LMFDB - Embedded newform 126.2.e.b.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(25,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("126.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.e (of order $3$, 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:	$1.00611506547$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.25
Dual form			126.2.e.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +1.73205i q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +1.73205i q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(-2.50000 - 4.33013i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(4.50000 + 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(-2.50000 - 4.33013i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +1.73205i q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 - 4.33013i) q^{26} -5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(1.50000 - 2.59808i) q^{29} +(4.50000 + 2.59808i) q^{30} -4.00000 q^{31} +1.00000 q^{32} +(-4.50000 + 2.59808i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.50000 + 7.79423i) q^{35} -3.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(-2.50000 - 4.33013i) q^{38} +(7.50000 - 4.33013i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 + 7.79423i) q^{41} +(-3.00000 - 3.46410i) q^{42} +(-5.50000 + 9.52628i) q^{43} +(1.50000 + 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{45} +(1.50000 - 2.59808i) q^{46} +1.73205i q^{48} +(1.00000 - 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} -5.19615i q^{54} +9.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(7.50000 - 4.33013i) q^{57} +(1.50000 - 2.59808i) q^{58} +12.0000 q^{59} +(4.50000 + 2.59808i) q^{60} +2.00000 q^{61} -4.00000 q^{62} +(6.00000 - 5.19615i) q^{63} +1.00000 q^{64} -15.0000 q^{65} +(-4.50000 + 2.59808i) q^{66} -4.00000 q^{67} +(-1.50000 + 2.59808i) q^{68} +(4.50000 + 2.59808i) q^{69} +(1.50000 + 7.79423i) q^{70} -3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(3.50000 + 6.06218i) q^{74} +(6.00000 - 3.46410i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-7.50000 - 2.59808i) q^{77} +(7.50000 - 4.33013i) q^{78} +8.00000 q^{79} +(1.50000 - 2.59808i) q^{80} +9.00000 q^{81} +(4.50000 + 7.79423i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-3.00000 - 3.46410i) q^{84} +(4.50000 + 7.79423i) q^{85} +(-5.50000 + 9.52628i) q^{86} +(4.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(12.5000 + 4.33013i) q^{91} +(1.50000 - 2.59808i) q^{92} -6.92820i q^{93} -15.0000 q^{95} +1.73205i q^{96} +(0.500000 - 0.866025i) q^{97} +(1.00000 - 6.92820i) q^{98} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - 4 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - 4 * q^7 + 2 * q^8 - 6 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - 4 q^{7} + 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} - 5 q^{13} - 4 q^{14} + 9 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 3 q^{22} + 3 q^{23} - 4 q^{25} - 5 q^{26} - 4 q^{28} + 3 q^{29} + 9 q^{30} - 8 q^{31} + 2 q^{32} - 9 q^{33} - 3 q^{34} + 3 q^{35} - 6 q^{36} + 7 q^{37} - 5 q^{38} + 15 q^{39} + 3 q^{40} + 9 q^{41} - 6 q^{42} - 11 q^{43} + 3 q^{44} - 9 q^{45} + 3 q^{46} + 2 q^{49} - 4 q^{50} - 9 q^{51} - 5 q^{52} + 3 q^{53} + 18 q^{55} - 4 q^{56} + 15 q^{57} + 3 q^{58} + 24 q^{59} + 9 q^{60} + 4 q^{61} - 8 q^{62} + 12 q^{63} + 2 q^{64} - 30 q^{65} - 9 q^{66} - 8 q^{67} - 3 q^{68} + 9 q^{69} + 3 q^{70} - 6 q^{72} - 11 q^{73} + 7 q^{74} + 12 q^{75} - 5 q^{76} - 15 q^{77} + 15 q^{78} + 16 q^{79} + 3 q^{80} + 18 q^{81} + 9 q^{82} - 3 q^{83} - 6 q^{84} + 9 q^{85} - 11 q^{86} + 9 q^{87} + 3 q^{88} - 15 q^{89} - 9 q^{90} + 25 q^{91} + 3 q^{92} - 30 q^{95} + q^{97} + 2 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - 4 * q^7 + 2 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 - 5 * q^13 - 4 * q^14 + 9 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 3 * q^22 + 3 * q^23 - 4 * q^25 - 5 * q^26 - 4 * q^28 + 3 * q^29 + 9 * q^30 - 8 * q^31 + 2 * q^32 - 9 * q^33 - 3 * q^34 + 3 * q^35 - 6 * q^36 + 7 * q^37 - 5 * q^38 + 15 * q^39 + 3 * q^40 + 9 * q^41 - 6 * q^42 - 11 * q^43 + 3 * q^44 - 9 * q^45 + 3 * q^46 + 2 * q^49 - 4 * q^50 - 9 * q^51 - 5 * q^52 + 3 * q^53 + 18 * q^55 - 4 * q^56 + 15 * q^57 + 3 * q^58 + 24 * q^59 + 9 * q^60 + 4 * q^61 - 8 * q^62 + 12 * q^63 + 2 * q^64 - 30 * q^65 - 9 * q^66 - 8 * q^67 - 3 * q^68 + 9 * q^69 + 3 * q^70 - 6 * q^72 - 11 * q^73 + 7 * q^74 + 12 * q^75 - 5 * q^76 - 15 * q^77 + 15 * q^78 + 16 * q^79 + 3 * q^80 + 18 * q^81 + 9 * q^82 - 3 * q^83 - 6 * q^84 + 9 * q^85 - 11 * q^86 + 9 * q^87 + 3 * q^88 - 15 * q^89 - 9 * q^90 + 25 * q^91 + 3 * q^92 - 30 * q^95 + q^97 + 2 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	1.00000			0.500000
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$			1.73205i			0.707107i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$	−3.00000			−1.00000
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$			1.73205i			0.500000i
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$	4.50000	+	2.59808i	1.16190	+	0.670820i
$16$	1.00000			0.250000
$17$	−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			−0.707107
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$			1.73205i			0.353553i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$		−	5.19615i		−	1.00000i
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$	4.50000	+	2.59808i	0.821584	+	0.474342i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000			0.176777
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	1.50000	+	7.79423i	0.253546	+	1.31747i
$36$	−3.00000			−0.500000
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	−2.50000	−	4.33013i	−0.405554	−	0.702439i
$39$	7.50000	−	4.33013i	1.20096	−	0.693375i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$	−3.00000	−	3.46410i	−0.462910	−	0.534522i
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	−4.50000	+	7.79423i	−0.670820	+	1.16190i
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$			1.73205i			0.250000i
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$		−	5.19615i		−	0.707107i
$55$	9.00000			1.21356
$56$	−2.00000	+	1.73205i	−0.267261	+	0.231455i
$57$	7.50000	−	4.33013i	0.993399	−	0.573539i
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	12.0000			1.56227			0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000			1.56227			0.781133	+	0.624364i	$0.214642\pi$
$60$	4.50000	+	2.59808i	0.580948	+	0.335410i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.00000			−0.508001
$63$	6.00000	−	5.19615i	0.755929	−	0.654654i
$64$	1.00000			0.125000
$65$	−15.0000			−1.86052
$66$	−4.50000	+	2.59808i	−0.553912	+	0.319801i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	4.50000	+	2.59808i	0.541736	+	0.312772i
$70$	1.50000	+	7.79423i	0.179284	+	0.931589i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−3.00000			−0.353553
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	0.340868	+	0.940111i	$0.389279\pi$
$73$	−5.50000	+	9.52628i	−0.643726	+	1.11497i	−0.984594	+	0.174855i	$0.944054\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	−7.50000	−	2.59808i	−0.854704	−	0.296078i
$78$	7.50000	−	4.33013i	0.849208	−	0.490290i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	9.00000			1.00000
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$	−3.00000	−	3.46410i	−0.327327	−	0.377964i
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$	−5.50000	+	9.52628i	−0.593080	+	1.02725i
$87$	4.50000	+	2.59808i	0.482451	+	0.278543i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$	−4.50000	+	7.79423i	−0.474342	+	0.821584i
$91$	12.5000	+	4.33013i	1.31036	+	0.453921i
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$		−	6.92820i		−	0.718421i
$94$		0			0
$95$	−15.0000			−1.53897
$96$			1.73205i			0.176777i
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−4.50000	−	7.79423i	−0.452267	−	0.783349i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	−0.962505	−	0.271263i	$-0.912559\pi$
$103$	−2.50000	+	4.33013i	−0.246332	+	0.426660i	0.716173	+	0.697923i	$0.245892\pi$
$104$	−2.50000	−	4.33013i	−0.245145	−	0.424604i
$105$	−13.5000	+	2.59808i	−1.31747	+	0.253546i
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	0.958952	+	0.283567i	$0.0915178\pi$
$107$	7.50000	+	12.9904i	0.725052	+	1.25583i	−0.233900	+	0.972261i	$0.575149\pi$
$108$		−	5.19615i		−	0.500000i
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$	9.00000			0.858116
$111$	−10.5000	+	6.06218i	−0.996616	+	0.575396i
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$	7.50000	−	4.33013i	0.702439	−	0.405554i
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	7.50000	+	12.9904i	0.693375	+	1.20096i
$118$	12.0000			1.10469
$119$	−1.50000	−	7.79423i	−0.137505	−	0.714496i
$120$	4.50000	+	2.59808i	0.410792	+	0.237171i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	2.00000			0.181071
$123$	−13.5000	+	7.79423i	−1.21725	+	0.702782i
$124$	−4.00000			−0.359211
$125$	3.00000			0.268328
$126$	6.00000	−	5.19615i	0.534522	−	0.462910i
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000			0.0883883
$129$	−16.5000	−	9.52628i	−1.45274	−	0.838742i
$130$	−15.0000			−1.31559
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$	−4.50000	+	2.59808i	−0.391675	+	0.226134i
$133$	12.5000	+	4.33013i	1.08389	+	0.375470i
$134$	−4.00000			−0.345547
$135$	−13.5000	−	7.79423i	−1.16190	−	0.670820i
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	4.50000	+	2.59808i	0.383065	+	0.221163i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$	1.50000	+	7.79423i	0.126773	+	0.658733i
$141$		0			0
$142$		0			0
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$	−3.00000			−0.250000
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	12.0000	+	1.73205i	0.989743	+	0.142857i
$148$	3.50000	+	6.06218i	0.287698	+	0.498308i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$	6.00000	−	3.46410i	0.489898	−	0.282843i
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$	−7.50000	−	2.59808i	−0.604367	−	0.209359i
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$	7.50000	−	4.33013i	0.600481	−	0.346688i
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	8.00000			0.636446
$159$	4.50000	+	2.59808i	0.356873	+	0.206041i
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	1.50000	+	7.79423i	0.118217	+	0.614271i
$162$	9.00000			0.707107
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	0.313304	−	0.949653i	$-0.398564\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$			15.5885i			1.21356i
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	0.802135	−	0.597143i	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$	−3.00000	−	3.46410i	−0.231455	−	0.267261i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	4.50000	+	7.79423i	0.345134	+	0.597790i
$171$	7.50000	+	12.9904i	0.573539	+	0.993399i
$172$	−5.50000	+	9.52628i	−0.419371	+	0.726372i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	4.50000	+	2.59808i	0.341144	+	0.196960i
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$			20.7846i			1.56227i
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	−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	$0.202429\pi$
$180$	−4.50000	+	7.79423i	−0.335410	+	0.580948i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	12.5000	+	4.33013i	0.926562	+	0.320970i
$183$			3.46410i			0.256074i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	21.0000			1.54395
$186$		−	6.92820i		−	0.508001i
$187$	−9.00000			−0.658145
$188$		0			0
$189$	9.00000	+	10.3923i	0.654654	+	0.755929i
$190$	−15.0000			−1.08821
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$			1.73205i			0.125000i
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	0.500000	−	0.866025i	0.0358979	−	0.0621770i
$195$		−	25.9808i		−	1.86052i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		−	6.92820i		−	0.488678i
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$	−4.50000	−	2.59808i	−0.315063	−	0.181902i
$205$	27.0000			1.88576
$206$	−2.50000	+	4.33013i	−0.174183	+	0.301694i
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$	7.50000	−	12.9904i	0.518786	−	0.898563i
$210$	−13.5000	+	2.59808i	−0.931589	+	0.179284i
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	16.5000	+	28.5788i	1.12529	+	1.94906i
$216$		−	5.19615i		−	0.353553i
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$	3.50000	−	6.06218i	0.237050	−	0.410582i
$219$	−16.5000	−	9.52628i	−1.11497	−	0.643726i
$220$	9.00000			0.606780
$221$	15.0000			1.00901
$222$	−10.5000	+	6.06218i	−0.704714	+	0.406867i
$223$	−8.50000	+	14.7224i	−0.569202	+	0.985887i	0.427443	+	0.904042i	$0.359414\pi$
$223$	−8.50000	+	14.7224i	−0.569202	+	0.985887i	−0.996645	+	0.0818447i	$0.973919\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$	−7.50000	−	12.9904i	−0.498893	−	0.864107i
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$	7.50000	−	4.33013i	0.496700	−	0.286770i
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	0.435653	+	0.900115i	$0.356518\pi$
$229$	−8.50000	+	14.7224i	−0.561696	+	0.972886i	−0.997349	+	0.0727709i	$0.976816\pi$
$230$	−4.50000	−	7.79423i	−0.296721	−	0.513936i
$231$	4.50000	−	12.9904i	0.296078	−	0.854704i
$232$	1.50000	−	2.59808i	0.0984798	−	0.170572i
$233$	−13.5000	−	23.3827i	−0.884414	−	1.53185i	−0.846383	−	0.532574i	$-0.821225\pi$
$233$	−13.5000	−	23.3827i	−0.884414	−	1.53185i	−0.0380310	−	0.999277i	$-0.512109\pi$
$234$	7.50000	+	12.9904i	0.490290	+	0.849208i
$235$		0			0
$236$	12.0000			0.781133
$237$			13.8564i			0.900070i
$238$	−1.50000	−	7.79423i	−0.0972306	−	0.505225i
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.858623	−	0.512607i	$-0.828680\pi$
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.0146191	−	0.999893i	$-0.504654\pi$
$240$	4.50000	+	2.59808i	0.290474	+	0.167705i
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$			15.5885i			1.00000i
$244$	2.00000			0.128037
$245$	−16.5000	−	12.9904i	−1.05415	−	0.829925i
$246$	−13.5000	+	7.79423i	−0.860729	+	0.496942i
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	−4.00000			−0.254000
$249$	−4.50000	−	2.59808i	−0.285176	−	0.164646i
$250$	3.00000			0.189737
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	6.00000	−	5.19615i	0.377964	−	0.327327i
$253$	9.00000			0.565825
$254$	−16.0000			−1.00393
$255$	−13.5000	+	7.79423i	−0.845403	+	0.488094i
$256$	1.00000			0.0625000
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$	−16.5000	−	9.52628i	−1.02725	−	0.593080i
$259$	−17.5000	−	6.06218i	−1.08740	−	0.376685i
$260$	−15.0000			−0.930261
$261$	−4.50000	+	7.79423i	−0.278543	+	0.482451i
$262$	−1.50000	+	2.59808i	−0.0926703	+	0.160510i
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$	−4.50000	+	2.59808i	−0.276956	+	0.159901i
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$	12.5000	+	4.33013i	0.766424	+	0.265497i
$267$	22.5000	−	12.9904i	1.37698	−	0.794998i
$268$	−4.00000			−0.244339
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$	−13.5000	−	7.79423i	−0.821584	−	0.474342i
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	0.993082	−	0.117426i	$-0.0374643\pi$
$271$	6.50000	+	11.2583i	0.394847	+	0.683895i	−0.598235	+	0.801321i	$0.704131\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	−7.50000	+	21.6506i	−0.453921	+	1.31036i
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	6.00000	−	10.3923i	0.361814	−	0.626680i
$276$	4.50000	+	2.59808i	0.270868	+	0.156386i
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	−2.50000	−	4.33013i	−0.149940	−	0.259704i
$279$	12.0000			0.718421
$280$	1.50000	+	7.79423i	0.0896421	+	0.465794i
$281$	−1.50000	+	2.59808i	−0.0894825	+	0.154988i	−0.907293	−	0.420500i	$-0.861855\pi$
$281$	−1.50000	+	2.59808i	−0.0894825	+	0.154988i	0.817810	+	0.575488i	$0.195188\pi$
$282$		0			0
$283$	8.00000			0.475551			0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000			0.475551			0.237775	+	0.971320i	$0.423582\pi$
$284$		0			0
$285$		−	25.9808i		−	1.53897i
$286$	7.50000	−	12.9904i	0.443484	−	0.768137i
$287$	−22.5000	−	7.79423i	−1.32813	−	0.460079i
$288$	−3.00000			−0.176777
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$	1.50000	+	0.866025i	0.0879316	+	0.0507673i
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	13.5000	+	23.3827i	0.788678	+	1.36603i	0.926777	+	0.375613i	$0.122568\pi$
$293$	13.5000	+	23.3827i	0.788678	+	1.36603i	−0.138098	+	0.990419i	$0.544099\pi$
$294$	12.0000	+	1.73205i	0.699854	+	0.101015i
$295$	18.0000	−	31.1769i	1.04800	−	1.81519i
$296$	3.50000	+	6.06218i	0.203433	+	0.352357i
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	−15.0000			−0.867472
$300$	6.00000	−	3.46410i	0.346410	−	0.200000i
$301$	−5.50000	−	28.5788i	−0.317015	−	1.64726i
$302$	−5.50000	−	9.52628i	−0.316489	−	0.548176i
$303$	−4.50000	+	2.59808i	−0.258518	+	0.149256i
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	4.50000	−	7.79423i	0.257248	−	0.445566i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−7.50000	−	2.59808i	−0.427352	−	0.148039i
$309$	−7.50000	−	4.33013i	−0.426660	−	0.246332i
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	7.50000	−	4.33013i	0.424604	−	0.245145i
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	14.0000			0.790066
$315$	−4.50000	−	23.3827i	−0.253546	−	1.31747i
$316$	8.00000			0.450035
$317$	30.0000			1.68497			0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000			1.68497			0.842484	+	0.538721i	$0.181092\pi$
$318$	4.50000	+	2.59808i	0.252347	+	0.145693i
$319$	9.00000			0.503903
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$	−22.5000	+	12.9904i	−1.25583	+	0.725052i
$322$	1.50000	+	7.79423i	0.0835917	+	0.434355i
$323$	15.0000			0.834622
$324$	9.00000			0.500000
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$	−8.50000	−	14.7224i	−0.470771	−	0.815400i
$327$	10.5000	+	6.06218i	0.580651	+	0.335239i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$			15.5885i			0.858116i
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−1.50000	+	2.59808i	−0.0823232	+	0.142588i
$333$	−10.5000	−	18.1865i	−0.575396	−	0.996616i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$	−3.00000	−	3.46410i	−0.163663	−	0.188982i
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	0.974701	+	0.223513i	$0.0717525\pi$
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	−0.293783	+	0.955872i	$0.594914\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	22.5000	−	12.9904i	1.22203	−	0.705541i
$340$	4.50000	+	7.79423i	0.244047	+	0.422701i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	7.50000	+	12.9904i	0.405554	+	0.702439i
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−5.50000	+	9.52628i	−0.296540	+	0.513623i
$345$	13.5000	−	7.79423i	0.726816	−	0.419627i
$346$	6.00000			0.322562
$347$	−12.0000			−0.644194			−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000			−0.644194			−0.322097	+	0.946707i	$0.604388\pi$
$348$	4.50000	+	2.59808i	0.241225	+	0.139272i
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$	10.0000	+	3.46410i	0.534522	+	0.185164i
$351$	−22.5000	+	12.9904i	−1.20096	+	0.693375i
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	0.960574	−	0.278024i	$-0.0896796\pi$
$353$	4.50000	+	7.79423i	0.239511	+	0.414845i	−0.721063	+	0.692869i	$0.756346\pi$
$354$			20.7846i			1.10469i
$355$		0			0
$356$	−7.50000	−	12.9904i	−0.397499	−	0.688489i
$357$	13.5000	−	2.59808i	0.714496	−	0.137505i
$358$	−1.50000	+	2.59808i	−0.0792775	+	0.137313i
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	0.597372	−	0.801964i	$-0.296211\pi$
$359$	−7.50000	−	12.9904i	−0.395835	−	0.685606i	−0.993207	+	0.116358i	$0.962878\pi$
$360$	−4.50000	+	7.79423i	−0.237171	+	0.410792i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−10.0000			−0.525588
$363$	3.00000	+	1.73205i	0.157459	+	0.0909091i
$364$	12.5000	+	4.33013i	0.655178	+	0.226960i
$365$	16.5000	+	28.5788i	0.863649	+	1.49588i
$366$			3.46410i			0.181071i
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	0.878780	−	0.477227i	$-0.158358\pi$
$367$	0.500000	+	0.866025i	0.0260998	+	0.0452062i	−0.852680	+	0.522433i	$0.825025\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$	−13.5000	−	23.3827i	−0.702782	−	1.21725i
$370$	21.0000			1.09174
$371$	1.50000	+	7.79423i	0.0778761	+	0.404656i
$372$		−	6.92820i		−	0.359211i
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	−0.997697	−	0.0678218i	$-0.978395\pi$
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	0.557584	+	0.830120i	$0.311728\pi$
$374$	−9.00000			−0.465379
$375$			5.19615i			0.268328i
$376$		0			0
$377$	−15.0000			−0.772539
$378$	9.00000	+	10.3923i	0.462910	+	0.534522i
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$	−15.0000			−0.769484
$381$		−	27.7128i		−	1.41977i
$382$	12.0000			0.613973
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$			1.73205i			0.0883883i
$385$	−18.0000	+	15.5885i	−0.917365	+	0.794461i
$386$	14.0000			0.712581
$387$	16.5000	−	28.5788i	0.838742	−	1.45274i
$388$	0.500000	−	0.866025i	0.0253837	−	0.0439658i
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$		−	25.9808i		−	1.31559i
$391$	4.50000	+	7.79423i	0.227575	+	0.394171i
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$	−4.50000	−	2.59808i	−0.226995	−	0.131056i
$394$	−6.00000			−0.302276
$395$	12.0000	−	20.7846i	0.603786	−	1.04579i
$396$	−4.50000	−	7.79423i	−0.226134	−	0.391675i
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	−0.957839	−	0.287307i	$-0.907240\pi$
$397$	−14.5000	−	25.1147i	−0.727734	−	1.26047i	0.230105	−	0.973166i	$-0.426093\pi$
$398$	3.50000	−	6.06218i	0.175439	−	0.303870i
$399$	−7.50000	+	21.6506i	−0.375470	+	1.08389i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	0.302556	+	0.953131i	$0.402160\pi$
$401$	−13.5000	+	23.3827i	−0.674158	+	1.16768i	−0.976714	+	0.214544i	$0.931173\pi$
$402$		−	6.92820i		−	0.345547i
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	13.5000	−	23.3827i	0.670820	−	1.16190i
$406$	1.50000	+	7.79423i	0.0744438	+	0.386821i
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$	−4.50000	−	2.59808i	−0.222783	−	0.128624i
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$	27.0000			1.33343
$411$	4.50000	−	2.59808i	0.221969	−	0.128154i
$412$	−2.50000	+	4.33013i	−0.123166	+	0.213330i
$413$	−24.0000	+	20.7846i	−1.18096	+	1.02274i
$414$	−4.50000	+	7.79423i	−0.221163	+	0.383065i
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$	−2.50000	−	4.33013i	−0.122573	−	0.212302i
$417$	7.50000	−	4.33013i	0.367277	−	0.212047i
$418$	7.50000	−	12.9904i	0.366837	−	0.635380i
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	0.900337	−	0.435194i	$-0.143320\pi$
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	−0.827057	+	0.562118i	$0.809987\pi$
$420$	−13.5000	+	2.59808i	−0.658733	+	0.126773i
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	−0.189740	−	0.981834i	$-0.560764\pi$
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	0.945163	−	0.326598i	$-0.105902\pi$
$422$	−2.50000	−	4.33013i	−0.121698	−	0.210787i
$423$		0			0
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	12.0000			0.582086
$426$		0			0
$427$	−4.00000	+	3.46410i	−0.193574	+	0.167640i
$428$	7.50000	+	12.9904i	0.362526	+	0.627914i
$429$	22.5000	+	12.9904i	1.08631	+	0.627182i
$430$	16.5000	+	28.5788i	0.795701	+	1.37819i
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	−0.827636	−	0.561266i	$-0.810315\pi$
$431$	1.50000	−	2.59808i	0.0722525	−	0.125145i	0.899888	+	0.436121i	$0.143648\pi$
$432$		−	5.19615i		−	0.250000i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	8.00000	−	6.92820i	0.384012	−	0.332564i
$435$	13.5000	−	7.79423i	0.647275	−	0.373705i
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−15.0000			−0.717547
$438$	−16.5000	−	9.52628i	−0.788400	−	0.455183i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	9.00000			0.429058
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$	15.0000			0.713477
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$	−10.5000	+	6.06218i	−0.498308	+	0.287698i
$445$	−45.0000			−2.13320
$446$	−8.50000	+	14.7224i	−0.402487	+	0.697127i
$447$	4.50000	+	2.59808i	0.212843	+	0.122885i
$448$	−2.00000	+	1.73205i	−0.0944911	+	0.0818317i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	6.00000	+	10.3923i	0.282843	+	0.489898i
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	16.5000	−	9.52628i	0.775238	−	0.447584i
$454$	−4.50000	−	7.79423i	−0.211195	−	0.365801i
$455$	30.0000	−	25.9808i	1.40642	−	1.21800i
$456$	7.50000	−	4.33013i	0.351220	−	0.202777i
$457$	−34.0000			−1.59045			−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000			−1.59045			−0.795226	+	0.606313i	$0.792648\pi$
$458$	−8.50000	+	14.7224i	−0.397179	+	0.687934i
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$	−4.50000	−	7.79423i	−0.209814	−	0.363408i
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$	4.50000	−	12.9904i	0.209359	−	0.604367i
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	−0.910546	−	0.413407i	$-0.864339\pi$
$463$	−17.5000	−	30.3109i	−0.813294	−	1.40867i	0.0972525	−	0.995260i	$-0.468995\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	−18.0000	−	10.3923i	−0.834730	−	0.481932i
$466$	−13.5000	−	23.3827i	−0.625375	−	1.08318i
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	0.898642	−	0.438682i	$-0.144554\pi$
$467$	1.50000	+	2.59808i	0.0694117	+	0.120225i	−0.829231	+	0.558906i	$0.811221\pi$
$468$	7.50000	+	12.9904i	0.346688	+	0.600481i
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$			24.2487i			1.11732i
$472$	12.0000			0.552345
$473$	−33.0000			−1.51734
$474$			13.8564i			0.636446i
$475$	−10.0000	+	17.3205i	−0.458831	+	0.794719i
$476$	−1.50000	−	7.79423i	−0.0687524	−	0.357248i
$477$	−4.50000	+	7.79423i	−0.206041	+	0.356873i
$478$	−13.5000	−	23.3827i	−0.617476	−	1.06950i
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	0.950327	−	0.311253i	$-0.100749\pi$
$479$	4.50000	+	7.79423i	0.205610	+	0.356127i	−0.744717	+	0.667381i	$0.767415\pi$
$480$	4.50000	+	2.59808i	0.205396	+	0.118585i
$481$	17.5000	−	30.3109i	0.797931	−	1.38206i
$482$	−11.5000	−	19.9186i	−0.523811	−	0.907267i
$483$	−13.5000	+	2.59808i	−0.614271	+	0.118217i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−1.50000	−	2.59808i	−0.0681115	−	0.117973i
$486$			15.5885i			0.707107i
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	−0.265260	−	0.964177i	$-0.585458\pi$
$487$	15.5000	−	26.8468i	0.702372	−	1.21654i	0.967632	−	0.252367i	$-0.0812090\pi$
$488$	2.00000			0.0905357
$489$	25.5000	−	14.7224i	1.15315	−	0.665771i
$490$	−16.5000	−	12.9904i	−0.745394	−	0.586846i
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.851314	+	0.524656i	$0.175806\pi$
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.0287085	+	0.999588i	$0.490861\pi$
$492$	−13.5000	+	7.79423i	−0.608627	+	0.351391i
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	−12.5000	+	21.6506i	−0.562402	+	0.974108i
$495$	−27.0000			−1.21356
$496$	−4.00000			−0.179605
$497$		0			0
$498$	−4.50000	−	2.59808i	−0.201650	−	0.116423i
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−5.50000	+	9.52628i	−0.246214	+	0.426455i	0.716258	+	0.697835i	$0.245853\pi$
$500$	3.00000			0.134164
$501$	4.50000	−	2.59808i	0.201045	−	0.116073i
$502$	12.0000			0.535586
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$	6.00000	−	5.19615i	0.267261	−	0.231455i
$505$	9.00000			0.400495
$506$	9.00000			0.400099
$507$	−18.0000	−	10.3923i	−0.799408	−	0.461538i
$508$	−16.0000			−0.709885
$509$	13.5000	−	23.3827i	0.598377	−	1.03642i	−0.394684	−	0.918817i	$-0.629146\pi$
$509$	13.5000	−	23.3827i	0.598377	−	1.03642i	0.993061	−	0.117602i	$-0.0375208\pi$
$510$	−13.5000	+	7.79423i	−0.597790	+	0.345134i
$511$	−5.50000	−	28.5788i	−0.243306	−	1.26425i
$512$	1.00000			0.0441942
$513$	−22.5000	+	12.9904i	−0.993399	+	0.573539i
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$	7.50000	+	12.9904i	0.330489	+	0.572425i
$516$	−16.5000	−	9.52628i	−0.726372	−	0.419371i
$517$		0			0
$518$	−17.5000	−	6.06218i	−0.768906	−	0.266357i
$519$			10.3923i			0.456172i
$520$	−15.0000			−0.657794
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	−0.897011	−	0.442007i	$-0.854267\pi$
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	0.831295	+	0.555831i	$0.187600\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	3.50000	+	6.06218i	0.153044	+	0.265081i	0.932345	−	0.361569i	$-0.117759\pi$
$523$	3.50000	+	6.06218i	0.153044	+	0.265081i	−0.779301	+	0.626650i	$0.784426\pi$
$524$	−1.50000	+	2.59808i	−0.0655278	+	0.113497i
$525$	−6.00000	+	17.3205i	−0.261861	+	0.755929i
$526$	4.50000	+	7.79423i	0.196209	+	0.339845i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	−4.50000	+	2.59808i	−0.195837	+	0.113067i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−4.50000	−	7.79423i	−0.195468	−	0.338560i
$531$	−36.0000			−1.56227
$532$	12.5000	+	4.33013i	0.541944	+	0.187735i
$533$	22.5000	−	38.9711i	0.974583	−	1.68803i
$534$	22.5000	−	12.9904i	0.973670	−	0.562149i
$535$	45.0000			1.94552
$536$	−4.00000			−0.172774
$537$	−4.50000	−	2.59808i	−0.194189	−	0.112115i
$538$	−10.5000	+	18.1865i	−0.452687	+	0.784077i
$539$	19.5000	−	7.79423i	0.839924	−	0.335721i
$540$	−13.5000	−	7.79423i	−0.580948	−	0.335410i
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	0.623404	−	0.781900i	$-0.285749\pi$
$541$	−8.50000	−	14.7224i	−0.365444	−	0.632967i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	6.50000	+	11.2583i	0.279199	+	0.483587i
$543$		−	17.3205i		−	0.743294i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−10.5000	−	18.1865i	−0.449771	−	0.779026i
$546$	−7.50000	+	21.6506i	−0.320970	+	0.926562i
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	−0.959320	−	0.282321i	$-0.908896\pi$
$547$	−5.50000	+	9.52628i	−0.235163	+	0.407314i	0.724157	+	0.689635i	$0.242229\pi$
$548$	−1.50000	−	2.59808i	−0.0640768	−	0.110984i
$549$	−6.00000			−0.256074
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	−15.0000			−0.639021
$552$	4.50000	+	2.59808i	0.191533	+	0.110581i
$553$	−16.0000	+	13.8564i	−0.680389	+	0.589234i
$554$	3.50000	+	6.06218i	0.148701	+	0.257557i
$555$			36.3731i			1.54395i
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$	12.0000			0.508001
$559$	55.0000			2.32625
$560$	1.50000	+	7.79423i	0.0633866	+	0.329366i
$561$		−	15.5885i		−	0.658145i
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$	−45.0000			−1.89316
$566$	8.00000			0.336265
$567$	−18.0000	+	15.5885i	−0.755929	+	0.654654i
$568$		0			0
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		−	25.9808i		−	1.08821i
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$	7.50000	−	12.9904i	0.313591	−	0.543155i
$573$			20.7846i			0.868290i
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$	−12.0000			−0.500435
$576$	−3.00000			−0.125000
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−5.50000	+	9.52628i	−0.228968	+	0.396584i	0.728535	+	0.685009i	$0.240202\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$			24.2487i			1.00774i
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	−1.50000	−	7.79423i	−0.0622305	−	0.323359i
$582$	1.50000	+	0.866025i	0.0621770	+	0.0358979i
$583$	9.00000			0.372742
$584$	−5.50000	+	9.52628i	−0.227592	+	0.394200i
$585$	45.0000			1.86052
$586$	13.5000	+	23.3827i	0.557680	+	0.965930i
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$	12.0000	+	1.73205i	0.494872	+	0.0714286i
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$	18.0000	−	31.1769i	0.741048	−	1.28353i
$591$		−	10.3923i		−	0.427482i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$	13.5000	−	7.79423i	0.553912	−	0.319801i
$595$	−22.5000	−	7.79423i	−0.922410	−	0.319532i
$596$	1.50000	−	2.59808i	0.0614424	−	0.106421i
$597$	10.5000	+	6.06218i	0.429736	+	0.248108i
$598$	−15.0000			−0.613396
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	6.00000	−	3.46410i	0.244949	−	0.141421i
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$	−5.50000	−	28.5788i	−0.224163	−	1.16479i
$603$	12.0000			0.488678
$604$	−5.50000	−	9.52628i	−0.223792	−	0.387619i
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$	−4.50000	+	2.59808i	−0.182800	+	0.105540i
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	−13.5000	+	2.59808i	−0.547048	+	0.105279i
$610$	3.00000	−	5.19615i	0.121466	−	0.210386i
$611$		0			0
$612$	4.50000	−	7.79423i	0.181902	−	0.315063i
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	−0.362300	−	0.932062i	$-0.618008\pi$
$613$	15.5000	−	26.8468i	0.626039	−	1.08433i	0.988339	−	0.152270i	$-0.0486583\pi$
$614$	−28.0000			−1.12999
$615$			46.7654i			1.88576i
$616$	−7.50000	−	2.59808i	−0.302184	−	0.104679i
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$	−7.50000	−	4.33013i	−0.301694	−	0.174183i
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$	−13.5000	−	7.79423i	−0.541736	−	0.312772i
$622$	−24.0000			−0.962312
$623$	37.5000	+	12.9904i	1.50241	+	0.520449i
$624$	7.50000	−	4.33013i	0.300240	−	0.173344i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	14.0000			0.559553
$627$	22.5000	+	12.9904i	0.898563	+	0.518786i
$628$	14.0000			0.558661
$629$	−21.0000			−0.837325
$630$	−4.50000	−	23.3827i	−0.179284	−	0.931589i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	8.00000			0.318223
$633$	7.50000	−	4.33013i	0.298098	−	0.172107i
$634$	30.0000			1.19145
$635$	−24.0000	+	41.5692i	−0.952411	+	1.64962i
$636$	4.50000	+	2.59808i	0.178437	+	0.103020i
$637$	−32.5000	+	12.9904i	−1.28770	+	0.514698i
$638$	9.00000			0.356313
$639$		0			0
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.841417	+	0.540386i	$0.181722\pi$
$641$	22.5000	+	38.9711i	0.888697	+	1.53927i	0.0472793	+	0.998882i	$0.484945\pi$
$642$	−22.5000	+	12.9904i	−0.888004	+	0.512689i
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	−0.996379	−	0.0850262i	$-0.972903\pi$
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	0.424555	−	0.905402i	$-0.360431\pi$
$644$	1.50000	+	7.79423i	0.0591083	+	0.307136i
$645$	−49.5000	+	28.5788i	−1.94906	+	1.12529i
$646$	15.0000			0.590167
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	−0.835033	−	0.550200i	$-0.814551\pi$
$647$	1.50000	−	2.59808i	0.0589711	−	0.102141i	0.894004	+	0.448059i	$0.147885\pi$
$648$	9.00000			0.353553
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$	−10.0000	+	17.3205i	−0.392232	+	0.679366i
$651$	12.0000	+	13.8564i	0.470317	+	0.543075i
$652$	−8.50000	−	14.7224i	−0.332886	−	0.576575i
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	−0.940541	−	0.339680i	$-0.889681\pi$
$653$	−4.50000	+	7.79423i	−0.176099	+	0.305012i	0.764442	+	0.644692i	$0.223014\pi$
$654$	10.5000	+	6.06218i	0.410582	+	0.237050i
$655$	4.50000	+	7.79423i	0.175830	+	0.304546i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$	16.5000	−	28.5788i	0.643726	−	1.11497i
$658$		0			0
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	0.183436	+	0.983032i	$0.441278\pi$
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	−0.943049	+	0.332655i	$0.892055\pi$
$660$			15.5885i			0.606780i
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	20.0000			0.777322
$663$			25.9808i			1.00901i
$664$	−1.50000	+	2.59808i	−0.0582113	+	0.100825i
$665$	30.0000	−	25.9808i	1.16335	−	1.00749i
$666$	−10.5000	−	18.1865i	−0.406867	−	0.704714i
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$	−1.50000	−	2.59808i	−0.0580367	−	0.100523i
$669$	−25.5000	−	14.7224i	−0.985887	−	0.569202i
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$	−3.00000	−	3.46410i	−0.115728	−	0.133631i
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$	12.5000	+	21.6506i	0.481482	+	0.833951i
$675$	−18.0000	+	10.3923i	−0.692820	+	0.400000i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	22.5000	−	12.9904i	0.864107	−	0.498893i
$679$	0.500000	+	2.59808i	0.0191882	+	0.0997050i
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$	13.5000	−	7.79423i	0.517321	−	0.298675i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	−0.355920	−	0.934516i	$-0.615832\pi$
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	0.987275	−	0.159022i	$-0.0508342\pi$
$684$	7.50000	+	12.9904i	0.286770	+	0.496700i
$685$	−9.00000			−0.343872
$686$	10.0000	+	15.5885i	0.381802	+	0.595170i
$687$	−25.5000	−	14.7224i	−0.972886	−	0.561696i
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	−15.0000			−0.571454
$690$	13.5000	−	7.79423i	0.513936	−	0.296721i
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$	6.00000			0.228086
$693$	22.5000	+	7.79423i	0.854704	+	0.296078i
$694$	−12.0000			−0.455514
$695$	−15.0000			−0.568982
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	−27.0000			−1.02270
$698$	−2.50000	+	4.33013i	−0.0946264	+	0.163898i
$699$	40.5000	−	23.3827i	1.53185	−	0.884414i
$700$	10.0000	+	3.46410i	0.377964	+	0.130931i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$	−22.5000	+	12.9904i	−0.849208	+	0.490290i
$703$	17.5000	−	30.3109i	0.660025	−	1.14320i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	4.50000	+	7.79423i	0.169360	+	0.293340i
$707$	−7.50000	−	2.59808i	−0.282067	−	0.0977107i
$708$			20.7846i			0.781133i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$	−24.0000			−0.900070
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$	13.5000	−	2.59808i	0.505225	−	0.0972306i
$715$	−22.5000	−	38.9711i	−0.841452	−	1.45744i
$716$	−1.50000	+	2.59808i	−0.0560576	+	0.0970947i
$717$	40.5000	−	23.3827i	1.51250	−	0.873242i
$718$	−7.50000	−	12.9904i	−0.279898	−	0.484797i
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	−0.958051	−	0.286599i	$-0.907475\pi$
$719$	−19.5000	−	33.7750i	−0.727227	−	1.25959i	0.230823	−	0.972996i	$-0.425858\pi$
$720$	−4.50000	+	7.79423i	−0.167705	+	0.290474i
$721$	−2.50000	−	12.9904i	−0.0931049	−	0.483787i
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$	34.5000	−	19.9186i	1.28307	−	0.740780i
$724$	−10.0000			−0.371647
$725$	−12.0000			−0.445669
$726$	3.00000	+	1.73205i	0.111340	+	0.0642824i
$727$	−2.50000	+	4.33013i	−0.0927199	+	0.160596i	−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−2.50000	+	4.33013i	−0.0927199	+	0.160596i	0.815935	+	0.578144i	$0.196223\pi$
$728$	12.5000	+	4.33013i	0.463281	+	0.160485i
$729$	−27.0000			−1.00000
$730$	16.5000	+	28.5788i	0.610692	+	1.05775i
$731$	−16.5000	−	28.5788i	−0.610275	−	1.05703i
$732$			3.46410i			0.128037i
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	0.187096	+	0.982342i	$0.440092\pi$
$733$	−20.5000	+	35.5070i	−0.757185	+	1.31148i	−0.944281	+	0.329141i	$0.893241\pi$
$734$	0.500000	+	0.866025i	0.0184553	+	0.0319656i
$735$	22.5000	−	28.5788i	0.829925	−	1.05415i
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	−13.5000	−	23.3827i	−0.496942	−	0.860729i
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	0.00311943	+	0.999995i	$0.499007\pi$
$739$	−23.5000	+	40.7032i	−0.864461	+	1.49729i	−0.867581	+	0.497296i	$0.834326\pi$
$740$	21.0000			0.771975
$741$	−37.5000	−	21.6506i	−1.37760	−	0.795356i
$742$	1.50000	+	7.79423i	0.0550667	+	0.286135i
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	0.837198	−	0.546899i	$-0.184192\pi$
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	−0.892228	+	0.451585i	$0.850859\pi$
$744$		−	6.92820i		−	0.254000i
$745$	−4.50000	−	7.79423i	−0.164867	−	0.285558i
$746$	−8.50000	+	14.7224i	−0.311207	+	0.539027i
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$	−9.00000			−0.329073
$749$	−37.5000	−	12.9904i	−1.37022	−	0.474658i
$750$			5.19615i			0.189737i
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$		0			0
$753$			20.7846i			0.757433i
$754$	−15.0000			−0.546268
$755$	−33.0000			−1.20099
$756$	9.00000	+	10.3923i	0.327327	+	0.377964i
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−16.0000			−0.581146
$759$			15.5885i			0.565825i
$760$	−15.0000			−0.544107
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	−0.891932	−	0.452170i	$-0.850650\pi$
$761$	−1.50000	+	2.59808i	−0.0543750	+	0.0941802i	0.837557	+	0.546350i	$0.183983\pi$
$762$		−	27.7128i		−	1.00393i
$763$	3.50000	+	18.1865i	0.126709	+	0.658397i
$764$	12.0000			0.434145
$765$	−13.5000	−	23.3827i	−0.488094	−	0.845403i
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$	−30.0000	−	51.9615i	−1.08324	−	1.87622i
$768$			1.73205i			0.0625000i
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$	−18.0000	+	15.5885i	−0.648675	+	0.561769i
$771$	−22.5000	−	12.9904i	−0.810318	−	0.467837i
$772$	14.0000			0.503871
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	−0.990721	−	0.135910i	$-0.956604\pi$
$773$	−10.5000	+	18.1865i	−0.377659	+	0.654124i	0.613062	+	0.790034i	$0.289937\pi$
$774$	16.5000	−	28.5788i	0.593080	−	1.02725i
$775$	8.00000	+	13.8564i	0.287368	+	0.497737i
$776$	0.500000	−	0.866025i	0.0179490	−	0.0310885i
$777$	10.5000	−	30.3109i	0.376685	−	1.08740i
$778$	−4.50000	−	7.79423i	−0.161333	−	0.279437i
$779$	22.5000	−	38.9711i	0.806146	−	1.39629i
$780$		−	25.9808i		−	0.930261i
$781$		0			0
$782$	4.50000	+	7.79423i	0.160920	+	0.278721i
$783$	−13.5000	−	7.79423i	−0.482451	−	0.278543i
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	21.0000	−	36.3731i	0.749522	−	1.29821i
$786$	−4.50000	−	2.59808i	−0.160510	−	0.0926703i
$787$	44.0000			1.56843			0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000			1.56843			0.784215	+	0.620489i	$0.213066\pi$
$788$	−6.00000			−0.213741
$789$	−13.5000	+	7.79423i	−0.480613	+	0.277482i
$790$	12.0000	−	20.7846i	0.426941	−	0.739483i
$791$	37.5000	+	12.9904i	1.33335	+	0.461885i
$792$	−4.50000	−	7.79423i	−0.159901	−	0.276956i
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	−14.5000	−	25.1147i	−0.514586	−	0.891289i
$795$	13.5000	−	7.79423i	0.478796	−	0.276433i
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	0.999687	−	0.0249984i	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$	−7.50000	+	21.6506i	−0.265497	+	0.766424i
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	22.5000	+	38.9711i	0.794998	+	1.37698i
$802$	−13.5000	+	23.3827i	−0.476702	+	0.825671i
$803$	−33.0000			−1.16454
$804$		−	6.92820i		−	0.244339i
$805$	22.5000	+	7.79423i	0.793021	+	0.274710i
$806$	10.0000	+	17.3205i	0.352235	+	0.610089i
$807$	−31.5000	−	18.1865i	−1.10885	−	0.640196i
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$	13.5000	−	23.3827i	0.474342	−	0.821584i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	1.50000	+	7.79423i	0.0526397	+	0.273524i
$813$	−19.5000	+	11.2583i	−0.683895	+	0.394847i
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$	−51.0000			−1.78645
$816$	−4.50000	−	2.59808i	−0.157532	−	0.0909509i
$817$	55.0000			1.92421
$818$	−22.0000			−0.769212
$819$	−37.5000	−	12.9904i	−1.31036	−	0.453921i
$820$	27.0000			0.942881
$821$	−54.0000			−1.88461			−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000			−1.88461			−0.942306	+	0.334751i	$0.891348\pi$
$822$	4.50000	−	2.59808i	0.156956	−	0.0906183i
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$	−2.50000	+	4.33013i	−0.0870916	+	0.150847i
$825$	18.0000	+	10.3923i	0.626680	+	0.361814i
$826$	−24.0000	+	20.7846i	−0.835067	+	0.723189i
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$	−4.50000	+	7.79423i	−0.156386	+	0.270868i
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$	−10.5000	+	6.06218i	−0.364241	+	0.210295i
$832$	−2.50000	−	4.33013i	−0.0866719	−	0.150120i
$833$	16.5000	+	12.9904i	0.571691	+	0.450090i
$834$	7.50000	−	4.33013i	0.259704	−	0.149940i
$835$	−9.00000			−0.311458
$836$	7.50000	−	12.9904i	0.259393	−	0.449282i
$837$			20.7846i			0.718421i
$838$	1.50000	+	2.59808i	0.0518166	+	0.0897491i
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	−0.303773	−	0.952745i	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$	−13.5000	+	2.59808i	−0.465794	+	0.0896421i
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	15.5000	−	26.8468i	0.534165	−	0.925201i
$843$	−4.50000	−	2.59808i	−0.154988	−	0.0894825i
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	18.0000	+	31.1769i	0.619219	+	1.07252i
$846$		0			0
$847$	1.00000	+	5.19615i	0.0343604	+	0.178542i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$			13.8564i			0.475551i
$850$	12.0000			0.411597
$851$	21.0000			0.719871
$852$		0			0
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	−0.974055	−	0.226313i	$-0.927333\pi$
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	0.683020	+	0.730400i	$0.260666\pi$
$854$	−4.00000	+	3.46410i	−0.136877	+	0.118539i
$855$	45.0000			1.53897
$856$	7.50000	+	12.9904i	0.256345	+	0.444002i
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	0.997176	+	0.0751033i	$0.0239287\pi$
$857$	16.5000	+	28.5788i	0.563629	+	0.976235i	−0.433546	+	0.901131i	$0.642738\pi$
$858$	22.5000	+	12.9904i	0.768137	+	0.443484i
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	−0.944469	−	0.328601i	$-0.893423\pi$
$859$	−5.50000	+	9.52628i	−0.187658	+	0.325032i	0.756811	+	0.653633i	$0.226756\pi$
$860$	16.5000	+	28.5788i	0.562645	+	0.974530i
$861$	13.5000	−	38.9711i	0.460079	−	1.32813i
$862$	1.50000	−	2.59808i	0.0510902	−	0.0884908i
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	0.709675	−	0.704529i	$-0.248842\pi$
$863$	−7.50000	−	12.9904i	−0.255303	−	0.442198i	−0.964978	+	0.262332i	$0.915509\pi$
$864$		−	5.19615i		−	0.176777i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	14.0000			0.475739
$867$	−12.0000	+	6.92820i	−0.407541	+	0.235294i
$868$	8.00000	−	6.92820i	0.271538	−	0.235159i
$869$	12.0000	+	20.7846i	0.407072	+	0.705070i
$870$	13.5000	−	7.79423i	0.457693	−	0.264249i
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$	3.50000	−	6.06218i	0.118525	−	0.205291i
$873$	−1.50000	+	2.59808i	−0.0507673	+	0.0879316i
$874$	−15.0000			−0.507383
$875$	−6.00000	+	5.19615i	−0.202837	+	0.175662i
$876$	−16.5000	−	9.52628i	−0.557483	−	0.321863i
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	−0.232556	−	0.972583i	$-0.574709\pi$
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	0.958560	−	0.284892i	$-0.0919577\pi$
$878$	8.00000			0.269987
$879$	−40.5000	+	23.3827i	−1.36603	+	0.788678i
$880$	9.00000			0.303390
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$	−3.00000	+	20.7846i	−0.101015	+	0.699854i
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	15.0000			0.504505
$885$	54.0000	+	31.1769i	1.81519	+	1.04800i
$886$		0			0
$887$	19.5000	−	33.7750i	0.654746	−	1.13405i	−0.327212	−	0.944951i	$-0.606109\pi$
$887$	19.5000	−	33.7750i	0.654746	−	1.13405i	0.981957	−	0.189102i	$-0.0605577\pi$
$888$	−10.5000	+	6.06218i	−0.352357	+	0.203433i
$889$	32.0000	−	27.7128i	1.07325	−	0.929458i
$890$	−45.0000			−1.50840
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	−8.50000	+	14.7224i	−0.284601	+	0.492943i
$893$		0			0
$894$	4.50000	+	2.59808i	0.150503	+	0.0868927i
$895$	4.50000	+	7.79423i	0.150418	+	0.260532i
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		−	25.9808i		−	0.867472i
$898$	30.0000			1.00111
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$	6.00000	+	10.3923i	0.200000	+	0.346410i
$901$	4.50000	+	7.79423i	0.149917	+	0.259663i
$902$	−13.5000	+	23.3827i	−0.449501	+	0.778558i
$903$	49.5000	−	9.52628i	1.64726	−	0.317015i
$904$	−7.50000	−	12.9904i	−0.249446	−	0.432054i
$905$	−15.0000	+	25.9808i	−0.498617	+	0.863630i
$906$	16.5000	−	9.52628i	0.548176	−	0.316489i
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	−4.50000	−	7.79423i	−0.149338	−	0.258661i
$909$	−4.50000	−	7.79423i	−0.149256	−	0.258518i
$910$	30.0000	−	25.9808i	0.994490	−	0.861254i
$911$	−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	$0.214302\pi$
$912$	7.50000	−	4.33013i	0.248350	−	0.143385i
$913$	−9.00000			−0.297857
$914$	−34.0000			−1.12462
$915$	9.00000	+	5.19615i	0.297531	+	0.171780i
$916$	−8.50000	+	14.7224i	−0.280848	+	0.486443i
$917$	−1.50000	−	7.79423i	−0.0495344	−	0.257388i
$918$	13.5000	+	7.79423i	0.445566	+	0.257248i
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	0.874154	−	0.485648i	$-0.161416\pi$
$919$	0.500000	+	0.866025i	0.0164935	+	0.0285675i	−0.857661	+	0.514216i	$0.828083\pi$
$920$	−4.50000	−	7.79423i	−0.148361	−	0.256968i
$921$		−	48.4974i		−	1.59804i
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$		0			0
$924$	4.50000	−	12.9904i	0.148039	−	0.427352i
$925$	14.0000	−	24.2487i	0.460317	−	0.797293i
$926$	−17.5000	−	30.3109i	−0.575086	−	0.996078i
$927$	7.50000	−	12.9904i	0.246332	−	0.426660i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	−18.0000			−0.590561			−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000			−0.590561			−0.295280	+	0.955411i	$0.595413\pi$
$930$	−18.0000	−	10.3923i	−0.590243	−	0.340777i
$931$	−32.5000	+	12.9904i	−1.06514	+	0.425743i
$932$	−13.5000	−	23.3827i	−0.442207	−	0.765925i
$933$		−	41.5692i		−	1.36092i
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$	−13.5000	+	23.3827i	−0.441497	+	0.764696i
$936$	7.50000	+	12.9904i	0.245145	+	0.424604i
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	8.00000	−	6.92820i	0.261209	−	0.226214i
$939$			24.2487i			0.791327i
$940$		0			0
$941$	54.0000			1.76035			0.880175	−	0.474650i	$-0.157425\pi$
$941$	54.0000			1.76035			0.880175	+	0.474650i	$0.157425\pi$
$942$			24.2487i			0.790066i
$943$	27.0000			0.879241
$944$	12.0000			0.390567
$945$	40.5000	−	7.79423i	1.31747	−	0.253546i
$946$	−33.0000			−1.07292
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$			13.8564i			0.450035i
$949$	55.0000			1.78538
$950$	−10.0000	+	17.3205i	−0.324443	+	0.561951i
$951$			51.9615i			1.68497i
$952$	−1.50000	−	7.79423i	−0.0486153	−	0.252612i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−4.50000	+	7.79423i	−0.145693	+	0.252347i
$955$	18.0000	−	31.1769i	0.582466	−	1.00886i
$956$	−13.5000	−	23.3827i	−0.436621	−	0.756250i
$957$			15.5885i			0.503903i
$958$	4.50000	+	7.79423i	0.145388	+	0.251820i
$959$	7.50000	+	2.59808i	0.242188	+	0.0838963i
$960$	4.50000	+	2.59808i	0.145237	+	0.0838525i
$961$	−15.0000			−0.483871
$962$	17.5000	−	30.3109i	0.564223	−	0.977262i
$963$	−22.5000	−	38.9711i	−0.725052	−	1.25583i
$964$	−11.5000	−	19.9186i	−0.370390	−	0.641534i
$965$	21.0000	−	36.3731i	0.676014	−	1.17089i
$966$	−13.5000	+	2.59808i	−0.434355	+	0.0835917i
$967$	24.5000	+	42.4352i	0.787867	+	1.36463i	0.927271	+	0.374390i	$0.122148\pi$
$967$	24.5000	+	42.4352i	0.787867	+	1.36463i	−0.139404	+	0.990236i	$0.544519\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$			25.9808i			0.834622i
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	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	$0.690705\pi$
$972$			15.5885i			0.500000i
$973$	12.5000	+	4.33013i	0.400732	+	0.138817i
$974$	15.5000	−	26.8468i	0.496652	−	0.860227i
$975$	−30.0000	−	17.3205i	−0.960769	−	0.554700i
$976$	2.00000			0.0640184
$977$	6.00000			0.191957			0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000			0.191957			0.0959785	+	0.995383i	$0.469402\pi$
$978$	25.5000	−	14.7224i	0.815400	−	0.470771i
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$	−16.5000	−	12.9904i	−0.527073	−	0.414963i
$981$	−10.5000	+	18.1865i	−0.335239	+	0.580651i
$982$	19.5000	+	33.7750i	0.622270	+	1.07780i
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	0.983465	−	0.181097i	$-0.0579648\pi$
$983$	10.5000	+	18.1865i	0.334898	+	0.580060i	−0.648567	+	0.761157i	$0.724631\pi$
$984$	−13.5000	+	7.79423i	−0.430364	+	0.248471i
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	4.50000	+	7.79423i	0.143309	+	0.248219i
$987$		0			0
$988$	−12.5000	+	21.6506i	−0.397678	+	0.688798i
$989$	16.5000	+	28.5788i	0.524669	+	0.908754i
$990$	−27.0000			−0.858116
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	−0.998991	−	0.0449040i	$-0.985702\pi$
$991$	−14.5000	+	25.1147i	−0.460608	+	0.797796i	0.538384	+	0.842700i	$0.319035\pi$
$992$	−4.00000			−0.127000
$993$			34.6410i			1.09930i
$994$		0			0
$995$	−10.5000	−	18.1865i	−0.332872	−	0.576552i
$996$	−4.50000	−	2.59808i	−0.142588	−	0.0823232i
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	−0.983304	−	0.181968i	$-0.941753\pi$
$997$	−20.5000	−	35.5070i	−0.649242	−	1.12452i	0.334063	−	0.942551i	$-0.391580\pi$
$998$	−5.50000	+	9.52628i	−0.174099	+	0.301549i
$999$	31.5000	−	18.1865i	0.996616	−	0.575396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.e.b.25.1	✓	2
3.2	odd	2		378.2.e.a.235.1		2
4.3	odd	2		1008.2.q.e.529.1		2
7.2	even	3		126.2.h.a.79.1	yes	2
7.3	odd	6		882.2.f.a.295.1		2
7.4	even	3		882.2.f.e.295.1		2
7.5	odd	6		882.2.h.e.79.1		2
7.6	odd	2		882.2.e.h.655.1		2
9.2	odd	6		1134.2.g.f.487.1		2
9.4	even	3		126.2.h.a.67.1	yes	2
9.5	odd	6		378.2.h.b.361.1		2
9.7	even	3		1134.2.g.d.487.1		2
12.11	even	2		3024.2.q.a.2881.1		2
21.2	odd	6		378.2.h.b.289.1		2
21.5	even	6		2646.2.h.f.667.1		2
21.11	odd	6		2646.2.f.e.883.1		2
21.17	even	6		2646.2.f.i.883.1		2
21.20	even	2		2646.2.e.e.2125.1		2
28.23	odd	6		1008.2.t.c.961.1		2
36.23	even	6		3024.2.t.f.1873.1		2
36.31	odd	6		1008.2.t.c.193.1		2
63.2	odd	6		1134.2.g.f.163.1		2
63.4	even	3		882.2.f.e.589.1		2
63.5	even	6		2646.2.e.e.1549.1		2
63.11	odd	6		7938.2.a.o.1.1		1
63.13	odd	6		882.2.h.e.67.1		2
63.16	even	3		1134.2.g.d.163.1		2
63.23	odd	6		378.2.e.a.37.1		2
63.25	even	3		7938.2.a.r.1.1		1
63.31	odd	6		882.2.f.a.589.1		2
63.32	odd	6		2646.2.f.e.1765.1		2
63.38	even	6		7938.2.a.c.1.1		1
63.40	odd	6		882.2.e.h.373.1		2
63.41	even	6		2646.2.h.f.361.1		2
63.52	odd	6		7938.2.a.bd.1.1		1
63.58	even	3	inner	126.2.e.b.121.1	yes	2
63.59	even	6		2646.2.f.i.1765.1		2
84.23	even	6		3024.2.t.f.289.1		2
252.23	even	6		3024.2.q.a.2305.1		2
252.247	odd	6		1008.2.q.e.625.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	1.1	even	1	trivial
126.2.e.b.121.1	yes	2	63.58	even	3	inner
126.2.h.a.67.1	yes	2	9.4	even	3
126.2.h.a.79.1	yes	2	7.2	even	3
378.2.e.a.37.1		2	63.23	odd	6
378.2.e.a.235.1		2	3.2	odd	2
378.2.h.b.289.1		2	21.2	odd	6
378.2.h.b.361.1		2	9.5	odd	6
882.2.e.h.373.1		2	63.40	odd	6
882.2.e.h.655.1		2	7.6	odd	2
882.2.f.a.295.1		2	7.3	odd	6
882.2.f.a.589.1		2	63.31	odd	6
882.2.f.e.295.1		2	7.4	even	3
882.2.f.e.589.1		2	63.4	even	3
882.2.h.e.67.1		2	63.13	odd	6
882.2.h.e.79.1		2	7.5	odd	6
1008.2.q.e.529.1		2	4.3	odd	2
1008.2.q.e.625.1		2	252.247	odd	6
1008.2.t.c.193.1		2	36.31	odd	6
1008.2.t.c.961.1		2	28.23	odd	6
1134.2.g.d.163.1		2	63.16	even	3
1134.2.g.d.487.1		2	9.7	even	3
1134.2.g.f.163.1		2	63.2	odd	6
1134.2.g.f.487.1		2	9.2	odd	6
2646.2.e.e.1549.1		2	63.5	even	6
2646.2.e.e.2125.1		2	21.20	even	2
2646.2.f.e.883.1		2	21.11	odd	6
2646.2.f.e.1765.1		2	63.32	odd	6
2646.2.f.i.883.1		2	21.17	even	6
2646.2.f.i.1765.1		2	63.59	even	6
2646.2.h.f.361.1		2	63.41	even	6
2646.2.h.f.667.1		2	21.5	even	6
3024.2.q.a.2305.1		2	252.23	even	6
3024.2.q.a.2881.1		2	12.11	even	2
3024.2.t.f.289.1		2	84.23	even	6
3024.2.t.f.1873.1		2	36.23	even	6
7938.2.a.c.1.1		1	63.38	even	6
7938.2.a.o.1.1		1	63.11	odd	6
7938.2.a.r.1.1		1	63.25	even	3
7938.2.a.bd.1.1		1	63.52	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +1.73205i q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.73205i q^{3} +1.00000 q^{4} +(1.50000 - 2.59808i) q^{5} +1.73205i q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +(1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.73205i q^{12} +(-2.50000 - 4.33013i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(4.50000 + 2.59808i) q^{15} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(-2.50000 - 4.33013i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +1.73205i q^{24} +(-2.00000 - 3.46410i) q^{25} +(-2.50000 - 4.33013i) q^{26} -5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(1.50000 - 2.59808i) q^{29} +(4.50000 + 2.59808i) q^{30} -4.00000 q^{31} +1.00000 q^{32} +(-4.50000 + 2.59808i) q^{33} +(-1.50000 + 2.59808i) q^{34} +(1.50000 + 7.79423i) q^{35} -3.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(-2.50000 - 4.33013i) q^{38} +(7.50000 - 4.33013i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 + 7.79423i) q^{41} +(-3.00000 - 3.46410i) q^{42} +(-5.50000 + 9.52628i) q^{43} +(1.50000 + 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{45} +(1.50000 - 2.59808i) q^{46} +1.73205i q^{48} +(1.00000 - 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(1.50000 - 2.59808i) q^{53} -5.19615i q^{54} +9.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +(7.50000 - 4.33013i) q^{57} +(1.50000 - 2.59808i) q^{58} +12.0000 q^{59} +(4.50000 + 2.59808i) q^{60} +2.00000 q^{61} -4.00000 q^{62} +(6.00000 - 5.19615i) q^{63} +1.00000 q^{64} -15.0000 q^{65} +(-4.50000 + 2.59808i) q^{66} -4.00000 q^{67} +(-1.50000 + 2.59808i) q^{68} +(4.50000 + 2.59808i) q^{69} +(1.50000 + 7.79423i) q^{70} -3.00000 q^{72} +(-5.50000 + 9.52628i) q^{73} +(3.50000 + 6.06218i) q^{74} +(6.00000 - 3.46410i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(-7.50000 - 2.59808i) q^{77} +(7.50000 - 4.33013i) q^{78} +8.00000 q^{79} +(1.50000 - 2.59808i) q^{80} +9.00000 q^{81} +(4.50000 + 7.79423i) q^{82} +(-1.50000 + 2.59808i) q^{83} +(-3.00000 - 3.46410i) q^{84} +(4.50000 + 7.79423i) q^{85} +(-5.50000 + 9.52628i) q^{86} +(4.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-7.50000 - 12.9904i) q^{89} +(-4.50000 + 7.79423i) q^{90} +(12.5000 + 4.33013i) q^{91} +(1.50000 - 2.59808i) q^{92} -6.92820i q^{93} -15.0000 q^{95} +1.73205i q^{96} +(0.500000 - 0.866025i) q^{97} +(1.00000 - 6.92820i) q^{98} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - 4 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - 4 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 3 q^{5} - 4 q^{7} + 2 q^{8} - 6 q^{9} + 3 q^{10} + 3 q^{11} - 5 q^{13} - 4 q^{14} + 9 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 3 q^{22} + 3 q^{23} - 4 q^{25} - 5 q^{26} - 4 q^{28} + 3 q^{29} + 9 q^{30} - 8 q^{31} + 2 q^{32} - 9 q^{33} - 3 q^{34} + 3 q^{35} - 6 q^{36} + 7 q^{37} - 5 q^{38} + 15 q^{39} + 3 q^{40} + 9 q^{41} - 6 q^{42} - 11 q^{43} + 3 q^{44} - 9 q^{45} + 3 q^{46} + 2 q^{49} - 4 q^{50} - 9 q^{51} - 5 q^{52} + 3 q^{53} + 18 q^{55} - 4 q^{56} + 15 q^{57} + 3 q^{58} + 24 q^{59} + 9 q^{60} + 4 q^{61} - 8 q^{62} + 12 q^{63} + 2 q^{64} - 30 q^{65} - 9 q^{66} - 8 q^{67} - 3 q^{68} + 9 q^{69} + 3 q^{70} - 6 q^{72} - 11 q^{73} + 7 q^{74} + 12 q^{75} - 5 q^{76} - 15 q^{77} + 15 q^{78} + 16 q^{79} + 3 q^{80} + 18 q^{81} + 9 q^{82} - 3 q^{83} - 6 q^{84} + 9 q^{85} - 11 q^{86} + 9 q^{87} + 3 q^{88} - 15 q^{89} - 9 q^{90} + 25 q^{91} + 3 q^{92} - 30 q^{95} + q^{97} + 2 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 3 * q^5 - 4 * q^7 + 2 * q^8 - 6 * q^9 + 3 * q^10 + 3 * q^11 - 5 * q^13 - 4 * q^14 + 9 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 3 * q^22 + 3 * q^23 - 4 * q^25 - 5 * q^26 - 4 * q^28 + 3 * q^29 + 9 * q^30 - 8 * q^31 + 2 * q^32 - 9 * q^33 - 3 * q^34 + 3 * q^35 - 6 * q^36 + 7 * q^37 - 5 * q^38 + 15 * q^39 + 3 * q^40 + 9 * q^41 - 6 * q^42 - 11 * q^43 + 3 * q^44 - 9 * q^45 + 3 * q^46 + 2 * q^49 - 4 * q^50 - 9 * q^51 - 5 * q^52 + 3 * q^53 + 18 * q^55 - 4 * q^56 + 15 * q^57 + 3 * q^58 + 24 * q^59 + 9 * q^60 + 4 * q^61 - 8 * q^62 + 12 * q^63 + 2 * q^64 - 30 * q^65 - 9 * q^66 - 8 * q^67 - 3 * q^68 + 9 * q^69 + 3 * q^70 - 6 * q^72 - 11 * q^73 + 7 * q^74 + 12 * q^75 - 5 * q^76 - 15 * q^77 + 15 * q^78 + 16 * q^79 + 3 * q^80 + 18 * q^81 + 9 * q^82 - 3 * q^83 - 6 * q^84 + 9 * q^85 - 11 * q^86 + 9 * q^87 + 3 * q^88 - 15 * q^89 - 9 * q^90 + 25 * q^91 + 3 * q^92 - 30 * q^95 + q^97 + 2 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more