LMFDB - Embedded newform 315.2.bh.a.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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([4, 3, 0]))

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

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (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			169.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.a.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(0.866025 + 0.500000i) q^{7} -3.00000i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(0.866025 + 0.500000i) q^{7} -3.00000i q^{8} +3.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-0.866025 - 1.50000i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.232051 + 3.86603i) q^{15} +(0.500000 - 0.866025i) q^{16} +7.00000i q^{17} +(2.59808 + 1.50000i) q^{18} -6.00000 q^{19} +(1.86603 - 1.23205i) q^{20} +(1.50000 + 0.866025i) q^{21} +(2.59808 - 1.50000i) q^{22} -5.19615i q^{24} +(-4.96410 + 0.598076i) q^{25} -1.00000 q^{26} +5.19615 q^{27} -1.00000i q^{28} +(5.00000 - 8.66025i) q^{29} +(-1.73205 + 3.46410i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-4.33013 + 2.50000i) q^{32} +(2.59808 - 4.50000i) q^{33} +(-3.50000 + 6.06218i) q^{34} +(-1.00000 + 2.00000i) q^{35} +(-1.50000 - 2.59808i) q^{36} +8.00000i q^{37} +(-5.19615 - 3.00000i) q^{38} +(-1.50000 + 0.866025i) q^{39} +(6.69615 - 0.401924i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.866025 + 1.50000i) q^{42} +(-3.46410 - 2.00000i) q^{43} -3.00000 q^{44} +(0.401924 + 6.69615i) q^{45} +(-7.79423 - 4.50000i) q^{47} +(0.866025 - 1.50000i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-4.59808 - 1.96410i) q^{50} +12.1244i q^{51} +(0.866025 + 0.500000i) q^{52} -6.00000i q^{53} +(4.50000 + 2.59808i) q^{54} +(6.00000 + 3.00000i) q^{55} +(1.50000 - 2.59808i) q^{56} -10.3923 q^{57} +(8.66025 - 5.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +(3.23205 - 2.13397i) q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000i q^{62} +(2.59808 + 1.50000i) q^{63} -7.00000 q^{64} +(-1.23205 - 1.86603i) q^{65} +(4.50000 - 2.59808i) q^{66} +(-3.46410 + 2.00000i) q^{67} +(6.06218 - 3.50000i) q^{68} +(-1.86603 + 1.23205i) q^{70} -5.00000 q^{71} -9.00000i q^{72} +3.00000i q^{73} +(-4.00000 + 6.92820i) q^{74} +(-8.59808 + 1.03590i) q^{75} +(3.00000 + 5.19615i) q^{76} +(2.59808 - 1.50000i) q^{77} -1.73205 q^{78} +(3.50000 - 6.06218i) q^{79} +(2.00000 + 1.00000i) q^{80} +9.00000 q^{81} -2.00000i q^{82} +(4.33013 + 2.50000i) q^{83} -1.73205i q^{84} +(-15.6244 + 0.937822i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(8.66025 - 15.0000i) q^{87} +(-7.79423 - 4.50000i) q^{88} +18.0000 q^{89} +(-3.00000 + 6.00000i) q^{90} -1.00000 q^{91} +(-6.92820 - 12.0000i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-0.803848 - 13.3923i) q^{95} +(-7.50000 + 4.33013i) q^{96} +(4.33013 + 2.50000i) q^{97} +1.00000i q^{98} +(4.50000 - 7.79423i) 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} + 6 q^{11} + 2 q^{14} - 6 q^{15} + 2 q^{16} - 24 q^{19} + 4 q^{20} + 6 q^{21} - 6 q^{25} - 4 q^{26} + 20 q^{29} - 16 q^{31} - 14 q^{34} - 4 q^{35} - 6 q^{36} - 6 q^{39} + 6 q^{40} - 4 q^{41} - 12 q^{44} + 12 q^{45} + 2 q^{49} - 8 q^{50} + 18 q^{54} + 24 q^{55} + 6 q^{56} + 8 q^{59} + 6 q^{60} - 20 q^{61} - 28 q^{64} + 2 q^{65} + 18 q^{66} - 4 q^{70} - 20 q^{71} - 16 q^{74} - 24 q^{75} + 12 q^{76} + 14 q^{79} + 8 q^{80} + 36 q^{81} - 14 q^{85} - 8 q^{86} + 72 q^{89} - 12 q^{90} - 4 q^{91} - 18 q^{94} - 24 q^{95} - 30 q^{96} + 18 q^{99}+O(q^{100}) $ 4 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^9 - 4 * q^10 + 6 * q^11 + 2 * q^14 - 6 * q^15 + 2 * q^16 - 24 * q^19 + 4 * q^20 + 6 * q^21 - 6 * q^25 - 4 * q^26 + 20 * q^29 - 16 * q^31 - 14 * q^34 - 4 * q^35 - 6 * q^36 - 6 * q^39 + 6 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 + 2 * q^49 - 8 * q^50 + 18 * q^54 + 24 * q^55 + 6 * q^56 + 8 * q^59 + 6 * q^60 - 20 * q^61 - 28 * q^64 + 2 * q^65 + 18 * q^66 - 4 * q^70 - 20 * q^71 - 16 * q^74 - 24 * q^75 + 12 * q^76 + 14 * q^79 + 8 * q^80 + 36 * q^81 - 14 * q^85 - 8 * q^86 + 72 * q^89 - 12 * q^90 - 4 * q^91 - 18 * q^94 - 24 * q^95 - 30 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	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
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	3.00000i		−	1.06066i
$9$	3.00000			1.00000
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	−0.866025	−	1.50000i	−0.250000	−	0.433013i
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	−0.615265	−	0.788320i	$-0.710951\pi$
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	0.375073	+	0.926995i	$0.377618\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	0.232051	+	3.86603i	0.0599153	+	0.998203i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$			7.00000i			1.69775i	0.528594	+	0.848875i	$0.322719\pi$
$17$			7.00000i			1.69775i	−0.528594	+	0.848875i	$0.677281\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	1.86603	−	1.23205i	0.417256	−	0.275495i
$21$	1.50000	+	0.866025i	0.327327	+	0.188982i
$22$	2.59808	−	1.50000i	0.553912	−	0.319801i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		−	5.19615i		−	1.06066i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−1.00000			−0.196116
$27$	5.19615			1.00000
$28$		−	1.00000i		−	0.188982i
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.142605	−	0.989780i	$-0.454452\pi$
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.785872	−	0.618389i	$-0.212214\pi$
$30$	−1.73205	+	3.46410i	−0.316228	+	0.632456i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−4.33013	+	2.50000i	−0.765466	+	0.441942i
$33$	2.59808	−	4.50000i	0.452267	−	0.783349i
$34$	−3.50000	+	6.06218i	−0.600245	+	1.03965i
$35$	−1.00000	+	2.00000i	−0.169031	+	0.338062i
$36$	−1.50000	−	2.59808i	−0.250000	−	0.433013i
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$	−5.19615	−	3.00000i	−0.842927	−	0.486664i
$39$	−1.50000	+	0.866025i	−0.240192	+	0.138675i
$40$	6.69615	−	0.401924i	1.05875	−	0.0635497i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$	0.866025	+	1.50000i	0.133631	+	0.231455i
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	0.212041	−	0.977261i	$-0.431989\pi$
$43$	−3.46410	−	2.00000i	−0.528271	−	0.304997i	−0.740312	+	0.672264i	$0.765322\pi$
$44$	−3.00000			−0.452267
$45$	0.401924	+	6.69615i	0.0599153	+	0.998203i
$46$		0			0
$47$	−7.79423	−	4.50000i	−1.13691	−	0.656392i	−0.191243	−	0.981543i	$-0.561252\pi$
$47$	−7.79423	−	4.50000i	−1.13691	−	0.656392i	−0.945662	+	0.325150i	$0.894585\pi$
$48$	0.866025	−	1.50000i	0.125000	−	0.216506i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−4.59808	−	1.96410i	−0.650266	−	0.277766i
$51$			12.1244i			1.69775i
$52$	0.866025	+	0.500000i	0.120096	+	0.0693375i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	6.00000	+	3.00000i	0.809040	+	0.404520i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	−10.3923			−1.37649
$58$	8.66025	−	5.00000i	1.13715	−	0.656532i
$59$	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	$0.749486\pi$
$60$	3.23205	−	2.13397i	0.417256	−	0.275495i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		−	8.00000i		−	1.01600i
$63$	2.59808	+	1.50000i	0.327327	+	0.188982i
$64$	−7.00000			−0.875000
$65$	−1.23205	−	1.86603i	−0.152817	−	0.231452i
$66$	4.50000	−	2.59808i	0.553912	−	0.319801i
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	6.06218	−	3.50000i	0.735147	−	0.424437i
$69$		0			0
$70$	−1.86603	+	1.23205i	−0.223033	+	0.147258i
$71$	−5.00000			−0.593391			−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000			−0.593391			−0.296695	+	0.954972i	$0.595885\pi$
$72$		−	9.00000i		−	1.06066i
$73$			3.00000i			0.351123i	0.984468	+	0.175562i	$0.0561742\pi$
$73$			3.00000i			0.351123i	−0.984468	+	0.175562i	$0.943826\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$	−8.59808	+	1.03590i	−0.992820	+	0.119615i
$76$	3.00000	+	5.19615i	0.344124	+	0.596040i
$77$	2.59808	−	1.50000i	0.296078	−	0.170941i
$78$	−1.73205			−0.196116
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	−0.599164	−	0.800626i	$-0.704500\pi$
$79$	3.50000	−	6.06218i	0.393781	−	0.682048i	0.992945	+	0.118578i	$0.0378336\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	9.00000			1.00000
$82$		−	2.00000i		−	0.220863i
$83$	4.33013	+	2.50000i	0.475293	+	0.274411i	0.718453	−	0.695576i	$-0.244851\pi$
$83$	4.33013	+	2.50000i	0.475293	+	0.274411i	−0.243160	+	0.969986i	$0.578184\pi$
$84$		−	1.73205i		−	0.188982i
$85$	−15.6244	+	0.937822i	−1.69470	+	0.101721i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	8.66025	−	15.0000i	0.928477	−	1.60817i
$88$	−7.79423	−	4.50000i	−0.830868	−	0.479702i
$89$	18.0000			1.90800			0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000			1.90800			0.953998	+	0.299813i	$0.0969242\pi$
$90$	−3.00000	+	6.00000i	−0.316228	+	0.632456i
$91$	−1.00000			−0.104828
$92$		0			0
$93$	−6.92820	−	12.0000i	−0.718421	−	1.24434i
$94$	−4.50000	−	7.79423i	−0.464140	−	0.803913i
$95$	−0.803848	−	13.3923i	−0.0824730	−	1.37402i
$96$	−7.50000	+	4.33013i	−0.765466	+	0.441942i
$97$	4.33013	+	2.50000i	0.439658	+	0.253837i	0.703452	−	0.710742i	$-0.251641\pi$
$97$	4.33013	+	2.50000i	0.439658	+	0.253837i	−0.263795	+	0.964579i	$0.584974\pi$
$98$			1.00000i			0.101015i
$99$	4.50000	−	7.79423i	0.452267	−	0.783349i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−6.06218	+	10.5000i	−0.600245	+	1.03965i
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	−0.319531	−	0.947576i	$-0.603525\pi$
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	0.660859	+	0.750510i	$0.270192\pi$
$104$	1.50000	+	2.59808i	0.147087	+	0.254762i
$105$	−1.73205	+	3.46410i	−0.169031	+	0.338062i
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$			10.0000i			0.966736i	0.875417	+	0.483368i	$0.160587\pi$
$107$			10.0000i			0.966736i	−0.875417	+	0.483368i	$0.839413\pi$
$108$	−2.59808	−	4.50000i	−0.250000	−	0.433013i
$109$	−5.00000			−0.478913			−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000			−0.478913			−0.239457	+	0.970907i	$0.576969\pi$
$110$	3.69615	+	5.59808i	0.352414	+	0.533756i
$111$			13.8564i			1.31519i
$112$	0.866025	−	0.500000i	0.0818317	−	0.0472456i
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	−0.235269	−	0.971930i	$-0.575597\pi$
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	0.724082	+	0.689714i	$0.242264\pi$
$114$	−9.00000	−	5.19615i	−0.842927	−	0.486664i
$115$		0			0
$116$	−10.0000			−0.928477
$117$	−2.59808	+	1.50000i	−0.240192	+	0.138675i
$118$			4.00000i			0.368230i
$119$	−3.50000	+	6.06218i	−0.320844	+	0.555719i
$120$	11.5981	−	0.696152i	1.05875	−	0.0635497i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−8.66025	+	5.00000i	−0.784063	+	0.452679i
$123$	−1.73205	−	3.00000i	−0.156174	−	0.270501i
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	1.50000	+	2.59808i	0.133631	+	0.231455i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	2.59808	+	1.50000i	0.229640	+	0.132583i
$129$	−6.00000	−	3.46410i	−0.528271	−	0.304997i
$130$	−0.133975	−	2.23205i	−0.0117503	−	0.195764i
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$	−5.19615			−0.452267
$133$	−5.19615	−	3.00000i	−0.450564	−	0.260133i
$134$	−4.00000			−0.345547
$135$	0.696152	+	11.5981i	0.0599153	+	0.998203i
$136$	21.0000			1.80074
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	0.905314	−	0.424743i	$-0.139635\pi$
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	−0.820495	+	0.571654i	$0.806302\pi$
$140$	2.23205	−	0.133975i	0.188643	−	0.0113229i
$141$	−13.5000	−	7.79423i	−1.13691	−	0.656392i
$142$	−4.33013	−	2.50000i	−0.363376	−	0.209795i
$143$			3.00000i			0.250873i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	20.0000	+	10.0000i	1.66091	+	0.830455i
$146$	−1.50000	+	2.59808i	−0.124141	+	0.215018i
$147$	0.866025	+	1.50000i	0.0714286	+	0.123718i
$148$	6.92820	−	4.00000i	0.569495	−	0.328798i
$149$	9.50000	+	16.4545i	0.778270	+	1.34800i	0.932938	+	0.360037i	$0.117236\pi$
$149$	9.50000	+	16.4545i	0.778270	+	1.34800i	−0.154668	+	0.987967i	$0.549431\pi$
$150$	−7.96410	−	3.40192i	−0.650266	−	0.277766i
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	0.935857	−	0.352381i	$-0.114628\pi$
$152$			18.0000i			1.45999i
$153$			21.0000i			1.69775i
$154$	3.00000			0.241747
$155$	14.9282	−	9.85641i	1.19906	−	0.791686i
$156$	1.50000	+	0.866025i	0.120096	+	0.0693375i
$157$	18.1865	−	10.5000i	1.45144	−	0.837991i	0.452880	−	0.891572i	$-0.350397\pi$
$157$	18.1865	−	10.5000i	1.45144	−	0.837991i	0.998564	+	0.0535803i	$0.0170633\pi$
$158$	6.06218	−	3.50000i	0.482281	−	0.278445i
$159$		−	10.3923i		−	0.824163i
$160$	−6.16025	−	9.33013i	−0.487011	−	0.737611i
$161$		0			0
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$		−	10.0000i		−	0.783260i	−0.920123	−	0.391630i	$-0.871911\pi$
$163$		−	10.0000i		−	0.783260i	0.920123	−	0.391630i	$-0.128089\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$	10.3923	+	5.19615i	0.809040	+	0.404520i
$166$	2.50000	+	4.33013i	0.194038	+	0.336083i
$167$	12.9904	−	7.50000i	1.00523	−	0.580367i	0.0954356	−	0.995436i	$-0.469576\pi$
$167$	12.9904	−	7.50000i	1.00523	−	0.580367i	0.909790	+	0.415068i	$0.136242\pi$
$168$	2.59808	−	4.50000i	0.200446	−	0.347183i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−14.0000	−	7.00000i	−1.07375	−	0.536875i
$171$	−18.0000			−1.37649
$172$			4.00000i			0.304997i
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$	15.0000	−	8.66025i	1.13715	−	0.656532i
$175$	−4.59808	−	1.96410i	−0.347582	−	0.148472i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	3.46410	+	6.00000i	0.260378	+	0.450988i
$178$	15.5885	+	9.00000i	1.16840	+	0.674579i
$179$	11.0000			0.822179			0.411089	−	0.911595i	$-0.365148\pi$
$179$	11.0000			0.822179			0.411089	+	0.911595i	$0.365148\pi$
$180$	5.59808	−	3.69615i	0.417256	−	0.275495i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$	−0.866025	−	0.500000i	−0.0641941	−	0.0370625i
$183$	−8.66025	+	15.0000i	−0.640184	+	1.10883i
$184$		0			0
$185$	−17.8564	+	1.07180i	−1.31283	+	0.0788001i
$186$		−	13.8564i		−	1.01600i
$187$	18.1865	+	10.5000i	1.32993	+	0.767836i
$188$			9.00000i			0.656392i
$189$	4.50000	+	2.59808i	0.327327	+	0.188982i
$190$	6.00000	−	12.0000i	0.435286	−	0.870572i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−12.1244			−0.875000
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	−0.619467	−	0.785022i	$-0.712651\pi$
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	0.370116	+	0.928986i	$0.379318\pi$
$194$	2.50000	+	4.33013i	0.179490	+	0.310885i
$195$	−2.13397	−	3.23205i	−0.152817	−	0.231452i
$196$	0.500000	−	0.866025i	0.0357143	−	0.0618590i
$197$		−	4.00000i		−	0.284988i	−0.989796	−	0.142494i	$-0.954488\pi$
$197$		−	4.00000i		−	0.284988i	0.989796	−	0.142494i	$-0.0455122\pi$
$198$	7.79423	−	4.50000i	0.553912	−	0.319801i
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$	1.79423	+	14.8923i	0.126871	+	1.05304i
$201$	−6.00000	+	3.46410i	−0.423207	+	0.244339i
$202$		0			0
$203$	8.66025	−	5.00000i	0.607831	−	0.350931i
$204$	10.5000	−	6.06218i	0.735147	−	0.424437i
$205$	3.73205	−	2.46410i	0.260658	−	0.172100i
$206$	4.00000			0.278693
$207$		0			0
$208$			1.00000i			0.0693375i
$209$	−9.00000	+	15.5885i	−0.622543	+	1.07828i
$210$	−3.23205	+	2.13397i	−0.223033	+	0.147258i
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$	−5.19615	+	3.00000i	−0.356873	+	0.206041i
$213$	−8.66025			−0.593391
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$		−	15.5885i		−	1.06066i
$217$		−	8.00000i		−	0.543075i
$218$	−4.33013	−	2.50000i	−0.293273	−	0.169321i
$219$			5.19615i			0.351123i
$220$	−0.401924	−	6.69615i	−0.0270977	−	0.451455i
$221$	−3.50000	−	6.06218i	−0.235435	−	0.407786i
$222$	−6.92820	+	12.0000i	−0.464991	+	0.805387i
$223$	−18.1865	−	10.5000i	−1.21786	−	0.703132i	−0.253401	−	0.967361i	$-0.581549\pi$
$223$	−18.1865	−	10.5000i	−1.21786	−	0.703132i	−0.964460	+	0.264229i	$0.914882\pi$
$224$	−5.00000			−0.334077
$225$	−14.8923	+	1.79423i	−0.992820	+	0.119615i
$226$	6.00000			0.399114
$227$	−9.52628	−	5.50000i	−0.632281	−	0.365048i	0.149354	−	0.988784i	$-0.452281\pi$
$227$	−9.52628	−	5.50000i	−0.632281	−	0.365048i	−0.781635	+	0.623736i	$0.785614\pi$
$228$	5.19615	+	9.00000i	0.344124	+	0.596040i
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$	4.50000	−	2.59808i	0.296078	−	0.170941i
$232$	−25.9808	−	15.0000i	−1.70572	−	0.984798i
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$	−3.00000			−0.196116
$235$	9.00000	−	18.0000i	0.587095	−	1.17419i
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$	6.06218	−	10.5000i	0.393781	−	0.682048i
$238$	−6.06218	+	3.50000i	−0.392953	+	0.226871i
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$	3.46410	+	1.73205i	0.223607	+	0.111803i
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	7.00000	−	12.1244i	0.450910	−	0.780998i	0.998443	+	0.0557856i	$0.0177663\pi$
$242$			2.00000i			0.128565i
$243$	15.5885			1.00000
$244$	10.0000			0.640184
$245$	−1.86603	+	1.23205i	−0.119216	+	0.0787128i
$246$		−	3.46410i		−	0.220863i
$247$	5.19615	−	3.00000i	0.330623	−	0.190885i
$248$	−20.7846	+	12.0000i	−1.31982	+	0.762001i
$249$	7.50000	+	4.33013i	0.475293	+	0.274411i
$250$	3.76795	−	10.5263i	0.238306	−	0.665740i
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$		−	3.00000i		−	0.188982i
$253$		0			0
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	−27.0622	+	1.62436i	−1.69470	+	0.101721i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	6.06218	−	3.50000i	0.378148	−	0.218324i	−0.298864	−	0.954296i	$-0.596608\pi$
$257$	6.06218	−	3.50000i	0.378148	−	0.218324i	0.677012	+	0.735972i	$0.263274\pi$
$258$	−3.46410	−	6.00000i	−0.215666	−	0.373544i
$259$	−4.00000	+	6.92820i	−0.248548	+	0.430498i
$260$	−1.00000	+	2.00000i	−0.0620174	+	0.124035i
$261$	15.0000	−	25.9808i	0.928477	−	1.60817i
$262$			8.00000i			0.494242i
$263$	15.5885	+	9.00000i	0.961225	+	0.554964i	0.896550	−	0.442943i	$-0.146065\pi$
$263$	15.5885	+	9.00000i	0.961225	+	0.554964i	0.0646755	+	0.997906i	$0.479399\pi$
$264$	−13.5000	−	7.79423i	−0.830868	−	0.479702i
$265$	13.3923	−	0.803848i	0.822683	−	0.0493800i
$266$	−3.00000	−	5.19615i	−0.183942	−	0.318597i
$267$	31.1769			1.90800
$268$	3.46410	+	2.00000i	0.211604	+	0.122169i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$	−5.19615	+	10.3923i	−0.316228	+	0.632456i
$271$	−14.0000			−0.850439			−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000			−0.850439			−0.425220	+	0.905090i	$0.639803\pi$
$272$	6.06218	+	3.50000i	0.367574	+	0.212219i
$273$	−1.73205			−0.104828
$274$		0			0
$275$	−5.89230	+	13.7942i	−0.355319	+	0.831823i
$276$		0			0
$277$	−22.5167	−	13.0000i	−1.35290	−	0.781094i	−0.364241	−	0.931305i	$-0.618672\pi$
$277$	−22.5167	−	13.0000i	−1.35290	−	0.781094i	−0.988654	+	0.150210i	$0.952005\pi$
$278$			2.00000i			0.119952i
$279$	−12.0000	−	20.7846i	−0.718421	−	1.24434i
$280$	6.00000	+	3.00000i	0.358569	+	0.179284i
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	0.430165	+	0.902750i	$0.358455\pi$
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	−0.996887	+	0.0788417i	$0.974878\pi$
$282$	−7.79423	−	13.5000i	−0.464140	−	0.803913i
$283$	−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	$0.439351\pi$
$284$	2.50000	+	4.33013i	0.148348	+	0.256946i
$285$	−1.39230	−	23.1962i	−0.0824730	−	1.37402i
$286$	−1.50000	+	2.59808i	−0.0886969	+	0.153627i
$287$		−	2.00000i		−	0.118056i
$288$	−12.9904	+	7.50000i	−0.765466	+	0.441942i
$289$	−32.0000			−1.88235
$290$	12.3205	+	18.6603i	0.723485	+	1.09577i
$291$	7.50000	+	4.33013i	0.439658	+	0.253837i
$292$	2.59808	−	1.50000i	0.152041	−	0.0877809i
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.880652	−	0.473763i	$-0.842895\pi$
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.0300351	+	0.999549i	$0.509562\pi$
$294$			1.73205i			0.101015i
$295$	−7.46410	+	4.92820i	−0.434577	+	0.286931i
$296$	24.0000			1.39497
$297$	7.79423	−	13.5000i	0.452267	−	0.783349i
$298$			19.0000i			1.10064i
$299$		0			0
$300$	5.19615	+	6.92820i	0.300000	+	0.400000i
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	16.4545	−	9.50000i	0.946849	−	0.546664i
$303$		0			0
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$	−20.0000	−	10.0000i	−1.14520	−	0.572598i
$306$	−10.5000	+	18.1865i	−0.600245	+	1.03965i
$307$		−	23.0000i		−	1.31268i	−0.754466	−	0.656340i	$-0.772104\pi$
$307$		−	23.0000i		−	1.31268i	0.754466	−	0.656340i	$-0.227896\pi$
$308$	−2.59808	−	1.50000i	−0.148039	−	0.0854704i
$309$	6.00000	−	3.46410i	0.341328	−	0.197066i
$310$	17.8564	−	1.07180i	1.01418	−	0.0608740i
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$	2.59808	+	4.50000i	0.147087	+	0.254762i
$313$	−5.19615	−	3.00000i	−0.293704	−	0.169570i	0.345907	−	0.938269i	$-0.387571\pi$
$313$	−5.19615	−	3.00000i	−0.293704	−	0.169570i	−0.639611	+	0.768699i	$0.720905\pi$
$314$	21.0000			1.18510
$315$	−3.00000	+	6.00000i	−0.169031	+	0.338062i
$316$	−7.00000			−0.393781
$317$	−10.3923	−	6.00000i	−0.583690	−	0.336994i	0.178908	−	0.983866i	$-0.442743\pi$
$317$	−10.3923	−	6.00000i	−0.583690	−	0.336994i	−0.762598	+	0.646872i	$0.776077\pi$
$318$	5.19615	−	9.00000i	0.291386	−	0.504695i
$319$	−15.0000	−	25.9808i	−0.839839	−	1.45464i
$320$	−0.937822	−	15.6244i	−0.0524259	−	0.873428i
$321$			17.3205i			0.966736i
$322$		0			0
$323$		−	42.0000i		−	2.33694i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	4.00000	−	3.00000i	0.221880	−	0.166410i
$326$	5.00000	−	8.66025i	0.276924	−	0.479647i
$327$	−8.66025			−0.478913
$328$	−5.19615	+	3.00000i	−0.286910	+	0.165647i
$329$	−4.50000	−	7.79423i	−0.248093	−	0.429710i
$330$	6.40192	+	9.69615i	0.352414	+	0.533756i
$331$	16.5000	−	28.5788i	0.906922	−	1.57084i	0.0886058	−	0.996067i	$-0.471759\pi$
$331$	16.5000	−	28.5788i	0.906922	−	1.57084i	0.818316	−	0.574768i	$-0.194908\pi$
$332$		−	5.00000i		−	0.274411i
$333$			24.0000i			1.31519i
$334$	15.0000			0.820763
$335$	−4.92820	−	7.46410i	−0.269257	−	0.407807i
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	−10.3923	+	6.00000i	−0.566105	+	0.326841i	−0.755592	−	0.655042i	$-0.772651\pi$
$337$	−10.3923	+	6.00000i	−0.566105	+	0.326841i	0.189487	+	0.981883i	$0.439317\pi$
$338$	−10.3923	+	6.00000i	−0.565267	+	0.326357i
$339$	9.00000	−	5.19615i	0.488813	−	0.282216i
$340$	8.62436	+	13.0622i	0.467721	+	0.708396i
$341$	−24.0000			−1.29967
$342$	−15.5885	−	9.00000i	−0.842927	−	0.486664i
$343$			1.00000i			0.0539949i
$344$	−6.00000	+	10.3923i	−0.323498	+	0.560316i
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$	−17.3205			−0.928477
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	−3.00000	−	4.00000i	−0.160357	−	0.213809i
$351$	−4.50000	+	2.59808i	−0.240192	+	0.138675i
$352$			15.0000i			0.799503i
$353$	12.1244	+	7.00000i	0.645314	+	0.372572i	0.786659	−	0.617388i	$-0.211809\pi$
$353$	12.1244	+	7.00000i	0.645314	+	0.372572i	−0.141344	+	0.989960i	$0.545142\pi$
$354$			6.92820i			0.368230i
$355$	−0.669873	−	11.1603i	−0.0355532	−	0.592325i
$356$	−9.00000	−	15.5885i	−0.476999	−	0.826187i
$357$	−6.06218	+	10.5000i	−0.320844	+	0.555719i
$358$	9.52628	+	5.50000i	0.503480	+	0.290684i
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$	20.0885	−	1.20577i	1.05875	−	0.0635497i
$361$	17.0000			0.894737
$362$	−15.5885	−	9.00000i	−0.819311	−	0.473029i
$363$	1.73205	+	3.00000i	0.0909091	+	0.157459i
$364$	0.500000	+	0.866025i	0.0262071	+	0.0453921i
$365$	−6.69615	+	0.401924i	−0.350493	+	0.0210377i
$366$	−15.0000	+	8.66025i	−0.784063	+	0.452679i
$367$	18.1865	+	10.5000i	0.949329	+	0.548096i	0.892873	−	0.450310i	$-0.148686\pi$
$367$	18.1865	+	10.5000i	0.949329	+	0.548096i	0.0564568	+	0.998405i	$0.482020\pi$
$368$		0			0
$369$	−3.00000	−	5.19615i	−0.156174	−	0.270501i
$370$	−16.0000	−	8.00000i	−0.831800	−	0.415900i
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$	−6.92820	+	12.0000i	−0.359211	+	0.622171i
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	−0.628454	−	0.777847i	$-0.716312\pi$
$373$	−5.19615	+	3.00000i	−0.269047	+	0.155334i	0.359408	+	0.933181i	$0.382979\pi$
$374$	10.5000	+	18.1865i	0.542942	+	0.940403i
$375$	−3.46410	−	19.0526i	−0.178885	−	0.983870i
$376$	−13.5000	+	23.3827i	−0.696209	+	1.20587i
$377$			10.0000i			0.515026i
$378$	2.59808	+	4.50000i	0.133631	+	0.231455i
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$	−11.1962	+	7.39230i	−0.574351	+	0.379217i
$381$			13.8564i			0.709885i
$382$		0			0
$383$	−16.4545	+	9.50000i	−0.840785	+	0.485427i	−0.857531	−	0.514432i	$-0.828003\pi$
$383$	−16.4545	+	9.50000i	−0.840785	+	0.485427i	0.0167461	+	0.999860i	$0.494669\pi$
$384$	4.50000	+	2.59808i	0.229640	+	0.132583i
$385$	3.69615	+	5.59808i	0.188373	+	0.285304i
$386$	−4.00000			−0.203595
$387$	−10.3923	−	6.00000i	−0.528271	−	0.304997i
$388$		−	5.00000i		−	0.253837i
$389$	14.5000	−	25.1147i	0.735179	−	1.27337i	−0.219465	−	0.975620i	$-0.570431\pi$
$389$	14.5000	−	25.1147i	0.735179	−	1.27337i	0.954645	−	0.297747i	$-0.0962353\pi$
$390$	−0.232051	−	3.86603i	−0.0117503	−	0.195764i
$391$		0			0
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	6.92820	+	12.0000i	0.349482	+	0.605320i
$394$	2.00000	−	3.46410i	0.100759	−	0.174519i
$395$	14.0000	+	7.00000i	0.704416	+	0.352208i
$396$	−9.00000			−0.452267
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	3.46410	+	2.00000i	0.173640	+	0.100251i
$399$	−9.00000	−	5.19615i	−0.450564	−	0.260133i
$400$	−1.96410	+	4.59808i	−0.0982051	+	0.229904i
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	−6.92820			−0.345547
$403$	6.92820	+	4.00000i	0.345118	+	0.199254i
$404$		0			0
$405$	1.20577	+	20.0885i	0.0599153	+	0.998203i
$406$	10.0000			0.496292
$407$	20.7846	+	12.0000i	1.03025	+	0.594818i
$408$	36.3731			1.80074
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	0.812333	−	0.583193i	$-0.198197\pi$
$409$	−2.00000	−	3.46410i	−0.0988936	−	0.171289i	−0.911227	+	0.411905i	$0.864864\pi$
$410$	4.46410	−	0.267949i	0.220466	−	0.0132331i
$411$		0			0
$412$	−3.46410	−	2.00000i	−0.170664	−	0.0985329i
$413$			4.00000i			0.196827i
$414$		0			0
$415$	−5.00000	+	10.0000i	−0.245440	+	0.490881i
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	1.73205	+	3.00000i	0.0848189	+	0.146911i
$418$	−15.5885	+	9.00000i	−0.762456	+	0.440204i
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$	3.86603	−	0.232051i	0.188643	−	0.0113229i
$421$	−10.5000	+	18.1865i	−0.511739	+	0.886357i	0.488169	+	0.872749i	$0.337665\pi$
$421$	−10.5000	+	18.1865i	−0.511739	+	0.886357i	−0.999907	+	0.0136081i	$0.995668\pi$
$422$			13.0000i			0.632830i
$423$	−23.3827	−	13.5000i	−1.13691	−	0.656392i
$424$	−18.0000			−0.874157
$425$	−4.18653	−	34.7487i	−0.203077	−	1.68556i
$426$	−7.50000	−	4.33013i	−0.363376	−	0.209795i
$427$	−8.66025	+	5.00000i	−0.419099	+	0.241967i
$428$	8.66025	−	5.00000i	0.418609	−	0.241684i
$429$			5.19615i			0.250873i
$430$	7.46410	−	4.92820i	0.359951	−	0.237659i
$431$	7.00000			0.337178			0.168589	−	0.985686i	$-0.446079\pi$
$431$	7.00000			0.337178			0.168589	+	0.985686i	$0.446079\pi$
$432$	2.59808	−	4.50000i	0.125000	−	0.216506i
$433$			22.0000i			1.05725i	0.848855	+	0.528626i	$0.177293\pi$
$433$			22.0000i			1.05725i	−0.848855	+	0.528626i	$0.822707\pi$
$434$	4.00000	−	6.92820i	0.192006	−	0.332564i
$435$	34.6410	+	17.3205i	1.66091	+	0.830455i
$436$	2.50000	+	4.33013i	0.119728	+	0.207375i
$437$		0			0
$438$	−2.59808	+	4.50000i	−0.124141	+	0.215018i
$439$	18.0000	−	31.1769i	0.859093	−	1.48799i	−0.0137020	−	0.999906i	$-0.504362\pi$
$439$	18.0000	−	31.1769i	0.859093	−	1.48799i	0.872795	−	0.488087i	$-0.162305\pi$
$440$	9.00000	−	18.0000i	0.429058	−	0.858116i
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		−	7.00000i		−	0.332956i
$443$	−13.8564	−	8.00000i	−0.658338	−	0.380091i	0.133306	−	0.991075i	$-0.457441\pi$
$443$	−13.8564	−	8.00000i	−0.658338	−	0.380091i	−0.791643	+	0.610984i	$0.790774\pi$
$444$	12.0000	−	6.92820i	0.569495	−	0.328798i
$445$	2.41154	+	40.1769i	0.114318	+	1.90457i
$446$	−10.5000	−	18.1865i	−0.497189	−	0.861157i
$447$	16.4545	+	28.5000i	0.778270	+	1.34800i
$448$	−6.06218	−	3.50000i	−0.286411	−	0.165359i
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	−13.7942	−	5.89230i	−0.650266	−	0.277766i
$451$	−6.00000			−0.282529
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$	16.4545	−	28.5000i	0.773099	−	1.33905i
$454$	−5.50000	−	9.52628i	−0.258128	−	0.447090i
$455$	−0.133975	−	2.23205i	−0.00628083	−	0.104640i
$456$			31.1769i			1.45999i
$457$	6.92820	+	4.00000i	0.324088	+	0.187112i	0.653213	−	0.757174i	$-0.273421\pi$
$457$	6.92820	+	4.00000i	0.324088	+	0.187112i	−0.329125	+	0.944286i	$0.606754\pi$
$458$		−	4.00000i		−	0.186908i
$459$			36.3731i			1.69775i
$460$		0			0
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	−0.691800	−	0.722089i	$-0.743182\pi$
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	0.971248	+	0.238071i	$0.0765153\pi$
$462$	5.19615			0.241747
$463$	10.3923	−	6.00000i	0.482971	−	0.278844i	−0.238683	−	0.971098i	$-0.576716\pi$
$463$	10.3923	−	6.00000i	0.482971	−	0.278844i	0.721654	+	0.692254i	$0.243382\pi$
$464$	−5.00000	−	8.66025i	−0.232119	−	0.402042i
$465$	25.8564	−	17.0718i	1.19906	−	0.791686i
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$		−	21.0000i		−	0.971764i	−0.874024	−	0.485882i	$-0.838498\pi$
$467$		−	21.0000i		−	0.971764i	0.874024	−	0.485882i	$-0.161502\pi$
$468$	2.59808	+	1.50000i	0.120096	+	0.0693375i
$469$	−4.00000			−0.184703
$470$	16.7942	−	11.0885i	0.774660	−	0.511472i
$471$	31.5000	−	18.1865i	1.45144	−	0.837991i
$472$	10.3923	−	6.00000i	0.478345	−	0.276172i
$473$	−10.3923	+	6.00000i	−0.477839	+	0.275880i
$474$	10.5000	−	6.06218i	0.482281	−	0.278445i
$475$	29.7846	−	3.58846i	1.36661	−	0.164650i
$476$	7.00000			0.320844
$477$		−	18.0000i		−	0.824163i
$478$			12.0000i			0.548867i
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$	−10.6699	−	16.1603i	−0.487011	−	0.737611i
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$	12.1244	−	7.00000i	0.552249	−	0.318841i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−5.00000	+	10.0000i	−0.227038	+	0.454077i
$486$	13.5000	+	7.79423i	0.612372	+	0.353553i
$487$		−	12.0000i		−	0.543772i	−0.962329	−	0.271886i	$-0.912353\pi$
$487$		−	12.0000i		−	0.543772i	0.962329	−	0.271886i	$-0.0876473\pi$
$488$	25.9808	+	15.0000i	1.17609	+	0.679018i
$489$		−	17.3205i		−	0.783260i
$490$	−2.23205	+	0.133975i	−0.100834	+	0.00605236i
$491$	5.50000	+	9.52628i	0.248212	+	0.429915i	0.963030	−	0.269395i	$-0.0868239\pi$
$491$	5.50000	+	9.52628i	0.248212	+	0.429915i	−0.714818	+	0.699310i	$0.753491\pi$
$492$	−1.73205	+	3.00000i	−0.0780869	+	0.135250i
$493$	60.6218	+	35.0000i	2.73027	+	1.57632i
$494$	6.00000			0.269953
$495$	18.0000	+	9.00000i	0.809040	+	0.404520i
$496$	−8.00000			−0.359211
$497$	−4.33013	−	2.50000i	−0.194233	−	0.112140i
$498$	4.33013	+	7.50000i	0.194038	+	0.336083i
$499$	9.50000	+	16.4545i	0.425278	+	0.736604i	0.996446	−	0.0842294i	$-0.0268429\pi$
$499$	9.50000	+	16.4545i	0.425278	+	0.736604i	−0.571168	+	0.820833i	$0.693510\pi$
$500$	−8.52628	+	7.23205i	−0.381307	+	0.323427i
$501$	22.5000	−	12.9904i	1.00523	−	0.580367i
$502$	5.19615	+	3.00000i	0.231916	+	0.133897i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$	4.50000	−	7.79423i	0.200446	−	0.347183i
$505$		0			0
$506$		0			0
$507$	−10.3923	+	18.0000i	−0.461538	+	0.799408i
$508$	6.92820	−	4.00000i	0.307389	−	0.177471i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$	−24.2487	−	12.1244i	−1.07375	−	0.536875i
$511$	−1.50000	+	2.59808i	−0.0663561	+	0.114932i
$512$			11.0000i			0.486136i
$513$	−31.1769			−1.37649
$514$	7.00000			0.308757
$515$	4.92820	+	7.46410i	0.217163	+	0.328908i
$516$			6.92820i			0.304997i
$517$	−23.3827	+	13.5000i	−1.02837	+	0.593729i
$518$	−6.92820	+	4.00000i	−0.304408	+	0.175750i
$519$	−9.00000	−	5.19615i	−0.395056	−	0.228086i
$520$	−5.59808	+	3.69615i	−0.245492	+	0.162087i
$521$	8.00000			0.350486			0.175243	−	0.984525i	$-0.443929\pi$
$521$	8.00000			0.350486			0.175243	+	0.984525i	$0.443929\pi$
$522$	25.9808	−	15.0000i	1.13715	−	0.656532i
$523$		−	11.0000i		−	0.480996i	−0.970650	−	0.240498i	$-0.922689\pi$
$523$		−	11.0000i		−	0.480996i	0.970650	−	0.240498i	$-0.0773108\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$	−7.96410	−	3.40192i	−0.347582	−	0.148472i
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	48.4974	−	28.0000i	2.11258	−	1.21970i
$528$	−2.59808	−	4.50000i	−0.113067	−	0.195837i
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$	12.0000	+	6.00000i	0.521247	+	0.260623i
$531$	6.00000	+	10.3923i	0.260378	+	0.450988i
$532$			6.00000i			0.260133i
$533$	1.73205	+	1.00000i	0.0750234	+	0.0433148i
$534$	27.0000	+	15.5885i	1.16840	+	0.674579i
$535$	−22.3205	+	1.33975i	−0.965000	+	0.0579223i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	19.0526			0.822179
$538$	−8.66025	−	5.00000i	−0.373370	−	0.215565i
$539$	3.00000			0.129219
$540$	9.69615	−	6.40192i	0.417256	−	0.275495i
$541$	−33.0000			−1.41878			−0.709390	−	0.704816i	$-0.751030\pi$
$541$	−33.0000			−1.41878			−0.709390	+	0.704816i	$0.751030\pi$
$542$	−12.1244	−	7.00000i	−0.520786	−	0.300676i
$543$	−31.1769			−1.33793
$544$	−17.5000	−	30.3109i	−0.750306	−	1.29957i
$545$	−0.669873	−	11.1603i	−0.0286942	−	0.478053i
$546$	−1.50000	−	0.866025i	−0.0641941	−	0.0370625i
$547$	3.46410	+	2.00000i	0.148114	+	0.0855138i	0.572226	−	0.820096i	$-0.306080\pi$
$547$	3.46410	+	2.00000i	0.148114	+	0.0855138i	−0.424111	+	0.905610i	$0.639413\pi$
$548$		0			0
$549$	−15.0000	+	25.9808i	−0.640184	+	1.10883i
$550$	−12.0000	+	9.00000i	−0.511682	+	0.383761i
$551$	−30.0000	+	51.9615i	−1.27804	+	2.21364i
$552$		0			0
$553$	6.06218	−	3.50000i	0.257790	−	0.148835i
$554$	−13.0000	−	22.5167i	−0.552317	−	0.956641i
$555$	−30.9282	+	1.85641i	−1.31283	+	0.0788001i
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$		−	4.00000i		−	0.169485i	−0.996403	−	0.0847427i	$-0.972993\pi$
$557$		−	4.00000i		−	0.169485i	0.996403	−	0.0847427i	$-0.0270068\pi$
$558$		−	24.0000i		−	1.01600i
$559$	4.00000			0.169182
$560$	1.23205	+	1.86603i	0.0520636	+	0.0788540i
$561$	31.5000	+	18.1865i	1.32993	+	0.767836i
$562$	−16.4545	+	9.50000i	−0.694090	+	0.400733i
$563$	−7.79423	+	4.50000i	−0.328488	+	0.189652i	−0.655169	−	0.755482i	$-0.727403\pi$
$563$	−7.79423	+	4.50000i	−0.328488	+	0.189652i	0.326682	+	0.945134i	$0.394069\pi$
$564$			15.5885i			0.656392i
$565$	7.39230	+	11.1962i	0.310997	+	0.471026i
$566$	−11.0000			−0.462364
$567$	7.79423	+	4.50000i	0.327327	+	0.188982i
$568$			15.0000i			0.629386i
$569$	16.5000	−	28.5788i	0.691716	−	1.19809i	−0.279559	−	0.960128i	$-0.590188\pi$
$569$	16.5000	−	28.5788i	0.691716	−	1.19809i	0.971275	−	0.237959i	$-0.0764783\pi$
$570$	10.3923	−	20.7846i	0.435286	−	0.870572i
$571$	−1.50000	−	2.59808i	−0.0627730	−	0.108726i	0.832931	−	0.553377i	$-0.186661\pi$
$571$	−1.50000	−	2.59808i	−0.0627730	−	0.108726i	−0.895704	+	0.444651i	$0.853328\pi$
$572$	2.59808	−	1.50000i	0.108631	−	0.0627182i
$573$		0			0
$574$	1.00000	−	1.73205i	0.0417392	−	0.0722944i
$575$		0			0
$576$	−21.0000			−0.875000
$577$		−	7.00000i		−	0.291414i	−0.989328	−	0.145707i	$-0.953454\pi$
$577$		−	7.00000i		−	0.291414i	0.989328	−	0.145707i	$-0.0465456\pi$
$578$	−27.7128	−	16.0000i	−1.15270	−	0.665512i
$579$	−6.00000	+	3.46410i	−0.249351	+	0.143963i
$580$	−1.33975	−	22.3205i	−0.0556299	−	0.926809i
$581$	2.50000	+	4.33013i	0.103717	+	0.179644i
$582$	4.33013	+	7.50000i	0.179490	+	0.310885i
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$	9.00000			0.372423
$585$	−3.69615	−	5.59808i	−0.152817	−	0.231452i
$586$	−18.0000			−0.743573
$587$	−31.1769	−	18.0000i	−1.28681	−	0.742940i	−0.308725	−	0.951151i	$-0.599902\pi$
$587$	−31.1769	−	18.0000i	−1.28681	−	0.742940i	−0.978084	+	0.208212i	$0.933236\pi$
$588$	0.866025	−	1.50000i	0.0357143	−	0.0618590i
$589$	24.0000	+	41.5692i	0.988903	+	1.71283i
$590$	−8.92820	+	0.535898i	−0.367568	+	0.0220626i
$591$		−	6.92820i		−	0.284988i
$592$	6.92820	+	4.00000i	0.284747	+	0.164399i
$593$			46.0000i			1.88899i	0.328521	+	0.944497i	$0.393450\pi$
$593$			46.0000i			1.88899i	−0.328521	+	0.944497i	$0.606550\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$	−14.0000	−	7.00000i	−0.573944	−	0.286972i
$596$	9.50000	−	16.4545i	0.389135	−	0.674002i
$597$	6.92820			0.283552
$598$		0			0
$599$	−2.50000	−	4.33013i	−0.102147	−	0.176924i	0.810422	−	0.585847i	$-0.199238\pi$
$599$	−2.50000	−	4.33013i	−0.102147	−	0.176924i	−0.912569	+	0.408923i	$0.865905\pi$
$600$	3.10770	+	25.7942i	0.126871	+	1.05304i
$601$	16.0000	−	27.7128i	0.652654	−	1.13043i	−0.329823	−	0.944043i	$-0.606989\pi$
$601$	16.0000	−	27.7128i	0.652654	−	1.13043i	0.982477	−	0.186386i	$-0.0596776\pi$
$602$		−	4.00000i		−	0.163028i
$603$	−10.3923	+	6.00000i	−0.423207	+	0.244339i
$604$	−19.0000			−0.773099
$605$	−3.73205	+	2.46410i	−0.151729	+	0.100180i
$606$		0			0
$607$	−31.1769	+	18.0000i	−1.26543	+	0.730597i	−0.974120	−	0.226031i	$-0.927425\pi$
$607$	−31.1769	+	18.0000i	−1.26543	+	0.730597i	−0.291312	+	0.956628i	$0.594092\pi$
$608$	25.9808	−	15.0000i	1.05366	−	0.608330i
$609$	15.0000	−	8.66025i	0.607831	−	0.350931i
$610$	−12.3205	−	18.6603i	−0.498843	−	0.755532i
$611$	9.00000			0.364101
$612$	18.1865	−	10.5000i	0.735147	−	0.424437i
$613$		−	46.0000i		−	1.85792i	−0.370177	−	0.928961i	$-0.620703\pi$
$613$		−	46.0000i		−	1.85792i	0.370177	−	0.928961i	$-0.379297\pi$
$614$	11.5000	−	19.9186i	0.464102	−	0.803849i
$615$	6.46410	−	4.26795i	0.260658	−	0.172100i
$616$	−4.50000	−	7.79423i	−0.181310	−	0.314038i
$617$	−22.5167	+	13.0000i	−0.906487	+	0.523360i	−0.879299	−	0.476270i	$-0.841988\pi$
$617$	−22.5167	+	13.0000i	−0.906487	+	0.523360i	−0.0271876	+	0.999630i	$0.508655\pi$
$618$	6.92820			0.278693
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.0376891	+	0.999290i	$0.512000\pi$
$619$	−22.0000	+	38.1051i	−0.884255	+	1.53157i	−0.846566	+	0.532284i	$0.821334\pi$
$620$	−16.0000	−	8.00000i	−0.642575	−	0.321288i
$621$		0			0
$622$			18.0000i			0.721734i
$623$	15.5885	+	9.00000i	0.624538	+	0.360577i
$624$			1.73205i			0.0693375i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	−15.5885	+	27.0000i	−0.622543	+	1.07828i
$628$	−18.1865	−	10.5000i	−0.725722	−	0.418996i
$629$	−56.0000			−2.23287
$630$	−5.59808	+	3.69615i	−0.223033	+	0.147258i
$631$	−23.0000			−0.915616			−0.457808	−	0.889051i	$-0.651365\pi$
$631$	−23.0000			−0.915616			−0.457808	+	0.889051i	$0.651365\pi$
$632$	−18.1865	−	10.5000i	−0.723421	−	0.417668i
$633$	11.2583	+	19.5000i	0.447478	+	0.775055i
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$	−17.8564	+	1.07180i	−0.708610	+	0.0425330i
$636$	−9.00000	+	5.19615i	−0.356873	+	0.206041i
$637$	−0.866025	−	0.500000i	−0.0343132	−	0.0198107i
$638$		−	30.0000i		−	1.18771i
$639$	−15.0000			−0.593391
$640$	−3.00000	+	6.00000i	−0.118585	+	0.237171i
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	−0.694025	−	0.719951i	$-0.744164\pi$
$641$	7.00000	−	12.1244i	0.276483	−	0.478883i	0.970508	+	0.241068i	$0.0774976\pi$
$642$	−8.66025	+	15.0000i	−0.341793	+	0.592003i
$643$	−0.866025	+	0.500000i	−0.0341527	+	0.0197181i	−0.516979	−	0.855998i	$-0.672944\pi$
$643$	−0.866025	+	0.500000i	−0.0341527	+	0.0197181i	0.482826	+	0.875716i	$0.339610\pi$
$644$		0			0
$645$	6.92820	−	13.8564i	0.272798	−	0.545595i
$646$	21.0000	−	36.3731i	0.826234	−	1.43108i
$647$			40.0000i			1.57256i	0.617869	+	0.786281i	$0.287996\pi$
$647$			40.0000i			1.57256i	−0.617869	+	0.786281i	$0.712004\pi$
$648$		−	27.0000i		−	1.06066i
$649$	12.0000			0.471041
$650$	4.96410	−	0.598076i	0.194708	−	0.0234585i
$651$		−	13.8564i		−	0.543075i
$652$	−8.66025	+	5.00000i	−0.339162	+	0.195815i
$653$	−1.73205	+	1.00000i	−0.0677804	+	0.0391330i	−0.533507	−	0.845796i	$-0.679126\pi$
$653$	−1.73205	+	1.00000i	−0.0677804	+	0.0391330i	0.465727	+	0.884929i	$0.345793\pi$
$654$	−7.50000	−	4.33013i	−0.293273	−	0.169321i
$655$	−14.9282	+	9.85641i	−0.583293	+	0.385122i
$656$	−2.00000			−0.0780869
$657$			9.00000i			0.351123i
$658$		−	9.00000i		−	0.350857i
$659$	−10.5000	+	18.1865i	−0.409022	+	0.708447i	−0.994780	−	0.102039i	$-0.967463\pi$
$659$	−10.5000	+	18.1865i	−0.409022	+	0.708447i	0.585758	+	0.810486i	$0.300797\pi$
$660$	−0.696152	−	11.5981i	−0.0270977	−	0.451455i
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$	28.5788	−	16.5000i	1.11075	−	0.641291i
$663$	−6.06218	−	10.5000i	−0.235435	−	0.407786i
$664$	7.50000	−	12.9904i	0.291056	−	0.504125i
$665$	6.00000	−	12.0000i	0.232670	−	0.465340i
$666$	−12.0000	+	20.7846i	−0.464991	+	0.805387i
$667$		0			0
$668$	−12.9904	−	7.50000i	−0.502613	−	0.290184i
$669$	−31.5000	−	18.1865i	−1.21786	−	0.703132i
$670$	−0.535898	−	8.92820i	−0.0207036	−	0.344927i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$	−8.66025			−0.334077
$673$	31.1769	+	18.0000i	1.20178	+	0.693849i	0.960951	−	0.276718i	$-0.0892468\pi$
$673$	31.1769	+	18.0000i	1.20178	+	0.693849i	0.240831	+	0.970567i	$0.422580\pi$
$674$	−12.0000			−0.462223
$675$	−25.7942	+	3.10770i	−0.992820	+	0.119615i
$676$	12.0000			0.461538
$677$	−14.7224	−	8.50000i	−0.565829	−	0.326682i	0.189653	−	0.981851i	$-0.439264\pi$
$677$	−14.7224	−	8.50000i	−0.565829	−	0.326682i	−0.755482	+	0.655170i	$0.772597\pi$
$678$	10.3923			0.399114
$679$	2.50000	+	4.33013i	0.0959412	+	0.166175i
$680$	2.81347	+	46.8731i	0.107892	+	1.79750i
$681$	−16.5000	−	9.52628i	−0.632281	−	0.365048i
$682$	−20.7846	−	12.0000i	−0.795884	−	0.459504i
$683$		−	40.0000i		−	1.53056i	−0.643699	−	0.765279i	$-0.722601\pi$
$683$		−	40.0000i		−	1.53056i	0.643699	−	0.765279i	$-0.277399\pi$
$684$	9.00000	+	15.5885i	0.344124	+	0.596040i
$685$		0			0
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−3.46410	−	6.00000i	−0.132164	−	0.228914i
$688$	−3.46410	+	2.00000i	−0.132068	+	0.0762493i
$689$	3.00000	+	5.19615i	0.114291	+	0.197958i
$690$		0			0
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$			6.00000i			0.228086i
$693$	7.79423	−	4.50000i	0.296078	−	0.170941i
$694$	12.0000			0.455514
$695$	−3.73205	+	2.46410i	−0.141565	+	0.0934687i
$696$	−45.0000	−	25.9808i	−1.70572	−	0.984798i
$697$	12.1244	−	7.00000i	0.459243	−	0.265144i
$698$	−12.1244	+	7.00000i	−0.458914	+	0.264954i
$699$			24.2487i			0.917170i
$700$	0.598076	+	4.96410i	0.0226052	+	0.187625i
$701$	−25.0000			−0.944237			−0.472118	−	0.881535i	$-0.656511\pi$
$701$	−25.0000			−0.944237			−0.472118	+	0.881535i	$0.656511\pi$
$702$	−5.19615			−0.196116
$703$		−	48.0000i		−	1.81035i
$704$	−10.5000	+	18.1865i	−0.395734	+	0.685431i
$705$	15.5885	−	31.1769i	0.587095	−	1.17419i
$706$	7.00000	+	12.1244i	0.263448	+	0.456306i
$707$		0			0
$708$	3.46410	−	6.00000i	0.130189	−	0.225494i
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	5.00000	−	10.0000i	0.187647	−	0.375293i
$711$	10.5000	−	18.1865i	0.393781	−	0.682048i
$712$		−	54.0000i		−	2.02374i
$713$		0			0
$714$	−10.5000	+	6.06218i	−0.392953	+	0.226871i
$715$	−6.69615	+	0.401924i	−0.250422	+	0.0150311i
$716$	−5.50000	−	9.52628i	−0.205545	−	0.356014i
$717$	10.3923	+	18.0000i	0.388108	+	0.672222i
$718$	6.92820	+	4.00000i	0.258558	+	0.149279i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	6.00000	+	3.00000i	0.223607	+	0.111803i
$721$	4.00000			0.148968
$722$	14.7224	+	8.50000i	0.547912	+	0.316337i
$723$	12.1244	−	21.0000i	0.450910	−	0.780998i
$724$	9.00000	+	15.5885i	0.334482	+	0.579340i
$725$	−19.6410	+	45.9808i	−0.729449	+	1.70768i
$726$			3.46410i			0.128565i
$727$	0.866025	+	0.500000i	0.0321191	+	0.0185440i	0.515974	−	0.856605i	$-0.327430\pi$
$727$	0.866025	+	0.500000i	0.0321191	+	0.0185440i	−0.483854	+	0.875148i	$0.660764\pi$
$728$			3.00000i			0.111187i
$729$	27.0000			1.00000
$730$	−6.00000	−	3.00000i	−0.222070	−	0.111035i
$731$	14.0000	−	24.2487i	0.517809	−	0.896871i
$732$	17.3205			0.640184
$733$	−19.0526	+	11.0000i	−0.703722	+	0.406294i	−0.808732	−	0.588177i	$-0.799846\pi$
$733$	−19.0526	+	11.0000i	−0.703722	+	0.406294i	0.105010	+	0.994471i	$0.466513\pi$
$734$	10.5000	+	18.1865i	0.387562	+	0.671277i
$735$	−3.23205	+	2.13397i	−0.119216	+	0.0787128i
$736$		0			0
$737$			12.0000i			0.442026i
$738$		−	6.00000i		−	0.220863i
$739$	−4.00000			−0.147142			−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000			−0.147142			−0.0735712	+	0.997290i	$0.523440\pi$
$740$	9.85641	+	14.9282i	0.362329	+	0.548772i
$741$	9.00000	−	5.19615i	0.330623	−	0.190885i
$742$	5.19615	−	3.00000i	0.190757	−	0.110133i
$743$	1.73205	−	1.00000i	0.0635428	−	0.0366864i	−0.467892	−	0.883786i	$-0.654986\pi$
$743$	1.73205	−	1.00000i	0.0635428	−	0.0366864i	0.531435	+	0.847099i	$0.321653\pi$
$744$	−36.0000	+	20.7846i	−1.31982	+	0.762001i
$745$	−35.4545	+	23.4090i	−1.29895	+	0.857638i
$746$	−6.00000			−0.219676
$747$	12.9904	+	7.50000i	0.475293	+	0.274411i
$748$		−	21.0000i		−	0.767836i
$749$	−5.00000	+	8.66025i	−0.182696	+	0.316439i
$750$	6.52628	−	18.2321i	0.238306	−	0.665740i
$751$	24.0000	+	41.5692i	0.875772	+	1.51688i	0.855938	+	0.517079i	$0.172981\pi$
$751$	24.0000	+	41.5692i	0.875772	+	1.51688i	0.0198348	+	0.999803i	$0.493686\pi$
$752$	−7.79423	+	4.50000i	−0.284226	+	0.164098i
$753$	10.3923			0.378717
$754$	−5.00000	+	8.66025i	−0.182089	+	0.315388i
$755$	38.0000	+	19.0000i	1.38296	+	0.691481i
$756$		−	5.19615i		−	0.188982i
$757$		−	34.0000i		−	1.23575i	−0.786276	−	0.617876i	$-0.787994\pi$
$757$		−	34.0000i		−	1.23575i	0.786276	−	0.617876i	$-0.212006\pi$
$758$	0.866025	+	0.500000i	0.0314555	+	0.0181608i
$759$		0			0
$760$	−40.1769	+	2.41154i	−1.45737	+	0.0874758i
$761$	2.00000	+	3.46410i	0.0724999	+	0.125574i	0.899996	−	0.435897i	$-0.143569\pi$
$761$	2.00000	+	3.46410i	0.0724999	+	0.125574i	−0.827496	+	0.561471i	$0.810236\pi$
$762$	−6.92820	+	12.0000i	−0.250982	+	0.434714i
$763$	−4.33013	−	2.50000i	−0.156761	−	0.0905061i
$764$		0			0
$765$	−46.8731	+	2.81347i	−1.69470	+	0.101721i
$766$	−19.0000			−0.686498
$767$	−3.46410	−	2.00000i	−0.125081	−	0.0722158i
$768$	14.7224	+	25.5000i	0.531250	+	0.920152i
$769$	24.0000	+	41.5692i	0.865462	+	1.49902i	0.866588	+	0.499025i	$0.166308\pi$
$769$	24.0000	+	41.5692i	0.865462	+	1.49902i	−0.00112544	+	0.999999i	$0.500358\pi$
$770$	0.401924	+	6.69615i	0.0144843	+	0.241313i
$771$	10.5000	−	6.06218i	0.378148	−	0.218324i
$772$	3.46410	+	2.00000i	0.124676	+	0.0719816i
$773$		−	33.0000i		−	1.18693i	−0.804861	−	0.593464i	$-0.797760\pi$
$773$		−	33.0000i		−	1.18693i	0.804861	−	0.593464i	$-0.202240\pi$
$774$	−6.00000	−	10.3923i	−0.215666	−	0.373544i
$775$	24.0000	+	32.0000i	0.862105	+	1.14947i
$776$	7.50000	−	12.9904i	0.269234	−	0.466328i
$777$	−6.92820	+	12.0000i	−0.248548	+	0.430498i
$778$	25.1147	−	14.5000i	0.900407	−	0.519850i
$779$	6.00000	+	10.3923i	0.214972	+	0.372343i
$780$	−1.73205	+	3.46410i	−0.0620174	+	0.124035i
$781$	−7.50000	+	12.9904i	−0.268371	+	0.464832i
$782$		0			0
$783$	25.9808	−	45.0000i	0.928477	−	1.60817i
$784$	1.00000			0.0357143
$785$	25.8731	+	39.1865i	0.923449	+	1.39863i
$786$			13.8564i			0.494242i
$787$	−21.6506	+	12.5000i	−0.771762	+	0.445577i	−0.833503	−	0.552515i	$-0.813668\pi$
$787$	−21.6506	+	12.5000i	−0.771762	+	0.445577i	0.0617409	+	0.998092i	$0.480335\pi$
$788$	−3.46410	+	2.00000i	−0.123404	+	0.0712470i
$789$	27.0000	+	15.5885i	0.961225	+	0.554964i
$790$	8.62436	+	13.0622i	0.306841	+	0.464731i
$791$	6.00000			0.213335
$792$	−23.3827	−	13.5000i	−0.830868	−	0.479702i
$793$		−	10.0000i		−	0.355110i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$	23.1962	−	1.39230i	0.822683	−	0.0493800i
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$	9.52628	−	5.50000i	0.337438	−	0.194820i	−0.321700	−	0.946841i	$-0.604254\pi$
$797$	9.52628	−	5.50000i	0.337438	−	0.194820i	0.659139	+	0.752022i	$0.270921\pi$
$798$	−5.19615	−	9.00000i	−0.183942	−	0.318597i
$799$	31.5000	−	54.5596i	1.11439	−	1.93018i
$800$	20.0000	−	15.0000i	0.707107	−	0.530330i
$801$	54.0000			1.90800
$802$		−	18.0000i		−	0.635602i
$803$	7.79423	+	4.50000i	0.275052	+	0.158802i
$804$	6.00000	+	3.46410i	0.211604	+	0.122169i
$805$		0			0
$806$	4.00000	+	6.92820i	0.140894	+	0.244036i
$807$	−17.3205			−0.609711
$808$		0			0
$809$	39.0000			1.37117			0.685583	−	0.727994i	$-0.259547\pi$
$809$	39.0000			1.37117			0.685583	+	0.727994i	$0.259547\pi$
$810$	−9.00000	+	18.0000i	−0.316228	+	0.632456i
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$	−8.66025	−	5.00000i	−0.303915	−	0.175466i
$813$	−24.2487			−0.850439
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	22.3205	−	1.33975i	0.781853	−	0.0469293i
$816$	10.5000	+	6.06218i	0.367574	+	0.212219i
$817$	20.7846	+	12.0000i	0.727161	+	0.419827i
$818$		−	4.00000i		−	0.139857i
$819$	−3.00000			−0.104828
$820$	−4.00000	−	2.00000i	−0.139686	−	0.0698430i
$821$	−6.50000	+	11.2583i	−0.226852	+	0.392918i	−0.956873	−	0.290505i	$-0.906177\pi$
$821$	−6.50000	+	11.2583i	−0.226852	+	0.392918i	0.730022	+	0.683424i	$0.239510\pi$
$822$		0			0
$823$	−12.1244	+	7.00000i	−0.422628	+	0.244005i	−0.696201	−	0.717847i	$-0.745128\pi$
$823$	−12.1244	+	7.00000i	−0.422628	+	0.244005i	0.273573	+	0.961851i	$0.411795\pi$
$824$	−6.00000	−	10.3923i	−0.209020	−	0.362033i
$825$	−10.2058	+	23.8923i	−0.355319	+	0.831823i
$826$	−2.00000	+	3.46410i	−0.0695889	+	0.120532i
$827$			30.0000i			1.04320i	0.853189	+	0.521601i	$0.174665\pi$
$827$			30.0000i			1.04320i	−0.853189	+	0.521601i	$0.825335\pi$
$828$		0			0
$829$	54.0000			1.87550			0.937749	−	0.347314i	$-0.112906\pi$
$829$	54.0000			1.87550			0.937749	+	0.347314i	$0.112906\pi$
$830$	−9.33013	+	6.16025i	−0.323853	+	0.213826i
$831$	−39.0000	−	22.5167i	−1.35290	−	0.781094i
$832$	6.06218	−	3.50000i	0.210168	−	0.121341i
$833$	−6.06218	+	3.50000i	−0.210042	+	0.121268i
$834$			3.46410i			0.119952i
$835$	18.4808	+	27.9904i	0.639553	+	0.968647i
$836$	18.0000			0.622543
$837$	−20.7846	−	36.0000i	−0.718421	−	1.24434i
$838$		−	30.0000i		−	1.03633i
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$	10.3923	+	5.19615i	0.358569	+	0.179284i
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	−18.1865	+	10.5000i	−0.626749	+	0.361854i
$843$	−16.4545	+	28.5000i	−0.566722	+	0.981592i
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$	−24.0000	−	12.0000i	−0.825625	−	0.412813i
$846$	−13.5000	−	23.3827i	−0.464140	−	0.803913i
$847$			2.00000i			0.0687208i
$848$	−5.19615	−	3.00000i	−0.178437	−	0.103020i
$849$	−16.5000	+	9.52628i	−0.566279	+	0.326941i
$850$	13.7487	−	32.1865i	0.471577	−	1.10399i
$851$		0			0
$852$	4.33013	+	7.50000i	0.148348	+	0.256946i
$853$	−36.3731	−	21.0000i	−1.24539	−	0.719026i	−0.275204	−	0.961386i	$-0.588745\pi$
$853$	−36.3731	−	21.0000i	−1.24539	−	0.719026i	−0.970186	+	0.242360i	$0.922079\pi$
$854$	−10.0000			−0.342193
$855$	−2.41154	−	40.1769i	−0.0824730	−	1.37402i
$856$	30.0000			1.02538
$857$	12.9904	+	7.50000i	0.443743	+	0.256195i	0.705184	−	0.709024i	$-0.250864\pi$
$857$	12.9904	+	7.50000i	0.443743	+	0.256195i	−0.261441	+	0.965219i	$0.584198\pi$
$858$	−2.59808	+	4.50000i	−0.0886969	+	0.153627i
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	−8.92820	+	0.535898i	−0.304449	+	0.0182740i
$861$		−	3.46410i		−	0.118056i
$862$	6.06218	+	3.50000i	0.206479	+	0.119210i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$	−22.5000	+	12.9904i	−0.765466	+	0.441942i
$865$	6.00000	−	12.0000i	0.204006	−	0.408012i
$866$	−11.0000	+	19.0526i	−0.373795	+	0.647432i
$867$	−55.4256			−1.88235
$868$	−6.92820	+	4.00000i	−0.235159	+	0.135769i
$869$	−10.5000	−	18.1865i	−0.356188	−	0.616936i
$870$	21.3397	+	32.3205i	0.723485	+	1.09577i
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$			15.0000i			0.507964i
$873$	12.9904	+	7.50000i	0.439658	+	0.253837i
$874$		0			0
$875$	3.76795	−	10.5263i	0.127380	−	0.355853i
$876$	4.50000	−	2.59808i	0.152041	−	0.0877809i
$877$	48.4974	−	28.0000i	1.63764	−	0.945493i	0.655999	−	0.754761i	$-0.272247\pi$
$877$	48.4974	−	28.0000i	1.63764	−	0.945493i	0.981642	−	0.190731i	$-0.0610859\pi$
$878$	31.1769	−	18.0000i	1.05217	−	0.607471i
$879$	−27.0000	+	15.5885i	−0.910687	+	0.525786i
$880$	5.59808	−	3.69615i	0.188711	−	0.124597i
$881$	−46.0000			−1.54978			−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000			−1.54978			−0.774890	+	0.632096i	$0.782195\pi$
$882$			3.00000i			0.101015i
$883$			36.0000i			1.21150i	0.795656	+	0.605748i	$0.207126\pi$
$883$			36.0000i			1.21150i	−0.795656	+	0.605748i	$0.792874\pi$
$884$	−3.50000	+	6.06218i	−0.117718	+	0.203893i
$885$	−12.9282	+	8.53590i	−0.434577	+	0.286931i
$886$	−8.00000	−	13.8564i	−0.268765	−	0.465515i
$887$	6.92820	−	4.00000i	0.232626	−	0.134307i	−0.379157	−	0.925332i	$-0.623786\pi$
$887$	6.92820	−	4.00000i	0.232626	−	0.134307i	0.611783	+	0.791026i	$0.290453\pi$
$888$	41.5692			1.39497
$889$	−4.00000	+	6.92820i	−0.134156	+	0.232364i
$890$	−18.0000	+	36.0000i	−0.603361	+	1.20672i
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$			21.0000i			0.703132i
$893$	46.7654	+	27.0000i	1.56494	+	0.903521i
$894$			32.9090i			1.10064i
$895$	1.47372	+	24.5526i	0.0492610	+	0.820702i
$896$	1.50000	+	2.59808i	0.0501115	+	0.0867956i
$897$		0			0
$898$	1.73205	+	1.00000i	0.0577993	+	0.0333704i
$899$	−80.0000			−2.66815
$900$	9.00000	+	12.0000i	0.300000	+	0.400000i
$901$	42.0000			1.39922
$902$	−5.19615	−	3.00000i	−0.173013	−	0.0998891i
$903$	−3.46410	−	6.00000i	−0.115278	−	0.199667i
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	−2.41154	−	40.1769i	−0.0801624	−	1.33553i
$906$	28.5000	−	16.4545i	0.946849	−	0.546664i
$907$	32.9090	+	19.0000i	1.09272	+	0.630885i	0.934300	−	0.356487i	$-0.116025\pi$
$907$	32.9090	+	19.0000i	1.09272	+	0.630885i	0.158424	+	0.987371i	$0.449359\pi$
$908$			11.0000i			0.365048i
$909$		0			0
$910$	1.00000	−	2.00000i	0.0331497	−	0.0662994i
$911$	−4.50000	+	7.79423i	−0.149092	+	0.258234i	−0.930892	−	0.365295i	$-0.880968\pi$
$911$	−4.50000	+	7.79423i	−0.149092	+	0.258234i	0.781800	+	0.623529i	$0.214302\pi$
$912$	−5.19615	+	9.00000i	−0.172062	+	0.298020i
$913$	12.9904	−	7.50000i	0.429919	−	0.248214i
$914$	4.00000	+	6.92820i	0.132308	+	0.229165i
$915$	−34.6410	−	17.3205i	−1.14520	−	0.572598i
$916$	−2.00000	+	3.46410i	−0.0660819	+	0.114457i
$917$			8.00000i			0.264183i
$918$	−18.1865	+	31.5000i	−0.600245	+	1.03965i
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$		0			0
$921$		−	39.8372i		−	1.31268i
$922$	10.3923	−	6.00000i	0.342252	−	0.197599i
$923$	4.33013	−	2.50000i	0.142528	−	0.0822885i
$924$	−4.50000	−	2.59808i	−0.148039	−	0.0854704i
$925$	−4.78461	−	39.7128i	−0.157317	−	1.30575i
$926$	12.0000			0.394344
$927$	10.3923	−	6.00000i	0.341328	−	0.197066i
$928$			50.0000i			1.64133i
$929$	11.0000	−	19.0526i	0.360898	−	0.625094i	−0.627211	−	0.778850i	$-0.715803\pi$
$929$	11.0000	−	19.0526i	0.360898	−	0.625094i	0.988109	+	0.153755i	$0.0491368\pi$
$930$	30.9282	−	1.85641i	1.01418	−	0.0608740i
$931$	−3.00000	−	5.19615i	−0.0983210	−	0.170297i
$932$	12.1244	−	7.00000i	0.397146	−	0.229293i
$933$	15.5885	+	27.0000i	0.510343	+	0.883940i
$934$	10.5000	−	18.1865i	0.343570	−	0.595082i
$935$	−21.0000	+	42.0000i	−0.686773	+	1.37355i
$936$	4.50000	+	7.79423i	0.147087	+	0.254762i
$937$			47.0000i			1.53542i	0.640796	+	0.767712i	$0.278605\pi$
$937$			47.0000i			1.53542i	−0.640796	+	0.767712i	$0.721395\pi$
$938$	−3.46410	−	2.00000i	−0.113107	−	0.0653023i
$939$	−9.00000	−	5.19615i	−0.293704	−	0.169570i
$940$	−20.0885	+	1.20577i	−0.655213	+	0.0393279i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	36.3731			1.18510
$943$		0			0
$944$	4.00000			0.130189
$945$	−5.19615	+	10.3923i	−0.169031	+	0.338062i
$946$	−12.0000			−0.390154
$947$	36.3731	+	21.0000i	1.18197	+	0.682408i	0.956469	−	0.291835i	$-0.0942660\pi$
$947$	36.3731	+	21.0000i	1.18197	+	0.682408i	0.225497	+	0.974244i	$0.427599\pi$
$948$	−12.1244			−0.393781
$949$	−1.50000	−	2.59808i	−0.0486921	−	0.0843371i
$950$	27.5885	+	11.7846i	0.895088	+	0.382343i
$951$	−18.0000	−	10.3923i	−0.583690	−	0.336994i
$952$	18.1865	+	10.5000i	0.589429	+	0.340307i
$953$		−	36.0000i		−	1.16615i	−0.812417	−	0.583077i	$-0.801849\pi$
$953$		−	36.0000i		−	1.16615i	0.812417	−	0.583077i	$-0.198151\pi$
$954$	9.00000	−	15.5885i	0.291386	−	0.504695i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−25.9808	−	45.0000i	−0.839839	−	1.45464i
$958$	−5.19615	+	3.00000i	−0.167880	+	0.0969256i
$959$		0			0
$960$	−1.62436	−	27.0622i	−0.0524259	−	0.873428i
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		−	8.00000i		−	0.257930i
$963$			30.0000i			0.966736i
$964$	−14.0000			−0.450910
$965$	−4.92820	−	7.46410i	−0.158644	−	0.240278i
$966$		0			0
$967$	−48.4974	+	28.0000i	−1.55957	+	0.900419i	−0.562274	+	0.826951i	$0.690074\pi$
$967$	−48.4974	+	28.0000i	−1.55957	+	0.900419i	−0.997298	+	0.0734686i	$0.976593\pi$
$968$	5.19615	−	3.00000i	0.167011	−	0.0964237i
$969$		−	72.7461i		−	2.33694i
$970$	−9.33013	+	6.16025i	−0.299572	+	0.197794i
$971$	4.00000			0.128366			0.0641831	−	0.997938i	$-0.479556\pi$
$971$	4.00000			0.128366			0.0641831	+	0.997938i	$0.479556\pi$
$972$	−7.79423	−	13.5000i	−0.250000	−	0.433013i
$973$			2.00000i			0.0641171i
$974$	6.00000	−	10.3923i	0.192252	−	0.332991i
$975$	6.92820	−	5.19615i	0.221880	−	0.166410i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	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	$0.271850\pi$
$978$	8.66025	−	15.0000i	0.276924	−	0.479647i
$979$	27.0000	−	46.7654i	0.862924	−	1.49463i
$980$	2.00000	+	1.00000i	0.0638877	+	0.0319438i
$981$	−15.0000			−0.478913
$982$			11.0000i			0.351024i
$983$	−7.79423	−	4.50000i	−0.248597	−	0.143528i	0.370525	−	0.928823i	$-0.379178\pi$
$983$	−7.79423	−	4.50000i	−0.248597	−	0.143528i	−0.619122	+	0.785295i	$0.712511\pi$
$984$	−9.00000	+	5.19615i	−0.286910	+	0.165647i
$985$	8.92820	−	0.535898i	0.284476	−	0.0170751i
$986$	35.0000	+	60.6218i	1.11463	+	1.93059i
$987$	−7.79423	−	13.5000i	−0.248093	−	0.429710i
$988$	−5.19615	−	3.00000i	−0.165312	−	0.0954427i
$989$		0			0
$990$	11.0885	+	16.7942i	0.352414	+	0.533756i
$991$	13.0000			0.412959			0.206479	−	0.978451i	$-0.433799\pi$
$991$	13.0000			0.412959			0.206479	+	0.978451i	$0.433799\pi$
$992$	34.6410	+	20.0000i	1.09985	+	0.635001i
$993$	28.5788	−	49.5000i	0.906922	−	1.57084i
$994$	−2.50000	−	4.33013i	−0.0792952	−	0.137343i
$995$	0.535898	+	8.92820i	0.0169891	+	0.283043i
$996$		−	8.66025i		−	0.274411i
$997$	−43.3013	−	25.0000i	−1.37136	−	0.791758i	−0.380265	−	0.924878i	$-0.624167\pi$
$997$	−43.3013	−	25.0000i	−1.37136	−	0.791758i	−0.991100	+	0.133120i	$0.957501\pi$
$998$			19.0000i			0.601434i
$999$			41.5692i			1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.a.169.2	yes	4
3.2	odd	2		945.2.bh.a.694.1		4
5.4	even	2	inner	315.2.bh.a.169.1	✓	4
9.4	even	3	inner	315.2.bh.a.274.1	yes	4
9.5	odd	6		945.2.bh.a.64.2		4
15.14	odd	2		945.2.bh.a.694.2		4
45.4	even	6	inner	315.2.bh.a.274.2	yes	4
45.14	odd	6		945.2.bh.a.64.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.a.169.1	✓	4	5.4	even	2	inner
315.2.bh.a.169.2	yes	4	1.1	even	1	trivial
315.2.bh.a.274.1	yes	4	9.4	even	3	inner
315.2.bh.a.274.2	yes	4	45.4	even	6	inner
945.2.bh.a.64.1		4	45.14	odd	6
945.2.bh.a.64.2		4	9.5	odd	6
945.2.bh.a.694.1		4	3.2	odd	2
945.2.bh.a.694.2		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.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(0.866025 + 0.500000i) q^{7} -3.00000i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +1.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(1.50000 + 0.866025i) q^{6} +(0.866025 + 0.500000i) q^{7} -3.00000i q^{8} +3.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} +(1.50000 - 2.59808i) q^{11} +(-0.866025 - 1.50000i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.232051 + 3.86603i) q^{15} +(0.500000 - 0.866025i) q^{16} +7.00000i q^{17} +(2.59808 + 1.50000i) q^{18} -6.00000 q^{19} +(1.86603 - 1.23205i) q^{20} +(1.50000 + 0.866025i) q^{21} +(2.59808 - 1.50000i) q^{22} -5.19615i q^{24} +(-4.96410 + 0.598076i) q^{25} -1.00000 q^{26} +5.19615 q^{27} -1.00000i q^{28} +(5.00000 - 8.66025i) q^{29} +(-1.73205 + 3.46410i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-4.33013 + 2.50000i) q^{32} +(2.59808 - 4.50000i) q^{33} +(-3.50000 + 6.06218i) q^{34} +(-1.00000 + 2.00000i) q^{35} +(-1.50000 - 2.59808i) q^{36} +8.00000i q^{37} +(-5.19615 - 3.00000i) q^{38} +(-1.50000 + 0.866025i) q^{39} +(6.69615 - 0.401924i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.866025 + 1.50000i) q^{42} +(-3.46410 - 2.00000i) q^{43} -3.00000 q^{44} +(0.401924 + 6.69615i) q^{45} +(-7.79423 - 4.50000i) q^{47} +(0.866025 - 1.50000i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-4.59808 - 1.96410i) q^{50} +12.1244i q^{51} +(0.866025 + 0.500000i) q^{52} -6.00000i q^{53} +(4.50000 + 2.59808i) q^{54} +(6.00000 + 3.00000i) q^{55} +(1.50000 - 2.59808i) q^{56} -10.3923 q^{57} +(8.66025 - 5.00000i) q^{58} +(2.00000 + 3.46410i) q^{59} +(3.23205 - 2.13397i) q^{60} +(-5.00000 + 8.66025i) q^{61} -8.00000i q^{62} +(2.59808 + 1.50000i) q^{63} -7.00000 q^{64} +(-1.23205 - 1.86603i) q^{65} +(4.50000 - 2.59808i) q^{66} +(-3.46410 + 2.00000i) q^{67} +(6.06218 - 3.50000i) q^{68} +(-1.86603 + 1.23205i) q^{70} -5.00000 q^{71} -9.00000i q^{72} +3.00000i q^{73} +(-4.00000 + 6.92820i) q^{74} +(-8.59808 + 1.03590i) q^{75} +(3.00000 + 5.19615i) q^{76} +(2.59808 - 1.50000i) q^{77} -1.73205 q^{78} +(3.50000 - 6.06218i) q^{79} +(2.00000 + 1.00000i) q^{80} +9.00000 q^{81} -2.00000i q^{82} +(4.33013 + 2.50000i) q^{83} -1.73205i q^{84} +(-15.6244 + 0.937822i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(8.66025 - 15.0000i) q^{87} +(-7.79423 - 4.50000i) q^{88} +18.0000 q^{89} +(-3.00000 + 6.00000i) q^{90} -1.00000 q^{91} +(-6.92820 - 12.0000i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-0.803848 - 13.3923i) q^{95} +(-7.50000 + 4.33013i) q^{96} +(4.33013 + 2.50000i) q^{97} +1.00000i q^{98} +(4.50000 - 7.79423i) 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	\( 4 q - 2 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{9} - 4 q^{10} + 6 q^{11} + 2 q^{14} - 6 q^{15} + 2 q^{16} - 24 q^{19} + 4 q^{20} + 6 q^{21} - 6 q^{25} - 4 q^{26} + 20 q^{29} - 16 q^{31} - 14 q^{34} - 4 q^{35} - 6 q^{36} - 6 q^{39} + 6 q^{40} - 4 q^{41} - 12 q^{44} + 12 q^{45} + 2 q^{49} - 8 q^{50} + 18 q^{54} + 24 q^{55} + 6 q^{56} + 8 q^{59} + 6 q^{60} - 20 q^{61} - 28 q^{64} + 2 q^{65} + 18 q^{66} - 4 q^{70} - 20 q^{71} - 16 q^{74} - 24 q^{75} + 12 q^{76} + 14 q^{79} + 8 q^{80} + 36 q^{81} - 14 q^{85} - 8 q^{86} + 72 q^{89} - 12 q^{90} - 4 q^{91} - 18 q^{94} - 24 q^{95} - 30 q^{96} + 18 q^{99}+O(q^{100}) \) 4 * q - 2 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^9 - 4 * q^10 + 6 * q^11 + 2 * q^14 - 6 * q^15 + 2 * q^16 - 24 * q^19 + 4 * q^20 + 6 * q^21 - 6 * q^25 - 4 * q^26 + 20 * q^29 - 16 * q^31 - 14 * q^34 - 4 * q^35 - 6 * q^36 - 6 * q^39 + 6 * q^40 - 4 * q^41 - 12 * q^44 + 12 * q^45 + 2 * q^49 - 8 * q^50 + 18 * q^54 + 24 * q^55 + 6 * q^56 + 8 * q^59 + 6 * q^60 - 20 * q^61 - 28 * q^64 + 2 * q^65 + 18 * q^66 - 4 * q^70 - 20 * q^71 - 16 * q^74 - 24 * q^75 + 12 * q^76 + 14 * q^79 + 8 * q^80 + 36 * q^81 - 14 * q^85 - 8 * q^86 + 72 * q^89 - 12 * q^90 - 4 * q^91 - 18 * q^94 - 24 * q^95 - 30 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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