LMFDB - Embedded newform 1134.2.m.b.377.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(377,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1134.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.m (of order $6$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			377.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.377
Dual form			1134.2.m.b.755.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +1.73205i q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.00000 + 1.73205i) q^{13} +(2.59808 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.92820 q^{17} -1.73205i q^{19} +(-0.866025 - 1.50000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(2.59808 + 1.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} -3.46410 q^{26} +(-2.00000 + 1.73205i) q^{28} +(-5.19615 + 3.00000i) q^{29} +(-4.50000 - 2.59808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.00000 - 3.46410i) q^{34} +(-3.46410 + 3.00000i) q^{35} +7.00000 q^{37} +(0.866025 + 1.50000i) q^{38} +(1.50000 + 0.866025i) q^{40} +(-6.06218 + 10.5000i) q^{41} +(1.00000 + 1.73205i) q^{43} +3.00000i q^{44} -3.00000 q^{46} +(-1.73205 - 3.00000i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.73205 - 1.00000i) q^{50} +(3.00000 - 1.73205i) q^{52} +12.0000i q^{53} +5.19615i q^{55} +(0.866025 - 2.50000i) q^{56} +(3.00000 - 5.19615i) q^{58} +(1.73205 - 3.00000i) q^{59} +(-6.00000 + 3.46410i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(5.19615 - 3.00000i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(1.50000 - 4.33013i) q^{70} +3.00000i q^{71} +3.46410i q^{73} +(-6.06218 + 3.50000i) q^{74} +(-1.50000 - 0.866025i) q^{76} +(7.79423 - 1.50000i) q^{77} +(5.00000 + 8.66025i) q^{79} -1.73205 q^{80} -12.1244i q^{82} +(-8.66025 - 15.0000i) q^{83} +(-6.00000 + 10.3923i) q^{85} +(-1.73205 - 1.00000i) q^{86} +(-1.50000 - 2.59808i) q^{88} +5.19615 q^{89} +(-6.00000 - 6.92820i) q^{91} +(2.59808 - 1.50000i) q^{92} +(3.00000 + 1.73205i) q^{94} +(-2.59808 - 1.50000i) q^{95} +(-12.0000 + 6.92820i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 10 q^{7} + 12 q^{13} - 2 q^{16} + 6 q^{22} + 4 q^{25} - 8 q^{28} - 18 q^{31} + 24 q^{34} + 28 q^{37} + 6 q^{40} + 4 q^{43} - 12 q^{46} + 22 q^{49} + 12 q^{52} + 12 q^{58} - 24 q^{61} - 4 q^{64}+ \cdots - 48 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 10 * q^7 + 12 * q^13 - 2 * q^16 + 6 * q^22 + 4 * q^25 - 8 * q^28 - 18 * q^31 + 24 * q^34 + 28 * q^37 + 6 * q^40 + 4 * q^43 - 12 * q^46 + 22 * q^49 + 12 * q^52 + 12 * q^58 - 24 * q^61 - 4 * q^64 - 4 * q^67 + 6 * q^70 - 6 * q^76 + 20 * q^79 - 24 * q^85 - 6 * q^88 - 24 * q^91 + 12 * q^94 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$	0.866025	−	1.50000i	0.387298	−	0.670820i	0.992085	+	0.125567i	$0.0400750\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$			1.00000i			0.353553i
$9$		0			0
$10$			1.73205i			0.547723i
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$	2.59808	−	0.500000i	0.694365	−	0.133631i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.92820			−1.68034			−0.840168	−	0.542326i	$-0.817544\pi$
$17$	−6.92820			−1.68034			−0.840168	+	0.542326i	$0.817544\pi$
$18$		0			0
$19$		−	1.73205i		−	0.397360i	−0.980064	−	0.198680i	$-0.936335\pi$
$19$		−	1.73205i		−	0.397360i	0.980064	−	0.198680i	$-0.0636654\pi$
$20$	−0.866025	−	1.50000i	−0.193649	−	0.335410i
$21$		0			0
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	−3.46410			−0.679366
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−5.19615	+	3.00000i	−0.964901	+	0.557086i	−0.897678	−	0.440652i	$-0.854747\pi$
$29$	−5.19615	+	3.00000i	−0.964901	+	0.557086i	−0.0672232	+	0.997738i	$0.521414\pi$
$30$		0			0
$31$	−4.50000	−	2.59808i	−0.808224	−	0.466628i	0.0381148	−	0.999273i	$-0.487865\pi$
$31$	−4.50000	−	2.59808i	−0.808224	−	0.466628i	−0.846339	+	0.532645i	$0.821198\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	6.00000	−	3.46410i	1.02899	−	0.594089i
$35$	−3.46410	+	3.00000i	−0.585540	+	0.507093i
$36$		0			0
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	0.866025	+	1.50000i	0.140488	+	0.243332i
$39$		0			0
$40$	1.50000	+	0.866025i	0.237171	+	0.136931i
$41$	−6.06218	+	10.5000i	−0.946753	+	1.63982i	−0.194551	+	0.980892i	$0.562325\pi$
$41$	−6.06218	+	10.5000i	−0.946753	+	1.63982i	−0.752202	+	0.658932i	$0.771008\pi$
$42$		0			0
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	−3.00000			−0.442326
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	0.711608	−	0.702577i	$-0.247967\pi$
$47$	−1.73205	−	3.00000i	−0.252646	−	0.437595i	−0.964253	+	0.264982i	$0.914634\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−1.73205	−	1.00000i	−0.244949	−	0.141421i
$51$		0			0
$52$	3.00000	−	1.73205i	0.416025	−	0.240192i
$53$			12.0000i			1.64833i	0.566352	+	0.824163i	$0.308354\pi$
$53$			12.0000i			1.64833i	−0.566352	+	0.824163i	$0.691646\pi$
$54$		0			0
$55$			5.19615i			0.700649i
$56$	0.866025	−	2.50000i	0.115728	−	0.334077i
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	−6.00000	+	3.46410i	−0.768221	+	0.443533i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−6.00000	+	3.46410i	−0.768221	+	0.443533i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	5.19615			0.659912
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.19615	−	3.00000i	0.644503	−	0.372104i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−3.46410	+	6.00000i	−0.420084	+	0.727607i
$69$		0			0
$70$	1.50000	−	4.33013i	0.179284	−	0.517549i
$71$			3.00000i			0.356034i	0.984027	+	0.178017i	$0.0569683\pi$
$71$			3.00000i			0.356034i	−0.984027	+	0.178017i	$0.943032\pi$
$72$		0			0
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$	−6.06218	+	3.50000i	−0.704714	+	0.406867i
$75$		0			0
$76$	−1.50000	−	0.866025i	−0.172062	−	0.0993399i
$77$	7.79423	−	1.50000i	0.888235	−	0.170941i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−1.73205			−0.193649
$81$		0			0
$82$		−	12.1244i		−	1.33891i
$83$	−8.66025	−	15.0000i	−0.950586	−	1.64646i	−0.744160	−	0.668002i	$-0.767150\pi$
$83$	−8.66025	−	15.0000i	−0.950586	−	1.64646i	−0.206427	−	0.978462i	$-0.566184\pi$
$84$		0			0
$85$	−6.00000	+	10.3923i	−0.650791	+	1.12720i
$86$	−1.73205	−	1.00000i	−0.186772	−	0.107833i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	5.19615			0.550791			0.275396	−	0.961331i	$-0.411191\pi$
$89$	5.19615			0.550791			0.275396	+	0.961331i	$0.411191\pi$
$90$		0			0
$91$	−6.00000	−	6.92820i	−0.628971	−	0.726273i
$92$	2.59808	−	1.50000i	0.270868	−	0.156386i
$93$		0			0
$94$	3.00000	+	1.73205i	0.309426	+	0.178647i
$95$	−2.59808	−	1.50000i	−0.266557	−	0.153897i
$96$		0			0
$97$	−12.0000	+	6.92820i	−1.21842	+	0.703452i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−12.0000	+	6.92820i	−1.21842	+	0.703452i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	−6.92820	−	1.00000i	−0.699854	−	0.101015i
$99$		0			0
$100$	2.00000			0.200000
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−16.5000	−	9.52628i	−1.62579	−	0.938652i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−16.5000	−	9.52628i	−1.62579	−	0.938652i	−0.640464	−	0.767988i	$-0.721258\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	−6.00000	−	10.3923i	−0.582772	−	1.00939i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$	13.0000			1.24517			0.622587	−	0.782551i	$-0.286082\pi$
$109$	13.0000			1.24517			0.622587	+	0.782551i	$0.286082\pi$
$110$	−2.59808	−	4.50000i	−0.247717	−	0.429058i
$111$		0			0
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−10.3923	−	6.00000i	−0.977626	−	0.564433i	−0.0760733	−	0.997102i	$-0.524238\pi$
$113$	−10.3923	−	6.00000i	−0.977626	−	0.564433i	−0.901553	+	0.432670i	$0.857572\pi$
$114$		0			0
$115$	4.50000	−	2.59808i	0.419627	−	0.242272i
$116$			6.00000i			0.557086i
$117$		0			0
$118$			3.46410i			0.318896i
$119$	17.3205	+	6.00000i	1.58777	+	0.550019i
$120$		0			0
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	3.46410	−	6.00000i	0.313625	−	0.543214i
$123$		0			0
$124$	−4.50000	+	2.59808i	−0.404112	+	0.233314i
$125$	12.1244			1.08444
$126$		0			0
$127$	−22.0000			−1.95218			−0.976092	−	0.217357i	$-0.930256\pi$
$127$	−22.0000			−1.95218			−0.976092	+	0.217357i	$0.930256\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	−5.19615	+	9.00000i	−0.453990	+	0.786334i	−0.998630	−	0.0523366i	$-0.983333\pi$
$131$	−5.19615	+	9.00000i	−0.453990	+	0.786334i	0.544640	+	0.838670i	$0.316666\pi$
$132$		0			0
$133$	−1.50000	+	4.33013i	−0.130066	+	0.375470i
$134$		−	2.00000i		−	0.172774i
$135$		0			0
$136$		−	6.92820i		−	0.594089i
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$		0			0
$139$	−3.00000	−	1.73205i	−0.254457	−	0.146911i	0.367347	−	0.930084i	$-0.380266\pi$
$139$	−3.00000	−	1.73205i	−0.254457	−	0.146911i	−0.621803	+	0.783174i	$0.713600\pi$
$140$	0.866025	+	4.50000i	0.0731925	+	0.380319i
$141$		0			0
$142$	−1.50000	−	2.59808i	−0.125877	−	0.218026i
$143$	−10.3923			−0.869048
$144$		0			0
$145$			10.3923i			0.863034i
$146$	−1.73205	−	3.00000i	−0.143346	−	0.248282i
$147$		0			0
$148$	3.50000	−	6.06218i	0.287698	−	0.498308i
$149$	10.3923	+	6.00000i	0.851371	+	0.491539i	0.861113	−	0.508413i	$-0.169768\pi$
$149$	10.3923	+	6.00000i	0.851371	+	0.491539i	−0.00974235	+	0.999953i	$0.503101\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	1.73205			0.140488
$153$		0			0
$154$	−6.00000	+	5.19615i	−0.483494	+	0.418718i
$155$	−7.79423	+	4.50000i	−0.626048	+	0.361449i
$156$		0			0
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	0.0958404	−	0.995397i	$-0.469446\pi$
$157$	−9.00000	−	5.19615i	−0.718278	−	0.414698i	−0.814119	+	0.580699i	$0.802779\pi$
$158$	−8.66025	−	5.00000i	−0.688973	−	0.397779i
$159$		0			0
$160$	1.50000	−	0.866025i	0.118585	−	0.0684653i
$161$	−5.19615	−	6.00000i	−0.409514	−	0.472866i
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	6.06218	+	10.5000i	0.473377	+	0.819912i
$165$		0			0
$166$	15.0000	+	8.66025i	1.16423	+	0.672166i
$167$	3.46410	−	6.00000i	0.268060	−	0.464294i	−0.700301	−	0.713848i	$-0.746951\pi$
$167$	3.46410	−	6.00000i	0.268060	−	0.464294i	0.968361	+	0.249554i	$0.0802840\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		−	12.0000i		−	0.920358i
$171$		0			0
$172$	2.00000			0.152499
$173$	2.59808	+	4.50000i	0.197528	+	0.342129i	0.947726	−	0.319084i	$-0.103375\pi$
$173$	2.59808	+	4.50000i	0.197528	+	0.342129i	−0.750198	+	0.661213i	$0.770042\pi$
$174$		0			0
$175$	−1.00000	−	5.19615i	−0.0755929	−	0.392792i
$176$	2.59808	+	1.50000i	0.195837	+	0.113067i
$177$		0			0
$178$	−4.50000	+	2.59808i	−0.337289	+	0.194734i
$179$		−	12.0000i		−	0.896922i	−0.893802	−	0.448461i	$-0.851972\pi$
$179$		−	12.0000i		−	0.896922i	0.893802	−	0.448461i	$-0.148028\pi$
$180$		0			0
$181$		−	13.8564i		−	1.02994i	−0.857209	−	0.514969i	$-0.827803\pi$
$181$		−	13.8564i		−	1.02994i	0.857209	−	0.514969i	$-0.172197\pi$
$182$	8.66025	+	3.00000i	0.641941	+	0.222375i
$183$		0			0
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$	6.06218	−	10.5000i	0.445700	−	0.771975i
$186$		0			0
$187$	18.0000	−	10.3923i	1.31629	−	0.759961i
$188$	−3.46410			−0.252646
$189$		0			0
$190$	3.00000			0.217643
$191$	18.1865	−	10.5000i	1.31593	−	0.759753i	0.332860	−	0.942976i	$-0.391986\pi$
$191$	18.1865	−	10.5000i	1.31593	−	0.759753i	0.983071	+	0.183223i	$0.0586530\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	6.92820	−	12.0000i	0.497416	−	0.861550i
$195$		0			0
$196$	6.50000	−	2.59808i	0.464286	−	0.185577i
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$		0			0
$199$			1.73205i			0.122782i	0.998114	+	0.0613909i	$0.0195536\pi$
$199$			1.73205i			0.122782i	−0.998114	+	0.0613909i	$0.980446\pi$
$200$	−1.73205	+	1.00000i	−0.122474	+	0.0707107i
$201$		0			0
$202$		0			0
$203$	15.5885	−	3.00000i	1.09410	−	0.210559i
$204$		0			0
$205$	10.5000	+	18.1865i	0.733352	+	1.27020i
$206$	19.0526			1.32745
$207$		0			0
$208$		−	3.46410i		−	0.240192i
$209$	2.59808	+	4.50000i	0.179713	+	0.311272i
$210$		0			0
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	10.3923	+	6.00000i	0.713746	+	0.412082i
$213$		0			0
$214$		0			0
$215$	3.46410			0.236250
$216$		0			0
$217$	9.00000	+	10.3923i	0.610960	+	0.705476i
$218$	−11.2583	+	6.50000i	−0.762510	+	0.440236i
$219$		0			0
$220$	4.50000	+	2.59808i	0.303390	+	0.175162i
$221$	−20.7846	−	12.0000i	−1.39812	−	0.807207i
$222$		0			0
$223$	13.5000	−	7.79423i	0.904027	−	0.521940i	0.0255224	−	0.999674i	$-0.491875\pi$
$223$	13.5000	−	7.79423i	0.904027	−	0.521940i	0.878504	+	0.477734i	$0.158542\pi$
$224$	−1.73205	−	2.00000i	−0.115728	−	0.133631i
$225$		0			0
$226$	12.0000			0.798228
$227$	10.3923	+	18.0000i	0.689761	+	1.19470i	0.971915	+	0.235333i	$0.0756180\pi$
$227$	10.3923	+	18.0000i	0.689761	+	1.19470i	−0.282153	+	0.959369i	$0.591049\pi$
$228$		0			0
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$	−2.59808	+	4.50000i	−0.171312	+	0.296721i
$231$		0			0
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$		−	24.0000i		−	1.57229i	−0.618041	−	0.786146i	$-0.712073\pi$
$233$		−	24.0000i		−	1.57229i	0.618041	−	0.786146i	$-0.287927\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$	−1.73205	−	3.00000i	−0.112747	−	0.195283i
$237$		0			0
$238$	−18.0000	+	3.46410i	−1.16677	+	0.224544i
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$		0			0
$241$	−15.0000	+	8.66025i	−0.966235	+	0.557856i	−0.898086	−	0.439819i	$-0.855043\pi$
$241$	−15.0000	+	8.66025i	−0.966235	+	0.557856i	−0.0681486	+	0.997675i	$0.521709\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$			6.92820i			0.443533i
$245$	11.2583	−	4.50000i	0.719268	−	0.287494i
$246$		0			0
$247$	3.00000	−	5.19615i	0.190885	−	0.330623i
$248$	2.59808	−	4.50000i	0.164978	−	0.285750i
$249$		0			0
$250$	−10.5000	+	6.06218i	−0.664078	+	0.383406i
$251$	13.8564			0.874609			0.437304	−	0.899314i	$-0.355933\pi$
$251$	13.8564			0.874609			0.437304	+	0.899314i	$0.355933\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$	19.0526	−	11.0000i	1.19546	−	0.690201i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.59808	−	4.50000i	0.162064	−	0.280702i	−0.773545	−	0.633741i	$-0.781518\pi$
$257$	2.59808	−	4.50000i	0.162064	−	0.280702i	0.935609	+	0.353039i	$0.114852\pi$
$258$		0			0
$259$	−17.5000	−	6.06218i	−1.08740	−	0.376685i
$260$		−	6.00000i		−	0.372104i
$261$		0			0
$262$		−	10.3923i		−	0.642039i
$263$	−23.3827	+	13.5000i	−1.44184	+	0.832446i	−0.997972	−	0.0636476i	$-0.979727\pi$
$263$	−23.3827	+	13.5000i	−1.44184	+	0.832446i	−0.443866	+	0.896093i	$0.646393\pi$
$264$		0			0
$265$	18.0000	+	10.3923i	1.10573	+	0.638394i
$266$	−0.866025	−	4.50000i	−0.0530994	−	0.275913i
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	1.73205			0.105605			0.0528025	−	0.998605i	$-0.483185\pi$
$269$	1.73205			0.105605			0.0528025	+	0.998605i	$0.483185\pi$
$270$		0			0
$271$			17.3205i			1.05215i	0.850439	+	0.526073i	$0.176336\pi$
$271$			17.3205i			1.05215i	−0.850439	+	0.526073i	$0.823664\pi$
$272$	3.46410	+	6.00000i	0.210042	+	0.363803i
$273$		0			0
$274$	9.00000	−	15.5885i	0.543710	−	0.941733i
$275$	−5.19615	−	3.00000i	−0.313340	−	0.180907i
$276$		0			0
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	0.652140	−	0.758099i	$-0.273872\pi$
$277$	−5.50000	−	9.52628i	−0.330463	−	0.572379i	−0.982603	+	0.185720i	$0.940538\pi$
$278$	3.46410			0.207763
$279$		0			0
$280$	−3.00000	−	3.46410i	−0.179284	−	0.207020i
$281$	25.9808	−	15.0000i	1.54988	−	0.894825i	0.551733	−	0.834021i	$-0.313967\pi$
$281$	25.9808	−	15.0000i	1.54988	−	0.894825i	0.998150	−	0.0608039i	$-0.0193664\pi$
$282$		0			0
$283$	27.0000	+	15.5885i	1.60498	+	0.926638i	0.990470	+	0.137732i	$0.0439811\pi$
$283$	27.0000	+	15.5885i	1.60498	+	0.926638i	0.614514	+	0.788906i	$0.289352\pi$
$284$	2.59808	+	1.50000i	0.154167	+	0.0890086i
$285$		0			0
$286$	9.00000	−	5.19615i	0.532181	−	0.307255i
$287$	24.2487	−	21.0000i	1.43136	−	1.23959i
$288$		0			0
$289$	31.0000			1.82353
$290$	−5.19615	−	9.00000i	−0.305129	−	0.528498i
$291$		0			0
$292$	3.00000	+	1.73205i	0.175562	+	0.101361i
$293$	−3.46410	+	6.00000i	−0.202375	+	0.350524i	−0.949293	−	0.314392i	$-0.898199\pi$
$293$	−3.46410	+	6.00000i	−0.202375	+	0.350524i	0.746918	+	0.664916i	$0.231533\pi$
$294$		0			0
$295$	−3.00000	−	5.19615i	−0.174667	−	0.302532i
$296$			7.00000i			0.406867i
$297$		0			0
$298$	−12.0000			−0.695141
$299$	5.19615	+	9.00000i	0.300501	+	0.520483i
$300$		0			0
$301$	−1.00000	−	5.19615i	−0.0576390	−	0.299501i
$302$	−6.92820	−	4.00000i	−0.398673	−	0.230174i
$303$		0			0
$304$	−1.50000	+	0.866025i	−0.0860309	+	0.0496700i
$305$			12.0000i			0.687118i
$306$		0			0
$307$		−	15.5885i		−	0.889680i	−0.895610	−	0.444840i	$-0.853260\pi$
$307$		−	15.5885i		−	0.889680i	0.895610	−	0.444840i	$-0.146740\pi$
$308$	2.59808	−	7.50000i	0.148039	−	0.427352i
$309$		0			0
$310$	4.50000	−	7.79423i	0.255583	−	0.442682i
$311$	−12.1244	+	21.0000i	−0.687509	+	1.19080i	0.285132	+	0.958488i	$0.407963\pi$
$311$	−12.1244	+	21.0000i	−0.687509	+	1.19080i	−0.972641	+	0.232313i	$0.925371\pi$
$312$		0			0
$313$	15.0000	−	8.66025i	0.847850	−	0.489506i	−0.0120748	−	0.999927i	$-0.503844\pi$
$313$	15.0000	−	8.66025i	0.847850	−	0.489506i	0.859925	+	0.510421i	$0.170510\pi$
$314$	10.3923			0.586472
$315$		0			0
$316$	10.0000			0.562544
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.00635137	−	0.999980i	$-0.497978\pi$
$317$	15.5885	−	9.00000i	0.875535	−	0.505490i	0.869184	+	0.494489i	$0.164645\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$	−0.866025	+	1.50000i	−0.0484123	+	0.0838525i
$321$		0			0
$322$	7.50000	+	2.59808i	0.417959	+	0.144785i
$323$			12.0000i			0.667698i
$324$		0			0
$325$			6.92820i			0.384308i
$326$	−1.73205	+	1.00000i	−0.0959294	+	0.0553849i
$327$		0			0
$328$	−10.5000	−	6.06218i	−0.579766	−	0.334728i
$329$	1.73205	+	9.00000i	0.0954911	+	0.496186i
$330$		0			0
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$	−17.3205			−0.950586
$333$		0			0
$334$			6.92820i			0.379094i
$335$	1.73205	+	3.00000i	0.0946320	+	0.163908i
$336$		0			0
$337$	2.50000	−	4.33013i	0.136184	−	0.235877i	−0.789865	−	0.613280i	$-0.789850\pi$
$337$	2.50000	−	4.33013i	0.136184	−	0.235877i	0.926049	+	0.377403i	$0.123183\pi$
$338$	0.866025	+	0.500000i	0.0471056	+	0.0271964i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	15.5885			0.844162
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−1.73205	+	1.00000i	−0.0933859	+	0.0539164i
$345$		0			0
$346$	−4.50000	−	2.59808i	−0.241921	−	0.139673i
$347$	−23.3827	−	13.5000i	−1.25525	−	0.724718i	−0.283101	−	0.959090i	$-0.591363\pi$
$347$	−23.3827	−	13.5000i	−1.25525	−	0.724718i	−0.972147	+	0.234372i	$0.924697\pi$
$348$		0			0
$349$	−24.0000	+	13.8564i	−1.28469	+	0.741716i	−0.977702	−	0.209997i	$-0.932655\pi$
$349$	−24.0000	+	13.8564i	−1.28469	+	0.741716i	−0.306988	+	0.951713i	$0.599321\pi$
$350$	3.46410	+	4.00000i	0.185164	+	0.213809i
$351$		0			0
$352$	−3.00000			−0.159901
$353$	−9.52628	−	16.5000i	−0.507033	−	0.878206i	−0.999967	−	0.00813978i	$-0.997409\pi$
$353$	−9.52628	−	16.5000i	−0.507033	−	0.878206i	0.492934	−	0.870067i	$-0.335924\pi$
$354$		0			0
$355$	4.50000	+	2.59808i	0.238835	+	0.137892i
$356$	2.59808	−	4.50000i	0.137698	−	0.238500i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	16.0000			0.842105
$362$	6.92820	+	12.0000i	0.364138	+	0.630706i
$363$		0			0
$364$	−9.00000	+	1.73205i	−0.471728	+	0.0907841i
$365$	5.19615	+	3.00000i	0.271979	+	0.157027i
$366$		0			0
$367$	1.50000	−	0.866025i	0.0782994	−	0.0452062i	−0.460339	−	0.887743i	$-0.652272\pi$
$367$	1.50000	−	0.866025i	0.0782994	−	0.0452062i	0.538639	+	0.842537i	$0.318939\pi$
$368$		−	3.00000i		−	0.156386i
$369$		0			0
$370$			12.1244i			0.630315i
$371$	10.3923	−	30.0000i	0.539542	−	1.55752i
$372$		0			0
$373$	−2.50000	+	4.33013i	−0.129445	+	0.224205i	−0.923462	−	0.383691i	$-0.874653\pi$
$373$	−2.50000	+	4.33013i	−0.129445	+	0.224205i	0.794017	+	0.607896i	$0.207986\pi$
$374$	−10.3923	+	18.0000i	−0.537373	+	0.930758i
$375$		0			0
$376$	3.00000	−	1.73205i	0.154713	−	0.0893237i
$377$	−20.7846			−1.07046
$378$		0			0
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$	−2.59808	+	1.50000i	−0.133278	+	0.0769484i
$381$		0			0
$382$	−10.5000	+	18.1865i	−0.537227	+	0.930504i
$383$	6.92820	−	12.0000i	0.354015	−	0.613171i	−0.632934	−	0.774206i	$-0.718150\pi$
$383$	6.92820	−	12.0000i	0.354015	−	0.613171i	0.986949	+	0.161034i	$0.0514830\pi$
$384$		0			0
$385$	4.50000	−	12.9904i	0.229341	−	0.662051i
$386$			14.0000i			0.712581i
$387$		0			0
$388$			13.8564i			0.703452i
$389$	−20.7846	+	12.0000i	−1.05382	+	0.608424i	−0.923717	−	0.383076i	$-0.874865\pi$
$389$	−20.7846	+	12.0000i	−1.05382	+	0.608424i	−0.130105	+	0.991500i	$0.541531\pi$
$390$		0			0
$391$	−18.0000	−	10.3923i	−0.910299	−	0.525561i
$392$	−4.33013	+	5.50000i	−0.218704	+	0.277792i
$393$		0			0
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	17.3205			0.871489
$396$		0			0
$397$			20.7846i			1.04315i	0.853206	+	0.521575i	$0.174655\pi$
$397$			20.7846i			1.04315i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−0.866025	−	1.50000i	−0.0434099	−	0.0751882i
$399$		0			0
$400$	1.00000	−	1.73205i	0.0500000	−	0.0866025i
$401$	15.5885	+	9.00000i	0.778450	+	0.449439i	0.835881	−	0.548911i	$-0.184957\pi$
$401$	15.5885	+	9.00000i	0.778450	+	0.449439i	−0.0574304	+	0.998350i	$0.518291\pi$
$402$		0			0
$403$	−9.00000	−	15.5885i	−0.448322	−	0.776516i
$404$		0			0
$405$		0			0
$406$	−12.0000	+	10.3923i	−0.595550	+	0.515761i
$407$	−18.1865	+	10.5000i	−0.901473	+	0.520466i
$408$		0			0
$409$	−3.00000	−	1.73205i	−0.148340	−	0.0856444i	0.423993	−	0.905666i	$-0.360628\pi$
$409$	−3.00000	−	1.73205i	−0.148340	−	0.0856444i	−0.572333	+	0.820021i	$0.693962\pi$
$410$	−18.1865	−	10.5000i	−0.898169	−	0.518558i
$411$		0			0
$412$	−16.5000	+	9.52628i	−0.812897	+	0.469326i
$413$	−6.92820	+	6.00000i	−0.340915	+	0.295241i
$414$		0			0
$415$	−30.0000			−1.47264
$416$	1.73205	+	3.00000i	0.0849208	+	0.147087i
$417$		0			0
$418$	−4.50000	−	2.59808i	−0.220102	−	0.127076i
$419$	3.46410	−	6.00000i	0.169232	−	0.293119i	−0.768918	−	0.639348i	$-0.779204\pi$
$419$	3.46410	−	6.00000i	0.169232	−	0.293119i	0.938150	+	0.346228i	$0.112538\pi$
$420$		0			0
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	0.979817	−	0.199899i	$-0.0640614\pi$
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	−0.663026	+	0.748596i	$0.730728\pi$
$422$		−	16.0000i		−	0.778868i
$423$		0			0
$424$	−12.0000			−0.582772
$425$	−6.92820	−	12.0000i	−0.336067	−	0.582086i
$426$		0			0
$427$	18.0000	−	3.46410i	0.871081	−	0.167640i
$428$		0			0
$429$		0			0
$430$	−3.00000	+	1.73205i	−0.144673	+	0.0835269i
$431$			21.0000i			1.01153i	0.862670	+	0.505767i	$0.168791\pi$
$431$			21.0000i			1.01153i	−0.862670	+	0.505767i	$0.831209\pi$
$432$		0			0
$433$		−	10.3923i		−	0.499422i	−0.968320	−	0.249711i	$-0.919664\pi$
$433$		−	10.3923i		−	0.499422i	0.968320	−	0.249711i	$-0.0803357\pi$
$434$	−12.9904	−	4.50000i	−0.623558	−	0.216007i
$435$		0			0
$436$	6.50000	−	11.2583i	0.311294	−	0.539176i
$437$	2.59808	−	4.50000i	0.124283	−	0.215264i
$438$		0			0
$439$	9.00000	−	5.19615i	0.429547	−	0.247999i	−0.269607	−	0.962970i	$-0.586894\pi$
$439$	9.00000	−	5.19615i	0.429547	−	0.247999i	0.699153	+	0.714972i	$0.253560\pi$
$440$	−5.19615			−0.247717
$441$		0			0
$442$	24.0000			1.14156
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	−0.303281	−	0.952901i	$-0.598082\pi$
$443$	7.79423	−	4.50000i	0.370315	−	0.213801i	0.673596	+	0.739100i	$0.264749\pi$
$444$		0			0
$445$	4.50000	−	7.79423i	0.213320	−	0.369482i
$446$	−7.79423	+	13.5000i	−0.369067	+	0.639244i
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$			12.0000i			0.566315i	0.959073	+	0.283158i	$0.0913819\pi$
$449$			12.0000i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$450$		0			0
$451$		−	36.3731i		−	1.71274i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$		0			0
$454$	−18.0000	−	10.3923i	−0.844782	−	0.487735i
$455$	−15.5885	+	3.00000i	−0.730798	+	0.140642i
$456$		0			0
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$		0			0
$459$		0			0
$460$		−	5.19615i		−	0.242272i
$461$	9.52628	+	16.5000i	0.443683	+	0.768482i	0.997959	−	0.0638511i	$-0.0203383\pi$
$461$	9.52628	+	16.5000i	0.443683	+	0.768482i	−0.554276	+	0.832333i	$0.687005\pi$
$462$		0			0
$463$	−16.0000	+	27.7128i	−0.743583	+	1.28792i	0.207271	+	0.978284i	$0.433542\pi$
$463$	−16.0000	+	27.7128i	−0.743583	+	1.28792i	−0.950854	+	0.309640i	$0.899791\pi$
$464$	5.19615	+	3.00000i	0.241225	+	0.139272i
$465$		0			0
$466$	12.0000	+	20.7846i	0.555889	+	0.962828i
$467$	−31.1769			−1.44270			−0.721348	−	0.692573i	$-0.756477\pi$
$467$	−31.1769			−1.44270			−0.721348	+	0.692573i	$0.756477\pi$
$468$		0			0
$469$	4.00000	−	3.46410i	0.184703	−	0.159957i
$470$	5.19615	−	3.00000i	0.239681	−	0.138380i
$471$		0			0
$472$	3.00000	+	1.73205i	0.138086	+	0.0797241i
$473$	−5.19615	−	3.00000i	−0.238919	−	0.137940i
$474$		0			0
$475$	3.00000	−	1.73205i	0.137649	−	0.0794719i
$476$	13.8564	−	12.0000i	0.635107	−	0.550019i
$477$		0			0
$478$		0			0
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	−0.986911	−	0.161265i	$-0.948443\pi$
$479$	−13.8564	−	24.0000i	−0.633115	−	1.09659i	0.353796	−	0.935323i	$-0.384891\pi$
$480$		0			0
$481$	21.0000	+	12.1244i	0.957518	+	0.552823i
$482$	8.66025	−	15.0000i	0.394464	−	0.683231i
$483$		0			0
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$			24.0000i			1.08978i
$486$		0			0
$487$	10.0000			0.453143			0.226572	−	0.973995i	$-0.427248\pi$
$487$	10.0000			0.453143			0.226572	+	0.973995i	$0.427248\pi$
$488$	−3.46410	−	6.00000i	−0.156813	−	0.271607i
$489$		0			0
$490$	−7.50000	+	9.52628i	−0.338815	+	0.430353i
$491$	7.79423	+	4.50000i	0.351749	+	0.203082i	0.665455	−	0.746438i	$-0.268237\pi$
$491$	7.79423	+	4.50000i	0.351749	+	0.203082i	−0.313707	+	0.949520i	$0.601571\pi$
$492$		0			0
$493$	36.0000	−	20.7846i	1.62136	−	0.936092i
$494$			6.00000i			0.269953i
$495$		0			0
$496$			5.19615i			0.233314i
$497$	2.59808	−	7.50000i	0.116540	−	0.336421i
$498$		0			0
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$		0			0
$502$	−12.0000	+	6.92820i	−0.535586	+	0.309221i
$503$	−24.2487			−1.08120			−0.540598	−	0.841281i	$-0.681802\pi$
$503$	−24.2487			−1.08120			−0.540598	+	0.841281i	$0.681802\pi$
$504$		0			0
$505$		0			0
$506$	7.79423	−	4.50000i	0.346496	−	0.200049i
$507$		0			0
$508$	−11.0000	+	19.0526i	−0.488046	+	0.845321i
$509$	6.92820	−	12.0000i	0.307087	−	0.531891i	−0.670637	−	0.741786i	$-0.733979\pi$
$509$	6.92820	−	12.0000i	0.307087	−	0.531891i	0.977724	+	0.209895i	$0.0673123\pi$
$510$		0			0
$511$	3.00000	−	8.66025i	0.132712	−	0.383107i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			5.19615i			0.229192i
$515$	−28.5788	+	16.5000i	−1.25933	+	0.727077i
$516$		0			0
$517$	9.00000	+	5.19615i	0.395820	+	0.228527i
$518$	18.1865	−	3.50000i	0.799070	−	0.153781i
$519$		0			0
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	22.5167			0.986473			0.493236	−	0.869895i	$-0.335814\pi$
$521$	22.5167			0.986473			0.493236	+	0.869895i	$0.335814\pi$
$522$		0			0
$523$		−	39.8372i		−	1.74196i	−0.491320	−	0.870979i	$-0.663486\pi$
$523$		−	39.8372i		−	1.74196i	0.491320	−	0.870979i	$-0.336514\pi$
$524$	5.19615	+	9.00000i	0.226995	+	0.393167i
$525$		0			0
$526$	13.5000	−	23.3827i	0.588628	−	1.01953i
$527$	31.1769	+	18.0000i	1.35809	+	0.784092i
$528$		0			0
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$	−20.7846			−0.902826
$531$		0			0
$532$	3.00000	+	3.46410i	0.130066	+	0.150188i
$533$	−36.3731	+	21.0000i	−1.57549	+	0.909611i
$534$		0			0
$535$		0			0
$536$	−1.73205	−	1.00000i	−0.0748132	−	0.0431934i
$537$		0			0
$538$	−1.50000	+	0.866025i	−0.0646696	+	0.0373370i
$539$	−20.7846	−	3.00000i	−0.895257	−	0.129219i
$540$		0			0
$541$	−25.0000			−1.07483			−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000			−1.07483			−0.537417	+	0.843317i	$0.680600\pi$
$542$	−8.66025	−	15.0000i	−0.371990	−	0.644305i
$543$		0			0
$544$	−6.00000	−	3.46410i	−0.257248	−	0.148522i
$545$	11.2583	−	19.5000i	0.482254	−	0.835288i
$546$		0			0
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	0.767752	−	0.640747i	$-0.221375\pi$
$547$	−4.00000	−	6.92820i	−0.171028	−	0.296229i	−0.938779	+	0.344519i	$0.888042\pi$
$548$			18.0000i			0.768922i
$549$		0			0
$550$	6.00000			0.255841
$551$	5.19615	+	9.00000i	0.221364	+	0.383413i
$552$		0			0
$553$	−5.00000	−	25.9808i	−0.212622	−	1.10481i
$554$	9.52628	+	5.50000i	0.404733	+	0.233673i
$555$		0			0
$556$	−3.00000	+	1.73205i	−0.127228	+	0.0734553i
$557$		−	12.0000i		−	0.508456i	−0.967144	−	0.254228i	$-0.918179\pi$
$557$		−	12.0000i		−	0.508456i	0.967144	−	0.254228i	$-0.0818214\pi$
$558$		0			0
$559$			6.92820i			0.293032i
$560$	4.33013	+	1.50000i	0.182981	+	0.0633866i
$561$		0			0
$562$	−15.0000	+	25.9808i	−0.632737	+	1.09593i
$563$	5.19615	−	9.00000i	0.218992	−	0.379305i	−0.735508	−	0.677516i	$-0.763057\pi$
$563$	5.19615	−	9.00000i	0.218992	−	0.379305i	0.954500	+	0.298211i	$0.0963899\pi$
$564$		0			0
$565$	−18.0000	+	10.3923i	−0.757266	+	0.437208i
$566$	−31.1769			−1.31046
$567$		0			0
$568$	−3.00000			−0.125877
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−5.19615	+	9.00000i	−0.217262	+	0.376309i
$573$		0			0
$574$	−10.5000	+	30.3109i	−0.438262	+	1.26515i
$575$			6.00000i			0.250217i
$576$		0			0
$577$			34.6410i			1.44212i	0.692870	+	0.721062i	$0.256346\pi$
$577$			34.6410i			1.44212i	−0.692870	+	0.721062i	$0.743654\pi$
$578$	−26.8468	+	15.5000i	−1.11668	+	0.644715i
$579$		0			0
$580$	9.00000	+	5.19615i	0.373705	+	0.215758i
$581$	8.66025	+	45.0000i	0.359288	+	1.86691i
$582$		0			0
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	−3.46410			−0.143346
$585$		0			0
$586$		−	6.92820i		−	0.286201i
$587$	20.7846	+	36.0000i	0.857873	+	1.48588i	0.873954	+	0.486008i	$0.161548\pi$
$587$	20.7846	+	36.0000i	0.857873	+	1.48588i	−0.0160815	+	0.999871i	$0.505119\pi$
$588$		0			0
$589$	−4.50000	+	7.79423i	−0.185419	+	0.321156i
$590$	5.19615	+	3.00000i	0.213922	+	0.123508i
$591$		0			0
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	−19.0526			−0.782395			−0.391197	−	0.920307i	$-0.627939\pi$
$593$	−19.0526			−0.782395			−0.391197	+	0.920307i	$0.627939\pi$
$594$		0			0
$595$	24.0000	−	20.7846i	0.983904	−	0.852086i
$596$	10.3923	−	6.00000i	0.425685	−	0.245770i
$597$		0			0
$598$	−9.00000	−	5.19615i	−0.368037	−	0.212486i
$599$	−7.79423	−	4.50000i	−0.318464	−	0.183865i	0.332244	−	0.943193i	$-0.392194\pi$
$599$	−7.79423	−	4.50000i	−0.318464	−	0.183865i	−0.650708	+	0.759328i	$0.725528\pi$
$600$		0			0
$601$	9.00000	−	5.19615i	0.367118	−	0.211955i	−0.305081	−	0.952326i	$-0.598683\pi$
$601$	9.00000	−	5.19615i	0.367118	−	0.211955i	0.672198	+	0.740371i	$0.265350\pi$
$602$	3.46410	+	4.00000i	0.141186	+	0.163028i
$603$		0			0
$604$	8.00000			0.325515
$605$	1.73205	+	3.00000i	0.0704179	+	0.121967i
$606$		0			0
$607$	−15.0000	−	8.66025i	−0.608831	−	0.351509i	0.163677	−	0.986514i	$-0.447665\pi$
$607$	−15.0000	−	8.66025i	−0.608831	−	0.351509i	−0.772508	+	0.635005i	$0.780998\pi$
$608$	0.866025	−	1.50000i	0.0351220	−	0.0608330i
$609$		0			0
$610$	−6.00000	−	10.3923i	−0.242933	−	0.420772i
$611$		−	12.0000i		−	0.485468i
$612$		0			0
$613$	−19.0000			−0.767403			−0.383701	−	0.923457i	$-0.625351\pi$
$613$	−19.0000			−0.767403			−0.383701	+	0.923457i	$0.625351\pi$
$614$	7.79423	+	13.5000i	0.314549	+	0.544816i
$615$		0			0
$616$	1.50000	+	7.79423i	0.0604367	+	0.314038i
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	0.779809	−	0.626017i	$-0.215316\pi$
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	−0.152242	+	0.988343i	$0.548649\pi$
$618$		0			0
$619$	−16.5000	+	9.52628i	−0.663191	+	0.382893i	−0.793492	−	0.608581i	$-0.791739\pi$
$619$	−16.5000	+	9.52628i	−0.663191	+	0.382893i	0.130301	+	0.991475i	$0.458406\pi$
$620$			9.00000i			0.361449i
$621$		0			0
$622$		−	24.2487i		−	0.972285i
$623$	−12.9904	−	4.50000i	−0.520449	−	0.180289i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	−8.66025	+	15.0000i	−0.346133	+	0.599521i
$627$		0			0
$628$	−9.00000	+	5.19615i	−0.359139	+	0.207349i
$629$	−48.4974			−1.93372
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−8.66025	+	5.00000i	−0.344486	+	0.198889i
$633$		0			0
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−19.0526	+	33.0000i	−0.756078	+	1.30957i
$636$		0			0
$637$	9.00000	+	22.5167i	0.356593	+	0.892143i
$638$			18.0000i			0.712627i
$639$		0			0
$640$		−	1.73205i		−	0.0684653i
$641$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$641$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$	−4.50000	−	2.59808i	−0.177463	−	0.102458i	0.408637	−	0.912697i	$-0.366004\pi$
$643$	−4.50000	−	2.59808i	−0.177463	−	0.102458i	−0.586100	+	0.810239i	$0.699337\pi$
$644$	−7.79423	+	1.50000i	−0.307136	+	0.0591083i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−10.3923			−0.408564			−0.204282	−	0.978912i	$-0.565486\pi$
$647$	−10.3923			−0.408564			−0.204282	+	0.978912i	$0.565486\pi$
$648$		0			0
$649$			10.3923i			0.407934i
$650$	−3.46410	−	6.00000i	−0.135873	−	0.235339i
$651$		0			0
$652$	1.00000	−	1.73205i	0.0391630	−	0.0678323i
$653$	−15.5885	−	9.00000i	−0.610023	−	0.352197i	0.162951	−	0.986634i	$-0.447899\pi$
$653$	−15.5885	−	9.00000i	−0.610023	−	0.352197i	−0.772975	+	0.634437i	$0.781232\pi$
$654$		0			0
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	12.1244			0.473377
$657$		0			0
$658$	−6.00000	−	6.92820i	−0.233904	−	0.270089i
$659$	18.1865	−	10.5000i	0.708447	−	0.409022i	−0.102039	−	0.994780i	$-0.532537\pi$
$659$	18.1865	−	10.5000i	0.708447	−	0.409022i	0.810486	+	0.585758i	$0.199203\pi$
$660$		0			0
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.306055	−	0.952014i	$-0.599009\pi$
$661$	−33.0000	−	19.0526i	−1.28355	−	0.741059i	−0.977496	+	0.210955i	$0.932343\pi$
$662$	24.2487	+	14.0000i	0.942453	+	0.544125i
$663$		0			0
$664$	15.0000	−	8.66025i	0.582113	−	0.336083i
$665$	5.19615	+	6.00000i	0.201498	+	0.232670i
$666$		0			0
$667$	−18.0000			−0.696963
$668$	−3.46410	−	6.00000i	−0.134030	−	0.232147i
$669$		0			0
$670$	−3.00000	−	1.73205i	−0.115900	−	0.0669150i
$671$	10.3923	−	18.0000i	0.401190	−	0.694882i
$672$		0			0
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	0.968818	−	0.247774i	$-0.0796991\pi$
$673$	7.00000	+	12.1244i	0.269830	+	0.467360i	−0.698988	+	0.715134i	$0.746366\pi$
$674$			5.00000i			0.192593i
$675$		0			0
$676$	−1.00000			−0.0384615
$677$	−12.9904	−	22.5000i	−0.499261	−	0.864745i	0.500739	−	0.865598i	$-0.333062\pi$
$677$	−12.9904	−	22.5000i	−0.499261	−	0.864745i	−1.00000		0.000853228i	$0.999728\pi$
$678$		0			0
$679$	36.0000	−	6.92820i	1.38155	−	0.265880i
$680$	−10.3923	−	6.00000i	−0.398527	−	0.230089i
$681$		0			0
$682$	−13.5000	+	7.79423i	−0.516942	+	0.298456i
$683$			33.0000i			1.26271i	0.775494	+	0.631355i	$0.217501\pi$
$683$			33.0000i			1.26271i	−0.775494	+	0.631355i	$0.782499\pi$
$684$		0			0
$685$			31.1769i			1.19121i
$686$	16.4545	+	8.50000i	0.628235	+	0.324532i
$687$		0			0
$688$	1.00000	−	1.73205i	0.0381246	−	0.0660338i
$689$	−20.7846	+	36.0000i	−0.791831	+	1.37149i
$690$		0			0
$691$	−9.00000	+	5.19615i	−0.342376	+	0.197671i	−0.661322	−	0.750102i	$-0.730004\pi$
$691$	−9.00000	+	5.19615i	−0.342376	+	0.197671i	0.318946	+	0.947773i	$0.396671\pi$
$692$	5.19615			0.197528
$693$		0			0
$694$	27.0000			1.02491
$695$	−5.19615	+	3.00000i	−0.197101	+	0.113796i
$696$		0			0
$697$	42.0000	−	72.7461i	1.59086	−	2.75546i
$698$	13.8564	−	24.0000i	0.524473	−	0.908413i
$699$		0			0
$700$	−5.00000	−	1.73205i	−0.188982	−	0.0654654i
$701$			6.00000i			0.226617i	0.993560	+	0.113308i	$0.0361448\pi$
$701$			6.00000i			0.226617i	−0.993560	+	0.113308i	$0.963855\pi$
$702$		0			0
$703$		−	12.1244i		−	0.457279i
$704$	2.59808	−	1.50000i	0.0979187	−	0.0565334i
$705$		0			0
$706$	16.5000	+	9.52628i	0.620986	+	0.358526i
$707$		0			0
$708$		0			0
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	0.856484	−	0.516174i	$-0.172644\pi$
$709$	−0.500000	−	0.866025i	−0.0187779	−	0.0325243i	−0.875262	+	0.483650i	$0.839311\pi$
$710$	−5.19615			−0.195008
$711$		0			0
$712$			5.19615i			0.194734i
$713$	−7.79423	−	13.5000i	−0.291896	−	0.505579i
$714$		0			0
$715$	−9.00000	+	15.5885i	−0.336581	+	0.582975i
$716$	−10.3923	−	6.00000i	−0.388379	−	0.224231i
$717$		0			0
$718$		0			0
$719$	−3.46410			−0.129189			−0.0645946	−	0.997912i	$-0.520575\pi$
$719$	−3.46410			−0.129189			−0.0645946	+	0.997912i	$0.520575\pi$
$720$		0			0
$721$	33.0000	+	38.1051i	1.22898	+	1.41911i
$722$	−13.8564	+	8.00000i	−0.515682	+	0.297729i
$723$		0			0
$724$	−12.0000	−	6.92820i	−0.445976	−	0.257485i
$725$	−10.3923	−	6.00000i	−0.385961	−	0.222834i
$726$		0			0
$727$	45.0000	−	25.9808i	1.66896	−	0.963573i	0.700756	−	0.713401i	$-0.252846\pi$
$727$	45.0000	−	25.9808i	1.66896	−	0.963573i	0.968201	−	0.250172i	$-0.0804873\pi$
$728$	6.92820	−	6.00000i	0.256776	−	0.222375i
$729$		0			0
$730$	−6.00000			−0.222070
$731$	−6.92820	−	12.0000i	−0.256249	−	0.443836i
$732$		0			0
$733$	−9.00000	−	5.19615i	−0.332423	−	0.191924i	0.324494	−	0.945888i	$-0.394806\pi$
$733$	−9.00000	−	5.19615i	−0.332423	−	0.191924i	−0.656916	+	0.753964i	$0.728139\pi$
$734$	−0.866025	+	1.50000i	−0.0319656	+	0.0553660i
$735$		0			0
$736$	1.50000	+	2.59808i	0.0552907	+	0.0957664i
$737$		−	6.00000i		−	0.221013i
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−6.06218	−	10.5000i	−0.222850	−	0.385988i
$741$		0			0
$742$	6.00000	+	31.1769i	0.220267	+	1.14454i
$743$	−23.3827	−	13.5000i	−0.857828	−	0.495267i	0.00545664	−	0.999985i	$-0.498263\pi$
$743$	−23.3827	−	13.5000i	−0.857828	−	0.495267i	−0.863284	+	0.504718i	$0.831596\pi$
$744$		0			0
$745$	18.0000	−	10.3923i	0.659469	−	0.380745i
$746$		−	5.00000i		−	0.183063i
$747$		0			0
$748$		−	20.7846i		−	0.759961i
$749$		0			0
$750$		0			0
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	−0.847203	−	0.531269i	$-0.821715\pi$
$751$	1.00000	−	1.73205i	0.0364905	−	0.0632034i	0.883694	+	0.468065i	$0.155049\pi$
$752$	−1.73205	+	3.00000i	−0.0631614	+	0.109399i
$753$		0			0
$754$	18.0000	−	10.3923i	0.655521	−	0.378465i
$755$	13.8564			0.504286
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	1.73205	−	1.00000i	0.0629109	−	0.0363216i
$759$		0			0
$760$	1.50000	−	2.59808i	0.0544107	−	0.0942421i
$761$	6.92820	−	12.0000i	0.251147	−	0.435000i	−0.712695	−	0.701474i	$-0.752526\pi$
$761$	6.92820	−	12.0000i	0.251147	−	0.435000i	0.963842	+	0.266475i	$0.0858589\pi$
$762$		0			0
$763$	−32.5000	−	11.2583i	−1.17658	−	0.407579i
$764$		−	21.0000i		−	0.759753i
$765$		0			0
$766$			13.8564i			0.500652i
$767$	10.3923	−	6.00000i	0.375244	−	0.216647i
$768$		0			0
$769$	33.0000	+	19.0526i	1.19001	+	0.687053i	0.958309	−	0.285734i	$-0.0922374\pi$
$769$	33.0000	+	19.0526i	1.19001	+	0.687053i	0.231701	+	0.972787i	$0.425571\pi$
$770$	2.59808	+	13.5000i	0.0936282	+	0.486506i
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	19.0526			0.685273			0.342636	−	0.939468i	$-0.388680\pi$
$773$	19.0526			0.685273			0.342636	+	0.939468i	$0.388680\pi$
$774$		0			0
$775$		−	10.3923i		−	0.373303i
$776$	−6.92820	−	12.0000i	−0.248708	−	0.430775i
$777$		0			0
$778$	12.0000	−	20.7846i	0.430221	−	0.745164i
$779$	18.1865	+	10.5000i	0.651600	+	0.376202i
$780$		0			0
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$	20.7846			0.743256
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	−15.5885	+	9.00000i	−0.556376	+	0.321224i
$786$		0			0
$787$	−15.0000	−	8.66025i	−0.534692	−	0.308705i	0.208233	−	0.978079i	$-0.433229\pi$
$787$	−15.0000	−	8.66025i	−0.534692	−	0.308705i	−0.742925	+	0.669375i	$0.766562\pi$
$788$	−10.3923	−	6.00000i	−0.370211	−	0.213741i
$789$		0			0
$790$	−15.0000	+	8.66025i	−0.533676	+	0.308118i
$791$	20.7846	+	24.0000i	0.739016	+	0.853342i
$792$		0			0
$793$	−24.0000			−0.852265
$794$	−10.3923	−	18.0000i	−0.368809	−	0.638796i
$795$		0			0
$796$	1.50000	+	0.866025i	0.0531661	+	0.0306955i
$797$	7.79423	−	13.5000i	0.276086	−	0.478195i	−0.694323	−	0.719664i	$-0.744296\pi$
$797$	7.79423	−	13.5000i	0.276086	−	0.478195i	0.970408	+	0.241469i	$0.0776293\pi$
$798$		0			0
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$			2.00000i			0.0707107i
$801$		0			0
$802$	−18.0000			−0.635602
$803$	−5.19615	−	9.00000i	−0.183368	−	0.317603i
$804$		0			0
$805$	−13.5000	+	2.59808i	−0.475812	+	0.0915702i
$806$	15.5885	+	9.00000i	0.549080	+	0.317011i
$807$		0			0
$808$		0			0
$809$			6.00000i			0.210949i	0.994422	+	0.105474i	$0.0336361\pi$
$809$			6.00000i			0.210949i	−0.994422	+	0.105474i	$0.966364\pi$
$810$		0			0
$811$			36.3731i			1.27723i	0.769526	+	0.638616i	$0.220493\pi$
$811$			36.3731i			1.27723i	−0.769526	+	0.638616i	$0.779507\pi$
$812$	5.19615	−	15.0000i	0.182349	−	0.526397i
$813$		0			0
$814$	10.5000	−	18.1865i	0.368025	−	0.637438i
$815$	1.73205	−	3.00000i	0.0606711	−	0.105085i
$816$		0			0
$817$	3.00000	−	1.73205i	0.104957	−	0.0605968i
$818$	3.46410			0.121119
$819$		0			0
$820$	21.0000			0.733352
$821$	25.9808	−	15.0000i	0.906735	−	0.523504i	0.0273557	−	0.999626i	$-0.491291\pi$
$821$	25.9808	−	15.0000i	0.906735	−	0.523504i	0.879379	+	0.476122i	$0.157958\pi$
$822$		0			0
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$	9.52628	−	16.5000i	0.331864	−	0.574805i
$825$		0			0
$826$	3.00000	−	8.66025i	0.104383	−	0.301329i
$827$			3.00000i			0.104320i	0.998639	+	0.0521601i	$0.0166106\pi$
$827$			3.00000i			0.104320i	−0.998639	+	0.0521601i	$0.983389\pi$
$828$		0			0
$829$			38.1051i			1.32345i	0.749749	+	0.661723i	$0.230174\pi$
$829$			38.1051i			1.32345i	−0.749749	+	0.661723i	$0.769826\pi$
$830$	25.9808	−	15.0000i	0.901805	−	0.520658i
$831$		0			0
$832$	−3.00000	−	1.73205i	−0.104006	−	0.0600481i
$833$	−38.1051	−	30.0000i	−1.32026	−	1.03944i
$834$		0			0
$835$	−6.00000	−	10.3923i	−0.207639	−	0.359641i
$836$	5.19615			0.179713
$837$		0			0
$838$			6.92820i			0.239331i
$839$	−12.1244	−	21.0000i	−0.418579	−	0.725001i	0.577218	−	0.816590i	$-0.304138\pi$
$839$	−12.1244	−	21.0000i	−0.418579	−	0.725001i	−0.995797	+	0.0915899i	$0.970805\pi$
$840$		0			0
$841$	3.50000	−	6.06218i	0.120690	−	0.209041i
$842$	−11.2583	−	6.50000i	−0.387988	−	0.224005i
$843$		0			0
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	−1.73205			−0.0595844
$846$		0			0
$847$	4.00000	−	3.46410i	0.137442	−	0.119028i
$848$	10.3923	−	6.00000i	0.356873	−	0.206041i
$849$		0			0
$850$	12.0000	+	6.92820i	0.411597	+	0.237635i
$851$	18.1865	+	10.5000i	0.623426	+	0.359935i
$852$		0			0
$853$	−12.0000	+	6.92820i	−0.410872	+	0.237217i	−0.691164	−	0.722698i	$-0.742902\pi$
$853$	−12.0000	+	6.92820i	−0.410872	+	0.237217i	0.280292	+	0.959915i	$0.409569\pi$
$854$	−13.8564	+	12.0000i	−0.474156	+	0.410632i
$855$		0			0
$856$		0			0
$857$	21.6506	+	37.5000i	0.739572	+	1.28098i	0.952688	+	0.303949i	$0.0983052\pi$
$857$	21.6506	+	37.5000i	0.739572	+	1.28098i	−0.213117	+	0.977027i	$0.568361\pi$
$858$		0			0
$859$	25.5000	+	14.7224i	0.870049	+	0.502323i	0.867364	−	0.497674i	$-0.165812\pi$
$859$	25.5000	+	14.7224i	0.870049	+	0.502323i	0.00268433	+	0.999996i	$0.499146\pi$
$860$	1.73205	−	3.00000i	0.0590624	−	0.102299i
$861$		0			0
$862$	−10.5000	−	18.1865i	−0.357631	−	0.619436i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$	9.00000			0.306009
$866$	5.19615	+	9.00000i	0.176572	+	0.305832i
$867$		0			0
$868$	13.5000	−	2.59808i	0.458220	−	0.0881845i
$869$	−25.9808	−	15.0000i	−0.881337	−	0.508840i
$870$		0			0
$871$	−6.00000	+	3.46410i	−0.203302	+	0.117377i
$872$			13.0000i			0.440236i
$873$		0			0
$874$			5.19615i			0.175762i
$875$	−30.3109	−	10.5000i	−1.02470	−	0.354965i
$876$		0			0
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$	−5.19615	+	9.00000i	−0.175362	+	0.303735i
$879$		0			0
$880$	4.50000	−	2.59808i	0.151695	−	0.0875811i
$881$	25.9808			0.875314			0.437657	−	0.899142i	$-0.355808\pi$
$881$	25.9808			0.875314			0.437657	+	0.899142i	$0.355808\pi$
$882$		0			0
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$	−20.7846	+	12.0000i	−0.699062	+	0.403604i
$885$		0			0
$886$	−4.50000	+	7.79423i	−0.151180	+	0.261852i
$887$	−12.1244	+	21.0000i	−0.407096	+	0.705111i	−0.994563	−	0.104137i	$-0.966792\pi$
$887$	−12.1244	+	21.0000i	−0.407096	+	0.705111i	0.587467	+	0.809248i	$0.300125\pi$
$888$		0			0
$889$	55.0000	+	19.0526i	1.84464	+	0.639002i
$890$			9.00000i			0.301681i
$891$		0			0
$892$		−	15.5885i		−	0.521940i
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$		0			0
$895$	−18.0000	−	10.3923i	−0.601674	−	0.347376i
$896$	−2.59808	+	0.500000i	−0.0867956	+	0.0167038i
$897$		0			0
$898$	−6.00000	−	10.3923i	−0.200223	−	0.346796i
$899$	31.1769			1.03981
$900$		0			0
$901$		−	83.1384i		−	2.76974i
$902$	18.1865	+	31.5000i	0.605545	+	1.04884i
$903$		0			0
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$	−20.7846	−	12.0000i	−0.690904	−	0.398893i
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$	20.7846			0.689761
$909$		0			0
$910$	12.0000	−	10.3923i	0.397796	−	0.344502i
$911$	10.3923	−	6.00000i	0.344312	−	0.198789i	−0.317865	−	0.948136i	$-0.602966\pi$
$911$	10.3923	−	6.00000i	0.344312	−	0.198789i	0.662177	+	0.749347i	$0.269633\pi$
$912$		0			0
$913$	45.0000	+	25.9808i	1.48928	+	0.859838i
$914$	−14.7224	−	8.50000i	−0.486975	−	0.281155i
$915$		0			0
$916$		0			0
$917$	20.7846	−	18.0000i	0.686368	−	0.594412i
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$	2.59808	+	4.50000i	0.0856560	+	0.148361i
$921$		0			0
$922$	−16.5000	−	9.52628i	−0.543399	−	0.313731i
$923$	−5.19615	+	9.00000i	−0.171033	+	0.296239i
$924$		0			0
$925$	7.00000	+	12.1244i	0.230159	+	0.398646i
$926$		−	32.0000i		−	1.05159i
$927$		0			0
$928$	−6.00000			−0.196960
$929$	13.8564	+	24.0000i	0.454614	+	0.787414i	0.998666	−	0.0516371i	$-0.0164439\pi$
$929$	13.8564	+	24.0000i	0.454614	+	0.787414i	−0.544052	+	0.839052i	$0.683111\pi$
$930$		0			0
$931$	7.50000	−	9.52628i	0.245803	−	0.312211i
$932$	−20.7846	−	12.0000i	−0.680823	−	0.393073i
$933$		0			0
$934$	27.0000	−	15.5885i	0.883467	−	0.510070i
$935$		−	36.0000i		−	1.17733i
$936$		0			0
$937$		−	6.92820i		−	0.226335i	−0.993576	−	0.113167i	$-0.963900\pi$
$937$		−	6.92820i		−	0.226335i	0.993576	−	0.113167i	$-0.0360996\pi$
$938$	−1.73205	+	5.00000i	−0.0565535	+	0.163256i
$939$		0			0
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$	−6.06218	+	10.5000i	−0.197621	+	0.342290i	−0.947757	−	0.318994i	$-0.896655\pi$
$941$	−6.06218	+	10.5000i	−0.197621	+	0.342290i	0.750135	+	0.661284i	$0.229988\pi$
$942$		0			0
$943$	−31.5000	+	18.1865i	−1.02578	+	0.592235i
$944$	−3.46410			−0.112747
$945$		0			0
$946$	6.00000			0.195077
$947$	12.9904	−	7.50000i	0.422131	−	0.243717i	−0.273858	−	0.961770i	$-0.588300\pi$
$947$	12.9904	−	7.50000i	0.422131	−	0.243717i	0.695988	+	0.718053i	$0.254966\pi$
$948$		0			0
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	−1.73205	+	3.00000i	−0.0561951	+	0.0973329i
$951$		0			0
$952$	−6.00000	+	17.3205i	−0.194461	+	0.561361i
$953$		−	18.0000i		−	0.583077i	−0.956559	−	0.291539i	$-0.905833\pi$
$953$		−	18.0000i		−	0.583077i	0.956559	−	0.291539i	$-0.0941672\pi$
$954$		0			0
$955$		−	36.3731i		−	1.17700i
$956$		0			0
$957$		0			0
$958$	24.0000	+	13.8564i	0.775405	+	0.447680i
$959$	46.7654	−	9.00000i	1.51013	−	0.290625i
$960$		0			0
$961$	−2.00000	−	3.46410i	−0.0645161	−	0.111745i
$962$	−24.2487			−0.781810
$963$		0			0
$964$			17.3205i			0.557856i
$965$	−12.1244	−	21.0000i	−0.390297	−	0.676014i
$966$		0			0
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$	−1.73205	−	1.00000i	−0.0556702	−	0.0321412i
$969$		0			0
$970$	−12.0000	−	20.7846i	−0.385297	−	0.667354i
$971$	−3.46410			−0.111168			−0.0555842	−	0.998454i	$-0.517702\pi$
$971$	−3.46410			−0.111168			−0.0555842	+	0.998454i	$0.517702\pi$
$972$		0			0
$973$	6.00000	+	6.92820i	0.192351	+	0.222108i
$974$	−8.66025	+	5.00000i	−0.277492	+	0.160210i
$975$		0			0
$976$	6.00000	+	3.46410i	0.192055	+	0.110883i
$977$	41.5692	+	24.0000i	1.32992	+	0.767828i	0.985287	−	0.170910i	$-0.0546709\pi$
$977$	41.5692	+	24.0000i	1.32992	+	0.767828i	0.344631	+	0.938738i	$0.388004\pi$
$978$		0			0
$979$	−13.5000	+	7.79423i	−0.431462	+	0.249105i
$980$	1.73205	−	12.0000i	0.0553283	−	0.383326i
$981$		0			0
$982$	−9.00000			−0.287202
$983$	1.73205	+	3.00000i	0.0552438	+	0.0956851i	0.892325	−	0.451394i	$-0.149073\pi$
$983$	1.73205	+	3.00000i	0.0552438	+	0.0956851i	−0.837081	+	0.547079i	$0.815740\pi$
$984$		0			0
$985$	−18.0000	−	10.3923i	−0.573528	−	0.331126i
$986$	−20.7846	+	36.0000i	−0.661917	+	1.14647i
$987$		0			0
$988$	−3.00000	−	5.19615i	−0.0954427	−	0.165312i
$989$			6.00000i			0.190789i
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	−2.59808	−	4.50000i	−0.0824890	−	0.142875i
$993$		0			0
$994$	1.50000	+	7.79423i	0.0475771	+	0.247218i
$995$	2.59808	+	1.50000i	0.0823646	+	0.0475532i
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		−	10.0000i		−	0.316544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.m.b.377.1		4
3.2	odd	2	inner	1134.2.m.b.377.2		4
7.6	odd	2		1134.2.m.c.377.1		4
9.2	odd	6		1134.2.m.c.755.1		4
9.4	even	3		378.2.d.b.377.1	✓	4
9.5	odd	6		378.2.d.b.377.4	yes	4
9.7	even	3		1134.2.m.c.755.2		4
21.20	even	2		1134.2.m.c.377.2		4
36.23	even	6		3024.2.k.e.1889.4		4
36.31	odd	6		3024.2.k.e.1889.2		4
63.13	odd	6		378.2.d.b.377.2	yes	4
63.20	even	6	inner	1134.2.m.b.755.1		4
63.34	odd	6	inner	1134.2.m.b.755.2		4
63.41	even	6		378.2.d.b.377.3	yes	4
252.139	even	6		3024.2.k.e.1889.3		4
252.167	odd	6		3024.2.k.e.1889.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.d.b.377.1	✓	4	9.4	even	3
378.2.d.b.377.2	yes	4	63.13	odd	6
378.2.d.b.377.3	yes	4	63.41	even	6
378.2.d.b.377.4	yes	4	9.5	odd	6
1134.2.m.b.377.1		4	1.1	even	1	trivial
1134.2.m.b.377.2		4	3.2	odd	2	inner
1134.2.m.b.755.1		4	63.20	even	6	inner
1134.2.m.b.755.2		4	63.34	odd	6	inner
1134.2.m.c.377.1		4	7.6	odd	2
1134.2.m.c.377.2		4	21.20	even	2
1134.2.m.c.755.1		4	9.2	odd	6
1134.2.m.c.755.2		4	9.7	even	3
3024.2.k.e.1889.1		4	252.167	odd	6
3024.2.k.e.1889.2		4	36.31	odd	6
3024.2.k.e.1889.3		4	252.139	even	6
3024.2.k.e.1889.4		4	36.23	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.866025 - 1.50000i) q^{5} +(-2.50000 - 0.866025i) q^{7} +1.00000i q^{8} +1.73205i q^{10} +(-2.59808 + 1.50000i) q^{11} +(3.00000 + 1.73205i) q^{13} +(2.59808 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.92820 q^{17} -1.73205i q^{19} +(-0.866025 - 1.50000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(2.59808 + 1.50000i) q^{23} +(1.00000 + 1.73205i) q^{25} -3.46410 q^{26} +(-2.00000 + 1.73205i) q^{28} +(-5.19615 + 3.00000i) q^{29} +(-4.50000 - 2.59808i) q^{31} +(0.866025 + 0.500000i) q^{32} +(6.00000 - 3.46410i) q^{34} +(-3.46410 + 3.00000i) q^{35} +7.00000 q^{37} +(0.866025 + 1.50000i) q^{38} +(1.50000 + 0.866025i) q^{40} +(-6.06218 + 10.5000i) q^{41} +(1.00000 + 1.73205i) q^{43} +3.00000i q^{44} -3.00000 q^{46} +(-1.73205 - 3.00000i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.73205 - 1.00000i) q^{50} +(3.00000 - 1.73205i) q^{52} +12.0000i q^{53} +5.19615i q^{55} +(0.866025 - 2.50000i) q^{56} +(3.00000 - 5.19615i) q^{58} +(1.73205 - 3.00000i) q^{59} +(-6.00000 + 3.46410i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(5.19615 - 3.00000i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(1.50000 - 4.33013i) q^{70} +3.00000i q^{71} +3.46410i q^{73} +(-6.06218 + 3.50000i) q^{74} +(-1.50000 - 0.866025i) q^{76} +(7.79423 - 1.50000i) q^{77} +(5.00000 + 8.66025i) q^{79} -1.73205 q^{80} -12.1244i q^{82} +(-8.66025 - 15.0000i) q^{83} +(-6.00000 + 10.3923i) q^{85} +(-1.73205 - 1.00000i) q^{86} +(-1.50000 - 2.59808i) q^{88} +5.19615 q^{89} +(-6.00000 - 6.92820i) q^{91} +(2.59808 - 1.50000i) q^{92} +(3.00000 + 1.73205i) q^{94} +(-2.59808 - 1.50000i) q^{95} +(-12.0000 + 6.92820i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 10 q^{7} + 12 q^{13} - 2 q^{16} + 6 q^{22} + 4 q^{25} - 8 q^{28} - 18 q^{31} + 24 q^{34} + 28 q^{37} + 6 q^{40} + 4 q^{43} - 12 q^{46} + 22 q^{49} + 12 q^{52} + 12 q^{58} - 24 q^{61} - 4 q^{64}+ \cdots - 48 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 10 * q^7 + 12 * q^13 - 2 * q^16 + 6 * q^22 + 4 * q^25 - 8 * q^28 - 18 * q^31 + 24 * q^34 + 28 * q^37 + 6 * q^40 + 4 * q^43 - 12 * q^46 + 22 * q^49 + 12 * q^52 + 12 * q^58 - 24 * q^61 - 4 * q^64 - 4 * q^67 + 6 * q^70 - 6 * q^76 + 20 * q^79 - 24 * q^85 - 6 * q^88 - 24 * q^91 + 12 * q^94 - 48 * q^97

Introduction

L-functions

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Varieties

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