LMFDB - Embedded newform 819.2.do.d.667.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (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			667.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	819.667
Dual form			819.2.do.d.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89564 + 1.09445i) q^{2} +(1.39564 - 2.41733i) q^{4} +(1.50000 + 0.866025i) q^{5} -2.64575i q^{7} +1.73205i q^{8} +O(q^{10})$	\(q+(-1.89564 + 1.09445i) q^{2} +(1.39564 - 2.41733i) q^{4} +(1.50000 + 0.866025i) q^{5} -2.64575i q^{7} +1.73205i q^{8} -3.79129 q^{10} -3.46410i q^{11} +(-1.00000 + 3.46410i) q^{13} +(2.89564 + 5.01540i) q^{14} +(0.895644 + 1.55130i) q^{16} +(0.500000 - 0.866025i) q^{17} -5.29150i q^{19} +(4.18693 - 2.41733i) q^{20} +(3.79129 + 6.56670i) q^{22} +(-4.29129 - 7.43273i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(-1.89564 - 7.66115i) q^{26} +(-6.39564 - 3.69253i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(-5.29129 + 3.05493i) q^{31} +(-6.39564 - 3.69253i) q^{32} +2.18890i q^{34} +(2.29129 - 3.96863i) q^{35} +(-6.08258 + 3.51178i) q^{37} +(5.79129 + 10.0308i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(3.08258 + 1.77973i) q^{41} +(-2.29129 - 3.96863i) q^{43} +(-8.37386 - 4.83465i) q^{44} +(16.2695 + 9.39320i) q^{46} +(-0.708712 - 0.409175i) q^{47} -7.00000 q^{49} +(3.79129 + 2.18890i) q^{50} +(6.97822 + 7.25198i) q^{52} +(-3.08258 - 5.33918i) q^{53} +(3.00000 - 5.19615i) q^{55} +4.58258 q^{56} -15.3223i q^{58} +(3.70871 + 2.14123i) q^{59} -5.16515 q^{61} +(6.68693 - 11.5821i) q^{62} +12.5826 q^{64} +(-4.50000 + 4.33013i) q^{65} -14.0471i q^{67} +(-1.39564 - 2.41733i) q^{68} +10.0308i q^{70} +(3.87386 - 2.23658i) q^{71} +(7.50000 - 4.33013i) q^{73} +(7.68693 - 13.3142i) q^{74} +(-12.7913 - 7.38505i) q^{76} -9.16515 q^{77} +(0.708712 - 1.22753i) q^{79} +3.10260i q^{80} -7.79129 q^{82} +3.46410i q^{83} +(1.50000 - 0.866025i) q^{85} +(8.68693 + 5.01540i) q^{86} +6.00000 q^{88} +(13.5000 - 7.79423i) q^{89} +(9.16515 + 2.64575i) q^{91} -23.9564 q^{92} +1.79129 q^{94} +(4.58258 - 7.93725i) q^{95} +(9.08258 - 5.24383i) q^{97} +(13.2695 - 7.66115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + q^{4} + 6 q^{5}+O(q^{10}) $ 4 * q - 3 * q^2 + q^4 + 6 * q^5	$ 4 q - 3 q^{2} + q^{4} + 6 q^{5} - 6 q^{10} - 4 q^{13} + 7 q^{14} - q^{16} + 2 q^{17} + 3 q^{20} + 6 q^{22} - 8 q^{23} - 4 q^{25} - 3 q^{26} - 21 q^{28} - 14 q^{29} - 12 q^{31} - 21 q^{32} - 6 q^{37} + 14 q^{38} - 6 q^{40} - 6 q^{41} - 6 q^{44} + 33 q^{46} - 12 q^{47} - 28 q^{49} + 6 q^{50} + 5 q^{52} + 6 q^{53} + 12 q^{55} + 24 q^{59} + 16 q^{61} + 13 q^{62} + 32 q^{64} - 18 q^{65} - q^{68} - 12 q^{71} + 30 q^{73} + 17 q^{74} - 42 q^{76} + 12 q^{79} - 22 q^{82} + 6 q^{85} + 21 q^{86} + 24 q^{88} + 54 q^{89} - 50 q^{92} - 2 q^{94} + 18 q^{97} + 21 q^{98}+O(q^{100}) $ 4 * q - 3 * q^2 + q^4 + 6 * q^5 - 6 * q^10 - 4 * q^13 + 7 * q^14 - q^16 + 2 * q^17 + 3 * q^20 + 6 * q^22 - 8 * q^23 - 4 * q^25 - 3 * q^26 - 21 * q^28 - 14 * q^29 - 12 * q^31 - 21 * q^32 - 6 * q^37 + 14 * q^38 - 6 * q^40 - 6 * q^41 - 6 * q^44 + 33 * q^46 - 12 * q^47 - 28 * q^49 + 6 * q^50 + 5 * q^52 + 6 * q^53 + 12 * q^55 + 24 * q^59 + 16 * q^61 + 13 * q^62 + 32 * q^64 - 18 * q^65 - q^68 - 12 * q^71 + 30 * q^73 + 17 * q^74 - 42 * q^76 + 12 * q^79 - 22 * q^82 + 6 * q^85 + 21 * q^86 + 24 * q^88 + 54 * q^89 - 50 * q^92 - 2 * q^94 + 18 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.89564	+	1.09445i	−1.34042	+	0.773893i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−1.89564	+	1.09445i	−1.34042	+	0.773893i	−0.353553	+	0.935414i	$0.615027\pi$
$3$		0			0
$3$		0			0
$4$	1.39564	−	2.41733i	0.697822	−	1.20866i
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$		0			0
$7$		−	2.64575i		−	1.00000i
$7$		−	2.64575i		−	1.00000i
$8$			1.73205i			0.612372i
$9$		0			0
$10$	−3.79129			−1.19891
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$		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
$16$	0.895644	+	1.55130i	0.223911	+	0.387825i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	−0.799000	−	0.601331i	$-0.794637\pi$
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i	0.920268	+	0.391289i	$0.127971\pi$
$18$		0			0
$19$		−	5.29150i		−	1.21395i	−0.794719	−	0.606977i	$-0.792382\pi$
$19$		−	5.29150i		−	1.21395i	0.794719	−	0.606977i	$-0.207618\pi$
$20$	4.18693	−	2.41733i	0.936226	−	0.540531i
$21$		0			0
$22$	3.79129	+	6.56670i	0.808305	+	1.40003i
$23$	−4.29129	−	7.43273i	−0.894795	−	1.54983i	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−4.29129	−	7.43273i	−0.894795	−	1.54983i	−0.0607377	−	0.998154i	$-0.519345\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−1.89564	−	7.66115i	−0.371766	−	1.50248i
$27$		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	$-0.851537\pi$
$31$	−5.29129	+	3.05493i	−0.950343	+	0.548681i	−0.0571558	+	0.998365i	$0.518203\pi$
$32$	−6.39564	−	3.69253i	−1.13060	−	0.652753i
$33$		0			0
$34$			2.18890i			0.375393i
$35$	2.29129	−	3.96863i	0.387298	−	0.670820i
$36$		0			0
$37$	−6.08258	+	3.51178i	−0.999969	+	0.577333i	−0.908239	−	0.418451i	$-0.862573\pi$
$37$	−6.08258	+	3.51178i	−0.999969	+	0.577333i	−0.0917301	+	0.995784i	$0.529240\pi$
$38$	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
$46$	16.2695	+	9.39320i	2.39881	+	1.38495i
$47$	−0.708712	−	0.409175i	−0.103376	−	0.0596843i	0.447421	−	0.894324i	$-0.352343\pi$
$47$	−0.708712	−	0.409175i	−0.103376	−	0.0596843i	−0.550797	+	0.834639i	$0.685676\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$	3.79129	+	2.18890i	0.536169	+	0.309557i
$51$		0			0
$52$	6.97822	+	7.25198i	0.967705	+	1.00567i
$53$	−3.08258	−	5.33918i	−0.423424	−	0.733392i	0.572848	−	0.819662i	$-0.305839\pi$
$53$	−3.08258	−	5.33918i	−0.423424	−	0.733392i	−0.996272	+	0.0862695i	$0.972505\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$	4.58258			0.612372
$57$		0			0
$58$		−	15.3223i		−	2.01192i
$59$	3.70871	+	2.14123i	0.482833	+	0.278764i	0.721596	−	0.692314i	$-0.243409\pi$
$59$	3.70871	+	2.14123i	0.482833	+	0.278764i	−0.238763	+	0.971078i	$0.576742\pi$
$60$		0			0
$61$	−5.16515			−0.661330			−0.330665	−	0.943748i	$-0.607273\pi$
$61$	−5.16515			−0.661330			−0.330665	+	0.943748i	$0.607273\pi$
$62$	6.68693	−	11.5821i	0.849241	−	1.47093i
$63$		0			0
$64$	12.5826			1.57282
$65$	−4.50000	+	4.33013i	−0.558156	+	0.537086i
$66$		0			0
$67$		−	14.0471i		−	1.71613i	−0.513543	−	0.858064i	$-0.671667\pi$
$67$		−	14.0471i		−	1.71613i	0.513543	−	0.858064i	$-0.328333\pi$
$68$	−1.39564	−	2.41733i	−0.169247	−	0.293144i
$69$		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	$-0.497494\pi$
$73$	7.50000	−	4.33013i	0.877809	−	0.506803i	0.869935	+	0.493166i	$0.164160\pi$
$74$	7.68693	−	13.3142i	0.893588	−	1.54774i
$75$		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	−0.823400	−	0.567462i	$-0.807925\pi$
$79$	0.708712	−	1.22753i	0.0797363	−	0.138107i	0.903136	+	0.429354i	$0.141259\pi$
$80$			3.10260i			0.346881i
$81$		0			0
$82$	−7.79129			−0.860404
$83$			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
$88$	6.00000			0.639602
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.433800	−	0.901009i	$-0.357172\pi$
$89$	13.5000	−	7.79423i	1.43100	−	0.826187i	0.997197	+	0.0748225i	$0.0238390\pi$
$90$		0			0
$91$	9.16515	+	2.64575i	0.960769	+	0.277350i
$92$	−23.9564			−2.49763
$93$		0			0
$94$	1.79129			0.184757
$95$	4.58258	−	7.93725i	0.470162	−	0.814345i
$96$		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
$100$	−5.58258			−0.558258
$101$	−13.1652			−1.30998			−0.654991	−	0.755637i	$-0.727327\pi$
$101$	−13.1652			−1.30998			−0.654991	+	0.755637i	$0.727327\pi$
$102$		0			0
$103$	−1.70871	+	2.95958i	−0.168364	+	0.291616i	−0.937845	−	0.347055i	$-0.887182\pi$
$103$	−1.70871	+	2.95958i	−0.168364	+	0.291616i	0.769481	+	0.638670i	$0.220515\pi$
$104$	−6.00000	−	1.73205i	−0.588348	−	0.169842i
$105$		0			0
$106$	11.6869	+	6.74745i	1.13514	+	0.655371i
$107$	−0.708712	−	1.22753i	−0.0685138	−	0.118669i	0.829733	−	0.558160i	$-0.188492\pi$
$107$	−0.708712	−	1.22753i	−0.0685138	−	0.118669i	−0.898247	+	0.439490i	$0.855159\pi$
$108$		0			0
$109$	16.6652	−	9.62163i	1.59623	−	0.921585i	0.604028	−	0.796963i	$-0.293562\pi$
$109$	16.6652	−	9.62163i	1.59623	−	0.921585i	0.992204	−	0.124622i	$-0.0397717\pi$
$110$			13.1334i			1.25222i
$111$		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
$115$		−	14.8655i		−	1.38621i
$116$	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
$121$	−1.00000			−0.0909091
$122$	9.79129	−	5.65300i	0.886462	−	0.511799i
$123$		0			0
$124$			17.0544i			1.53153i
$125$		−	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	$0.261006\pi$
$128$	−11.0608	+	6.38595i	−0.977645	+	0.564444i
$129$		0			0
$130$	3.79129	−	13.1334i	0.332518	−	1.15188i
$131$	0.708712	−	1.22753i	0.0619205	−	0.107249i	−0.833403	−	0.552665i	$-0.813611\pi$
$131$	0.708712	−	1.22753i	0.0619205	−	0.107249i	0.895324	+	0.445416i	$0.146944\pi$
$132$		0			0
$133$	−14.0000			−1.21395
$134$	15.3739	+	26.6283i	1.32810	+	2.30034i
$135$		0			0
$136$	1.50000	+	0.866025i	0.128624	+	0.0742611i
$137$	7.50000	+	4.33013i	0.640768	+	0.369948i	0.784910	−	0.619609i	$-0.212709\pi$
$137$	7.50000	+	4.33013i	0.640768	+	0.369948i	−0.144142	+	0.989557i	$0.546042\pi$
$138$		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	$0.743276\pi$
$140$	−6.39564	−	11.0776i	−0.540531	−	0.936226i
$141$		0			0
$142$	−4.89564	+	8.47950i	−0.410833	+	0.711584i
$143$	12.0000	+	3.46410i	1.00349	+	0.289683i
$144$		0			0
$145$	−10.5000	+	6.06218i	−0.871978	+	0.503436i
$146$	−9.47822	+	16.4168i	−0.784423	+	1.35866i
$147$		0			0
$148$			19.6048i			1.61150i
$149$			3.65480i			0.299413i	0.988730	+	0.149707i	$0.0478329\pi$
$149$			3.65480i			0.299413i	−0.988730	+	0.149707i	$0.952167\pi$
$150$		0			0
$151$	−14.4564	+	8.34643i	−1.17645	+	0.679223i	−0.955190	−	0.295993i	$-0.904350\pi$
$151$	−14.4564	+	8.34643i	−1.17645	+	0.679223i	−0.221258	+	0.975215i	$0.571016\pi$
$152$	9.16515			0.743392
$153$		0			0
$154$	17.3739	−	10.0308i	1.40003	−	0.808305i
$155$	−10.5826			−0.850013
$156$		0			0
$157$	−5.08258	−	8.80328i	−0.405634	−	0.702578i	0.588761	−	0.808307i	$-0.299616\pi$
$157$	−5.08258	−	8.80328i	−0.405634	−	0.702578i	−0.994395	+	0.105729i	$0.966282\pi$
$158$			3.10260i			0.246830i
$159$		0			0
$160$	−6.39564	−	11.0776i	−0.505620	−	0.875760i
$161$	−19.6652	+	11.3537i	−1.54983	+	0.894795i
$162$		0			0
$163$		−	3.46410i		−	0.271329i	−0.990755	−	0.135665i	$-0.956683\pi$
$163$		−	3.46410i		−	0.271329i	0.990755	−	0.135665i	$-0.0433170\pi$
$164$	8.60436	−	4.96773i	0.671887	−	0.387914i
$165$		0			0
$166$	−3.79129	−	6.56670i	−0.294261	−	0.509675i
$167$	−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
$172$	−12.7913			−0.975327
$173$	−24.3303			−1.84980			−0.924899	−	0.380212i	$-0.875851\pi$
$173$	−24.3303			−1.84980			−0.924899	+	0.380212i	$0.875851\pi$
$174$		0			0
$175$	−4.58258	+	2.64575i	−0.346410	+	0.200000i
$176$	5.37386	−	3.10260i	0.405070	−	0.233867i
$177$		0			0
$178$	−17.0608	+	29.5502i	−1.27876	+	2.21488i
$179$	−0.834849			−0.0623995			−0.0311998	−	0.999513i	$-0.509933\pi$
$179$	−0.834849			−0.0623995			−0.0311998	+	0.999513i	$0.509933\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	−20.2695	+	5.01540i	−1.50248	+	0.371766i
$183$		0			0
$184$	12.8739	−	7.43273i	0.949074	−	0.547948i
$185$	−12.1652			−0.894400
$186$		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
$191$	14.3303			1.03690			0.518452	−	0.855107i	$-0.326508\pi$
$191$	14.3303			1.03690			0.518452	+	0.855107i	$0.326508\pi$
$192$		0			0
$193$		−	3.65480i		−	0.263078i	−0.991311	−	0.131539i	$-0.958008\pi$
$193$		−	3.65480i		−	0.263078i	0.991311	−	0.131539i	$-0.0419919\pi$
$194$	−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
$199$	−1.29129	+	2.23658i	−0.0915370	+	0.158547i	−0.908158	−	0.418627i	$-0.862511\pi$
$199$	−1.29129	+	2.23658i	−0.0915370	+	0.158547i	0.816621	+	0.577174i	$0.195845\pi$
$200$	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
$205$	3.08258	+	5.33918i	0.215296	+	0.372904i
$206$		−	7.48040i		−	0.521184i
$207$		0			0
$208$	−6.26951	+	1.55130i	−0.434712	+	0.107563i
$209$	−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	$0.239422\pi$
$212$	−17.2087			−1.18190
$213$		0			0
$214$	2.68693	+	1.55130i	0.183675	+	0.106045i
$215$		−	7.93725i		−	0.541316i
$216$		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
$221$	2.50000	+	2.59808i	0.168168	+	0.174766i
$222$		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
$227$	23.6216	+	13.6379i	1.56782	+	0.905181i	0.996423	+	0.0845077i	$0.0269317\pi$
$227$	23.6216	+	13.6379i	1.56782	+	0.905181i	0.571397	+	0.820674i	$0.306402\pi$
$228$		0			0
$229$	9.08258	+	5.24383i	0.600193	+	0.346522i	0.769118	−	0.639107i	$-0.220696\pi$
$229$	9.08258	+	5.24383i	0.600193	+	0.346522i	−0.168924	+	0.985629i	$0.554029\pi$
$230$	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	−0.319945	−	0.947436i	$-0.603664\pi$
$233$	10.0826	−	17.4635i	0.660531	−	1.14407i	0.980476	−	0.196638i	$-0.0630023\pi$
$234$		0			0
$235$	−0.708712	−	1.22753i	−0.0462313	−	0.0800749i
$236$	10.3521	−	5.97678i	0.673863	−	0.389055i
$237$		0			0
$238$	5.79129			0.375393
$239$		−	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
$241$	12.2477	+	7.07123i	0.788945	+	0.455498i	0.839591	−	0.543219i	$-0.182795\pi$
$241$	12.2477	+	7.07123i	0.788945	+	0.455498i	−0.0506457	+	0.998717i	$0.516128\pi$
$242$	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
$247$	18.3303	+	5.29150i	1.16633	+	0.336690i
$248$	−5.29129	−	9.16478i	−0.335997	−	0.581964i
$249$		0			0
$250$	13.2695	+	22.9835i	0.839237	+	1.45360i
$251$	−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
$254$		−	14.4086i		−	0.904076i
$255$		0			0
$256$	1.39564	−	2.41733i	0.0872277	−	0.151083i
$257$	−4.66515	−	8.08028i	−0.291004	−	0.504034i	0.683043	−	0.730378i	$-0.260656\pi$
$257$	−4.66515	−	8.08028i	−0.291004	−	0.504034i	−0.974047	+	0.226344i	$0.927323\pi$
$258$		0			0
$259$	9.29129	+	16.0930i	0.577333	+	0.999969i
$260$	4.18693	+	16.9213i	0.259662	+	1.04941i
$261$		0			0
$262$			3.10260i			0.191679i
$263$	4.83485			0.298130			0.149065	−	0.988827i	$-0.452374\pi$
$263$	4.83485			0.298130			0.149065	+	0.988827i	$0.452374\pi$
$264$		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
$269$	8.08258	−	13.9994i	0.492803	−	0.853560i	−0.507162	−	0.861851i	$-0.669306\pi$
$269$	8.08258	−	13.9994i	0.492803	−	0.853560i	0.999966	+	0.00829015i	$0.00263887\pi$
$270$		0			0
$271$	−10.0390	+	5.79603i	−0.609827	+	0.352084i	−0.772898	−	0.634531i	$-0.781193\pi$
$271$	−10.0390	+	5.79603i	−0.609827	+	0.352084i	0.163071	+	0.986614i	$0.447860\pi$
$272$	1.79129			0.108613
$273$		0			0
$274$	−18.9564			−1.14520
$275$	−6.00000	+	3.46410i	−0.361814	+	0.208893i
$276$		0			0
$277$	−4.66515	+	8.08028i	−0.280302	+	0.485497i	−0.971459	−	0.237208i	$-0.923768\pi$
$277$	−4.66515	+	8.08028i	−0.280302	+	0.485497i	0.691157	+	0.722704i	$0.257101\pi$
$278$	−12.4782	−	7.20430i	−0.748394	−	0.432085i
$279$		0			0
$280$	6.87386	+	3.96863i	0.410792	+	0.237171i
$281$		−	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
$283$	−30.3303			−1.80295			−0.901475	−	0.432832i	$-0.857514\pi$
$283$	−30.3303			−1.80295			−0.901475	+	0.432832i	$0.857514\pi$
$284$		−	12.4859i		−	0.740899i
$285$		0			0
$286$	−26.5390	+	6.56670i	−1.56928	+	0.388297i
$287$	4.70871	−	8.15573i	0.277946	−	0.481417i
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	13.2695	−	22.9835i	0.779212	−	1.34964i
$291$		0			0
$292$		−	24.1733i		−	1.41463i
$293$	−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
$296$	−6.08258	−	10.5353i	−0.353543	−	0.612354i
$297$		0			0
$298$	−4.00000	−	6.92820i	−0.231714	−	0.401340i
$299$	30.0390	−	7.43273i	1.73720	−	0.429846i
$300$		0			0
$301$	−10.5000	+	6.06218i	−0.605210	+	0.349418i
$302$	18.2695	−	31.6437i	1.05129	−	1.82089i
$303$		0			0
$304$	8.20871	−	4.73930i	0.470802	−	0.271818i
$305$	−7.74773	−	4.47315i	−0.443634	−	0.256132i
$306$		0			0
$307$		−	20.9753i		−	1.19712i	−0.801076	−	0.598562i	$-0.795739\pi$
$307$		−	20.9753i		−	1.19712i	0.801076	−	0.598562i	$-0.204261\pi$
$308$	−12.7913	+	22.1552i	−0.728851	+	1.26241i
$309$		0			0
$310$	20.0608	−	11.5821i	1.13938	−	0.657819i
$311$	−4.29129	−	7.43273i	−0.243337	−	0.421471i	0.718326	−	0.695707i	$-0.244909\pi$
$311$	−4.29129	−	7.43273i	−0.243337	−	0.421471i	−0.961663	+	0.274235i	$0.911575\pi$
$312$		0			0
$313$	6.91742	−	11.9813i	0.390996	−	0.677225i	−0.601585	−	0.798809i	$-0.705464\pi$
$313$	6.91742	−	11.9813i	0.390996	−	0.677225i	0.992581	+	0.121584i	$0.0387973\pi$
$314$	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	$-0.350529\pi$
$317$	−1.66515	−	0.961376i	−0.0935242	−	0.0539962i	−0.546033	+	0.837764i	$0.683863\pi$
$318$		0			0
$319$	21.0000	+	12.1244i	1.17577	+	0.678834i
$320$	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
$325$	7.00000	−	1.73205i	0.388290	−	0.0960769i
$326$	3.79129	+	6.56670i	0.209980	+	0.363696i
$327$		0			0
$328$	−3.08258	+	5.33918i	−0.170207	+	0.294807i
$329$	−1.08258	+	1.87508i	−0.0596843	+	0.103376i
$330$		0			0
$331$			26.0761i			1.43327i	0.697447	+	0.716636i	$0.254319\pi$
$331$			26.0761i			1.43327i	−0.697447	+	0.716636i	$0.745681\pi$
$332$	8.37386	+	4.83465i	0.459575	+	0.265336i
$333$		0			0
$334$	9.79129			0.535755
$335$	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	$0.278959\pi$
$338$	28.4347	+	1.09445i	1.54664	+	0.0595303i
$339$		0			0
$340$		−	4.83465i		−	0.262196i
$341$	10.5826	+	18.3296i	0.573079	+	0.992601i
$342$		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
$347$	−12.8739	+	22.2982i	−0.691105	+	1.19703i	0.280371	+	0.959892i	$0.409543\pi$
$347$	−12.8739	+	22.2982i	−0.691105	+	1.19703i	−0.971476	+	0.237138i	$0.923791\pi$
$348$		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
$353$			19.3386i			1.02929i	0.857403	+	0.514645i	$0.172076\pi$
$353$			19.3386i			1.02929i	−0.857403	+	0.514645i	$0.827924\pi$
$354$		0			0
$355$	7.74773			0.411207
$356$		−	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	$-0.170793\pi$
$359$	16.0390	+	9.26013i	0.846507	+	0.488731i	−0.0129639	+	0.999916i	$0.504127\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	−41.7042	+	24.0779i	−2.19192	+	1.26551i
$363$		0			0
$364$	19.1869	−	18.4626i	1.00567	−	0.967705i
$365$	15.0000			0.785136
$366$		0			0
$367$	15.1652			0.791614			0.395807	−	0.918334i	$-0.370465\pi$
$367$	15.1652			0.791614			0.395807	+	0.918334i	$0.370465\pi$
$368$	7.68693	−	13.3142i	0.400709	−	0.694048i
$369$		0			0
$370$	23.0608	−	13.3142i	1.19887	−	0.692170i
$371$	−14.1261	+	8.15573i	−0.733392	+	0.423424i
$372$		0			0
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	7.58258			0.392086
$375$		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	$0.508876\pi$
$380$	−12.7913	−	22.1552i	−0.656179	−	1.13654i
$381$		0			0
$382$	−27.1652	+	15.6838i	−1.38989	+	0.802453i
$383$		−	17.7019i		−	0.904525i	−0.891885	−	0.452263i	$-0.850617\pi$
$383$		−	17.7019i		−	0.904525i	0.891885	−	0.452263i	$-0.149383\pi$
$384$		0			0
$385$	−13.7477	−	7.93725i	−0.700649	−	0.404520i
$386$	4.00000	+	6.92820i	0.203595	+	0.352636i
$387$		0			0
$388$		−	29.2741i		−	1.48617i
$389$	13.6652	+	23.6687i	0.692851	+	1.20005i	0.970900	+	0.239486i	$0.0769788\pi$
$389$	13.6652	+	23.6687i	0.692851	+	1.20005i	−0.278049	+	0.960567i	$0.589688\pi$
$390$		0			0
$391$	−8.58258			−0.434040
$392$		−	12.1244i		−	0.612372i
$393$		0			0
$394$	38.5390			1.94157
$395$	2.12614	−	1.22753i	0.106978	−	0.0617635i
$396$		0			0
$397$		−	36.8498i		−	1.84944i	−0.380649	−	0.924720i	$-0.624299\pi$
$397$		−	36.8498i		−	1.84944i	0.380649	−	0.924720i	$-0.375701\pi$
$398$		−	5.65300i		−	0.283359i
$399$		0			0
$400$	1.79129	−	3.10260i	0.0895644	−	0.155130i
$401$	−30.0826	+	17.3682i	−1.50225	+	0.867326i	−0.502256	+	0.864719i	$0.667496\pi$
$401$	−30.0826	+	17.3682i	−1.50225	+	0.867326i	−0.999997	+	0.00260643i	$0.999170\pi$
$402$		0			0
$403$	−5.29129	−	21.3845i	−0.263578	−	1.06524i
$404$	−18.3739	+	31.8245i	−0.914134	+	1.58333i
$405$		0			0
$406$	−40.5390			−2.01192
$407$	12.1652	+	21.0707i	0.603004	+	1.04443i
$408$		0			0
$409$	27.0826	+	15.6361i	1.33915	+	0.773157i	0.986681	−	0.162668i	$-0.0520098\pi$
$409$	27.0826	+	15.6361i	1.33915	+	0.773157i	0.352466	+	0.935825i	$0.385343\pi$
$410$	−11.6869	−	6.74745i	−0.577176	−	0.333233i
$411$		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
$416$	19.1869	−	18.4626i	0.940717	−	0.905205i
$417$		0			0
$418$	34.7477	−	20.0616i	1.69957	−	0.981245i
$419$	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	$-0.448692\pi$
$422$		−	14.4086i		−	0.701400i
$423$		0			0
$424$	9.24773	−	5.33918i	0.449109	−	0.259293i
$425$	−2.00000			−0.0970143
$426$		0			0
$427$			13.6657i			0.661330i
$428$	−3.95644			−0.191242
$429$		0			0
$430$	8.68693	+	15.0462i	0.418921	+	0.725593i
$431$			8.56490i			0.412557i	0.978493	+	0.206278i	$0.0661353\pi$
$431$			8.56490i			0.412557i	−0.978493	+	0.206278i	$0.933865\pi$
$432$		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
$436$		−	53.7135i		−	2.57241i
$437$	−39.3303	+	22.7074i	−1.88142	+	1.08624i
$438$		0			0
$439$	5.29129	+	9.16478i	0.252539	+	0.437411i	0.964224	−	0.265088i	$-0.0854009\pi$
$439$	5.29129	+	9.16478i	0.252539	+	0.437411i	−0.711685	+	0.702499i	$0.752068\pi$
$440$	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	−0.926185	−	0.377069i	$-0.876932\pi$
$443$	−2.87386	+	4.97768i	−0.136541	+	0.236497i	0.789644	+	0.613565i	$0.210265\pi$
$444$		0			0
$445$	27.0000			1.27992
$446$	5.79129			0.274225
$447$		0			0
$448$		−	33.2904i		−	1.57282i
$449$	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
$451$	6.16515	−	10.6784i	0.290306	−	0.502824i
$452$	33.9564			1.59718
$453$		0			0
$454$	−59.7042			−2.80206
$455$	11.4564	+	11.9059i	0.537086	+	0.558156i
$456$		0			0
$457$	−3.24773	+	1.87508i	−0.151922	+	0.0877124i	−0.574034	−	0.818831i	$-0.694622\pi$
$457$	−3.24773	+	1.87508i	−0.151922	+	0.0877124i	0.422112	+	0.906544i	$0.361289\pi$
$458$	−22.9564			−1.07268
$459$		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	$-0.352333\pi$
$464$	−12.5390			−0.582109
$465$		0			0
$466$			44.1395i			2.04472i
$467$	−14.4564	+	25.0393i	−0.668964	+	1.15868i	0.309230	+	0.950987i	$0.399929\pi$
$467$	−14.4564	+	25.0393i	−0.668964	+	1.15868i	−0.978194	+	0.207693i	$0.933405\pi$
$468$		0			0
$469$	−37.1652			−1.71613
$470$	2.68693	+	1.55130i	0.123939	+	0.0715562i
$471$		0			0
$472$	−3.70871	+	6.42368i	−0.170707	+	0.295674i
$473$	−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
$478$	2.20871	+	3.82560i	0.101024	+	0.174979i
$479$		−	28.2849i		−	1.29237i	−0.763181	−	0.646185i	$-0.776363\pi$
$479$		−	28.2849i		−	1.29237i	0.763181	−	0.646185i	$-0.223637\pi$
$480$		0			0
$481$	−6.08258	−	24.5824i	−0.277342	−	1.12086i
$482$	−30.9564			−1.41003
$483$		0			0
$484$	−1.39564	+	2.41733i	−0.0634384	+	0.109878i
$485$	18.1652			0.824837
$486$		0			0
$487$	−9.54356	−	5.50998i	−0.432460	−	0.249681i	0.267934	−	0.963437i	$-0.413659\pi$
$487$	−9.54356	−	5.50998i	−0.432460	−	0.249681i	−0.700394	+	0.713756i	$0.746992\pi$
$488$		−	8.94630i		−	0.404980i
$489$		0			0
$490$	26.5390			1.19891
$491$	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
$494$	−40.5390	+	10.0308i	−1.82394	+	0.451307i
$495$		0			0
$496$	−9.47822	−	5.47225i	−0.425585	−	0.245711i
$497$	−5.91742	−	10.2493i	−0.265433	−	0.459743i
$498$		0			0
$499$	21.7087	+	12.5335i	0.971815	+	0.561078i	0.899789	−	0.436325i	$-0.143720\pi$
$499$	21.7087	+	12.5335i	0.971815	+	0.561078i	0.0720262	+	0.997403i	$0.477053\pi$
$500$	−29.3085	−	16.9213i	−1.31072	−	0.756743i
$501$		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
$509$	24.2477	−	13.9994i	1.07476	−	0.620514i	0.145283	−	0.989390i	$-0.453591\pi$
$509$	24.2477	−	13.9994i	1.07476	−	0.620514i	0.929479	+	0.368876i	$0.120257\pi$
$510$		0			0
$511$	−11.4564	−	19.8431i	−0.506803	−	0.877809i
$512$		−	19.4340i		−	0.858868i
$513$		0			0
$514$	17.6869	+	10.2116i	0.780137	+	0.450412i
$515$	−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
$520$	−7.50000	−	7.79423i	−0.328897	−	0.341800i
$521$	1.66515	+	2.88413i	0.0729516	+	0.126356i	0.900194	−	0.435490i	$-0.143425\pi$
$521$	1.66515	+	2.88413i	0.0729516	+	0.126356i	−0.827242	+	0.561846i	$0.810091\pi$
$522$		0			0
$523$	4.87386	+	8.44178i	0.213119	+	0.369133i	0.952689	−	0.303946i	$-0.0983044\pi$
$523$	4.87386	+	8.44178i	0.213119	+	0.369133i	−0.739570	+	0.673080i	$0.764971\pi$
$524$	−1.97822	−	3.42638i	−0.0864189	−	0.149682i
$525$		0			0
$526$	−9.16515	+	5.29150i	−0.399620	+	0.230720i
$527$			6.10985i			0.266149i
$528$		0			0
$529$	−25.3303	+	43.8734i	−1.10132	+	1.90754i
$530$	11.6869	+	20.2424i	0.507648	+	0.879272i
$531$		0			0
$532$	−19.5390	+	33.8426i	−0.847124	+	1.46726i
$533$	−9.24773	+	8.89863i	−0.400564	+	0.385442i
$534$		0			0
$535$		−	2.45505i		−	0.106141i
$536$	24.3303			1.05091
$537$		0			0
$538$			35.3839i			1.52551i
$539$			24.2487i			1.04447i
$540$		0			0
$541$	−7.33485	−	4.23478i	−0.315350	−	0.182067i	0.333968	−	0.942584i	$-0.391612\pi$
$541$	−7.33485	−	4.23478i	−0.315350	−	0.182067i	−0.649318	+	0.760517i	$0.724946\pi$
$542$	12.6869	−	21.9744i	0.544950	−	0.943882i
$543$		0			0
$544$	−6.39564	+	3.69253i	−0.274211	+	0.158316i
$545$	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	$0.554709\pi$
$548$	20.9347	−	12.0866i	0.894284	−	0.516315i
$549$		0			0
$550$	7.58258	−	13.1334i	0.323322	−	0.560010i
$551$	32.0780	+	18.5203i	1.36657	+	0.788990i
$552$		0			0
$553$	−3.24773	−	1.87508i	−0.138107	−	0.0797363i
$554$		−	20.4231i		−	0.867695i
$555$		0			0
$556$	18.3739			0.779225
$557$			24.4394i			1.03553i	0.855523	+	0.517766i	$0.173236\pi$
$557$			24.4394i			1.03553i	−0.855523	+	0.517766i	$0.826764\pi$
$558$		0			0
$559$	16.0390	−	3.96863i	0.678378	−	0.167855i
$560$	8.20871			0.346881
$561$		0			0
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	2.70871	−	4.69163i	0.114159	−	0.197729i	−0.803284	−	0.595596i	$-0.796916\pi$
$563$	2.70871	−	4.69163i	0.114159	−	0.197729i	0.917443	+	0.397867i	$0.130249\pi$
$564$		0			0
$565$			21.0707i			0.886449i
$566$	57.4955	−	33.1950i	2.41671	−	1.39529i
$567$		0			0
$568$	3.87386	+	6.70973i	0.162544	+	0.281534i
$569$	−2.66515	−	4.61618i	−0.111729	−	0.193520i	0.804738	−	0.593629i	$-0.202306\pi$
$569$	−2.66515	−	4.61618i	−0.111729	−	0.193520i	−0.916467	+	0.400109i	$0.868972\pi$
$570$		0			0
$571$	−23.8739	−	41.3507i	−0.999090	−	1.73047i	−0.536481	−	0.843913i	$-0.680247\pi$
$571$	−23.8739	−	41.3507i	−0.999090	−	1.73047i	−0.462609	−	0.886562i	$-0.653087\pi$
$572$	25.1216	−	24.1733i	1.05039	−	1.01073i
$573$		0			0
$574$			20.6138i			0.860404i
$575$	−8.58258	+	14.8655i	−0.357918	+	0.619932i
$576$		0			0
$577$	−12.0826	+	6.97588i	−0.503004	+	0.290410i	−0.729953	−	0.683497i	$-0.760458\pi$
$577$	−12.0826	+	6.97588i	−0.503004	+	0.290410i	0.226949	+	0.973907i	$0.427125\pi$
$578$	−30.3303	−	17.5112i	−1.26157	−	0.728370i
$579$		0			0
$580$			33.8426i			1.40524i
$581$	9.16515			0.380235
$582$		0			0
$583$	−18.4955	+	10.6784i	−0.766003	+	0.442252i
$584$	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
$592$	−10.8956	−	6.29060i	−0.447808	−	0.258542i
$593$	−15.2477	−	8.80328i	−0.626149	−	0.361507i	0.153110	−	0.988209i	$-0.451071\pi$
$593$	−15.2477	−	8.80328i	−0.626149	−	0.361507i	−0.779259	+	0.626702i	$0.784404\pi$
$594$		0			0
$595$	−2.29129	−	3.96863i	−0.0939336	−	0.162698i
$596$	8.83485	+	5.10080i	0.361889	+	0.208937i
$597$		0			0
$598$	−48.8085	+	46.9660i	−1.99593	+	1.92058i
$599$	4.12614	+	7.14668i	0.168589	+	0.292005i	0.937924	−	0.346841i	$-0.112745\pi$
$599$	4.12614	+	7.14668i	0.168589	+	0.292005i	−0.769335	+	0.638846i	$0.779412\pi$
$600$		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	$0.987487\pi$
$602$	13.2695	−	22.9835i	0.540825	−	0.936736i
$603$		0			0
$604$			46.5946i			1.89591i
$605$	−1.50000	−	0.866025i	−0.0609837	−	0.0352089i
$606$		0			0
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$	−19.5390	+	33.8426i	−0.792412	+	1.37250i
$609$		0			0
$610$	19.5826			0.792875
$611$	2.12614	−	2.04588i	0.0860143	−	0.0827673i
$612$		0			0
$613$			24.4394i			0.987099i	0.869718	+	0.493549i	$0.164301\pi$
$613$			24.4394i			0.987099i	−0.869718	+	0.493549i	$0.835699\pi$
$614$	22.9564	+	39.7617i	0.926446	+	1.60465i
$615$		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	$-0.658991\pi$
$619$	1.03901	−	0.599876i	0.0417615	−	0.0241110i	0.520735	+	0.853718i	$0.325658\pi$
$620$	−14.7695	+	25.5815i	−0.593158	+	1.02738i
$621$		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
$626$			30.2831i			1.21036i
$627$		0			0
$628$	−28.3739			−1.13224
$629$			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
$634$	4.20871			0.167149
$635$	−9.87386	+	5.70068i	−0.391832	+	0.226224i
$636$		0			0
$637$	7.00000	−	24.2487i	0.277350	−	0.960769i
$638$	−53.0780			−2.10138
$639$		0			0
$640$	−22.1216			−0.874433
$641$	−8.24773	+	14.2855i	−0.325766	+	0.564243i	−0.981667	−	0.190604i	$-0.938955\pi$
$641$	−8.24773	+	14.2855i	−0.325766	+	0.564243i	0.655901	+	0.754847i	$0.272289\pi$
$642$		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	$0.0993365\pi$
$644$			63.3828i			2.49763i
$645$		0			0
$646$	11.5826			0.455710
$647$	38.3303			1.50692			0.753460	−	0.657494i	$-0.228383\pi$
$647$	38.3303			1.50692			0.753460	+	0.657494i	$0.228383\pi$
$648$		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
$653$	13.2477	+	22.9457i	0.518424	+	0.897936i	0.999771	+	0.0214061i	$0.00681428\pi$
$653$	13.2477	+	22.9457i	0.518424	+	0.897936i	−0.481347	+	0.876530i	$0.659852\pi$
$654$		0			0
$655$	2.12614	−	1.22753i	0.0830750	−	0.0479634i
$656$			6.37600i			0.248941i
$657$		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
$661$			5.48220i			0.213233i	0.994300	+	0.106616i	$0.0340017\pi$
$661$			5.48220i			0.213233i	−0.994300	+	0.106616i	$0.965998\pi$
$662$	−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
$667$	60.0780			2.32623
$668$	−10.8131	+	6.24293i	−0.418370	+	0.241546i
$669$		0			0
$670$			53.2566i			2.05748i
$671$			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	$-0.0717626\pi$
$674$	−44.5390	+	25.7146i	−1.71558	+	0.990490i
$675$		0			0
$676$	−32.0998	+	16.9213i	−1.23461	+	0.650819i
$677$	14.9174	−	25.8377i	0.573323	−	0.993025i	−0.422898	−	0.906177i	$-0.638987\pi$
$677$	14.9174	−	25.8377i	0.573323	−	0.993025i	0.996222	−	0.0868478i	$-0.0276794\pi$
$678$		0			0
$679$	−13.8739	−	24.0302i	−0.532430	−	0.922196i
$680$	1.50000	+	2.59808i	0.0575224	+	0.0996317i
$681$		0			0
$682$	−40.1216	−	23.1642i	−1.53634	−	0.887003i
$683$	−33.8739	−	19.5571i	−1.29615	−	0.748331i	−0.316411	−	0.948622i	$-0.602478\pi$
$683$	−33.8739	−	19.5571i	−1.29615	−	0.748331i	−0.979736	+	0.200291i	$0.935811\pi$
$684$		0			0
$685$	7.50000	+	12.9904i	0.286560	+	0.496337i
$686$	−20.2695	−	35.1078i	−0.773893	−	1.34042i
$687$		0			0
$688$	4.10436	−	7.10895i	0.156477	−	0.271026i
$689$	21.5780	−	5.33918i	0.822057	−	0.203406i
$690$		0			0
$691$	−6.54356	+	3.77793i	−0.248929	+	0.143719i	−0.619274	−	0.785175i	$-0.712573\pi$
$691$	−6.54356	+	3.77793i	−0.248929	+	0.143719i	0.370345	+	0.928894i	$0.379240\pi$
$692$	−33.9564	+	58.8143i	−1.29083	+	2.23578i
$693$		0			0
$694$		−	56.3592i		−	2.13937i
$695$			11.4014i			0.432478i
$696$		0			0
$697$	3.08258	−	1.77973i	0.116761	−	0.0674119i
$698$	−22.9564			−0.868914
$699$		0			0
$700$			14.7701i			0.558258i
$701$	−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
$704$		−	43.5873i		−	1.64276i
$705$		0			0
$706$	−21.1652	−	36.6591i	−0.796561	−	1.37968i
$707$			34.8317i			1.30998i
$708$		0			0
$709$		−	29.5402i		−	1.10941i	−0.832048	−	0.554703i	$-0.812832\pi$
$709$		−	29.5402i		−	1.10941i	0.832048	−	0.554703i	$-0.187168\pi$
$710$	−14.6869	+	8.47950i	−0.551191	+	0.318230i
$711$		0			0
$712$	13.5000	+	23.3827i	0.505934	+	0.876303i
$713$	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
$718$	−40.5390			−1.51290
$719$	34.3303			1.28030			0.640152	−	0.768248i	$-0.278871\pi$
$719$	34.3303			1.28030			0.640152	+	0.768248i	$0.278871\pi$
$720$		0			0
$721$	7.83030	+	4.52083i	0.291616	+	0.168364i
$722$	17.0608	−	9.85005i	0.634937	−	0.366581i
$723$		0			0
$724$	30.7042	−	53.1812i	1.14111	−	1.97646i
$725$	14.0000			0.519947
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−4.58258	+	15.8745i	−0.169842	+	0.588348i
$729$		0			0
$730$	−28.4347	+	16.4168i	−1.05241	+	0.607611i
$731$	−4.58258			−0.169493
$732$		0			0
$733$	25.8303	+	14.9131i	0.954064	+	0.550829i	0.894341	−	0.447386i	$-0.147645\pi$
$733$	25.8303	+	14.9131i	0.954064	+	0.550829i	0.0597230	+	0.998215i	$0.480978\pi$
$734$	−28.7477	+	16.5975i	−1.06110	+	0.612625i
$735$		0			0
$736$			63.3828i			2.33632i
$737$	−48.6606			−1.79244
$738$		0			0
$739$			19.1479i			0.704367i	0.935931	+	0.352184i	$0.114561\pi$
$739$			19.1479i			0.704367i	−0.935931	+	0.352184i	$0.885439\pi$
$740$	−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
$745$	−3.16515	+	5.48220i	−0.115962	+	0.200852i
$746$	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
$751$	6.45644	+	11.1829i	0.235599	+	0.408069i	0.959447	−	0.281891i	$-0.0909615\pi$
$751$	6.45644	+	11.1829i	0.235599	+	0.408069i	−0.723848	+	0.689960i	$0.757628\pi$
$752$		−	1.46590i		−	0.0534559i
$753$		0			0
$754$	53.0780	+	15.3223i	1.93299	+	0.558006i
$755$	−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	$0.192700\pi$
$758$	−40.5390			−1.47244
$759$		0			0
$760$	13.7477	+	7.93725i	0.498682	+	0.287914i
$761$		−	1.44600i		−	0.0524175i	−0.999656	−	0.0262087i	$-0.991657\pi$
$761$		−	1.44600i		−	0.0524175i	0.999656	−	0.0262087i	$-0.00834345\pi$
$762$		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
$767$	−11.1261	+	10.7061i	−0.401742	+	0.386576i
$768$		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	$0.686013\pi$
$770$	34.7477			1.25222
$771$		0			0
$772$	−8.83485	−	5.10080i	−0.317973	−	0.183582i
$773$	−21.2477	−	12.2674i	−0.764228	−	0.441227i	0.0665839	−	0.997781i	$-0.478790\pi$
$773$	−21.2477	−	12.2674i	−0.764228	−	0.441227i	−0.830812	+	0.556554i	$0.812123\pi$
$774$		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
$782$	16.2695	−	9.39320i	0.581796	−	0.335900i
$783$		0			0
$784$	−6.26951	−	10.8591i	−0.223911	−	0.387825i
$785$		−	17.6066i		−	0.628405i
$786$		0			0
$787$	−26.2913	−	15.1793i	−0.937183	−	0.541083i	−0.0481070	−	0.998842i	$-0.515319\pi$
$787$	−26.2913	−	15.1793i	−0.937183	−	0.541083i	−0.889076	+	0.457759i	$0.848652\pi$
$788$	−42.5608	+	24.5725i	−1.51617	+	0.875359i
$789$		0			0
$790$	−2.68693	+	4.65390i	−0.0955967	+	0.165578i
$791$	27.8739	−	16.0930i	0.991080	−	0.572201i
$792$		0			0
$793$	5.16515	−	17.8926i	0.183420	−	0.635385i
$794$	40.3303	+	69.8541i	1.43127	+	2.47903i
$795$		0			0
$796$	3.60436	+	6.24293i	0.127753	+	0.221275i
$797$	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
$800$			14.7701i			0.522202i
$801$		0			0
$802$	38.0172	−	65.8478i	1.34244	−	2.32517i
$803$	−15.0000	−	25.9808i	−0.529339	−	0.916841i
$804$		0			0
$805$	−39.3303			−1.38621
$806$	33.4347	+	34.7463i	1.17769	+	1.22389i
$807$		0			0
$808$		−	22.8027i		−	0.802197i
$809$	33.1652			1.16602			0.583012	−	0.812463i	$-0.301874\pi$
$809$	33.1652			1.16602			0.583012	+	0.812463i	$0.301874\pi$
$810$		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
$815$	3.00000	−	5.19615i	0.105085	−	0.182013i
$816$		0			0
$817$	−21.0000	+	12.1244i	−0.734697	+	0.424178i
$818$	−68.4519			−2.39336
$819$		0			0
$820$	17.2087			0.600954
$821$	−33.2477	+	19.1956i	−1.16035	+	0.669931i	−0.951389	−	0.307993i	$-0.900343\pi$
$821$	−33.2477	+	19.1956i	−1.16035	+	0.669931i	−0.208965	+	0.977923i	$0.567009\pi$
$822$		0			0
$823$	−15.2913	+	26.4853i	−0.533021	+	0.923219i	0.466236	+	0.884661i	$0.345610\pi$
$823$	−15.2913	+	26.4853i	−0.533021	+	0.923219i	−0.999256	+	0.0385585i	$0.987723\pi$
$824$	−5.12614	−	2.95958i	−0.178577	−	0.103102i
$825$		0			0
$826$			24.8009i			0.862934i
$827$		−	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
$829$	−46.6606			−1.62059			−0.810295	−	0.586022i	$-0.800693\pi$
$829$	−46.6606			−1.62059			−0.810295	+	0.586022i	$0.800693\pi$
$830$		−	13.1334i		−	0.455867i
$831$		0			0
$832$	−12.5826	+	43.5873i	−0.436222	+	1.51112i
$833$	−3.50000	+	6.06218i	−0.121268	+	0.210042i
$834$		0			0
$835$	−3.87386	−	6.70973i	−0.134061	−	0.232200i
$836$	−25.5826	+	44.3103i	−0.884792	+	1.53250i
$837$		0			0
$838$			25.7146i			0.888297i
$839$	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
$842$	44.3303	+	76.7823i	1.52772	+	2.64609i
$843$		0			0
$844$	9.18693	+	15.9122i	0.316227	+	0.547722i
$845$	−10.5000	−	19.9186i	−0.361211	−	0.685220i
$846$		0			0
$847$			2.64575i			0.0909091i
$848$	5.52178	−	9.56400i	0.189619	−	0.328429i
$849$		0			0
$850$	3.79129	−	2.18890i	0.130040	−	0.0750787i
$851$	52.2042	+	30.1401i	1.78954	+	1.03319i
$852$		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
$856$	2.12614	−	1.22753i	0.0726698	−	0.0419560i
$857$	5.66515	+	9.81233i	0.193518	+	0.335183i	0.946414	−	0.322957i	$-0.104677\pi$
$857$	5.66515	+	9.81233i	0.193518	+	0.335183i	−0.752896	+	0.658140i	$0.771344\pi$
$858$		0			0
$859$	23.4564	−	40.6277i	0.800323	−	1.38620i	−0.119080	−	0.992885i	$-0.537994\pi$
$859$	23.4564	−	40.6277i	0.800323	−	1.38620i	0.919403	−	0.393316i	$-0.128672\pi$
$860$	−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	$-0.444802\pi$
$863$	−17.4564	−	10.0785i	−0.594224	−	0.343075i	−0.766766	+	0.641927i	$0.778135\pi$
$864$		0			0
$865$	−36.4955	−	21.0707i	−1.24088	−	0.716424i
$866$	−29.0608	−	16.7783i	−0.987526	−	0.570148i
$867$		0			0
$868$	45.1216			1.53153
$869$	−4.25227	−	2.45505i	−0.144248	−	0.0832819i
$870$		0			0
$871$	48.6606	+	14.0471i	1.64880	+	0.475968i
$872$	16.6652	+	28.8649i	0.564353	+	0.977488i
$873$		0			0
$874$	49.7042	−	86.0901i	1.68127	−	2.91204i
$875$	−32.0780			−1.08444
$876$		0			0
$877$			16.0652i			0.542484i	0.962511	+	0.271242i	$0.0874343\pi$
$877$			16.0652i			0.542484i	−0.962511	+	0.271242i	$0.912566\pi$
$878$	−20.0608	−	11.5821i	−0.677019	−	0.390877i
$879$		0			0
$880$	10.7477			0.362306
$881$	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	$0.178481\pi$
$884$	9.76951	−	2.41733i	0.328584	−	0.0813035i
$885$		0			0
$886$		−	12.5812i		−	0.422674i
$887$	−18.7087	−	32.4044i	−0.628177	−	1.08803i	−0.987917	−	0.154982i	$-0.950468\pi$
$887$	−18.7087	−	32.4044i	−0.628177	−	1.08803i	0.359740	−	0.933053i	$-0.382865\pi$
$888$		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
$893$	−2.16515	+	3.75015i	−0.0724540	+	0.125494i
$894$		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
$899$		−	42.7690i		−	1.42643i
$900$		0			0
$901$	−6.16515			−0.205391
$902$			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
$907$	8.83485			0.293356			0.146678	−	0.989184i	$-0.453142\pi$
$907$	8.83485			0.293356			0.146678	+	0.989184i	$0.453142\pi$
$908$	65.9347	−	38.0674i	2.18812	−	1.26331i
$909$		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
$913$	12.0000			0.397142
$914$	4.10436	−	7.10895i	0.135760	−	0.235143i
$915$		0			0
$916$	25.3521	−	14.6370i	0.837656	−	0.483621i
$917$	−3.24773	−	1.87508i	−0.107249	−	0.0619205i
$918$		0			0
$919$	−4.83485			−0.159487			−0.0797435	−	0.996815i	$-0.525410\pi$
$919$	−4.83485			−0.159487			−0.0797435	+	0.996815i	$0.525410\pi$
$920$	25.7477			0.848877
$921$		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
$926$	42.1216	+	72.9567i	1.38420	+	2.39751i
$927$		0			0
$928$	44.7695	−	25.8477i	1.46963	−	0.848492i
$929$		−	42.3320i		−	1.38887i	−0.719556	−	0.694434i	$-0.755655\pi$
$929$		−	42.3320i		−	1.38887i	0.719556	−	0.694434i	$-0.244345\pi$
$930$		0			0
$931$			37.0405i			1.21395i
$932$	−28.1434	−	48.7457i	−0.921867	−	1.59672i
$933$		0			0
$934$		−	63.2874i		−	2.07083i
$935$	−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	$0.497377\pi$
$938$	70.4519	−	40.6754i	2.30034	−	1.32810i
$939$		0			0
$940$	−3.95644			−0.129045
$941$	−28.8303	+	16.6452i	−0.939841	+	0.542617i	−0.889910	−	0.456135i	$-0.849233\pi$
$941$	−28.8303	+	16.6452i	−0.939841	+	0.542617i	−0.0499305	+	0.998753i	$0.515900\pi$
$942$		0			0
$943$		−	30.5493i		−	0.994821i
$944$			7.67110i			0.249673i
$945$		0			0
$946$	17.3739	−	30.0924i	0.564873	−	0.978389i
$947$	13.0390	−	7.52808i	0.423711	−	0.244630i	−0.272953	−	0.962027i	$-0.588000\pi$
$947$	13.0390	−	7.52808i	0.423711	−	0.244630i	0.696664	+	0.717398i	$0.254667\pi$
$948$		0			0
$949$	7.50000	+	30.3109i	0.243460	+	0.983933i
$950$	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
$955$	21.4955	+	12.4104i	0.695577	+	0.401591i
$956$	−4.87841	−	2.81655i	−0.157779	−	0.0910938i
$957$		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
$962$	38.4347	+	39.9425i	1.23918	+	1.28780i
$963$		0			0
$964$	34.1869	−	19.7378i	1.10109	−	0.635713i
$965$	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	$-0.0271151\pi$
$968$		−	1.73205i		−	0.0556702i
$969$		0			0
$970$	−34.4347	+	19.8809i	−1.10563	+	0.638336i
$971$	−50.3303			−1.61518			−0.807588	−	0.589747i	$-0.799228\pi$
$971$	−50.3303			−1.61518			−0.807588	+	0.589747i	$0.799228\pi$
$972$		0			0
$973$	15.0826	−	8.70793i	0.483525	−	0.279163i
$974$	24.1216			0.772906
$975$		0			0
$976$	−4.62614	−	8.01270i	−0.148079	−	0.256480i
$977$		−	3.65480i		−	0.116927i	−0.998290	−	0.0584637i	$-0.981380\pi$
$977$		−	3.65480i		−	0.116927i	0.998290	−	0.0584637i	$-0.0186202\pi$
$978$		0			0
$979$	−27.0000	−	46.7654i	−0.862924	−	1.49463i
$980$	−29.3085	+	16.9213i	−0.936226	+	0.540531i
$981$		0			0
$982$			8.20340i			0.261781i
$983$	20.2913	−	11.7152i	0.647192	−	0.373656i	−0.140188	−	0.990125i	$-0.544771\pi$
$983$	20.2913	−	11.7152i	0.647192	−	0.373656i	0.787379	+	0.616469i	$0.211437\pi$
$984$		0			0
$985$	−15.2477	−	26.4098i	−0.485833	−	0.841487i
$986$	−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
$991$	32.6606			1.03750			0.518749	−	0.854926i	$-0.326398\pi$
$991$	32.6606			1.03750			0.518749	+	0.854926i	$0.326398\pi$
$992$	45.1216			1.43261
$993$		0			0
$994$	22.4347	+	12.9527i	0.711584	+	0.410833i
$995$	−3.87386	+	2.23658i	−0.122810	+	0.0709042i
$996$		0			0
$997$	23.6652	−	40.9892i	0.749483	−	1.29814i	−0.198588	−	0.980083i	$-0.563636\pi$
$997$	23.6652	−	40.9892i	0.749483	−	1.29814i	0.948071	−	0.318059i	$-0.103031\pi$
$998$	−54.8693			−1.73686
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.2	✓	4	21.11	odd	6
273.2.t.b.205.1	yes	4	39.23	odd	6
273.2.bl.b.88.2	yes	4	273.179	odd	6
273.2.bl.b.121.2	yes	4	3.2	odd	2
819.2.bm.d.478.2		4	13.10	even	6
819.2.bm.d.550.1		4	7.4	even	3
819.2.do.d.361.1		4	91.88	even	6	inner
819.2.do.d.667.1		4	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q+(-1.89564 + 1.09445i) q^{2} +(1.39564 - 2.41733i) q^{4} +(1.50000 + 0.866025i) q^{5} -2.64575i q^{7} +1.73205i q^{8} +O(q^{10})\)	\(q+(-1.89564 + 1.09445i) q^{2} +(1.39564 - 2.41733i) q^{4} +(1.50000 + 0.866025i) q^{5} -2.64575i q^{7} +1.73205i q^{8} -3.79129 q^{10} -3.46410i q^{11} +(-1.00000 + 3.46410i) q^{13} +(2.89564 + 5.01540i) q^{14} +(0.895644 + 1.55130i) q^{16} +(0.500000 - 0.866025i) q^{17} -5.29150i q^{19} +(4.18693 - 2.41733i) q^{20} +(3.79129 + 6.56670i) q^{22} +(-4.29129 - 7.43273i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(-1.89564 - 7.66115i) q^{26} +(-6.39564 - 3.69253i) q^{28} +(-3.50000 + 6.06218i) q^{29} +(-5.29129 + 3.05493i) q^{31} +(-6.39564 - 3.69253i) q^{32} +2.18890i q^{34} +(2.29129 - 3.96863i) q^{35} +(-6.08258 + 3.51178i) q^{37} +(5.79129 + 10.0308i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(3.08258 + 1.77973i) q^{41} +(-2.29129 - 3.96863i) q^{43} +(-8.37386 - 4.83465i) q^{44} +(16.2695 + 9.39320i) q^{46} +(-0.708712 - 0.409175i) q^{47} -7.00000 q^{49} +(3.79129 + 2.18890i) q^{50} +(6.97822 + 7.25198i) q^{52} +(-3.08258 - 5.33918i) q^{53} +(3.00000 - 5.19615i) q^{55} +4.58258 q^{56} -15.3223i q^{58} +(3.70871 + 2.14123i) q^{59} -5.16515 q^{61} +(6.68693 - 11.5821i) q^{62} +12.5826 q^{64} +(-4.50000 + 4.33013i) q^{65} -14.0471i q^{67} +(-1.39564 - 2.41733i) q^{68} +10.0308i q^{70} +(3.87386 - 2.23658i) q^{71} +(7.50000 - 4.33013i) q^{73} +(7.68693 - 13.3142i) q^{74} +(-12.7913 - 7.38505i) q^{76} -9.16515 q^{77} +(0.708712 - 1.22753i) q^{79} +3.10260i q^{80} -7.79129 q^{82} +3.46410i q^{83} +(1.50000 - 0.866025i) q^{85} +(8.68693 + 5.01540i) q^{86} +6.00000 q^{88} +(13.5000 - 7.79423i) q^{89} +(9.16515 + 2.64575i) q^{91} -23.9564 q^{92} +1.79129 q^{94} +(4.58258 - 7.93725i) q^{95} +(9.08258 - 5.24383i) q^{97} +(13.2695 - 7.66115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + q^{4} + 6 q^{5}+O(q^{10}) \) 4 * q - 3 * q^2 + q^4 + 6 * q^5	\( 4 q - 3 q^{2} + q^{4} + 6 q^{5} - 6 q^{10} - 4 q^{13} + 7 q^{14} - q^{16} + 2 q^{17} + 3 q^{20} + 6 q^{22} - 8 q^{23} - 4 q^{25} - 3 q^{26} - 21 q^{28} - 14 q^{29} - 12 q^{31} - 21 q^{32} - 6 q^{37} + 14 q^{38} - 6 q^{40} - 6 q^{41} - 6 q^{44} + 33 q^{46} - 12 q^{47} - 28 q^{49} + 6 q^{50} + 5 q^{52} + 6 q^{53} + 12 q^{55} + 24 q^{59} + 16 q^{61} + 13 q^{62} + 32 q^{64} - 18 q^{65} - q^{68} - 12 q^{71} + 30 q^{73} + 17 q^{74} - 42 q^{76} + 12 q^{79} - 22 q^{82} + 6 q^{85} + 21 q^{86} + 24 q^{88} + 54 q^{89} - 50 q^{92} - 2 q^{94} + 18 q^{97} + 21 q^{98}+O(q^{100}) \) 4 * q - 3 * q^2 + q^4 + 6 * q^5 - 6 * q^10 - 4 * q^13 + 7 * q^14 - q^16 + 2 * q^17 + 3 * q^20 + 6 * q^22 - 8 * q^23 - 4 * q^25 - 3 * q^26 - 21 * q^28 - 14 * q^29 - 12 * q^31 - 21 * q^32 - 6 * q^37 + 14 * q^38 - 6 * q^40 - 6 * q^41 - 6 * q^44 + 33 * q^46 - 12 * q^47 - 28 * q^49 + 6 * q^50 + 5 * q^52 + 6 * q^53 + 12 * q^55 + 24 * q^59 + 16 * q^61 + 13 * q^62 + 32 * q^64 - 18 * q^65 - q^68 - 12 * q^71 + 30 * q^73 + 17 * q^74 - 42 * q^76 + 12 * q^79 - 22 * q^82 + 6 * q^85 + 21 * q^86 + 24 * q^88 + 54 * q^89 - 50 * q^92 - 2 * q^94 + 18 * q^97 + 21 * q^98

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