LMFDB - Embedded newform 315.2.bo.a.4.2

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			4.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.a.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} -1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.866025 - 2.50000i) q^{7} -3.00000i q^{8} +3.00000 q^{9} +O(q^{10})$	\(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} +(-0.133975 + 2.23205i) 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} +(1.23205 - 1.86603i) 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} +(0.232051 - 3.86603i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-4.33013 + 2.50000i) q^{32} -10.3923 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} -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} +(-4.59808 + 1.96410i) 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} +(-2.13397 + 3.23205i) q^{60} +(-3.50000 + 6.06218i) q^{61} +4.00000i q^{62} +(-2.59808 - 7.50000i) q^{63} -7.00000 q^{64} +(-0.535898 + 8.92820i) q^{65} +(-9.00000 - 5.19615i) q^{66} +(-6.06218 + 3.50000i) q^{67} -2.00000i q^{68} +5.19615i q^{69} +(5.69615 - 1.59808i) 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} +(2.23205 + 0.133975i) q^{80} +9.00000 q^{81} +(-1.73205 + 1.00000i) q^{82} +(3.46410 - 2.00000i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-0.267949 + 4.46410i) q^{85} +1.00000 q^{86} +(1.73205 + 3.00000i) q^{87} -18.0000i q^{88} +(-1.50000 - 2.59808i) q^{89} +(-0.401924 + 6.69615i) 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} +(7.39230 - 11.1962i) 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	0.773893	−	0.633316i	$-0.218307\pi$
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i	−0.161521	+	0.986869i	$0.551640\pi$
$3$	−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
$10$	−0.133975	+	2.23205i	−0.0423665	+	0.705836i
$11$	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	0.896410	−	0.443227i	$-0.146166\pi$
$13$	3.46410	+	2.00000i	0.960769	+	0.554700i	0.0643593	+	0.997927i	$0.479500\pi$
$14$	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	0.695113	−	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	$-0.408286\pi$
$20$	1.23205	−	1.86603i	0.275495	−	0.417256i
$21$	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	$-0.898743\pi$
$23$		−	3.00000i		−	0.625543i	0.949828	−	0.312772i	$-0.101257\pi$
$24$			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	$0.892787\pi$
$30$	0.232051	−	3.86603i	0.0423665	−	0.705836i
$31$	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
$35$	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	$0.104907\pi$
$38$		−	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	−0.432511	−	0.901629i	$-0.642372\pi$
$43$	0.866025	−	0.500000i	0.132068	−	0.0762493i	0.564578	+	0.825380i	$0.309039\pi$
$44$	−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	0.677369	−	0.735643i	$-0.263120\pi$
$47$	2.59808	+	1.50000i	0.378968	+	0.218797i	−0.298401	+	0.954441i	$0.596453\pi$
$48$	−0.866025	+	1.50000i	−0.125000	+	0.216506i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	−4.59808	+	1.96410i	−0.650266	+	0.277766i
$51$	−3.00000	−	1.73205i	−0.420084	−	0.242536i
$52$		−	4.00000i		−	0.554700i
$53$	−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	$0.975021\pi$
$54$	−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	$0.749486\pi$
$60$	−2.13397	+	3.23205i	−0.275495	+	0.417256i
$61$	−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
$65$	−0.535898	+	8.92820i	−0.0664700	+	1.10741i
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$		−	2.00000i		−	0.242536i
$69$			5.19615i			0.625543i
$70$	5.69615	−	1.59808i	0.680820	−	0.191007i
$71$	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	$0.878010\pi$
$80$	2.23205	+	0.133975i	0.249551	+	0.0149788i
$81$	9.00000			1.00000
$82$	−1.73205	+	1.00000i	−0.191273	+	0.110432i
$83$	3.46410	−	2.00000i	0.380235	−	0.219529i	−0.297686	−	0.954664i	$-0.596215\pi$
$83$	3.46410	−	2.00000i	0.380235	−	0.219529i	0.677920	+	0.735135i	$0.262881\pi$
$84$	3.00000	−	3.46410i	0.327327	−	0.377964i
$85$	−0.267949	+	4.46410i	−0.0290632	+	0.484200i
$86$	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	$0.884160\pi$
$90$	−0.401924	+	6.69615i	−0.0423665	+	0.705836i
$91$	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
$95$	7.39230	−	11.1962i	0.758434	−	1.14870i
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	−1.73205	+	1.00000i	−0.175863	+	0.101535i	−0.585348	−	0.810782i	$-0.699042\pi$
$97$	−1.73205	+	1.00000i	−0.175863	+	0.101535i	0.409484	+	0.912317i	$0.365709\pi$
$98$	−6.92820	+	1.00000i	−0.699854	+	0.101015i
$99$	18.0000			1.80907
$100$	4.96410	+	0.598076i	0.496410	+	0.0598076i
$101$	−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	$0.0156884\pi$
$103$			1.00000i			0.0985329i	−0.998786	+	0.0492665i	$0.984312\pi$
$104$	6.00000	−	10.3923i	0.588348	−	1.01905i
$105$	−7.16025	+	7.33013i	−0.698769	+	0.715347i
$106$	−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	$0.271399\pi$
$108$	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	$0.325636\pi$
$110$	−0.803848	+	13.3923i	−0.0766439	+	1.27691i
$111$	−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	0.999295	−	0.0375328i	$-0.0119499\pi$
$113$	15.5885	+	9.00000i	1.46644	+	0.846649i	0.467143	+	0.884182i	$0.345283\pi$
$114$			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	$-0.899478\pi$
$127$		−	7.00000i		−	0.621150i	0.950549	−	0.310575i	$-0.100522\pi$
$128$	2.59808	+	1.50000i	0.229640	+	0.132583i
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	−4.92820	+	7.46410i	−0.432232	+	0.654645i
$131$	−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	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$	−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	$0.139635\pi$
$140$	−5.73205	−	1.46410i	−0.484447	−	0.123739i
$141$	−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
$145$	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
$149$	23.0000			1.88423			0.942117	−	0.335285i	$-0.108833\pi$
$149$	23.0000			1.88423			0.942117	+	0.335285i	$0.108833\pi$
$150$	7.96410	−	3.40192i	0.650266	−	0.277766i
$151$	−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
$155$	−4.92820	+	7.46410i	−0.395843	+	0.599531i
$156$			6.92820i			0.554700i
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−10.3923	+	6.00000i	−0.829396	+	0.478852i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	−12.1244	+	7.00000i	−0.964562	+	0.556890i
$159$	18.0000	+	10.3923i	1.42749	+	0.824163i
$160$	−9.33013	−	6.16025i	−0.737611	−	0.487011i
$161$	−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	$0.383403\pi$
$164$	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	0.396098	−	0.918208i	$-0.370364\pi$
$167$	−2.59808	−	1.50000i	−0.201045	−	0.116073i	−0.597143	+	0.802135i	$0.703697\pi$
$168$	12.9904	−	4.50000i	1.00223	−	0.347183i
$169$	1.50000	+	2.59808i	0.115385	+	0.199852i
$170$	−2.46410	+	3.73205i	−0.188988	+	0.286235i
$171$	−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	−0.227964	−	0.973670i	$-0.573207\pi$
$173$	−15.5885	−	9.00000i	−1.18517	−	0.684257i	−0.957205	+	0.289412i	$0.906540\pi$
$174$			3.46410i			0.262613i
$175$	12.5981	+	4.03590i	0.952325	+	0.305085i
$176$	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	$0.190480\pi$
$180$	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	$0.428419\pi$
$182$	6.92820	−	8.00000i	0.513553	−	0.592999i
$183$	6.06218	−	10.5000i	0.448129	−	0.776182i
$184$	−9.00000			−0.663489
$185$	14.9282	+	9.85641i	1.09754	+	0.724657i
$186$		−	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	−0.778183	−	0.628037i	$-0.783859\pi$
$193$	−8.66025	+	5.00000i	−0.623379	+	0.359908i	0.154805	+	0.987945i	$0.450525\pi$
$194$	−2.00000			−0.143592
$195$	0.928203	−	15.4641i	0.0664700	−	1.10741i
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$			14.0000i			0.997459i	0.866758	+	0.498729i	$0.166200\pi$
$197$			14.0000i			0.997459i	−0.866758	+	0.498729i	$0.833800\pi$
$198$	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
$205$	−4.46410	−	0.267949i	−0.311786	−	0.0187144i
$206$	−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
$210$	−9.86603	+	2.76795i	−0.680820	+	0.191007i
$211$	−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
$215$	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
$220$	7.39230	−	11.1962i	0.498389	−	0.754844i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	−13.8564			−0.929981
$223$	−2.59808	+	1.50000i	−0.173980	+	0.100447i	−0.584461	−	0.811422i	$-0.698694\pi$
$223$	−2.59808	+	1.50000i	−0.173980	+	0.100447i	0.410481	+	0.911869i	$0.365361\pi$
$224$	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	$-0.957621\pi$
$227$		−	4.00000i		−	0.265489i	0.991150	−	0.132745i	$-0.0423790\pi$
$228$	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	$0.774772\pi$
$230$	6.69615	+	0.401924i	0.441531	+	0.0265021i
$231$	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	$0.181690\pi$
$234$	6.00000	+	10.3923i	0.392232	+	0.679366i
$235$	−0.401924	+	6.69615i	−0.0262186	+	0.436809i
$236$	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	$0.883804\pi$
$240$	−3.86603	−	0.232051i	−0.249551	−	0.0149788i
$241$	−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
$245$	−14.1603	−	6.66987i	−0.904665	−	0.426123i
$246$	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
$250$	−8.52628	−	7.23205i	−0.539249	−	0.457395i
$251$	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
$255$	0.464102	−	7.73205i	0.0290632	−	0.484200i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$		−	8.00000i		−	0.499026i	−0.968371	−	0.249513i	$-0.919729\pi$
$257$		−	8.00000i		−	0.499026i	0.968371	−	0.249513i	$-0.0802706\pi$
$258$	−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	$0.224168\pi$
$263$			21.0000i			1.29492i	−0.762101	+	0.647458i	$0.775832\pi$
$264$			31.1769i			1.91881i
$265$	1.60770	−	26.7846i	0.0987599	−	1.64537i
$266$	−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	$0.0369565\pi$
$270$	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
$273$	−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	$-0.770164\pi$
$277$		−	22.0000i		−	1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$	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	0.973111	+	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	−0.755662	−	0.654962i	$-0.772685\pi$
$283$	−9.52628	+	5.50000i	−0.566279	+	0.326941i	0.189383	+	0.981903i	$0.439351\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$	−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
$290$	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	0.771839	−	0.635818i	$-0.219337\pi$
$293$	10.3923	+	6.00000i	0.607125	+	0.350524i	−0.164714	+	0.986341i	$0.552670\pi$
$294$	12.0000	−	1.73205i	0.699854	−	0.101015i
$295$	−4.92820	+	7.46410i	−0.286931	+	0.434577i
$296$	−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
$300$	−8.59808	−	1.03590i	−0.496410	−	0.0598076i
$301$	−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
$305$	−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	$0.705351\pi$
$308$	−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	0.871025	−	0.491239i	$-0.163456\pi$
$313$	15.5885	+	9.00000i	0.881112	+	0.508710i	0.0100869	+	0.999949i	$0.496789\pi$
$314$	−12.0000			−0.677199
$315$	12.4019	−	12.6962i	0.698769	−	0.715347i
$316$	14.0000			0.787562
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.00635137	−	0.999980i	$-0.502022\pi$
$317$	−15.5885	−	9.00000i	−0.875535	−	0.505490i	−0.869184	+	0.494489i	$0.835355\pi$
$318$	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
$325$	−18.3923	+	7.85641i	−1.02022	+	0.435795i
$326$	−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
$330$	1.39230	−	23.1962i	0.0766439	−	1.27691i
$331$	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
$335$	−13.0622	−	8.62436i	−0.713663	−	0.471199i
$336$	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	−0.428640	−	0.903475i	$-0.641007\pi$
$347$	2.59808	−	1.50000i	0.139472	−	0.0805242i	0.568112	+	0.822951i	$0.307674\pi$
$348$	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	$0.521847\pi$
$350$	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
$353$			10.0000i			0.532246i	0.963939	+	0.266123i	$0.0857428\pi$
$353$			10.0000i			0.532246i	−0.963939	+	0.266123i	$0.914257\pi$
$354$		−	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	$0.0249490\pi$
$367$			3.00000i			0.156599i	−0.996930	+	0.0782994i	$0.975051\pi$
$368$	−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	$0.213410\pi$
$373$			24.0000i			1.24267i	−0.783544	+	0.621336i	$0.786590\pi$
$374$	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	$0.671713\pi$
$380$	−13.3923	−	0.803848i	−0.687011	−	0.0412365i
$381$			12.1244i			0.621150i
$382$	5.19615	−	3.00000i	0.265858	−	0.153493i
$383$		−	1.00000i		−	0.0510976i	−0.999674	−	0.0255488i	$-0.991867\pi$
$383$		−	1.00000i		−	0.0510976i	0.999674	−	0.0255488i	$-0.00813332\pi$
$384$	−4.50000	−	2.59808i	−0.229640	−	0.132583i
$385$	24.8038	−	25.3923i	1.26412	−	1.29411i
$386$	−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	$0.340031\pi$
$390$	8.53590	−	12.9282i	0.432232	−	0.654645i
$391$	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
$395$	−31.2487	−	1.87564i	−1.57229	−	0.0943739i
$396$	−9.00000	−	15.5885i	−0.452267	−	0.783349i
$397$	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
$399$	18.0000	−	20.7846i	0.901127	−	1.04053i
$400$	1.96410	+	4.59808i	0.0982051	+	0.229904i
$401$	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	$0.500449\pi$
$410$	−3.73205	−	2.46410i	−0.184313	−	0.121693i
$411$		−	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
$415$	7.46410	+	4.92820i	0.366398	+	0.241916i
$416$	−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	$0.0217590\pi$
$420$	9.92820	+	2.53590i	0.484447	+	0.123739i
$421$	−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
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$	−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	$-0.720799\pi$
$433$		−	32.0000i		−	1.53782i	0.639356	−	0.768911i	$-0.279201\pi$
$434$	10.0000	−	3.46410i	0.480015	−	0.166282i
$435$	−4.26795	+	6.46410i	−0.204633	+	0.309930i
$436$	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	0.415445	−	0.909618i	$-0.363626\pi$
$443$	−3.46410	−	2.00000i	−0.164584	−	0.0950229i	−0.580030	+	0.814595i	$0.696959\pi$
$444$	12.0000	+	6.92820i	0.569495	+	0.328798i
$445$	3.69615	−	5.59808i	0.175214	−	0.265374i
$446$	−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	$0.462357\pi$
$450$	−13.7942	+	5.89230i	−0.650266	+	0.277766i
$451$	−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
$455$	22.7846	−	6.39230i	1.06816	−	0.299676i
$456$	27.0000	−	15.5885i	1.26439	−	0.729996i
$457$	17.3205	+	10.0000i	0.810219	+	0.467780i	0.847032	−	0.531542i	$-0.178387\pi$
$457$	17.3205	+	10.0000i	0.810219	+	0.467780i	−0.0368128	+	0.999322i	$0.511721\pi$
$458$	−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	0.510887	−	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	0.932692	−	0.360674i	$-0.117453\pi$
$463$	23.3827	+	13.5000i	1.08669	+	0.627398i	0.153993	+	0.988072i	$0.450787\pi$
$464$	−2.00000			−0.0928477
$465$	8.53590	−	12.9282i	0.395843	−	0.599531i
$466$	14.0000			0.648537
$467$	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
$470$	−3.69615	+	5.59808i	−0.170491	+	0.258220i
$471$	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
$475$	29.7846	+	3.58846i	1.36661	+	0.164650i
$476$	−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	$0.5\pi$
$480$	16.1603	+	10.6699i	0.737611	+	0.487011i
$481$	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
$485$	−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	$0.754314\pi$
$488$	18.1865	+	10.5000i	0.823266	+	0.475313i
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$	−8.92820	−	12.8564i	−0.403335	−	0.580793i
$491$	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	$0.715605\pi$
$500$	3.76795	+	10.5263i	0.168508	+	0.470750i
$501$	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	$0.0862064\pi$
$503$			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
$506$	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	$0.731510\pi$
$510$	4.26795	−	6.46410i	0.188988	−	0.286235i
$511$		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
$520$	26.7846	+	1.60770i	1.17458	+	0.0705021i
$521$	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	$0.687162\pi$
$523$	−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
$527$			8.00000i			0.348485i
$528$	−5.19615	+	9.00000i	−0.226134	+	0.391675i
$529$	14.0000			0.608696
$530$	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
$534$			5.19615i			0.224860i
$535$	7.46410	+	4.92820i	0.322701	+	0.213065i
$536$	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
$540$	−6.40192	+	9.69615i	−0.275495	+	0.417256i
$541$	−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
$545$	−22.3205	−	1.33975i	−0.956106	−	0.0573884i
$546$	−12.0000	+	13.8564i	−0.513553	+	0.592999i
$547$	−24.2487	+	14.0000i	−1.03680	+	0.598597i	−0.918925	−	0.394432i	$-0.870941\pi$
$547$	−24.2487	+	14.0000i	−1.03680	+	0.598597i	−0.117875	+	0.993028i	$0.537608\pi$
$548$	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
$551$	−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
$555$	−25.8564	−	17.0718i	−1.09754	−	0.724657i
$556$	−2.00000			−0.0848189
$557$	−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	$0.680158\pi$
$558$			12.0000i			0.508001i
$559$	4.00000			0.169182
$560$	−1.59808	−	5.69615i	−0.0675310	−	0.240706i
$561$	−18.0000	−	10.3923i	−0.759961	−	0.438763i
$562$			23.0000i			0.970196i
$563$	−23.3827	+	13.5000i	−0.985463	+	0.568957i	−0.903915	−	0.427712i	$-0.859320\pi$
$563$	−23.3827	+	13.5000i	−0.985463	+	0.568957i	−0.0815478	+	0.996669i	$0.525986\pi$
$564$			5.19615i			0.218797i
$565$	−2.41154	+	40.1769i	−0.101454	+	1.69026i
$566$	−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	0.997991	−	0.0633500i	$-0.0201784\pi$
$577$	34.6410	+	20.0000i	1.44212	+	0.832611i	0.444133	+	0.895961i	$0.353512\pi$
$578$		−	13.0000i		−	0.540729i
$579$	15.0000	−	8.66025i	0.623379	−	0.359908i
$580$	−4.46410	−	0.267949i	−0.185362	−	0.0111260i
$581$	−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
$585$	−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	0.618808	−	0.785543i	$-0.287616\pi$
$587$	38.9711	−	22.5000i	1.60851	−	0.928674i	0.989704	−	0.143132i	$-0.0457173\pi$
$588$	−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	−0.811530	−	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
$597$	−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
$610$	−13.0622	−	8.62436i	−0.528872	−	0.349190i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		−	6.00000i		−	0.242536i
$613$	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	$0.425759\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$	7.73205	+	0.464102i	0.311786	+	0.0187144i
$616$	−45.0000	+	15.5885i	−1.81310	+	0.628077i
$617$	−24.2487	−	14.0000i	−0.976216	−	0.563619i	−0.0750907	−	0.997177i	$-0.523925\pi$
$617$	−24.2487	−	14.0000i	−0.976216	−	0.563619i	−0.901126	+	0.433558i	$0.857258\pi$
$618$	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	$0.223393\pi$
$620$	8.92820	+	0.535898i	0.358565	+	0.0215222i
$621$			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
$630$	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	$0.512675\pi$
$632$	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
$640$	−0.401924	+	6.69615i	−0.0158874	+	0.264689i
$641$	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	$-0.955924\pi$
$643$	−40.7032	−	23.5000i	−1.60518	−	0.926750i	−0.614749	−	0.788723i	$-0.710743\pi$
$644$	6.00000	+	5.19615i	0.236433	+	0.204757i
$645$	−3.23205	−	2.13397i	−0.127262	−	0.0840252i
$646$	6.00000	−	10.3923i	0.236067	−	0.408880i
$647$	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	$0.616402\pi$
$648$		−	27.0000i		−	1.06066i
$649$	12.0000	+	20.7846i	0.471041	+	0.815867i
$650$	−19.8564	−	2.39230i	−0.778832	−	0.0938339i
$651$	−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	$-0.733151\pi$
$653$		−	38.0000i		−	1.48705i	0.668705	−	0.743527i	$-0.266849\pi$
$654$	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	$0.634696\pi$
$660$	−12.8038	+	19.3923i	−0.498389	+	0.754844i
$661$	−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
$665$	−34.3923	−	8.78461i	−1.33368	−	0.340653i
$666$	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	−0.0426985	−	0.999088i	$-0.513595\pi$
$673$	20.7846	−	12.0000i	0.801188	−	0.462566i	0.843886	+	0.536522i	$0.180262\pi$
$674$		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	0.360920	−	0.932597i	$-0.382463\pi$
$677$	−6.92820	−	4.00000i	−0.266272	−	0.153732i	−0.627192	+	0.778864i	$0.715796\pi$
$678$	−15.5885	−	27.0000i	−0.598671	−	1.03693i
$679$	4.00000	+	3.46410i	0.153506	+	0.132940i
$680$	13.3923	+	0.803848i	0.513571	+	0.0308261i
$681$			6.92820i			0.265489i
$682$			24.0000i			0.919007i
$683$	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	$0.623909\pi$
$684$	−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
$690$	−11.5981	−	0.696152i	−0.441531	−	0.0265021i
$691$	−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
$695$	4.46410	+	0.267949i	0.169333	+	0.0101639i
$696$	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
$700$	−2.80385	−	12.9282i	−0.105975	−	0.488640i
$701$	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
$705$	0.696152	−	11.5981i	0.0262186	−	0.436809i
$706$	−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	$0.245163\pi$
$710$	−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
$715$	−3.21539	+	53.5692i	−0.120249	+	2.00338i
$716$	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	$0.797646\pi$
$720$	6.69615	+	0.401924i	0.249551	+	0.0149788i
$721$	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
$725$	9.92820	+	1.19615i	0.368724	+	0.0444240i
$726$	−37.5000	−	21.6506i	−1.39176	−	0.803530i
$727$	−11.2583	+	6.50000i	−0.417548	+	0.241072i	−0.694028	−	0.719948i	$-0.744166\pi$
$727$	−11.2583	+	6.50000i	−0.417548	+	0.241072i	0.276479	+	0.961020i	$0.410832\pi$
$728$	−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	$-0.735432\pi$
$733$		−	40.0000i		−	1.47743i	0.674016	−	0.738717i	$-0.264568\pi$
$734$	−1.50000	+	2.59808i	−0.0553660	+	0.0958967i
$735$	24.5263	+	11.5526i	0.904665	+	0.426123i
$736$	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	$-0.0483792\pi$
$740$	1.07180	−	17.8564i	0.0394000	−	0.656415i
$741$			41.5692i			1.52708i
$742$	−20.7846	+	24.0000i	−0.763027	+	0.881068i
$743$	−6.92820	−	4.00000i	−0.254171	−	0.146746i	0.367502	−	0.930023i	$-0.380213\pi$
$743$	−6.92820	−	4.00000i	−0.254171	−	0.146746i	−0.621673	+	0.783277i	$0.713547\pi$
$744$	−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
$750$	14.7679	+	12.5263i	0.539249	+	0.457395i
$751$	−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	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	−17.3205	−	10.0000i	−0.629109	−	0.363216i
$759$			31.1769i			1.13165i
$760$	−33.5885	−	22.1769i	−1.21838	−	0.804441i
$761$	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
$765$	−0.803848	+	13.3923i	−0.0290632	+	0.484200i
$766$	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	$-0.0361834\pi$
$770$	34.1769	−	9.58846i	1.23165	−	0.345544i
$771$			13.8564i			0.499026i
$772$	8.66025	+	5.00000i	0.311689	+	0.179954i
$773$	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	$0.632253\pi$
$774$	3.00000			0.107833
$775$	−19.8564	−	2.39230i	−0.713263	−	0.0859341i
$776$	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
$785$	−22.3923	−	14.7846i	−0.799216	−	0.527685i
$786$	21.0000	+	12.1244i	0.749045	+	0.432461i
$787$	19.9186	−	11.5000i	0.710021	−	0.409931i	−0.101048	−	0.994882i	$-0.532220\pi$
$787$	19.9186	−	11.5000i	0.710021	−	0.409931i	0.811069	+	0.584951i	$0.198886\pi$
$788$	12.1244	−	7.00000i	0.431912	−	0.249365i
$789$		−	36.3731i		−	1.29492i
$790$	−26.1244	−	17.2487i	−0.929463	−	0.613682i
$791$	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
$795$	−2.78461	+	46.3923i	−0.0987599	+	1.64537i
$796$	−14.0000			−0.496217
$797$	−12.1244	−	7.00000i	−0.429467	−	0.247953i	0.269653	−	0.962958i	$-0.413091\pi$
$797$	−12.1244	−	7.00000i	−0.429467	−	0.247953i	−0.699119	+	0.715005i	$0.746424\pi$
$798$	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
$801$	−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
$805$	−12.6962	−	12.4019i	−0.447481	−	0.437110i
$806$	−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	$0.183461\pi$
$810$	−1.20577	+	20.0885i	−0.0423665	+	0.705836i
$811$	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
$815$	−7.46410	−	4.92820i	−0.261456	−	0.172627i
$816$	−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	−0.985031	−	0.172379i	$-0.944854\pi$
$823$	−38.1051	+	22.0000i	−1.32826	+	0.766872i	−0.343230	+	0.939251i	$0.611521\pi$
$824$	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	$-0.933096\pi$
$827$		−	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	$0.820379\pi$
$830$	4.00000	+	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
$835$	0.401924	−	6.69615i	0.0139091	−	0.231730i
$836$	−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	$0.660063\pi$
$840$	21.9904	+	21.4808i	0.758740	+	0.741157i
$841$	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
$845$	−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
$850$	−9.92820	−	1.19615i	−0.340535	−	0.0410277i
$851$	−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	−0.208799	−	0.977959i	$-0.566955\pi$
$853$	15.5885	−	9.00000i	0.533739	−	0.308154i	0.742538	+	0.669804i	$0.233622\pi$
$854$	14.0000	+	12.1244i	0.479070	+	0.414887i
$855$	22.1769	−	33.5885i	0.758434	−	1.14870i
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$			18.0000i			0.614868i	0.951569	+	0.307434i	$0.0994704\pi$
$857$			18.0000i			0.614868i	−0.951569	+	0.307434i	$0.900530\pi$
$858$	−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	$0.275492\pi$
$860$	0.133975	−	2.23205i	0.00456850	−	0.0761123i
$861$	−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	−0.262332	−	0.964978i	$-0.584491\pi$
$863$	12.9904	−	7.50000i	0.442198	−	0.255303i	0.704529	+	0.709675i	$0.251158\pi$
$864$	22.5000	−	12.9904i	0.765466	−	0.441942i
$865$	2.41154	−	40.1769i	0.0819949	−	1.36606i
$866$	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
$875$	4.52628	+	29.2321i	0.153016	+	0.988224i
$876$		0			0
$877$		−	10.0000i		−	0.337676i	−0.985644	−	0.168838i	$-0.945999\pi$
$877$		−	10.0000i		−	0.337676i	0.985644	−	0.168838i	$-0.0540015\pi$
$878$	25.9808	−	15.0000i	0.876808	−	0.506225i
$879$	−18.0000	−	10.3923i	−0.607125	−	0.350524i
$880$	13.3923	+	0.803848i	0.451455	+	0.0270977i
$881$	−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	$0.0160748\pi$
$883$			3.00000i			0.100958i	−0.998725	+	0.0504790i	$0.983925\pi$
$884$	4.00000	−	6.92820i	0.134535	−	0.233021i
$885$	8.53590	−	12.9282i	0.286931	−	0.434577i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$			23.0000i			0.772264i	0.922443	+	0.386132i	$0.126189\pi$
$887$			23.0000i			0.772264i	−0.922443	+	0.386132i	$0.873811\pi$
$888$	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
$895$	−4.46410	−	0.267949i	−0.149218	−	0.00895655i
$896$	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
$900$	14.8923	+	1.79423i	0.496410	+	0.0598076i
$901$	−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	$-0.892262\pi$
$907$		−	20.0000i		−	0.664089i	0.943264	−	0.332045i	$-0.107738\pi$
$908$	−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	−0.922740	−	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
$915$	27.0622	+	1.62436i	0.894648	+	0.0536995i
$916$	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
$925$	−4.78461	+	39.7128i	−0.157317	+	1.30575i
$926$	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
$935$	−1.60770	+	26.7846i	−0.0525773	+	0.875950i
$936$	18.0000	−	31.1769i	0.588348	−	1.01905i
$937$			2.00000i			0.0653372i	0.999466	+	0.0326686i	$0.0104006\pi$
$937$			2.00000i			0.0653372i	−0.999466	+	0.0326686i	$0.989599\pi$
$938$	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
$945$	−21.4808	+	21.9904i	−0.698769	+	0.715347i
$946$	6.00000			0.195077
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	0.541619	−	0.840624i	$-0.317812\pi$
$947$	2.59808	+	1.50000i	0.0844261	+	0.0487435i	−0.457193	+	0.889368i	$0.651145\pi$
$948$	−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	$0.198151\pi$
$953$			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
$956$	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
$965$	−18.6603	−	12.3205i	−0.600695	−	0.396611i
$966$	13.5000	+	2.59808i	0.434355	+	0.0835917i
$967$	−32.0429	−	18.5000i	−1.03043	−	0.594920i	−0.113323	−	0.993558i	$-0.536150\pi$
$967$	−32.0429	−	18.5000i	−1.03043	−	0.594920i	−0.917108	+	0.398638i	$0.869483\pi$
$968$		−	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
$975$	31.8564	−	13.6077i	1.02022	−	0.435795i
$976$	3.50000	+	6.06218i	0.112032	+	0.194046i
$977$	−10.3923	+	6.00000i	−0.332479	+	0.191957i	−0.656941	−	0.753942i	$-0.728150\pi$
$977$	−10.3923	+	6.00000i	−0.332479	+	0.191957i	0.324462	+	0.945899i	$0.394817\pi$
$978$	6.92820			0.221540
$979$	−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
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	−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
$990$	−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	$0.947534\pi$
$992$	−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
$995$	31.2487	+	1.87564i	0.990651	+	0.0594619i
$996$	6.00000	+	3.46410i	0.190117	+	0.109764i
$997$		−	10.0000i		−	0.316703i	−0.987383	−	0.158352i	$-0.949382\pi$
$997$		−	10.0000i		−	0.316703i	0.987383	−	0.158352i	$-0.0506179\pi$
$998$	−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.4.2	yes	4
3.2	odd	2		945.2.bo.a.739.1		4
5.4	even	2	inner	315.2.bo.a.4.1	yes	4
7.2	even	3		315.2.r.a.184.1	✓	4
9.2	odd	6		945.2.r.a.424.2		4
9.7	even	3		315.2.r.a.214.1	yes	4
15.14	odd	2		945.2.bo.a.739.2		4
21.2	odd	6		945.2.r.a.604.2		4
35.9	even	6		315.2.r.a.184.2	yes	4
45.29	odd	6		945.2.r.a.424.1		4
45.34	even	6		315.2.r.a.214.2	yes	4
63.2	odd	6		945.2.bo.a.289.2		4
63.16	even	3	inner	315.2.bo.a.79.1	yes	4
105.44	odd	6		945.2.r.a.604.1		4
315.79	even	6	inner	315.2.bo.a.79.2	yes	4
315.254	odd	6		945.2.bo.a.289.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.a.184.1	✓	4	7.2	even	3
315.2.r.a.184.2	yes	4	35.9	even	6
315.2.r.a.214.1	yes	4	9.7	even	3
315.2.r.a.214.2	yes	4	45.34	even	6
315.2.bo.a.4.1	yes	4	5.4	even	2	inner
315.2.bo.a.4.2	yes	4	1.1	even	1	trivial
315.2.bo.a.79.1	yes	4	63.16	even	3	inner
315.2.bo.a.79.2	yes	4	315.79	even	6	inner
945.2.r.a.424.1		4	45.29	odd	6
945.2.r.a.424.2		4	9.2	odd	6
945.2.r.a.604.1		4	105.44	odd	6
945.2.r.a.604.2		4	21.2	odd	6
945.2.bo.a.289.1		4	315.254	odd	6
945.2.bo.a.289.2		4	63.2	odd	6
945.2.bo.a.739.1		4	3.2	odd	2
945.2.bo.a.739.2		4	15.14	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} +(-0.133975 + 2.23205i) 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} +(1.23205 - 1.86603i) 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} +(0.232051 - 3.86603i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-4.33013 + 2.50000i) q^{32} -10.3923 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} -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} +(-4.59808 + 1.96410i) 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} +(-2.13397 + 3.23205i) q^{60} +(-3.50000 + 6.06218i) q^{61} +4.00000i q^{62} +(-2.59808 - 7.50000i) q^{63} -7.00000 q^{64} +(-0.535898 + 8.92820i) q^{65} +(-9.00000 - 5.19615i) q^{66} +(-6.06218 + 3.50000i) q^{67} -2.00000i q^{68} +5.19615i q^{69} +(5.69615 - 1.59808i) 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} +(2.23205 + 0.133975i) q^{80} +9.00000 q^{81} +(-1.73205 + 1.00000i) q^{82} +(3.46410 - 2.00000i) q^{83} +(3.00000 - 3.46410i) q^{84} +(-0.267949 + 4.46410i) q^{85} +1.00000 q^{86} +(1.73205 + 3.00000i) q^{87} -18.0000i q^{88} +(-1.50000 - 2.59808i) q^{89} +(-0.401924 + 6.69615i) 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} +(7.39230 - 11.1962i) 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

Properties

Related objects

Downloads

Learn more