LMFDB - Embedded newform 819.2.do.d.361.2

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			361.2
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	819.361
Dual form			819.2.do.d.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395644 + 0.228425i) q^{2} +(-0.895644 - 1.55130i) q^{4} +(1.50000 - 0.866025i) q^{5} -2.64575i q^{7} -1.73205i q^{8} +O(q^{10})$	\(q+(0.395644 + 0.228425i) q^{2} +(-0.895644 - 1.55130i) q^{4} +(1.50000 - 0.866025i) q^{5} -2.64575i q^{7} -1.73205i q^{8} +0.791288 q^{10} +3.46410i q^{11} +(-1.00000 - 3.46410i) q^{13} +(0.604356 - 1.04678i) q^{14} +(-1.39564 + 2.41733i) q^{16} +(0.500000 + 0.866025i) q^{17} -5.29150i q^{19} +(-2.68693 - 1.55130i) q^{20} +(-0.791288 + 1.37055i) q^{22} +(0.291288 - 0.504525i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(0.395644 - 1.59898i) q^{26} +(-4.10436 + 2.36965i) q^{28} +(-3.50000 - 6.06218i) q^{29} +(-0.708712 - 0.409175i) q^{31} +(-4.10436 + 2.36965i) q^{32} +0.456850i q^{34} +(-2.29129 - 3.96863i) q^{35} +(3.08258 + 1.77973i) q^{37} +(1.20871 - 2.09355i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-6.08258 + 3.51178i) q^{41} +(2.29129 - 3.96863i) q^{43} +(5.37386 - 3.10260i) q^{44} +(0.230493 - 0.133075i) q^{46} +(-5.29129 + 3.05493i) q^{47} -7.00000 q^{49} +(-0.791288 + 0.456850i) q^{50} +(-4.47822 + 4.65390i) q^{52} +(6.08258 - 10.5353i) q^{53} +(3.00000 + 5.19615i) q^{55} -4.58258 q^{56} -3.19795i q^{58} +(8.29129 - 4.78698i) q^{59} +13.1652 q^{61} +(-0.186932 - 0.323775i) q^{62} +3.41742 q^{64} +(-4.50000 - 4.33013i) q^{65} -7.11890i q^{67} +(0.895644 - 1.55130i) q^{68} -2.09355i q^{70} +(-9.87386 - 5.70068i) q^{71} +(7.50000 + 4.33013i) q^{73} +(0.813068 + 1.40828i) q^{74} +(-8.20871 + 4.73930i) q^{76} +9.16515 q^{77} +(5.29129 + 9.16478i) q^{79} +4.83465i q^{80} -3.20871 q^{82} -3.46410i q^{83} +(1.50000 + 0.866025i) q^{85} +(1.81307 - 1.04678i) q^{86} +6.00000 q^{88} +(13.5000 + 7.79423i) q^{89} +(-9.16515 + 2.64575i) q^{91} -1.04356 q^{92} -2.79129 q^{94} +(-4.58258 - 7.93725i) q^{95} +(-0.0825757 - 0.0476751i) q^{97} +(-2.76951 - 1.59898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.395644	+	0.228425i	0.279763	+	0.161521i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	0.395644	+	0.228425i	0.279763	+	0.161521i	−0.353553	+	0.935414i	$0.615027\pi$
$3$		0			0
$3$		0			0
$4$	−0.895644	−	1.55130i	−0.447822	−	0.775650i
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		0			0
$7$		−	2.64575i		−	1.00000i
$7$		−	2.64575i		−	1.00000i
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	0.791288			0.250227
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	0.604356	−	1.04678i	0.161521	−	0.279763i
$15$		0			0
$16$	−1.39564	+	2.41733i	−0.348911	+	0.604332i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	0.920268	−	0.391289i	$-0.127971\pi$
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	−0.799000	+	0.601331i	$0.794637\pi$
$18$		0			0
$19$		−	5.29150i		−	1.21395i	−0.794719	−	0.606977i	$-0.792382\pi$
$19$		−	5.29150i		−	1.21395i	0.794719	−	0.606977i	$-0.207618\pi$
$20$	−2.68693	−	1.55130i	−0.600816	−	0.346881i
$21$		0			0
$22$	−0.791288	+	1.37055i	−0.168703	+	0.292202i
$23$	0.291288	−	0.504525i	0.0607377	−	0.105201i	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	0.291288	−	0.504525i	0.0607377	−	0.105201i	0.894795	+	0.446476i	$0.147321\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	0.395644	−	1.59898i	0.0775922	−	0.313585i
$27$		0			0
$28$	−4.10436	+	2.36965i	−0.775650	+	0.447822i
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	−0.983138	−	0.182864i	$-0.941463\pi$
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	0.333205	−	0.942855i	$-0.391870\pi$
$30$		0			0
$31$	−0.708712	−	0.409175i	−0.127288	−	0.0734900i	0.435004	−	0.900429i	$-0.356747\pi$
$31$	−0.708712	−	0.409175i	−0.127288	−	0.0734900i	−0.562292	+	0.826939i	$0.690080\pi$
$32$	−4.10436	+	2.36965i	−0.725555	+	0.418899i
$33$		0			0
$34$			0.456850i			0.0783492i
$35$	−2.29129	−	3.96863i	−0.387298	−	0.670820i
$36$		0			0
$37$	3.08258	+	1.77973i	0.506772	+	0.292585i	0.731506	−	0.681835i	$-0.238818\pi$
$37$	3.08258	+	1.77973i	0.506772	+	0.292585i	−0.224734	+	0.974420i	$0.572151\pi$
$38$	1.20871	−	2.09355i	0.196079	−	0.339619i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−6.08258	+	3.51178i	−0.949939	+	0.548447i	−0.893062	−	0.449934i	$-0.851448\pi$
$41$	−6.08258	+	3.51178i	−0.949939	+	0.548447i	−0.0568768	+	0.998381i	$0.518114\pi$
$42$		0			0
$43$	2.29129	−	3.96863i	0.349418	−	0.605210i	−0.636728	−	0.771088i	$-0.719713\pi$
$43$	2.29129	−	3.96863i	0.349418	−	0.605210i	0.986146	+	0.165878i	$0.0530460\pi$
$44$	5.37386	−	3.10260i	0.810140	−	0.467735i
$45$		0			0
$46$	0.230493	−	0.133075i	0.0339843	−	0.0196208i
$47$	−5.29129	+	3.05493i	−0.771814	+	0.445607i	−0.833521	−	0.552487i	$-0.813679\pi$
$47$	−5.29129	+	3.05493i	−0.771814	+	0.445607i	0.0617076	+	0.998094i	$0.480345\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$	−0.791288	+	0.456850i	−0.111905	+	0.0646084i
$51$		0			0
$52$	−4.47822	+	4.65390i	−0.621017	+	0.645380i
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	−0.0581117	−	0.998310i	$-0.518508\pi$
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	0.893618	−	0.448829i	$-0.148159\pi$
$54$		0			0
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	−4.58258			−0.612372
$57$		0			0
$58$		−	3.19795i		−	0.419912i
$59$	8.29129	−	4.78698i	1.07943	−	0.623211i	0.148690	−	0.988884i	$-0.452494\pi$
$59$	8.29129	−	4.78698i	1.07943	−	0.623211i	0.930744	+	0.365672i	$0.119161\pi$
$60$		0			0
$61$	13.1652			1.68562			0.842812	−	0.538207i	$-0.180898\pi$
$61$	13.1652			1.68562			0.842812	+	0.538207i	$0.180898\pi$
$62$	−0.186932	−	0.323775i	−0.0237404	−	0.0411195i
$63$		0			0
$64$	3.41742			0.427178
$65$	−4.50000	−	4.33013i	−0.558156	−	0.537086i
$66$		0			0
$67$		−	7.11890i		−	0.869713i	−0.900500	−	0.434856i	$-0.856799\pi$
$67$		−	7.11890i		−	0.869713i	0.900500	−	0.434856i	$-0.143201\pi$
$68$	0.895644	−	1.55130i	0.108613	−	0.188123i
$69$		0			0
$70$		−	2.09355i		−	0.250227i
$71$	−9.87386	−	5.70068i	−1.17181	−	0.676546i	−0.217706	−	0.976014i	$-0.569857\pi$
$71$	−9.87386	−	5.70068i	−1.17181	−	0.676546i	−0.954106	+	0.299468i	$0.903191\pi$
$72$		0			0
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.869935	−	0.493166i	$-0.164160\pi$
$73$	7.50000	+	4.33013i	0.877809	+	0.506803i	0.00787336	+	0.999969i	$0.497494\pi$
$74$	0.813068	+	1.40828i	0.0945173	+	0.163709i
$75$		0			0
$76$	−8.20871	+	4.73930i	−0.941604	+	0.543635i
$77$	9.16515			1.04447
$78$		0			0
$79$	5.29129	+	9.16478i	0.595316	+	1.03112i	0.993502	+	0.113813i	$0.0363066\pi$
$79$	5.29129	+	9.16478i	0.595316	+	1.03112i	−0.398186	+	0.917305i	$0.630360\pi$
$80$			4.83465i			0.540531i
$81$		0			0
$82$	−3.20871			−0.354343
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$		0			0
$85$	1.50000	+	0.866025i	0.162698	+	0.0939336i
$86$	1.81307	−	1.04678i	0.195508	−	0.112877i
$87$		0			0
$88$	6.00000			0.639602
$89$	13.5000	+	7.79423i	1.43100	+	0.826187i	0.997197	−	0.0748225i	$-0.0238390\pi$
$89$	13.5000	+	7.79423i	1.43100	+	0.826187i	0.433800	+	0.901009i	$0.357172\pi$
$90$		0			0
$91$	−9.16515	+	2.64575i	−0.960769	+	0.277350i
$92$	−1.04356			−0.108799
$93$		0			0
$94$	−2.79129			−0.287899
$95$	−4.58258	−	7.93725i	−0.470162	−	0.814345i
$96$		0			0
$97$	−0.0825757	−	0.0476751i	−0.00838429	−	0.00484067i	0.495802	−	0.868436i	$-0.334874\pi$
$97$	−0.0825757	−	0.0476751i	−0.00838429	−	0.00484067i	−0.504186	+	0.863595i	$0.668208\pi$
$98$	−2.76951	−	1.59898i	−0.279763	−	0.161521i
$99$		0			0
$100$	3.58258			0.358258
$101$	5.16515			0.513952			0.256976	−	0.966418i	$-0.417274\pi$
$101$	5.16515			0.513952			0.256976	+	0.966418i	$0.417274\pi$
$102$		0			0
$103$	−6.29129	−	10.8968i	−0.619899	−	1.07370i	−0.989504	−	0.144507i	$-0.953840\pi$
$103$	−6.29129	−	10.8968i	−0.619899	−	1.07370i	0.369605	−	0.929189i	$-0.379493\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	4.81307	−	2.77883i	0.467487	−	0.269903i
$107$	−5.29129	+	9.16478i	−0.511528	+	0.885993i	0.488383	+	0.872630i	$0.337587\pi$
$107$	−5.29129	+	9.16478i	−0.511528	+	0.885993i	−0.999911	+	0.0133631i	$0.995746\pi$
$108$		0			0
$109$	−1.66515	−	0.961376i	−0.159493	−	0.0920831i	0.418129	−	0.908387i	$-0.362686\pi$
$109$	−1.66515	−	0.961376i	−0.159493	−	0.0920831i	−0.577622	+	0.816304i	$0.696019\pi$
$110$			2.74110i			0.261354i
$111$		0			0
$112$	6.39564	+	3.69253i	0.604332	+	0.348911i
$113$	−3.08258	+	5.33918i	−0.289984	+	0.502268i	−0.973806	−	0.227382i	$-0.926983\pi$
$113$	−3.08258	+	5.33918i	−0.289984	+	0.502268i	0.683821	+	0.729649i	$0.260317\pi$
$114$		0			0
$115$		−	1.00905i		−	0.0940945i
$116$	−6.26951	+	10.8591i	−0.582109	+	1.00824i
$117$		0			0
$118$	4.37386			0.402647
$119$	2.29129	−	1.32288i	0.210042	−	0.121268i
$120$		0			0
$121$	−1.00000			−0.0909091
$122$	5.20871	+	3.00725i	0.471575	+	0.272264i
$123$		0			0
$124$			1.46590i			0.131642i
$125$			12.1244i			1.08444i
$126$		0			0
$127$	1.29129	+	2.23658i	0.114583	+	0.198464i	0.917613	−	0.397475i	$-0.130113\pi$
$127$	1.29129	+	2.23658i	0.114583	+	0.198464i	−0.803030	+	0.595939i	$0.796780\pi$
$128$	9.56080	+	5.51993i	0.845063	+	0.487897i
$129$		0			0
$130$	−0.791288	−	2.74110i	−0.0694005	−	0.240411i
$131$	5.29129	+	9.16478i	0.462302	+	0.800730i	0.999075	−	0.0429960i	$-0.0136903\pi$
$131$	5.29129	+	9.16478i	0.462302	+	0.800730i	−0.536773	+	0.843727i	$0.680357\pi$
$132$		0			0
$133$	−14.0000			−1.21395
$134$	1.62614	−	2.81655i	0.140477	−	0.243313i
$135$		0			0
$136$	1.50000	−	0.866025i	0.128624	−	0.0742611i
$137$	7.50000	−	4.33013i	0.640768	−	0.369948i	−0.144142	−	0.989557i	$-0.546042\pi$
$137$	7.50000	−	4.33013i	0.640768	−	0.369948i	0.784910	+	0.619609i	$0.212709\pi$
$138$		0			0
$139$	−1.29129	+	2.23658i	−0.109526	+	0.189704i	−0.915578	−	0.402140i	$-0.868266\pi$
$139$	−1.29129	+	2.23658i	−0.109526	+	0.189704i	0.806053	+	0.591844i	$0.201600\pi$
$140$	−4.10436	+	7.10895i	−0.346881	+	0.600816i
$141$		0			0
$142$	−2.60436	−	4.51088i	−0.218553	−	0.378544i
$143$	12.0000	−	3.46410i	1.00349	−	0.289683i
$144$		0			0
$145$	−10.5000	−	6.06218i	−0.871978	−	0.503436i
$146$	1.97822	+	3.42638i	0.163719	+	0.283569i
$147$		0			0
$148$		−	6.37600i		−	0.524104i
$149$			17.5112i			1.43457i	0.696778	+	0.717287i	$0.254616\pi$
$149$			17.5112i			1.43457i	−0.696778	+	0.717287i	$0.745384\pi$
$150$		0			0
$151$	8.45644	+	4.88233i	0.688175	+	0.397318i	0.802928	−	0.596076i	$-0.203274\pi$
$151$	8.45644	+	4.88233i	0.688175	+	0.397318i	−0.114753	+	0.993394i	$0.536608\pi$
$152$	−9.16515			−0.743392
$153$		0			0
$154$	3.62614	+	2.09355i	0.292202	+	0.168703i
$155$	−1.41742			−0.113850
$156$		0			0
$157$	4.08258	−	7.07123i	0.325825	−	0.564345i	−0.655854	−	0.754888i	$-0.727691\pi$
$157$	4.08258	−	7.07123i	0.325825	−	0.564345i	0.981679	+	0.190542i	$0.0610246\pi$
$158$			4.83465i			0.384624i
$159$		0			0
$160$	−4.10436	+	7.10895i	−0.324478	+	0.562012i
$161$	−1.33485	−	0.770675i	−0.105201	−	0.0607377i
$162$		0			0
$163$			3.46410i			0.271329i	0.990755	+	0.135665i	$0.0433170\pi$
$163$			3.46410i			0.271329i	−0.990755	+	0.135665i	$0.956683\pi$
$164$	10.8956	+	6.29060i	0.850807	+	0.491214i
$165$		0			0
$166$	0.791288	−	1.37055i	0.0614158	−	0.106375i
$167$	9.87386	−	5.70068i	0.764063	−	0.441132i	−0.0666899	−	0.997774i	$-0.521244\pi$
$167$	9.87386	−	5.70068i	0.764063	−	0.441132i	0.830752	+	0.556642i	$0.187911\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	0.395644	+	0.685275i	0.0303445	+	0.0525582i
$171$		0			0
$172$	−8.20871			−0.625908
$173$	12.3303			0.937456			0.468728	−	0.883343i	$-0.344713\pi$
$173$	12.3303			0.937456			0.468728	+	0.883343i	$0.344713\pi$
$174$		0			0
$175$	4.58258	+	2.64575i	0.346410	+	0.200000i
$176$	−8.37386	−	4.83465i	−0.631204	−	0.364426i
$177$		0			0
$178$	3.56080	+	6.16748i	0.266893	+	0.462272i
$179$	−19.1652			−1.43247			−0.716235	−	0.697859i	$-0.754136\pi$
$179$	−19.1652			−1.43247			−0.716235	+	0.697859i	$0.754136\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	−4.23049	−	1.04678i	−0.313585	−	0.0775922i
$183$		0			0
$184$	−0.873864	−	0.504525i	−0.0644221	−	0.0371941i
$185$	6.16515			0.453271
$186$		0			0
$187$	−3.00000	+	1.73205i	−0.219382	+	0.126660i
$188$	9.47822	+	5.47225i	0.691270	+	0.399105i
$189$		0			0
$190$		−	4.18710i		−	0.303764i
$191$	−22.3303			−1.61576			−0.807882	−	0.589344i	$-0.799386\pi$
$191$	−22.3303			−1.61576			−0.807882	+	0.589344i	$0.799386\pi$
$192$		0			0
$193$		−	17.5112i		−	1.26048i	−0.776399	−	0.630242i	$-0.782956\pi$
$193$		−	17.5112i		−	1.26048i	0.776399	−	0.630242i	$-0.217044\pi$
$194$	−0.0217804	−	0.0377247i	−0.00156374	−	0.00270848i
$195$		0			0
$196$	6.26951	+	10.8591i	0.447822	+	0.775650i
$197$	12.2477	−	7.07123i	0.872614	−	0.503804i	0.00439826	−	0.999990i	$-0.498600\pi$
$197$	12.2477	−	7.07123i	0.872614	−	0.503804i	0.868216	+	0.496186i	$0.165267\pi$
$198$		0			0
$199$	3.29129	+	5.70068i	0.233313	+	0.404110i	0.958781	−	0.284146i	$-0.0917099\pi$
$199$	3.29129	+	5.70068i	0.233313	+	0.404110i	−0.725468	+	0.688256i	$0.758377\pi$
$200$	3.00000	+	1.73205i	0.212132	+	0.122474i
$201$		0			0
$202$	2.04356	+	1.17985i	0.143784	+	0.0830140i
$203$	−16.0390	+	9.26013i	−1.12572	+	0.649934i
$204$		0			0
$205$	−6.08258	+	10.5353i	−0.424826	+	0.735819i
$206$		−	5.74835i		−	0.400507i
$207$		0			0
$208$	9.76951	+	2.41733i	0.677393	+	0.167611i
$209$	18.3303			1.26793
$210$		0			0
$211$	1.29129	+	2.23658i	0.0888959	+	0.153972i	0.907045	−	0.421034i	$-0.138333\pi$
$211$	1.29129	+	2.23658i	0.0888959	+	0.153972i	−0.818149	+	0.575007i	$0.804999\pi$
$212$	−21.7913			−1.49663
$213$		0			0
$214$	−4.18693	+	2.41733i	−0.286213	+	0.165245i
$215$		−	7.93725i		−	0.541316i
$216$		0			0
$217$	−1.08258	+	1.87508i	−0.0734900	+	0.127288i
$218$	−0.439205	−	0.760725i	−0.0297467	−	0.0515228i
$219$		0			0
$220$	5.37386	−	9.30780i	0.362306	−	0.627532i
$221$	2.50000	−	2.59808i	0.168168	−	0.174766i
$222$		0			0
$223$	2.29129	−	1.32288i	0.153436	−	0.0885863i	−0.421316	−	0.906914i	$-0.638432\pi$
$223$	2.29129	−	1.32288i	0.153436	−	0.0885863i	0.574752	+	0.818327i	$0.305098\pi$
$224$	6.26951	+	10.8591i	0.418899	+	0.725555i
$225$		0			0
$226$	−2.43920	+	1.40828i	−0.162253	+	0.0936771i
$227$	−17.6216	+	10.1738i	−1.16959	+	0.675261i	−0.953583	−	0.301132i	$-0.902636\pi$
$227$	−17.6216	+	10.1738i	−1.16959	+	0.675261i	−0.216004	+	0.976393i	$0.569302\pi$
$228$		0			0
$229$	−0.0825757	+	0.0476751i	−0.00545676	+	0.00315046i	−0.502726	−	0.864446i	$-0.667669\pi$
$229$	−0.0825757	+	0.0476751i	−0.00545676	+	0.00315046i	0.497269	+	0.867596i	$0.334336\pi$
$230$	0.230493	−	0.399225i	0.0151982	−	0.0263241i
$231$		0			0
$232$	−10.5000	+	6.06218i	−0.689359	+	0.398001i
$233$	0.917424	+	1.58903i	0.0601025	+	0.104101i	0.894511	−	0.447046i	$-0.147524\pi$
$233$	0.917424	+	1.58903i	0.0601025	+	0.104101i	−0.834409	+	0.551146i	$0.814191\pi$
$234$		0			0
$235$	−5.29129	+	9.16478i	−0.345166	+	0.597844i
$236$	−14.8521	−	8.57485i	−0.966788	−	0.558175i
$237$		0			0
$238$	1.20871			0.0783492
$239$		−	29.7309i		−	1.92313i	−0.274572	−	0.961566i	$-0.588536\pi$
$239$		−	29.7309i		−	1.92313i	0.274572	−	0.961566i	$-0.411464\pi$
$240$		0			0
$241$	−15.2477	+	8.80328i	−0.982192	+	0.567069i	−0.902931	−	0.429785i	$-0.858589\pi$
$241$	−15.2477	+	8.80328i	−0.982192	+	0.567069i	−0.0792611	+	0.996854i	$0.525256\pi$
$242$	−0.395644	−	0.228425i	−0.0254330	−	0.0146837i
$243$		0			0
$244$	−11.7913	−	20.4231i	−0.754860	−	1.30746i
$245$	−10.5000	+	6.06218i	−0.670820	+	0.387298i
$246$		0			0
$247$	−18.3303	+	5.29150i	−1.16633	+	0.336690i
$248$	−0.708712	+	1.22753i	−0.0450033	+	0.0779479i
$249$		0			0
$250$	−2.76951	+	4.79693i	−0.175159	+	0.303384i
$251$	−5.70871	+	9.88778i	−0.360331	+	0.624111i	−0.988015	−	0.154357i	$-0.950669\pi$
$251$	−5.70871	+	9.88778i	−0.360331	+	0.624111i	0.627684	+	0.778468i	$0.284003\pi$
$252$		0			0
$253$	1.74773	+	1.00905i	0.109879	+	0.0634385i
$254$			1.17985i			0.0740304i
$255$		0			0
$256$	−0.895644	−	1.55130i	−0.0559777	−	0.0969563i
$257$	13.6652	−	23.6687i	0.852409	−	1.47642i	−0.0266196	−	0.999646i	$-0.508474\pi$
$257$	13.6652	−	23.6687i	0.852409	−	1.47642i	0.879028	−	0.476770i	$-0.158192\pi$
$258$		0			0
$259$	4.70871	−	8.15573i	0.292585	−	0.506772i
$260$	−2.68693	+	10.8591i	−0.166636	+	0.673453i
$261$		0			0
$262$			4.83465i			0.298686i
$263$	23.1652			1.42842			0.714212	−	0.699929i	$-0.246785\pi$
$263$	23.1652			1.42842			0.714212	+	0.699929i	$0.246785\pi$
$264$		0			0
$265$		−	21.0707i		−	1.29436i
$266$	−5.53901	−	3.19795i	−0.339619	−	0.196079i
$267$		0			0
$268$	−11.0436	+	6.37600i	−0.674593	+	0.389476i
$269$	−1.08258	−	1.87508i	−0.0660058	−	0.114325i	0.831134	−	0.556072i	$-0.187692\pi$
$269$	−1.08258	−	1.87508i	−0.0660058	−	0.114325i	−0.897140	+	0.441747i	$0.854359\pi$
$270$		0			0
$271$	22.0390	+	12.7242i	1.33877	+	0.772942i	0.986626	−	0.163002i	$-0.0521177\pi$
$271$	22.0390	+	12.7242i	1.33877	+	0.772942i	0.352149	+	0.935944i	$0.385451\pi$
$272$	−2.79129			−0.169247
$273$		0			0
$274$	3.95644			0.239017
$275$	−6.00000	−	3.46410i	−0.361814	−	0.208893i
$276$		0			0
$277$	13.6652	+	23.6687i	0.821059	+	1.42212i	0.904894	+	0.425637i	$0.139950\pi$
$277$	13.6652	+	23.6687i	0.821059	+	1.42212i	−0.0838347	+	0.996480i	$0.526717\pi$
$278$	−1.02178	+	0.589925i	−0.0612823	+	0.0353814i
$279$		0			0
$280$	−6.87386	+	3.96863i	−0.410792	+	0.237171i
$281$		−	17.5112i		−	1.04463i	−0.852752	−	0.522316i	$-0.825068\pi$
$281$		−	17.5112i		−	1.04463i	0.852752	−	0.522316i	$-0.174932\pi$
$282$		0			0
$283$	6.33030			0.376297			0.188149	−	0.982141i	$-0.439751\pi$
$283$	6.33030			0.376297			0.188149	+	0.982141i	$0.439751\pi$
$284$			20.4231i			1.21189i
$285$		0			0
$286$	5.53901	+	1.37055i	0.327529	+	0.0810424i
$287$	9.29129	+	16.0930i	0.548447	+	0.949939i
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$	−2.76951	−	4.79693i	−0.162631	−	0.281685i
$291$		0			0
$292$		−	15.5130i		−	0.907830i
$293$	19.8303	+	11.4490i	1.15850	+	0.668860i	0.950944	−	0.309364i	$-0.100116\pi$
$293$	19.8303	+	11.4490i	1.15850	+	0.668860i	0.207555	+	0.978223i	$0.433449\pi$
$294$		0			0
$295$	8.29129	−	14.3609i	0.482737	−	0.836126i
$296$	3.08258	−	5.33918i	0.179171	−	0.310333i
$297$		0			0
$298$	−4.00000	+	6.92820i	−0.231714	+	0.401340i
$299$	−2.03901	−	0.504525i	−0.117919	−	0.0291775i
$300$		0			0
$301$	−10.5000	−	6.06218i	−0.605210	−	0.349418i
$302$	2.23049	+	3.86333i	0.128350	+	0.222309i
$303$		0			0
$304$	12.7913	+	7.38505i	0.733631	+	0.423562i
$305$	19.7477	−	11.4014i	1.13075	−	0.652840i
$306$		0			0
$307$		−	0.190700i		−	0.0108838i	−0.999985	−	0.00544192i	$-0.998268\pi$
$307$		−	0.190700i		−	0.0108838i	0.999985	−	0.00544192i	$-0.00173223\pi$
$308$	−8.20871	−	14.2179i	−0.467735	−	0.810140i
$309$		0			0
$310$	−0.560795	−	0.323775i	−0.0318510	−	0.0183892i
$311$	0.291288	−	0.504525i	0.0165174	−	0.0286090i	−0.857649	−	0.514236i	$-0.828075\pi$
$311$	0.291288	−	0.504525i	0.0165174	−	0.0286090i	0.874166	+	0.485627i	$0.161409\pi$
$312$		0			0
$313$	16.0826	+	27.8558i	0.909041	+	1.57451i	0.815399	+	0.578899i	$0.196517\pi$
$313$	16.0826	+	27.8558i	0.909041	+	1.57451i	0.0936417	+	0.995606i	$0.470149\pi$
$314$	3.23049	−	1.86513i	0.182307	−	0.105255i
$315$		0			0
$316$	9.47822	−	16.4168i	0.533192	−	0.923515i
$317$	16.6652	−	9.62163i	0.936008	−	0.540405i	0.0473014	−	0.998881i	$-0.484938\pi$
$317$	16.6652	−	9.62163i	0.936008	−	0.540405i	0.888707	+	0.458476i	$0.151605\pi$
$318$		0			0
$319$	21.0000	−	12.1244i	1.17577	−	0.678834i
$320$	5.12614	−	2.95958i	0.286560	−	0.165445i
$321$		0			0
$322$	−0.352083	−	0.609826i	−0.0196208	−	0.0339843i
$323$	4.58258	−	2.64575i	0.254981	−	0.147214i
$324$		0			0
$325$	7.00000	+	1.73205i	0.388290	+	0.0960769i
$326$	−0.791288	+	1.37055i	−0.0438254	+	0.0759078i
$327$		0			0
$328$	6.08258	+	10.5353i	0.335854	+	0.581716i
$329$	8.08258	+	13.9994i	0.445607	+	0.771814i
$330$		0			0
$331$		−	15.4931i		−	0.851578i	−0.904822	−	0.425789i	$-0.859997\pi$
$331$		−	15.4931i		−	0.851578i	0.904822	−	0.425789i	$-0.140003\pi$
$332$	−5.37386	+	3.10260i	−0.294929	+	0.170277i
$333$		0			0
$334$	5.20871			0.285008
$335$	−6.16515	−	10.6784i	−0.336838	−	0.583421i
$336$		0			0
$337$	−31.4955			−1.71567			−0.857833	−	0.513928i	$-0.828190\pi$
$337$	−31.4955			−1.71567			−0.857833	+	0.513928i	$0.828190\pi$
$338$	−5.93466	+	0.228425i	−0.322803	+	0.0124247i
$339$		0			0
$340$		−	3.10260i		−	0.168262i
$341$	1.41742	−	2.45505i	0.0767578	−	0.132948i
$342$		0			0
$343$			18.5203i			1.00000i
$344$	−6.87386	−	3.96863i	−0.370614	−	0.213974i
$345$		0			0
$346$	4.87841	+	2.81655i	0.262265	+	0.151419i
$347$	0.873864	+	1.51358i	0.0469115	+	0.0812530i	0.888528	−	0.458823i	$-0.151729\pi$
$347$	0.873864	+	1.51358i	0.0469115	+	0.0812530i	−0.841616	+	0.540076i	$0.818395\pi$
$348$		0			0
$349$	−0.0825757	+	0.0476751i	−0.00442018	+	0.00255199i	−0.502208	−	0.864747i	$-0.667479\pi$
$349$	−0.0825757	+	0.0476751i	−0.00442018	+	0.00255199i	0.497788	+	0.867299i	$0.334146\pi$
$350$	1.20871	+	2.09355i	0.0646084	+	0.111905i
$351$		0			0
$352$	−8.20871	−	14.2179i	−0.437526	−	0.757817i
$353$			12.4104i			0.660539i	0.943887	+	0.330270i	$0.107140\pi$
$353$			12.4104i			0.660539i	−0.943887	+	0.330270i	$0.892860\pi$
$354$		0			0
$355$	−19.7477			−1.04810
$356$		−	27.9234i		−	1.47994i
$357$		0			0
$358$	−7.58258	−	4.37780i	−0.400752	−	0.231374i
$359$	−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
$361$	−9.00000			−0.473684
$362$	8.70417	+	5.02535i	0.457481	+	0.264127i
$363$		0			0
$364$	12.3131	+	11.8483i	0.645380	+	0.621017i
$365$	15.0000			0.785136
$366$		0			0
$367$	−3.16515			−0.165220			−0.0826098	−	0.996582i	$-0.526326\pi$
$367$	−3.16515			−0.165220			−0.0826098	+	0.996582i	$0.526326\pi$
$368$	0.813068	+	1.40828i	0.0423841	+	0.0734114i
$369$		0			0
$370$	2.43920	+	1.40828i	0.126808	+	0.0732128i
$371$	−27.8739	−	16.0930i	−1.44714	−	0.835506i
$372$		0			0
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	−1.58258			−0.0818330
$375$		0			0
$376$	5.29129	+	9.16478i	0.272877	+	0.472637i
$377$	−17.5000	+	18.1865i	−0.901296	+	0.936654i
$378$		0			0
$379$	−16.0390	+	9.26013i	−0.823869	+	0.475661i	−0.851749	−	0.523950i	$-0.824458\pi$
$379$	−16.0390	+	9.26013i	−0.823869	+	0.475661i	0.0278799	+	0.999611i	$0.491124\pi$
$380$	−8.20871	+	14.2179i	−0.421098	+	0.729363i
$381$		0			0
$382$	−8.83485	−	5.10080i	−0.452030	−	0.260980i
$383$		−	24.6301i		−	1.25854i	−0.777187	−	0.629270i	$-0.783354\pi$
$383$		−	24.6301i		−	1.25854i	0.777187	−	0.629270i	$-0.216646\pi$
$384$		0			0
$385$	13.7477	−	7.93725i	0.700649	−	0.404520i
$386$	4.00000	−	6.92820i	0.203595	−	0.352636i
$387$		0			0
$388$			0.170800i			0.00867104i
$389$	−4.66515	+	8.08028i	−0.236533	+	0.409686i	−0.959717	−	0.280969i	$-0.909344\pi$
$389$	−4.66515	+	8.08028i	−0.236533	+	0.409686i	0.723184	+	0.690655i	$0.242678\pi$
$390$		0			0
$391$	0.582576			0.0294621
$392$			12.1244i			0.612372i
$393$		0			0
$394$	6.46099			0.325500
$395$	15.8739	+	9.16478i	0.798701	+	0.461130i
$396$		0			0
$397$		−	16.0652i		−	0.806290i	−0.915136	−	0.403145i	$-0.867917\pi$
$397$		−	16.0652i		−	0.806290i	0.915136	−	0.403145i	$-0.132083\pi$
$398$			3.00725i			0.150740i
$399$		0			0
$400$	−2.79129	−	4.83465i	−0.139564	−	0.241733i
$401$	−20.9174	−	12.0767i	−1.04457	−	0.603081i	−0.123443	−	0.992352i	$-0.539394\pi$
$401$	−20.9174	−	12.0767i	−1.04457	−	0.603081i	−0.921123	+	0.389271i	$0.872727\pi$
$402$		0			0
$403$	−0.708712	+	2.86423i	−0.0353035	+	0.142677i
$404$	−4.62614	−	8.01270i	−0.230159	−	0.398647i
$405$		0			0
$406$	−8.46099			−0.419912
$407$	−6.16515	+	10.6784i	−0.305595	+	0.529306i
$408$		0			0
$409$	17.9174	−	10.3446i	0.885960	−	0.511509i	0.0133409	−	0.999911i	$-0.495753\pi$
$409$	17.9174	−	10.3446i	0.885960	−	0.511509i	0.872619	+	0.488402i	$0.162420\pi$
$410$	−4.81307	+	2.77883i	−0.237700	+	0.137236i
$411$		0			0
$412$	−11.2695	+	19.5194i	−0.555209	+	0.961650i
$413$	−12.6652	−	21.9367i	−0.623211	−	1.07943i
$414$		0			0
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	12.3131	+	11.8483i	0.603698	+	0.580909i
$417$		0			0
$418$	7.25227	+	4.18710i	0.354720	+	0.204798i
$419$	−7.87386	−	13.6379i	−0.384663	−	0.666257i	0.607059	−	0.794657i	$-0.292349\pi$
$419$	−7.87386	−	13.6379i	−0.384663	−	0.666257i	−0.991722	+	0.128400i	$0.959016\pi$
$420$		0			0
$421$		−	33.5764i		−	1.63641i	−0.574923	−	0.818207i	$-0.694968\pi$
$421$		−	33.5764i		−	1.63641i	0.574923	−	0.818207i	$-0.305032\pi$
$422$			1.17985i			0.0574342i
$423$		0			0
$424$	−18.2477	−	10.5353i	−0.886188	−	0.511641i
$425$	−2.00000			−0.0970143
$426$		0			0
$427$		−	34.8317i		−	1.68562i
$428$	18.9564			0.916294
$429$		0			0
$430$	1.81307	−	3.14033i	0.0874339	−	0.151440i
$431$		−	19.1479i		−	0.922322i	−0.887316	−	0.461161i	$-0.847433\pi$
$431$		−	19.1479i		−	0.922322i	0.887316	−	0.461161i	$-0.152567\pi$
$432$		0			0
$433$	−10.6652	+	18.4726i	−0.512534	+	0.887736i	0.487360	+	0.873201i	$0.337960\pi$
$433$	−10.6652	+	18.4726i	−0.512534	+	0.887736i	−0.999894	+	0.0145345i	$0.995373\pi$
$434$	−0.856629	+	0.494575i	−0.0411195	+	0.0237404i
$435$		0			0
$436$			3.44420i			0.164947i
$437$	−2.66970	−	1.54135i	−0.127709	−	0.0737328i
$438$		0			0
$439$	0.708712	−	1.22753i	0.0338250	−	0.0585866i	−0.848617	−	0.529007i	$-0.822564\pi$
$439$	0.708712	−	1.22753i	0.0338250	−	0.0585866i	0.882442	+	0.470421i	$0.155898\pi$
$440$	9.00000	−	5.19615i	0.429058	−	0.247717i
$441$		0			0
$442$	1.58258	−	0.456850i	0.0752754	−	0.0217302i
$443$	10.8739	+	18.8341i	0.516633	+	0.894834i	0.999813	+	0.0193136i	$0.00614811\pi$
$443$	10.8739	+	18.8341i	0.516633	+	0.894834i	−0.483181	+	0.875521i	$0.660519\pi$
$444$		0			0
$445$	27.0000			1.27992
$446$	1.20871			0.0572342
$447$		0			0
$448$		−	9.04165i		−	0.427178i
$449$	−7.66515	−	4.42548i	−0.361741	−	0.208851i	0.308103	−	0.951353i	$-0.400306\pi$
$449$	−7.66515	−	4.42548i	−0.361741	−	0.208851i	−0.669844	+	0.742502i	$0.733639\pi$
$450$		0			0
$451$	−12.1652	−	21.0707i	−0.572835	−	0.992179i
$452$	11.0436			0.519445
$453$		0			0
$454$	−9.29583			−0.436275
$455$	−11.4564	+	11.9059i	−0.537086	+	0.558156i
$456$		0			0
$457$	24.2477	+	13.9994i	1.13426	+	0.654866i	0.945003	−	0.327062i	$-0.106058\pi$
$457$	24.2477	+	13.9994i	1.13426	+	0.654866i	0.189258	+	0.981927i	$0.439392\pi$
$458$	−0.0435608			−0.00203546
$459$		0			0
$460$	−1.56534	+	0.903750i	−0.0729844	+	0.0421376i
$461$	−18.4129	−	10.6307i	−0.857573	−	0.495120i	0.00562564	−	0.999984i	$-0.498209\pi$
$461$	−18.4129	−	10.6307i	−0.857573	−	0.495120i	−0.863199	+	0.504864i	$0.831543\pi$
$462$		0			0
$463$		−	3.84550i		−	0.178716i	−0.996000	−	0.0893578i	$-0.971519\pi$
$463$		−	3.84550i		−	0.178716i	0.996000	−	0.0893578i	$-0.0284815\pi$
$464$	19.5390			0.907076
$465$		0			0
$466$			0.838251i			0.0388312i
$467$	8.45644	+	14.6470i	0.391317	+	0.677782i	0.992624	−	0.121237i	$-0.0386862\pi$
$467$	8.45644	+	14.6470i	0.391317	+	0.677782i	−0.601306	+	0.799019i	$0.705353\pi$
$468$		0			0
$469$	−18.8348			−0.869713
$470$	−4.18693	+	2.41733i	−0.193129	+	0.111503i
$471$		0			0
$472$	−8.29129	−	14.3609i	−0.381637	−	0.661015i
$473$	13.7477	+	7.93725i	0.632121	+	0.364955i
$474$		0			0
$475$	9.16515	+	5.29150i	0.420526	+	0.242791i
$476$	−4.10436	−	2.36965i	−0.188123	−	0.108613i
$477$		0			0
$478$	6.79129	−	11.7629i	0.310626	−	0.538020i
$479$		−	35.2131i		−	1.60893i	−0.594001	−	0.804464i	$-0.702453\pi$
$479$		−	35.2131i		−	1.60893i	0.594001	−	0.804464i	$-0.297547\pi$
$480$		0			0
$481$	3.08258	−	12.4581i	0.140553	−	0.568040i
$482$	−8.04356			−0.366374
$483$		0			0
$484$	0.895644	+	1.55130i	0.0407111	+	0.0705137i
$485$	−0.165151			−0.00749914
$486$		0			0
$487$	−32.4564	+	18.7387i	−1.47074	+	0.849133i	−0.999460	−	0.0328498i	$-0.989542\pi$
$487$	−32.4564	+	18.7387i	−1.47074	+	0.849133i	−0.471281	+	0.881983i	$0.656208\pi$
$488$		−	22.8027i		−	1.03223i
$489$		0			0
$490$	−5.53901			−0.250227
$491$	−11.8739	−	20.5661i	−0.535860	−	0.928137i	−0.999121	−	0.0419149i	$-0.986654\pi$
$491$	−11.8739	−	20.5661i	−0.535860	−	0.928137i	0.463261	−	0.886222i	$-0.346679\pi$
$492$		0			0
$493$	3.50000	−	6.06218i	0.157632	−	0.273027i
$494$	−8.46099	−	2.09355i	−0.380678	−	0.0941933i
$495$		0			0
$496$	1.97822	−	1.14213i	0.0888247	−	0.0512830i
$497$	−15.0826	+	26.1238i	−0.676546	+	1.17181i
$498$		0			0
$499$	26.2913	−	15.1793i	1.17696	−	0.679518i	0.221650	−	0.975126i	$-0.428856\pi$
$499$	26.2913	−	15.1793i	1.17696	−	0.679518i	0.955309	+	0.295608i	$0.0955223\pi$
$500$	18.8085	−	10.8591i	0.841143	−	0.485634i
$501$		0			0
$502$	−4.51723	+	2.60803i	−0.201614	+	0.116402i
$503$	−12.8739	+	22.2982i	−0.574017	+	0.994227i	0.422130	+	0.906535i	$0.361282\pi$
$503$	−12.8739	+	22.2982i	−0.574017	+	0.994227i	−0.996148	+	0.0876919i	$0.972051\pi$
$504$		0			0
$505$	7.74773	−	4.47315i	0.344769	−	0.199053i
$506$	0.460985	+	0.798450i	0.0204933	+	0.0354954i
$507$		0			0
$508$	2.31307	−	4.00635i	0.102626	−	0.177753i
$509$	−3.24773	−	1.87508i	−0.143953	−	0.0831113i	0.426294	−	0.904585i	$-0.359819\pi$
$509$	−3.24773	−	1.87508i	−0.143953	−	0.0831113i	−0.570247	+	0.821474i	$0.693152\pi$
$510$		0			0
$511$	11.4564	−	19.8431i	0.506803	−	0.877809i
$512$		−	22.8981i		−	1.01196i
$513$		0			0
$514$	10.8131	−	6.24293i	0.476944	−	0.275364i
$515$	−18.8739	−	10.8968i	−0.831682	−	0.480172i
$516$		0			0
$517$	−10.5826	−	18.3296i	−0.465421	−	0.806133i
$518$	3.72595	−	2.15118i	0.163709	−	0.0945173i
$519$		0			0
$520$	−7.50000	+	7.79423i	−0.328897	+	0.341800i
$521$	−16.6652	+	28.8649i	−0.730114	+	1.26459i	0.226721	+	0.973960i	$0.427200\pi$
$521$	−16.6652	+	28.8649i	−0.730114	+	1.26459i	−0.956834	+	0.290634i	$0.906134\pi$
$522$		0			0
$523$	−8.87386	+	15.3700i	−0.388027	+	0.672082i	−0.992184	−	0.124783i	$-0.960177\pi$
$523$	−8.87386	+	15.3700i	−0.388027	+	0.672082i	0.604157	+	0.796865i	$0.293510\pi$
$524$	9.47822	−	16.4168i	0.414058	−	0.717169i
$525$		0			0
$526$	9.16515	+	5.29150i	0.399620	+	0.230720i
$527$		−	0.818350i		−	0.0356479i
$528$		0			0
$529$	11.3303	+	19.6247i	0.492622	+	0.853246i
$530$	4.81307	−	8.33648i	0.209066	−	0.362113i
$531$		0			0
$532$	12.5390	+	21.7182i	0.543635	+	0.941604i
$533$	18.2477	+	17.5589i	0.790397	+	0.760560i
$534$		0			0
$535$			18.3296i			0.792456i
$536$	−12.3303			−0.532588
$537$		0			0
$538$		−	0.989150i		−	0.0426453i
$539$		−	24.2487i		−	1.04447i
$540$		0			0
$541$	−25.6652	+	14.8178i	−1.10343	+	0.637066i	−0.937120	−	0.349007i	$-0.886519\pi$
$541$	−25.6652	+	14.8178i	−1.10343	+	0.637066i	−0.166311	+	0.986073i	$0.553186\pi$
$542$	5.81307	+	10.0685i	0.249693	+	0.432480i
$543$		0			0
$544$	−4.10436	−	2.36965i	−0.175973	−	0.101598i
$545$	−3.33030			−0.142654
$546$		0			0
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$	−13.4347	−	7.75650i	−0.573900	−	0.331341i
$549$		0			0
$550$	−1.58258	−	2.74110i	−0.0674813	−	0.116881i
$551$	−32.0780	+	18.5203i	−1.36657	+	0.788990i
$552$		0			0
$553$	24.2477	−	13.9994i	1.03112	−	0.595316i
$554$			12.4859i			0.530473i
$555$		0			0
$556$	4.62614			0.196192
$557$		−	3.27340i		−	0.138698i	−0.997592	−	0.0693492i	$-0.977908\pi$
$557$		−	3.27340i		−	0.138698i	0.997592	−	0.0693492i	$-0.0220923\pi$
$558$		0			0
$559$	−16.0390	−	3.96863i	−0.678378	−	0.167855i
$560$	12.7913			0.540531
$561$		0			0
$562$	4.00000	−	6.92820i	0.168730	−	0.292249i
$563$	7.29129	+	12.6289i	0.307291	+	0.532244i	0.977769	−	0.209686i	$-0.0672441\pi$
$563$	7.29129	+	12.6289i	0.307291	+	0.532244i	−0.670478	+	0.741930i	$0.733911\pi$
$564$		0			0
$565$			10.6784i			0.449242i
$566$	2.50455	+	1.44600i	0.105274	+	0.0607799i
$567$		0			0
$568$	−9.87386	+	17.1020i	−0.414298	+	0.717585i
$569$	15.6652	−	27.1328i	0.656717	−	1.13747i	−0.324743	−	0.945802i	$-0.605278\pi$
$569$	15.6652	−	27.1328i	0.656717	−	1.13747i	0.981460	−	0.191665i	$-0.0613889\pi$
$570$		0			0
$571$	−10.1261	+	17.5390i	−0.423766	+	0.733984i	−0.996304	−	0.0858941i	$-0.972625\pi$
$571$	−10.1261	+	17.5390i	−0.423766	+	0.733984i	0.572539	+	0.819878i	$0.305959\pi$
$572$	−16.1216	−	15.5130i	−0.674078	−	0.648631i
$573$		0			0
$574$			8.48945i			0.354343i
$575$	0.582576	+	1.00905i	0.0242951	+	0.0420803i
$576$		0			0
$577$	−2.91742	−	1.68438i	−0.121454	−	0.0701215i	0.438042	−	0.898954i	$-0.355672\pi$
$577$	−2.91742	−	1.68438i	−0.121454	−	0.0701215i	−0.559496	+	0.828833i	$0.689005\pi$
$578$	6.33030	−	3.65480i	0.263306	−	0.152020i
$579$		0			0
$580$			21.7182i			0.901800i
$581$	−9.16515			−0.380235
$582$		0			0
$583$	36.4955	+	21.0707i	1.51149	+	0.872658i
$584$	7.50000	−	12.9904i	0.310352	−	0.537546i
$585$		0			0
$586$	5.23049	+	9.05948i	0.216070	+	0.374244i
$587$	5.12614	−	2.95958i	0.211578	−	0.122155i	−0.390466	−	0.920617i	$-0.627686\pi$
$587$	5.12614	−	2.95958i	0.211578	−	0.122155i	0.602045	+	0.798462i	$0.294353\pi$
$588$		0			0
$589$	−2.16515	+	3.75015i	−0.0892135	+	0.154522i
$590$	6.56080	−	3.78788i	0.270104	−	0.155944i
$591$		0			0
$592$	−8.60436	+	4.96773i	−0.353637	+	0.204172i
$593$	12.2477	−	7.07123i	0.502954	−	0.290381i	−0.226979	−	0.973900i	$-0.572885\pi$
$593$	12.2477	−	7.07123i	0.502954	−	0.290381i	0.729933	+	0.683519i	$0.239551\pi$
$594$		0			0
$595$	2.29129	−	3.96863i	0.0939336	−	0.162698i
$596$	27.1652	−	15.6838i	1.11273	−	0.642434i
$597$		0			0
$598$	−0.691478	−	0.665375i	−0.0282766	−	0.0272092i
$599$	17.8739	−	30.9584i	0.730306	−	1.26493i	−0.226446	−	0.974024i	$-0.572711\pi$
$599$	17.8739	−	30.9584i	0.730306	−	1.26493i	0.956752	−	0.290904i	$-0.0939560\pi$
$600$		0			0
$601$	−3.91742	−	6.78518i	−0.159795	−	0.276773i	0.775000	−	0.631962i	$-0.217750\pi$
$601$	−3.91742	−	6.78518i	−0.159795	−	0.276773i	−0.934795	+	0.355189i	$0.884417\pi$
$602$	−2.76951	−	4.79693i	−0.112877	−	0.195508i
$603$		0			0
$604$		−	17.4913i		−	0.711711i
$605$	−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	$0.551909\pi$
$608$	12.5390	+	21.7182i	0.508524	+	0.880790i
$609$		0			0
$610$	10.4174			0.421789
$611$	15.8739	+	15.2746i	0.642188	+	0.617945i
$612$		0			0
$613$		−	3.27340i		−	0.132211i	−0.997813	−	0.0661057i	$-0.978943\pi$
$613$		−	3.27340i		−	0.132211i	0.997813	−	0.0661057i	$-0.0210575\pi$
$614$	0.0435608	−	0.0754495i	0.00175797	−	0.00304489i
$615$		0			0
$616$		−	15.8745i		−	0.639602i
$617$	−9.24773	−	5.33918i	−0.372299	−	0.214947i	0.302163	−	0.953256i	$-0.402291\pi$
$617$	−9.24773	−	5.33918i	−0.372299	−	0.214947i	−0.674463	+	0.738309i	$0.735625\pi$
$618$		0			0
$619$	−31.0390	−	17.9204i	−1.24756	−	0.720281i	−0.276940	−	0.960887i	$-0.589320\pi$
$619$	−31.0390	−	17.9204i	−1.24756	−	0.720281i	−0.970623	+	0.240606i	$0.922654\pi$
$620$	1.26951	+	2.19885i	0.0509846	+	0.0883080i
$621$		0			0
$622$	0.230493	−	0.133075i	0.00924191	−	0.00533582i
$623$	20.6216	−	35.7176i	0.826187	−	1.43100i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$			14.6947i			0.587317i
$627$		0			0
$628$	−14.6261			−0.583646
$629$			3.55945i			0.141925i
$630$		0			0
$631$	−17.1261	−	9.88778i	−0.681781	−	0.393626i	0.118745	−	0.992925i	$-0.462113\pi$
$631$	−17.1261	−	9.88778i	−0.681781	−	0.393626i	−0.800526	+	0.599299i	$0.795446\pi$
$632$	15.8739	−	9.16478i	0.631428	−	0.364555i
$633$		0			0
$634$	8.79129			0.349147
$635$	3.87386	+	2.23658i	0.153730	+	0.0887558i
$636$		0			0
$637$	7.00000	+	24.2487i	0.277350	+	0.960769i
$638$	11.0780			0.438583
$639$		0			0
$640$	19.1216			0.755847
$641$	19.2477	+	33.3380i	0.760240	+	1.31677i	0.942727	+	0.333565i	$0.108252\pi$
$641$	19.2477	+	33.3380i	0.760240	+	1.31677i	−0.182487	+	0.983208i	$0.558415\pi$
$642$		0			0
$643$	6.54356	+	3.77793i	0.258053	+	0.148987i	0.623446	−	0.781866i	$-0.285732\pi$
$643$	6.54356	+	3.77793i	0.258053	+	0.148987i	−0.365393	+	0.930853i	$0.619065\pi$
$644$			2.76100i			0.108799i
$645$		0			0
$646$	2.41742			0.0951123
$647$	1.66970			0.0656426			0.0328213	−	0.999461i	$-0.489551\pi$
$647$	1.66970			0.0656426			0.0328213	+	0.999461i	$0.489551\pi$
$648$		0			0
$649$	16.5826	+	28.7219i	0.650923	+	1.12743i
$650$	2.37386	+	2.28425i	0.0931106	+	0.0895957i
$651$		0			0
$652$	5.37386	−	3.10260i	0.210457	−	0.121507i
$653$	−14.2477	+	24.6778i	−0.557557	+	0.965716i	0.440143	+	0.897928i	$0.354928\pi$
$653$	−14.2477	+	24.6778i	−0.557557	+	0.965716i	−0.997700	+	0.0677888i	$0.978406\pi$
$654$		0			0
$655$	15.8739	+	9.16478i	0.620243	+	0.358098i
$656$		−	19.6048i		−	0.765437i
$657$		0			0
$658$			7.38505i			0.287899i
$659$	−22.0390	+	38.1727i	−0.858518	+	1.48700i	0.0148242	+	0.999890i	$0.495281\pi$
$659$	−22.0390	+	38.1727i	−0.858518	+	1.48700i	−0.873342	+	0.487107i	$0.838052\pi$
$660$		0			0
$661$			26.2668i			1.02166i	0.859682	+	0.510830i	$0.170662\pi$
$661$			26.2668i			1.02166i	−0.859682	+	0.510830i	$0.829338\pi$
$662$	3.53901	−	6.12975i	0.137548	−	0.238240i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	−21.0000	+	12.1244i	−0.814345	+	0.470162i
$666$		0			0
$667$	−4.07803			−0.157902
$668$	−17.6869	−	10.2116i	−0.684328	−	0.395097i
$669$		0			0
$670$		−	5.63310i		−	0.217626i
$671$			45.6054i			1.76058i
$672$		0			0
$673$	−0.665151	−	1.15208i	−0.0256397	−	0.0444093i	0.852921	−	0.522040i	$-0.174829\pi$
$673$	−0.665151	−	1.15208i	−0.0256397	−	0.0444093i	−0.878561	+	0.477631i	$0.841496\pi$
$674$	−12.4610	−	7.19435i	−0.479979	−	0.277116i
$675$		0			0
$676$	20.5998	+	10.8591i	0.792300	+	0.417658i
$677$	24.0826	+	41.7122i	0.925569	+	1.60313i	0.790644	+	0.612276i	$0.209746\pi$
$677$	24.0826	+	41.7122i	0.925569	+	1.60313i	0.134924	+	0.990856i	$0.456921\pi$
$678$		0			0
$679$	−0.126136	+	0.218475i	−0.00484067	+	0.00838429i
$680$	1.50000	−	2.59808i	0.0575224	−	0.0996317i
$681$		0			0
$682$	1.12159	−	0.647551i	0.0429479	−	0.0247960i
$683$	−20.1261	+	11.6198i	−0.770105	+	0.444620i	−0.832912	−	0.553405i	$-0.813328\pi$
$683$	−20.1261	+	11.6198i	−0.770105	+	0.444620i	0.0628069	+	0.998026i	$0.479995\pi$
$684$		0			0
$685$	7.50000	−	12.9904i	0.286560	−	0.496337i
$686$	−4.23049	+	7.32743i	−0.161521	+	0.279763i
$687$		0			0
$688$	6.39564	+	11.0776i	0.243832	+	0.422329i
$689$	−42.5780	−	10.5353i	−1.62209	−	0.401364i
$690$		0			0
$691$	−29.4564	−	17.0067i	−1.12058	−	0.646965i	−0.179028	−	0.983844i	$-0.557295\pi$
$691$	−29.4564	−	17.0067i	−1.12058	−	0.646965i	−0.941548	+	0.336879i	$0.890629\pi$
$692$	−11.0436	−	19.1280i	−0.419813	−	0.727138i
$693$		0			0
$694$			0.798450i			0.0303087i
$695$			4.47315i			0.169676i
$696$		0			0
$697$	−6.08258	−	3.51178i	−0.230394	−	0.133018i
$698$	−0.0435608			−0.00164880
$699$		0			0
$700$		−	9.47860i		−	0.358258i
$701$	−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
$703$	9.41742	−	16.3115i	0.355185	−	0.615198i
$704$			11.8383i			0.446173i
$705$		0			0
$706$	−2.83485	+	4.91010i	−0.106691	+	0.184794i
$707$		−	13.6657i		−	0.513952i
$708$		0			0
$709$			18.9572i			0.711953i	0.934495	+	0.355976i	$0.115852\pi$
$709$			18.9572i			0.711953i	−0.934495	+	0.355976i	$0.884148\pi$
$710$	−7.81307	−	4.51088i	−0.293219	−	0.169290i
$711$		0			0
$712$	13.5000	−	23.3827i	0.505934	−	0.876303i
$713$	−0.412878	+	0.238375i	−0.0154624	+	0.00892723i
$714$		0			0
$715$	15.0000	−	15.5885i	0.560968	−	0.582975i
$716$	17.1652	+	29.7309i	0.641492	+	1.11110i
$717$		0			0
$718$	−8.46099			−0.315761
$719$	−2.33030			−0.0869056			−0.0434528	−	0.999055i	$-0.513836\pi$
$719$	−2.33030			−0.0869056			−0.0434528	+	0.999055i	$0.513836\pi$
$720$		0			0
$721$	−28.8303	+	16.6452i	−1.07370	+	0.619899i
$722$	−3.56080	−	2.05583i	−0.132519	−	0.0765099i
$723$		0			0
$724$	−19.7042	−	34.1286i	−0.732300	−	1.26838i
$725$	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
$730$	5.93466	+	3.42638i	0.219652	+	0.126816i
$731$	4.58258			0.169493
$732$		0			0
$733$	−10.8303	+	6.25288i	−0.400026	+	0.230955i	−0.686495	−	0.727134i	$-0.740852\pi$
$733$	−10.8303	+	6.25288i	−0.400026	+	0.230955i	0.286469	+	0.958090i	$0.407518\pi$
$734$	−1.25227	−	0.723000i	−0.0462222	−	0.0266864i
$735$		0			0
$736$			2.76100i			0.101772i
$737$	24.6606			0.908385
$738$		0			0
$739$		−	8.56490i		−	0.315065i	−0.987514	−	0.157533i	$-0.949646\pi$
$739$		−	8.56490i		−	0.315065i	0.987514	−	0.157533i	$-0.0503539\pi$
$740$	−5.52178	−	9.56400i	−0.202985	−	0.351580i
$741$		0			0
$742$	−7.35208	−	12.7342i	−0.269903	−	0.467487i
$743$	−11.2913	+	6.51903i	−0.414237	+	0.239160i	−0.692609	−	0.721314i	$-0.743539\pi$
$743$	−11.2913	+	6.51903i	−0.414237	+	0.239160i	0.278372	+	0.960473i	$0.410205\pi$
$744$		0			0
$745$	15.1652	+	26.2668i	0.555608	+	0.962342i
$746$	−10.2867	−	5.93905i	−0.376624	−	0.217444i
$747$		0			0
$748$	5.37386	+	3.10260i	0.196488	+	0.113442i
$749$	24.2477	+	13.9994i	0.885993	+	0.511528i
$750$		0			0
$751$	−16.4564	+	28.5034i	−0.600504	+	1.04010i	0.392241	+	0.919863i	$0.371700\pi$
$751$	−16.4564	+	28.5034i	−0.600504	+	1.04010i	−0.992745	+	0.120241i	$0.961633\pi$
$752$		−	17.0544i		−	0.621908i
$753$		0			0
$754$	−11.0780	+	3.19795i	−0.403438	+	0.116463i
$755$	16.9129			0.615523
$756$		0			0
$757$	25.2477	+	43.7303i	0.917644	+	1.58941i	0.802983	+	0.596002i	$0.203245\pi$
$757$	25.2477	+	43.7303i	0.917644	+	1.58941i	0.114661	+	0.993405i	$0.463422\pi$
$758$	−8.46099			−0.307317
$759$		0			0
$760$	−13.7477	+	7.93725i	−0.498682	+	0.287914i
$761$			33.1950i			1.20332i	0.798753	+	0.601659i	$0.205493\pi$
$761$			33.1950i			1.20332i	−0.798753	+	0.601659i	$0.794507\pi$
$762$		0			0
$763$	−2.54356	+	4.40558i	−0.0920831	+	0.159493i
$764$	20.0000	+	34.6410i	0.723575	+	1.25327i
$765$		0			0
$766$	5.62614	−	9.74475i	0.203281	−	0.352092i
$767$	−24.8739	−	23.9349i	−0.898143	−	0.864239i
$768$		0			0
$769$	−12.0826	+	6.97588i	−0.435709	+	0.251557i	−0.701776	−	0.712398i	$-0.747609\pi$
$769$	−12.0826	+	6.97588i	−0.435709	+	0.251557i	0.266067	+	0.963955i	$0.414276\pi$
$770$	7.25227			0.261354
$771$		0			0
$772$	−27.1652	+	15.6838i	−0.977695	+	0.564473i
$773$	6.24773	−	3.60713i	0.224715	−	0.129739i	−0.383417	−	0.923576i	$-0.625253\pi$
$773$	6.24773	−	3.60713i	0.224715	−	0.129739i	0.608132	+	0.793836i	$0.291919\pi$
$774$		0			0
$775$	1.41742	−	0.818350i	0.0509154	−	0.0293960i
$776$	−0.0825757	+	0.143025i	−0.00296429	+	0.00513431i
$777$		0			0
$778$	−3.69148	+	2.13128i	−0.132346	+	0.0764099i
$779$	18.5826	+	32.1860i	0.665790	+	1.15318i
$780$		0			0
$781$	19.7477	−	34.2041i	0.706629	−	1.22392i
$782$	0.230493	+	0.133075i	0.00824240	+	0.00475875i
$783$		0			0
$784$	9.76951	−	16.9213i	0.348911	−	0.604332i
$785$		−	14.1425i		−	0.504766i
$786$		0			0
$787$	−21.7087	+	12.5335i	−0.773832	+	0.446772i	−0.834240	−	0.551402i	$-0.814093\pi$
$787$	−21.7087	+	12.5335i	−0.773832	+	0.446772i	0.0604079	+	0.998174i	$0.480760\pi$
$788$	−21.9392	−	12.6666i	−0.781552	−	0.451229i
$789$		0			0
$790$	4.18693	+	7.25198i	0.148964	+	0.258014i
$791$	14.1261	+	8.15573i	0.502268	+	0.289984i
$792$		0			0
$793$	−13.1652	−	45.6054i	−0.467508	−	1.61950i
$794$	3.66970	−	6.35610i	0.130233	−	0.225570i
$795$		0			0
$796$	5.89564	−	10.2116i	0.208966	−	0.361939i
$797$	2.91742	−	5.05313i	0.103340	−	0.178991i	−0.809719	−	0.586818i	$-0.800380\pi$
$797$	2.91742	−	5.05313i	0.103340	−	0.178991i	0.913059	+	0.407828i	$0.133714\pi$
$798$		0			0
$799$	−5.29129	−	3.05493i	−0.187192	−	0.108076i
$800$		−	9.47860i		−	0.335119i
$801$		0			0
$802$	−5.51723	−	9.55613i	−0.194820	−	0.337439i
$803$	−15.0000	+	25.9808i	−0.529339	+	0.916841i
$804$		0			0
$805$	−2.66970			−0.0940945
$806$	−0.934659	+	0.971326i	−0.0329220	+	0.0342135i
$807$		0			0
$808$		−	8.94630i		−	0.314730i
$809$	14.8348			0.521566			0.260783	−	0.965398i	$-0.416019\pi$
$809$	14.8348			0.521566			0.260783	+	0.965398i	$0.416019\pi$
$810$		0			0
$811$			20.9753i			0.736543i	0.929718	+	0.368271i	$0.120050\pi$
$811$			20.9753i			0.736543i	−0.929718	+	0.368271i	$0.879950\pi$
$812$	28.7305	+	16.5876i	1.00824	+	0.582109i
$813$		0			0
$814$	−4.87841	+	2.81655i	−0.170988	+	0.0987201i
$815$	3.00000	+	5.19615i	0.105085	+	0.182013i
$816$		0			0
$817$	−21.0000	−	12.1244i	−0.734697	−	0.424178i
$818$	9.45189			0.330478
$819$		0			0
$820$	21.7913			0.760985
$821$	−5.75227	−	3.32108i	−0.200756	−	0.115906i	0.396252	−	0.918142i	$-0.370311\pi$
$821$	−5.75227	−	3.32108i	−0.200756	−	0.115906i	−0.597008	+	0.802235i	$0.703644\pi$
$822$		0			0
$823$	−10.7087	−	18.5480i	−0.373282	−	0.646544i	0.616786	−	0.787131i	$-0.288434\pi$
$823$	−10.7087	−	18.5480i	−0.373282	−	0.646544i	−0.990068	+	0.140587i	$0.955101\pi$
$824$	−18.8739	+	10.8968i	−0.657502	+	0.379609i
$825$		0			0
$826$		−	11.5722i		−	0.402647i
$827$			4.91010i			0.170741i	0.996349	+	0.0853705i	$0.0272074\pi$
$827$			4.91010i			0.170741i	−0.996349	+	0.0853705i	$0.972793\pi$
$828$		0			0
$829$	26.6606			0.925961			0.462981	−	0.886368i	$-0.346780\pi$
$829$	26.6606			0.925961			0.462981	+	0.886368i	$0.346780\pi$
$830$		−	2.74110i		−	0.0951450i
$831$		0			0
$832$	−3.41742	−	11.8383i	−0.118478	−	0.410419i
$833$	−3.50000	−	6.06218i	−0.121268	−	0.210042i
$834$		0			0
$835$	9.87386	−	17.1020i	0.341699	−	0.591840i
$836$	−16.4174	−	28.4358i	−0.567808	−	0.983473i
$837$		0			0
$838$		−	7.19435i		−	0.248525i
$839$	36.8739	+	21.2891i	1.27303	+	0.734983i	0.975557	−	0.219748i	$-0.0705237\pi$
$839$	36.8739	+	21.2891i	1.27303	+	0.734983i	0.297471	+	0.954731i	$0.403857\pi$
$840$		0			0
$841$	−10.0000	+	17.3205i	−0.344828	+	0.597259i
$842$	7.66970	−	13.2843i	0.264315	−	0.457807i
$843$		0			0
$844$	2.31307	−	4.00635i	0.0796191	−	0.137904i
$845$	−10.5000	+	19.9186i	−0.361211	+	0.685220i
$846$		0			0
$847$			2.64575i			0.0909091i
$848$	16.9782	+	29.4071i	0.583034	+	1.00985i
$849$		0			0
$850$	−0.791288	−	0.456850i	−0.0271409	−	0.0156698i
$851$	1.79583	−	1.03683i	0.0615604	−	0.0355419i
$852$		0			0
$853$		−	52.1522i		−	1.78566i	−0.450396	−	0.892829i	$-0.648717\pi$
$853$		−	52.1522i		−	1.78566i	0.450396	−	0.892829i	$-0.351283\pi$
$854$	7.95644	−	13.7810i	0.272264	−	0.471575i
$855$		0			0
$856$	15.8739	+	9.16478i	0.542557	+	0.313246i
$857$	−12.6652	+	21.9367i	−0.432633	+	0.749343i	−0.997099	−	0.0761135i	$-0.975749\pi$
$857$	−12.6652	+	21.9367i	−0.432633	+	0.749343i	0.564466	+	0.825456i	$0.309082\pi$
$858$		0			0
$859$	0.543561	+	0.941475i	0.0185461	+	0.0321227i	0.875149	−	0.483853i	$-0.160763\pi$
$859$	0.543561	+	0.941475i	0.0185461	+	0.0321227i	−0.856603	+	0.515975i	$0.827430\pi$
$860$	−12.3131	+	7.10895i	−0.419872	+	0.242413i
$861$		0			0
$862$	4.37386	−	7.57575i	0.148974	−	0.258031i
$863$	5.45644	−	3.15028i	0.185739	−	0.107237i	−0.404247	−	0.914650i	$-0.632466\pi$
$863$	5.45644	−	3.15028i	0.185739	−	0.107237i	0.589986	+	0.807413i	$0.299133\pi$
$864$		0			0
$865$	18.4955	−	10.6784i	0.628864	−	0.363075i
$866$	−8.43920	+	4.87238i	−0.286776	+	0.165570i
$867$		0			0
$868$	3.87841			0.131642
$869$	−31.7477	+	18.3296i	−1.07697	+	0.621788i
$870$		0			0
$871$	−24.6606	+	7.11890i	−0.835593	+	0.241215i
$872$	−1.66515	+	2.88413i	−0.0563891	+	0.0976689i
$873$		0			0
$874$	−0.704166	−	1.21965i	−0.0238188	−	0.0412553i
$875$	32.0780			1.08444
$876$		0			0
$877$			36.8498i			1.24433i	0.782886	+	0.622165i	$0.213747\pi$
$877$			36.8498i			1.24433i	−0.782886	+	0.622165i	$0.786253\pi$
$878$	0.560795	−	0.323775i	0.0189259	−	0.0109269i
$879$		0			0
$880$	−16.7477			−0.564566
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	−0.990423	−	0.138068i	$-0.955911\pi$
$881$	−18.2477	−	31.6060i	−0.614782	−	1.06483i	0.375641	−	0.926765i	$-0.377422\pi$
$882$		0			0
$883$	13.6697			0.460022			0.230011	−	0.973188i	$-0.426124\pi$
$883$	13.6697			0.460022			0.230011	+	0.973188i	$0.426124\pi$
$884$	−6.26951	−	1.55130i	−0.210866	−	0.0521759i
$885$		0			0
$886$			9.93545i			0.333788i
$887$	−23.2913	+	40.3417i	−0.782045	+	1.35454i	0.148704	+	0.988882i	$0.452490\pi$
$887$	−23.2913	+	40.3417i	−0.782045	+	1.35454i	−0.930749	+	0.365660i	$0.880843\pi$
$888$		0			0
$889$	5.91742	−	3.41643i	0.198464	−	0.114583i
$890$	10.6824	+	6.16748i	0.358074	+	0.206734i
$891$		0			0
$892$	−4.10436	−	2.36965i	−0.137424	−	0.0793418i
$893$	16.1652	+	27.9989i	0.540946	+	0.936946i
$894$		0			0
$895$	−28.7477	+	16.5975i	−0.960931	+	0.554794i
$896$	14.6044	−	25.2955i	0.487897	−	0.845063i
$897$		0			0
$898$	−2.02178	−	3.50183i	−0.0674677	−	0.116857i
$899$			5.72845i			0.191055i
$900$		0			0
$901$	12.1652			0.405280
$902$		−	11.1153i		−	0.370099i
$903$		0			0
$904$	9.24773	+	5.33918i	0.307575	+	0.177578i
$905$	33.0000	−	19.0526i	1.09696	−	0.633328i
$906$		0			0
$907$	27.1652			0.902004			0.451002	−	0.892523i	$-0.351067\pi$
$907$	27.1652			0.902004			0.451002	+	0.892523i	$0.351067\pi$
$908$	31.5653	+	18.2243i	1.04753	+	0.604793i
$909$		0			0
$910$	−7.25227	+	2.09355i	−0.240411	+	0.0694005i
$911$	24.6606			0.817042			0.408521	−	0.912749i	$-0.366045\pi$
$911$	24.6606			0.817042			0.408521	+	0.912749i	$0.366045\pi$
$912$		0			0
$913$	12.0000			0.397142
$914$	6.39564	+	11.0776i	0.211549	+	0.366414i
$915$		0			0
$916$	0.147917	+	0.0853998i	0.00488731	+	0.00282169i
$917$	24.2477	−	13.9994i	0.800730	−	0.462302i
$918$		0			0
$919$	−23.1652			−0.764148			−0.382074	−	0.924132i	$-0.624790\pi$
$919$	−23.1652			−0.764148			−0.382074	+	0.924132i	$0.624790\pi$
$920$	−1.74773			−0.0576209
$921$		0			0
$922$	−4.85663	−	8.41193i	−0.159945	−	0.277032i
$923$	−9.87386	+	39.9047i	−0.325002	+	1.31348i
$924$		0			0
$925$	−6.16515	+	3.55945i	−0.202709	+	0.117034i
$926$	0.878409	−	1.52145i	0.0288663	−	0.0499979i
$927$		0			0
$928$	28.7305	+	16.5876i	0.943125	+	0.544513i
$929$		−	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
$932$	1.64337	−	2.84640i	0.0538304	−	0.0932370i
$933$		0			0
$934$			7.72665i			0.252824i
$935$	−3.00000	+	5.19615i	−0.0981105	+	0.169932i
$936$		0			0
$937$	55.4955			1.81296			0.906479	−	0.422251i	$-0.138760\pi$
$937$	55.4955			1.81296			0.906479	+	0.422251i	$0.138760\pi$
$938$	−7.45189	−	4.30235i	−0.243313	−	0.140477i
$939$		0			0
$940$	18.9564			0.618291
$941$	7.83030	+	4.52083i	0.255261	+	0.147375i	0.622171	−	0.782882i	$-0.286251\pi$
$941$	7.83030	+	4.52083i	0.255261	+	0.147375i	−0.366910	+	0.930256i	$0.619584\pi$
$942$		0			0
$943$			4.09175i			0.133246i
$944$			26.7237i			0.869781i
$945$		0			0
$946$	3.62614	+	6.28065i	0.117896	+	0.204202i
$947$	−19.0390	−	10.9922i	−0.618685	−	0.357198i	0.157672	−	0.987492i	$-0.449601\pi$
$947$	−19.0390	−	10.9922i	−0.618685	−	0.357198i	−0.776357	+	0.630294i	$0.782934\pi$
$948$		0			0
$949$	7.50000	−	30.3109i	0.243460	−	0.983933i
$950$	2.41742	+	4.18710i	0.0784316	+	0.135848i
$951$		0			0
$952$	−2.29129	−	3.96863i	−0.0742611	−	0.128624i
$953$	5.33485	−	9.24023i	0.172813	−	0.299320i	−0.766589	−	0.642138i	$-0.778048\pi$
$953$	5.33485	−	9.24023i	0.172813	−	0.299320i	0.939402	+	0.342817i	$0.111381\pi$
$954$		0			0
$955$	−33.4955	+	19.3386i	−1.08389	+	0.625783i
$956$	−46.1216	+	26.6283i	−1.49168	+	0.861221i
$957$		0			0
$958$	8.04356	−	13.9319i	0.259876	−	0.450118i
$959$	−11.4564	−	19.8431i	−0.369948	−	0.640768i
$960$		0			0
$961$	−15.1652	−	26.2668i	−0.489198	−	0.847317i
$962$	4.06534	−	4.22483i	0.131072	−	0.136214i
$963$		0			0
$964$	27.3131	+	15.7692i	0.879695	+	0.507892i
$965$	−15.1652	−	26.2668i	−0.488183	−	0.845559i
$966$		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
$970$	−0.0653411	−	0.0377247i	−0.00209798	−	0.00121127i
$971$	−13.6697			−0.438681			−0.219341	−	0.975648i	$-0.570391\pi$
$971$	−13.6697			−0.438681			−0.219341	+	0.975648i	$0.570391\pi$
$972$		0			0
$973$	5.91742	+	3.41643i	0.189704	+	0.109526i
$974$	−17.1216			−0.548611
$975$		0			0
$976$	−18.3739	+	31.8245i	−0.588133	+	1.01868i
$977$		−	17.5112i		−	0.560233i	−0.959966	−	0.280117i	$-0.909627\pi$
$977$		−	17.5112i		−	0.560233i	0.959966	−	0.280117i	$-0.0903731\pi$
$978$		0			0
$979$	−27.0000	+	46.7654i	−0.862924	+	1.49463i
$980$	18.8085	+	10.8591i	0.600816	+	0.346881i
$981$		0			0
$982$		−	10.8492i		−	0.346210i
$983$	15.7087	+	9.06943i	0.501030	+	0.289270i	0.729139	−	0.684366i	$-0.239921\pi$
$983$	15.7087	+	9.06943i	0.501030	+	0.289270i	−0.228109	+	0.973636i	$0.573254\pi$
$984$		0			0
$985$	12.2477	−	21.2137i	0.390245	−	0.675924i
$986$	2.76951	−	1.59898i	0.0881991	−	0.0509218i
$987$		0			0
$988$	24.6261	+	23.6965i	0.783462	+	0.753886i
$989$	−1.33485	−	2.31203i	−0.0424457	−	0.0735181i
$990$		0			0
$991$	−40.6606			−1.29163			−0.645813	−	0.763495i	$-0.723482\pi$
$991$	−40.6606			−1.29163			−0.645813	+	0.763495i	$0.723482\pi$
$992$	3.87841			0.123140
$993$		0			0
$994$	−11.9347	+	6.89048i	−0.378544	+	0.218553i
$995$	9.87386	+	5.70068i	0.313023	+	0.180724i
$996$		0			0
$997$	5.33485	+	9.24023i	0.168956	+	0.292641i	0.938053	−	0.346491i	$-0.112627\pi$
$997$	5.33485	+	9.24023i	0.168956	+	0.292641i	−0.769097	+	0.639132i	$0.779294\pi$
$998$	13.8693			0.439026
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.d.361.2		4
3.2	odd	2		273.2.bl.b.88.1	yes	4
7.2	even	3		819.2.bm.d.478.1		4
13.4	even	6		819.2.bm.d.550.2		4
21.2	odd	6		273.2.t.b.205.2	yes	4
39.17	odd	6		273.2.t.b.4.1	✓	4
91.30	even	6	inner	819.2.do.d.667.2		4
273.212	odd	6		273.2.bl.b.121.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.1	✓	4	39.17	odd	6
273.2.t.b.205.2	yes	4	21.2	odd	6
273.2.bl.b.88.1	yes	4	3.2	odd	2
273.2.bl.b.121.1	yes	4	273.212	odd	6
819.2.bm.d.478.1		4	7.2	even	3
819.2.bm.d.550.2		4	13.4	even	6
819.2.do.d.361.2		4	1.1	even	1	trivial
819.2.do.d.667.2		4	91.30	even	6	inner

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)

\(f(q)\)	\(=\)	\(q+(0.395644 + 0.228425i) q^{2} +(-0.895644 - 1.55130i) q^{4} +(1.50000 - 0.866025i) q^{5} -2.64575i q^{7} -1.73205i q^{8} +O(q^{10})\)	\(q+(0.395644 + 0.228425i) q^{2} +(-0.895644 - 1.55130i) q^{4} +(1.50000 - 0.866025i) q^{5} -2.64575i q^{7} -1.73205i q^{8} +0.791288 q^{10} +3.46410i q^{11} +(-1.00000 - 3.46410i) q^{13} +(0.604356 - 1.04678i) q^{14} +(-1.39564 + 2.41733i) q^{16} +(0.500000 + 0.866025i) q^{17} -5.29150i q^{19} +(-2.68693 - 1.55130i) q^{20} +(-0.791288 + 1.37055i) q^{22} +(0.291288 - 0.504525i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(0.395644 - 1.59898i) q^{26} +(-4.10436 + 2.36965i) q^{28} +(-3.50000 - 6.06218i) q^{29} +(-0.708712 - 0.409175i) q^{31} +(-4.10436 + 2.36965i) q^{32} +0.456850i q^{34} +(-2.29129 - 3.96863i) q^{35} +(3.08258 + 1.77973i) q^{37} +(1.20871 - 2.09355i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-6.08258 + 3.51178i) q^{41} +(2.29129 - 3.96863i) q^{43} +(5.37386 - 3.10260i) q^{44} +(0.230493 - 0.133075i) q^{46} +(-5.29129 + 3.05493i) q^{47} -7.00000 q^{49} +(-0.791288 + 0.456850i) q^{50} +(-4.47822 + 4.65390i) q^{52} +(6.08258 - 10.5353i) q^{53} +(3.00000 + 5.19615i) q^{55} -4.58258 q^{56} -3.19795i q^{58} +(8.29129 - 4.78698i) q^{59} +13.1652 q^{61} +(-0.186932 - 0.323775i) q^{62} +3.41742 q^{64} +(-4.50000 - 4.33013i) q^{65} -7.11890i q^{67} +(0.895644 - 1.55130i) q^{68} -2.09355i q^{70} +(-9.87386 - 5.70068i) q^{71} +(7.50000 + 4.33013i) q^{73} +(0.813068 + 1.40828i) q^{74} +(-8.20871 + 4.73930i) q^{76} +9.16515 q^{77} +(5.29129 + 9.16478i) q^{79} +4.83465i q^{80} -3.20871 q^{82} -3.46410i q^{83} +(1.50000 + 0.866025i) q^{85} +(1.81307 - 1.04678i) q^{86} +6.00000 q^{88} +(13.5000 + 7.79423i) q^{89} +(-9.16515 + 2.64575i) q^{91} -1.04356 q^{92} -2.79129 q^{94} +(-4.58258 - 7.93725i) q^{95} +(-0.0825757 - 0.0476751i) q^{97} +(-2.76951 - 1.59898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + q^{4} + 6 q^{5}+O(q^{10}) \) 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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