LMFDB - Embedded newform 805.2.s.c.254.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(254,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 0]))

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

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

chi := DirichletCharacter("805.254");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			254.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	805.254
Dual form			805.2.s.c.599.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} -4.00000 q^{6} +(-2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} -4.00000 q^{6} +(-2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(2.46410 - 3.73205i) q^{10} +(-3.46410 - 2.00000i) q^{12} -2.00000i q^{13} +(-4.00000 - 3.46410i) q^{14} +(2.00000 + 4.00000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(1.73205 - 1.00000i) q^{17} +(1.73205 - 1.00000i) q^{18} +(3.00000 - 5.19615i) q^{19} +(4.00000 - 2.00000i) q^{20} +(5.00000 - 1.73205i) q^{21} +(0.866025 + 0.500000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +(2.00000 - 3.46410i) q^{26} -4.00000i q^{27} +(-1.73205 - 5.00000i) q^{28} +5.00000 q^{29} +(-0.535898 + 8.92820i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(6.92820 - 4.00000i) q^{32} +4.00000 q^{34} +(-1.46410 + 5.73205i) q^{35} +2.00000 q^{36} +(-6.06218 - 3.50000i) q^{37} +(10.3923 - 6.00000i) q^{38} +(2.00000 + 3.46410i) q^{39} -7.00000 q^{41} +(10.3923 + 2.00000i) q^{42} +11.0000i q^{43} +(-1.86603 - 1.23205i) q^{45} +(1.00000 + 1.73205i) q^{46} +(-10.3923 - 6.00000i) q^{47} +8.00000i q^{48} +(6.50000 + 2.59808i) q^{49} +(-8.00000 - 6.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(3.46410 - 2.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(4.00000 - 6.92820i) q^{54} +12.0000i q^{57} +(8.66025 + 5.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-4.92820 + 7.46410i) q^{60} +(4.00000 - 6.92820i) q^{61} -10.0000i q^{62} +(-1.73205 + 2.00000i) q^{63} +8.00000 q^{64} +(-4.46410 - 0.267949i) q^{65} +(0.866025 - 0.500000i) q^{67} +(3.46410 + 2.00000i) q^{68} -2.00000 q^{69} +(-8.26795 + 8.46410i) q^{70} -8.00000 q^{71} +(5.19615 - 3.00000i) q^{73} +(-7.00000 - 12.1244i) q^{74} +(9.19615 - 3.92820i) q^{75} +12.0000 q^{76} +8.00000i q^{78} +(-7.00000 + 12.1244i) q^{79} +(-7.46410 - 4.92820i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-12.1244 - 7.00000i) q^{82} +17.0000i q^{83} +(8.00000 + 6.92820i) q^{84} +(-2.00000 - 4.00000i) q^{85} +(-11.0000 + 19.0526i) q^{86} +(-8.66025 + 5.00000i) q^{87} +(-2.00000 - 4.00000i) q^{90} +(-1.00000 + 5.19615i) q^{91} +2.00000i q^{92} +(8.66025 + 5.00000i) q^{93} +(-12.0000 - 20.7846i) q^{94} +(-11.1962 - 7.39230i) q^{95} +(-8.00000 + 13.8564i) q^{96} -7.00000i q^{97} +(8.66025 + 11.0000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 4 q^{5} - 16 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 + 4 * q^5 - 16 * q^6 + 2 * q^9	$ 4 q + 4 q^{4} + 4 q^{5} - 16 q^{6} + 2 q^{9} - 4 q^{10} - 16 q^{14} + 8 q^{15} + 8 q^{16} + 12 q^{19} + 16 q^{20} + 20 q^{21} - 6 q^{25} + 8 q^{26} + 20 q^{29} - 16 q^{30} - 10 q^{31} + 16 q^{34} + 8 q^{35} + 8 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{45} + 4 q^{46} + 26 q^{49} - 32 q^{50} - 8 q^{51} + 16 q^{54} + 8 q^{59} + 8 q^{60} + 16 q^{61} + 32 q^{64} - 4 q^{65} - 8 q^{69} - 40 q^{70} - 32 q^{71} - 28 q^{74} + 16 q^{75} + 48 q^{76} - 28 q^{79} - 16 q^{80} + 22 q^{81} + 32 q^{84} - 8 q^{85} - 44 q^{86} - 8 q^{90} - 4 q^{91} - 48 q^{94} - 24 q^{95} - 32 q^{96}+O(q^{100}) $ 4 * q + 4 * q^4 + 4 * q^5 - 16 * q^6 + 2 * q^9 - 4 * q^10 - 16 * q^14 + 8 * q^15 + 8 * q^16 + 12 * q^19 + 16 * q^20 + 20 * q^21 - 6 * q^25 + 8 * q^26 + 20 * q^29 - 16 * q^30 - 10 * q^31 + 16 * q^34 + 8 * q^35 + 8 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^45 + 4 * q^46 + 26 * q^49 - 32 * q^50 - 8 * q^51 + 16 * q^54 + 8 * q^59 + 8 * q^60 + 16 * q^61 + 32 * q^64 - 4 * q^65 - 8 * q^69 - 40 * q^70 - 32 * q^71 - 28 * q^74 + 16 * q^75 + 48 * q^76 - 28 * q^79 - 16 * q^80 + 22 * q^81 + 32 * q^84 - 8 * q^85 - 44 * q^86 - 8 * q^90 - 4 * q^91 - 48 * q^94 - 24 * q^95 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73205	+	1.00000i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	1.73205	+	1.00000i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$3$	−1.73205	+	1.00000i	−1.00000	+	0.577350i	−0.908248	−	0.418432i	$-0.862580\pi$
$3$	−1.73205	+	1.00000i	−1.00000	+	0.577350i	−0.0917517	+	0.995782i	$0.529247\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$5$	0.133975	−	2.23205i	0.0599153	−	0.998203i
$6$	−4.00000			−1.63299
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$7$	−2.59808	−	0.500000i	−0.981981	−	0.188982i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.46410	−	3.73205i	0.779217	−	1.18018i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−3.46410	−	2.00000i	−1.00000	−	0.577350i
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$	−4.00000	−	3.46410i	−1.06904	−	0.925820i
$15$	2.00000	+	4.00000i	0.516398	+	1.03280i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	−0.275029	−	0.961436i	$-0.588688\pi$
$17$	1.73205	−	1.00000i	0.420084	−	0.242536i	0.695113	+	0.718900i	$0.255354\pi$
$18$	1.73205	−	1.00000i	0.408248	−	0.235702i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	4.00000	−	2.00000i	0.894427	−	0.447214i
$21$	5.00000	−	1.73205i	1.09109	−	0.377964i
$22$		0			0
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$		0			0
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$		−	4.00000i		−	0.769800i
$28$	−1.73205	−	5.00000i	−0.327327	−	0.944911i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$	−0.535898	+	8.92820i	−0.0978412	+	1.63006i
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	6.92820	−	4.00000i	1.22474	−	0.707107i
$33$		0			0
$34$	4.00000			0.685994
$35$	−1.46410	+	5.73205i	−0.247478	+	0.968893i
$36$	2.00000			0.333333
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.0893706	−	0.995998i	$-0.528486\pi$
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.907245	+	0.420602i	$0.861819\pi$
$38$	10.3923	−	6.00000i	1.68585	−	0.973329i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$	10.3923	+	2.00000i	1.60357	+	0.308607i
$43$			11.0000i			1.67748i	0.544529	+	0.838742i	$0.316708\pi$
$43$			11.0000i			1.67748i	−0.544529	+	0.838742i	$0.683292\pi$
$44$		0			0
$45$	−1.86603	−	1.23205i	−0.278171	−	0.183663i
$46$	1.00000	+	1.73205i	0.147442	+	0.255377i
$47$	−10.3923	−	6.00000i	−1.51587	−	0.875190i	−0.999826	−	0.0186297i	$-0.994070\pi$
$47$	−10.3923	−	6.00000i	−1.51587	−	0.875190i	−0.516047	−	0.856560i	$-0.672597\pi$
$48$			8.00000i			1.15470i
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$	−8.00000	−	6.00000i	−1.13137	−	0.848528i
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	3.46410	−	2.00000i	0.480384	−	0.277350i
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$	4.00000	−	6.92820i	0.544331	−	0.942809i
$55$		0			0
$56$		0			0
$57$			12.0000i			1.58944i
$58$	8.66025	+	5.00000i	1.13715	+	0.656532i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−4.92820	+	7.46410i	−0.636228	+	0.963611i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$		−	10.0000i		−	1.27000i
$63$	−1.73205	+	2.00000i	−0.218218	+	0.251976i
$64$	8.00000			1.00000
$65$	−4.46410	−	0.267949i	−0.553704	−	0.0332350i
$66$		0			0
$67$	0.866025	−	0.500000i	0.105802	−	0.0610847i	−0.446165	−	0.894951i	$-0.647211\pi$
$67$	0.866025	−	0.500000i	0.105802	−	0.0610847i	0.551967	+	0.833866i	$0.313877\pi$
$68$	3.46410	+	2.00000i	0.420084	+	0.242536i
$69$	−2.00000			−0.240772
$70$	−8.26795	+	8.46410i	−0.988209	+	1.01165i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	−0.164083	−	0.986447i	$-0.552466\pi$
$73$	5.19615	−	3.00000i	0.608164	−	0.351123i	0.772246	+	0.635323i	$0.219133\pi$
$74$	−7.00000	−	12.1244i	−0.813733	−	1.40943i
$75$	9.19615	−	3.92820i	1.06188	−	0.453590i
$76$	12.0000			1.37649
$77$		0			0
$78$			8.00000i			0.905822i
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	−7.46410	−	4.92820i	−0.834512	−	0.550990i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−12.1244	−	7.00000i	−1.33891	−	0.773021i
$83$			17.0000i			1.86599i	0.359886	+	0.932996i	$0.382816\pi$
$83$			17.0000i			1.86599i	−0.359886	+	0.932996i	$0.617184\pi$
$84$	8.00000	+	6.92820i	0.872872	+	0.755929i
$85$	−2.00000	−	4.00000i	−0.216930	−	0.433861i
$86$	−11.0000	+	19.0526i	−1.18616	+	2.05449i
$87$	−8.66025	+	5.00000i	−0.928477	+	0.536056i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	−2.00000	−	4.00000i	−0.210819	−	0.421637i
$91$	−1.00000	+	5.19615i	−0.104828	+	0.544705i
$92$			2.00000i			0.208514i
$93$	8.66025	+	5.00000i	0.898027	+	0.518476i
$94$	−12.0000	−	20.7846i	−1.23771	−	2.14377i
$95$	−11.1962	−	7.39230i	−1.14870	−	0.758434i
$96$	−8.00000	+	13.8564i	−0.816497	+	1.41421i
$97$		−	7.00000i		−	0.710742i	−0.934725	−	0.355371i	$-0.884354\pi$
$97$		−	7.00000i		−	0.710742i	0.934725	−	0.355371i	$-0.115646\pi$
$98$	8.66025	+	11.0000i	0.874818	+	1.11117i
$99$		0			0
$100$	−3.92820	−	9.19615i	−0.392820	−	0.919615i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	−6.92820	+	4.00000i	−0.685994	+	0.396059i
$103$	6.06218	+	3.50000i	0.597324	+	0.344865i	0.767988	−	0.640464i	$-0.221258\pi$
$103$	6.06218	+	3.50000i	0.597324	+	0.344865i	−0.170664	+	0.985329i	$0.554591\pi$
$104$		0			0
$105$	−3.19615	−	11.3923i	−0.311913	−	1.11178i
$106$	12.0000			1.16554
$107$	13.8564	+	8.00000i	1.33955	+	0.773389i	0.986740	−	0.162306i	$-0.0518932\pi$
$107$	13.8564	+	8.00000i	1.33955	+	0.773389i	0.352809	+	0.935695i	$0.385227\pi$
$108$	6.92820	−	4.00000i	0.666667	−	0.384900i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$	14.0000			1.32882
$112$	−6.92820	+	8.00000i	−0.654654	+	0.755929i
$113$		−	15.0000i		−	1.41108i	−0.708669	−	0.705541i	$-0.750704\pi$
$113$		−	15.0000i		−	1.41108i	0.708669	−	0.705541i	$-0.249296\pi$
$114$	−12.0000	+	20.7846i	−1.12390	+	1.94666i
$115$	1.23205	−	1.86603i	0.114889	−	0.174008i
$116$	5.00000	+	8.66025i	0.464238	+	0.804084i
$117$	−1.73205	−	1.00000i	−0.160128	−	0.0924500i
$118$			8.00000i			0.736460i
$119$	−5.00000	+	1.73205i	−0.458349	+	0.158777i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	13.8564	−	8.00000i	1.25450	−	0.724286i
$123$	12.1244	−	7.00000i	1.09322	−	0.631169i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−5.00000	+	1.73205i	−0.445435	+	0.154303i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$		0			0
$129$	−11.0000	−	19.0526i	−0.968496	−	1.67748i
$130$	−7.46410	−	4.92820i	−0.654645	−	0.432232i
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$		0			0
$133$	−10.3923	+	12.0000i	−0.901127	+	1.04053i
$134$	2.00000			0.172774
$135$	−8.92820	−	0.535898i	−0.768417	−	0.0461228i
$136$		0			0
$137$	12.9904	−	7.50000i	1.10984	−	0.640768i	0.171054	−	0.985262i	$-0.445283\pi$
$137$	12.9904	−	7.50000i	1.10984	−	0.640768i	0.938789	+	0.344493i	$0.111949\pi$
$138$	−3.46410	−	2.00000i	−0.294884	−	0.170251i
$139$	−5.00000			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$140$	−11.3923	+	3.19615i	−0.962825	+	0.270124i
$141$	24.0000			2.02116
$142$	−13.8564	−	8.00000i	−1.16280	−	0.671345i
$143$		0			0
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	0.669873	−	11.1603i	0.0556299	−	0.926809i
$146$	12.0000			0.993127
$147$	−13.8564	+	2.00000i	−1.14286	+	0.164957i
$148$		−	14.0000i		−	1.15079i
$149$	−7.00000	+	12.1244i	−0.573462	+	0.993266i	0.422744	+	0.906249i	$0.361067\pi$
$149$	−7.00000	+	12.1244i	−0.573462	+	0.993266i	−0.996207	+	0.0870170i	$0.972267\pi$
$150$	19.8564	+	2.39230i	1.62127	+	0.195331i
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	0.999430	+	0.0337724i	$0.0107521\pi$
$151$	6.50000	+	11.2583i	0.528962	+	0.916190i	−0.470467	+	0.882418i	$0.655915\pi$
$152$		0			0
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	−10.0000	+	5.00000i	−0.803219	+	0.401610i
$156$	−4.00000	+	6.92820i	−0.320256	+	0.554700i
$157$	−2.59808	+	1.50000i	−0.207349	+	0.119713i	−0.600079	−	0.799941i	$-0.704864\pi$
$157$	−2.59808	+	1.50000i	−0.207349	+	0.119713i	0.392730	+	0.919654i	$0.371531\pi$
$158$	−24.2487	+	14.0000i	−1.92912	+	1.11378i
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$	−8.00000	−	16.0000i	−0.632456	−	1.26491i
$161$	−2.00000	−	1.73205i	−0.157622	−	0.136505i
$162$			22.0000i			1.72848i
$163$	−8.66025	−	5.00000i	−0.678323	−	0.391630i	0.120900	−	0.992665i	$-0.461422\pi$
$163$	−8.66025	−	5.00000i	−0.678323	−	0.391630i	−0.799223	+	0.601035i	$0.794755\pi$
$164$	−7.00000	−	12.1244i	−0.546608	−	0.946753i
$165$		0			0
$166$	−17.0000	+	29.4449i	−1.31946	+	2.28536i
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$	0.535898	−	8.92820i	0.0411015	−	0.684762i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	−19.0526	+	11.0000i	−1.45274	+	0.838742i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$	−20.0000			−1.51620
$175$	12.5981	+	4.03590i	0.952325	+	0.305085i
$176$		0			0
$177$	−6.92820	−	4.00000i	−0.520756	−	0.300658i
$178$		0			0
$179$	−5.50000	−	9.52628i	−0.411089	−	0.712028i	0.583920	−	0.811811i	$-0.301518\pi$
$179$	−5.50000	−	9.52628i	−0.411089	−	0.712028i	−0.995009	+	0.0997838i	$0.968185\pi$
$180$	0.267949	−	4.46410i	0.0199718	−	0.332734i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−6.92820	+	8.00000i	−0.513553	+	0.592999i
$183$			16.0000i			1.18275i
$184$		0			0
$185$	−8.62436	+	13.0622i	−0.634075	+	0.960350i
$186$	10.0000	+	17.3205i	0.733236	+	1.27000i
$187$		0			0
$188$		−	24.0000i		−	1.75038i
$189$	−2.00000	+	10.3923i	−0.145479	+	0.755929i
$190$	−12.0000	−	24.0000i	−0.870572	−	1.74114i
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$	−13.8564	+	8.00000i	−1.00000	+	0.577350i
$193$	13.8564	−	8.00000i	0.997406	−	0.575853i	0.0899262	−	0.995948i	$-0.471337\pi$
$193$	13.8564	−	8.00000i	0.997406	−	0.575853i	0.907480	+	0.420096i	$0.138004\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$	8.00000	−	4.00000i	0.572892	−	0.286446i
$196$	2.00000	+	13.8564i	0.142857	+	0.989743i
$197$		−	14.0000i		−	0.997459i	−0.866758	−	0.498729i	$-0.833800\pi$
$197$		−	14.0000i		−	0.997459i	0.866758	−	0.498729i	$-0.166200\pi$
$198$		0			0
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.797025	+	0.603947i	$0.206406\pi$
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.124521	+	0.992217i	$0.460261\pi$
$200$		0			0
$201$	−1.00000	+	1.73205i	−0.0705346	+	0.122169i
$202$		−	12.0000i		−	0.844317i
$203$	−12.9904	−	2.50000i	−0.911746	−	0.175466i
$204$	−8.00000			−0.560112
$205$	−0.937822	+	15.6244i	−0.0655003	+	1.09125i
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	0.866025	−	0.500000i	0.0601929	−	0.0347524i
$208$	−6.92820	−	4.00000i	−0.480384	−	0.277350i
$209$		0			0
$210$	5.85641	−	22.9282i	0.404130	−	1.58220i
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	10.3923	+	6.00000i	0.713746	+	0.412082i
$213$	13.8564	−	8.00000i	0.949425	−	0.548151i
$214$	16.0000	+	27.7128i	1.09374	+	1.89441i
$215$	24.5526	+	1.47372i	1.67447	+	0.100507i
$216$		0			0
$217$	4.33013	+	12.5000i	0.293948	+	0.848555i
$218$		−	20.0000i		−	1.35457i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$		0			0
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$	24.2487	+	14.0000i	1.62747	+	0.939618i
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	−20.0000	+	6.92820i	−1.33631	+	0.462910i
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$	15.0000	−	25.9808i	0.997785	−	1.72821i
$227$	6.06218	−	3.50000i	0.402361	−	0.232303i	−0.285141	−	0.958485i	$-0.592041\pi$
$227$	6.06218	−	3.50000i	0.402361	−	0.232303i	0.687502	+	0.726182i	$0.258707\pi$
$228$	−20.7846	+	12.0000i	−1.37649	+	0.794719i
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$	4.00000	−	2.00000i	0.263752	−	0.131876i
$231$		0			0
$232$		0			0
$233$	6.92820	+	4.00000i	0.453882	+	0.262049i	0.709468	−	0.704737i	$-0.248935\pi$
$233$	6.92820	+	4.00000i	0.453882	+	0.262049i	−0.255586	+	0.966786i	$0.582269\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	−14.7846	+	22.3923i	−0.964442	+	1.46071i
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$		−	28.0000i		−	1.81880i
$238$	−10.3923	−	2.00000i	−0.673633	−	0.129641i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	17.8564	+	1.07180i	1.15263	+	0.0691842i
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	0.984496	+	0.175409i	$0.0561248\pi$
$241$	10.0000	+	17.3205i	0.644157	+	1.11571i	−0.340339	+	0.940303i	$0.610542\pi$
$242$	19.0526	−	11.0000i	1.22474	−	0.707107i
$243$	−8.66025	−	5.00000i	−0.555556	−	0.320750i
$244$	16.0000			1.02430
$245$	6.66987	−	14.1603i	0.426123	−	0.904665i
$246$	28.0000			1.78521
$247$	−10.3923	−	6.00000i	−0.661247	−	0.381771i
$248$		0			0
$249$	−17.0000	−	29.4449i	−1.07733	−	1.86599i
$250$	−14.4641	+	17.0526i	−0.914790	+	1.07850i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	−5.19615	−	1.00000i	−0.327327	−	0.0629941i
$253$		0			0
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$	7.46410	+	4.92820i	0.467420	+	0.308616i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	0.268101	−	0.963391i	$-0.413604\pi$
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	−0.700270	+	0.713878i	$0.746937\pi$
$258$		−	44.0000i		−	2.73932i
$259$	14.0000	+	12.1244i	0.869918	+	0.753371i
$260$	−4.00000	−	8.00000i	−0.248069	−	0.496139i
$261$	2.50000	−	4.33013i	0.154746	−	0.268028i
$262$	−12.1244	+	7.00000i	−0.749045	+	0.432461i
$263$	12.9904	−	7.50000i	0.801021	−	0.462470i	−0.0428069	−	0.999083i	$-0.513630\pi$
$263$	12.9904	−	7.50000i	0.801021	−	0.462470i	0.843828	+	0.536614i	$0.180297\pi$
$264$		0			0
$265$	−6.00000	−	12.0000i	−0.368577	−	0.737154i
$266$	−30.0000	+	10.3923i	−1.83942	+	0.637193i
$267$		0			0
$268$	1.73205	+	1.00000i	0.105802	+	0.0610847i
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	0.880866	−	0.473366i	$-0.156961\pi$
$269$	0.500000	+	0.866025i	0.0304855	+	0.0528025i	−0.850380	+	0.526169i	$0.823628\pi$
$270$	−14.9282	−	9.85641i	−0.908502	−	0.599842i
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−0.500000	+	0.866025i	−0.0303728	+	0.0526073i	0.850439	+	0.526073i	$0.176336\pi$
$272$		−	8.00000i		−	0.485071i
$273$	−3.46410	−	10.0000i	−0.209657	−	0.605228i
$274$	30.0000			1.81237
$275$		0			0
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	−8.66025	−	5.00000i	−0.519408	−	0.299880i
$279$	−5.00000			−0.299342
$280$		0			0
$281$	16.0000			0.954480			0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000			0.954480			0.477240	+	0.878773i	$0.341637\pi$
$282$	41.5692	+	24.0000i	2.47541	+	1.42918i
$283$	14.7224	−	8.50000i	0.875158	−	0.505273i	0.00609896	−	0.999981i	$-0.498059\pi$
$283$	14.7224	−	8.50000i	0.875158	−	0.505273i	0.869059	+	0.494709i	$0.164725\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$	26.7846	+	1.60770i	1.58658	+	0.0952316i
$286$		0			0
$287$	18.1865	+	3.50000i	1.07352	+	0.206598i
$288$		−	8.00000i		−	0.471405i
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$	12.3205	−	18.6603i	0.723485	−	1.09577i
$291$	7.00000	+	12.1244i	0.410347	+	0.710742i
$292$	10.3923	+	6.00000i	0.608164	+	0.351123i
$293$			27.0000i			1.57736i	0.614806	+	0.788678i	$0.289234\pi$
$293$			27.0000i			1.57736i	−0.614806	+	0.788678i	$0.710766\pi$
$294$	−26.0000	−	10.3923i	−1.51635	−	0.606092i
$295$	8.00000	−	4.00000i	0.465778	−	0.232889i
$296$		0			0
$297$		0			0
$298$	−24.2487	+	14.0000i	−1.40469	+	0.810998i
$299$	1.00000	−	1.73205i	0.0578315	−	0.100167i
$300$	16.0000	+	12.0000i	0.923760	+	0.692820i
$301$	5.50000	−	28.5788i	0.317015	−	1.64726i
$302$			26.0000i			1.49613i
$303$	10.3923	+	6.00000i	0.597022	+	0.344691i
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$	−14.9282	−	9.85641i	−0.854786	−	0.564376i
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$			14.0000i			0.799022i	0.916728	+	0.399511i	$0.130820\pi$
$307$			14.0000i			0.799022i	−0.916728	+	0.399511i	$0.869180\pi$
$308$		0			0
$309$	−14.0000			−0.796432
$310$	−22.3205	−	1.33975i	−1.26772	−	0.0760925i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	18.1865	+	10.5000i	1.02796	+	0.593495i	0.916401	−	0.400262i	$-0.131081\pi$
$313$	18.1865	+	10.5000i	1.02796	+	0.593495i	0.111563	+	0.993757i	$0.464414\pi$
$314$	−6.00000			−0.338600
$315$	4.23205	+	4.13397i	0.238449	+	0.232923i
$316$	−28.0000			−1.57512
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	−20.7846	+	12.0000i	−1.16554	+	0.672927i
$319$		0			0
$320$	1.07180	−	17.8564i	0.0599153	−	0.998203i
$321$	−32.0000			−1.78607
$322$	−1.73205	−	5.00000i	−0.0965234	−	0.278639i
$323$		−	12.0000i		−	0.667698i
$324$	−11.0000	+	19.0526i	−0.611111	+	1.05848i
$325$	−1.19615	+	9.92820i	−0.0663506	+	0.550718i
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$	17.3205	+	10.0000i	0.957826	+	0.553001i
$328$		0			0
$329$	24.0000	+	20.7846i	1.32316	+	1.14589i
$330$		0			0
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	−0.652680	−	0.757634i	$-0.726355\pi$
$331$	6.00000	−	10.3923i	0.329790	−	0.571213i	0.982470	+	0.186421i	$0.0596888\pi$
$332$	−29.4449	+	17.0000i	−1.61600	+	0.932996i
$333$	−6.06218	+	3.50000i	−0.332205	+	0.191799i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$	−1.00000	−	2.00000i	−0.0546358	−	0.109272i
$336$	4.00000	−	20.7846i	0.218218	−	1.13389i
$337$			30.0000i			1.63420i	0.576493	+	0.817102i	$0.304421\pi$
$337$			30.0000i			1.63420i	−0.576493	+	0.817102i	$0.695579\pi$
$338$	15.5885	+	9.00000i	0.847900	+	0.489535i
$339$	15.0000	+	25.9808i	0.814688	+	1.41108i
$340$	4.92820	−	7.46410i	0.267269	−	0.404798i
$341$		0			0
$342$		−	12.0000i		−	0.648886i
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$	−0.267949	+	4.46410i	−0.0144259	+	0.240339i
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	5.19615	−	3.00000i	0.278944	−	0.161048i	−0.354001	−	0.935245i	$-0.615179\pi$
$347$	5.19615	−	3.00000i	0.278944	−	0.161048i	0.632945	+	0.774197i	$0.281846\pi$
$348$	−17.3205	−	10.0000i	−0.928477	−	0.536056i
$349$	−19.0000			−1.01705			−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000			−1.01705			−0.508523	+	0.861048i	$0.669808\pi$
$350$	17.7846	+	19.5885i	0.950627	+	1.04705i
$351$	−8.00000			−0.427008
$352$		0			0
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	−0.141344	−	0.989960i	$-0.545142\pi$
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	0.786659	+	0.617388i	$0.211809\pi$
$354$	−8.00000	−	13.8564i	−0.425195	−	0.736460i
$355$	−1.07180	+	17.8564i	−0.0568851	+	0.947720i
$356$		0			0
$357$	6.92820	−	8.00000i	0.366679	−	0.423405i
$358$		−	22.0000i		−	1.16274i
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	−0.414855	−	0.909887i	$-0.636168\pi$
$359$	11.0000	−	19.0526i	0.580558	−	1.00556i	0.995413	−	0.0956683i	$-0.0304988\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$		0			0
$363$			22.0000i			1.15470i
$364$	−10.0000	+	3.46410i	−0.524142	+	0.181568i
$365$	−6.00000	−	12.0000i	−0.314054	−	0.628109i
$366$	−16.0000	+	27.7128i	−0.836333	+	1.44857i
$367$	−23.3827	+	13.5000i	−1.22057	+	0.704694i	−0.965039	−	0.262108i	$-0.915582\pi$
$367$	−23.3827	+	13.5000i	−1.22057	+	0.704694i	−0.255528	+	0.966802i	$0.582249\pi$
$368$	3.46410	−	2.00000i	0.180579	−	0.104257i
$369$	−3.50000	+	6.06218i	−0.182203	+	0.315584i
$370$	−28.0000	+	14.0000i	−1.45565	+	0.727825i
$371$	−15.0000	+	5.19615i	−0.778761	+	0.269771i
$372$			20.0000i			1.03695i
$373$	−12.9904	−	7.50000i	−0.672616	−	0.388335i	0.124451	−	0.992226i	$-0.460283\pi$
$373$	−12.9904	−	7.50000i	−0.672616	−	0.388335i	−0.797067	+	0.603890i	$0.793616\pi$
$374$		0			0
$375$	−7.53590	−	21.0526i	−0.389152	−	1.08715i
$376$		0			0
$377$		−	10.0000i		−	0.515026i
$378$	−13.8564	+	16.0000i	−0.712697	+	0.822951i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	1.60770	−	26.7846i	0.0824730	−	1.37402i
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	−10.3923	+	6.00000i	−0.531717	+	0.306987i
$383$	−21.6506	−	12.5000i	−1.10630	−	0.638720i	−0.168428	−	0.985714i	$-0.553869\pi$
$383$	−21.6506	−	12.5000i	−1.10630	−	0.638720i	−0.937867	+	0.346994i	$0.887203\pi$
$384$		0			0
$385$		0			0
$386$	32.0000			1.62876
$387$	9.52628	+	5.50000i	0.484248	+	0.279581i
$388$	12.1244	−	7.00000i	0.615521	−	0.355371i
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	0.949432	−	0.313972i	$-0.101660\pi$
$389$	4.00000	+	6.92820i	0.202808	+	0.351274i	−0.746624	+	0.665246i	$0.768327\pi$
$390$	17.8564	+	1.07180i	0.904194	+	0.0542725i
$391$	2.00000			0.101144
$392$		0			0
$393$		−	14.0000i		−	0.706207i
$394$	14.0000	−	24.2487i	0.705310	−	1.22163i
$395$	26.1244	+	17.2487i	1.31446	+	0.867877i
$396$		0			0
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	0.455905	−	0.890028i	$-0.349316\pi$
$397$	−1.73205	−	1.00000i	−0.0869291	−	0.0501886i	−0.542834	+	0.839840i	$0.682649\pi$
$398$			52.0000i			2.60652i
$399$	6.00000	−	31.1769i	0.300376	−	1.56080i
$400$	−12.0000	+	16.0000i	−0.600000	+	0.800000i
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	−3.46410	+	2.00000i	−0.172774	+	0.0997509i
$403$	−8.66025	+	5.00000i	−0.431398	+	0.249068i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$	22.0000	−	11.0000i	1.09319	−	0.546594i
$406$	−20.0000	−	17.3205i	−0.992583	−	0.859602i
$407$		0			0
$408$		0			0
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$	−17.2487	+	26.1244i	−0.851853	+	1.29019i
$411$	−15.0000	+	25.9808i	−0.739895	+	1.28154i
$412$			14.0000i			0.689730i
$413$	−3.46410	−	10.0000i	−0.170457	−	0.492068i
$414$	2.00000			0.0982946
$415$	37.9449	+	2.27757i	1.86264	+	0.111801i
$416$	−8.00000	−	13.8564i	−0.392232	−	0.679366i
$417$	8.66025	−	5.00000i	0.424094	−	0.244851i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$	16.5359	−	16.9282i	0.806869	−	0.826012i
$421$	−18.0000			−0.877266			−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000			−0.877266			−0.438633	+	0.898666i	$0.644537\pi$
$422$	8.66025	+	5.00000i	0.421575	+	0.243396i
$423$	−10.3923	+	6.00000i	−0.505291	+	0.291730i
$424$		0			0
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$	32.0000			1.55041
$427$	−13.8564	+	16.0000i	−0.670559	+	0.774294i
$428$			32.0000i			1.54678i
$429$		0			0
$430$	41.0526	+	27.1051i	1.97973	+	1.30712i
$431$	−8.00000	−	13.8564i	−0.385346	−	0.667440i	0.606471	−	0.795106i	$-0.292585\pi$
$431$	−8.00000	−	13.8564i	−0.385346	−	0.667440i	−0.991817	+	0.127666i	$0.959251\pi$
$432$	−13.8564	−	8.00000i	−0.666667	−	0.384900i
$433$		−	19.0000i		−	0.913082i	−0.889702	−	0.456541i	$-0.849088\pi$
$433$		−	19.0000i		−	0.913082i	0.889702	−	0.456541i	$-0.150912\pi$
$434$	−5.00000	+	25.9808i	−0.240008	+	1.24712i
$435$	10.0000	+	20.0000i	0.479463	+	0.958927i
$436$	10.0000	−	17.3205i	0.478913	−	0.829502i
$437$	5.19615	−	3.00000i	0.248566	−	0.143509i
$438$	−20.7846	+	12.0000i	−0.993127	+	0.573382i
$439$	−10.5000	+	18.1865i	−0.501138	+	0.867996i	0.498861	+	0.866682i	$0.333752\pi$
$439$	−10.5000	+	18.1865i	−0.501138	+	0.867996i	−0.999999	+	0.00131415i	$0.999582\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		−	8.00000i		−	0.380521i
$443$	8.66025	+	5.00000i	0.411461	+	0.237557i	0.691417	−	0.722456i	$-0.256987\pi$
$443$	8.66025	+	5.00000i	0.411461	+	0.237557i	−0.279956	+	0.960013i	$0.590320\pi$
$444$	14.0000	+	24.2487i	0.664411	+	1.15079i
$445$		0			0
$446$		0			0
$447$		−	28.0000i		−	1.32435i
$448$	−20.7846	−	4.00000i	−0.981981	−	0.188982i
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$	−9.19615	+	3.92820i	−0.433511	+	0.185177i
$451$		0			0
$452$	25.9808	−	15.0000i	1.22203	−	0.705541i
$453$	−22.5167	−	13.0000i	−1.05792	−	0.610793i
$454$	14.0000			0.657053
$455$	11.4641	+	2.92820i	0.537445	+	0.137276i
$456$		0			0
$457$	19.0526	+	11.0000i	0.891241	+	0.514558i	0.874348	−	0.485299i	$-0.161289\pi$
$457$	19.0526	+	11.0000i	0.891241	+	0.514558i	0.0168929	+	0.999857i	$0.494623\pi$
$458$	−6.92820	+	4.00000i	−0.323734	+	0.186908i
$459$	−4.00000	−	6.92820i	−0.186704	−	0.323381i
$460$	4.46410	+	0.267949i	0.208140	+	0.0124932i
$461$	−3.00000			−0.139724			−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000			−0.139724			−0.0698620	+	0.997557i	$0.522256\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$	10.0000	−	17.3205i	0.464238	−	0.804084i
$465$	12.3205	−	18.6603i	0.571350	−	0.865349i
$466$	8.00000	+	13.8564i	0.370593	+	0.641886i
$467$	−31.1769	−	18.0000i	−1.44270	−	0.832941i	−0.444667	−	0.895696i	$-0.646678\pi$
$467$	−31.1769	−	18.0000i	−1.44270	−	0.832941i	−0.998029	+	0.0627555i	$0.980011\pi$
$468$		−	4.00000i		−	0.184900i
$469$	−2.50000	+	0.866025i	−0.115439	+	0.0399893i
$470$	−48.0000	+	24.0000i	−2.21407	+	1.10704i
$471$	3.00000	−	5.19615i	0.138233	−	0.239426i
$472$		0			0
$473$		0			0
$474$	28.0000	−	48.4974i	1.28608	−	2.22756i
$475$	−18.0000	+	24.0000i	−0.825897	+	1.10120i
$476$	−8.00000	−	6.92820i	−0.366679	−	0.317554i
$477$		−	6.00000i		−	0.274721i
$478$	25.9808	+	15.0000i	1.18833	+	0.686084i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	29.8564	+	19.7128i	1.36275	+	0.899763i
$481$	−7.00000	+	12.1244i	−0.319173	+	0.552823i
$482$			40.0000i			1.82195i
$483$	5.19615	+	1.00000i	0.236433	+	0.0455016i
$484$	22.0000			1.00000
$485$	−15.6244	−	0.937822i	−0.709465	−	0.0425843i
$486$	−10.0000	−	17.3205i	−0.453609	−	0.785674i
$487$	−20.7846	+	12.0000i	−0.941841	+	0.543772i	−0.890537	−	0.454911i	$-0.849671\pi$
$487$	−20.7846	+	12.0000i	−0.941841	+	0.543772i	−0.0513038	+	0.998683i	$0.516338\pi$
$488$		0			0
$489$	20.0000			0.904431
$490$	25.7128	−	17.8564i	1.16159	−	0.806670i
$491$	4.00000			0.180517			0.0902587	−	0.995918i	$-0.471231\pi$
$491$	4.00000			0.180517			0.0902587	+	0.995918i	$0.471231\pi$
$492$	24.2487	+	14.0000i	1.09322	+	0.631169i
$493$	8.66025	−	5.00000i	0.390038	−	0.225189i
$494$	−12.0000	−	20.7846i	−0.539906	−	0.935144i
$495$		0			0
$496$	−20.0000			−0.898027
$497$	20.7846	+	4.00000i	0.932317	+	0.179425i
$498$		−	68.0000i		−	3.04715i
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$	−21.0526	+	7.53590i	−0.941499	+	0.337016i
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	41.5692	+	24.0000i	1.85533	+	1.07117i
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$		0			0
$505$	−12.0000	+	6.00000i	−0.533993	+	0.266996i
$506$		0			0
$507$	−15.5885	+	9.00000i	−0.692308	+	0.399704i
$508$	13.8564	−	8.00000i	0.614779	−	0.354943i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	8.00000	+	16.0000i	0.354246	+	0.708492i
$511$	−15.0000	+	5.19615i	−0.663561	+	0.229864i
$512$		−	32.0000i		−	1.41421i
$513$	−20.7846	−	12.0000i	−0.917663	−	0.529813i
$514$	−8.00000	−	13.8564i	−0.352865	−	0.611180i
$515$	8.62436	−	13.0622i	0.380035	−	0.575588i
$516$	22.0000	−	38.1051i	0.968496	−	1.67748i
$517$		0			0
$518$	12.1244	+	35.0000i	0.532714	+	1.53781i
$519$	−12.0000			−0.526742
$520$		0			0
$521$	11.0000	+	19.0526i	0.481919	+	0.834708i	0.999785	−	0.0207541i	$-0.00660670\pi$
$521$	11.0000	+	19.0526i	0.481919	+	0.834708i	−0.517866	+	0.855462i	$0.673273\pi$
$522$	8.66025	−	5.00000i	0.379049	−	0.218844i
$523$	−30.3109	−	17.5000i	−1.32540	−	0.765222i	−0.340818	−	0.940129i	$-0.610704\pi$
$523$	−30.3109	−	17.5000i	−1.32540	−	0.765222i	−0.984585	+	0.174908i	$0.944037\pi$
$524$	−14.0000			−0.611593
$525$	−25.8564	+	5.60770i	−1.12847	+	0.244740i
$526$	30.0000			1.30806
$527$	−8.66025	−	5.00000i	−0.377247	−	0.217803i
$528$		0			0
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	1.60770	−	26.7846i	0.0698338	−	1.16345i
$531$	4.00000			0.173585
$532$	−31.1769	−	6.00000i	−1.35169	−	0.260133i
$533$			14.0000i			0.606407i
$534$		0			0
$535$	19.7128	−	29.8564i	0.852259	−	1.29081i
$536$		0			0
$537$	19.0526	+	11.0000i	0.822179	+	0.474685i
$538$			2.00000i			0.0862261i
$539$		0			0
$540$	−8.00000	−	16.0000i	−0.344265	−	0.688530i
$541$	−10.5000	+	18.1865i	−0.451430	+	0.781900i	−0.998475	−	0.0552031i	$-0.982419\pi$
$541$	−10.5000	+	18.1865i	−0.451430	+	0.781900i	0.547045	+	0.837103i	$0.315753\pi$
$542$	−1.73205	+	1.00000i	−0.0743980	+	0.0429537i
$543$		0			0
$544$	8.00000	−	13.8564i	0.342997	−	0.594089i
$545$	−20.0000	+	10.0000i	−0.856706	+	0.428353i
$546$	4.00000	−	20.7846i	0.171184	−	0.889499i
$547$		−	38.0000i		−	1.62476i	−0.583127	−	0.812381i	$-0.698171\pi$
$547$		−	38.0000i		−	1.62476i	0.583127	−	0.812381i	$-0.301829\pi$
$548$	25.9808	+	15.0000i	1.10984	+	0.640768i
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$		0			0
$551$	15.0000	−	25.9808i	0.639021	−	1.10682i
$552$		0			0
$553$	24.2487	−	28.0000i	1.03116	−	1.19068i
$554$	−4.00000			−0.169944
$555$	1.87564	−	31.2487i	0.0796167	−	1.32643i
$556$	−5.00000	−	8.66025i	−0.212047	−	0.367277i
$557$	16.4545	−	9.50000i	0.697199	−	0.402528i	−0.109104	−	0.994030i	$-0.534798\pi$
$557$	16.4545	−	9.50000i	0.697199	−	0.402528i	0.806303	+	0.591502i	$0.201465\pi$
$558$	−8.66025	−	5.00000i	−0.366618	−	0.211667i
$559$	22.0000			0.930501
$560$	16.9282	+	16.5359i	0.715347	+	0.698769i
$561$		0			0
$562$	27.7128	+	16.0000i	1.16899	+	0.674919i
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	−0.553748	−	0.832684i	$-0.686803\pi$
$563$	−2.59808	+	1.50000i	−0.109496	+	0.0632175i	0.444252	+	0.895902i	$0.353470\pi$
$564$	24.0000	+	41.5692i	1.01058	+	1.75038i
$565$	−33.4808	−	2.00962i	−1.40855	−	0.0845453i
$566$	34.0000			1.42913
$567$	−9.52628	−	27.5000i	−0.400066	−	1.15489i
$568$		0			0
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	−0.963948	−	0.266090i	$-0.914268\pi$
$569$	−6.00000	+	10.3923i	−0.251533	+	0.435668i	0.712415	+	0.701758i	$0.247601\pi$
$570$	44.7846	+	29.5692i	1.87582	+	1.23852i
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	0.613933	−	0.789359i	$-0.289587\pi$
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	−0.990571	+	0.137002i	$0.956253\pi$
$572$		0			0
$573$		−	12.0000i		−	0.501307i
$574$	28.0000	+	24.2487i	1.16870	+	1.01212i
$575$	−4.00000	−	3.00000i	−0.166812	−	0.125109i
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	19.0526	−	11.0000i	0.793168	−	0.457936i	−0.0479084	−	0.998852i	$-0.515256\pi$
$577$	19.0526	−	11.0000i	0.793168	−	0.457936i	0.841077	+	0.540916i	$0.181922\pi$
$578$	−22.5167	+	13.0000i	−0.936570	+	0.540729i
$579$	−16.0000	+	27.7128i	−0.664937	+	1.15171i
$580$	20.0000	−	10.0000i	0.830455	−	0.415227i
$581$	8.50000	−	44.1673i	0.352639	−	1.83237i
$582$			28.0000i			1.16064i
$583$		0			0
$584$		0			0
$585$	−2.46410	+	3.73205i	−0.101878	+	0.154301i
$586$	−27.0000	+	46.7654i	−1.11536	+	1.93186i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	−17.3205	−	22.0000i	−0.714286	−	0.907265i
$589$	−30.0000			−1.23613
$590$	17.8564	+	1.07180i	0.735137	+	0.0441252i
$591$	14.0000	+	24.2487i	0.575883	+	0.997459i
$592$	−24.2487	+	14.0000i	−0.996616	+	0.575396i
$593$	13.8564	+	8.00000i	0.569014	+	0.328521i	0.756756	−	0.653698i	$-0.226783\pi$
$593$	13.8564	+	8.00000i	0.569014	+	0.328521i	−0.187741	+	0.982219i	$0.560117\pi$
$594$		0			0
$595$	3.19615	+	11.3923i	0.131029	+	0.467039i
$596$	−28.0000			−1.14692
$597$	−45.0333	−	26.0000i	−1.84309	−	1.06411i
$598$	3.46410	−	2.00000i	0.141658	−	0.0817861i
$599$	0.500000	+	0.866025i	0.0204294	+	0.0353848i	0.876059	−	0.482203i	$-0.160163\pi$
$599$	0.500000	+	0.866025i	0.0204294	+	0.0353848i	−0.855630	+	0.517588i	$0.826830\pi$
$600$		0			0
$601$	−17.0000			−0.693444			−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000			−0.693444			−0.346722	+	0.937968i	$0.612705\pi$
$602$	38.1051	−	44.0000i	1.55305	−	1.79331i
$603$		−	1.00000i		−	0.0407231i
$604$	−13.0000	+	22.5167i	−0.528962	+	0.916190i
$605$	−20.5263	−	13.5526i	−0.834512	−	0.550990i
$606$	12.0000	+	20.7846i	0.487467	+	0.844317i
$607$	−15.5885	−	9.00000i	−0.632716	−	0.365299i	0.149087	−	0.988824i	$-0.452366\pi$
$607$	−15.5885	−	9.00000i	−0.632716	−	0.365299i	−0.781803	+	0.623525i	$0.785700\pi$
$608$		−	48.0000i		−	1.94666i
$609$	25.0000	−	8.66025i	1.01305	−	0.350931i
$610$	−16.0000	−	32.0000i	−0.647821	−	1.29564i
$611$	−12.0000	+	20.7846i	−0.485468	+	0.840855i
$612$	3.46410	−	2.00000i	0.140028	−	0.0808452i
$613$	29.4449	−	17.0000i	1.18927	−	0.686624i	0.231127	−	0.972924i	$-0.425759\pi$
$613$	29.4449	−	17.0000i	1.18927	−	0.686624i	0.958140	+	0.286300i	$0.0924254\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$	−14.0000	−	28.0000i	−0.564534	−	1.12907i
$616$		0			0
$617$			5.00000i			0.201292i	0.994922	+	0.100646i	$0.0320910\pi$
$617$			5.00000i			0.201292i	−0.994922	+	0.100646i	$0.967909\pi$
$618$	−24.2487	−	14.0000i	−0.975426	−	0.563163i
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−16.0000	−	27.7128i	−0.643094	−	1.11387i	0.341644	−	0.939829i	$-0.389016\pi$
$620$	−18.6603	−	12.3205i	−0.749414	−	0.494804i
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$		−	48.0000i		−	1.92462i
$623$		0			0
$624$	16.0000			0.640513
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	21.0000	+	36.3731i	0.839329	+	1.45376i
$627$		0			0
$628$	−5.19615	−	3.00000i	−0.207349	−	0.119713i
$629$	−14.0000			−0.558217
$630$	3.19615	+	11.3923i	0.127338	+	0.453880i
$631$	22.0000			0.875806			0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000			0.875806			0.437903	+	0.899022i	$0.355721\pi$
$632$		0			0
$633$	−8.66025	+	5.00000i	−0.344214	+	0.198732i
$634$	18.0000	+	31.1769i	0.714871	+	1.23819i
$635$	−17.8564	−	1.07180i	−0.708610	−	0.0425330i
$636$	−24.0000			−0.951662
$637$	5.19615	−	13.0000i	0.205879	−	0.515079i
$638$		0			0
$639$	−4.00000	+	6.92820i	−0.158238	+	0.274075i
$640$		0			0
$641$	−2.00000	−	3.46410i	−0.0789953	−	0.136824i	0.823821	−	0.566849i	$-0.191838\pi$
$641$	−2.00000	−	3.46410i	−0.0789953	−	0.136824i	−0.902817	+	0.430026i	$0.858505\pi$
$642$	−55.4256	−	32.0000i	−2.18747	−	1.26294i
$643$			19.0000i			0.749287i	0.927169	+	0.374643i	$0.122235\pi$
$643$			19.0000i			0.749287i	−0.927169	+	0.374643i	$0.877765\pi$
$644$	1.00000	−	5.19615i	0.0394055	−	0.204757i
$645$	−44.0000	+	22.0000i	−1.73250	+	0.866249i
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	32.9090	−	19.0000i	1.29378	−	0.746967i	0.314462	−	0.949270i	$-0.398176\pi$
$647$	32.9090	−	19.0000i	1.29378	−	0.746967i	0.979323	+	0.202303i	$0.0648426\pi$
$648$		0			0
$649$		0			0
$650$	−12.0000	+	16.0000i	−0.470679	+	0.627572i
$651$	−20.0000	−	17.3205i	−0.783862	−	0.678844i
$652$		−	20.0000i		−	0.783260i
$653$	−38.1051	−	22.0000i	−1.49117	−	0.860927i	−0.491220	−	0.871036i	$-0.663449\pi$
$653$	−38.1051	−	22.0000i	−1.49117	−	0.860927i	−0.999949	+	0.0101092i	$0.996782\pi$
$654$	20.0000	+	34.6410i	0.782062	+	1.35457i
$655$	13.0622	+	8.62436i	0.510382	+	0.336981i
$656$	−14.0000	+	24.2487i	−0.546608	+	0.946753i
$657$		−	6.00000i		−	0.234082i
$658$	20.7846	+	60.0000i	0.810268	+	2.33904i
$659$	48.0000			1.86981			0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000			1.86981			0.934907	+	0.354892i	$0.115482\pi$
$660$		0			0
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	−0.995069	−	0.0991864i	$-0.968376\pi$
$661$	−15.0000	−	25.9808i	−0.583432	−	1.01053i	0.411636	−	0.911348i	$-0.364957\pi$
$662$	20.7846	−	12.0000i	0.807817	−	0.466393i
$663$	6.92820	+	4.00000i	0.269069	+	0.155347i
$664$		0			0
$665$	25.3923	+	24.8038i	0.984671	+	0.961852i
$666$	−14.0000			−0.542489
$667$	4.33013	+	2.50000i	0.167663	+	0.0968004i
$668$	20.7846	−	12.0000i	0.804181	−	0.464294i
$669$		0			0
$670$	0.267949	−	4.46410i	0.0103518	−	0.172463i
$671$		0			0
$672$	27.7128	−	32.0000i	1.06904	−	1.23443i
$673$			24.0000i			0.925132i	0.886585	+	0.462566i	$0.153071\pi$
$673$			24.0000i			0.925132i	−0.886585	+	0.462566i	$0.846929\pi$
$674$	−30.0000	+	51.9615i	−1.15556	+	2.00148i
$675$	−2.39230	+	19.8564i	−0.0920799	+	0.764273i
$676$	9.00000	+	15.5885i	0.346154	+	0.599556i
$677$	−21.6506	−	12.5000i	−0.832102	−	0.480414i	0.0224702	−	0.999748i	$-0.492847\pi$
$677$	−21.6506	−	12.5000i	−0.832102	−	0.480414i	−0.854572	+	0.519333i	$0.826180\pi$
$678$			60.0000i			2.30429i
$679$	−3.50000	+	18.1865i	−0.134318	+	0.697935i
$680$		0			0
$681$	−7.00000	+	12.1244i	−0.268241	+	0.464606i
$682$		0			0
$683$	39.8372	−	23.0000i	1.52433	−	0.880071i	0.524742	−	0.851261i	$-0.324162\pi$
$683$	39.8372	−	23.0000i	1.52433	−	0.880071i	0.999585	−	0.0288092i	$-0.00917152\pi$
$684$	6.00000	−	10.3923i	0.229416	−	0.397360i
$685$	−15.0000	−	30.0000i	−0.573121	−	1.14624i
$686$	−17.0000	−	32.9090i	−0.649063	−	1.25647i
$687$		−	8.00000i		−	0.305219i
$688$	38.1051	+	22.0000i	1.45274	+	0.838742i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$	−4.92820	+	7.46410i	−0.187613	+	0.284153i
$691$	−24.5000	+	42.4352i	−0.932024	+	1.61431i	−0.152167	+	0.988355i	$0.548625\pi$
$691$	−24.5000	+	42.4352i	−0.932024	+	1.61431i	−0.779857	+	0.625958i	$0.784708\pi$
$692$			12.0000i			0.456172i
$693$		0			0
$694$	12.0000			0.455514
$695$	−0.669873	+	11.1603i	−0.0254097	+	0.423333i
$696$		0			0
$697$	−12.1244	+	7.00000i	−0.459243	+	0.265144i
$698$	−32.9090	−	19.0000i	−1.24562	−	0.719161i
$699$	−16.0000			−0.605176
$700$	5.60770	+	25.8564i	0.211951	+	0.977280i
$701$	−28.0000			−1.05755			−0.528773	−	0.848763i	$-0.677348\pi$
$701$	−28.0000			−1.05755			−0.528773	+	0.848763i	$0.677348\pi$
$702$	−13.8564	−	8.00000i	−0.522976	−	0.301941i
$703$	−36.3731	+	21.0000i	−1.37184	+	0.792030i
$704$		0			0
$705$	3.21539	−	53.5692i	0.121099	−	2.01753i
$706$	28.0000			1.05379
$707$	5.19615	+	15.0000i	0.195421	+	0.564133i
$708$		−	16.0000i		−	0.601317i
$709$	16.0000	−	27.7128i	0.600893	−	1.04078i	−0.391794	−	0.920053i	$-0.628145\pi$
$709$	16.0000	−	27.7128i	0.600893	−	1.04078i	0.992686	−	0.120723i	$-0.0385214\pi$
$710$	−19.7128	+	29.8564i	−0.739809	+	1.12049i
$711$	7.00000	+	12.1244i	0.262521	+	0.454699i
$712$		0			0
$713$		−	5.00000i		−	0.187251i
$714$	20.0000	−	6.92820i	0.748481	−	0.259281i
$715$		0			0
$716$	11.0000	−	19.0526i	0.411089	−	0.712028i
$717$	−25.9808	+	15.0000i	−0.970269	+	0.560185i
$718$	38.1051	−	22.0000i	1.42207	−	0.821033i
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$	−8.00000	+	4.00000i	−0.298142	+	0.149071i
$721$	−14.0000	−	12.1244i	−0.521387	−	0.451535i
$722$		−	34.0000i		−	1.26535i
$723$	−34.6410	−	20.0000i	−1.28831	−	0.743808i
$724$		0			0
$725$	−24.8205	−	2.99038i	−0.921811	−	0.111060i
$726$	−22.0000	+	38.1051i	−0.816497	+	1.41421i
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$	1.60770	−	26.7846i	0.0595035	−	0.991343i
$731$	11.0000	+	19.0526i	0.406850	+	0.704684i
$732$	−27.7128	+	16.0000i	−1.02430	+	0.591377i
$733$	30.3109	+	17.5000i	1.11956	+	0.646377i	0.941288	−	0.337604i	$-0.109617\pi$
$733$	30.3109	+	17.5000i	1.11956	+	0.646377i	0.178270	+	0.983982i	$0.442950\pi$
$734$	−54.0000			−1.99318
$735$	2.60770	+	31.1962i	0.0961863	+	1.15069i
$736$	8.00000			0.294884
$737$		0			0
$738$	−12.1244	+	7.00000i	−0.446304	+	0.257674i
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	0.999849	+	0.0174060i	$0.00554079\pi$
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	−0.484850	+	0.874597i	$0.661126\pi$
$740$	−31.2487	−	1.87564i	−1.14873	−	0.0689501i
$741$	24.0000			0.881662
$742$	−31.1769	−	6.00000i	−1.14454	−	0.220267i
$743$			31.0000i			1.13728i	0.822587	+	0.568640i	$0.192530\pi$
$743$			31.0000i			1.13728i	−0.822587	+	0.568640i	$0.807470\pi$
$744$		0			0
$745$	26.1244	+	17.2487i	0.957122	+	0.631944i
$746$	−15.0000	−	25.9808i	−0.549189	−	0.951223i
$747$	14.7224	+	8.50000i	0.538666	+	0.310999i
$748$		0			0
$749$	−32.0000	−	27.7128i	−1.16925	−	1.01260i
$750$	8.00000	−	44.0000i	0.292119	−	1.60665i
$751$	21.0000	−	36.3731i	0.766301	−	1.32727i	−0.173255	−	0.984877i	$-0.555429\pi$
$751$	21.0000	−	36.3731i	0.766301	−	1.32727i	0.939556	−	0.342395i	$-0.111238\pi$
$752$	−41.5692	+	24.0000i	−1.51587	+	0.875190i
$753$	−41.5692	+	24.0000i	−1.51487	+	0.874609i
$754$	10.0000	−	17.3205i	0.364179	−	0.630776i
$755$	26.0000	−	13.0000i	0.946237	−	0.473118i
$756$	−20.0000	+	6.92820i	−0.727393	+	0.251976i
$757$			49.0000i			1.78094i	0.455047	+	0.890468i	$0.349623\pi$
$757$			49.0000i			1.78094i	−0.455047	+	0.890468i	$0.650377\pi$
$758$	−34.6410	−	20.0000i	−1.25822	−	0.726433i
$759$		0			0
$760$		0			0
$761$	−8.50000	+	14.7224i	−0.308125	+	0.533688i	−0.977952	−	0.208829i	$-0.933035\pi$
$761$	−8.50000	+	14.7224i	−0.308125	+	0.533688i	0.669827	+	0.742517i	$0.266368\pi$
$762$			32.0000i			1.15924i
$763$	8.66025	+	25.0000i	0.313522	+	0.905061i
$764$	−12.0000			−0.434145
$765$	−4.46410	−	0.267949i	−0.161400	−	0.00968772i
$766$	−25.0000	−	43.3013i	−0.903287	−	1.56454i
$767$	6.92820	−	4.00000i	0.250163	−	0.144432i
$768$	27.7128	+	16.0000i	1.00000	+	0.577350i
$769$	−18.0000			−0.649097			−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000			−0.649097			−0.324548	+	0.945869i	$0.605212\pi$
$770$		0			0
$771$	16.0000			0.576226
$772$	27.7128	+	16.0000i	0.997406	+	0.575853i
$773$	−18.1865	+	10.5000i	−0.654124	+	0.377659i	−0.790034	−	0.613062i	$-0.789937\pi$
$773$	−18.1865	+	10.5000i	−0.654124	+	0.377659i	0.135910	+	0.990721i	$0.456604\pi$
$774$	11.0000	+	19.0526i	0.395387	+	0.684830i
$775$	9.82051	+	22.9904i	0.352763	+	0.825839i
$776$		0			0
$777$	−36.3731	−	7.00000i	−1.30488	−	0.251124i
$778$			16.0000i			0.573628i
$779$	−21.0000	+	36.3731i	−0.752403	+	1.30320i
$780$	14.9282	+	9.85641i	0.534515	+	0.352916i
$781$		0			0
$782$	3.46410	+	2.00000i	0.123876	+	0.0715199i
$783$		−	20.0000i		−	0.714742i
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	3.00000	+	6.00000i	0.107075	+	0.214149i
$786$	14.0000	−	24.2487i	0.499363	−	0.864923i
$787$	−27.7128	+	16.0000i	−0.987855	+	0.570338i	−0.904632	−	0.426193i	$-0.859855\pi$
$787$	−27.7128	+	16.0000i	−0.987855	+	0.570338i	−0.0832226	+	0.996531i	$0.526521\pi$
$788$	24.2487	−	14.0000i	0.863825	−	0.498729i
$789$	−15.0000	+	25.9808i	−0.534014	+	0.924940i
$790$	28.0000	+	56.0000i	0.996195	+	1.99239i
$791$	−7.50000	+	38.9711i	−0.266669	+	1.38565i
$792$		0			0
$793$	−13.8564	−	8.00000i	−0.492055	−	0.284088i
$794$	−2.00000	−	3.46410i	−0.0709773	−	0.122936i
$795$	22.3923	+	14.7846i	0.794173	+	0.524356i
$796$	−26.0000	+	45.0333i	−0.921546	+	1.59616i
$797$			13.0000i			0.460484i	0.973133	+	0.230242i	$0.0739517\pi$
$797$			13.0000i			0.460484i	−0.973133	+	0.230242i	$0.926048\pi$
$798$	41.5692	−	48.0000i	1.47153	−	1.69918i
$799$	−24.0000			−0.849059
$800$	−36.7846	+	15.7128i	−1.30053	+	0.555532i
$801$		0			0
$802$	20.7846	−	12.0000i	0.733930	−	0.423735i
$803$		0			0
$804$	−4.00000			−0.141069
$805$	−4.13397	+	4.23205i	−0.145703	+	0.149160i
$806$	−20.0000			−0.704470
$807$	−1.73205	−	1.00000i	−0.0609711	−	0.0352017i
$808$		0			0
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	0.663316	−	0.748340i	$-0.269149\pi$
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	−0.979739	+	0.200279i	$0.935815\pi$
$810$	49.1051	+	2.94744i	1.72538	+	0.103563i
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$	−8.66025	−	25.0000i	−0.303915	−	0.877328i
$813$		−	2.00000i		−	0.0701431i
$814$		0			0
$815$	−12.3205	+	18.6603i	−0.431569	+	0.653640i
$816$	8.00000	+	13.8564i	0.280056	+	0.485071i
$817$	57.1577	+	33.0000i	1.99969	+	1.15452i
$818$			52.0000i			1.81814i
$819$	4.00000	+	3.46410i	0.139771	+	0.121046i
$820$	−28.0000	+	14.0000i	−0.977802	+	0.488901i
$821$	23.5000	−	40.7032i	0.820156	−	1.42055i	−0.0854103	−	0.996346i	$-0.527220\pi$
$821$	23.5000	−	40.7032i	0.820156	−	1.42055i	0.905566	−	0.424205i	$-0.139447\pi$
$822$	−51.9615	+	30.0000i	−1.81237	+	1.04637i
$823$	43.3013	−	25.0000i	1.50939	−	0.871445i	0.509447	−	0.860502i	$-0.329850\pi$
$823$	43.3013	−	25.0000i	1.50939	−	0.871445i	0.999940	−	0.0109433i	$-0.00348344\pi$
$824$		0			0
$825$		0			0
$826$	4.00000	−	20.7846i	0.139178	−	0.723189i
$827$			9.00000i			0.312961i	0.987681	+	0.156480i	$0.0500148\pi$
$827$			9.00000i			0.312961i	−0.987681	+	0.156480i	$0.949985\pi$
$828$	1.73205	+	1.00000i	0.0601929	+	0.0347524i
$829$	16.5000	+	28.5788i	0.573069	+	0.992584i	0.996249	+	0.0865384i	$0.0275805\pi$
$829$	16.5000	+	28.5788i	0.573069	+	0.992584i	−0.423180	+	0.906046i	$0.639086\pi$
$830$	63.4449	+	41.8897i	2.20220	+	1.45401i
$831$	2.00000	−	3.46410i	0.0693792	−	0.120168i
$832$		−	16.0000i		−	0.554700i
$833$	13.8564	−	2.00000i	0.480096	−	0.0692959i
$834$	20.0000			0.692543
$835$	−26.7846	−	1.60770i	−0.926920	−	0.0556366i
$836$		0			0
$837$	−17.3205	+	10.0000i	−0.598684	+	0.345651i
$838$	20.7846	+	12.0000i	0.717992	+	0.414533i
$839$	42.0000			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−31.1769	−	18.0000i	−1.07443	−	0.620321i
$843$	−27.7128	+	16.0000i	−0.954480	+	0.551069i
$844$	5.00000	+	8.66025i	0.172107	+	0.298098i
$845$	1.20577	−	20.0885i	0.0414798	−	0.691064i
$846$	−24.0000			−0.825137
$847$	−19.0526	+	22.0000i	−0.654654	+	0.755929i
$848$		−	24.0000i		−	0.824163i
$849$	−17.0000	+	29.4449i	−0.583438	+	1.01055i
$850$	−19.8564	−	2.39230i	−0.681069	−	0.0820554i
$851$	−3.50000	−	6.06218i	−0.119978	−	0.207809i
$852$	27.7128	+	16.0000i	0.949425	+	0.548151i
$853$			48.0000i			1.64349i	0.569856	+	0.821744i	$0.306999\pi$
$853$			48.0000i			1.64349i	−0.569856	+	0.821744i	$0.693001\pi$
$854$	−40.0000	+	13.8564i	−1.36877	+	0.474156i
$855$	−12.0000	+	6.00000i	−0.410391	+	0.205196i
$856$		0			0
$857$	20.7846	−	12.0000i	0.709989	−	0.409912i	−0.101068	−	0.994880i	$-0.532226\pi$
$857$	20.7846	−	12.0000i	0.709989	−	0.409912i	0.811057	+	0.584967i	$0.198893\pi$
$858$		0			0
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	−0.999982	−	0.00607046i	$-0.998068\pi$
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	0.505248	+	0.862974i	$0.331401\pi$
$860$	22.0000	+	44.0000i	0.750194	+	1.50039i
$861$	−35.0000	+	12.1244i	−1.19280	+	0.413197i
$862$		−	32.0000i		−	1.08992i
$863$	−20.7846	−	12.0000i	−0.707516	−	0.408485i	0.102624	−	0.994720i	$-0.467276\pi$
$863$	−20.7846	−	12.0000i	−0.707516	−	0.408485i	−0.810141	+	0.586235i	$0.800609\pi$
$864$	−16.0000	−	27.7128i	−0.544331	−	0.942809i
$865$	7.39230	−	11.1962i	0.251346	−	0.380681i
$866$	19.0000	−	32.9090i	0.645646	−	1.11829i
$867$		−	26.0000i		−	0.883006i
$868$	−17.3205	+	20.0000i	−0.587896	+	0.678844i
$869$		0			0
$870$	−2.67949	+	44.6410i	−0.0908433	+	1.51347i
$871$	−1.00000	−	1.73205i	−0.0338837	−	0.0586883i
$872$		0			0
$873$	−6.06218	−	3.50000i	−0.205174	−	0.118457i
$874$	12.0000			0.405906
$875$	10.6962	−	27.5788i	0.361596	−	0.932335i
$876$	−24.0000			−0.810885
$877$	43.3013	+	25.0000i	1.46218	+	0.844190i	0.999112	−	0.0421327i	$-0.0134152\pi$
$877$	43.3013	+	25.0000i	1.46218	+	0.844190i	0.463068	+	0.886323i	$0.346749\pi$
$878$	−36.3731	+	21.0000i	−1.22753	+	0.708716i
$879$	−27.0000	−	46.7654i	−0.910687	−	1.57736i
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	13.8564	−	2.00000i	0.466569	−	0.0673435i
$883$		−	6.00000i		−	0.201916i	−0.994891	−	0.100958i	$-0.967809\pi$
$883$		−	6.00000i		−	0.201916i	0.994891	−	0.100958i	$-0.0321908\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$	−9.85641	+	14.9282i	−0.331319	+	0.501806i
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	12.1244	+	7.00000i	0.407096	+	0.235037i	0.689541	−	0.724246i	$-0.257812\pi$
$887$	12.1244	+	7.00000i	0.407096	+	0.235037i	−0.282445	+	0.959283i	$0.591146\pi$
$888$		0			0
$889$	−4.00000	+	20.7846i	−0.134156	+	0.697093i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−62.3538	+	36.0000i	−2.08659	+	1.20469i
$894$	28.0000	−	48.4974i	0.936460	−	1.62200i
$895$	−22.0000	+	11.0000i	−0.735379	+	0.367689i
$896$		0			0
$897$			4.00000i			0.133556i
$898$	−38.1051	−	22.0000i	−1.27158	−	0.734150i
$899$	−12.5000	−	21.6506i	−0.416898	−	0.722089i
$900$	−9.92820	−	1.19615i	−0.330940	−	0.0398717i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$		0			0
$903$	19.0526	+	55.0000i	0.634029	+	1.83029i
$904$		0			0
$905$		0			0
$906$	−26.0000	−	45.0333i	−0.863792	−	1.49613i
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	−0.712084	−	0.702094i	$-0.752248\pi$
$907$	−13.8564	+	8.00000i	−0.460094	+	0.265636i	0.251990	+	0.967730i	$0.418915\pi$
$908$	12.1244	+	7.00000i	0.402361	+	0.232303i
$909$	−6.00000			−0.199007
$910$	16.9282	+	16.5359i	0.561164	+	0.548160i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	41.5692	+	24.0000i	1.37649	+	0.794719i
$913$		0			0
$914$	22.0000	+	38.1051i	0.727695	+	1.26041i
$915$	35.7128	+	2.14359i	1.18063	+	0.0708650i
$916$	−8.00000			−0.264327
$917$	12.1244	−	14.0000i	0.400381	−	0.462321i
$918$		−	16.0000i		−	0.528079i
$919$	2.00000	−	3.46410i	0.0659739	−	0.114270i	−0.831152	−	0.556046i	$-0.812318\pi$
$919$	2.00000	−	3.46410i	0.0659739	−	0.114270i	0.897126	+	0.441776i	$0.145651\pi$
$920$		0			0
$921$	−14.0000	−	24.2487i	−0.461316	−	0.799022i
$922$	−5.19615	−	3.00000i	−0.171126	−	0.0987997i
$923$			16.0000i			0.526646i
$924$		0			0
$925$	28.0000	+	21.0000i	0.920634	+	0.690476i
$926$	−24.0000	+	41.5692i	−0.788689	+	1.36605i
$927$	6.06218	−	3.50000i	0.199108	−	0.114955i
$928$	34.6410	−	20.0000i	1.13715	−	0.656532i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$	40.0000	−	20.0000i	1.31165	−	0.655826i
$931$	33.0000	−	25.9808i	1.08153	−	0.851485i
$932$			16.0000i			0.524097i
$933$	41.5692	+	24.0000i	1.36092	+	0.785725i
$934$	−36.0000	−	62.3538i	−1.17796	−	2.04028i
$935$		0			0
$936$		0			0
$937$		−	23.0000i		−	0.751377i	−0.926746	−	0.375689i	$-0.877406\pi$
$937$		−	23.0000i		−	0.751377i	0.926746	−	0.375689i	$-0.122594\pi$
$938$	−5.19615	−	1.00000i	−0.169660	−	0.0326512i
$939$	−42.0000			−1.37062
$940$	−53.5692	−	3.21539i	−1.74724	−	0.104874i
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.851146	−	0.524929i	$-0.824092\pi$
$941$	−27.0000	−	46.7654i	−0.880175	−	1.52451i	−0.0290288	−	0.999579i	$-0.509241\pi$
$942$	10.3923	−	6.00000i	0.338600	−	0.195491i
$943$	−6.06218	−	3.50000i	−0.197412	−	0.113976i
$944$	16.0000			0.520756
$945$	22.9282	+	5.85641i	0.745855	+	0.190509i
$946$		0			0
$947$	−36.3731	−	21.0000i	−1.18197	−	0.682408i	−0.225497	−	0.974244i	$-0.572401\pi$
$947$	−36.3731	−	21.0000i	−1.18197	−	0.682408i	−0.956469	+	0.291835i	$0.905734\pi$
$948$	48.4974	−	28.0000i	1.57512	−	0.909398i
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$	−55.1769	+	23.5692i	−1.79018	+	0.764686i
$951$	−36.0000			−1.16738
$952$		0			0
$953$		−	9.00000i		−	0.291539i	−0.989319	−	0.145769i	$-0.953434\pi$
$953$		−	9.00000i		−	0.291539i	0.989319	−	0.145769i	$-0.0465657\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$	11.1962	+	7.39230i	0.362299	+	0.239209i
$956$	15.0000	+	25.9808i	0.485135	+	0.840278i
$957$		0			0
$958$		0			0
$959$	−37.5000	+	12.9904i	−1.21094	+	0.419481i
$960$	16.0000	+	32.0000i	0.516398	+	1.03280i
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	−24.2487	+	14.0000i	−0.781810	+	0.451378i
$963$	13.8564	−	8.00000i	0.446516	−	0.257796i
$964$	−20.0000	+	34.6410i	−0.644157	+	1.11571i
$965$	−16.0000	−	32.0000i	−0.515058	−	1.03012i
$966$	8.00000	+	6.92820i	0.257396	+	0.222911i
$967$		−	10.0000i		−	0.321578i	−0.986989	−	0.160789i	$-0.948596\pi$
$967$		−	10.0000i		−	0.321578i	0.986989	−	0.160789i	$-0.0514039\pi$
$968$		0			0
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	−26.1244	−	17.2487i	−0.838803	−	0.553823i
$971$	−17.0000	+	29.4449i	−0.545556	+	0.944931i	0.453016	+	0.891503i	$0.350348\pi$
$971$	−17.0000	+	29.4449i	−0.545556	+	0.944931i	−0.998572	+	0.0534281i	$0.982985\pi$
$972$		−	20.0000i		−	0.641500i
$973$	12.9904	+	2.50000i	0.416452	+	0.0801463i
$974$	−48.0000			−1.53802
$975$	−7.85641	−	18.3923i	−0.251606	−	0.589025i
$976$	−16.0000	−	27.7128i	−0.512148	−	0.887066i
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	−0.229465	−	0.973317i	$-0.573698\pi$
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	0.728184	+	0.685381i	$0.240364\pi$
$978$	34.6410	+	20.0000i	1.10770	+	0.639529i
$979$		0			0
$980$	31.1962	−	2.60770i	0.996525	−	0.0832998i
$981$	−10.0000			−0.319275
$982$	6.92820	+	4.00000i	0.221088	+	0.127645i
$983$	18.1865	−	10.5000i	0.580060	−	0.334898i	−0.181097	−	0.983465i	$-0.557965\pi$
$983$	18.1865	−	10.5000i	0.580060	−	0.334898i	0.761157	+	0.648567i	$0.224631\pi$
$984$		0			0
$985$	−31.2487	−	1.87564i	−0.995667	−	0.0597630i
$986$	20.0000			0.636930
$987$	−62.3538	−	12.0000i	−1.98474	−	0.381964i
$988$		−	24.0000i		−	0.763542i
$989$	−5.50000	+	9.52628i	−0.174890	+	0.302918i
$990$		0			0
$991$	11.5000	+	19.9186i	0.365310	+	0.632735i	0.988826	−	0.149076i	$-0.0476298\pi$
$991$	11.5000	+	19.9186i	0.365310	+	0.632735i	−0.623516	+	0.781810i	$0.714296\pi$
$992$	−34.6410	−	20.0000i	−1.09985	−	0.635001i
$993$			24.0000i			0.761617i
$994$	32.0000	+	27.7128i	1.01498	+	0.878997i
$995$	52.0000	−	26.0000i	1.64851	−	0.824255i
$996$	34.0000	−	58.8897i	1.07733	−	1.86599i
$997$	−6.92820	+	4.00000i	−0.219418	+	0.126681i	−0.605681	−	0.795708i	$-0.707099\pi$
$997$	−6.92820	+	4.00000i	−0.219418	+	0.126681i	0.386263	+	0.922389i	$0.373766\pi$
$998$	53.6936	−	31.0000i	1.69964	−	0.981288i
$999$	−14.0000	+	24.2487i	−0.442940	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.s.c.254.2	yes	4
5.4	even	2	inner	805.2.s.c.254.1	✓	4
7.4	even	3	inner	805.2.s.c.599.1	yes	4
35.4	even	6	inner	805.2.s.c.599.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.s.c.254.1	✓	4	5.4	even	2	inner
805.2.s.c.254.2	yes	4	1.1	even	1	trivial
805.2.s.c.599.1	yes	4	7.4	even	3	inner
805.2.s.c.599.2	yes	4	35.4	even	6	inner

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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} -4.00000 q^{6} +(-2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.133975 - 2.23205i) q^{5} -4.00000 q^{6} +(-2.59808 - 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(2.46410 - 3.73205i) q^{10} +(-3.46410 - 2.00000i) q^{12} -2.00000i q^{13} +(-4.00000 - 3.46410i) q^{14} +(2.00000 + 4.00000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(1.73205 - 1.00000i) q^{17} +(1.73205 - 1.00000i) q^{18} +(3.00000 - 5.19615i) q^{19} +(4.00000 - 2.00000i) q^{20} +(5.00000 - 1.73205i) q^{21} +(0.866025 + 0.500000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +(2.00000 - 3.46410i) q^{26} -4.00000i q^{27} +(-1.73205 - 5.00000i) q^{28} +5.00000 q^{29} +(-0.535898 + 8.92820i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(6.92820 - 4.00000i) q^{32} +4.00000 q^{34} +(-1.46410 + 5.73205i) q^{35} +2.00000 q^{36} +(-6.06218 - 3.50000i) q^{37} +(10.3923 - 6.00000i) q^{38} +(2.00000 + 3.46410i) q^{39} -7.00000 q^{41} +(10.3923 + 2.00000i) q^{42} +11.0000i q^{43} +(-1.86603 - 1.23205i) q^{45} +(1.00000 + 1.73205i) q^{46} +(-10.3923 - 6.00000i) q^{47} +8.00000i q^{48} +(6.50000 + 2.59808i) q^{49} +(-8.00000 - 6.00000i) q^{50} +(-2.00000 + 3.46410i) q^{51} +(3.46410 - 2.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(4.00000 - 6.92820i) q^{54} +12.0000i q^{57} +(8.66025 + 5.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-4.92820 + 7.46410i) q^{60} +(4.00000 - 6.92820i) q^{61} -10.0000i q^{62} +(-1.73205 + 2.00000i) q^{63} +8.00000 q^{64} +(-4.46410 - 0.267949i) q^{65} +(0.866025 - 0.500000i) q^{67} +(3.46410 + 2.00000i) q^{68} -2.00000 q^{69} +(-8.26795 + 8.46410i) q^{70} -8.00000 q^{71} +(5.19615 - 3.00000i) q^{73} +(-7.00000 - 12.1244i) q^{74} +(9.19615 - 3.92820i) q^{75} +12.0000 q^{76} +8.00000i q^{78} +(-7.00000 + 12.1244i) q^{79} +(-7.46410 - 4.92820i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-12.1244 - 7.00000i) q^{82} +17.0000i q^{83} +(8.00000 + 6.92820i) q^{84} +(-2.00000 - 4.00000i) q^{85} +(-11.0000 + 19.0526i) q^{86} +(-8.66025 + 5.00000i) q^{87} +(-2.00000 - 4.00000i) q^{90} +(-1.00000 + 5.19615i) q^{91} +2.00000i q^{92} +(8.66025 + 5.00000i) q^{93} +(-12.0000 - 20.7846i) q^{94} +(-11.1962 - 7.39230i) q^{95} +(-8.00000 + 13.8564i) q^{96} -7.00000i q^{97} +(8.66025 + 11.0000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 4 q^{5} - 16 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 + 4 * q^5 - 16 * q^6 + 2 * q^9	\( 4 q + 4 q^{4} + 4 q^{5} - 16 q^{6} + 2 q^{9} - 4 q^{10} - 16 q^{14} + 8 q^{15} + 8 q^{16} + 12 q^{19} + 16 q^{20} + 20 q^{21} - 6 q^{25} + 8 q^{26} + 20 q^{29} - 16 q^{30} - 10 q^{31} + 16 q^{34} + 8 q^{35} + 8 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{45} + 4 q^{46} + 26 q^{49} - 32 q^{50} - 8 q^{51} + 16 q^{54} + 8 q^{59} + 8 q^{60} + 16 q^{61} + 32 q^{64} - 4 q^{65} - 8 q^{69} - 40 q^{70} - 32 q^{71} - 28 q^{74} + 16 q^{75} + 48 q^{76} - 28 q^{79} - 16 q^{80} + 22 q^{81} + 32 q^{84} - 8 q^{85} - 44 q^{86} - 8 q^{90} - 4 q^{91} - 48 q^{94} - 24 q^{95} - 32 q^{96}+O(q^{100}) \) 4 * q + 4 * q^4 + 4 * q^5 - 16 * q^6 + 2 * q^9 - 4 * q^10 - 16 * q^14 + 8 * q^15 + 8 * q^16 + 12 * q^19 + 16 * q^20 + 20 * q^21 - 6 * q^25 + 8 * q^26 + 20 * q^29 - 16 * q^30 - 10 * q^31 + 16 * q^34 + 8 * q^35 + 8 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^45 + 4 * q^46 + 26 * q^49 - 32 * q^50 - 8 * q^51 + 16 * q^54 + 8 * q^59 + 8 * q^60 + 16 * q^61 + 32 * q^64 - 4 * q^65 - 8 * q^69 - 40 * q^70 - 32 * q^71 - 28 * q^74 + 16 * q^75 + 48 * q^76 - 28 * q^79 - 16 * q^80 + 22 * q^81 + 32 * q^84 - 8 * q^85 - 44 * q^86 - 8 * q^90 - 4 * q^91 - 48 * q^94 - 24 * q^95 - 32 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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