LMFDB - Embedded newform 315.2.r.a.214.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 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("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.214
Dual form			315.2.r.a.184.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.866025 - 1.50000i) q^{3} +1.00000 q^{4} +(-2.23205 - 0.133975i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.866025 - 1.50000i) q^{3} +1.00000 q^{4} +(-2.23205 - 0.133975i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.133975 + 2.23205i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.866025 - 1.50000i) q^{12} +(-3.46410 + 2.00000i) q^{13} +(2.00000 + 1.73205i) q^{14} +(1.73205 + 3.46410i) q^{15} -1.00000 q^{16} +(1.73205 + 1.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-2.23205 - 0.133975i) q^{20} +(4.50000 + 0.866025i) q^{21} +(-5.19615 + 3.00000i) q^{22} +(2.59808 + 1.50000i) q^{23} +(-4.50000 + 2.59808i) q^{24} +(4.96410 + 0.598076i) q^{25} +(2.00000 + 3.46410i) q^{26} +5.19615 q^{27} +(-1.73205 + 2.00000i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.46410 - 1.73205i) q^{30} -4.00000 q^{31} -5.00000i q^{32} +(-5.19615 + 9.00000i) q^{33} +(1.00000 - 1.73205i) q^{34} +(4.13397 - 4.23205i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(6.92820 - 4.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(6.00000 + 3.46410i) q^{39} +(-0.401924 + 6.69615i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.866025 - 4.50000i) q^{42} +(-0.866025 - 0.500000i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(3.69615 - 5.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} -3.00000i q^{47} +(0.866025 + 1.50000i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(0.598076 - 4.96410i) q^{50} -3.46410i q^{51} +(-3.46410 + 2.00000i) q^{52} +(-10.3923 - 6.00000i) q^{53} -5.19615i q^{54} +(6.00000 + 12.0000i) q^{55} +(6.00000 + 5.19615i) q^{56} +(-5.19615 + 9.00000i) q^{57} +(1.73205 + 1.00000i) q^{58} -4.00000 q^{59} +(1.73205 + 3.46410i) q^{60} +7.00000 q^{61} +4.00000i q^{62} +(-2.59808 - 7.50000i) q^{63} -7.00000 q^{64} +(8.00000 - 4.00000i) q^{65} +(9.00000 + 5.19615i) q^{66} -7.00000i q^{67} +(1.73205 + 1.00000i) q^{68} -5.19615i q^{69} +(-4.23205 - 4.13397i) q^{70} +4.00000 q^{71} +(7.79423 + 4.50000i) q^{72} +(-4.00000 - 6.92820i) q^{74} +(-3.40192 - 7.96410i) q^{75} +(-3.00000 - 5.19615i) q^{76} +(15.5885 + 3.00000i) q^{77} +(3.46410 - 6.00000i) q^{78} +14.0000 q^{79} +(2.23205 + 0.133975i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.73205 + 1.00000i) q^{82} +(-3.46410 - 2.00000i) q^{83} +(4.50000 + 0.866025i) q^{84} +(-3.73205 - 2.46410i) q^{85} +(-0.500000 + 0.866025i) q^{86} +3.46410 q^{87} +(-15.5885 + 9.00000i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-5.59808 - 3.69615i) q^{90} +(2.00000 - 10.3923i) q^{91} +(2.59808 + 1.50000i) q^{92} +(3.46410 + 6.00000i) q^{93} -3.00000 q^{94} +(6.00000 + 12.0000i) q^{95} +(-7.50000 + 4.33013i) q^{96} +(1.73205 + 1.00000i) q^{97} +(-6.92820 + 1.00000i) q^{98} +18.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 - 2 * q^5 - 6 * q^6 - 6 * q^9	$ 4 q + 4 q^{4} - 2 q^{5} - 6 q^{6} - 6 q^{9} - 4 q^{10} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 12 q^{19} - 2 q^{20} + 18 q^{21} - 18 q^{24} + 6 q^{25} + 8 q^{26} - 4 q^{29} - 16 q^{31} + 4 q^{34} + 20 q^{35} - 6 q^{36} + 24 q^{39} - 12 q^{40} - 4 q^{41} - 12 q^{44} - 6 q^{45} + 6 q^{46} - 4 q^{49} - 8 q^{50} + 24 q^{55} + 24 q^{56} - 16 q^{59} + 28 q^{61} - 28 q^{64} + 32 q^{65} + 36 q^{66} - 10 q^{70} + 16 q^{71} - 16 q^{74} - 24 q^{75} - 12 q^{76} + 56 q^{79} + 2 q^{80} - 18 q^{81} + 18 q^{84} - 8 q^{85} - 2 q^{86} - 6 q^{89} - 12 q^{90} + 8 q^{91} - 12 q^{94} + 24 q^{95} - 30 q^{96} + 72 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 - 2 * q^5 - 6 * q^6 - 6 * q^9 - 4 * q^10 - 12 * q^11 + 8 * q^14 - 4 * q^16 - 12 * q^19 - 2 * q^20 + 18 * q^21 - 18 * q^24 + 6 * q^25 + 8 * q^26 - 4 * q^29 - 16 * q^31 + 4 * q^34 + 20 * q^35 - 6 * q^36 + 24 * q^39 - 12 * q^40 - 4 * q^41 - 12 * q^44 - 6 * q^45 + 6 * q^46 - 4 * q^49 - 8 * q^50 + 24 * q^55 + 24 * q^56 - 16 * q^59 + 28 * q^61 - 28 * q^64 + 32 * q^65 + 36 * q^66 - 10 * q^70 + 16 * q^71 - 16 * q^74 - 24 * q^75 - 12 * q^76 + 56 * q^79 + 2 * q^80 - 18 * q^81 + 18 * q^84 - 8 * q^85 - 2 * q^86 - 6 * q^89 - 12 * q^90 + 8 * q^91 - 12 * q^94 + 24 * q^95 - 30 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$	1.00000			0.500000
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$5$	−2.23205	−	0.133975i	−0.998203	−	0.0599153i
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$		−	3.00000i		−	1.06066i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	−0.133975	+	2.23205i	−0.0423665	+	0.705836i
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	−0.866025	−	1.50000i	−0.250000	−	0.433013i
$13$	−3.46410	+	2.00000i	−0.960769	+	0.554700i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.46410	+	2.00000i	−0.960769	+	0.554700i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$	1.73205	+	3.46410i	0.447214	+	0.894427i
$16$	−1.00000			−0.250000
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	−2.23205	−	0.133975i	−0.499102	−	0.0299576i
$21$	4.50000	+	0.866025i	0.981981	+	0.188982i
$22$	−5.19615	+	3.00000i	−1.10782	+	0.639602i
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$	−4.50000	+	2.59808i	−0.918559	+	0.530330i
$25$	4.96410	+	0.598076i	0.992820	+	0.119615i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	5.19615			1.00000
$28$	−1.73205	+	2.00000i	−0.327327	+	0.377964i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$	3.46410	−	1.73205i	0.632456	−	0.316228i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		−	5.00000i		−	0.883883i
$33$	−5.19615	+	9.00000i	−0.904534	+	1.56670i
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$	4.13397	−	4.23205i	0.698769	−	0.715347i
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	6.92820	−	4.00000i	1.13899	−	0.657596i	0.192809	−	0.981236i	$-0.438240\pi$
$37$	6.92820	−	4.00000i	1.13899	−	0.657596i	0.946180	+	0.323640i	$0.104907\pi$
$38$	−5.19615	+	3.00000i	−0.842927	+	0.486664i
$39$	6.00000	+	3.46410i	0.960769	+	0.554700i
$40$	−0.401924	+	6.69615i	−0.0635497	+	1.05875i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$	0.866025	−	4.50000i	0.133631	−	0.694365i
$43$	−0.866025	−	0.500000i	−0.132068	−	0.0762493i	0.432511	−	0.901629i	$-0.357628\pi$
$43$	−0.866025	−	0.500000i	−0.132068	−	0.0762493i	−0.564578	+	0.825380i	$0.690961\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$	3.69615	−	5.59808i	0.550990	−	0.834512i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	0.866025	+	1.50000i	0.125000	+	0.216506i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	0.598076	−	4.96410i	0.0845807	−	0.702030i
$51$		−	3.46410i		−	0.485071i
$52$	−3.46410	+	2.00000i	−0.480384	+	0.277350i
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.430570	−	0.902557i	$-0.641688\pi$
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.996922	+	0.0783936i	$0.975021\pi$
$54$		−	5.19615i		−	0.707107i
$55$	6.00000	+	12.0000i	0.809040	+	1.61808i
$56$	6.00000	+	5.19615i	0.801784	+	0.694365i
$57$	−5.19615	+	9.00000i	−0.688247	+	1.19208i
$58$	1.73205	+	1.00000i	0.227429	+	0.131306i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$	1.73205	+	3.46410i	0.223607	+	0.447214i
$61$	7.00000			0.896258			0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000			0.896258			0.448129	+	0.893969i	$0.352090\pi$
$62$			4.00000i			0.508001i
$63$	−2.59808	−	7.50000i	−0.327327	−	0.944911i
$64$	−7.00000			−0.875000
$65$	8.00000	−	4.00000i	0.992278	−	0.496139i
$66$	9.00000	+	5.19615i	1.10782	+	0.639602i
$67$		−	7.00000i		−	0.855186i	−0.903971	−	0.427593i	$-0.859362\pi$
$67$		−	7.00000i		−	0.855186i	0.903971	−	0.427593i	$-0.140638\pi$
$68$	1.73205	+	1.00000i	0.210042	+	0.121268i
$69$		−	5.19615i		−	0.625543i
$70$	−4.23205	−	4.13397i	−0.505827	−	0.494104i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$	7.79423	+	4.50000i	0.918559	+	0.530330i
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$	−4.00000	−	6.92820i	−0.464991	−	0.805387i
$75$	−3.40192	−	7.96410i	−0.392820	−	0.919615i
$76$	−3.00000	−	5.19615i	−0.344124	−	0.596040i
$77$	15.5885	+	3.00000i	1.77647	+	0.341882i
$78$	3.46410	−	6.00000i	0.392232	−	0.679366i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	2.23205	+	0.133975i	0.249551	+	0.0149788i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−1.73205	+	1.00000i	−0.191273	+	0.110432i
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	0.297686	−	0.954664i	$-0.403785\pi$
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	−0.677920	+	0.735135i	$0.737119\pi$
$84$	4.50000	+	0.866025i	0.490990	+	0.0944911i
$85$	−3.73205	−	2.46410i	−0.404798	−	0.267269i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	3.46410			0.371391
$88$	−15.5885	+	9.00000i	−1.66174	+	0.959403i
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$	−5.59808	−	3.69615i	−0.590089	−	0.389609i
$91$	2.00000	−	10.3923i	0.209657	−	1.08941i
$92$	2.59808	+	1.50000i	0.270868	+	0.156386i
$93$	3.46410	+	6.00000i	0.359211	+	0.622171i
$94$	−3.00000			−0.309426
$95$	6.00000	+	12.0000i	0.615587	+	1.23117i
$96$	−7.50000	+	4.33013i	−0.765466	+	0.441942i
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$98$	−6.92820	+	1.00000i	−0.699854	+	0.101015i
$99$	18.0000			1.80907
$100$	4.96410	+	0.598076i	0.496410	+	0.0598076i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$	−3.46410			−0.342997
$103$	−0.866025	−	0.500000i	−0.0853320	−	0.0492665i	0.456727	−	0.889607i	$-0.349022\pi$
$103$	−0.866025	−	0.500000i	−0.0853320	−	0.0492665i	−0.542059	+	0.840341i	$0.682355\pi$
$104$	6.00000	+	10.3923i	0.588348	+	1.01905i
$105$	−9.92820	−	2.53590i	−0.968893	−	0.247478i
$106$	−6.00000	+	10.3923i	−0.582772	+	1.00939i
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	−0.323122	−	0.946357i	$-0.604732\pi$
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	0.658009	+	0.753010i	$0.271399\pi$
$108$	5.19615			0.500000
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	−0.999708	−	0.0241802i	$-0.992302\pi$
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	0.520794	+	0.853682i	$0.325636\pi$
$110$	12.0000	−	6.00000i	1.14416	−	0.572078i
$111$	−12.0000	−	6.92820i	−1.13899	−	0.657596i
$112$	1.73205	−	2.00000i	0.163663	−	0.188982i
$113$	−15.5885	+	9.00000i	−1.46644	+	0.846649i	−0.999295	−	0.0375328i	$-0.988050\pi$
$113$	−15.5885	+	9.00000i	−1.46644	+	0.846649i	−0.467143	+	0.884182i	$0.654717\pi$
$114$	9.00000	+	5.19615i	0.842927	+	0.486664i
$115$	−5.59808	−	3.69615i	−0.522023	−	0.344668i
$116$	−1.00000	+	1.73205i	−0.0928477	+	0.160817i
$117$		−	12.0000i		−	1.10940i
$118$			4.00000i			0.368230i
$119$	−5.00000	+	1.73205i	−0.458349	+	0.158777i
$120$	10.3923	−	5.19615i	0.948683	−	0.474342i
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		−	7.00000i		−	0.633750i
$123$	−1.73205	+	3.00000i	−0.156174	+	0.270501i
$124$	−4.00000			−0.359211
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−7.50000	+	2.59808i	−0.668153	+	0.231455i
$127$		−	7.00000i		−	0.621150i	−0.950549	−	0.310575i	$-0.899478\pi$
$127$		−	7.00000i		−	0.621150i	0.950549	−	0.310575i	$-0.100522\pi$
$128$		−	3.00000i		−	0.265165i
$129$			1.73205i			0.152499i
$130$	−4.00000	−	8.00000i	−0.350823	−	0.701646i
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	−0.379379	−	0.925241i	$-0.623862\pi$
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	0.990972	−	0.134069i	$-0.0428042\pi$
$132$	−5.19615	+	9.00000i	−0.452267	+	0.783349i
$133$	15.5885	+	3.00000i	1.35169	+	0.260133i
$134$	−7.00000			−0.604708
$135$	−11.5981	−	0.696152i	−0.998203	−	0.0599153i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	5.19615	−	3.00000i	0.443937	−	0.256307i	−0.261329	−	0.965250i	$-0.584161\pi$
$137$	5.19615	−	3.00000i	0.443937	−	0.256307i	0.705266	+	0.708942i	$0.250827\pi$
$138$	−5.19615			−0.442326
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	0.905314	−	0.424743i	$-0.139635\pi$
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	−0.820495	+	0.571654i	$0.806302\pi$
$140$	4.13397	−	4.23205i	0.349385	−	0.357674i
$141$	−4.50000	+	2.59808i	−0.378968	+	0.218797i
$142$		−	4.00000i		−	0.335673i
$143$	20.7846	+	12.0000i	1.73810	+	1.00349i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	2.46410	−	3.73205i	0.204633	−	0.309930i
$146$		0			0
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	6.92820	−	4.00000i	0.569495	−	0.328798i
$149$	−11.5000	+	19.9186i	−0.942117	+	1.63179i	−0.180693	+	0.983540i	$0.557834\pi$
$149$	−11.5000	+	19.9186i	−0.942117	+	1.63179i	−0.761424	+	0.648254i	$0.775499\pi$
$150$	−7.96410	+	3.40192i	−0.650266	+	0.277766i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	−15.5885	+	9.00000i	−1.26439	+	0.729996i
$153$	−5.19615	+	3.00000i	−0.420084	+	0.242536i
$154$	3.00000	−	15.5885i	0.241747	−	1.25615i
$155$	8.92820	+	0.535898i	0.717131	+	0.0430444i
$156$	6.00000	+	3.46410i	0.480384	+	0.277350i
$157$		−	12.0000i		−	0.957704i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$		−	12.0000i		−	0.957704i	0.877896	−	0.478852i	$-0.158947\pi$
$158$		−	14.0000i		−	1.11378i
$159$			20.7846i			1.64833i
$160$	−0.669873	+	11.1603i	−0.0529581	+	0.882296i
$161$	−7.50000	+	2.59808i	−0.591083	+	0.204757i
$162$	−7.79423	+	4.50000i	−0.612372	+	0.353553i
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	−0.629492	−	0.777007i	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$	−1.00000	−	1.73205i	−0.0780869	−	0.135250i
$165$	12.8038	−	19.3923i	0.996778	−	1.50969i
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	2.59808	−	1.50000i	0.201045	−	0.116073i	−0.396098	−	0.918208i	$-0.629636\pi$
$167$	2.59808	−	1.50000i	0.201045	−	0.116073i	0.597143	+	0.802135i	$0.296303\pi$
$168$	2.59808	−	13.5000i	0.200446	−	1.04155i
$169$	1.50000	−	2.59808i	0.115385	−	0.199852i
$170$	−2.46410	+	3.73205i	−0.188988	+	0.286235i
$171$	18.0000			1.37649
$172$	−0.866025	−	0.500000i	−0.0660338	−	0.0381246i
$173$			18.0000i			1.36851i	0.729241	+	0.684257i	$0.239873\pi$
$173$			18.0000i			1.36851i	−0.729241	+	0.684257i	$0.760127\pi$
$174$		−	3.46410i		−	0.262613i
$175$	−9.79423	+	8.89230i	−0.740374	+	0.672195i
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$	3.46410	+	6.00000i	0.260378	+	0.450988i
$178$	−2.59808	+	1.50000i	−0.194734	+	0.112430i
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	−0.900975	−	0.433872i	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$	3.69615	−	5.59808i	0.275495	−	0.417256i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−10.3923	−	2.00000i	−0.770329	−	0.148250i
$183$	−6.06218	−	10.5000i	−0.448129	−	0.776182i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$	−16.0000	+	8.00000i	−1.17634	+	0.588172i
$186$	6.00000	−	3.46410i	0.439941	−	0.254000i
$187$		−	12.0000i		−	0.877527i
$188$		−	3.00000i		−	0.218797i
$189$	−9.00000	+	10.3923i	−0.654654	+	0.755929i
$190$	12.0000	−	6.00000i	0.870572	−	0.435286i
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$	6.06218	+	10.5000i	0.437500	+	0.757772i
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$	−12.9282	−	8.53590i	−0.925808	−	0.611268i
$196$	−1.00000	−	6.92820i	−0.0714286	−	0.494872i
$197$			14.0000i			0.997459i	0.866758	+	0.498729i	$0.166200\pi$
$197$			14.0000i			0.997459i	−0.866758	+	0.498729i	$0.833800\pi$
$198$		−	18.0000i		−	1.27920i
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$	1.79423	−	14.8923i	0.126871	−	1.05304i
$201$	−10.5000	+	6.06218i	−0.740613	+	0.427593i
$202$	2.59808	−	1.50000i	0.182800	−	0.105540i
$203$	−1.73205	−	5.00000i	−0.121566	−	0.350931i
$204$		−	3.46410i		−	0.242536i
$205$	2.00000	+	4.00000i	0.139686	+	0.279372i
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$	−7.79423	+	4.50000i	−0.541736	+	0.312772i
$208$	3.46410	−	2.00000i	0.240192	−	0.138675i
$209$	−18.0000	+	31.1769i	−1.24509	+	2.15655i
$210$	−2.53590	+	9.92820i	−0.174994	+	0.685111i
$211$	−1.00000	−	1.73205i	−0.0688428	−	0.119239i	0.829549	−	0.558433i	$-0.188597\pi$
$211$	−1.00000	−	1.73205i	−0.0688428	−	0.119239i	−0.898392	+	0.439194i	$0.855264\pi$
$212$	−10.3923	−	6.00000i	−0.713746	−	0.412082i
$213$	−3.46410	−	6.00000i	−0.237356	−	0.411113i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	1.86603	+	1.23205i	0.127262	+	0.0840252i
$216$		−	15.5885i		−	1.06066i
$217$	6.92820	−	8.00000i	0.470317	−	0.543075i
$218$	8.66025	+	5.00000i	0.586546	+	0.338643i
$219$		0			0
$220$	6.00000	+	12.0000i	0.404520	+	0.809040i
$221$	−8.00000			−0.538138
$222$	−6.92820	+	12.0000i	−0.464991	+	0.805387i
$223$	2.59808	+	1.50000i	0.173980	+	0.100447i	0.584461	−	0.811422i	$-0.301306\pi$
$223$	2.59808	+	1.50000i	0.173980	+	0.100447i	−0.410481	+	0.911869i	$0.634639\pi$
$224$	10.0000	+	8.66025i	0.668153	+	0.578638i
$225$	−9.00000	+	12.0000i	−0.600000	+	0.800000i
$226$	9.00000	+	15.5885i	0.598671	+	1.03693i
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	−0.610535	−	0.791989i	$-0.709046\pi$
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	0.380615	+	0.924734i	$0.375712\pi$
$228$	−5.19615	+	9.00000i	−0.344124	+	0.596040i
$229$	11.5000	−	19.9186i	0.759941	−	1.31626i	−0.182939	−	0.983124i	$-0.558561\pi$
$229$	11.5000	−	19.9186i	0.759941	−	1.31626i	0.942880	−	0.333133i	$-0.108106\pi$
$230$	−3.69615	+	5.59808i	−0.243717	+	0.369126i
$231$	−9.00000	−	25.9808i	−0.592157	−	1.70941i
$232$	5.19615	+	3.00000i	0.341144	+	0.196960i
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	−0.0471787	−	0.998886i	$-0.515023\pi$
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	0.841472	+	0.540301i	$0.181690\pi$
$234$	−12.0000			−0.784465
$235$	−0.401924	+	6.69615i	−0.0262186	+	0.436809i
$236$	−4.00000			−0.260378
$237$	−12.1244	−	21.0000i	−0.787562	−	1.36410i
$238$	1.73205	+	5.00000i	0.112272	+	0.324102i
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	−0.934109	−	0.356988i	$-0.883804\pi$
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	0.157893	−	0.987456i	$-0.449530\pi$
$240$	−1.73205	−	3.46410i	−0.111803	−	0.223607i
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	0.952141	+	0.305661i	$0.0988773\pi$
$241$	11.5000	+	19.9186i	0.740780	+	1.28307i	−0.211360	+	0.977408i	$0.567789\pi$
$242$	21.6506	+	12.5000i	1.39176	+	0.803530i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$	7.00000			0.448129
$245$	1.30385	+	15.5981i	0.0832998	+	0.996525i
$246$	3.00000	+	1.73205i	0.191273	+	0.110432i
$247$	20.7846	+	12.0000i	1.32249	+	0.763542i
$248$			12.0000i			0.762001i
$249$			6.92820i			0.439057i
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−2.59808	−	7.50000i	−0.163663	−	0.472456i
$253$		−	18.0000i		−	1.13165i
$254$	−7.00000			−0.439219
$255$	−0.464102	+	7.73205i	−0.0290632	+	0.484200i
$256$	−17.0000			−1.06250
$257$	6.92820	+	4.00000i	0.432169	+	0.249513i	0.700270	−	0.713878i	$-0.253063\pi$
$257$	6.92820	+	4.00000i	0.432169	+	0.249513i	−0.268101	+	0.963391i	$0.586396\pi$
$258$	1.73205			0.107833
$259$	−4.00000	+	20.7846i	−0.248548	+	1.29149i
$260$	8.00000	−	4.00000i	0.496139	−	0.248069i
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$	−12.1244	−	7.00000i	−0.749045	−	0.432461i
$263$	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	$0.109166\pi$
$264$	27.0000	+	15.5885i	1.66174	+	0.959403i
$265$	22.3923	+	14.7846i	1.37555	+	0.908211i
$266$	3.00000	−	15.5885i	0.183942	−	0.955790i
$267$	−2.59808	+	4.50000i	−0.159000	+	0.275396i
$268$		−	7.00000i		−	0.427593i
$269$	6.50000	−	11.2583i	0.396312	−	0.686433i	−0.596956	−	0.802274i	$-0.703623\pi$
$269$	6.50000	−	11.2583i	0.396312	−	0.686433i	0.993268	+	0.115842i	$0.0369565\pi$
$270$	−0.696152	+	11.5981i	−0.0423665	+	0.705836i
$271$	−14.0000	−	24.2487i	−0.850439	−	1.47300i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−14.0000	−	24.2487i	−0.850439	−	1.47300i	0.0303728	−	0.999539i	$-0.490331\pi$
$272$	−1.73205	−	1.00000i	−0.105021	−	0.0606339i
$273$	−17.3205	+	6.00000i	−1.04828	+	0.363137i
$274$	−3.00000	−	5.19615i	−0.181237	−	0.313911i
$275$	−11.7846	−	27.5885i	−0.710639	−	1.66365i
$276$		−	5.19615i		−	0.312772i
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.947604	−	0.319447i	$-0.896503\pi$
$277$	−19.0526	+	11.0000i	−1.14476	+	0.660926i	−0.197153	+	0.980373i	$0.563170\pi$
$278$	1.73205	−	1.00000i	0.103882	−	0.0599760i
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$	−12.6962	−	12.4019i	−0.758740	−	0.741157i
$281$	11.5000	−	19.9186i	0.686032	−	1.18824i	−0.287079	−	0.957907i	$-0.592684\pi$
$281$	11.5000	−	19.9186i	0.686032	−	1.18824i	0.973111	−	0.230336i	$-0.0739826\pi$
$282$	2.59808	+	4.50000i	0.154713	+	0.267971i
$283$		−	11.0000i		−	0.653882i	−0.945045	−	0.326941i	$-0.893982\pi$
$283$		−	11.0000i		−	0.653882i	0.945045	−	0.326941i	$-0.106018\pi$
$284$	4.00000			0.237356
$285$	12.8038	−	19.3923i	0.758434	−	1.14870i
$286$	12.0000	−	20.7846i	0.709575	−	1.22902i
$287$	5.19615	+	1.00000i	0.306719	+	0.0590281i
$288$	12.9904	+	7.50000i	0.765466	+	0.441942i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	−3.73205	−	2.46410i	−0.219154	−	0.144697i
$291$		−	3.46410i		−	0.203069i
$292$		0			0
$293$	−10.3923	+	6.00000i	−0.607125	+	0.350524i	−0.771839	−	0.635818i	$-0.780663\pi$
$293$	−10.3923	+	6.00000i	−0.607125	+	0.350524i	0.164714	+	0.986341i	$0.447330\pi$
$294$	7.50000	+	9.52628i	0.437409	+	0.555584i
$295$	8.92820	+	0.535898i	0.519820	+	0.0312012i
$296$	−12.0000	−	20.7846i	−0.697486	−	1.20808i
$297$	−15.5885	−	27.0000i	−0.904534	−	1.56670i
$298$	19.9186	+	11.5000i	1.15385	+	0.666177i
$299$	−12.0000			−0.693978
$300$	−3.40192	−	7.96410i	−0.196410	−	0.459808i
$301$	2.50000	−	0.866025i	0.144098	−	0.0499169i
$302$	13.8564	−	8.00000i	0.797347	−	0.460348i
$303$	2.59808	−	4.50000i	0.149256	−	0.258518i
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$	−15.6244	−	0.937822i	−0.894648	−	0.0536995i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$			28.0000i			1.59804i	0.601302	+	0.799022i	$0.294649\pi$
$307$			28.0000i			1.59804i	−0.601302	+	0.799022i	$0.705351\pi$
$308$	15.5885	+	3.00000i	0.888235	+	0.170941i
$309$			1.73205i			0.0985329i
$310$	0.535898	−	8.92820i	0.0304370	−	0.507088i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	10.3923	−	18.0000i	0.588348	−	1.01905i
$313$		−	18.0000i		−	1.01742i	−0.860938	−	0.508710i	$-0.830123\pi$
$313$		−	18.0000i		−	1.01742i	0.860938	−	0.508710i	$-0.169877\pi$
$314$	−12.0000			−0.677199
$315$	4.79423	+	17.0885i	0.270124	+	0.962825i
$316$	14.0000			0.787562
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$	20.7846			1.16554
$319$	12.0000			0.671871
$320$	15.6244	+	0.937822i	0.873428	+	0.0524259i
$321$	−6.00000	−	3.46410i	−0.334887	−	0.193347i
$322$	2.59808	+	7.50000i	0.144785	+	0.417959i
$323$		−	12.0000i		−	0.667698i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−18.3923	+	7.85641i	−1.02022	+	0.435795i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	17.3205			0.957826
$328$	−5.19615	+	3.00000i	−0.286910	+	0.165647i
$329$	6.00000	+	5.19615i	0.330791	+	0.286473i
$330$	−19.3923	−	12.8038i	−1.06751	−	0.704829i
$331$	−6.00000			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$332$	−3.46410	−	2.00000i	−0.190117	−	0.109764i
$333$			24.0000i			1.31519i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$	−0.937822	+	15.6244i	−0.0512387	+	0.853650i
$336$	−4.50000	−	0.866025i	−0.245495	−	0.0472456i
$337$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$337$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$338$	−2.59808	−	1.50000i	−0.141317	−	0.0815892i
$339$	27.0000	+	15.5885i	1.46644	+	0.846649i
$340$	−3.73205	−	2.46410i	−0.202399	−	0.133635i
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$		−	18.0000i		−	0.973329i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−1.50000	+	2.59808i	−0.0808746	+	0.140079i
$345$	−0.696152	+	11.5981i	−0.0374796	+	0.624419i
$346$	18.0000			0.967686
$347$			3.00000i			0.161048i	0.996753	+	0.0805242i	$0.0256594\pi$
$347$			3.00000i			0.161048i	−0.996753	+	0.0805242i	$0.974341\pi$
$348$	3.46410			0.185695
$349$	15.5000	−	26.8468i	0.829696	−	1.43708i	−0.0685808	−	0.997646i	$-0.521847\pi$
$349$	15.5000	−	26.8468i	0.829696	−	1.43708i	0.898277	−	0.439430i	$-0.144820\pi$
$350$	8.89230	+	9.79423i	0.475314	+	0.523524i
$351$	−18.0000	+	10.3923i	−0.960769	+	0.554700i
$352$	−25.9808	+	15.0000i	−1.38478	+	0.799503i
$353$	8.66025	−	5.00000i	0.460939	−	0.266123i	−0.251500	−	0.967857i	$-0.580924\pi$
$353$	8.66025	−	5.00000i	0.460939	−	0.266123i	0.712439	+	0.701734i	$0.247591\pi$
$354$	6.00000	−	3.46410i	0.318896	−	0.184115i
$355$	−8.92820	−	0.535898i	−0.473860	−	0.0284425i
$356$	−1.50000	−	2.59808i	−0.0794998	−	0.137698i
$357$	6.92820	+	6.00000i	0.366679	+	0.317554i
$358$	1.73205	+	1.00000i	0.0915417	+	0.0528516i
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	0.838429	−	0.545010i	$-0.183474\pi$
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	−0.891207	+	0.453596i	$0.850141\pi$
$360$	−16.7942	−	11.0885i	−0.885134	−	0.584413i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		−	6.00000i		−	0.315353i
$363$	43.3013			2.27273
$364$	2.00000	−	10.3923i	0.104828	−	0.544705i
$365$		0			0
$366$	−10.5000	+	6.06218i	−0.548844	+	0.316875i
$367$	2.59808	−	1.50000i	0.135618	−	0.0782994i	−0.430656	−	0.902516i	$-0.641718\pi$
$367$	2.59808	−	1.50000i	0.135618	−	0.0782994i	0.566274	+	0.824217i	$0.308384\pi$
$368$	−2.59808	−	1.50000i	−0.135434	−	0.0781929i
$369$	6.00000			0.312348
$370$	8.00000	+	16.0000i	0.415900	+	0.831800i
$371$	30.0000	−	10.3923i	1.55752	−	0.539542i
$372$	3.46410	+	6.00000i	0.179605	+	0.311086i
$373$	−20.7846	−	12.0000i	−1.07619	−	0.621336i	−0.146321	−	0.989237i	$-0.546743\pi$
$373$	−20.7846	−	12.0000i	−1.07619	−	0.621336i	−0.929865	+	0.367901i	$0.880077\pi$
$374$	−12.0000			−0.620505
$375$	6.52628	+	18.2321i	0.337016	+	0.941499i
$376$	−9.00000			−0.464140
$377$		−	8.00000i		−	0.412021i
$378$	10.3923	+	9.00000i	0.534522	+	0.462910i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	6.00000	+	12.0000i	0.307794	+	0.615587i
$381$	−10.5000	+	6.06218i	−0.537931	+	0.310575i
$382$			6.00000i			0.306987i
$383$	0.866025	+	0.500000i	0.0442518	+	0.0255488i	0.521963	−	0.852968i	$-0.325200\pi$
$383$	0.866025	+	0.500000i	0.0442518	+	0.0255488i	−0.477711	+	0.878517i	$0.658533\pi$
$384$	−4.50000	+	2.59808i	−0.229640	+	0.132583i
$385$	−34.3923	−	8.78461i	−1.75279	−	0.447705i
$386$	−10.0000			−0.508987
$387$	2.59808	−	1.50000i	0.132068	−	0.0762493i
$388$	1.73205	+	1.00000i	0.0879316	+	0.0507673i
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$	−8.53590	+	12.9282i	−0.432232	+	0.654645i
$391$	3.00000	+	5.19615i	0.151717	+	0.262781i
$392$	−20.7846	+	3.00000i	−1.04978	+	0.151523i
$393$	−24.2487			−1.22319
$394$	14.0000			0.705310
$395$	−31.2487	−	1.87564i	−1.57229	−	0.0943739i
$396$	18.0000			0.904534
$397$	8.66025	−	5.00000i	0.434646	−	0.250943i	−0.266678	−	0.963786i	$-0.585926\pi$
$397$	8.66025	−	5.00000i	0.434646	−	0.250943i	0.701324	+	0.712843i	$0.252593\pi$
$398$	−12.1244	−	7.00000i	−0.607739	−	0.350878i
$399$	−9.00000	−	25.9808i	−0.450564	−	1.30066i
$400$	−4.96410	−	0.598076i	−0.248205	−	0.0299038i
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$	6.06218	+	10.5000i	0.302354	+	0.523692i
$403$	13.8564	−	8.00000i	0.690237	−	0.398508i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	9.00000	+	18.0000i	0.447214	+	0.894427i
$406$	−5.00000	+	1.73205i	−0.248146	+	0.0859602i
$407$	−41.5692	−	24.0000i	−2.06051	−	1.18964i
$408$	−10.3923			−0.514496
$409$	−35.0000			−1.73064			−0.865319	−	0.501221i	$-0.832884\pi$
$409$	−35.0000			−1.73064			−0.865319	+	0.501221i	$0.832884\pi$
$410$	4.00000	−	2.00000i	0.197546	−	0.0987730i
$411$	−9.00000	−	5.19615i	−0.443937	−	0.256307i
$412$	−0.866025	−	0.500000i	−0.0426660	−	0.0246332i
$413$	6.92820	−	8.00000i	0.340915	−	0.393654i
$414$	4.50000	+	7.79423i	0.221163	+	0.383065i
$415$	7.46410	+	4.92820i	0.366398	+	0.241916i
$416$	10.0000	+	17.3205i	0.490290	+	0.849208i
$417$	1.73205	−	3.00000i	0.0848189	−	0.146911i
$418$	31.1769	+	18.0000i	1.52491	+	0.880409i
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	0.997665	−	0.0683046i	$-0.0217590\pi$
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	−0.557986	+	0.829851i	$0.688426\pi$
$420$	−9.92820	−	2.53590i	−0.484447	−	0.123739i
$421$	−1.50000	+	2.59808i	−0.0731055	+	0.126622i	−0.900261	−	0.435351i	$-0.856624\pi$
$421$	−1.50000	+	2.59808i	−0.0731055	+	0.126622i	0.827155	+	0.561973i	$0.189958\pi$
$422$	−1.73205	+	1.00000i	−0.0843149	+	0.0486792i
$423$	7.79423	+	4.50000i	0.378968	+	0.218797i
$424$	−18.0000	+	31.1769i	−0.874157	+	1.51408i
$425$	8.00000	+	6.00000i	0.388057	+	0.291043i
$426$	−6.00000	+	3.46410i	−0.290701	+	0.167836i
$427$	−12.1244	+	14.0000i	−0.586739	+	0.677507i
$428$	3.46410	−	2.00000i	0.167444	−	0.0966736i
$429$		−	41.5692i		−	2.00698i
$430$	1.23205	−	1.86603i	0.0594148	−	0.0899877i
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	−0.840936	−	0.541135i	$-0.817995\pi$
$431$	1.00000	−	1.73205i	0.0481683	−	0.0834300i	0.889104	+	0.457705i	$0.151328\pi$
$432$	−5.19615			−0.250000
$433$		−	32.0000i		−	1.53782i	−0.639356	−	0.768911i	$-0.720799\pi$
$433$		−	32.0000i		−	1.53782i	0.639356	−	0.768911i	$-0.279201\pi$
$434$	−8.00000	−	6.92820i	−0.384012	−	0.332564i
$435$	−7.73205	−	0.464102i	−0.370723	−	0.0222520i
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$		−	18.0000i		−	0.861057i
$438$		0			0
$439$	−30.0000			−1.43182			−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000			−1.43182			−0.715911	+	0.698192i	$0.753988\pi$
$440$	36.0000	−	18.0000i	1.71623	−	0.858116i
$441$	19.5000	+	7.79423i	0.928571	+	0.371154i
$442$			8.00000i			0.380521i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$	−12.0000	−	6.92820i	−0.569495	−	0.328798i
$445$	3.00000	+	6.00000i	0.142214	+	0.284427i
$446$	1.50000	−	2.59808i	0.0710271	−	0.123022i
$447$	39.8372			1.88423
$448$	12.1244	−	14.0000i	0.572822	−	0.661438i
$449$	5.00000			0.235965			0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000			0.235965			0.117982	+	0.993016i	$0.462357\pi$
$450$	12.0000	+	9.00000i	0.565685	+	0.424264i
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$	−15.5885	+	9.00000i	−0.733219	+	0.423324i
$453$	13.8564	−	24.0000i	0.651031	−	1.12762i
$454$	2.00000	+	3.46410i	0.0938647	+	0.162578i
$455$	−5.85641	+	22.9282i	−0.274553	+	1.07489i
$456$	27.0000	+	15.5885i	1.26439	+	0.729996i
$457$		−	20.0000i		−	0.935561i	−0.883845	−	0.467780i	$-0.845054\pi$
$457$		−	20.0000i		−	0.935561i	0.883845	−	0.467780i	$-0.154946\pi$
$458$	−19.9186	−	11.5000i	−0.930734	−	0.537360i
$459$	9.00000	+	5.19615i	0.420084	+	0.242536i
$460$	−5.59808	−	3.69615i	−0.261012	−	0.172334i
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	−0.999920	−	0.0126168i	$-0.995984\pi$
$461$	−10.5000	+	18.1865i	−0.489034	+	0.847031i	0.510887	+	0.859648i	$0.329317\pi$
$462$	−25.9808	+	9.00000i	−1.20873	+	0.418718i
$463$	−23.3827	+	13.5000i	−1.08669	+	0.627398i	−0.932692	−	0.360674i	$-0.882547\pi$
$463$	−23.3827	+	13.5000i	−1.08669	+	0.627398i	−0.153993	+	0.988072i	$0.549213\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$	−6.92820	−	13.8564i	−0.321288	−	0.642575i
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	2.59808	−	1.50000i	0.120225	−	0.0694117i	−0.438682	−	0.898642i	$-0.644554\pi$
$467$	2.59808	−	1.50000i	0.120225	−	0.0694117i	0.558906	+	0.829231i	$0.311221\pi$
$468$		−	12.0000i		−	0.554700i
$469$	14.0000	+	12.1244i	0.646460	+	0.559851i
$470$	6.69615	+	0.401924i	0.308870	+	0.0185394i
$471$	−18.0000	+	10.3923i	−0.829396	+	0.478852i
$472$			12.0000i			0.552345i
$473$			6.00000i			0.275880i
$474$	−21.0000	+	12.1244i	−0.964562	+	0.556890i
$475$	−11.7846	−	27.5885i	−0.540715	−	1.26585i
$476$	−5.00000	+	1.73205i	−0.229175	+	0.0793884i
$477$	31.1769	−	18.0000i	1.42749	−	0.824163i
$478$	−20.7846	+	12.0000i	−0.950666	+	0.548867i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	17.3205	−	8.66025i	0.790569	−	0.395285i
$481$	−16.0000	+	27.7128i	−0.729537	+	1.26360i
$482$	19.9186	−	11.5000i	0.907267	−	0.523811i
$483$	10.3923	+	9.00000i	0.472866	+	0.409514i
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−3.73205	−	2.46410i	−0.169464	−	0.111889i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	0.245705	−	0.969345i	$-0.420981\pi$
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	−0.716625	+	0.697459i	$0.754314\pi$
$488$		−	21.0000i		−	0.950625i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$	15.5981	−	1.30385i	0.704649	−	0.0589018i
$491$	16.0000	+	27.7128i	0.722070	+	1.25066i	0.960169	+	0.279421i	$0.0901424\pi$
$491$	16.0000	+	27.7128i	0.722070	+	1.25066i	−0.238099	+	0.971241i	$0.576524\pi$
$492$	−1.73205	+	3.00000i	−0.0780869	+	0.135250i
$493$	−3.46410	+	2.00000i	−0.156015	+	0.0900755i
$494$	12.0000	−	20.7846i	0.539906	−	0.935144i
$495$	−40.1769	−	2.41154i	−1.80582	−	0.108391i
$496$	4.00000			0.179605
$497$	−6.92820	+	8.00000i	−0.310772	+	0.358849i
$498$	6.92820			0.310460
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$	−4.50000	−	2.59808i	−0.201045	−	0.116073i
$502$		−	12.0000i		−	0.535586i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$	−22.5000	+	7.79423i	−1.00223	+	0.347183i
$505$	−3.00000	−	6.00000i	−0.133498	−	0.266996i
$506$	−18.0000			−0.800198
$507$	−5.19615			−0.230769
$508$		−	7.00000i		−	0.310575i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	7.73205	+	0.464102i	0.342381	+	0.0205508i
$511$		0			0
$512$			11.0000i			0.486136i
$513$	−15.5885	−	27.0000i	−0.688247	−	1.19208i
$514$	4.00000	−	6.92820i	0.176432	−	0.305590i
$515$	1.86603	+	1.23205i	0.0822269	+	0.0542906i
$516$			1.73205i			0.0762493i
$517$	−15.5885	+	9.00000i	−0.685580	+	0.395820i
$518$	20.7846	+	4.00000i	0.913223	+	0.175750i
$519$	27.0000	−	15.5885i	1.18517	−	0.684257i
$520$	−12.0000	−	24.0000i	−0.526235	−	1.05247i
$521$	18.5000	−	32.0429i	0.810500	−	1.40383i	−0.102015	−	0.994783i	$-0.532529\pi$
$521$	18.5000	−	32.0429i	0.810500	−	1.40383i	0.912515	−	0.409044i	$-0.134138\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$	−35.5070	+	20.5000i	−1.55261	+	0.896402i	−0.554687	+	0.832059i	$0.687162\pi$
$523$	−35.5070	+	20.5000i	−1.55261	+	0.896402i	−0.997928	+	0.0643431i	$0.979505\pi$
$524$	7.00000	−	12.1244i	0.305796	−	0.529655i
$525$	21.8205	+	6.99038i	0.952325	+	0.305085i
$526$	−10.5000	−	18.1865i	−0.457822	−	0.792971i
$527$	−6.92820	−	4.00000i	−0.301797	−	0.174243i
$528$	5.19615	−	9.00000i	0.226134	−	0.391675i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$	14.7846	−	22.3923i	0.642202	−	0.972660i
$531$	6.00000	−	10.3923i	0.260378	−	0.450988i
$532$	15.5885	+	3.00000i	0.675845	+	0.130066i
$533$	6.92820	+	4.00000i	0.300094	+	0.173259i
$534$	4.50000	+	2.59808i	0.194734	+	0.112430i
$535$	−8.00000	+	4.00000i	−0.345870	+	0.172935i
$536$	−21.0000			−0.907062
$537$	3.46410			0.149487
$538$	−11.2583	−	6.50000i	−0.485381	−	0.280235i
$539$	−33.0000	+	25.9808i	−1.42141	+	1.11907i
$540$	−11.5981	−	0.696152i	−0.499102	−	0.0299576i
$541$	−10.5000	−	18.1865i	−0.451430	−	0.781900i	0.547045	−	0.837103i	$-0.315753\pi$
$541$	−10.5000	−	18.1865i	−0.451430	−	0.781900i	−0.998475	+	0.0552031i	$0.982419\pi$
$542$	−24.2487	+	14.0000i	−1.04157	+	0.601351i
$543$	−5.19615	−	9.00000i	−0.222988	−	0.386227i
$544$	5.00000	−	8.66025i	0.214373	−	0.371305i
$545$	12.3205	−	18.6603i	0.527753	−	0.799317i
$546$	6.00000	+	17.3205i	0.256776	+	0.741249i
$547$	24.2487	+	14.0000i	1.03680	+	0.598597i	0.918925	−	0.394432i	$-0.129059\pi$
$547$	24.2487	+	14.0000i	1.03680	+	0.598597i	0.117875	+	0.993028i	$0.462392\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$	−10.5000	+	18.1865i	−0.448129	+	0.776182i
$550$	−27.5885	+	11.7846i	−1.17638	+	0.502497i
$551$	12.0000			0.511217
$552$	−15.5885			−0.663489
$553$	−24.2487	+	28.0000i	−1.03116	+	1.19068i
$554$	11.0000	+	19.0526i	0.467345	+	0.809466i
$555$	25.8564	+	17.0718i	1.09754	+	0.724657i
$556$	1.00000	+	1.73205i	0.0424094	+	0.0734553i
$557$	−1.73205	−	1.00000i	−0.0733893	−	0.0423714i	0.462856	−	0.886433i	$-0.346825\pi$
$557$	−1.73205	−	1.00000i	−0.0733893	−	0.0423714i	−0.536246	+	0.844062i	$0.680158\pi$
$558$	−10.3923	−	6.00000i	−0.439941	−	0.254000i
$559$	4.00000			0.169182
$560$	−4.13397	+	4.23205i	−0.174692	+	0.178837i
$561$	−18.0000	+	10.3923i	−0.759961	+	0.438763i
$562$	−19.9186	−	11.5000i	−0.840215	−	0.485098i
$563$		−	27.0000i		−	1.13791i	−0.822367	−	0.568957i	$-0.807347\pi$
$563$		−	27.0000i		−	1.13791i	0.822367	−	0.568957i	$-0.192653\pi$
$564$	−4.50000	+	2.59808i	−0.189484	+	0.109399i
$565$	36.0000	−	18.0000i	1.51453	−	0.757266i
$566$	−11.0000			−0.462364
$567$	23.3827	+	4.50000i	0.981981	+	0.188982i
$568$		−	12.0000i		−	0.503509i
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$	−19.3923	−	12.8038i	−0.812254	−	0.536294i
$571$	6.00000			0.251092			0.125546	−	0.992088i	$-0.459932\pi$
$571$	6.00000			0.251092			0.125546	+	0.992088i	$0.459932\pi$
$572$	20.7846	+	12.0000i	0.869048	+	0.501745i
$573$	5.19615	+	9.00000i	0.217072	+	0.375980i
$574$	1.00000	−	5.19615i	0.0417392	−	0.216883i
$575$	12.0000	+	9.00000i	0.500435	+	0.375326i
$576$	10.5000	−	18.1865i	0.437500	−	0.757772i
$577$	34.6410	+	20.0000i	1.44212	+	0.832611i	0.997991	−	0.0633500i	$-0.0201784\pi$
$577$	34.6410	+	20.0000i	1.44212	+	0.832611i	0.444133	+	0.895961i	$0.353512\pi$
$578$	−11.2583	+	6.50000i	−0.468285	+	0.270364i
$579$	−15.0000	+	8.66025i	−0.623379	+	0.359908i
$580$	2.46410	−	3.73205i	0.102316	−	0.154965i
$581$	10.0000	−	3.46410i	0.414870	−	0.143715i
$582$	−3.46410			−0.143592
$583$			72.0000i			2.98194i
$584$		0			0
$585$	−1.60770	+	26.7846i	−0.0664700	+	1.10741i
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$	−38.9711	−	22.5000i	−1.60851	−	0.928674i	−0.989704	−	0.143132i	$-0.954283\pi$
$587$	−38.9711	−	22.5000i	−1.60851	−	0.928674i	−0.618808	−	0.785543i	$-0.712384\pi$
$588$	−9.52628	+	7.50000i	−0.392857	+	0.309295i
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$	0.535898	−	8.92820i	0.0220626	−	0.367568i
$591$	21.0000	−	12.1244i	0.863825	−	0.498729i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$	−17.3205	+	10.0000i	−0.711268	+	0.410651i	−0.811530	−	0.584310i	$-0.801365\pi$
$593$	−17.3205	+	10.0000i	−0.711268	+	0.410651i	0.100262	+	0.994961i	$0.468032\pi$
$594$	−27.0000	+	15.5885i	−1.10782	+	0.639602i
$595$	11.3923	−	3.19615i	0.467039	−	0.131029i
$596$	−11.5000	+	19.9186i	−0.471058	+	0.815897i
$597$	−24.2487			−0.992434
$598$			12.0000i			0.490716i
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$	−23.8923	+	10.2058i	−0.975399	+	0.416649i
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$	−0.866025	−	2.50000i	−0.0352966	−	0.101892i
$603$	18.1865	+	10.5000i	0.740613	+	0.427593i
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	30.8013	−	46.6506i	1.25225	−	1.89662i
$606$	−4.50000	−	2.59808i	−0.182800	−	0.105540i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−25.9808	+	15.0000i	−1.05366	+	0.608330i
$609$	−6.00000	+	6.92820i	−0.243132	+	0.280745i
$610$	−0.937822	+	15.6244i	−0.0379713	+	0.632612i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	−5.19615	+	3.00000i	−0.210042	+	0.121268i
$613$	29.4449	+	17.0000i	1.18927	+	0.686624i	0.958140	−	0.286300i	$-0.0924254\pi$
$613$	29.4449	+	17.0000i	1.18927	+	0.686624i	0.231127	+	0.972924i	$0.425759\pi$
$614$	28.0000			1.12999
$615$	4.26795	−	6.46410i	0.172100	−	0.260658i
$616$	9.00000	−	46.7654i	0.362620	−	1.88423i
$617$	24.2487	−	14.0000i	0.976216	−	0.563619i	0.0750907	−	0.997177i	$-0.476075\pi$
$617$	24.2487	−	14.0000i	0.976216	−	0.563619i	0.901126	+	0.433558i	$0.142742\pi$
$618$	1.73205			0.0696733
$619$	−19.0000	−	32.9090i	−0.763674	−	1.32272i	−0.940945	−	0.338561i	$-0.890060\pi$
$619$	−19.0000	−	32.9090i	−0.763674	−	1.32272i	0.177270	−	0.984162i	$-0.443273\pi$
$620$	8.92820	+	0.535898i	0.358565	+	0.0215222i
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		−	12.0000i		−	0.481156i
$623$	7.79423	+	1.50000i	0.312269	+	0.0600962i
$624$	−6.00000	−	3.46410i	−0.240192	−	0.138675i
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	−18.0000			−0.719425
$627$	62.3538			2.49017
$628$		−	12.0000i		−	0.478852i
$629$	16.0000			0.637962
$630$	17.0885	−	4.79423i	0.680820	−	0.191007i
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$		−	42.0000i		−	1.67067i
$633$	−1.73205	+	3.00000i	−0.0688428	+	0.119239i
$634$	18.0000			0.714871
$635$	−0.937822	+	15.6244i	−0.0372163	+	0.620034i
$636$			20.7846i			0.824163i
$637$	17.3205	+	22.0000i	0.686264	+	0.871672i
$638$		−	12.0000i		−	0.475085i
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$	−0.401924	+	6.69615i	−0.0158874	+	0.264689i
$641$	−18.5000	−	32.0429i	−0.730706	−	1.26562i	−0.956582	−	0.291464i	$-0.905858\pi$
$641$	−18.5000	−	32.0429i	−0.730706	−	1.26562i	0.225876	−	0.974156i	$-0.427476\pi$
$642$	−3.46410	+	6.00000i	−0.136717	+	0.236801i
$643$	40.7032	−	23.5000i	1.60518	−	0.926750i	0.614749	−	0.788723i	$-0.289257\pi$
$643$	40.7032	−	23.5000i	1.60518	−	0.926750i	0.990429	−	0.138027i	$-0.0440759\pi$
$644$	−7.50000	+	2.59808i	−0.295541	+	0.102379i
$645$	0.232051	−	3.86603i	0.00913699	−	0.152225i
$646$	−12.0000			−0.472134
$647$	6.92820	+	4.00000i	0.272376	+	0.157256i	0.629967	−	0.776622i	$-0.283068\pi$
$647$	6.92820	+	4.00000i	0.272376	+	0.157256i	−0.357591	+	0.933878i	$0.616402\pi$
$648$	−23.3827	+	13.5000i	−0.918559	+	0.530330i
$649$	12.0000	+	20.7846i	0.471041	+	0.815867i
$650$	7.85641	+	18.3923i	0.308154	+	0.721406i
$651$	−18.0000	−	3.46410i	−0.705476	−	0.135769i
$652$	−3.46410	+	2.00000i	−0.135665	+	0.0783260i
$653$	32.9090	+	19.0000i	1.28783	+	0.743527i	0.978266	−	0.207352i	$-0.0664846\pi$
$653$	32.9090	+	19.0000i	1.28783	+	0.743527i	0.309561	+	0.950880i	$0.399818\pi$
$654$		−	17.3205i		−	0.677285i
$655$	−17.2487	+	26.1244i	−0.673963	+	1.02076i
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$		0			0
$658$	5.19615	−	6.00000i	0.202567	−	0.233904i
$659$	15.0000	−	25.9808i	0.584317	−	1.01207i	−0.410643	−	0.911796i	$-0.634696\pi$
$659$	15.0000	−	25.9808i	0.584317	−	1.01207i	0.994960	−	0.100271i	$-0.0319709\pi$
$660$	12.8038	−	19.3923i	0.498389	−	0.754844i
$661$	39.0000			1.51692			0.758462	−	0.651717i	$-0.225951\pi$
$661$	39.0000			1.51692			0.758462	+	0.651717i	$0.225951\pi$
$662$			6.00000i			0.233197i
$663$	6.92820	+	12.0000i	0.269069	+	0.466041i
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$	−34.3923	−	8.78461i	−1.33368	−	0.340653i
$666$	24.0000			0.929981
$667$	−5.19615	+	3.00000i	−0.201196	+	0.116160i
$668$	2.59808	−	1.50000i	0.100523	−	0.0580367i
$669$		−	5.19615i		−	0.200895i
$670$	15.6244	+	0.937822i	0.603622	+	0.0362312i
$671$	−21.0000	−	36.3731i	−0.810696	−	1.40417i
$672$	4.33013	−	22.5000i	0.167038	−	0.867956i
$673$	−20.7846	−	12.0000i	−0.801188	−	0.462566i	0.0426985	−	0.999088i	$-0.486405\pi$
$673$	−20.7846	−	12.0000i	−0.801188	−	0.462566i	−0.843886	+	0.536522i	$0.819738\pi$
$674$		0			0
$675$	25.7942	+	3.10770i	0.992820	+	0.119615i
$676$	1.50000	−	2.59808i	0.0576923	−	0.0999260i
$677$			8.00000i			0.307465i	0.988113	+	0.153732i	$0.0491294\pi$
$677$			8.00000i			0.307465i	−0.988113	+	0.153732i	$0.950871\pi$
$678$	15.5885	−	27.0000i	0.598671	−	1.03693i
$679$	−5.00000	+	1.73205i	−0.191882	+	0.0664700i
$680$	−7.39230	+	11.1962i	−0.283482	+	0.429353i
$681$	6.00000	+	3.46410i	0.229920	+	0.132745i
$682$	20.7846	−	12.0000i	0.795884	−	0.459504i
$683$	6.06218	+	3.50000i	0.231963	+	0.133924i	0.611477	−	0.791262i	$-0.290576\pi$
$683$	6.06218	+	3.50000i	0.231963	+	0.133924i	−0.379514	+	0.925186i	$0.623909\pi$
$684$	18.0000			0.688247
$685$	−12.0000	+	6.00000i	−0.458496	+	0.229248i
$686$	10.0000	−	15.5885i	0.381802	−	0.595170i
$687$	−39.8372			−1.51988
$688$	0.866025	+	0.500000i	0.0330169	+	0.0190623i
$689$	48.0000			1.82865
$690$	11.5981	+	0.696152i	0.441531	+	0.0265021i
$691$	10.0000			0.380418			0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000			0.380418			0.190209	+	0.981744i	$0.439083\pi$
$692$			18.0000i			0.684257i
$693$	−31.1769	+	36.0000i	−1.18431	+	1.36753i
$694$	3.00000			0.113878
$695$	−2.00000	−	4.00000i	−0.0758643	−	0.151729i
$696$		−	10.3923i		−	0.393919i
$697$		−	4.00000i		−	0.151511i
$698$	−26.8468	−	15.5000i	−1.01617	−	0.586684i
$699$	−21.0000	−	12.1244i	−0.794293	−	0.458585i
$700$	−9.79423	+	8.89230i	−0.370187	+	0.336098i
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$	10.3923	+	18.0000i	0.392232	+	0.679366i
$703$	−41.5692	−	24.0000i	−1.56781	−	0.905177i
$704$	21.0000	+	36.3731i	0.791467	+	1.37086i
$705$	10.3923	−	5.19615i	0.391397	−	0.195698i
$706$	−5.00000	−	8.66025i	−0.188177	−	0.325933i
$707$	−7.79423	−	1.50000i	−0.293132	−	0.0564133i
$708$	3.46410	+	6.00000i	0.130189	+	0.225494i
$709$	13.0000			0.488225			0.244113	−	0.969747i	$-0.421503\pi$
$709$	13.0000			0.488225			0.244113	+	0.969747i	$0.421503\pi$
$710$	−0.535898	+	8.92820i	−0.0201119	+	0.335069i
$711$	−21.0000	+	36.3731i	−0.787562	+	1.36410i
$712$	−7.79423	+	4.50000i	−0.292101	+	0.168645i
$713$	−10.3923	−	6.00000i	−0.389195	−	0.224702i
$714$	6.00000	−	6.92820i	0.224544	−	0.259281i
$715$	−44.7846	−	29.5692i	−1.67485	−	1.10583i
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	−20.7846	+	36.0000i	−0.776215	+	1.34444i
$718$	−1.73205	+	1.00000i	−0.0646396	+	0.0373197i
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	0.916529	−	0.399969i	$-0.130979\pi$
$719$	3.00000	+	5.19615i	0.111881	+	0.193784i	−0.804648	+	0.593753i	$0.797646\pi$
$720$	−3.69615	+	5.59808i	−0.137747	+	0.208628i
$721$	2.50000	−	0.866025i	0.0931049	−	0.0322525i
$722$	14.7224	+	8.50000i	0.547912	+	0.316337i
$723$	19.9186	−	34.5000i	0.740780	−	1.28307i
$724$	6.00000			0.222988
$725$	−6.00000	+	8.00000i	−0.222834	+	0.297113i
$726$		−	43.3013i		−	1.60706i
$727$	11.2583	+	6.50000i	0.417548	+	0.241072i	0.694028	−	0.719948i	$-0.255834\pi$
$727$	11.2583	+	6.50000i	0.417548	+	0.241072i	−0.276479	+	0.961020i	$0.589168\pi$
$728$	−31.1769	−	6.00000i	−1.15549	−	0.222375i
$729$	27.0000			1.00000
$730$		0			0
$731$	−1.00000	−	1.73205i	−0.0369863	−	0.0640622i
$732$	−6.06218	−	10.5000i	−0.224065	−	0.388091i
$733$	34.6410	+	20.0000i	1.27950	+	0.738717i	0.976756	−	0.214356i	$-0.0687654\pi$
$733$	34.6410	+	20.0000i	1.27950	+	0.738717i	0.302740	+	0.953073i	$0.402099\pi$
$734$	−1.50000	−	2.59808i	−0.0553660	−	0.0958967i
$735$	22.2679	−	15.4641i	0.821366	−	0.570402i
$736$	7.50000	−	12.9904i	0.276454	−	0.478832i
$737$	−36.3731	+	21.0000i	−1.33982	+	0.773545i
$738$		−	6.00000i		−	0.220863i
$739$	17.0000	−	29.4449i	0.625355	−	1.08315i	−0.363117	−	0.931744i	$-0.618287\pi$
$739$	17.0000	−	29.4449i	0.625355	−	1.08315i	0.988472	−	0.151403i	$-0.0483792\pi$
$740$	−16.0000	+	8.00000i	−0.588172	+	0.294086i
$741$		−	41.5692i		−	1.52708i
$742$	−10.3923	−	30.0000i	−0.381514	−	1.10133i
$743$	6.92820	−	4.00000i	0.254171	−	0.146746i	−0.367502	−	0.930023i	$-0.619787\pi$
$743$	6.92820	−	4.00000i	0.254171	−	0.146746i	0.621673	+	0.783277i	$0.286453\pi$
$744$	18.0000	−	10.3923i	0.659912	−	0.381000i
$745$	28.3372	−	42.9186i	1.03819	−	1.57242i
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	10.3923	−	6.00000i	0.380235	−	0.219529i
$748$		−	12.0000i		−	0.438763i
$749$	−2.00000	+	10.3923i	−0.0730784	+	0.379727i
$750$	18.2321	−	6.52628i	0.665740	−	0.238306i
$751$	9.00000	−	15.5885i	0.328415	−	0.568831i	−0.653783	−	0.756682i	$-0.726819\pi$
$751$	9.00000	−	15.5885i	0.328415	−	0.568831i	0.982197	+	0.187851i	$0.0601523\pi$
$752$			3.00000i			0.109399i
$753$	−10.3923	−	18.0000i	−0.378717	−	0.655956i
$754$	−8.00000			−0.291343
$755$	−16.0000	−	32.0000i	−0.582300	−	1.16460i
$756$	−9.00000	+	10.3923i	−0.327327	+	0.377964i
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$			20.0000i			0.726433i
$759$	−27.0000	+	15.5885i	−0.980038	+	0.565825i
$760$	36.0000	−	18.0000i	1.30586	−	0.652929i
$761$	−17.5000	+	30.3109i	−0.634375	+	1.09877i	0.352273	+	0.935897i	$0.385409\pi$
$761$	−17.5000	+	30.3109i	−0.634375	+	1.09877i	−0.986647	+	0.162872i	$0.947924\pi$
$762$	6.06218	+	10.5000i	0.219610	+	0.380375i
$763$	−8.66025	−	25.0000i	−0.313522	−	0.905061i
$764$	−6.00000			−0.217072
$765$	12.0000	−	6.00000i	0.433861	−	0.216930i
$766$	0.500000	−	0.866025i	0.0180657	−	0.0312908i
$767$	13.8564	−	8.00000i	0.500326	−	0.288863i
$768$	14.7224	+	25.5000i	0.531250	+	0.920152i
$769$	16.5000	+	28.5788i	0.595005	+	1.03058i	0.993546	+	0.113429i	$0.0361834\pi$
$769$	16.5000	+	28.5788i	0.595005	+	1.03058i	−0.398541	+	0.917151i	$0.630483\pi$
$770$	−8.78461	+	34.3923i	−0.316575	+	1.23941i
$771$		−	13.8564i		−	0.499026i
$772$		−	10.0000i		−	0.359908i
$773$	5.19615	+	3.00000i	0.186893	+	0.107903i	0.590527	−	0.807018i	$-0.298920\pi$
$773$	5.19615	+	3.00000i	0.186893	+	0.107903i	−0.403634	+	0.914920i	$0.632253\pi$
$774$	−1.50000	−	2.59808i	−0.0539164	−	0.0933859i
$775$	−19.8564	−	2.39230i	−0.713263	−	0.0859341i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	34.6410	−	12.0000i	1.24274	−	0.430498i
$778$	−16.4545	+	9.50000i	−0.589922	+	0.340592i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	−12.9282	−	8.53590i	−0.462904	−	0.305634i
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$	5.19615	−	3.00000i	0.185814	−	0.107280i
$783$	−5.19615	+	9.00000i	−0.185695	+	0.321634i
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−1.60770	+	26.7846i	−0.0573811	+	0.955984i
$786$			24.2487i			0.864923i
$787$			23.0000i			0.819861i	0.912117	+	0.409931i	$0.134447\pi$
$787$			23.0000i			0.819861i	−0.912117	+	0.409931i	$0.865553\pi$
$788$			14.0000i			0.498729i
$789$	−31.5000	−	18.1865i	−1.12143	−	0.647458i
$790$	−1.87564	+	31.2487i	−0.0667324	+	1.11178i
$791$	9.00000	−	46.7654i	0.320003	−	1.66279i
$792$		−	54.0000i		−	1.91881i
$793$	−24.2487	+	14.0000i	−0.861097	+	0.497155i
$794$	−5.00000	−	8.66025i	−0.177443	−	0.307341i
$795$	2.78461	−	46.3923i	0.0987599	−	1.64537i
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	12.1244	−	7.00000i	0.429467	−	0.247953i	−0.269653	−	0.962958i	$-0.586909\pi$
$797$	12.1244	−	7.00000i	0.429467	−	0.247953i	0.699119	+	0.715005i	$0.253576\pi$
$798$	−25.9808	+	9.00000i	−0.919709	+	0.318597i
$799$	3.00000	−	5.19615i	0.106132	−	0.183827i
$800$	2.99038	−	24.8205i	0.105726	−	0.877537i
$801$	9.00000			0.317999
$802$	23.3827	+	13.5000i	0.825671	+	0.476702i
$803$		0			0
$804$	−10.5000	+	6.06218i	−0.370306	+	0.213797i
$805$	17.0885	−	4.79423i	0.602289	−	0.168974i
$806$	−8.00000	−	13.8564i	−0.281788	−	0.488071i
$807$	−22.5167			−0.792624
$808$	7.79423	−	4.50000i	0.274200	−	0.158309i
$809$	−1.50000	+	2.59808i	−0.0527372	+	0.0913435i	−0.891189	−	0.453632i	$-0.850128\pi$
$809$	−1.50000	+	2.59808i	−0.0527372	+	0.0913435i	0.838452	+	0.544976i	$0.183461\pi$
$810$	18.0000	−	9.00000i	0.632456	−	0.316228i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$	−1.73205	−	5.00000i	−0.0607831	−	0.175466i
$813$	−24.2487	+	42.0000i	−0.850439	+	1.47300i
$814$	−24.0000	+	41.5692i	−0.841200	+	1.45700i
$815$	8.00000	−	4.00000i	0.280228	−	0.140114i
$816$			3.46410i			0.121268i
$817$			6.00000i			0.209913i
$818$			35.0000i			1.22375i
$819$	24.0000	+	20.7846i	0.838628	+	0.726273i
$820$	2.00000	+	4.00000i	0.0698430	+	0.139686i
$821$	31.0000			1.08191			0.540954	−	0.841052i	$-0.318063\pi$
$821$	31.0000			1.08191			0.540954	+	0.841052i	$0.318063\pi$
$822$	−5.19615	+	9.00000i	−0.181237	+	0.313911i
$823$		−	44.0000i		−	1.53374i	−0.641800	−	0.766872i	$-0.721812\pi$
$823$		−	44.0000i		−	1.53374i	0.641800	−	0.766872i	$-0.278188\pi$
$824$	−1.50000	+	2.59808i	−0.0522550	+	0.0905083i
$825$	−31.1769	+	41.5692i	−1.08544	+	1.44725i
$826$	−8.00000	−	6.92820i	−0.278356	−	0.241063i
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	−7.79423	+	4.50000i	−0.270868	+	0.156386i
$829$	−25.5000	+	44.1673i	−0.885652	+	1.53399i	−0.0406866	+	0.999172i	$0.512955\pi$
$829$	−25.5000	+	44.1673i	−0.885652	+	1.53399i	−0.844965	+	0.534822i	$0.820379\pi$
$830$	4.92820	−	7.46410i	0.171060	−	0.259083i
$831$	33.0000	+	19.0526i	1.14476	+	0.660926i
$832$	24.2487	−	14.0000i	0.840673	−	0.485363i
$833$	5.19615	−	13.0000i	0.180036	−	0.450423i
$834$	−3.00000	−	1.73205i	−0.103882	−	0.0599760i
$835$	−6.00000	+	3.00000i	−0.207639	+	0.103819i
$836$	−18.0000	+	31.1769i	−0.622543	+	1.07828i
$837$	−20.7846			−0.718421
$838$	15.5885	−	9.00000i	0.538494	−	0.310900i
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$	−7.60770	+	29.7846i	−0.262490	+	1.02767i
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	2.59808	+	1.50000i	0.0895356	+	0.0516934i
$843$	−39.8372			−1.37206
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$	−3.69615	+	5.59808i	−0.127152	+	0.192580i
$846$	4.50000	−	7.79423i	0.154713	−	0.267971i
$847$	−21.6506	−	62.5000i	−0.743925	−	2.14753i
$848$	10.3923	+	6.00000i	0.356873	+	0.206041i
$849$	−16.5000	+	9.52628i	−0.566279	+	0.326941i
$850$	6.00000	−	8.00000i	0.205798	−	0.274398i
$851$	24.0000			0.822709
$852$	−3.46410	−	6.00000i	−0.118678	−	0.205557i
$853$	−15.5885	−	9.00000i	−0.533739	−	0.308154i	0.208799	−	0.977959i	$-0.433045\pi$
$853$	−15.5885	−	9.00000i	−0.533739	−	0.308154i	−0.742538	+	0.669804i	$0.766378\pi$
$854$	14.0000	+	12.1244i	0.479070	+	0.414887i
$855$	−40.1769	−	2.41154i	−1.37402	−	0.0824730i
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	15.5885	−	9.00000i	0.532492	−	0.307434i	−0.209539	−	0.977800i	$-0.567196\pi$
$857$	15.5885	−	9.00000i	0.532492	−	0.307434i	0.742030	+	0.670366i	$0.233863\pi$
$858$	−41.5692			−1.41915
$859$	−19.0000	+	32.9090i	−0.648272	+	1.12284i	0.335264	+	0.942124i	$0.391175\pi$
$859$	−19.0000	+	32.9090i	−0.648272	+	1.12284i	−0.983535	+	0.180715i	$0.942159\pi$
$860$	1.86603	+	1.23205i	0.0636309	+	0.0420126i
$861$	−3.00000	−	8.66025i	−0.102240	−	0.295141i
$862$	−1.73205	−	1.00000i	−0.0589939	−	0.0340601i
$863$	12.9904	−	7.50000i	0.442198	−	0.255303i	−0.262332	−	0.964978i	$-0.584491\pi$
$863$	12.9904	−	7.50000i	0.442198	−	0.255303i	0.704529	+	0.709675i	$0.251158\pi$
$864$		−	25.9808i		−	0.883883i
$865$	2.41154	−	40.1769i	0.0819949	−	1.36606i
$866$	−32.0000			−1.08740
$867$	−11.2583	+	19.5000i	−0.382353	+	0.662255i
$868$	6.92820	−	8.00000i	0.235159	−	0.271538i
$869$	−42.0000	−	72.7461i	−1.42475	−	2.46774i
$870$	−0.464102	+	7.73205i	−0.0157345	+	0.262141i
$871$	14.0000	+	24.2487i	0.474372	+	0.821636i
$872$	25.9808	+	15.0000i	0.879820	+	0.507964i
$873$	−5.19615	+	3.00000i	−0.175863	+	0.101535i
$874$	−18.0000			−0.608859
$875$	23.0526	−	18.5359i	0.779319	−	0.626628i
$876$		0			0
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	0.639040	−	0.769174i	$-0.279332\pi$
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	−0.346604	+	0.938012i	$0.612665\pi$
$878$			30.0000i			1.01245i
$879$	18.0000	+	10.3923i	0.607125	+	0.350524i
$880$	−6.00000	−	12.0000i	−0.202260	−	0.404520i
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	7.79423	−	19.5000i	0.262445	−	0.656599i
$883$			3.00000i			0.100958i	0.998725	+	0.0504790i	$0.0160748\pi$
$883$			3.00000i			0.100958i	−0.998725	+	0.0504790i	$0.983925\pi$
$884$	−8.00000			−0.269069
$885$	−6.92820	−	13.8564i	−0.232889	−	0.465778i
$886$	4.00000			0.134383
$887$	−19.9186	−	11.5000i	−0.668801	−	0.386132i	0.126821	−	0.991926i	$-0.459522\pi$
$887$	−19.9186	−	11.5000i	−0.668801	−	0.386132i	−0.795622	+	0.605793i	$0.792856\pi$
$888$	−20.7846	+	36.0000i	−0.697486	+	1.20808i
$889$	14.0000	+	12.1244i	0.469545	+	0.406638i
$890$	6.00000	−	3.00000i	0.201120	−	0.100560i
$891$	−27.0000	+	46.7654i	−0.904534	+	1.56670i
$892$	2.59808	+	1.50000i	0.0869900	+	0.0502237i
$893$	−15.5885	+	9.00000i	−0.521648	+	0.301174i
$894$		−	39.8372i		−	1.33235i
$895$	2.46410	−	3.73205i	0.0823658	−	0.124749i
$896$	6.00000	+	5.19615i	0.200446	+	0.173591i
$897$	10.3923	+	18.0000i	0.346989	+	0.601003i
$898$		−	5.00000i		−	0.166852i
$899$	4.00000	−	6.92820i	0.133407	−	0.231069i
$900$	−9.00000	+	12.0000i	−0.300000	+	0.400000i
$901$	−12.0000	−	20.7846i	−0.399778	−	0.692436i
$902$	10.3923	+	6.00000i	0.346026	+	0.199778i
$903$	−3.46410	−	3.00000i	−0.115278	−	0.0998337i
$904$	27.0000	+	46.7654i	0.898007	+	1.55539i
$905$	−13.3923	−	0.803848i	−0.445175	−	0.0267208i
$906$	−24.0000	−	13.8564i	−0.797347	−	0.460348i
$907$	−17.3205	+	10.0000i	−0.575118	+	0.332045i	−0.759191	−	0.650868i	$-0.774405\pi$
$907$	−17.3205	+	10.0000i	−0.575118	+	0.332045i	0.184073	+	0.982913i	$0.441072\pi$
$908$	−3.46410	+	2.00000i	−0.114960	+	0.0663723i
$909$	−9.00000			−0.298511
$910$	22.9282	+	5.85641i	0.760063	+	0.194138i
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	0.127585	+	0.991828i	$0.459277\pi$
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	−0.922740	+	0.385422i	$0.874056\pi$
$912$	5.19615	−	9.00000i	0.172062	−	0.298020i
$913$			24.0000i			0.794284i
$914$	−20.0000			−0.661541
$915$	12.1244	+	24.2487i	0.400819	+	0.801638i
$916$	11.5000	−	19.9186i	0.379971	−	0.658129i
$917$	12.1244	+	35.0000i	0.400381	+	1.15580i
$918$	5.19615	−	9.00000i	0.171499	−	0.297044i
$919$	11.0000	+	19.0526i	0.362857	+	0.628486i	0.988430	−	0.151680i	$-0.0484682\pi$
$919$	11.0000	+	19.0526i	0.362857	+	0.628486i	−0.625573	+	0.780165i	$0.715135\pi$
$920$	−11.0885	+	16.7942i	−0.365576	+	0.553689i
$921$	42.0000	−	24.2487i	1.38395	−	0.799022i
$922$	18.1865	+	10.5000i	0.598942	+	0.345799i
$923$	−13.8564	+	8.00000i	−0.456089	+	0.263323i
$924$	−9.00000	−	25.9808i	−0.296078	−	0.854704i
$925$	36.7846	−	15.7128i	1.20947	−	0.516634i
$926$	13.5000	+	23.3827i	0.443638	+	0.768403i
$927$	2.59808	−	1.50000i	0.0853320	−	0.0492665i
$928$	8.66025	+	5.00000i	0.284287	+	0.164133i
$929$	−7.00000			−0.229663			−0.114831	−	0.993385i	$-0.536633\pi$
$929$	−7.00000			−0.229663			−0.114831	+	0.993385i	$0.536633\pi$
$930$	−13.8564	+	6.92820i	−0.454369	+	0.227185i
$931$	−33.0000	+	25.9808i	−1.08153	+	0.851485i
$932$	12.1244	−	7.00000i	0.397146	−	0.229293i
$933$	−10.3923	−	18.0000i	−0.340229	−	0.589294i
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$	−1.60770	+	26.7846i	−0.0525773	+	0.875950i
$936$	−36.0000			−1.17670
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$	12.1244	−	14.0000i	0.395874	−	0.457116i
$939$	−27.0000	+	15.5885i	−0.881112	+	0.508710i
$940$	−0.401924	+	6.69615i	−0.0131093	+	0.218404i
$941$	45.0000			1.46696			0.733479	−	0.679712i	$-0.237895\pi$
$941$	45.0000			1.46696			0.733479	+	0.679712i	$0.237895\pi$
$942$	10.3923	+	18.0000i	0.338600	+	0.586472i
$943$		−	6.00000i		−	0.195387i
$944$	4.00000			0.130189
$945$	21.4808	−	21.9904i	0.698769	−	0.715347i
$946$	6.00000			0.195077
$947$		−	3.00000i		−	0.0974869i	−0.998811	−	0.0487435i	$-0.984478\pi$
$947$		−	3.00000i		−	0.0974869i	0.998811	−	0.0487435i	$-0.0155217\pi$
$948$	−12.1244	−	21.0000i	−0.393781	−	0.682048i
$949$		0			0
$950$	−27.5885	+	11.7846i	−0.895088	+	0.382343i
$951$	27.0000	−	15.5885i	0.875535	−	0.505490i
$952$	5.19615	+	15.0000i	0.168408	+	0.486153i
$953$			36.0000i			1.16615i	0.812417	+	0.583077i	$0.198151\pi$
$953$			36.0000i			1.16615i	−0.812417	+	0.583077i	$0.801849\pi$
$954$	−18.0000	−	31.1769i	−0.582772	−	1.00939i
$955$	13.3923	+	0.803848i	0.433365	+	0.0260119i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$	−10.3923	−	18.0000i	−0.335936	−	0.581857i
$958$		0			0
$959$	−3.00000	+	15.5885i	−0.0968751	+	0.503378i
$960$	−12.1244	−	24.2487i	−0.391312	−	0.782624i
$961$	−15.0000			−0.483871
$962$	27.7128	+	16.0000i	0.893497	+	0.515861i
$963$			12.0000i			0.386695i
$964$	11.5000	+	19.9186i	0.370390	+	0.641534i
$965$	−1.33975	+	22.3205i	−0.0431279	+	0.718523i
$966$	9.00000	−	10.3923i	0.289570	−	0.334367i
$967$	32.0429	−	18.5000i	1.03043	−	0.594920i	0.113323	−	0.993558i	$-0.463850\pi$
$967$	32.0429	−	18.5000i	1.03043	−	0.594920i	0.917108	+	0.398638i	$0.130517\pi$
$968$	64.9519	+	37.5000i	2.08763	+	1.20530i
$969$	−18.0000	+	10.3923i	−0.578243	+	0.333849i
$970$	−2.46410	+	3.73205i	−0.0791175	+	0.119829i
$971$	−14.0000	−	24.2487i	−0.449281	−	0.778178i	0.549058	−	0.835784i	$-0.314987\pi$
$971$	−14.0000	−	24.2487i	−0.449281	−	0.778178i	−0.998339	+	0.0576061i	$0.981653\pi$
$972$	−7.79423	+	13.5000i	−0.250000	+	0.433013i
$973$	−5.19615	−	1.00000i	−0.166581	−	0.0320585i
$974$	−6.00000	+	10.3923i	−0.192252	+	0.332991i
$975$	27.7128	+	20.7846i	0.887520	+	0.665640i
$976$	−7.00000			−0.224065
$977$		−	12.0000i		−	0.383914i	−0.981403	−	0.191957i	$-0.938517\pi$
$977$		−	12.0000i		−	0.383914i	0.981403	−	0.191957i	$-0.0614834\pi$
$978$	3.46410	−	6.00000i	0.110770	−	0.191859i
$979$	−9.00000	+	15.5885i	−0.287641	+	0.498209i
$980$	1.30385	+	15.5981i	0.0416499	+	0.498262i
$981$	−15.0000	−	25.9808i	−0.478913	−	0.829502i
$982$	27.7128	−	16.0000i	0.884351	−	0.510581i
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	−0.793391	−	0.608712i	$-0.791686\pi$
$983$	−20.7846	+	12.0000i	−0.662926	+	0.382741i	0.130465	+	0.991453i	$0.458353\pi$
$984$	9.00000	+	5.19615i	0.286910	+	0.165647i
$985$	1.87564	−	31.2487i	0.0597630	−	0.995667i
$986$	2.00000	+	3.46410i	0.0636930	+	0.110319i
$987$	2.59808	−	13.5000i	0.0826977	−	0.429710i
$988$	20.7846	+	12.0000i	0.661247	+	0.381771i
$989$	−1.50000	−	2.59808i	−0.0476972	−	0.0826140i
$990$	−2.41154	+	40.1769i	−0.0766439	+	1.27691i
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	0.351126	+	0.936328i	$0.385799\pi$
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	−0.986447	+	0.164080i	$0.947534\pi$
$992$			20.0000i			0.635001i
$993$	5.19615	+	9.00000i	0.164895	+	0.285606i
$994$	8.00000	+	6.92820i	0.253745	+	0.219749i
$995$	−17.2487	+	26.1244i	−0.546821	+	0.828198i
$996$			6.92820i			0.219529i
$997$	−8.66025	+	5.00000i	−0.274273	+	0.158352i	−0.630828	−	0.775923i	$-0.717285\pi$
$997$	−8.66025	+	5.00000i	−0.274273	+	0.158352i	0.356555	+	0.934274i	$0.383951\pi$
$998$	−24.2487	−	14.0000i	−0.767580	−	0.443162i
$999$	36.0000	−	20.7846i	1.13899	−	0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.a.214.1	yes	4
3.2	odd	2		945.2.r.a.424.2		4
5.4	even	2	inner	315.2.r.a.214.2	yes	4
7.2	even	3		315.2.bo.a.79.1	yes	4
9.4	even	3		315.2.bo.a.4.2	yes	4
9.5	odd	6		945.2.bo.a.739.1		4
15.14	odd	2		945.2.r.a.424.1		4
21.2	odd	6		945.2.bo.a.289.2		4
35.9	even	6		315.2.bo.a.79.2	yes	4
45.4	even	6		315.2.bo.a.4.1	yes	4
45.14	odd	6		945.2.bo.a.739.2		4
63.23	odd	6		945.2.r.a.604.2		4
63.58	even	3	inner	315.2.r.a.184.1	✓	4
105.44	odd	6		945.2.bo.a.289.1		4
315.149	odd	6		945.2.r.a.604.1		4
315.184	even	6	inner	315.2.r.a.184.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.a.184.1	✓	4	63.58	even	3	inner
315.2.r.a.184.2	yes	4	315.184	even	6	inner
315.2.r.a.214.1	yes	4	1.1	even	1	trivial
315.2.r.a.214.2	yes	4	5.4	even	2	inner
315.2.bo.a.4.1	yes	4	45.4	even	6
315.2.bo.a.4.2	yes	4	9.4	even	3
315.2.bo.a.79.1	yes	4	7.2	even	3
315.2.bo.a.79.2	yes	4	35.9	even	6
945.2.r.a.424.1		4	15.14	odd	2
945.2.r.a.424.2		4	3.2	odd	2
945.2.r.a.604.1		4	315.149	odd	6
945.2.r.a.604.2		4	63.23	odd	6
945.2.bo.a.289.1		4	105.44	odd	6
945.2.bo.a.289.2		4	21.2	odd	6
945.2.bo.a.739.1		4	9.5	odd	6
945.2.bo.a.739.2		4	45.14	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.866025 - 1.50000i) q^{3} +1.00000 q^{4} +(-2.23205 - 0.133975i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.866025 - 1.50000i) q^{3} +1.00000 q^{4} +(-2.23205 - 0.133975i) q^{5} +(-1.50000 + 0.866025i) q^{6} +(-1.73205 + 2.00000i) q^{7} -3.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.133975 + 2.23205i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.866025 - 1.50000i) q^{12} +(-3.46410 + 2.00000i) q^{13} +(2.00000 + 1.73205i) q^{14} +(1.73205 + 3.46410i) q^{15} -1.00000 q^{16} +(1.73205 + 1.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-3.00000 - 5.19615i) q^{19} +(-2.23205 - 0.133975i) q^{20} +(4.50000 + 0.866025i) q^{21} +(-5.19615 + 3.00000i) q^{22} +(2.59808 + 1.50000i) q^{23} +(-4.50000 + 2.59808i) q^{24} +(4.96410 + 0.598076i) q^{25} +(2.00000 + 3.46410i) q^{26} +5.19615 q^{27} +(-1.73205 + 2.00000i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.46410 - 1.73205i) q^{30} -4.00000 q^{31} -5.00000i q^{32} +(-5.19615 + 9.00000i) q^{33} +(1.00000 - 1.73205i) q^{34} +(4.13397 - 4.23205i) q^{35} +(-1.50000 + 2.59808i) q^{36} +(6.92820 - 4.00000i) q^{37} +(-5.19615 + 3.00000i) q^{38} +(6.00000 + 3.46410i) q^{39} +(-0.401924 + 6.69615i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.866025 - 4.50000i) q^{42} +(-0.866025 - 0.500000i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(3.69615 - 5.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} -3.00000i q^{47} +(0.866025 + 1.50000i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(0.598076 - 4.96410i) q^{50} -3.46410i q^{51} +(-3.46410 + 2.00000i) q^{52} +(-10.3923 - 6.00000i) q^{53} -5.19615i q^{54} +(6.00000 + 12.0000i) q^{55} +(6.00000 + 5.19615i) q^{56} +(-5.19615 + 9.00000i) q^{57} +(1.73205 + 1.00000i) q^{58} -4.00000 q^{59} +(1.73205 + 3.46410i) q^{60} +7.00000 q^{61} +4.00000i q^{62} +(-2.59808 - 7.50000i) q^{63} -7.00000 q^{64} +(8.00000 - 4.00000i) q^{65} +(9.00000 + 5.19615i) q^{66} -7.00000i q^{67} +(1.73205 + 1.00000i) q^{68} -5.19615i q^{69} +(-4.23205 - 4.13397i) q^{70} +4.00000 q^{71} +(7.79423 + 4.50000i) q^{72} +(-4.00000 - 6.92820i) q^{74} +(-3.40192 - 7.96410i) q^{75} +(-3.00000 - 5.19615i) q^{76} +(15.5885 + 3.00000i) q^{77} +(3.46410 - 6.00000i) q^{78} +14.0000 q^{79} +(2.23205 + 0.133975i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-1.73205 + 1.00000i) q^{82} +(-3.46410 - 2.00000i) q^{83} +(4.50000 + 0.866025i) q^{84} +(-3.73205 - 2.46410i) q^{85} +(-0.500000 + 0.866025i) q^{86} +3.46410 q^{87} +(-15.5885 + 9.00000i) q^{88} +(-1.50000 - 2.59808i) q^{89} +(-5.59808 - 3.69615i) q^{90} +(2.00000 - 10.3923i) q^{91} +(2.59808 + 1.50000i) q^{92} +(3.46410 + 6.00000i) q^{93} -3.00000 q^{94} +(6.00000 + 12.0000i) q^{95} +(-7.50000 + 4.33013i) q^{96} +(1.73205 + 1.00000i) q^{97} +(-6.92820 + 1.00000i) q^{98} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 2 q^{5} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 - 2 * q^5 - 6 * q^6 - 6 * q^9	\( 4 q + 4 q^{4} - 2 q^{5} - 6 q^{6} - 6 q^{9} - 4 q^{10} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 12 q^{19} - 2 q^{20} + 18 q^{21} - 18 q^{24} + 6 q^{25} + 8 q^{26} - 4 q^{29} - 16 q^{31} + 4 q^{34} + 20 q^{35} - 6 q^{36} + 24 q^{39} - 12 q^{40} - 4 q^{41} - 12 q^{44} - 6 q^{45} + 6 q^{46} - 4 q^{49} - 8 q^{50} + 24 q^{55} + 24 q^{56} - 16 q^{59} + 28 q^{61} - 28 q^{64} + 32 q^{65} + 36 q^{66} - 10 q^{70} + 16 q^{71} - 16 q^{74} - 24 q^{75} - 12 q^{76} + 56 q^{79} + 2 q^{80} - 18 q^{81} + 18 q^{84} - 8 q^{85} - 2 q^{86} - 6 q^{89} - 12 q^{90} + 8 q^{91} - 12 q^{94} + 24 q^{95} - 30 q^{96} + 72 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 - 2 * q^5 - 6 * q^6 - 6 * q^9 - 4 * q^10 - 12 * q^11 + 8 * q^14 - 4 * q^16 - 12 * q^19 - 2 * q^20 + 18 * q^21 - 18 * q^24 + 6 * q^25 + 8 * q^26 - 4 * q^29 - 16 * q^31 + 4 * q^34 + 20 * q^35 - 6 * q^36 + 24 * q^39 - 12 * q^40 - 4 * q^41 - 12 * q^44 - 6 * q^45 + 6 * q^46 - 4 * q^49 - 8 * q^50 + 24 * q^55 + 24 * q^56 - 16 * q^59 + 28 * q^61 - 28 * q^64 + 32 * q^65 + 36 * q^66 - 10 * q^70 + 16 * q^71 - 16 * q^74 - 24 * q^75 - 12 * q^76 + 56 * q^79 + 2 * q^80 - 18 * q^81 + 18 * q^84 - 8 * q^85 - 2 * q^86 - 6 * q^89 - 12 * q^90 + 8 * q^91 - 12 * q^94 + 24 * q^95 - 30 * q^96 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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