			33.8426i			1.40524i
$581$	−4.58258	+	7.93725i	−0.190117	+	0.329293i
$582$		0			0
$583$		−	21.3567i		−	0.884505i
$584$	7.50000	−	12.9904i	0.310352	−	0.537546i
$585$		0			0
$586$	21.2695	+	36.8399i	0.878635	+	1.52184i
$587$	18.8739	+	10.8968i	0.779008	+	0.449760i	0.836079	−	0.548610i	$-0.184843\pi$
$587$	18.8739	+	10.8968i	0.779008	+	0.449760i	−0.0570708	+	0.998370i	$0.518176\pi$
$588$		0			0
$589$	16.1652	+	27.9989i	0.666073	+	1.15367i
$590$	14.0608	−	8.11800i	0.578874	−	0.334213i
$591$		0			0
$592$			12.5812i			0.517084i
$593$	15.2477	−	8.80328i	0.626149	−	0.361507i	−0.153110	−	0.988209i	$-0.548929\pi$
$593$	15.2477	−	8.80328i	0.626149	−	0.361507i	0.779259	+	0.626702i	$0.215596\pi$
$594$		0			0
$595$	4.58258			0.187867
$596$	8.83485	+	5.10080i	0.361889	+	0.208937i
$597$		0			0
$598$	65.0780	+	18.7864i	2.66124	+	0.768233i
$599$	4.12614	−	7.14668i	0.168589	−	0.292005i	−0.769335	−	0.638846i	$-0.779412\pi$
$599$	4.12614	−	7.14668i	0.168589	−	0.292005i	0.937924	+	0.346841i	$0.112745\pi$
$600$		0			0
$601$	−13.0826	+	22.6597i	−0.533649	+	0.924308i	0.465578	+	0.885007i	$0.345846\pi$
$601$	−13.0826	+	22.6597i	−0.533649	+	0.924308i	−0.999227	+	0.0393010i	$0.987487\pi$
$602$	−26.5390			−1.08165
$603$		0			0
$604$	−40.3521	−	23.2973i	−1.64190	−	0.947953i
$605$			1.73205i			0.0704179i
$606$		0			0
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−19.5390	+	33.8426i	−0.792412	+	1.37250i
$609$		0			0
$610$	19.5826			0.792875
$611$	0.708712	+	2.86423i	0.0286714	+	0.115874i
$612$		0			0
$613$	21.1652	−	12.2197i	0.854852	−	0.493549i	−0.00743271	−	0.999972i	$-0.502366\pi$
$613$	21.1652	−	12.2197i	0.854852	−	0.493549i	0.862285	+	0.506423i	$0.169033\pi$
$614$	−45.9129			−1.85289
$615$		0			0
$616$		−	15.8745i		−	0.639602i
$617$	18.2477	−	10.5353i	0.734626	−	0.424136i	−0.0854862	−	0.996339i	$-0.527244\pi$
$617$	18.2477	−	10.5353i	0.734626	−	0.424136i	0.820112	+	0.572203i	$0.193911\pi$
$618$		0			0
$619$	−1.03901	−	0.599876i	−0.0417615	−	0.0241110i	0.478974	−	0.877829i	$-0.341009\pi$
$619$	−1.03901	−	0.599876i	−0.0417615	−	0.0241110i	−0.520735	+	0.853718i	$0.674342\pi$
$620$	29.5390			1.18632
$621$		0			0
$622$	16.2695	+	9.39320i	0.652348	+	0.376633i
$623$	−20.6216	+	35.7176i	−0.826187	+	1.43100i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	26.2259	−	15.1416i	1.04820	−	0.605178i
$627$		0			0
$628$	14.1869	−	24.5725i	0.566120	−	0.980549i
$629$			7.02355i			0.280047i
$630$		0			0
$631$	−30.8739	+	17.8250i	−1.22907	+	0.709603i	−0.966835	−	0.255401i	$-0.917793\pi$
$631$	−30.8739	+	17.8250i	−1.22907	+	0.709603i	−0.262234	+	0.965004i	$0.584459\pi$
$632$	−2.12614	+	1.22753i	−0.0845732	+	0.0488283i
$633$		0			0
$634$	−2.10436	−	3.64485i	−0.0835747	−	0.144756i
$635$		−	11.4014i		−	0.452449i
$636$		0			0
$637$	−24.5000	+	6.06218i	−0.970725	+	0.240192i
$638$	−53.0780			−2.10138
$639$		0			0
$640$	11.0608	+	19.1579i	0.437216	+	0.757281i
$641$	16.4955			0.651531			0.325766	−	0.945451i	$-0.394378\pi$
$641$	16.4955			0.651531			0.325766	+	0.945451i	$0.394378\pi$
$642$		0			0
$643$	29.4564	−	17.0067i	1.16165	−	0.670678i	0.209950	−	0.977712i	$-0.432670\pi$
$643$	29.4564	−	17.0067i	1.16165	−	0.670678i	0.951699	+	0.307034i	$0.0993365\pi$
$644$	−54.8911	−	31.6914i	−2.16301	−	1.24882i
$645$		0			0
$646$	−5.79129	+	10.0308i	−0.227855	+	0.394657i
$647$	−19.1652	−	33.1950i	−0.753460	−	1.30503i	−0.946136	−	0.323768i	$-0.895050\pi$
$647$	−19.1652	−	33.1950i	−0.753460	−	1.30503i	0.192677	−	0.981262i	$-0.438283\pi$
$648$		0			0
$649$	7.41742	+	12.8474i	0.291159	+	0.504303i
$650$	−11.3739	+	10.9445i	−0.446120	+	0.429279i
$651$		0			0
$652$	−8.37386	−	4.83465i	−0.327946	−	0.189340i
$653$	−26.4955			−1.03685			−0.518424	−	0.855124i	$-0.673481\pi$
$653$	−26.4955			−1.03685			−0.518424	+	0.855124i	$0.673481\pi$
$654$		0			0
$655$	−2.12614	−	1.22753i	−0.0830750	−	0.0479634i
$656$	−5.52178	−	3.18800i	−0.215589	−	0.124471i
$657$		0			0
$658$		−	4.73930i		−	0.184757i
$659$	10.0390	+	17.3881i	0.391064	+	0.677344i	0.992590	−	0.121510i	$-0.0387736\pi$
$659$	10.0390	+	17.3881i	0.391064	+	0.677344i	−0.601526	+	0.798853i	$0.705440\pi$
$660$		0			0
$661$	4.74773	−	2.74110i	0.184665	−	0.106616i	−0.404818	−	0.914397i	$-0.632665\pi$
$661$	4.74773	−	2.74110i	0.184665	−	0.106616i	0.589483	+	0.807781i	$0.299332\pi$
$662$	−28.5390	+	49.4310i	−1.10920	+	1.92119i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	−21.0000	−	12.1244i	−0.814345	−	0.470162i
$666$		0			0
$667$	−30.0390	+	52.0291i	−1.16312	+	2.01457i
$668$	10.8131	+	6.24293i	0.418370	+	0.241546i
$669$		0			0
$670$	−46.1216	−	26.6283i	−1.78183	−	1.02874i
$671$			17.8926i			0.690737i
$672$		0			0
$673$	17.6652	−	30.5969i	0.680942	−	1.17943i	−0.293752	−	0.955882i	$-0.594904\pi$
$673$	17.6652	−	30.5969i	0.680942	−	1.17943i	0.974694	−	0.223544i	$-0.0717626\pi$
$674$		−	51.4292i		−	1.98098i
$675$		0			0
$676$	30.7042	+	19.3386i	1.18093	+	0.743793i
$677$	14.9174	+	25.8377i	0.573323	+	0.993025i	0.996222	+	0.0868478i	$0.0276794\pi$
$677$	14.9174	+	25.8377i	0.573323	+	0.993025i	−0.422898	+	0.906177i	$0.638987\pi$
$678$		0			0
$679$	27.7477			1.06486
$680$	1.50000	+	2.59808i	0.0575224	+	0.0996317i
$681$		0			0
$682$			46.3284i			1.77401i
$683$			39.1142i			1.49666i	0.663325	+	0.748331i	$0.269145\pi$
$683$			39.1142i			1.49666i	−0.663325	+	0.748331i	$0.730855\pi$
$684$		0			0
$685$	7.50000	+	12.9904i	0.286560	+	0.496337i
$686$	40.5390			1.54779
$687$		0			0
$688$	4.10436	+	7.10895i	0.156477	+	0.271026i
$689$	−15.4129	−	16.0175i	−0.587184	−	0.610219i
$690$		0			0
$691$		−	7.55585i		−	0.287438i	−0.989619	−	0.143719i	$-0.954094\pi$
$691$		−	7.55585i		−	0.287438i	0.989619	−	0.143719i	$-0.0459062\pi$
$692$	−33.9564	+	58.8143i	−1.29083	+	2.23578i
$693$		0			0
$694$		−	56.3592i		−	2.13937i
$695$	−9.87386	−	5.70068i	−0.374537	−	0.216239i
$696$		0			0
$697$	−3.08258	−	1.77973i	−0.116761	−	0.0674119i
$698$	11.4782	−	19.8809i	0.434457	−	0.752502i
$699$		0			0
$700$	12.7913	−	7.38505i	0.483465	−	0.279129i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$		0			0
$703$	18.5826	−	32.1860i	0.700855	−	1.21392i
$704$	−37.7477	+	21.7937i	−1.42267	+	0.821379i
$705$		0			0
$706$	−21.1652	−	36.6591i	−0.796561	−	1.37968i
$707$			34.8317i			1.30998i
$708$		0			0
$709$	25.5826	+	14.7701i	0.960774	+	0.554703i	0.896411	−	0.443224i	$-0.146165\pi$
$709$	25.5826	+	14.7701i	0.960774	+	0.554703i	0.0643627	+	0.997927i	$0.479499\pi$
$710$	14.6869	+	8.47950i	0.551191	+	0.318230i
$711$		0			0
$712$	−27.0000			−1.01187
$713$	45.4129	+	26.2191i	1.70073	+	0.981914i
$714$		0			0
$715$	15.0000	+	15.5885i	0.560968	+	0.582975i
$716$	−1.16515	−	2.01810i	−0.0435438	−	0.0754200i
$717$		0			0
$718$	20.2695	+	35.1078i	0.756451	+	1.31021i
$719$	−17.1652	+	29.7309i	−0.640152	+	1.10878i	0.345246	+	0.938512i	$0.387795\pi$
$719$	−17.1652	+	29.7309i	−0.640152	+	1.10878i	−0.985398	+	0.170264i	$0.945538\pi$
$720$		0			0
$721$		−	9.04165i		−	0.336729i
$722$	17.0608	−	9.85005i	0.634937	−	0.366581i
$723$		0			0
$724$	−61.4083			−2.28222
$725$	−7.00000	−	12.1244i	−0.259973	−	0.450287i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−11.4564	−	11.9059i	−0.424604	−	0.441261i
$729$		0			0
$730$		−	32.8335i		−	1.21522i
$731$	2.29129	+	3.96863i	0.0847463	+	0.146785i
$732$		0			0
$733$	−25.8303	+	14.9131i	−0.954064	+	0.550829i	−0.894341	−	0.447386i	$-0.852355\pi$
$733$	−25.8303	+	14.9131i	−0.954064	+	0.550829i	−0.0597230	+	0.998215i	$0.519022\pi$
$734$	−28.7477	+	16.5975i	−1.06110	+	0.612625i
$735$		0			0
$736$			63.3828i			2.33632i
$737$	24.3303	−	42.1413i	0.896218	−	1.55230i
$738$		0			0
$739$	16.5826	−	9.57395i	0.610000	−	0.352184i	−0.162966	−	0.986632i	$-0.552106\pi$
$739$	16.5826	−	9.57395i	0.610000	−	0.352184i	0.772965	+	0.634448i	$0.218773\pi$
$740$	−16.9782	−	29.4071i	−0.624132	−	1.08103i
$741$		0			0
$742$	17.8521	+	30.9207i	0.655371	+	1.13514i
$743$	−6.70871	−	3.87328i	−0.246119	−	0.142097i	0.371867	−	0.928286i	$-0.378718\pi$
$743$	−6.70871	−	3.87328i	−0.246119	−	0.142097i	−0.617986	+	0.786189i	$0.712051\pi$
$744$		0			0
$745$	6.33030			0.231924
$746$	−49.2867	−	28.4557i	−1.80452	−	1.04184i
$747$		0			0
$748$	−8.37386	+	4.83465i	−0.306179	+	0.176772i
$749$	3.24773	+	1.87508i	0.118669	+	0.0685138i
$750$		0			0
$751$	−12.9129			−0.471198			−0.235599	−	0.971850i	$-0.575705\pi$
$751$	−12.9129			−0.471198			−0.235599	+	0.971850i	$0.575705\pi$
$752$	−1.26951	+	0.732950i	−0.0462942	+	0.0267280i
$753$		0			0
$754$	−39.8085	+	38.3058i	−1.44974	+	1.39501i
$755$	−28.9129			−1.05225
$756$		0			0
$757$	−2.24773	+	3.89318i	−0.0816950	+	0.141500i	−0.903978	−	0.427579i	$-0.859367\pi$
$757$	−2.24773	+	3.89318i	−0.0816950	+	0.141500i	0.822283	+	0.569079i	$0.192700\pi$
$758$	20.2695	−	35.1078i	0.736222	−	1.27517i
$759$		0			0
$760$		−	15.8745i		−	0.575829i
$761$	1.25227	+	0.723000i	0.0453949	+	0.0262087i	0.522526	−	0.852624i	$-0.324990\pi$
$761$	1.25227	+	0.723000i	0.0453949	+	0.0262087i	−0.477131	+	0.878832i	$0.658323\pi$
$762$		0			0
$763$	−25.4564	−	44.0918i	−0.921585	−	1.59623i
$764$	20.0000	−	34.6410i	0.723575	−	1.25327i
$765$		0			0
$766$	19.3739	−	33.5565i	0.700006	−	1.21245i
$767$	14.8348	+	4.28245i	0.535655	+	0.154630i
$768$		0			0
$769$	−2.91742	−	1.68438i	−0.105205	−	0.0607401i	0.446474	−	0.894796i	$-0.352679\pi$
$769$	−2.91742	−	1.68438i	−0.105205	−	0.0607401i	−0.551679	+	0.834056i	$0.686013\pi$
$770$	−17.3739	−	30.0924i	−0.626111	−	1.08446i
$771$		0			0
$772$	8.83485	−	5.10080i	0.317973	−	0.183582i
$773$			24.5348i			0.882454i	0.897396	+	0.441227i	$0.145457\pi$
$773$			24.5348i			0.882454i	−0.897396	+	0.441227i	$0.854543\pi$
$774$		0			0
$775$	−10.5826	+	6.10985i	−0.380137	+	0.219472i
$776$	9.08258	+	15.7315i	0.326045	+	0.564727i
$777$		0			0
$778$	−51.8085	−	29.9117i	−1.85743	−	1.07239i
$779$	9.41742	+	16.3115i	0.337414	+	0.584419i
$780$		0			0
$781$	−7.74773	+	13.4195i	−0.277235	+	0.480186i
$782$			18.7864i			0.671801i
$783$		0			0
$784$	−6.26951	−	10.8591i	−0.223911	−	0.387825i
$785$		−	17.6066i		−	0.628405i
$786$		0			0
$787$			30.3586i			1.08217i	0.840969	+	0.541083i	$0.181986\pi$
$787$			30.3586i			1.08217i	−0.840969	+	0.541083i	$0.818014\pi$
$788$	42.5608	+	24.5725i	1.51617	+	0.875359i
$789$		0			0
$790$	−2.68693	+	4.65390i	−0.0955967	+	0.165578i
$791$			32.1860i			1.14440i
$792$		0			0
$793$	12.9129	+	13.4195i	0.458550	+	0.476539i
$794$	40.3303	−	69.8541i	1.43127	−	2.47903i
$795$		0			0
$796$	−7.20871			−0.255506
$797$	12.0826	+	20.9276i	0.427987	+	0.741295i	0.996694	−	0.0812451i	$-0.0258896\pi$
$797$	12.0826	+	20.9276i	0.427987	+	0.741295i	−0.568707	+	0.822540i	$0.692556\pi$
$798$		0			0
$799$	−0.708712	+	0.409175i	−0.0250724	+	0.0144756i
$800$	−12.7913	−	7.38505i	−0.452240	−	0.261101i
$801$		0			0
$802$	−76.0345			−2.68487
$803$	30.0000			1.05868
$804$		0			0
$805$	−39.3303			−1.38621
$806$	33.4347	+	34.7463i	1.17769	+	1.22389i
$807$		0			0
$808$	−19.7477	+	11.4014i	−0.694723	+	0.401098i
$809$	−16.5826	−	28.7219i	−0.583012	−	1.00981i	−0.995120	−	0.0986718i	$-0.968541\pi$
$809$	−16.5826	−	28.7219i	−0.583012	−	1.00981i	0.412108	−	0.911135i	$-0.364793\pi$
$810$		0			0
$811$			0.190700i			0.00669640i	0.999994	+	0.00334820i	$0.00106577\pi$
$811$			0.190700i			0.00669640i	−0.999994	+	0.00334820i	$0.998934\pi$
$812$	44.7695	−	25.8477i	1.57110	−	0.907076i
$813$		0			0
$814$	46.1216	−	26.6283i	1.61656	−	0.933322i
$815$	−6.00000			−0.210171
$816$		0			0
$817$		−	24.2487i		−	0.848355i
$818$	−68.4519			−2.39336
$819$		0			0
$820$	17.2087			0.600954
$821$		−	38.3912i		−	1.33986i	−0.742424	−	0.669931i	$-0.766324\pi$
$821$		−	38.3912i		−	1.33986i	0.742424	−	0.669931i	$-0.233676\pi$
$822$		0			0
$823$	30.5826			1.06604			0.533021	−	0.846102i	$-0.321057\pi$
$823$	30.5826			1.06604			0.533021	+	0.846102i	$0.321057\pi$
$824$	5.12614	−	2.95958i	0.178577	−	0.103102i
$825$		0			0
$826$	−21.4782	−	12.4005i	−0.747323	−	0.431467i
$827$		−	36.6591i		−	1.27476i	−0.770549	−	0.637381i	$-0.780018\pi$
$827$		−	36.6591i		−	1.27476i	0.770549	−	0.637381i	$-0.219982\pi$
$828$		0			0
$829$	23.3303	+	40.4093i	0.810295	+	1.40347i	0.912658	+	0.408725i	$0.134026\pi$
$829$	23.3303	+	40.4093i	0.810295	+	1.40347i	−0.102363	+	0.994747i	$0.532640\pi$
$830$	−11.3739	+	6.56670i	−0.394793	+	0.227934i
$831$		0			0
$832$	−12.5826	+	43.5873i	−0.436222	+	1.51112i
$833$	−3.50000	−	6.06218i	−0.121268	−	0.210042i
$834$		0			0
$835$	7.74773			0.268121
$836$	51.1652			1.76958
$837$		0			0
$838$	−22.2695	−	12.8573i	−0.769287	−	0.444148i
$839$	23.1261	−	13.3519i	0.798403	−	0.460958i	−0.0445095	−	0.999009i	$-0.514172\pi$
$839$	23.1261	−	13.3519i	0.798403	−	0.460958i	0.842912	+	0.538051i	$0.180839\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	−88.6606			−3.05545
$843$		0			0
$844$	9.18693	−	15.9122i	0.316227	−	0.547722i
$845$	22.5000	+	0.866025i	0.774024	+	0.0297922i
$846$		0			0
$847$	2.29129	−	1.32288i	0.0787296	−	0.0454545i
$848$	5.52178	−	9.56400i	0.189619	−	0.328429i
$849$		0			0
$850$	−3.79129	−	2.18890i	−0.130040	−	0.0750787i
$851$		−	60.2802i		−	2.06638i
$852$		0			0
$853$			30.9862i			1.06095i	0.847701	+	0.530474i	$0.177986\pi$
$853$			30.9862i			1.06095i	−0.847701	+	0.530474i	$0.822014\pi$
$854$	−14.9564	−	25.9053i	−0.511799	−	0.886462i
$855$		0			0
$856$			2.45505i			0.0839119i
$857$	5.66515	−	9.81233i	0.193518	−	0.335183i	−0.752896	−	0.658140i	$-0.771344\pi$
$857$	5.66515	−	9.81233i	0.193518	−	0.335183i	0.946414	+	0.322957i	$0.104677\pi$
$858$		0			0
$859$	23.4564	+	40.6277i	0.800323	+	1.38620i	0.919403	+	0.393316i	$0.128672\pi$
$859$	23.4564	+	40.6277i	0.800323	+	1.38620i	−0.119080	+	0.992885i	$0.537994\pi$
$860$	−19.1869	−	11.0776i	−0.654269	−	0.377742i
$861$		0			0
$862$	−9.37386	−	16.2360i	−0.319275	−	0.553001i
$863$	17.4564	−	10.0785i	0.594224	−	0.343075i	−0.172542	−	0.985002i	$-0.555198\pi$
$863$	17.4564	−	10.0785i	0.594224	−	0.343075i	0.766766	+	0.641927i	$0.221865\pi$
$864$		0			0
$865$			42.1413i			1.43285i
$866$	29.0608	−	16.7783i	0.987526	−	0.570148i
$867$		0			0
$868$	−22.5608	−	39.0764i	−0.765763	−	1.32634i
$869$	−4.25227	−	2.45505i	−0.144248	−	0.0832819i
$870$		0			0
$871$	−12.1652	−	49.1649i	−0.412200	−	1.66589i
$872$	16.6652	−	28.8649i	0.564353	−	0.977488i
$873$		0			0
$874$	49.7042	−	86.0901i	1.68127	−	2.91204i
$875$	16.0390	−	27.7804i	0.542218	−	0.939149i
$876$		0			0
$877$	−13.9129	−	8.03260i	−0.469805	−	0.271242i	0.246353	−	0.969180i	$-0.420768\pi$
$877$	−13.9129	−	8.03260i	−0.469805	−	0.271242i	−0.716158	+	0.697938i	$0.754101\pi$
$878$			23.1642i			0.781754i
$879$		0			0
$880$	−5.37386	+	9.30780i	−0.181153	+	0.313766i
$881$	9.24773	−	16.0175i	0.311564	−	0.539644i	−0.667137	−	0.744935i	$-0.732481\pi$
$881$	9.24773	−	16.0175i	0.311564	−	0.539644i	0.978701	+	0.205290i	$0.0658139\pi$
$882$		0			0
$883$	50.3303			1.69375			0.846875	−	0.531792i	$-0.178481\pi$
$883$	50.3303			1.69375			0.846875	+	0.531792i	$0.178481\pi$
$884$	−2.79129	+	9.66930i	−0.0938812	+	0.325214i
$885$		0			0
$886$	−10.8956	+	6.29060i	−0.366046	+	0.211337i
$887$	37.4174			1.25635			0.628177	−	0.778070i	$-0.283801\pi$
$887$	37.4174			1.25635			0.628177	+	0.778070i	$0.283801\pi$
$888$		0			0
$889$	−15.0826	+	8.70793i	−0.505853	+	0.292055i
$890$	−51.1824	+	29.5502i	−1.71564	+	0.990524i
$891$		0			0
$892$	6.39564	+	3.69253i	0.214142	+	0.123635i
$893$	4.33030			0.144908
$894$		0			0
$895$	−1.25227	−	0.723000i	−0.0418589	−	0.0241672i
$896$	16.8956	−	29.2641i	0.564444	−	0.977645i
$897$		0			0
$898$	−13.4782	−	23.3450i	−0.449774	−	0.779031i
$899$	−37.0390	+	21.3845i	−1.23532	+	0.713213i
$900$		0			0
$901$	3.08258	−	5.33918i	0.102695	−	0.177874i
$902$			26.9898i			0.898662i
$903$		0			0
$904$	−18.2477	+	10.5353i	−0.606910	+	0.350400i
$905$	−33.0000	+	19.0526i	−1.09696	+	0.633328i
$906$		0			0
$907$	−4.41742	−	7.65120i	−0.146678	−	0.254054i	0.783320	−	0.621619i	$-0.213525\pi$
$907$	−4.41742	−	7.65120i	−0.146678	−	0.254054i	−0.929998	+	0.367565i	$0.880192\pi$
$908$			76.1348i			2.52662i
$909$		0			0
$910$	−34.7477	−	10.0308i	−1.15188	−	0.332518i
$911$	−48.6606			−1.61220			−0.806099	−	0.591781i	$-0.798425\pi$
$911$	−48.6606			−1.61220			−0.806099	+	0.591781i	$0.798425\pi$
$912$		0			0
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−8.20871			−0.271520
$915$		0			0
$916$	25.3521	−	14.6370i	0.837656	−	0.483621i
$917$			3.75015i			0.123841i
$918$		0			0
$919$	2.41742	−	4.18710i	0.0797435	−	0.138120i	−0.823396	−	0.567468i	$-0.807923\pi$
$919$	2.41742	−	4.18710i	0.0797435	−	0.138120i	0.903139	+	0.429348i	$0.141257\pi$
$920$	−12.8739	−	22.2982i	−0.424439	−	0.735149i
$921$		0			0
$922$	−34.6434	−	60.0041i	−1.14092	−	1.97613i
$923$	3.87386	+	15.6560i	0.127510	+	0.515325i
$924$		0			0
$925$	12.1652	+	7.02355i	0.399988	+	0.230933i
$926$	−84.2432			−2.76840
$927$		0			0
$928$	−44.7695	−	25.8477i	−1.46963	−	0.848492i
$929$	36.6606	+	21.1660i	1.20280	+	0.694434i	0.961176	−	0.275937i	$-0.0889880\pi$
$929$	36.6606	+	21.1660i	1.20280	+	0.694434i	0.241620	+	0.970371i	$0.422321\pi$
$930$		0			0
$931$			37.0405i			1.21395i
$932$	−28.1434	−	48.7457i	−0.921867	−	1.59672i
$933$		0			0
$934$	−54.8085	+	31.6437i	−1.79339	+	1.03541i
$935$	−3.00000	+	5.19615i	−0.0981105	+	0.169932i
$936$		0			0
$937$	0.504546			0.0164828			0.00824140	−	0.999966i	$-0.497377\pi$
$937$	0.504546			0.0164828			0.00824140	+	0.999966i	$0.497377\pi$
$938$			81.3508i			2.65620i
$939$		0			0
$940$	1.97822	−	3.42638i	0.0645224	−	0.111756i
$941$	28.8303	+	16.6452i	0.939841	+	0.542617i	0.889910	−	0.456135i	$-0.150767\pi$
$941$	28.8303	+	16.6452i	0.939841	+	0.542617i	0.0499305	+	0.998753i	$0.484100\pi$
$942$		0			0
$943$	26.4564	+	15.2746i	0.861540	+	0.497410i
$944$			7.67110i			0.249673i
$945$		0			0
$946$	17.3739	−	30.0924i	0.564873	−	0.978389i
$947$			15.0562i			0.489259i	0.969617	+	0.244630i	$0.0786664\pi$
$947$			15.0562i			0.489259i	−0.969617	+	0.244630i	$0.921334\pi$
$948$		0			0
$949$	22.5000	−	21.6506i	0.730381	−	0.702809i
$950$	11.5826	+	20.0616i	0.375788	+	0.650885i
$951$		0			0
$952$	2.29129	−	3.96863i	0.0742611	−	0.128624i
$953$	23.6652	+	40.9892i	0.766589	+	1.32777i	0.939402	+	0.342817i	$0.111381\pi$
$953$	23.6652	+	40.9892i	0.766589	+	1.32777i	−0.172813	+	0.984955i	$0.555286\pi$
$954$		0			0
$955$		−	24.8208i		−	0.803183i
$956$			5.63310i			0.182188i
$957$		0			0
$958$	30.9564	+	53.6181i	1.00016	+	1.73232i
$959$	11.4564	−	19.8431i	0.369948	−	0.640768i
$960$		0			0
$961$	3.16515	+	5.48220i	0.102102	+	0.176845i
$962$	15.3739	−	53.2566i	0.495673	−	1.71706i
$963$		0			0
$964$			39.4757i			1.27143i
$965$	3.16515	−	5.48220i	0.101890	−	0.176478i
$966$		0			0
$967$		−	5.29150i		−	0.170163i	−0.996374	−	0.0850816i	$-0.972885\pi$
$967$		−	5.29150i		−	0.170163i	0.996374	−	0.0850816i	$-0.0271151\pi$
$968$	1.50000	+	0.866025i	0.0482118	+	0.0278351i
$969$		0			0
$970$	34.4347	+	19.8809i	1.10563	+	0.638336i
$971$	25.1652	−	43.5873i	0.807588	−	1.39878i	−0.106942	−	0.994265i	$-0.534106\pi$
$971$	25.1652	−	43.5873i	0.807588	−	1.39878i	0.914530	−	0.404518i	$-0.132561\pi$
$972$		0			0
$973$			17.4159i			0.558327i
$974$	24.1216			0.772906
$975$		0			0
$976$	−4.62614	+	8.01270i	−0.148079	+	0.256480i
$977$	−3.16515	+	1.82740i	−0.101262	+	0.0584637i	−0.549776	−	0.835312i	$-0.685287\pi$
$977$	−3.16515	+	1.82740i	−0.101262	+	0.0584637i	0.448514	+	0.893776i	$0.351954\pi$
$978$		0			0
$979$	−27.0000	−	46.7654i	−0.862924	−	1.49463i
$980$	29.3085	+	16.9213i	0.936226	+	0.540531i
$981$		0			0
$982$	−7.10436	−	4.10170i	−0.226709	−	0.130891i
$983$	−20.2913	−	11.7152i	−0.647192	−	0.373656i	0.140188	−	0.990125i	$-0.455229\pi$
$983$	−20.2913	−	11.7152i	−0.647192	−	0.373656i	−0.787379	+	0.616469i	$0.788563\pi$
$984$		0			0
$985$	30.4955			0.971666
$986$	−13.2695	−	7.66115i	−0.422587	−	0.243981i
$987$		0			0
$988$	38.3739	−	36.9253i	1.22084	−	1.17475i
$989$	−19.6652	−	34.0610i	−0.625315	−	1.08308i
$990$		0			0
$991$	−16.3303	−	28.2849i	−0.518749	−	0.898500i	−0.999763	−	0.0217867i	$-0.993065\pi$
$991$	−16.3303	−	28.2849i	−0.518749	−	0.898500i	0.481013	−	0.876713i	$-0.340269\pi$
$992$	−22.5608	+	39.0764i	−0.716306	+	1.24068i
$993$		0			0
$994$		−	25.9053i		−	0.821667i
$995$	−3.87386	+	2.23658i	−0.122810	+	0.0709042i
$996$		0			0
$997$	−47.3303			−1.49897			−0.749483	−	0.662024i	$-0.769698\pi$
$997$	−47.3303			−1.49897			−0.749483	+	0.662024i	$0.769698\pi$
$998$	27.4347	+	47.5182i	0.868429	+	1.50416i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.d.550.1		4
3.2	odd	2		273.2.t.b.4.2	✓	4
7.2	even	3		819.2.do.d.667.1		4
13.10	even	6		819.2.do.d.361.1		4
21.2	odd	6		273.2.bl.b.121.2	yes	4
39.23	odd	6		273.2.bl.b.88.2	yes	4
91.23	even	6	inner	819.2.bm.d.478.2		4
273.23	odd	6		273.2.t.b.205.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.2	✓	4	3.2	odd	2
273.2.t.b.205.1	yes	4	273.23	odd	6
273.2.bl.b.88.2	yes	4	39.23	odd	6
273.2.bl.b.121.2	yes	4	21.2	odd	6
819.2.bm.d.478.2		4	91.23	even	6	inner
819.2.bm.d.550.1		4	1.1	even	1	trivial
819.2.do.d.361.1		4	13.10	even	6
819.2.do.d.667.1		4	7.2	even	3

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.18890i q^{2} -2.79129 q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +1.73205i q^{8} +O(q^{10})\)	\(q-2.18890i q^{2} -2.79129 q^{4} +(-1.50000 + 0.866025i) q^{5} +(2.29129 + 1.32288i) q^{7} +1.73205i q^{8} +(1.89564 + 3.28335i) q^{10} +(-3.00000 + 1.73205i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(2.89564 - 5.01540i) q^{14} -1.79129 q^{16} -1.00000 q^{17} +(4.58258 + 2.64575i) q^{19} +(4.18693 - 2.41733i) q^{20} +(3.79129 + 6.56670i) q^{22} +8.58258 q^{23} +(-1.00000 + 1.73205i) q^{25} +(7.58258 + 2.18890i) q^{26} +(-6.39564 - 3.69253i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(5.29129 + 3.05493i) q^{31} +7.38505i q^{32} +2.18890i q^{34} -4.58258 q^{35} -7.02355i q^{37} +(5.79129 - 10.0308i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(3.08258 + 1.77973i) q^{41} +(-2.29129 - 3.96863i) q^{43} +(8.37386 - 4.83465i) q^{44} -18.7864i q^{46} +(0.708712 - 0.409175i) q^{47} +(3.50000 + 6.06218i) q^{49} +(3.79129 + 2.18890i) q^{50} +(2.79129 - 9.66930i) q^{52} +(-3.08258 + 5.33918i) q^{53} +(3.00000 - 5.19615i) q^{55} +(-2.29129 + 3.96863i) q^{56} +(13.2695 + 7.66115i) q^{58} -4.28245i q^{59} +(2.58258 - 4.47315i) q^{61} +(6.68693 - 11.5821i) q^{62} +12.5826 q^{64} +(-1.50000 - 6.06218i) q^{65} +(-12.1652 + 7.02355i) q^{67} +2.79129 q^{68} +10.0308i q^{70} +(3.87386 - 2.23658i) q^{71} +(-7.50000 - 4.33013i) q^{73} -15.3739 q^{74} +(-12.7913 - 7.38505i) q^{76} -9.16515 q^{77} +(0.708712 + 1.22753i) q^{79} +(2.68693 - 1.55130i) q^{80} +(3.89564 - 6.74745i) q^{82} +3.46410i q^{83} +(1.50000 - 0.866025i) q^{85} +(-8.68693 + 5.01540i) q^{86} +(-3.00000 - 5.19615i) q^{88} +15.5885i q^{89} +(-6.87386 + 6.61438i) q^{91} -23.9564 q^{92} +(-0.895644 - 1.55130i) q^{94} -9.16515 q^{95} +(9.08258 - 5.24383i) q^{97} +(13.2695 - 7.66115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} - 6 q^{5}+O(q^{10}) \) 4 * q - 2 * q^4 - 6 * q^5	\( 4 q - 2 q^{4} - 6 q^{5} + 3 q^{10} - 12 q^{11} - 4 q^{13} + 7 q^{14} + 2 q^{16} - 4 q^{17} + 3 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 12 q^{26} - 21 q^{28} - 14 q^{29} + 12 q^{31} + 14 q^{38} - 6 q^{40} - 6 q^{41} + 6 q^{44} + 12 q^{47} + 14 q^{49} + 6 q^{50} + 2 q^{52} + 6 q^{53} + 12 q^{55} + 21 q^{58} - 8 q^{61} + 13 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 2 q^{68} - 12 q^{71} - 30 q^{73} - 34 q^{74} - 42 q^{76} + 12 q^{79} - 3 q^{80} + 11 q^{82} + 6 q^{85} - 21 q^{86} - 12 q^{88} - 50 q^{92} + q^{94} + 18 q^{97} + 21 q^{98}+O(q^{100}) \) 4 * q - 2 * q^4 - 6 * q^5 + 3 * q^10 - 12 * q^11 - 4 * q^13 + 7 * q^14 + 2 * q^16 - 4 * q^17 + 3 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 12 * q^26 - 21 * q^28 - 14 * q^29 + 12 * q^31 + 14 * q^38 - 6 * q^40 - 6 * q^41 + 6 * q^44 + 12 * q^47 + 14 * q^49 + 6 * q^50 + 2 * q^52 + 6 * q^53 + 12 * q^55 + 21 * q^58 - 8 * q^61 + 13 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 2 * q^68 - 12 * q^71 - 30 * q^73 - 34 * q^74 - 42 * q^76 + 12 * q^79 - 3 * q^80 + 11 * q^82 + 6 * q^85 - 21 * q^86 - 12 * q^88 - 50 * q^92 + q^94 + 18 * q^97 + 21 * q^98

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