LMFDB - Embedded newform 1134.2.m.c.755.2

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			755.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.755
Dual form			1134.2.m.c.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +1.73205i q^{10} +(2.59808 + 1.50000i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(-0.866025 + 2.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.92820 q^{17} -1.73205i q^{19} +(-0.866025 + 1.50000i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.59808 + 1.50000i) q^{23} +(1.00000 - 1.73205i) q^{25} -3.46410 q^{26} +(-2.00000 + 1.73205i) q^{28} +(5.19615 + 3.00000i) q^{29} +(4.50000 - 2.59808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(-3.46410 + 3.00000i) q^{35} +7.00000 q^{37} +(0.866025 - 1.50000i) q^{38} +(-1.50000 + 0.866025i) q^{40} +(-6.06218 - 10.5000i) q^{41} +(1.00000 - 1.73205i) q^{43} +3.00000i q^{44} -3.00000 q^{46} +(-1.73205 + 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-3.00000 - 1.73205i) q^{52} +12.0000i q^{53} +5.19615i q^{55} +(-2.59808 + 0.500000i) q^{56} +(3.00000 + 5.19615i) q^{58} +(1.73205 + 3.00000i) q^{59} +(6.00000 + 3.46410i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(-5.19615 - 3.00000i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-3.46410 - 6.00000i) q^{68} +(-4.50000 + 0.866025i) q^{70} +3.00000i q^{71} +3.46410i q^{73} +(6.06218 + 3.50000i) q^{74} +(1.50000 - 0.866025i) q^{76} +(-2.59808 + 7.50000i) q^{77} +(5.00000 - 8.66025i) q^{79} -1.73205 q^{80} -12.1244i q^{82} +(-8.66025 + 15.0000i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(1.73205 - 1.00000i) q^{86} +(-1.50000 + 2.59808i) q^{88} +5.19615 q^{89} +(-6.00000 - 6.92820i) q^{91} +(-2.59808 - 1.50000i) q^{92} +(-3.00000 + 1.73205i) q^{94} +(2.59808 - 1.50000i) q^{95} +(12.0000 + 6.92820i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^7	$ 4 q + 2 q^{4} + 2 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} - 26 q^{49} - 12 q^{52} + 12 q^{58} + 24 q^{61} - 4 q^{64} - 4 q^{67} - 18 q^{70} + 6 q^{76} + 20 q^{79} - 24 q^{85} - 6 q^{88} - 24 q^{91} - 12 q^{94} + 48 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * 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 - 26 * q^49 - 12 * q^52 + 12 * q^58 + 24 * q^61 - 4 * q^64 - 4 * q^67 - 18 * q^70 + 6 * q^76 + 20 * q^79 - 24 * q^85 - 6 * q^88 - 24 * q^91 - 12 * q^94 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		0			0
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$			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	$-0.183949\pi$
$11$	2.59808	+	1.50000i	0.783349	+	0.452267i	−0.0542666	+	0.998526i	$0.517282\pi$
$12$		0			0
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	−0.854554	−	0.519362i	$-0.826170\pi$
$13$	−3.00000	+	1.73205i	−0.832050	+	0.480384i	0.0225039	+	0.999747i	$0.492836\pi$
$14$	−0.866025	+	2.50000i	−0.231455	+	0.668153i
$15$		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	$-0.767924\pi$
$23$	−2.59808	+	1.50000i	−0.541736	+	0.312772i	0.204046	+	0.978961i	$0.434591\pi$
$24$		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	$-0.145253\pi$
$29$	5.19615	+	3.00000i	0.964901	+	0.557086i	0.0672232	+	0.997738i	$0.478586\pi$
$30$		0			0
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	−0.0381148	−	0.999273i	$-0.512135\pi$
$31$	4.50000	−	2.59808i	0.808224	−	0.466628i	0.846339	+	0.532645i	$0.178802\pi$
$32$	−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	−0.752202	−	0.658932i	$-0.771008\pi$
$41$	−6.06218	−	10.5000i	−0.946753	−	1.63982i	−0.194551	−	0.980892i	$-0.562325\pi$
$42$		0			0
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	−0.779647	−	0.626219i	$-0.784601\pi$
$43$	1.00000	−	1.73205i	0.152499	−	0.264135i	0.932145	+	0.362084i	$0.117935\pi$
$44$			3.00000i			0.452267i
$45$		0			0
$46$	−3.00000			−0.442326
$47$	−1.73205	+	3.00000i	−0.252646	+	0.437595i	−0.964253	−	0.264982i	$-0.914634\pi$
$47$	−1.73205	+	3.00000i	−0.252646	+	0.437595i	0.711608	+	0.702577i	$0.247967\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	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
$56$	−2.59808	+	0.500000i	−0.347183	+	0.0668153i
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	0.956467	−	0.291839i	$-0.0942671\pi$
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	−0.730974	+	0.682406i	$0.760934\pi$
$60$		0			0
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	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	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−3.46410	−	6.00000i	−0.420084	−	0.727607i
$69$		0			0
$70$	−4.50000	+	0.866025i	−0.537853	+	0.103510i
$71$			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
$77$	−2.59808	+	7.50000i	−0.296078	+	0.854704i
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	−1.73205			−0.193649
$81$		0			0
$82$		−	12.1244i		−	1.33891i
$83$	−8.66025	+	15.0000i	−0.950586	+	1.64646i	−0.206427	+	0.978462i	$0.566184\pi$
$83$	−8.66025	+	15.0000i	−0.950586	+	1.64646i	−0.744160	+	0.668002i	$0.767150\pi$
$84$		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	$-0.0849741\pi$
$97$	12.0000	+	6.92820i	1.21842	+	0.703452i	0.253837	+	0.967247i	$0.418307\pi$
$98$	−6.92820	−	1.00000i	−0.699854	−	0.101015i
$99$		0			0
$100$	2.00000			0.200000
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	16.5000	−	9.52628i	1.62579	−	0.938652i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	16.5000	−	9.52628i	1.62579	−	0.938652i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−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
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	10.3923	−	6.00000i	0.977626	−	0.564433i	0.0760733	−	0.997102i	$-0.475762\pi$
$113$	10.3923	−	6.00000i	0.977626	−	0.564433i	0.901553	+	0.432670i	$0.142428\pi$
$114$		0			0
$115$	−4.50000	−	2.59808i	−0.419627	−	0.242272i
$116$			6.00000i			0.557086i
$117$		0			0
$118$			3.46410i			0.318896i
$119$	−3.46410	−	18.0000i	−0.317554	−	1.65006i
$120$		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	0.544640	−	0.838670i	$-0.316666\pi$
$131$	−5.19615	−	9.00000i	−0.453990	−	0.786334i	−0.998630	+	0.0523366i	$0.983333\pi$
$132$		0			0
$133$	4.50000	−	0.866025i	0.390199	−	0.0750939i
$134$		−	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	$-0.0541268\pi$
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.346235	+	0.938148i	$0.387460\pi$
$138$		0			0
$139$	3.00000	−	1.73205i	0.254457	−	0.146911i	−0.367347	−	0.930084i	$-0.619734\pi$
$139$	3.00000	−	1.73205i	0.254457	−	0.146911i	0.621803	+	0.783174i	$0.286400\pi$
$140$	−4.33013	−	1.50000i	−0.365963	−	0.126773i
$141$		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	$-0.830232\pi$
$149$	−10.3923	+	6.00000i	−0.851371	+	0.491539i	0.00974235	+	0.999953i	$0.496899\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	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	$-0.530554\pi$
$157$	9.00000	−	5.19615i	0.718278	−	0.414698i	0.814119	+	0.580699i	$0.197221\pi$
$158$	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	0.968361	−	0.249554i	$-0.0802840\pi$
$167$	3.46410	+	6.00000i	0.268060	+	0.464294i	−0.700301	+	0.713848i	$0.746951\pi$
$168$		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	−0.750198	−	0.661213i	$-0.770042\pi$
$173$	2.59808	−	4.50000i	0.197528	−	0.342129i	0.947726	+	0.319084i	$0.103375\pi$
$174$		0			0
$175$	5.00000	+	1.73205i	0.377964	+	0.130931i
$176$	−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	$-0.172197\pi$
$182$	−1.73205	−	9.00000i	−0.128388	−	0.667124i
$183$		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	$-0.608014\pi$
$191$	−18.1865	−	10.5000i	−1.31593	−	0.759753i	−0.983071	+	0.183223i	$0.941347\pi$
$192$		0			0
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	6.92820	+	12.0000i	0.497416	+	0.861550i
$195$		0			0
$196$	−5.50000	−	4.33013i	−0.392857	−	0.309295i
$197$		−	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
$203$	−5.19615	+	15.0000i	−0.364698	+	1.05279i
$204$		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	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−8.00000	−	13.8564i	−0.550743	−	0.953914i	0.447478	−	0.894295i	$-0.352322\pi$
$212$	−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	$-0.508125\pi$
$223$	−13.5000	−	7.79423i	−0.904027	−	0.521940i	−0.878504	+	0.477734i	$0.841458\pi$
$224$	−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	−0.282153	−	0.959369i	$-0.591049\pi$
$227$	10.3923	−	18.0000i	0.689761	−	1.19470i	0.971915	−	0.235333i	$-0.0756180\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$	−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
$238$	6.00000	−	17.3205i	0.388922	−	1.12272i
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$		0			0
$241$	15.0000	+	8.66025i	0.966235	+	0.557856i	0.898086	−	0.439819i	$-0.144957\pi$
$241$	15.0000	+	8.66025i	0.966235	+	0.557856i	0.0681486	+	0.997675i	$0.478291\pi$
$242$		−	2.00000i		−	0.128565i
$243$		0			0
$244$			6.92820i			0.443533i
$245$	−9.52628	−	7.50000i	−0.608612	−	0.479157i
$246$		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	0.935609	−	0.353039i	$-0.114852\pi$
$257$	2.59808	+	4.50000i	0.162064	+	0.280702i	−0.773545	+	0.633741i	$0.781518\pi$
$258$		0			0
$259$	3.50000	+	18.1865i	0.217479	+	1.13006i
$260$		−	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	$-0.0202734\pi$
$263$	23.3827	+	13.5000i	1.44184	+	0.832446i	0.443866	+	0.896093i	$0.353607\pi$
$264$		0			0
$265$	−18.0000	+	10.3923i	−1.10573	+	0.638394i
$266$	4.33013	+	1.50000i	0.265497	+	0.0919709i
$267$		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	−0.982603	−	0.185720i	$-0.940538\pi$
$277$	−5.50000	+	9.52628i	−0.330463	+	0.572379i	0.652140	+	0.758099i	$0.273872\pi$
$278$	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	−0.998150	−	0.0608039i	$-0.980634\pi$
$281$	−25.9808	−	15.0000i	−1.54988	−	0.894825i	−0.551733	−	0.834021i	$-0.686033\pi$
$282$		0			0
$283$	−27.0000	+	15.5885i	−1.60498	+	0.926638i	−0.614514	+	0.788906i	$0.710648\pi$
$283$	−27.0000	+	15.5885i	−1.60498	+	0.926638i	−0.990470	+	0.137732i	$0.956019\pi$
$284$	−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	0.746918	−	0.664916i	$-0.231533\pi$
$293$	−3.46410	−	6.00000i	−0.202375	−	0.350524i	−0.949293	+	0.314392i	$0.898199\pi$
$294$		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
$301$	5.00000	+	1.73205i	0.288195	+	0.0998337i
$302$	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	$-0.146740\pi$
$308$	−7.79423	+	1.50000i	−0.444117	+	0.0854704i
$309$		0			0
$310$	4.50000	+	7.79423i	0.255583	+	0.442682i
$311$	−12.1244	−	21.0000i	−0.687509	−	1.19080i	−0.972641	−	0.232313i	$-0.925371\pi$
$311$	−12.1244	−	21.0000i	−0.687509	−	1.19080i	0.285132	−	0.958488i	$-0.407963\pi$
$312$		0			0
$313$	−15.0000	−	8.66025i	−0.847850	−	0.489506i	0.0120748	−	0.999927i	$-0.496156\pi$
$313$	−15.0000	−	8.66025i	−0.847850	−	0.489506i	−0.859925	+	0.510421i	$0.829490\pi$
$314$	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	$-0.502022\pi$
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.869184	+	0.494489i	$0.835355\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$		0			0
$322$	−1.50000	−	7.79423i	−0.0835917	−	0.434355i
$323$			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
$329$	−8.66025	−	3.00000i	−0.477455	−	0.165395i
$330$		0			0
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	0.168320	+	0.985732i	$0.446166\pi$
$331$	−14.0000	+	24.2487i	−0.769510	+	1.33283i	−0.937829	+	0.347097i	$0.887167\pi$
$332$	−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	0.926049	−	0.377403i	$-0.123183\pi$
$337$	2.50000	+	4.33013i	0.136184	+	0.235877i	−0.789865	+	0.613280i	$0.789850\pi$
$338$	−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	$-0.408637\pi$
$347$	23.3827	−	13.5000i	1.25525	−	0.724718i	0.972147	+	0.234372i	$0.0753034\pi$
$348$		0			0
$349$	24.0000	+	13.8564i	1.28469	+	0.741716i	0.977702	−	0.209997i	$-0.0673454\pi$
$349$	24.0000	+	13.8564i	1.28469	+	0.741716i	0.306988	+	0.951713i	$0.400679\pi$
$350$	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	0.492934	+	0.870067i	$0.335924\pi$
$353$	−9.52628	+	16.5000i	−0.507033	+	0.878206i	−0.999967	+	0.00813978i	$0.997409\pi$
$354$		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
$364$	3.00000	−	8.66025i	0.157243	−	0.453921i
$365$	−5.19615	+	3.00000i	−0.271979	+	0.157027i
$366$		0			0
$367$	−1.50000	−	0.866025i	−0.0782994	−	0.0452062i	0.460339	−	0.887743i	$-0.347728\pi$
$367$	−1.50000	−	0.866025i	−0.0782994	−	0.0452062i	−0.538639	+	0.842537i	$0.681061\pi$
$368$		−	3.00000i		−	0.156386i
$369$		0			0
$370$			12.1244i			0.630315i
$371$	−31.1769	+	6.00000i	−1.61862	+	0.311504i
$372$		0			0
$373$	−2.50000	−	4.33013i	−0.129445	−	0.224205i	0.794017	−	0.607896i	$-0.207986\pi$
$373$	−2.50000	−	4.33013i	−0.129445	−	0.224205i	−0.923462	+	0.383691i	$0.874653\pi$
$374$	−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	0.986949	−	0.161034i	$-0.0514830\pi$
$383$	6.92820	+	12.0000i	0.354015	+	0.613171i	−0.632934	+	0.774206i	$0.718150\pi$
$384$		0			0
$385$	−13.5000	+	2.59808i	−0.688024	+	0.132410i
$386$			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	$-0.125135\pi$
$389$	20.7846	+	12.0000i	1.05382	+	0.608424i	0.130105	+	0.991500i	$0.458469\pi$
$390$		0			0
$391$	18.0000	−	10.3923i	0.910299	−	0.525561i
$392$	−2.59808	−	6.50000i	−0.131223	−	0.328300i
$393$		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	$-0.815043\pi$
$401$	−15.5885	+	9.00000i	−0.778450	+	0.449439i	0.0574304	+	0.998350i	$0.481709\pi$
$402$		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	$-0.639372\pi$
$409$	3.00000	−	1.73205i	0.148340	−	0.0856444i	0.572333	+	0.820021i	$0.306038\pi$
$410$	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	0.938150	−	0.346228i	$-0.112538\pi$
$419$	3.46410	+	6.00000i	0.169232	+	0.293119i	−0.768918	+	0.639348i	$0.779204\pi$
$420$		0			0
$421$	6.50000	−	11.2583i	0.316791	−	0.548697i	−0.663026	−	0.748596i	$-0.730728\pi$
$421$	6.50000	−	11.2583i	0.316791	−	0.548697i	0.979817	+	0.199899i	$0.0640614\pi$
$422$		−	16.0000i		−	0.778868i
$423$		0			0
$424$	−12.0000			−0.582772
$425$	−6.92820	+	12.0000i	−0.336067	+	0.582086i
$426$		0			0
$427$	−6.00000	+	17.3205i	−0.290360	+	0.838198i
$428$		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	$-0.0803357\pi$
$434$	2.59808	+	13.5000i	0.124712	+	0.648021i
$435$		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	$-0.413106\pi$
$439$	−9.00000	−	5.19615i	−0.429547	−	0.247999i	−0.699153	+	0.714972i	$0.746440\pi$
$440$	−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	$-0.401918\pi$
$443$	−7.79423	−	4.50000i	−0.370315	−	0.213801i	−0.673596	+	0.739100i	$0.735251\pi$
$444$		0			0
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$	−7.79423	−	13.5000i	−0.369067	−	0.639244i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$			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
$455$	5.19615	−	15.0000i	0.243599	−	0.703211i
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$		0			0
$459$		0			0
$460$		−	5.19615i		−	0.242272i
$461$	9.52628	−	16.5000i	0.443683	−	0.768482i	−0.554276	−	0.832333i	$-0.687005\pi$
$461$	9.52628	−	16.5000i	0.443683	−	0.768482i	0.997959	+	0.0638511i	$0.0203383\pi$
$462$		0			0
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	−0.950854	−	0.309640i	$-0.899791\pi$
$463$	−16.0000	−	27.7128i	−0.743583	−	1.28792i	0.207271	−	0.978284i	$-0.433542\pi$
$464$	−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	0.353796	+	0.935323i	$0.384891\pi$
$479$	−13.8564	+	24.0000i	−0.633115	+	1.09659i	−0.986911	+	0.161265i	$0.948443\pi$
$480$		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
$490$	−4.50000	−	11.2583i	−0.203289	−	0.508600i
$491$	−7.79423	+	4.50000i	−0.351749	+	0.203082i	−0.665455	−	0.746438i	$-0.731763\pi$
$491$	−7.79423	+	4.50000i	−0.351749	+	0.203082i	0.313707	+	0.949520i	$0.398429\pi$
$492$		0			0
$493$	−36.0000	−	20.7846i	−1.62136	−	0.936092i
$494$			6.00000i			0.269953i
$495$		0			0
$496$			5.19615i			0.233314i
$497$	−7.79423	+	1.50000i	−0.349619	+	0.0672842i
$498$		0			0
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	0.732137	−	0.681157i	$-0.238523\pi$
$499$	−5.00000	−	8.66025i	−0.223831	−	0.387686i	−0.955968	+	0.293471i	$0.905190\pi$
$500$	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	0.977724	−	0.209895i	$-0.0673123\pi$
$509$	6.92820	+	12.0000i	0.307087	+	0.531891i	−0.670637	+	0.741786i	$0.733979\pi$
$510$		0			0
$511$	−9.00000	+	1.73205i	−0.398137	+	0.0766214i
$512$		−	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
$518$	−6.06218	+	17.5000i	−0.266357	+	0.768906i
$519$		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	−0.938779	−	0.344519i	$-0.888042\pi$
$547$	−4.00000	+	6.92820i	−0.171028	+	0.296229i	0.767752	+	0.640747i	$0.221375\pi$
$548$			18.0000i			0.768922i
$549$		0			0
$550$	6.00000			0.255841
$551$	5.19615	−	9.00000i	0.221364	−	0.383413i
$552$		0			0
$553$	25.0000	+	8.66025i	1.06311	+	0.368271i
$554$	−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
$560$	−0.866025	−	4.50000i	−0.0365963	−	0.190160i
$561$		0			0
$562$	−15.0000	−	25.9808i	−0.632737	−	1.09593i
$563$	5.19615	+	9.00000i	0.218992	+	0.379305i	0.954500	−	0.298211i	$-0.0963899\pi$
$563$	5.19615	+	9.00000i	0.218992	+	0.379305i	−0.735508	+	0.677516i	$0.763057\pi$
$564$		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	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	−5.19615	−	9.00000i	−0.217262	−	0.376309i
$573$		0			0
$574$	31.5000	−	6.06218i	1.31478	−	0.253030i
$575$			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
$581$	−43.3013	−	15.0000i	−1.79644	−	0.622305i
$582$		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	−0.0160815	−	0.999871i	$-0.505119\pi$
$587$	20.7846	−	36.0000i	0.857873	−	1.48588i	0.873954	−	0.486008i	$-0.161548\pi$
$588$		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	$-0.607806\pi$
$599$	7.79423	−	4.50000i	0.318464	−	0.183865i	0.650708	+	0.759328i	$0.274472\pi$
$600$		0			0
$601$	−9.00000	−	5.19615i	−0.367118	−	0.211955i	0.305081	−	0.952326i	$-0.401317\pi$
$601$	−9.00000	−	5.19615i	−0.367118	−	0.211955i	−0.672198	+	0.740371i	$0.734650\pi$
$602$	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	$-0.552335\pi$
$607$	15.0000	−	8.66025i	0.608831	−	0.351509i	0.772508	+	0.635005i	$0.219002\pi$
$608$	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
$616$	−7.50000	−	2.59808i	−0.302184	−	0.104679i
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	−0.779809	−	0.626017i	$-0.784684\pi$
$617$	−15.5885	+	9.00000i	−0.627568	+	0.362326i	0.152242	+	0.988343i	$0.451351\pi$
$618$		0			0
$619$	16.5000	+	9.52628i	0.663191	+	0.382893i	0.793492	−	0.608581i	$-0.208261\pi$
$619$	16.5000	+	9.52628i	0.663191	+	0.382893i	−0.130301	+	0.991475i	$0.541594\pi$
$620$			9.00000i			0.361449i
$621$		0			0
$622$		−	24.2487i		−	0.972285i
$623$	2.59808	+	13.5000i	0.104090	+	0.540866i
$624$		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
$637$	15.0000	−	19.0526i	0.594322	−	0.754890i
$638$			18.0000i			0.712627i
$639$		0			0
$640$		−	1.73205i		−	0.0684653i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	4.50000	−	2.59808i	0.177463	−	0.102458i	−0.408637	−	0.912697i	$-0.633996\pi$
$643$	4.50000	−	2.59808i	0.177463	−	0.102458i	0.586100	+	0.810239i	$0.300663\pi$
$644$	2.59808	−	7.50000i	0.102379	−	0.295541i
$645$		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	$-0.552101\pi$
$653$	15.5885	−	9.00000i	0.610023	−	0.352197i	0.772975	+	0.634437i	$0.218768\pi$
$654$		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	$-0.467463\pi$
$659$	−18.1865	−	10.5000i	−0.708447	−	0.409022i	−0.810486	+	0.585758i	$0.800797\pi$
$660$		0			0
$661$	33.0000	−	19.0526i	1.28355	−	0.741059i	0.306055	−	0.952014i	$-0.400991\pi$
$661$	33.0000	−	19.0526i	1.28355	−	0.741059i	0.977496	+	0.210955i	$0.0676574\pi$
$662$	−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	−0.698988	−	0.715134i	$-0.746366\pi$
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	0.968818	+	0.247774i	$0.0796991\pi$
$674$			5.00000i			0.192593i
$675$		0			0
$676$	−1.00000			−0.0384615
$677$	−12.9904	+	22.5000i	−0.499261	+	0.864745i	−1.00000		0.000853228i	$-0.999728\pi$
$677$	−12.9904	+	22.5000i	−0.499261	+	0.864745i	0.500739	+	0.865598i	$0.333062\pi$
$678$		0			0
$679$	−12.0000	+	34.6410i	−0.460518	+	1.32940i
$680$	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
$686$	−0.866025	−	18.5000i	−0.0330650	−	0.706333i
$687$		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	$-0.269996\pi$
$691$	9.00000	+	5.19615i	0.342376	+	0.197671i	−0.318946	+	0.947773i	$0.603329\pi$
$692$	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
$700$	1.00000	+	5.19615i	0.0377964	+	0.196396i
$701$			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	−0.875262	−	0.483650i	$-0.839311\pi$
$709$	−0.500000	+	0.866025i	−0.0187779	+	0.0325243i	0.856484	+	0.516174i	$0.172644\pi$
$710$	−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	−0.968201	−	0.250172i	$-0.919513\pi$
$727$	−45.0000	−	25.9808i	−1.66896	−	0.963573i	−0.700756	−	0.713401i	$-0.747154\pi$
$728$	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	$-0.605194\pi$
$733$	9.00000	−	5.19615i	0.332423	−	0.191924i	0.656916	+	0.753964i	$0.271861\pi$
$734$	−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
$742$	−30.0000	−	10.3923i	−1.10133	−	0.381514i
$743$	23.3827	−	13.5000i	0.857828	−	0.495267i	−0.00545664	−	0.999985i	$-0.501737\pi$
$743$	23.3827	−	13.5000i	0.857828	−	0.495267i	0.863284	+	0.504718i	$0.168404\pi$
$744$		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	0.883694	−	0.468065i	$-0.155049\pi$
$751$	1.00000	+	1.73205i	0.0364905	+	0.0632034i	−0.847203	+	0.531269i	$0.821715\pi$
$752$	−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	0.963842	−	0.266475i	$-0.0858589\pi$
$761$	6.92820	+	12.0000i	0.251147	+	0.435000i	−0.712695	+	0.701474i	$0.752526\pi$
$762$		0			0
$763$	6.50000	+	33.7750i	0.235316	+	1.22274i
$764$		−	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	$-0.907763\pi$
$769$	−33.0000	+	19.0526i	−1.19001	+	0.687053i	−0.231701	+	0.972787i	$0.574429\pi$
$770$	−12.9904	−	4.50000i	−0.468141	−	0.162169i
$771$		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	$-0.566771\pi$
$787$	15.0000	−	8.66025i	0.534692	−	0.308705i	0.742925	+	0.669375i	$0.233438\pi$
$788$	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	0.970408	−	0.241469i	$-0.0776293\pi$
$797$	7.79423	+	13.5000i	0.276086	+	0.478195i	−0.694323	+	0.719664i	$0.744296\pi$
$798$		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
$805$	4.50000	−	12.9904i	0.158604	−	0.457851i
$806$	−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	$0.779507\pi$
$812$	−15.5885	+	3.00000i	−0.547048	+	0.105279i
$813$		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	$-0.508709\pi$
$821$	−25.9808	−	15.0000i	−0.906735	−	0.523504i	−0.879379	+	0.476122i	$0.842042\pi$
$822$		0			0
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	9.52628	+	16.5000i	0.331864	+	0.574805i
$825$		0			0
$826$	−9.00000	+	1.73205i	−0.313150	+	0.0602658i
$827$			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
$833$	45.0333	−	18.0000i	1.56031	−	0.623663i
$834$		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	−0.995797	−	0.0915899i	$-0.970805\pi$
$839$	−12.1244	+	21.0000i	−0.418579	+	0.725001i	0.577218	+	0.816590i	$0.304138\pi$
$840$		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	$-0.257098\pi$
$853$	12.0000	+	6.92820i	0.410872	+	0.237217i	−0.280292	+	0.959915i	$0.590431\pi$
$854$	−13.8564	+	12.0000i	−0.474156	+	0.410632i
$855$		0			0
$856$		0			0
$857$	21.6506	−	37.5000i	0.739572	−	1.28098i	−0.213117	−	0.977027i	$-0.568361\pi$
$857$	21.6506	−	37.5000i	0.739572	−	1.28098i	0.952688	−	0.303949i	$-0.0983052\pi$
$858$		0			0
$859$	−25.5000	+	14.7224i	−0.870049	+	0.502323i	−0.867364	−	0.497674i	$-0.834188\pi$
$859$	−25.5000	+	14.7224i	−0.870049	+	0.502323i	−0.00268433	+	0.999996i	$0.500854\pi$
$860$	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
$868$	−4.50000	+	12.9904i	−0.152740	+	0.440922i
$869$	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
$875$	6.06218	+	31.5000i	0.204939	+	1.06489i
$876$		0			0
$877$	−25.0000	−	43.3013i	−0.844190	−	1.46218i	−0.886323	−	0.463068i	$-0.846749\pi$
$877$	−25.0000	−	43.3013i	−0.844190	−	1.46218i	0.0421327	−	0.999112i	$-0.486585\pi$
$878$	−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	0.587467	−	0.809248i	$-0.300125\pi$
$887$	−12.1244	−	21.0000i	−0.407096	−	0.705111i	−0.994563	+	0.104137i	$0.966792\pi$
$888$		0			0
$889$	−11.0000	−	57.1577i	−0.368928	−	1.91701i
$890$			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
$896$	0.866025	−	2.50000i	0.0289319	−	0.0835191i
$897$		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	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$	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	$-0.397034\pi$
$911$	−10.3923	−	6.00000i	−0.344312	−	0.198789i	−0.662177	+	0.749347i	$0.730367\pi$
$912$		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	−0.544052	−	0.839052i	$-0.683111\pi$
$929$	13.8564	−	24.0000i	0.454614	−	0.787414i	0.998666	+	0.0516371i	$0.0164439\pi$
$930$		0			0
$931$	4.50000	+	11.2583i	0.147482	+	0.368977i
$932$	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	$-0.0360996\pi$
$938$	5.19615	−	1.00000i	0.169660	−	0.0326512i
$939$		0			0
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−6.06218	−	10.5000i	−0.197621	−	0.342290i	0.750135	−	0.661284i	$-0.229988\pi$
$941$	−6.06218	−	10.5000i	−0.197621	−	0.342290i	−0.947757	+	0.318994i	$0.896655\pi$
$942$		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	$-0.411700\pi$
$947$	−12.9904	−	7.50000i	−0.422131	−	0.243717i	−0.695988	+	0.718053i	$0.745034\pi$
$948$		0			0
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$	−1.73205	−	3.00000i	−0.0561951	−	0.0973329i
$951$		0			0
$952$	18.0000	−	3.46410i	0.583383	−	0.112272i
$953$		−	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
$959$	−15.5885	+	45.0000i	−0.503378	+	1.45313i
$960$		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	0.965508	−	0.260375i	$-0.0838461\pi$
$967$	8.00000	+	13.8564i	0.257263	+	0.445592i	−0.708245	+	0.705967i	$0.750513\pi$
$968$	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	$-0.945329\pi$
$977$	−41.5692	+	24.0000i	−1.32992	+	0.767828i	−0.344631	+	0.938738i	$0.611996\pi$
$978$		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	−0.837081	−	0.547079i	$-0.815740\pi$
$983$	1.73205	−	3.00000i	0.0552438	−	0.0956851i	0.892325	+	0.451394i	$0.149073\pi$
$984$		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
$994$	−7.50000	−	2.59808i	−0.237886	−	0.0824060i
$995$	−2.59808	+	1.50000i	−0.0823646	+	0.0475532i
$996$		0			0
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		−	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.c.755.2		4
3.2	odd	2	inner	1134.2.m.c.755.1		4
7.6	odd	2		1134.2.m.b.755.2		4
9.2	odd	6		378.2.d.b.377.4	yes	4
9.4	even	3		1134.2.m.b.377.1		4
9.5	odd	6		1134.2.m.b.377.2		4
9.7	even	3		378.2.d.b.377.1	✓	4
21.20	even	2		1134.2.m.b.755.1		4
36.7	odd	6		3024.2.k.e.1889.2		4
36.11	even	6		3024.2.k.e.1889.4		4
63.13	odd	6	inner	1134.2.m.c.377.1		4
63.20	even	6		378.2.d.b.377.3	yes	4
63.34	odd	6		378.2.d.b.377.2	yes	4
63.41	even	6	inner	1134.2.m.c.377.2		4
252.83	odd	6		3024.2.k.e.1889.1		4
252.223	even	6		3024.2.k.e.1889.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.d.b.377.1	✓	4	9.7	even	3
378.2.d.b.377.2	yes	4	63.34	odd	6
378.2.d.b.377.3	yes	4	63.20	even	6
378.2.d.b.377.4	yes	4	9.2	odd	6
1134.2.m.b.377.1		4	9.4	even	3
1134.2.m.b.377.2		4	9.5	odd	6
1134.2.m.b.755.1		4	21.20	even	2
1134.2.m.b.755.2		4	7.6	odd	2
1134.2.m.c.377.1		4	63.13	odd	6	inner
1134.2.m.c.377.2		4	63.41	even	6	inner
1134.2.m.c.755.1		4	3.2	odd	2	inner
1134.2.m.c.755.2		4	1.1	even	1	trivial
3024.2.k.e.1889.1		4	252.83	odd	6
3024.2.k.e.1889.2		4	36.7	odd	6
3024.2.k.e.1889.3		4	252.223	even	6
3024.2.k.e.1889.4		4	36.11	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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +(0.500000 + 2.59808i) q^{7} +1.00000i q^{8} +1.73205i q^{10} +(2.59808 + 1.50000i) q^{11} +(-3.00000 + 1.73205i) q^{13} +(-0.866025 + 2.50000i) q^{14} +(-0.500000 + 0.866025i) q^{16} -6.92820 q^{17} -1.73205i q^{19} +(-0.866025 + 1.50000i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-2.59808 + 1.50000i) q^{23} +(1.00000 - 1.73205i) q^{25} -3.46410 q^{26} +(-2.00000 + 1.73205i) q^{28} +(5.19615 + 3.00000i) q^{29} +(4.50000 - 2.59808i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(-3.46410 + 3.00000i) q^{35} +7.00000 q^{37} +(0.866025 - 1.50000i) q^{38} +(-1.50000 + 0.866025i) q^{40} +(-6.06218 - 10.5000i) q^{41} +(1.00000 - 1.73205i) q^{43} +3.00000i q^{44} -3.00000 q^{46} +(-1.73205 + 3.00000i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(1.73205 - 1.00000i) q^{50} +(-3.00000 - 1.73205i) q^{52} +12.0000i q^{53} +5.19615i q^{55} +(-2.59808 + 0.500000i) q^{56} +(3.00000 + 5.19615i) q^{58} +(1.73205 + 3.00000i) q^{59} +(6.00000 + 3.46410i) q^{61} +5.19615 q^{62} -1.00000 q^{64} +(-5.19615 - 3.00000i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-3.46410 - 6.00000i) q^{68} +(-4.50000 + 0.866025i) q^{70} +3.00000i q^{71} +3.46410i q^{73} +(6.06218 + 3.50000i) q^{74} +(1.50000 - 0.866025i) q^{76} +(-2.59808 + 7.50000i) q^{77} +(5.00000 - 8.66025i) q^{79} -1.73205 q^{80} -12.1244i q^{82} +(-8.66025 + 15.0000i) q^{83} +(-6.00000 - 10.3923i) q^{85} +(1.73205 - 1.00000i) q^{86} +(-1.50000 + 2.59808i) q^{88} +5.19615 q^{89} +(-6.00000 - 6.92820i) q^{91} +(-2.59808 - 1.50000i) q^{92} +(-3.00000 + 1.73205i) q^{94} +(2.59808 - 1.50000i) q^{95} +(12.0000 + 6.92820i) q^{97} +(-6.92820 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^7	\( 4 q + 2 q^{4} + 2 q^{7} - 12 q^{13} - 2 q^{16} + 6 q^{22} + 4 q^{25} - 8 q^{28} + 18 q^{31} - 24 q^{34} + 28 q^{37} - 6 q^{40} + 4 q^{43} - 12 q^{46} - 26 q^{49} - 12 q^{52} + 12 q^{58} + 24 q^{61} - 4 q^{64} - 4 q^{67} - 18 q^{70} + 6 q^{76} + 20 q^{79} - 24 q^{85} - 6 q^{88} - 24 q^{91} - 12 q^{94} + 48 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * 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 - 26 * q^49 - 12 * q^52 + 12 * q^58 + 24 * q^61 - 4 * q^64 - 4 * q^67 - 18 * 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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