LMFDB - Embedded newform 273.2.n.b.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(8,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("273.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.n (of order $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	273.8
Dual form			273.2.n.b.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(-1.70711 + 0.292893i) q^{3} +(2.70711 - 2.70711i) q^{5} +(-1.41421 + 2.00000i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(-1.70711 + 0.292893i) q^{3} +(2.70711 - 2.70711i) q^{5} +(-1.41421 + 2.00000i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.82843 - 1.00000i) q^{9} -5.41421i q^{10} +(-1.41421 - 1.41421i) q^{11} +(0.707107 - 3.53553i) q^{13} +1.41421i q^{14} +(-3.82843 + 5.41421i) q^{15} +4.00000 q^{16} +4.00000 q^{17} +(1.82843 - 3.82843i) q^{18} +(-1.87868 - 1.87868i) q^{19} +(1.00000 - 1.41421i) q^{21} -2.82843 q^{22} -1.82843 q^{23} +(-4.00000 - 2.82843i) q^{24} -9.65685i q^{25} +(-2.82843 - 4.24264i) q^{26} +(-4.53553 + 2.53553i) q^{27} +6.65685i q^{29} +(1.58579 + 9.24264i) q^{30} +(2.94975 + 2.94975i) q^{31} +(2.82843 + 2.00000i) q^{33} +(4.00000 - 4.00000i) q^{34} +3.82843i q^{35} +(-6.41421 + 6.41421i) q^{37} -3.75736 q^{38} +(-0.171573 + 6.24264i) q^{39} +10.8284 q^{40} +(0.242641 - 0.242641i) q^{41} +(-0.414214 - 2.41421i) q^{42} +6.65685i q^{43} +(4.94975 - 10.3640i) q^{45} +(-1.82843 + 1.82843i) q^{46} +(-1.87868 - 1.87868i) q^{47} +(-6.82843 + 1.17157i) q^{48} -1.00000i q^{49} +(-9.65685 - 9.65685i) q^{50} +(-6.82843 + 1.17157i) q^{51} +12.3137i q^{53} +(-2.00000 + 7.07107i) q^{54} -7.65685 q^{55} -2.82843 q^{56} +(3.75736 + 2.65685i) q^{57} +(6.65685 + 6.65685i) q^{58} +(1.41421 + 1.41421i) q^{59} -13.8995 q^{61} +5.89949 q^{62} +(-1.29289 + 2.70711i) q^{63} +8.00000i q^{64} +(-7.65685 - 11.4853i) q^{65} +(4.82843 - 0.828427i) q^{66} +(-9.07107 - 9.07107i) q^{67} +(3.12132 - 0.535534i) q^{69} +(3.82843 + 3.82843i) q^{70} +(11.2426 - 11.2426i) q^{71} +(7.65685 + 3.65685i) q^{72} +(0.121320 - 0.121320i) q^{73} +12.8284i q^{74} +(2.82843 + 16.4853i) q^{75} +2.00000 q^{77} +(6.07107 + 6.41421i) q^{78} +5.82843 q^{79} +(10.8284 - 10.8284i) q^{80} +(7.00000 - 5.65685i) q^{81} -0.485281i q^{82} +(0.707107 - 0.707107i) q^{83} +(10.8284 - 10.8284i) q^{85} +(6.65685 + 6.65685i) q^{86} +(-1.94975 - 11.3640i) q^{87} -5.65685i q^{88} +(5.87868 + 5.87868i) q^{89} +(-5.41421 - 15.3137i) q^{90} +(2.00000 + 3.00000i) q^{91} +(-5.89949 - 4.17157i) q^{93} -3.75736 q^{94} -10.1716 q^{95} +(-7.29289 - 7.29289i) q^{97} +(-1.00000 - 1.00000i) q^{98} +(-5.41421 - 2.58579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8	$ 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8} - 4 q^{15} + 16 q^{16} + 16 q^{17} - 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{23} - 16 q^{24} - 4 q^{27} + 12 q^{30} - 8 q^{31} + 16 q^{34} - 20 q^{37} - 32 q^{38} - 12 q^{39} + 32 q^{40} - 16 q^{41} + 4 q^{42} + 4 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{50} - 16 q^{51} - 8 q^{54} - 8 q^{55} + 32 q^{57} + 4 q^{58} - 16 q^{61} - 16 q^{62} - 8 q^{63} - 8 q^{65} + 8 q^{66} - 8 q^{67} + 4 q^{69} + 4 q^{70} + 28 q^{71} + 8 q^{72} - 8 q^{73} + 8 q^{77} - 4 q^{78} + 12 q^{79} + 32 q^{80} + 28 q^{81} + 32 q^{85} + 4 q^{86} + 12 q^{87} + 32 q^{89} - 16 q^{90} + 8 q^{91} + 16 q^{93} - 32 q^{94} - 52 q^{95} - 32 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8 - 4 * q^15 + 16 * q^16 + 16 * q^17 - 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^23 - 16 * q^24 - 4 * q^27 + 12 * q^30 - 8 * q^31 + 16 * q^34 - 20 * q^37 - 32 * q^38 - 12 * q^39 + 32 * q^40 - 16 * q^41 + 4 * q^42 + 4 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^50 - 16 * q^51 - 8 * q^54 - 8 * q^55 + 32 * q^57 + 4 * q^58 - 16 * q^61 - 16 * q^62 - 8 * q^63 - 8 * q^65 + 8 * q^66 - 8 * q^67 + 4 * q^69 + 4 * q^70 + 28 * q^71 + 8 * q^72 - 8 * q^73 + 8 * q^77 - 4 * q^78 + 12 * q^79 + 32 * q^80 + 28 * q^81 + 32 * q^85 + 4 * q^86 + 12 * q^87 + 32 * q^89 - 16 * q^90 + 8 * q^91 + 16 * q^93 - 32 * q^94 - 52 * q^95 - 32 * q^97 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.00000	−	1.00000i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.00000i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$3$	−1.70711	+	0.292893i	−0.985599	+	0.169102i
$4$		0			0
$5$	2.70711	−	2.70711i	1.21065	−	1.21065i	0.239843	−	0.970812i	$-0.422904\pi$
$5$	2.70711	−	2.70711i	1.21065	−	1.21065i	0.970812	−	0.239843i	$-0.0770961\pi$
$6$	−1.41421	+	2.00000i	−0.577350	+	0.816497i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	2.82843	−	1.00000i	0.942809	−	0.333333i
$10$		−	5.41421i		−	1.71212i
$11$	−1.41421	−	1.41421i	−0.426401	−	0.426401i	0.460999	−	0.887401i	$-0.347491\pi$
$11$	−1.41421	−	1.41421i	−0.426401	−	0.426401i	−0.887401	+	0.460999i	$0.847491\pi$
$12$		0			0
$13$	0.707107	−	3.53553i	0.196116	−	0.980581i
$13$	0.707107	−	3.53553i	0.196116	−	0.980581i
$14$			1.41421i			0.377964i
$15$	−3.82843	+	5.41421i	−0.988496	+	1.39794i
$16$	4.00000			1.00000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	1.82843	−	3.82843i	0.430964	−	0.902369i
$19$	−1.87868	−	1.87868i	−0.430999	−	0.430999i	0.457969	−	0.888968i	$-0.348577\pi$
$19$	−1.87868	−	1.87868i	−0.430999	−	0.430999i	−0.888968	+	0.457969i	$0.848577\pi$
$20$		0			0
$21$	1.00000	−	1.41421i	0.218218	−	0.308607i
$22$	−2.82843			−0.603023
$23$	−1.82843			−0.381253			−0.190627	−	0.981663i	$-0.561052\pi$
$23$	−1.82843			−0.381253			−0.190627	+	0.981663i	$0.561052\pi$
$24$	−4.00000	−	2.82843i	−0.816497	−	0.577350i
$25$		−	9.65685i		−	1.93137i
$26$	−2.82843	−	4.24264i	−0.554700	−	0.832050i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$		0			0
$29$			6.65685i			1.23615i	0.786120	+	0.618073i	$0.212087\pi$
$29$			6.65685i			1.23615i	−0.786120	+	0.618073i	$0.787913\pi$
$30$	1.58579	+	9.24264i	0.289524	+	1.68747i
$31$	2.94975	+	2.94975i	0.529790	+	0.529790i	0.920510	−	0.390720i	$-0.127774\pi$
$31$	2.94975	+	2.94975i	0.529790	+	0.529790i	−0.390720	+	0.920510i	$0.627774\pi$
$32$		0			0
$33$	2.82843	+	2.00000i	0.492366	+	0.348155i
$34$	4.00000	−	4.00000i	0.685994	−	0.685994i
$35$			3.82843i			0.647122i
$36$		0			0
$37$	−6.41421	+	6.41421i	−1.05449	+	1.05449i	−0.0560630	+	0.998427i	$0.517855\pi$
$37$	−6.41421	+	6.41421i	−1.05449	+	1.05449i	−0.998427	+	0.0560630i	$0.982145\pi$
$38$	−3.75736			−0.609524
$39$	−0.171573	+	6.24264i	−0.0274736	+	0.999623i
$40$	10.8284			1.71212
$41$	0.242641	−	0.242641i	0.0378941	−	0.0378941i	−0.687906	−	0.725800i	$-0.741470\pi$
$41$	0.242641	−	0.242641i	0.0378941	−	0.0378941i	0.725800	+	0.687906i	$0.241470\pi$
$42$	−0.414214	−	2.41421i	−0.0639145	−	0.372521i
$43$			6.65685i			1.01516i	0.861604	+	0.507580i	$0.169460\pi$
$43$			6.65685i			1.01516i	−0.861604	+	0.507580i	$0.830540\pi$
$44$		0			0
$45$	4.94975	−	10.3640i	0.737865	−	1.54497i
$46$	−1.82843	+	1.82843i	−0.269587	+	0.269587i
$47$	−1.87868	−	1.87868i	−0.274034	−	0.274034i	0.556688	−	0.830722i	$-0.312072\pi$
$47$	−1.87868	−	1.87868i	−0.274034	−	0.274034i	−0.830722	+	0.556688i	$0.812072\pi$
$48$	−6.82843	+	1.17157i	−0.985599	+	0.169102i
$49$		−	1.00000i		−	0.142857i
$50$	−9.65685	−	9.65685i	−1.36569	−	1.36569i
$51$	−6.82843	+	1.17157i	−0.956171	+	0.164053i
$52$		0			0
$53$			12.3137i			1.69142i	0.533644	+	0.845709i	$0.320822\pi$
$53$			12.3137i			1.69142i	−0.533644	+	0.845709i	$0.679178\pi$
$54$	−2.00000	+	7.07107i	−0.272166	+	0.962250i
$55$	−7.65685			−1.03245
$56$	−2.82843			−0.377964
$57$	3.75736	+	2.65685i	0.497674	+	0.351909i
$58$	6.65685	+	6.65685i	0.874088	+	0.874088i
$59$	1.41421	+	1.41421i	0.184115	+	0.184115i	0.793146	−	0.609031i	$-0.208442\pi$
$59$	1.41421	+	1.41421i	0.184115	+	0.184115i	−0.609031	+	0.793146i	$0.708442\pi$
$60$		0			0
$61$	−13.8995			−1.77965			−0.889824	−	0.456304i	$-0.849173\pi$
$61$	−13.8995			−1.77965			−0.889824	+	0.456304i	$0.849173\pi$
$62$	5.89949			0.749237
$63$	−1.29289	+	2.70711i	−0.162889	+	0.341063i
$64$			8.00000i			1.00000i
$65$	−7.65685	−	11.4853i	−0.949716	−	1.42457i
$66$	4.82843	−	0.828427i	0.594338	−	0.101972i
$67$	−9.07107	−	9.07107i	−1.10821	−	1.10821i	−0.993386	−	0.114821i	$-0.963371\pi$
$67$	−9.07107	−	9.07107i	−1.10821	−	1.10821i	−0.114821	−	0.993386i	$-0.536629\pi$
$68$		0			0
$69$	3.12132	−	0.535534i	0.375763	−	0.0644707i
$70$	3.82843	+	3.82843i	0.457585	+	0.457585i
$71$	11.2426	−	11.2426i	1.33426	−	1.33426i	0.432735	−	0.901521i	$-0.357549\pi$
$71$	11.2426	−	11.2426i	1.33426	−	1.33426i	0.901521	−	0.432735i	$-0.142451\pi$
$72$	7.65685	+	3.65685i	0.902369	+	0.430964i
$73$	0.121320	−	0.121320i	0.0141995	−	0.0141995i	−0.699971	−	0.714171i	$-0.746804\pi$
$73$	0.121320	−	0.121320i	0.0141995	−	0.0141995i	0.714171	+	0.699971i	$0.246804\pi$
$74$			12.8284i			1.49127i
$75$	2.82843	+	16.4853i	0.326599	+	1.90356i
$76$		0			0
$77$	2.00000			0.227921
$78$	6.07107	+	6.41421i	0.687413	+	0.726267i
$79$	5.82843			0.655749			0.327875	−	0.944721i	$-0.393668\pi$
$79$	5.82843			0.655749			0.327875	+	0.944721i	$0.393668\pi$
$80$	10.8284	−	10.8284i	1.21065	−	1.21065i
$81$	7.00000	−	5.65685i	0.777778	−	0.628539i
$82$		−	0.485281i		−	0.0535904i
$83$	0.707107	−	0.707107i	0.0776151	−	0.0776151i	−0.667234	−	0.744849i	$-0.732522\pi$
$83$	0.707107	−	0.707107i	0.0776151	−	0.0776151i	0.744849	+	0.667234i	$0.232522\pi$
$84$		0			0
$85$	10.8284	−	10.8284i	1.17451	−	1.17451i
$86$	6.65685	+	6.65685i	0.717827	+	0.717827i
$87$	−1.94975	−	11.3640i	−0.209035	−	1.21834i
$88$		−	5.65685i		−	0.603023i
$89$	5.87868	+	5.87868i	0.623139	+	0.623139i	0.946333	−	0.323194i	$-0.104757\pi$
$89$	5.87868	+	5.87868i	0.623139	+	0.623139i	−0.323194	+	0.946333i	$0.604757\pi$
$90$	−5.41421	−	15.3137i	−0.570708	−	1.61421i
$91$	2.00000	+	3.00000i	0.209657	+	0.314485i
$92$		0			0
$93$	−5.89949	−	4.17157i	−0.611749	−	0.432572i
$94$	−3.75736			−0.387542
$95$	−10.1716			−1.04358
$96$		0			0
$97$	−7.29289	−	7.29289i	−0.740481	−	0.740481i	0.232189	−	0.972671i	$-0.425411\pi$
$97$	−7.29289	−	7.29289i	−0.740481	−	0.740481i	−0.972671	+	0.232189i	$0.925411\pi$
$98$	−1.00000	−	1.00000i	−0.101015	−	0.101015i
$99$	−5.41421	−	2.58579i	−0.544149	−	0.259881i
$100$		0			0
$101$	−7.65685			−0.761885			−0.380943	−	0.924599i	$-0.624401\pi$
$101$	−7.65685			−0.761885			−0.380943	+	0.924599i	$0.624401\pi$
$102$	−5.65685	+	8.00000i	−0.560112	+	0.792118i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	8.48528	−	5.65685i	0.832050	−	0.554700i
$105$	−1.12132	−	6.53553i	−0.109430	−	0.637803i
$106$	12.3137	+	12.3137i	1.19601	+	1.19601i
$107$		−	0.828427i		−	0.0800871i	−0.999198	−	0.0400435i	$-0.987250\pi$
$107$		−	0.828427i		−	0.0800871i	0.999198	−	0.0400435i	$-0.0127497\pi$
$108$		0			0
$109$	4.17157	+	4.17157i	0.399564	+	0.399564i	0.878079	−	0.478515i	$-0.158825\pi$
$109$	4.17157	+	4.17157i	0.399564	+	0.399564i	−0.478515	+	0.878079i	$0.658825\pi$
$110$	−7.65685	+	7.65685i	−0.730052	+	0.730052i
$111$	9.07107	−	12.8284i	0.860988	−	1.21762i
$112$	−2.82843	+	2.82843i	−0.267261	+	0.267261i
$113$			9.82843i			0.924581i	0.886729	+	0.462290i	$0.152972\pi$
$113$			9.82843i			0.924581i	−0.886729	+	0.462290i	$0.847028\pi$
$114$	6.41421	−	1.10051i	0.600746	−	0.103072i
$115$	−4.94975	+	4.94975i	−0.461566	+	0.461566i
$116$		0			0
$117$	−1.53553	−	10.7071i	−0.141960	−	0.989872i
$118$	2.82843			0.260378
$119$	−2.82843	+	2.82843i	−0.259281	+	0.259281i
$120$	−18.4853	+	3.17157i	−1.68747	+	0.289524i
$121$		−	7.00000i		−	0.636364i
$122$	−13.8995	+	13.8995i	−1.25840	+	1.25840i
$123$	−0.343146	+	0.485281i	−0.0309404	+	0.0437563i
$124$		0			0
$125$	−12.6066	−	12.6066i	−1.12757	−	1.12757i
$126$	1.41421	+	4.00000i	0.125988	+	0.356348i
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	8.00000	+	8.00000i	0.707107	+	0.707107i
$129$	−1.94975	−	11.3640i	−0.171666	−	1.00054i
$130$	−19.1421	−	3.82843i	−1.67888	−	0.335775i
$131$			9.07107i			0.792543i	0.918133	+	0.396271i	$0.129696\pi$
$131$			9.07107i			0.792543i	−0.918133	+	0.396271i	$0.870304\pi$
$132$		0			0
$133$	2.65685			0.230378
$134$	−18.1421			−1.56724
$135$	−5.41421	+	19.1421i	−0.465981	+	1.64749i
$136$	8.00000	+	8.00000i	0.685994	+	0.685994i
$137$	−6.41421	−	6.41421i	−0.548003	−	0.548003i	0.377860	−	0.925863i	$-0.376660\pi$
$137$	−6.41421	−	6.41421i	−0.548003	−	0.548003i	−0.925863	+	0.377860i	$0.876660\pi$
$138$	2.58579	−	3.65685i	0.220117	−	0.311292i
$139$	−8.82843			−0.748817			−0.374409	−	0.927264i	$-0.622154\pi$
$139$	−8.82843			−0.748817			−0.374409	+	0.927264i	$0.622154\pi$
$140$		0			0
$141$	3.75736	+	2.65685i	0.316427	+	0.223747i
$142$		−	22.4853i		−	1.88692i
$143$	−6.00000	+	4.00000i	−0.501745	+	0.334497i
$144$	11.3137	−	4.00000i	0.942809	−	0.333333i
$145$	18.0208	+	18.0208i	1.49655	+	1.49655i
$146$		−	0.242641i		−	0.0200811i
$147$	0.292893	+	1.70711i	0.0241574	+	0.140800i
$148$		0			0
$149$	4.24264	−	4.24264i	0.347571	−	0.347571i	−0.511633	−	0.859204i	$-0.670959\pi$
$149$	4.24264	−	4.24264i	0.347571	−	0.347571i	0.859204	+	0.511633i	$0.170959\pi$
$150$	19.3137	+	13.6569i	1.57696	+	1.11508i
$151$	10.8995	−	10.8995i	0.886988	−	0.886988i	−0.107244	−	0.994233i	$-0.534203\pi$
$151$	10.8995	−	10.8995i	0.886988	−	0.886988i	0.994233	+	0.107244i	$0.0342027\pi$
$152$		−	7.51472i		−	0.609524i
$153$	11.3137	−	4.00000i	0.914659	−	0.323381i
$154$	2.00000	−	2.00000i	0.161165	−	0.161165i
$155$	15.9706			1.28279
$156$		0			0
$157$	−8.48528			−0.677199			−0.338600	−	0.940931i	$-0.609953\pi$
$157$	−8.48528			−0.677199			−0.338600	+	0.940931i	$0.609953\pi$
$158$	5.82843	−	5.82843i	0.463685	−	0.463685i
$159$	−3.60660	−	21.0208i	−0.286022	−	1.66706i
$160$		0			0
$161$	1.29289	−	1.29289i	0.101894	−	0.101894i
$162$	1.34315	−	12.6569i	0.105527	−	0.994416i
$163$	−15.2426	+	15.2426i	−1.19390	+	1.19390i	−0.217932	+	0.975964i	$0.569931\pi$
$163$	−15.2426	+	15.2426i	−1.19390	+	1.19390i	−0.975964	+	0.217932i	$0.930069\pi$
$164$		0			0
$165$	13.0711	−	2.24264i	1.01758	−	0.174589i
$166$		−	1.41421i		−	0.109764i
$167$	−2.94975	−	2.94975i	−0.228258	−	0.228258i	0.583706	−	0.811965i	$-0.301602\pi$
$167$	−2.94975	−	2.94975i	−0.228258	−	0.228258i	−0.811965	+	0.583706i	$0.801602\pi$
$168$	4.82843	−	0.828427i	0.372521	−	0.0639145i
$169$	−12.0000	−	5.00000i	−0.923077	−	0.384615i
$170$		−	21.6569i		−	1.66100i
$171$	−7.19239	−	3.43503i	−0.550016	−	0.262683i
$172$		0			0
$173$	9.75736			0.741838			0.370919	−	0.928665i	$-0.379043\pi$
$173$	9.75736			0.741838			0.370919	+	0.928665i	$0.379043\pi$
$174$	−13.3137	−	9.41421i	−1.00931	−	0.713690i
$175$	6.82843	+	6.82843i	0.516181	+	0.516181i
$176$	−5.65685	−	5.65685i	−0.426401	−	0.426401i
$177$	−2.82843	−	2.00000i	−0.212598	−	0.150329i
$178$	11.7574			0.881251
$179$	23.8284			1.78102			0.890510	−	0.454963i	$-0.150348\pi$
$179$	23.8284			1.78102			0.890510	+	0.454963i	$0.150348\pi$
$180$		0			0
$181$		−	2.00000i		−	0.148659i	−0.997234	−	0.0743294i	$-0.976318\pi$
$181$		−	2.00000i		−	0.148659i	0.997234	−	0.0743294i	$-0.0236816\pi$
$182$	5.00000	+	1.00000i	0.370625	+	0.0741249i
$183$	23.7279	−	4.07107i	1.75402	−	0.300942i
$184$	−3.65685	−	3.65685i	−0.269587	−	0.269587i
$185$			34.7279i			2.55325i
$186$	−10.0711	+	1.72792i	−0.738447	+	0.126697i
$187$	−5.65685	−	5.65685i	−0.413670	−	0.413670i
$188$		0			0
$189$	1.41421	−	5.00000i	0.102869	−	0.363696i
$190$	−10.1716	+	10.1716i	−0.737923	+	0.737923i
$191$		−	9.31371i		−	0.673916i	−0.941520	−	0.336958i	$-0.890602\pi$
$191$		−	9.31371i		−	0.673916i	0.941520	−	0.336958i	$-0.109398\pi$
$192$	−2.34315	−	13.6569i	−0.169102	−	0.985599i
$193$	−3.75736	+	3.75736i	−0.270461	+	0.270461i	−0.829286	−	0.558825i	$-0.811252\pi$
$193$	−3.75736	+	3.75736i	−0.270461	+	0.270461i	0.558825	+	0.829286i	$0.311252\pi$
$194$	−14.5858			−1.04720
$195$	16.4350	+	17.3640i	1.17694	+	1.24346i
$196$		0			0
$197$	−8.65685	+	8.65685i	−0.616775	+	0.616775i	−0.944703	−	0.327928i	$-0.893650\pi$
$197$	−8.65685	+	8.65685i	−0.616775	+	0.616775i	0.327928	+	0.944703i	$0.393650\pi$
$198$	−8.00000	+	2.82843i	−0.568535	+	0.201008i
$199$			17.6569i			1.25166i	0.779959	+	0.625831i	$0.215240\pi$
$199$			17.6569i			1.25166i	−0.779959	+	0.625831i	$0.784760\pi$
$200$	19.3137	−	19.3137i	1.36569	−	1.36569i
$201$	18.1421	+	12.8284i	1.27965	+	0.904847i
$202$	−7.65685	+	7.65685i	−0.538734	+	0.538734i
$203$	−4.70711	−	4.70711i	−0.330374	−	0.330374i
$204$		0			0
$205$		−	1.31371i		−	0.0917534i
$206$		0			0
$207$	−5.17157	+	1.82843i	−0.359449	+	0.127084i
$208$	2.82843	−	14.1421i	0.196116	−	0.980581i
$209$			5.31371i			0.367557i
$210$	−7.65685	−	5.41421i	−0.528373	−	0.373616i
$211$	17.4853			1.20374			0.601868	−	0.798595i	$-0.294423\pi$
$211$	17.4853			1.20374			0.601868	+	0.798595i	$0.294423\pi$
$212$		0			0
$213$	−15.8995	+	22.4853i	−1.08942	+	1.54067i
$214$	−0.828427	−	0.828427i	−0.0566301	−	0.0566301i
$215$	18.0208	+	18.0208i	1.22901	+	1.22901i
$216$	−14.1421	−	4.00000i	−0.962250	−	0.272166i
$217$	−4.17157			−0.283185
$218$	8.34315			0.565069
$219$	−0.171573	+	0.242641i	−0.0115938	+	0.0163961i
$220$		0			0
$221$	2.82843	−	14.1421i	0.190261	−	0.951303i
$222$	−3.75736	−	21.8995i	−0.252177	−	1.46980i
$223$	11.7782	+	11.7782i	0.788725	+	0.788725i	0.981285	−	0.192560i	$-0.0616791\pi$
$223$	11.7782	+	11.7782i	0.788725	+	0.788725i	−0.192560	+	0.981285i	$0.561679\pi$
$224$		0			0
$225$	−9.65685	−	27.3137i	−0.643790	−	1.82091i
$226$	9.82843	+	9.82843i	0.653777	+	0.653777i
$227$	0.928932	−	0.928932i	0.0616554	−	0.0616554i	−0.675607	−	0.737262i	$-0.736118\pi$
$227$	0.928932	−	0.928932i	0.0616554	−	0.0616554i	0.737262	+	0.675607i	$0.236118\pi$
$228$		0			0
$229$	6.48528	−	6.48528i	0.428559	−	0.428559i	−0.459578	−	0.888137i	$-0.651999\pi$
$229$	6.48528	−	6.48528i	0.428559	−	0.428559i	0.888137	+	0.459578i	$0.151999\pi$
$230$			9.89949i			0.652753i
$231$	−3.41421	+	0.585786i	−0.224639	+	0.0385419i
$232$	−13.3137	+	13.3137i	−0.874088	+	0.874088i
$233$	16.3137			1.06875			0.534373	−	0.845249i	$-0.320548\pi$
$233$	16.3137			1.06875			0.534373	+	0.845249i	$0.320548\pi$
$234$	−12.2426	−	9.17157i	−0.800326	−	0.599564i
$235$	−10.1716			−0.663520
$236$		0			0
$237$	−9.94975	+	1.70711i	−0.646306	+	0.110889i
$238$			5.65685i			0.366679i
$239$	10.0711	−	10.0711i	0.651443	−	0.651443i	−0.301897	−	0.953340i	$-0.597620\pi$
$239$	10.0711	−	10.0711i	0.651443	−	0.651443i	0.953340	+	0.301897i	$0.0976200\pi$
$240$	−15.3137	+	21.6569i	−0.988496	+	1.39794i
$241$	6.70711	−	6.70711i	0.432043	−	0.432043i	−0.457280	−	0.889323i	$-0.651176\pi$
$241$	6.70711	−	6.70711i	0.432043	−	0.432043i	0.889323	+	0.457280i	$0.151176\pi$
$242$	−7.00000	−	7.00000i	−0.449977	−	0.449977i
$243$	−10.2929	+	11.7071i	−0.660289	+	0.751011i
$244$		0			0
$245$	−2.70711	−	2.70711i	−0.172951	−	0.172951i
$246$	0.142136	+	0.828427i	0.00906224	+	0.0528186i
$247$	−7.97056	+	5.31371i	−0.507155	+	0.338103i
$248$			11.7990i			0.749237i
$249$	−1.00000	+	1.41421i	−0.0633724	+	0.0896221i
$250$	−25.2132			−1.59462
$251$	18.9706			1.19741			0.598706	−	0.800969i	$-0.295682\pi$
$251$	18.9706			1.19741			0.598706	+	0.800969i	$0.295682\pi$
$252$		0			0
$253$	2.58579	+	2.58579i	0.162567	+	0.162567i
$254$	−2.00000	−	2.00000i	−0.125491	−	0.125491i
$255$	−15.3137	+	21.6569i	−0.958982	+	1.35620i
$256$		0			0
$257$	−28.1421			−1.75546			−0.877729	−	0.479157i	$-0.840942\pi$
$257$	−28.1421			−1.75546			−0.877729	+	0.479157i	$0.840942\pi$
$258$	−13.3137	−	9.41421i	−0.828875	−	0.586103i
$259$		−	9.07107i		−	0.563649i
$260$		0			0
$261$	6.65685	+	18.8284i	0.412049	+	1.16545i
$262$	9.07107	+	9.07107i	0.560412	+	0.560412i
$263$		−	27.4853i		−	1.69482i	−0.530943	−	0.847408i	$-0.678162\pi$
$263$		−	27.4853i		−	1.69482i	0.530943	−	0.847408i	$-0.321838\pi$
$264$	1.65685	+	9.65685i	0.101972	+	0.594338i
$265$	33.3345	+	33.3345i	2.04772	+	2.04772i
$266$	2.65685	−	2.65685i	0.162902	−	0.162902i
$267$	−11.7574	−	8.31371i	−0.719539	−	0.508791i
$268$		0			0
$269$		−	31.6985i		−	1.93269i	−0.257248	−	0.966345i	$-0.582816\pi$
$269$		−	31.6985i		−	1.93269i	0.257248	−	0.966345i	$-0.417184\pi$
$270$	13.7279	+	24.5563i	0.835455	+	1.49445i
$271$	−11.8995	+	11.8995i	−0.722843	+	0.722843i	−0.969183	−	0.246341i	$-0.920772\pi$
$271$	−11.8995	+	11.8995i	−0.722843	+	0.722843i	0.246341	+	0.969183i	$0.420772\pi$
$272$	16.0000			0.970143
$273$	−4.29289	−	4.53553i	−0.259818	−	0.274503i
$274$	−12.8284			−0.774994
$275$	−13.6569	+	13.6569i	−0.823539	+	0.823539i
$276$		0			0
$277$		−	2.51472i		−	0.151095i	−0.997142	−	0.0755474i	$-0.975930\pi$
$277$		−	2.51472i		−	0.151095i	0.997142	−	0.0755474i	$-0.0240704\pi$
$278$	−8.82843	+	8.82843i	−0.529494	+	0.529494i
$279$	11.2929	+	5.39340i	0.676088	+	0.322894i
$280$	−7.65685	+	7.65685i	−0.457585	+	0.457585i
$281$	11.1421	+	11.1421i	0.664684	+	0.664684i	0.956480	−	0.291796i	$-0.0942530\pi$
$281$	11.1421	+	11.1421i	0.664684	+	0.664684i	−0.291796	+	0.956480i	$0.594253\pi$
$282$	6.41421	−	1.10051i	0.381961	−	0.0655341i
$283$			6.82843i			0.405908i	0.979188	+	0.202954i	$0.0650542\pi$
$283$			6.82843i			0.405908i	−0.979188	+	0.202954i	$0.934946\pi$
$284$		0			0
$285$	17.3640	−	2.97918i	1.02855	−	0.176472i
$286$	−2.00000	+	10.0000i	−0.118262	+	0.591312i
$287$			0.343146i			0.0202553i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	36.0416			2.11644
$291$	14.5858	+	10.3137i	0.855034	+	0.604600i
$292$		0			0
$293$	−12.9497	−	12.9497i	−0.756532	−	0.756532i	0.219157	−	0.975690i	$-0.429669\pi$
$293$	−12.9497	−	12.9497i	−0.756532	−	0.756532i	−0.975690	+	0.219157i	$0.929669\pi$
$294$	2.00000	+	1.41421i	0.116642	+	0.0824786i
$295$	7.65685			0.445799
$296$	−25.6569			−1.49127
$297$	10.0000	+	2.82843i	0.580259	+	0.164122i
$298$		−	8.48528i		−	0.491539i
$299$	−1.29289	+	6.46447i	−0.0747699	+	0.373850i
$300$		0			0
$301$	−4.70711	−	4.70711i	−0.271313	−	0.271313i
$302$		−	21.7990i		−	1.25439i
$303$	13.0711	−	2.24264i	0.750913	−	0.128836i
$304$	−7.51472	−	7.51472i	−0.430999	−	0.430999i
$305$	−37.6274	+	37.6274i	−2.15454	+	2.15454i
$306$	7.31371	−	15.3137i	0.418097	−	0.875426i
$307$	4.36396	−	4.36396i	0.249064	−	0.249064i	−0.571522	−	0.820587i	$-0.693647\pi$
$307$	4.36396	−	4.36396i	0.249064	−	0.249064i	0.820587	+	0.571522i	$0.193647\pi$
$308$		0			0
$309$		0			0
$310$	15.9706	−	15.9706i	0.907067	−	0.907067i
$311$	−31.5563			−1.78940			−0.894698	−	0.446671i	$-0.852609\pi$
$311$	−31.5563			−1.78940			−0.894698	+	0.446671i	$0.852609\pi$
$312$	−12.8284	+	12.1421i	−0.726267	+	0.687413i
$313$	−12.1421			−0.686314			−0.343157	−	0.939278i	$-0.611496\pi$
$313$	−12.1421			−0.686314			−0.343157	+	0.939278i	$0.611496\pi$
$314$	−8.48528	+	8.48528i	−0.478852	+	0.478852i
$315$	3.82843	+	10.8284i	0.215707	+	0.610113i
$316$		0			0
$317$	11.2426	−	11.2426i	0.631450	−	0.631450i	−0.316982	−	0.948432i	$-0.602669\pi$
$317$	11.2426	−	11.2426i	0.631450	−	0.631450i	0.948432	+	0.316982i	$0.102669\pi$
$318$	−24.6274	−	17.4142i	−1.38104	−	0.976541i
$319$	9.41421	−	9.41421i	0.527095	−	0.527095i
$320$	21.6569	+	21.6569i	1.21065	+	1.21065i
$321$	0.242641	+	1.41421i	0.0135429	+	0.0789337i
$322$		−	2.58579i		−	0.144100i
$323$	−7.51472	−	7.51472i	−0.418130	−	0.418130i
$324$		0			0
$325$	−34.1421	−	6.82843i	−1.89386	−	0.378773i
$326$			30.4853i			1.68842i
$327$	−8.34315	−	5.89949i	−0.461377	−	0.326243i
$328$	0.970563			0.0535904
$329$	2.65685			0.146477
$330$	10.8284	−	15.3137i	0.596085	−	0.842992i
$331$	−8.65685	−	8.65685i	−0.475824	−	0.475824i	0.427969	−	0.903793i	$-0.359229\pi$
$331$	−8.65685	−	8.65685i	−0.475824	−	0.475824i	−0.903793	+	0.427969i	$0.859229\pi$
$332$		0			0
$333$	−11.7279	+	24.5563i	−0.642686	+	1.34568i
$334$	−5.89949			−0.322806
$335$	−49.1127			−2.68331
$336$	4.00000	−	5.65685i	0.218218	−	0.308607i
$337$			21.1421i			1.15169i	0.817560	+	0.575843i	$0.195326\pi$
$337$			21.1421i			1.15169i	−0.817560	+	0.575843i	$0.804674\pi$
$338$	−17.0000	+	7.00000i	−0.924678	+	0.380750i
$339$	−2.87868	−	16.7782i	−0.156348	−	0.911265i
$340$		0			0
$341$		−	8.34315i		−	0.451807i
$342$	−10.6274	+	3.75736i	−0.574665	+	0.203175i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−13.3137	+	13.3137i	−0.717827	+	0.717827i
$345$	7.00000	−	9.89949i	0.376867	−	0.532971i
$346$	9.75736	−	9.75736i	0.524559	−	0.524559i
$347$		−	6.00000i		−	0.322097i	−0.986947	−	0.161048i	$-0.948512\pi$
$347$		−	6.00000i		−	0.322097i	0.986947	−	0.161048i	$-0.0514875\pi$
$348$		0			0
$349$	13.0503	−	13.0503i	0.698564	−	0.698564i	−0.265537	−	0.964101i	$-0.585549\pi$
$349$	13.0503	−	13.0503i	0.698564	−	0.698564i	0.964101	+	0.265537i	$0.0855492\pi$
$350$	13.6569			0.729990
$351$	5.75736	+	17.8284i	0.307305	+	0.951611i
$352$		0			0
$353$	17.3137	−	17.3137i	0.921516	−	0.921516i	−0.0756209	−	0.997137i	$-0.524094\pi$
$353$	17.3137	−	17.3137i	0.921516	−	0.921516i	0.997137	+	0.0756209i	$0.0240939\pi$
$354$	−4.82843	+	0.828427i	−0.256628	+	0.0440304i
$355$		−	60.8701i		−	3.23065i
$356$		0			0
$357$	4.00000	−	5.65685i	0.211702	−	0.299392i
$358$	23.8284	−	23.8284i	1.25937	−	1.25937i
$359$	16.8284	+	16.8284i	0.888170	+	0.888170i	0.994347	−	0.106177i	$-0.0338610\pi$
$359$	16.8284	+	16.8284i	0.888170	+	0.888170i	−0.106177	+	0.994347i	$0.533861\pi$
$360$	30.6274	−	10.8284i	1.61421	−	0.570708i
$361$		−	11.9411i		−	0.628480i
$362$	−2.00000	−	2.00000i	−0.105118	−	0.105118i
$363$	2.05025	+	11.9497i	0.107610	+	0.627199i
$364$		0			0
$365$		−	0.656854i		−	0.0343813i
$366$	19.6569	−	27.7990i	1.02748	−	1.45308i
$367$	25.6985			1.34145			0.670725	−	0.741706i	$-0.265983\pi$
$367$	25.6985			1.34145			0.670725	+	0.741706i	$0.265983\pi$
$368$	−7.31371			−0.381253
$369$	0.443651	−	0.928932i	0.0230955	−	0.0483583i
$370$	34.7279	+	34.7279i	1.80542	+	1.80542i
$371$	−8.70711	−	8.70711i	−0.452050	−	0.452050i
$372$		0			0
$373$	−22.6274			−1.17160			−0.585802	−	0.810454i	$-0.699220\pi$
$373$	−22.6274			−1.17160			−0.585802	+	0.810454i	$0.699220\pi$
$374$	−11.3137			−0.585018
$375$	25.2132	+	17.8284i	1.30200	+	0.920656i
$376$		−	7.51472i		−	0.387542i
$377$	23.5355	+	4.70711i	1.21214	+	0.242428i
$378$	−3.58579	−	6.41421i	−0.184433	−	0.329912i
$379$	−4.58579	−	4.58579i	−0.235556	−	0.235556i	0.579451	−	0.815007i	$-0.303267\pi$
$379$	−4.58579	−	4.58579i	−0.235556	−	0.235556i	−0.815007	+	0.579451i	$0.803267\pi$
$380$		0			0
$381$	0.585786	+	3.41421i	0.0300107	+	0.174915i
$382$	−9.31371	−	9.31371i	−0.476531	−	0.476531i
$383$	−6.10051	+	6.10051i	−0.311721	+	0.311721i	−0.845576	−	0.533855i	$-0.820743\pi$
$383$	−6.10051	+	6.10051i	−0.311721	+	0.311721i	0.533855	+	0.845576i	$0.320743\pi$
$384$	−16.0000	−	11.3137i	−0.816497	−	0.577350i
$385$	5.41421	−	5.41421i	0.275934	−	0.275934i
$386$			7.51472i			0.382489i
$387$	6.65685	+	18.8284i	0.338387	+	0.957103i
$388$		0			0
$389$	6.82843			0.346215			0.173107	−	0.984903i	$-0.444619\pi$
$389$	6.82843			0.346215			0.173107	+	0.984903i	$0.444619\pi$
$390$	33.7990	+	0.928932i	1.71148	+	0.0470383i
$391$	−7.31371			−0.369870
$392$	2.00000	−	2.00000i	0.101015	−	0.101015i
$393$	−2.65685	−	15.4853i	−0.134021	−	0.781129i
$394$			17.3137i			0.872252i
$395$	15.7782	−	15.7782i	0.793886	−	0.793886i
$396$		0			0
$397$	−3.39340	+	3.39340i	−0.170310	+	0.170310i	−0.787115	−	0.616806i	$-0.788426\pi$
$397$	−3.39340	+	3.39340i	−0.170310	+	0.170310i	0.616806	+	0.787115i	$0.288426\pi$
$398$	17.6569	+	17.6569i	0.885058	+	0.885058i
$399$	−4.53553	+	0.778175i	−0.227061	+	0.0389575i
$400$		−	38.6274i		−	1.93137i
$401$	3.92893	+	3.92893i	0.196202	+	0.196202i	0.798369	−	0.602168i	$-0.205696\pi$
$401$	3.92893	+	3.92893i	0.196202	+	0.196202i	−0.602168	+	0.798369i	$0.705696\pi$
$402$	30.9706	−	5.31371i	1.54467	−	0.265024i
$403$	12.5147	−	8.34315i	0.623403	−	0.415602i
$404$		0			0
$405$	3.63604	−	34.2635i	0.180676	−	1.70256i
$406$	−9.41421			−0.467220
$407$	18.1421			0.899272
$408$	−16.0000	−	11.3137i	−0.792118	−	0.560112i
$409$	−2.36396	−	2.36396i	−0.116890	−	0.116890i	0.646242	−	0.763132i	$-0.276340\pi$
$409$	−2.36396	−	2.36396i	−0.116890	−	0.116890i	−0.763132	+	0.646242i	$0.776340\pi$
$410$	−1.31371	−	1.31371i	−0.0648794	−	0.0648794i
$411$	12.8284	+	9.07107i	0.632780	+	0.447443i
$412$		0			0
$413$	−2.00000			−0.0984136
$414$	−3.34315	+	7.00000i	−0.164307	+	0.344031i
$415$		−	3.82843i		−	0.187930i
$416$		0			0
$417$	15.0711	−	2.58579i	0.738033	−	0.126627i
$418$	5.31371	+	5.31371i	0.259902	+	0.259902i
$419$			16.6274i			0.812302i	0.913806	+	0.406151i	$0.133129\pi$
$419$			16.6274i			0.812302i	−0.913806	+	0.406151i	$0.866871\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	17.4853	−	17.4853i	0.851170	−	0.851170i
$423$	−7.19239	−	3.43503i	−0.349706	−	0.167017i
$424$	−24.6274	+	24.6274i	−1.19601	+	1.19601i
$425$		−	38.6274i		−	1.87370i
$426$	6.58579	+	38.3848i	0.319082	+	1.85975i
$427$	9.82843	−	9.82843i	0.475631	−	0.475631i
$428$		0			0
$429$	9.07107	−	8.58579i	0.437955	−	0.414526i
$430$	36.0416			1.73808
$431$	−15.4853	+	15.4853i	−0.745900	+	0.745900i	−0.973706	−	0.227807i	$-0.926845\pi$
$431$	−15.4853	+	15.4853i	−0.745900	+	0.745900i	0.227807	+	0.973706i	$0.426845\pi$
$432$	−18.1421	+	10.1421i	−0.872864	+	0.487964i
$433$			11.4142i			0.548532i	0.961654	+	0.274266i	$0.0884349\pi$
$433$			11.4142i			0.548532i	−0.961654	+	0.274266i	$0.911565\pi$
$434$	−4.17157	+	4.17157i	−0.200242	+	0.200242i
$435$	−36.0416	−	25.4853i	−1.72806	−	1.22193i
$436$		0			0
$437$	3.43503	+	3.43503i	0.164320	+	0.164320i
$438$	0.0710678	+	0.414214i	0.00339575	+	0.0197919i
$439$		−	21.2132i		−	1.01245i	−0.862401	−	0.506225i	$-0.831040\pi$
$439$		−	21.2132i		−	1.01245i	0.862401	−	0.506225i	$-0.168960\pi$
$440$	−15.3137	−	15.3137i	−0.730052	−	0.730052i
$441$	−1.00000	−	2.82843i	−0.0476190	−	0.134687i
$442$	−11.3137	−	16.9706i	−0.538138	−	0.807207i
$443$		−	7.34315i		−	0.348883i	−0.984668	−	0.174442i	$-0.944188\pi$
$443$		−	7.34315i		−	0.348883i	0.984668	−	0.174442i	$-0.0558121\pi$
$444$		0			0
$445$	31.8284			1.50881
$446$	23.5563			1.11543
$447$	−6.00000	+	8.48528i	−0.283790	+	0.401340i
$448$	−5.65685	−	5.65685i	−0.267261	−	0.267261i
$449$	18.4142	+	18.4142i	0.869020	+	0.869020i	0.992364	−	0.123344i	$-0.0393617\pi$
$449$	18.4142	+	18.4142i	0.869020	+	0.869020i	−0.123344	+	0.992364i	$0.539362\pi$
$450$	−36.9706	−	17.6569i	−1.74281	−	0.832352i
$451$	−0.686292			−0.0323162
$452$		0			0
$453$	−15.4142	+	21.7990i	−0.724223	+	1.02421i
$454$		−	1.85786i		−	0.0871939i
$455$	13.5355	+	2.70711i	0.634556	+	0.126911i
$456$	2.20101	+	12.8284i	0.103072	+	0.600746i
$457$	−5.17157	−	5.17157i	−0.241916	−	0.241916i	0.575726	−	0.817642i	$-0.304719\pi$
$457$	−5.17157	−	5.17157i	−0.241916	−	0.241916i	−0.817642	+	0.575726i	$0.804719\pi$
$458$		−	12.9706i		−	0.606075i
$459$	−18.1421	+	10.1421i	−0.846802	+	0.473394i
$460$		0			0
$461$	1.51472	−	1.51472i	0.0705475	−	0.0705475i	−0.670953	−	0.741500i	$-0.734115\pi$
$461$	1.51472	−	1.51472i	0.0705475	−	0.0705475i	0.741500	+	0.670953i	$0.234115\pi$
$462$	−2.82843	+	4.00000i	−0.131590	+	0.186097i
$463$	3.34315	−	3.34315i	0.155369	−	0.155369i	−0.625142	−	0.780511i	$-0.714959\pi$
$463$	3.34315	−	3.34315i	0.155369	−	0.155369i	0.780511	+	0.625142i	$0.214959\pi$
$464$			26.6274i			1.23615i
$465$	−27.2635	+	4.67767i	−1.26431	+	0.216922i
$466$	16.3137	−	16.3137i	0.755718	−	0.755718i
$467$	−33.2132			−1.53692			−0.768462	−	0.639896i	$-0.778978\pi$
$467$	−33.2132			−1.53692			−0.768462	+	0.639896i	$0.778978\pi$
$468$		0			0
$469$	12.8284			0.592362
$470$	−10.1716	+	10.1716i	−0.469180	+	0.469180i
$471$	14.4853	−	2.48528i	0.667447	−	0.114516i
$472$			5.65685i			0.260378i
$473$	9.41421	−	9.41421i	0.432866	−	0.432866i
$474$	−8.24264	+	11.6569i	−0.378597	+	0.535417i
$475$	−18.1421	+	18.1421i	−0.832418	+	0.832418i
$476$		0			0
$477$	12.3137	+	34.8284i	0.563806	+	1.59468i
$478$		−	20.1421i		−	0.921280i
$479$	−8.02082	−	8.02082i	−0.366480	−	0.366480i	0.499712	−	0.866192i	$-0.333439\pi$
$479$	−8.02082	−	8.02082i	−0.366480	−	0.366480i	−0.866192	+	0.499712i	$0.833439\pi$
$480$		0			0
$481$	18.1421	+	27.2132i	0.827210	+	1.24082i
$482$		−	13.4142i		−	0.611001i
$483$	−1.82843	+	2.58579i	−0.0831963	+	0.117657i
$484$		0			0
$485$	−39.4853			−1.79293
$486$	1.41421	+	22.0000i	0.0641500	+	0.997940i
$487$	−20.1716	−	20.1716i	−0.914061	−	0.914061i	0.0825276	−	0.996589i	$-0.473701\pi$
$487$	−20.1716	−	20.1716i	−0.914061	−	0.914061i	−0.996589	+	0.0825276i	$0.973701\pi$
$488$	−27.7990	−	27.7990i	−1.25840	−	1.25840i
$489$	21.5563	−	30.4853i	0.974812	−	1.37859i
$490$	−5.41421			−0.244589
$491$	−28.9706			−1.30742			−0.653712	−	0.756744i	$-0.726789\pi$
$491$	−28.9706			−1.30742			−0.653712	+	0.756744i	$0.726789\pi$
$492$		0			0
$493$			26.6274i			1.19924i
$494$	−2.65685	+	13.2843i	−0.119538	+	0.597688i
$495$	−21.6569	+	7.65685i	−0.973403	+	0.344150i
$496$	11.7990	+	11.7990i	0.529790	+	0.529790i
$497$			15.8995i			0.713190i
$498$	0.414214	+	2.41421i	0.0185614	+	0.108183i
$499$	−14.0000	−	14.0000i	−0.626726	−	0.626726i	0.320517	−	0.947243i	$-0.396143\pi$
$499$	−14.0000	−	14.0000i	−0.626726	−	0.626726i	−0.947243	+	0.320517i	$0.896143\pi$
$500$		0			0
$501$	5.89949	+	4.17157i	0.263570	+	0.186372i
$502$	18.9706	−	18.9706i	0.846698	−	0.846698i
$503$			3.07107i			0.136932i	0.997653	+	0.0684661i	$0.0218105\pi$
$503$			3.07107i			0.136932i	−0.997653	+	0.0684661i	$0.978190\pi$
$504$	−8.00000	+	2.82843i	−0.356348	+	0.125988i
$505$	−20.7279	+	20.7279i	−0.922380	+	0.922380i
$506$	5.17157			0.229904
$507$	21.9497	+	5.02082i	0.974823	+	0.222982i
$508$		0			0
$509$	26.1213	−	26.1213i	1.15781	−	1.15781i	0.172861	−	0.984946i	$-0.444699\pi$
$509$	26.1213	−	26.1213i	1.15781	−	1.15781i	0.984946	−	0.172861i	$-0.0553011\pi$
$510$	6.34315	+	36.9706i	0.280879	+	1.63708i
$511$			0.171573i			0.00758994i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	13.2843	+	3.75736i	0.586515	+	0.165891i
$514$	−28.1421	+	28.1421i	−1.24130	+	1.24130i
$515$		0			0
$516$		0			0
$517$			5.31371i			0.233697i
$518$	−9.07107	−	9.07107i	−0.398560	−	0.398560i
$519$	−16.6569	+	2.85786i	−0.731155	+	0.125446i
$520$	7.65685	−	38.2843i	0.335775	−	1.67888i
$521$		−	16.2843i		−	0.713427i	−0.934214	−	0.356713i	$-0.883897\pi$
$521$		−	16.2843i		−	0.713427i	0.934214	−	0.356713i	$-0.116103\pi$
$522$	25.4853	+	12.1716i	1.11546	+	0.532735i
$523$	−4.72792			−0.206738			−0.103369	−	0.994643i	$-0.532962\pi$
$523$	−4.72792			−0.206738			−0.103369	+	0.994643i	$0.532962\pi$
$524$		0			0
$525$	−13.6569	−	9.65685i	−0.596034	−	0.421460i
$526$	−27.4853	−	27.4853i	−1.19842	−	1.19842i
$527$	11.7990	+	11.7990i	0.513972	+	0.513972i
$528$	11.3137	+	8.00000i	0.492366	+	0.348155i
$529$	−19.6569			−0.854646
$530$	66.6690			2.89592
$531$	5.41421	+	2.58579i	0.234957	+	0.112214i
$532$		0			0
$533$	−0.686292	−	1.02944i	−0.0297266	−	0.0445899i
$534$	−20.0711	+	3.44365i	−0.868560	+	0.149021i
$535$	−2.24264	−	2.24264i	−0.0969578	−	0.0969578i
$536$		−	36.2843i		−	1.56724i
$537$	−40.6777	+	6.97918i	−1.75537	+	0.301174i
$538$	−31.6985	−	31.6985i	−1.36662	−	1.36662i
$539$	−1.41421	+	1.41421i	−0.0609145	+	0.0609145i
$540$		0			0
$541$	14.0711	−	14.0711i	0.604962	−	0.604962i	−0.336663	−	0.941625i	$-0.609298\pi$
$541$	14.0711	−	14.0711i	0.604962	−	0.604962i	0.941625	+	0.336663i	$0.109298\pi$
$542$			23.7990i			1.02225i
$543$	0.585786	+	3.41421i	0.0251385	+	0.146518i
$544$		0			0
$545$	22.5858			0.967469
$546$	−8.82843	−	0.242641i	−0.377822	−	0.0103841i
$547$	−14.6569			−0.626682			−0.313341	−	0.949641i	$-0.601448\pi$
$547$	−14.6569			−0.626682			−0.313341	+	0.949641i	$0.601448\pi$
$548$		0			0
$549$	−39.3137	+	13.8995i	−1.67787	+	0.593216i
$550$			27.3137i			1.16466i
$551$	12.5061	−	12.5061i	0.532778	−	0.532778i
$552$	7.31371	+	5.17157i	0.311292	+	0.220117i
$553$	−4.12132	+	4.12132i	−0.175256	+	0.175256i
$554$	−2.51472	−	2.51472i	−0.106840	−	0.106840i
$555$	−10.1716	−	59.2843i	−0.431759	−	2.51648i
$556$		0			0
$557$	27.7990	+	27.7990i	1.17788	+	1.17788i	0.980283	+	0.197598i	$0.0633140\pi$
$557$	27.7990	+	27.7990i	1.17788	+	1.17788i	0.197598	+	0.980283i	$0.436686\pi$
$558$	16.6863	−	5.89949i	0.706387	−	0.249746i
$559$	23.5355	+	4.70711i	0.995447	+	0.199089i
$560$			15.3137i			0.647122i
$561$	11.3137	+	8.00000i	0.477665	+	0.337760i
$562$	22.2843			0.940005
$563$	−1.07107			−0.0451401			−0.0225701	−	0.999745i	$-0.507185\pi$
$563$	−1.07107			−0.0451401			−0.0225701	+	0.999745i	$0.507185\pi$
$564$		0			0
$565$	26.6066	+	26.6066i	1.11935	+	1.11935i
$566$	6.82843	+	6.82843i	0.287020	+	0.287020i
$567$	−0.949747	+	8.94975i	−0.0398856	+	0.375854i
$568$	44.9706			1.88692
$569$	7.48528			0.313799			0.156900	−	0.987615i	$-0.449850\pi$
$569$	7.48528			0.313799			0.156900	+	0.987615i	$0.449850\pi$
$570$	14.3848	−	20.3431i	0.602512	−	0.852081i
$571$			36.4558i			1.52563i	0.646617	+	0.762815i	$0.276183\pi$
$571$			36.4558i			1.52563i	−0.646617	+	0.762815i	$0.723817\pi$
$572$		0			0
$573$	2.72792	+	15.8995i	0.113961	+	0.664211i
$574$	0.343146	+	0.343146i	0.0143226	+	0.0143226i
$575$			17.6569i			0.736342i
$576$	8.00000	+	22.6274i	0.333333	+	0.942809i
$577$	−14.8284	−	14.8284i	−0.617315	−	0.617315i	0.327526	−	0.944842i	$-0.393785\pi$
$577$	−14.8284	−	14.8284i	−0.617315	−	0.617315i	−0.944842	+	0.327526i	$0.893785\pi$
$578$	−1.00000	+	1.00000i	−0.0415945	+	0.0415945i
$579$	5.31371	−	7.51472i	0.220830	−	0.312301i
$580$		0			0
$581$			1.00000i			0.0414870i
$582$	24.8995	−	4.27208i	1.03212	−	0.177083i
$583$	17.4142	−	17.4142i	0.721223	−	0.721223i
$584$	0.485281			0.0200811
$585$	−33.1421	−	24.8284i	−1.37026	−	1.02653i
$586$	−25.8995			−1.06990
$587$	−11.1924	+	11.1924i	−0.461959	+	0.461959i	−0.899297	−	0.437338i	$-0.855921\pi$
$587$	−11.1924	+	11.1924i	−0.461959	+	0.461959i	0.437338	+	0.899297i	$0.355921\pi$
$588$		0			0
$589$		−	11.0833i		−	0.456678i
$590$	7.65685	−	7.65685i	0.315228	−	0.315228i
$591$	12.2426	−	17.3137i	0.503595	−	0.712191i
$592$	−25.6569	+	25.6569i	−1.05449	+	1.05449i
$593$	−21.0919	−	21.0919i	−0.866140	−	0.866140i	0.125903	−	0.992043i	$-0.459817\pi$
$593$	−21.0919	−	21.0919i	−0.866140	−	0.866140i	−0.992043	+	0.125903i	$0.959817\pi$
$594$	12.8284	−	7.17157i	0.526357	−	0.294253i
$595$			15.3137i			0.627801i
$596$		0			0
$597$	−5.17157	−	30.1421i	−0.211658	−	1.23364i
$598$	5.17157	+	7.75736i	0.211481	+	0.317222i
$599$		−	16.4558i		−	0.672368i	−0.941796	−	0.336184i	$-0.890864\pi$
$599$		−	16.4558i		−	0.672368i	0.941796	−	0.336184i	$-0.109136\pi$
$600$	−27.3137	+	38.6274i	−1.11508	+	1.57696i
$601$	2.48528			0.101377			0.0506884	−	0.998715i	$-0.483858\pi$
$601$	2.48528			0.101377			0.0506884	+	0.998715i	$0.483858\pi$
$602$	−9.41421			−0.383695
$603$	−34.7279	−	16.5858i	−1.41423	−	0.675425i
$604$		0			0
$605$	−18.9497	−	18.9497i	−0.770417	−	0.770417i
$606$	10.8284	−	15.3137i	0.439875	−	0.622077i
$607$	8.82843			0.358335			0.179167	−	0.983819i	$-0.442660\pi$
$607$	8.82843			0.358335			0.179167	+	0.983819i	$0.442660\pi$
$608$		0			0
$609$	9.41421	+	6.65685i	0.381483	+	0.269749i
$610$			75.2548i			3.04698i
$611$	−7.97056	+	5.31371i	−0.322454	+	0.214970i
$612$		0			0
$613$	10.7574	+	10.7574i	0.434486	+	0.434486i	0.890151	−	0.455665i	$-0.150599\pi$
$613$	10.7574	+	10.7574i	0.434486	+	0.434486i	−0.455665	+	0.890151i	$0.650599\pi$
$614$		−	8.72792i		−	0.352230i
$615$	0.384776	+	2.24264i	0.0155157	+	0.0904320i
$616$	4.00000	+	4.00000i	0.161165	+	0.161165i
$617$	9.68629	−	9.68629i	0.389955	−	0.389955i	−0.484716	−	0.874672i	$-0.661077\pi$
$617$	9.68629	−	9.68629i	0.389955	−	0.389955i	0.874672	+	0.484716i	$0.161077\pi$
$618$		0			0
$619$	−15.8995	+	15.8995i	−0.639055	+	0.639055i	−0.950322	−	0.311268i	$-0.899246\pi$
$619$	−15.8995	+	15.8995i	−0.639055	+	0.639055i	0.311268	+	0.950322i	$0.399246\pi$
$620$		0			0
$621$	8.29289	−	4.63604i	0.332782	−	0.186038i
$622$	−31.5563	+	31.5563i	−1.26529	+	1.26529i
$623$	−8.31371			−0.333082
$624$	−0.686292	+	24.9706i	−0.0274736	+	0.999623i
$625$	−19.9706			−0.798823
$626$	−12.1421	+	12.1421i	−0.485297	+	0.485297i
$627$	−1.55635	−	9.07107i	−0.0621546	−	0.362264i
$628$		0			0
$629$	−25.6569	+	25.6569i	−1.02301	+	1.02301i
$630$	14.6569	+	7.00000i	0.583943	+	0.278887i
$631$	20.6569	−	20.6569i	0.822336	−	0.822336i	−0.164106	−	0.986443i	$-0.552474\pi$
$631$	20.6569	−	20.6569i	0.822336	−	0.822336i	0.986443	+	0.164106i	$0.0524740\pi$
$632$	11.6569	+	11.6569i	0.463685	+	0.463685i
$633$	−29.8492	+	5.12132i	−1.18640	+	0.203554i
$634$		−	22.4853i		−	0.893005i
$635$	−5.41421	−	5.41421i	−0.214857	−	0.214857i
$636$		0			0
$637$	−3.53553	−	0.707107i	−0.140083	−	0.0280166i
$638$		−	18.8284i		−	0.745425i
$639$	20.5563	−	43.0416i	0.813197	−	1.70270i
$640$	43.3137			1.71212
$641$	−31.0000			−1.22443			−0.612213	−	0.790693i	$-0.709721\pi$
$641$	−31.0000			−1.22443			−0.612213	+	0.790693i	$0.709721\pi$
$642$	1.65685	+	1.17157i	0.0653908	+	0.0462383i
$643$	4.92893	+	4.92893i	0.194378	+	0.194378i	0.797585	−	0.603207i	$-0.206111\pi$
$643$	4.92893	+	4.92893i	0.194378	+	0.194378i	−0.603207	+	0.797585i	$0.706111\pi$
$644$		0			0
$645$	−36.0416	−	25.4853i	−1.41914	−	1.00348i
$646$	−15.0294			−0.591325
$647$	33.8995			1.33273			0.666363	−	0.745627i	$-0.267850\pi$
$647$	33.8995			1.33273			0.666363	+	0.745627i	$0.267850\pi$
$648$	25.3137	+	2.68629i	0.994416	+	0.105527i
$649$		−	4.00000i		−	0.157014i
$650$	−40.9706	+	27.3137i	−1.60700	+	1.07133i
$651$	7.12132	−	1.22183i	0.279107	−	0.0478871i
$652$		0			0
$653$		−	11.5147i		−	0.450606i	−0.974289	−	0.225303i	$-0.927663\pi$
$653$		−	11.5147i		−	0.450606i	0.974289	−	0.225303i	$-0.0723372\pi$
$654$	−14.2426	+	2.44365i	−0.556931	+	0.0955543i
$655$	24.5563	+	24.5563i	0.959496	+	0.959496i
$656$	0.970563	−	0.970563i	0.0378941	−	0.0378941i
$657$	0.221825	−	0.464466i	0.00865423	−	0.0181205i
$658$	2.65685	−	2.65685i	0.103575	−	0.103575i
$659$		−	27.9706i		−	1.08958i	−0.838573	−	0.544789i	$-0.816610\pi$
$659$		−	27.9706i		−	1.08958i	0.838573	−	0.544789i	$-0.183390\pi$
$660$		0			0
$661$	0.849242	−	0.849242i	0.0330317	−	0.0330317i	−0.690398	−	0.723430i	$-0.742565\pi$
$661$	0.849242	−	0.849242i	0.0330317	−	0.0330317i	0.723430	+	0.690398i	$0.242565\pi$
$662$	−17.3137			−0.672916
$663$	−0.686292	+	24.9706i	−0.0266534	+	0.969776i
$664$	2.82843			0.109764
$665$	7.19239	−	7.19239i	0.278909	−	0.278909i
$666$	12.8284	+	36.2843i	0.497091	+	1.40599i
$667$		−	12.1716i		−	0.471285i
$668$		0			0
$669$	−23.5563	−	16.6569i	−0.910741	−	0.643991i
$670$	−49.1127	+	49.1127i	−1.89739	+	1.89739i
$671$	19.6569	+	19.6569i	0.758844	+	0.758844i
$672$		0			0
$673$		−	27.0000i		−	1.04077i	−0.853931	−	0.520387i	$-0.825788\pi$
$673$		−	27.0000i		−	1.04077i	0.853931	−	0.520387i	$-0.174212\pi$
$674$	21.1421	+	21.1421i	0.814365	+	0.814365i
$675$	24.4853	+	43.7990i	0.942439	+	1.68582i
$676$		0			0
$677$			5.41421i			0.208085i	0.994573	+	0.104043i	$0.0331778\pi$
$677$			5.41421i			0.208085i	−0.994573	+	0.104043i	$0.966822\pi$
$678$	−19.6569	−	13.8995i	−0.754917	−	0.533807i
$679$	10.3137			0.395804
$680$	43.3137			1.66100
$681$	−1.31371	+	1.85786i	−0.0503414	+	0.0711935i
$682$	−8.34315	−	8.34315i	−0.319476	−	0.319476i
$683$	11.7990	+	11.7990i	0.451476	+	0.451476i	0.895844	−	0.444368i	$-0.146572\pi$
$683$	11.7990	+	11.7990i	0.451476	+	0.451476i	−0.444368	+	0.895844i	$0.646572\pi$
$684$		0			0
$685$	−34.7279			−1.32689
$686$	1.41421			0.0539949
$687$	−9.17157	+	12.9706i	−0.349917	+	0.494858i
$688$			26.6274i			1.01516i
$689$	43.5355	+	8.70711i	1.65857	+	0.331714i
$690$	−2.89949	−	16.8995i	−0.110382	−	0.643353i
$691$	−26.6066	−	26.6066i	−1.01216	−	1.01216i	−0.999925	−	0.0122377i	$-0.996105\pi$
$691$	−26.6066	−	26.6066i	−1.01216	−	1.01216i	−0.0122377	−	0.999925i	$-0.503895\pi$
$692$		0			0
$693$	5.65685	−	2.00000i	0.214886	−	0.0759737i
$694$	−6.00000	−	6.00000i	−0.227757	−	0.227757i
$695$	−23.8995	+	23.8995i	−0.906560	+	0.906560i
$696$	18.8284	−	26.6274i	0.713690	−	1.00931i
$697$	0.970563	−	0.970563i	0.0367627	−	0.0367627i
$698$		−	26.1005i		−	0.987919i
$699$	−27.8492	+	4.77817i	−1.05336	+	0.180727i
$700$		0			0
$701$	7.48528			0.282715			0.141358	−	0.989959i	$-0.454853\pi$
$701$	7.48528			0.282715			0.141358	+	0.989959i	$0.454853\pi$
$702$	23.5858	+	12.0711i	0.890188	+	0.455593i
$703$	24.1005			0.908968
$704$	11.3137	−	11.3137i	0.426401	−	0.426401i
$705$	17.3640	−	2.97918i	0.653965	−	0.112203i
$706$		−	34.6274i		−	1.30322i
$707$	5.41421	−	5.41421i	0.203622	−	0.203622i
$708$		0			0
$709$	−31.6985	+	31.6985i	−1.19046	+	1.19046i	−0.213524	+	0.976938i	$0.568494\pi$
$709$	−31.6985	+	31.6985i	−1.19046	+	1.19046i	−0.976938	+	0.213524i	$0.931506\pi$
$710$	−60.8701	−	60.8701i	−2.28441	−	2.28441i
$711$	16.4853	−	5.82843i	0.618246	−	0.218583i
$712$			23.5147i			0.881251i
$713$	−5.39340	−	5.39340i	−0.201984	−	0.201984i
$714$	−1.65685	−	9.65685i	−0.0620062	−	0.361399i
$715$	−5.41421	+	27.0711i	−0.202480	+	1.01240i
$716$		0			0
$717$	−14.2426	+	20.1421i	−0.531901	+	0.752222i
$718$	33.6569			1.25606
$719$	−6.38478			−0.238112			−0.119056	−	0.992888i	$-0.537987\pi$
$719$	−6.38478			−0.238112			−0.119056	+	0.992888i	$0.537987\pi$
$720$	19.7990	−	41.4558i	0.737865	−	1.54497i
$721$		0			0
$722$	−11.9411	−	11.9411i	−0.444403	−	0.444403i
$723$	−9.48528	+	13.4142i	−0.352761	+	0.498880i
$724$		0			0
$725$	64.2843			2.38746
$726$	14.0000	+	9.89949i	0.519589	+	0.367405i
$727$		−	7.45584i		−	0.276522i	−0.990396	−	0.138261i	$-0.955849\pi$
$727$		−	7.45584i		−	0.276522i	0.990396	−	0.138261i	$-0.0441513\pi$
$728$	−2.00000	+	10.0000i	−0.0741249	+	0.370625i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−0.656854	−	0.656854i	−0.0243113	−	0.0243113i
$731$			26.6274i			0.984851i
$732$		0			0
$733$	19.8787	+	19.8787i	0.734236	+	0.734236i	0.971456	−	0.237220i	$-0.0762363\pi$
$733$	19.8787	+	19.8787i	0.734236	+	0.734236i	−0.237220	+	0.971456i	$0.576236\pi$
$734$	25.6985	−	25.6985i	0.948548	−	0.948548i
$735$	5.41421	+	3.82843i	0.199706	+	0.141214i
$736$		0			0
$737$			25.6569i			0.945082i
$738$	−0.485281	−	1.37258i	−0.0178635	−	0.0505255i
$739$	16.0416	−	16.0416i	0.590101	−	0.590101i	−0.347558	−	0.937659i	$-0.612989\pi$
$739$	16.0416	−	16.0416i	0.590101	−	0.590101i	0.937659	+	0.347558i	$0.112989\pi$
$740$		0			0
$741$	12.0503	−	11.4056i	0.442677	−	0.418995i
$742$	−17.4142			−0.639296
$743$	12.2132	−	12.2132i	0.448059	−	0.448059i	−0.446650	−	0.894709i	$-0.647383\pi$
$743$	12.2132	−	12.2132i	0.448059	−	0.448059i	0.894709	+	0.446650i	$0.147383\pi$
$744$	−3.45584	−	20.1421i	−0.126697	−	0.738447i
$745$		−	22.9706i		−	0.841576i
$746$	−22.6274	+	22.6274i	−0.828449	+	0.828449i
$747$	1.29289	−	2.70711i	0.0473045	−	0.0990479i
$748$		0			0
$749$	0.585786	+	0.585786i	0.0214042	+	0.0214042i
$750$	43.0416	−	7.38478i	1.57166	−	0.269654i
$751$			49.6274i			1.81093i	0.424421	+	0.905465i	$0.360478\pi$
$751$			49.6274i			1.81093i	−0.424421	+	0.905465i	$0.639522\pi$
$752$	−7.51472	−	7.51472i	−0.274034	−	0.274034i
$753$	−32.3848	+	5.55635i	−1.18017	+	0.202485i
$754$	28.2426	−	18.8284i	1.02854	−	0.685691i
$755$		−	59.0122i		−	2.14767i
$756$		0			0
$757$	−7.68629			−0.279363			−0.139682	−	0.990196i	$-0.544608\pi$
$757$	−7.68629			−0.279363			−0.139682	+	0.990196i	$0.544608\pi$
$758$	−9.17157			−0.333127
$759$	−5.17157	−	3.65685i	−0.187716	−	0.132735i
$760$	−20.3431	−	20.3431i	−0.737923	−	0.737923i
$761$	36.8492	+	36.8492i	1.33578	+	1.33578i	0.900099	+	0.435685i	$0.143494\pi$
$761$	36.8492	+	36.8492i	1.33578	+	1.33578i	0.435685	+	0.900099i	$0.356506\pi$
$762$	4.00000	+	2.82843i	0.144905	+	0.102463i
$763$	−5.89949			−0.213576
$764$		0			0
$765$	19.7990	−	41.4558i	0.715834	−	1.49884i
$766$			12.2010i			0.440840i
$767$	6.00000	−	4.00000i	0.216647	−	0.144432i
$768$		0			0
$769$	−6.36396	−	6.36396i	−0.229490	−	0.229490i	0.582989	−	0.812480i	$-0.301883\pi$
$769$	−6.36396	−	6.36396i	−0.229490	−	0.229490i	−0.812480	+	0.582989i	$0.801883\pi$
$770$		−	10.8284i		−	0.390229i
$771$	48.0416	−	8.24264i	1.73018	−	0.296851i
$772$		0			0
$773$	22.1421	−	22.1421i	0.796397	−	0.796397i	−0.186128	−	0.982525i	$-0.559594\pi$
$773$	22.1421	−	22.1421i	0.796397	−	0.796397i	0.982525	+	0.186128i	$0.0595940\pi$
$774$	25.4853	+	12.1716i	0.916050	+	0.437498i
$775$	28.4853	−	28.4853i	1.02322	−	1.02322i
$776$		−	29.1716i		−	1.04720i
$777$	2.65685	+	15.4853i	0.0953141	+	0.555531i
$778$	6.82843	−	6.82843i	0.244811	−	0.244811i
$779$	−0.911688			−0.0326646
$780$		0			0
$781$	−31.7990			−1.13786
$782$	−7.31371	+	7.31371i	−0.261538	+	0.261538i
$783$	−16.8787	−	30.1924i	−0.603195	−	1.07899i
$784$		−	4.00000i		−	0.142857i
$785$	−22.9706	+	22.9706i	−0.819855	+	0.819855i
$786$	−18.1421	−	12.8284i	−0.647109	−	0.457575i
$787$	33.5355	−	33.5355i	1.19541	−	1.19541i	0.219887	−	0.975525i	$-0.429431\pi$
$787$	33.5355	−	33.5355i	1.19541	−	1.19541i	0.975525	−	0.219887i	$-0.0705690\pi$
$788$		0			0
$789$	8.05025	+	46.9203i	0.286597	+	1.67041i
$790$		−	31.5563i		−	1.12272i
$791$	−6.94975	−	6.94975i	−0.247105	−	0.247105i
$792$	−5.65685	−	16.0000i	−0.201008	−	0.568535i
$793$	−9.82843	+	49.1421i	−0.349018	+	1.74509i
$794$			6.78680i			0.240854i
$795$	−66.6690	−	47.1421i	−2.36451	−	1.67196i
$796$		0			0
$797$	−17.7990			−0.630473			−0.315236	−	0.949013i	$-0.602084\pi$
$797$	−17.7990			−0.630473			−0.315236	+	0.949013i	$0.602084\pi$
$798$	−3.75736	+	5.31371i	−0.133009	+	0.188103i
$799$	−7.51472	−	7.51472i	−0.265852	−	0.265852i
$800$		0			0
$801$	22.5061	+	10.7487i	0.795214	+	0.379788i
$802$	7.85786			0.277471
$803$	−0.343146			−0.0121094
$804$		0			0
$805$		−	7.00000i		−	0.246718i
$806$	4.17157	−	20.8579i	0.146937	−	0.734687i
$807$	9.28427	+	54.1127i	0.326822	+	1.90486i
$808$	−15.3137	−	15.3137i	−0.538734	−	0.538734i
$809$			3.97056i			0.139598i	0.997561	+	0.0697988i	$0.0222357\pi$
$809$			3.97056i			0.139598i	−0.997561	+	0.0697988i	$0.977764\pi$
$810$	−30.6274	−	37.8995i	−1.07614	−	1.33165i
$811$	−11.7574	−	11.7574i	−0.412857	−	0.412857i	0.469876	−	0.882733i	$-0.344299\pi$
$811$	−11.7574	−	11.7574i	−0.412857	−	0.412857i	−0.882733	+	0.469876i	$0.844299\pi$
$812$		0			0
$813$	16.8284	−	23.7990i	0.590199	−	0.834667i
$814$	18.1421	−	18.1421i	0.635882	−	0.635882i
$815$			82.5269i			2.89079i
$816$	−27.3137	+	4.68629i	−0.956171	+	0.164053i
$817$	12.5061	−	12.5061i	0.437533	−	0.437533i
$818$	−4.72792			−0.165308
$819$	8.65685	+	6.48528i	0.302495	+	0.226614i
$820$		0			0
$821$	−30.2426	+	30.2426i	−1.05548	+	1.05548i	−0.0571074	+	0.998368i	$0.518188\pi$
$821$	−30.2426	+	30.2426i	−1.05548	+	1.05548i	−0.998368	+	0.0571074i	$0.981812\pi$
$822$	21.8995	−	3.75736i	0.763833	−	0.131053i
$823$			11.3137i			0.394371i	0.980366	+	0.197186i	$0.0631801\pi$
$823$			11.3137i			0.394371i	−0.980366	+	0.197186i	$0.936820\pi$
$824$		0			0
$825$	19.3137	−	27.3137i	0.672417	−	0.950941i
$826$	−2.00000	+	2.00000i	−0.0695889	+	0.0695889i
$827$	−27.8701	−	27.8701i	−0.969137	−	0.969137i	0.0304009	−	0.999538i	$-0.490322\pi$
$827$	−27.8701	−	27.8701i	−0.969137	−	0.969137i	−0.999538	+	0.0304009i	$0.990322\pi$
$828$		0			0
$829$		−	5.89949i		−	0.204898i	−0.994738	−	0.102449i	$-0.967332\pi$
$829$		−	5.89949i		−	0.204898i	0.994738	−	0.102449i	$-0.0326678\pi$
$830$	−3.82843	−	3.82843i	−0.132887	−	0.132887i
$831$	0.736544	+	4.29289i	0.0255504	+	0.148919i
$832$	28.2843	+	5.65685i	0.980581	+	0.196116i
$833$		−	4.00000i		−	0.138592i
$834$	12.4853	−	17.6569i	0.432330	−	0.611407i
$835$	−15.9706			−0.552684
$836$		0			0
$837$	−20.8579	−	5.89949i	−0.720953	−	0.203916i
$838$	16.6274	+	16.6274i	0.574385	+	0.574385i
$839$	37.2132	+	37.2132i	1.28474	+	1.28474i	0.937937	+	0.346805i	$0.112734\pi$
$839$	37.2132	+	37.2132i	1.28474	+	1.28474i	0.346805	+	0.937937i	$0.387266\pi$
$840$	10.8284	−	15.3137i	0.373616	−	0.528373i
$841$	−15.3137			−0.528059
$842$		0			0
$843$	−22.2843	−	15.7574i	−0.767511	−	0.542712i
$844$		0			0
$845$	−46.0208	+	18.9497i	−1.58316	+	0.651891i
$846$	−10.6274	+	3.75736i	−0.365378	+	0.129181i
$847$	4.94975	+	4.94975i	0.170075	+	0.170075i
$848$			49.2548i			1.69142i
$849$	−2.00000	−	11.6569i	−0.0686398	−	0.400062i
$850$	−38.6274	−	38.6274i	−1.32491	−	1.32491i
$851$	11.7279	−	11.7279i	0.402028	−	0.402028i
$852$		0			0
$853$	6.02082	−	6.02082i	0.206149	−	0.206149i	−0.596480	−	0.802628i	$-0.703434\pi$
$853$	6.02082	−	6.02082i	0.206149	−	0.206149i	0.802628	+	0.596480i	$0.203434\pi$
$854$		−	19.6569i		−	0.672644i
$855$	−28.7696	+	10.1716i	−0.983898	+	0.347860i
$856$	1.65685	−	1.65685i	0.0566301	−	0.0566301i
$857$	1.21320			0.0414422			0.0207211	−	0.999785i	$-0.493404\pi$
$857$	1.21320			0.0414422			0.0207211	+	0.999785i	$0.493404\pi$
$858$	0.485281	−	17.6569i	0.0165672	−	0.602795i
$859$	−23.6569			−0.807161			−0.403581	−	0.914944i	$-0.632235\pi$
$859$	−23.6569			−0.807161			−0.403581	+	0.914944i	$0.632235\pi$
$860$		0			0
$861$	−0.100505	−	0.585786i	−0.00342520	−	0.0199635i
$862$			30.9706i			1.05486i
$863$	−13.7990	+	13.7990i	−0.469723	+	0.469723i	−0.901825	−	0.432102i	$-0.857772\pi$
$863$	−13.7990	+	13.7990i	−0.469723	+	0.469723i	0.432102	+	0.901825i	$0.357772\pi$
$864$		0			0
$865$	26.4142	−	26.4142i	0.898110	−	0.898110i
$866$	11.4142	+	11.4142i	0.387871	+	0.387871i
$867$	1.70711	−	0.292893i	0.0579764	−	0.00994718i
$868$		0			0
$869$	−8.24264	−	8.24264i	−0.279612	−	0.279612i
$870$	−61.5269	+	10.5563i	−2.08596	+	0.357894i
$871$	−38.4853	+	25.6569i	−1.30402	+	0.869349i
$872$			16.6863i			0.565069i
$873$	−27.9203	−	13.3345i	−0.944959	−	0.451305i
$874$	6.87006			0.232383
$875$	17.8284			0.602711
$876$		0			0
$877$	26.4853	+	26.4853i	0.894344	+	0.894344i	0.994929	−	0.100584i	$-0.0320712\pi$
$877$	26.4853	+	26.4853i	0.894344	+	0.894344i	−0.100584	+	0.994929i	$0.532071\pi$
$878$	−21.2132	−	21.2132i	−0.715911	−	0.715911i
$879$	25.8995	+	18.3137i	0.873568	+	0.617706i
$880$	−30.6274			−1.03245
$881$	10.2843			0.346486			0.173243	−	0.984879i	$-0.444575\pi$
$881$	10.2843			0.346486			0.173243	+	0.984879i	$0.444575\pi$
$882$	−3.82843	−	1.82843i	−0.128910	−	0.0615663i
$883$			8.68629i			0.292317i	0.989261	+	0.146158i	$0.0466909\pi$
$883$			8.68629i			0.292317i	−0.989261	+	0.146158i	$0.953309\pi$
$884$		0			0
$885$	−13.0711	+	2.24264i	−0.439379	+	0.0753855i
$886$	−7.34315	−	7.34315i	−0.246698	−	0.246698i
$887$		−	24.8701i		−	0.835055i	−0.908664	−	0.417527i	$-0.862897\pi$
$887$		−	24.8701i		−	0.835055i	0.908664	−	0.417527i	$-0.137103\pi$
$888$	43.7990	−	7.51472i	1.46980	−	0.252177i
$889$	1.41421	+	1.41421i	0.0474312	+	0.0474312i
$890$	31.8284	−	31.8284i	1.06689	−	1.06689i
$891$	−17.8995	−	1.89949i	−0.599656	−	0.0636355i
$892$		0			0
$893$			7.05887i			0.236216i
$894$	2.48528	+	14.4853i	0.0831202	+	0.484460i
$895$	64.5061	−	64.5061i	2.15620	−	2.15620i
$896$	−11.3137			−0.377964
$897$	0.313708	−	11.4142i	0.0104744	−	0.381109i
$898$	36.8284			1.22898
$899$	−19.6360	+	19.6360i	−0.654899	+	0.654899i
$900$		0			0
$901$			49.2548i			1.64092i
$902$	−0.686292	+	0.686292i	−0.0228510	+	0.0228510i
$903$	9.41421	+	6.65685i	0.313285	+	0.221526i
$904$	−19.6569	+	19.6569i	−0.653777	+	0.653777i
$905$	−5.41421	−	5.41421i	−0.179975	−	0.179975i
$906$	6.38478	+	37.2132i	0.212120	+	1.23633i
$907$		−	0.372583i		−	0.0123714i	−0.999981	−	0.00618571i	$-0.998031\pi$
$907$		−	0.372583i		−	0.0123714i	0.999981	−	0.00618571i	$-0.00196898\pi$
$908$		0			0
$909$	−21.6569	+	7.65685i	−0.718313	+	0.253962i
$910$	16.2426	−	10.8284i	0.538438	−	0.358959i
$911$			18.1716i			0.602051i	0.953616	+	0.301026i	$0.0973289\pi$
$911$			18.1716i			0.602051i	−0.953616	+	0.301026i	$0.902671\pi$
$912$	15.0294	+	10.6274i	0.497674	+	0.351909i
$913$	−2.00000			−0.0661903
$914$	−10.3431			−0.342121
$915$	53.2132	−	75.2548i	1.75917	−	2.48785i
$916$		0			0
$917$	−6.41421	−	6.41421i	−0.211816	−	0.211816i
$918$	−8.00000	+	28.2843i	−0.264039	+	0.933520i
$919$	47.1716			1.55605			0.778023	−	0.628235i	$-0.216223\pi$
$919$	47.1716			1.55605			0.778023	+	0.628235i	$0.216223\pi$
$920$	−19.7990			−0.652753
$921$	−6.17157	+	8.72792i	−0.203360	+	0.287595i
$922$		−	3.02944i		−	0.0997692i
$923$	−31.7990	−	47.6985i	−1.04668	−	1.57001i
$924$		0			0
$925$	61.9411	+	61.9411i	2.03661	+	2.03661i
$926$		−	6.68629i		−	0.219725i
$927$		0			0
$928$		0			0
$929$	−35.9203	+	35.9203i	−1.17851	+	1.17851i	−0.198382	+	0.980125i	$0.563569\pi$
$929$	−35.9203	+	35.9203i	−1.17851	+	1.17851i	−0.980125	+	0.198382i	$0.936431\pi$
$930$	−22.5858	+	31.9411i	−0.740617	+	1.04739i
$931$	−1.87868	+	1.87868i	−0.0615712	+	0.0615712i
$932$		0			0
$933$	53.8701	−	9.24264i	1.76363	−	0.302590i
$934$	−33.2132	+	33.2132i	−1.08677	+	1.08677i
$935$	−30.6274			−1.00162
$936$	18.3431	−	24.4853i	0.599564	−	0.800326i
$937$	−32.8701			−1.07382			−0.536909	−	0.843640i	$-0.680408\pi$
$937$	−32.8701			−1.07382			−0.536909	+	0.843640i	$0.680408\pi$
$938$	12.8284	−	12.8284i	0.418863	−	0.418863i
$939$	20.7279	−	3.55635i	0.676430	−	0.116057i
$940$		0			0
$941$	26.6066	−	26.6066i	0.867350	−	0.867350i	−0.124828	−	0.992178i	$-0.539838\pi$
$941$	26.6066	−	26.6066i	0.867350	−	0.867350i	0.992178	+	0.124828i	$0.0398379\pi$
$942$	12.0000	−	16.9706i	0.390981	−	0.552931i
$943$	−0.443651	+	0.443651i	−0.0144473	+	0.0144473i
$944$	5.65685	+	5.65685i	0.184115	+	0.184115i
$945$	−9.70711	−	17.3640i	−0.315772	−	0.564850i
$946$		−	18.8284i		−	0.612165i
$947$	−16.5858	−	16.5858i	−0.538966	−	0.538966i	0.384259	−	0.923225i	$-0.374457\pi$
$947$	−16.5858	−	16.5858i	−0.538966	−	0.538966i	−0.923225	+	0.384259i	$0.874457\pi$
$948$		0			0
$949$	−0.343146	−	0.514719i	−0.0111390	−	0.0167085i
$950$			36.2843i			1.17722i
$951$	−15.8995	+	22.4853i	−0.515576	+	0.729135i
$952$	−11.3137			−0.366679
$953$	3.97056			0.128619			0.0643096	−	0.997930i	$-0.479515\pi$
$953$	3.97056			0.128619			0.0643096	+	0.997930i	$0.479515\pi$
$954$	47.1421	+	22.5147i	1.52628	+	0.728941i
$955$	−25.2132	−	25.2132i	−0.815880	−	0.815880i
$956$		0			0
$957$	−13.3137	+	18.8284i	−0.430371	+	0.608637i
$958$	−16.0416			−0.518282
$959$	9.07107			0.292920
$960$	−43.3137	−	30.6274i	−1.39794	−	0.988496i
$961$		−	13.5980i		−	0.438645i
$962$	45.3553	+	9.07107i	1.46231	+	0.292463i
$963$	−0.828427	−	2.34315i	−0.0266957	−	0.0755068i
$964$		0			0
$965$			20.3431i			0.654869i
$966$	0.757359	+	4.41421i	0.0243676	+	0.142025i
$967$	−16.3848	−	16.3848i	−0.526899	−	0.526899i	0.392747	−	0.919646i	$-0.371525\pi$
$967$	−16.3848	−	16.3848i	−0.526899	−	0.526899i	−0.919646	+	0.392747i	$0.871525\pi$
$968$	14.0000	−	14.0000i	0.449977	−	0.449977i
$969$	15.0294	+	10.6274i	0.482815	+	0.341402i
$970$	−39.4853	+	39.4853i	−1.26780	+	1.26780i
$971$			8.52691i			0.273642i	0.990596	+	0.136821i	$0.0436885\pi$
$971$			8.52691i			0.273642i	−0.990596	+	0.136821i	$0.956312\pi$
$972$		0			0
$973$	6.24264	−	6.24264i	0.200130	−	0.200130i
$974$	−40.3431			−1.29268
$975$	60.2843	+	1.65685i	1.93064	+	0.0530618i
$976$	−55.5980			−1.77965
$977$	23.5563	−	23.5563i	0.753634	−	0.753634i	−0.221521	−	0.975156i	$-0.571102\pi$
$977$	23.5563	−	23.5563i	0.753634	−	0.753634i	0.975156	+	0.221521i	$0.0711022\pi$
$978$	−8.92893	−	52.0416i	−0.285516	−	1.66411i
$979$		−	16.6274i		−	0.531415i
$980$		0			0
$981$	15.9706	+	7.62742i	0.509901	+	0.243525i
$982$	−28.9706	+	28.9706i	−0.924488	+	0.924488i
$983$	11.1924	+	11.1924i	0.356982	+	0.356982i	0.862699	−	0.505717i	$-0.168772\pi$
$983$	11.1924	+	11.1924i	0.356982	+	0.356982i	−0.505717	+	0.862699i	$0.668772\pi$
$984$	−1.65685	+	0.284271i	−0.0528186	+	0.00906224i
$985$			46.8701i			1.49340i
$986$	26.6274	+	26.6274i	0.847990	+	0.847990i
$987$	−4.53553	+	0.778175i	−0.144368	+	0.0247696i
$988$		0			0
$989$		−	12.1716i		−	0.387034i
$990$	−14.0000	+	29.3137i	−0.444949	+	0.931651i
$991$	−42.9706			−1.36500			−0.682502	−	0.730883i	$-0.739108\pi$
$991$	−42.9706			−1.36500			−0.682502	+	0.730883i	$0.739108\pi$
$992$		0			0
$993$	17.3137	+	12.2426i	0.549434	+	0.388508i
$994$	15.8995	+	15.8995i	0.504301	+	0.504301i
$995$	47.7990	+	47.7990i	1.51533	+	1.51533i
$996$		0			0
$997$	51.3137			1.62512			0.812561	−	0.582877i	$-0.198073\pi$
$997$	51.3137			1.62512			0.812561	+	0.582877i	$0.198073\pi$
$998$	−28.0000			−0.886325
$999$	12.8284	−	45.3553i	0.405873	−	1.43498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.n.b.8.1	yes	4
3.2	odd	2		273.2.n.a.8.1	✓	4
13.5	odd	4		273.2.n.a.239.1	yes	4
39.5	even	4	inner	273.2.n.b.239.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.n.a.8.1	✓	4	3.2	odd	2
273.2.n.a.239.1	yes	4	13.5	odd	4
273.2.n.b.8.1	yes	4	1.1	even	1	trivial
273.2.n.b.239.1	yes	4	39.5	even	4	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.70711 + 0.292893i) q^{3} +(2.70711 - 2.70711i) q^{5} +(-1.41421 + 2.00000i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.82843 - 1.00000i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(-1.70711 + 0.292893i) q^{3} +(2.70711 - 2.70711i) q^{5} +(-1.41421 + 2.00000i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.82843 - 1.00000i) q^{9} -5.41421i q^{10} +(-1.41421 - 1.41421i) q^{11} +(0.707107 - 3.53553i) q^{13} +1.41421i q^{14} +(-3.82843 + 5.41421i) q^{15} +4.00000 q^{16} +4.00000 q^{17} +(1.82843 - 3.82843i) q^{18} +(-1.87868 - 1.87868i) q^{19} +(1.00000 - 1.41421i) q^{21} -2.82843 q^{22} -1.82843 q^{23} +(-4.00000 - 2.82843i) q^{24} -9.65685i q^{25} +(-2.82843 - 4.24264i) q^{26} +(-4.53553 + 2.53553i) q^{27} +6.65685i q^{29} +(1.58579 + 9.24264i) q^{30} +(2.94975 + 2.94975i) q^{31} +(2.82843 + 2.00000i) q^{33} +(4.00000 - 4.00000i) q^{34} +3.82843i q^{35} +(-6.41421 + 6.41421i) q^{37} -3.75736 q^{38} +(-0.171573 + 6.24264i) q^{39} +10.8284 q^{40} +(0.242641 - 0.242641i) q^{41} +(-0.414214 - 2.41421i) q^{42} +6.65685i q^{43} +(4.94975 - 10.3640i) q^{45} +(-1.82843 + 1.82843i) q^{46} +(-1.87868 - 1.87868i) q^{47} +(-6.82843 + 1.17157i) q^{48} -1.00000i q^{49} +(-9.65685 - 9.65685i) q^{50} +(-6.82843 + 1.17157i) q^{51} +12.3137i q^{53} +(-2.00000 + 7.07107i) q^{54} -7.65685 q^{55} -2.82843 q^{56} +(3.75736 + 2.65685i) q^{57} +(6.65685 + 6.65685i) q^{58} +(1.41421 + 1.41421i) q^{59} -13.8995 q^{61} +5.89949 q^{62} +(-1.29289 + 2.70711i) q^{63} +8.00000i q^{64} +(-7.65685 - 11.4853i) q^{65} +(4.82843 - 0.828427i) q^{66} +(-9.07107 - 9.07107i) q^{67} +(3.12132 - 0.535534i) q^{69} +(3.82843 + 3.82843i) q^{70} +(11.2426 - 11.2426i) q^{71} +(7.65685 + 3.65685i) q^{72} +(0.121320 - 0.121320i) q^{73} +12.8284i q^{74} +(2.82843 + 16.4853i) q^{75} +2.00000 q^{77} +(6.07107 + 6.41421i) q^{78} +5.82843 q^{79} +(10.8284 - 10.8284i) q^{80} +(7.00000 - 5.65685i) q^{81} -0.485281i q^{82} +(0.707107 - 0.707107i) q^{83} +(10.8284 - 10.8284i) q^{85} +(6.65685 + 6.65685i) q^{86} +(-1.94975 - 11.3640i) q^{87} -5.65685i q^{88} +(5.87868 + 5.87868i) q^{89} +(-5.41421 - 15.3137i) q^{90} +(2.00000 + 3.00000i) q^{91} +(-5.89949 - 4.17157i) q^{93} -3.75736 q^{94} -10.1716 q^{95} +(-7.29289 - 7.29289i) q^{97} +(-1.00000 - 1.00000i) q^{98} +(-5.41421 - 2.58579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8	\( 4 q + 4 q^{2} - 4 q^{3} + 8 q^{5} + 8 q^{8} - 4 q^{15} + 16 q^{16} + 16 q^{17} - 4 q^{18} - 16 q^{19} + 4 q^{21} + 4 q^{23} - 16 q^{24} - 4 q^{27} + 12 q^{30} - 8 q^{31} + 16 q^{34} - 20 q^{37} - 32 q^{38} - 12 q^{39} + 32 q^{40} - 16 q^{41} + 4 q^{42} + 4 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{50} - 16 q^{51} - 8 q^{54} - 8 q^{55} + 32 q^{57} + 4 q^{58} - 16 q^{61} - 16 q^{62} - 8 q^{63} - 8 q^{65} + 8 q^{66} - 8 q^{67} + 4 q^{69} + 4 q^{70} + 28 q^{71} + 8 q^{72} - 8 q^{73} + 8 q^{77} - 4 q^{78} + 12 q^{79} + 32 q^{80} + 28 q^{81} + 32 q^{85} + 4 q^{86} + 12 q^{87} + 32 q^{89} - 16 q^{90} + 8 q^{91} + 16 q^{93} - 32 q^{94} - 52 q^{95} - 32 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 8 * q^5 + 8 * q^8 - 4 * q^15 + 16 * q^16 + 16 * q^17 - 4 * q^18 - 16 * q^19 + 4 * q^21 + 4 * q^23 - 16 * q^24 - 4 * q^27 + 12 * q^30 - 8 * q^31 + 16 * q^34 - 20 * q^37 - 32 * q^38 - 12 * q^39 + 32 * q^40 - 16 * q^41 + 4 * q^42 + 4 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^50 - 16 * q^51 - 8 * q^54 - 8 * q^55 + 32 * q^57 + 4 * q^58 - 16 * q^61 - 16 * q^62 - 8 * q^63 - 8 * q^65 + 8 * q^66 - 8 * q^67 + 4 * q^69 + 4 * q^70 + 28 * q^71 + 8 * q^72 - 8 * q^73 + 8 * q^77 - 4 * q^78 + 12 * q^79 + 32 * q^80 + 28 * q^81 + 32 * q^85 + 4 * q^86 + 12 * q^87 + 32 * q^89 - 16 * q^90 + 8 * q^91 + 16 * q^93 - 32 * q^94 - 52 * q^95 - 32 * q^97 - 4 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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Database

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