LMFDB - Embedded newform 819.2.bm.d.478.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			478.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	819.478
Dual form			819.2.bm.d.550.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.456850i q^{2} +1.79129 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-2.29129 + 1.32288i) q^{7} -1.73205i q^{8} +O(q^{10})$	\(q-0.456850i q^{2} +1.79129 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-2.29129 + 1.32288i) q^{7} -1.73205i q^{8} +(-0.395644 + 0.685275i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(0.604356 + 1.04678i) q^{14} +2.79129 q^{16} -1.00000 q^{17} +(-4.58258 + 2.64575i) q^{19} +(-2.68693 - 1.55130i) q^{20} +(-0.791288 + 1.37055i) q^{22} -0.582576 q^{23} +(-1.00000 - 1.73205i) q^{25} +(-1.58258 + 0.456850i) q^{26} +(-4.10436 + 2.36965i) q^{28} +(-3.50000 - 6.06218i) q^{29} +(0.708712 - 0.409175i) q^{31} -4.73930i q^{32} +0.456850i q^{34} +4.58258 q^{35} -3.55945i q^{37} +(1.20871 + 2.09355i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-6.08258 + 3.51178i) q^{41} +(2.29129 - 3.96863i) q^{43} +(-5.37386 - 3.10260i) q^{44} +0.266150i q^{46} +(5.29129 + 3.05493i) q^{47} +(3.50000 - 6.06218i) q^{49} +(-0.791288 + 0.456850i) q^{50} +(-1.79129 - 6.20520i) q^{52} +(6.08258 + 10.5353i) q^{53} +(3.00000 + 5.19615i) q^{55} +(2.29129 + 3.96863i) q^{56} +(-2.76951 + 1.59898i) q^{58} +9.57395i q^{59} +(-6.58258 - 11.4014i) q^{61} +(-0.186932 - 0.323775i) q^{62} +3.41742 q^{64} +(-1.50000 + 6.06218i) q^{65} +(6.16515 + 3.55945i) q^{67} -1.79129 q^{68} -2.09355i q^{70} +(-9.87386 - 5.70068i) q^{71} +(-7.50000 + 4.33013i) q^{73} -1.62614 q^{74} +(-8.20871 + 4.73930i) q^{76} +9.16515 q^{77} +(5.29129 - 9.16478i) q^{79} +(-4.18693 - 2.41733i) q^{80} +(1.60436 + 2.77883i) q^{82} -3.46410i q^{83} +(1.50000 + 0.866025i) q^{85} +(-1.81307 - 1.04678i) q^{86} +(-3.00000 + 5.19615i) q^{88} -15.5885i q^{89} +(6.87386 + 6.61438i) q^{91} -1.04356 q^{92} +(1.39564 - 2.41733i) q^{94} +9.16515 q^{95} +(-0.0825757 - 0.0476751i) q^{97} +(-2.76951 - 1.59898i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} - 6 q^{5}+O(q^{10}) $ 4 * q - 2 * q^4 - 6 * q^5	$ 4 q - 2 q^{4} - 6 q^{5} + 3 q^{10} - 12 q^{11} - 4 q^{13} + 7 q^{14} + 2 q^{16} - 4 q^{17} + 3 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 12 q^{26} - 21 q^{28} - 14 q^{29} + 12 q^{31} + 14 q^{38} - 6 q^{40} - 6 q^{41} + 6 q^{44} + 12 q^{47} + 14 q^{49} + 6 q^{50} + 2 q^{52} + 6 q^{53} + 12 q^{55} + 21 q^{58} - 8 q^{61} + 13 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 2 q^{68} - 12 q^{71} - 30 q^{73} - 34 q^{74} - 42 q^{76} + 12 q^{79} - 3 q^{80} + 11 q^{82} + 6 q^{85} - 21 q^{86} - 12 q^{88} - 50 q^{92} + q^{94} + 18 q^{97} + 21 q^{98}+O(q^{100}) $ 4 * q - 2 * q^4 - 6 * q^5 + 3 * q^10 - 12 * q^11 - 4 * q^13 + 7 * q^14 + 2 * q^16 - 4 * q^17 + 3 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 12 * q^26 - 21 * q^28 - 14 * q^29 + 12 * q^31 + 14 * q^38 - 6 * q^40 - 6 * q^41 + 6 * q^44 + 12 * q^47 + 14 * q^49 + 6 * q^50 + 2 * q^52 + 6 * q^53 + 12 * q^55 + 21 * q^58 - 8 * q^61 + 13 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 2 * q^68 - 12 * q^71 - 30 * q^73 - 34 * q^74 - 42 * q^76 + 12 * q^79 - 3 * q^80 + 11 * q^82 + 6 * q^85 - 21 * q^86 - 12 * q^88 - 50 * q^92 + q^94 + 18 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	0.456850i		−	0.323042i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$		−	0.456850i		−	0.323042i	0.986869	−	0.161521i	$-0.0516399\pi$
$3$		0			0
$3$		0			0
$4$	1.79129			0.895644
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$		0			0
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i
$7$	−2.29129	+	1.32288i	−0.866025	+	0.500000i
$8$		−	1.73205i		−	0.612372i
$9$		0			0
$10$	−0.395644	+	0.685275i	−0.125114	+	0.216703i
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$		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
$16$	2.79129			0.697822
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		0			0
$19$	−4.58258	+	2.64575i	−1.05131	+	0.606977i	−0.923017	−	0.384759i	$-0.874285\pi$
$19$	−4.58258	+	2.64575i	−1.05131	+	0.606977i	−0.128298	+	0.991736i	$0.540951\pi$
$20$	−2.68693	−	1.55130i	−0.600816	−	0.346881i
$21$		0			0
$22$	−0.791288	+	1.37055i	−0.168703	+	0.292202i
$23$	−0.582576			−0.121475			−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	−0.582576			−0.121475			−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−1.58258	+	0.456850i	−0.310369	+	0.0895957i
$27$		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	$-0.643253\pi$
$31$	0.708712	−	0.409175i	0.127288	−	0.0734900i	0.562292	+	0.826939i	$0.309920\pi$
$32$		−	4.73930i		−	0.837798i
$33$		0			0
$34$			0.456850i			0.0783492i
$35$	4.58258			0.774597
$36$		0			0
$37$		−	3.55945i		−	0.585170i	−0.956239	−	0.292585i	$-0.905485\pi$
$37$		−	3.55945i		−	0.585170i	0.956239	−	0.292585i	$-0.0945155\pi$
$38$	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
$46$			0.266150i			0.0392417i
$47$	5.29129	+	3.05493i	0.771814	+	0.445607i	0.833521	−	0.552487i	$-0.186321\pi$
$47$	5.29129	+	3.05493i	0.771814	+	0.445607i	−0.0617076	+	0.998094i	$0.519655\pi$
$48$		0			0
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	−0.791288	+	0.456850i	−0.111905	+	0.0646084i
$51$		0			0
$52$	−1.79129	−	6.20520i	−0.248407	−	0.860507i
$53$	6.08258	+	10.5353i	0.835506	+	1.44714i	0.893618	+	0.448829i	$0.148159\pi$
$53$	6.08258	+	10.5353i	0.835506	+	1.44714i	−0.0581117	+	0.998310i	$0.518508\pi$
$54$		0			0
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	2.29129	+	3.96863i	0.306186	+	0.530330i
$57$		0			0
$58$	−2.76951	+	1.59898i	−0.363654	+	0.209956i
$59$			9.57395i			1.24642i	0.782053	+	0.623211i	$0.214172\pi$
$59$			9.57395i			1.24642i	−0.782053	+	0.623211i	$0.785828\pi$
$60$		0			0
$61$	−6.58258	−	11.4014i	−0.842812	−	1.45979i	−0.887507	−	0.460793i	$-0.847565\pi$
$61$	−6.58258	−	11.4014i	−0.842812	−	1.45979i	0.0446950	−	0.999001i	$-0.485768\pi$
$62$	−0.186932	−	0.323775i	−0.0237404	−	0.0411195i
$63$		0			0
$64$	3.41742			0.427178
$65$	−1.50000	+	6.06218i	−0.186052	+	0.751921i
$66$		0			0
$67$	6.16515	+	3.55945i	0.753193	+	0.434856i	0.826847	−	0.562428i	$-0.190133\pi$
$67$	6.16515	+	3.55945i	0.753193	+	0.434856i	−0.0736534	+	0.997284i	$0.523466\pi$
$68$	−1.79129			−0.217226
$69$		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	$-0.835840\pi$
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.00787336	+	0.999969i	$0.502506\pi$
$74$	−1.62614			−0.189035
$75$		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	−0.398186	−	0.917305i	$-0.630360\pi$
$79$	5.29129	−	9.16478i	0.595316	−	1.03112i	0.993502	−	0.113813i	$-0.0363066\pi$
$80$	−4.18693	−	2.41733i	−0.468113	−	0.270265i
$81$		0			0
$82$	1.60436	+	2.77883i	0.177171	+	0.306870i
$83$		−	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
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$		−	15.5885i		−	1.65237i	−0.563397	−	0.826187i	$-0.690506\pi$
$89$		−	15.5885i		−	1.65237i	0.563397	−	0.826187i	$-0.309494\pi$
$90$		0			0
$91$	6.87386	+	6.61438i	0.720577	+	0.693375i
$92$	−1.04356			−0.108799
$93$		0			0
$94$	1.39564	−	2.41733i	0.143950	−	0.249328i
$95$	9.16515			0.940325
$96$		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
$100$	−1.79129	−	3.10260i	−0.179129	−	0.310260i
$101$	−2.58258	+	4.47315i	−0.256976	+	0.445095i	−0.965430	−	0.260661i	$-0.916059\pi$
$101$	−2.58258	+	4.47315i	−0.256976	+	0.445095i	0.708454	+	0.705757i	$0.249393\pi$
$102$		0			0
$103$	−6.29129	+	10.8968i	−0.619899	+	1.07370i	0.369605	+	0.929189i	$0.379493\pi$
$103$	−6.29129	+	10.8968i	−0.619899	+	1.07370i	−0.989504	+	0.144507i	$0.953840\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	4.81307	−	2.77883i	0.467487	−	0.269903i
$107$	10.5826			1.02306			0.511528	−	0.859267i	$-0.329080\pi$
$107$	10.5826			1.02306			0.511528	+	0.859267i	$0.329080\pi$
$108$		0			0
$109$	1.66515	−	0.961376i	0.159493	−	0.0920831i	−0.418129	−	0.908387i	$-0.637314\pi$
$109$	1.66515	−	0.961376i	0.159493	−	0.0920831i	0.577622	+	0.816304i	$0.303981\pi$
$110$	2.37386	−	1.37055i	0.226339	−	0.130677i
$111$		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
$115$	0.873864	+	0.504525i	0.0814882	+	0.0470472i
$116$	−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
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	−5.20871	+	3.00725i	−0.471575	+	0.272264i
$123$		0			0
$124$	1.26951	−	0.732950i	0.114005	−	0.0658209i
$125$			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	$0.796780\pi$
$128$		−	11.0399i		−	0.975795i
$129$		0			0
$130$	2.76951	+	0.685275i	0.242902	+	0.0601026i
$131$	5.29129	−	9.16478i	0.462302	−	0.800730i	−0.536773	−	0.843727i	$-0.680357\pi$
$131$	5.29129	−	9.16478i	0.462302	−	0.800730i	0.999075	+	0.0429960i	$0.0136903\pi$
$132$		0			0
$133$	7.00000	−	12.1244i	0.606977	−	1.05131i
$134$	1.62614	−	2.81655i	0.140477	−	0.243313i
$135$		0			0
$136$			1.73205i			0.148522i
$137$			8.66025i			0.739895i	0.929053	+	0.369948i	$0.120624\pi$
$137$			8.66025i			0.739895i	−0.929053	+	0.369948i	$0.879376\pi$
$138$		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	$0.201600\pi$
$140$	8.20871			0.693763
$141$		0			0
$142$	−2.60436	+	4.51088i	−0.218553	+	0.378544i
$143$	−3.00000	+	12.1244i	−0.250873	+	1.01389i
$144$		0			0
$145$			12.1244i			1.00687i
$146$	1.97822	+	3.42638i	0.163719	+	0.283569i
$147$		0			0
$148$		−	6.37600i		−	0.524104i
$149$	15.1652	−	8.75560i	1.24238	−	0.717287i	0.272800	−	0.962071i	$-0.412050\pi$
$149$	15.1652	−	8.75560i	1.24238	−	0.717287i	0.969578	+	0.244784i	$0.0787170\pi$
$150$		0			0
$151$	−8.45644	+	4.88233i	−0.688175	+	0.397318i	−0.802928	−	0.596076i	$-0.796726\pi$
$151$	−8.45644	+	4.88233i	−0.688175	+	0.397318i	0.114753	+	0.993394i	$0.463392\pi$
$152$	4.58258	+	7.93725i	0.371696	+	0.643796i
$153$		0			0
$154$		−	4.18710i		−	0.337406i
$155$	−1.41742			−0.113850
$156$		0			0
$157$	4.08258	+	7.07123i	0.325825	+	0.564345i	0.981679	−	0.190542i	$-0.0610246\pi$
$157$	4.08258	+	7.07123i	0.325825	+	0.564345i	−0.655854	+	0.754888i	$0.727691\pi$
$158$	−4.18693	−	2.41733i	−0.333094	−	0.192312i
$159$		0			0
$160$	−4.10436	+	7.10895i	−0.324478	+	0.562012i
$161$	1.33485	−	0.770675i	0.105201	−	0.0607377i
$162$		0			0
$163$	3.00000	−	1.73205i	0.234978	−	0.135665i	−0.377888	−	0.925851i	$-0.623350\pi$
$163$	3.00000	−	1.73205i	0.234978	−	0.135665i	0.612866	+	0.790186i	$0.290016\pi$
$164$	−10.8956	+	6.29060i	−0.850807	+	0.491214i
$165$		0			0
$166$	−1.58258			−0.122832
$167$	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
$172$	4.10436	−	7.10895i	0.312954	−	0.542053i
$173$	−6.16515	−	10.6784i	−0.468728	−	0.811860i	0.530633	−	0.847601i	$-0.321954\pi$
$173$	−6.16515	−	10.6784i	−0.468728	−	0.811860i	−0.999361	+	0.0357412i	$0.988621\pi$
$174$		0			0
$175$	4.58258	+	2.64575i	0.346410	+	0.200000i
$176$	−8.37386	−	4.83465i	−0.631204	−	0.364426i
$177$		0			0
$178$	−7.12159			−0.533786
$179$	9.58258	−	16.5975i	0.716235	−	1.24056i	−0.246246	−	0.969207i	$-0.579197\pi$
$179$	9.58258	−	16.5975i	0.716235	−	1.24056i	0.962481	−	0.271349i	$-0.0874696\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$	3.02178	−	3.14033i	0.223989	−	0.232776i
$183$		0			0
$184$			1.00905i			0.0743882i
$185$	−3.08258	+	5.33918i	−0.226635	+	0.392544i
$186$		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
$191$	11.1652	+	19.3386i	0.807882	+	1.39929i	0.914328	+	0.404974i	$0.132720\pi$
$191$	11.1652	+	19.3386i	0.807882	+	1.39929i	−0.106446	+	0.994318i	$0.533947\pi$
$192$		0			0
$193$	15.1652	+	8.75560i	1.09161	+	0.630242i	0.934005	−	0.357260i	$-0.116289\pi$
$193$	15.1652	+	8.75560i	1.09161	+	0.630242i	0.157606	+	0.987502i	$0.449622\pi$
$194$	−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
$199$	−6.58258			−0.466626			−0.233313	−	0.972402i	$-0.574957\pi$
$199$	−6.58258			−0.466626			−0.233313	+	0.972402i	$0.574957\pi$
$200$	−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
$205$	12.1652			0.849651
$206$	4.97822	+	2.87418i	0.346849	+	0.200253i
$207$		0			0
$208$	−2.79129	−	9.66930i	−0.193541	−	0.670446i
$209$	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	$0.804999\pi$
$212$	10.8956	+	18.8718i	0.748316	+	1.29612i
$213$		0			0
$214$		−	4.83465i		−	0.330490i
$215$	−6.87386	+	3.96863i	−0.468794	+	0.270658i
$216$		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
$221$	1.00000	+	3.46410i	0.0672673	+	0.233021i
$222$		0			0
$223$	2.29129	−	1.32288i	0.153436	−	0.0885863i	−0.421316	−	0.906914i	$-0.638432\pi$
$223$	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
$227$		−	20.3477i		−	1.35052i	−0.737579	−	0.675261i	$-0.764031\pi$
$227$		−	20.3477i		−	1.35052i	0.737579	−	0.675261i	$-0.235969\pi$
$228$		0			0
$229$	0.0825757	+	0.0476751i	0.00545676	+	0.00315046i	0.502726	−	0.864446i	$-0.332331\pi$
$229$	0.0825757	+	0.0476751i	0.00545676	+	0.00315046i	−0.497269	+	0.867596i	$0.665664\pi$
$230$	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	−0.834409	−	0.551146i	$-0.814191\pi$
$233$	0.917424	−	1.58903i	0.0601025	−	0.104101i	0.894511	+	0.447046i	$0.147524\pi$
$234$		0			0
$235$	−5.29129	−	9.16478i	−0.345166	−	0.597844i
$236$			17.1497i			1.11635i
$237$		0			0
$238$	−0.604356	−	1.04678i	−0.0391746	−	0.0678524i
$239$		−	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
$241$		−	17.6066i		−	1.13414i	−0.823670	−	0.567069i	$-0.808077\pi$
$241$		−	17.6066i		−	1.13414i	0.823670	−	0.567069i	$-0.191923\pi$
$242$	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
$247$	13.7477	+	13.2288i	0.874747	+	0.841726i
$248$	−0.708712	−	1.22753i	−0.0450033	−	0.0779479i
$249$		0			0
$250$	5.53901			0.350318
$251$	−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
$254$	1.02178	−	0.589925i	0.0641122	−	0.0370152i
$255$		0			0
$256$	1.79129			0.111955
$257$	−27.3303			−1.70482			−0.852409	−	0.522876i	$-0.824859\pi$
$257$	−27.3303			−1.70482			−0.852409	+	0.522876i	$0.824859\pi$
$258$		0			0
$259$	4.70871	+	8.15573i	0.292585	+	0.506772i
$260$	−2.68693	+	10.8591i	−0.166636	+	0.673453i
$261$		0			0
$262$	−4.18693	−	2.41733i	−0.258670	−	0.149343i
$263$	−11.5826	+	20.0616i	−0.714212	+	1.23705i	0.249050	+	0.968491i	$0.419882\pi$
$263$	−11.5826	+	20.0616i	−0.714212	+	1.23705i	−0.963263	+	0.268561i	$0.913452\pi$
$264$		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
$269$	2.16515			0.132012			0.0660058	−	0.997819i	$-0.478974\pi$
$269$	2.16515			0.132012			0.0660058	+	0.997819i	$0.478974\pi$
$270$		0			0
$271$		−	25.4485i		−	1.54588i	−0.634477	−	0.772942i	$-0.718784\pi$
$271$		−	25.4485i		−	1.54588i	0.634477	−	0.772942i	$-0.281216\pi$
$272$	−2.79129			−0.169247
$273$		0			0
$274$	3.95644			0.239017
$275$			6.92820i			0.417786i
$276$		0			0
$277$	−27.3303			−1.64212			−0.821059	−	0.570843i	$-0.806617\pi$
$277$	−27.3303			−1.64212			−0.821059	+	0.570843i	$0.806617\pi$
$278$	1.02178	+	0.589925i	0.0612823	+	0.0353814i
$279$		0			0
$280$		−	7.93725i		−	0.474342i
$281$		−	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
$283$	−3.16515	+	5.48220i	−0.188149	+	0.325883i	−0.944633	−	0.328129i	$-0.893582\pi$
$283$	−3.16515	+	5.48220i	−0.188149	+	0.325883i	0.756484	+	0.654012i	$0.226915\pi$
$284$	−17.6869	−	10.2116i	−1.04953	−	0.605944i
$285$		0			0
$286$	5.53901	+	1.37055i	0.327529	+	0.0810424i
$287$	9.29129	−	16.0930i	0.548447	−	0.949939i
$288$		0			0
$289$	−16.0000			−0.941176
$290$	5.53901			0.325262
$291$		0			0
$292$	−13.4347	+	7.75650i	−0.786204	+	0.453915i
$293$	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
$296$	−6.16515			−0.358342
$297$		0			0
$298$	−4.00000	−	6.92820i	−0.231714	−	0.401340i
$299$	0.582576	+	2.01810i	0.0336912	+	0.116710i
$300$		0			0
$301$			12.1244i			0.698836i
$302$	2.23049	+	3.86333i	0.128350	+	0.222309i
$303$		0			0
$304$	−12.7913	+	7.38505i	−0.733631	+	0.423562i
$305$			22.8027i			1.30568i
$306$		0			0
$307$		−	0.190700i		−	0.0108838i	−0.999985	−	0.00544192i	$-0.998268\pi$
$307$		−	0.190700i		−	0.0108838i	0.999985	−	0.00544192i	$-0.00173223\pi$
$308$	16.4174			0.935470
$309$		0			0
$310$			0.647551i			0.0367784i
$311$	0.291288	+	0.504525i	0.0165174	+	0.0286090i	0.874166	−	0.485627i	$-0.161409\pi$
$311$	0.291288	+	0.504525i	0.0165174	+	0.0286090i	−0.857649	+	0.514236i	$0.828075\pi$
$312$		0			0
$313$	16.0826	−	27.8558i	0.909041	−	1.57451i	0.0936417	−	0.995606i	$-0.470149\pi$
$313$	16.0826	−	27.8558i	0.909041	−	1.57451i	0.815399	−	0.578899i	$-0.196517\pi$
$314$	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	$-0.515062\pi$
$317$	−16.6652	−	9.62163i	−0.936008	−	0.540405i	−0.888707	+	0.458476i	$0.848395\pi$
$318$		0			0
$319$			24.2487i			1.35767i
$320$	−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
$325$	−5.00000	+	5.19615i	−0.277350	+	0.288231i
$326$	−0.791288	−	1.37055i	−0.0438254	−	0.0759078i
$327$		0			0
$328$	6.08258	+	10.5353i	0.335854	+	0.581716i
$329$	−16.1652			−0.891214
$330$		0			0
$331$	−13.4174	+	7.74655i	−0.737488	+	0.425789i	−0.821155	−	0.570705i	$-0.806670\pi$
$331$	−13.4174	+	7.74655i	−0.737488	+	0.425789i	0.0836671	+	0.996494i	$0.473337\pi$
$332$		−	6.20520i		−	0.340555i
$333$		0			0
$334$	−2.60436	−	4.51088i	−0.142504	−	0.246824i
$335$	−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	$0.828190\pi$
$338$	3.16515	+	5.02535i	0.172162	+	0.273343i
$339$		0			0
$340$	2.68693	+	1.55130i	0.145719	+	0.0841311i
$341$	−2.83485			−0.153516
$342$		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
$347$	−1.74773			−0.0938229			−0.0469115	−	0.998899i	$-0.514938\pi$
$347$	−1.74773			−0.0938229			−0.0469115	+	0.998899i	$0.514938\pi$
$348$		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
$353$	−10.7477	−	6.20520i	−0.572044	−	0.330270i	0.185921	−	0.982565i	$-0.440473\pi$
$353$	−10.7477	−	6.20520i	−0.572044	−	0.330270i	−0.757965	+	0.652295i	$0.773806\pi$
$354$		0			0
$355$	9.87386	+	17.1020i	0.524050	+	0.907682i
$356$		−	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	$-0.170793\pi$
$359$	16.0390	+	9.26013i	0.846507	+	0.488731i	−0.0129639	+	0.999916i	$0.504127\pi$
$360$		0			0
$361$	4.50000	−	7.79423i	0.236842	−	0.410223i
$362$		−	10.0507i		−	0.528253i
$363$		0			0
$364$	12.3131	+	11.8483i	0.645380	+	0.621017i
$365$	15.0000			0.785136
$366$		0			0
$367$	1.58258	−	2.74110i	0.0826098	−	0.143084i	−0.821760	−	0.569833i	$-0.807008\pi$
$367$	1.58258	−	2.74110i	0.0826098	−	0.143084i	0.904370	+	0.426749i	$0.140341\pi$
$368$	−1.62614			−0.0847682
$369$		0			0
$370$	2.43920	+	1.40828i	0.126808	+	0.0732128i
$371$	−27.8739	−	16.0930i	−1.44714	−	0.835506i
$372$		0			0
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	0.977016	+	0.213165i	$0.0683772\pi$
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$374$	0.791288	−	1.37055i	0.0409165	−	0.0708695i
$375$		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	$0.491124\pi$
$380$	16.4174			0.842196
$381$		0			0
$382$	8.83485	−	5.10080i	0.452030	−	0.260980i
$383$	−21.3303	+	12.3151i	−1.08993	+	0.629270i	−0.933557	−	0.358429i	$-0.883313\pi$
$383$	−21.3303	+	12.3151i	−1.08993	+	0.629270i	−0.156370	+	0.987698i	$0.549979\pi$
$384$		0			0
$385$	−13.7477	−	7.93725i	−0.700649	−	0.404520i
$386$	4.00000	−	6.92820i	0.203595	−	0.352636i
$387$		0			0
$388$	−0.147917	−	0.0853998i	−0.00750934	−	0.00433552i
$389$	−4.66515	−	8.08028i	−0.236533	−	0.409686i	0.723184	−	0.690655i	$-0.242678\pi$
$389$	−4.66515	−	8.08028i	−0.236533	−	0.409686i	−0.959717	+	0.280969i	$0.909344\pi$
$390$		0			0
$391$	0.582576			0.0294621
$392$	−10.5000	−	6.06218i	−0.530330	−	0.306186i
$393$		0			0
$394$	−3.23049	−	5.59538i	−0.162750	−	0.281891i
$395$	−15.8739	+	9.16478i	−0.798701	+	0.461130i
$396$		0			0
$397$	−13.9129	+	8.03260i	−0.698267	+	0.403145i	−0.806702	−	0.590959i	$-0.798750\pi$
$397$	−13.9129	+	8.03260i	−0.698267	+	0.403145i	0.108434	+	0.994104i	$0.465416\pi$
$398$			3.00725i			0.150740i
$399$		0			0
$400$	−2.79129	−	4.83465i	−0.139564	−	0.241733i
$401$			24.1534i			1.20616i	0.797680	+	0.603081i	$0.206060\pi$
$401$			24.1534i			1.20616i	−0.797680	+	0.603081i	$0.793940\pi$
$402$		0			0
$403$	−2.12614	−	2.04588i	−0.105910	−	0.101912i
$404$	−4.62614	+	8.01270i	−0.230159	+	0.398647i
$405$		0			0
$406$	4.23049	−	7.32743i	0.209956	−	0.363654i
$407$	−6.16515	+	10.6784i	−0.305595	+	0.529306i
$408$		0			0
$409$			20.6893i			1.02302i	0.859278	+	0.511509i	$0.170913\pi$
$409$			20.6893i			1.02302i	−0.859278	+	0.511509i	$0.829087\pi$
$410$		−	5.55765i		−	0.274473i
$411$		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
$416$	−16.4174	+	4.73930i	−0.804930	+	0.232363i
$417$		0			0
$418$		−	8.37420i		−	0.409596i
$419$	−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	$-0.305032\pi$
$422$	1.02178	−	0.589925i	0.0497395	−	0.0287171i
$423$		0			0
$424$	18.2477	−	10.5353i	0.886188	−	0.511641i
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	30.1652	+	17.4159i	1.45979	+	0.842812i
$428$	18.9564			0.916294
$429$		0			0
$430$	1.81307	+	3.14033i	0.0874339	+	0.151440i
$431$	16.5826	+	9.57395i	0.798755	+	0.461161i	0.843035	−	0.537858i	$-0.180766\pi$
$431$	16.5826	+	9.57395i	0.798755	+	0.461161i	−0.0442809	+	0.999019i	$0.514100\pi$
$432$		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
$436$	2.98277	−	1.72210i	0.142849	−	0.0824737i
$437$	2.66970	−	1.54135i	0.127709	−	0.0737328i
$438$		0			0
$439$	−1.41742			−0.0676500			−0.0338250	−	0.999428i	$-0.510769\pi$
$439$	−1.41742			−0.0676500			−0.0338250	+	0.999428i	$0.510769\pi$
$440$	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	−0.483181	−	0.875521i	$-0.660519\pi$
$443$	10.8739	−	18.8341i	0.516633	−	0.894834i	0.999813	−	0.0193136i	$-0.00614811\pi$
$444$		0			0
$445$	−13.5000	+	23.3827i	−0.639961	+	1.10845i
$446$	−0.604356	−	1.04678i	−0.0286171	−	0.0495663i
$447$		0			0
$448$	−7.83030	+	4.52083i	−0.369947	+	0.213589i
$449$	−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
$451$	24.3303			1.14567
$452$	−5.52178	+	9.56400i	−0.259723	+	0.449853i
$453$		0			0
$454$	−9.29583			−0.436275
$455$	−4.58258	−	15.8745i	−0.214834	−	0.744208i
$456$		0			0
$457$		−	27.9989i		−	1.30973i	−0.755745	−	0.654866i	$-0.772725\pi$
$457$		−	27.9989i		−	1.30973i	0.755745	−	0.654866i	$-0.227275\pi$
$458$	0.0217804	−	0.0377247i	0.00101773	−	0.00176276i
$459$		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	$-0.0284815\pi$
$464$	−9.76951	−	16.9213i	−0.453538	−	0.785551i
$465$		0			0
$466$	−0.725947	−	0.419126i	−0.0336288	−	0.0194156i
$467$	8.45644	−	14.6470i	0.391317	−	0.677782i	−0.601306	−	0.799019i	$-0.705353\pi$
$467$	8.45644	−	14.6470i	0.391317	−	0.677782i	0.992624	+	0.121237i	$0.0386862\pi$
$468$		0			0
$469$	−18.8348			−0.869713
$470$	−4.18693	+	2.41733i	−0.193129	+	0.111503i
$471$		0			0
$472$	16.5826			0.763275
$473$	−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
$478$	−13.5826			−0.621253
$479$	30.4955	+	17.6066i	1.39337	+	0.804464i	0.993687	−	0.112188i	$-0.0357859\pi$
$479$	30.4955	+	17.6066i	1.39337	+	0.804464i	0.399686	+	0.916652i	$0.369119\pi$
$480$		0			0
$481$	−12.3303	+	3.55945i	−0.562213	+	0.162297i
$482$	−8.04356			−0.366374
$483$		0			0
$484$	0.895644	+	1.55130i	0.0407111	+	0.0705137i
$485$	0.0825757	+	0.143025i	0.00374957	+	0.00649444i
$486$		0			0
$487$		−	37.4775i		−	1.69827i	−0.528179	−	0.849133i	$-0.677125\pi$
$487$		−	37.4775i		−	1.69827i	0.528179	−	0.849133i	$-0.322875\pi$
$488$	−19.7477	+	11.4014i	−0.893938	+	0.516115i
$489$		0			0
$490$	2.76951	+	4.79693i	0.125114	+	0.216703i
$491$	−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
$494$	6.04356	−	6.28065i	0.271913	−	0.282580i
$495$		0			0
$496$	1.97822	−	1.14213i	0.0888247	−	0.0512830i
$497$	30.1652			1.35309
$498$		0			0
$499$	−26.2913	−	15.1793i	−1.17696	−	0.679518i	−0.221650	−	0.975126i	$-0.571144\pi$
$499$	−26.2913	−	15.1793i	−1.17696	−	0.679518i	−0.955309	+	0.295608i	$0.904478\pi$
$500$			21.7182i			0.971268i
$501$		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
$509$			3.75015i			0.166223i	0.996540	+	0.0831113i	$0.0264857\pi$
$509$			3.75015i			0.166223i	−0.996540	+	0.0831113i	$0.973514\pi$
$510$		0			0
$511$	11.4564	−	19.8431i	0.506803	−	0.877809i
$512$		−	22.8981i		−	1.01196i
$513$		0			0
$514$			12.4859i			0.550727i
$515$	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
$520$	10.5000	+	2.59808i	0.460455	+	0.113933i
$521$	−16.6652	−	28.8649i	−0.730114	−	1.26459i	−0.956834	−	0.290634i	$-0.906134\pi$
$521$	−16.6652	−	28.8649i	−0.730114	−	1.26459i	0.226721	−	0.973960i	$-0.427200\pi$
$522$		0			0
$523$	17.7477			0.776054			0.388027	−	0.921648i	$-0.373157\pi$
$523$	17.7477			0.776054			0.388027	+	0.921648i	$0.373157\pi$
$524$	9.47822	−	16.4168i	0.414058	−	0.717169i
$525$		0			0
$526$	9.16515	+	5.29150i	0.399620	+	0.230720i
$527$	−0.708712	+	0.409175i	−0.0308720	+	0.0178239i
$528$		0			0
$529$	−22.6606			−0.985244
$530$	−9.62614			−0.418133
$531$		0			0
$532$	12.5390	−	21.7182i	0.543635	−	0.941604i
$533$	18.2477	+	17.5589i	0.790397	+	0.760560i
$534$		0			0
$535$	−15.8739	−	9.16478i	−0.686287	−	0.396228i
$536$	6.16515	−	10.6784i	0.266294	−	0.461235i
$537$		0			0
$538$		−	0.989150i		−	0.0426453i
$539$	−21.0000	+	12.1244i	−0.904534	+	0.522233i
$540$		0			0
$541$	25.6652	+	14.8178i	1.10343	+	0.637066i	0.937120	−	0.349007i	$-0.113481\pi$
$541$	25.6652	+	14.8178i	1.10343	+	0.637066i	0.166311	+	0.986073i	$0.446814\pi$
$542$	−11.6261			−0.499385
$543$		0			0
$544$			4.73930i			0.203196i
$545$	−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	$0.554709\pi$
$548$			15.5130i			0.662683i
$549$		0			0
$550$	3.16515			0.134963
$551$	32.0780	+	18.5203i	1.36657	+	0.788990i
$552$		0			0
$553$			27.9989i			1.19063i
$554$			12.4859i			0.530473i
$555$		0			0
$556$	−2.31307	+	4.00635i	−0.0980959	+	0.169907i
$557$	2.83485	+	1.63670i	0.120116	+	0.0693492i	0.558854	−	0.829266i	$-0.311241\pi$
$557$	2.83485	+	1.63670i	0.120116	+	0.0693492i	−0.438738	+	0.898615i	$0.644574\pi$
$558$		0			0
$559$	−16.0390	−	3.96863i	−0.678378	−	0.167855i
$560$	12.7913			0.540531
$561$		0			0
$562$	−8.00000			−0.337460
$563$	−14.5826			−0.614582			−0.307291	−	0.951616i	$-0.599423\pi$
$563$	−14.5826			−0.614582			−0.307291	+	0.951616i	$0.599423\pi$
$564$		0			0
$565$	9.24773	−	5.33918i	0.389055	−	0.224621i
$566$	2.50455	+	1.44600i	0.105274	+	0.0607799i
$567$		0			0
$568$	−9.87386	+	17.1020i	−0.414298	+	0.717585i
$569$	−31.3303			−1.31343			−0.656717	−	0.754137i	$-0.728056\pi$
$569$	−31.3303			−1.31343			−0.656717	+	0.754137i	$0.728056\pi$
$570$		0			0
$571$	−10.1261	−	17.5390i	−0.423766	−	0.733984i	0.572539	−	0.819878i	$-0.305959\pi$
$571$	−10.1261	−	17.5390i	−0.423766	−	0.733984i	−0.996304	+	0.0858941i	$0.972625\pi$
$572$	−5.37386	+	21.7182i	−0.224693	+	0.908084i
$573$		0			0
$574$	−7.35208	−	4.24473i	−0.306870	−	0.177171i
$575$	0.582576	+	1.00905i	0.0242951	+	0.0420803i
$576$		0			0
$577$	2.91742	−	1.68438i	0.121454	−	0.0701215i	−0.438042	−	0.898954i	$-0.644328\pi$
$577$	2.91742	−	1.68438i	0.121454	−	0.0701215i	0.559496	+	0.828833i	$0.310995\pi$
$578$			7.30960i			0.304039i
$579$		0			0
$580$			21.7182i			0.901800i
$581$	4.58258	+	7.93725i	0.190117	+	0.329293i
$582$		0			0
$583$		−	42.1413i		−	1.74532i
$584$	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
$592$		−	9.93545i		−	0.408345i
$593$	−12.2477	−	7.07123i	−0.502954	−	0.290381i	0.226979	−	0.973900i	$-0.427115\pi$
$593$	−12.2477	−	7.07123i	−0.502954	−	0.290381i	−0.729933	+	0.683519i	$0.760449\pi$
$594$		0			0
$595$	−4.58258			−0.187867
$596$	27.1652	−	15.6838i	1.11273	−	0.642434i
$597$		0			0
$598$	0.921970	−	0.266150i	0.0377022	−	0.0108837i
$599$	17.8739	+	30.9584i	0.730306	+	1.26493i	0.956752	+	0.290904i	$0.0939560\pi$
$599$	17.8739	+	30.9584i	0.730306	+	1.26493i	−0.226446	+	0.974024i	$0.572711\pi$
$600$		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	$0.884417\pi$
$602$	5.53901			0.225753
$603$		0			0
$604$	−15.1479	+	8.74565i	−0.616360	+	0.355856i
$605$		−	1.73205i		−	0.0704179i
$606$		0			0
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	0.935713	−	0.352763i	$-0.114758\pi$
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	−0.773358	+	0.633970i	$0.781424\pi$
$608$	12.5390	+	21.7182i	0.508524	+	0.880790i
$609$		0			0
$610$	10.4174			0.421789
$611$	5.29129	−	21.3845i	0.214063	−	0.865124i
$612$		0			0
$613$	2.83485	+	1.63670i	0.114498	+	0.0661057i	0.556156	−	0.831078i	$-0.312276\pi$
$613$	2.83485	+	1.63670i	0.114498	+	0.0661057i	−0.441657	+	0.897184i	$0.645609\pi$
$614$	−0.0871215			−0.00351594
$615$		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	$-0.410680\pi$
$619$	31.0390	−	17.9204i	1.24756	−	0.720281i	0.970623	+	0.240606i	$0.0773462\pi$
$620$	−2.53901			−0.101969
$621$		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
$626$	−12.7259	−	7.34733i	−0.508631	−	0.293658i
$627$		0			0
$628$	7.31307	+	12.6666i	0.291823	+	0.505453i
$629$			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
$634$	−4.39564	+	7.61348i	−0.174573	+	0.302370i
$635$		−	4.47315i		−	0.177512i
$636$		0			0
$637$	−24.5000	−	6.06218i	−0.970725	−	0.240192i
$638$	11.0780			0.438583
$639$		0			0
$640$	−9.56080	+	16.5598i	−0.377924	+	0.654583i
$641$	−38.4955			−1.52048			−0.760240	−	0.649643i	$-0.774918\pi$
$641$	−38.4955			−1.52048			−0.760240	+	0.649643i	$0.774918\pi$
$642$		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	$0.619065\pi$
$644$	2.39110	−	1.38050i	0.0942225	−	0.0543994i
$645$		0			0
$646$	−1.20871	−	2.09355i	−0.0475561	−	0.0823697i
$647$	−0.834849	+	1.44600i	−0.0328213	+	0.0568481i	−0.881969	−	0.471307i	$-0.843783\pi$
$647$	−0.834849	+	1.44600i	−0.0328213	+	0.0568481i	0.849148	+	0.528155i	$0.177116\pi$
$648$		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
$653$	28.4955			1.11511			0.557557	−	0.830139i	$-0.311739\pi$
$653$	28.4955			1.11511			0.557557	+	0.830139i	$0.311739\pi$
$654$		0			0
$655$	−15.8739	+	9.16478i	−0.620243	+	0.358098i
$656$	−16.9782	+	9.80238i	−0.662888	+	0.382719i
$657$		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
$661$	−22.7477	−	13.1334i	−0.884784	−	0.510830i	−0.0125512	−	0.999921i	$-0.503995\pi$
$661$	−22.7477	−	13.1334i	−0.884784	−	0.510830i	−0.872233	+	0.489091i	$0.837329\pi$
$662$	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
$667$	2.03901	+	3.53168i	0.0789510	+	0.136747i
$668$	17.6869	−	10.2116i	0.684328	−	0.395097i
$669$		0			0
$670$	−4.87841	+	2.81655i	−0.188469	+	0.108813i
$671$			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	$0.841496\pi$
$674$			14.3887i			0.554232i
$675$		0			0
$676$	−19.7042	+	12.4104i	−0.757853	+	0.477323i
$677$	24.0826	−	41.7122i	0.925569	−	1.60313i	0.134924	−	0.990856i	$-0.456921\pi$
$677$	24.0826	−	41.7122i	0.925569	−	1.60313i	0.790644	−	0.612276i	$-0.209746\pi$
$678$		0			0
$679$	0.252273			0.00968135
$680$	1.50000	−	2.59808i	0.0575224	−	0.0996317i
$681$		0			0
$682$			1.29510i			0.0495920i
$683$		−	23.2397i		−	0.889241i	−0.895719	−	0.444620i	$-0.853339\pi$
$683$		−	23.2397i		−	0.889241i	0.895719	−	0.444620i	$-0.146661\pi$
$684$		0			0
$685$	7.50000	−	12.9904i	0.286560	−	0.496337i
$686$	8.46099			0.323042
$687$		0			0
$688$	6.39564	−	11.0776i	0.243832	−	0.422329i
$689$	30.4129	−	31.6060i	1.15864	−	1.20409i
$690$		0			0
$691$			34.0134i			1.29393i	0.762520	+	0.646965i	$0.223962\pi$
$691$			34.0134i			1.29393i	−0.762520	+	0.646965i	$0.776038\pi$
$692$	−11.0436	−	19.1280i	−0.419813	−	0.727138i
$693$		0			0
$694$			0.798450i			0.0303087i
$695$	3.87386	−	2.23658i	0.146944	−	0.0848382i
$696$		0			0
$697$	6.08258	−	3.51178i	0.230394	−	0.133018i
$698$	0.0217804	+	0.0377247i	0.000824400	+	0.00142790i
$699$		0			0
$700$	8.20871	+	4.73930i	0.310260	+	0.179129i
$701$	−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
$704$	−10.2523	−	5.91915i	−0.386397	−	0.223086i
$705$		0			0
$706$	−2.83485	+	4.91010i	−0.106691	+	0.184794i
$707$		−	13.6657i		−	0.513952i
$708$		0			0
$709$	16.4174	−	9.47860i	0.616569	−	0.355976i	−0.158963	−	0.987285i	$-0.550815\pi$
$709$	16.4174	−	9.47860i	0.616569	−	0.355976i	0.775532	+	0.631308i	$0.217482\pi$
$710$	7.81307	−	4.51088i	0.293219	−	0.169290i
$711$		0			0
$712$	−27.0000			−1.01187
$713$	−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
$718$	4.23049	−	7.32743i	0.157881	−	0.273457i
$719$	1.16515	+	2.01810i	0.0434528	+	0.0752625i	0.886934	−	0.461896i	$-0.152831\pi$
$719$	1.16515	+	2.01810i	0.0434528	+	0.0752625i	−0.843481	+	0.537159i	$0.819498\pi$
$720$		0			0
$721$		−	33.2904i		−	1.23980i
$722$	−3.56080	−	2.05583i	−0.132519	−	0.0765099i
$723$		0			0
$724$	39.4083			1.46460
$725$	−7.00000	+	12.1244i	−0.259973	+	0.450287i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	11.4564	−	11.9059i	0.424604	−	0.441261i
$729$		0			0
$730$		−	6.85275i		−	0.253632i
$731$	−2.29129	+	3.96863i	−0.0847463	+	0.146785i
$732$		0			0
$733$	10.8303	+	6.25288i	0.400026	+	0.230955i	0.686495	−	0.727134i	$-0.259148\pi$
$733$	10.8303	+	6.25288i	0.400026	+	0.230955i	−0.286469	+	0.958090i	$0.592482\pi$
$734$	−1.25227	−	0.723000i	−0.0462222	−	0.0266864i
$735$		0			0
$736$			2.76100i			0.101772i
$737$	−12.3303	−	21.3567i	−0.454193	−	0.786685i
$738$		0			0
$739$	7.41742	+	4.28245i	0.272854	+	0.157533i	0.630184	−	0.776446i	$-0.282979\pi$
$739$	7.41742	+	4.28245i	0.272854	+	0.157533i	−0.357330	+	0.933978i	$0.616313\pi$
$740$	−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
$745$	−30.3303			−1.11122
$746$	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
$751$	32.9129			1.20101			0.600504	−	0.799622i	$-0.294967\pi$
$751$	32.9129			1.20101			0.600504	+	0.799622i	$0.294967\pi$
$752$	14.7695	+	8.52718i	0.538589	+	0.310954i
$753$		0			0
$754$	8.30852	+	7.99488i	0.302579	+	0.291156i
$755$	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	$0.463422\pi$
$758$	4.23049	+	7.32743i	0.153658	+	0.266144i
$759$		0			0
$760$		−	15.8745i		−	0.575829i
$761$	28.7477	−	16.5975i	1.04210	−	0.601659i	0.121676	−	0.992570i	$-0.461173\pi$
$761$	28.7477	−	16.5975i	1.04210	−	0.601659i	0.920429	+	0.390911i	$0.127840\pi$
$762$		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
$767$	33.1652	−	9.57395i	1.19752	−	0.345695i
$768$		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	$0.414276\pi$
$770$	−3.62614	+	6.28065i	−0.130677	+	0.226339i
$771$		0			0
$772$	27.1652	+	15.6838i	0.977695	+	0.564473i
$773$			7.21425i			0.259479i	0.991548	+	0.129739i	$0.0414141\pi$
$773$			7.21425i			0.259479i	−0.991548	+	0.129739i	$0.958586\pi$
$774$		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
$782$		−	0.266150i		−	0.00951750i
$783$		0			0
$784$	9.76951	−	16.9213i	0.348911	−	0.604332i
$785$		−	14.1425i		−	0.504766i
$786$		0			0
$787$		−	25.0671i		−	0.893544i	−0.894648	−	0.446772i	$-0.852573\pi$
$787$		−	25.0671i		−	0.893544i	0.894648	−	0.446772i	$-0.147427\pi$
$788$	21.9392	−	12.6666i	0.781552	−	0.451229i
$789$		0			0
$790$	4.18693	+	7.25198i	0.148964	+	0.258014i
$791$		−	16.3115i		−	0.579969i
$792$		0			0
$793$	−32.9129	+	34.2041i	−1.16877	+	1.21462i
$794$	3.66970	+	6.35610i	0.130233	+	0.225570i
$795$		0			0
$796$	−11.7913			−0.417931
$797$	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
$800$	−8.20871	+	4.73930i	−0.290222	+	0.167560i
$801$		0			0
$802$	11.0345			0.389641
$803$	30.0000			1.05868
$804$		0			0
$805$	−2.66970			−0.0940945
$806$	−0.934659	+	0.971326i	−0.0329220	+	0.0342135i
$807$		0			0
$808$	7.74773	+	4.47315i	0.272564	+	0.157365i
$809$	−7.41742	+	12.8474i	−0.260783	+	0.451689i	−0.966450	−	0.256854i	$-0.917314\pi$
$809$	−7.41742	+	12.8474i	−0.260783	+	0.451689i	0.705667	+	0.708543i	$0.250647\pi$
$810$		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
$815$	−6.00000			−0.210171
$816$		0			0
$817$			24.2487i			0.848355i
$818$	9.45189			0.330478
$819$		0			0
$820$	21.7913			0.760985
$821$			6.64215i			0.231813i	0.993260	+	0.115906i	$0.0369773\pi$
$821$			6.64215i			0.231813i	−0.993260	+	0.115906i	$0.963023\pi$
$822$		0			0
$823$	21.4174			0.746564			0.373282	−	0.927718i	$-0.378232\pi$
$823$	21.4174			0.746564			0.373282	+	0.927718i	$0.378232\pi$
$824$	18.8739	+	10.8968i	0.657502	+	0.379609i
$825$		0			0
$826$	−10.0218	+	5.78608i	−0.348702	+	0.201323i
$827$			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
$829$	−13.3303	+	23.0888i	−0.462981	+	0.801906i	−0.999108	−	0.0422313i	$-0.986553\pi$
$829$	−13.3303	+	23.0888i	−0.462981	+	0.801906i	0.536127	+	0.844137i	$0.319887\pi$
$830$	2.37386	+	1.37055i	0.0823980	+	0.0475725i
$831$		0			0
$832$	−3.41742	−	11.8383i	−0.118478	−	0.410419i
$833$	−3.50000	+	6.06218i	−0.121268	+	0.210042i
$834$		0			0
$835$	−19.7477			−0.683398
$836$	32.8348			1.13562
$837$		0			0
$838$	−6.23049	+	3.59718i	−0.215229	+	0.124262i
$839$	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
$842$	−15.3394			−0.528630
$843$		0			0
$844$	2.31307	+	4.00635i	0.0796191	+	0.137904i
$845$	22.5000	−	0.866025i	0.774024	−	0.0297922i
$846$		0			0
$847$	−2.29129	−	1.32288i	−0.0787296	−	0.0454545i
$848$	16.9782	+	29.4071i	0.583034	+	1.00985i
$849$		0			0
$850$	0.791288	−	0.456850i	0.0271409	−	0.0156698i
$851$			2.07365i			0.0710838i
$852$		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
$856$		−	18.3296i		−	0.626491i
$857$	−12.6652	−	21.9367i	−0.432633	−	0.749343i	0.564466	−	0.825456i	$-0.309082\pi$
$857$	−12.6652	−	21.9367i	−0.432633	−	0.749343i	−0.997099	+	0.0761135i	$0.975749\pi$
$858$		0			0
$859$	0.543561	−	0.941475i	0.0185461	−	0.0321227i	−0.856603	−	0.515975i	$-0.827430\pi$
$859$	0.543561	−	0.941475i	0.0185461	−	0.0321227i	0.875149	+	0.483853i	$0.160763\pi$
$860$	−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	$-0.367534\pi$
$863$	−5.45644	−	3.15028i	−0.185739	−	0.107237i	−0.589986	+	0.807413i	$0.700867\pi$
$864$		0			0
$865$			21.3567i			0.726150i
$866$	8.43920	+	4.87238i	0.286776	+	0.165570i
$867$		0			0
$868$	−1.93920	+	3.35880i	−0.0658209	+	0.114005i
$869$	−31.7477	+	18.3296i	−1.07697	+	0.621788i
$870$		0			0
$871$	6.16515	−	24.9162i	0.208898	−	0.844252i
$872$	−1.66515	−	2.88413i	−0.0563891	−	0.0976689i
$873$		0			0
$874$	−0.704166	−	1.21965i	−0.0238188	−	0.0412553i
$875$	−16.0390	−	27.7804i	−0.542218	−	0.939149i
$876$		0			0
$877$	31.9129	−	18.4249i	1.07762	−	0.622165i	0.147368	−	0.989082i	$-0.452920\pi$
$877$	31.9129	−	18.4249i	1.07762	−	0.622165i	0.930254	+	0.366917i	$0.119587\pi$
$878$			0.647551i			0.0218538i
$879$		0			0
$880$	8.37386	+	14.5040i	0.282283	+	0.488928i
$881$	−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	$0.426124\pi$
$884$	1.79129	+	6.20520i	0.0602475	+	0.208704i
$885$		0			0
$886$	−8.60436	−	4.96773i	−0.289069	−	0.166894i
$887$	46.5826			1.56409			0.782045	−	0.623222i	$-0.214177\pi$
$887$	46.5826			1.56409			0.782045	+	0.623222i	$0.214177\pi$
$888$		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
$893$	−32.3303			−1.08189
$894$		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
$899$	−4.96099	−	2.86423i	−0.165458	−	0.0955273i
$900$		0			0
$901$	−6.08258	−	10.5353i	−0.202640	−	0.350983i
$902$		−	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
$907$	−13.5826	+	23.5257i	−0.451002	+	0.781158i	−0.998449	−	0.0556823i	$-0.982267\pi$
$907$	−13.5826	+	23.5257i	−0.451002	+	0.781158i	0.547447	+	0.836841i	$0.315600\pi$
$908$		−	36.4485i		−	1.20959i
$909$		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
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	−12.7913			−0.423098
$915$		0			0
$916$	0.147917	+	0.0853998i	0.00488731	+	0.00282169i
$917$			27.9989i			0.924604i
$918$		0			0
$919$	11.5826	+	20.0616i	0.382074	+	0.661771i	0.991359	−	0.131180i	$-0.0418766\pi$
$919$	11.5826	+	20.0616i	0.382074	+	0.661771i	−0.609285	+	0.792952i	$0.708543\pi$
$920$	0.873864	−	1.51358i	0.0288104	−	0.0499011i
$921$		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
$926$	−1.75682			−0.0577326
$927$		0			0
$928$	−28.7305	+	16.5876i	−0.943125	+	0.544513i
$929$	−36.6606	+	21.1660i	−1.20280	+	0.694434i	−0.961176	−	0.275937i	$-0.911012\pi$
$929$	−36.6606	+	21.1660i	−1.20280	+	0.694434i	−0.241620	+	0.970371i	$0.577679\pi$
$930$		0			0
$931$			37.0405i			1.21395i
$932$	1.64337	−	2.84640i	0.0538304	−	0.0932370i
$933$		0			0
$934$	−6.69148	−	3.86333i	−0.218952	−	0.126412i
$935$	−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	$0.138760\pi$
$938$			8.60471i			0.280954i
$939$		0			0
$940$	−9.47822	−	16.4168i	−0.309145	−	0.535456i
$941$	−7.83030	+	4.52083i	−0.255261	+	0.147375i	−0.622171	−	0.782882i	$-0.713749\pi$
$941$	−7.83030	+	4.52083i	−0.255261	+	0.147375i	0.366910	+	0.930256i	$0.380416\pi$
$942$		0			0
$943$	3.54356	−	2.04588i	0.115394	−	0.0666229i
$944$			26.7237i			0.869781i
$945$		0			0
$946$	3.62614	+	6.28065i	0.117896	+	0.204202i
$947$			21.9844i			0.714396i	0.934029	+	0.357198i	$0.116268\pi$
$947$			21.9844i			0.714396i	−0.934029	+	0.357198i	$0.883732\pi$
$948$		0			0
$949$	22.5000	+	21.6506i	0.730381	+	0.702809i
$950$	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
$955$		−	38.6772i		−	1.25157i
$956$		−	53.2566i		−	1.72244i
$957$		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
$962$	1.62614	+	5.63310i	0.0524287	+	0.181618i
$963$		0			0
$964$		−	31.5384i		−	1.01578i
$965$	−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	$-0.0271151\pi$
$968$	1.50000	−	0.866025i	0.0482118	−	0.0278351i
$969$		0			0
$970$	0.0653411	−	0.0377247i	0.00209798	−	0.00121127i
$971$	6.83485	+	11.8383i	0.219341	+	0.379909i	0.954607	−	0.297870i	$-0.0962760\pi$
$971$	6.83485	+	11.8383i	0.219341	+	0.379909i	−0.735266	+	0.677779i	$0.762943\pi$
$972$		0			0
$973$		−	6.83285i		−	0.219051i
$974$	−17.1216			−0.548611
$975$		0			0
$976$	−18.3739	−	31.8245i	−0.588133	−	1.01868i
$977$	15.1652	+	8.75560i	0.485176	+	0.280117i	0.722571	−	0.691297i	$-0.242960\pi$
$977$	15.1652	+	8.75560i	0.485176	+	0.280117i	−0.237395	+	0.971413i	$0.576294\pi$
$978$		0			0
$979$	−27.0000	+	46.7654i	−0.862924	+	1.49463i
$980$	−18.8085	+	10.8591i	−0.600816	+	0.346881i
$981$		0			0
$982$	−9.39564	+	5.42458i	−0.299827	+	0.173105i
$983$	−15.7087	+	9.06943i	−0.501030	+	0.289270i	−0.729139	−	0.684366i	$-0.760079\pi$
$983$	−15.7087	+	9.06943i	−0.501030	+	0.289270i	0.228109	+	0.973636i	$0.426746\pi$
$984$		0			0
$985$	−24.4955			−0.780490
$986$	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
$991$	20.3303	−	35.2131i	0.645813	−	1.11858i	−0.338300	−	0.941038i	$-0.609852\pi$
$991$	20.3303	−	35.2131i	0.645813	−	1.11858i	0.984113	−	0.177543i	$-0.0568149\pi$
$992$	−1.93920	−	3.35880i	−0.0615698	−	0.106642i
$993$		0			0
$994$		−	13.7810i		−	0.437105i
$995$	9.87386	+	5.70068i	0.313023	+	0.180724i
$996$		0			0
$997$	−10.6697			−0.337913			−0.168956	−	0.985624i	$-0.554040\pi$
$997$	−10.6697			−0.337913			−0.168956	+	0.985624i	$0.554040\pi$
$998$	−6.93466	+	12.0112i	−0.219513	+	0.380207i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.b.4.1	✓	4	273.95	odd	6
273.2.t.b.205.2	yes	4	3.2	odd	2
273.2.bl.b.88.1	yes	4	21.11	odd	6
273.2.bl.b.121.1	yes	4	39.17	odd	6
819.2.bm.d.478.1		4	1.1	even	1	trivial
819.2.bm.d.550.2		4	91.4	even	6	inner
819.2.do.d.361.2		4	7.4	even	3
819.2.do.d.667.2		4	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.456850i q^{2} +1.79129 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-2.29129 + 1.32288i) q^{7} -1.73205i q^{8} +O(q^{10})\)	\(q-0.456850i q^{2} +1.79129 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-2.29129 + 1.32288i) q^{7} -1.73205i q^{8} +(-0.395644 + 0.685275i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(0.604356 + 1.04678i) q^{14} +2.79129 q^{16} -1.00000 q^{17} +(-4.58258 + 2.64575i) q^{19} +(-2.68693 - 1.55130i) q^{20} +(-0.791288 + 1.37055i) q^{22} -0.582576 q^{23} +(-1.00000 - 1.73205i) q^{25} +(-1.58258 + 0.456850i) q^{26} +(-4.10436 + 2.36965i) q^{28} +(-3.50000 - 6.06218i) q^{29} +(0.708712 - 0.409175i) q^{31} -4.73930i q^{32} +0.456850i q^{34} +4.58258 q^{35} -3.55945i q^{37} +(1.20871 + 2.09355i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-6.08258 + 3.51178i) q^{41} +(2.29129 - 3.96863i) q^{43} +(-5.37386 - 3.10260i) q^{44} +0.266150i q^{46} +(5.29129 + 3.05493i) q^{47} +(3.50000 - 6.06218i) q^{49} +(-0.791288 + 0.456850i) q^{50} +(-1.79129 - 6.20520i) q^{52} +(6.08258 + 10.5353i) q^{53} +(3.00000 + 5.19615i) q^{55} +(2.29129 + 3.96863i) q^{56} +(-2.76951 + 1.59898i) q^{58} +9.57395i q^{59} +(-6.58258 - 11.4014i) q^{61} +(-0.186932 - 0.323775i) q^{62} +3.41742 q^{64} +(-1.50000 + 6.06218i) q^{65} +(6.16515 + 3.55945i) q^{67} -1.79129 q^{68} -2.09355i q^{70} +(-9.87386 - 5.70068i) q^{71} +(-7.50000 + 4.33013i) q^{73} -1.62614 q^{74} +(-8.20871 + 4.73930i) q^{76} +9.16515 q^{77} +(5.29129 - 9.16478i) q^{79} +(-4.18693 - 2.41733i) q^{80} +(1.60436 + 2.77883i) q^{82} -3.46410i q^{83} +(1.50000 + 0.866025i) q^{85} +(-1.81307 - 1.04678i) q^{86} +(-3.00000 + 5.19615i) q^{88} -15.5885i q^{89} +(6.87386 + 6.61438i) q^{91} -1.04356 q^{92} +(1.39564 - 2.41733i) q^{94} +9.16515 q^{95} +(-0.0825757 - 0.0476751i) q^{97} +(-2.76951 - 1.59898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} - 6 q^{5}+O(q^{10}) \) 4 * q - 2 * q^4 - 6 * q^5	\( 4 q - 2 q^{4} - 6 q^{5} + 3 q^{10} - 12 q^{11} - 4 q^{13} + 7 q^{14} + 2 q^{16} - 4 q^{17} + 3 q^{20} + 6 q^{22} + 16 q^{23} - 4 q^{25} + 12 q^{26} - 21 q^{28} - 14 q^{29} + 12 q^{31} + 14 q^{38} - 6 q^{40} - 6 q^{41} + 6 q^{44} + 12 q^{47} + 14 q^{49} + 6 q^{50} + 2 q^{52} + 6 q^{53} + 12 q^{55} + 21 q^{58} - 8 q^{61} + 13 q^{62} + 32 q^{64} - 6 q^{65} - 12 q^{67} + 2 q^{68} - 12 q^{71} - 30 q^{73} - 34 q^{74} - 42 q^{76} + 12 q^{79} - 3 q^{80} + 11 q^{82} + 6 q^{85} - 21 q^{86} - 12 q^{88} - 50 q^{92} + q^{94} + 18 q^{97} + 21 q^{98}+O(q^{100}) \) 4 * q - 2 * q^4 - 6 * q^5 + 3 * q^10 - 12 * q^11 - 4 * q^13 + 7 * q^14 + 2 * q^16 - 4 * q^17 + 3 * q^20 + 6 * q^22 + 16 * q^23 - 4 * q^25 + 12 * q^26 - 21 * q^28 - 14 * q^29 + 12 * q^31 + 14 * q^38 - 6 * q^40 - 6 * q^41 + 6 * q^44 + 12 * q^47 + 14 * q^49 + 6 * q^50 + 2 * q^52 + 6 * q^53 + 12 * q^55 + 21 * q^58 - 8 * q^61 + 13 * q^62 + 32 * q^64 - 6 * q^65 - 12 * q^67 + 2 * q^68 - 12 * q^71 - 30 * q^73 - 34 * q^74 - 42 * q^76 + 12 * q^79 - 3 * q^80 + 11 * q^82 + 6 * q^85 - 21 * q^86 - 12 * q^88 - 50 * q^92 + q^94 + 18 * q^97 + 21 * q^98

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