LMFDB - Embedded newform 560.2.bw.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(289,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("560.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bw (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
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:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	560.289
Dual form			560.2.bw.c.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59808 + 1.50000i) q^{3} +(-2.23205 - 0.133975i) q^{5} +(0.866025 - 2.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-2.59808 + 1.50000i) q^{3} +(-2.23205 - 0.133975i) q^{5} +(0.866025 - 2.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +2.00000i q^{13} +(6.00000 - 3.00000i) q^{15} +(-1.73205 + 1.00000i) q^{17} +(1.00000 - 1.73205i) q^{19} +(1.50000 + 7.79423i) q^{21} +(0.866025 + 0.500000i) q^{23} +(4.96410 + 0.598076i) q^{25} +9.00000i q^{27} +1.00000 q^{29} +(5.00000 + 8.66025i) q^{31} +(-2.26795 + 5.46410i) q^{35} +(6.92820 + 4.00000i) q^{37} +(-3.00000 - 5.19615i) q^{39} -3.00000 q^{41} +5.00000i q^{43} +(-7.39230 + 11.1962i) q^{45} +(6.92820 + 4.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(3.00000 - 5.19615i) q^{51} +(5.19615 - 3.00000i) q^{53} +6.00000i q^{57} +(-1.00000 - 1.73205i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-10.3923 - 12.0000i) q^{63} +(0.267949 - 4.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} -3.00000 q^{69} -6.00000 q^{71} +(8.66025 - 5.00000i) q^{73} +(-13.7942 + 5.89230i) q^{75} +(5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} -9.00000i q^{83} +(4.00000 - 2.00000i) q^{85} +(-2.59808 + 1.50000i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(5.00000 + 1.73205i) q^{91} +(-25.9808 - 15.0000i) q^{93} +(-2.46410 + 3.73205i) q^{95} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} + 12 q^{9}+O(q^{10}) $ 4 * q - 2 * q^5 + 12 * q^9	$ 4 q - 2 q^{5} + 12 q^{9} + 24 q^{15} + 4 q^{19} + 6 q^{21} + 6 q^{25} + 4 q^{29} + 20 q^{31} - 16 q^{35} - 12 q^{39} - 12 q^{41} + 12 q^{45} - 22 q^{49} + 12 q^{51} - 4 q^{59} + 18 q^{61} + 8 q^{65} - 12 q^{69} - 24 q^{71} - 24 q^{75} + 20 q^{79} - 18 q^{81} + 16 q^{85} - 14 q^{89} + 20 q^{91} + 4 q^{95}+O(q^{100}) $ 4 * q - 2 * q^5 + 12 * q^9 + 24 * q^15 + 4 * q^19 + 6 * q^21 + 6 * q^25 + 4 * q^29 + 20 * q^31 - 16 * q^35 - 12 * q^39 - 12 * q^41 + 12 * q^45 - 22 * q^49 + 12 * q^51 - 4 * q^59 + 18 * q^61 + 8 * q^65 - 12 * q^69 - 24 * q^71 - 24 * q^75 + 20 * q^79 - 18 * q^81 + 16 * q^85 - 14 * q^89 + 20 * q^91 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$6$		0			0
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		0			0
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$	6.00000	−	3.00000i	1.54919	−	0.774597i
$16$		0			0
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$	1.50000	+	7.79423i	0.327327	+	1.70084i
$22$		0			0
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	0.587565	−	0.809177i	$-0.300087\pi$
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	−0.406986	+	0.913434i	$0.633420\pi$
$24$		0			0
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$		0			0
$27$			9.00000i			1.73205i
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.830014	+	0.557743i	$0.188333\pi$
$31$	5.00000	+	8.66025i	0.898027	+	1.55543i	0.0680129	+	0.997684i	$0.478334\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.26795	+	5.46410i	−0.383353	+	0.923602i
$36$		0			0
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.946180	−	0.323640i	$-0.104907\pi$
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.192809	+	0.981236i	$0.438240\pi$
$38$		0			0
$39$	−3.00000	−	5.19615i	−0.480384	−	0.832050i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$			5.00000i			0.762493i	0.924473	+	0.381246i	$0.124505\pi$
$43$			5.00000i			0.762493i	−0.924473	+	0.381246i	$0.875495\pi$
$44$		0			0
$45$	−7.39230	+	11.1962i	−1.10198	+	1.66902i
$46$		0			0
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.911362	−	0.411606i	$-0.135032\pi$
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.0992202	+	0.995066i	$0.468365\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$		0			0
$53$	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	$0.198135\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$		0			0
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$		0			0
$63$	−10.3923	−	12.0000i	−1.30931	−	1.51186i
$64$		0			0
$65$	0.267949	−	4.46410i	0.0332350	−	0.553704i
$66$		0			0
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$		0			0
$69$	−3.00000			−0.361158
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.101361	−	0.994850i	$-0.467680\pi$
$73$	8.66025	−	5.00000i	1.01361	−	0.585206i	0.912245	+	0.409644i	$0.134347\pi$
$74$		0			0
$75$	−13.7942	+	5.89230i	−1.59282	+	0.680385i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$		−	9.00000i		−	0.987878i	−0.869496	−	0.493939i	$-0.835557\pi$
$83$		−	9.00000i		−	0.987878i	0.869496	−	0.493939i	$-0.164443\pi$
$84$		0			0
$85$	4.00000	−	2.00000i	0.433861	−	0.216930i
$86$		0			0
$87$	−2.59808	+	1.50000i	−0.278543	+	0.160817i
$88$		0			0
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$		0			0
$91$	5.00000	+	1.73205i	0.524142	+	0.181568i
$92$		0			0
$93$	−25.9808	−	15.0000i	−2.69408	−	1.55543i
$94$		0			0
$95$	−2.46410	+	3.73205i	−0.252811	+	0.382900i
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$		0			0
$103$	9.52628	+	5.50000i	0.938652	+	0.541931i	0.889538	−	0.456862i	$-0.151027\pi$
$103$	9.52628	+	5.50000i	0.938652	+	0.541931i	0.0491146	+	0.998793i	$0.484360\pi$
$104$		0			0
$105$	−2.30385	−	17.5981i	−0.224833	−	1.71740i
$106$		0			0
$107$	−6.06218	−	3.50000i	−0.586053	−	0.338358i	0.177482	−	0.984124i	$-0.443205\pi$
$107$	−6.06218	−	3.50000i	−0.586053	−	0.338358i	−0.763535	+	0.645766i	$0.776538\pi$
$108$		0			0
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$		0			0
$111$	−24.0000			−2.27798
$112$		0			0
$113$			10.0000i			0.940721i	0.882474	+	0.470360i	$0.155876\pi$
$113$			10.0000i			0.940721i	−0.882474	+	0.470360i	$0.844124\pi$
$114$		0			0
$115$	−1.86603	−	1.23205i	−0.174008	−	0.114889i
$116$		0			0
$117$	10.3923	+	6.00000i	0.960769	+	0.554700i
$118$		0			0
$119$	1.00000	+	5.19615i	0.0916698	+	0.476331i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$	7.79423	−	4.50000i	0.702782	−	0.405751i
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		0			0
$129$	−7.50000	−	12.9904i	−0.660338	−	1.14374i
$130$		0			0
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.0155672	−	0.999879i	$-0.495045\pi$
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$132$		0			0
$133$	−3.46410	−	4.00000i	−0.300376	−	0.346844i
$134$		0			0
$135$	1.20577	−	20.0885i	0.103776	−	1.72894i
$136$		0			0
$137$	13.8564	−	8.00000i	1.18383	−	0.683486i	0.226935	−	0.973910i	$-0.427130\pi$
$137$	13.8564	−	8.00000i	1.18383	−	0.683486i	0.956898	+	0.290424i	$0.0937963\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−24.0000			−2.02116
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−2.23205	−	0.133975i	−0.185362	−	0.0111260i
$146$		0			0
$147$	20.7846	+	3.00000i	1.71429	+	0.247436i
$148$		0			0
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$		0			0
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	0.961888	−	0.273442i	$-0.0881622\pi$
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	−0.717752	+	0.696299i	$0.754829\pi$
$152$		0			0
$153$			12.0000i			0.970143i
$154$		0			0
$155$	−10.0000	−	20.0000i	−0.803219	−	1.60644i
$156$		0			0
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	0.0242497	+	0.999706i	$0.492280\pi$
$158$		0			0
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$		0			0
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$		0			0
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	0.0343508	−	0.999410i	$-0.489064\pi$
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	−0.848339	+	0.529454i	$0.822397\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			9.00000i			0.696441i	0.937413	+	0.348220i	$0.113214\pi$
$167$			9.00000i			0.696441i	−0.937413	+	0.348220i	$0.886786\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−6.00000	−	10.3923i	−0.458831	−	0.794719i
$172$		0			0
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	0.840002	−	0.542583i	$-0.182554\pi$
$173$	10.3923	+	6.00000i	0.790112	+	0.456172i	−0.0498898	+	0.998755i	$0.515887\pi$
$174$		0			0
$175$	5.79423	−	11.8923i	0.438003	−	0.898974i
$176$		0			0
$177$	5.19615	+	3.00000i	0.390567	+	0.225494i
$178$		0			0
$179$	13.0000	+	22.5167i	0.971666	+	1.68297i	0.690526	+	0.723307i	$0.257379\pi$
$179$	13.0000	+	22.5167i	0.971666	+	1.68297i	0.281139	+	0.959667i	$0.409288\pi$
$180$		0			0
$181$	5.00000			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$182$		0			0
$183$			27.0000i			1.99590i
$184$		0			0
$185$	−14.9282	−	9.85641i	−1.09754	−	0.724657i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	22.5000	+	7.79423i	1.63663	+	0.566947i
$190$		0			0
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$		0			0
$193$	−17.3205	+	10.0000i	−1.24676	+	0.719816i	−0.970461	−	0.241257i	$-0.922440\pi$
$193$	−17.3205	+	10.0000i	−1.24676	+	0.719816i	−0.276296	+	0.961073i	$0.589107\pi$
$194$		0			0
$195$	6.00000	+	12.0000i	0.429669	+	0.859338i
$196$		0			0
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	0.571122	−	0.820865i	$-0.306508\pi$
$199$	−6.00000	−	10.3923i	−0.425329	−	0.736691i	−0.996451	+	0.0841740i	$0.973175\pi$
$200$		0			0
$201$	−10.5000	+	18.1865i	−0.740613	+	1.28278i
$202$		0			0
$203$	0.866025	−	2.50000i	0.0607831	−	0.175466i
$204$		0			0
$205$	6.69615	+	0.401924i	0.467680	+	0.0280716i
$206$		0			0
$207$	5.19615	−	3.00000i	0.361158	−	0.208514i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	18.0000			1.23917			0.619586	−	0.784929i	$-0.287301\pi$
$211$	18.0000			1.23917			0.619586	+	0.784929i	$0.287301\pi$
$212$		0			0
$213$	15.5885	−	9.00000i	1.06810	−	0.616670i
$214$		0			0
$215$	0.669873	−	11.1603i	0.0456850	−	0.761123i
$216$		0			0
$217$	25.9808	−	5.00000i	1.76369	−	0.339422i
$218$		0			0
$219$	−15.0000	+	25.9808i	−1.01361	+	1.75562i
$220$		0			0
$221$	−2.00000	−	3.46410i	−0.134535	−	0.233021i
$222$		0			0
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	18.0000	−	24.0000i	1.20000	−	1.60000i
$226$		0			0
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	−0.803523	−	0.595274i	$-0.797043\pi$
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	0.113761	+	0.993508i	$0.463710\pi$
$228$		0			0
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	0.0471787	−	0.998886i	$-0.484977\pi$
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	−0.841472	+	0.540301i	$0.818310\pi$
$234$		0			0
$235$	−14.9282	−	9.85641i	−0.973809	−	0.642961i
$236$		0			0
$237$			30.0000i			1.94871i
$238$		0			0
$239$	−10.0000			−0.646846			−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000			−0.646846			−0.323423	+	0.946254i	$0.604834\pi$
$240$		0			0
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.6962	+	10.4019i	0.747240	+	0.664555i
$246$		0			0
$247$	3.46410	+	2.00000i	0.220416	+	0.127257i
$248$		0			0
$249$	13.5000	+	23.3827i	0.855528	+	1.48182i
$250$		0			0
$251$	10.0000			0.631194			0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000			0.631194			0.315597	+	0.948893i	$0.397795\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−7.39230	+	11.1962i	−0.462924	+	0.701130i
$256$		0			0
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	16.0000	−	13.8564i	0.994192	−	0.860995i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	18.1865	−	10.5000i	1.12143	−	0.647458i	0.179664	−	0.983728i	$-0.442499\pi$
$263$	18.1865	−	10.5000i	1.12143	−	0.647458i	0.941766	+	0.336270i	$0.109166\pi$
$264$		0			0
$265$	−12.0000	+	6.00000i	−0.737154	+	0.368577i
$266$		0			0
$267$		−	21.0000i		−	1.28518i
$268$		0			0
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	0.932119	−	0.362151i	$-0.117958\pi$
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	−0.779692	+	0.626164i	$0.784624\pi$
$270$		0			0
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	−0.760405	−	0.649449i	$-0.775000\pi$
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	0.942642	+	0.333805i	$0.108333\pi$
$272$		0			0
$273$	−15.5885	+	3.00000i	−0.943456	+	0.181568i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.988654	−	0.150210i	$-0.952005\pi$
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.364241	+	0.931305i	$0.618672\pi$
$278$		0			0
$279$	60.0000			3.59211
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	6.92820	−	4.00000i	0.411839	−	0.237775i	−0.279741	−	0.960076i	$-0.590248\pi$
$283$	6.92820	−	4.00000i	0.411839	−	0.237775i	0.691580	+	0.722300i	$0.256915\pi$
$284$		0			0
$285$	0.803848	−	13.3923i	0.0476158	−	0.793292i
$286$		0			0
$287$	−2.59808	+	7.50000i	−0.153360	+	0.442711i
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	24.0000i		−	1.40209i	−0.713115	−	0.701047i	$-0.752716\pi$
$293$		−	24.0000i		−	1.40209i	0.713115	−	0.701047i	$-0.247284\pi$
$294$		0			0
$295$	2.00000	+	4.00000i	0.116445	+	0.232889i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.00000	+	1.73205i	−0.0578315	+	0.100167i
$300$		0			0
$301$	12.5000	+	4.33013i	0.720488	+	0.249584i
$302$		0			0
$303$	−38.9711	−	22.5000i	−2.23883	−	1.29259i
$304$		0			0
$305$	−11.0885	+	16.7942i	−0.634923	+	0.961635i
$306$		0			0
$307$			19.0000i			1.08439i	0.840254	+	0.542194i	$0.182406\pi$
$307$			19.0000i			1.08439i	−0.840254	+	0.542194i	$0.817594\pi$
$308$		0			0
$309$	−33.0000			−1.87730
$310$		0			0
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	0.938460	−	0.345389i	$-0.112253\pi$
$311$	3.00000	+	5.19615i	0.170114	+	0.294647i	−0.768345	+	0.640036i	$0.778920\pi$
$312$		0			0
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	0.682855	−	0.730554i	$-0.260738\pi$
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	−0.291250	+	0.956647i	$0.594071\pi$
$314$		0			0
$315$	21.5885	+	28.1769i	1.21637	+	1.58759i
$316$		0			0
$317$	−19.0526	−	11.0000i	−1.07010	−	0.617822i	−0.141890	−	0.989882i	$-0.545318\pi$
$317$	−19.0526	−	11.0000i	−1.07010	−	0.617822i	−0.928208	+	0.372061i	$0.878651\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	21.0000			1.17211
$322$		0			0
$323$			4.00000i			0.222566i
$324$		0			0
$325$	−1.19615	+	9.92820i	−0.0663506	+	0.550718i
$326$		0			0
$327$	−12.9904	−	7.50000i	−0.718370	−	0.414751i
$328$		0			0
$329$	16.0000	−	13.8564i	0.882109	−	0.763928i
$330$		0			0
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	−0.606980	−	0.794717i	$-0.707619\pi$
$331$	7.00000	−	12.1244i	0.384755	−	0.666415i	0.991735	+	0.128302i	$0.0409527\pi$
$332$		0			0
$333$	41.5692	−	24.0000i	2.27798	−	1.31519i
$334$		0			0
$335$	−14.0000	+	7.00000i	−0.764902	+	0.382451i
$336$		0			0
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$		0			0
$339$	−15.0000	−	25.9808i	−0.814688	−	1.41108i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$	6.69615	+	0.401924i	0.360509	+	0.0216388i
$346$		0			0
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.901152	−	0.433503i	$-0.857278\pi$
$347$	−18.1865	+	10.5000i	−0.976304	+	0.563670i	−0.0751519	+	0.997172i	$0.523944\pi$
$348$		0			0
$349$	9.00000			0.481759			0.240879	−	0.970555i	$-0.422564\pi$
$349$	9.00000			0.481759			0.240879	+	0.970555i	$0.422564\pi$
$350$		0			0
$351$	−18.0000			−0.960769
$352$		0			0
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	−0.355303	−	0.934751i	$-0.615622\pi$
$353$	5.19615	−	3.00000i	0.276563	−	0.159674i	0.631867	+	0.775077i	$0.282289\pi$
$354$		0			0
$355$	13.3923	+	0.803848i	0.710790	+	0.0426638i
$356$		0			0
$357$	−10.3923	−	12.0000i	−0.550019	−	0.635107i
$358$		0			0
$359$	7.00000	−	12.1244i	0.369446	−	0.639899i	−0.620033	−	0.784576i	$-0.712881\pi$
$359$	7.00000	−	12.1244i	0.369446	−	0.639899i	0.989479	+	0.144677i	$0.0462142\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$			33.0000i			1.73205i
$364$		0			0
$365$	−20.0000	+	10.0000i	−1.04685	+	0.523424i
$366$		0			0
$367$	19.9186	−	11.5000i	1.03974	−	0.600295i	0.119982	−	0.992776i	$-0.461716\pi$
$367$	19.9186	−	11.5000i	1.03974	−	0.600295i	0.919760	+	0.392481i	$0.128383\pi$
$368$		0			0
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$		0			0
$371$	−3.00000	−	15.5885i	−0.155752	−	0.809312i
$372$		0			0
$373$	6.92820	+	4.00000i	0.358729	+	0.207112i	0.668523	−	0.743691i	$-0.266927\pi$
$373$	6.92820	+	4.00000i	0.358729	+	0.207112i	−0.309794	+	0.950804i	$0.600260\pi$
$374$		0			0
$375$	31.5788	−	11.3038i	1.63072	−	0.583728i
$376$		0			0
$377$			2.00000i			0.103005i
$378$		0			0
$379$	−2.00000			−0.102733			−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000			−0.102733			−0.0513665	+	0.998680i	$0.516358\pi$
$380$		0			0
$381$	−12.0000	−	20.7846i	−0.614779	−	1.06483i
$382$		0			0
$383$	7.79423	+	4.50000i	0.398266	+	0.229939i	0.685736	−	0.727851i	$-0.259481\pi$
$383$	7.79423	+	4.50000i	0.398266	+	0.229939i	−0.287469	+	0.957790i	$0.592814\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	25.9808	+	15.0000i	1.32068	+	0.762493i
$388$		0			0
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$	−2.00000			−0.101144
$392$		0			0
$393$			60.0000i			3.02660i
$394$		0			0
$395$	−12.3205	+	18.6603i	−0.619912	+	0.938899i
$396$		0			0
$397$	27.7128	+	16.0000i	1.39087	+	0.803017i	0.993411	−	0.114605i	$-0.0365601\pi$
$397$	27.7128	+	16.0000i	1.39087	+	0.803017i	0.397455	+	0.917622i	$0.369893\pi$
$398$		0			0
$399$	15.0000	+	5.19615i	0.750939	+	0.260133i
$400$		0			0
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	−0.901046	−	0.433724i	$-0.857199\pi$
$401$	−1.50000	+	2.59808i	−0.0749064	+	0.129742i	0.826139	+	0.563466i	$0.190532\pi$
$402$		0			0
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$		0			0
$405$	9.00000	+	18.0000i	0.447214	+	0.894427i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	0.575670	−	0.817682i	$-0.304741\pi$
$409$	−8.50000	−	14.7224i	−0.420298	−	0.727977i	−0.995968	+	0.0897044i	$0.971408\pi$
$410$		0			0
$411$	−24.0000	+	41.5692i	−1.18383	+	2.05046i
$412$		0			0
$413$	−5.19615	+	1.00000i	−0.255686	+	0.0492068i
$414$		0			0
$415$	−1.20577	+	20.0885i	−0.0591890	+	0.986104i
$416$		0			0
$417$	20.7846	−	12.0000i	1.01783	−	0.587643i
$418$		0			0
$419$	−40.0000			−1.95413			−0.977064	−	0.212946i	$-0.931694\pi$
$419$	−40.0000			−1.95413			−0.977064	+	0.212946i	$0.931694\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$		0			0
$423$	41.5692	−	24.0000i	2.02116	−	1.16692i
$424$		0			0
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$		0			0
$427$	−15.5885	−	18.0000i	−0.754378	−	0.871081i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	0.937184	+	0.348836i	$0.113423\pi$
$431$	16.0000	+	27.7128i	0.770693	+	1.33488i	−0.166491	+	0.986043i	$0.553244\pi$
$432$		0			0
$433$			14.0000i			0.672797i	0.941720	+	0.336399i	$0.109209\pi$
$433$			14.0000i			0.672797i	−0.941720	+	0.336399i	$0.890791\pi$
$434$		0			0
$435$	6.00000	−	3.00000i	0.287678	−	0.143839i
$436$		0			0
$437$	1.73205	−	1.00000i	0.0828552	−	0.0478365i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$	−39.0000	+	15.5885i	−1.85714	+	0.742307i
$442$		0			0
$443$	2.59808	+	1.50000i	0.123438	+	0.0712672i	0.560448	−	0.828190i	$-0.310629\pi$
$443$	2.59808	+	1.50000i	0.123438	+	0.0712672i	−0.437009	+	0.899457i	$0.643962\pi$
$444$		0			0
$445$	8.62436	−	13.0622i	0.408834	−	0.619207i
$446$		0			0
$447$		−	45.0000i		−	2.12843i
$448$		0			0
$449$	−23.0000			−1.08544			−0.542719	−	0.839915i	$-0.682605\pi$
$449$	−23.0000			−1.08544			−0.542719	+	0.839915i	$0.682605\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−15.5885	−	9.00000i	−0.732410	−	0.422857i
$454$		0			0
$455$	−10.9282	−	4.53590i	−0.512322	−	0.212646i
$456$		0			0
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.316579	−	0.948566i	$-0.602534\pi$
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.979772	+	0.200118i	$0.935868\pi$
$458$		0			0
$459$	−9.00000	−	15.5885i	−0.420084	−	0.727607i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$			25.0000i			1.16185i	0.813958	+	0.580924i	$0.197309\pi$
$463$			25.0000i			1.16185i	−0.813958	+	0.580924i	$0.802691\pi$
$464$		0			0
$465$	55.9808	+	36.9615i	2.59605	+	1.71405i
$466$		0			0
$467$	0.866025	+	0.500000i	0.0400749	+	0.0231372i	0.519904	−	0.854225i	$-0.325968\pi$
$467$	0.866025	+	0.500000i	0.0400749	+	0.0231372i	−0.479829	+	0.877362i	$0.659301\pi$
$468$		0			0
$469$	−3.50000	−	18.1865i	−0.161615	−	0.839776i
$470$		0			0
$471$	18.0000	−	31.1769i	0.829396	−	1.43656i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	6.00000	−	8.00000i	0.275299	−	0.367065i
$476$		0			0
$477$		−	36.0000i		−	1.64833i
$478$		0			0
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$		0			0
$483$	−2.59808	+	7.50000i	−0.118217	+	0.341262i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.46410	+	2.00000i	−0.156973	+	0.0906287i	−0.576429	−	0.817147i	$-0.695554\pi$
$487$	−3.46410	+	2.00000i	−0.156973	+	0.0906287i	0.419456	+	0.907776i	$0.362221\pi$
$488$		0			0
$489$	36.0000			1.62798
$490$		0			0
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$		0			0
$493$	−1.73205	+	1.00000i	−0.0780076	+	0.0450377i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.19615	+	15.0000i	−0.233079	+	0.672842i
$498$		0			0
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	−0.987648	−	0.156687i	$-0.949919\pi$
$499$	−8.00000	+	13.8564i	−0.358129	+	0.620298i	0.629519	+	0.776985i	$0.283252\pi$
$500$		0			0
$501$	−13.5000	−	23.3827i	−0.603136	−	1.04466i
$502$		0			0
$503$		−	5.00000i		−	0.222939i	−0.993768	−	0.111469i	$-0.964444\pi$
$503$		−	5.00000i		−	0.222939i	0.993768	−	0.111469i	$-0.0355557\pi$
$504$		0			0
$505$	−15.0000	−	30.0000i	−0.667491	−	1.33498i
$506$		0			0
$507$	−23.3827	+	13.5000i	−1.03846	+	0.599556i
$508$		0			0
$509$	17.5000	−	30.3109i	0.775674	−	1.34351i	−0.158741	−	0.987320i	$-0.550744\pi$
$509$	17.5000	−	30.3109i	0.775674	−	1.34351i	0.934415	−	0.356186i	$-0.115923\pi$
$510$		0			0
$511$	−5.00000	−	25.9808i	−0.221187	−	1.14932i
$512$		0			0
$513$	15.5885	+	9.00000i	0.688247	+	0.397360i
$514$		0			0
$515$	−20.5263	−	13.5526i	−0.904496	−	0.597197i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−36.0000			−1.58022
$520$		0			0
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	0.422347	−	0.906434i	$-0.361206\pi$
$523$	−3.46410	−	2.00000i	−0.151475	−	0.0874539i	−0.573822	+	0.818980i	$0.694540\pi$
$524$		0			0
$525$	2.78461	+	39.5885i	0.121530	+	1.72778i
$526$		0			0
$527$	−17.3205	−	10.0000i	−0.754493	−	0.435607i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	−12.0000			−0.520756
$532$		0			0
$533$		−	6.00000i		−	0.259889i
$534$		0			0
$535$	13.0622	+	8.62436i	0.564727	+	0.372863i
$536$		0			0
$537$	−67.5500	−	39.0000i	−2.91500	−	1.68297i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$		0			0
$543$	−12.9904	+	7.50000i	−0.557471	+	0.321856i
$544$		0			0
$545$	−5.00000	−	10.0000i	−0.214176	−	0.428353i
$546$		0			0
$547$		−	37.0000i		−	1.58201i	−0.611812	−	0.791003i	$-0.709559\pi$
$547$		−	37.0000i		−	1.58201i	0.611812	−	0.791003i	$-0.290441\pi$
$548$		0			0
$549$	−27.0000	−	46.7654i	−1.15233	−	1.99590i
$550$		0			0
$551$	1.00000	−	1.73205i	0.0426014	−	0.0737878i
$552$		0			0
$553$	−17.3205	−	20.0000i	−0.736543	−	0.850487i
$554$		0			0
$555$	53.5692	+	3.21539i	2.27389	+	0.136486i
$556$		0			0
$557$	−3.46410	+	2.00000i	−0.146779	+	0.0847427i	−0.571591	−	0.820539i	$-0.693674\pi$
$557$	−3.46410	+	2.00000i	−0.146779	+	0.0847427i	0.424812	+	0.905282i	$0.360340\pi$
$558$		0			0
$559$	−10.0000			−0.422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.52628	−	5.50000i	0.401485	−	0.231797i	−0.285640	−	0.958337i	$-0.592206\pi$
$563$	9.52628	−	5.50000i	0.401485	−	0.231797i	0.687124	+	0.726540i	$0.258873\pi$
$564$		0			0
$565$	1.33975	−	22.3205i	0.0563635	−	0.939031i
$566$		0			0
$567$	−23.3827	+	4.50000i	−0.981981	+	0.188982i
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	−5.00000	−	8.66025i	−0.209243	−	0.362420i	0.742233	−	0.670142i	$-0.233767\pi$
$571$	−5.00000	−	8.66025i	−0.209243	−	0.362420i	−0.951476	+	0.307722i	$0.900433\pi$
$572$		0			0
$573$		−	60.0000i		−	2.50654i
$574$		0			0
$575$	4.00000	+	3.00000i	0.166812	+	0.125109i
$576$		0			0
$577$	−13.8564	+	8.00000i	−0.576850	+	0.333044i	−0.759880	−	0.650063i	$-0.774743\pi$
$577$	−13.8564	+	8.00000i	−0.576850	+	0.333044i	0.183031	+	0.983107i	$0.441409\pi$
$578$		0			0
$579$	30.0000	−	51.9615i	1.24676	−	2.15945i
$580$		0			0
$581$	−22.5000	−	7.79423i	−0.933457	−	0.323359i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−22.3923	−	14.7846i	−0.925808	−	0.611268i
$586$		0			0
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$		0			0
$589$	20.0000			0.824086
$590$		0			0
$591$	12.0000	+	20.7846i	0.493614	+	0.854965i
$592$		0			0
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.999974	−	0.00727173i	$-0.00231468\pi$
$593$	36.3731	+	21.0000i	1.49366	+	0.862367i	0.493689	+	0.869638i	$0.335648\pi$
$594$		0			0
$595$	−1.53590	−	11.7321i	−0.0629657	−	0.480967i
$596$		0			0
$597$	31.1769	+	18.0000i	1.27599	+	0.736691i
$598$		0			0
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$		−	42.0000i		−	1.71037i
$604$		0			0
$605$	−13.5526	+	20.5263i	−0.550990	+	0.834512i
$606$		0			0
$607$	4.33013	+	2.50000i	0.175754	+	0.101472i	0.585296	−	0.810819i	$-0.300978\pi$
$607$	4.33013	+	2.50000i	0.175754	+	0.101472i	−0.409542	+	0.912291i	$0.634311\pi$
$608$		0			0
$609$	1.50000	+	7.79423i	0.0607831	+	0.315838i
$610$		0			0
$611$	−8.00000	+	13.8564i	−0.323645	+	0.560570i
$612$		0			0
$613$	−15.5885	+	9.00000i	−0.629612	+	0.363507i	−0.780602	−	0.625029i	$-0.785087\pi$
$613$	−15.5885	+	9.00000i	−0.629612	+	0.363507i	0.150990	+	0.988535i	$0.451754\pi$
$614$		0			0
$615$	−18.0000	+	9.00000i	−0.725830	+	0.362915i
$616$		0			0
$617$			20.0000i			0.805170i	0.915383	+	0.402585i	$0.131888\pi$
$617$			20.0000i			0.805170i	−0.915383	+	0.402585i	$0.868112\pi$
$618$		0			0
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$		0			0
$621$	−4.50000	+	7.79423i	−0.180579	+	0.312772i
$622$		0			0
$623$	12.1244	+	14.0000i	0.485752	+	0.560898i
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.0000			−0.637962
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	−46.7654	+	27.0000i	−1.85876	+	1.07315i
$634$		0			0
$635$	1.07180	−	17.8564i	0.0425330	−	0.708610i
$636$		0			0
$637$	8.66025	−	11.0000i	0.343132	−	0.435836i
$638$		0			0
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$		0			0
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	0.971442	+	0.237276i	$0.0762547\pi$
$641$	17.5000	+	30.3109i	0.691208	+	1.19721i	−0.280234	+	0.959932i	$0.590412\pi$
$642$		0			0
$643$		−	20.0000i		−	0.788723i	−0.918955	−	0.394362i	$-0.870966\pi$
$643$		−	20.0000i		−	0.788723i	0.918955	−	0.394362i	$-0.129034\pi$
$644$		0			0
$645$	15.0000	+	30.0000i	0.590624	+	1.18125i
$646$		0			0
$647$	−18.1865	+	10.5000i	−0.714986	+	0.412798i	−0.812905	−	0.582397i	$-0.802115\pi$
$647$	−18.1865	+	10.5000i	−0.714986	+	0.412798i	0.0979182	+	0.995194i	$0.468782\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−60.0000	+	51.9615i	−2.35159	+	2.03653i
$652$		0			0
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.996587	−	0.0825519i	$-0.0263070\pi$
$653$	36.3731	+	21.0000i	1.42339	+	0.821794i	0.426801	+	0.904345i	$0.359640\pi$
$654$		0			0
$655$	−24.6410	+	37.3205i	−0.962804	+	1.45823i
$656$		0			0
$657$		−	60.0000i		−	2.34082i
$658$		0			0
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	0.921331	+	0.388778i	$0.127103\pi$
$661$	20.5000	+	35.5070i	0.797358	+	1.38106i	−0.123974	+	0.992286i	$0.539564\pi$
$662$		0			0
$663$	10.3923	+	6.00000i	0.403604	+	0.233021i
$664$		0			0
$665$	7.19615	+	9.39230i	0.279055	+	0.364218i
$666$		0			0
$667$	0.866025	+	0.500000i	0.0335326	+	0.0193601i
$668$		0			0
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	20.0000i		−	0.770943i	−0.922720	−	0.385472i	$-0.874039\pi$
$673$		−	20.0000i		−	0.770943i	0.922720	−	0.385472i	$-0.125961\pi$
$674$		0			0
$675$	−5.38269	+	44.6769i	−0.207180	+	1.71962i
$676$		0			0
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	0.532915	−	0.846169i	$-0.321097\pi$
$677$	1.73205	+	1.00000i	0.0665681	+	0.0384331i	−0.466347	+	0.884602i	$0.654430\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	18.0000	−	31.1769i	0.689761	−	1.19470i
$682$		0			0
$683$	21.6506	−	12.5000i	0.828439	−	0.478299i	−0.0248792	−	0.999690i	$-0.507920\pi$
$683$	21.6506	−	12.5000i	0.828439	−	0.478299i	0.853318	+	0.521391i	$0.174587\pi$
$684$		0			0
$685$	−32.0000	+	16.0000i	−1.22266	+	0.611329i
$686$		0			0
$687$			30.0000i			1.14457i
$688$		0			0
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17.8564	+	1.07180i	0.677332	+	0.0406556i
$696$		0			0
$697$	5.19615	−	3.00000i	0.196818	−	0.113633i
$698$		0			0
$699$	42.0000			1.58859
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$		0			0
$703$	13.8564	−	8.00000i	0.522604	−	0.301726i
$704$		0			0
$705$	53.5692	+	3.21539i	2.01753	+	0.121099i
$706$		0			0
$707$	38.9711	−	7.50000i	1.46566	−	0.282067i
$708$		0			0
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	−0.938069	−	0.346449i	$-0.887387\pi$
$709$	−4.50000	+	7.79423i	−0.169001	+	0.292718i	0.769068	+	0.639167i	$0.220721\pi$
$710$		0			0
$711$	−30.0000	−	51.9615i	−1.12509	−	1.94871i
$712$		0			0
$713$			10.0000i			0.374503i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	25.9808	−	15.0000i	0.970269	−	0.560185i
$718$		0			0
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	−0.990016	−	0.140955i	$-0.954983\pi$
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	0.617079	+	0.786901i	$0.288316\pi$
$720$		0			0
$721$	22.0000	−	19.0526i	0.819323	−	0.709554i
$722$		0			0
$723$	46.7654	+	27.0000i	1.73922	+	1.00414i
$724$		0			0
$725$	4.96410	+	0.598076i	0.184362	+	0.0222120i
$726$		0			0
$727$			29.0000i			1.07555i	0.843088	+	0.537775i	$0.180735\pi$
$727$			29.0000i			1.07555i	−0.843088	+	0.537775i	$0.819265\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−5.00000	−	8.66025i	−0.184932	−	0.320311i
$732$		0			0
$733$	−13.8564	−	8.00000i	−0.511798	−	0.295487i	0.221774	−	0.975098i	$-0.428815\pi$
$733$	−13.8564	−	8.00000i	−0.511798	−	0.295487i	−0.733572	+	0.679611i	$0.762148\pi$
$734$		0			0
$735$	−45.9904	−	9.48076i	−1.69638	−	0.349703i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	16.0000	+	27.7128i	0.588570	+	1.01943i	0.994420	+	0.105493i	$0.0336420\pi$
$739$	16.0000	+	27.7128i	0.588570	+	1.01943i	−0.405851	+	0.913939i	$0.633025\pi$
$740$		0			0
$741$	−12.0000			−0.440831
$742$		0			0
$743$		−	3.00000i		−	0.110059i	−0.998485	−	0.0550297i	$-0.982475\pi$
$743$		−	3.00000i		−	0.110059i	0.998485	−	0.0550297i	$-0.0175253\pi$
$744$		0			0
$745$	18.4808	−	27.9904i	0.677083	−	1.02549i
$746$		0			0
$747$	−46.7654	−	27.0000i	−1.71106	−	0.987878i
$748$		0			0
$749$	−14.0000	+	12.1244i	−0.511549	+	0.443014i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$		0			0
$753$	−25.9808	+	15.0000i	−0.946792	+	0.546630i
$754$		0			0
$755$	−6.00000	−	12.0000i	−0.218362	−	0.436725i
$756$		0			0
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.0000	−	43.3013i	0.906249	−	1.56967i	0.0870179	−	0.996207i	$-0.472266\pi$
$761$	25.0000	−	43.3013i	0.906249	−	1.56967i	0.819231	−	0.573463i	$-0.194400\pi$
$762$		0			0
$763$	12.9904	−	2.50000i	0.470283	−	0.0905061i
$764$		0			0
$765$	1.60770	−	26.7846i	0.0581263	−	0.968400i
$766$		0			0
$767$	3.46410	−	2.00000i	0.125081	−	0.0722158i
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	36.0000			1.29651
$772$		0			0
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$		0			0
$775$	19.6410	+	45.9808i	0.705526	+	1.65168i
$776$		0			0
$777$	−20.7846	+	60.0000i	−0.745644	+	2.15249i
$778$		0			0
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$		0			0
$782$		0			0
$783$			9.00000i			0.321634i
$784$		0			0
$785$	24.0000	−	12.0000i	0.856597	−	0.428298i
$786$		0			0
$787$	−18.1865	+	10.5000i	−0.648280	+	0.374285i	−0.787797	−	0.615935i	$-0.788778\pi$
$787$	−18.1865	+	10.5000i	−0.648280	+	0.374285i	0.139517	+	0.990220i	$0.455445\pi$
$788$		0			0
$789$	−31.5000	+	54.5596i	−1.12143	+	1.94237i
$790$		0			0
$791$	25.0000	+	8.66025i	0.888898	+	0.307923i
$792$		0			0
$793$	15.5885	+	9.00000i	0.553562	+	0.319599i
$794$		0			0
$795$	22.1769	−	33.5885i	0.786534	−	1.19126i
$796$		0			0
$797$		−	8.00000i		−	0.283375i	−0.989911	−	0.141687i	$-0.954747\pi$
$797$		−	8.00000i		−	0.283375i	0.989911	−	0.141687i	$-0.0452527\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$		0			0
$801$	21.0000	+	36.3731i	0.741999	+	1.28518i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−4.69615	+	3.59808i	−0.165518	+	0.126816i
$806$		0			0
$807$	−12.9904	−	7.50000i	−0.457283	−	0.264013i
$808$		0			0
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	0.997649	−	0.0685291i	$-0.0218306\pi$
$809$	12.5000	+	21.6506i	0.439477	+	0.761196i	−0.558173	+	0.829725i	$0.688497\pi$
$810$		0			0
$811$	−6.00000			−0.210688			−0.105344	−	0.994436i	$-0.533594\pi$
$811$	−6.00000			−0.210688			−0.105344	+	0.994436i	$0.533594\pi$
$812$		0			0
$813$			18.0000i			0.631288i
$814$		0			0
$815$	22.3923	+	14.7846i	0.784368	+	0.517882i
$816$		0			0
$817$	8.66025	+	5.00000i	0.302984	+	0.174928i
$818$		0			0
$819$	24.0000	−	20.7846i	0.838628	−	0.726273i
$820$		0			0
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$		0			0
$823$	−38.9711	+	22.5000i	−1.35845	+	0.784301i	−0.989415	−	0.145115i	$-0.953645\pi$
$823$	−38.9711	+	22.5000i	−1.35845	+	0.784301i	−0.369034	+	0.929416i	$0.620311\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			37.0000i			1.28662i	0.765607	+	0.643308i	$0.222439\pi$
$827$			37.0000i			1.28662i	−0.765607	+	0.643308i	$0.777561\pi$
$828$		0			0
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	0.994174	+	0.107788i	$0.0343769\pi$
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	−0.403739	+	0.914874i	$0.632290\pi$
$830$		0			0
$831$	39.0000	−	67.5500i	1.35290	−	2.34328i
$832$		0			0
$833$	13.8564	+	2.00000i	0.480096	+	0.0692959i
$834$		0			0
$835$	1.20577	−	20.0885i	0.0417274	−	0.695190i
$836$		0			0
$837$	−77.9423	+	45.0000i	−2.69408	+	1.55543i
$838$		0			0
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	−46.7654	+	27.0000i	−1.61068	+	0.929929i
$844$		0			0
$845$	−20.0885	−	1.20577i	−0.691064	−	0.0414798i
$846$		0			0
$847$	−19.0526	−	22.0000i	−0.654654	−	0.755929i
$848$		0			0
$849$	−12.0000	+	20.7846i	−0.411839	+	0.713326i
$850$		0			0
$851$	4.00000	+	6.92820i	0.137118	+	0.237496i
$852$		0			0
$853$			10.0000i			0.342393i	0.985237	+	0.171197i	$0.0547634\pi$
$853$			10.0000i			0.342393i	−0.985237	+	0.171197i	$0.945237\pi$
$854$		0			0
$855$	12.0000	+	24.0000i	0.410391	+	0.820783i
$856$		0			0
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	−0.557998	−	0.829843i	$-0.688430\pi$
$857$	−3.46410	+	2.00000i	−0.118331	+	0.0683187i	0.439666	+	0.898161i	$0.355097\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$		0			0
$861$	−4.50000	−	23.3827i	−0.153360	−	0.796880i
$862$		0			0
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	0.653298	−	0.757101i	$-0.273385\pi$
$863$	9.52628	+	5.50000i	0.324278	+	0.187222i	−0.329020	+	0.944323i	$0.606718\pi$
$864$		0			0
$865$	−22.3923	−	14.7846i	−0.761361	−	0.502692i
$866$		0			0
$867$		−	39.0000i		−	1.32451i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−14.5263	+	25.7679i	−0.491078	+	0.871116i
$876$		0			0
$877$	12.1244	+	7.00000i	0.409410	+	0.236373i	0.690536	−	0.723298i	$-0.257375\pi$
$877$	12.1244	+	7.00000i	0.409410	+	0.236373i	−0.281126	+	0.959671i	$0.590708\pi$
$878$		0			0
$879$	36.0000	+	62.3538i	1.21425	+	2.10314i
$880$		0			0
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$		0			0
$883$			4.00000i			0.134611i	0.997732	+	0.0673054i	$0.0214402\pi$
$883$			4.00000i			0.134611i	−0.997732	+	0.0673054i	$0.978560\pi$
$884$		0			0
$885$	−11.1962	−	7.39230i	−0.376355	−	0.248490i
$886$		0			0
$887$	7.79423	+	4.50000i	0.261705	+	0.151095i	0.625112	−	0.780535i	$-0.285053\pi$
$887$	7.79423	+	4.50000i	0.261705	+	0.151095i	−0.363407	+	0.931630i	$0.618387\pi$
$888$		0			0
$889$	20.0000	+	6.92820i	0.670778	+	0.232364i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.8564	−	8.00000i	0.463687	−	0.267710i
$894$		0			0
$895$	−26.0000	−	52.0000i	−0.869084	−	1.73817i
$896$		0			0
$897$		−	6.00000i		−	0.200334i
$898$		0			0
$899$	5.00000	+	8.66025i	0.166759	+	0.288836i
$900$		0			0
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$	−38.9711	+	7.50000i	−1.29688	+	0.249584i
$904$		0			0
$905$	−11.1603	−	0.669873i	−0.370979	−	0.0222673i
$906$		0			0
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	−0.0954492	−	0.995434i	$-0.530429\pi$
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	0.814347	+	0.580379i	$0.197095\pi$
$908$		0			0
$909$	90.0000			2.98511
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	3.61731	−	60.2654i	0.119585	−	1.99231i
$916$		0			0
$917$	−34.6410	−	40.0000i	−1.14395	−	1.32092i
$918$		0			0
$919$	−13.0000	+	22.5167i	−0.428830	+	0.742756i	−0.996770	−	0.0803145i	$-0.974408\pi$
$919$	−13.0000	+	22.5167i	−0.428830	+	0.742756i	0.567939	+	0.823071i	$0.307741\pi$
$920$		0			0
$921$	−28.5000	−	49.3634i	−0.939107	−	1.62658i
$922$		0			0
$923$		−	12.0000i		−	0.394985i
$924$		0			0
$925$	32.0000	+	24.0000i	1.05215	+	0.789115i
$926$		0			0
$927$	57.1577	−	33.0000i	1.87730	−	1.08386i
$928$		0			0
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$		0			0
$931$	−13.0000	+	5.19615i	−0.426058	+	0.170297i
$932$		0			0
$933$	−15.5885	−	9.00000i	−0.510343	−	0.294647i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	56.0000i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$937$		−	56.0000i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$938$		0			0
$939$	−24.0000			−0.783210
$940$		0			0
$941$	−7.00000	−	12.1244i	−0.228193	−	0.395243i	0.729079	−	0.684429i	$-0.239949\pi$
$941$	−7.00000	−	12.1244i	−0.228193	−	0.395243i	−0.957273	+	0.289187i	$0.906615\pi$
$942$		0			0
$943$	−2.59808	−	1.50000i	−0.0846050	−	0.0488467i
$944$		0			0
$945$	−49.1769	−	20.4115i	−1.59973	−	0.663988i
$946$		0			0
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	0.457193	−	0.889368i	$-0.348855\pi$
$947$	−2.59808	−	1.50000i	−0.0844261	−	0.0487435i	−0.541619	+	0.840624i	$0.682188\pi$
$948$		0			0
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$		0			0
$951$	66.0000			2.14020
$952$		0			0
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$		0			0
$955$	24.6410	−	37.3205i	0.797365	−	1.20766i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−8.00000	−	41.5692i	−0.258333	−	1.34234i
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$		0			0
$963$	−36.3731	+	21.0000i	−1.17211	+	0.676716i
$964$		0			0
$965$	40.0000	−	20.0000i	1.28765	−	0.643823i
$966$		0			0
$967$		−	17.0000i		−	0.546683i	−0.961917	−	0.273342i	$-0.911871\pi$
$967$		−	17.0000i		−	0.546683i	0.961917	−	0.273342i	$-0.0881289\pi$
$968$		0			0
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	−6.92820	+	20.0000i	−0.222108	+	0.641171i
$974$		0			0
$975$	−11.7846	−	27.5885i	−0.377410	−	0.883538i
$976$		0			0
$977$	31.1769	−	18.0000i	0.997438	−	0.575871i	0.0899487	−	0.995946i	$-0.471330\pi$
$977$	31.1769	−	18.0000i	0.997438	−	0.575871i	0.907489	+	0.420075i	$0.137996\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	30.0000			0.957826
$982$		0			0
$983$	21.6506	−	12.5000i	0.690548	−	0.398688i	−0.113269	−	0.993564i	$-0.536132\pi$
$983$	21.6506	−	12.5000i	0.690548	−	0.398688i	0.803817	+	0.594876i	$0.202799\pi$
$984$		0			0
$985$	−1.07180	+	17.8564i	−0.0341503	+	0.568952i
$986$		0			0
$987$	−20.7846	+	60.0000i	−0.661581	+	1.90982i
$988$		0			0
$989$	−2.50000	+	4.33013i	−0.0794954	+	0.137690i
$990$		0			0
$991$	−13.0000	−	22.5167i	−0.412959	−	0.715265i	0.582253	−	0.813008i	$-0.302171\pi$
$991$	−13.0000	−	22.5167i	−0.412959	−	0.715265i	−0.995212	+	0.0977423i	$0.968838\pi$
$992$		0			0
$993$			42.0000i			1.33283i
$994$		0			0
$995$	12.0000	+	24.0000i	0.380426	+	0.760851i
$996$		0			0
$997$	29.4449	−	17.0000i	0.932528	−	0.538395i	0.0449179	−	0.998991i	$-0.485697\pi$
$997$	29.4449	−	17.0000i	0.932528	−	0.538395i	0.887610	+	0.460595i	$0.152364\pi$
$998$		0			0
$999$	−36.0000	+	62.3538i	−1.13899	+	1.97279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bw.c.289.1		4
4.3	odd	2		70.2.i.a.9.1	✓	4
5.4	even	2	inner	560.2.bw.c.289.2		4
7.4	even	3	inner	560.2.bw.c.529.2		4
12.11	even	2		630.2.u.b.289.2		4
20.3	even	4		350.2.e.f.51.1		2
20.7	even	4		350.2.e.g.51.1		2
20.19	odd	2		70.2.i.a.9.2	yes	4
28.3	even	6		490.2.i.b.459.2		4
28.11	odd	6		70.2.i.a.39.2	yes	4
28.19	even	6		490.2.c.b.99.2		2
28.23	odd	6		490.2.c.c.99.2		2
28.27	even	2		490.2.i.b.79.1		4
35.4	even	6	inner	560.2.bw.c.529.1		4
60.59	even	2		630.2.u.b.289.1		4
84.11	even	6		630.2.u.b.109.1		4
140.19	even	6		490.2.c.b.99.1		2
140.23	even	12		2450.2.a.s.1.1		1
140.39	odd	6		70.2.i.a.39.1	yes	4
140.47	odd	12		2450.2.a.c.1.1		1
140.59	even	6		490.2.i.b.459.1		4
140.67	even	12		350.2.e.g.151.1		2
140.79	odd	6		490.2.c.c.99.1		2
140.103	odd	12		2450.2.a.bh.1.1		1
140.107	even	12		2450.2.a.r.1.1		1
140.123	even	12		350.2.e.f.151.1		2
140.139	even	2		490.2.i.b.79.2		4
420.179	even	6		630.2.u.b.109.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.i.a.9.1	✓	4	4.3	odd	2
70.2.i.a.9.2	yes	4	20.19	odd	2
70.2.i.a.39.1	yes	4	140.39	odd	6
70.2.i.a.39.2	yes	4	28.11	odd	6
350.2.e.f.51.1		2	20.3	even	4
350.2.e.f.151.1		2	140.123	even	12
350.2.e.g.51.1		2	20.7	even	4
350.2.e.g.151.1		2	140.67	even	12
490.2.c.b.99.1		2	140.19	even	6
490.2.c.b.99.2		2	28.19	even	6
490.2.c.c.99.1		2	140.79	odd	6
490.2.c.c.99.2		2	28.23	odd	6
490.2.i.b.79.1		4	28.27	even	2
490.2.i.b.79.2		4	140.139	even	2
490.2.i.b.459.1		4	140.59	even	6
490.2.i.b.459.2		4	28.3	even	6
560.2.bw.c.289.1		4	1.1	even	1	trivial
560.2.bw.c.289.2		4	5.4	even	2	inner
560.2.bw.c.529.1		4	35.4	even	6	inner
560.2.bw.c.529.2		4	7.4	even	3	inner
630.2.u.b.109.1		4	84.11	even	6
630.2.u.b.109.2		4	420.179	even	6
630.2.u.b.289.1		4	60.59	even	2
630.2.u.b.289.2		4	12.11	even	2
2450.2.a.c.1.1		1	140.47	odd	12
2450.2.a.r.1.1		1	140.107	even	12
2450.2.a.s.1.1		1	140.23	even	12
2450.2.a.bh.1.1		1	140.103	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bw (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 + 1.50000i) q^{3} +(-2.23205 - 0.133975i) q^{5} +(0.866025 - 2.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-2.59808 + 1.50000i) q^{3} +(-2.23205 - 0.133975i) q^{5} +(0.866025 - 2.50000i) q^{7} +(3.00000 - 5.19615i) q^{9} +2.00000i q^{13} +(6.00000 - 3.00000i) q^{15} +(-1.73205 + 1.00000i) q^{17} +(1.00000 - 1.73205i) q^{19} +(1.50000 + 7.79423i) q^{21} +(0.866025 + 0.500000i) q^{23} +(4.96410 + 0.598076i) q^{25} +9.00000i q^{27} +1.00000 q^{29} +(5.00000 + 8.66025i) q^{31} +(-2.26795 + 5.46410i) q^{35} +(6.92820 + 4.00000i) q^{37} +(-3.00000 - 5.19615i) q^{39} -3.00000 q^{41} +5.00000i q^{43} +(-7.39230 + 11.1962i) q^{45} +(6.92820 + 4.00000i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(3.00000 - 5.19615i) q^{51} +(5.19615 - 3.00000i) q^{53} +6.00000i q^{57} +(-1.00000 - 1.73205i) q^{59} +(4.50000 - 7.79423i) q^{61} +(-10.3923 - 12.0000i) q^{63} +(0.267949 - 4.46410i) q^{65} +(6.06218 - 3.50000i) q^{67} -3.00000 q^{69} -6.00000 q^{71} +(8.66025 - 5.00000i) q^{73} +(-13.7942 + 5.89230i) q^{75} +(5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} -9.00000i q^{83} +(4.00000 - 2.00000i) q^{85} +(-2.59808 + 1.50000i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(5.00000 + 1.73205i) q^{91} +(-25.9808 - 15.0000i) q^{93} +(-2.46410 + 3.73205i) q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} + 12 q^{9}+O(q^{10}) \) 4 * q - 2 * q^5 + 12 * q^9	\( 4 q - 2 q^{5} + 12 q^{9} + 24 q^{15} + 4 q^{19} + 6 q^{21} + 6 q^{25} + 4 q^{29} + 20 q^{31} - 16 q^{35} - 12 q^{39} - 12 q^{41} + 12 q^{45} - 22 q^{49} + 12 q^{51} - 4 q^{59} + 18 q^{61} + 8 q^{65} - 12 q^{69} - 24 q^{71} - 24 q^{75} + 20 q^{79} - 18 q^{81} + 16 q^{85} - 14 q^{89} + 20 q^{91} + 4 q^{95}+O(q^{100}) \) 4 * q - 2 * q^5 + 12 * q^9 + 24 * q^15 + 4 * q^19 + 6 * q^21 + 6 * q^25 + 4 * q^29 + 20 * q^31 - 16 * q^35 - 12 * q^39 - 12 * q^41 + 12 * q^45 - 22 * q^49 + 12 * q^51 - 4 * q^59 + 18 * q^61 + 8 * q^65 - 12 * q^69 - 24 * q^71 - 24 * q^75 + 20 * q^79 - 18 * q^81 + 16 * q^85 - 14 * q^89 + 20 * q^91 + 4 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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