LMFDB - Embedded newform 810.2.m.c.593.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(53,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("810.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.m (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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			593.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	810.593
Dual form			810.2.m.c.377.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(2.19067 - 0.448288i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(2.19067 - 0.448288i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.00000 + 1.00000i) q^{10} +(2.44949 + 1.41421i) q^{11} +(-1.09808 + 4.09808i) q^{13} +(-1.41421 - 2.44949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.82843 - 2.82843i) q^{17} +8.00000i q^{19} +(1.67303 - 1.48356i) q^{20} +(-2.73205 - 0.732051i) q^{22} +(-3.86370 - 1.03528i) q^{23} +(4.59808 - 1.96410i) q^{25} -4.24264i q^{26} +(2.00000 + 2.00000i) q^{28} +(-0.707107 + 1.22474i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.46410 + 2.00000i) q^{34} +(2.82843 + 5.65685i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-2.07055 - 7.72741i) q^{38} +(-1.23205 + 1.86603i) q^{40} +(8.57321 - 4.94975i) q^{41} +2.82843 q^{44} +4.00000 q^{46} +(-0.866025 + 0.500000i) q^{49} +(-3.93305 + 3.08725i) q^{50} +(1.09808 + 4.09808i) q^{52} +(-2.82843 + 2.82843i) q^{53} +(6.00000 + 2.00000i) q^{55} +(-2.44949 - 1.41421i) q^{56} +(0.366025 - 1.36603i) q^{58} +(1.41421 + 2.44949i) q^{59} +(2.82843 + 2.82843i) q^{62} -1.00000i q^{64} +(-0.568406 + 9.46979i) q^{65} +(5.46410 + 1.46410i) q^{67} +(-3.86370 - 1.03528i) q^{68} +(-4.19615 - 4.73205i) q^{70} -5.65685i q^{71} +(1.00000 + 1.00000i) q^{73} +(2.12132 - 3.67423i) q^{74} +(4.00000 + 6.92820i) q^{76} +(-2.07055 + 7.72741i) q^{77} +(10.3923 + 6.00000i) q^{79} +(0.707107 - 2.12132i) q^{80} +(-7.00000 + 7.00000i) q^{82} +(3.10583 + 11.5911i) q^{83} +(-7.46410 - 4.92820i) q^{85} +(-2.73205 + 0.732051i) q^{88} -9.89949 q^{89} -12.0000 q^{91} +(-3.86370 + 1.03528i) q^{92} +(3.58630 + 17.5254i) q^{95} +(-1.09808 - 4.09808i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7}+O(q^{10}) $ 8 * q - 8 * q^7	$ 8 q - 8 q^{7} - 16 q^{10} + 12 q^{13} + 4 q^{16} - 8 q^{22} + 16 q^{25} + 16 q^{28} - 16 q^{31} - 24 q^{37} + 4 q^{40} + 32 q^{46} - 12 q^{52} + 48 q^{55} - 4 q^{58} + 16 q^{67} + 8 q^{70} + 8 q^{73} + 32 q^{76} - 56 q^{82} - 32 q^{85} - 8 q^{88} - 96 q^{91} + 12 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 - 16 * q^10 + 12 * q^13 + 4 * q^16 - 8 * q^22 + 16 * q^25 + 16 * q^28 - 16 * q^31 - 24 * q^37 + 4 * q^40 + 32 * q^46 - 12 * q^52 + 48 * q^55 - 4 * q^58 + 16 * q^67 + 8 * q^70 + 8 * q^73 + 32 * q^76 - 56 * q^82 - 32 * q^85 - 8 * q^88 - 96 * q^91 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	2.19067	−	0.448288i	0.979698	−	0.200480i
$5$	2.19067	−	0.448288i	0.979698	−	0.200480i
$6$		0			0
$7$	0.732051	+	2.73205i	0.276689	+	1.03262i	0.954701	+	0.297567i	$0.0961752\pi$
$7$	0.732051	+	2.73205i	0.276689	+	1.03262i	−0.678012	+	0.735051i	$0.737158\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$	2.44949	+	1.41421i	0.738549	+	0.426401i	0.821541	−	0.570149i	$-0.193114\pi$
$11$	2.44949	+	1.41421i	0.738549	+	0.426401i	−0.0829925	+	0.996550i	$0.526448\pi$
$12$		0			0
$13$	−1.09808	+	4.09808i	−0.304552	+	1.13660i	0.628779	+	0.777584i	$0.283555\pi$
$13$	−1.09808	+	4.09808i	−0.304552	+	1.13660i	−0.933331	+	0.359018i	$0.883112\pi$
$14$	−1.41421	−	2.44949i	−0.377964	−	0.654654i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.82843	−	2.82843i	−0.685994	−	0.685994i	0.275350	−	0.961344i	$-0.411206\pi$
$17$	−2.82843	−	2.82843i	−0.685994	−	0.685994i	−0.961344	+	0.275350i	$0.911206\pi$
$18$		0			0
$19$			8.00000i			1.83533i	0.397360	+	0.917663i	$0.369927\pi$
$19$			8.00000i			1.83533i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	1.67303	−	1.48356i	0.374101	−	0.331735i
$21$		0			0
$22$	−2.73205	−	0.732051i	−0.582475	−	0.156074i
$23$	−3.86370	−	1.03528i	−0.805638	−	0.215870i	−0.167580	−	0.985858i	$-0.553595\pi$
$23$	−3.86370	−	1.03528i	−0.805638	−	0.215870i	−0.638058	+	0.769988i	$0.720262\pi$
$24$		0			0
$25$	4.59808	−	1.96410i	0.919615	−	0.392820i
$26$		−	4.24264i		−	0.832050i
$27$		0			0
$28$	2.00000	+	2.00000i	0.377964	+	0.377964i
$29$	−0.707107	+	1.22474i	−0.131306	+	0.227429i	−0.924180	−	0.381956i	$-0.875251\pi$
$29$	−0.707107	+	1.22474i	−0.131306	+	0.227429i	0.792874	+	0.609386i	$0.208584\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	3.46410	+	2.00000i	0.594089	+	0.342997i
$35$	2.82843	+	5.65685i	0.478091	+	0.956183i
$36$		0			0
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$	−2.07055	−	7.72741i	−0.335888	−	1.25355i
$39$		0			0
$40$	−1.23205	+	1.86603i	−0.194804	+	0.295045i
$41$	8.57321	−	4.94975i	1.33891	−	0.773021i	0.352265	−	0.935900i	$-0.385412\pi$
$41$	8.57321	−	4.94975i	1.33891	−	0.773021i	0.986646	+	0.162880i	$0.0520782\pi$
$42$		0			0
$43$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$43$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$44$	2.82843			0.426401
$45$		0			0
$46$	4.00000			0.589768
$47$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$47$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$48$		0			0
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−3.93305	+	3.08725i	−0.556218	+	0.436603i
$51$		0			0
$52$	1.09808	+	4.09808i	0.152276	+	0.568301i
$53$	−2.82843	+	2.82843i	−0.388514	+	0.388514i	−0.874157	−	0.485643i	$-0.838586\pi$
$53$	−2.82843	+	2.82843i	−0.388514	+	0.388514i	0.485643	+	0.874157i	$0.338586\pi$
$54$		0			0
$55$	6.00000	+	2.00000i	0.809040	+	0.269680i
$56$	−2.44949	−	1.41421i	−0.327327	−	0.188982i
$57$		0			0
$58$	0.366025	−	1.36603i	0.0480615	−	0.179368i
$59$	1.41421	+	2.44949i	0.184115	+	0.318896i	0.943278	−	0.332004i	$-0.107725\pi$
$59$	1.41421	+	2.44949i	0.184115	+	0.318896i	−0.759163	+	0.650901i	$0.774391\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	2.82843	+	2.82843i	0.359211	+	0.359211i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.568406	+	9.46979i	−0.0705021	+	1.17458i
$66$		0			0
$67$	5.46410	+	1.46410i	0.667546	+	0.178868i	0.576649	−	0.816992i	$-0.304360\pi$
$67$	5.46410	+	1.46410i	0.667546	+	0.178868i	0.0908970	+	0.995860i	$0.471027\pi$
$68$	−3.86370	−	1.03528i	−0.468543	−	0.125546i
$69$		0			0
$70$	−4.19615	−	4.73205i	−0.501536	−	0.565588i
$71$		−	5.65685i		−	0.671345i	−0.941979	−	0.335673i	$-0.891036\pi$
$71$		−	5.65685i		−	0.671345i	0.941979	−	0.335673i	$-0.108964\pi$
$72$		0			0
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	0.763202	−	0.646160i	$-0.223626\pi$
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	−0.646160	+	0.763202i	$0.723626\pi$
$74$	2.12132	−	3.67423i	0.246598	−	0.427121i
$75$		0			0
$76$	4.00000	+	6.92820i	0.458831	+	0.794719i
$77$	−2.07055	+	7.72741i	−0.235961	+	0.880620i
$78$		0			0
$79$	10.3923	+	6.00000i	1.16923	+	0.675053i	0.953498	−	0.301401i	$-0.0974542\pi$
$79$	10.3923	+	6.00000i	1.16923	+	0.675053i	0.215728	+	0.976453i	$0.430788\pi$
$80$	0.707107	−	2.12132i	0.0790569	−	0.237171i
$81$		0			0
$82$	−7.00000	+	7.00000i	−0.773021	+	0.773021i
$83$	3.10583	+	11.5911i	0.340909	+	1.27229i	0.897319	+	0.441382i	$0.145512\pi$
$83$	3.10583	+	11.5911i	0.340909	+	1.27229i	−0.556410	+	0.830908i	$0.687822\pi$
$84$		0			0
$85$	−7.46410	−	4.92820i	−0.809595	−	0.534539i
$86$		0			0
$87$		0			0
$88$	−2.73205	+	0.732051i	−0.291238	+	0.0780369i
$89$	−9.89949			−1.04934			−0.524672	−	0.851304i	$-0.675812\pi$
$89$	−9.89949			−1.04934			−0.524672	+	0.851304i	$0.675812\pi$
$90$		0			0
$91$	−12.0000			−1.25794
$92$	−3.86370	+	1.03528i	−0.402819	+	0.107935i
$93$		0			0
$94$		0			0
$95$	3.58630	+	17.5254i	0.367947	+	1.79806i
$96$		0			0
$97$	−1.09808	−	4.09808i	−0.111493	−	0.416097i	0.887508	−	0.460793i	$-0.152435\pi$
$97$	−1.09808	−	4.09808i	−0.111493	−	0.416097i	−0.999001	+	0.0446959i	$0.985768\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	1.22474	+	0.707107i	0.121867	+	0.0703598i	0.559694	−	0.828699i	$-0.310919\pi$
$101$	1.22474	+	0.707107i	0.121867	+	0.0703598i	−0.437828	+	0.899059i	$0.644252\pi$
$102$		0			0
$103$	−0.732051	+	2.73205i	−0.0721311	+	0.269197i	−0.992567	−	0.121695i	$-0.961167\pi$
$103$	−0.732051	+	2.73205i	−0.0721311	+	0.269197i	0.920436	+	0.390892i	$0.127834\pi$
$104$	−2.12132	−	3.67423i	−0.208013	−	0.360288i
$105$		0			0
$106$	2.00000	−	3.46410i	0.194257	−	0.336463i
$107$	14.1421	+	14.1421i	1.36717	+	1.36717i	0.864446	+	0.502726i	$0.167670\pi$
$107$	14.1421	+	14.1421i	1.36717	+	1.36717i	0.502726	+	0.864446i	$0.332330\pi$
$108$		0			0
$109$		−	8.00000i		−	0.766261i	−0.923694	−	0.383131i	$-0.874846\pi$
$109$		−	8.00000i		−	0.766261i	0.923694	−	0.383131i	$-0.125154\pi$
$110$	−6.31319	−	0.378937i	−0.601939	−	0.0361303i
$111$		0			0
$112$	2.73205	+	0.732051i	0.258155	+	0.0691723i
$113$	−1.93185	−	0.517638i	−0.181733	−	0.0486953i	0.166805	−	0.985990i	$-0.446655\pi$
$113$	−1.93185	−	0.517638i	−0.181733	−	0.0486953i	−0.348538	+	0.937295i	$0.613322\pi$
$114$		0			0
$115$	−8.92820	−	0.535898i	−0.832559	−	0.0499728i
$116$			1.41421i			0.131306i
$117$		0			0
$118$	−2.00000	−	2.00000i	−0.184115	−	0.184115i
$119$	5.65685	−	9.79796i	0.518563	−	0.898177i
$120$		0			0
$121$	−1.50000	−	2.59808i	−0.136364	−	0.236189i
$122$		0			0
$123$		0			0
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$	9.19239	−	6.36396i	0.822192	−	0.569210i
$126$		0			0
$127$	14.0000	−	14.0000i	1.24230	−	1.24230i	0.283254	−	0.959045i	$-0.408586\pi$
$127$	14.0000	−	14.0000i	1.24230	−	1.24230i	0.959045	−	0.283254i	$-0.0914140\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	−1.90192	−	9.29423i	−0.166810	−	0.815158i
$131$	12.2474	−	7.07107i	1.07006	−	0.617802i	0.141865	−	0.989886i	$-0.454690\pi$
$131$	12.2474	−	7.07107i	1.07006	−	0.617802i	0.928199	+	0.372084i	$0.121357\pi$
$132$		0			0
$133$	−21.8564	+	5.85641i	−1.89519	+	0.507815i
$134$	−5.65685			−0.488678
$135$		0			0
$136$	4.00000			0.342997
$137$	−5.79555	+	1.55291i	−0.495148	+	0.132674i	−0.497747	−	0.867322i	$-0.665839\pi$
$137$	−5.79555	+	1.55291i	−0.495148	+	0.132674i	0.00259945	+	0.999997i	$0.499173\pi$
$138$		0			0
$139$	3.46410	−	2.00000i	0.293821	−	0.169638i	−0.345843	−	0.938293i	$-0.612407\pi$
$139$	3.46410	−	2.00000i	0.293821	−	0.169638i	0.639664	+	0.768655i	$0.279074\pi$
$140$	5.27792	+	3.48477i	0.446065	+	0.294516i
$141$		0			0
$142$	1.46410	+	5.46410i	0.122865	+	0.458537i
$143$	−8.48528	+	8.48528i	−0.709575	+	0.709575i
$144$		0			0
$145$	−1.00000	+	3.00000i	−0.0830455	+	0.249136i
$146$	−1.22474	−	0.707107i	−0.101361	−	0.0585206i
$147$		0			0
$148$	−1.09808	+	4.09808i	−0.0902613	+	0.336860i
$149$	−10.6066	−	18.3712i	−0.868927	−	1.50503i	−0.863095	−	0.505042i	$-0.831477\pi$
$149$	−10.6066	−	18.3712i	−0.868927	−	1.50503i	−0.00583199	−	0.999983i	$-0.501856\pi$
$150$		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	$0.0611289\pi$
$152$	−5.65685	−	5.65685i	−0.458831	−	0.458831i
$153$		0			0
$154$		−	8.00000i		−	0.644658i
$155$	−5.93426	−	6.69213i	−0.476651	−	0.537525i
$156$		0			0
$157$	12.2942	+	3.29423i	0.981186	+	0.262908i	0.713544	−	0.700610i	$-0.247089\pi$
$157$	12.2942	+	3.29423i	0.981186	+	0.262908i	0.267642	+	0.963518i	$0.413756\pi$
$158$	−11.5911	−	3.10583i	−0.922139	−	0.247086i
$159$		0			0
$160$	−0.133975	+	2.23205i	−0.0105916	+	0.176459i
$161$		−	11.3137i		−	0.891645i
$162$		0			0
$163$	−16.0000	−	16.0000i	−1.25322	−	1.25322i	−0.954270	−	0.298947i	$-0.903365\pi$
$163$	−16.0000	−	16.0000i	−1.25322	−	1.25322i	−0.298947	−	0.954270i	$-0.596635\pi$
$164$	4.94975	−	8.57321i	0.386510	−	0.669456i
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	1.03528	−	3.86370i	0.0801121	−	0.298982i	−0.914232	−	0.405192i	$-0.867205\pi$
$167$	1.03528	−	3.86370i	0.0801121	−	0.298982i	0.994344	+	0.106209i	$0.0338714\pi$
$168$		0			0
$169$	−4.33013	−	2.50000i	−0.333087	−	0.192308i
$170$	8.48528	+	2.82843i	0.650791	+	0.216930i
$171$		0			0
$172$		0			0
$173$	−3.62347	−	13.5230i	−0.275487	−	1.02813i	−0.955514	−	0.294945i	$-0.904699\pi$
$173$	−3.62347	−	13.5230i	−0.275487	−	1.02813i	0.680027	−	0.733187i	$-0.261968\pi$
$174$		0			0
$175$	8.73205	+	11.1244i	0.660081	+	0.840922i
$176$	2.44949	−	1.41421i	0.184637	−	0.106600i
$177$		0			0
$178$	9.56218	−	2.56218i	0.716716	−	0.192043i
$179$	2.82843			0.211407			0.105703	−	0.994398i	$-0.466291\pi$
$179$	2.82843			0.211407			0.105703	+	0.994398i	$0.466291\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	11.5911	−	3.10583i	0.859190	−	0.230219i
$183$		0			0
$184$	3.46410	−	2.00000i	0.255377	−	0.147442i
$185$	−5.22715	+	7.91688i	−0.384308	+	0.582060i
$186$		0			0
$187$	−2.92820	−	10.9282i	−0.214131	−	0.799149i
$188$		0			0
$189$		0			0
$190$	−8.00000	−	16.0000i	−0.580381	−	1.16076i
$191$	19.5959	+	11.3137i	1.41791	+	0.818631i	0.996115	−	0.0880597i	$-0.0280666\pi$
$191$	19.5959	+	11.3137i	1.41791	+	0.818631i	0.421796	+	0.906691i	$0.361400\pi$
$192$		0			0
$193$	3.29423	−	12.2942i	0.237124	−	0.884958i	−0.740056	−	0.672545i	$-0.765201\pi$
$193$	3.29423	−	12.2942i	0.237124	−	0.884958i	0.977180	−	0.212413i	$-0.0681322\pi$
$194$	2.12132	+	3.67423i	0.152302	+	0.263795i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−12.7279	−	12.7279i	−0.906827	−	0.906827i	0.0891879	−	0.996015i	$-0.471573\pi$
$197$	−12.7279	−	12.7279i	−0.906827	−	0.906827i	−0.996015	+	0.0891879i	$0.971573\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−1.86250	+	4.64016i	−0.131699	+	0.328109i
$201$		0			0
$202$	−1.36603	−	0.366025i	−0.0961132	−	0.0257535i
$203$	−3.86370	−	1.03528i	−0.271179	−	0.0726621i
$204$		0			0
$205$	16.5622	−	14.6865i	1.15675	−	1.02575i
$206$		−	2.82843i		−	0.197066i
$207$		0			0
$208$	3.00000	+	3.00000i	0.208013	+	0.208013i
$209$	−11.3137	+	19.5959i	−0.782586	+	1.35548i
$210$		0			0
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	0.926620	−	0.375999i	$-0.122700\pi$
$211$	2.00000	+	3.46410i	0.137686	+	0.238479i	−0.788935	+	0.614477i	$0.789367\pi$
$212$	−1.03528	+	3.86370i	−0.0711031	+	0.265360i
$213$		0			0
$214$	−17.3205	−	10.0000i	−1.18401	−	0.683586i
$215$		0			0
$216$		0			0
$217$	8.00000	−	8.00000i	0.543075	−	0.543075i
$218$	2.07055	+	7.72741i	0.140236	+	0.523366i
$219$		0			0
$220$	6.19615	−	1.26795i	0.417745	−	0.0854851i
$221$	14.6969	−	8.48528i	0.988623	−	0.570782i
$222$		0			0
$223$	−8.19615	+	2.19615i	−0.548855	+	0.147065i	−0.522581	−	0.852590i	$-0.675031\pi$
$223$	−8.19615	+	2.19615i	−0.548855	+	0.147065i	−0.0262738	+	0.999655i	$0.508364\pi$
$224$	−2.82843			−0.188982
$225$		0			0
$226$	2.00000			0.133038
$227$	7.72741	−	2.07055i	0.512886	−	0.137427i	0.00691198	−	0.999976i	$-0.497800\pi$
$227$	7.72741	−	2.07055i	0.512886	−	0.137427i	0.505974	+	0.862549i	$0.331133\pi$
$228$		0			0
$229$	5.19615	−	3.00000i	0.343371	−	0.198246i	−0.318390	−	0.947960i	$-0.603142\pi$
$229$	5.19615	−	3.00000i	0.343371	−	0.198246i	0.661762	+	0.749714i	$0.269809\pi$
$230$	8.76268	−	1.79315i	0.577794	−	0.118237i
$231$		0			0
$232$	−0.366025	−	1.36603i	−0.0240307	−	0.0896840i
$233$	−8.48528	+	8.48528i	−0.555889	+	0.555889i	−0.928134	−	0.372245i	$-0.878588\pi$
$233$	−8.48528	+	8.48528i	−0.555889	+	0.555889i	0.372245	+	0.928134i	$0.378588\pi$
$234$		0			0
$235$		0			0
$236$	2.44949	+	1.41421i	0.159448	+	0.0920575i
$237$		0			0
$238$	−2.92820	+	10.9282i	−0.189807	+	0.708370i
$239$	−8.48528	−	14.6969i	−0.548867	−	0.950666i	−0.998353	−	0.0573782i	$-0.981726\pi$
$239$	−8.48528	−	14.6969i	−0.548867	−	0.950666i	0.449485	−	0.893288i	$-0.351607\pi$
$240$		0			0
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	0.256814	+	0.966461i	$0.417327\pi$
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	−0.965387	+	0.260822i	$0.916006\pi$
$242$	2.12132	+	2.12132i	0.136364	+	0.136364i
$243$		0			0
$244$		0			0
$245$	−1.67303	+	1.48356i	−0.106886	+	0.0947814i
$246$		0			0
$247$	−32.7846	−	8.78461i	−2.08603	−	0.558951i
$248$	3.86370	+	1.03528i	0.245345	+	0.0657401i
$249$		0			0
$250$	−7.23205	+	8.52628i	−0.457395	+	0.539249i
$251$		−	8.48528i		−	0.535586i	−0.963476	−	0.267793i	$-0.913706\pi$
$251$		−	8.48528i		−	0.535586i	0.963476	−	0.267793i	$-0.0862944\pi$
$252$		0			0
$253$	−8.00000	−	8.00000i	−0.502956	−	0.502956i
$254$	−9.89949	+	17.1464i	−0.621150	+	1.07586i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.62347	+	13.5230i	−0.226026	+	0.843539i	0.755965	+	0.654612i	$0.227168\pi$
$257$	−3.62347	+	13.5230i	−0.226026	+	0.843539i	−0.981991	+	0.188928i	$0.939499\pi$
$258$		0			0
$259$	−10.3923	−	6.00000i	−0.645746	−	0.372822i
$260$	4.24264	+	8.48528i	0.263117	+	0.526235i
$261$		0			0
$262$	−10.0000	+	10.0000i	−0.617802	+	0.617802i
$263$	−7.24693	−	27.0459i	−0.446865	−	1.66772i	−0.710965	−	0.703228i	$-0.751741\pi$
$263$	−7.24693	−	27.0459i	−0.446865	−	1.66772i	0.264100	−	0.964495i	$-0.414925\pi$
$264$		0			0
$265$	−4.92820	+	7.46410i	−0.302737	+	0.458516i
$266$	19.5959	−	11.3137i	1.20150	−	0.693688i
$267$		0			0
$268$	5.46410	−	1.46410i	0.333773	−	0.0894342i
$269$	−15.5563			−0.948487			−0.474244	−	0.880394i	$-0.657278\pi$
$269$	−15.5563			−0.948487			−0.474244	+	0.880394i	$0.657278\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−3.86370	+	1.03528i	−0.234271	+	0.0627728i
$273$		0			0
$274$	5.19615	−	3.00000i	0.313911	−	0.181237i
$275$	14.0406	+	1.69161i	0.846680	+	0.102008i
$276$		0			0
$277$	3.29423	+	12.2942i	0.197931	+	0.738689i	0.991489	+	0.130193i	$0.0415598\pi$
$277$	3.29423	+	12.2942i	0.197931	+	0.738689i	−0.793558	+	0.608495i	$0.791773\pi$
$278$	−2.82843	+	2.82843i	−0.169638	+	0.169638i
$279$		0			0
$280$	−6.00000	−	2.00000i	−0.358569	−	0.119523i
$281$	−11.0227	−	6.36396i	−0.657559	−	0.379642i	0.133787	−	0.991010i	$-0.457286\pi$
$281$	−11.0227	−	6.36396i	−0.657559	−	0.379642i	−0.791346	+	0.611368i	$0.790620\pi$
$282$		0			0
$283$	2.92820	−	10.9282i	0.174064	−	0.649614i	−0.822646	−	0.568554i	$-0.807503\pi$
$283$	2.92820	−	10.9282i	0.174064	−	0.649614i	0.996709	−	0.0810598i	$-0.0258305\pi$
$284$	−2.82843	−	4.89898i	−0.167836	−	0.290701i
$285$		0			0
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$	19.7990	+	19.7990i	1.16870	+	1.16870i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	0.189469	−	3.15660i	0.0111260	−	0.185362i
$291$		0			0
$292$	1.36603	+	0.366025i	0.0799406	+	0.0214200i
$293$	−17.3867	−	4.65874i	−1.01574	−	0.272167i	−0.287714	−	0.957716i	$-0.592895\pi$
$293$	−17.3867	−	4.65874i	−1.01574	−	0.272167i	−0.728026	+	0.685550i	$0.759562\pi$
$294$		0			0
$295$	4.19615	+	4.73205i	0.244309	+	0.275511i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	15.0000	+	15.0000i	0.868927	+	0.868927i
$299$	8.48528	−	14.6969i	0.490716	−	0.849946i
$300$		0			0
$301$		0			0
$302$	−2.07055	+	7.72741i	−0.119147	+	0.444662i
$303$		0			0
$304$	6.92820	+	4.00000i	0.397360	+	0.229416i
$305$		0			0
$306$		0			0
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	2.07055	+	7.72741i	0.117981	+	0.440310i
$309$		0			0
$310$	7.46410	+	4.92820i	0.423932	+	0.279903i
$311$	−19.5959	+	11.3137i	−1.11118	+	0.641542i	−0.939135	−	0.343547i	$-0.888371\pi$
$311$	−19.5959	+	11.3137i	−1.11118	+	0.641542i	−0.172047	+	0.985089i	$0.555038\pi$
$312$		0			0
$313$	28.6865	−	7.68653i	1.62146	−	0.434469i	0.670029	−	0.742335i	$-0.266282\pi$
$313$	28.6865	−	7.68653i	1.62146	−	0.434469i	0.951430	+	0.307866i	$0.0996149\pi$
$314$	−12.7279			−0.718278
$315$		0			0
$316$	12.0000			0.675053
$317$	−11.5911	+	3.10583i	−0.651022	+	0.174441i	−0.569191	−	0.822206i	$-0.692743\pi$
$317$	−11.5911	+	3.10583i	−0.651022	+	0.174441i	−0.0818309	+	0.996646i	$0.526077\pi$
$318$		0			0
$319$	−3.46410	+	2.00000i	−0.193952	+	0.111979i
$320$	−0.448288	−	2.19067i	−0.0250600	−	0.122462i
$321$		0			0
$322$	2.92820	+	10.9282i	0.163182	+	0.609005i
$323$	22.6274	−	22.6274i	1.25902	−	1.25902i
$324$		0			0
$325$	3.00000	+	21.0000i	0.166410	+	1.16487i
$326$	19.5959	+	11.3137i	1.08532	+	0.626608i
$327$		0			0
$328$	−2.56218	+	9.56218i	−0.141473	+	0.527983i
$329$		0			0
$330$		0			0
$331$	−8.00000	+	13.8564i	−0.439720	+	0.761617i	−0.997668	−	0.0682590i	$-0.978256\pi$
$331$	−8.00000	+	13.8564i	−0.439720	+	0.761617i	0.557948	+	0.829876i	$0.311589\pi$
$332$	8.48528	+	8.48528i	0.465690	+	0.465690i
$333$		0			0
$334$			4.00000i			0.218870i
$335$	12.6264	+	0.757875i	0.689853	+	0.0414071i
$336$		0			0
$337$	28.6865	+	7.68653i	1.56266	+	0.418712i	0.933503	−	0.358570i	$-0.116736\pi$
$337$	28.6865	+	7.68653i	1.56266	+	0.418712i	0.629152	+	0.777282i	$0.283402\pi$
$338$	4.82963	+	1.29410i	0.262697	+	0.0703895i
$339$		0			0
$340$	−8.92820	−	0.535898i	−0.484200	−	0.0290632i
$341$		−	11.3137i		−	0.612672i
$342$		0			0
$343$	12.0000	+	12.0000i	0.647939	+	0.647939i
$344$		0			0
$345$		0			0
$346$	7.00000	+	12.1244i	0.376322	+	0.651809i
$347$	−4.14110	+	15.4548i	−0.222306	+	0.829658i	0.761160	+	0.648564i	$0.224630\pi$
$347$	−4.14110	+	15.4548i	−0.222306	+	0.829658i	−0.983466	+	0.181093i	$0.942036\pi$
$348$		0			0
$349$	13.8564	+	8.00000i	0.741716	+	0.428230i	0.822693	−	0.568486i	$-0.192471\pi$
$349$	13.8564	+	8.00000i	0.741716	+	0.428230i	−0.0809766	+	0.996716i	$0.525804\pi$
$350$	−11.3137	−	8.48528i	−0.604743	−	0.453557i
$351$		0			0
$352$	−2.00000	+	2.00000i	−0.106600	+	0.106600i
$353$	−3.10583	−	11.5911i	−0.165307	−	0.616933i	−0.998001	−	0.0631996i	$-0.979870\pi$
$353$	−3.10583	−	11.5911i	−0.165307	−	0.616933i	0.832694	−	0.553733i	$-0.186797\pi$
$354$		0			0
$355$	−2.53590	−	12.3923i	−0.134592	−	0.657715i
$356$	−8.57321	+	4.94975i	−0.454379	+	0.262336i
$357$		0			0
$358$	−2.73205	+	0.732051i	−0.144393	+	0.0386901i
$359$	11.3137			0.597115			0.298557	−	0.954392i	$-0.403495\pi$
$359$	11.3137			0.597115			0.298557	+	0.954392i	$0.403495\pi$
$360$		0			0
$361$	−45.0000			−2.36842
$362$	−7.72741	+	2.07055i	−0.406143	+	0.108826i
$363$		0			0
$364$	−10.3923	+	6.00000i	−0.544705	+	0.314485i
$365$	2.63896	+	1.74238i	0.138129	+	0.0912005i
$366$		0			0
$367$	−8.05256	−	30.0526i	−0.420340	−	1.56873i	−0.773893	−	0.633316i	$-0.781693\pi$
$367$	−8.05256	−	30.0526i	−0.420340	−	1.56873i	0.353553	−	0.935415i	$-0.384973\pi$
$368$	−2.82843	+	2.82843i	−0.147442	+	0.147442i
$369$		0			0
$370$	3.00000	−	9.00000i	0.155963	−	0.467888i
$371$	−9.79796	−	5.65685i	−0.508685	−	0.293689i
$372$		0			0
$373$	−1.83013	+	6.83013i	−0.0947604	+	0.353651i	−0.996983	−	0.0776200i	$-0.975268\pi$
$373$	−1.83013	+	6.83013i	−0.0947604	+	0.353651i	0.902223	+	0.431271i	$0.141935\pi$
$374$	5.65685	+	9.79796i	0.292509	+	0.506640i
$375$		0			0
$376$		0			0
$377$	−4.24264	−	4.24264i	−0.218507	−	0.218507i
$378$		0			0
$379$			20.0000i			1.02733i	0.857991	+	0.513665i	$0.171713\pi$
$379$			20.0000i			1.02733i	−0.857991	+	0.513665i	$0.828287\pi$
$380$	11.8685	+	13.3843i	0.608842	+	0.686598i
$381$		0			0
$382$	−21.8564	−	5.85641i	−1.11827	−	0.299640i
$383$	−23.1822	−	6.21166i	−1.18456	−	0.317401i	−0.387824	−	0.921733i	$-0.626773\pi$
$383$	−23.1822	−	6.21166i	−1.18456	−	0.317401i	−0.796732	+	0.604333i	$0.793440\pi$
$384$		0			0
$385$	−1.07180	+	17.8564i	−0.0546238	+	0.910047i
$386$			12.7279i			0.647834i
$387$		0			0
$388$	−3.00000	−	3.00000i	−0.152302	−	0.152302i
$389$	10.6066	−	18.3712i	0.537776	−	0.931455i	−0.461247	−	0.887272i	$-0.652598\pi$
$389$	10.6066	−	18.3712i	0.537776	−	0.931455i	0.999023	−	0.0441839i	$-0.0140687\pi$
$390$		0			0
$391$	8.00000	+	13.8564i	0.404577	+	0.700749i
$392$	0.258819	−	0.965926i	0.0130723	−	0.0487866i
$393$		0			0
$394$	15.5885	+	9.00000i	0.785335	+	0.453413i
$395$	25.4558	+	8.48528i	1.28082	+	0.426941i
$396$		0			0
$397$	7.00000	−	7.00000i	0.351320	−	0.351320i	−0.509281	−	0.860601i	$-0.670088\pi$
$397$	7.00000	−	7.00000i	0.351320	−	0.351320i	0.860601	+	0.509281i	$0.170088\pi$
$398$		0			0
$399$		0			0
$400$	0.598076	−	4.96410i	0.0299038	−	0.248205i
$401$	11.0227	−	6.36396i	0.550448	−	0.317801i	−0.198855	−	0.980029i	$-0.563722\pi$
$401$	11.0227	−	6.36396i	0.550448	−	0.317801i	0.749302	+	0.662228i	$0.230389\pi$
$402$		0			0
$403$	16.3923	−	4.39230i	0.816559	−	0.218796i
$404$	1.41421			0.0703598
$405$		0			0
$406$	4.00000			0.198517
$407$	−11.5911	+	3.10583i	−0.574550	+	0.153950i
$408$		0			0
$409$	−20.7846	+	12.0000i	−1.02773	+	0.593362i	−0.916334	−	0.400414i	$-0.868866\pi$
$409$	−20.7846	+	12.0000i	−1.02773	+	0.593362i	−0.111398	+	0.993776i	$0.535533\pi$
$410$	−12.1967	+	18.4727i	−0.602351	+	0.912302i
$411$		0			0
$412$	0.732051	+	2.73205i	0.0360656	+	0.134598i
$413$	−5.65685	+	5.65685i	−0.278356	+	0.278356i
$414$		0			0
$415$	12.0000	+	24.0000i	0.589057	+	1.17811i
$416$	−3.67423	−	2.12132i	−0.180144	−	0.104006i
$417$		0			0
$418$	5.85641	−	21.8564i	0.286446	−	1.06903i
$419$	12.7279	+	22.0454i	0.621800	+	1.07699i	0.989150	+	0.146906i	$0.0469315\pi$
$419$	12.7279	+	22.0454i	0.621800	+	1.07699i	−0.367351	+	0.930082i	$0.619735\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	−2.82843	−	2.82843i	−0.137686	−	0.137686i
$423$		0			0
$424$		−	4.00000i		−	0.194257i
$425$	−18.5606	−	7.45001i	−0.900323	−	0.361378i
$426$		0			0
$427$		0			0
$428$	19.3185	+	5.17638i	0.933796	+	0.250210i
$429$		0			0
$430$		0			0
$431$			39.5980i			1.90737i	0.300811	+	0.953684i	$0.402743\pi$
$431$			39.5980i			1.90737i	−0.300811	+	0.953684i	$0.597257\pi$
$432$		0			0
$433$	23.0000	+	23.0000i	1.10531	+	1.10531i	0.993759	+	0.111551i	$0.0355818\pi$
$433$	23.0000	+	23.0000i	1.10531	+	1.10531i	0.111551	+	0.993759i	$0.464418\pi$
$434$	−5.65685	+	9.79796i	−0.271538	+	0.470317i
$435$		0			0
$436$	−4.00000	−	6.92820i	−0.191565	−	0.331801i
$437$	8.28221	−	30.9096i	0.396192	−	1.47861i
$438$		0			0
$439$	6.92820	+	4.00000i	0.330665	+	0.190910i	0.656136	−	0.754642i	$-0.272190\pi$
$439$	6.92820	+	4.00000i	0.330665	+	0.190910i	−0.325471	+	0.945552i	$0.605523\pi$
$440$	−5.65685	+	2.82843i	−0.269680	+	0.134840i
$441$		0			0
$442$	−12.0000	+	12.0000i	−0.570782	+	0.570782i
$443$	6.21166	+	23.1822i	0.295125	+	1.10142i	0.941118	+	0.338078i	$0.109777\pi$
$443$	6.21166	+	23.1822i	0.295125	+	1.10142i	−0.645994	+	0.763343i	$0.723557\pi$
$444$		0			0
$445$	−21.6865	+	4.43782i	−1.02804	+	0.210373i
$446$	7.34847	−	4.24264i	0.347960	−	0.200895i
$447$		0			0
$448$	2.73205	−	0.732051i	0.129077	−	0.0345861i
$449$	1.41421			0.0667409			0.0333704	−	0.999443i	$-0.489376\pi$
$449$	1.41421			0.0667409			0.0333704	+	0.999443i	$0.489376\pi$
$450$		0			0
$451$	28.0000			1.31847
$452$	−1.93185	+	0.517638i	−0.0908667	+	0.0243476i
$453$		0			0
$454$	−6.92820	+	4.00000i	−0.325157	+	0.187729i
$455$	−26.2880	+	5.37945i	−1.23240	+	0.252193i
$456$		0			0
$457$	−5.49038	−	20.4904i	−0.256829	−	0.958500i	−0.967064	−	0.254534i	$-0.918078\pi$
$457$	−5.49038	−	20.4904i	−0.256829	−	0.958500i	0.710235	−	0.703965i	$-0.248589\pi$
$458$	−4.24264	+	4.24264i	−0.198246	+	0.198246i
$459$		0			0
$460$	−8.00000	+	4.00000i	−0.373002	+	0.186501i
$461$	−15.9217	−	9.19239i	−0.741547	−	0.428132i	0.0810847	−	0.996707i	$-0.474162\pi$
$461$	−15.9217	−	9.19239i	−0.741547	−	0.428132i	−0.822631	+	0.568575i	$0.807495\pi$
$462$		0			0
$463$	5.12436	−	19.1244i	0.238149	−	0.888784i	−0.738555	−	0.674193i	$-0.764491\pi$
$463$	5.12436	−	19.1244i	0.238149	−	0.888784i	0.976704	−	0.214591i	$-0.0688418\pi$
$464$	0.707107	+	1.22474i	0.0328266	+	0.0568574i
$465$		0			0
$466$	6.00000	−	10.3923i	0.277945	−	0.481414i
$467$	−19.7990	−	19.7990i	−0.916188	−	0.916188i	0.0805616	−	0.996750i	$-0.474329\pi$
$467$	−19.7990	−	19.7990i	−0.916188	−	0.916188i	−0.996750	+	0.0805616i	$0.974329\pi$
$468$		0			0
$469$			16.0000i			0.738811i
$470$		0			0
$471$		0			0
$472$	−2.73205	−	0.732051i	−0.125753	−	0.0336954i
$473$		0			0
$474$		0			0
$475$	15.7128	+	36.7846i	0.720953	+	1.68779i
$476$		−	11.3137i		−	0.518563i
$477$		0			0
$478$	12.0000	+	12.0000i	0.548867	+	0.548867i
$479$	−2.82843	+	4.89898i	−0.129234	+	0.223840i	−0.923380	−	0.383887i	$-0.874585\pi$
$479$	−2.82843	+	4.89898i	−0.129234	+	0.223840i	0.794146	+	0.607727i	$0.207919\pi$
$480$		0			0
$481$	−9.00000	−	15.5885i	−0.410365	−	0.710772i
$482$	5.69402	−	21.2504i	0.259355	−	0.967928i
$483$		0			0
$484$	−2.59808	−	1.50000i	−0.118094	−	0.0681818i
$485$	−4.24264	−	8.48528i	−0.192648	−	0.385297i
$486$		0			0
$487$	−18.0000	+	18.0000i	−0.815658	+	0.815658i	−0.985476	−	0.169818i	$-0.945682\pi$
$487$	−18.0000	+	18.0000i	−0.815658	+	0.815658i	0.169818	+	0.985476i	$0.445682\pi$
$488$		0			0
$489$		0			0
$490$	1.23205	−	1.86603i	0.0556584	−	0.0842984i
$491$	2.44949	−	1.41421i	0.110544	−	0.0638226i	−0.443709	−	0.896171i	$-0.646337\pi$
$491$	2.44949	−	1.41421i	0.110544	−	0.0638226i	0.554253	+	0.832349i	$0.313004\pi$
$492$		0			0
$493$	5.46410	−	1.46410i	0.246091	−	0.0659398i
$494$	33.9411			1.52708
$495$		0			0
$496$	−4.00000			−0.179605
$497$	15.4548	−	4.14110i	0.693243	−	0.185754i
$498$		0			0
$499$	−27.7128	+	16.0000i	−1.24060	+	0.716258i	−0.969216	−	0.246214i	$-0.920813\pi$
$499$	−27.7128	+	16.0000i	−1.24060	+	0.716258i	−0.271380	+	0.962472i	$0.587480\pi$
$500$	4.77886	−	10.1075i	0.213717	−	0.452023i
$501$		0			0
$502$	2.19615	+	8.19615i	0.0980191	+	0.365812i
$503$	−16.9706	+	16.9706i	−0.756680	+	0.756680i	−0.975717	−	0.219037i	$-0.929709\pi$
$503$	−16.9706	+	16.9706i	−0.756680	+	0.756680i	0.219037	+	0.975717i	$0.429709\pi$
$504$		0			0
$505$	3.00000	+	1.00000i	0.133498	+	0.0444994i
$506$	9.79796	+	5.65685i	0.435572	+	0.251478i
$507$		0			0
$508$	5.12436	−	19.1244i	0.227357	−	0.848506i
$509$	12.0208	+	20.8207i	0.532813	+	0.922860i	0.999266	+	0.0383134i	$0.0121985\pi$
$509$	12.0208	+	20.8207i	0.532813	+	0.922860i	−0.466453	+	0.884546i	$0.654468\pi$
$510$		0			0
$511$	−2.00000	+	3.46410i	−0.0884748	+	0.153243i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	14.0000i		−	0.617514i
$515$	−0.378937	+	6.31319i	−0.0166980	+	0.278193i
$516$		0			0
$517$		0			0
$518$	11.5911	+	3.10583i	0.509284	+	0.136462i
$519$		0			0
$520$	−6.29423	−	7.09808i	−0.276020	−	0.311271i
$521$		−	29.6985i		−	1.30111i	−0.759457	−	0.650557i	$-0.774535\pi$
$521$		−	29.6985i		−	1.30111i	0.759457	−	0.650557i	$-0.225465\pi$
$522$		0			0
$523$	−24.0000	−	24.0000i	−1.04945	−	1.04945i	−0.998712	−	0.0507346i	$-0.983844\pi$
$523$	−24.0000	−	24.0000i	−1.04945	−	1.04945i	−0.0507346	−	0.998712i	$-0.516156\pi$
$524$	7.07107	−	12.2474i	0.308901	−	0.535032i
$525$		0			0
$526$	14.0000	+	24.2487i	0.610429	+	1.05729i
$527$	−4.14110	+	15.4548i	−0.180389	+	0.673222i
$528$		0			0
$529$	−6.06218	−	3.50000i	−0.263573	−	0.152174i
$530$	2.82843	−	8.48528i	0.122859	−	0.368577i
$531$		0			0
$532$	−16.0000	+	16.0000i	−0.693688	+	0.693688i
$533$	10.8704	+	40.5689i	0.470849	+	1.75723i
$534$		0			0
$535$	37.3205	+	24.6410i	1.61351	+	1.06532i
$536$	−4.89898	+	2.82843i	−0.211604	+	0.122169i
$537$		0			0
$538$	15.0263	−	4.02628i	0.647829	−	0.173585i
$539$	−2.82843			−0.121829
$540$		0			0
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$		0			0
$543$		0			0
$544$	3.46410	−	2.00000i	0.148522	−	0.0857493i
$545$	−3.58630	−	17.5254i	−0.153620	−	0.750704i
$546$		0			0
$547$	4.39230	+	16.3923i	0.187801	+	0.700884i	0.994013	+	0.109258i	$0.0348474\pi$
$547$	4.39230	+	16.3923i	0.187801	+	0.700884i	−0.806212	+	0.591627i	$0.798486\pi$
$548$	−4.24264	+	4.24264i	−0.181237	+	0.181237i
$549$		0			0
$550$	−14.0000	+	2.00000i	−0.596962	+	0.0852803i
$551$	−9.79796	−	5.65685i	−0.417407	−	0.240990i
$552$		0			0
$553$	−8.78461	+	32.7846i	−0.373560	+	1.39414i
$554$	−6.36396	−	11.0227i	−0.270379	−	0.468310i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	−8.48528	−	8.48528i	−0.359533	−	0.359533i	0.504108	−	0.863641i	$-0.331821\pi$
$557$	−8.48528	−	8.48528i	−0.359533	−	0.359533i	−0.863641	+	0.504108i	$0.831821\pi$
$558$		0			0
$559$		0			0
$560$	6.31319	+	0.378937i	0.266781	+	0.0160130i
$561$		0			0
$562$	12.2942	+	3.29423i	0.518601	+	0.138959i
$563$	23.1822	+	6.21166i	0.977014	+	0.261790i	0.711787	−	0.702396i	$-0.247886\pi$
$563$	23.1822	+	6.21166i	0.977014	+	0.261790i	0.265227	+	0.964186i	$0.414553\pi$
$564$		0			0
$565$	−4.46410	−	0.267949i	−0.187806	−	0.0112727i
$566$			11.3137i			0.475551i
$567$		0			0
$568$	4.00000	+	4.00000i	0.167836	+	0.167836i
$569$	9.19239	−	15.9217i	0.385365	−	0.667472i	−0.606455	−	0.795118i	$-0.707409\pi$
$569$	9.19239	−	15.9217i	0.385365	−	0.667472i	0.991820	+	0.127646i	$0.0407422\pi$
$570$		0			0
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	0.770108	−	0.637913i	$-0.220202\pi$
$571$	−4.00000	−	6.92820i	−0.167395	−	0.289936i	−0.937503	+	0.347977i	$0.886869\pi$
$572$	−3.10583	+	11.5911i	−0.129861	+	0.484649i
$573$		0			0
$574$	−24.2487	−	14.0000i	−1.01212	−	0.584349i
$575$	−19.7990	+	2.82843i	−0.825675	+	0.117954i
$576$		0			0
$577$	31.0000	−	31.0000i	1.29055	−	1.29055i	0.356098	−	0.934448i	$-0.384107\pi$
$577$	31.0000	−	31.0000i	1.29055	−	1.29055i	0.934448	−	0.356098i	$-0.115893\pi$
$578$	0.258819	+	0.965926i	0.0107655	+	0.0401772i
$579$		0			0
$580$	0.633975	+	3.09808i	0.0263244	+	0.128641i
$581$	−29.3939	+	16.9706i	−1.21946	+	0.704058i
$582$		0			0
$583$	−10.9282	+	2.92820i	−0.452600	+	0.121274i
$584$	−1.41421			−0.0585206
$585$		0			0
$586$	18.0000			0.743573
$587$	34.7733	−	9.31749i	1.43525	−	0.384574i	0.544382	−	0.838838i	$-0.316764\pi$
$587$	34.7733	−	9.31749i	1.43525	−	0.384574i	0.890867	+	0.454264i	$0.150098\pi$
$588$		0			0
$589$	27.7128	−	16.0000i	1.14189	−	0.659269i
$590$	−5.27792	−	3.48477i	−0.217288	−	0.143466i
$591$		0			0
$592$	1.09808	+	4.09808i	0.0451307	+	0.168430i
$593$	24.0416	−	24.0416i	0.987271	−	0.987271i	−0.0126486	−	0.999920i	$-0.504026\pi$
$593$	24.0416	−	24.0416i	0.987271	−	0.987271i	0.999920	+	0.0126486i	$0.00402627\pi$
$594$		0			0
$595$	8.00000	−	24.0000i	0.327968	−	0.983904i
$596$	−18.3712	−	10.6066i	−0.752513	−	0.434463i
$597$		0			0
$598$	−4.39230	+	16.3923i	−0.179615	+	0.670331i
$599$	−19.7990	−	34.2929i	−0.808965	−	1.40117i	−0.913582	−	0.406656i	$-0.866695\pi$
$599$	−19.7990	−	34.2929i	−0.808965	−	1.40117i	0.104617	−	0.994513i	$-0.466638\pi$
$600$		0			0
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	−0.936002	−	0.351996i	$-0.885503\pi$
$601$	−4.00000	+	6.92820i	−0.163163	+	0.282607i	0.772838	+	0.634603i	$0.218836\pi$
$602$		0			0
$603$		0			0
$604$		−	8.00000i		−	0.325515i
$605$	−4.45069	−	5.01910i	−0.180946	−	0.204055i
$606$		0			0
$607$	8.19615	+	2.19615i	0.332672	+	0.0891391i	0.421288	−	0.906927i	$-0.361578\pi$
$607$	8.19615	+	2.19615i	0.332672	+	0.0891391i	−0.0886169	+	0.996066i	$0.528245\pi$
$608$	−7.72741	−	2.07055i	−0.313388	−	0.0839720i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−3.00000	−	3.00000i	−0.121169	−	0.121169i	0.643922	−	0.765091i	$-0.277306\pi$
$613$	−3.00000	−	3.00000i	−0.121169	−	0.121169i	−0.765091	+	0.643922i	$0.777306\pi$
$614$		0			0
$615$		0			0
$616$	−4.00000	−	6.92820i	−0.161165	−	0.279145i
$617$	9.31749	−	34.7733i	0.375108	−	1.39992i	−0.478079	−	0.878317i	$-0.658667\pi$
$617$	9.31749	−	34.7733i	0.375108	−	1.39992i	0.853187	−	0.521605i	$-0.174666\pi$
$618$		0			0
$619$	−10.3923	−	6.00000i	−0.417702	−	0.241160i	0.276392	−	0.961045i	$-0.410861\pi$
$619$	−10.3923	−	6.00000i	−0.417702	−	0.241160i	−0.694094	+	0.719885i	$0.744195\pi$
$620$	−8.48528	−	2.82843i	−0.340777	−	0.113592i
$621$		0			0
$622$	16.0000	−	16.0000i	0.641542	−	0.641542i
$623$	−7.24693	−	27.0459i	−0.290342	−	1.08357i
$624$		0			0
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$	−25.7196	+	14.8492i	−1.02796	+	0.593495i
$627$		0			0
$628$	12.2942	−	3.29423i	0.490593	−	0.131454i
$629$	16.9706			0.676661
$630$		0			0
$631$	−20.0000			−0.796187			−0.398094	−	0.917345i	$-0.630328\pi$
$631$	−20.0000			−0.796187			−0.398094	+	0.917345i	$0.630328\pi$
$632$	−11.5911	+	3.10583i	−0.461070	+	0.123543i
$633$		0			0
$634$	10.3923	−	6.00000i	0.412731	−	0.238290i
$635$	24.3934	−	36.9454i	0.968021	−	1.46613i
$636$		0			0
$637$	−1.09808	−	4.09808i	−0.0435074	−	0.162372i
$638$	2.82843	−	2.82843i	0.111979	−	0.111979i
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	15.9217	+	9.19239i	0.628869	+	0.363078i	0.780314	−	0.625388i	$-0.215059\pi$
$641$	15.9217	+	9.19239i	0.628869	+	0.363078i	−0.151445	+	0.988466i	$0.548393\pi$
$642$		0			0
$643$	4.39230	−	16.3923i	0.173216	−	0.646449i	−0.823633	−	0.567123i	$-0.808056\pi$
$643$	4.39230	−	16.3923i	0.173216	−	0.646449i	0.996849	−	0.0793264i	$-0.0252769\pi$
$644$	−5.65685	−	9.79796i	−0.222911	−	0.386094i
$645$		0			0
$646$	−16.0000	+	27.7128i	−0.629512	+	1.09035i
$647$	11.3137	+	11.3137i	0.444788	+	0.444788i	0.893617	−	0.448830i	$-0.148159\pi$
$647$	11.3137	+	11.3137i	0.444788	+	0.444788i	−0.448830	+	0.893617i	$0.648159\pi$
$648$		0			0
$649$			8.00000i			0.314027i
$650$	−8.33298	−	19.5080i	−0.326846	−	0.765166i
$651$		0			0
$652$	−21.8564	−	5.85641i	−0.855963	−	0.229355i
$653$	34.7733	+	9.31749i	1.36079	+	0.364621i	0.864105	−	0.503312i	$-0.167885\pi$
$653$	34.7733	+	9.31749i	1.36079	+	0.364621i	0.496681	+	0.867933i	$0.334552\pi$
$654$		0			0
$655$	23.6603	−	20.9808i	0.924483	−	0.819786i
$656$		−	9.89949i		−	0.386510i
$657$		0			0
$658$		0			0
$659$	−1.41421	+	2.44949i	−0.0550899	+	0.0954186i	−0.892255	−	0.451531i	$-0.850878\pi$
$659$	−1.41421	+	2.44949i	−0.0550899	+	0.0954186i	0.837165	+	0.546950i	$0.184211\pi$
$660$		0			0
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	4.14110	−	15.4548i	0.160949	−	0.600668i
$663$		0			0
$664$	−10.3923	−	6.00000i	−0.403300	−	0.232845i
$665$	−45.2548	+	22.6274i	−1.75491	+	0.877454i
$666$		0			0
$667$	4.00000	−	4.00000i	0.154881	−	0.154881i
$668$	−1.03528	−	3.86370i	−0.0400560	−	0.149491i
$669$		0			0
$670$	−12.3923	+	2.53590i	−0.478757	+	0.0979703i
$671$		0			0
$672$		0			0
$673$	−34.1506	+	9.15064i	−1.31641	+	0.352731i	−0.847632	−	0.530585i	$-0.821972\pi$
$673$	−34.1506	+	9.15064i	−1.31641	+	0.352731i	−0.468778	+	0.883316i	$0.655306\pi$
$674$	−29.6985			−1.14394
$675$		0			0
$676$	−5.00000			−0.192308
$677$	−19.3185	+	5.17638i	−0.742471	+	0.198944i	−0.610176	−	0.792266i	$-0.708901\pi$
$677$	−19.3185	+	5.17638i	−0.742471	+	0.198944i	−0.132295	+	0.991210i	$0.542235\pi$
$678$		0			0
$679$	10.3923	−	6.00000i	0.398820	−	0.230259i
$680$	8.76268	−	1.79315i	0.336034	−	0.0687642i
$681$		0			0
$682$	2.92820	+	10.9282i	0.112127	+	0.418463i
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	−0.525879	−	0.850559i	$-0.676264\pi$
$683$	8.48528	−	8.48528i	0.324680	−	0.324680i	0.850559	+	0.525879i	$0.176264\pi$
$684$		0			0
$685$	−12.0000	+	6.00000i	−0.458496	+	0.229248i
$686$	−14.6969	−	8.48528i	−0.561132	−	0.323970i
$687$		0			0
$688$		0			0
$689$	−8.48528	−	14.6969i	−0.323263	−	0.559909i
$690$		0			0
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	−9.89949	−	9.89949i	−0.376322	−	0.376322i
$693$		0			0
$694$		−	16.0000i		−	0.607352i
$695$	6.69213	−	5.93426i	0.253847	−	0.225099i
$696$		0			0
$697$	−38.2487	−	10.2487i	−1.44877	−	0.388198i
$698$	−15.4548	−	4.14110i	−0.584973	−	0.156743i
$699$		0			0
$700$	13.1244	+	5.26795i	0.496054	+	0.199110i
$701$			35.3553i			1.33535i	0.744452	+	0.667676i	$0.232711\pi$
$701$			35.3553i			1.33535i	−0.744452	+	0.667676i	$0.767289\pi$
$702$		0			0
$703$	−24.0000	−	24.0000i	−0.905177	−	0.905177i
$704$	1.41421	−	2.44949i	0.0533002	−	0.0923186i
$705$		0			0
$706$	6.00000	+	10.3923i	0.225813	+	0.391120i
$707$	−1.03528	+	3.86370i	−0.0389356	+	0.145310i
$708$		0			0
$709$	−22.5167	−	13.0000i	−0.845631	−	0.488225i	0.0135434	−	0.999908i	$-0.495689\pi$
$709$	−22.5167	−	13.0000i	−0.845631	−	0.488225i	−0.859174	+	0.511683i	$0.829022\pi$
$710$	5.65685	+	11.3137i	0.212298	+	0.424596i
$711$		0			0
$712$	7.00000	−	7.00000i	0.262336	−	0.262336i
$713$	4.14110	+	15.4548i	0.155086	+	0.578787i
$714$		0			0
$715$	−14.7846	+	22.3923i	−0.552913	+	0.837425i
$716$	2.44949	−	1.41421i	0.0915417	−	0.0528516i
$717$		0			0
$718$	−10.9282	+	2.92820i	−0.407837	+	0.109280i
$719$	22.6274			0.843860			0.421930	−	0.906628i	$-0.361353\pi$
$719$	22.6274			0.843860			0.421930	+	0.906628i	$0.361353\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	43.4667	−	11.6469i	1.61766	−	0.433451i
$723$		0			0
$724$	6.92820	−	4.00000i	0.257485	−	0.148659i
$725$	−0.845807	+	7.02030i	−0.0314125	+	0.260727i
$726$		0			0
$727$	−2.19615	−	8.19615i	−0.0814508	−	0.303978i	0.913168	−	0.407584i	$-0.133629\pi$
$727$	−2.19615	−	8.19615i	−0.0814508	−	0.303978i	−0.994618	+	0.103606i	$0.966962\pi$
$728$	8.48528	−	8.48528i	0.314485	−	0.314485i
$729$		0			0
$730$	−3.00000	−	1.00000i	−0.111035	−	0.0370117i
$731$		0			0
$732$		0			0
$733$	−4.02628	+	15.0263i	−0.148714	+	0.555008i	0.850848	+	0.525412i	$0.176089\pi$
$733$	−4.02628	+	15.0263i	−0.148714	+	0.555008i	−0.999562	+	0.0295962i	$0.990578\pi$
$734$	15.5563	+	26.9444i	0.574195	+	0.994535i
$735$		0			0
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	11.3137	+	11.3137i	0.416746	+	0.416746i
$738$		0			0
$739$		−	8.00000i		−	0.294285i	−0.989115	−	0.147142i	$-0.952992\pi$
$739$		−	8.00000i		−	0.294285i	0.989115	−	0.147142i	$-0.0470076\pi$
$740$	−0.568406	+	9.46979i	−0.0208950	+	0.348116i
$741$		0			0
$742$	10.9282	+	2.92820i	0.401187	+	0.107498i
$743$	38.6370	+	10.3528i	1.41746	+	0.379806i	0.884580	−	0.466388i	$-0.154445\pi$
$743$	38.6370	+	10.3528i	1.41746	+	0.379806i	0.532875	+	0.846194i	$0.321112\pi$
$744$		0			0
$745$	−31.4711	−	35.4904i	−1.15301	−	1.30027i
$746$		−	7.07107i		−	0.258890i
$747$		0			0
$748$	−8.00000	−	8.00000i	−0.292509	−	0.292509i
$749$	−28.2843	+	48.9898i	−1.03348	+	1.79005i
$750$		0			0
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	0.954485	−	0.298259i	$-0.0964058\pi$
$751$	6.00000	+	10.3923i	0.218943	+	0.379221i	−0.735542	+	0.677479i	$0.763072\pi$
$752$		0			0
$753$		0			0
$754$	5.19615	+	3.00000i	0.189233	+	0.109254i
$755$	5.65685	−	16.9706i	0.205874	−	0.617622i
$756$		0			0
$757$	15.0000	−	15.0000i	0.545184	−	0.545184i	−0.379860	−	0.925044i	$-0.624028\pi$
$757$	15.0000	−	15.0000i	0.545184	−	0.545184i	0.925044	+	0.379860i	$0.124028\pi$
$758$	−5.17638	−	19.3185i	−0.188015	−	0.701680i
$759$		0			0
$760$	−14.9282	−	9.85641i	−0.541503	−	0.357529i
$761$	−35.5176	+	20.5061i	−1.28751	+	0.743345i	−0.978210	−	0.207618i	$-0.933429\pi$
$761$	−35.5176	+	20.5061i	−1.28751	+	0.743345i	−0.309302	+	0.950964i	$0.600095\pi$
$762$		0			0
$763$	21.8564	−	5.85641i	0.791255	−	0.212016i
$764$	22.6274			0.818631
$765$		0			0
$766$	24.0000			0.867155
$767$	−11.5911	+	3.10583i	−0.418531	+	0.112145i
$768$		0			0
$769$	34.6410	−	20.0000i	1.24919	−	0.721218i	0.278240	−	0.960512i	$-0.410249\pi$
$769$	34.6410	−	20.0000i	1.24919	−	0.721218i	0.970947	+	0.239293i	$0.0769157\pi$
$770$	−3.58630	−	17.5254i	−0.129241	−	0.631570i
$771$		0			0
$772$	−3.29423	−	12.2942i	−0.118562	−	0.442479i
$773$	8.48528	−	8.48528i	0.305194	−	0.305194i	−0.537848	−	0.843042i	$-0.680762\pi$
$773$	8.48528	−	8.48528i	0.305194	−	0.305194i	0.843042	+	0.537848i	$0.180762\pi$
$774$		0			0
$775$	−16.0000	−	12.0000i	−0.574737	−	0.431053i
$776$	3.67423	+	2.12132i	0.131897	+	0.0761510i
$777$		0			0
$778$	−5.49038	+	20.4904i	−0.196840	+	0.734616i
$779$	39.5980	+	68.5857i	1.41874	+	2.45734i
$780$		0			0
$781$	8.00000	−	13.8564i	0.286263	−	0.495821i
$782$	−11.3137	−	11.3137i	−0.404577	−	0.404577i
$783$		0			0
$784$			1.00000i			0.0357143i
$785$	28.4094	+	1.70522i	1.01397	+	0.0608618i
$786$		0			0
$787$	27.3205	+	7.32051i	0.973871	+	0.260948i	0.710461	−	0.703736i	$-0.248486\pi$
$787$	27.3205	+	7.32051i	0.973871	+	0.260948i	0.263410	+	0.964684i	$0.415153\pi$
$788$	−17.3867	−	4.65874i	−0.619374	−	0.165961i
$789$		0			0
$790$	−26.7846	−	1.60770i	−0.952954	−	0.0571992i
$791$		−	5.65685i		−	0.201135i
$792$		0			0
$793$		0			0
$794$	−4.94975	+	8.57321i	−0.175660	+	0.304252i
$795$		0			0
$796$		0			0
$797$	−7.76457	+	28.9778i	−0.275035	+	1.02645i	0.680783	+	0.732486i	$0.261640\pi$
$797$	−7.76457	+	28.9778i	−0.275035	+	1.02645i	−0.955818	+	0.293960i	$0.905027\pi$
$798$		0			0
$799$		0			0
$800$	0.707107	+	4.94975i	0.0250000	+	0.175000i
$801$		0			0
$802$	−9.00000	+	9.00000i	−0.317801	+	0.317801i
$803$	1.03528	+	3.86370i	0.0365341	+	0.136347i
$804$		0			0
$805$	−5.07180	−	24.7846i	−0.178757	−	0.873543i
$806$	−14.6969	+	8.48528i	−0.517678	+	0.298881i
$807$		0			0
$808$	−1.36603	+	0.366025i	−0.0480566	+	0.0128767i
$809$	−1.41421			−0.0497211			−0.0248606	−	0.999691i	$-0.507914\pi$
$809$	−1.41421			−0.0497211			−0.0248606	+	0.999691i	$0.507914\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−3.86370	+	1.03528i	−0.135589	+	0.0363311i
$813$		0			0
$814$	10.3923	−	6.00000i	0.364250	−	0.210300i
$815$	−42.2233	−	27.8781i	−1.47902	−	0.976528i
$816$		0			0
$817$		0			0
$818$	16.9706	−	16.9706i	0.593362	−	0.593362i
$819$		0			0
$820$	7.00000	−	21.0000i	0.244451	−	0.733352i
$821$	35.5176	+	20.5061i	1.23957	+	0.715668i	0.969007	−	0.247034i	$-0.0794559\pi$
$821$	35.5176	+	20.5061i	1.23957	+	0.715668i	0.270566	+	0.962701i	$0.412789\pi$
$822$		0			0
$823$	13.9090	−	51.9090i	0.484836	−	1.80943i	−0.0959619	−	0.995385i	$-0.530593\pi$
$823$	13.9090	−	51.9090i	0.484836	−	1.80943i	0.580798	−	0.814048i	$-0.302741\pi$
$824$	−1.41421	−	2.44949i	−0.0492665	−	0.0853320i
$825$		0			0
$826$	4.00000	−	6.92820i	0.139178	−	0.241063i
$827$	−33.9411	−	33.9411i	−1.18025	−	1.18025i	−0.979680	−	0.200569i	$-0.935721\pi$
$827$	−33.9411	−	33.9411i	−1.18025	−	1.18025i	−0.200569	−	0.979680i	$-0.564279\pi$
$828$		0			0
$829$		−	56.0000i		−	1.94496i	−0.232986	−	0.972480i	$-0.574849\pi$
$829$		−	56.0000i		−	1.94496i	0.232986	−	0.972480i	$-0.425151\pi$
$830$	−17.8028	−	20.0764i	−0.617943	−	0.696862i
$831$		0			0
$832$	4.09808	+	1.09808i	0.142075	+	0.0380689i
$833$	3.86370	+	1.03528i	0.133869	+	0.0358702i
$834$		0			0
$835$	0.535898	−	8.92820i	0.0185455	−	0.308973i
$836$			22.6274i			0.782586i
$837$		0			0
$838$	−18.0000	−	18.0000i	−0.621800	−	0.621800i
$839$	−22.6274	+	39.1918i	−0.781185	+	1.35305i	0.150067	+	0.988676i	$0.452051\pi$
$839$	−22.6274	+	39.1918i	−0.781185	+	1.35305i	−0.931252	+	0.364377i	$0.881282\pi$
$840$		0			0
$841$	13.5000	+	23.3827i	0.465517	+	0.806300i
$842$	−2.58819	+	9.65926i	−0.0891949	+	0.332880i
$843$		0			0
$844$	3.46410	+	2.00000i	0.119239	+	0.0688428i
$845$	−10.6066	−	3.53553i	−0.364878	−	0.121626i
$846$		0			0
$847$	6.00000	−	6.00000i	0.206162	−	0.206162i
$848$	1.03528	+	3.86370i	0.0355515	+	0.132680i
$849$		0			0
$850$	19.8564	+	2.39230i	0.681069	+	0.0820554i
$851$	14.6969	−	8.48528i	0.503805	−	0.290872i
$852$		0			0
$853$	−25.9545	+	6.95448i	−0.888665	+	0.238117i	−0.674142	−	0.738602i	$-0.735486\pi$
$853$	−25.9545	+	6.95448i	−0.888665	+	0.238117i	−0.214523	+	0.976719i	$0.568820\pi$
$854$		0			0
$855$		0			0
$856$	−20.0000			−0.683586
$857$	−11.5911	+	3.10583i	−0.395945	+	0.106093i	−0.451297	−	0.892374i	$-0.649038\pi$
$857$	−11.5911	+	3.10583i	−0.395945	+	0.106093i	0.0553522	+	0.998467i	$0.482372\pi$
$858$		0			0
$859$	−38.1051	+	22.0000i	−1.30013	+	0.750630i	−0.980426	−	0.196887i	$-0.936917\pi$
$859$	−38.1051	+	22.0000i	−1.30013	+	0.750630i	−0.319704	+	0.947518i	$0.603583\pi$
$860$		0			0
$861$		0			0
$862$	−10.2487	−	38.2487i	−0.349072	−	1.30276i
$863$	−31.1127	+	31.1127i	−1.05909	+	1.05909i	−0.0609476	+	0.998141i	$0.519412\pi$
$863$	−31.1127	+	31.1127i	−1.05909	+	1.05909i	−0.998141	+	0.0609476i	$0.980588\pi$
$864$		0			0
$865$	−14.0000	−	28.0000i	−0.476014	−	0.952029i
$866$	−28.1691	−	16.2635i	−0.957226	−	0.552655i
$867$		0			0
$868$	2.92820	−	10.9282i	0.0993897	−	0.370927i
$869$	16.9706	+	29.3939i	0.575687	+	0.997119i
$870$		0			0
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	5.65685	+	5.65685i	0.191565	+	0.191565i
$873$		0			0
$874$			32.0000i			1.08242i
$875$	24.1160	+	20.4553i	0.815268	+	0.691516i
$876$		0			0
$877$	20.4904	+	5.49038i	0.691911	+	0.185397i	0.587605	−	0.809148i	$-0.300071\pi$
$877$	20.4904	+	5.49038i	0.691911	+	0.185397i	0.104306	+	0.994545i	$0.466738\pi$
$878$	−7.72741	−	2.07055i	−0.260787	−	0.0698778i
$879$		0			0
$880$	4.73205	−	4.19615i	0.159517	−	0.141452i
$881$			52.3259i			1.76290i	0.472273	+	0.881452i	$0.343434\pi$
$881$			52.3259i			1.76290i	−0.472273	+	0.881452i	$0.656566\pi$
$882$		0			0
$883$	16.0000	+	16.0000i	0.538443	+	0.538443i	0.923071	−	0.384629i	$-0.125670\pi$
$883$	16.0000	+	16.0000i	0.538443	+	0.538443i	−0.384629	+	0.923071i	$0.625670\pi$
$884$	8.48528	−	14.6969i	0.285391	−	0.494312i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	9.31749	−	34.7733i	0.312851	−	1.16757i	−0.613124	−	0.789987i	$-0.710087\pi$
$887$	9.31749	−	34.7733i	0.312851	−	1.16757i	0.925974	−	0.377587i	$-0.123246\pi$
$888$		0			0
$889$	48.4974	+	28.0000i	1.62655	+	0.939090i
$890$	19.7990	−	9.89949i	0.663664	−	0.331832i
$891$		0			0
$892$	−6.00000	+	6.00000i	−0.200895	+	0.200895i
$893$		0			0
$894$		0			0
$895$	6.19615	−	1.26795i	0.207115	−	0.0423829i
$896$	−2.44949	+	1.41421i	−0.0818317	+	0.0472456i
$897$		0			0
$898$	−1.36603	+	0.366025i	−0.0455849	+	0.0122144i
$899$	5.65685			0.188667
$900$		0			0
$901$	16.0000			0.533037
$902$	−27.0459	+	7.24693i	−0.900531	+	0.241296i
$903$		0			0
$904$	1.73205	−	1.00000i	0.0576072	−	0.0332595i
$905$	17.5254	−	3.58630i	0.582563	−	0.119213i
$906$		0			0
$907$	1.46410	+	5.46410i	0.0486147	+	0.181433i	0.985964	−	0.166959i	$-0.0533947\pi$
$907$	1.46410	+	5.46410i	0.0486147	+	0.181433i	−0.937349	+	0.348391i	$0.886728\pi$
$908$	5.65685	−	5.65685i	0.187729	−	0.187729i
$909$		0			0
$910$	24.0000	−	12.0000i	0.795592	−	0.397796i
$911$	−9.79796	−	5.65685i	−0.324621	−	0.187420i	0.328830	−	0.944389i	$-0.393346\pi$
$911$	−9.79796	−	5.65685i	−0.324621	−	0.187420i	−0.653450	+	0.756969i	$0.726679\pi$
$912$		0			0
$913$	−8.78461	+	32.7846i	−0.290728	+	1.08501i
$914$	10.6066	+	18.3712i	0.350835	+	0.607664i
$915$		0			0
$916$	3.00000	−	5.19615i	0.0991228	−	0.171686i
$917$	28.2843	+	28.2843i	0.934029	+	0.934029i
$918$		0			0
$919$		−	20.0000i		−	0.659739i	−0.944027	−	0.329870i	$-0.892995\pi$
$919$		−	20.0000i		−	0.659739i	0.944027	−	0.329870i	$-0.107005\pi$
$920$	6.69213	−	5.93426i	0.220633	−	0.195647i
$921$		0			0
$922$	17.7583	+	4.75833i	0.584839	+	0.156707i
$923$	23.1822	+	6.21166i	0.763052	+	0.204459i
$924$		0			0
$925$	−7.90192	+	19.6865i	−0.259814	+	0.647289i
$926$			19.7990i			0.650635i
$927$		0			0
$928$	−1.00000	−	1.00000i	−0.0328266	−	0.0328266i
$929$	16.2635	−	28.1691i	0.533587	−	0.924199i	−0.465644	−	0.884972i	$-0.654177\pi$
$929$	16.2635	−	28.1691i	0.533587	−	0.924199i	0.999230	−	0.0392269i	$-0.0124895\pi$
$930$		0			0
$931$	−4.00000	−	6.92820i	−0.131095	−	0.227063i
$932$	−3.10583	+	11.5911i	−0.101735	+	0.379679i
$933$		0			0
$934$	24.2487	+	14.0000i	0.793442	+	0.458094i
$935$	−11.3137	−	22.6274i	−0.369998	−	0.739996i
$936$		0			0
$937$	−11.0000	+	11.0000i	−0.359354	+	0.359354i	−0.863575	−	0.504221i	$-0.831780\pi$
$937$	−11.0000	+	11.0000i	−0.359354	+	0.359354i	0.504221	+	0.863575i	$0.331780\pi$
$938$	−4.14110	−	15.4548i	−0.135212	−	0.504618i
$939$		0			0
$940$		0			0
$941$	−25.7196	+	14.8492i	−0.838436	+	0.484071i	−0.856732	−	0.515761i	$-0.827509\pi$
$941$	−25.7196	+	14.8492i	−0.838436	+	0.484071i	0.0182960	+	0.999833i	$0.494176\pi$
$942$		0			0
$943$	−38.2487	+	10.2487i	−1.24555	+	0.333744i
$944$	2.82843			0.0920575
$945$		0			0
$946$		0			0
$947$	7.72741	−	2.07055i	0.251107	−	0.0672839i	−0.131070	−	0.991373i	$-0.541841\pi$
$947$	7.72741	−	2.07055i	0.251107	−	0.0672839i	0.382177	+	0.924089i	$0.375175\pi$
$948$		0			0
$949$	−5.19615	+	3.00000i	−0.168674	+	0.0973841i
$950$	−24.6980	−	31.4644i	−0.801308	−	1.02084i
$951$		0			0
$952$	2.92820	+	10.9282i	0.0949036	+	0.354185i
$953$	4.24264	−	4.24264i	0.137433	−	0.137433i	−0.635044	−	0.772476i	$-0.719018\pi$
$953$	4.24264	−	4.24264i	0.137433	−	0.137433i	0.772476	+	0.635044i	$0.219018\pi$
$954$		0			0
$955$	48.0000	+	16.0000i	1.55324	+	0.517748i
$956$	−14.6969	−	8.48528i	−0.475333	−	0.274434i
$957$		0			0
$958$	1.46410	−	5.46410i	0.0473030	−	0.176537i
$959$	−8.48528	−	14.6969i	−0.274004	−	0.474589i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	12.7279	+	12.7279i	0.410365	+	0.410365i
$963$		0			0
$964$			22.0000i			0.708572i
$965$	1.70522	−	28.4094i	0.0548929	−	0.914530i
$966$		0			0
$967$	−13.6603	−	3.66025i	−0.439284	−	0.117706i	0.0323969	−	0.999475i	$-0.489686\pi$
$967$	−13.6603	−	3.66025i	−0.439284	−	0.117706i	−0.471681	+	0.881769i	$0.656353\pi$
$968$	2.89778	+	0.776457i	0.0931381	+	0.0249563i
$969$		0			0
$970$	6.29423	+	7.09808i	0.202096	+	0.227905i
$971$			36.7696i			1.17999i	0.807406	+	0.589996i	$0.200871\pi$
$971$			36.7696i			1.17999i	−0.807406	+	0.589996i	$0.799129\pi$
$972$		0			0
$973$	8.00000	+	8.00000i	0.256468	+	0.256468i
$974$	12.7279	−	22.0454i	0.407829	−	0.706380i
$975$		0			0
$976$		0			0
$977$	3.10583	−	11.5911i	0.0993643	−	0.370832i	−0.898281	−	0.439422i	$-0.855183\pi$
$977$	3.10583	−	11.5911i	0.0993643	−	0.370832i	0.997645	+	0.0685896i	$0.0218499\pi$
$978$		0			0
$979$	−24.2487	−	14.0000i	−0.774992	−	0.447442i
$980$	−0.707107	+	2.12132i	−0.0225877	+	0.0677631i
$981$		0			0
$982$	−2.00000	+	2.00000i	−0.0638226	+	0.0638226i
$983$	2.07055	+	7.72741i	0.0660404	+	0.246466i	0.991053	−	0.133471i	$-0.0426123\pi$
$983$	2.07055	+	7.72741i	0.0660404	+	0.246466i	−0.925012	+	0.379937i	$0.875946\pi$
$984$		0			0
$985$	−33.5885	−	22.1769i	−1.07022	−	0.706615i
$986$	−4.89898	+	2.82843i	−0.156015	+	0.0900755i
$987$		0			0
$988$	−32.7846	+	8.78461i	−1.04302	+	0.279476i
$989$		0			0
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$	3.86370	−	1.03528i	0.122673	−	0.0328701i
$993$		0			0
$994$	−13.8564	+	8.00000i	−0.439499	+	0.253745i
$995$		0			0
$996$		0			0
$997$	4.75833	+	17.7583i	0.150698	+	0.562412i	0.999435	+	0.0335977i	$0.0106965\pi$
$997$	4.75833	+	17.7583i	0.150698	+	0.562412i	−0.848738	+	0.528814i	$0.822637\pi$
$998$	22.6274	−	22.6274i	0.716258	−	0.716258i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.m.c.593.1		8
3.2	odd	2	inner	810.2.m.c.593.2		8
5.2	odd	4	inner	810.2.m.c.107.1		8
9.2	odd	6		90.2.f.a.53.1	yes	4
9.4	even	3	inner	810.2.m.c.53.2		8
9.5	odd	6	inner	810.2.m.c.53.1		8
9.7	even	3		90.2.f.a.53.2	yes	4
15.2	even	4	inner	810.2.m.c.107.2		8
36.7	odd	6		720.2.w.a.593.1		4
36.11	even	6		720.2.w.a.593.2		4
45.2	even	12		90.2.f.a.17.2	yes	4
45.7	odd	12		90.2.f.a.17.1	✓	4
45.22	odd	12	inner	810.2.m.c.377.2		8
45.29	odd	6		450.2.f.b.143.2		4
45.32	even	12	inner	810.2.m.c.377.1		8
45.34	even	6		450.2.f.b.143.1		4
45.38	even	12		450.2.f.b.107.1		4
45.43	odd	12		450.2.f.b.107.2		4
72.11	even	6		2880.2.w.c.2753.1		4
72.29	odd	6		2880.2.w.l.2753.1		4
72.43	odd	6		2880.2.w.c.2753.2		4
72.61	even	6		2880.2.w.l.2753.2		4
180.7	even	12		720.2.w.a.17.2		4
180.43	even	12		3600.2.w.g.1457.2		4
180.47	odd	12		720.2.w.a.17.1		4
180.79	odd	6		3600.2.w.g.593.2		4
180.83	odd	12		3600.2.w.g.1457.1		4
180.119	even	6		3600.2.w.g.593.1		4
360.187	even	12		2880.2.w.c.2177.1		4
360.227	odd	12		2880.2.w.c.2177.2		4
360.277	odd	12		2880.2.w.l.2177.1		4
360.317	even	12		2880.2.w.l.2177.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.f.a.17.1	✓	4	45.7	odd	12
90.2.f.a.17.2	yes	4	45.2	even	12
90.2.f.a.53.1	yes	4	9.2	odd	6
90.2.f.a.53.2	yes	4	9.7	even	3
450.2.f.b.107.1		4	45.38	even	12
450.2.f.b.107.2		4	45.43	odd	12
450.2.f.b.143.1		4	45.34	even	6
450.2.f.b.143.2		4	45.29	odd	6
720.2.w.a.17.1		4	180.47	odd	12
720.2.w.a.17.2		4	180.7	even	12
720.2.w.a.593.1		4	36.7	odd	6
720.2.w.a.593.2		4	36.11	even	6
810.2.m.c.53.1		8	9.5	odd	6	inner
810.2.m.c.53.2		8	9.4	even	3	inner
810.2.m.c.107.1		8	5.2	odd	4	inner
810.2.m.c.107.2		8	15.2	even	4	inner
810.2.m.c.377.1		8	45.32	even	12	inner
810.2.m.c.377.2		8	45.22	odd	12	inner
810.2.m.c.593.1		8	1.1	even	1	trivial
810.2.m.c.593.2		8	3.2	odd	2	inner
2880.2.w.c.2177.1		4	360.187	even	12
2880.2.w.c.2177.2		4	360.227	odd	12
2880.2.w.c.2753.1		4	72.11	even	6
2880.2.w.c.2753.2		4	72.43	odd	6
2880.2.w.l.2177.1		4	360.277	odd	12
2880.2.w.l.2177.2		4	360.317	even	12
2880.2.w.l.2753.1		4	72.29	odd	6
2880.2.w.l.2753.2		4	72.61	even	6
3600.2.w.g.593.1		4	180.119	even	6
3600.2.w.g.593.2		4	180.79	odd	6
3600.2.w.g.1457.1		4	180.83	odd	12
3600.2.w.g.1457.2		4	180.43	even	12

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(2.19067 - 0.448288i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(2.19067 - 0.448288i) q^{5} +(0.732051 + 2.73205i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.00000 + 1.00000i) q^{10} +(2.44949 + 1.41421i) q^{11} +(-1.09808 + 4.09808i) q^{13} +(-1.41421 - 2.44949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-2.82843 - 2.82843i) q^{17} +8.00000i q^{19} +(1.67303 - 1.48356i) q^{20} +(-2.73205 - 0.732051i) q^{22} +(-3.86370 - 1.03528i) q^{23} +(4.59808 - 1.96410i) q^{25} -4.24264i q^{26} +(2.00000 + 2.00000i) q^{28} +(-0.707107 + 1.22474i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(3.46410 + 2.00000i) q^{34} +(2.82843 + 5.65685i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(-2.07055 - 7.72741i) q^{38} +(-1.23205 + 1.86603i) q^{40} +(8.57321 - 4.94975i) q^{41} +2.82843 q^{44} +4.00000 q^{46} +(-0.866025 + 0.500000i) q^{49} +(-3.93305 + 3.08725i) q^{50} +(1.09808 + 4.09808i) q^{52} +(-2.82843 + 2.82843i) q^{53} +(6.00000 + 2.00000i) q^{55} +(-2.44949 - 1.41421i) q^{56} +(0.366025 - 1.36603i) q^{58} +(1.41421 + 2.44949i) q^{59} +(2.82843 + 2.82843i) q^{62} -1.00000i q^{64} +(-0.568406 + 9.46979i) q^{65} +(5.46410 + 1.46410i) q^{67} +(-3.86370 - 1.03528i) q^{68} +(-4.19615 - 4.73205i) q^{70} -5.65685i q^{71} +(1.00000 + 1.00000i) q^{73} +(2.12132 - 3.67423i) q^{74} +(4.00000 + 6.92820i) q^{76} +(-2.07055 + 7.72741i) q^{77} +(10.3923 + 6.00000i) q^{79} +(0.707107 - 2.12132i) q^{80} +(-7.00000 + 7.00000i) q^{82} +(3.10583 + 11.5911i) q^{83} +(-7.46410 - 4.92820i) q^{85} +(-2.73205 + 0.732051i) q^{88} -9.89949 q^{89} -12.0000 q^{91} +(-3.86370 + 1.03528i) q^{92} +(3.58630 + 17.5254i) q^{95} +(-1.09808 - 4.09808i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7}+O(q^{10}) \) 8 * q - 8 * q^7	\( 8 q - 8 q^{7} - 16 q^{10} + 12 q^{13} + 4 q^{16} - 8 q^{22} + 16 q^{25} + 16 q^{28} - 16 q^{31} - 24 q^{37} + 4 q^{40} + 32 q^{46} - 12 q^{52} + 48 q^{55} - 4 q^{58} + 16 q^{67} + 8 q^{70} + 8 q^{73} + 32 q^{76} - 56 q^{82} - 32 q^{85} - 8 q^{88} - 96 q^{91} + 12 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 - 16 * q^10 + 12 * q^13 + 4 * q^16 - 8 * q^22 + 16 * q^25 + 16 * q^28 - 16 * q^31 - 24 * q^37 + 4 * q^40 + 32 * q^46 - 12 * q^52 + 48 * q^55 - 4 * q^58 + 16 * q^67 + 8 * q^70 + 8 * q^73 + 32 * q^76 - 56 * q^82 - 32 * q^85 - 8 * q^88 - 96 * q^91 + 12 * q^97

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