LMFDB - Embedded newform 546.2.l.c.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (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:	$4.35983195036$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.c.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.50000 + 6.06218i) q^{17} -1.00000 q^{18} +(2.50000 + 4.33013i) q^{19} +(1.00000 + 1.73205i) q^{20} -1.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-1.00000 - 1.73205i) q^{30} -2.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +7.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 - 1.73205i) q^{37} +5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +2.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +3.00000 q^{44} +(1.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{46} -1.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} -7.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +3.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{55} +(-0.500000 - 0.866025i) q^{56} -5.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(3.00000 + 5.19615i) q^{59} -2.00000 q^{60} +(-3.50000 - 6.06218i) q^{61} +(-1.00000 + 1.73205i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-7.00000 + 1.73205i) q^{65} -3.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(3.50000 - 6.06218i) q^{68} +(-3.00000 - 5.19615i) q^{69} -2.00000 q^{70} +(-4.00000 - 6.92820i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +(2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(2.50000 + 2.59808i) q^{78} +3.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -8.00000 q^{83} +(0.500000 + 0.866025i) q^{84} +(-7.00000 - 12.1244i) q^{85} -2.00000 q^{86} +(-2.50000 - 4.33013i) q^{87} +(1.50000 - 2.59808i) q^{88} +(5.50000 - 9.52628i) q^{89} +2.00000 q^{90} +(2.50000 + 2.59808i) q^{91} +6.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(-5.00000 - 8.66025i) q^{95} -1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(0.500000 + 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} + 2 q^{12} + 7 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} + 7 q^{17} - 2 q^{18} + 5 q^{19} + 2 q^{20} - 2 q^{21} + 3 q^{22} - 6 q^{23} + q^{24} - 2 q^{25} + 2 q^{26} + 2 q^{27} + q^{28} - 5 q^{29} - 2 q^{30} - 4 q^{31} + q^{32} - 3 q^{33} + 14 q^{34} - 2 q^{35} - q^{36} + 2 q^{37} + 10 q^{38} - 2 q^{39} + 4 q^{40} + 5 q^{41} - q^{42} - 2 q^{43} + 6 q^{44} + 2 q^{45} + 6 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 14 q^{51} - 5 q^{52} + 6 q^{53} + q^{54} + 6 q^{55} - q^{56} - 10 q^{57} + 5 q^{58} + 6 q^{59} - 4 q^{60} - 7 q^{61} - 2 q^{62} + q^{63} + 2 q^{64} - 14 q^{65} - 6 q^{66} - 2 q^{67} + 7 q^{68} - 6 q^{69} - 4 q^{70} - 8 q^{71} + q^{72} + 24 q^{73} - 2 q^{74} + q^{75} + 5 q^{76} - 6 q^{77} + 5 q^{78} + 6 q^{79} + 2 q^{80} - q^{81} - 5 q^{82} - 16 q^{83} + q^{84} - 14 q^{85} - 4 q^{86} - 5 q^{87} + 3 q^{88} + 11 q^{89} + 4 q^{90} + 5 q^{91} + 12 q^{92} + 2 q^{93} - q^{94} - 10 q^{95} - 2 q^{96} + 2 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 + 2 * q^12 + 7 * q^13 + 2 * q^14 + 2 * q^15 - q^16 + 7 * q^17 - 2 * q^18 + 5 * q^19 + 2 * q^20 - 2 * q^21 + 3 * q^22 - 6 * q^23 + q^24 - 2 * q^25 + 2 * q^26 + 2 * q^27 + q^28 - 5 * q^29 - 2 * q^30 - 4 * q^31 + q^32 - 3 * q^33 + 14 * q^34 - 2 * q^35 - q^36 + 2 * q^37 + 10 * q^38 - 2 * q^39 + 4 * q^40 + 5 * q^41 - q^42 - 2 * q^43 + 6 * q^44 + 2 * q^45 + 6 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 14 * q^51 - 5 * q^52 + 6 * q^53 + q^54 + 6 * q^55 - q^56 - 10 * q^57 + 5 * q^58 + 6 * q^59 - 4 * q^60 - 7 * q^61 - 2 * q^62 + q^63 + 2 * q^64 - 14 * q^65 - 6 * q^66 - 2 * q^67 + 7 * q^68 - 6 * q^69 - 4 * q^70 - 8 * q^71 + q^72 + 24 * q^73 - 2 * q^74 + q^75 + 5 * q^76 - 6 * q^77 + 5 * q^78 + 6 * q^79 + 2 * q^80 - q^81 - 5 * q^82 - 16 * q^83 + q^84 - 14 * q^85 - 4 * q^86 - 5 * q^87 + 3 * q^88 + 11 * q^89 + 4 * q^90 + 5 * q^91 + 12 * q^92 + 2 * q^93 - q^94 - 10 * q^95 - 2 * q^96 + 2 * q^97 + q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	1.00000			0.288675
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	1.00000			0.267261
$15$	1.00000	−	1.73205i	0.258199	−	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	0.882213	+	0.470850i	$0.156053\pi$
$17$	3.50000	+	6.06218i	0.848875	+	1.47029i	−0.0333386	+	0.999444i	$0.510614\pi$
$18$	−1.00000			−0.235702
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$	−1.00000			−0.218218
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−1.00000			−0.200000
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$	1.00000			0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	7.00000			1.20049
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	5.00000			0.811107
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$	2.00000			0.316228
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	3.00000			0.452267
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−1.00000			−0.145865			−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000			−0.145865			−0.0729325	+	0.997337i	$0.523236\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−7.00000			−0.980196
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	3.00000			0.412082			0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000			0.412082			0.206041	+	0.978543i	$0.433942\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−5.00000			−0.662266
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$	−2.00000			−0.258199
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$	−1.00000	+	1.73205i	−0.127000	+	0.219971i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	−7.00000	+	1.73205i	−0.868243	+	0.214834i
$66$	−3.00000			−0.369274
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	3.50000	−	6.06218i	0.424437	−	0.735147i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$	−2.00000			−0.239046
$71$	−4.00000	−	6.92820i	−0.474713	−	0.822226i	0.524868	−	0.851184i	$-0.324115\pi$
$71$	−4.00000	−	6.92820i	−0.474713	−	0.822226i	−0.999581	+	0.0289572i	$0.990781\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$	−3.00000			−0.341882
$78$	2.50000	+	2.59808i	0.283069	+	0.294174i
$79$	3.00000			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−7.00000	−	12.1244i	−0.759257	−	1.31507i
$86$	−2.00000			−0.215666
$87$	−2.50000	−	4.33013i	−0.268028	−	0.464238i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	5.50000	−	9.52628i	0.582999	−	1.00978i	−0.412123	−	0.911128i	$-0.635213\pi$
$89$	5.50000	−	9.52628i	0.582999	−	1.00978i	0.995122	−	0.0986553i	$-0.0314541\pi$
$90$	2.00000			0.210819
$91$	2.50000	+	2.59808i	0.262071	+	0.272352i
$92$	6.00000			0.625543
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$	−0.500000	+	0.866025i	−0.0515711	+	0.0893237i
$95$	−5.00000	−	8.66025i	−0.512989	−	0.888523i
$96$	−1.00000			−0.102062
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$	3.00000			0.301511
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$	−3.50000	+	6.06218i	−0.346552	+	0.600245i
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	−3.50000	+	0.866025i	−0.343203	+	0.0849208i
$105$	2.00000			0.195180
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	0.233900	+	0.972261i	$0.424851\pi$
$107$	−7.50000	+	12.9904i	−0.725052	+	1.25583i	−0.958952	+	0.283567i	$0.908482\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$	1.00000	+	1.73205i	0.0949158	+	0.164399i
$112$	−1.00000			−0.0944911
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	−2.50000	+	4.33013i	−0.234146	+	0.405554i
$115$	6.00000	−	10.3923i	0.559503	−	0.969087i
$116$	5.00000			0.464238
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	6.00000			0.552345
$119$	−3.50000	+	6.06218i	−0.320844	+	0.555719i
$120$	−1.00000	+	1.73205i	−0.0912871	+	0.158114i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−7.00000			−0.633750
$123$	2.50000	+	4.33013i	0.225417	+	0.390434i
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	12.0000			1.07331
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	−0.466870	−	0.884326i	$-0.654618\pi$
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	0.999284	−	0.0378419i	$-0.0120483\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	2.00000			0.176090
$130$	−2.00000	+	6.92820i	−0.175412	+	0.607644i
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$	−1.50000	+	2.59808i	−0.130558	+	0.226134i
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$	−2.00000			−0.172133
$136$	−3.50000	−	6.06218i	−0.300123	−	0.519827i
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$	−6.00000			−0.510754
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$	−1.00000	+	1.73205i	−0.0845154	+	0.146385i
$141$	0.500000	−	0.866025i	0.0421076	−	0.0729325i
$142$	−8.00000			−0.671345
$143$	−3.00000	+	10.3923i	−0.250873	+	0.869048i
$144$	1.00000			0.0833333
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	6.00000	−	10.3923i	0.496564	−	0.860073i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−2.00000			−0.164399
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	13.0000			1.05792			0.528962	−	0.848645i	$-0.322581\pi$
$151$	13.0000			1.05792			0.528962	+	0.848645i	$0.322581\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	3.50000	−	6.06218i	0.282958	−	0.490098i
$154$	−1.50000	+	2.59808i	−0.120873	+	0.209359i
$155$	4.00000			0.321288
$156$	3.50000	−	0.866025i	0.280224	−	0.0693375i
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	1.50000	−	2.59808i	0.119334	−	0.206692i
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	−6.00000			−0.472866
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	0.998392	+	0.0566798i	$0.0180514\pi$
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	−0.450110	+	0.892973i	$0.648615\pi$
$164$	−5.00000			−0.390434
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	1.00000			0.0771517
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−14.0000			−1.07375
$171$	2.50000	−	4.33013i	0.191180	−	0.331133i
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	0.542583	−	0.840002i	$-0.317446\pi$
$173$	−6.00000	−	10.3923i	−0.456172	−	0.790112i	−0.998755	+	0.0498898i	$0.984113\pi$
$174$	−5.00000			−0.379049
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−6.00000			−0.450988
$178$	−5.50000	−	9.52628i	−0.412242	−	0.714025i
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	−9.00000			−0.668965			−0.334482	−	0.942402i	$-0.608561\pi$
$181$	−9.00000			−0.668965			−0.334482	+	0.942402i	$0.608561\pi$
$182$	3.50000	−	0.866025i	0.259437	−	0.0641941i
$183$	7.00000			0.517455
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	−21.0000			−1.53567
$188$	0.500000	+	0.866025i	0.0364662	+	0.0631614i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−10.0000			−0.725476
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	0.929267	−	0.369410i	$-0.120440\pi$
$191$	2.00000	+	3.46410i	0.144715	+	0.250654i	−0.784552	+	0.620063i	$0.787107\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$	2.00000			0.143592
$195$	2.00000	−	6.92820i	0.143223	−	0.496139i
$196$	1.00000			0.0714286
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	−0.660003	−	0.751263i	$-0.729445\pi$
$197$	4.50000	−	7.79423i	0.320612	−	0.555316i	0.980614	+	0.195947i	$0.0627782\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.797025	+	0.603947i	$0.206406\pi$
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.124521	+	0.992217i	$0.460261\pi$
$200$	1.00000			0.0707107
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	−5.00000			−0.350931
$204$	3.50000	+	6.06218i	0.245049	+	0.424437i
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$	6.00000			0.417029
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	−15.0000			−1.03757
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	−0.640996	−	0.767544i	$-0.721479\pi$
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	0.985211	+	0.171347i	$0.0548120\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	8.00000			0.548151
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$	−1.00000			−0.0680414
$217$	−1.00000	−	1.73205i	−0.0678844	−	0.117579i
$218$	−8.00000	+	13.8564i	−0.541828	+	0.938474i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	−6.00000			−0.404520
$221$	17.5000	+	18.1865i	1.17718	+	1.22336i
$222$	2.00000			0.134231
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	−6.00000			−0.399114
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$	2.50000	+	4.33013i	0.165567	+	0.286770i
$229$	27.0000			1.78421			0.892105	−	0.451828i	$-0.149228\pi$
$229$	27.0000			1.78421			0.892105	+	0.451828i	$0.149228\pi$
$230$	−6.00000	−	10.3923i	−0.395628	−	0.685248i
$231$	1.50000	−	2.59808i	0.0986928	−	0.170941i
$232$	2.50000	−	4.33013i	0.164133	−	0.284287i
$233$	26.0000			1.70332			0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000			1.70332			0.851658	+	0.524097i	$0.175597\pi$
$234$	−3.50000	+	0.866025i	−0.228802	+	0.0566139i
$235$	2.00000			0.130466
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	−1.50000	+	2.59808i	−0.0974355	+	0.168763i
$238$	3.50000	+	6.06218i	0.226871	+	0.392953i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	−14.0000	−	24.2487i	−0.901819	−	1.56200i	−0.825131	−	0.564942i	$-0.808899\pi$
$241$	−14.0000	−	24.2487i	−0.901819	−	1.56200i	−0.0766885	−	0.997055i	$-0.524435\pi$
$242$	2.00000			0.128565
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	5.00000			0.318788
$247$	12.5000	+	12.9904i	0.795356	+	0.826558i
$248$	2.00000			0.127000
$249$	4.00000	−	6.92820i	0.253490	−	0.439057i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$	−1.00000			−0.0629941
$253$	−9.00000	−	15.5885i	−0.565825	−	0.980038i
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	14.0000			0.876714
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$	1.00000	−	1.73205i	0.0622573	−	0.107833i
$259$	2.00000			0.124274
$260$	5.00000	+	5.19615i	0.310087	+	0.322252i
$261$	5.00000			0.309492
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$	−6.00000			−0.368577
$266$	2.50000	+	4.33013i	0.153285	+	0.265497i
$267$	5.50000	+	9.52628i	0.336595	+	0.582999i
$268$	2.00000			0.122169
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$	−1.00000	+	1.73205i	−0.0608581	+	0.105409i
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	−7.00000			−0.424437
$273$	−3.50000	+	0.866025i	−0.211830	+	0.0524142i
$274$	−18.0000			−1.08742
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	0.761714	−	0.647913i	$-0.224358\pi$
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	−0.941966	+	0.335707i	$0.891025\pi$
$278$	19.0000			1.13954
$279$	1.00000	+	1.73205i	0.0598684	+	0.103695i
$280$	1.00000	+	1.73205i	0.0597614	+	0.103510i
$281$	16.0000			0.954480			0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000			0.954480			0.477240	+	0.878773i	$0.341637\pi$
$282$	−0.500000	−	0.866025i	−0.0297746	−	0.0515711i
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	−4.00000	+	6.92820i	−0.237356	+	0.411113i
$285$	10.0000			0.592349
$286$	7.50000	+	7.79423i	0.443484	+	0.460882i
$287$	5.00000			0.295141
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$	−2.00000			−0.117242
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$	−1.00000			−0.0583212
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	−1.50000	+	2.59808i	−0.0870388	+	0.150756i
$298$	−14.0000			−0.810998
$299$	−6.00000	+	20.7846i	−0.346989	+	1.20201i
$300$	−1.00000			−0.0577350
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	6.50000	−	11.2583i	0.374033	−	0.647844i
$303$	−7.00000	−	12.1244i	−0.402139	−	0.696526i
$304$	−5.00000			−0.286770
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$	−3.50000	−	6.06218i	−0.200082	−	0.346552i
$307$	9.00000			0.513657			0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000			0.513657			0.256829	+	0.966457i	$0.417322\pi$
$308$	1.50000	+	2.59808i	0.0854704	+	0.148039i
$309$	−5.00000	+	8.66025i	−0.284440	+	0.492665i
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	23.0000			1.30421			0.652105	−	0.758129i	$-0.273886\pi$
$311$	23.0000			1.30421			0.652105	+	0.758129i	$0.273886\pi$
$312$	1.00000	−	3.46410i	0.0566139	−	0.196116i
$313$	28.0000			1.58265			0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000			1.58265			0.791327	+	0.611393i	$0.209391\pi$
$314$	−9.00000	+	15.5885i	−0.507899	+	0.879708i
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$	−1.50000	−	2.59808i	−0.0843816	−	0.146153i
$317$	30.0000			1.68497			0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000			1.68497			0.842484	+	0.538721i	$0.181092\pi$
$318$	1.50000	+	2.59808i	0.0841158	+	0.145693i
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$	−2.00000			−0.111803
$321$	−7.50000	−	12.9904i	−0.418609	−	0.725052i
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	−17.5000	+	30.3109i	−0.973726	+	1.68654i
$324$	1.00000			0.0555556
$325$	−3.50000	+	0.866025i	−0.194145	+	0.0480384i
$326$	14.0000			0.775388
$327$	8.00000	−	13.8564i	0.442401	−	0.766261i
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	−0.500000	−	0.866025i	−0.0275659	−	0.0477455i
$330$	6.00000			0.330289
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	−0.992112	−	0.125353i	$-0.959994\pi$
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	0.387498	−	0.921871i	$-0.373340\pi$
$332$	4.00000	+	6.92820i	0.219529	+	0.380235i
$333$	−2.00000			−0.109599
$334$		0			0
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	−17.0000			−0.926049			−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000			−0.926049			−0.463025	+	0.886345i	$0.653236\pi$
$338$	0.500000	−	12.9904i	0.0271964	−	0.706584i
$339$	6.00000			0.325875
$340$	−7.00000	+	12.1244i	−0.379628	+	0.657536i
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$	−2.50000	−	4.33013i	−0.135185	−	0.234146i
$343$	−1.00000			−0.0539949
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$	6.00000	+	10.3923i	0.323029	+	0.559503i
$346$	−12.0000			−0.645124
$347$	−8.50000	−	14.7224i	−0.456304	−	0.790342i	0.542458	−	0.840083i	$-0.317494\pi$
$347$	−8.50000	−	14.7224i	−0.456304	−	0.790342i	−0.998762	+	0.0497412i	$0.984160\pi$
$348$	−2.50000	+	4.33013i	−0.134014	+	0.232119i
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	−0.518022	−	0.855367i	$-0.673331\pi$
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	0.999781	+	0.0209364i	$0.00666475\pi$
$350$	−1.00000			−0.0534522
$351$	3.50000	−	0.866025i	0.186816	−	0.0462250i
$352$	−3.00000			−0.159901
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	−11.0000			−0.582999
$357$	−3.50000	−	6.06218i	−0.185240	−	0.320844i
$358$	10.0000	+	17.3205i	0.528516	+	0.915417i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−4.50000	+	7.79423i	−0.236515	+	0.409656i
$363$	−2.00000			−0.104973
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$	−24.0000			−1.25622
$366$	3.50000	−	6.06218i	0.182948	−	0.316875i
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	−5.00000			−0.260290
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$	1.50000	+	2.59808i	0.0778761	+	0.134885i
$372$	−2.00000			−0.103695
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	−10.5000	+	18.1865i	−0.542942	+	0.940403i
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$	1.00000			0.0515711
$377$	−5.00000	+	17.3205i	−0.257513	+	0.892052i
$378$	1.00000			0.0514344
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	−5.00000	+	8.66025i	−0.256495	+	0.444262i
$381$	6.00000	+	10.3923i	0.307389	+	0.532414i
$382$	4.00000			0.204658
$383$	−15.5000	−	26.8468i	−0.792013	−	1.37181i	−0.924719	−	0.380651i	$-0.875700\pi$
$383$	−15.5000	−	26.8468i	−0.792013	−	1.37181i	0.132706	−	0.991155i	$-0.457633\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	6.00000			0.305788
$386$	6.50000	+	11.2583i	0.330841	+	0.573034i
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$	−5.00000	−	5.19615i	−0.253185	−	0.263117i
$391$	−42.0000			−2.12403
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$	−4.00000	+	6.92820i	−0.201773	+	0.349482i
$394$	−4.50000	−	7.79423i	−0.226707	−	0.392668i
$395$	−6.00000			−0.301893
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	0.990538	−	0.137241i	$-0.0438236\pi$
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$398$	26.0000			1.30326
$399$	−2.50000	−	4.33013i	−0.125157	−	0.216777i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	−2.00000			−0.0997509
$403$	−7.00000	+	1.73205i	−0.348695	+	0.0862796i
$404$	14.0000			0.696526
$405$	1.00000	−	1.73205i	0.0496904	−	0.0860663i
$406$	−2.50000	+	4.33013i	−0.124073	+	0.214901i
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$	7.00000			0.346552
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$	5.00000	+	8.66025i	0.246932	+	0.427699i
$411$	18.0000			0.887875
$412$	−5.00000	−	8.66025i	−0.246332	−	0.426660i
$413$	−3.00000	+	5.19615i	−0.147620	+	0.255686i
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	16.0000			0.785409
$416$	2.50000	+	2.59808i	0.122573	+	0.127381i
$417$	−19.0000			−0.930434
$418$	−7.50000	+	12.9904i	−0.366837	+	0.635380i
$419$	−2.00000	+	3.46410i	−0.0977064	+	0.169232i	−0.910735	−	0.412991i	$-0.864484\pi$
$419$	−2.00000	+	3.46410i	−0.0977064	+	0.169232i	0.813029	+	0.582224i	$0.197817\pi$
$420$	−1.00000	−	1.73205i	−0.0487950	−	0.0845154i
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	−5.00000	−	8.66025i	−0.243396	−	0.421575i
$423$	0.500000	+	0.866025i	0.0243108	+	0.0421076i
$424$	−3.00000			−0.145693
$425$	−3.50000	−	6.06218i	−0.169775	−	0.294059i
$426$	4.00000	−	6.92820i	0.193801	−	0.335673i
$427$	3.50000	−	6.06218i	0.169377	−	0.293369i
$428$	15.0000			0.725052
$429$	−7.50000	−	7.79423i	−0.362103	−	0.376309i
$430$	4.00000			0.192897
$431$	4.00000	−	6.92820i	0.192673	−	0.333720i	−0.753462	−	0.657491i	$-0.771618\pi$
$431$	4.00000	−	6.92820i	0.192673	−	0.333720i	0.946135	+	0.323772i	$0.104951\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−13.0000	−	22.5167i	−0.624740	−	1.08208i	−0.988591	−	0.150624i	$-0.951872\pi$
$433$	−13.0000	−	22.5167i	−0.624740	−	1.08208i	0.363851	−	0.931457i	$-0.381462\pi$
$434$	−2.00000			−0.0960031
$435$	5.00000	+	8.66025i	0.239732	+	0.415227i
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	−30.0000			−1.43509
$438$	6.00000	+	10.3923i	0.286691	+	0.496564i
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$	−3.00000	+	5.19615i	−0.143019	+	0.247717i
$441$	1.00000			0.0476190
$442$	24.5000	−	6.06218i	1.16535	−	0.288348i
$443$	15.0000			0.712672			0.356336	−	0.934358i	$-0.384026\pi$
$443$	15.0000			0.712672			0.356336	+	0.934358i	$0.384026\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	−11.0000	+	19.0526i	−0.521450	+	0.903178i
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$	14.0000			0.662177
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	19.0000	+	32.9090i	0.896665	+	1.55307i	0.831730	+	0.555181i	$0.187351\pi$
$449$	19.0000	+	32.9090i	0.896665	+	1.55307i	0.0649356	+	0.997889i	$0.479316\pi$
$450$	1.00000			0.0471405
$451$	7.50000	+	12.9904i	0.353161	+	0.611693i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−6.50000	+	11.2583i	−0.305397	+	0.528962i
$454$	−14.0000			−0.657053
$455$	−5.00000	−	5.19615i	−0.234404	−	0.243599i
$456$	5.00000			0.234146
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	0.383437	+	0.923567i	$0.374740\pi$
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	−0.991551	+	0.129718i	$0.958593\pi$
$458$	13.5000	−	23.3827i	0.630814	−	1.09260i
$459$	3.50000	+	6.06218i	0.163366	+	0.282958i
$460$	−12.0000			−0.559503
$461$	−4.00000	−	6.92820i	−0.186299	−	0.322679i	0.757715	−	0.652586i	$-0.226316\pi$
$461$	−4.00000	−	6.92820i	−0.186299	−	0.322679i	−0.944013	+	0.329907i	$0.892983\pi$
$462$	−1.50000	−	2.59808i	−0.0697863	−	0.120873i
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	13.0000	−	22.5167i	0.602213	−	1.04306i
$467$	−12.0000			−0.555294			−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000			−0.555294			−0.277647	+	0.960683i	$0.589555\pi$
$468$	−1.00000	+	3.46410i	−0.0462250	+	0.160128i
$469$	−2.00000			−0.0923514
$470$	1.00000	−	1.73205i	0.0461266	−	0.0798935i
$471$	9.00000	−	15.5885i	0.414698	−	0.718278i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	6.00000			0.275880
$474$	1.50000	+	2.59808i	0.0688973	+	0.119334i
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$	7.00000			0.320844
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	−0.999730	−	0.0232187i	$-0.992609\pi$
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	0.519973	+	0.854183i	$0.325942\pi$
$480$	2.00000			0.0912871
$481$	2.00000	−	6.92820i	0.0911922	−	0.315899i
$482$	−28.0000			−1.27537
$483$	3.00000	−	5.19615i	0.136505	−	0.236433i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	−2.00000	−	3.46410i	−0.0908153	−	0.157297i
$486$	−1.00000			−0.0453609
$487$	−17.5000	−	30.3109i	−0.793001	−	1.37352i	−0.924101	−	0.382148i	$-0.875184\pi$
$487$	−17.5000	−	30.3109i	−0.793001	−	1.37352i	0.131100	−	0.991369i	$-0.458149\pi$
$488$	3.50000	+	6.06218i	0.158438	+	0.274422i
$489$	−14.0000			−0.633102
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	−0.761539	−	0.648119i	$-0.775556\pi$
$491$	4.00000	−	6.92820i	0.180517	−	0.312665i	0.942057	+	0.335453i	$0.108889\pi$
$492$	2.50000	−	4.33013i	0.112709	−	0.195217i
$493$	−35.0000			−1.57632
$494$	17.5000	−	4.33013i	0.787362	−	0.194822i
$495$	−6.00000			−0.269680
$496$	1.00000	−	1.73205i	0.0449013	−	0.0777714i
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$	−4.00000	−	6.92820i	−0.179244	−	0.310460i
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		0			0
$502$	12.0000			0.535586
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	−0.999161	−	0.0409609i	$-0.986958\pi$
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	0.464107	−	0.885779i	$-0.346375\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	14.0000	−	24.2487i	0.622992	−	1.07905i
$506$	−18.0000			−0.800198
$507$	−0.500000	+	12.9904i	−0.0222058	+	0.576923i
$508$	−12.0000			−0.532414
$509$	20.0000	−	34.6410i	0.886484	−	1.53544i	0.0424816	−	0.999097i	$-0.486474\pi$
$509$	20.0000	−	34.6410i	0.886484	−	1.53544i	0.844003	−	0.536339i	$-0.180193\pi$
$510$	7.00000	−	12.1244i	0.309965	−	0.536875i
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	−1.00000			−0.0441942
$513$	2.50000	+	4.33013i	0.110378	+	0.191180i
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	−20.0000			−0.881305
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	12.0000			0.526742
$520$	7.00000	−	1.73205i	0.306970	−	0.0759555i
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	2.50000	−	4.33013i	0.109422	−	0.189525i
$523$	−19.5000	+	33.7750i	−0.852675	+	1.47688i	0.0261094	+	0.999659i	$0.491688\pi$
$523$	−19.5000	+	33.7750i	−0.852675	+	1.47688i	−0.878785	+	0.477218i	$0.841645\pi$
$524$	−4.00000	−	6.92820i	−0.174741	−	0.302660i
$525$	1.00000			0.0436436
$526$	−12.0000	−	20.7846i	−0.523225	−	0.906252i
$527$	−7.00000	−	12.1244i	−0.304925	−	0.528145i
$528$	3.00000			0.130558
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	3.00000	−	5.19615i	0.130189	−	0.225494i
$532$	5.00000			0.216777
$533$	5.00000	−	17.3205i	0.216574	−	0.750234i
$534$	11.0000			0.476017
$535$	15.0000	−	25.9808i	0.648507	−	1.12325i
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$	−10.0000	−	17.3205i	−0.431532	−	0.747435i
$538$	24.0000			1.03471
$539$	−1.50000	−	2.59808i	−0.0646096	−	0.111907i
$540$	1.00000	+	1.73205i	0.0430331	+	0.0745356i
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	1.00000	+	1.73205i	0.0429537	+	0.0743980i
$543$	4.50000	−	7.79423i	0.193113	−	0.334482i
$544$	−3.50000	+	6.06218i	−0.150061	+	0.259914i
$545$	32.0000			1.37073
$546$	−1.00000	+	3.46410i	−0.0427960	+	0.148250i
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$	−3.50000	+	6.06218i	−0.149376	+	0.258727i
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	−25.0000			−1.06504
$552$	3.00000	+	5.19615i	0.127688	+	0.221163i
$553$	1.50000	+	2.59808i	0.0637865	+	0.110481i
$554$	−6.00000			−0.254916
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	−0.662240	−	0.749291i	$-0.730394\pi$
$557$	7.50000	−	12.9904i	0.317785	−	0.550420i	0.980026	+	0.198871i	$0.0637276\pi$
$558$	2.00000			0.0846668
$559$	−5.00000	−	5.19615i	−0.211477	−	0.219774i
$560$	2.00000			0.0845154
$561$	10.5000	−	18.1865i	0.443310	−	0.767836i
$562$	8.00000	−	13.8564i	0.337460	−	0.584497i
$563$	−15.0000	−	25.9808i	−0.632175	−	1.09496i	−0.987106	−	0.160066i	$-0.948829\pi$
$563$	−15.0000	−	25.9808i	−0.632175	−	1.09496i	0.354932	−	0.934892i	$-0.384504\pi$
$564$	−1.00000			−0.0421076
$565$	6.00000	+	10.3923i	0.252422	+	0.437208i
$566$	14.0000	+	24.2487i	0.588464	+	1.01925i
$567$	−1.00000			−0.0419961
$568$	4.00000	+	6.92820i	0.167836	+	0.290701i
$569$	22.0000	−	38.1051i	0.922288	−	1.59745i	0.126422	−	0.991977i	$-0.459651\pi$
$569$	22.0000	−	38.1051i	0.922288	−	1.59745i	0.795866	−	0.605473i	$-0.207016\pi$
$570$	5.00000	−	8.66025i	0.209427	−	0.362738i
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	10.5000	−	2.59808i	0.439027	−	0.108631i
$573$	−4.00000			−0.167102
$574$	2.50000	−	4.33013i	0.104348	−	0.180736i
$575$	3.00000	−	5.19615i	0.125109	−	0.216695i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$	16.0000	+	27.7128i	0.665512	+	1.15270i
$579$	−6.50000	−	11.2583i	−0.270131	−	0.467880i
$580$	−10.0000			−0.415227
$581$	−4.00000	−	6.92820i	−0.165948	−	0.287430i
$582$	−1.00000	+	1.73205i	−0.0414513	+	0.0717958i
$583$	−4.50000	+	7.79423i	−0.186371	+	0.322804i
$584$	−12.0000			−0.496564
$585$	5.00000	+	5.19615i	0.206725	+	0.214834i
$586$	−12.0000			−0.495715
$587$	−5.00000	+	8.66025i	−0.206372	+	0.357447i	−0.950569	−	0.310513i	$-0.899499\pi$
$587$	−5.00000	+	8.66025i	−0.206372	+	0.357447i	0.744197	+	0.667960i	$0.232832\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	−12.0000			−0.494032
$591$	4.50000	+	7.79423i	0.185105	+	0.320612i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−13.0000			−0.533846			−0.266923	−	0.963718i	$-0.586007\pi$
$593$	−13.0000			−0.533846			−0.266923	+	0.963718i	$0.586007\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$	7.00000	−	12.1244i	0.286972	−	0.497050i
$596$	−7.00000	+	12.1244i	−0.286731	+	0.496633i
$597$	−26.0000			−1.06411
$598$	15.0000	+	15.5885i	0.613396	+	0.637459i
$599$	−26.0000			−1.06233			−0.531166	−	0.847268i	$-0.678246\pi$
$599$	−26.0000			−1.06233			−0.531166	+	0.847268i	$0.678246\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	0.159754	+	0.987157i	$0.448930\pi$
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	−0.934780	+	0.355228i	$0.884403\pi$
$602$	−1.00000	−	1.73205i	−0.0407570	−	0.0705931i
$603$	2.00000			0.0814463
$604$	−6.50000	−	11.2583i	−0.264481	−	0.458095i
$605$	−2.00000	−	3.46410i	−0.0813116	−	0.140836i
$606$	−14.0000			−0.568711
$607$	15.0000	+	25.9808i	0.608831	+	1.05453i	0.991433	+	0.130613i	$0.0416947\pi$
$607$	15.0000	+	25.9808i	0.608831	+	1.05453i	−0.382602	+	0.923913i	$0.624972\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$	2.50000	−	4.33013i	0.101305	−	0.175466i
$610$	14.0000			0.566843
$611$	−3.50000	+	0.866025i	−0.141595	+	0.0350356i
$612$	−7.00000			−0.282958
$613$	14.0000	−	24.2487i	0.565455	−	0.979396i	−0.431553	−	0.902088i	$-0.642034\pi$
$613$	14.0000	−	24.2487i	0.565455	−	0.979396i	0.997007	−	0.0773084i	$-0.0246326\pi$
$614$	4.50000	−	7.79423i	0.181605	−	0.314549i
$615$	−5.00000	−	8.66025i	−0.201619	−	0.349215i
$616$	3.00000			0.120873
$617$	10.0000	+	17.3205i	0.402585	+	0.697297i	0.994037	−	0.109043i	$-0.0347785\pi$
$617$	10.0000	+	17.3205i	0.402585	+	0.697297i	−0.591452	+	0.806340i	$0.701445\pi$
$618$	5.00000	+	8.66025i	0.201129	+	0.348367i
$619$	41.0000			1.64793			0.823965	−	0.566641i	$-0.191757\pi$
$619$	41.0000			1.64793			0.823965	+	0.566641i	$0.191757\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	11.5000	−	19.9186i	0.461108	−	0.798662i
$623$	11.0000			0.440706
$624$	−2.50000	−	2.59808i	−0.100080	−	0.104006i
$625$	−19.0000			−0.760000
$626$	14.0000	−	24.2487i	0.559553	−	0.969173i
$627$	7.50000	−	12.9904i	0.299521	−	0.518786i
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	14.0000			0.558217
$630$	1.00000	+	1.73205i	0.0398410	+	0.0690066i
$631$	−7.50000	−	12.9904i	−0.298570	−	0.517139i	0.677239	−	0.735763i	$-0.263176\pi$
$631$	−7.50000	−	12.9904i	−0.298570	−	0.517139i	−0.975809	+	0.218624i	$0.929843\pi$
$632$	−3.00000			−0.119334
$633$	5.00000	+	8.66025i	0.198732	+	0.344214i
$634$	15.0000	−	25.9808i	0.595726	−	1.03183i
$635$	−12.0000	+	20.7846i	−0.476205	+	0.824812i
$636$	3.00000			0.118958
$637$	−1.00000	+	3.46410i	−0.0396214	+	0.137253i
$638$	−15.0000			−0.593856
$639$	−4.00000	+	6.92820i	−0.158238	+	0.274075i
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	−15.0000			−0.592003
$643$	24.5000	+	42.4352i	0.966186	+	1.67348i	0.706395	+	0.707818i	$0.250320\pi$
$643$	24.5000	+	42.4352i	0.966186	+	1.67348i	0.259791	+	0.965665i	$0.416346\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$	−4.00000			−0.157500
$646$	17.5000	+	30.3109i	0.688528	+	1.19257i
$647$	−0.500000	+	0.866025i	−0.0196570	+	0.0340470i	−0.875687	−	0.482880i	$-0.839591\pi$
$647$	−0.500000	+	0.866025i	−0.0196570	+	0.0340470i	0.856030	+	0.516927i	$0.172924\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−18.0000			−0.706562
$650$	−1.00000	+	3.46410i	−0.0392232	+	0.135873i
$651$	2.00000			0.0783862
$652$	7.00000	−	12.1244i	0.274141	−	0.474826i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	−8.00000	−	13.8564i	−0.312825	−	0.541828i
$655$	−16.0000			−0.625172
$656$	2.50000	+	4.33013i	0.0976086	+	0.169063i
$657$	−6.00000	−	10.3923i	−0.234082	−	0.405442i
$658$	−1.00000			−0.0389841
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	0.999545	+	0.0301523i	$0.00959924\pi$
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	−0.473660	+	0.880708i	$0.657067\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	−22.0000			−0.855054
$663$	−24.5000	+	6.06218i	−0.951501	+	0.235435i
$664$	8.00000			0.310460
$665$	5.00000	−	8.66025i	0.193892	−	0.335830i
$666$	−1.00000	+	1.73205i	−0.0387492	+	0.0671156i
$667$	−15.0000	−	25.9808i	−0.580802	−	1.00598i
$668$		0			0
$669$	2.00000	+	3.46410i	0.0773245	+	0.133930i
$670$	−2.00000	−	3.46410i	−0.0772667	−	0.133830i
$671$	21.0000			0.810696
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	−0.997932	−	0.0642860i	$-0.979523\pi$
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	0.554639	+	0.832091i	$0.312856\pi$
$674$	−8.50000	+	14.7224i	−0.327408	+	0.567087i
$675$	−1.00000			−0.0384900
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$	7.00000	+	12.1244i	0.268438	+	0.464948i
$681$	14.0000			0.536481
$682$	−3.00000	−	5.19615i	−0.114876	−	0.198971i
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$	−5.00000			−0.191180
$685$	18.0000	+	31.1769i	0.687745	+	1.19121i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−13.5000	+	23.3827i	−0.515057	+	0.892105i
$688$	2.00000			0.0762493
$689$	10.5000	−	2.59808i	0.400018	−	0.0989788i
$690$	12.0000			0.456832
$691$	−20.0000	+	34.6410i	−0.760836	+	1.31781i	0.181584	+	0.983375i	$0.441877\pi$
$691$	−20.0000	+	34.6410i	−0.760836	+	1.31781i	−0.942420	+	0.334431i	$0.891456\pi$
$692$	−6.00000	+	10.3923i	−0.228086	+	0.395056i
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$	−17.0000			−0.645311
$695$	−19.0000	−	32.9090i	−0.720711	−	1.24831i
$696$	2.50000	+	4.33013i	0.0947623	+	0.164133i
$697$	35.0000			1.32572
$698$	−9.00000	−	15.5885i	−0.340655	−	0.590032i
$699$	−13.0000	+	22.5167i	−0.491705	+	0.851658i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$	1.00000	−	3.46410i	0.0377426	−	0.130744i
$703$	10.0000			0.377157
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$	−1.00000	+	1.73205i	−0.0376622	+	0.0652328i
$706$	7.00000	+	12.1244i	0.263448	+	0.456306i
$707$	−14.0000			−0.526524
$708$	3.00000	+	5.19615i	0.112747	+	0.195283i
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$	16.0000			0.600469
$711$	−1.50000	−	2.59808i	−0.0562544	−	0.0974355i
$712$	−5.50000	+	9.52628i	−0.206121	+	0.357012i
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$	−7.00000			−0.261968
$715$	6.00000	−	20.7846i	0.224387	−	0.777300i
$716$	20.0000			0.747435
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	0.971311	−	0.237814i	$-0.0764307\pi$
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	−0.691608	+	0.722273i	$0.743097\pi$
$720$	−2.00000			−0.0745356
$721$	5.00000	+	8.66025i	0.186210	+	0.322525i
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$	28.0000			1.04133
$724$	4.50000	+	7.79423i	0.167241	+	0.289670i
$725$	2.50000	−	4.33013i	0.0928477	−	0.160817i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−2.50000	−	2.59808i	−0.0926562	−	0.0962911i
$729$	1.00000			0.0370370
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	7.00000	−	12.1244i	0.258904	−	0.448435i
$732$	−3.50000	−	6.06218i	−0.129364	−	0.224065i
$733$	−7.00000			−0.258551			−0.129275	−	0.991609i	$-0.541265\pi$
$733$	−7.00000			−0.258551			−0.129275	+	0.991609i	$0.541265\pi$
$734$	−5.00000	−	8.66025i	−0.184553	−	0.319656i
$735$	1.00000	+	1.73205i	0.0368856	+	0.0638877i
$736$	−6.00000			−0.221163
$737$	−3.00000	−	5.19615i	−0.110506	−	0.191403i
$738$	−2.50000	+	4.33013i	−0.0920263	+	0.159394i
$739$	7.00000	−	12.1244i	0.257499	−	0.446002i	−0.708072	−	0.706140i	$-0.750435\pi$
$739$	7.00000	−	12.1244i	0.257499	−	0.446002i	0.965571	+	0.260138i	$0.0837682\pi$
$740$	4.00000			0.147043
$741$	−17.5000	+	4.33013i	−0.642879	+	0.159071i
$742$	3.00000			0.110133
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$	−1.00000	+	1.73205i	−0.0366618	+	0.0635001i
$745$	14.0000	+	24.2487i	0.512920	+	0.888404i
$746$	−4.00000			−0.146450
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$	10.5000	+	18.1865i	0.383918	+	0.664966i
$749$	−15.0000			−0.548088
$750$	6.00000	+	10.3923i	0.219089	+	0.379473i
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	−0.390410	−	0.920641i	$-0.627667\pi$
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	0.992504	−	0.122216i	$-0.0389999\pi$
$752$	0.500000	−	0.866025i	0.0182331	−	0.0315807i
$753$	−12.0000			−0.437304
$754$	12.5000	+	12.9904i	0.455223	+	0.473082i
$755$	−26.0000			−0.946237
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	0.413768	+	0.910382i	$0.364212\pi$
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	−0.995298	+	0.0968571i	$0.969121\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$	18.0000			0.653359
$760$	5.00000	+	8.66025i	0.181369	+	0.314140i
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$	12.0000			0.434714
$763$	−8.00000	−	13.8564i	−0.289619	−	0.501636i
$764$	2.00000	−	3.46410i	0.0723575	−	0.125327i
$765$	−7.00000	+	12.1244i	−0.253086	+	0.438357i
$766$	−31.0000			−1.12008
$767$	15.0000	+	15.5885i	0.541619	+	0.562867i
$768$	1.00000			0.0360844
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	0.0691074	+	0.997609i	$0.477985\pi$
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	−0.898509	+	0.438956i	$0.855348\pi$
$770$	3.00000	−	5.19615i	0.108112	−	0.187256i
$771$	7.50000	+	12.9904i	0.270106	+	0.467837i
$772$	13.0000			0.467880
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	0.941825	−	0.336104i	$-0.109109\pi$
$773$	5.00000	+	8.66025i	0.179838	+	0.311488i	−0.761987	+	0.647592i	$0.775776\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	2.00000			0.0718421
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$	−1.00000	+	1.73205i	−0.0358748	+	0.0621370i
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$	25.0000			0.895718
$780$	−7.00000	+	1.73205i	−0.250640	+	0.0620174i
$781$	24.0000			0.858788
$782$	−21.0000	+	36.3731i	−0.750958	+	1.30070i
$783$	−2.50000	+	4.33013i	−0.0893427	+	0.154746i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	36.0000			1.28490
$786$	4.00000	+	6.92820i	0.142675	+	0.247121i
$787$	−12.5000	−	21.6506i	−0.445577	−	0.771762i	0.552515	−	0.833503i	$-0.313668\pi$
$787$	−12.5000	−	21.6506i	−0.445577	−	0.771762i	−0.998092	+	0.0617409i	$0.980335\pi$
$788$	−9.00000			−0.320612
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$	3.00000	−	5.19615i	0.106668	−	0.184754i
$792$	−3.00000			−0.106600
$793$	−17.5000	−	18.1865i	−0.621443	−	0.645823i
$794$	15.0000			0.532330
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$	13.0000	−	22.5167i	0.460773	−	0.798082i
$797$	−28.0000	−	48.4974i	−0.991811	−	1.71787i	−0.606510	−	0.795076i	$-0.707431\pi$
$797$	−28.0000	−	48.4974i	−0.991811	−	1.71787i	−0.385301	−	0.922791i	$-0.625902\pi$
$798$	−5.00000			−0.176998
$799$	−3.50000	−	6.06218i	−0.123821	−	0.214464i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−11.0000			−0.388666
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	−18.0000	+	31.1769i	−0.635206	+	1.10021i
$804$	−1.00000	+	1.73205i	−0.0352673	+	0.0610847i
$805$	12.0000			0.422944
$806$	−2.00000	+	6.92820i	−0.0704470	+	0.244036i
$807$	−24.0000			−0.844840
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	−26.0000	+	45.0333i	−0.914111	+	1.58329i	−0.105914	+	0.994375i	$0.533777\pi$
$809$	−26.0000	+	45.0333i	−0.914111	+	1.58329i	−0.808197	+	0.588912i	$0.799556\pi$
$810$	−1.00000	−	1.73205i	−0.0351364	−	0.0608581i
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	2.50000	+	4.33013i	0.0877328	+	0.151958i
$813$	−1.00000	−	1.73205i	−0.0350715	−	0.0607457i
$814$	6.00000			0.210300
$815$	−14.0000	−	24.2487i	−0.490399	−	0.849395i
$816$	3.50000	−	6.06218i	0.122525	−	0.212219i
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$		0			0
$819$	1.00000	−	3.46410i	0.0349428	−	0.121046i
$820$	10.0000			0.349215
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	−0.966708	−	0.255884i	$-0.917634\pi$
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	0.704956	+	0.709251i	$0.250967\pi$
$822$	9.00000	−	15.5885i	0.313911	−	0.543710i
$823$	24.0000	+	41.5692i	0.836587	+	1.44901i	0.892731	+	0.450589i	$0.148786\pi$
$823$	24.0000	+	41.5692i	0.836587	+	1.44901i	−0.0561440	+	0.998423i	$0.517881\pi$
$824$	−10.0000			−0.348367
$825$	1.50000	+	2.59808i	0.0522233	+	0.0904534i
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	3.50000	−	6.06218i	0.121560	−	0.210548i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	3.50000	−	6.06218i	0.121560	−	0.210548i	0.920383	+	0.391018i	$0.127877\pi$
$830$	8.00000	−	13.8564i	0.277684	−	0.480963i
$831$	6.00000			0.208138
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	−7.00000			−0.242536
$834$	−9.50000	+	16.4545i	−0.328958	+	0.569772i
$835$		0			0
$836$	7.50000	+	12.9904i	0.259393	+	0.449282i
$837$	−2.00000			−0.0691301
$838$	2.00000	+	3.46410i	0.0690889	+	0.119665i
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	0.995353	−	0.0962912i	$-0.0306980\pi$
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	−0.581067	+	0.813856i	$0.697365\pi$
$840$	−2.00000			−0.0690066
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	−11.0000	+	19.0526i	−0.379085	+	0.656595i
$843$	−8.00000	+	13.8564i	−0.275535	+	0.477240i
$844$	−10.0000			−0.344214
$845$	−23.0000	+	12.1244i	−0.791224	+	0.417091i
$846$	1.00000			0.0343807
$847$	−1.00000	+	1.73205i	−0.0343604	+	0.0595140i
$848$	−1.50000	+	2.59808i	−0.0515102	+	0.0892183i
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$	−7.00000			−0.240098
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	−4.00000	−	6.92820i	−0.137038	−	0.237356i
$853$	41.0000			1.40381			0.701907	−	0.712269i	$-0.252332\pi$
$853$	41.0000			1.40381			0.701907	+	0.712269i	$0.252332\pi$
$854$	−3.50000	−	6.06218i	−0.119768	−	0.207443i
$855$	−5.00000	+	8.66025i	−0.170996	+	0.296174i
$856$	7.50000	−	12.9904i	0.256345	−	0.444002i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$	−10.5000	+	2.59808i	−0.358464	+	0.0886969i
$859$	35.0000			1.19418			0.597092	−	0.802173i	$-0.296323\pi$
$859$	35.0000			1.19418			0.597092	+	0.802173i	$0.296323\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$	−2.50000	+	4.33013i	−0.0851998	+	0.147570i
$862$	−4.00000	−	6.92820i	−0.136241	−	0.235976i
$863$	34.0000			1.15737			0.578687	−	0.815550i	$-0.303565\pi$
$863$	34.0000			1.15737			0.578687	+	0.815550i	$0.303565\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	12.0000	+	20.7846i	0.408012	+	0.706698i
$866$	−26.0000			−0.883516
$867$	−16.0000	−	27.7128i	−0.543388	−	0.941176i
$868$	−1.00000	+	1.73205i	−0.0339422	+	0.0587896i
$869$	−4.50000	+	7.79423i	−0.152652	+	0.264401i
$870$	10.0000			0.339032
$871$	−2.00000	+	6.92820i	−0.0677674	+	0.234753i
$872$	16.0000			0.541828
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$	−15.0000	+	25.9808i	−0.507383	+	0.878812i
$875$	6.00000	+	10.3923i	0.202837	+	0.351324i
$876$	12.0000			0.405442
$877$	−20.0000	−	34.6410i	−0.675352	−	1.16974i	−0.976366	−	0.216124i	$-0.930658\pi$
$877$	−20.0000	−	34.6410i	−0.675352	−	1.16974i	0.301014	−	0.953620i	$-0.402675\pi$
$878$	2.00000	+	3.46410i	0.0674967	+	0.116908i
$879$	12.0000			0.404750
$880$	3.00000	+	5.19615i	0.101130	+	0.175162i
$881$	13.0000	−	22.5167i	0.437981	−	0.758606i	−0.559553	−	0.828795i	$-0.689027\pi$
$881$	13.0000	−	22.5167i	0.437981	−	0.758606i	0.997534	+	0.0701893i	$0.0223603\pi$
$882$	0.500000	−	0.866025i	0.0168359	−	0.0291606i
$883$	−14.0000			−0.471138			−0.235569	−	0.971858i	$-0.575695\pi$
$883$	−14.0000			−0.471138			−0.235569	+	0.971858i	$0.575695\pi$
$884$	7.00000	−	24.2487i	0.235435	−	0.815572i
$885$	12.0000			0.403376
$886$	7.50000	−	12.9904i	0.251967	−	0.436420i
$887$	−18.5000	+	32.0429i	−0.621169	+	1.07590i	0.368099	+	0.929787i	$0.380009\pi$
$887$	−18.5000	+	32.0429i	−0.621169	+	1.07590i	−0.989268	+	0.146110i	$0.953325\pi$
$888$	−1.00000	−	1.73205i	−0.0335578	−	0.0581238i
$889$	12.0000			0.402467
$890$	11.0000	+	19.0526i	0.368721	+	0.638643i
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	−4.00000			−0.133930
$893$	−2.50000	−	4.33013i	−0.0836593	−	0.144902i
$894$	7.00000	−	12.1244i	0.234115	−	0.405499i
$895$	20.0000	−	34.6410i	0.668526	−	1.15792i
$896$	1.00000			0.0334077
$897$	−15.0000	−	15.5885i	−0.500835	−	0.520483i
$898$	38.0000			1.26808
$899$	5.00000	−	8.66025i	0.166759	−	0.288836i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	10.5000	+	18.1865i	0.349806	+	0.605881i
$902$	15.0000			0.499445
$903$	1.00000	+	1.73205i	0.0332779	+	0.0576390i
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	18.0000			0.598340
$906$	6.50000	+	11.2583i	0.215948	+	0.374033i
$907$	19.0000	−	32.9090i	0.630885	−	1.09272i	−0.356487	−	0.934300i	$-0.616025\pi$
$907$	19.0000	−	32.9090i	0.630885	−	1.09272i	0.987371	−	0.158424i	$-0.0506412\pi$
$908$	−7.00000	+	12.1244i	−0.232303	+	0.402361i
$909$	14.0000			0.464351
$910$	−7.00000	+	1.73205i	−0.232048	+	0.0574169i
$911$	−52.0000			−1.72284			−0.861418	−	0.507896i	$-0.830423\pi$
$911$	−52.0000			−1.72284			−0.861418	+	0.507896i	$0.830423\pi$
$912$	2.50000	−	4.33013i	0.0827833	−	0.143385i
$913$	12.0000	−	20.7846i	0.397142	−	0.687870i
$914$	13.0000	+	22.5167i	0.430002	+	0.744785i
$915$	−14.0000			−0.462826
$916$	−13.5000	−	23.3827i	−0.446053	−	0.772586i
$917$	4.00000	+	6.92820i	0.132092	+	0.228789i
$918$	7.00000			0.231034
$919$	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	$0.775261\pi$
$920$	−6.00000	+	10.3923i	−0.197814	+	0.342624i
$921$	−4.50000	+	7.79423i	−0.148280	+	0.256829i
$922$	−8.00000			−0.263466
$923$	−20.0000	−	20.7846i	−0.658308	−	0.684134i
$924$	−3.00000			−0.0986928
$925$	−1.00000	+	1.73205i	−0.0328798	+	0.0569495i
$926$	−15.5000	+	26.8468i	−0.509362	+	0.882240i
$927$	−5.00000	−	8.66025i	−0.164222	−	0.284440i
$928$	−5.00000			−0.164133
$929$	6.50000	+	11.2583i	0.213258	+	0.369374i	0.952732	−	0.303811i	$-0.0982592\pi$
$929$	6.50000	+	11.2583i	0.213258	+	0.369374i	−0.739474	+	0.673185i	$0.764926\pi$
$930$	2.00000	+	3.46410i	0.0655826	+	0.113592i
$931$	−5.00000			−0.163868
$932$	−13.0000	−	22.5167i	−0.425829	−	0.737558i
$933$	−11.5000	+	19.9186i	−0.376493	+	0.652105i
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	42.0000			1.37355
$936$	2.50000	+	2.59808i	0.0817151	+	0.0849208i
$937$	52.0000			1.69877			0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000			1.69877			0.849383	+	0.527777i	$0.176974\pi$
$938$	−1.00000	+	1.73205i	−0.0326512	+	0.0565535i
$939$	−14.0000	+	24.2487i	−0.456873	+	0.791327i
$940$	−1.00000	−	1.73205i	−0.0326164	−	0.0564933i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	−9.00000	−	15.5885i	−0.293236	−	0.507899i
$943$	15.0000	+	25.9808i	0.488467	+	0.846050i
$944$	−6.00000			−0.195283
$945$	−1.00000	−	1.73205i	−0.0325300	−	0.0563436i
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	15.5000	−	26.8468i	0.503682	−	0.872403i	−0.496309	−	0.868146i	$-0.665312\pi$
$947$	15.5000	−	26.8468i	0.503682	−	0.872403i	0.999991	−	0.00425721i	$-0.00135512\pi$
$948$	3.00000			0.0974355
$949$	42.0000	−	10.3923i	1.36338	−	0.337348i
$950$	−5.00000			−0.162221
$951$	−15.0000	+	25.9808i	−0.486408	+	0.842484i
$952$	3.50000	−	6.06218i	0.113436	−	0.196476i
$953$	7.00000	+	12.1244i	0.226752	+	0.392746i	0.956844	−	0.290603i	$-0.0938559\pi$
$953$	7.00000	+	12.1244i	0.226752	+	0.392746i	−0.730091	+	0.683349i	$0.760523\pi$
$954$	−3.00000			−0.0971286
$955$	−4.00000	−	6.92820i	−0.129437	−	0.224191i
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$	15.0000			0.484881
$958$	10.5000	+	18.1865i	0.339240	+	0.587580i
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$	1.00000	−	1.73205i	0.0322749	−	0.0559017i
$961$	−27.0000			−0.870968
$962$	−5.00000	−	5.19615i	−0.161206	−	0.167531i
$963$	15.0000			0.483368
$964$	−14.0000	+	24.2487i	−0.450910	+	0.780998i
$965$	13.0000	−	22.5167i	0.418485	−	0.724837i
$966$	−3.00000	−	5.19615i	−0.0965234	−	0.167183i
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−1.00000	−	1.73205i	−0.0321412	−	0.0556702i
$969$	−17.5000	−	30.3109i	−0.562181	−	0.973726i
$970$	−4.00000			−0.128432
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	0.633768	−	0.773523i	$-0.281507\pi$
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	−0.986775	+	0.162098i	$0.948174\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−9.50000	+	16.4545i	−0.304556	+	0.527506i
$974$	−35.0000			−1.12147
$975$	1.00000	−	3.46410i	0.0320256	−	0.110940i
$976$	7.00000			0.224065
$977$	−4.00000	+	6.92820i	−0.127971	+	0.221653i	−0.922890	−	0.385063i	$-0.874180\pi$
$977$	−4.00000	+	6.92820i	−0.127971	+	0.221653i	0.794919	+	0.606715i	$0.207513\pi$
$978$	−7.00000	+	12.1244i	−0.223835	+	0.387694i
$979$	16.5000	+	28.5788i	0.527342	+	0.913384i
$980$	−2.00000			−0.0638877
$981$	8.00000	+	13.8564i	0.255420	+	0.442401i
$982$	−4.00000	−	6.92820i	−0.127645	−	0.221088i
$983$	−32.0000			−1.02064			−0.510321	−	0.859984i	$-0.670473\pi$
$983$	−32.0000			−1.02064			−0.510321	+	0.859984i	$0.670473\pi$
$984$	−2.50000	−	4.33013i	−0.0796971	−	0.138039i
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−17.5000	+	30.3109i	−0.557314	+	0.965295i
$987$	1.00000			0.0318304
$988$	5.00000	−	17.3205i	0.159071	−	0.551039i
$989$	12.0000			0.381578
$990$	−3.00000	+	5.19615i	−0.0953463	+	0.165145i
$991$	1.50000	−	2.59808i	0.0476491	−	0.0825306i	−0.841217	−	0.540697i	$-0.818160\pi$
$991$	1.50000	−	2.59808i	0.0476491	−	0.0825306i	0.888866	+	0.458167i	$0.151494\pi$
$992$	−1.00000	−	1.73205i	−0.0317500	−	0.0549927i
$993$	22.0000			0.698149
$994$	−4.00000	−	6.92820i	−0.126872	−	0.219749i
$995$	−26.0000	−	45.0333i	−0.824255	−	1.42765i
$996$	−8.00000			−0.253490
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	0.805266	−	0.592914i	$-0.202023\pi$
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	−0.916112	+	0.400923i	$0.868689\pi$
$998$	7.00000	−	12.1244i	0.221581	−	0.383790i
$999$	1.00000	−	1.73205i	0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.c.295.1	yes	2
3.2	odd	2		1638.2.r.l.1387.1		2
13.3	even	3	inner	546.2.l.c.211.1	✓	2
13.4	even	6		7098.2.a.bd.1.1		1
13.9	even	3		7098.2.a.i.1.1		1
39.29	odd	6		1638.2.r.l.757.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.c.211.1	✓	2	13.3	even	3	inner
546.2.l.c.295.1	yes	2	1.1	even	1	trivial
1638.2.r.l.757.1		2	39.29	odd	6
1638.2.r.l.1387.1		2	3.2	odd	2
7098.2.a.i.1.1		1	13.9	even	3
7098.2.a.bd.1.1		1	13.4	even	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 - 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.50000 + 6.06218i) q^{17} -1.00000 q^{18} +(2.50000 + 4.33013i) q^{19} +(1.00000 + 1.73205i) q^{20} -1.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-1.00000 - 1.73205i) q^{30} -2.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +7.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.00000 - 1.73205i) q^{37} +5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +2.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +3.00000 q^{44} +(1.00000 + 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{46} -1.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} -7.00000 q^{51} +(-2.50000 - 2.59808i) q^{52} +3.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{55} +(-0.500000 - 0.866025i) q^{56} -5.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(3.00000 + 5.19615i) q^{59} -2.00000 q^{60} +(-3.50000 - 6.06218i) q^{61} +(-1.00000 + 1.73205i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(-7.00000 + 1.73205i) q^{65} -3.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(3.50000 - 6.06218i) q^{68} +(-3.00000 - 5.19615i) q^{69} -2.00000 q^{70} +(-4.00000 - 6.92820i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +(2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(2.50000 + 2.59808i) q^{78} +3.00000 q^{79} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.50000 - 4.33013i) q^{82} -8.00000 q^{83} +(0.500000 + 0.866025i) q^{84} +(-7.00000 - 12.1244i) q^{85} -2.00000 q^{86} +(-2.50000 - 4.33013i) q^{87} +(1.50000 - 2.59808i) q^{88} +(5.50000 - 9.52628i) q^{89} +2.00000 q^{90} +(2.50000 + 2.59808i) q^{91} +6.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(-5.00000 - 8.66025i) q^{95} -1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(0.500000 + 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} - 4 q^{5} + q^{6} + q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} + 2 q^{12} + 7 q^{13} + 2 q^{14} + 2 q^{15} - q^{16} + 7 q^{17} - 2 q^{18} + 5 q^{19} + 2 q^{20} - 2 q^{21} + 3 q^{22} - 6 q^{23} + q^{24} - 2 q^{25} + 2 q^{26} + 2 q^{27} + q^{28} - 5 q^{29} - 2 q^{30} - 4 q^{31} + q^{32} - 3 q^{33} + 14 q^{34} - 2 q^{35} - q^{36} + 2 q^{37} + 10 q^{38} - 2 q^{39} + 4 q^{40} + 5 q^{41} - q^{42} - 2 q^{43} + 6 q^{44} + 2 q^{45} + 6 q^{46} - 2 q^{47} - q^{48} - q^{49} - q^{50} - 14 q^{51} - 5 q^{52} + 6 q^{53} + q^{54} + 6 q^{55} - q^{56} - 10 q^{57} + 5 q^{58} + 6 q^{59} - 4 q^{60} - 7 q^{61} - 2 q^{62} + q^{63} + 2 q^{64} - 14 q^{65} - 6 q^{66} - 2 q^{67} + 7 q^{68} - 6 q^{69} - 4 q^{70} - 8 q^{71} + q^{72} + 24 q^{73} - 2 q^{74} + q^{75} + 5 q^{76} - 6 q^{77} + 5 q^{78} + 6 q^{79} + 2 q^{80} - q^{81} - 5 q^{82} - 16 q^{83} + q^{84} - 14 q^{85} - 4 q^{86} - 5 q^{87} + 3 q^{88} + 11 q^{89} + 4 q^{90} + 5 q^{91} + 12 q^{92} + 2 q^{93} - q^{94} - 10 q^{95} - 2 q^{96} + 2 q^{97} + q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 - 4 * q^5 + q^6 + q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 + 2 * q^12 + 7 * q^13 + 2 * q^14 + 2 * q^15 - q^16 + 7 * q^17 - 2 * q^18 + 5 * q^19 + 2 * q^20 - 2 * q^21 + 3 * q^22 - 6 * q^23 + q^24 - 2 * q^25 + 2 * q^26 + 2 * q^27 + q^28 - 5 * q^29 - 2 * q^30 - 4 * q^31 + q^32 - 3 * q^33 + 14 * q^34 - 2 * q^35 - q^36 + 2 * q^37 + 10 * q^38 - 2 * q^39 + 4 * q^40 + 5 * q^41 - q^42 - 2 * q^43 + 6 * q^44 + 2 * q^45 + 6 * q^46 - 2 * q^47 - q^48 - q^49 - q^50 - 14 * q^51 - 5 * q^52 + 6 * q^53 + q^54 + 6 * q^55 - q^56 - 10 * q^57 + 5 * q^58 + 6 * q^59 - 4 * q^60 - 7 * q^61 - 2 * q^62 + q^63 + 2 * q^64 - 14 * q^65 - 6 * q^66 - 2 * q^67 + 7 * q^68 - 6 * q^69 - 4 * q^70 - 8 * q^71 + q^72 + 24 * q^73 - 2 * q^74 + q^75 + 5 * q^76 - 6 * q^77 + 5 * q^78 + 6 * q^79 + 2 * q^80 - q^81 - 5 * q^82 - 16 * q^83 + q^84 - 14 * q^85 - 4 * q^86 - 5 * q^87 + 3 * q^88 + 11 * q^89 + 4 * q^90 + 5 * q^91 + 12 * q^92 + 2 * q^93 - q^94 - 10 * q^95 - 2 * q^96 + 2 * q^97 + q^98 + 6 * q^99

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