LMFDB - Embedded newform 315.2.bo.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

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, 4]))

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

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

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.866025 + 2.50000i) q^{7} +3.00000i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.866025 + 2.50000i) q^{7} +3.00000i q^{8} +3.00000 q^{9} +(-1.86603 + 1.23205i) q^{10} +6.00000 q^{11} +(-0.866025 - 1.50000i) q^{12} +(-3.46410 - 2.00000i) q^{13} +(0.500000 - 2.59808i) q^{14} +(1.73205 - 3.46410i) q^{15} +(0.500000 - 0.866025i) 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} +(1.50000 + 4.33013i) q^{21} +(-5.19615 - 3.00000i) q^{22} +3.00000i q^{23} +5.19615i q^{24} +(-3.00000 - 4.00000i) q^{25} +(2.00000 + 3.46410i) q^{26} +5.19615 q^{27} +(1.73205 - 2.00000i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-3.23205 + 2.13397i) q^{30} +(2.00000 + 3.46410i) q^{31} +(4.33013 - 2.50000i) q^{32} +10.3923 q^{33} +(1.00000 + 1.73205i) q^{34} +(5.86603 + 0.767949i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(-6.92820 + 4.00000i) q^{37} +6.00000i q^{38} +(-6.00000 - 3.46410i) q^{39} +(6.00000 + 3.00000i) 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} +(3.00000 - 6.00000i) q^{45} +(1.50000 - 2.59808i) q^{46} +(-2.59808 - 1.50000i) q^{47} +(0.866025 - 1.50000i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(0.598076 + 4.96410i) q^{50} +(-3.00000 - 1.73205i) q^{51} +4.00000i q^{52} +(10.3923 + 6.00000i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(6.00000 - 12.0000i) q^{55} +(-7.50000 + 2.59808i) q^{56} +(-5.19615 - 9.00000i) q^{57} +2.00000i q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.86603 + 0.232051i) q^{60} +(-3.50000 + 6.06218i) q^{61} -4.00000i q^{62} +(2.59808 + 7.50000i) q^{63} -7.00000 q^{64} +(-7.46410 + 4.92820i) q^{65} +(-9.00000 - 5.19615i) q^{66} +(6.06218 - 3.50000i) q^{67} +2.00000i q^{68} +5.19615i q^{69} +(-4.69615 - 3.59808i) q^{70} +4.00000 q^{71} +9.00000i q^{72} +8.00000 q^{74} +(-5.19615 - 6.92820i) q^{75} +(-3.00000 + 5.19615i) q^{76} +(5.19615 + 15.0000i) q^{77} +(3.46410 + 6.00000i) q^{78} +(-7.00000 + 12.1244i) q^{79} +(-1.23205 - 1.86603i) q^{80} +9.00000 q^{81} +(1.73205 - 1.00000i) q^{82} +(-3.46410 + 2.00000i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-3.73205 + 2.46410i) q^{85} +1.00000 q^{86} +(-1.73205 - 3.00000i) q^{87} +18.0000i 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} +(1.50000 + 2.59808i) q^{94} +(-13.3923 + 0.803848i) 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 - 2 q^{4} + 4 q^{5} - 6 q^{6} + 12 q^{9}+O(q^{10}) $ 4 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 + 12 * q^9	$ 4 q - 2 q^{4} + 4 q^{5} - 6 q^{6} + 12 q^{9} - 4 q^{10} + 24 q^{11} + 2 q^{14} + 2 q^{16} - 12 q^{19} - 2 q^{20} + 6 q^{21} - 12 q^{25} + 8 q^{26} - 4 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{34} + 20 q^{35} - 6 q^{36} - 24 q^{39} + 24 q^{40} - 4 q^{41} - 12 q^{44} + 12 q^{45} + 6 q^{46} - 22 q^{49} - 8 q^{50} - 12 q^{51} - 18 q^{54} + 24 q^{55} - 30 q^{56} + 8 q^{59} - 12 q^{60} - 14 q^{61} - 28 q^{64} - 16 q^{65} - 36 q^{66} + 2 q^{70} + 16 q^{71} + 32 q^{74} - 12 q^{76} - 28 q^{79} + 2 q^{80} + 36 q^{81} + 12 q^{84} - 8 q^{85} + 4 q^{86} - 6 q^{89} - 12 q^{90} + 8 q^{91} + 6 q^{94} - 12 q^{95} + 30 q^{96} + 72 q^{99}+O(q^{100}) $ 4 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 + 12 * q^9 - 4 * q^10 + 24 * q^11 + 2 * q^14 + 2 * q^16 - 12 * q^19 - 2 * q^20 + 6 * q^21 - 12 * q^25 + 8 * q^26 - 4 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^34 + 20 * q^35 - 6 * q^36 - 24 * q^39 + 24 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 + 6 * q^46 - 22 * q^49 - 8 * q^50 - 12 * q^51 - 18 * q^54 + 24 * q^55 - 30 * q^56 + 8 * q^59 - 12 * q^60 - 14 * q^61 - 28 * q^64 - 16 * q^65 - 36 * q^66 + 2 * q^70 + 16 * q^71 + 32 * q^74 - 12 * q^76 - 28 * q^79 + 2 * q^80 + 36 * q^81 + 12 * q^84 - 8 * q^85 + 4 * q^86 - 6 * q^89 - 12 * q^90 + 8 * q^91 + 6 * q^94 - 12 * q^95 + 30 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	0.161521	−	0.986869i	$-0.448360\pi$
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	−0.773893	+	0.633316i	$0.781693\pi$
$3$	1.73205			1.00000
$3$	1.73205			1.00000
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$8$			3.00000i			1.06066i
$9$	3.00000			1.00000
$10$	−1.86603	+	1.23205i	−0.590089	+	0.389609i
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$	−0.866025	−	1.50000i	−0.250000	−	0.433013i
$13$	−3.46410	−	2.00000i	−0.960769	−	0.554700i	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	−3.46410	−	2.00000i	−0.960769	−	0.554700i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$	1.73205	−	3.46410i	0.447214	−	0.894427i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	−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
$21$	1.50000	+	4.33013i	0.327327	+	0.944911i
$22$	−5.19615	−	3.00000i	−1.10782	−	0.639602i
$23$			3.00000i			0.625543i	0.949828	+	0.312772i	$0.101257\pi$
$23$			3.00000i			0.625543i	−0.949828	+	0.312772i	$0.898743\pi$
$24$			5.19615i			1.06066i
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$	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	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$	−3.23205	+	2.13397i	−0.590089	+	0.389609i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	4.33013	−	2.50000i	0.765466	−	0.441942i
$33$	10.3923			1.80907
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	5.86603	+	0.767949i	0.991539	+	0.129807i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$			6.00000i			0.973329i
$39$	−6.00000	−	3.46410i	−0.960769	−	0.554700i
$40$	6.00000	+	3.00000i	0.948683	+	0.474342i
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	0.777312	+	0.629115i	$0.216583\pi$
$42$	0.866025	−	4.50000i	0.133631	−	0.694365i
$43$	−0.866025	+	0.500000i	−0.132068	+	0.0762493i	−0.564578	−	0.825380i	$-0.690961\pi$
$43$	−0.866025	+	0.500000i	−0.132068	+	0.0762493i	0.432511	+	0.901629i	$0.357628\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$	3.00000	−	6.00000i	0.447214	−	0.894427i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$	−2.59808	−	1.50000i	−0.378968	−	0.218797i	0.298401	−	0.954441i	$-0.403547\pi$
$47$	−2.59808	−	1.50000i	−0.378968	−	0.218797i	−0.677369	+	0.735643i	$0.736880\pi$
$48$	0.866025	−	1.50000i	0.125000	−	0.216506i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	0.598076	+	4.96410i	0.0845807	+	0.702030i
$51$	−3.00000	−	1.73205i	−0.420084	−	0.242536i
$52$			4.00000i			0.554700i
$53$	10.3923	+	6.00000i	1.42749	+	0.824163i	0.996922	−	0.0783936i	$-0.0249791\pi$
$53$	10.3923	+	6.00000i	1.42749	+	0.824163i	0.430570	+	0.902557i	$0.358312\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	6.00000	−	12.0000i	0.809040	−	1.61808i
$56$	−7.50000	+	2.59808i	−1.00223	+	0.347183i
$57$	−5.19615	−	9.00000i	−0.688247	−	1.19208i
$58$			2.00000i			0.262613i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	−3.86603	+	0.232051i	−0.499102	+	0.0299576i
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		−	4.00000i		−	0.508001i
$63$	2.59808	+	7.50000i	0.327327	+	0.944911i
$64$	−7.00000			−0.875000
$65$	−7.46410	+	4.92820i	−0.925808	+	0.611268i
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	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	$0.192695\pi$
$68$			2.00000i			0.242536i
$69$			5.19615i			0.625543i
$70$	−4.69615	−	3.59808i	−0.561298	−	0.430052i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$			9.00000i			1.06066i
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$	8.00000			0.929981
$75$	−5.19615	−	6.92820i	−0.600000	−	0.800000i
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	5.19615	+	15.0000i	0.592157	+	1.70941i
$78$	3.46410	+	6.00000i	0.392232	+	0.679366i
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	−1.23205	−	1.86603i	−0.137747	−	0.208628i
$81$	9.00000			1.00000
$82$	1.73205	−	1.00000i	0.191273	−	0.110432i
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	−0.677920	−	0.735135i	$-0.737119\pi$
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	0.297686	+	0.954664i	$0.403785\pi$
$84$	3.00000	−	3.46410i	0.327327	−	0.377964i
$85$	−3.73205	+	2.46410i	−0.404798	+	0.267269i
$86$	1.00000			0.107833
$87$	−1.73205	−	3.00000i	−0.185695	−	0.321634i
$88$			18.0000i			1.91881i
$89$	−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
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	−13.3923	+	0.803848i	−1.37402	+	0.0824730i
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	−0.409484	−	0.912317i	$-0.634291\pi$
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$98$	6.92820	−	1.00000i	0.699854	−	0.101015i
$99$	18.0000			1.80907
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	1.73205	+	3.00000i	0.171499	+	0.297044i
$103$		−	1.00000i		−	0.0985329i	−0.998786	−	0.0492665i	$-0.984312\pi$
$103$		−	1.00000i		−	0.0985329i	0.998786	−	0.0492665i	$-0.0156884\pi$
$104$	6.00000	−	10.3923i	0.588348	−	1.01905i
$105$	10.1603	+	1.33013i	0.991539	+	0.129807i
$106$	−6.00000	−	10.3923i	−0.582772	−	1.00939i
$107$	−3.46410	+	2.00000i	−0.334887	+	0.193347i	−0.658009	−	0.753010i	$-0.728601\pi$
$107$	−3.46410	+	2.00000i	−0.334887	+	0.193347i	0.323122	+	0.946357i	$0.395268\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	−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	$0.325636\pi$
$110$	−11.1962	+	7.39230i	−1.06751	+	0.704829i
$111$	−12.0000	+	6.92820i	−1.13899	+	0.657596i
$112$	2.59808	+	0.500000i	0.245495	+	0.0472456i
$113$	−15.5885	−	9.00000i	−1.46644	−	0.846649i	−0.467143	−	0.884182i	$-0.654717\pi$
$113$	−15.5885	−	9.00000i	−1.46644	−	0.846649i	−0.999295	+	0.0375328i	$0.988050\pi$
$114$			10.3923i			0.973329i
$115$	6.00000	+	3.00000i	0.559503	+	0.279751i
$116$	−1.00000	+	1.73205i	−0.0928477	+	0.160817i
$117$	−10.3923	−	6.00000i	−0.960769	−	0.554700i
$118$		−	4.00000i		−	0.368230i
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$	10.3923	+	5.19615i	0.948683	+	0.474342i
$121$	25.0000			2.27273
$122$	6.06218	−	3.50000i	0.548844	−	0.316875i
$123$	−1.73205	+	3.00000i	−0.156174	+	0.270501i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	1.50000	−	7.79423i	0.133631	−	0.694365i
$127$			7.00000i			0.621150i	0.950549	+	0.310575i	$0.100522\pi$
$127$			7.00000i			0.621150i	−0.950549	+	0.310575i	$0.899478\pi$
$128$	−2.59808	−	1.50000i	−0.229640	−	0.132583i
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	8.92820	−	0.535898i	0.783055	−	0.0470014i
$131$	−14.0000			−1.22319			−0.611593	−	0.791173i	$-0.709471\pi$
$131$	−14.0000			−1.22319			−0.611593	+	0.791173i	$0.709471\pi$
$132$	−5.19615	−	9.00000i	−0.452267	−	0.783349i
$133$	10.3923	−	12.0000i	0.901127	−	1.04053i
$134$	−7.00000			−0.604708
$135$	5.19615	−	10.3923i	0.447214	−	0.894427i
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$	2.59808	−	4.50000i	0.221163	−	0.383065i
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	−0.820495	−	0.571654i	$-0.806302\pi$
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	0.905314	+	0.424743i	$0.139635\pi$
$140$	−2.26795	−	5.46410i	−0.191677	−	0.461801i
$141$	−4.50000	−	2.59808i	−0.378968	−	0.218797i
$142$	−3.46410	−	2.00000i	−0.290701	−	0.167836i
$143$	−20.7846	−	12.0000i	−1.73810	−	1.00349i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−4.46410	+	0.267949i	−0.370723	+	0.0222520i
$146$		0			0
$147$	−9.52628	+	7.50000i	−0.785714	+	0.618590i
$148$	6.92820	+	4.00000i	0.569495	+	0.328798i
$149$	23.0000			1.88423			0.942117	−	0.335285i	$-0.108833\pi$
$149$	23.0000			1.88423			0.942117	+	0.335285i	$0.108833\pi$
$150$	1.03590	+	8.59808i	0.0845807	+	0.702030i
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	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
$156$			6.92820i			0.554700i
$157$	10.3923	−	6.00000i	0.829396	−	0.478852i	−0.0242497	−	0.999706i	$-0.507720\pi$
$157$	10.3923	−	6.00000i	0.829396	−	0.478852i	0.853646	+	0.520854i	$0.174386\pi$
$158$	12.1244	−	7.00000i	0.964562	−	0.556890i
$159$	18.0000	+	10.3923i	1.42749	+	0.824163i
$160$	−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	−0.358162	−	0.933659i	$-0.616597\pi$
$163$	3.46410	−	2.00000i	0.271329	−	0.156652i	0.629492	+	0.777007i	$0.283263\pi$
$164$	2.00000			0.156174
$165$	10.3923	−	20.7846i	0.809040	−	1.61808i
$166$	4.00000			0.310460
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$167$	2.59808	+	1.50000i	0.201045	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$168$	−12.9904	+	4.50000i	−1.00223	+	0.347183i
$169$	1.50000	+	2.59808i	0.115385	+	0.199852i
$170$	4.46410	−	0.267949i	0.342381	−	0.0205508i
$171$	−9.00000	−	15.5885i	−0.688247	−	1.19208i
$172$	0.866025	+	0.500000i	0.0660338	+	0.0381246i
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.957205	−	0.289412i	$-0.0934598\pi$
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.227964	+	0.973670i	$0.426793\pi$
$174$			3.46410i			0.262613i
$175$	7.40192	−	10.9641i	0.559533	−	0.828808i
$176$	3.00000	−	5.19615i	0.226134	−	0.391675i
$177$	3.46410	+	6.00000i	0.260378	+	0.450988i
$178$			3.00000i			0.224860i
$179$	−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	$0.190480\pi$
$180$	−6.69615	+	0.401924i	−0.499102	+	0.0299576i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−6.92820	+	8.00000i	−0.513553	+	0.592999i
$183$	−6.06218	+	10.5000i	−0.448129	+	0.776182i
$184$	−9.00000			−0.663489
$185$	1.07180	+	17.8564i	0.0788001	+	1.31283i
$186$		−	6.92820i		−	0.508001i
$187$	−10.3923	−	6.00000i	−0.759961	−	0.438763i
$188$			3.00000i			0.218797i
$189$	4.50000	+	12.9904i	0.327327	+	0.944911i
$190$	12.0000	+	6.00000i	0.870572	+	0.435286i
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−12.1244			−0.875000
$193$	8.66025	−	5.00000i	0.623379	−	0.359908i	−0.154805	−	0.987945i	$-0.549475\pi$
$193$	8.66025	−	5.00000i	0.623379	−	0.359908i	0.778183	+	0.628037i	$0.216141\pi$
$194$	−2.00000			−0.143592
$195$	−12.9282	+	8.53590i	−0.925808	+	0.611268i
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$		−	14.0000i		−	0.997459i	−0.866758	−	0.498729i	$-0.833800\pi$
$197$		−	14.0000i		−	0.997459i	0.866758	−	0.498729i	$-0.166200\pi$
$198$	−15.5885	−	9.00000i	−1.10782	−	0.639602i
$199$	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	$0.00138876\pi$
$200$	12.0000	−	9.00000i	0.848528	−	0.636396i
$201$	10.5000	−	6.06218i	0.740613	−	0.427593i
$202$	2.59808	+	1.50000i	0.182800	+	0.105540i
$203$	3.46410	−	4.00000i	0.243132	−	0.280745i
$204$			3.46410i			0.242536i
$205$	2.46410	+	3.73205i	0.172100	+	0.260658i
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$			9.00000i			0.625543i
$208$	−3.46410	+	2.00000i	−0.240192	+	0.138675i
$209$	−18.0000	−	31.1769i	−1.24509	−	2.15655i
$210$	−8.13397	−	6.23205i	−0.561298	−	0.430052i
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	−0.898392	−	0.439194i	$-0.855264\pi$
$211$	−1.00000	+	1.73205i	−0.0688428	+	0.119239i	0.829549	+	0.558433i	$0.188597\pi$
$212$		−	12.0000i		−	0.824163i
$213$	6.92820			0.474713
$214$	4.00000			0.273434
$215$	0.133975	+	2.23205i	0.00913699	+	0.152225i
$216$			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
$220$	−13.3923	+	0.803848i	−0.902909	+	0.0541954i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	13.8564			0.929981
$223$	2.59808	−	1.50000i	0.173980	−	0.100447i	−0.410481	−	0.911869i	$-0.634639\pi$
$223$	2.59808	−	1.50000i	0.173980	−	0.100447i	0.584461	+	0.811422i	$0.301306\pi$
$224$	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
$227$			4.00000i			0.265489i	0.991150	+	0.132745i	$0.0423790\pi$
$227$			4.00000i			0.265489i	−0.991150	+	0.132745i	$0.957621\pi$
$228$	−5.19615	+	9.00000i	−0.344124	+	0.596040i
$229$	−23.0000			−1.51988			−0.759941	−	0.649992i	$-0.774772\pi$
$229$	−23.0000			−1.51988			−0.759941	+	0.649992i	$0.774772\pi$
$230$	−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	−0.841472	−	0.540301i	$-0.818310\pi$
$233$	−12.1244	+	7.00000i	−0.794293	+	0.458585i	0.0471787	+	0.998886i	$0.484977\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$	−5.59808	+	3.69615i	−0.365178	+	0.241110i
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$	−12.1244	+	21.0000i	−0.787562	+	1.36410i
$238$	−3.46410	+	4.00000i	−0.224544	+	0.259281i
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$	−2.13397	−	3.23205i	−0.137747	−	0.208628i
$241$	−23.0000			−1.48156			−0.740780	−	0.671748i	$-0.765544\pi$
$241$	−23.0000			−1.48156			−0.740780	+	0.671748i	$0.765544\pi$
$242$	−21.6506	−	12.5000i	−1.39176	−	0.803530i
$243$	15.5885			1.00000
$244$	7.00000			0.448129
$245$	3.16025	+	15.3301i	0.201901	+	0.979406i
$246$	3.00000	−	1.73205i	0.191273	−	0.110432i
$247$			24.0000i			1.52708i
$248$	−10.3923	+	6.00000i	−0.659912	+	0.381000i
$249$	−6.00000	+	3.46410i	−0.380235	+	0.219529i
$250$	10.5263	+	3.76795i	0.665740	+	0.238306i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	5.19615	−	6.00000i	0.327327	−	0.377964i
$253$			18.0000i			1.13165i
$254$	3.50000	−	6.06218i	0.219610	−	0.380375i
$255$	−6.46410	+	4.26795i	−0.404798	+	0.267269i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$			8.00000i			0.499026i	0.968371	+	0.249513i	$0.0802706\pi$
$257$			8.00000i			0.499026i	−0.968371	+	0.249513i	$0.919729\pi$
$258$	1.73205			0.107833
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$	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
$263$		−	21.0000i		−	1.29492i	−0.762101	−	0.647458i	$-0.775832\pi$
$263$		−	21.0000i		−	1.29492i	0.762101	−	0.647458i	$-0.224168\pi$
$264$			31.1769i			1.91881i
$265$	22.3923	−	14.7846i	1.37555	−	0.908211i
$266$	−15.0000	+	5.19615i	−0.919709	+	0.318597i
$267$	−2.59808	−	4.50000i	−0.159000	−	0.275396i
$268$	−6.06218	−	3.50000i	−0.370306	−	0.213797i
$269$	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	$0.0369565\pi$
$270$	−9.69615	+	6.40192i	−0.590089	+	0.389609i
$271$	−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
$273$	3.46410	−	18.0000i	0.209657	−	1.08941i
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	−18.0000	−	24.0000i	−1.08544	−	1.44725i
$276$	4.50000	−	2.59808i	0.270868	−	0.156386i
$277$			22.0000i			1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$			22.0000i			1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	−1.73205	+	1.00000i	−0.103882	+	0.0599760i
$279$	6.00000	+	10.3923i	0.359211	+	0.622171i
$280$	−2.30385	+	17.5981i	−0.137681	+	1.05169i
$281$	11.5000	+	19.9186i	0.686032	+	1.18824i	0.973111	+	0.230336i	$0.0739826\pi$
$281$	11.5000	+	19.9186i	0.686032	+	1.18824i	−0.287079	+	0.957907i	$0.592684\pi$
$282$	2.59808	+	4.50000i	0.154713	+	0.267971i
$283$	9.52628	−	5.50000i	0.566279	−	0.326941i	−0.189383	−	0.981903i	$-0.560649\pi$
$283$	9.52628	−	5.50000i	0.566279	−	0.326941i	0.755662	+	0.654962i	$0.227315\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$	−23.1962	+	1.39230i	−1.37402	+	0.0824730i
$286$	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
$290$	4.00000	+	2.00000i	0.234888	+	0.117444i
$291$	3.00000	−	1.73205i	0.175863	−	0.101535i
$292$		0			0
$293$	−10.3923	−	6.00000i	−0.607125	−	0.350524i	0.164714	−	0.986341i	$-0.447330\pi$
$293$	−10.3923	−	6.00000i	−0.607125	−	0.350524i	−0.771839	+	0.635818i	$0.780663\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$	8.92820	−	0.535898i	0.519820	−	0.0312012i
$296$	−12.0000	−	20.7846i	−0.697486	−	1.20808i
$297$	31.1769			1.80907
$298$	−19.9186	−	11.5000i	−1.15385	−	0.666177i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	−3.40192	+	7.96410i	−0.196410	+	0.459808i
$301$	−2.00000	−	1.73205i	−0.115278	−	0.0998337i
$302$	13.8564	+	8.00000i	0.797347	+	0.460348i
$303$	−5.19615			−0.298511
$304$	−6.00000			−0.344124
$305$	8.62436	+	13.0622i	0.493829	+	0.747938i
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$		−	28.0000i		−	1.59804i	−0.601302	−	0.799022i	$-0.705351\pi$
$307$		−	28.0000i		−	1.59804i	0.601302	−	0.799022i	$-0.294649\pi$
$308$	10.3923	−	12.0000i	0.592157	−	0.683763i
$309$		−	1.73205i		−	0.0985329i
$310$	−8.00000	−	4.00000i	−0.454369	−	0.227185i
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$	10.3923	−	18.0000i	0.588348	−	1.01905i
$313$	−15.5885	−	9.00000i	−0.881112	−	0.508710i	−0.0100869	−	0.999949i	$-0.503211\pi$
$313$	−15.5885	−	9.00000i	−0.881112	−	0.508710i	−0.871025	+	0.491239i	$0.836544\pi$
$314$	−12.0000			−0.677199
$315$	17.5981	+	2.30385i	0.991539	+	0.129807i
$316$	14.0000			0.787562
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.869184	−	0.494489i	$-0.164645\pi$
$317$	15.5885	+	9.00000i	0.875535	+	0.505490i	0.00635137	+	0.999980i	$0.497978\pi$
$318$	−10.3923	−	18.0000i	−0.582772	−	1.00939i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	−7.00000	+	14.0000i	−0.391312	+	0.782624i
$321$	−6.00000	+	3.46410i	−0.334887	+	0.193347i
$322$	7.79423	+	1.50000i	0.434355	+	0.0835917i
$323$			12.0000i			0.667698i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	2.39230	+	19.8564i	0.132701	+	1.10144i
$326$	−4.00000			−0.221540
$327$	−8.66025	+	15.0000i	−0.478913	+	0.829502i
$328$	−5.19615	−	3.00000i	−0.286910	−	0.165647i
$329$	1.50000	−	7.79423i	0.0826977	−	0.429710i
$330$	−19.3923	+	12.8038i	−1.06751	+	0.704829i
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	−0.771723	−	0.635959i	$-0.780605\pi$
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	0.936618	+	0.350352i	$0.113938\pi$
$332$	3.46410	+	2.00000i	0.190117	+	0.109764i
$333$	−20.7846	+	12.0000i	−1.13899	+	0.657596i
$334$	−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	$-0.333333\pi$
$337$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$338$		−	3.00000i		−	0.163178i
$339$	−27.0000	−	15.5885i	−1.46644	−	0.846649i
$340$	4.00000	+	2.00000i	0.216930	+	0.108465i
$341$	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
$345$	10.3923	+	5.19615i	0.559503	+	0.279751i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−2.59808	+	1.50000i	−0.139472	+	0.0805242i	−0.568112	−	0.822951i	$-0.692326\pi$
$347$	−2.59808	+	1.50000i	−0.139472	+	0.0805242i	0.428640	+	0.903475i	$0.358993\pi$
$348$	−1.73205	+	3.00000i	−0.0928477	+	0.160817i
$349$	15.5000	+	26.8468i	0.829696	+	1.43708i	0.898277	+	0.439430i	$0.144820\pi$
$349$	15.5000	+	26.8468i	0.829696	+	1.43708i	−0.0685808	+	0.997646i	$0.521847\pi$
$350$	−11.8923	+	5.79423i	−0.635670	+	0.309715i
$351$	−18.0000	−	10.3923i	−0.960769	−	0.554700i
$352$	25.9808	−	15.0000i	1.38478	−	0.799503i
$353$		−	10.0000i		−	0.532246i	−0.963939	−	0.266123i	$-0.914257\pi$
$353$		−	10.0000i		−	0.532246i	0.963939	−	0.266123i	$-0.0857428\pi$
$354$		−	6.92820i		−	0.368230i
$355$	4.00000	−	8.00000i	0.212298	−	0.424596i
$356$	−1.50000	+	2.59808i	−0.0794998	+	0.137698i
$357$	1.73205	−	9.00000i	0.0916698	−	0.476331i
$358$	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	$0.850141\pi$
$360$	18.0000	+	9.00000i	0.948683	+	0.474342i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−5.19615	−	3.00000i	−0.273104	−	0.157676i
$363$	43.3013			2.27273
$364$	−10.0000	+	3.46410i	−0.524142	+	0.181568i
$365$		0			0
$366$	10.5000	−	6.06218i	0.548844	−	0.316875i
$367$		−	3.00000i		−	0.156599i	−0.996930	−	0.0782994i	$-0.975051\pi$
$367$		−	3.00000i		−	0.156599i	0.996930	−	0.0782994i	$-0.0249490\pi$
$368$	2.59808	+	1.50000i	0.135434	+	0.0781929i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$	8.00000	−	16.0000i	0.415900	−	0.831800i
$371$	−6.00000	+	31.1769i	−0.311504	+	1.61862i
$372$	3.46410	−	6.00000i	0.179605	−	0.311086i
$373$		−	24.0000i		−	1.24267i	−0.783544	−	0.621336i	$-0.786590\pi$
$373$		−	24.0000i		−	1.24267i	0.783544	−	0.621336i	$-0.213410\pi$
$374$	6.00000	+	10.3923i	0.310253	+	0.537373i
$375$	−19.0526	+	3.46410i	−0.983870	+	0.178885i
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$			8.00000i			0.412021i
$378$	2.59808	−	13.5000i	0.133631	−	0.694365i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	7.39230	+	11.1962i	0.379217	+	0.574351i
$381$			12.1244i			0.621150i
$382$	−5.19615	+	3.00000i	−0.265858	+	0.153493i
$383$			1.00000i			0.0510976i	0.999674	+	0.0255488i	$0.00813332\pi$
$383$			1.00000i			0.0510976i	−0.999674	+	0.0255488i	$0.991867\pi$
$384$	−4.50000	−	2.59808i	−0.229640	−	0.132583i
$385$	35.1962	+	4.60770i	1.79376	+	0.234830i
$386$	−10.0000			−0.508987
$387$	−2.59808	+	1.50000i	−0.132068	+	0.0762493i
$388$	−1.73205	−	1.00000i	−0.0879316	−	0.0507673i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$	15.4641	−	0.928203i	0.783055	−	0.0470014i
$391$	3.00000	−	5.19615i	0.151717	−	0.262781i
$392$	−12.9904	−	16.5000i	−0.656113	−	0.833376i
$393$	−24.2487			−1.22319
$394$	−7.00000	+	12.1244i	−0.352655	+	0.610816i
$395$	17.2487	+	26.1244i	0.867877	+	1.31446i
$396$	−9.00000	−	15.5885i	−0.452267	−	0.783349i
$397$	−8.66025	+	5.00000i	−0.434646	+	0.250943i	−0.701324	−	0.712843i	$-0.747407\pi$
$397$	−8.66025	+	5.00000i	−0.434646	+	0.250943i	0.266678	+	0.963786i	$0.414074\pi$
$398$	−12.1244	+	7.00000i	−0.607739	+	0.350878i
$399$	18.0000	−	20.7846i	0.901127	−	1.04053i
$400$	−4.96410	+	0.598076i	−0.248205	+	0.0299038i
$401$	27.0000			1.34832			0.674158	−	0.738587i	$-0.264507\pi$
$401$	27.0000			1.34832			0.674158	+	0.738587i	$0.264507\pi$
$402$	−12.1244			−0.604708
$403$		−	16.0000i		−	0.797017i
$404$	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
$408$	5.19615	−	9.00000i	0.257248	−	0.445566i
$409$	17.5000	+	30.3109i	0.865319	+	1.49878i	0.866730	+	0.498778i	$0.166218\pi$
$409$	17.5000	+	30.3109i	0.865319	+	1.49878i	−0.00141047	+	0.999999i	$0.500449\pi$
$410$	−0.267949	−	4.46410i	−0.0132331	−	0.220466i
$411$		−	10.3923i		−	0.512615i
$412$	−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
$415$	0.535898	+	8.92820i	0.0263062	+	0.438268i
$416$	−20.0000			−0.980581
$417$	1.73205	−	3.00000i	0.0848189	−	0.146911i
$418$			36.0000i			1.76082i
$419$	9.00000	−	15.5885i	0.439679	−	0.761546i	−0.557986	−	0.829851i	$-0.688426\pi$
$419$	9.00000	−	15.5885i	0.439679	−	0.761546i	0.997665	+	0.0683046i	$0.0217590\pi$
$420$	−3.92820	−	9.46410i	−0.191677	−	0.461801i
$421$	−1.50000	−	2.59808i	−0.0731055	−	0.126622i	0.827155	−	0.561973i	$-0.189958\pi$
$421$	−1.50000	−	2.59808i	−0.0731055	−	0.126622i	−0.900261	+	0.435351i	$0.856624\pi$
$422$	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
$425$	1.19615	+	9.92820i	0.0580219	+	0.481589i
$426$	−6.00000	−	3.46410i	−0.290701	−	0.167836i
$427$	−18.1865	−	3.50000i	−0.880108	−	0.169377i
$428$	3.46410	+	2.00000i	0.167444	+	0.0966736i
$429$	−36.0000	−	20.7846i	−1.73810	−	1.00349i
$430$	1.00000	−	2.00000i	0.0482243	−	0.0964486i
$431$	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	$0.151328\pi$
$432$	2.59808	−	4.50000i	0.125000	−	0.216506i
$433$			32.0000i			1.53782i	0.639356	+	0.768911i	$0.279201\pi$
$433$			32.0000i			1.53782i	−0.639356	+	0.768911i	$0.720799\pi$
$434$	10.0000	−	3.46410i	0.480015	−	0.166282i
$435$	−7.73205	+	0.464102i	−0.370723	+	0.0222520i
$436$	10.0000			0.478913
$437$	15.5885	−	9.00000i	0.745697	−	0.430528i
$438$		0			0
$439$	15.0000	−	25.9808i	0.715911	−	1.23999i	−0.246696	−	0.969093i	$-0.579345\pi$
$439$	15.0000	−	25.9808i	0.715911	−	1.23999i	0.962607	−	0.270901i	$-0.0873217\pi$
$440$	36.0000	+	18.0000i	1.71623	+	0.858116i
$441$	−16.5000	+	12.9904i	−0.785714	+	0.618590i
$442$		−	8.00000i		−	0.380521i
$443$	3.46410	+	2.00000i	0.164584	+	0.0950229i	0.580030	−	0.814595i	$-0.303041\pi$
$443$	3.46410	+	2.00000i	0.164584	+	0.0950229i	−0.415445	+	0.909618i	$0.636374\pi$
$444$	12.0000	+	6.92820i	0.569495	+	0.328798i
$445$	−6.69615	+	0.401924i	−0.317428	+	0.0190530i
$446$	−3.00000			−0.142054
$447$	39.8372			1.88423
$448$	−6.06218	−	17.5000i	−0.286411	−	0.826797i
$449$	5.00000			0.235965			0.117982	−	0.993016i	$-0.462357\pi$
$449$	5.00000			0.235965			0.117982	+	0.993016i	$0.462357\pi$
$450$	1.79423	+	14.8923i	0.0845807	+	0.702030i
$451$	−6.00000	+	10.3923i	−0.282529	+	0.489355i
$452$			18.0000i			0.846649i
$453$	−27.7128			−1.30206
$454$	2.00000	−	3.46410i	0.0938647	−	0.162578i
$455$	−18.7846	−	14.3923i	−0.880636	−	0.674722i
$456$	27.0000	−	15.5885i	1.26439	−	0.729996i
$457$	−17.3205	−	10.0000i	−0.810219	−	0.467780i	0.0368128	−	0.999322i	$-0.488279\pi$
$457$	−17.3205	−	10.0000i	−0.810219	−	0.467780i	−0.847032	+	0.531542i	$0.821613\pi$
$458$	19.9186	+	11.5000i	0.930734	+	0.537360i
$459$	−9.00000	−	5.19615i	−0.420084	−	0.242536i
$460$	−0.401924	−	6.69615i	−0.0187398	−	0.312210i
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	0.510887	−	0.859648i	$-0.329317\pi$
$461$	−10.5000	−	18.1865i	−0.489034	−	0.847031i	−0.999920	+	0.0126168i	$0.995984\pi$
$462$	5.19615	−	27.0000i	0.241747	−	1.25615i
$463$	−23.3827	−	13.5000i	−1.08669	−	0.627398i	−0.153993	−	0.988072i	$-0.549213\pi$
$463$	−23.3827	−	13.5000i	−1.08669	−	0.627398i	−0.932692	+	0.360674i	$0.882547\pi$
$464$	−2.00000			−0.0928477
$465$	15.4641	−	0.928203i	0.717131	−	0.0430444i
$466$	14.0000			0.648537
$467$	−2.59808	+	1.50000i	−0.120225	+	0.0694117i	−0.558906	−	0.829231i	$-0.688779\pi$
$467$	−2.59808	+	1.50000i	−0.120225	+	0.0694117i	0.438682	+	0.898642i	$0.355446\pi$
$468$			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
$472$	−10.3923	+	6.00000i	−0.478345	+	0.276172i
$473$	−5.19615	+	3.00000i	−0.238919	+	0.137940i
$474$	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			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	−1.16025	−	19.3301i	−0.0529581	−	0.882296i
$481$	32.0000			1.45907
$482$	19.9186	+	11.5000i	0.907267	+	0.523811i
$483$	−12.9904	+	4.50000i	−0.591083	+	0.204757i
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$	−0.267949	−	4.46410i	−0.0121669	−	0.202704i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$	−18.1865	−	10.5000i	−0.823266	−	0.475313i
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$	4.92820	−	14.8564i	0.222634	−	0.671144i
$491$	16.0000	−	27.7128i	0.722070	−	1.25066i	−0.238099	−	0.971241i	$-0.576524\pi$
$491$	16.0000	−	27.7128i	0.722070	−	1.25066i	0.960169	−	0.279421i	$-0.0901424\pi$
$492$	3.46410			0.156174
$493$			4.00000i			0.180151i
$494$	12.0000	−	20.7846i	0.539906	−	0.935144i
$495$	18.0000	−	36.0000i	0.809040	−	1.61808i
$496$	4.00000			0.179605
$497$	3.46410	+	10.0000i	0.155386	+	0.448561i
$498$	6.92820			0.310460
$499$	−28.0000			−1.25345			−0.626726	−	0.779240i	$-0.715605\pi$
$499$	−28.0000			−1.25345			−0.626726	+	0.779240i	$0.715605\pi$
$500$	7.23205	+	8.52628i	0.323427	+	0.381307i
$501$	4.50000	+	2.59808i	0.201045	+	0.116073i
$502$	−10.3923	−	6.00000i	−0.463831	−	0.267793i
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$	−22.5000	+	7.79423i	−1.00223	+	0.347183i
$505$	−3.00000	+	6.00000i	−0.133498	+	0.266996i
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$	2.59808	+	4.50000i	0.115385	+	0.199852i
$508$	6.06218	−	3.50000i	0.268966	−	0.155287i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$	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
$515$	−2.00000	−	1.00000i	−0.0881305	−	0.0440653i
$516$	1.50000	+	0.866025i	0.0660338	+	0.0381246i
$517$	−15.5885	−	9.00000i	−0.685580	−	0.395820i
$518$	6.92820	+	20.0000i	0.304408	+	0.878750i
$519$	27.0000	+	15.5885i	1.18517	+	0.684257i
$520$	−14.7846	−	22.3923i	−0.648348	−	0.981968i
$521$	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	$-0.134138\pi$
$522$			6.00000i			0.262613i
$523$	35.5070	−	20.5000i	1.55261	−	0.896402i	0.554687	−	0.832059i	$-0.312838\pi$
$523$	35.5070	−	20.5000i	1.55261	−	0.896402i	0.997928	−	0.0643431i	$-0.0204952\pi$
$524$	7.00000	+	12.1244i	0.305796	+	0.529655i
$525$	12.8205	−	18.9904i	0.559533	−	0.828808i
$526$	−10.5000	+	18.1865i	−0.457822	+	0.792971i
$527$		−	8.00000i		−	0.348485i
$528$	5.19615	−	9.00000i	0.226134	−	0.391675i
$529$	14.0000			0.608696
$530$	−26.7846	+	1.60770i	−1.16345	+	0.0698338i
$531$	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
$534$			5.19615i			0.224860i
$535$	0.535898	+	8.92820i	0.0231689	+	0.386000i
$536$	10.5000	+	18.1865i	0.453531	+	0.785539i
$537$	−1.73205	+	3.00000i	−0.0747435	+	0.129460i
$538$	−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	$0.982419\pi$
$542$			28.0000i			1.20270i
$543$	10.3923			0.445976
$544$	−10.0000			−0.428746
$545$	12.3205	+	18.6603i	0.527753	+	0.799317i
$546$	−12.0000	+	13.8564i	−0.513553	+	0.592999i
$547$	24.2487	−	14.0000i	1.03680	−	0.598597i	0.117875	−	0.993028i	$-0.462392\pi$
$547$	24.2487	−	14.0000i	1.03680	−	0.598597i	0.918925	+	0.394432i	$0.129059\pi$
$548$	−5.19615	+	3.00000i	−0.221969	+	0.128154i
$549$	−10.5000	+	18.1865i	−0.448129	+	0.776182i
$550$	3.58846	+	29.7846i	0.153012	+	1.27002i
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$	−15.5885			−0.663489
$553$	−36.3731	−	7.00000i	−1.54674	−	0.297670i
$554$	11.0000	−	19.0526i	0.467345	−	0.809466i
$555$	1.85641	+	30.9282i	0.0788001	+	1.31283i
$556$	−2.00000			−0.0848189
$557$	1.73205	+	1.00000i	0.0733893	+	0.0423714i	0.536246	−	0.844062i	$-0.319842\pi$
$557$	1.73205	+	1.00000i	0.0733893	+	0.0423714i	−0.462856	+	0.886433i	$0.653175\pi$
$558$		−	12.0000i		−	0.508001i
$559$	4.00000			0.169182
$560$	3.59808	−	4.69615i	0.152046	−	0.198449i
$561$	−18.0000	−	10.3923i	−0.759961	−	0.438763i
$562$		−	23.0000i		−	0.970196i
$563$	23.3827	−	13.5000i	0.985463	−	0.568957i	0.0815478	−	0.996669i	$-0.474014\pi$
$563$	23.3827	−	13.5000i	0.985463	−	0.568957i	0.903915	+	0.427712i	$0.140680\pi$
$564$			5.19615i			0.218797i
$565$	−33.5885	+	22.1769i	−1.41308	+	0.932990i
$566$	−11.0000			−0.462364
$567$	7.79423	+	22.5000i	0.327327	+	0.944911i
$568$			12.0000i			0.503509i
$569$	−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	$0.289814\pi$
$570$	20.7846	+	10.3923i	0.870572	+	0.435286i
$571$	−3.00000	−	5.19615i	−0.125546	−	0.217452i	0.796400	−	0.604770i	$-0.206735\pi$
$571$	−3.00000	−	5.19615i	−0.125546	−	0.217452i	−0.921946	+	0.387318i	$0.873402\pi$
$572$			24.0000i			1.00349i
$573$	5.19615	−	9.00000i	0.217072	−	0.375980i
$574$	4.00000	+	3.46410i	0.166957	+	0.144589i
$575$	12.0000	−	9.00000i	0.500435	−	0.375326i
$576$	−21.0000			−0.875000
$577$	−34.6410	−	20.0000i	−1.44212	−	0.832611i	−0.444133	−	0.895961i	$-0.646488\pi$
$577$	−34.6410	−	20.0000i	−1.44212	−	0.832611i	−0.997991	+	0.0633500i	$0.979822\pi$
$578$			13.0000i			0.540729i
$579$	15.0000	−	8.66025i	0.623379	−	0.359908i
$580$	2.46410	+	3.73205i	0.102316	+	0.154965i
$581$	−8.00000	−	6.92820i	−0.331896	−	0.287430i
$582$	−3.46410			−0.143592
$583$	62.3538	+	36.0000i	2.58243	+	1.49097i
$584$		0			0
$585$	−22.3923	+	14.7846i	−0.925808	+	0.611268i
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$	−38.9711	+	22.5000i	−1.60851	+	0.928674i	−0.618808	+	0.785543i	$0.712384\pi$
$587$	−38.9711	+	22.5000i	−1.60851	+	0.928674i	−0.989704	+	0.143132i	$0.954283\pi$
$588$	11.2583	+	4.50000i	0.464286	+	0.185577i
$589$	12.0000	−	20.7846i	0.494451	−	0.856415i
$590$	−8.00000	−	4.00000i	−0.329355	−	0.164677i
$591$		−	24.2487i		−	0.997459i
$592$			8.00000i			0.328798i
$593$	17.3205	−	10.0000i	0.711268	−	0.410651i	−0.100262	−	0.994961i	$-0.531968\pi$
$593$	17.3205	−	10.0000i	0.711268	−	0.410651i	0.811530	+	0.584310i	$0.198635\pi$
$594$	−27.0000	−	15.5885i	−1.10782	−	0.639602i
$595$	−9.39230	−	7.19615i	−0.385047	−	0.295013i
$596$	−11.5000	−	19.9186i	−0.471058	−	0.815897i
$597$	12.1244	−	21.0000i	0.496217	−	0.859473i
$598$	−10.3923	+	6.00000i	−0.424973	+	0.245358i
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	0.981889	−	0.189456i	$-0.0606724\pi$
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	−0.655018	+	0.755613i	$0.727339\pi$
$600$	20.7846	−	15.5885i	0.848528	−	0.636396i
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	0.745845	−	0.666120i	$-0.232046\pi$
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	−0.949799	+	0.312861i	$0.898713\pi$
$602$	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
$605$	25.0000	−	50.0000i	1.01639	−	2.03279i
$606$	4.50000	+	2.59808i	0.182800	+	0.105540i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−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
$612$			6.00000i			0.242536i
$613$	−29.4449	−	17.0000i	−1.18927	−	0.686624i	−0.231127	−	0.972924i	$-0.574241\pi$
$613$	−29.4449	−	17.0000i	−1.18927	−	0.686624i	−0.958140	+	0.286300i	$0.907575\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$	4.26795	+	6.46410i	0.172100	+	0.260658i
$616$	−45.0000	+	15.5885i	−1.81310	+	0.628077i
$617$	24.2487	+	14.0000i	0.976216	+	0.563619i	0.901126	−	0.433558i	$-0.142742\pi$
$617$	24.2487	+	14.0000i	0.976216	+	0.563619i	0.0750907	+	0.997177i	$0.476075\pi$
$618$	−0.866025	+	1.50000i	−0.0348367	+	0.0603388i
$619$	38.0000			1.52735			0.763674	−	0.645601i	$-0.223393\pi$
$619$	38.0000			1.52735			0.763674	+	0.645601i	$0.223393\pi$
$620$	−4.92820	−	7.46410i	−0.197921	−	0.299766i
$621$			15.5885i			0.625543i
$622$			12.0000i			0.481156i
$623$	5.19615	−	6.00000i	0.208179	−	0.240385i
$624$	−6.00000	+	3.46410i	−0.240192	+	0.138675i
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	9.00000	+	15.5885i	0.359712	+	0.623040i
$627$	−31.1769	−	54.0000i	−1.24509	−	2.15655i
$628$	−10.3923	−	6.00000i	−0.414698	−	0.239426i
$629$	16.0000			0.637962
$630$	−14.0885	−	10.7942i	−0.561298	−	0.430052i
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$	−36.3731	−	21.0000i	−1.44684	−	0.835335i
$633$	−1.73205	+	3.00000i	−0.0688428	+	0.119239i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	14.0000	+	7.00000i	0.555573	+	0.277787i
$636$		−	20.7846i		−	0.824163i
$637$	27.7128	−	4.00000i	1.09802	−	0.158486i
$638$			12.0000i			0.475085i
$639$	12.0000			0.474713
$640$	−5.59808	+	3.69615i	−0.221283	+	0.146103i
$641$	37.0000			1.46141			0.730706	−	0.682692i	$-0.239191\pi$
$641$	37.0000			1.46141			0.730706	+	0.682692i	$0.239191\pi$
$642$	6.92820			0.273434
$643$	40.7032	+	23.5000i	1.60518	+	0.926750i	0.990429	+	0.138027i	$0.0440759\pi$
$643$	40.7032	+	23.5000i	1.60518	+	0.926750i	0.614749	+	0.788723i	$0.289257\pi$
$644$	6.00000	+	5.19615i	0.236433	+	0.204757i
$645$	0.232051	+	3.86603i	0.00913699	+	0.152225i
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	−6.92820	−	4.00000i	−0.272376	−	0.157256i	0.357591	−	0.933878i	$-0.383598\pi$
$647$	−6.92820	−	4.00000i	−0.272376	−	0.157256i	−0.629967	+	0.776622i	$0.716932\pi$
$648$			27.0000i			1.06066i
$649$	12.0000	+	20.7846i	0.471041	+	0.815867i
$650$	7.85641	−	18.3923i	0.308154	−	0.721406i
$651$	−12.0000	+	13.8564i	−0.470317	+	0.543075i
$652$	−3.46410	−	2.00000i	−0.135665	−	0.0783260i
$653$			38.0000i			1.48705i	0.668705	+	0.743527i	$0.266849\pi$
$653$			38.0000i			1.48705i	−0.668705	+	0.743527i	$0.733151\pi$
$654$	15.0000	−	8.66025i	0.586546	−	0.338643i
$655$	−14.0000	+	28.0000i	−0.547025	+	1.09405i
$656$	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	0.994960	+	0.100271i	$0.0319709\pi$
$659$	15.0000	+	25.9808i	0.584317	+	1.01207i	−0.410643	+	0.911796i	$0.634696\pi$
$660$	−23.1962	+	1.39230i	−0.902909	+	0.0541954i
$661$	−19.5000	−	33.7750i	−0.758462	−	1.31369i	−0.943635	−	0.330989i	$-0.892618\pi$
$661$	−19.5000	−	33.7750i	−0.758462	−	1.31369i	0.185173	−	0.982706i	$-0.440716\pi$
$662$	−5.19615	+	3.00000i	−0.201954	+	0.116598i
$663$	6.92820	+	12.0000i	0.269069	+	0.466041i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	−13.6077	−	32.7846i	−0.527684	−	1.27133i
$666$	24.0000			0.929981
$667$	5.19615	−	3.00000i	0.201196	−	0.116160i
$668$		−	3.00000i		−	0.116073i
$669$	4.50000	−	2.59808i	0.173980	−	0.100447i
$670$	−7.00000	+	14.0000i	−0.270434	+	0.540867i
$671$	−21.0000	+	36.3731i	−0.810696	+	1.40417i
$672$	17.3205	+	15.0000i	0.668153	+	0.578638i
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	−0.843886	−	0.536522i	$-0.819738\pi$
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	0.0426985	+	0.999088i	$0.486405\pi$
$674$		0			0
$675$	−15.5885	−	20.7846i	−0.600000	−	0.800000i
$676$	1.50000	−	2.59808i	0.0576923	−	0.0999260i
$677$	6.92820	+	4.00000i	0.266272	+	0.153732i	0.627192	−	0.778864i	$-0.284204\pi$
$677$	6.92820	+	4.00000i	0.266272	+	0.153732i	−0.360920	+	0.932597i	$0.617537\pi$
$678$	15.5885	+	27.0000i	0.598671	+	1.03693i
$679$	4.00000	+	3.46410i	0.153506	+	0.132940i
$680$	−7.39230	−	11.1962i	−0.283482	−	0.429353i
$681$			6.92820i			0.265489i
$682$		−	24.0000i		−	0.919007i
$683$	−6.06218	−	3.50000i	−0.231963	−	0.133924i	0.379514	−	0.925186i	$-0.376091\pi$
$683$	−6.06218	−	3.50000i	−0.231963	−	0.133924i	−0.611477	+	0.791262i	$0.709424\pi$
$684$	−9.00000	+	15.5885i	−0.344124	+	0.596040i
$685$	−12.0000	−	6.00000i	−0.458496	−	0.229248i
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	−39.8372			−1.51988
$688$			1.00000i			0.0381246i
$689$	−24.0000	−	41.5692i	−0.914327	−	1.58366i
$690$	−6.40192	−	9.69615i	−0.243717	−	0.369126i
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	−0.945319	−	0.326146i	$-0.894250\pi$
$691$	−5.00000	+	8.66025i	−0.190209	+	0.329452i	0.755110	+	0.655598i	$0.227583\pi$
$692$		−	18.0000i		−	0.684257i
$693$	15.5885	+	45.0000i	0.592157	+	1.70941i
$694$	3.00000			0.113878
$695$	−2.46410	−	3.73205i	−0.0934687	−	0.141565i
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$	3.46410	−	2.00000i	0.131212	−	0.0757554i
$698$		−	31.0000i		−	1.17337i
$699$	−21.0000	+	12.1244i	−0.794293	+	0.458585i
$700$	−13.1962	−	0.928203i	−0.498768	−	0.0350828i
$701$	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
$704$	−42.0000			−1.58293
$705$	−9.69615	+	6.40192i	−0.365178	+	0.241110i
$706$	−5.00000	+	8.66025i	−0.188177	+	0.325933i
$707$	−2.59808	−	7.50000i	−0.0977107	−	0.282067i
$708$	3.46410	−	6.00000i	0.130189	−	0.225494i
$709$	−6.50000	+	11.2583i	−0.244113	+	0.422815i	−0.961882	−	0.273466i	$-0.911830\pi$
$709$	−6.50000	+	11.2583i	−0.244113	+	0.422815i	0.717769	+	0.696281i	$0.245163\pi$
$710$	−7.46410	+	4.92820i	−0.280123	+	0.184952i
$711$	−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
$716$	2.00000			0.0747435
$717$	−20.7846	+	36.0000i	−0.776215	+	1.34444i
$718$			2.00000i			0.0746393i
$719$	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
$723$	−39.8372			−1.48156
$724$	−3.00000	−	5.19615i	−0.111494	−	0.193113i
$725$	−3.92820	+	9.19615i	−0.145890	+	0.341537i
$726$	−37.5000	−	21.6506i	−1.39176	−	0.803530i
$727$	11.2583	−	6.50000i	0.417548	−	0.241072i	−0.276479	−	0.961020i	$-0.589168\pi$
$727$	11.2583	−	6.50000i	0.417548	−	0.241072i	0.694028	+	0.719948i	$0.255834\pi$
$728$	31.1769	+	6.00000i	1.15549	+	0.222375i
$729$	27.0000			1.00000
$730$		0			0
$731$	2.00000			0.0739727
$732$	12.1244			0.448129
$733$			40.0000i			1.47743i	0.674016	+	0.738717i	$0.264568\pi$
$733$			40.0000i			1.47743i	−0.674016	+	0.738717i	$0.735432\pi$
$734$	−1.50000	+	2.59808i	−0.0553660	+	0.0958967i
$735$	5.47372	+	26.5526i	0.201901	+	0.979406i
$736$	7.50000	+	12.9904i	0.276454	+	0.478832i
$737$	36.3731	−	21.0000i	1.33982	−	0.773545i
$738$	5.19615	−	3.00000i	0.191273	−	0.110432i
$739$	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	$-0.0483792\pi$
$740$	14.9282	−	9.85641i	0.548772	−	0.362329i
$741$			41.5692i			1.52708i
$742$	20.7846	−	24.0000i	0.763027	−	0.881068i
$743$	6.92820	+	4.00000i	0.254171	+	0.146746i	0.621673	−	0.783277i	$-0.286453\pi$
$743$	6.92820	+	4.00000i	0.254171	+	0.146746i	−0.367502	+	0.930023i	$0.619787\pi$
$744$	−18.0000	+	10.3923i	−0.659912	+	0.381000i
$745$	23.0000	−	46.0000i	0.842655	−	1.68531i
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	−10.3923	+	6.00000i	−0.380235	+	0.219529i
$748$			12.0000i			0.438763i
$749$	−8.00000	−	6.92820i	−0.292314	−	0.253151i
$750$	18.2321	+	6.52628i	0.665740	+	0.238306i
$751$	−18.0000			−0.656829			−0.328415	−	0.944534i	$-0.606514\pi$
$751$	−18.0000			−0.656829			−0.328415	+	0.944534i	$0.606514\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$	20.7846			0.757433
$754$	4.00000	−	6.92820i	0.145671	−	0.252310i
$755$	−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	$0.0581691\pi$
$757$			10.0000i			0.363456i	−0.983349	+	0.181728i	$0.941831\pi$
$758$	17.3205	+	10.0000i	0.629109	+	0.363216i
$759$			31.1769i			1.13165i
$760$	−2.41154	−	40.1769i	−0.0874758	−	1.45737i
$761$	35.0000			1.26875			0.634375	−	0.773026i	$-0.281258\pi$
$761$	35.0000			1.26875			0.634375	+	0.773026i	$0.281258\pi$
$762$	6.06218	−	10.5000i	0.219610	−	0.380375i
$763$	−25.9808	−	5.00000i	−0.940567	−	0.181012i
$764$	−6.00000			−0.217072
$765$	−11.1962	+	7.39230i	−0.404798	+	0.267269i
$766$	0.500000	−	0.866025i	0.0180657	−	0.0312908i
$767$		−	16.0000i		−	0.577727i
$768$	14.7224	+	25.5000i	0.531250	+	0.920152i
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$	−28.1769	−	21.5885i	−1.01543	−	0.777994i
$771$			13.8564i			0.499026i
$772$	−8.66025	−	5.00000i	−0.311689	−	0.179954i
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	0.403634	−	0.914920i	$-0.367747\pi$
$773$	−5.19615	−	3.00000i	−0.186893	−	0.107903i	−0.590527	+	0.807018i	$0.701080\pi$
$774$	3.00000			0.107833
$775$	7.85641	−	18.3923i	0.282210	−	0.660671i
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	−27.7128	−	24.0000i	−0.994192	−	0.860995i
$778$	−16.4545	−	9.50000i	−0.589922	−	0.340592i
$779$	12.0000			0.429945
$780$	13.8564	+	6.92820i	0.496139	+	0.248069i
$781$	24.0000			0.858788
$782$	−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
$786$	21.0000	+	12.1244i	0.749045	+	0.432461i
$787$	−19.9186	+	11.5000i	−0.710021	+	0.409931i	−0.811069	−	0.584951i	$-0.801114\pi$
$787$	−19.9186	+	11.5000i	−0.710021	+	0.409931i	0.101048	+	0.994882i	$0.467780\pi$
$788$	−12.1244	+	7.00000i	−0.431912	+	0.249365i
$789$		−	36.3731i		−	1.29492i
$790$	−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
$794$	10.0000			0.354887
$795$	38.7846	−	25.6077i	1.37555	−	0.908211i
$796$	−14.0000			−0.496217
$797$	12.1244	+	7.00000i	0.429467	+	0.247953i	0.699119	−	0.715005i	$-0.253576\pi$
$797$	12.1244	+	7.00000i	0.429467	+	0.247953i	−0.269653	+	0.962958i	$0.586909\pi$
$798$	−25.9808	+	9.00000i	−0.919709	+	0.318597i
$799$	3.00000	+	5.19615i	0.106132	+	0.183827i
$800$	−22.9904	−	9.82051i	−0.812833	−	0.347207i
$801$	−4.50000	−	7.79423i	−0.159000	−	0.275396i
$802$	−23.3827	−	13.5000i	−0.825671	−	0.476702i
$803$		0			0
$804$	−10.5000	−	6.06218i	−0.370306	−	0.213797i
$805$	−2.30385	+	17.5981i	−0.0812000	+	0.620251i
$806$	−8.00000	+	13.8564i	−0.281788	+	0.488071i
$807$	11.2583	−	19.5000i	0.396312	−	0.686433i
$808$		−	9.00000i		−	0.316619i
$809$	−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	$0.183461\pi$
$810$	−16.7942	+	11.0885i	−0.590089	+	0.389609i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$	−5.19615	−	1.00000i	−0.182349	−	0.0350931i
$813$	−24.2487	−	42.0000i	−0.850439	−	1.47300i
$814$	48.0000			1.68240
$815$	−0.535898	−	8.92820i	−0.0187717	−	0.312741i
$816$	−3.00000	+	1.73205i	−0.105021	+	0.0606339i
$817$	5.19615	+	3.00000i	0.181790	+	0.104957i
$818$		−	35.0000i		−	1.22375i
$819$	6.00000	−	31.1769i	0.209657	−	1.08941i
$820$	2.00000	−	4.00000i	0.0698430	−	0.139686i
$821$	−15.5000	+	26.8468i	−0.540954	+	0.936959i	0.457896	+	0.889006i	$0.348603\pi$
$821$	−15.5000	+	26.8468i	−0.540954	+	0.936959i	−0.998850	+	0.0479535i	$0.984730\pi$
$822$	−5.19615	+	9.00000i	−0.181237	+	0.313911i
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.343230	−	0.939251i	$-0.388479\pi$
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.985031	+	0.172379i	$0.0551455\pi$
$824$	3.00000			0.104510
$825$	−31.1769	−	41.5692i	−1.08544	−	1.44725i
$826$	10.0000	−	3.46410i	0.347945	−	0.120532i
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$	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	$0.820379\pi$
$830$	4.00000	−	8.00000i	0.138842	−	0.277684i
$831$			38.1051i			1.32185i
$832$	24.2487	+	14.0000i	0.840673	+	0.485363i
$833$	13.8564	−	2.00000i	0.480096	−	0.0692959i
$834$	−3.00000	+	1.73205i	−0.103882	+	0.0599760i
$835$	5.59808	−	3.69615i	0.193729	−	0.127911i
$836$	−18.0000	+	31.1769i	−0.622543	+	1.07828i
$837$	10.3923	+	18.0000i	0.359211	+	0.622171i
$838$	−15.5885	+	9.00000i	−0.538494	+	0.310900i
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$	−3.99038	+	30.4808i	−0.137681	+	1.05169i
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$			3.00000i			0.103387i
$843$	19.9186	+	34.5000i	0.686032	+	1.18824i
$844$	2.00000			0.0688428
$845$	6.69615	−	0.401924i	0.230355	−	0.0138266i
$846$	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
$850$	3.92820	−	9.19615i	0.134736	−	0.315425i
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−3.46410	−	6.00000i	−0.118678	−	0.205557i
$853$	−15.5885	+	9.00000i	−0.533739	+	0.308154i	−0.742538	−	0.669804i	$-0.766378\pi$
$853$	−15.5885	+	9.00000i	−0.533739	+	0.308154i	0.208799	+	0.977959i	$0.433045\pi$
$854$	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
$857$		−	18.0000i		−	0.614868i	−0.951569	−	0.307434i	$-0.900530\pi$
$857$		−	18.0000i		−	0.614868i	0.951569	−	0.307434i	$-0.0994704\pi$
$858$	20.7846	+	36.0000i	0.709575	+	1.22902i
$859$	38.0000			1.29654			0.648272	−	0.761409i	$-0.275492\pi$
$859$	38.0000			1.29654			0.648272	+	0.761409i	$0.275492\pi$
$860$	1.86603	−	1.23205i	0.0636309	−	0.0420126i
$861$	−9.00000	−	1.73205i	−0.306719	−	0.0590281i
$862$	−1.73205	+	1.00000i	−0.0589939	+	0.0340601i
$863$	−12.9904	+	7.50000i	−0.442198	+	0.255303i	−0.704529	−	0.709675i	$-0.748842\pi$
$863$	−12.9904	+	7.50000i	−0.442198	+	0.255303i	0.262332	+	0.964978i	$0.415509\pi$
$864$	22.5000	−	12.9904i	0.765466	−	0.441942i
$865$	33.5885	−	22.1769i	1.14204	−	0.754038i
$866$	16.0000	−	27.7128i	0.543702	−	0.941720i
$867$	−11.2583	−	19.5000i	−0.382353	−	0.662255i
$868$	10.3923	+	2.00000i	0.352738	+	0.0678844i
$869$	−42.0000	+	72.7461i	−1.42475	+	2.46774i
$870$	6.92820	+	3.46410i	0.234888	+	0.117444i
$871$	−28.0000			−0.948744
$872$	−25.9808	−	15.0000i	−0.879820	−	0.507964i
$873$	5.19615	−	3.00000i	0.175863	−	0.101535i
$874$	−18.0000			−0.608859
$875$	−14.5263	−	25.7679i	−0.491078	−	0.871116i
$876$		0			0
$877$			10.0000i			0.337676i	0.985644	+	0.168838i	$0.0540015\pi$
$877$			10.0000i			0.337676i	−0.985644	+	0.168838i	$0.945999\pi$
$878$	−25.9808	+	15.0000i	−0.876808	+	0.506225i
$879$	−18.0000	−	10.3923i	−0.607125	−	0.350524i
$880$	−7.39230	−	11.1962i	−0.249195	−	0.377422i
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	20.7846	−	3.00000i	0.699854	−	0.101015i
$883$		−	3.00000i		−	0.100958i	−0.998725	−	0.0504790i	$-0.983925\pi$
$883$		−	3.00000i		−	0.100958i	0.998725	−	0.0504790i	$-0.0160748\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$	15.4641	−	0.928203i	0.519820	−	0.0312012i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$		−	23.0000i		−	0.772264i	−0.922443	−	0.386132i	$-0.873811\pi$
$887$		−	23.0000i		−	0.772264i	0.922443	−	0.386132i	$-0.126189\pi$
$888$	−20.7846	−	36.0000i	−0.697486	−	1.20808i
$889$	−17.5000	+	6.06218i	−0.586931	+	0.203319i
$890$	6.00000	+	3.00000i	0.201120	+	0.100560i
$891$	54.0000			1.80907
$892$	−2.59808	−	1.50000i	−0.0869900	−	0.0502237i
$893$			18.0000i			0.602347i
$894$	−34.5000	−	19.9186i	−1.15385	−	0.666177i
$895$	2.46410	+	3.73205i	0.0823658	+	0.124749i
$896$	1.50000	−	7.79423i	0.0501115	−	0.260387i
$897$	10.3923	−	18.0000i	0.346989	−	0.601003i
$898$	−4.33013	−	2.50000i	−0.144498	−	0.0834261i
$899$	4.00000	−	6.92820i	0.133407	−	0.231069i
$900$	−5.89230	+	13.7942i	−0.196410	+	0.459808i
$901$	−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
$905$	6.00000	−	12.0000i	0.199447	−	0.398893i
$906$	24.0000	+	13.8564i	0.797347	+	0.460348i
$907$			20.0000i			0.664089i	0.943264	+	0.332045i	$0.107738\pi$
$907$			20.0000i			0.664089i	−0.943264	+	0.332045i	$0.892262\pi$
$908$	3.46410	−	2.00000i	0.114960	−	0.0663723i
$909$	−9.00000			−0.298511
$910$	9.07180	+	21.8564i	0.300727	+	0.724533i
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	−0.922740	−	0.385422i	$-0.874056\pi$
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	0.127585	−	0.991828i	$-0.459277\pi$
$912$	−10.3923			−0.344124
$913$	−20.7846	+	12.0000i	−0.687870	+	0.397142i
$914$	10.0000	+	17.3205i	0.330771	+	0.572911i
$915$	14.9378	+	22.6244i	0.493829	+	0.747938i
$916$	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	$0.715135\pi$
$920$	−9.00000	+	18.0000i	−0.296721	+	0.593442i
$921$		−	48.4974i		−	1.59804i
$922$			21.0000i			0.691598i
$923$	−13.8564	−	8.00000i	−0.456089	−	0.263323i
$924$	18.0000	−	20.7846i	0.592157	−	0.683763i
$925$	36.7846	+	15.7128i	1.20947	+	0.516634i
$926$	13.5000	+	23.3827i	0.443638	+	0.768403i
$927$		−	3.00000i		−	0.0985329i
$928$	−8.66025	−	5.00000i	−0.284287	−	0.164133i
$929$	3.50000	−	6.06218i	0.114831	−	0.198894i	−0.802881	−	0.596139i	$-0.796701\pi$
$929$	3.50000	−	6.06218i	0.114831	−	0.198894i	0.917712	+	0.397246i	$0.130034\pi$
$930$	−13.8564	−	6.92820i	−0.454369	−	0.227185i
$931$	39.0000	+	15.5885i	1.27817	+	0.510891i
$932$	12.1244	+	7.00000i	0.397146	+	0.229293i
$933$	−10.3923	−	18.0000i	−0.340229	−	0.589294i
$934$	3.00000			0.0981630
$935$	−22.3923	+	14.7846i	−0.732307	+	0.483508i
$936$	18.0000	−	31.1769i	0.588348	−	1.01905i
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	−6.06218	−	17.5000i	−0.197937	−	0.571395i
$939$	−27.0000	−	15.5885i	−0.881112	−	0.508710i
$940$	6.00000	+	3.00000i	0.195698	+	0.0978492i
$941$	−22.5000	−	38.9711i	−0.733479	−	1.27042i	−0.955387	−	0.295355i	$-0.904562\pi$
$941$	−22.5000	−	38.9711i	−0.733479	−	1.27042i	0.221908	−	0.975068i	$-0.428771\pi$
$942$	−20.7846			−0.677199
$943$	−5.19615	−	3.00000i	−0.169210	−	0.0976934i
$944$	4.00000			0.130189
$945$	30.4808	+	3.99038i	0.991539	+	0.129807i
$946$	6.00000			0.195077
$947$	−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	$0.682188\pi$
$948$	24.2487			0.787562
$949$		0			0
$950$	24.0000	−	18.0000i	0.778663	−	0.583997i
$951$	27.0000	+	15.5885i	0.875535	+	0.505490i
$952$	15.5885	+	3.00000i	0.505225	+	0.0972306i
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$	−18.0000	−	31.1769i	−0.582772	−	1.00939i
$955$	−7.39230	−	11.1962i	−0.239209	−	0.362299i
$956$	24.0000			0.776215
$957$	−10.3923	−	18.0000i	−0.335936	−	0.581857i
$958$		0			0
$959$	15.0000	−	5.19615i	0.484375	−	0.167793i
$960$	−12.1244	+	24.2487i	−0.391312	+	0.782624i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	−27.7128	−	16.0000i	−0.893497	−	0.515861i
$963$	−10.3923	+	6.00000i	−0.334887	+	0.193347i
$964$	11.5000	+	19.9186i	0.370390	+	0.641534i
$965$	−1.33975	−	22.3205i	−0.0431279	−	0.718523i
$966$	13.5000	+	2.59808i	0.434355	+	0.0835917i
$967$	32.0429	+	18.5000i	1.03043	+	0.594920i	0.917108	−	0.398638i	$-0.130517\pi$
$967$	32.0429	+	18.5000i	1.03043	+	0.594920i	0.113323	+	0.993558i	$0.463850\pi$
$968$			75.0000i			2.41059i
$969$			20.7846i			0.667698i
$970$	−2.00000	+	4.00000i	−0.0642161	+	0.128432i
$971$	−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
$975$	4.14359	+	34.3923i	0.132701	+	1.10144i
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	−0.324462	−	0.945899i	$-0.605183\pi$
$977$	10.3923	−	6.00000i	0.332479	−	0.191957i	0.656941	+	0.753942i	$0.271850\pi$
$978$	−6.92820			−0.221540
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	11.6962	−	10.4019i	0.373620	−	0.332277i
$981$	−15.0000	+	25.9808i	−0.478913	+	0.829502i
$982$	−27.7128	+	16.0000i	−0.884351	+	0.510581i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	−9.00000	−	5.19615i	−0.286910	−	0.165647i
$985$	−28.0000	−	14.0000i	−0.892154	−	0.446077i
$986$	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
$990$	−33.5885	+	22.1769i	−1.06751	+	0.704829i
$991$	−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	$0.947534\pi$
$992$	17.3205	+	10.0000i	0.549927	+	0.317500i
$993$	5.19615	−	9.00000i	0.164895	−	0.285606i
$994$	2.00000	−	10.3923i	0.0634361	−	0.329624i
$995$	−17.2487	−	26.1244i	−0.546821	−	0.828198i
$996$	6.00000	+	3.46410i	0.190117	+	0.109764i
$997$			10.0000i			0.316703i	0.987383	+	0.158352i	$0.0506179\pi$
$997$			10.0000i			0.316703i	−0.987383	+	0.158352i	$0.949382\pi$
$998$	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.bo.a.4.1	yes	4
3.2	odd	2		945.2.bo.a.739.2		4
5.4	even	2	inner	315.2.bo.a.4.2	yes	4
7.2	even	3		315.2.r.a.184.2	yes	4
9.2	odd	6		945.2.r.a.424.1		4
9.7	even	3		315.2.r.a.214.2	yes	4
15.14	odd	2		945.2.bo.a.739.1		4
21.2	odd	6		945.2.r.a.604.1		4
35.9	even	6		315.2.r.a.184.1	✓	4
45.29	odd	6		945.2.r.a.424.2		4
45.34	even	6		315.2.r.a.214.1	yes	4
63.2	odd	6		945.2.bo.a.289.1		4
63.16	even	3	inner	315.2.bo.a.79.2	yes	4
105.44	odd	6		945.2.r.a.604.2		4
315.79	even	6	inner	315.2.bo.a.79.1	yes	4
315.254	odd	6		945.2.bo.a.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.a.184.1	✓	4	35.9	even	6
315.2.r.a.184.2	yes	4	7.2	even	3
315.2.r.a.214.1	yes	4	45.34	even	6
315.2.r.a.214.2	yes	4	9.7	even	3
315.2.bo.a.4.1	yes	4	1.1	even	1	trivial
315.2.bo.a.4.2	yes	4	5.4	even	2	inner
315.2.bo.a.79.1	yes	4	315.79	even	6	inner
315.2.bo.a.79.2	yes	4	63.16	even	3	inner
945.2.r.a.424.1		4	9.2	odd	6
945.2.r.a.424.2		4	45.29	odd	6
945.2.r.a.604.1		4	21.2	odd	6
945.2.r.a.604.2		4	105.44	odd	6
945.2.bo.a.289.1		4	63.2	odd	6
945.2.bo.a.289.2		4	315.254	odd	6
945.2.bo.a.739.1		4	15.14	odd	2
945.2.bo.a.739.2		4	3.2	odd	2

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.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.866025 + 2.50000i) q^{7} +3.00000i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(0.866025 + 2.50000i) q^{7} +3.00000i q^{8} +3.00000 q^{9} +(-1.86603 + 1.23205i) q^{10} +6.00000 q^{11} +(-0.866025 - 1.50000i) q^{12} +(-3.46410 - 2.00000i) q^{13} +(0.500000 - 2.59808i) q^{14} +(1.73205 - 3.46410i) q^{15} +(0.500000 - 0.866025i) 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} +(1.50000 + 4.33013i) q^{21} +(-5.19615 - 3.00000i) q^{22} +3.00000i q^{23} +5.19615i q^{24} +(-3.00000 - 4.00000i) q^{25} +(2.00000 + 3.46410i) q^{26} +5.19615 q^{27} +(1.73205 - 2.00000i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(-3.23205 + 2.13397i) q^{30} +(2.00000 + 3.46410i) q^{31} +(4.33013 - 2.50000i) q^{32} +10.3923 q^{33} +(1.00000 + 1.73205i) q^{34} +(5.86603 + 0.767949i) q^{35} +(-1.50000 - 2.59808i) q^{36} +(-6.92820 + 4.00000i) q^{37} +6.00000i q^{38} +(-6.00000 - 3.46410i) q^{39} +(6.00000 + 3.00000i) 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} +(3.00000 - 6.00000i) q^{45} +(1.50000 - 2.59808i) q^{46} +(-2.59808 - 1.50000i) q^{47} +(0.866025 - 1.50000i) q^{48} +(-5.50000 + 4.33013i) q^{49} +(0.598076 + 4.96410i) q^{50} +(-3.00000 - 1.73205i) q^{51} +4.00000i q^{52} +(10.3923 + 6.00000i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(6.00000 - 12.0000i) q^{55} +(-7.50000 + 2.59808i) q^{56} +(-5.19615 - 9.00000i) q^{57} +2.00000i q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.86603 + 0.232051i) q^{60} +(-3.50000 + 6.06218i) q^{61} -4.00000i q^{62} +(2.59808 + 7.50000i) q^{63} -7.00000 q^{64} +(-7.46410 + 4.92820i) q^{65} +(-9.00000 - 5.19615i) q^{66} +(6.06218 - 3.50000i) q^{67} +2.00000i q^{68} +5.19615i q^{69} +(-4.69615 - 3.59808i) q^{70} +4.00000 q^{71} +9.00000i q^{72} +8.00000 q^{74} +(-5.19615 - 6.92820i) q^{75} +(-3.00000 + 5.19615i) q^{76} +(5.19615 + 15.0000i) q^{77} +(3.46410 + 6.00000i) q^{78} +(-7.00000 + 12.1244i) q^{79} +(-1.23205 - 1.86603i) q^{80} +9.00000 q^{81} +(1.73205 - 1.00000i) q^{82} +(-3.46410 + 2.00000i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-3.73205 + 2.46410i) q^{85} +1.00000 q^{86} +(-1.73205 - 3.00000i) q^{87} +18.0000i 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} +(1.50000 + 2.59808i) q^{94} +(-13.3923 + 0.803848i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 4 q^{5} - 6 q^{6} + 12 q^{9}+O(q^{10}) \) 4 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 + 12 * q^9	\( 4 q - 2 q^{4} + 4 q^{5} - 6 q^{6} + 12 q^{9} - 4 q^{10} + 24 q^{11} + 2 q^{14} + 2 q^{16} - 12 q^{19} - 2 q^{20} + 6 q^{21} - 12 q^{25} + 8 q^{26} - 4 q^{29} - 6 q^{30} + 8 q^{31} + 4 q^{34} + 20 q^{35} - 6 q^{36} - 24 q^{39} + 24 q^{40} - 4 q^{41} - 12 q^{44} + 12 q^{45} + 6 q^{46} - 22 q^{49} - 8 q^{50} - 12 q^{51} - 18 q^{54} + 24 q^{55} - 30 q^{56} + 8 q^{59} - 12 q^{60} - 14 q^{61} - 28 q^{64} - 16 q^{65} - 36 q^{66} + 2 q^{70} + 16 q^{71} + 32 q^{74} - 12 q^{76} - 28 q^{79} + 2 q^{80} + 36 q^{81} + 12 q^{84} - 8 q^{85} + 4 q^{86} - 6 q^{89} - 12 q^{90} + 8 q^{91} + 6 q^{94} - 12 q^{95} + 30 q^{96} + 72 q^{99}+O(q^{100}) \) 4 * q - 2 * q^4 + 4 * q^5 - 6 * q^6 + 12 * q^9 - 4 * q^10 + 24 * q^11 + 2 * q^14 + 2 * q^16 - 12 * q^19 - 2 * q^20 + 6 * q^21 - 12 * q^25 + 8 * q^26 - 4 * q^29 - 6 * q^30 + 8 * q^31 + 4 * q^34 + 20 * q^35 - 6 * q^36 - 24 * q^39 + 24 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 + 6 * q^46 - 22 * q^49 - 8 * q^50 - 12 * q^51 - 18 * q^54 + 24 * q^55 - 30 * q^56 + 8 * q^59 - 12 * q^60 - 14 * q^61 - 28 * q^64 - 16 * q^65 - 36 * q^66 + 2 * q^70 + 16 * q^71 + 32 * q^74 - 12 * q^76 - 28 * q^79 + 2 * q^80 + 36 * q^81 + 12 * q^84 - 8 * q^85 + 4 * q^86 - 6 * q^89 - 12 * q^90 + 8 * q^91 + 6 * q^94 - 12 * q^95 + 30 * q^96 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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