LMFDB - Embedded newform 403.2.l.a.129.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	403.129
Dual form			403.2.l.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+1.73205i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-4.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.50000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{14} +1.73205i q^{15} -5.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(-3.00000 + 1.73205i) q^{18} +(4.50000 + 2.59808i) q^{19} +(1.50000 - 0.866025i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(-4.50000 - 7.79423i) q^{22} +(1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-1.50000 + 6.06218i) q^{26} +5.00000 q^{27} +(1.50000 + 0.866025i) q^{28} -6.00000 q^{29} -3.00000 q^{30} +(2.00000 - 5.19615i) q^{31} -5.19615i q^{32} +5.19615i q^{33} +(-4.50000 - 2.59808i) q^{34} +3.00000 q^{35} +(-1.00000 - 1.73205i) q^{36} +(4.50000 + 2.59808i) q^{37} +(-4.50000 + 7.79423i) q^{38} +(2.50000 - 2.59808i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(0.500000 - 0.866025i) q^{43} +(4.50000 - 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} -3.46410i q^{47} +(-2.50000 + 4.33013i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-3.00000 - 1.73205i) q^{50} +(1.50000 + 2.59808i) q^{51} +(-3.50000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} +8.66025i q^{54} +(4.50000 - 7.79423i) q^{55} +(1.50000 - 2.59808i) q^{56} +(4.50000 - 2.59808i) q^{57} -10.3923i q^{58} +(-1.50000 - 0.866025i) q^{59} -1.73205i q^{60} +10.0000 q^{61} +(9.00000 + 3.46410i) q^{62} -3.46410i q^{63} -1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} -9.00000 q^{66} +(7.50000 - 4.33013i) q^{67} +(1.50000 - 2.59808i) q^{68} +5.19615i q^{70} +(7.50000 - 4.33013i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-7.50000 + 4.33013i) q^{73} +(-4.50000 + 7.79423i) q^{74} +(1.00000 + 1.73205i) q^{75} +(-4.50000 - 2.59808i) q^{76} +9.00000 q^{77} +(4.50000 + 4.33013i) q^{78} +(2.50000 - 4.33013i) q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +(-10.5000 + 6.06218i) q^{83} +(1.50000 - 0.866025i) q^{84} -5.19615i q^{85} +(1.50000 + 0.866025i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(-4.50000 - 7.79423i) q^{88} +6.92820i q^{89} +(3.00000 - 5.19615i) q^{90} +(-4.50000 - 4.33013i) q^{91} +(-3.50000 - 4.33013i) q^{93} +6.00000 q^{94} -9.00000 q^{95} +(-4.50000 - 2.59808i) q^{96} +6.92820i q^{97} +(6.00000 - 3.46410i) q^{98} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 2 * q^9	$ 2 q + q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 2 q^{9} - 3 q^{10} - 9 q^{11} - q^{12} + 7 q^{13} + 3 q^{14} - 10 q^{16} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{22} + 3 q^{24} - 2 q^{25} - 3 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 6 q^{30} + 4 q^{31} - 9 q^{34} + 6 q^{35} - 2 q^{36} + 9 q^{37} - 9 q^{38} + 5 q^{39} - 3 q^{40} + 9 q^{41} - 3 q^{42} + q^{43} + 9 q^{44} - 6 q^{45} - 5 q^{48} - 4 q^{49} - 6 q^{50} + 3 q^{51} - 7 q^{52} - 3 q^{53} + 9 q^{55} + 3 q^{56} + 9 q^{57} - 3 q^{59} + 20 q^{61} + 18 q^{62} - 2 q^{64} - 12 q^{65} - 18 q^{66} + 15 q^{67} + 3 q^{68} + 15 q^{71} - 6 q^{72} - 15 q^{73} - 9 q^{74} + 2 q^{75} - 9 q^{76} + 18 q^{77} + 9 q^{78} + 5 q^{79} + 15 q^{80} - q^{81} + 9 q^{82} - 21 q^{83} + 3 q^{84} + 3 q^{86} - 6 q^{87} - 9 q^{88} + 6 q^{90} - 9 q^{91} - 7 q^{93} + 12 q^{94} - 18 q^{95} - 9 q^{96} + 12 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q + q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 2 * q^9 - 3 * q^10 - 9 * q^11 - q^12 + 7 * q^13 + 3 * q^14 - 10 * q^16 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 3 * q^20 - 3 * q^21 - 9 * q^22 + 3 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 6 * q^30 + 4 * q^31 - 9 * q^34 + 6 * q^35 - 2 * q^36 + 9 * q^37 - 9 * q^38 + 5 * q^39 - 3 * q^40 + 9 * q^41 - 3 * q^42 + q^43 + 9 * q^44 - 6 * q^45 - 5 * q^48 - 4 * q^49 - 6 * q^50 + 3 * q^51 - 7 * q^52 - 3 * q^53 + 9 * q^55 + 3 * q^56 + 9 * q^57 - 3 * q^59 + 20 * q^61 + 18 * q^62 - 2 * q^64 - 12 * q^65 - 18 * q^66 + 15 * q^67 + 3 * q^68 + 15 * q^71 - 6 * q^72 - 15 * q^73 - 9 * q^74 + 2 * q^75 - 9 * q^76 + 18 * q^77 + 9 * q^78 + 5 * q^79 + 15 * q^80 - q^81 + 9 * q^82 - 21 * q^83 + 3 * q^84 + 3 * q^86 - 6 * q^87 - 9 * q^88 + 6 * q^90 - 9 * q^91 - 7 * q^93 + 12 * q^94 - 18 * q^95 - 9 * q^96 + 12 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.73205i			1.22474i	0.790569	+	0.612372i	$0.209785\pi$
$2$			1.73205i			1.22474i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−1.00000			−0.500000
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	−1.50000	−	0.866025i	−0.566947	−	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$			1.73205i			0.612372i
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.989191	−	0.146631i	$-0.953157\pi$
$11$	−4.50000	+	2.59808i	−1.35680	+	0.783349i	−0.367610	+	0.929980i	$0.619824\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$			1.73205i			0.447214i
$16$	−5.00000			−1.25000
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−3.00000	+	1.73205i	−0.707107	+	0.408248i
$19$	4.50000	+	2.59808i	1.03237	+	0.596040i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	4.50000	+	2.59808i	1.03237	+	0.596040i	0.114708	+	0.993399i	$0.463407\pi$
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$	−1.50000	+	0.866025i	−0.327327	+	0.188982i
$22$	−4.50000	−	7.79423i	−0.959403	−	1.66174i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	−1.50000	+	6.06218i	−0.294174	+	1.18889i
$27$	5.00000			0.962250
$28$	1.50000	+	0.866025i	0.283473	+	0.163663i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	−3.00000			−0.547723
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$31$	2.00000	−	5.19615i	0.359211	−	0.933257i
$32$		−	5.19615i		−	0.918559i
$33$			5.19615i			0.904534i
$34$	−4.50000	−	2.59808i	−0.771744	−	0.445566i
$35$	3.00000			0.507093
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	4.50000	+	2.59808i	0.739795	+	0.427121i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	4.50000	+	2.59808i	0.739795	+	0.427121i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−4.50000	+	7.79423i	−0.729996	+	1.26439i
$39$	2.50000	−	2.59808i	0.400320	−	0.416025i
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	4.50000	−	2.59808i	0.678401	−	0.391675i
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$		0			0
$47$		−	3.46410i		−	0.505291i	−0.967559	−	0.252646i	$-0.918699\pi$
$47$		−	3.46410i		−	0.505291i	0.967559	−	0.252646i	$-0.0813007\pi$
$48$	−2.50000	+	4.33013i	−0.360844	+	0.625000i
$49$	−2.00000	−	3.46410i	−0.285714	−	0.494872i
$50$	−3.00000	−	1.73205i	−0.424264	−	0.244949i
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$	−3.50000	−	0.866025i	−0.485363	−	0.120096i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$			8.66025i			1.17851i
$55$	4.50000	−	7.79423i	0.606780	−	1.05097i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	4.50000	−	2.59808i	0.596040	−	0.344124i
$58$		−	10.3923i		−	1.36458i
$59$	−1.50000	−	0.866025i	−0.195283	−	0.112747i	0.399170	−	0.916877i	$-0.369298\pi$
$59$	−1.50000	−	0.866025i	−0.195283	−	0.112747i	−0.594454	+	0.804130i	$0.702632\pi$
$60$		−	1.73205i		−	0.223607i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	9.00000	+	3.46410i	1.14300	+	0.439941i
$63$		−	3.46410i		−	0.436436i
$64$	−1.00000			−0.125000
$65$	−6.00000	+	1.73205i	−0.744208	+	0.214834i
$66$	−9.00000			−1.10782
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.0338274	−	0.999428i	$-0.489230\pi$
$67$	7.50000	−	4.33013i	0.916271	−	0.529009i	0.882443	+	0.470418i	$0.155897\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$			5.19615i			0.621059i
$71$	7.50000	−	4.33013i	0.890086	−	0.513892i	0.0161155	−	0.999870i	$-0.494870\pi$
$71$	7.50000	−	4.33013i	0.890086	−	0.513892i	0.873971	+	0.485979i	$0.161537\pi$
$72$	−3.00000	+	1.73205i	−0.353553	+	0.204124i
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.869935	−	0.493166i	$-0.835840\pi$
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.00787336	+	0.999969i	$0.502506\pi$
$74$	−4.50000	+	7.79423i	−0.523114	+	0.906061i
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$	−4.50000	−	2.59808i	−0.516185	−	0.298020i
$77$	9.00000			1.02565
$78$	4.50000	+	4.33013i	0.509525	+	0.490290i
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$	7.50000	−	4.33013i	0.838525	−	0.484123i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	−10.5000	+	6.06218i	−1.15252	+	0.665410i	−0.949501	−	0.313763i	$-0.898410\pi$
$83$	−10.5000	+	6.06218i	−1.15252	+	0.665410i	−0.203024	+	0.979174i	$0.565077\pi$
$84$	1.50000	−	0.866025i	0.163663	−	0.0944911i
$85$		−	5.19615i		−	0.563602i
$86$	1.50000	+	0.866025i	0.161749	+	0.0933859i
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	−4.50000	−	7.79423i	−0.479702	−	0.830868i
$89$			6.92820i			0.734388i	0.930144	+	0.367194i	$0.119682\pi$
$89$			6.92820i			0.734388i	−0.930144	+	0.367194i	$0.880318\pi$
$90$	3.00000	−	5.19615i	0.316228	−	0.547723i
$91$	−4.50000	−	4.33013i	−0.471728	−	0.453921i
$92$		0			0
$93$	−3.50000	−	4.33013i	−0.362933	−	0.449013i
$94$	6.00000			0.618853
$95$	−9.00000			−0.923381
$96$	−4.50000	−	2.59808i	−0.459279	−	0.265165i
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$	6.00000	−	3.46410i	0.606092	−	0.349927i
$99$	−9.00000	−	5.19615i	−0.904534	−	0.522233i
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	18.0000			1.79107			0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000			1.79107			0.895533	+	0.444994i	$0.146794\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.772728	+	0.634738i	$0.218892\pi$
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.163335	+	0.986571i	$0.447775\pi$
$104$	−1.50000	+	6.06218i	−0.147087	+	0.594445i
$105$	1.50000	−	2.59808i	0.146385	−	0.253546i
$106$	4.50000	−	2.59808i	0.437079	−	0.252347i
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	−0.562267	−	0.826956i	$-0.690071\pi$
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	0.997298	+	0.0734594i	$0.0234039\pi$
$108$	−5.00000			−0.481125
$109$			13.8564i			1.32720i	0.748086	+	0.663602i	$0.230973\pi$
$109$			13.8564i			1.32720i	−0.748086	+	0.663602i	$0.769027\pi$
$110$	13.5000	+	7.79423i	1.28717	+	0.743151i
$111$	4.50000	−	2.59808i	0.427121	−	0.246598i
$112$	7.50000	+	4.33013i	0.708683	+	0.409159i
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	0.996262	−	0.0863794i	$-0.0275297\pi$
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	−0.572938	+	0.819599i	$0.694196\pi$
$114$	4.50000	+	7.79423i	0.421464	+	0.729996i
$115$		0			0
$116$	6.00000			0.557086
$117$	2.00000	+	6.92820i	0.184900	+	0.640513i
$118$	1.50000	−	2.59808i	0.138086	−	0.239172i
$119$	4.50000	−	2.59808i	0.412514	−	0.238165i
$120$	−3.00000			−0.273861
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$			17.3205i			1.56813i
$123$		−	5.19615i		−	0.468521i
$124$	−2.00000	+	5.19615i	−0.179605	+	0.466628i
$125$		−	12.1244i		−	1.08444i
$126$	6.00000			0.534522
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	−0.978487	−	0.206309i	$-0.933855\pi$
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	0.667912	+	0.744240i	$0.267188\pi$
$128$		−	12.1244i		−	1.07165i
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$	−3.00000	−	10.3923i	−0.263117	−	0.911465i
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$		−	5.19615i		−	0.452267i
$133$	−4.50000	−	7.79423i	−0.390199	−	0.675845i
$134$	7.50000	+	12.9904i	0.647901	+	1.12220i
$135$	−7.50000	+	4.33013i	−0.645497	+	0.372678i
$136$	−4.50000	−	2.59808i	−0.385872	−	0.222783i
$137$	4.50000	−	2.59808i	0.384461	−	0.221969i	−0.295296	−	0.955406i	$-0.595418\pi$
$137$	4.50000	−	2.59808i	0.384461	−	0.221969i	0.679757	+	0.733437i	$0.262085\pi$
$138$		0			0
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−3.00000			−0.253546
$141$	−3.00000	−	1.73205i	−0.252646	−	0.145865i
$142$	7.50000	+	12.9904i	0.629386	+	1.09013i
$143$	−18.0000	+	5.19615i	−1.50524	+	0.434524i
$144$	−5.00000	−	8.66025i	−0.416667	−	0.721688i
$145$	9.00000	−	5.19615i	0.747409	−	0.431517i
$146$	−7.50000	−	12.9904i	−0.620704	−	1.07509i
$147$	−4.00000			−0.329914
$148$	−4.50000	−	2.59808i	−0.369898	−	0.213561i
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.988492	−	0.151272i	$-0.0483370\pi$
$149$	16.5000	+	9.52628i	1.35173	+	0.780423i	0.363241	+	0.931695i	$0.381670\pi$
$150$	−3.00000	+	1.73205i	−0.244949	+	0.141421i
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$	−4.50000	+	7.79423i	−0.364998	+	0.632195i
$153$	−6.00000			−0.485071
$154$			15.5885i			1.25615i
$155$	1.50000	+	9.52628i	0.120483	+	0.765169i
$156$	−2.50000	+	2.59808i	−0.200160	+	0.208013i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	7.50000	+	4.33013i	0.596668	+	0.344486i
$159$	−3.00000			−0.237915
$160$	4.50000	+	7.79423i	0.355756	+	0.616188i
$161$		0			0
$162$	−1.50000	−	0.866025i	−0.117851	−	0.0680414i
$163$		−	10.3923i		−	0.813988i	−0.913431	−	0.406994i	$-0.866577\pi$
$163$		−	10.3923i		−	0.813988i	0.913431	−	0.406994i	$-0.133423\pi$
$164$	−4.50000	+	2.59808i	−0.351391	+	0.202876i
$165$	−4.50000	−	7.79423i	−0.350325	−	0.606780i
$166$	−10.5000	−	18.1865i	−0.814958	−	1.41155i
$167$	−7.50000	−	4.33013i	−0.580367	−	0.335075i	0.180912	−	0.983499i	$-0.442095\pi$
$167$	−7.50000	−	4.33013i	−0.580367	−	0.335075i	−0.761279	+	0.648424i	$0.775428\pi$
$168$	−1.50000	−	2.59808i	−0.115728	−	0.200446i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	9.00000			0.690268
$171$			10.3923i			0.794719i
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$	−9.00000	−	5.19615i	−0.682288	−	0.393919i
$175$	3.00000	−	1.73205i	0.226779	−	0.130931i
$176$	22.5000	−	12.9904i	1.69600	−	0.979187i
$177$	−1.50000	+	0.866025i	−0.112747	+	0.0650945i
$178$	−12.0000			−0.899438
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$	3.00000	+	1.73205i	0.223607	+	0.129099i
$181$	−11.5000	−	19.9186i	−0.854788	−	1.48054i	−0.876841	−	0.480780i	$-0.840354\pi$
$181$	−11.5000	−	19.9186i	−0.854788	−	1.48054i	0.0220530	−	0.999757i	$-0.492980\pi$
$182$	7.50000	−	7.79423i	0.555937	−	0.577747i
$183$	5.00000	−	8.66025i	0.369611	−	0.640184i
$184$		0			0
$185$	−9.00000			−0.661693
$186$	7.50000	−	6.06218i	0.549927	−	0.444500i
$187$		−	15.5885i		−	1.13994i
$188$			3.46410i			0.252646i
$189$	−7.50000	−	4.33013i	−0.545545	−	0.314970i
$190$		−	15.5885i		−	1.13091i
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	0.998749	+	0.0500060i	$0.0159241\pi$
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	−0.456068	+	0.889945i	$0.650743\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−19.5000	−	11.2583i	−1.40364	−	0.810392i	−0.408877	−	0.912590i	$-0.634079\pi$
$193$	−19.5000	−	11.2583i	−1.40364	−	0.810392i	−0.994764	+	0.102197i	$0.967413\pi$
$194$	−12.0000			−0.861550
$195$	−1.50000	+	6.06218i	−0.107417	+	0.434122i
$196$	2.00000	+	3.46410i	0.142857	+	0.247436i
$197$	−7.50000	+	4.33013i	−0.534353	+	0.308509i	−0.742787	−	0.669528i	$-0.766497\pi$
$197$	−7.50000	+	4.33013i	−0.534353	+	0.308509i	0.208434	+	0.978036i	$0.433163\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.844446	−	0.535641i	$-0.820070\pi$
$199$	−12.5000	−	21.6506i	−0.886102	−	1.53477i	−0.0416556	−	0.999132i	$-0.513263\pi$
$200$	−3.00000	−	1.73205i	−0.212132	−	0.122474i
$201$		−	8.66025i		−	0.610847i
$202$			31.1769i			2.19360i
$203$	9.00000	+	5.19615i	0.631676	+	0.364698i
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	−28.5000	+	16.4545i	−1.98569	+	1.14644i
$207$		0			0
$208$	−17.5000	−	4.33013i	−1.21341	−	0.300240i
$209$	−27.0000			−1.86763
$210$	4.50000	+	2.59808i	0.310530	+	0.179284i
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	−0.767049	−	0.641588i	$-0.778276\pi$
$211$	2.50000	−	4.33013i	0.172107	−	0.298098i	0.939156	+	0.343490i	$0.111609\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$		−	8.66025i		−	0.593391i
$214$	13.5000	+	7.79423i	0.922841	+	0.532803i
$215$			1.73205i			0.118125i
$216$			8.66025i			0.589256i
$217$	−7.50000	+	6.06218i	−0.509133	+	0.411527i
$218$	−24.0000			−1.62549
$219$			8.66025i			0.585206i
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$	−7.50000	+	7.79423i	−0.504505	+	0.524297i
$222$	4.50000	+	7.79423i	0.302020	+	0.523114i
$223$	−1.50000	−	0.866025i	−0.100447	−	0.0579934i	0.448935	−	0.893565i	$-0.351804\pi$
$223$	−1.50000	−	0.866025i	−0.100447	−	0.0579934i	−0.549382	+	0.835571i	$0.685137\pi$
$224$	−4.50000	+	7.79423i	−0.300669	+	0.520774i
$225$	−4.00000			−0.266667
$226$	−13.5000	+	7.79423i	−0.898007	+	0.518464i
$227$	7.50000	−	4.33013i	0.497792	−	0.287401i	−0.230009	−	0.973189i	$-0.573876\pi$
$227$	7.50000	−	4.33013i	0.497792	−	0.287401i	0.727801	+	0.685788i	$0.240542\pi$
$228$	−4.50000	+	2.59808i	−0.298020	+	0.172062i
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	0.449619	−	0.893220i	$-0.351560\pi$
$229$	−1.50000	−	0.866025i	−0.0991228	−	0.0572286i	−0.548742	+	0.835992i	$0.684893\pi$
$230$		0			0
$231$	4.50000	−	7.79423i	0.296078	−	0.512823i
$232$		−	10.3923i		−	0.682288i
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$	−12.0000	+	3.46410i	−0.784465	+	0.226455i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	1.50000	+	0.866025i	0.0976417	+	0.0563735i
$237$	−2.50000	−	4.33013i	−0.162392	−	0.281272i
$238$	4.50000	+	7.79423i	0.291692	+	0.505225i
$239$	13.5000	−	7.79423i	0.873242	−	0.504167i	0.00481804	−	0.999988i	$-0.498466\pi$
$239$	13.5000	−	7.79423i	0.873242	−	0.504167i	0.868424	+	0.495822i	$0.165133\pi$
$240$		−	8.66025i		−	0.559017i
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	0.450910	−	0.892570i	$-0.351100\pi$
$241$	−1.50000	−	0.866025i	−0.0966235	−	0.0557856i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	24.0000	+	13.8564i	1.54278	+	0.890724i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−10.0000			−0.640184
$245$	6.00000	+	3.46410i	0.383326	+	0.221313i
$246$	9.00000			0.573819
$247$	13.5000	+	12.9904i	0.858984	+	0.826558i
$248$	9.00000	+	3.46410i	0.571501	+	0.219971i
$249$			12.1244i			0.768350i
$250$	21.0000			1.32816
$251$	10.5000	−	18.1865i	0.662754	−	1.14792i	−0.317135	−	0.948380i	$-0.602721\pi$
$251$	10.5000	−	18.1865i	0.662754	−	1.14792i	0.979889	−	0.199543i	$-0.0639459\pi$
$252$			3.46410i			0.218218i
$253$		0			0
$254$	−10.5000	−	6.06218i	−0.658829	−	0.380375i
$255$	−4.50000	−	2.59808i	−0.281801	−	0.162698i
$256$	19.0000			1.18750
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	1.50000	−	0.866025i	0.0933859	−	0.0539164i
$259$	−4.50000	−	7.79423i	−0.279616	−	0.484310i
$260$	6.00000	−	1.73205i	0.372104	−	0.107417i
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$	13.5000	+	7.79423i	0.834033	+	0.481529i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−9.00000			−0.553912
$265$	4.50000	+	2.59808i	0.276433	+	0.159599i
$266$	13.5000	−	7.79423i	0.827738	−	0.477895i
$267$	6.00000	+	3.46410i	0.367194	+	0.212000i
$268$	−7.50000	+	4.33013i	−0.458135	+	0.264505i
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$	−7.50000	−	12.9904i	−0.456435	−	0.790569i
$271$			10.3923i			0.631288i	0.948878	+	0.315644i	$0.102220\pi$
$271$			10.3923i			0.631288i	−0.948878	+	0.315644i	$0.897780\pi$
$272$	7.50000	−	12.9904i	0.454754	−	0.787658i
$273$	−6.00000	+	1.73205i	−0.363137	+	0.104828i
$274$	4.50000	+	7.79423i	0.271855	+	0.470867i
$275$		−	10.3923i		−	0.626680i
$276$		0			0
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$		−	6.92820i		−	0.415526i
$279$	11.0000	−	1.73205i	0.658553	−	0.103695i
$280$			5.19615i			0.310530i
$281$			13.8564i			0.826604i	0.910594	+	0.413302i	$0.135625\pi$
$281$			13.8564i			0.826604i	−0.910594	+	0.413302i	$0.864375\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$	−7.50000	+	4.33013i	−0.445043	+	0.256946i
$285$	−4.50000	+	7.79423i	−0.266557	+	0.461690i
$286$	−9.00000	−	31.1769i	−0.532181	−	1.84353i
$287$	−9.00000			−0.531253
$288$	9.00000	−	5.19615i	0.530330	−	0.306186i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	9.00000	+	15.5885i	0.528498	+	0.915386i
$291$	6.00000	+	3.46410i	0.351726	+	0.203069i
$292$	7.50000	−	4.33013i	0.438904	−	0.253402i
$293$	22.5000	+	12.9904i	1.31446	+	0.758906i	0.982832	−	0.184503i	$-0.0590674\pi$
$293$	22.5000	+	12.9904i	1.31446	+	0.758906i	0.331632	+	0.943409i	$0.392401\pi$
$294$		−	6.92820i		−	0.404061i
$295$	3.00000			0.174667
$296$	−4.50000	+	7.79423i	−0.261557	+	0.453030i
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	−16.5000	+	28.5788i	−0.955819	+	1.65553i
$299$		0			0
$300$	−1.00000	−	1.73205i	−0.0577350	−	0.100000i
$301$	−1.50000	+	0.866025i	−0.0864586	+	0.0499169i
$302$	−6.00000			−0.345261
$303$	9.00000	−	15.5885i	0.517036	−	0.895533i
$304$	−22.5000	−	12.9904i	−1.29046	−	0.745049i
$305$	−15.0000	+	8.66025i	−0.858898	+	0.495885i
$306$		−	10.3923i		−	0.594089i
$307$	−1.50000	−	0.866025i	−0.0856095	−	0.0494267i	0.456584	−	0.889680i	$-0.349073\pi$
$307$	−1.50000	−	0.866025i	−0.0856095	−	0.0494267i	−0.542194	+	0.840254i	$0.682406\pi$
$308$	−9.00000			−0.512823
$309$	19.0000			1.08087
$310$	−16.5000	+	2.59808i	−0.937137	+	0.147561i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	4.50000	+	4.33013i	0.254762	+	0.245145i
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	0.462093	+	0.886831i	$0.347098\pi$
$313$	−9.50000	+	16.4545i	−0.536972	+	0.930062i	−0.999065	+	0.0432311i	$0.986235\pi$
$314$		−	38.1051i		−	2.15040i
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	−13.5000	−	7.79423i	−0.758236	−	0.437767i	0.0704263	−	0.997517i	$-0.477564\pi$
$317$	−13.5000	−	7.79423i	−0.758236	−	0.437767i	−0.828662	+	0.559749i	$0.810897\pi$
$318$		−	5.19615i		−	0.291386i
$319$	27.0000	−	15.5885i	1.51171	−	0.872786i
$320$	1.50000	−	0.866025i	0.0838525	−	0.0484123i
$321$	−4.50000	−	7.79423i	−0.251166	−	0.435031i
$322$		0			0
$323$	−13.5000	+	7.79423i	−0.751160	+	0.433682i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−5.00000	+	5.19615i	−0.277350	+	0.288231i
$326$	18.0000			0.996928
$327$	12.0000	+	6.92820i	0.663602	+	0.383131i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$	13.5000	−	7.79423i	0.743151	−	0.429058i
$331$	−10.5000	+	6.06218i	−0.577132	+	0.333207i	−0.759993	−	0.649931i	$-0.774798\pi$
$331$	−10.5000	+	6.06218i	−0.577132	+	0.333207i	0.182861	+	0.983139i	$0.441464\pi$
$332$	10.5000	−	6.06218i	0.576262	−	0.332705i
$333$			10.3923i			0.569495i
$334$	7.50000	−	12.9904i	0.410382	−	0.710802i
$335$	−7.50000	+	12.9904i	−0.409769	+	0.709740i
$336$	7.50000	−	4.33013i	0.409159	−	0.236228i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−10.5000	+	19.9186i	−0.571125	+	1.08343i
$339$	9.00000			0.488813
$340$			5.19615i			0.281801i
$341$	4.50000	+	28.5788i	0.243689	+	1.54763i
$342$	−18.0000			−0.973329
$343$			19.0526i			1.02874i
$344$	1.50000	+	0.866025i	0.0808746	+	0.0466930i
$345$		0			0
$346$	−13.5000	+	7.79423i	−0.725764	+	0.419020i
$347$	16.5000	−	28.5788i	0.885766	−	1.53419i	0.0409337	−	0.999162i	$-0.486967\pi$
$347$	16.5000	−	28.5788i	0.885766	−	1.53419i	0.844833	−	0.535031i	$-0.179700\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	3.00000	+	5.19615i	0.160357	+	0.277746i
$351$	17.5000	+	4.33013i	0.934081	+	0.231125i
$352$	13.5000	+	23.3827i	0.719552	+	1.24630i
$353$	−25.5000	−	14.7224i	−1.35723	−	0.783596i	−0.367979	−	0.929834i	$-0.619950\pi$
$353$	−25.5000	−	14.7224i	−1.35723	−	0.783596i	−0.989249	+	0.146238i	$0.953283\pi$
$354$	−1.50000	−	2.59808i	−0.0797241	−	0.138086i
$355$	−7.50000	+	12.9904i	−0.398059	+	0.689458i
$356$		−	6.92820i		−	0.367194i
$357$		−	5.19615i		−	0.275010i
$358$	−4.50000	−	2.59808i	−0.237832	−	0.137313i
$359$	7.50000	−	4.33013i	0.395835	−	0.228535i	−0.288850	−	0.957374i	$-0.593273\pi$
$359$	7.50000	−	4.33013i	0.395835	−	0.228535i	0.684685	+	0.728839i	$0.259940\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	4.00000	+	6.92820i	0.210526	+	0.364642i
$362$	34.5000	−	19.9186i	1.81328	−	1.04690i
$363$	−8.00000	−	13.8564i	−0.419891	−	0.727273i
$364$	4.50000	+	4.33013i	0.235864	+	0.226960i
$365$	7.50000	−	12.9904i	0.392568	−	0.679948i
$366$	15.0000	+	8.66025i	0.784063	+	0.452679i
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	0.913493	+	0.406855i	$0.133375\pi$
$367$	15.5000	+	26.8468i	0.809093	+	1.40139i	−0.104399	+	0.994535i	$0.533292\pi$
$368$		0			0
$369$	9.00000	+	5.19615i	0.468521	+	0.270501i
$370$		−	15.5885i		−	0.810405i
$371$			5.19615i			0.269771i
$372$	3.50000	+	4.33013i	0.181467	+	0.224507i
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	27.0000			1.39614
$375$	−10.5000	−	6.06218i	−0.542218	−	0.313050i
$376$	6.00000			0.309426
$377$	−21.0000	−	5.19615i	−1.08156	−	0.267615i
$378$	7.50000	−	12.9904i	0.385758	−	0.668153i
$379$	10.5000	+	6.06218i	0.539349	+	0.311393i	0.744815	−	0.667271i	$-0.232538\pi$
$379$	10.5000	+	6.06218i	0.539349	+	0.311393i	−0.205466	+	0.978664i	$0.565871\pi$
$380$	9.00000			0.461690
$381$	3.50000	+	6.06218i	0.179310	+	0.310575i
$382$	−22.5000	+	12.9904i	−1.15120	+	0.664646i
$383$	−22.5000	+	12.9904i	−1.14970	+	0.663777i	−0.948813	−	0.315838i	$-0.897714\pi$
$383$	−22.5000	+	12.9904i	−1.14970	+	0.663777i	−0.200883	+	0.979615i	$0.564381\pi$
$384$	−10.5000	−	6.06218i	−0.535826	−	0.309359i
$385$	−13.5000	+	7.79423i	−0.688024	+	0.397231i
$386$	19.5000	−	33.7750i	0.992524	−	1.71910i
$387$	2.00000			0.101666
$388$		−	6.92820i		−	0.351726i
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	−0.0561516	−	0.998422i	$-0.517883\pi$
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	0.892735	−	0.450582i	$-0.148784\pi$
$390$	−10.5000	−	2.59808i	−0.531688	−	0.131559i
$391$		0			0
$392$	6.00000	−	3.46410i	0.303046	−	0.174964i
$393$	−4.50000	−	7.79423i	−0.226995	−	0.393167i
$394$	−7.50000	−	12.9904i	−0.377845	−	0.654446i
$395$			8.66025i			0.435745i
$396$	9.00000	+	5.19615i	0.452267	+	0.261116i
$397$	−13.5000	−	7.79423i	−0.677546	−	0.391181i	0.121384	−	0.992606i	$-0.461267\pi$
$397$	−13.5000	−	7.79423i	−0.677546	−	0.391181i	−0.798930	+	0.601424i	$0.794600\pi$
$398$	37.5000	−	21.6506i	1.87971	−	1.08525i
$399$	−9.00000			−0.450564
$400$	5.00000	−	8.66025i	0.250000	−	0.433013i
$401$			6.92820i			0.345978i	0.984924	+	0.172989i	$0.0553425\pi$
$401$			6.92820i			0.345978i	−0.984924	+	0.172989i	$0.944657\pi$
$402$	15.0000			0.748132
$403$	11.5000	−	16.4545i	0.572856	−	0.819656i
$404$	−18.0000			−0.895533
$405$		−	1.73205i		−	0.0860663i
$406$	−9.00000	+	15.5885i	−0.446663	+	0.773642i
$407$	−27.0000			−1.33834
$408$	−4.50000	+	2.59808i	−0.222783	+	0.128624i
$409$	22.5000	+	12.9904i	1.11255	+	0.642333i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	22.5000	+	12.9904i	1.11255	+	0.642333i	0.173064	+	0.984911i	$0.444633\pi$
$410$	−13.5000	−	7.79423i	−0.666717	−	0.384930i
$411$		−	5.19615i		−	0.256307i
$412$	−9.50000	−	16.4545i	−0.468031	−	0.810654i
$413$	1.50000	+	2.59808i	0.0738102	+	0.127843i
$414$		0			0
$415$	10.5000	−	18.1865i	0.515425	−	0.892742i
$416$	4.50000	−	18.1865i	0.220631	−	0.891668i
$417$	−2.00000	+	3.46410i	−0.0979404	+	0.169638i
$418$		−	46.7654i		−	2.28737i
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	28.5000	−	16.4545i	1.38901	−	0.801942i	0.395802	−	0.918336i	$-0.370467\pi$
$421$	28.5000	−	16.4545i	1.38901	−	0.801942i	0.993203	+	0.116394i	$0.0371334\pi$
$422$	7.50000	+	4.33013i	0.365094	+	0.210787i
$423$	6.00000	−	3.46410i	0.291730	−	0.168430i
$424$	4.50000	−	2.59808i	0.218539	−	0.126174i
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$	15.0000			0.726752
$427$	−15.0000	−	8.66025i	−0.725901	−	0.419099i
$428$	−4.50000	+	7.79423i	−0.217516	+	0.376748i
$429$	−4.50000	+	18.1865i	−0.217262	+	0.878054i
$430$	−3.00000			−0.144673
$431$	−19.5000	−	11.2583i	−0.939282	−	0.542295i	−0.0495468	−	0.998772i	$-0.515778\pi$
$431$	−19.5000	−	11.2583i	−0.939282	−	0.542295i	−0.889735	+	0.456477i	$0.849111\pi$
$432$	−25.0000			−1.20281
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$	−10.5000	−	12.9904i	−0.504016	−	0.623558i
$435$		−	10.3923i		−	0.498273i
$436$		−	13.8564i		−	0.663602i
$437$		0			0
$438$	−15.0000			−0.716728
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	0.998595	−	0.0529862i	$-0.0168739\pi$
$439$	9.50000	+	16.4545i	0.453410	+	0.785330i	−0.545185	+	0.838316i	$0.683541\pi$
$440$	13.5000	+	7.79423i	0.643587	+	0.371575i
$441$	4.00000	−	6.92820i	0.190476	−	0.329914i
$442$	−13.5000	−	12.9904i	−0.642130	−	0.617889i
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	0.987346	−	0.158583i	$-0.0506926\pi$
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	−0.631010	+	0.775775i	$0.717359\pi$
$444$	−4.50000	+	2.59808i	−0.213561	+	0.123299i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	1.50000	−	2.59808i	0.0710271	−	0.123022i
$447$	16.5000	−	9.52628i	0.780423	−	0.450578i
$448$	1.50000	+	0.866025i	0.0708683	+	0.0409159i
$449$			13.8564i			0.653924i	0.945037	+	0.326962i	$0.106025\pi$
$449$			13.8564i			0.653924i	−0.945037	+	0.326962i	$0.893975\pi$
$450$		−	6.92820i		−	0.326599i
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$	3.00000	+	1.73205i	0.140952	+	0.0813788i
$454$	7.50000	+	12.9904i	0.351992	+	0.609669i
$455$	10.5000	+	2.59808i	0.492248	+	0.121800i
$456$	4.50000	+	7.79423i	0.210732	+	0.364998i
$457$			6.92820i			0.324088i	0.986784	+	0.162044i	$0.0518086\pi$
$457$			6.92820i			0.324088i	−0.986784	+	0.162044i	$0.948191\pi$
$458$	1.50000	−	2.59808i	0.0700904	−	0.121400i
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		0			0
$461$		−	13.8564i		−	0.645357i	−0.946509	−	0.322679i	$-0.895417\pi$
$461$		−	13.8564i		−	0.645357i	0.946509	−	0.322679i	$-0.104583\pi$
$462$	13.5000	+	7.79423i	0.628077	+	0.362620i
$463$		−	17.3205i		−	0.804952i	−0.915430	−	0.402476i	$-0.868150\pi$
$463$		−	17.3205i		−	0.804952i	0.915430	−	0.402476i	$-0.131850\pi$
$464$	30.0000			1.39272
$465$	9.00000	+	3.46410i	0.417365	+	0.160644i
$466$		−	31.1769i		−	1.44424i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$	−2.00000	−	6.92820i	−0.0924500	−	0.320256i
$469$	−15.0000			−0.692636
$470$	−9.00000	+	5.19615i	−0.415139	+	0.239681i
$471$	−11.0000	+	19.0526i	−0.506853	+	0.877896i
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$			5.19615i			0.238919i
$474$	7.50000	−	4.33013i	0.344486	−	0.198889i
$475$	−9.00000	+	5.19615i	−0.412948	+	0.238416i
$476$	−4.50000	+	2.59808i	−0.206257	+	0.119083i
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$	13.5000	+	23.3827i	0.617476	+	1.06950i
$479$	−1.50000	−	0.866025i	−0.0685367	−	0.0395697i	0.465340	−	0.885132i	$-0.345932\pi$
$479$	−1.50000	−	0.866025i	−0.0685367	−	0.0395697i	−0.533877	+	0.845562i	$0.679265\pi$
$480$	9.00000			0.410792
$481$	13.5000	+	12.9904i	0.615547	+	0.592310i
$482$	1.50000	−	2.59808i	0.0683231	−	0.118339i
$483$		0			0
$484$	−8.00000	+	13.8564i	−0.363636	+	0.629837i
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$	−24.0000	+	13.8564i	−1.08866	+	0.628539i
$487$	19.5000	−	11.2583i	0.883629	−	0.510164i	0.0117760	−	0.999931i	$-0.496251\pi$
$487$	19.5000	−	11.2583i	0.883629	−	0.510164i	0.871853	+	0.489767i	$0.162918\pi$
$488$			17.3205i			0.784063i
$489$	−9.00000	−	5.19615i	−0.406994	−	0.234978i
$490$	−6.00000	+	10.3923i	−0.271052	+	0.469476i
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$			5.19615i			0.234261i
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	−22.5000	+	23.3827i	−1.01232	+	1.05204i
$495$	18.0000			0.809040
$496$	−10.0000	+	25.9808i	−0.449013	+	1.16657i
$497$	−15.0000			−0.672842
$498$	−21.0000			−0.941033
$499$	−31.5000	−	18.1865i	−1.41013	−	0.814141i	−0.414733	−	0.909943i	$-0.636125\pi$
$499$	−31.5000	−	18.1865i	−1.41013	−	0.814141i	−0.995400	+	0.0958020i	$0.969458\pi$
$500$			12.1244i			0.542218i
$501$	−7.50000	+	4.33013i	−0.335075	+	0.193456i
$502$	31.5000	+	18.1865i	1.40591	+	0.811705i
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	−0.531167	−	0.847267i	$-0.678246\pi$
$503$	10.5000	−	18.1865i	0.468172	−	0.810897i	0.999338	+	0.0363700i	$0.0115795\pi$
$504$	6.00000			0.267261
$505$	−27.0000	+	15.5885i	−1.20148	+	0.693677i
$506$		0			0
$507$	11.0000	−	6.92820i	0.488527	−	0.307692i
$508$	3.50000	−	6.06218i	0.155287	−	0.268966i
$509$	−7.50000	+	4.33013i	−0.332432	+	0.191930i	−0.656920	−	0.753960i	$-0.728141\pi$
$509$	−7.50000	+	4.33013i	−0.332432	+	0.191930i	0.324489	+	0.945890i	$0.394808\pi$
$510$	4.50000	−	7.79423i	0.199263	−	0.345134i
$511$	15.0000			0.663561
$512$			8.66025i			0.382733i
$513$	22.5000	+	12.9904i	0.993399	+	0.573539i
$514$	22.5000	−	12.9904i	0.992432	−	0.572981i
$515$	−28.5000	−	16.4545i	−1.25586	−	0.725071i
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$	13.5000	−	7.79423i	0.593156	−	0.342459i
$519$	9.00000			0.395056
$520$	−3.00000	−	10.3923i	−0.131559	−	0.455733i
$521$	10.5000	−	18.1865i	0.460013	−	0.796766i	−0.538948	−	0.842339i	$-0.681178\pi$
$521$	10.5000	−	18.1865i	0.460013	−	0.796766i	0.998961	+	0.0455727i	$0.0145113\pi$
$522$	18.0000	−	10.3923i	0.787839	−	0.454859i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$		−	3.46410i		−	0.151186i
$526$		0			0
$527$	10.5000	+	12.9904i	0.457387	+	0.565870i
$528$		−	25.9808i		−	1.13067i
$529$	−23.0000			−1.00000
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		−	3.46410i		−	0.150329i
$532$	4.50000	+	7.79423i	0.195100	+	0.337923i
$533$	18.0000	−	5.19615i	0.779667	−	0.225070i
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$			15.5885i			0.673948i
$536$	7.50000	+	12.9904i	0.323951	+	0.561099i
$537$	1.50000	+	2.59808i	0.0647298	+	0.112115i
$538$	−31.5000	+	18.1865i	−1.35806	+	0.784077i
$539$	18.0000	+	10.3923i	0.775315	+	0.447628i
$540$	7.50000	−	4.33013i	0.322749	−	0.186339i
$541$	−7.50000	−	4.33013i	−0.322450	−	0.186167i	0.330034	−	0.943969i	$-0.392940\pi$
$541$	−7.50000	−	4.33013i	−0.322450	−	0.186167i	−0.652484	+	0.757802i	$0.726273\pi$
$542$	−18.0000			−0.773166
$543$	−23.0000			−0.987024
$544$	13.5000	+	7.79423i	0.578808	+	0.334175i
$545$	−12.0000	−	20.7846i	−0.514024	−	0.890315i
$546$	−3.00000	−	10.3923i	−0.128388	−	0.444750i
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	0.994459	−	0.105123i	$-0.0335235\pi$
$547$	9.50000	+	16.4545i	0.406191	+	0.703543i	−0.588269	+	0.808666i	$0.700190\pi$
$548$	−4.50000	+	2.59808i	−0.192230	+	0.110984i
$549$	10.0000	+	17.3205i	0.426790	+	0.739221i
$550$	18.0000			0.767523
$551$	−27.0000	−	15.5885i	−1.15024	−	0.664091i
$552$		0			0
$553$	−7.50000	+	4.33013i	−0.318932	+	0.184136i
$554$			45.0333i			1.91328i
$555$	−4.50000	+	7.79423i	−0.191014	+	0.330847i
$556$	4.00000			0.169638
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$	3.00000	+	19.0526i	0.127000	+	0.806559i
$559$	2.50000	−	2.59808i	0.105739	−	0.109887i
$560$	−15.0000			−0.633866
$561$	−13.5000	−	7.79423i	−0.569970	−	0.329073i
$562$	−24.0000			−1.01238
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	0.895902	−	0.444252i	$-0.146530\pi$
$563$	1.50000	+	2.59808i	0.0632175	+	0.109496i	−0.832684	+	0.553748i	$0.813197\pi$
$564$	3.00000	+	1.73205i	0.126323	+	0.0729325i
$565$	−13.5000	−	7.79423i	−0.567949	−	0.327906i
$566$			6.92820i			0.291214i
$567$	1.50000	−	0.866025i	0.0629941	−	0.0363696i
$568$	7.50000	+	12.9904i	0.314693	+	0.545064i
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	0.997703	−	0.0677445i	$-0.0215803\pi$
$569$	10.5000	+	18.1865i	0.440183	+	0.762419i	−0.557520	+	0.830164i	$0.688247\pi$
$570$	−13.5000	−	7.79423i	−0.565453	−	0.326464i
$571$	−18.5000	−	32.0429i	−0.774201	−	1.34096i	−0.935243	−	0.354008i	$-0.884819\pi$
$571$	−18.5000	−	32.0429i	−0.774201	−	1.34096i	0.161042	−	0.986948i	$-0.448515\pi$
$572$	18.0000	−	5.19615i	0.752618	−	0.217262i
$573$	15.0000			0.626634
$574$		−	15.5885i		−	0.650650i
$575$		0			0
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$	34.5000	+	19.9186i	1.43625	+	0.829222i	0.997587	−	0.0694283i	$-0.0221175\pi$
$577$	34.5000	+	19.9186i	1.43625	+	0.829222i	0.438667	+	0.898650i	$0.355451\pi$
$578$	−12.0000	+	6.92820i	−0.499134	+	0.288175i
$579$	−19.5000	+	11.2583i	−0.810392	+	0.467880i
$580$	−9.00000	+	5.19615i	−0.373705	+	0.215758i
$581$	21.0000			0.871227
$582$	−6.00000	+	10.3923i	−0.248708	+	0.430775i
$583$	13.5000	+	7.79423i	0.559113	+	0.322804i
$584$	−7.50000	−	12.9904i	−0.310352	−	0.537546i
$585$	−9.00000	−	8.66025i	−0.372104	−	0.358057i
$586$	−22.5000	+	38.9711i	−0.929466	+	1.60988i
$587$			10.3923i			0.428936i	0.976731	+	0.214468i	$0.0688018\pi$
$587$			10.3923i			0.428936i	−0.976731	+	0.214468i	$0.931198\pi$
$588$	4.00000			0.164957
$589$	22.5000	−	18.1865i	0.927096	−	0.749363i
$590$			5.19615i			0.213922i
$591$			8.66025i			0.356235i
$592$	−22.5000	−	12.9904i	−0.924744	−	0.533901i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−22.5000	−	38.9711i	−0.923186	−	1.59901i
$595$	−4.50000	+	7.79423i	−0.184482	+	0.319532i
$596$	−16.5000	−	9.52628i	−0.675866	−	0.390212i
$597$	−25.0000			−1.02318
$598$		0			0
$599$	−16.5000	−	28.5788i	−0.674172	−	1.16770i	−0.976710	−	0.214563i	$-0.931167\pi$
$599$	−16.5000	−	28.5788i	−0.674172	−	1.16770i	0.302539	−	0.953137i	$-0.402166\pi$
$600$	−3.00000	+	1.73205i	−0.122474	+	0.0707107i
$601$	14.5000	−	25.1147i	0.591467	−	1.02445i	−0.402568	−	0.915390i	$-0.631882\pi$
$601$	14.5000	−	25.1147i	0.591467	−	1.02445i	0.994035	−	0.109061i	$-0.0347845\pi$
$602$	−1.50000	−	2.59808i	−0.0611354	−	0.105890i
$603$	15.0000	+	8.66025i	0.610847	+	0.352673i
$604$		−	3.46410i		−	0.140952i
$605$			27.7128i			1.12669i
$606$	27.0000	+	15.5885i	1.09680	+	0.633238i
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$	13.5000	−	23.3827i	0.547497	−	0.948293i
$609$	9.00000	−	5.19615i	0.364698	−	0.210559i
$610$	−15.0000	−	25.9808i	−0.607332	−	1.05193i
$611$	3.00000	−	12.1244i	0.121367	−	0.490499i
$612$	6.00000			0.242536
$613$	40.5000	+	23.3827i	1.63578	+	0.944418i	0.982264	+	0.187505i	$0.0600401\pi$
$613$	40.5000	+	23.3827i	1.63578	+	0.944418i	0.653516	+	0.756913i	$0.273293\pi$
$614$	1.50000	−	2.59808i	0.0605351	−	0.104850i
$615$	4.50000	+	7.79423i	0.181458	+	0.314294i
$616$			15.5885i			0.628077i
$617$	10.5000	+	6.06218i	0.422714	+	0.244054i	0.696238	−	0.717811i	$-0.254856\pi$
$617$	10.5000	+	6.06218i	0.422714	+	0.244054i	−0.273524	+	0.961865i	$0.588189\pi$
$618$			32.9090i			1.32379i
$619$			10.3923i			0.417702i	0.977947	+	0.208851i	$0.0669724\pi$
$619$			10.3923i			0.417702i	−0.977947	+	0.208851i	$0.933028\pi$
$620$	−1.50000	−	9.52628i	−0.0602414	−	0.382585i
$621$		0			0
$622$			41.5692i			1.66677i
$623$	6.00000	−	10.3923i	0.240385	−	0.416359i
$624$	−12.5000	+	12.9904i	−0.500400	+	0.520031i
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	−28.5000	−	16.4545i	−1.13909	−	0.657653i
$627$	−13.5000	+	23.3827i	−0.539138	+	0.933815i
$628$	22.0000			0.877896
$629$	−13.5000	+	7.79423i	−0.538280	+	0.310776i
$630$	−9.00000	+	5.19615i	−0.358569	+	0.207020i
$631$	19.5000	−	11.2583i	0.776283	−	0.448187i	−0.0588285	−	0.998268i	$-0.518737\pi$
$631$	19.5000	−	11.2583i	0.776283	−	0.448187i	0.835111	+	0.550081i	$0.185403\pi$
$632$	7.50000	+	4.33013i	0.298334	+	0.172243i
$633$	−2.50000	−	4.33013i	−0.0993661	−	0.172107i
$634$	13.5000	−	23.3827i	0.536153	−	0.928645i
$635$		−	12.1244i		−	0.481140i
$636$	3.00000			0.118958
$637$	−4.00000	−	13.8564i	−0.158486	−	0.549011i
$638$	27.0000	+	46.7654i	1.06894	+	1.85146i
$639$	15.0000	+	8.66025i	0.593391	+	0.342594i
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$	13.5000	−	7.79423i	0.532803	−	0.307614i
$643$			17.3205i			0.683054i	0.939872	+	0.341527i	$0.110944\pi$
$643$			17.3205i			0.683054i	−0.939872	+	0.341527i	$0.889056\pi$
$644$		0			0
$645$	1.50000	+	0.866025i	0.0590624	+	0.0340997i
$646$	−13.5000	−	23.3827i	−0.531150	−	0.919979i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	−1.50000	−	0.866025i	−0.0589256	−	0.0340207i
$649$	9.00000			0.353281
$650$	−9.00000	−	8.66025i	−0.353009	−	0.339683i
$651$	1.50000	+	9.52628i	0.0587896	+	0.373364i
$652$			10.3923i			0.406994i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$	−12.0000	+	20.7846i	−0.469237	+	0.812743i
$655$			15.5885i			0.609091i
$656$	−22.5000	+	12.9904i	−0.878477	+	0.507189i
$657$	−15.0000	−	8.66025i	−0.585206	−	0.337869i
$658$	−9.00000	−	5.19615i	−0.350857	−	0.202567i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$	4.50000	+	7.79423i	0.175162	+	0.303390i
$661$	4.50000	−	2.59808i	0.175030	−	0.101053i	−0.409926	−	0.912119i	$-0.634445\pi$
$661$	4.50000	−	2.59808i	0.175030	−	0.101053i	0.584955	+	0.811065i	$0.301112\pi$
$662$	−10.5000	−	18.1865i	−0.408094	−	0.706840i
$663$	3.00000	+	10.3923i	0.116510	+	0.403604i
$664$	−10.5000	−	18.1865i	−0.407479	−	0.705774i
$665$	13.5000	+	7.79423i	0.523508	+	0.302247i
$666$	−18.0000			−0.697486
$667$		0			0
$668$	7.50000	+	4.33013i	0.290184	+	0.167538i
$669$	−1.50000	+	0.866025i	−0.0579934	+	0.0334825i
$670$	−22.5000	−	12.9904i	−0.869251	−	0.501862i
$671$	−45.0000	+	25.9808i	−1.73721	+	1.00298i
$672$	4.50000	+	7.79423i	0.173591	+	0.300669i
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$		−	24.2487i		−	0.934025i
$675$	−5.00000	+	8.66025i	−0.192450	+	0.333333i
$676$	−11.5000	−	6.06218i	−0.442308	−	0.233161i
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	0.939450	−	0.342687i	$-0.111337\pi$
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	−0.766501	+	0.642244i	$0.778004\pi$
$678$			15.5885i			0.598671i
$679$	6.00000	−	10.3923i	0.230259	−	0.398820i
$680$	9.00000			0.345134
$681$		−	8.66025i		−	0.331862i
$682$	−49.5000	+	7.79423i	−1.89545	+	0.298456i
$683$		−	38.1051i		−	1.45805i	−0.684486	−	0.729026i	$-0.739973\pi$
$683$		−	38.1051i		−	1.45805i	0.684486	−	0.729026i	$-0.260027\pi$
$684$		−	10.3923i		−	0.397360i
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	−33.0000			−1.25995
$687$	−1.50000	+	0.866025i	−0.0572286	+	0.0330409i
$688$	−2.50000	+	4.33013i	−0.0953116	+	0.165085i
$689$	−3.00000	−	10.3923i	−0.114291	−	0.395915i
$690$		0			0
$691$	−4.50000	+	2.59808i	−0.171188	+	0.0988355i	−0.583146	−	0.812367i	$-0.698178\pi$
$691$	−4.50000	+	2.59808i	−0.171188	+	0.0988355i	0.411958	+	0.911203i	$0.364845\pi$
$692$	−4.50000	−	7.79423i	−0.171064	−	0.296292i
$693$	9.00000	+	15.5885i	0.341882	+	0.592157i
$694$	49.5000	+	28.5788i	1.87899	+	1.08484i
$695$	6.00000	−	3.46410i	0.227593	−	0.131401i
$696$	−9.00000	−	5.19615i	−0.341144	−	0.196960i
$697$			15.5885i			0.590455i
$698$		0			0
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$	−3.00000	+	1.73205i	−0.113389	+	0.0654654i
$701$	4.50000	−	7.79423i	0.169963	−	0.294384i	−0.768444	−	0.639917i	$-0.778969\pi$
$701$	4.50000	−	7.79423i	0.169963	−	0.294384i	0.938406	+	0.345533i	$0.112302\pi$
$702$	−7.50000	+	30.3109i	−0.283069	+	1.14401i
$703$	13.5000	+	23.3827i	0.509162	+	0.881895i
$704$	4.50000	−	2.59808i	0.169600	−	0.0979187i
$705$	6.00000			0.225973
$706$	25.5000	−	44.1673i	0.959705	−	1.66226i
$707$	−27.0000	−	15.5885i	−1.01544	−	0.586264i
$708$	1.50000	−	0.866025i	0.0563735	−	0.0325472i
$709$		−	48.4974i		−	1.82136i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$		−	48.4974i		−	1.82136i	0.413114	−	0.910679i	$-0.364441\pi$
$710$	−22.5000	−	12.9904i	−0.844410	−	0.487520i
$711$	10.0000			0.375029
$712$	−12.0000			−0.449719
$713$		0			0
$714$	9.00000			0.336817
$715$	22.5000	−	23.3827i	0.841452	−	0.874463i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$		−	15.5885i		−	0.582162i
$718$	7.50000	+	12.9904i	0.279898	+	0.484797i
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$	15.0000	+	8.66025i	0.559017	+	0.322749i
$721$		−	32.9090i		−	1.22559i
$722$	−12.0000	+	6.92820i	−0.446594	+	0.257841i
$723$	−1.50000	+	0.866025i	−0.0557856	+	0.0322078i
$724$	11.5000	+	19.9186i	0.427394	+	0.740268i
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$	24.0000	−	13.8564i	0.890724	−	0.514259i
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	0.908655	+	0.417548i	$0.137111\pi$
$728$	7.50000	−	7.79423i	0.277968	−	0.288873i
$729$	13.0000			0.481481
$730$	22.5000	+	12.9904i	0.832762	+	0.480796i
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$	−5.00000	+	8.66025i	−0.184805	+	0.320092i
$733$	10.5000	−	6.06218i	0.387826	−	0.223912i	−0.293392	−	0.955992i	$-0.594784\pi$
$733$	10.5000	−	6.06218i	0.387826	−	0.223912i	0.681218	+	0.732081i	$0.261451\pi$
$734$	−46.5000	+	26.8468i	−1.71635	+	0.990933i
$735$	6.00000	−	3.46410i	0.221313	−	0.127775i
$736$		0			0
$737$	−22.5000	+	38.9711i	−0.828798	+	1.43552i
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	19.5000	−	11.2583i	0.717319	−	0.414144i	−0.0964461	−	0.995338i	$-0.530748\pi$
$739$	19.5000	−	11.2583i	0.717319	−	0.414144i	0.813765	+	0.581194i	$0.197414\pi$
$740$	9.00000			0.330847
$741$	18.0000	−	5.19615i	0.661247	−	0.190885i
$742$	−9.00000			−0.330400
$743$		−	17.3205i		−	0.635428i	−0.948187	−	0.317714i	$-0.897085\pi$
$743$		−	17.3205i		−	0.635428i	0.948187	−	0.317714i	$-0.102915\pi$
$744$	7.50000	−	6.06218i	0.274963	−	0.222250i
$745$	−33.0000			−1.20903
$746$		−	45.0333i		−	1.64879i
$747$	−21.0000	−	12.1244i	−0.768350	−	0.443607i
$748$			15.5885i			0.569970i
$749$	−13.5000	+	7.79423i	−0.493279	+	0.284795i
$750$	10.5000	−	18.1865i	0.383406	−	0.664078i
$751$	−23.5000	+	40.7032i	−0.857527	+	1.48528i	0.0167534	+	0.999860i	$0.494667\pi$
$751$	−23.5000	+	40.7032i	−0.857527	+	1.48528i	−0.874281	+	0.485421i	$0.838666\pi$
$752$			17.3205i			0.631614i
$753$	−10.5000	−	18.1865i	−0.382641	−	0.662754i
$754$	9.00000	−	36.3731i	0.327761	−	1.32463i
$755$	−3.00000	−	5.19615i	−0.109181	−	0.189107i
$756$	7.50000	+	4.33013i	0.272772	+	0.157485i
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	0.978130	−	0.207993i	$-0.0666932\pi$
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	−0.669193	+	0.743089i	$0.733360\pi$
$758$	−10.5000	+	18.1865i	−0.381377	+	0.660565i
$759$		0			0
$760$		−	15.5885i		−	0.565453i
$761$	−7.50000	−	4.33013i	−0.271875	−	0.156967i	0.357865	−	0.933774i	$-0.383505\pi$
$761$	−7.50000	−	4.33013i	−0.271875	−	0.156967i	−0.629739	+	0.776807i	$0.716838\pi$
$762$	−10.5000	+	6.06218i	−0.380375	+	0.219610i
$763$	12.0000	−	20.7846i	0.434429	−	0.752453i
$764$	−7.50000	−	12.9904i	−0.271340	−	0.469975i
$765$	9.00000	−	5.19615i	0.325396	−	0.187867i
$766$	−22.5000	−	38.9711i	−0.812958	−	1.40808i
$767$	−4.50000	−	4.33013i	−0.162486	−	0.156352i
$768$	9.50000	−	16.4545i	0.342802	−	0.593750i
$769$	−43.5000	−	25.1147i	−1.56865	−	0.905661i	−0.996327	−	0.0856325i	$-0.972709\pi$
$769$	−43.5000	−	25.1147i	−1.56865	−	0.905661i	−0.572323	−	0.820028i	$-0.693958\pi$
$770$	−13.5000	−	23.3827i	−0.486506	−	0.842654i
$771$	−15.0000			−0.540212
$772$	19.5000	+	11.2583i	0.701820	+	0.405196i
$773$		−	34.6410i		−	1.24595i	−0.782241	−	0.622975i	$-0.785924\pi$
$773$		−	34.6410i		−	1.24595i	0.782241	−	0.622975i	$-0.214076\pi$
$774$			3.46410i			0.124515i
$775$	7.00000	+	8.66025i	0.251447	+	0.311086i
$776$	−12.0000			−0.430775
$777$	−9.00000			−0.322873
$778$	49.5000	+	28.5788i	1.77466	+	1.02460i
$779$	27.0000			0.967375
$780$	1.50000	−	6.06218i	0.0537086	−	0.217061i
$781$	−22.5000	+	38.9711i	−0.805113	+	1.39450i
$782$		0			0
$783$	−30.0000			−1.07211
$784$	10.0000	+	17.3205i	0.357143	+	0.618590i
$785$	33.0000	−	19.0526i	1.17782	−	0.680015i
$786$	13.5000	−	7.79423i	0.481529	−	0.278011i
$787$	22.5000	+	12.9904i	0.802038	+	0.463057i	0.844183	−	0.536054i	$-0.180086\pi$
$787$	22.5000	+	12.9904i	0.802038	+	0.463057i	−0.0421450	+	0.999112i	$0.513419\pi$
$788$	7.50000	−	4.33013i	0.267176	−	0.154254i
$789$		0			0
$790$	−15.0000			−0.533676
$791$		−	15.5885i		−	0.554262i
$792$	9.00000	−	15.5885i	0.319801	−	0.553912i
$793$	35.0000	+	8.66025i	1.24289	+	0.307535i
$794$	13.5000	−	23.3827i	0.479097	−	0.829820i
$795$	4.50000	−	2.59808i	0.159599	−	0.0921443i
$796$	12.5000	+	21.6506i	0.443051	+	0.767386i
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$		−	15.5885i		−	0.551825i
$799$	9.00000	+	5.19615i	0.318397	+	0.183827i
$800$	9.00000	+	5.19615i	0.318198	+	0.183712i
$801$	−12.0000	+	6.92820i	−0.423999	+	0.244796i
$802$	−12.0000			−0.423735
$803$	22.5000	−	38.9711i	0.794008	−	1.37526i
$804$			8.66025i			0.305424i
$805$		0			0
$806$	28.5000	+	19.9186i	1.00387	+	0.701602i
$807$	21.0000			0.739235
$808$			31.1769i			1.09680i
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	−0.967219	−	0.253946i	$-0.918272\pi$
$809$	−7.50000	+	12.9904i	−0.263686	+	0.456717i	0.703533	+	0.710663i	$0.251605\pi$
$810$	3.00000			0.105409
$811$	43.5000	−	25.1147i	1.52749	−	0.881898i	0.528025	−	0.849229i	$-0.322933\pi$
$811$	43.5000	−	25.1147i	1.52749	−	0.881898i	0.999466	−	0.0326691i	$-0.0104007\pi$
$812$	−9.00000	−	5.19615i	−0.315838	−	0.182349i
$813$	9.00000	+	5.19615i	0.315644	+	0.182237i
$814$		−	46.7654i		−	1.63913i
$815$	9.00000	+	15.5885i	0.315256	+	0.546040i
$816$	−7.50000	−	12.9904i	−0.262553	−	0.454754i
$817$	4.50000	−	2.59808i	0.157435	−	0.0908952i
$818$	−22.5000	+	38.9711i	−0.786694	+	1.36259i
$819$	3.00000	−	12.1244i	0.104828	−	0.423659i
$820$	4.50000	−	7.79423i	0.157147	−	0.272186i
$821$		−	41.5692i		−	1.45078i	−0.688340	−	0.725388i	$-0.741660\pi$
$821$		−	41.5692i		−	1.45078i	0.688340	−	0.725388i	$-0.258340\pi$
$822$	9.00000			0.313911
$823$	24.5000	−	42.4352i	0.854016	−	1.47920i	−0.0235383	−	0.999723i	$-0.507493\pi$
$823$	24.5000	−	42.4352i	0.854016	−	1.47920i	0.877555	−	0.479477i	$-0.159174\pi$
$824$	−28.5000	+	16.4545i	−0.992845	+	0.573219i
$825$	−9.00000	−	5.19615i	−0.313340	−	0.180907i
$826$	−4.50000	+	2.59808i	−0.156575	+	0.0903986i
$827$	−4.50000	+	2.59808i	−0.156480	+	0.0903440i	−0.576195	−	0.817312i	$-0.695463\pi$
$827$	−4.50000	+	2.59808i	−0.156480	+	0.0903440i	0.419715	+	0.907656i	$0.362130\pi$
$828$		0			0
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$	31.5000	+	18.1865i	1.09338	+	0.631264i
$831$	13.0000	−	22.5167i	0.450965	−	0.781094i
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$	12.0000			0.415775
$834$	−6.00000	−	3.46410i	−0.207763	−	0.119952i
$835$	15.0000			0.519096
$836$	27.0000			0.933815
$837$	10.0000	−	25.9808i	0.345651	−	0.898027i
$838$			20.7846i			0.717992i
$839$		−	17.3205i		−	0.597970i	−0.954258	−	0.298985i	$-0.903352\pi$
$839$		−	17.3205i		−	0.597970i	0.954258	−	0.298985i	$-0.0966481\pi$
$840$	4.50000	+	2.59808i	0.155265	+	0.0896421i
$841$	7.00000			0.241379
$842$	28.5000	+	49.3634i	0.982175	+	1.70118i
$843$	12.0000	+	6.92820i	0.413302	+	0.238620i
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$	−22.5000	+	0.866025i	−0.774024	+	0.0297922i
$846$	6.00000	+	10.3923i	0.206284	+	0.357295i
$847$	−24.0000	+	13.8564i	−0.824650	+	0.476112i
$848$	7.50000	+	12.9904i	0.257551	+	0.446092i
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	9.00000	−	5.19615i	0.308697	−	0.178227i
$851$		0			0
$852$			8.66025i			0.296695i
$853$		−	13.8564i		−	0.474434i	−0.971457	−	0.237217i	$-0.923765\pi$
$853$		−	13.8564i		−	0.474434i	0.971457	−	0.237217i	$-0.0762353\pi$
$854$	15.0000	−	25.9808i	0.513289	−	0.889043i
$855$	−9.00000	−	15.5885i	−0.307794	−	0.533114i
$856$	13.5000	+	7.79423i	0.461421	+	0.266401i
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$	−31.5000	−	7.79423i	−1.07539	−	0.266091i
$859$	5.50000	+	9.52628i	0.187658	+	0.325032i	0.944469	−	0.328601i	$-0.106577\pi$
$859$	5.50000	+	9.52628i	0.187658	+	0.325032i	−0.756811	+	0.653633i	$0.773244\pi$
$860$		−	1.73205i		−	0.0590624i
$861$	−4.50000	+	7.79423i	−0.153360	+	0.265627i
$862$	19.5000	−	33.7750i	0.664173	−	1.15038i
$863$	−10.5000	+	6.06218i	−0.357424	+	0.206359i	−0.667950	−	0.744206i	$-0.732828\pi$
$863$	−10.5000	+	6.06218i	−0.357424	+	0.206359i	0.310526	+	0.950565i	$0.399495\pi$
$864$		−	25.9808i		−	0.883883i
$865$	−13.5000	−	7.79423i	−0.459014	−	0.265012i
$866$		−	45.0333i		−	1.53029i
$867$	8.00000			0.271694
$868$	7.50000	−	6.06218i	0.254567	−	0.205764i
$869$			25.9808i			0.881337i
$870$	18.0000			0.610257
$871$	30.0000	−	8.66025i	1.01651	−	0.293442i
$872$	−24.0000			−0.812743
$873$	−12.0000	+	6.92820i	−0.406138	+	0.234484i
$874$		0			0
$875$	−10.5000	+	18.1865i	−0.354965	+	0.614817i
$876$		−	8.66025i		−	0.292603i
$877$	16.5000	−	9.52628i	0.557165	−	0.321680i	−0.194842	−	0.980835i	$-0.562419\pi$
$877$	16.5000	−	9.52628i	0.557165	−	0.321680i	0.752007	+	0.659155i	$0.229086\pi$
$878$	−28.5000	+	16.4545i	−0.961828	+	0.555312i
$879$	22.5000	−	12.9904i	0.758906	−	0.438155i
$880$	−22.5000	+	38.9711i	−0.758475	+	1.31372i
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	0.711582	−	0.702603i	$-0.247979\pi$
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	−0.964263	+	0.264946i	$0.914646\pi$
$882$	12.0000	+	6.92820i	0.404061	+	0.233285i
$883$	−56.0000			−1.88455			−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000			−1.88455			−0.942275	+	0.334840i	$0.891318\pi$
$884$	7.50000	−	7.79423i	0.252252	−	0.262148i
$885$	1.50000	−	2.59808i	0.0504219	−	0.0873334i
$886$	−22.5000	+	12.9904i	−0.755902	+	0.436420i
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	−0.998588	−	0.0531258i	$-0.983082\pi$
$887$	−13.5000	+	23.3827i	−0.453286	+	0.785114i	0.545302	+	0.838240i	$0.316415\pi$
$888$	4.50000	+	7.79423i	0.151010	+	0.261557i
$889$	10.5000	−	6.06218i	0.352159	−	0.203319i
$890$	18.0000	−	10.3923i	0.603361	−	0.348351i
$891$		−	5.19615i		−	0.174078i
$892$	1.50000	+	0.866025i	0.0502237	+	0.0289967i
$893$	9.00000	−	15.5885i	0.301174	−	0.521648i
$894$	16.5000	+	28.5788i	0.551843	+	0.955819i
$895$		−	5.19615i		−	0.173688i
$896$	−10.5000	+	18.1865i	−0.350780	+	0.607569i
$897$		0			0
$898$	−24.0000			−0.800890
$899$	−12.0000	+	31.1769i	−0.400222	+	1.03981i
$900$	4.00000			0.133333
$901$	9.00000			0.299833
$902$	−40.5000	−	23.3827i	−1.34850	−	0.778558i
$903$			1.73205i			0.0576390i
$904$	−13.5000	+	7.79423i	−0.449003	+	0.259232i
$905$	34.5000	+	19.9186i	1.14682	+	0.662116i
$906$	−3.00000	+	5.19615i	−0.0996683	+	0.172631i
$907$	28.0000			0.929725			0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000			0.929725			0.464862	+	0.885383i	$0.346104\pi$
$908$	−7.50000	+	4.33013i	−0.248896	+	0.143700i
$909$	18.0000	+	31.1769i	0.597022	+	1.03407i
$910$	−4.50000	+	18.1865i	−0.149174	+	0.602878i
$911$	10.5000	−	18.1865i	0.347881	−	0.602547i	−0.637992	−	0.770043i	$-0.720235\pi$
$911$	10.5000	−	18.1865i	0.347881	−	0.602547i	0.985873	+	0.167496i	$0.0535682\pi$
$912$	−22.5000	+	12.9904i	−0.745049	+	0.430155i
$913$	31.5000	−	54.5596i	1.04250	−	1.80566i
$914$	−12.0000			−0.396925
$915$			17.3205i			0.572598i
$916$	1.50000	+	0.866025i	0.0495614	+	0.0286143i
$917$	−13.5000	+	7.79423i	−0.445809	+	0.257388i
$918$	−22.5000	−	12.9904i	−0.742611	−	0.428746i
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	0.942367	−	0.334581i	$-0.108595\pi$
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	−0.760939	+	0.648824i	$0.775261\pi$
$920$		0			0
$921$	−1.50000	+	0.866025i	−0.0494267	+	0.0285365i
$922$	24.0000			0.790398
$923$	30.0000	−	8.66025i	0.987462	−	0.285056i
$924$	−4.50000	+	7.79423i	−0.148039	+	0.256411i
$925$	−9.00000	+	5.19615i	−0.295918	+	0.170848i
$926$	30.0000			0.985861
$927$	−19.0000	+	32.9090i	−0.624042	+	1.08087i
$928$			31.1769i			1.02343i
$929$			20.7846i			0.681921i	0.940078	+	0.340960i	$0.110752\pi$
$929$			20.7846i			0.681921i	−0.940078	+	0.340960i	$0.889248\pi$
$930$	−6.00000	+	15.5885i	−0.196748	+	0.511166i
$931$		−	20.7846i		−	0.681188i
$932$	18.0000			0.589610
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		−	62.3538i		−	2.04028i
$935$	13.5000	+	23.3827i	0.441497	+	0.764696i
$936$	−12.0000	+	3.46410i	−0.392232	+	0.113228i
$937$	−3.50000	+	6.06218i	−0.114340	+	0.198043i	−0.917516	−	0.397699i	$-0.869809\pi$
$937$	−3.50000	+	6.06218i	−0.114340	+	0.198043i	0.803176	+	0.595742i	$0.203142\pi$
$938$		−	25.9808i		−	0.848302i
$939$	9.50000	+	16.4545i	0.310021	+	0.536972i
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	22.5000	−	12.9904i	0.733479	−	0.423474i	−0.0862145	−	0.996277i	$-0.527477\pi$
$941$	22.5000	−	12.9904i	0.733479	−	0.423474i	0.819694	+	0.572802i	$0.194144\pi$
$942$	−33.0000	−	19.0526i	−1.07520	−	0.620766i
$943$		0			0
$944$	7.50000	+	4.33013i	0.244104	+	0.140934i
$945$	15.0000			0.487950
$946$	−9.00000			−0.292615
$947$	−37.5000	−	21.6506i	−1.21859	−	0.703551i	−0.253971	−	0.967212i	$-0.581737\pi$
$947$	−37.5000	−	21.6506i	−1.21859	−	0.703551i	−0.964615	+	0.263661i	$0.915070\pi$
$948$	2.50000	+	4.33013i	0.0811962	+	0.140636i
$949$	−30.0000	+	8.66025i	−0.973841	+	0.281124i
$950$	−9.00000	−	15.5885i	−0.291999	−	0.505756i
$951$	−13.5000	+	7.79423i	−0.437767	+	0.252745i
$952$	4.50000	+	7.79423i	0.145846	+	0.252612i
$953$	54.0000			1.74923			0.874616	−	0.484817i	$-0.161114\pi$
$953$	54.0000			1.74923			0.874616	+	0.484817i	$0.161114\pi$
$954$	9.00000	+	5.19615i	0.291386	+	0.168232i
$955$	−22.5000	−	12.9904i	−0.728083	−	0.420359i
$956$	−13.5000	+	7.79423i	−0.436621	+	0.252083i
$957$		−	31.1769i		−	1.00781i
$958$	1.50000	−	2.59808i	0.0484628	−	0.0839400i
$959$	−9.00000			−0.290625
$960$		−	1.73205i		−	0.0559017i
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$	−22.5000	+	23.3827i	−0.725429	+	0.753888i
$963$	18.0000			0.580042
$964$	1.50000	+	0.866025i	0.0483117	+	0.0278928i
$965$	39.0000			1.25545
$966$		0			0
$967$	−37.5000	−	21.6506i	−1.20592	−	0.696237i	−0.244054	−	0.969762i	$-0.578477\pi$
$967$	−37.5000	−	21.6506i	−1.20592	−	0.696237i	−0.961865	+	0.273524i	$0.911811\pi$
$968$	24.0000	+	13.8564i	0.771389	+	0.445362i
$969$			15.5885i			0.500773i
$970$	18.0000	−	10.3923i	0.577945	−	0.333677i
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	0.997150	−	0.0754473i	$-0.0240385\pi$
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	−0.563914	+	0.825833i	$0.690705\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	6.00000	+	3.46410i	0.192351	+	0.111054i
$974$	19.5000	+	33.7750i	0.624820	+	1.08222i
$975$	2.00000	+	6.92820i	0.0640513	+	0.221880i
$976$	−50.0000			−1.60046
$977$			34.6410i			1.10826i	0.832429	+	0.554132i	$0.186950\pi$
$977$			34.6410i			1.10826i	−0.832429	+	0.554132i	$0.813050\pi$
$978$	9.00000	−	15.5885i	0.287788	−	0.498464i
$979$	−18.0000	−	31.1769i	−0.575282	−	0.996419i
$980$	−6.00000	−	3.46410i	−0.191663	−	0.110657i
$981$	−24.0000	+	13.8564i	−0.766261	+	0.442401i
$982$	13.5000	−	7.79423i	0.430802	−	0.248724i
$983$	−40.5000	+	23.3827i	−1.29175	+	0.745792i	−0.978964	−	0.204032i	$-0.934595\pi$
$983$	−40.5000	+	23.3827i	−1.29175	+	0.745792i	−0.312785	+	0.949824i	$0.601262\pi$
$984$	9.00000			0.286910
$985$	7.50000	−	12.9904i	0.238970	−	0.413908i
$986$	27.0000	+	15.5885i	0.859855	+	0.496438i
$987$	3.00000	+	5.19615i	0.0954911	+	0.165395i
$988$	−13.5000	−	12.9904i	−0.429492	−	0.413279i
$989$		0			0
$990$			31.1769i			0.990867i
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$	−27.0000	−	10.3923i	−0.857251	−	0.329956i
$993$			12.1244i			0.384755i
$994$		−	25.9808i		−	0.824060i
$995$	37.5000	+	21.6506i	1.18883	+	0.686371i
$996$		−	12.1244i		−	0.384175i
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	0.993213	−	0.116310i	$-0.0371066\pi$
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	−0.597334	+	0.801993i	$0.703773\pi$
$998$	31.5000	−	54.5596i	0.997115	−	1.72705i
$999$	22.5000	+	12.9904i	0.711868	+	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.a.129.1	yes	2
13.12	even	2		403.2.l.b.129.1	yes	2
31.25	even	3		403.2.l.b.25.1	yes	2
403.25	even	6	inner	403.2.l.a.25.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.a.25.1	✓	2	403.25	even	6	inner
403.2.l.a.129.1	yes	2	1.1	even	1	trivial
403.2.l.b.25.1	yes	2	31.25	even	3
403.2.l.b.129.1	yes	2	13.12	even	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+1.73205i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(1.50000 + 0.866025i) q^{6} +(-1.50000 - 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-4.50000 + 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.50000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{14} +1.73205i q^{15} -5.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(-3.00000 + 1.73205i) q^{18} +(4.50000 + 2.59808i) q^{19} +(1.50000 - 0.866025i) q^{20} +(-1.50000 + 0.866025i) q^{21} +(-4.50000 - 7.79423i) q^{22} +(1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-1.50000 + 6.06218i) q^{26} +5.00000 q^{27} +(1.50000 + 0.866025i) q^{28} -6.00000 q^{29} -3.00000 q^{30} +(2.00000 - 5.19615i) q^{31} -5.19615i q^{32} +5.19615i q^{33} +(-4.50000 - 2.59808i) q^{34} +3.00000 q^{35} +(-1.00000 - 1.73205i) q^{36} +(4.50000 + 2.59808i) q^{37} +(-4.50000 + 7.79423i) q^{38} +(2.50000 - 2.59808i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-1.50000 - 2.59808i) q^{42} +(0.500000 - 0.866025i) q^{43} +(4.50000 - 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} -3.46410i q^{47} +(-2.50000 + 4.33013i) q^{48} +(-2.00000 - 3.46410i) q^{49} +(-3.00000 - 1.73205i) q^{50} +(1.50000 + 2.59808i) q^{51} +(-3.50000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} +8.66025i q^{54} +(4.50000 - 7.79423i) q^{55} +(1.50000 - 2.59808i) q^{56} +(4.50000 - 2.59808i) q^{57} -10.3923i q^{58} +(-1.50000 - 0.866025i) q^{59} -1.73205i q^{60} +10.0000 q^{61} +(9.00000 + 3.46410i) q^{62} -3.46410i q^{63} -1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} -9.00000 q^{66} +(7.50000 - 4.33013i) q^{67} +(1.50000 - 2.59808i) q^{68} +5.19615i q^{70} +(7.50000 - 4.33013i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-7.50000 + 4.33013i) q^{73} +(-4.50000 + 7.79423i) q^{74} +(1.00000 + 1.73205i) q^{75} +(-4.50000 - 2.59808i) q^{76} +9.00000 q^{77} +(4.50000 + 4.33013i) q^{78} +(2.50000 - 4.33013i) q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} +(-10.5000 + 6.06218i) q^{83} +(1.50000 - 0.866025i) q^{84} -5.19615i q^{85} +(1.50000 + 0.866025i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(-4.50000 - 7.79423i) q^{88} +6.92820i q^{89} +(3.00000 - 5.19615i) q^{90} +(-4.50000 - 4.33013i) q^{91} +(-3.50000 - 4.33013i) q^{93} +6.00000 q^{94} -9.00000 q^{95} +(-4.50000 - 2.59808i) q^{96} +6.92820i q^{97} +(6.00000 - 3.46410i) q^{98} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 2 * q^9	\( 2 q + q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{6} - 3 q^{7} + 2 q^{9} - 3 q^{10} - 9 q^{11} - q^{12} + 7 q^{13} + 3 q^{14} - 10 q^{16} - 3 q^{17} - 6 q^{18} + 9 q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{22} + 3 q^{24} - 2 q^{25} - 3 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 6 q^{30} + 4 q^{31} - 9 q^{34} + 6 q^{35} - 2 q^{36} + 9 q^{37} - 9 q^{38} + 5 q^{39} - 3 q^{40} + 9 q^{41} - 3 q^{42} + q^{43} + 9 q^{44} - 6 q^{45} - 5 q^{48} - 4 q^{49} - 6 q^{50} + 3 q^{51} - 7 q^{52} - 3 q^{53} + 9 q^{55} + 3 q^{56} + 9 q^{57} - 3 q^{59} + 20 q^{61} + 18 q^{62} - 2 q^{64} - 12 q^{65} - 18 q^{66} + 15 q^{67} + 3 q^{68} + 15 q^{71} - 6 q^{72} - 15 q^{73} - 9 q^{74} + 2 q^{75} - 9 q^{76} + 18 q^{77} + 9 q^{78} + 5 q^{79} + 15 q^{80} - q^{81} + 9 q^{82} - 21 q^{83} + 3 q^{84} + 3 q^{86} - 6 q^{87} - 9 q^{88} + 6 q^{90} - 9 q^{91} - 7 q^{93} + 12 q^{94} - 18 q^{95} - 9 q^{96} + 12 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q + q^3 - 2 * q^4 - 3 * q^5 + 3 * q^6 - 3 * q^7 + 2 * q^9 - 3 * q^10 - 9 * q^11 - q^12 + 7 * q^13 + 3 * q^14 - 10 * q^16 - 3 * q^17 - 6 * q^18 + 9 * q^19 + 3 * q^20 - 3 * q^21 - 9 * q^22 + 3 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 6 * q^30 + 4 * q^31 - 9 * q^34 + 6 * q^35 - 2 * q^36 + 9 * q^37 - 9 * q^38 + 5 * q^39 - 3 * q^40 + 9 * q^41 - 3 * q^42 + q^43 + 9 * q^44 - 6 * q^45 - 5 * q^48 - 4 * q^49 - 6 * q^50 + 3 * q^51 - 7 * q^52 - 3 * q^53 + 9 * q^55 + 3 * q^56 + 9 * q^57 - 3 * q^59 + 20 * q^61 + 18 * q^62 - 2 * q^64 - 12 * q^65 - 18 * q^66 + 15 * q^67 + 3 * q^68 + 15 * q^71 - 6 * q^72 - 15 * q^73 - 9 * q^74 + 2 * q^75 - 9 * q^76 + 18 * q^77 + 9 * q^78 + 5 * q^79 + 15 * q^80 - q^81 + 9 * q^82 - 21 * q^83 + 3 * q^84 + 3 * q^86 - 6 * q^87 - 9 * q^88 + 6 * q^90 - 9 * q^91 - 7 * q^93 + 12 * q^94 - 18 * q^95 - 9 * q^96 + 12 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more