LMFDB - Embedded newform 546.2.s.c.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(43,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.127
Dual form			546.2.s.c.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.73205 + 3.00000i) q^{10} +(3.46410 - 2.00000i) q^{11} -1.00000 q^{12} +(2.59808 + 2.50000i) q^{13} -1.00000 q^{14} +(3.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.23205 - 5.59808i) q^{17} +1.00000i q^{18} +(6.46410 + 3.73205i) q^{19} +(3.00000 + 1.73205i) q^{20} +1.00000i q^{21} +(2.00000 - 3.46410i) q^{22} +(2.86603 + 4.96410i) q^{23} +(-0.866025 + 0.500000i) q^{24} -7.00000 q^{25} +(3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-4.00000 - 6.92820i) q^{29} +(1.73205 - 3.00000i) q^{30} +6.46410i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} -6.46410i q^{34} +(1.73205 - 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.26795 + 2.46410i) q^{37} +7.46410 q^{38} +(0.866025 - 3.50000i) q^{39} +3.46410 q^{40} +(-6.00000 + 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{42} +(2.23205 - 3.86603i) q^{43} -4.00000i q^{44} +(-3.00000 - 1.73205i) q^{45} +(4.96410 + 2.86603i) q^{46} -0.535898i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.06218 + 3.50000i) q^{50} -6.46410 q^{51} +(3.46410 - 1.00000i) q^{52} -8.26795 q^{53} +(0.866025 - 0.500000i) q^{54} +(6.92820 + 12.0000i) q^{55} +(-0.500000 + 0.866025i) q^{56} -7.46410i q^{57} +(-6.92820 - 4.00000i) q^{58} +(-5.42820 - 3.13397i) q^{59} -3.46410i q^{60} +(2.59808 - 4.50000i) q^{61} +(3.23205 + 5.59808i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(-8.66025 + 9.00000i) q^{65} -4.00000 q^{66} +(6.23205 - 3.59808i) q^{67} +(-3.23205 - 5.59808i) q^{68} +(2.86603 - 4.96410i) q^{69} -3.46410i q^{70} +(1.66987 + 0.964102i) q^{71} +(0.866025 + 0.500000i) q^{72} -10.9282i q^{73} +(-2.46410 + 4.26795i) q^{74} +(3.50000 + 6.06218i) q^{75} +(6.46410 - 3.73205i) q^{76} -4.00000 q^{77} +(-1.00000 - 3.46410i) q^{78} -9.46410 q^{79} +(3.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.46410 + 6.00000i) q^{82} -1.73205i q^{83} +(0.866025 + 0.500000i) q^{84} +(19.3923 + 11.1962i) q^{85} -4.46410i q^{86} +(-4.00000 + 6.92820i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-10.1603 + 5.86603i) q^{89} -3.46410 q^{90} +(-1.00000 - 3.46410i) q^{91} +5.73205 q^{92} +(5.59808 - 3.23205i) q^{93} +(-0.267949 - 0.464102i) q^{94} +(-12.9282 + 22.3923i) q^{95} +1.00000i q^{96} +(10.7321 + 6.19615i) q^{97} +(0.866025 + 0.500000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	$ 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{12} - 4 q^{14} + 12 q^{15} - 2 q^{16} + 6 q^{17} + 12 q^{19} + 12 q^{20} + 8 q^{22} + 8 q^{23} - 28 q^{25} + 14 q^{26} + 4 q^{27} - 16 q^{29} + 2 q^{36} - 24 q^{37} + 16 q^{38} - 24 q^{41} + 2 q^{42} + 2 q^{43} - 12 q^{45} + 6 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{51} - 40 q^{53} - 2 q^{56} + 6 q^{59} + 6 q^{62} - 4 q^{64} - 16 q^{66} + 18 q^{67} - 6 q^{68} + 8 q^{69} + 24 q^{71} + 4 q^{74} + 14 q^{75} + 12 q^{76} - 16 q^{77} - 4 q^{78} - 24 q^{79} + 12 q^{80} - 2 q^{81} + 36 q^{85} - 16 q^{87} - 8 q^{88} - 6 q^{89} - 4 q^{91} + 16 q^{92} + 12 q^{93} - 8 q^{94} - 24 q^{95} + 36 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 4 * q^12 - 4 * q^14 + 12 * q^15 - 2 * q^16 + 6 * q^17 + 12 * q^19 + 12 * q^20 + 8 * q^22 + 8 * q^23 - 28 * q^25 + 14 * q^26 + 4 * q^27 - 16 * q^29 + 2 * q^36 - 24 * q^37 + 16 * q^38 - 24 * q^41 + 2 * q^42 + 2 * q^43 - 12 * q^45 + 6 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^51 - 40 * q^53 - 2 * q^56 + 6 * q^59 + 6 * q^62 - 4 * q^64 - 16 * q^66 + 18 * q^67 - 6 * q^68 + 8 * q^69 + 24 * q^71 + 4 * q^74 + 14 * q^75 + 12 * q^76 - 16 * q^77 - 4 * q^78 - 24 * q^79 + 12 * q^80 - 2 * q^81 + 36 * q^85 - 16 * q^87 - 8 * q^88 - 6 * q^89 - 4 * q^91 + 16 * q^92 + 12 * q^93 - 8 * q^94 - 24 * q^95 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−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
$5$			3.46410i			1.54919i	0.632456	+	0.774597i	$0.282047\pi$
$5$			3.46410i			1.54919i	−0.632456	+	0.774597i	$0.717953\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.73205	+	3.00000i	0.547723	+	0.948683i
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.123371	−	0.992361i	$-0.460630\pi$
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.921095	+	0.389338i	$0.127296\pi$
$12$	−1.00000			−0.288675
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	−1.00000			−0.267261
$15$	3.00000	−	1.73205i	0.774597	−	0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.23205	−	5.59808i	0.783887	−	1.35773i	−0.145774	−	0.989318i	$-0.546567\pi$
$17$	3.23205	−	5.59808i	0.783887	−	1.35773i	0.929661	−	0.368415i	$-0.120099\pi$
$18$			1.00000i			0.235702i
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.999813	−	0.0193444i	$-0.00615788\pi$
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.483154	+	0.875536i	$0.339491\pi$
$20$	3.00000	+	1.73205i	0.670820	+	0.387298i
$21$			1.00000i			0.218218i
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	2.86603	+	4.96410i	0.597608	+	1.03509i	0.993173	+	0.116649i	$0.0372153\pi$
$23$	2.86603	+	4.96410i	0.597608	+	1.03509i	−0.395566	+	0.918438i	$0.629451\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−7.00000			−1.40000
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$	1.00000			0.192450
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−4.00000	−	6.92820i	−0.742781	−	1.28654i	−0.951224	−	0.308500i	$-0.900173\pi$
$29$	−4.00000	−	6.92820i	−0.742781	−	1.28654i	0.208443	−	0.978035i	$-0.433160\pi$
$30$	1.73205	−	3.00000i	0.316228	−	0.547723i
$31$			6.46410i			1.16099i	0.814265	+	0.580493i	$0.197140\pi$
$31$			6.46410i			1.16099i	−0.814265	+	0.580493i	$0.802860\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−3.46410	−	2.00000i	−0.603023	−	0.348155i
$34$		−	6.46410i		−	1.10858i
$35$	1.73205	−	3.00000i	0.292770	−	0.507093i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−4.26795	+	2.46410i	−0.701647	+	0.405096i	−0.807960	−	0.589237i	$-0.799429\pi$
$37$	−4.26795	+	2.46410i	−0.701647	+	0.405096i	0.106314	+	0.994333i	$0.466095\pi$
$38$	7.46410			1.21084
$39$	0.866025	−	3.50000i	0.138675	−	0.560449i
$40$	3.46410			0.547723
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.889032	−	0.457845i	$-0.848621\pi$
$41$	−6.00000	+	3.46410i	−0.937043	+	0.541002i	−0.0480106	+	0.998847i	$0.515288\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	2.23205	−	3.86603i	0.340385	−	0.589563i	−0.644120	−	0.764925i	$-0.722776\pi$
$43$	2.23205	−	3.86603i	0.340385	−	0.589563i	0.984504	+	0.175361i	$0.0561094\pi$
$44$		−	4.00000i		−	0.603023i
$45$	−3.00000	−	1.73205i	−0.447214	−	0.258199i
$46$	4.96410	+	2.86603i	0.731917	+	0.422572i
$47$		−	0.535898i		−	0.0781688i	−0.999236	−	0.0390844i	$-0.987556\pi$
$47$		−	0.535898i		−	0.0781688i	0.999236	−	0.0390844i	$-0.0124441\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−6.06218	+	3.50000i	−0.857321	+	0.494975i
$51$	−6.46410			−0.905155
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$	−8.26795			−1.13569			−0.567845	−	0.823135i	$-0.692223\pi$
$53$	−8.26795			−1.13569			−0.567845	+	0.823135i	$0.692223\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	6.92820	+	12.0000i	0.934199	+	1.61808i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		−	7.46410i		−	0.988644i
$58$	−6.92820	−	4.00000i	−0.909718	−	0.525226i
$59$	−5.42820	−	3.13397i	−0.706692	−	0.408009i	0.103143	−	0.994667i	$-0.467110\pi$
$59$	−5.42820	−	3.13397i	−0.706692	−	0.408009i	−0.809835	+	0.586658i	$0.800443\pi$
$60$		−	3.46410i		−	0.447214i
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	−0.650381	−	0.759608i	$-0.725391\pi$
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	0.983030	+	0.183442i	$0.0587240\pi$
$62$	3.23205	+	5.59808i	0.410471	+	0.710956i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	−1.00000			−0.125000
$65$	−8.66025	+	9.00000i	−1.07417	+	1.11631i
$66$	−4.00000			−0.492366
$67$	6.23205	−	3.59808i	0.761366	−	0.439575i	−0.0684199	−	0.997657i	$-0.521796\pi$
$67$	6.23205	−	3.59808i	0.761366	−	0.439575i	0.829786	+	0.558082i	$0.188462\pi$
$68$	−3.23205	−	5.59808i	−0.391944	−	0.678866i
$69$	2.86603	−	4.96410i	0.345029	−	0.597608i
$70$		−	3.46410i		−	0.414039i
$71$	1.66987	+	0.964102i	0.198177	+	0.114418i	0.595805	−	0.803129i	$-0.296833\pi$
$71$	1.66987	+	0.964102i	0.198177	+	0.114418i	−0.397628	+	0.917547i	$0.630166\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	10.9282i		−	1.27905i	−0.768771	−	0.639525i	$-0.779131\pi$
$73$		−	10.9282i		−	1.27905i	0.768771	−	0.639525i	$-0.220869\pi$
$74$	−2.46410	+	4.26795i	−0.286446	+	0.496139i
$75$	3.50000	+	6.06218i	0.404145	+	0.700000i
$76$	6.46410	−	3.73205i	0.741483	−	0.428096i
$77$	−4.00000			−0.455842
$78$	−1.00000	−	3.46410i	−0.113228	−	0.392232i
$79$	−9.46410			−1.06479			−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410			−1.06479			−0.532397	+	0.846495i	$0.678709\pi$
$80$	3.00000	−	1.73205i	0.335410	−	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.46410	+	6.00000i	−0.382546	+	0.662589i
$83$		−	1.73205i		−	0.190117i	−0.995472	−	0.0950586i	$-0.969696\pi$
$83$		−	1.73205i		−	0.190117i	0.995472	−	0.0950586i	$-0.0303039\pi$
$84$	0.866025	+	0.500000i	0.0944911	+	0.0545545i
$85$	19.3923	+	11.1962i	2.10339	+	1.21439i
$86$		−	4.46410i		−	0.481376i
$87$	−4.00000	+	6.92820i	−0.428845	+	0.742781i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−10.1603	+	5.86603i	−1.07698	+	0.621797i	−0.930081	−	0.367353i	$-0.880264\pi$
$89$	−10.1603	+	5.86603i	−1.07698	+	0.621797i	−0.146903	+	0.989151i	$0.546931\pi$
$90$	−3.46410			−0.365148
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	5.73205			0.597608
$93$	5.59808	−	3.23205i	0.580493	−	0.335148i
$94$	−0.267949	−	0.464102i	−0.0276368	−	0.0478684i
$95$	−12.9282	+	22.3923i	−1.32641	+	2.29740i
$96$			1.00000i			0.102062i
$97$	10.7321	+	6.19615i	1.08967	+	0.629124i	0.933490	−	0.358604i	$-0.116747\pi$
$97$	10.7321	+	6.19615i	1.08967	+	0.629124i	0.156185	+	0.987728i	$0.450080\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$			4.00000i			0.402015i
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−5.59808	+	3.23205i	−0.554292	+	0.320021i
$103$	−10.6603			−1.05039			−0.525193	−	0.850983i	$-0.676007\pi$
$103$	−10.6603			−1.05039			−0.525193	+	0.850983i	$0.676007\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$	−3.46410			−0.338062
$106$	−7.16025	+	4.13397i	−0.695465	+	0.401527i
$107$	−4.26795	−	7.39230i	−0.412598	−	0.714641i	0.582575	−	0.812777i	$-0.302045\pi$
$107$	−4.26795	−	7.39230i	−0.412598	−	0.714641i	−0.995173	+	0.0981360i	$0.968712\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			12.0000i			1.14939i	0.818367	+	0.574696i	$0.194880\pi$
$109$			12.0000i			1.14939i	−0.818367	+	0.574696i	$0.805120\pi$
$110$	12.0000	+	6.92820i	1.14416	+	0.660578i
$111$	4.26795	+	2.46410i	0.405096	+	0.233882i
$112$			1.00000i			0.0944911i
$113$	2.19615	−	3.80385i	0.206597	−	0.357836i	−0.744044	−	0.668131i	$-0.767095\pi$
$113$	2.19615	−	3.80385i	0.206597	−	0.357836i	0.950640	+	0.310295i	$0.100428\pi$
$114$	−3.73205	−	6.46410i	−0.349539	−	0.605419i
$115$	−17.1962	+	9.92820i	−1.60355	+	0.925810i
$116$	−8.00000			−0.742781
$117$	−3.46410	+	1.00000i	−0.320256	+	0.0924500i
$118$	−6.26795			−0.577011
$119$	−5.59808	+	3.23205i	−0.513175	+	0.296282i
$120$	−1.73205	−	3.00000i	−0.158114	−	0.273861i
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$		−	5.19615i		−	0.470438i
$123$	6.00000	+	3.46410i	0.541002	+	0.312348i
$124$	5.59808	+	3.23205i	0.502722	+	0.290247i
$125$		−	6.92820i		−	0.619677i
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	2.53590	+	4.39230i	0.225025	+	0.389754i	0.956327	−	0.292300i	$-0.0944204\pi$
$127$	2.53590	+	4.39230i	0.225025	+	0.389754i	−0.731302	+	0.682054i	$0.761087\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−4.46410			−0.393042
$130$	−3.00000	+	12.1244i	−0.263117	+	1.06338i
$131$	19.0000			1.66004			0.830019	−	0.557735i	$-0.188330\pi$
$131$	19.0000			1.66004			0.830019	+	0.557735i	$0.188330\pi$
$132$	−3.46410	+	2.00000i	−0.301511	+	0.174078i
$133$	−3.73205	−	6.46410i	−0.323610	−	0.560509i
$134$	3.59808	−	6.23205i	0.310826	−	0.538367i
$135$			3.46410i			0.298142i
$136$	−5.59808	−	3.23205i	−0.480031	−	0.277146i
$137$	−12.0000	−	6.92820i	−1.02523	−	0.591916i	−0.109615	−	0.993974i	$-0.534962\pi$
$137$	−12.0000	−	6.92820i	−1.02523	−	0.591916i	−0.915614	+	0.402058i	$0.868295\pi$
$138$		−	5.73205i		−	0.487945i
$139$	−1.46410	+	2.53590i	−0.124183	+	0.215092i	−0.921413	−	0.388584i	$-0.872964\pi$
$139$	−1.46410	+	2.53590i	−0.124183	+	0.215092i	0.797230	+	0.603676i	$0.206298\pi$
$140$	−1.73205	−	3.00000i	−0.146385	−	0.253546i
$141$	−0.464102	+	0.267949i	−0.0390844	+	0.0225654i
$142$	1.92820			0.161811
$143$	14.0000	+	3.46410i	1.17074	+	0.289683i
$144$	1.00000			0.0833333
$145$	24.0000	−	13.8564i	1.99309	−	1.15071i
$146$	−5.46410	−	9.46410i	−0.452212	−	0.783255i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$			4.92820i			0.405096i
$149$	−9.99038	−	5.76795i	−0.818444	−	0.472529i	0.0314357	−	0.999506i	$-0.489992\pi$
$149$	−9.99038	−	5.76795i	−0.818444	−	0.472529i	−0.849880	+	0.526977i	$0.823325\pi$
$150$	6.06218	+	3.50000i	0.494975	+	0.285774i
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	3.73205	−	6.46410i	0.302709	−	0.524308i
$153$	3.23205	+	5.59808i	0.261296	+	0.452578i
$154$	−3.46410	+	2.00000i	−0.279145	+	0.161165i
$155$	−22.3923			−1.79859
$156$	−2.59808	−	2.50000i	−0.208013	−	0.200160i
$157$	−2.92820			−0.233696			−0.116848	−	0.993150i	$-0.537279\pi$
$157$	−2.92820			−0.233696			−0.116848	+	0.993150i	$0.537279\pi$
$158$	−8.19615	+	4.73205i	−0.652051	+	0.376462i
$159$	4.13397	+	7.16025i	0.327846	+	0.567845i
$160$	1.73205	−	3.00000i	0.136931	−	0.237171i
$161$		−	5.73205i		−	0.451749i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	1.16025	+	0.669873i	0.0908781	+	0.0524685i	0.544750	−	0.838598i	$-0.316624\pi$
$163$	1.16025	+	0.669873i	0.0908781	+	0.0524685i	−0.453872	+	0.891067i	$0.649958\pi$
$164$			6.92820i			0.541002i
$165$	6.92820	−	12.0000i	0.539360	−	0.934199i
$166$	−0.866025	−	1.50000i	−0.0672166	−	0.116423i
$167$	17.3205	−	10.0000i	1.34030	−	0.773823i	0.353450	−	0.935454i	$-0.385009\pi$
$167$	17.3205	−	10.0000i	1.34030	−	0.773823i	0.986851	+	0.161630i	$0.0516752\pi$
$168$	1.00000			0.0771517
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	22.3923			1.71741
$171$	−6.46410	+	3.73205i	−0.494322	+	0.285397i
$172$	−2.23205	−	3.86603i	−0.170192	−	0.294782i
$173$	0.535898	−	0.928203i	0.0407436	−	0.0705700i	−0.844934	−	0.534870i	$-0.820361\pi$
$173$	0.535898	−	0.928203i	0.0407436	−	0.0705700i	0.885678	+	0.464300i	$0.153694\pi$
$174$			8.00000i			0.606478i
$175$	6.06218	+	3.50000i	0.458258	+	0.264575i
$176$	−3.46410	−	2.00000i	−0.261116	−	0.150756i
$177$			6.26795i			0.471128i
$178$	−5.86603	+	10.1603i	−0.439677	+	0.761543i
$179$	−8.46410	−	14.6603i	−0.632637	−	1.09576i	−0.987011	−	0.160655i	$-0.948639\pi$
$179$	−8.46410	−	14.6603i	−0.632637	−	1.09576i	0.354374	−	0.935104i	$-0.384694\pi$
$180$	−3.00000	+	1.73205i	−0.223607	+	0.129099i
$181$	−24.7846			−1.84223			−0.921113	−	0.389296i	$-0.872718\pi$
$181$	−24.7846			−1.84223			−0.921113	+	0.389296i	$0.872718\pi$
$182$	−2.59808	−	2.50000i	−0.192582	−	0.185312i
$183$	−5.19615			−0.384111
$184$	4.96410	−	2.86603i	0.365958	−	0.211286i
$185$	−8.53590	−	14.7846i	−0.627572	−	1.08699i
$186$	3.23205	−	5.59808i	0.236985	−	0.410471i
$187$		−	25.8564i		−	1.89081i
$188$	−0.464102	−	0.267949i	−0.0338481	−	0.0195422i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$			25.8564i			1.87582i
$191$	13.2583	−	22.9641i	0.959339	−	1.66162i	0.235229	−	0.971940i	$-0.424416\pi$
$191$	13.2583	−	22.9641i	0.959339	−	1.66162i	0.724110	−	0.689684i	$-0.242251\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	15.4641	−	8.92820i	1.11313	−	0.642666i	0.173492	−	0.984835i	$-0.444495\pi$
$193$	15.4641	−	8.92820i	1.11313	−	0.642666i	0.939638	+	0.342169i	$0.111162\pi$
$194$	12.3923			0.889716
$195$	12.1244	+	3.00000i	0.868243	+	0.214834i
$196$	1.00000			0.0714286
$197$	2.25833	−	1.30385i	0.160899	−	0.0928953i	−0.417388	−	0.908728i	$-0.637054\pi$
$197$	2.25833	−	1.30385i	0.160899	−	0.0928953i	0.578288	+	0.815833i	$0.303721\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	−11.0622	+	19.1603i	−0.784177	+	1.35823i	0.145312	+	0.989386i	$0.453581\pi$
$199$	−11.0622	+	19.1603i	−0.784177	+	1.35823i	−0.929489	+	0.368849i	$0.879752\pi$
$200$			7.00000i			0.494975i
$201$	−6.23205	−	3.59808i	−0.439575	−	0.253789i
$202$		0			0
$203$			8.00000i			0.561490i
$204$	−3.23205	+	5.59808i	−0.226289	+	0.391944i
$205$	−12.0000	−	20.7846i	−0.838116	−	1.45166i
$206$	−9.23205	+	5.33013i	−0.643227	+	0.371368i
$207$	−5.73205			−0.398405
$208$	0.866025	−	3.50000i	0.0600481	−	0.242681i
$209$	29.8564			2.06521
$210$	−3.00000	+	1.73205i	−0.207020	+	0.119523i
$211$	4.53590	+	7.85641i	0.312264	+	0.540857i	0.978852	−	0.204569i	$-0.0655793\pi$
$211$	4.53590	+	7.85641i	0.312264	+	0.540857i	−0.666588	+	0.745426i	$0.732246\pi$
$212$	−4.13397	+	7.16025i	−0.283923	+	0.491768i
$213$		−	1.92820i		−	0.132118i
$214$	−7.39230	−	4.26795i	−0.505328	−	0.291751i
$215$	13.3923	+	7.73205i	0.913348	+	0.527321i
$216$		−	1.00000i		−	0.0680414i
$217$	3.23205	−	5.59808i	0.219406	−	0.380022i
$218$	6.00000	+	10.3923i	0.406371	+	0.703856i
$219$	−9.46410	+	5.46410i	−0.639525	+	0.369230i
$220$	13.8564			0.934199
$221$	22.3923	−	6.46410i	1.50627	−	0.434823i
$222$	4.92820			0.330759
$223$	−6.52628	+	3.76795i	−0.437032	+	0.252321i	−0.702338	−	0.711844i	$-0.747860\pi$
$223$	−6.52628	+	3.76795i	−0.437032	+	0.252321i	0.265306	+	0.964164i	$0.414527\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	3.50000	−	6.06218i	0.233333	−	0.404145i
$226$		−	4.39230i		−	0.292172i
$227$	−11.5359	−	6.66025i	−0.765664	−	0.442057i	0.0656613	−	0.997842i	$-0.479084\pi$
$227$	−11.5359	−	6.66025i	−0.765664	−	0.442057i	−0.831326	+	0.555785i	$0.812418\pi$
$228$	−6.46410	−	3.73205i	−0.428096	−	0.247161i
$229$			19.9282i			1.31689i	0.752628	+	0.658446i	$0.228786\pi$
$229$			19.9282i			1.31689i	−0.752628	+	0.658446i	$0.771214\pi$
$230$	−9.92820	+	17.1962i	−0.654646	+	1.13388i
$231$	2.00000	+	3.46410i	0.131590	+	0.227921i
$232$	−6.92820	+	4.00000i	−0.454859	+	0.262613i
$233$	−13.4641			−0.882063			−0.441031	−	0.897492i	$-0.645387\pi$
$233$	−13.4641			−0.882063			−0.441031	+	0.897492i	$0.645387\pi$
$234$	−2.50000	+	2.59808i	−0.163430	+	0.169842i
$235$	1.85641			0.121099
$236$	−5.42820	+	3.13397i	−0.353346	+	0.204004i
$237$	4.73205	+	8.19615i	0.307380	+	0.532397i
$238$	−3.23205	+	5.59808i	−0.209503	+	0.362869i
$239$		−	12.8564i		−	0.831612i	−0.909453	−	0.415806i	$-0.863500\pi$
$239$		−	12.8564i		−	0.831612i	0.909453	−	0.415806i	$-0.136500\pi$
$240$	−3.00000	−	1.73205i	−0.193649	−	0.111803i
$241$	13.7321	+	7.92820i	0.884559	+	0.510700i	0.872159	−	0.489223i	$-0.162719\pi$
$241$	13.7321	+	7.92820i	0.884559	+	0.510700i	0.0124002	+	0.999923i	$0.496053\pi$
$242$		−	5.00000i		−	0.321412i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.59808	−	4.50000i	−0.166325	−	0.288083i
$245$	−3.00000	+	1.73205i	−0.191663	+	0.110657i
$246$	6.92820			0.441726
$247$	7.46410	+	25.8564i	0.474929	+	1.64520i
$248$	6.46410			0.410471
$249$	−1.50000	+	0.866025i	−0.0950586	+	0.0548821i
$250$	−3.46410	−	6.00000i	−0.219089	−	0.379473i
$251$	−5.03590	+	8.72243i	−0.317863	+	0.550555i	−0.980042	−	0.198791i	$-0.936299\pi$
$251$	−5.03590	+	8.72243i	−0.317863	+	0.550555i	0.662179	+	0.749346i	$0.269632\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	19.8564	+	11.4641i	1.24836	+	0.720742i
$254$	4.39230	+	2.53590i	0.275598	+	0.159116i
$255$		−	22.3923i		−	1.40226i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.232051	+	0.401924i	0.0144749	+	0.0250713i	0.873172	−	0.487412i	$-0.162059\pi$
$257$	0.232051	+	0.401924i	0.0144749	+	0.0250713i	−0.858697	+	0.512483i	$0.828726\pi$
$258$	−3.86603	+	2.23205i	−0.240688	+	0.138961i
$259$	4.92820			0.306224
$260$	3.46410	+	12.0000i	0.214834	+	0.744208i
$261$	8.00000			0.495188
$262$	16.4545	−	9.50000i	1.01656	−	0.586912i
$263$	8.66025	+	15.0000i	0.534014	+	0.924940i	0.999210	+	0.0397320i	$0.0126504\pi$
$263$	8.66025	+	15.0000i	0.534014	+	0.924940i	−0.465196	+	0.885208i	$0.654016\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$		−	28.6410i		−	1.75940i
$266$	−6.46410	−	3.73205i	−0.396339	−	0.228827i
$267$	10.1603	+	5.86603i	0.621797	+	0.358995i
$268$		−	7.19615i		−	0.439575i
$269$	−11.1962	+	19.3923i	−0.682641	+	1.18237i	0.291530	+	0.956562i	$0.405836\pi$
$269$	−11.1962	+	19.3923i	−0.682641	+	1.18237i	−0.974172	+	0.225808i	$0.927498\pi$
$270$	1.73205	+	3.00000i	0.105409	+	0.182574i
$271$	10.7942	−	6.23205i	0.655703	−	0.378570i	−0.134935	−	0.990854i	$-0.543083\pi$
$271$	10.7942	−	6.23205i	0.655703	−	0.378570i	0.790638	+	0.612284i	$0.209749\pi$
$272$	−6.46410			−0.391944
$273$	−2.50000	+	2.59808i	−0.151307	+	0.157243i
$274$	−13.8564			−0.837096
$275$	−24.2487	+	14.0000i	−1.46225	+	0.844232i
$276$	−2.86603	−	4.96410i	−0.172514	−	0.298804i
$277$	3.66025	−	6.33975i	0.219923	−	0.380918i	−0.734861	−	0.678218i	$-0.762753\pi$
$277$	3.66025	−	6.33975i	0.219923	−	0.380918i	0.954784	+	0.297299i	$0.0960859\pi$
$278$			2.92820i			0.175622i
$279$	−5.59808	−	3.23205i	−0.335148	−	0.193498i
$280$	−3.00000	−	1.73205i	−0.179284	−	0.103510i
$281$		−	2.39230i		−	0.142713i	−0.997451	−	0.0713565i	$-0.977267\pi$
$281$		−	2.39230i		−	0.142713i	0.997451	−	0.0713565i	$-0.0227328\pi$
$282$	−0.267949	+	0.464102i	−0.0159561	+	0.0276368i
$283$	−5.73205	−	9.92820i	−0.340735	−	0.590170i	0.643834	−	0.765165i	$-0.277343\pi$
$283$	−5.73205	−	9.92820i	−0.340735	−	0.590170i	−0.984569	+	0.174994i	$0.944009\pi$
$284$	1.66987	−	0.964102i	0.0990887	−	0.0572089i
$285$	25.8564			1.53160
$286$	13.8564	−	4.00000i	0.819346	−	0.236525i
$287$	6.92820			0.408959
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−12.3923	−	21.4641i	−0.728959	−	1.26259i
$290$	13.8564	−	24.0000i	0.813676	−	1.40933i
$291$		−	12.3923i		−	0.726450i
$292$	−9.46410	−	5.46410i	−0.553845	−	0.319762i
$293$	−28.9808	−	16.7321i	−1.69307	−	0.977497i	−0.952012	−	0.306060i	$-0.900989\pi$
$293$	−28.9808	−	16.7321i	−1.69307	−	0.977497i	−0.741062	−	0.671437i	$-0.765678\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	10.8564	−	18.8038i	0.632084	−	1.09480i
$296$	2.46410	+	4.26795i	0.143223	+	0.248070i
$297$	3.46410	−	2.00000i	0.201008	−	0.116052i
$298$	−11.5359			−0.668257
$299$	−4.96410	+	20.0622i	−0.287081	+	1.16023i
$300$	7.00000			0.404145
$301$	−3.86603	+	2.23205i	−0.222834	+	0.128653i
$302$	−6.00000	−	10.3923i	−0.345261	−	0.598010i
$303$		0			0
$304$		−	7.46410i		−	0.428096i
$305$	15.5885	+	9.00000i	0.892592	+	0.515339i
$306$	5.59808	+	3.23205i	0.320021	+	0.184764i
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$	−2.00000	+	3.46410i	−0.113961	+	0.197386i
$309$	5.33013	+	9.23205i	0.303220	+	0.525193i
$310$	−19.3923	+	11.1962i	−1.10141	+	0.635899i
$311$	−13.3205			−0.755337			−0.377668	−	0.925941i	$-0.623274\pi$
$311$	−13.3205			−0.755337			−0.377668	+	0.925941i	$0.623274\pi$
$312$	−3.50000	−	0.866025i	−0.198148	−	0.0490290i
$313$	0.679492			0.0384072			0.0192036	−	0.999816i	$-0.493887\pi$
$313$	0.679492			0.0384072			0.0192036	+	0.999816i	$0.493887\pi$
$314$	−2.53590	+	1.46410i	−0.143109	+	0.0826240i
$315$	1.73205	+	3.00000i	0.0975900	+	0.169031i
$316$	−4.73205	+	8.19615i	−0.266199	+	0.461070i
$317$		−	16.4641i		−	0.924716i	−0.886693	−	0.462358i	$-0.847003\pi$
$317$		−	16.4641i		−	0.924716i	0.886693	−	0.462358i	$-0.152997\pi$
$318$	7.16025	+	4.13397i	0.401527	+	0.231822i
$319$	−27.7128	−	16.0000i	−1.55162	−	0.895828i
$320$		−	3.46410i		−	0.193649i
$321$	−4.26795	+	7.39230i	−0.238214	+	0.412598i
$322$	−2.86603	−	4.96410i	−0.159717	−	0.276639i
$323$	41.7846	−	24.1244i	2.32496	−	1.34232i
$324$	−1.00000			−0.0555556
$325$	−18.1865	−	17.5000i	−1.00881	−	0.970725i
$326$	1.33975			0.0742017
$327$	10.3923	−	6.00000i	0.574696	−	0.331801i
$328$	3.46410	+	6.00000i	0.191273	+	0.331295i
$329$	−0.267949	+	0.464102i	−0.0147725	+	0.0255868i
$330$		−	13.8564i		−	0.762770i
$331$	18.4641	+	10.6603i	1.01488	+	0.585941i	0.912616	−	0.408817i	$-0.134059\pi$
$331$	18.4641	+	10.6603i	1.01488	+	0.585941i	0.102262	+	0.994757i	$0.467392\pi$
$332$	−1.50000	−	0.866025i	−0.0823232	−	0.0475293i
$333$		−	4.92820i		−	0.270064i
$334$	10.0000	−	17.3205i	0.547176	−	0.947736i
$335$	12.4641	+	21.5885i	0.680987	+	1.17950i
$336$	0.866025	−	0.500000i	0.0472456	−	0.0272772i
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	6.92820	+	11.0000i	0.376845	+	0.598321i
$339$	−4.39230			−0.238557
$340$	19.3923	−	11.1962i	1.05170	−	0.607197i
$341$	12.9282	+	22.3923i	0.700101	+	1.21261i
$342$	−3.73205	+	6.46410i	−0.201806	+	0.349539i
$343$		−	1.00000i		−	0.0539949i
$344$	−3.86603	−	2.23205i	−0.208442	−	0.120344i
$345$	17.1962	+	9.92820i	0.925810	+	0.534516i
$346$		−	1.07180i		−	0.0576202i
$347$	−12.8564	+	22.2679i	−0.690168	+	1.19541i	0.281614	+	0.959528i	$0.409130\pi$
$347$	−12.8564	+	22.2679i	−0.690168	+	1.19541i	−0.971783	+	0.235879i	$0.924203\pi$
$348$	4.00000	+	6.92820i	0.214423	+	0.371391i
$349$	−30.8660	+	17.8205i	−1.65222	+	0.953910i	−0.676064	+	0.736843i	$0.736316\pi$
$349$	−30.8660	+	17.8205i	−1.65222	+	0.953910i	−0.976157	+	0.217067i	$0.930351\pi$
$350$	7.00000			0.374166
$351$	2.59808	+	2.50000i	0.138675	+	0.133440i
$352$	−4.00000			−0.213201
$353$	8.08846	−	4.66987i	0.430505	−	0.248552i	−0.269057	−	0.963124i	$-0.586712\pi$
$353$	8.08846	−	4.66987i	0.430505	−	0.248552i	0.699562	+	0.714572i	$0.253379\pi$
$354$	3.13397	+	5.42820i	0.166569	+	0.288506i
$355$	−3.33975	+	5.78461i	−0.177255	+	0.307015i
$356$			11.7321i			0.621797i
$357$	5.59808	+	3.23205i	0.296282	+	0.171058i
$358$	−14.6603	−	8.46410i	−0.774819	−	0.447342i
$359$		−	8.00000i		−	0.422224i	−0.977462	−	0.211112i	$-0.932292\pi$
$359$		−	8.00000i		−	0.422224i	0.977462	−	0.211112i	$-0.0677085\pi$
$360$	−1.73205	+	3.00000i	−0.0912871	+	0.158114i
$361$	18.3564	+	31.7942i	0.966127	+	1.67338i
$362$	−21.4641	+	12.3923i	−1.12813	+	0.651325i
$363$	−5.00000			−0.262432
$364$	−3.50000	−	0.866025i	−0.183450	−	0.0453921i
$365$	37.8564			1.98149
$366$	−4.50000	+	2.59808i	−0.235219	+	0.135804i
$367$	16.5263	+	28.6244i	0.862665	+	1.49418i	0.869347	+	0.494202i	$0.164540\pi$
$367$	16.5263	+	28.6244i	0.862665	+	1.49418i	−0.00668260	+	0.999978i	$0.502127\pi$
$368$	2.86603	−	4.96410i	0.149402	−	0.258772i
$369$		−	6.92820i		−	0.360668i
$370$	−14.7846	−	8.53590i	−0.768615	−	0.443760i
$371$	7.16025	+	4.13397i	0.371742	+	0.214625i
$372$		−	6.46410i		−	0.335148i
$373$	13.1244	−	22.7321i	0.679553	−	1.17702i	−0.295562	−	0.955324i	$-0.595507\pi$
$373$	13.1244	−	22.7321i	0.679553	−	1.17702i	0.975116	−	0.221697i	$-0.0711597\pi$
$374$	−12.9282	−	22.3923i	−0.668501	−	1.15788i
$375$	−6.00000	+	3.46410i	−0.309839	+	0.178885i
$376$	−0.535898			−0.0276368
$377$	6.92820	−	28.0000i	0.356821	−	1.44207i
$378$	−1.00000			−0.0514344
$379$	−8.32051	+	4.80385i	−0.427396	+	0.246757i	−0.698237	−	0.715867i	$-0.746032\pi$
$379$	−8.32051	+	4.80385i	−0.427396	+	0.246757i	0.270841	+	0.962624i	$0.412698\pi$
$380$	12.9282	+	22.3923i	0.663203	+	1.14870i
$381$	2.53590	−	4.39230i	0.129918	−	0.225025i
$382$		−	26.5167i		−	1.35671i
$383$	6.33975	+	3.66025i	0.323946	+	0.187030i	0.653150	−	0.757229i	$-0.273447\pi$
$383$	6.33975	+	3.66025i	0.323946	+	0.187030i	−0.329204	+	0.944259i	$0.606780\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		−	13.8564i		−	0.706188i
$386$	8.92820	−	15.4641i	0.454434	−	0.787102i
$387$	2.23205	+	3.86603i	0.113462	+	0.196521i
$388$	10.7321	−	6.19615i	0.544837	−	0.314562i
$389$	14.6603			0.743304			0.371652	−	0.928372i	$-0.378791\pi$
$389$	14.6603			0.743304			0.371652	+	0.928372i	$0.378791\pi$
$390$	12.0000	−	3.46410i	0.607644	−	0.175412i
$391$	37.0526			1.87383
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$	−9.50000	−	16.4545i	−0.479212	−	0.830019i
$394$	1.30385	−	2.25833i	0.0656869	−	0.113773i
$395$		−	32.7846i		−	1.64957i
$396$	3.46410	+	2.00000i	0.174078	+	0.100504i
$397$	−25.7942	−	14.8923i	−1.29458	−	0.747423i	−0.315114	−	0.949054i	$-0.602043\pi$
$397$	−25.7942	−	14.8923i	−1.29458	−	0.747423i	−0.979462	+	0.201631i	$0.935376\pi$
$398$			22.1244i			1.10899i
$399$	−3.73205	+	6.46410i	−0.186836	+	0.323610i
$400$	3.50000	+	6.06218i	0.175000	+	0.303109i
$401$	−14.1962	+	8.19615i	−0.708922	+	0.409296i	−0.810662	−	0.585515i	$-0.800892\pi$
$401$	−14.1962	+	8.19615i	−0.708922	+	0.409296i	0.101740	+	0.994811i	$0.467559\pi$
$402$	−7.19615			−0.358911
$403$	−16.1603	+	16.7942i	−0.805000	+	0.836580i
$404$		0			0
$405$	3.00000	−	1.73205i	0.149071	−	0.0860663i
$406$	4.00000	+	6.92820i	0.198517	+	0.343841i
$407$	−9.85641	+	17.0718i	−0.488564	+	0.846218i
$408$			6.46410i			0.320021i
$409$	5.53590	+	3.19615i	0.273733	+	0.158040i	0.630583	−	0.776122i	$-0.282816\pi$
$409$	5.53590	+	3.19615i	0.273733	+	0.158040i	−0.356850	+	0.934162i	$0.616149\pi$
$410$	−20.7846	−	12.0000i	−1.02648	−	0.592638i
$411$			13.8564i			0.683486i
$412$	−5.33013	+	9.23205i	−0.262597	+	0.454830i
$413$	3.13397	+	5.42820i	0.154213	+	0.267104i
$414$	−4.96410	+	2.86603i	−0.243972	+	0.140857i
$415$	6.00000			0.294528
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$	2.92820			0.143395
$418$	25.8564	−	14.9282i	1.26468	−	0.730162i
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	0.920609	−	0.390487i	$-0.127693\pi$
$419$	2.50000	+	4.33013i	0.122133	+	0.211541i	−0.798476	+	0.602027i	$0.794360\pi$
$420$	−1.73205	+	3.00000i	−0.0845154	+	0.146385i
$421$			1.60770i			0.0783543i	0.999232	+	0.0391771i	$0.0124737\pi$
$421$			1.60770i			0.0783543i	−0.999232	+	0.0391771i	$0.987526\pi$
$422$	7.85641	+	4.53590i	0.382444	+	0.220804i
$423$	0.464102	+	0.267949i	0.0225654	+	0.0130281i
$424$			8.26795i			0.401527i
$425$	−22.6244	+	39.1865i	−1.09744	+	1.90083i
$426$	−0.964102	−	1.66987i	−0.0467109	−	0.0809056i
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	−8.53590			−0.412598
$429$	−4.00000	−	13.8564i	−0.193122	−	0.668994i
$430$	15.4641			0.745745
$431$	4.20577	−	2.42820i	0.202585	−	0.116962i	−0.395276	−	0.918563i	$-0.629351\pi$
$431$	4.20577	−	2.42820i	0.202585	−	0.116962i	0.597861	+	0.801600i	$0.296018\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	4.92820	−	8.53590i	0.236834	−	0.410209i	−0.722970	−	0.690880i	$-0.757223\pi$
$433$	4.92820	−	8.53590i	0.236834	−	0.410209i	0.959804	+	0.280670i	$0.0905568\pi$
$434$		−	6.46410i		−	0.310287i
$435$	−24.0000	−	13.8564i	−1.15071	−	0.664364i
$436$	10.3923	+	6.00000i	0.497701	+	0.287348i
$437$			42.7846i			2.04667i
$438$	−5.46410	+	9.46410i	−0.261085	+	0.452212i
$439$	−6.80385	−	11.7846i	−0.324730	−	0.562449i	0.656728	−	0.754128i	$-0.271940\pi$
$439$	−6.80385	−	11.7846i	−0.324730	−	0.562449i	−0.981458	+	0.191679i	$0.938607\pi$
$440$	12.0000	−	6.92820i	0.572078	−	0.330289i
$441$	−1.00000			−0.0476190
$442$	16.1603	−	16.7942i	0.768665	−	0.798820i
$443$	−22.3923			−1.06389			−0.531945	−	0.846779i	$-0.678539\pi$
$443$	−22.3923			−1.06389			−0.531945	+	0.846779i	$0.678539\pi$
$444$	4.26795	−	2.46410i	0.202548	−	0.116941i
$445$	−20.3205	−	35.1962i	−0.963284	−	1.66846i
$446$	−3.76795	+	6.52628i	−0.178418	+	0.309028i
$447$			11.5359i			0.545629i
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	0.820491	−	0.571660i	$-0.193700\pi$
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	−0.0848262	+	0.996396i	$0.527033\pi$
$450$		−	7.00000i		−	0.329983i
$451$	−13.8564	+	24.0000i	−0.652473	+	1.13012i
$452$	−2.19615	−	3.80385i	−0.103298	−	0.178918i
$453$	−10.3923	+	6.00000i	−0.488273	+	0.281905i
$454$	−13.3205			−0.625162
$455$	12.0000	−	3.46410i	0.562569	−	0.162400i
$456$	−7.46410			−0.349539
$457$	1.03590	−	0.598076i	0.0484573	−	0.0279768i	−0.475576	−	0.879675i	$-0.657760\pi$
$457$	1.03590	−	0.598076i	0.0484573	−	0.0279768i	0.524033	+	0.851698i	$0.324427\pi$
$458$	9.96410	+	17.2583i	0.465592	+	0.806429i
$459$	3.23205	−	5.59808i	0.150859	−	0.261296i
$460$			19.8564i			0.925810i
$461$	−4.39230	−	2.53590i	−0.204570	−	0.118109i	0.394215	−	0.919018i	$-0.371016\pi$
$461$	−4.39230	−	2.53590i	−0.204570	−	0.118109i	−0.598785	+	0.800910i	$0.704350\pi$
$462$	3.46410	+	2.00000i	0.161165	+	0.0930484i
$463$			8.24871i			0.383350i	0.981458	+	0.191675i	$0.0613920\pi$
$463$			8.24871i			0.383350i	−0.981458	+	0.191675i	$0.938608\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$	11.1962	+	19.3923i	0.519209	+	0.899297i
$466$	−11.6603	+	6.73205i	−0.540151	+	0.311856i
$467$	39.6410			1.83437			0.917184	−	0.398465i	$-0.130457\pi$
$467$	39.6410			1.83437			0.917184	+	0.398465i	$0.130457\pi$
$468$	−0.866025	+	3.50000i	−0.0400320	+	0.161788i
$469$	−7.19615			−0.332287
$470$	1.60770	−	0.928203i	0.0741574	−	0.0428148i
$471$	1.46410	+	2.53590i	0.0674622	+	0.116848i
$472$	−3.13397	+	5.42820i	−0.144253	+	0.249853i
$473$		−	17.8564i		−	0.821038i
$474$	8.19615	+	4.73205i	0.376462	+	0.217350i
$475$	−45.2487	−	26.1244i	−2.07615	−	1.19867i
$476$			6.46410i			0.296282i
$477$	4.13397	−	7.16025i	0.189282	−	0.327846i
$478$	−6.42820	−	11.1340i	−0.294019	−	0.509256i
$479$	−3.80385	+	2.19615i	−0.173802	+	0.100345i	−0.584377	−	0.811482i	$-0.698661\pi$
$479$	−3.80385	+	2.19615i	−0.173802	+	0.100345i	0.410575	+	0.911827i	$0.365328\pi$
$480$	−3.46410			−0.158114
$481$	−17.2487	−	4.26795i	−0.786474	−	0.194602i
$482$	15.8564			0.722240
$483$	−4.96410	+	2.86603i	−0.225874	+	0.130409i
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−21.4641	+	37.1769i	−0.974635	+	1.68812i
$486$			1.00000i			0.0453609i
$487$	0.339746	+	0.196152i	0.0153954	+	0.00888851i	0.507678	−	0.861547i	$-0.330504\pi$
$487$	0.339746	+	0.196152i	0.0153954	+	0.00888851i	−0.492283	+	0.870435i	$0.663837\pi$
$488$	−4.50000	−	2.59808i	−0.203705	−	0.117609i
$489$		−	1.33975i		−	0.0605854i
$490$	−1.73205	+	3.00000i	−0.0782461	+	0.135526i
$491$	−4.92820	−	8.53590i	−0.222407	−	0.385220i	0.733132	−	0.680087i	$-0.238058\pi$
$491$	−4.92820	−	8.53590i	−0.222407	−	0.385220i	−0.955538	+	0.294867i	$0.904725\pi$
$492$	6.00000	−	3.46410i	0.270501	−	0.156174i
$493$	−51.7128			−2.32903
$494$	19.3923	+	18.6603i	0.872501	+	0.839565i
$495$	−13.8564			−0.622799
$496$	5.59808	−	3.23205i	0.251361	−	0.145123i
$497$	−0.964102	−	1.66987i	−0.0432459	−	0.0749040i
$498$	−0.866025	+	1.50000i	−0.0388075	+	0.0672166i
$499$			0.267949i			0.0119951i	0.999982	+	0.00599753i	$0.00190908\pi$
$499$			0.267949i			0.0119951i	−0.999982	+	0.00599753i	$0.998091\pi$
$500$	−6.00000	−	3.46410i	−0.268328	−	0.154919i
$501$	−17.3205	−	10.0000i	−0.773823	−	0.446767i
$502$			10.0718i			0.449526i
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	−0.778404	−	0.627763i	$-0.783971\pi$
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	0.932861	+	0.360236i	$0.117304\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$		0			0
$506$	22.9282			1.01928
$507$	11.0000	−	6.92820i	0.488527	−	0.307692i
$508$	5.07180			0.225025
$509$	−29.6603	+	17.1244i	−1.31467	+	0.759024i	−0.982865	−	0.184325i	$-0.940990\pi$
$509$	−29.6603	+	17.1244i	−1.31467	+	0.759024i	−0.331802	+	0.943349i	$0.607657\pi$
$510$	−11.1962	−	19.3923i	−0.495774	−	0.858706i
$511$	−5.46410	+	9.46410i	−0.241718	+	0.418667i
$512$			1.00000i			0.0441942i
$513$	6.46410	+	3.73205i	0.285397	+	0.164774i
$514$	0.401924	+	0.232051i	0.0177281	+	0.0102353i
$515$		−	36.9282i		−	1.62725i
$516$	−2.23205	+	3.86603i	−0.0982606	+	0.170192i
$517$	−1.07180	−	1.85641i	−0.0471376	−	0.0816447i
$518$	4.26795	−	2.46410i	0.187523	−	0.108266i
$519$	−1.07180			−0.0470467
$520$	9.00000	+	8.66025i	0.394676	+	0.379777i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	6.92820	−	4.00000i	0.303239	−	0.175075i
$523$	−7.46410	−	12.9282i	−0.326382	−	0.565311i	0.655409	−	0.755274i	$-0.272496\pi$
$523$	−7.46410	−	12.9282i	−0.326382	−	0.565311i	−0.981791	+	0.189963i	$0.939163\pi$
$524$	9.50000	−	16.4545i	0.415009	−	0.718817i
$525$		−	7.00000i		−	0.305505i
$526$	15.0000	+	8.66025i	0.654031	+	0.377605i
$527$	36.1865	+	20.8923i	1.57631	+	0.910083i
$528$			4.00000i			0.174078i
$529$	−4.92820	+	8.53590i	−0.214270	+	0.371126i
$530$	−14.3205	−	24.8038i	−0.622043	−	1.07741i
$531$	5.42820	−	3.13397i	0.235564	−	0.136003i
$532$	−7.46410			−0.323610
$533$	−24.2487	−	6.00000i	−1.05033	−	0.259889i
$534$	11.7321			0.507695
$535$	25.6077	−	14.7846i	1.10712	−	0.639194i
$536$	−3.59808	−	6.23205i	−0.155413	−	0.269184i
$537$	−8.46410	+	14.6603i	−0.365253	+	0.632637i
$538$			22.3923i			0.965401i
$539$	3.46410	+	2.00000i	0.149209	+	0.0861461i
$540$	3.00000	+	1.73205i	0.129099	+	0.0745356i
$541$		−	17.3205i		−	0.744667i	−0.928099	−	0.372333i	$-0.878558\pi$
$541$		−	17.3205i		−	0.744667i	0.928099	−	0.372333i	$-0.121442\pi$
$542$	6.23205	−	10.7942i	0.267690	−	0.463652i
$543$	12.3923	+	21.4641i	0.531805	+	0.921113i
$544$	−5.59808	+	3.23205i	−0.240016	+	0.138573i
$545$	−41.5692			−1.78063
$546$	−0.866025	+	3.50000i	−0.0370625	+	0.149786i
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	−12.0000	+	6.92820i	−0.512615	+	0.295958i
$549$	2.59808	+	4.50000i	0.110883	+	0.192055i
$550$	−14.0000	+	24.2487i	−0.596962	+	1.03397i
$551$		−	59.7128i		−	2.54385i
$552$	−4.96410	−	2.86603i	−0.211286	−	0.121986i
$553$	8.19615	+	4.73205i	0.348536	+	0.201227i
$554$		−	7.32051i		−	0.311019i
$555$	−8.53590	+	14.7846i	−0.362329	+	0.627572i
$556$	1.46410	+	2.53590i	0.0620917	+	0.107546i
$557$	21.3109	−	12.3038i	0.902971	−	0.521331i	0.0248083	−	0.999692i	$-0.492102\pi$
$557$	21.3109	−	12.3038i	0.902971	−	0.521331i	0.878163	+	0.478361i	$0.158769\pi$
$558$	−6.46410			−0.273647
$559$	15.4641	−	4.46410i	0.654062	−	0.188811i
$560$	−3.46410			−0.146385
$561$	−22.3923	+	12.9282i	−0.945404	+	0.545829i
$562$	−1.19615	−	2.07180i	−0.0504566	−	0.0873935i
$563$	−6.92820	+	12.0000i	−0.291989	+	0.505740i	−0.974280	−	0.225341i	$-0.927650\pi$
$563$	−6.92820	+	12.0000i	−0.291989	+	0.505740i	0.682291	+	0.731081i	$0.260984\pi$
$564$			0.535898i			0.0225654i
$565$	13.1769	+	7.60770i	0.554357	+	0.320058i
$566$	−9.92820	−	5.73205i	−0.417314	−	0.240936i
$567$			1.00000i			0.0419961i
$568$	0.964102	−	1.66987i	0.0404528	−	0.0700663i
$569$	7.73205	+	13.3923i	0.324144	+	0.561435i	0.981339	−	0.192286i	$-0.0615903\pi$
$569$	7.73205	+	13.3923i	0.324144	+	0.561435i	−0.657194	+	0.753721i	$0.728257\pi$
$570$	22.3923	−	12.9282i	0.937910	−	0.541503i
$571$	3.39230			0.141964			0.0709818	−	0.997478i	$-0.477387\pi$
$571$	3.39230			0.141964			0.0709818	+	0.997478i	$0.477387\pi$
$572$	10.0000	−	10.3923i	0.418121	−	0.434524i
$573$	−26.5167			−1.10775
$574$	6.00000	−	3.46410i	0.250435	−	0.144589i
$575$	−20.0622	−	34.7487i	−0.836651	−	1.44912i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	1.21539i		−	0.0505974i	−0.999680	−	0.0252987i	$-0.991946\pi$
$577$		−	1.21539i		−	0.0505974i	0.999680	−	0.0252987i	$-0.00805368\pi$
$578$	−21.4641	−	12.3923i	−0.892789	−	0.515452i
$579$	−15.4641	−	8.92820i	−0.642666	−	0.371043i
$580$		−	27.7128i		−	1.15071i
$581$	−0.866025	+	1.50000i	−0.0359288	+	0.0622305i
$582$	−6.19615	−	10.7321i	−0.256839	−	0.444858i
$583$	−28.6410	+	16.5359i	−1.18619	+	0.684847i
$584$	−10.9282			−0.452212
$585$	−3.46410	−	12.0000i	−0.143223	−	0.496139i
$586$	−33.4641			−1.38239
$587$	7.03590	−	4.06218i	0.290403	−	0.167664i	−0.347721	−	0.937598i	$-0.613044\pi$
$587$	7.03590	−	4.06218i	0.290403	−	0.167664i	0.638123	+	0.769934i	$0.279711\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	−24.1244	+	41.7846i	−0.994027	+	1.72170i
$590$		−	21.7128i		−	0.893902i
$591$	−2.25833	−	1.30385i	−0.0928953	−	0.0536331i
$592$	4.26795	+	2.46410i	0.175412	+	0.101274i
$593$			4.26795i			0.175264i	0.996153	+	0.0876318i	$0.0279299\pi$
$593$			4.26795i			0.175264i	−0.996153	+	0.0876318i	$0.972070\pi$
$594$	2.00000	−	3.46410i	0.0820610	−	0.142134i
$595$	−11.1962	−	19.3923i	−0.458997	−	0.795007i
$596$	−9.99038	+	5.76795i	−0.409222	+	0.236264i
$597$	22.1244			0.905490
$598$	5.73205	+	19.8564i	0.234401	+	0.811989i
$599$	−19.0526			−0.778466			−0.389233	−	0.921139i	$-0.627260\pi$
$599$	−19.0526			−0.778466			−0.389233	+	0.921139i	$0.627260\pi$
$600$	6.06218	−	3.50000i	0.247487	−	0.142887i
$601$	12.1244	+	21.0000i	0.494563	+	0.856608i	0.999980	−	0.00626702i	$-0.00199487\pi$
$601$	12.1244	+	21.0000i	0.494563	+	0.856608i	−0.505418	+	0.862875i	$0.668662\pi$
$602$	−2.23205	+	3.86603i	−0.0909716	+	0.157567i
$603$			7.19615i			0.293050i
$604$	−10.3923	−	6.00000i	−0.422857	−	0.244137i
$605$	15.0000	+	8.66025i	0.609837	+	0.352089i
$606$		0			0
$607$	7.59808	−	13.1603i	0.308396	−	0.534158i	−0.669615	−	0.742708i	$-0.733541\pi$
$607$	7.59808	−	13.1603i	0.308396	−	0.534158i	0.978012	+	0.208550i	$0.0668744\pi$
$608$	−3.73205	−	6.46410i	−0.151355	−	0.262154i
$609$	6.92820	−	4.00000i	0.280745	−	0.162088i
$610$	18.0000			0.728799
$611$	1.33975	−	1.39230i	0.0542003	−	0.0563266i
$612$	6.46410			0.261296
$613$	29.7846	−	17.1962i	1.20299	−	0.694546i	0.241770	−	0.970333i	$-0.422272\pi$
$613$	29.7846	−	17.1962i	1.20299	−	0.694546i	0.961219	+	0.275787i	$0.0889386\pi$
$614$	−11.0000	−	19.0526i	−0.443924	−	0.768899i
$615$	−12.0000	+	20.7846i	−0.483887	+	0.838116i
$616$			4.00000i			0.161165i
$617$	−5.07180	−	2.92820i	−0.204183	−	0.117885i	0.394422	−	0.918929i	$-0.370945\pi$
$617$	−5.07180	−	2.92820i	−0.204183	−	0.117885i	−0.598605	+	0.801044i	$0.704278\pi$
$618$	9.23205	+	5.33013i	0.371368	+	0.214409i
$619$			30.7846i			1.23734i	0.785652	+	0.618669i	$0.212328\pi$
$619$			30.7846i			1.23734i	−0.785652	+	0.618669i	$0.787672\pi$
$620$	−11.1962	+	19.3923i	−0.449648	+	0.778814i
$621$	2.86603	+	4.96410i	0.115010	+	0.199203i
$622$	−11.5359	+	6.66025i	−0.462547	+	0.267052i
$623$	11.7321			0.470035
$624$	−3.46410	+	1.00000i	−0.138675	+	0.0400320i
$625$	−11.0000			−0.440000
$626$	0.588457	−	0.339746i	0.0235195	−	0.0135790i
$627$	−14.9282	−	25.8564i	−0.596175	−	1.03261i
$628$	−1.46410	+	2.53590i	−0.0584240	+	0.101193i
$629$			31.8564i			1.27020i
$630$	3.00000	+	1.73205i	0.119523	+	0.0690066i
$631$	30.2487	+	17.4641i	1.20418	+	0.695235i	0.961482	−	0.274867i	$-0.0886337\pi$
$631$	30.2487	+	17.4641i	1.20418	+	0.695235i	0.242700	+	0.970101i	$0.421967\pi$
$632$			9.46410i			0.376462i
$633$	4.53590	−	7.85641i	0.180286	−	0.312264i
$634$	−8.23205	−	14.2583i	−0.326937	−	0.566271i
$635$	−15.2154	+	8.78461i	−0.603804	+	0.348607i
$636$	8.26795			0.327846
$637$	−0.866025	+	3.50000i	−0.0343132	+	0.138675i
$638$	−32.0000			−1.26689
$639$	−1.66987	+	0.964102i	−0.0660592	+	0.0381393i
$640$	−1.73205	−	3.00000i	−0.0684653	−	0.118585i
$641$	−13.3205	+	23.0718i	−0.526128	+	0.911281i	0.473408	+	0.880843i	$0.343024\pi$
$641$	−13.3205	+	23.0718i	−0.526128	+	0.911281i	−0.999537	+	0.0304380i	$0.990310\pi$
$642$			8.53590i			0.336885i
$643$	−17.5359	−	10.1244i	−0.691548	−	0.399266i	0.112643	−	0.993635i	$-0.464068\pi$
$643$	−17.5359	−	10.1244i	−0.691548	−	0.399266i	−0.804192	+	0.594370i	$0.797402\pi$
$644$	−4.96410	−	2.86603i	−0.195613	−	0.112937i
$645$		−	15.4641i		−	0.608898i
$646$	24.1244	−	41.7846i	0.949160	−	1.64399i
$647$	18.6603	+	32.3205i	0.733610	+	1.27065i	0.955330	+	0.295540i	$0.0954995\pi$
$647$	18.6603	+	32.3205i	0.733610	+	1.27065i	−0.221720	+	0.975110i	$0.571167\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−25.0718			−0.984154
$650$	−24.5000	−	6.06218i	−0.960969	−	0.237778i
$651$	−6.46410			−0.253348
$652$	1.16025	−	0.669873i	0.0454391	−	0.0262343i
$653$	18.7942	+	32.5526i	0.735475	+	1.27388i	0.954515	+	0.298164i	$0.0963743\pi$
$653$	18.7942	+	32.5526i	0.735475	+	1.27388i	−0.219040	+	0.975716i	$0.570292\pi$
$654$	6.00000	−	10.3923i	0.234619	−	0.406371i
$655$			65.8179i			2.57172i
$656$	6.00000	+	3.46410i	0.234261	+	0.135250i
$657$	9.46410	+	5.46410i	0.369230	+	0.213175i
$658$			0.535898i			0.0208915i
$659$	−0.803848	+	1.39230i	−0.0313135	+	0.0542365i	−0.881257	−	0.472637i	$-0.843302\pi$
$659$	−0.803848	+	1.39230i	−0.0313135	+	0.0542365i	0.849944	+	0.526873i	$0.176636\pi$
$660$	−6.92820	−	12.0000i	−0.269680	−	0.467099i
$661$	43.9186	−	25.3564i	1.70823	−	0.986250i	0.771487	−	0.636245i	$-0.219513\pi$
$661$	43.9186	−	25.3564i	1.70823	−	0.986250i	0.936748	−	0.350005i	$-0.113820\pi$
$662$	21.3205			0.828645
$663$	−16.7942	−	16.1603i	−0.652234	−	0.627612i
$664$	−1.73205			−0.0672166
$665$	22.3923	−	12.9282i	0.868336	−	0.501334i
$666$	−2.46410	−	4.26795i	−0.0954820	−	0.165380i
$667$	22.9282	−	39.7128i	0.887784	−	1.53769i
$668$		−	20.0000i		−	0.773823i
$669$	6.52628	+	3.76795i	0.252321	+	0.145677i
$670$	21.5885	+	12.4641i	0.834035	+	0.481530i
$671$		−	20.7846i		−	0.802381i
$672$	0.500000	−	0.866025i	0.0192879	−	0.0334077i
$673$	19.8205	+	34.3301i	0.764024	+	1.32333i	0.940761	+	0.339071i	$0.110113\pi$
$673$	19.8205	+	34.3301i	0.764024	+	1.32333i	−0.176736	+	0.984258i	$0.556554\pi$
$674$	−5.19615	+	3.00000i	−0.200148	+	0.115556i
$675$	−7.00000			−0.269430
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	1.07180			0.0411925			0.0205962	−	0.999788i	$-0.493444\pi$
$677$	1.07180			0.0411925			0.0205962	+	0.999788i	$0.493444\pi$
$678$	−3.80385	+	2.19615i	−0.146086	+	0.0843427i
$679$	−6.19615	−	10.7321i	−0.237787	−	0.411858i
$680$	11.1962	−	19.3923i	0.429353	−	0.743661i
$681$			13.3205i			0.510443i
$682$	22.3923	+	12.9282i	0.857446	+	0.495046i
$683$	44.3205	+	25.5885i	1.69588	+	0.979115i	0.949592	+	0.313489i	$0.101498\pi$
$683$	44.3205	+	25.5885i	1.69588	+	0.979115i	0.746285	+	0.665626i	$0.231836\pi$
$684$			7.46410i			0.285397i
$685$	24.0000	−	41.5692i	0.916993	−	1.58828i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	17.2583	−	9.96410i	0.658446	−	0.380154i
$688$	−4.46410			−0.170192
$689$	−21.4808	−	20.6699i	−0.818352	−	0.787459i
$690$	19.8564			0.755920
$691$	−35.6603	+	20.5885i	−1.35658	+	0.783222i	−0.989161	−	0.146834i	$-0.953092\pi$
$691$	−35.6603	+	20.5885i	−1.35658	+	0.783222i	−0.367419	+	0.930056i	$0.619758\pi$
$692$	−0.535898	−	0.928203i	−0.0203718	−	0.0352850i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$			25.7128i			0.976045i
$695$	−8.78461	−	5.07180i	−0.333219	−	0.192384i
$696$	6.92820	+	4.00000i	0.262613	+	0.151620i
$697$			44.7846i			1.69634i
$698$	−17.8205	+	30.8660i	−0.674516	+	1.16830i
$699$	6.73205	+	11.6603i	0.254630	+	0.441031i
$700$	6.06218	−	3.50000i	0.229129	−	0.132288i
$701$	2.12436			0.0802358			0.0401179	−	0.999195i	$-0.487227\pi$
$701$	2.12436			0.0802358			0.0401179	+	0.999195i	$0.487227\pi$
$702$	3.50000	+	0.866025i	0.132099	+	0.0326860i
$703$	−36.7846			−1.38736
$704$	−3.46410	+	2.00000i	−0.130558	+	0.0753778i
$705$	−0.928203	−	1.60770i	−0.0349582	−	0.0605493i
$706$	4.66987	−	8.08846i	0.175753	−	0.304413i
$707$		0			0
$708$	5.42820	+	3.13397i	0.204004	+	0.117782i
$709$	−6.67949	−	3.85641i	−0.250854	−	0.144830i	0.369301	−	0.929310i	$-0.379597\pi$
$709$	−6.67949	−	3.85641i	−0.250854	−	0.144830i	−0.620155	+	0.784479i	$0.712930\pi$
$710$			6.67949i			0.250677i
$711$	4.73205	−	8.19615i	0.177466	−	0.307380i
$712$	5.86603	+	10.1603i	0.219839	+	0.380772i
$713$	−32.0885	+	18.5263i	−1.20172	+	0.693815i
$714$	6.46410			0.241913
$715$	−12.0000	+	48.4974i	−0.448775	+	1.81370i
$716$	−16.9282			−0.632637
$717$	−11.1340	+	6.42820i	−0.415806	+	0.240066i
$718$	−4.00000	−	6.92820i	−0.149279	−	0.258558i
$719$	17.2679	−	29.9090i	0.643986	−	1.11542i	−0.340549	−	0.940227i	$-0.610613\pi$
$719$	17.2679	−	29.9090i	0.643986	−	1.11542i	0.984535	−	0.175189i	$-0.0560538\pi$
$720$			3.46410i			0.129099i
$721$	9.23205	+	5.33013i	0.343820	+	0.198504i
$722$	31.7942	+	18.3564i	1.18326	+	0.683155i
$723$		−	15.8564i		−	0.589706i
$724$	−12.3923	+	21.4641i	−0.460556	+	0.797707i
$725$	28.0000	+	48.4974i	1.03989	+	1.80115i
$726$	−4.33013	+	2.50000i	−0.160706	+	0.0927837i
$727$	22.9090			0.849646			0.424823	−	0.905276i	$-0.360336\pi$
$727$	22.9090			0.849646			0.424823	+	0.905276i	$0.360336\pi$
$728$	−3.46410	+	1.00000i	−0.128388	+	0.0370625i
$729$	1.00000			0.0370370
$730$	32.7846	−	18.9282i	1.21341	−	0.700564i
$731$	−14.4282	−	24.9904i	−0.533646	−	0.924303i
$732$	−2.59808	+	4.50000i	−0.0960277	+	0.166325i
$733$		−	4.85641i		−	0.179375i	−0.995970	−	0.0896877i	$-0.971413\pi$
$733$		−	4.85641i		−	0.179375i	0.995970	−	0.0896877i	$-0.0285869\pi$
$734$	28.6244	+	16.5263i	1.05654	+	0.609996i
$735$	3.00000	+	1.73205i	0.110657	+	0.0638877i
$736$		−	5.73205i		−	0.211286i
$737$	14.3923	−	24.9282i	0.530147	−	0.918242i
$738$	−3.46410	−	6.00000i	−0.127515	−	0.220863i
$739$	6.69615	−	3.86603i	0.246322	−	0.142214i	−0.371757	−	0.928330i	$-0.621245\pi$
$739$	6.69615	−	3.86603i	0.246322	−	0.142214i	0.618079	+	0.786116i	$0.287911\pi$
$740$	−17.0718			−0.627572
$741$	18.6603	−	19.3923i	0.685502	−	0.712394i
$742$	8.26795			0.303526
$743$	1.54552	−	0.892305i	0.0566995	−	0.0327355i	−0.471382	−	0.881929i	$-0.656245\pi$
$743$	1.54552	−	0.892305i	0.0566995	−	0.0327355i	0.528082	+	0.849194i	$0.322911\pi$
$744$	−3.23205	−	5.59808i	−0.118493	−	0.205235i
$745$	19.9808	−	34.6077i	0.732038	−	1.26793i
$746$		−	26.2487i		−	0.961034i
$747$	1.50000	+	0.866025i	0.0548821	+	0.0316862i
$748$	−22.3923	−	12.9282i	−0.818744	−	0.472702i
$749$			8.53590i			0.311895i
$750$	−3.46410	+	6.00000i	−0.126491	+	0.219089i
$751$	14.6603	+	25.3923i	0.534960	+	0.926578i	0.999165	+	0.0408506i	$0.0130068\pi$
$751$	14.6603	+	25.3923i	0.534960	+	0.926578i	−0.464205	+	0.885728i	$0.653660\pi$
$752$	−0.464102	+	0.267949i	−0.0169240	+	0.00977110i
$753$	10.0718			0.367037
$754$	−8.00000	−	27.7128i	−0.291343	−	1.00924i
$755$	41.5692			1.51286
$756$	−0.866025	+	0.500000i	−0.0314970	+	0.0181848i
$757$	−9.92820	−	17.1962i	−0.360847	−	0.625005i	0.627254	−	0.778815i	$-0.284179\pi$
$757$	−9.92820	−	17.1962i	−0.360847	−	0.625005i	−0.988100	+	0.153810i	$0.950846\pi$
$758$	−4.80385	+	8.32051i	−0.174484	+	0.302214i
$759$		−	22.9282i		−	0.832241i
$760$	22.3923	+	12.9282i	0.812254	+	0.468955i
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	0.604792	−	0.796383i	$-0.293256\pi$
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	−0.387292	+	0.921957i	$0.626590\pi$
$762$		−	5.07180i		−	0.183732i
$763$	6.00000	−	10.3923i	0.217215	−	0.376227i
$764$	−13.2583	−	22.9641i	−0.479670	−	0.830812i
$765$	−19.3923	+	11.1962i	−0.701130	+	0.404798i
$766$	7.32051			0.264501
$767$	−6.26795	−	21.7128i	−0.226323	−	0.784004i
$768$	1.00000			0.0360844
$769$	36.9282	−	21.3205i	1.33167	−	0.768837i	0.346110	−	0.938194i	$-0.387502\pi$
$769$	36.9282	−	21.3205i	1.33167	−	0.768837i	0.985555	+	0.169357i	$0.0541690\pi$
$770$	−6.92820	−	12.0000i	−0.249675	−	0.432450i
$771$	0.232051	−	0.401924i	0.00835711	−	0.0144749i
$772$		−	17.8564i		−	0.642666i
$773$	11.1962	+	6.46410i	0.402698	+	0.232498i	0.687647	−	0.726045i	$-0.258644\pi$
$773$	11.1962	+	6.46410i	0.402698	+	0.232498i	−0.284950	+	0.958542i	$0.591977\pi$
$774$	3.86603	+	2.23205i	0.138961	+	0.0802294i
$775$		−	45.2487i		−	1.62538i
$776$	6.19615	−	10.7321i	0.222429	−	0.385258i
$777$	−2.46410	−	4.26795i	−0.0883992	−	0.153112i
$778$	12.6962	−	7.33013i	0.455179	−	0.262798i
$779$	−51.7128			−1.85280
$780$	8.66025	−	9.00000i	0.310087	−	0.322252i
$781$	7.71281			0.275986
$782$	32.0885	−	18.5263i	1.14748	−	0.662498i
$783$	−4.00000	−	6.92820i	−0.142948	−	0.247594i
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	10.1436i		−	0.362040i
$786$	−16.4545	−	9.50000i	−0.586912	−	0.338854i
$787$	−7.26795	−	4.19615i	−0.259074	−	0.149577i	0.364838	−	0.931071i	$-0.381124\pi$
$787$	−7.26795	−	4.19615i	−0.259074	−	0.149577i	−0.623912	+	0.781494i	$0.714458\pi$
$788$		−	2.60770i		−	0.0928953i
$789$	8.66025	−	15.0000i	0.308313	−	0.534014i
$790$	−16.3923	−	28.3923i	−0.583212	−	1.01015i
$791$	−3.80385	+	2.19615i	−0.135249	+	0.0780862i
$792$	4.00000			0.142134
$793$	18.0000	−	5.19615i	0.639199	−	0.184521i
$794$	−29.7846			−1.05702
$795$	−24.8038	+	14.3205i	−0.879702	+	0.507896i
$796$	11.0622	+	19.1603i	0.392088	+	0.679117i
$797$	21.1244	−	36.5885i	0.748263	−	1.29603i	−0.200392	−	0.979716i	$-0.564221\pi$
$797$	21.1244	−	36.5885i	0.748263	−	1.29603i	0.948655	−	0.316314i	$-0.102445\pi$
$798$			7.46410i			0.264226i
$799$	−3.00000	−	1.73205i	−0.106132	−	0.0612756i
$800$	6.06218	+	3.50000i	0.214330	+	0.123744i
$801$		−	11.7321i		−	0.414532i
$802$	−8.19615	+	14.1962i	−0.289416	+	0.501284i
$803$	−21.8564	−	37.8564i	−0.771296	−	1.33592i
$804$	−6.23205	+	3.59808i	−0.219787	+	0.126894i
$805$	19.8564			0.699846
$806$	−5.59808	+	22.6244i	−0.197184	+	0.796909i
$807$	22.3923			0.788246
$808$		0			0
$809$	−7.85641	−	13.6077i	−0.276217	−	0.478421i	0.694225	−	0.719758i	$-0.255747\pi$
$809$	−7.85641	−	13.6077i	−0.276217	−	0.478421i	−0.970441	+	0.241337i	$0.922414\pi$
$810$	1.73205	−	3.00000i	0.0608581	−	0.105409i
$811$		−	2.14359i		−	0.0752717i	−0.999292	−	0.0376359i	$-0.988017\pi$
$811$		−	2.14359i		−	0.0752717i	0.999292	−	0.0376359i	$-0.0119827\pi$
$812$	6.92820	+	4.00000i	0.243132	+	0.140372i
$813$	−10.7942	−	6.23205i	−0.378570	−	0.218568i
$814$			19.7128i			0.690934i
$815$	−2.32051	+	4.01924i	−0.0812839	+	0.140788i
$816$	3.23205	+	5.59808i	0.113144	+	0.195972i
$817$	28.8564	−	16.6603i	1.00956	−	0.582869i
$818$	6.39230			0.223502
$819$	3.50000	+	0.866025i	0.122300	+	0.0302614i
$820$	−24.0000			−0.838116
$821$	27.0622	−	15.6244i	0.944477	−	0.545294i	0.0531158	−	0.998588i	$-0.483085\pi$
$821$	27.0622	−	15.6244i	0.944477	−	0.545294i	0.891361	+	0.453295i	$0.149751\pi$
$822$	6.92820	+	12.0000i	0.241649	+	0.418548i
$823$	11.8038	−	20.4449i	0.411456	−	0.712663i	−0.583593	−	0.812046i	$-0.698354\pi$
$823$	11.8038	−	20.4449i	0.411456	−	0.712663i	0.995049	+	0.0993832i	$0.0316870\pi$
$824$			10.6603i			0.371368i
$825$	24.2487	+	14.0000i	0.844232	+	0.487417i
$826$	5.42820	+	3.13397i	0.188871	+	0.109045i
$827$			36.3923i			1.26548i	0.774363	+	0.632742i	$0.218071\pi$
$827$			36.3923i			1.26548i	−0.774363	+	0.632742i	$0.781929\pi$
$828$	−2.86603	+	4.96410i	−0.0996013	+	0.172514i
$829$	3.60770	+	6.24871i	0.125300	+	0.217027i	0.921850	−	0.387546i	$-0.126677\pi$
$829$	3.60770	+	6.24871i	0.125300	+	0.217027i	−0.796550	+	0.604573i	$0.793344\pi$
$830$	5.19615	−	3.00000i	0.180361	−	0.104132i
$831$	−7.32051			−0.253946
$832$	−2.59808	−	2.50000i	−0.0900721	−	0.0866719i
$833$	6.46410			0.223968
$834$	2.53590	−	1.46410i	0.0878110	−	0.0506977i
$835$	34.6410	+	60.0000i	1.19880	+	2.07639i
$836$	14.9282	−	25.8564i	0.516303	−	0.894263i
$837$			6.46410i			0.223432i
$838$	4.33013	+	2.50000i	0.149582	+	0.0863611i
$839$	−1.39230	−	0.803848i	−0.0480677	−	0.0277519i	0.475774	−	0.879568i	$-0.342168\pi$
$839$	−1.39230	−	0.803848i	−0.0480677	−	0.0277519i	−0.523841	+	0.851816i	$0.675502\pi$
$840$			3.46410i			0.119523i
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$	0.803848	+	1.39230i	0.0277024	+	0.0479820i
$843$	−2.07180	+	1.19615i	−0.0713565	+	0.0411977i
$844$	9.07180			0.312264
$845$	−45.0000	+	1.73205i	−1.54805	+	0.0595844i
$846$	0.535898			0.0184246
$847$	−4.33013	+	2.50000i	−0.148785	+	0.0859010i
$848$	4.13397	+	7.16025i	0.141961	+	0.245884i
$849$	−5.73205	+	9.92820i	−0.196723	+	0.340735i
$850$			45.2487i			1.55202i
$851$	−24.4641	−	14.1244i	−0.838619	−	0.484177i
$852$	−1.66987	−	0.964102i	−0.0572089	−	0.0330296i
$853$			47.6410i			1.63120i	0.578618	+	0.815599i	$0.303592\pi$
$853$			47.6410i			1.63120i	−0.578618	+	0.815599i	$0.696408\pi$
$854$	−2.59808	+	4.50000i	−0.0889043	+	0.153987i
$855$	−12.9282	−	22.3923i	−0.442135	−	0.765801i
$856$	−7.39230	+	4.26795i	−0.252664	+	0.145876i
$857$	33.7128			1.15161			0.575804	−	0.817588i	$-0.304689\pi$
$857$	33.7128			1.15161			0.575804	+	0.817588i	$0.304689\pi$
$858$	−10.3923	−	10.0000i	−0.354787	−	0.341394i
$859$	−15.8564			−0.541014			−0.270507	−	0.962718i	$-0.587191\pi$
$859$	−15.8564			−0.541014			−0.270507	+	0.962718i	$0.587191\pi$
$860$	13.3923	−	7.73205i	0.456674	−	0.263661i
$861$	−3.46410	−	6.00000i	−0.118056	−	0.204479i
$862$	2.42820	−	4.20577i	0.0827049	−	0.143249i
$863$		−	42.9282i		−	1.46129i	−0.682756	−	0.730647i	$-0.739219\pi$
$863$		−	42.9282i		−	1.46129i	0.682756	−	0.730647i	$-0.260781\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	3.21539	+	1.85641i	0.109327	+	0.0631197i
$866$		−	9.85641i		−	0.334934i
$867$	−12.3923	+	21.4641i	−0.420865	+	0.728959i
$868$	−3.23205	−	5.59808i	−0.109703	−	0.190011i
$869$	−32.7846	+	18.9282i	−1.11214	+	0.642095i
$870$	−27.7128			−0.939552
$871$	25.1865	+	6.23205i	0.853413	+	0.211165i
$872$	12.0000			0.406371
$873$	−10.7321	+	6.19615i	−0.363225	+	0.209708i
$874$	21.3923	+	37.0526i	0.723606	+	1.25332i
$875$	−3.46410	+	6.00000i	−0.117108	+	0.202837i
$876$			10.9282i			0.369230i
$877$	22.2679	+	12.8564i	0.751935	+	0.434130i	0.826393	−	0.563094i	$-0.190389\pi$
$877$	22.2679	+	12.8564i	0.751935	+	0.434130i	−0.0744575	+	0.997224i	$0.523723\pi$
$878$	−11.7846	−	6.80385i	−0.397711	−	0.229619i
$879$			33.4641i			1.12872i
$880$	6.92820	−	12.0000i	0.233550	−	0.404520i
$881$	16.0167	+	27.7417i	0.539615	+	0.934641i	0.998925	+	0.0463644i	$0.0147635\pi$
$881$	16.0167	+	27.7417i	0.539615	+	0.934641i	−0.459310	+	0.888276i	$0.651903\pi$
$882$	−0.866025	+	0.500000i	−0.0291606	+	0.0168359i
$883$	0.320508			0.0107860			0.00539298	−	0.999985i	$-0.498283\pi$
$883$	0.320508			0.0107860			0.00539298	+	0.999985i	$0.498283\pi$
$884$	5.59808	−	22.6244i	0.188284	−	0.760939i
$885$	−21.7128			−0.729868
$886$	−19.3923	+	11.1962i	−0.651497	+	0.376142i
$887$	−5.92820	−	10.2679i	−0.199050	−	0.344764i	0.749171	−	0.662377i	$-0.230452\pi$
$887$	−5.92820	−	10.2679i	−0.199050	−	0.344764i	−0.948221	+	0.317613i	$0.897119\pi$
$888$	2.46410	−	4.26795i	0.0826898	−	0.143223i
$889$		−	5.07180i		−	0.170103i
$890$	−35.1962	−	20.3205i	−1.17978	−	0.681145i
$891$	−3.46410	−	2.00000i	−0.116052	−	0.0670025i
$892$			7.53590i			0.252321i
$893$	2.00000	−	3.46410i	0.0669274	−	0.115922i
$894$	5.76795	+	9.99038i	0.192909	+	0.334128i
$895$	50.7846	−	29.3205i	1.69754	−	0.980076i
$896$	1.00000			0.0334077
$897$	19.8564	−	5.73205i	0.662986	−	0.191388i
$898$	18.0000			0.600668
$899$	44.7846	−	25.8564i	1.49365	−	0.862359i
$900$	−3.50000	−	6.06218i	−0.116667	−	0.202073i
$901$	−26.7224	+	46.2846i	−0.890253	+	1.54196i
$902$			27.7128i			0.922736i
$903$	3.86603	+	2.23205i	0.128653	+	0.0742780i
$904$	−3.80385	−	2.19615i	−0.126514	−	0.0730429i
$905$		−	85.8564i		−	2.85396i
$906$	−6.00000	+	10.3923i	−0.199337	+	0.345261i
$907$	−9.23205	−	15.9904i	−0.306545	−	0.530952i	0.671059	−	0.741404i	$-0.265840\pi$
$907$	−9.23205	−	15.9904i	−0.306545	−	0.530952i	−0.977604	+	0.210452i	$0.932506\pi$
$908$	−11.5359	+	6.66025i	−0.382832	+	0.221028i
$909$		0			0
$910$	8.66025	−	9.00000i	0.287085	−	0.298347i
$911$	27.1769			0.900411			0.450206	−	0.892925i	$-0.351351\pi$
$911$	27.1769			0.900411			0.450206	+	0.892925i	$0.351351\pi$
$912$	−6.46410	+	3.73205i	−0.214048	+	0.123581i
$913$	−3.46410	−	6.00000i	−0.114645	−	0.198571i
$914$	0.598076	−	1.03590i	0.0197826	−	0.0342645i
$915$		−	18.0000i		−	0.595062i
$916$	17.2583	+	9.96410i	0.570231	+	0.329223i
$917$	−16.4545	−	9.50000i	−0.543375	−	0.313718i
$918$		−	6.46410i		−	0.213347i
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	0.996770	+	0.0803145i	$0.0255924\pi$
$920$	9.92820	+	17.1962i	0.327323	+	0.566940i
$921$	−19.0526	+	11.0000i	−0.627803	+	0.362462i
$922$	−5.07180			−0.167031
$923$	1.92820	+	6.67949i	0.0634676	+	0.219858i
$924$	4.00000			0.131590
$925$	29.8756	−	17.2487i	0.982305	−	0.567134i
$926$	4.12436	+	7.14359i	0.135535	+	0.234753i
$927$	5.33013	−	9.23205i	0.175064	−	0.303220i
$928$			8.00000i			0.262613i
$929$	5.08846	+	2.93782i	0.166947	+	0.0963868i	0.581145	−	0.813800i	$-0.302605\pi$
$929$	5.08846	+	2.93782i	0.166947	+	0.0963868i	−0.414199	+	0.910187i	$0.635938\pi$
$930$	19.3923	+	11.1962i	0.635899	+	0.367136i
$931$			7.46410i			0.244626i
$932$	−6.73205	+	11.6603i	−0.220516	+	0.381944i
$933$	6.66025	+	11.5359i	0.218047	+	0.377668i
$934$	34.3301	−	19.8205i	1.12332	−	0.648547i
$935$	89.5692			2.92923
$936$	1.00000	+	3.46410i	0.0326860	+	0.113228i
$937$	−44.9282			−1.46774			−0.733870	−	0.679290i	$-0.762288\pi$
$937$	−44.9282			−1.46774			−0.733870	+	0.679290i	$0.762288\pi$
$938$	−6.23205	+	3.59808i	−0.203484	+	0.117481i
$939$	−0.339746	−	0.588457i	−0.0110872	−	0.0192036i
$940$	0.928203	−	1.60770i	0.0302747	−	0.0524372i
$941$			19.6077i			0.639193i	0.947554	+	0.319596i	$0.103547\pi$
$941$			19.6077i			0.639193i	−0.947554	+	0.319596i	$0.896453\pi$
$942$	2.53590	+	1.46410i	0.0826240	+	0.0477030i
$943$	−34.3923	−	19.8564i	−1.11997	−	0.646614i
$944$			6.26795i			0.204004i
$945$	1.73205	−	3.00000i	0.0563436	−	0.0975900i
$946$	−8.92820	−	15.4641i	−0.290281	−	0.502781i
$947$	26.1962	−	15.1244i	0.851261	−	0.491476i	−0.00981541	−	0.999952i	$-0.503124\pi$
$947$	26.1962	−	15.1244i	0.851261	−	0.491476i	0.861076	+	0.508476i	$0.169791\pi$
$948$	9.46410			0.307380
$949$	27.3205	−	28.3923i	0.886861	−	0.921653i
$950$	−52.2487			−1.69517
$951$	−14.2583	+	8.23205i	−0.462358	+	0.266943i
$952$	3.23205	+	5.59808i	0.104751	+	0.181435i
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	−0.513971	−	0.857808i	$-0.671826\pi$
$953$	15.0000	−	25.9808i	0.485898	−	0.841599i	0.999869	+	0.0162081i	$0.00515944\pi$
$954$		−	8.26795i		−	0.267685i
$955$	79.5500	+	45.9282i	2.57418	+	1.48620i
$956$	−11.1340	−	6.42820i	−0.360098	−	0.207903i
$957$			32.0000i			1.03441i
$958$	−2.19615	+	3.80385i	−0.0709545	+	0.122897i
$959$	6.92820	+	12.0000i	0.223723	+	0.387500i
$960$	−3.00000	+	1.73205i	−0.0968246	+	0.0559017i
$961$	−10.7846			−0.347891
$962$	−17.0718	+	4.92820i	−0.550417	+	0.158892i
$963$	8.53590			0.275065
$964$	13.7321	−	7.92820i	0.442280	−	0.255350i
$965$	30.9282	+	53.5692i	0.995614	+	1.72445i
$966$	−2.86603	+	4.96410i	−0.0922129	+	0.159717i
$967$		−	16.5359i		−	0.531759i	−0.964006	−	0.265879i	$-0.914338\pi$
$967$		−	16.5359i		−	0.531759i	0.964006	−	0.265879i	$-0.0856623\pi$
$968$	−4.33013	−	2.50000i	−0.139176	−	0.0803530i
$969$	−41.7846	−	24.1244i	−1.34232	−	0.774986i
$970$			42.9282i			1.37834i
$971$	−11.9641	+	20.7224i	−0.383946	+	0.665014i	−0.991622	−	0.129170i	$-0.958769\pi$
$971$	−11.9641	+	20.7224i	−0.383946	+	0.665014i	0.607676	+	0.794185i	$0.292102\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	2.53590	−	1.46410i	0.0812972	−	0.0469369i
$974$	0.392305			0.0125703
$975$	−6.06218	+	24.5000i	−0.194145	+	0.784628i
$976$	−5.19615			−0.166325
$977$	−22.3923	+	12.9282i	−0.716393	+	0.413610i	−0.813424	−	0.581672i	$-0.802399\pi$
$977$	−22.3923	+	12.9282i	−0.716393	+	0.413610i	0.0970305	+	0.995281i	$0.469066\pi$
$978$	−0.669873	−	1.16025i	−0.0214202	−	0.0371008i
$979$	−23.4641	+	40.6410i	−0.749916	+	1.29889i
$980$			3.46410i			0.110657i
$981$	−10.3923	−	6.00000i	−0.331801	−	0.191565i
$982$	−8.53590	−	4.92820i	−0.272391	−	0.157265i
$983$			19.0718i			0.608296i	0.952625	+	0.304148i	$0.0983717\pi$
$983$			19.0718i			0.608296i	−0.952625	+	0.304148i	$0.901628\pi$
$984$	3.46410	−	6.00000i	0.110432	−	0.191273i
$985$	4.51666	+	7.82309i	0.143913	+	0.249264i
$986$	−44.7846	+	25.8564i	−1.42623	+	0.823436i
$987$	0.535898			0.0170578
$988$	26.1244	+	6.46410i	0.831126	+	0.205650i
$989$	25.5885			0.813666
$990$	−12.0000	+	6.92820i	−0.381385	+	0.220193i
$991$	−0.0717968	−	0.124356i	−0.00228070	−	0.00395029i	0.864883	−	0.501974i	$-0.167393\pi$
$991$	−0.0717968	−	0.124356i	−0.00228070	−	0.00395029i	−0.867164	+	0.498024i	$0.834059\pi$
$992$	3.23205	−	5.59808i	0.102618	−	0.177739i
$993$		−	21.3205i		−	0.676586i
$994$	−1.66987	−	0.964102i	−0.0529652	−	0.0305794i
$995$	−66.3731	−	38.3205i	−2.10417	−	1.21484i
$996$			1.73205i			0.0548821i
$997$	−16.9904	+	29.4282i	−0.538091	+	0.932001i	0.460916	+	0.887444i	$0.347521\pi$
$997$	−16.9904	+	29.4282i	−0.538091	+	0.932001i	−0.999007	+	0.0445568i	$0.985812\pi$
$998$	0.133975	+	0.232051i	0.00424089	+	0.00734544i
$999$	−4.26795	+	2.46410i	−0.135032	+	0.0779607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.s.c.127.2	yes	4
3.2	odd	2		1638.2.bj.e.127.1		4
13.2	odd	12		7098.2.a.bz.1.2		2
13.4	even	6	inner	546.2.s.c.43.2	✓	4
13.11	odd	12		7098.2.a.bn.1.1		2
39.17	odd	6		1638.2.bj.e.1135.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.c.43.2	✓	4	13.4	even	6	inner
546.2.s.c.127.2	yes	4	1.1	even	1	trivial
1638.2.bj.e.127.1		4	3.2	odd	2
1638.2.bj.e.1135.1		4	39.17	odd	6
7098.2.a.bn.1.1		2	13.11	odd	12
7098.2.a.bz.1.2		2	13.2	odd	12

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.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +3.46410i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.73205 + 3.00000i) q^{10} +(3.46410 - 2.00000i) q^{11} -1.00000 q^{12} +(2.59808 + 2.50000i) q^{13} -1.00000 q^{14} +(3.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.23205 - 5.59808i) q^{17} +1.00000i q^{18} +(6.46410 + 3.73205i) q^{19} +(3.00000 + 1.73205i) q^{20} +1.00000i q^{21} +(2.00000 - 3.46410i) q^{22} +(2.86603 + 4.96410i) q^{23} +(-0.866025 + 0.500000i) q^{24} -7.00000 q^{25} +(3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-4.00000 - 6.92820i) q^{29} +(1.73205 - 3.00000i) q^{30} +6.46410i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.46410 - 2.00000i) q^{33} -6.46410i q^{34} +(1.73205 - 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-4.26795 + 2.46410i) q^{37} +7.46410 q^{38} +(0.866025 - 3.50000i) q^{39} +3.46410 q^{40} +(-6.00000 + 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{42} +(2.23205 - 3.86603i) q^{43} -4.00000i q^{44} +(-3.00000 - 1.73205i) q^{45} +(4.96410 + 2.86603i) q^{46} -0.535898i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-6.06218 + 3.50000i) q^{50} -6.46410 q^{51} +(3.46410 - 1.00000i) q^{52} -8.26795 q^{53} +(0.866025 - 0.500000i) q^{54} +(6.92820 + 12.0000i) q^{55} +(-0.500000 + 0.866025i) q^{56} -7.46410i q^{57} +(-6.92820 - 4.00000i) q^{58} +(-5.42820 - 3.13397i) q^{59} -3.46410i q^{60} +(2.59808 - 4.50000i) q^{61} +(3.23205 + 5.59808i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(-8.66025 + 9.00000i) q^{65} -4.00000 q^{66} +(6.23205 - 3.59808i) q^{67} +(-3.23205 - 5.59808i) q^{68} +(2.86603 - 4.96410i) q^{69} -3.46410i q^{70} +(1.66987 + 0.964102i) q^{71} +(0.866025 + 0.500000i) q^{72} -10.9282i q^{73} +(-2.46410 + 4.26795i) q^{74} +(3.50000 + 6.06218i) q^{75} +(6.46410 - 3.73205i) q^{76} -4.00000 q^{77} +(-1.00000 - 3.46410i) q^{78} -9.46410 q^{79} +(3.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.46410 + 6.00000i) q^{82} -1.73205i q^{83} +(0.866025 + 0.500000i) q^{84} +(19.3923 + 11.1962i) q^{85} -4.46410i q^{86} +(-4.00000 + 6.92820i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-10.1603 + 5.86603i) q^{89} -3.46410 q^{90} +(-1.00000 - 3.46410i) q^{91} +5.73205 q^{92} +(5.59808 - 3.23205i) q^{93} +(-0.267949 - 0.464102i) q^{94} +(-12.9282 + 22.3923i) q^{95} +1.00000i q^{96} +(10.7321 + 6.19615i) q^{97} +(0.866025 + 0.500000i) q^{98} +4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{12} - 4 q^{14} + 12 q^{15} - 2 q^{16} + 6 q^{17} + 12 q^{19} + 12 q^{20} + 8 q^{22} + 8 q^{23} - 28 q^{25} + 14 q^{26} + 4 q^{27} - 16 q^{29} + 2 q^{36} - 24 q^{37} + 16 q^{38} - 24 q^{41} + 2 q^{42} + 2 q^{43} - 12 q^{45} + 6 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{51} - 40 q^{53} - 2 q^{56} + 6 q^{59} + 6 q^{62} - 4 q^{64} - 16 q^{66} + 18 q^{67} - 6 q^{68} + 8 q^{69} + 24 q^{71} + 4 q^{74} + 14 q^{75} + 12 q^{76} - 16 q^{77} - 4 q^{78} - 24 q^{79} + 12 q^{80} - 2 q^{81} + 36 q^{85} - 16 q^{87} - 8 q^{88} - 6 q^{89} - 4 q^{91} + 16 q^{92} + 12 q^{93} - 8 q^{94} - 24 q^{95} + 36 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 4 * q^12 - 4 * q^14 + 12 * q^15 - 2 * q^16 + 6 * q^17 + 12 * q^19 + 12 * q^20 + 8 * q^22 + 8 * q^23 - 28 * q^25 + 14 * q^26 + 4 * q^27 - 16 * q^29 + 2 * q^36 - 24 * q^37 + 16 * q^38 - 24 * q^41 + 2 * q^42 + 2 * q^43 - 12 * q^45 + 6 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^51 - 40 * q^53 - 2 * q^56 + 6 * q^59 + 6 * q^62 - 4 * q^64 - 16 * q^66 + 18 * q^67 - 6 * q^68 + 8 * q^69 + 24 * q^71 + 4 * q^74 + 14 * q^75 + 12 * q^76 - 16 * q^77 - 4 * q^78 - 24 * q^79 + 12 * q^80 - 2 * q^81 + 36 * q^85 - 16 * q^87 - 8 * q^88 - 6 * q^89 - 4 * q^91 + 16 * q^92 + 12 * q^93 - 8 * q^94 - 24 * q^95 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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