LMFDB - Embedded newform 918.2.o.b.829.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [918,2,Mod(361,918)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(918, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("918.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 918 = 2 \cdot 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	918.o (of order $12$, degree $4$, 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:	$7.33026690555$
Analytic rank:	$0$
Dimension:	$4$
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 306)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			829.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	918.829
Dual form			918.2.o.b.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.732051 + 2.73205i) q^{5} +(-0.267949 - 1.00000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.732051 + 2.73205i) q^{5} +(-0.267949 - 1.00000i) q^{7} -1.00000i q^{8} +(2.00000 - 2.00000i) q^{10} +(-0.598076 - 2.23205i) q^{11} +(-1.73205 - 3.00000i) q^{13} +(-0.267949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 - 2.96410i) q^{17} -1.00000i q^{19} +(-2.73205 + 0.732051i) q^{20} +(-0.598076 + 2.23205i) q^{22} +(1.73205 + 0.464102i) q^{23} +(-2.59808 - 1.50000i) q^{25} +3.46410i q^{26} +(0.732051 - 0.732051i) q^{28} +(8.46410 - 2.26795i) q^{29} +(0.866025 - 0.500000i) q^{32} +(-3.96410 + 1.13397i) q^{34} +2.92820 q^{35} +(3.46410 + 3.46410i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(2.73205 + 0.732051i) q^{40} +(9.96410 + 2.66987i) q^{41} +(4.50000 + 2.59808i) q^{43} +(1.63397 - 1.63397i) q^{44} +(-1.26795 - 1.26795i) q^{46} +(-5.00000 + 8.66025i) q^{47} +(5.13397 - 2.96410i) q^{49} +(1.50000 + 2.59808i) q^{50} +(1.73205 - 3.00000i) q^{52} +2.53590i q^{53} +6.53590 q^{55} +(-1.00000 + 0.267949i) q^{56} +(-8.46410 - 2.26795i) q^{58} +(1.50000 - 0.866025i) q^{59} +(-2.73205 - 10.1962i) q^{61} -1.00000 q^{64} +(9.46410 - 2.53590i) q^{65} +(2.33013 + 4.03590i) q^{67} +(4.00000 + 1.00000i) q^{68} +(-2.53590 - 1.46410i) q^{70} +(-5.46410 - 5.46410i) q^{71} +(3.90192 + 3.90192i) q^{73} +(-1.26795 - 4.73205i) q^{74} +(0.866025 - 0.500000i) q^{76} +(-2.07180 + 1.19615i) q^{77} +(-3.26795 - 12.1962i) q^{79} +(-2.00000 - 2.00000i) q^{80} +(-7.29423 - 7.29423i) q^{82} +(3.92820 + 2.26795i) q^{83} +(6.00000 + 10.0000i) q^{85} +(-2.59808 - 4.50000i) q^{86} +(-2.23205 + 0.598076i) q^{88} -6.92820 q^{89} +(-2.53590 + 2.53590i) q^{91} +(0.464102 + 1.73205i) q^{92} +(8.66025 - 5.00000i) q^{94} +(2.73205 + 0.732051i) q^{95} +(2.50000 - 0.669873i) q^{97} -5.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 - 8 * q^7	$ 4 q + 2 q^{4} + 4 q^{5} - 8 q^{7} + 8 q^{10} + 8 q^{11} - 8 q^{14} - 2 q^{16} + 8 q^{17} - 4 q^{20} + 8 q^{22} - 4 q^{28} + 20 q^{29} - 2 q^{34} - 16 q^{35} - 2 q^{38} + 4 q^{40} + 26 q^{41} + 18 q^{43} + 10 q^{44} - 12 q^{46} - 20 q^{47} + 24 q^{49} + 6 q^{50} + 40 q^{55} - 4 q^{56} - 20 q^{58} + 6 q^{59} - 4 q^{61} - 4 q^{64} + 24 q^{65} - 8 q^{67} + 16 q^{68} - 24 q^{70} - 8 q^{71} + 26 q^{73} - 12 q^{74} - 36 q^{77} - 20 q^{79} - 8 q^{80} + 2 q^{82} - 12 q^{83} + 24 q^{85} - 2 q^{88} - 24 q^{91} - 12 q^{92} + 4 q^{95} + 10 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 - 8 * q^7 + 8 * q^10 + 8 * q^11 - 8 * q^14 - 2 * q^16 + 8 * q^17 - 4 * q^20 + 8 * q^22 - 4 * q^28 + 20 * q^29 - 2 * q^34 - 16 * q^35 - 2 * q^38 + 4 * q^40 + 26 * q^41 + 18 * q^43 + 10 * q^44 - 12 * q^46 - 20 * q^47 + 24 * q^49 + 6 * q^50 + 40 * q^55 - 4 * q^56 - 20 * q^58 + 6 * q^59 - 4 * q^61 - 4 * q^64 + 24 * q^65 - 8 * q^67 + 16 * q^68 - 24 * q^70 - 8 * q^71 + 26 * q^73 - 12 * q^74 - 36 * q^77 - 20 * q^79 - 8 * q^80 + 2 * q^82 - 12 * q^83 + 24 * q^85 - 2 * q^88 - 24 * q^91 - 12 * q^92 + 4 * q^95 + 10 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/918\mathbb{Z}\right)^\times$.

$n$	$137$	$649$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

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
$5$	−0.732051	+	2.73205i	−0.327383	+	1.22181i	0.584511	+	0.811386i	$0.301286\pi$
$5$	−0.732051	+	2.73205i	−0.327383	+	1.22181i	−0.911894	+	0.410425i	$0.865380\pi$
$6$		0			0
$7$	−0.267949	−	1.00000i	−0.101275	−	0.377964i	0.896621	−	0.442799i	$-0.146015\pi$
$7$	−0.267949	−	1.00000i	−0.101275	−	0.377964i	−0.997896	+	0.0648349i	$0.979348\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$	−0.598076	−	2.23205i	−0.180327	−	0.672989i	−0.995583	−	0.0938879i	$-0.970070\pi$
$11$	−0.598076	−	2.23205i	−0.180327	−	0.672989i	0.815256	−	0.579101i	$-0.196596\pi$
$12$		0			0
$13$	−1.73205	−	3.00000i	−0.480384	−	0.832050i	0.519362	−	0.854554i	$-0.326170\pi$
$13$	−1.73205	−	3.00000i	−0.480384	−	0.832050i	−0.999747	+	0.0225039i	$0.992836\pi$
$14$	−0.267949	+	1.00000i	−0.0716124	+	0.267261i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.86603	−	2.96410i	0.695113	−	0.718900i
$17$	2.86603	−	2.96410i	0.695113	−	0.718900i
$18$		0			0
$19$		−	1.00000i		−	0.229416i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$		−	1.00000i		−	0.229416i	0.993399	−	0.114708i	$-0.0365932\pi$
$20$	−2.73205	+	0.732051i	−0.610905	+	0.163692i
$21$		0			0
$22$	−0.598076	+	2.23205i	−0.127510	+	0.475875i
$23$	1.73205	+	0.464102i	0.361158	+	0.0967719i	0.434835	−	0.900510i	$-0.356807\pi$
$23$	1.73205	+	0.464102i	0.361158	+	0.0967719i	−0.0736772	+	0.997282i	$0.523473\pi$
$24$		0			0
$25$	−2.59808	−	1.50000i	−0.519615	−	0.300000i
$26$			3.46410i			0.679366i
$27$		0			0
$28$	0.732051	−	0.732051i	0.138345	−	0.138345i
$29$	8.46410	−	2.26795i	1.57174	−	0.421148i	0.635386	−	0.772194i	$-0.280841\pi$
$29$	8.46410	−	2.26795i	1.57174	−	0.421148i	0.936358	+	0.351047i	$0.114174\pi$
$30$		0			0
$31$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$31$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−3.96410	+	1.13397i	−0.679838	+	0.194475i
$35$	2.92820			0.494957
$36$		0			0
$37$	3.46410	+	3.46410i	0.569495	+	0.569495i	0.931987	−	0.362492i	$-0.118074\pi$
$37$	3.46410	+	3.46410i	0.569495	+	0.569495i	−0.362492	+	0.931987i	$0.618074\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$		0			0
$40$	2.73205	+	0.732051i	0.431975	+	0.115747i
$41$	9.96410	+	2.66987i	1.55613	+	0.416964i	0.931436	−	0.363905i	$-0.118557\pi$
$41$	9.96410	+	2.66987i	1.55613	+	0.416964i	0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$	4.50000	+	2.59808i	0.686244	+	0.396203i	0.802203	−	0.597051i	$-0.203661\pi$
$43$	4.50000	+	2.59808i	0.686244	+	0.396203i	−0.115960	+	0.993254i	$0.536994\pi$
$44$	1.63397	−	1.63397i	0.246331	−	0.246331i
$45$		0			0
$46$	−1.26795	−	1.26795i	−0.186949	−	0.186949i
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	0.227844	+	0.973698i	$0.426832\pi$
$47$	−5.00000	+	8.66025i	−0.729325	+	1.26323i	−0.957169	+	0.289530i	$0.906501\pi$
$48$		0			0
$49$	5.13397	−	2.96410i	0.733425	−	0.423443i
$50$	1.50000	+	2.59808i	0.212132	+	0.367423i
$51$		0			0
$52$	1.73205	−	3.00000i	0.240192	−	0.416025i
$53$			2.53590i			0.348332i	0.984716	+	0.174166i	$0.0557230\pi$
$53$			2.53590i			0.348332i	−0.984716	+	0.174166i	$0.944277\pi$
$54$		0			0
$55$	6.53590			0.881300
$56$	−1.00000	+	0.267949i	−0.133631	+	0.0358062i
$57$		0			0
$58$	−8.46410	−	2.26795i	−1.11139	−	0.297796i
$59$	1.50000	−	0.866025i	0.195283	−	0.112747i	−0.399170	−	0.916877i	$-0.630702\pi$
$59$	1.50000	−	0.866025i	0.195283	−	0.112747i	0.594454	+	0.804130i	$0.297368\pi$
$60$		0			0
$61$	−2.73205	−	10.1962i	−0.349803	−	1.30548i	−0.886899	−	0.461963i	$-0.847145\pi$
$61$	−2.73205	−	10.1962i	−0.349803	−	1.30548i	0.537096	−	0.843521i	$-0.319521\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	9.46410	−	2.53590i	1.17388	−	0.314539i
$66$		0			0
$67$	2.33013	+	4.03590i	0.284670	+	0.493063i	0.972529	−	0.232781i	$-0.0747825\pi$
$67$	2.33013	+	4.03590i	0.284670	+	0.493063i	−0.687859	+	0.725844i	$0.741449\pi$
$68$	4.00000	+	1.00000i	0.485071	+	0.121268i
$69$		0			0
$70$	−2.53590	−	1.46410i	−0.303098	−	0.174994i
$71$	−5.46410	−	5.46410i	−0.648470	−	0.648470i	0.304153	−	0.952623i	$-0.401626\pi$
$71$	−5.46410	−	5.46410i	−0.648470	−	0.648470i	−0.952623	+	0.304153i	$0.901626\pi$
$72$		0			0
$73$	3.90192	+	3.90192i	0.456686	+	0.456686i	0.897566	−	0.440880i	$-0.145334\pi$
$73$	3.90192	+	3.90192i	0.456686	+	0.456686i	−0.440880	+	0.897566i	$0.645334\pi$
$74$	−1.26795	−	4.73205i	−0.147396	−	0.550090i
$75$		0			0
$76$	0.866025	−	0.500000i	0.0993399	−	0.0573539i
$77$	−2.07180	+	1.19615i	−0.236103	+	0.136314i
$78$		0			0
$79$	−3.26795	−	12.1962i	−0.367673	−	1.37217i	−0.863761	−	0.503902i	$-0.831897\pi$
$79$	−3.26795	−	12.1962i	−0.367673	−	1.37217i	0.496088	−	0.868272i	$-0.334769\pi$
$80$	−2.00000	−	2.00000i	−0.223607	−	0.223607i
$81$		0			0
$82$	−7.29423	−	7.29423i	−0.805513	−	0.805513i
$83$	3.92820	+	2.26795i	0.431176	+	0.248940i	0.699848	−	0.714292i	$-0.253251\pi$
$83$	3.92820	+	2.26795i	0.431176	+	0.248940i	−0.268671	+	0.963232i	$0.586585\pi$
$84$		0			0
$85$	6.00000	+	10.0000i	0.650791	+	1.08465i
$86$	−2.59808	−	4.50000i	−0.280158	−	0.485247i
$87$		0			0
$88$	−2.23205	+	0.598076i	−0.237937	+	0.0637551i
$89$	−6.92820			−0.734388			−0.367194	−	0.930144i	$-0.619682\pi$
$89$	−6.92820			−0.734388			−0.367194	+	0.930144i	$0.619682\pi$
$90$		0			0
$91$	−2.53590	+	2.53590i	−0.265834	+	0.265834i
$92$	0.464102	+	1.73205i	0.0483859	+	0.180579i
$93$		0			0
$94$	8.66025	−	5.00000i	0.893237	−	0.515711i
$95$	2.73205	+	0.732051i	0.280302	+	0.0751068i
$96$		0			0
$97$	2.50000	−	0.669873i	0.253837	−	0.0680153i	−0.129657	−	0.991559i	$-0.541388\pi$
$97$	2.50000	−	0.669873i	0.253837	−	0.0680153i	0.383493	+	0.923544i	$0.374721\pi$
$98$	−5.92820			−0.598839
$99$		0			0
$100$		−	3.00000i		−	0.300000i
$101$	8.73205	−	15.1244i	0.868872	−	1.50493i	0.00572059	−	0.999984i	$-0.498179\pi$
$101$	8.73205	−	15.1244i	0.868872	−	1.50493i	0.863151	−	0.504946i	$-0.168488\pi$
$102$		0			0
$103$	−3.73205	−	6.46410i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$103$	−3.73205	−	6.46410i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$104$	−3.00000	+	1.73205i	−0.294174	+	0.169842i
$105$		0			0
$106$	1.26795	−	2.19615i	0.123154	−	0.213309i
$107$	−13.2942	−	13.2942i	−1.28520	−	1.28520i	−0.937667	−	0.347534i	$-0.887019\pi$
$107$	−13.2942	−	13.2942i	−1.28520	−	1.28520i	−0.347534	−	0.937667i	$-0.612981\pi$
$108$		0			0
$109$	−4.92820	+	4.92820i	−0.472036	+	0.472036i	−0.902573	−	0.430537i	$-0.858324\pi$
$109$	−4.92820	+	4.92820i	−0.472036	+	0.472036i	0.430537	+	0.902573i	$0.358324\pi$
$110$	−5.66025	−	3.26795i	−0.539684	−	0.311587i
$111$		0			0
$112$	1.00000	+	0.267949i	0.0944911	+	0.0253188i
$113$	6.09808	+	1.63397i	0.573659	+	0.153711i	0.533974	−	0.845501i	$-0.320698\pi$
$113$	6.09808	+	1.63397i	0.573659	+	0.153711i	0.0396847	+	0.999212i	$0.487365\pi$
$114$		0			0
$115$	−2.53590	+	4.39230i	−0.236474	+	0.409585i
$116$	6.19615	+	6.19615i	0.575298	+	0.575298i
$117$		0			0
$118$	−1.73205			−0.159448
$119$	−3.73205	−	2.07180i	−0.342117	−	0.189921i
$120$		0			0
$121$	4.90192	−	2.83013i	0.445629	−	0.257284i
$122$	−2.73205	+	10.1962i	−0.247348	+	0.923116i
$123$		0			0
$124$		0			0
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$		0			0
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−9.46410	−	2.53590i	−0.830057	−	0.222413i
$131$	−4.63397	+	17.2942i	−0.404872	+	1.51100i	0.399419	+	0.916768i	$0.369212\pi$
$131$	−4.63397	+	17.2942i	−0.404872	+	1.51100i	−0.804291	+	0.594235i	$0.797455\pi$
$132$		0			0
$133$	−1.00000	+	0.267949i	−0.0867110	+	0.0232341i
$134$		−	4.66025i		−	0.402585i
$135$		0			0
$136$	−2.96410	−	2.86603i	−0.254170	−	0.245760i
$137$	10.9641	−	18.9904i	0.936726	−	1.62246i	0.165200	−	0.986260i	$-0.447173\pi$
$137$	10.9641	−	18.9904i	0.936726	−	1.62246i	0.771526	−	0.636198i	$-0.219494\pi$
$138$		0			0
$139$	5.69615	−	21.2583i	0.483141	−	1.80311i	−0.105147	−	0.994457i	$-0.533531\pi$
$139$	5.69615	−	21.2583i	0.483141	−	1.80311i	0.588288	−	0.808651i	$-0.299802\pi$
$140$	1.46410	+	2.53590i	0.123739	+	0.214323i
$141$		0			0
$142$	2.00000	+	7.46410i	0.167836	+	0.626373i
$143$	−5.66025	+	5.66025i	−0.473334	+	0.473334i
$144$		0			0
$145$			24.7846i			2.05825i
$146$	−1.42820	−	5.33013i	−0.118199	−	0.441124i
$147$		0			0
$148$	−1.26795	+	4.73205i	−0.104225	+	0.388972i
$149$	−5.73205	−	9.92820i	−0.469588	−	0.813350i	0.529808	−	0.848118i	$-0.322264\pi$
$149$	−5.73205	−	9.92820i	−0.469588	−	0.813350i	−0.999395	+	0.0347678i	$0.988931\pi$
$150$		0			0
$151$	18.1244	+	10.4641i	1.47494	+	0.851557i	0.999601	−	0.0282467i	$-0.00899239\pi$
$151$	18.1244	+	10.4641i	1.47494	+	0.851557i	0.475338	+	0.879803i	$0.342326\pi$
$152$	−1.00000			−0.0811107
$153$		0			0
$154$	2.39230			0.192777
$155$		0			0
$156$		0			0
$157$	10.1962	+	17.6603i	0.813742	+	1.40944i	0.910228	+	0.414107i	$0.135906\pi$
$157$	10.1962	+	17.6603i	0.813742	+	1.40944i	−0.0964865	+	0.995334i	$0.530760\pi$
$158$	−3.26795	+	12.1962i	−0.259984	+	0.970274i
$159$		0			0
$160$	0.732051	+	2.73205i	0.0578737	+	0.215988i
$161$		−	1.85641i		−	0.146305i
$162$		0			0
$163$	−4.26795	+	4.26795i	−0.334292	+	0.334292i	−0.854214	−	0.519922i	$-0.825961\pi$
$163$	−4.26795	+	4.26795i	−0.334292	+	0.334292i	0.519922	+	0.854214i	$0.325961\pi$
$164$	2.66987	+	9.96410i	0.208482	+	0.778066i
$165$		0			0
$166$	−2.26795	−	3.92820i	−0.176027	−	0.304888i
$167$	6.19615	−	23.1244i	0.479473	−	1.78942i	−0.124283	−	0.992247i	$-0.539663\pi$
$167$	6.19615	−	23.1244i	0.479473	−	1.78942i	0.603756	−	0.797170i	$-0.293670\pi$
$168$		0			0
$169$	0.500000	−	0.866025i	0.0384615	−	0.0666173i
$170$	−0.196152	−	11.6603i	−0.0150442	−	0.894301i
$171$		0			0
$172$			5.19615i			0.396203i
$173$	−3.73205	+	1.00000i	−0.283743	+	0.0760286i	−0.397883	−	0.917436i	$-0.630255\pi$
$173$	−3.73205	+	1.00000i	−0.283743	+	0.0760286i	0.114141	+	0.993465i	$0.463588\pi$
$174$		0			0
$175$	−0.803848	+	3.00000i	−0.0607652	+	0.226779i
$176$	2.23205	+	0.598076i	0.168247	+	0.0450817i
$177$		0			0
$178$	6.00000	+	3.46410i	0.449719	+	0.259645i
$179$			9.07180i			0.678058i	0.940776	+	0.339029i	$0.110098\pi$
$179$			9.07180i			0.678058i	−0.940776	+	0.339029i	$0.889902\pi$
$180$		0			0
$181$	−11.2679	+	11.2679i	−0.837540	+	0.837540i	−0.988535	−	0.150995i	$-0.951752\pi$
$181$	−11.2679	+	11.2679i	−0.837540	+	0.837540i	0.150995	+	0.988535i	$0.451752\pi$
$182$	3.46410	−	0.928203i	0.256776	−	0.0688030i
$183$		0			0
$184$	0.464102	−	1.73205i	0.0342140	−	0.127688i
$185$	−12.0000	+	6.92820i	−0.882258	+	0.509372i
$186$		0			0
$187$	−8.33013	−	4.62436i	−0.609159	−	0.338166i
$188$	−10.0000			−0.729325
$189$		0			0
$190$	−2.00000	−	2.00000i	−0.145095	−	0.145095i
$191$	−3.92820	+	6.80385i	−0.284235	+	0.492309i	−0.972423	−	0.233223i	$-0.925073\pi$
$191$	−3.92820	+	6.80385i	−0.284235	+	0.492309i	0.688189	+	0.725532i	$0.258406\pi$
$192$		0			0
$193$	−5.59808	−	1.50000i	−0.402958	−	0.107972i	0.0516469	−	0.998665i	$-0.483553\pi$
$193$	−5.59808	−	1.50000i	−0.402958	−	0.107972i	−0.454605	+	0.890693i	$0.650220\pi$
$194$	−2.50000	−	0.669873i	−0.179490	−	0.0480941i
$195$		0			0
$196$	5.13397	+	2.96410i	0.366712	+	0.211722i
$197$	−9.46410	+	9.46410i	−0.674289	+	0.674289i	−0.958702	−	0.284413i	$-0.908201\pi$
$197$	−9.46410	+	9.46410i	−0.674289	+	0.674289i	0.284413	+	0.958702i	$0.408201\pi$
$198$		0			0
$199$	−3.66025	−	3.66025i	−0.259469	−	0.259469i	0.565369	−	0.824838i	$-0.308734\pi$
$199$	−3.66025	−	3.66025i	−0.259469	−	0.259469i	−0.824838	+	0.565369i	$0.808734\pi$
$200$	−1.50000	+	2.59808i	−0.106066	+	0.183712i
$201$		0			0
$202$	−15.1244	+	8.73205i	−1.06415	+	0.614385i
$203$	−4.53590	−	7.85641i	−0.318358	−	0.551412i
$204$		0			0
$205$	−14.5885	+	25.2679i	−1.01890	+	1.76479i
$206$			7.46410i			0.520049i
$207$		0			0
$208$	3.46410			0.240192
$209$	−2.23205	+	0.598076i	−0.154394	+	0.0413698i
$210$		0			0
$211$	15.2942	+	4.09808i	1.05290	+	0.282123i	0.743449	−	0.668793i	$-0.233189\pi$
$211$	15.2942	+	4.09808i	1.05290	+	0.282123i	0.309449	+	0.950916i	$0.399855\pi$
$212$	−2.19615	+	1.26795i	−0.150832	+	0.0870831i
$213$		0			0
$214$	4.86603	+	18.1603i	0.332635	+	1.24141i
$215$	−10.3923	+	10.3923i	−0.708749	+	0.708749i
$216$		0			0
$217$		0			0
$218$	6.73205	−	1.80385i	0.455952	−	0.122172i
$219$		0			0
$220$	3.26795	+	5.66025i	0.220325	+	0.381614i
$221$	−13.8564	−	3.46410i	−0.932083	−	0.233021i
$222$		0			0
$223$	−2.07180	−	1.19615i	−0.138738	−	0.0801003i	0.429025	−	0.903293i	$-0.358857\pi$
$223$	−2.07180	−	1.19615i	−0.138738	−	0.0801003i	−0.567762	+	0.823193i	$0.692191\pi$
$224$	−0.732051	−	0.732051i	−0.0489122	−	0.0489122i
$225$		0			0
$226$	−4.46410	−	4.46410i	−0.296948	−	0.296948i
$227$	−1.69615	−	6.33013i	−0.112578	−	0.420145i	0.886517	−	0.462697i	$-0.153118\pi$
$227$	−1.69615	−	6.33013i	−0.112578	−	0.420145i	−0.999094	+	0.0425513i	$0.986451\pi$
$228$		0			0
$229$	−11.5359	+	6.66025i	−0.762314	+	0.440122i	−0.830126	−	0.557576i	$-0.811731\pi$
$229$	−11.5359	+	6.66025i	−0.762314	+	0.440122i	0.0678122	+	0.997698i	$0.478398\pi$
$230$	4.39230	−	2.53590i	0.289620	−	0.167212i
$231$		0			0
$232$	−2.26795	−	8.46410i	−0.148898	−	0.555695i
$233$	9.75833	+	9.75833i	0.639289	+	0.639289i	0.950380	−	0.311091i	$-0.100694\pi$
$233$	9.75833	+	9.75833i	0.639289	+	0.639289i	−0.311091	+	0.950380i	$0.600694\pi$
$234$		0			0
$235$	−20.0000	−	20.0000i	−1.30466	−	1.30466i
$236$	1.50000	+	0.866025i	0.0976417	+	0.0563735i
$237$		0			0
$238$	2.19615	+	3.66025i	0.142355	+	0.237259i
$239$	8.46410	+	14.6603i	0.547497	+	0.948293i	0.998445	+	0.0557428i	$0.0177527\pi$
$239$	8.46410	+	14.6603i	0.547497	+	0.948293i	−0.450948	+	0.892550i	$0.648914\pi$
$240$		0			0
$241$	11.5981	−	3.10770i	0.747098	−	0.200184i	0.134867	−	0.990864i	$-0.456939\pi$
$241$	11.5981	−	3.10770i	0.747098	−	0.200184i	0.612230	+	0.790679i	$0.290272\pi$
$242$	−5.66025			−0.363855
$243$		0			0
$244$	7.46410	−	7.46410i	0.477840	−	0.477840i
$245$	4.33975	+	16.1962i	0.277256	+	1.03473i
$246$		0			0
$247$	−3.00000	+	1.73205i	−0.190885	+	0.110208i
$248$		0			0
$249$		0			0
$250$	5.46410	−	1.46410i	0.345580	−	0.0925979i
$251$	6.80385			0.429455			0.214728	−	0.976674i	$-0.431114\pi$
$251$	6.80385			0.429455			0.214728	+	0.976674i	$0.431114\pi$
$252$		0			0
$253$		−	4.14359i		−	0.260505i
$254$	−1.00000	+	1.73205i	−0.0627456	+	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.0359	+	5.79423i	−0.626022	+	0.361434i	−0.779210	−	0.626763i	$-0.784379\pi$
$257$	−10.0359	+	5.79423i	−0.626022	+	0.361434i	0.153188	+	0.988197i	$0.451046\pi$
$258$		0			0
$259$	2.53590	−	4.39230i	0.157573	−	0.272925i
$260$	6.92820	+	6.92820i	0.429669	+	0.429669i
$261$		0			0
$262$	12.6603	−	12.6603i	0.782153	−	0.782153i
$263$	−26.6603	−	15.3923i	−1.64394	−	0.949130i	−0.979413	−	0.201868i	$-0.935299\pi$
$263$	−26.6603	−	15.3923i	−1.64394	−	0.949130i	−0.664529	−	0.747263i	$-0.731368\pi$
$264$		0			0
$265$	−6.92820	−	1.85641i	−0.425596	−	0.114038i
$266$	1.00000	+	0.267949i	0.0613139	+	0.0164290i
$267$		0			0
$268$	−2.33013	+	4.03590i	−0.142335	+	0.246532i
$269$	−1.46410	−	1.46410i	−0.0892679	−	0.0892679i	0.661063	−	0.750331i	$-0.270106\pi$
$269$	−1.46410	−	1.46410i	−0.0892679	−	0.0892679i	−0.750331	+	0.661063i	$0.770106\pi$
$270$		0			0
$271$	17.4641			1.06087			0.530434	−	0.847726i	$-0.322029\pi$
$271$	17.4641			1.06087			0.530434	+	0.847726i	$0.322029\pi$
$272$	1.13397	+	3.96410i	0.0687573	+	0.240359i
$273$		0			0
$274$	−18.9904	+	10.9641i	−1.14725	+	0.662366i
$275$	−1.79423	+	6.69615i	−0.108196	+	0.403793i
$276$		0			0
$277$	−28.3205	+	7.58846i	−1.70161	+	0.455946i	−0.973345	−	0.229345i	$-0.926342\pi$
$277$	−28.3205	+	7.58846i	−1.70161	+	0.455946i	−0.728269	+	0.685291i	$0.759675\pi$
$278$	−15.5622	+	15.5622i	−0.933357	+	0.933357i
$279$		0			0
$280$		−	2.92820i		−	0.174994i
$281$	4.26795	+	2.46410i	0.254605	+	0.146996i	0.621871	−	0.783120i	$-0.286373\pi$
$281$	4.26795	+	2.46410i	0.254605	+	0.146996i	−0.367266	+	0.930116i	$0.619706\pi$
$282$		0			0
$283$	−28.7583	−	7.70577i	−1.70951	−	0.458061i	−0.734202	−	0.678931i	$-0.762444\pi$
$283$	−28.7583	−	7.70577i	−1.70951	−	0.458061i	−0.975303	+	0.220870i	$0.929110\pi$
$284$	2.00000	−	7.46410i	0.118678	−	0.442913i
$285$		0			0
$286$	7.73205	−	2.07180i	0.457206	−	0.122508i
$287$		−	10.6795i		−	0.630390i
$288$		0			0
$289$	−0.571797	−	16.9904i	−0.0336351	−	0.999434i
$290$	12.3923	−	21.4641i	0.727701	−	1.26042i
$291$		0			0
$292$	−1.42820	+	5.33013i	−0.0835793	+	0.311922i
$293$	7.73205	+	13.3923i	0.451711	+	0.782387i	0.998492	−	0.0548887i	$-0.0174804\pi$
$293$	7.73205	+	13.3923i	0.451711	+	0.782387i	−0.546781	+	0.837276i	$0.684147\pi$
$294$		0			0
$295$	1.26795	+	4.73205i	0.0738229	+	0.275511i
$296$	3.46410	−	3.46410i	0.201347	−	0.201347i
$297$		0			0
$298$			11.4641i			0.664098i
$299$	−1.60770	−	6.00000i	−0.0929754	−	0.346989i
$300$		0			0
$301$	1.39230	−	5.19615i	0.0802511	−	0.299501i
$302$	−10.4641	−	18.1244i	−0.602141	−	1.04294i
$303$		0			0
$304$	0.866025	+	0.500000i	0.0496700	+	0.0286770i
$305$	29.8564			1.70957
$306$		0			0
$307$	6.07180			0.346536			0.173268	−	0.984875i	$-0.444567\pi$
$307$	6.07180			0.346536			0.173268	+	0.984875i	$0.444567\pi$
$308$	−2.07180	−	1.19615i	−0.118052	−	0.0681571i
$309$		0			0
$310$		0			0
$311$	4.60770	−	17.1962i	0.261278	−	0.975104i	−0.703211	−	0.710982i	$-0.748251\pi$
$311$	4.60770	−	17.1962i	0.261278	−	0.975104i	0.964489	−	0.264123i	$-0.0850824\pi$
$312$		0			0
$313$	−2.52628	−	9.42820i	−0.142794	−	0.532914i	−0.999844	−	0.0176802i	$-0.994372\pi$
$313$	−2.52628	−	9.42820i	−0.142794	−	0.532914i	0.857050	−	0.515233i	$-0.172295\pi$
$314$		−	20.3923i		−	1.15080i
$315$		0			0
$316$	8.92820	−	8.92820i	0.502251	−	0.502251i
$317$	6.66025	+	24.8564i	0.374077	+	1.39607i	0.854689	+	0.519141i	$0.173748\pi$
$317$	6.66025	+	24.8564i	0.374077	+	1.39607i	−0.480611	+	0.876934i	$0.659585\pi$
$318$		0			0
$319$	−10.1244	−	17.5359i	−0.566855	−	0.981822i
$320$	0.732051	−	2.73205i	0.0409229	−	0.152726i
$321$		0			0
$322$	−0.928203	+	1.60770i	−0.0517267	+	0.0895933i
$323$	−2.96410	−	2.86603i	−0.164927	−	0.159470i
$324$		0			0
$325$			10.3923i			0.576461i
$326$	5.83013	−	1.56218i	0.322901	−	0.0865210i
$327$		0			0
$328$	2.66987	−	9.96410i	0.147419	−	0.550175i
$329$	10.0000	+	2.67949i	0.551318	+	0.147725i
$330$		0			0
$331$	3.00000	+	1.73205i	0.164895	+	0.0952021i	0.580176	−	0.814491i	$-0.302984\pi$
$331$	3.00000	+	1.73205i	0.164895	+	0.0952021i	−0.415282	+	0.909693i	$0.636317\pi$
$332$			4.53590i			0.248940i
$333$		0			0
$334$	−16.9282	+	16.9282i	−0.926270	+	0.926270i
$335$	−12.7321	+	3.41154i	−0.695626	+	0.186392i
$336$		0			0
$337$	−0.964102	+	3.59808i	−0.0525180	+	0.196000i	−0.987201	−	0.159484i	$-0.949017\pi$
$337$	−0.964102	+	3.59808i	−0.0525180	+	0.196000i	0.934683	+	0.355483i	$0.115684\pi$
$338$	−0.866025	+	0.500000i	−0.0471056	+	0.0271964i
$339$		0			0
$340$	−5.66025	+	10.1962i	−0.306970	+	0.552964i
$341$		0			0
$342$		0			0
$343$	−9.46410	−	9.46410i	−0.511013	−	0.511013i
$344$	2.59808	−	4.50000i	0.140079	−	0.242624i
$345$		0			0
$346$	3.73205	+	1.00000i	0.200636	+	0.0537603i
$347$	9.79423	+	2.62436i	0.525782	+	0.140883i	0.511940	−	0.859021i	$-0.328927\pi$
$347$	9.79423	+	2.62436i	0.525782	+	0.140883i	0.0138421	+	0.999904i	$0.495594\pi$
$348$		0			0
$349$	−17.0718	−	9.85641i	−0.913832	−	0.527601i	−0.0321701	−	0.999482i	$-0.510242\pi$
$349$	−17.0718	−	9.85641i	−0.913832	−	0.527601i	−0.881662	+	0.471881i	$0.843575\pi$
$350$	2.19615	−	2.19615i	0.117389	−	0.117389i
$351$		0			0
$352$	−1.63397	−	1.63397i	−0.0870911	−	0.0870911i
$353$	−10.8660	+	18.8205i	−0.578340	+	1.00171i	0.417330	+	0.908755i	$0.362966\pi$
$353$	−10.8660	+	18.8205i	−0.578340	+	1.00171i	−0.995670	+	0.0929594i	$0.970367\pi$
$354$		0			0
$355$	18.9282	−	10.9282i	1.00460	−	0.580009i
$356$	−3.46410	−	6.00000i	−0.183597	−	0.317999i
$357$		0			0
$358$	4.53590	−	7.85641i	0.239730	−	0.415224i
$359$			18.3923i			0.970709i	0.874318	+	0.485354i	$0.161309\pi$
$359$			18.3923i			0.970709i	−0.874318	+	0.485354i	$0.838691\pi$
$360$		0			0
$361$	18.0000			0.947368
$362$	15.3923	−	4.12436i	0.809002	−	0.216771i
$363$		0			0
$364$	−3.46410	−	0.928203i	−0.181568	−	0.0486511i
$365$	−13.5167	+	7.80385i	−0.707494	+	0.408472i
$366$		0			0
$367$	2.19615	+	8.19615i	0.114638	+	0.427836i	0.999260	−	0.0384744i	$-0.0122498\pi$
$367$	2.19615	+	8.19615i	0.114638	+	0.427836i	−0.884621	+	0.466310i	$0.845583\pi$
$368$	−1.26795	+	1.26795i	−0.0660964	+	0.0660964i
$369$		0			0
$370$	13.8564			0.720360
$371$	2.53590	−	0.679492i	0.131657	−	0.0352775i
$372$		0			0
$373$	1.19615	+	2.07180i	0.0619344	+	0.107274i	0.895330	−	0.445403i	$-0.146940\pi$
$373$	1.19615	+	2.07180i	0.0619344	+	0.107274i	−0.833396	+	0.552677i	$0.813606\pi$
$374$	4.90192	+	8.16987i	0.253472	+	0.422454i
$375$		0			0
$376$	8.66025	+	5.00000i	0.446619	+	0.257855i
$377$	−21.4641	−	21.4641i	−1.10546	−	1.10546i
$378$		0			0
$379$	−3.16987	−	3.16987i	−0.162825	−	0.162825i	0.620992	−	0.783817i	$-0.286730\pi$
$379$	−3.16987	−	3.16987i	−0.162825	−	0.162825i	−0.783817	+	0.620992i	$0.786730\pi$
$380$	0.732051	+	2.73205i	0.0375534	+	0.140151i
$381$		0			0
$382$	6.80385	−	3.92820i	0.348115	−	0.200984i
$383$	−1.26795	+	0.732051i	−0.0647892	+	0.0374060i	−0.532045	−	0.846716i	$-0.678576\pi$
$383$	−1.26795	+	0.732051i	−0.0647892	+	0.0374060i	0.467255	+	0.884122i	$0.345243\pi$
$384$		0			0
$385$	−1.75129	−	6.53590i	−0.0892539	−	0.333100i
$386$	4.09808	+	4.09808i	0.208587	+	0.208587i
$387$		0			0
$388$	1.83013	+	1.83013i	0.0929106	+	0.0929106i
$389$	9.58846	+	5.53590i	0.486154	+	0.280681i	0.722978	−	0.690872i	$-0.242773\pi$
$389$	9.58846	+	5.53590i	0.486154	+	0.280681i	−0.236823	+	0.971553i	$0.576106\pi$
$390$		0			0
$391$	6.33975	−	3.80385i	0.320615	−	0.192369i
$392$	−2.96410	−	5.13397i	−0.149710	−	0.259305i
$393$		0			0
$394$	12.9282	−	3.46410i	0.651313	−	0.174519i
$395$	35.7128			1.79691
$396$		0			0
$397$	5.07180	−	5.07180i	0.254546	−	0.254546i	−0.568285	−	0.822832i	$-0.692393\pi$
$397$	5.07180	−	5.07180i	0.254546	−	0.254546i	0.822832	+	0.568285i	$0.192393\pi$
$398$	1.33975	+	5.00000i	0.0671554	+	0.250627i
$399$		0			0
$400$	2.59808	−	1.50000i	0.129904	−	0.0750000i
$401$	19.3564	+	5.18653i	0.966613	+	0.259003i	0.707397	−	0.706816i	$-0.249869\pi$
$401$	19.3564	+	5.18653i	0.966613	+	0.259003i	0.259216	+	0.965819i	$0.416536\pi$
$402$		0			0
$403$		0			0
$404$	17.4641			0.868872
$405$		0			0
$406$			9.07180i			0.450226i
$407$	5.66025	−	9.80385i	0.280568	−	0.485959i
$408$		0			0
$409$	15.5263	+	26.8923i	0.767725	+	1.32974i	0.938794	+	0.344480i	$0.111945\pi$
$409$	15.5263	+	26.8923i	0.767725	+	1.32974i	−0.171069	+	0.985259i	$0.554722\pi$
$410$	25.2679	−	14.5885i	1.24790	−	0.720473i
$411$		0			0
$412$	3.73205	−	6.46410i	0.183865	−	0.318463i
$413$	−1.26795	−	1.26795i	−0.0623917	−	0.0623917i
$414$		0			0
$415$	−9.07180	+	9.07180i	−0.445317	+	0.445317i
$416$	−3.00000	−	1.73205i	−0.147087	−	0.0849208i
$417$		0			0
$418$	2.23205	+	0.598076i	0.109173	+	0.0292529i
$419$	−7.63397	−	2.04552i	−0.372944	−	0.0999301i	0.0674783	−	0.997721i	$-0.478505\pi$
$419$	−7.63397	−	2.04552i	−0.372944	−	0.0999301i	−0.440422	+	0.897791i	$0.645171\pi$
$420$		0			0
$421$	8.39230	−	14.5359i	0.409016	−	0.708436i	−0.585764	−	0.810482i	$-0.699205\pi$
$421$	8.39230	−	14.5359i	0.409016	−	0.708436i	0.994780	+	0.102045i	$0.0325387\pi$
$422$	−11.1962	−	11.1962i	−0.545020	−	0.545020i
$423$		0			0
$424$	2.53590			0.123154
$425$	−11.8923	+	3.40192i	−0.576862	+	0.165018i
$426$		0			0
$427$	−9.46410	+	5.46410i	−0.458000	+	0.264426i
$428$	4.86603	−	18.1603i	0.235208	−	0.877809i
$429$		0			0
$430$	14.1962	−	3.80385i	0.684599	−	0.183438i
$431$	20.5885	−	20.5885i	0.991711	−	0.991711i	−0.00825484	−	0.999966i	$-0.502628\pi$
$431$	20.5885	−	20.5885i	0.991711	−	0.991711i	0.999966	+	0.00825484i	$0.00262763\pi$
$432$		0			0
$433$			4.07180i			0.195678i	0.995202	+	0.0978390i	$0.0311930\pi$
$433$			4.07180i			0.195678i	−0.995202	+	0.0978390i	$0.968807\pi$
$434$		0			0
$435$		0			0
$436$	−6.73205	−	1.80385i	−0.322407	−	0.0863886i
$437$	0.464102	−	1.73205i	0.0222010	−	0.0828552i
$438$		0			0
$439$	6.73205	−	1.80385i	0.321303	−	0.0860929i	−0.0945626	−	0.995519i	$-0.530145\pi$
$439$	6.73205	−	1.80385i	0.321303	−	0.0860929i	0.415866	+	0.909426i	$0.363479\pi$
$440$		−	6.53590i		−	0.311587i
$441$		0			0
$442$	10.2679	+	9.92820i	0.488397	+	0.472236i
$443$	−6.06218	+	10.5000i	−0.288023	+	0.498870i	−0.973338	−	0.229377i	$-0.926331\pi$
$443$	−6.06218	+	10.5000i	−0.288023	+	0.498870i	0.685315	+	0.728247i	$0.259665\pi$
$444$		0			0
$445$	5.07180	−	18.9282i	0.240426	−	0.897283i
$446$	1.19615	+	2.07180i	0.0566395	+	0.0981024i
$447$		0			0
$448$	0.267949	+	1.00000i	0.0126594	+	0.0472456i
$449$	8.36603	−	8.36603i	0.394817	−	0.394817i	−0.481583	−	0.876400i	$-0.659938\pi$
$449$	8.36603	−	8.36603i	0.394817	−	0.394817i	0.876400	+	0.481583i	$0.159938\pi$
$450$		0			0
$451$		−	23.8372i		−	1.12245i
$452$	1.63397	+	6.09808i	0.0768557	+	0.286829i
$453$		0			0
$454$	−1.69615	+	6.33013i	−0.0796044	+	0.297088i
$455$	−5.07180	−	8.78461i	−0.237769	−	0.411829i
$456$		0			0
$457$	23.1340	+	13.3564i	1.08216	+	0.624786i	0.931479	−	0.363796i	$-0.118519\pi$
$457$	23.1340	+	13.3564i	1.08216	+	0.624786i	0.150683	+	0.988582i	$0.451853\pi$
$458$	13.3205			0.622426
$459$		0			0
$460$	−5.07180			−0.236474
$461$	−15.5885	−	9.00000i	−0.726027	−	0.419172i	0.0909401	−	0.995856i	$-0.471013\pi$
$461$	−15.5885	−	9.00000i	−0.726027	−	0.419172i	−0.816967	+	0.576685i	$0.804346\pi$
$462$		0			0
$463$	13.8564	+	24.0000i	0.643962	+	1.11537i	0.984540	+	0.175158i	$0.0560438\pi$
$463$	13.8564	+	24.0000i	0.643962	+	1.11537i	−0.340578	+	0.940216i	$0.610623\pi$
$464$	−2.26795	+	8.46410i	−0.105287	+	0.392936i
$465$		0			0
$466$	−3.57180	−	13.3301i	−0.165460	−	0.617506i
$467$		−	36.8564i		−	1.70551i	−0.522310	−	0.852756i	$-0.674930\pi$
$467$		−	36.8564i		−	1.70551i	0.522310	−	0.852756i	$-0.325070\pi$
$468$		0			0
$469$	3.41154	−	3.41154i	0.157530	−	0.157530i
$470$	7.32051	+	27.3205i	0.337670	+	1.26020i
$471$		0			0
$472$	−0.866025	−	1.50000i	−0.0398621	−	0.0690431i
$473$	3.10770	−	11.5981i	0.142892	−	0.533280i
$474$		0			0
$475$	−1.50000	+	2.59808i	−0.0688247	+	0.119208i
$476$	−0.0717968	−	4.26795i	−0.00329080	−	0.195621i
$477$		0			0
$478$		−	16.9282i		−	0.774278i
$479$	−29.5885	+	7.92820i	−1.35193	+	0.362249i	−0.860847	−	0.508863i	$-0.830066\pi$
$479$	−29.5885	+	7.92820i	−1.35193	+	0.362249i	−0.491084	+	0.871112i	$0.663399\pi$
$480$		0			0
$481$	4.39230	−	16.3923i	0.200272	−	0.747425i
$482$	−11.5981	−	3.10770i	−0.528278	−	0.141552i
$483$		0			0
$484$	4.90192	+	2.83013i	0.222815	+	0.128642i
$485$			7.32051i			0.332407i
$486$		0			0
$487$	12.5885	−	12.5885i	0.570437	−	0.570437i	−0.361813	−	0.932251i	$-0.617842\pi$
$487$	12.5885	−	12.5885i	0.570437	−	0.570437i	0.932251	+	0.361813i	$0.117842\pi$
$488$	−10.1962	+	2.73205i	−0.461558	+	0.123674i
$489$		0			0
$490$	4.33975	−	16.1962i	0.196050	−	0.731668i
$491$	−10.3301	+	5.96410i	−0.466192	+	0.269156i	−0.714644	−	0.699488i	$-0.753411\pi$
$491$	−10.3301	+	5.96410i	−0.466192	+	0.269156i	0.248452	+	0.968644i	$0.420078\pi$
$492$		0			0
$493$	17.5359	−	31.5885i	0.789777	−	1.42267i
$494$	3.46410			0.155857
$495$		0			0
$496$		0			0
$497$	−4.00000	+	6.92820i	−0.179425	+	0.310772i
$498$		0			0
$499$	−29.2583	−	7.83975i	−1.30978	−	0.350955i	−0.464642	−	0.885499i	$-0.653817\pi$
$499$	−29.2583	−	7.83975i	−1.30978	−	0.350955i	−0.845141	+	0.534544i	$0.820484\pi$
$500$	−5.46410	−	1.46410i	−0.244362	−	0.0654766i
$501$		0			0
$502$	−5.89230	−	3.40192i	−0.262986	−	0.151835i
$503$	−16.3923	+	16.3923i	−0.730897	+	0.730897i	−0.970797	−	0.239901i	$-0.922885\pi$
$503$	−16.3923	+	16.3923i	−0.730897	+	0.730897i	0.239901	+	0.970797i	$0.422885\pi$
$504$		0			0
$505$	34.9282	+	34.9282i	1.55428	+	1.55428i
$506$	−2.07180	+	3.58846i	−0.0921026	+	0.159526i
$507$		0			0
$508$	1.73205	−	1.00000i	0.0768473	−	0.0443678i
$509$	5.85641	+	10.1436i	0.259581	+	0.449607i	0.966130	−	0.258057i	$-0.0830823\pi$
$509$	5.85641	+	10.1436i	0.259581	+	0.449607i	−0.706549	+	0.707664i	$0.749749\pi$
$510$		0			0
$511$	2.85641	−	4.94744i	0.126360	−	0.218862i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	11.5885			0.511145
$515$	20.3923	−	5.46410i	0.898592	−	0.240777i
$516$		0			0
$517$	22.3205	+	5.98076i	0.981655	+	0.263034i
$518$	−4.39230	+	2.53590i	−0.192987	+	0.111421i
$519$		0			0
$520$	−2.53590	−	9.46410i	−0.111207	−	0.415028i
$521$	−25.7583	+	25.7583i	−1.12849	+	1.12849i	−0.138071	+	0.990422i	$0.544090\pi$
$521$	−25.7583	+	25.7583i	−1.12849	+	1.12849i	−0.990422	+	0.138071i	$0.955910\pi$
$522$		0			0
$523$	−43.1769			−1.88799			−0.943997	−	0.329953i	$-0.892967\pi$
$523$	−43.1769			−1.88799			−0.943997	+	0.329953i	$0.892967\pi$
$524$	−17.2942	+	4.63397i	−0.755502	+	0.202436i
$525$		0			0
$526$	15.3923	+	26.6603i	0.671136	+	1.16244i
$527$		0			0
$528$		0			0
$529$	−17.1340	−	9.89230i	−0.744955	−	0.430100i
$530$	5.07180	+	5.07180i	0.220305	+	0.220305i
$531$		0			0
$532$	−0.732051	−	0.732051i	−0.0317384	−	0.0317384i
$533$	−9.24871	−	34.5167i	−0.400606	−	1.49508i
$534$		0			0
$535$	46.0526	−	26.5885i	1.99103	−	1.14952i
$536$	4.03590	−	2.33013i	0.174324	−	0.100646i
$537$		0			0
$538$	0.535898	+	2.00000i	0.0231042	+	0.0862261i
$539$	−9.68653	−	9.68653i	−0.417229	−	0.417229i
$540$		0			0
$541$	−18.9282	−	18.9282i	−0.813787	−	0.813787i	0.171412	−	0.985199i	$-0.445167\pi$
$541$	−18.9282	−	18.9282i	−0.813787	−	0.813787i	−0.985199	+	0.171412i	$0.945167\pi$
$542$	−15.1244	−	8.73205i	−0.649647	−	0.375074i
$543$		0			0
$544$	1.00000	−	4.00000i	0.0428746	−	0.171499i
$545$	−9.85641	−	17.0718i	−0.422202	−	0.731275i
$546$		0			0
$547$	−31.5526	+	8.45448i	−1.34909	+	0.361488i	−0.859799	−	0.510633i	$-0.829411\pi$
$547$	−31.5526	+	8.45448i	−1.34909	+	0.361488i	−0.489291	+	0.872120i	$0.662744\pi$
$548$	21.9282			0.936726
$549$		0			0
$550$	4.90192	−	4.90192i	0.209019	−	0.209019i
$551$	−2.26795	−	8.46410i	−0.0966179	−	0.360583i
$552$		0			0
$553$	−11.3205	+	6.53590i	−0.481397	+	0.277935i
$554$	28.3205	+	7.58846i	1.20322	+	0.322403i
$555$		0			0
$556$	21.2583	−	5.69615i	0.901554	−	0.241571i
$557$	38.7846			1.64336			0.821678	−	0.569952i	$-0.193038\pi$
$557$	38.7846			1.64336			0.821678	+	0.569952i	$0.193038\pi$
$558$		0			0
$559$		−	18.0000i		−	0.761319i
$560$	−1.46410	+	2.53590i	−0.0618696	+	0.107161i
$561$		0			0
$562$	−2.46410	−	4.26795i	−0.103942	−	0.180033i
$563$	8.89230	−	5.13397i	0.374766	−	0.216371i	−0.300773	−	0.953696i	$-0.597245\pi$
$563$	8.89230	−	5.13397i	0.374766	−	0.216371i	0.675539	+	0.737325i	$0.263911\pi$
$564$		0			0
$565$	−8.92820	+	15.4641i	−0.375612	+	0.650580i
$566$	21.0526	+	21.0526i	0.884905	+	0.884905i
$567$		0			0
$568$	−5.46410	+	5.46410i	−0.229269	+	0.229269i
$569$	15.8205	+	9.13397i	0.663230	+	0.382916i	0.793507	−	0.608562i	$-0.208253\pi$
$569$	15.8205	+	9.13397i	0.663230	+	0.382916i	−0.130276	+	0.991478i	$0.541586\pi$
$570$		0			0
$571$	14.1603	+	3.79423i	0.592588	+	0.158784i	0.542636	−	0.839968i	$-0.317426\pi$
$571$	14.1603	+	3.79423i	0.592588	+	0.158784i	0.0499524	+	0.998752i	$0.484093\pi$
$572$	−7.73205	−	2.07180i	−0.323293	−	0.0866262i
$573$		0			0
$574$	−5.33975	+	9.24871i	−0.222877	+	0.386034i
$575$	−3.80385	−	3.80385i	−0.158631	−	0.158631i
$576$		0			0
$577$	5.14359			0.214131			0.107065	−	0.994252i	$-0.465855\pi$
$577$	5.14359			0.214131			0.107065	+	0.994252i	$0.465855\pi$
$578$	−8.00000	+	15.0000i	−0.332756	+	0.623918i
$579$		0			0
$580$	−21.4641	+	12.3923i	−0.891248	+	0.514562i
$581$	1.21539	−	4.53590i	0.0504229	−	0.188181i
$582$		0			0
$583$	5.66025	−	1.51666i	0.234424	−	0.0628137i
$584$	3.90192	−	3.90192i	0.161463	−	0.161463i
$585$		0			0
$586$		−	15.4641i		−	0.638816i
$587$	−8.47372	−	4.89230i	−0.349748	−	0.201927i	0.314826	−	0.949149i	$-0.398054\pi$
$587$	−8.47372	−	4.89230i	−0.349748	−	0.201927i	−0.664574	+	0.747222i	$0.731387\pi$
$588$		0			0
$589$		0			0
$590$	1.26795	−	4.73205i	0.0522006	−	0.194815i
$591$		0			0
$592$	−4.73205	+	1.26795i	−0.194486	+	0.0521124i
$593$			6.92820i			0.284507i	0.989830	+	0.142254i	$0.0454349\pi$
$593$			6.92820i			0.284507i	−0.989830	+	0.142254i	$0.954565\pi$
$594$		0			0
$595$	8.39230	−	8.67949i	0.344051	−	0.355824i
$596$	5.73205	−	9.92820i	0.234794	−	0.406675i
$597$		0			0
$598$	−1.60770	+	6.00000i	−0.0657435	+	0.245358i
$599$	−4.73205	−	8.19615i	−0.193346	−	0.334886i	0.753011	−	0.658008i	$-0.228601\pi$
$599$	−4.73205	−	8.19615i	−0.193346	−	0.334886i	−0.946357	+	0.323122i	$0.895267\pi$
$600$		0			0
$601$	−10.1340	−	37.8205i	−0.413373	−	1.54273i	−0.788071	−	0.615584i	$-0.788920\pi$
$601$	−10.1340	−	37.8205i	−0.413373	−	1.54273i	0.374698	−	0.927147i	$-0.377746\pi$
$602$	−3.80385	+	3.80385i	−0.155033	+	0.155033i
$603$		0			0
$604$			20.9282i			0.851557i
$605$	4.14359	+	15.4641i	0.168461	+	0.628705i
$606$		0			0
$607$	−12.5885	+	46.9808i	−0.510950	+	1.90689i	−0.100701	+	0.994917i	$0.532108\pi$
$607$	−12.5885	+	46.9808i	−0.510950	+	1.90689i	−0.410249	+	0.911974i	$0.634558\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$	−25.8564	−	14.9282i	−1.04690	−	0.604425i
$611$	34.6410			1.40143
$612$		0			0
$613$	−25.8564			−1.04433			−0.522165	−	0.852844i	$-0.674876\pi$
$613$	−25.8564			−1.04433			−0.522165	+	0.852844i	$0.674876\pi$
$614$	−5.25833	−	3.03590i	−0.212209	−	0.122519i
$615$		0			0
$616$	1.19615	+	2.07180i	0.0481944	+	0.0834751i
$617$	0.428203	−	1.59808i	0.0172388	−	0.0643361i	−0.956771	−	0.290844i	$-0.906064\pi$
$617$	0.428203	−	1.59808i	0.0172388	−	0.0643361i	0.974009	+	0.226507i	$0.0727308\pi$
$618$		0			0
$619$	−5.38269	−	20.0885i	−0.216348	−	0.807423i	−0.985688	−	0.168583i	$-0.946081\pi$
$619$	−5.38269	−	20.0885i	−0.216348	−	0.807423i	0.769339	−	0.638841i	$-0.220586\pi$
$620$		0			0
$621$		0			0
$622$	−12.5885	+	12.5885i	−0.504751	+	0.504751i
$623$	1.85641	+	6.92820i	0.0743754	+	0.277573i
$624$		0			0
$625$	−15.5000	−	26.8468i	−0.620000	−	1.07387i
$626$	−2.52628	+	9.42820i	−0.100970	+	0.376827i
$627$		0			0
$628$	−10.1962	+	17.6603i	−0.406871	+	0.704721i
$629$	20.1962	−	0.339746i	0.805273	−	0.0135466i
$630$		0			0
$631$			21.4641i			0.854472i	0.904140	+	0.427236i	$0.140513\pi$
$631$			21.4641i			0.854472i	−0.904140	+	0.427236i	$0.859487\pi$
$632$	−12.1962	+	3.26795i	−0.485137	+	0.129992i
$633$		0			0
$634$	6.66025	−	24.8564i	0.264512	−	0.987174i
$635$	5.46410	+	1.46410i	0.216836	+	0.0581011i
$636$		0			0
$637$	−17.7846	−	10.2679i	−0.704652	−	0.406831i
$638$			20.2487i			0.801654i
$639$		0			0
$640$	−2.00000	+	2.00000i	−0.0790569	+	0.0790569i
$641$	44.9186	−	12.0359i	1.77418	−	0.475389i	0.784675	−	0.619907i	$-0.212830\pi$
$641$	44.9186	−	12.0359i	1.77418	−	0.475389i	0.989502	+	0.144518i	$0.0461631\pi$
$642$		0			0
$643$	−6.16025	+	22.9904i	−0.242937	+	0.906652i	0.731473	+	0.681871i	$0.238833\pi$
$643$	−6.16025	+	22.9904i	−0.242937	+	0.906652i	−0.974409	+	0.224781i	$0.927833\pi$
$644$	1.60770	−	0.928203i	0.0633521	−	0.0365763i
$645$		0			0
$646$	1.13397	+	3.96410i	0.0446156	+	0.155965i
$647$	−15.4641			−0.607957			−0.303978	−	0.952679i	$-0.598315\pi$
$647$	−15.4641			−0.607957			−0.303978	+	0.952679i	$0.598315\pi$
$648$		0			0
$649$	−2.83013	−	2.83013i	−0.111092	−	0.111092i
$650$	5.19615	−	9.00000i	0.203810	−	0.353009i
$651$		0			0
$652$	−5.83013	−	1.56218i	−0.228325	−	0.0611796i
$653$	23.3923	+	6.26795i	0.915412	+	0.245284i	0.685623	−	0.727957i	$-0.259530\pi$
$653$	23.3923	+	6.26795i	0.915412	+	0.245284i	0.229789	+	0.973241i	$0.426197\pi$
$654$		0			0
$655$	−43.8564	−	25.3205i	−1.71361	−	0.989354i
$656$	−7.29423	+	7.29423i	−0.284792	+	0.284792i
$657$		0			0
$658$	−7.32051	−	7.32051i	−0.285383	−	0.285383i
$659$	−16.9282	+	29.3205i	−0.659429	+	1.14216i	0.321334	+	0.946966i	$0.395869\pi$
$659$	−16.9282	+	29.3205i	−0.659429	+	1.14216i	−0.980764	+	0.195199i	$0.937465\pi$
$660$		0			0
$661$	−30.2487	+	17.4641i	−1.17654	+	0.679275i	−0.955211	−	0.295925i	$-0.904372\pi$
$661$	−30.2487	+	17.4641i	−1.17654	+	0.679275i	−0.221327	+	0.975200i	$0.571039\pi$
$662$	−1.73205	−	3.00000i	−0.0673181	−	0.116598i
$663$		0			0
$664$	2.26795	−	3.92820i	0.0880135	−	0.152444i
$665$		−	2.92820i		−	0.113551i
$666$		0			0
$667$	15.7128			0.608403
$668$	23.1244	−	6.19615i	0.894708	−	0.239736i
$669$		0			0
$670$	12.7321	+	3.41154i	0.491882	+	0.131799i
$671$	−21.1244	+	12.1962i	−0.815497	+	0.470827i
$672$		0			0
$673$	6.75833	+	25.2224i	0.260514	+	0.972253i	0.964939	+	0.262474i	$0.0845385\pi$
$673$	6.75833	+	25.2224i	0.260514	+	0.972253i	−0.704424	+	0.709779i	$0.748795\pi$
$674$	2.63397	−	2.63397i	0.101457	−	0.101457i
$675$		0			0
$676$	1.00000			0.0384615
$677$	−40.0526	+	10.7321i	−1.53934	+	0.412466i	−0.926054	−	0.377391i	$-0.876821\pi$
$677$	−40.0526	+	10.7321i	−1.53934	+	0.412466i	−0.613291	+	0.789857i	$0.710155\pi$
$678$		0			0
$679$	−1.33975	−	2.32051i	−0.0514147	−	0.0890529i
$680$	10.0000	−	6.00000i	0.383482	−	0.230089i
$681$		0			0
$682$		0			0
$683$	−14.8827	−	14.8827i	−0.569470	−	0.569470i	0.362510	−	0.931980i	$-0.381920\pi$
$683$	−14.8827	−	14.8827i	−0.569470	−	0.569470i	−0.931980	+	0.362510i	$0.881920\pi$
$684$		0			0
$685$	43.8564	+	43.8564i	1.67567	+	1.67567i
$686$	3.46410	+	12.9282i	0.132260	+	0.493601i
$687$		0			0
$688$	−4.50000	+	2.59808i	−0.171561	+	0.0990507i
$689$	7.60770	−	4.39230i	0.289830	−	0.167333i
$690$		0			0
$691$	12.2417	+	45.6865i	0.465695	+	1.73800i	0.654575	+	0.755997i	$0.272848\pi$
$691$	12.2417	+	45.6865i	0.465695	+	1.73800i	−0.188880	+	0.982000i	$0.560486\pi$
$692$	−2.73205	−	2.73205i	−0.103857	−	0.103857i
$693$		0			0
$694$	−7.16987	−	7.16987i	−0.272165	−	0.272165i
$695$	53.9090	+	31.1244i	2.04488	+	1.18061i
$696$		0			0
$697$	36.4711	−	21.8827i	1.38144	−	0.828866i
$698$	9.85641	+	17.0718i	0.373070	+	0.646177i
$699$		0			0
$700$	−3.00000	+	0.803848i	−0.113389	+	0.0303826i
$701$	38.7846			1.46487			0.732437	−	0.680835i	$-0.238383\pi$
$701$	38.7846			1.46487			0.732437	+	0.680835i	$0.238383\pi$
$702$		0			0
$703$	3.46410	−	3.46410i	0.130651	−	0.130651i
$704$	0.598076	+	2.23205i	0.0225408	+	0.0841236i
$705$		0			0
$706$	18.8205	−	10.8660i	0.708319	−	0.408948i
$707$	−17.4641	−	4.67949i	−0.656805	−	0.175990i
$708$		0			0
$709$	−16.9282	+	4.53590i	−0.635752	+	0.170349i	−0.562279	−	0.826948i	$-0.690075\pi$
$709$	−16.9282	+	4.53590i	−0.635752	+	0.170349i	−0.0734735	+	0.997297i	$0.523408\pi$
$710$	−21.8564			−0.820256
$711$		0			0
$712$			6.92820i			0.259645i
$713$		0			0
$714$		0			0
$715$	−11.3205	−	19.6077i	−0.423363	−	0.733286i
$716$	−7.85641	+	4.53590i	−0.293608	+	0.169514i
$717$		0			0
$718$	9.19615	−	15.9282i	0.343197	−	0.594435i
$719$	3.85641	+	3.85641i	0.143820	+	0.143820i	0.775351	−	0.631531i	$-0.217573\pi$
$719$	3.85641	+	3.85641i	0.143820	+	0.143820i	−0.631531	+	0.775351i	$0.717573\pi$
$720$		0			0
$721$	−5.46410	+	5.46410i	−0.203494	+	0.203494i
$722$	−15.5885	−	9.00000i	−0.580142	−	0.334945i
$723$		0			0
$724$	−15.3923	−	4.12436i	−0.572051	−	0.153280i
$725$	−25.3923	−	6.80385i	−0.943047	−	0.252689i
$726$		0			0
$727$	3.53590	−	6.12436i	0.131139	−	0.227140i	−0.792977	−	0.609252i	$-0.791470\pi$
$727$	3.53590	−	6.12436i	0.131139	−	0.227140i	0.924116	+	0.382112i	$0.124803\pi$
$728$	2.53590	+	2.53590i	0.0939866	+	0.0939866i
$729$		0			0
$730$	15.6077			0.577667
$731$	20.5981	−	5.89230i	0.761847	−	0.217935i
$732$		0			0
$733$	−10.8564	+	6.26795i	−0.400991	+	0.231512i	−0.686911	−	0.726741i	$-0.741034\pi$
$733$	−10.8564	+	6.26795i	−0.400991	+	0.231512i	0.285921	+	0.958253i	$0.407701\pi$
$734$	2.19615	−	8.19615i	0.0810615	−	0.302526i
$735$		0			0
$736$	1.73205	−	0.464102i	0.0638442	−	0.0171070i
$737$	7.61474	−	7.61474i	0.280492	−	0.280492i
$738$		0			0
$739$		−	0.215390i		−	0.00792326i	−0.999992	−	0.00396163i	$-0.998739\pi$
$739$		−	0.215390i		−	0.00792326i	0.999992	−	0.00396163i	$-0.00126103\pi$
$740$	−12.0000	−	6.92820i	−0.441129	−	0.254686i
$741$		0			0
$742$	−2.53590	−	0.679492i	−0.0930958	−	0.0249449i
$743$	4.85641	−	18.1244i	0.178164	−	0.664918i	−0.817827	−	0.575465i	$-0.804821\pi$
$743$	4.85641	−	18.1244i	0.178164	−	0.664918i	0.995991	−	0.0894536i	$-0.0285121\pi$
$744$		0			0
$745$	31.3205	−	8.39230i	1.14749	−	0.307470i
$746$		−	2.39230i		−	0.0875885i
$747$		0			0
$748$	−0.160254	−	9.52628i	−0.00585947	−	0.348315i
$749$	−9.73205	+	16.8564i	−0.355601	+	0.615920i
$750$		0			0
$751$	4.73205	−	17.6603i	0.172675	−	0.644432i	−0.824261	−	0.566210i	$-0.808409\pi$
$751$	4.73205	−	17.6603i	0.172675	−	0.644432i	0.996936	−	0.0782218i	$-0.0249242\pi$
$752$	−5.00000	−	8.66025i	−0.182331	−	0.315807i
$753$		0			0
$754$	7.85641	+	29.3205i	0.286113	+	1.06779i
$755$	−41.8564	+	41.8564i	−1.52331	+	1.52331i
$756$		0			0
$757$			35.8564i			1.30322i	0.758553	+	0.651612i	$0.225907\pi$
$757$			35.8564i			1.30322i	−0.758553	+	0.651612i	$0.774093\pi$
$758$	1.16025	+	4.33013i	0.0421423	+	0.157277i
$759$		0			0
$760$	0.732051	−	2.73205i	0.0265543	−	0.0991019i
$761$	−1.92820	−	3.33975i	−0.0698973	−	0.121066i	0.828959	−	0.559310i	$-0.188934\pi$
$761$	−1.92820	−	3.33975i	−0.0698973	−	0.121066i	−0.898856	+	0.438244i	$0.855600\pi$
$762$		0			0
$763$	6.24871	+	3.60770i	0.226219	+	0.130607i
$764$	−7.85641			−0.284235
$765$		0			0
$766$	1.46410			0.0529001
$767$	−5.19615	−	3.00000i	−0.187622	−	0.108324i
$768$		0			0
$769$	1.53590	+	2.66025i	0.0553859	+	0.0959312i	0.892389	−	0.451267i	$-0.149028\pi$
$769$	1.53590	+	2.66025i	0.0553859	+	0.0959312i	−0.837003	+	0.547198i	$0.815694\pi$
$770$	−1.75129	+	6.53590i	−0.0631121	+	0.235537i
$771$		0			0
$772$	−1.50000	−	5.59808i	−0.0539862	−	0.201479i
$773$			23.1769i			0.833616i	0.908995	+	0.416808i	$0.136851\pi$
$773$			23.1769i			0.833616i	−0.908995	+	0.416808i	$0.863149\pi$
$774$		0			0
$775$		0			0
$776$	−0.669873	−	2.50000i	−0.0240470	−	0.0897448i
$777$		0			0
$778$	−5.53590	−	9.58846i	−0.198472	−	0.343763i
$779$	2.66987	−	9.96410i	0.0956581	−	0.357001i
$780$		0			0
$781$	−8.92820	+	15.4641i	−0.319476	+	0.553349i
$782$	−7.39230	+	0.124356i	−0.264348	+	0.00444695i
$783$		0			0
$784$			5.92820i			0.211722i
$785$	−55.7128	+	14.9282i	−1.98848	+	0.532810i
$786$		0			0
$787$	−11.0263	+	41.1506i	−0.393044	+	1.46686i	0.432041	+	0.901854i	$0.357794\pi$
$787$	−11.0263	+	41.1506i	−0.393044	+	1.46686i	−0.825086	+	0.565008i	$0.808873\pi$
$788$	−12.9282	−	3.46410i	−0.460548	−	0.123404i
$789$		0			0
$790$	−30.9282	−	17.8564i	−1.10038	−	0.635302i
$791$		−	6.53590i		−	0.232390i
$792$		0			0
$793$	−25.8564	+	25.8564i	−0.918188	+	0.918188i
$794$	−6.92820	+	1.85641i	−0.245873	+	0.0658814i
$795$		0			0
$796$	1.33975	−	5.00000i	0.0474860	−	0.177220i
$797$	−19.1769	+	11.0718i	−0.679281	+	0.392183i	−0.799584	−	0.600554i	$-0.794947\pi$
$797$	−19.1769	+	11.0718i	−0.679281	+	0.392183i	0.120303	+	0.992737i	$0.461613\pi$
$798$		0			0
$799$	11.3397	+	39.6410i	0.401171	+	1.40240i
$800$	−3.00000			−0.106066
$801$		0			0
$802$	−14.1699	−	14.1699i	−0.500356	−	0.500356i
$803$	6.37564	−	11.0429i	0.224992	−	0.389697i
$804$		0			0
$805$	5.07180	+	1.35898i	0.178757	+	0.0478979i
$806$		0			0
$807$		0			0
$808$	−15.1244	−	8.73205i	−0.532073	−	0.307192i
$809$	−22.1506	+	22.1506i	−0.778775	+	0.778775i	−0.979622	−	0.200848i	$-0.935630\pi$
$809$	−22.1506	+	22.1506i	−0.778775	+	0.778775i	0.200848	+	0.979622i	$0.435630\pi$
$810$		0			0
$811$	−13.9737	−	13.9737i	−0.490684	−	0.490684i	0.417838	−	0.908522i	$-0.362788\pi$
$811$	−13.9737	−	13.9737i	−0.490684	−	0.490684i	−0.908522	+	0.417838i	$0.862788\pi$
$812$	4.53590	−	7.85641i	0.159179	−	0.275706i
$813$		0			0
$814$	−9.80385	+	5.66025i	−0.343625	+	0.198392i
$815$	−8.53590	−	14.7846i	−0.298999	−	0.517882i
$816$		0			0
$817$	2.59808	−	4.50000i	0.0908952	−	0.157435i
$818$		−	31.0526i		−	1.08573i
$819$		0			0
$820$	−29.1769			−1.01890
$821$	29.0526	−	7.78461i	1.01394	−	0.271685i	0.286666	−	0.958031i	$-0.407453\pi$
$821$	29.0526	−	7.78461i	1.01394	−	0.271685i	0.727275	+	0.686346i	$0.240786\pi$
$822$		0			0
$823$	6.92820	+	1.85641i	0.241502	+	0.0647103i	0.377540	−	0.925993i	$-0.376770\pi$
$823$	6.92820	+	1.85641i	0.241502	+	0.0647103i	−0.136038	+	0.990704i	$0.543437\pi$
$824$	−6.46410	+	3.73205i	−0.225188	+	0.130012i
$825$		0			0
$826$	0.464102	+	1.73205i	0.0161482	+	0.0602658i
$827$	13.3397	−	13.3397i	0.463868	−	0.463868i	−0.436053	−	0.899921i	$-0.643624\pi$
$827$	13.3397	−	13.3397i	0.463868	−	0.463868i	0.899921	+	0.436053i	$0.143624\pi$
$828$		0			0
$829$	−22.0000			−0.764092			−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000			−0.764092			−0.382046	+	0.924143i	$0.624780\pi$
$830$	12.3923	−	3.32051i	0.430143	−	0.115257i
$831$		0			0
$832$	1.73205	+	3.00000i	0.0600481	+	0.104006i
$833$	5.92820	−	23.7128i	0.205400	−	0.821600i
$834$		0			0
$835$	58.6410	+	33.8564i	2.02936	+	1.17165i
$836$	−1.63397	−	1.63397i	−0.0565122	−	0.0565122i
$837$		0			0
$838$	5.58846	+	5.58846i	0.193050	+	0.193050i
$839$	−5.85641	−	21.8564i	−0.202186	−	0.754567i	−0.990289	−	0.139024i	$-0.955603\pi$
$839$	−5.85641	−	21.8564i	−0.202186	−	0.754567i	0.788103	−	0.615543i	$-0.211063\pi$
$840$		0			0
$841$	41.3827	−	23.8923i	1.42699	−	0.823873i
$842$	−14.5359	+	8.39230i	−0.500940	+	0.289218i
$843$		0			0
$844$	4.09808	+	15.2942i	0.141062	+	0.526449i
$845$	2.00000	+	2.00000i	0.0688021	+	0.0688021i
$846$		0			0
$847$	−4.14359	−	4.14359i	−0.142376	−	0.142376i
$848$	−2.19615	−	1.26795i	−0.0754162	−	0.0435416i
$849$		0			0
$850$	12.0000	+	3.00000i	0.411597	+	0.102899i
$851$	4.39230	+	7.60770i	0.150566	+	0.260788i
$852$		0			0
$853$	−2.46410	+	0.660254i	−0.0843692	+	0.0226067i	−0.300757	−	0.953701i	$-0.597239\pi$
$853$	−2.46410	+	0.660254i	−0.0843692	+	0.0226067i	0.216387	+	0.976308i	$0.430573\pi$
$854$	10.9282			0.373955
$855$		0			0
$856$	−13.2942	+	13.2942i	−0.454387	+	0.454387i
$857$	−6.50962	−	24.2942i	−0.222364	−	0.829875i	−0.983443	−	0.181216i	$-0.941997\pi$
$857$	−6.50962	−	24.2942i	−0.222364	−	0.829875i	0.761079	−	0.648659i	$-0.224670\pi$
$858$		0			0
$859$	−29.8923	+	17.2583i	−1.01991	+	0.588847i	−0.914079	−	0.405537i	$-0.867084\pi$
$859$	−29.8923	+	17.2583i	−1.01991	+	0.588847i	−0.105834	+	0.994384i	$0.533751\pi$
$860$	−14.1962	−	3.80385i	−0.484085	−	0.129710i
$861$		0			0
$862$	−28.1244	+	7.53590i	−0.957919	+	0.256674i
$863$	−33.8564			−1.15249			−0.576243	−	0.817279i	$-0.695482\pi$
$863$	−33.8564			−1.15249			−0.576243	+	0.817279i	$0.695482\pi$
$864$		0			0
$865$		−	10.9282i		−	0.371570i
$866$	2.03590	−	3.52628i	0.0691826	−	0.119828i
$867$		0			0
$868$		0			0
$869$	−25.2679	+	14.5885i	−0.857156	+	0.494880i
$870$		0			0
$871$	8.07180	−	13.9808i	0.273502	−	0.473720i
$872$	4.92820	+	4.92820i	0.166890	+	0.166890i
$873$		0			0
$874$	−1.26795	+	1.26795i	−0.0428890	+	0.0428890i
$875$	5.07180	+	2.92820i	0.171458	+	0.0989913i
$876$		0			0
$877$	−9.26795	−	2.48334i	−0.312956	−	0.0838564i	0.0989221	−	0.995095i	$-0.468461\pi$
$877$	−9.26795	−	2.48334i	−0.312956	−	0.0838564i	−0.411879	+	0.911239i	$0.635127\pi$
$878$	−6.73205	−	1.80385i	−0.227196	−	0.0608769i
$879$		0			0
$880$	−3.26795	+	5.66025i	−0.110163	+	0.190807i
$881$	−4.32051	−	4.32051i	−0.145562	−	0.145562i	0.630570	−	0.776132i	$-0.282821\pi$
$881$	−4.32051	−	4.32051i	−0.145562	−	0.145562i	−0.776132	+	0.630570i	$0.782821\pi$
$882$		0			0
$883$	48.3731			1.62788			0.813942	−	0.580947i	$-0.197318\pi$
$883$	48.3731			1.62788			0.813942	+	0.580947i	$0.197318\pi$
$884$	−3.92820	−	13.7321i	−0.132120	−	0.461859i
$885$		0			0
$886$	10.5000	−	6.06218i	0.352754	−	0.203663i
$887$	−5.71281	+	21.3205i	−0.191817	+	0.715873i	0.801250	+	0.598329i	$0.204169\pi$
$887$	−5.71281	+	21.3205i	−0.191817	+	0.715873i	−0.993068	+	0.117543i	$0.962498\pi$
$888$		0			0
$889$	−2.00000	+	0.535898i	−0.0670778	+	0.0179735i
$890$	−13.8564	+	13.8564i	−0.464468	+	0.464468i
$891$		0			0
$892$		−	2.39230i		−	0.0801003i
$893$	8.66025	+	5.00000i	0.289804	+	0.167319i
$894$		0			0
$895$	−24.7846	−	6.64102i	−0.828458	−	0.221985i
$896$	0.267949	−	1.00000i	0.00895155	−	0.0334077i
$897$		0			0
$898$	−11.4282	+	3.06218i	−0.381364	+	0.102186i
$899$		0			0
$900$		0			0
$901$	7.51666	+	7.26795i	0.250416	+	0.242130i
$902$	−11.9186	+	20.6436i	−0.396845	+	0.687356i
$903$		0			0
$904$	1.63397	−	6.09808i	0.0543452	−	0.202819i
$905$	−22.5359	−	39.0333i	−0.749119	−	1.29751i
$906$		0			0
$907$	9.91858	+	37.0167i	0.329341	+	1.22912i	0.909875	+	0.414882i	$0.136177\pi$
$907$	9.91858	+	37.0167i	0.329341	+	1.22912i	−0.580534	+	0.814236i	$0.697156\pi$
$908$	4.63397	−	4.63397i	0.153784	−	0.153784i
$909$		0			0
$910$			10.1436i			0.336257i
$911$	9.66025	+	36.0526i	0.320058	+	1.19447i	0.919187	+	0.393822i	$0.128847\pi$
$911$	9.66025	+	36.0526i	0.320058	+	1.19447i	−0.599128	+	0.800653i	$0.704486\pi$
$912$		0			0
$913$	2.71281	−	10.1244i	0.0897810	−	0.335067i
$914$	−13.3564	−	23.1340i	−0.441791	−	0.765204i
$915$		0			0
$916$	−11.5359	−	6.66025i	−0.381157	−	0.220061i
$917$	18.5359			0.612109
$918$		0			0
$919$	8.92820			0.294514			0.147257	−	0.989098i	$-0.452956\pi$
$919$	8.92820			0.294514			0.147257	+	0.989098i	$0.452956\pi$
$920$	4.39230	+	2.53590i	0.144810	+	0.0836061i
$921$		0			0
$922$	9.00000	+	15.5885i	0.296399	+	0.513378i
$923$	−6.92820	+	25.8564i	−0.228045	+	0.851074i
$924$		0			0
$925$	−3.80385	−	14.1962i	−0.125070	−	0.466767i
$926$		−	27.7128i		−	0.910700i
$927$		0			0
$928$	6.19615	−	6.19615i	0.203399	−	0.203399i
$929$	−7.04552	−	26.2942i	−0.231156	−	0.862686i	−0.979844	−	0.199763i	$-0.935983\pi$
$929$	−7.04552	−	26.2942i	−0.231156	−	0.862686i	0.748688	−	0.662922i	$-0.230684\pi$
$930$		0			0
$931$	−2.96410	−	5.13397i	−0.0971445	−	0.168259i
$932$	−3.57180	+	13.3301i	−0.116998	+	0.436643i
$933$		0			0
$934$	−18.4282	+	31.9186i	−0.602989	+	1.04441i
$935$	18.7321	−	19.3731i	0.612604	−	0.633567i
$936$		0			0
$937$		−	41.7128i		−	1.36270i	−0.731959	−	0.681349i	$-0.761394\pi$
$937$		−	41.7128i		−	1.36270i	0.731959	−	0.681349i	$-0.238606\pi$
$938$	−4.66025	+	1.24871i	−0.152163	+	0.0407719i
$939$		0			0
$940$	7.32051	−	27.3205i	0.238769	−	0.891097i
$941$	4.73205	+	1.26795i	0.154260	+	0.0413340i	0.335123	−	0.942174i	$-0.391222\pi$
$941$	4.73205	+	1.26795i	0.154260	+	0.0413340i	−0.180862	+	0.983508i	$0.557889\pi$
$942$		0			0
$943$	16.0192	+	9.24871i	0.521658	+	0.301179i
$944$			1.73205i			0.0563735i
$945$		0			0
$946$	−8.49038	+	8.49038i	−0.276046	+	0.276046i
$947$	−15.6962	+	4.20577i	−0.510056	+	0.136669i	−0.504663	−	0.863316i	$-0.668383\pi$
$947$	−15.6962	+	4.20577i	−0.510056	+	0.136669i	−0.00539312	+	0.999985i	$0.501717\pi$
$948$		0			0
$949$	4.94744	−	18.4641i	0.160601	−	0.599370i
$950$	2.59808	−	1.50000i	0.0842927	−	0.0486664i
$951$		0			0
$952$	−2.07180	+	3.73205i	−0.0671473	+	0.120956i
$953$	−4.66025			−0.150960			−0.0754802	−	0.997147i	$-0.524049\pi$
$953$	−4.66025			−0.150960			−0.0754802	+	0.997147i	$0.524049\pi$
$954$		0			0
$955$	−15.7128	−	15.7128i	−0.508455	−	0.508455i
$956$	−8.46410	+	14.6603i	−0.273749	+	0.474147i
$957$		0			0
$958$	29.5885	+	7.92820i	0.955960	+	0.256149i
$959$	−21.9282	−	5.87564i	−0.708099	−	0.189734i
$960$		0			0
$961$	26.8468	+	15.5000i	0.866025	+	0.500000i
$962$	−12.0000	+	12.0000i	−0.386896	+	0.386896i
$963$		0			0
$964$	8.49038	+	8.49038i	0.273457	+	0.273457i
$965$	8.19615	−	14.1962i	0.263843	−	0.456990i
$966$		0			0
$967$	−19.1436	+	11.0526i	−0.615616	+	0.355426i	−0.775160	−	0.631764i	$-0.782331\pi$
$967$	−19.1436	+	11.0526i	−0.615616	+	0.355426i	0.159544	+	0.987191i	$0.448998\pi$
$968$	−2.83013	−	4.90192i	−0.0909637	−	0.157554i
$969$		0			0
$970$	3.66025	−	6.33975i	0.117524	−	0.203557i
$971$			22.3923i			0.718603i	0.933221	+	0.359302i	$0.116985\pi$
$971$			22.3923i			0.718603i	−0.933221	+	0.359302i	$0.883015\pi$
$972$		0			0
$973$	−22.7846			−0.730441
$974$	−17.1962	+	4.60770i	−0.551000	+	0.147640i
$975$		0			0
$976$	10.1962	+	2.73205i	0.326371	+	0.0874508i
$977$	38.4282	−	22.1865i	1.22943	−	0.709810i	0.262517	−	0.964927i	$-0.415447\pi$
$977$	38.4282	−	22.1865i	1.22943	−	0.709810i	0.966910	+	0.255117i	$0.0821141\pi$
$978$		0			0
$979$	4.14359	+	15.4641i	0.132430	+	0.494235i
$980$	−11.8564	+	11.8564i	−0.378739	+	0.378739i
$981$		0			0
$982$	11.9282			0.380644
$983$	−25.6603	+	6.87564i	−0.818435	+	0.219299i	−0.643662	−	0.765310i	$-0.722586\pi$
$983$	−25.6603	+	6.87564i	−0.818435	+	0.219299i	−0.174773	+	0.984609i	$0.555919\pi$
$984$		0			0
$985$	−18.9282	−	32.7846i	−0.603103	−	1.04460i
$986$	−30.9808	+	18.5885i	−0.986628	+	0.591977i
$987$		0			0
$988$	−3.00000	−	1.73205i	−0.0954427	−	0.0551039i
$989$	6.58846	+	6.58846i	0.209501	+	0.209501i
$990$		0			0
$991$	2.14359	+	2.14359i	0.0680935	+	0.0680935i	0.740333	−	0.672240i	$-0.234668\pi$
$991$	2.14359	+	2.14359i	0.0680935	+	0.0680935i	−0.672240	+	0.740333i	$0.734668\pi$
$992$		0			0
$993$		0			0
$994$	6.92820	−	4.00000i	0.219749	−	0.126872i
$995$	12.6795	−	7.32051i	0.401967	−	0.232076i
$996$		0			0
$997$	4.39230	+	16.3923i	0.139106	+	0.519150i	0.999947	+	0.0102763i	$0.00327112\pi$
$997$	4.39230	+	16.3923i	0.139106	+	0.519150i	−0.860842	+	0.508873i	$0.830062\pi$
$998$	21.4186	+	21.4186i	0.677993	+	0.677993i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	918.2.o.b.829.1		4
3.2	odd	2		306.2.n.c.115.1	yes	4
9.4	even	3		918.2.o.c.523.1		4
9.5	odd	6		306.2.n.b.13.1	✓	4
17.4	even	4		918.2.o.c.667.1		4
51.38	odd	4		306.2.n.b.259.1	yes	4
153.4	even	12	inner	918.2.o.b.361.1		4
153.140	odd	12		306.2.n.c.157.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
306.2.n.b.13.1	✓	4	9.5	odd	6
306.2.n.b.259.1	yes	4	51.38	odd	4
306.2.n.c.115.1	yes	4	3.2	odd	2
306.2.n.c.157.1	yes	4	153.140	odd	12
918.2.o.b.361.1		4	153.4	even	12	inner
918.2.o.b.829.1		4	1.1	even	1	trivial
918.2.o.c.523.1		4	9.4	even	3
918.2.o.c.667.1		4	17.4	even	4

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:	\( N \)	\(=\)	\( 918 = 2 \cdot 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	918.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.732051 + 2.73205i) q^{5} +(-0.267949 - 1.00000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.732051 + 2.73205i) q^{5} +(-0.267949 - 1.00000i) q^{7} -1.00000i q^{8} +(2.00000 - 2.00000i) q^{10} +(-0.598076 - 2.23205i) q^{11} +(-1.73205 - 3.00000i) q^{13} +(-0.267949 + 1.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.86603 - 2.96410i) q^{17} -1.00000i q^{19} +(-2.73205 + 0.732051i) q^{20} +(-0.598076 + 2.23205i) q^{22} +(1.73205 + 0.464102i) q^{23} +(-2.59808 - 1.50000i) q^{25} +3.46410i q^{26} +(0.732051 - 0.732051i) q^{28} +(8.46410 - 2.26795i) q^{29} +(0.866025 - 0.500000i) q^{32} +(-3.96410 + 1.13397i) q^{34} +2.92820 q^{35} +(3.46410 + 3.46410i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(2.73205 + 0.732051i) q^{40} +(9.96410 + 2.66987i) q^{41} +(4.50000 + 2.59808i) q^{43} +(1.63397 - 1.63397i) q^{44} +(-1.26795 - 1.26795i) q^{46} +(-5.00000 + 8.66025i) q^{47} +(5.13397 - 2.96410i) q^{49} +(1.50000 + 2.59808i) q^{50} +(1.73205 - 3.00000i) q^{52} +2.53590i q^{53} +6.53590 q^{55} +(-1.00000 + 0.267949i) q^{56} +(-8.46410 - 2.26795i) q^{58} +(1.50000 - 0.866025i) q^{59} +(-2.73205 - 10.1962i) q^{61} -1.00000 q^{64} +(9.46410 - 2.53590i) q^{65} +(2.33013 + 4.03590i) q^{67} +(4.00000 + 1.00000i) q^{68} +(-2.53590 - 1.46410i) q^{70} +(-5.46410 - 5.46410i) q^{71} +(3.90192 + 3.90192i) q^{73} +(-1.26795 - 4.73205i) q^{74} +(0.866025 - 0.500000i) q^{76} +(-2.07180 + 1.19615i) q^{77} +(-3.26795 - 12.1962i) q^{79} +(-2.00000 - 2.00000i) q^{80} +(-7.29423 - 7.29423i) q^{82} +(3.92820 + 2.26795i) q^{83} +(6.00000 + 10.0000i) q^{85} +(-2.59808 - 4.50000i) q^{86} +(-2.23205 + 0.598076i) q^{88} -6.92820 q^{89} +(-2.53590 + 2.53590i) q^{91} +(0.464102 + 1.73205i) q^{92} +(8.66025 - 5.00000i) q^{94} +(2.73205 + 0.732051i) q^{95} +(2.50000 - 0.669873i) q^{97} -5.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 - 8 * q^7	\( 4 q + 2 q^{4} + 4 q^{5} - 8 q^{7} + 8 q^{10} + 8 q^{11} - 8 q^{14} - 2 q^{16} + 8 q^{17} - 4 q^{20} + 8 q^{22} - 4 q^{28} + 20 q^{29} - 2 q^{34} - 16 q^{35} - 2 q^{38} + 4 q^{40} + 26 q^{41} + 18 q^{43} + 10 q^{44} - 12 q^{46} - 20 q^{47} + 24 q^{49} + 6 q^{50} + 40 q^{55} - 4 q^{56} - 20 q^{58} + 6 q^{59} - 4 q^{61} - 4 q^{64} + 24 q^{65} - 8 q^{67} + 16 q^{68} - 24 q^{70} - 8 q^{71} + 26 q^{73} - 12 q^{74} - 36 q^{77} - 20 q^{79} - 8 q^{80} + 2 q^{82} - 12 q^{83} + 24 q^{85} - 2 q^{88} - 24 q^{91} - 12 q^{92} + 4 q^{95} + 10 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 - 8 * q^7 + 8 * q^10 + 8 * q^11 - 8 * q^14 - 2 * q^16 + 8 * q^17 - 4 * q^20 + 8 * q^22 - 4 * q^28 + 20 * q^29 - 2 * q^34 - 16 * q^35 - 2 * q^38 + 4 * q^40 + 26 * q^41 + 18 * q^43 + 10 * q^44 - 12 * q^46 - 20 * q^47 + 24 * q^49 + 6 * q^50 + 40 * q^55 - 4 * q^56 - 20 * q^58 + 6 * q^59 - 4 * q^61 - 4 * q^64 + 24 * q^65 - 8 * q^67 + 16 * q^68 - 24 * q^70 - 8 * q^71 + 26 * q^73 - 12 * q^74 - 36 * q^77 - 20 * q^79 - 8 * q^80 + 2 * q^82 - 12 * q^83 + 24 * q^85 - 2 * q^88 - 24 * q^91 - 12 * q^92 + 4 * q^95 + 10 * q^97 + 4 * q^98

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