LMFDB - Embedded newform 546.2.s.c.43.1

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			43.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	546.43
Dual form			546.2.s.c.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -3.46410i q^{5} +(0.866025 - 0.500000i) q^{6} +(0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.232051 - 0.401924i) q^{17} +1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} +(3.00000 - 1.73205i) q^{20} +1.00000i q^{21} +(2.00000 + 3.46410i) q^{22} +(1.13397 - 1.96410i) 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} -0.464102i q^{31} +(0.866025 - 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} +0.464102i q^{34} +(-1.73205 - 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.73205 - 4.46410i) q^{37} +0.535898 q^{38} +(-0.866025 - 3.50000i) q^{39} -3.46410 q^{40} +(-6.00000 - 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-1.23205 - 2.13397i) q^{43} -4.00000i q^{44} +(-3.00000 + 1.73205i) q^{45} +(-1.96410 + 1.13397i) q^{46} -7.46410i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(6.06218 + 3.50000i) q^{50} +0.464102 q^{51} +(-3.46410 - 1.00000i) q^{52} -11.7321 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-6.92820 + 12.0000i) q^{55} +(-0.500000 - 0.866025i) q^{56} -0.535898i q^{57} +(6.92820 - 4.00000i) q^{58} +(8.42820 - 4.86603i) q^{59} +3.46410i q^{60} +(-2.59808 - 4.50000i) q^{61} +(-0.232051 + 0.401924i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(8.66025 + 9.00000i) q^{65} -4.00000 q^{66} +(2.76795 + 1.59808i) q^{67} +(0.232051 - 0.401924i) q^{68} +(1.13397 + 1.96410i) q^{69} +3.46410i q^{70} +(10.3301 - 5.96410i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.92820i q^{73} +(4.46410 + 7.73205i) q^{74} +(3.50000 - 6.06218i) q^{75} +(-0.464102 - 0.267949i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -2.53590 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} +(-1.39230 + 0.803848i) q^{85} +2.46410i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(7.16025 + 4.13397i) q^{89} +3.46410 q^{90} +(-1.00000 + 3.46410i) q^{91} +2.26795 q^{92} +(0.401924 + 0.232051i) q^{93} +(-3.73205 + 6.46410i) q^{94} +(0.928203 + 1.60770i) q^{95} +1.00000i q^{96} +(7.26795 - 4.19615i) 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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	$-0.717953\pi$
$5$		−	3.46410i		−	1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$	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	$-0.539370\pi$
$11$	−3.46410	−	2.00000i	−1.04447	−	0.603023i	−0.921095	+	0.389338i	$0.872704\pi$
$12$	−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
$17$	−0.232051	−	0.401924i	−0.0562806	−	0.0974808i	0.836512	−	0.547948i	$-0.184591\pi$
$17$	−0.232051	−	0.401924i	−0.0562806	−	0.0974808i	−0.892793	+	0.450467i	$0.851257\pi$
$18$			1.00000i			0.235702i
$19$	−0.464102	+	0.267949i	−0.106472	+	0.0614718i	−0.552291	−	0.833652i	$-0.686246\pi$
$19$	−0.464102	+	0.267949i	−0.106472	+	0.0614718i	0.445818	+	0.895123i	$0.352913\pi$
$20$	3.00000	−	1.73205i	0.670820	−	0.387298i
$21$			1.00000i			0.218218i
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$	1.13397	−	1.96410i	0.236450	−	0.409543i	−0.723243	−	0.690594i	$-0.757349\pi$
$23$	1.13397	−	1.96410i	0.236450	−	0.409543i	0.959693	+	0.281050i	$0.0906827\pi$
$24$	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	0.208443	+	0.978035i	$0.433160\pi$
$29$	−4.00000	+	6.92820i	−0.742781	+	1.28654i	−0.951224	+	0.308500i	$0.900173\pi$
$30$	−1.73205	−	3.00000i	−0.316228	−	0.547723i
$31$		−	0.464102i		−	0.0833551i	−0.999131	−	0.0416776i	$-0.986730\pi$
$31$		−	0.464102i		−	0.0833551i	0.999131	−	0.0416776i	$-0.0132702\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.46410	−	2.00000i	0.603023	−	0.348155i
$34$			0.464102i			0.0795928i
$35$	−1.73205	−	3.00000i	−0.292770	−	0.507093i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−7.73205	−	4.46410i	−1.27114	−	0.733894i	−0.295939	−	0.955207i	$-0.595632\pi$
$37$	−7.73205	−	4.46410i	−1.27114	−	0.733894i	−0.975203	+	0.221313i	$0.928966\pi$
$38$	0.535898			0.0869342
$39$	−0.866025	−	3.50000i	−0.138675	−	0.560449i
$40$	−3.46410			−0.547723
$41$	−6.00000	−	3.46410i	−0.937043	−	0.541002i	−0.0480106	−	0.998847i	$-0.515288\pi$
$41$	−6.00000	−	3.46410i	−0.937043	−	0.541002i	−0.889032	+	0.457845i	$0.848621\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	−1.23205	−	2.13397i	−0.187886	−	0.325428i	0.756659	−	0.653809i	$-0.226830\pi$
$43$	−1.23205	−	2.13397i	−0.187886	−	0.325428i	−0.944545	+	0.328381i	$0.893497\pi$
$44$		−	4.00000i		−	0.603023i
$45$	−3.00000	+	1.73205i	−0.447214	+	0.258199i
$46$	−1.96410	+	1.13397i	−0.289591	+	0.167195i
$47$		−	7.46410i		−	1.08875i	−0.838842	−	0.544376i	$-0.816767\pi$
$47$		−	7.46410i		−	1.08875i	0.838842	−	0.544376i	$-0.183233\pi$
$48$	−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
$51$	0.464102			0.0649872
$52$	−3.46410	−	1.00000i	−0.480384	−	0.138675i
$53$	−11.7321			−1.61152			−0.805761	−	0.592241i	$-0.798243\pi$
$53$	−11.7321			−1.61152			−0.805761	+	0.592241i	$0.798243\pi$
$54$	−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
$57$		−	0.535898i		−	0.0709815i
$58$	6.92820	−	4.00000i	0.909718	−	0.525226i
$59$	8.42820	−	4.86603i	1.09726	−	0.633503i	0.161759	−	0.986830i	$-0.448283\pi$
$59$	8.42820	−	4.86603i	1.09726	−	0.633503i	0.935500	+	0.353328i	$0.114950\pi$
$60$			3.46410i			0.447214i
$61$	−2.59808	−	4.50000i	−0.332650	−	0.576166i	0.650381	−	0.759608i	$-0.274609\pi$
$61$	−2.59808	−	4.50000i	−0.332650	−	0.576166i	−0.983030	+	0.183442i	$0.941276\pi$
$62$	−0.232051	+	0.401924i	−0.0294705	+	0.0510444i
$63$	−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
$67$	2.76795	+	1.59808i	0.338159	+	0.195236i	0.659458	−	0.751742i	$-0.270786\pi$
$67$	2.76795	+	1.59808i	0.338159	+	0.195236i	−0.321299	+	0.946978i	$0.604119\pi$
$68$	0.232051	−	0.401924i	0.0281403	−	0.0487404i
$69$	1.13397	+	1.96410i	0.136514	+	0.236450i
$70$			3.46410i			0.414039i
$71$	10.3301	−	5.96410i	1.22596	−	0.707809i	0.259778	−	0.965668i	$-0.416351\pi$
$71$	10.3301	−	5.96410i	1.22596	−	0.707809i	0.966182	+	0.257860i	$0.0830172\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			2.92820i			0.342720i	0.985208	+	0.171360i	$0.0548162\pi$
$73$			2.92820i			0.342720i	−0.985208	+	0.171360i	$0.945184\pi$
$74$	4.46410	+	7.73205i	0.518941	+	0.898833i
$75$	3.50000	−	6.06218i	0.404145	−	0.700000i
$76$	−0.464102	−	0.267949i	−0.0532361	−	0.0307359i
$77$	−4.00000			−0.455842
$78$	−1.00000	+	3.46410i	−0.113228	+	0.392232i
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$	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	$0.0303039\pi$
$83$			1.73205i			0.190117i	−0.995472	+	0.0950586i	$0.969696\pi$
$84$	−0.866025	+	0.500000i	−0.0944911	+	0.0545545i
$85$	−1.39230	+	0.803848i	−0.151017	+	0.0871895i
$86$			2.46410i			0.265711i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	7.16025	+	4.13397i	0.758985	+	0.438200i	0.828931	−	0.559350i	$-0.188949\pi$
$89$	7.16025	+	4.13397i	0.758985	+	0.438200i	−0.0699459	+	0.997551i	$0.522283\pi$
$90$	3.46410			0.365148
$91$	−1.00000	+	3.46410i	−0.104828	+	0.363137i
$92$	2.26795			0.236450
$93$	0.401924	+	0.232051i	0.0416776	+	0.0240625i
$94$	−3.73205	+	6.46410i	−0.384932	+	0.666721i
$95$	0.928203	+	1.60770i	0.0952316	+	0.164946i
$96$			1.00000i			0.102062i
$97$	7.26795	−	4.19615i	0.737948	−	0.426055i	−0.0833745	−	0.996518i	$-0.526570\pi$
$97$	7.26795	−	4.19615i	0.737948	−	0.426055i	0.821323	+	0.570464i	$0.193236\pi$
$98$	−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	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	−0.401924	−	0.232051i	−0.0397964	−	0.0229765i
$103$	6.66025			0.656254			0.328127	−	0.944634i	$-0.393583\pi$
$103$	6.66025			0.656254			0.328127	+	0.944634i	$0.393583\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$	3.46410			0.338062
$106$	10.1603	+	5.86603i	0.986851	+	0.569759i
$107$	−7.73205	+	13.3923i	−0.747486	+	1.29468i	0.201539	+	0.979481i	$0.435406\pi$
$107$	−7.73205	+	13.3923i	−0.747486	+	1.29468i	−0.949024	+	0.315202i	$0.897928\pi$
$108$	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
$111$	7.73205	−	4.46410i	0.733894	−	0.423714i
$112$			1.00000i			0.0944911i
$113$	−8.19615	−	14.1962i	−0.771029	−	1.33546i	−0.936999	−	0.349331i	$-0.886409\pi$
$113$	−8.19615	−	14.1962i	−0.771029	−	1.33546i	0.165970	−	0.986131i	$-0.446924\pi$
$114$	−0.267949	+	0.464102i	−0.0250957	+	0.0434671i
$115$	−6.80385	−	3.92820i	−0.634462	−	0.366307i
$116$	−8.00000			−0.742781
$117$	3.46410	+	1.00000i	0.320256	+	0.0924500i
$118$	−9.73205			−0.895908
$119$	−0.401924	−	0.232051i	−0.0368443	−	0.0212721i
$120$	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
$124$	0.401924	−	0.232051i	0.0360938	−	0.0208388i
$125$			6.92820i			0.619677i
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	9.46410	−	16.3923i	0.839803	−	1.45458i	−0.0502557	−	0.998736i	$-0.516004\pi$
$127$	9.46410	−	16.3923i	0.839803	−	1.45458i	0.890059	−	0.455845i	$-0.150663\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.46410			0.216952
$130$	−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
$133$	−0.267949	+	0.464102i	−0.0232341	+	0.0402427i
$134$	−1.59808	−	2.76795i	−0.138053	−	0.239114i
$135$		−	3.46410i		−	0.298142i
$136$	−0.401924	+	0.232051i	−0.0344647	+	0.0198982i
$137$	−12.0000	+	6.92820i	−1.02523	+	0.591916i	−0.915614	−	0.402058i	$-0.868295\pi$
$137$	−12.0000	+	6.92820i	−1.02523	+	0.591916i	−0.109615	+	0.993974i	$0.534962\pi$
$138$		−	2.26795i		−	0.193061i
$139$	5.46410	+	9.46410i	0.463459	+	0.802735i	0.999131	−	0.0416919i	$-0.0132748\pi$
$139$	5.46410	+	9.46410i	0.463459	+	0.802735i	−0.535671	+	0.844426i	$0.679941\pi$
$140$	1.73205	−	3.00000i	0.146385	−	0.253546i
$141$	6.46410	+	3.73205i	0.544376	+	0.314295i
$142$	−11.9282			−1.00099
$143$	14.0000	−	3.46410i	1.17074	−	0.289683i
$144$	1.00000			0.0833333
$145$	24.0000	+	13.8564i	1.99309	+	1.15071i
$146$	1.46410	−	2.53590i	0.121170	−	0.209872i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$		−	8.92820i		−	0.733894i
$149$	15.9904	−	9.23205i	1.30998	−	0.756319i	0.327890	−	0.944716i	$-0.393662\pi$
$149$	15.9904	−	9.23205i	1.30998	−	0.756319i	0.982093	+	0.188397i	$0.0603291\pi$
$150$	−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	$-0.162373\pi$
$152$	0.267949	+	0.464102i	0.0217335	+	0.0376436i
$153$	−0.232051	+	0.401924i	−0.0187602	+	0.0324936i
$154$	3.46410	+	2.00000i	0.279145	+	0.161165i
$155$	−1.60770			−0.129133
$156$	2.59808	−	2.50000i	0.208013	−	0.200160i
$157$	10.9282			0.872166			0.436083	−	0.899907i	$-0.356365\pi$
$157$	10.9282			0.872166			0.436083	+	0.899907i	$0.356365\pi$
$158$	2.19615	+	1.26795i	0.174717	+	0.100873i
$159$	5.86603	−	10.1603i	0.465206	−	0.805761i
$160$	−1.73205	−	3.00000i	−0.136931	−	0.237171i
$161$		−	2.26795i		−	0.178739i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−16.1603	+	9.33013i	−1.26577	+	0.730792i	−0.974185	−	0.225753i	$-0.927516\pi$
$163$	−16.1603	+	9.33013i	−1.26577	+	0.730792i	−0.291584	+	0.956545i	$0.594182\pi$
$164$		−	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	$-0.614991\pi$
$167$	−17.3205	−	10.0000i	−1.34030	−	0.773823i	−0.986851	+	0.161630i	$0.948325\pi$
$168$	1.00000			0.0771517
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$	1.60770			0.123305
$171$	0.464102	+	0.267949i	0.0354907	+	0.0204906i
$172$	1.23205	−	2.13397i	0.0939430	−	0.162714i
$173$	7.46410	+	12.9282i	0.567485	+	0.982913i	0.996814	+	0.0797647i	$0.0254169\pi$
$173$	7.46410	+	12.9282i	0.567485	+	0.982913i	−0.429329	+	0.903148i	$0.641250\pi$
$174$			8.00000i			0.606478i
$175$	−6.06218	+	3.50000i	−0.458258	+	0.264575i
$176$	3.46410	−	2.00000i	0.261116	−	0.150756i
$177$			9.73205i			0.731506i
$178$	−4.13397	−	7.16025i	−0.309854	−	0.536684i
$179$	−1.53590	+	2.66025i	−0.114798	+	0.198837i	−0.917699	−	0.397276i	$-0.869956\pi$
$179$	−1.53590	+	2.66025i	−0.114798	+	0.198837i	0.802901	+	0.596113i	$0.203289\pi$
$180$	−3.00000	−	1.73205i	−0.223607	−	0.129099i
$181$	16.7846			1.24759			0.623795	−	0.781588i	$-0.285590\pi$
$181$	16.7846			1.24759			0.623795	+	0.781588i	$0.285590\pi$
$182$	2.59808	−	2.50000i	0.192582	−	0.185312i
$183$	5.19615			0.384111
$184$	−1.96410	−	1.13397i	−0.144795	−	0.0835977i
$185$	−15.4641	+	26.7846i	−1.13694	+	1.96924i
$186$	−0.232051	−	0.401924i	−0.0170148	−	0.0294705i
$187$			1.85641i			0.135754i
$188$	6.46410	−	3.73205i	0.471443	−	0.272188i
$189$	0.866025	−	0.500000i	0.0629941	−	0.0363696i
$190$		−	1.85641i		−	0.134678i
$191$	−9.25833	−	16.0359i	−0.669909	−	1.16032i	−0.977929	−	0.208937i	$-0.933000\pi$
$191$	−9.25833	−	16.0359i	−0.669909	−	1.16032i	0.308020	−	0.951380i	$-0.400334\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	8.53590	+	4.92820i	0.614427	+	0.354740i	0.774696	−	0.632334i	$-0.217903\pi$
$193$	8.53590	+	4.92820i	0.614427	+	0.354740i	−0.160269	+	0.987073i	$0.551236\pi$
$194$	−8.39230			−0.602532
$195$	−12.1244	+	3.00000i	−0.868243	+	0.214834i
$196$	1.00000			0.0714286
$197$	−20.2583	−	11.6962i	−1.44335	−	0.833316i	−0.445275	−	0.895394i	$-0.646894\pi$
$197$	−20.2583	−	11.6962i	−1.44335	−	0.833316i	−0.998071	+	0.0620775i	$0.980227\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	1.06218	+	1.83975i	0.0752958	+	0.130416i	0.901215	−	0.433373i	$-0.142677\pi$
$199$	1.06218	+	1.83975i	0.0752958	+	0.130416i	−0.825919	+	0.563789i	$0.809343\pi$
$200$			7.00000i			0.494975i
$201$	−2.76795	+	1.59808i	−0.195236	+	0.112720i
$202$		0			0
$203$			8.00000i			0.561490i
$204$	0.232051	+	0.401924i	0.0162468	+	0.0281403i
$205$	−12.0000	+	20.7846i	−0.838116	+	1.45166i
$206$	−5.76795	−	3.33013i	−0.401872	−	0.232021i
$207$	−2.26795			−0.157633
$208$	−0.866025	−	3.50000i	−0.0600481	−	0.242681i
$209$	2.14359			0.148275
$210$	−3.00000	−	1.73205i	−0.207020	−	0.119523i
$211$	11.4641	−	19.8564i	0.789221	−	1.36697i	−0.137223	−	0.990540i	$-0.543818\pi$
$211$	11.4641	−	19.8564i	0.789221	−	1.36697i	0.926445	−	0.376431i	$-0.122849\pi$
$212$	−5.86603	−	10.1603i	−0.402880	−	0.697809i
$213$			11.9282i			0.817307i
$214$	13.3923	−	7.73205i	0.915479	−	0.528552i
$215$	−7.39230	+	4.26795i	−0.504151	+	0.291072i
$216$		−	1.00000i		−	0.0680414i
$217$	−0.232051	−	0.401924i	−0.0157526	−	0.0272844i
$218$	6.00000	−	10.3923i	0.406371	−	0.703856i
$219$	−2.53590	−	1.46410i	−0.171360	−	0.0989348i
$220$	−13.8564			−0.934199
$221$	1.60770	+	0.464102i	0.108145	+	0.0312189i
$222$	−8.92820			−0.599222
$223$	12.5263	+	7.23205i	0.838822	+	0.484294i	0.856864	−	0.515543i	$-0.172410\pi$
$223$	12.5263	+	7.23205i	0.838822	+	0.484294i	−0.0180418	+	0.999837i	$0.505743\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	3.50000	+	6.06218i	0.233333	+	0.404145i
$226$			16.3923i			1.09040i
$227$	−18.4641	+	10.6603i	−1.22551	+	0.707546i	−0.966086	−	0.258219i	$-0.916864\pi$
$227$	−18.4641	+	10.6603i	−1.22551	+	0.707546i	−0.259419	+	0.965765i	$0.583531\pi$
$228$	0.464102	−	0.267949i	0.0307359	−	0.0177454i
$229$			6.07180i			0.401236i	0.979670	+	0.200618i	$0.0642949\pi$
$229$			6.07180i			0.401236i	−0.979670	+	0.200618i	$0.935705\pi$
$230$	3.92820	+	6.80385i	0.259018	+	0.448632i
$231$	2.00000	−	3.46410i	0.131590	−	0.227921i
$232$	6.92820	+	4.00000i	0.454859	+	0.262613i
$233$	−6.53590			−0.428181			−0.214090	−	0.976814i	$-0.568679\pi$
$233$	−6.53590			−0.428181			−0.214090	+	0.976814i	$0.568679\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$	−25.8564			−1.68669
$236$	8.42820	+	4.86603i	0.548629	+	0.316751i
$237$	1.26795	−	2.19615i	0.0823622	−	0.142655i
$238$	0.232051	+	0.401924i	0.0150416	+	0.0260528i
$239$			14.8564i			0.960981i	0.877000	+	0.480491i	$0.159541\pi$
$239$			14.8564i			0.960981i	−0.877000	+	0.480491i	$0.840459\pi$
$240$	−3.00000	+	1.73205i	−0.193649	+	0.111803i
$241$	10.2679	−	5.92820i	0.661417	−	0.381869i	−0.131400	−	0.991329i	$-0.541947\pi$
$241$	10.2679	−	5.92820i	0.661417	−	0.381869i	0.792817	+	0.609460i	$0.208614\pi$
$242$		−	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
$247$	0.535898	−	1.85641i	0.0340984	−	0.118120i
$248$	−0.464102			−0.0294705
$249$	−1.50000	−	0.866025i	−0.0950586	−	0.0548821i
$250$	3.46410	−	6.00000i	0.219089	−	0.379473i
$251$	−11.9641	−	20.7224i	−0.755167	−	1.30799i	−0.945291	−	0.326228i	$-0.894222\pi$
$251$	−11.9641	−	20.7224i	−0.755167	−	1.30799i	0.190124	−	0.981760i	$-0.439111\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	−7.85641	+	4.53590i	−0.493928	+	0.285169i
$254$	−16.3923	+	9.46410i	−1.02854	+	0.593831i
$255$		−	1.60770i		−	0.100678i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.23205	+	5.59808i	−0.201610	+	0.349198i	−0.949047	−	0.315134i	$-0.897951\pi$
$257$	−3.23205	+	5.59808i	−0.201610	+	0.349198i	0.747437	+	0.664332i	$0.231284\pi$
$258$	−2.13397	−	1.23205i	−0.132855	−	0.0767041i
$259$	−8.92820			−0.554772
$260$	−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	0.465196	+	0.885208i	$0.345984\pi$
$263$	−8.66025	+	15.0000i	−0.534014	+	0.924940i	−0.999210	+	0.0397320i	$0.987350\pi$
$264$	−2.00000	−	3.46410i	−0.123091	−	0.213201i
$265$			40.6410i			2.49656i
$266$	0.464102	−	0.267949i	0.0284559	−	0.0164290i
$267$	−7.16025	+	4.13397i	−0.438200	+	0.252995i
$268$			3.19615i			0.195236i
$269$	−0.803848	−	1.39230i	−0.0490115	−	0.0848903i	0.840479	−	0.541844i	$-0.182274\pi$
$269$	−0.803848	−	1.39230i	−0.0490115	−	0.0848903i	−0.889490	+	0.456954i	$0.848940\pi$
$270$	−1.73205	+	3.00000i	−0.105409	+	0.182574i
$271$	−4.79423	−	2.76795i	−0.291229	−	0.168141i	0.347267	−	0.937766i	$-0.387110\pi$
$271$	−4.79423	−	2.76795i	−0.291229	−	0.168141i	−0.638496	+	0.769625i	$0.720443\pi$
$272$	0.464102			0.0281403
$273$	−2.50000	−	2.59808i	−0.151307	−	0.157243i
$274$	13.8564			0.837096
$275$	24.2487	+	14.0000i	1.46225	+	0.844232i
$276$	−1.13397	+	1.96410i	−0.0682572	+	0.118225i
$277$	−13.6603	−	23.6603i	−0.820765	−	1.42161i	−0.905113	−	0.425171i	$-0.860214\pi$
$277$	−13.6603	−	23.6603i	−0.820765	−	1.42161i	0.0843481	−	0.996436i	$-0.473119\pi$
$278$		−	10.9282i		−	0.655430i
$279$	−0.401924	+	0.232051i	−0.0240625	+	0.0138925i
$280$	−3.00000	+	1.73205i	−0.179284	+	0.103510i
$281$			18.3923i			1.09719i	0.836087	+	0.548596i	$0.184838\pi$
$281$			18.3923i			1.09719i	−0.836087	+	0.548596i	$0.815162\pi$
$282$	−3.73205	−	6.46410i	−0.222240	−	0.384932i
$283$	−2.26795	+	3.92820i	−0.134816	+	0.233507i	−0.925527	−	0.378682i	$-0.876378\pi$
$283$	−2.26795	+	3.92820i	−0.134816	+	0.233507i	0.790711	+	0.612189i	$0.209711\pi$
$284$	10.3301	+	5.96410i	0.612980	+	0.353904i
$285$	−1.85641			−0.109964
$286$	−13.8564	−	4.00000i	−0.819346	−	0.236525i
$287$	−6.92820			−0.408959
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	8.39230	−	14.5359i	0.493665	−	0.855053i
$290$	−13.8564	−	24.0000i	−0.813676	−	1.40933i
$291$			8.39230i			0.491966i
$292$	−2.53590	+	1.46410i	−0.148402	+	0.0856801i
$293$	22.9808	−	13.2679i	1.34255	−	0.775122i	0.355369	−	0.934726i	$-0.384355\pi$
$293$	22.9808	−	13.2679i	1.34255	−	0.775122i	0.987181	+	0.159604i	$0.0510218\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	−16.8564	−	29.1962i	−0.981418	−	1.69987i
$296$	−4.46410	+	7.73205i	−0.259471	+	0.449416i
$297$	−3.46410	−	2.00000i	−0.201008	−	0.116052i
$298$	−18.4641			−1.06960
$299$	1.96410	+	7.93782i	0.113587	+	0.459056i
$300$	7.00000			0.404145
$301$	−2.13397	−	1.23205i	−0.123000	−	0.0710142i
$302$	−6.00000	+	10.3923i	−0.345261	+	0.598010i
$303$		0			0
$304$		−	0.535898i		−	0.0307359i
$305$	−15.5885	+	9.00000i	−0.892592	+	0.515339i
$306$	0.401924	−	0.232051i	0.0229765	−	0.0132655i
$307$		−	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
$309$	−3.33013	+	5.76795i	−0.189444	+	0.328127i
$310$	1.39230	+	0.803848i	0.0790776	+	0.0456555i
$311$	21.3205			1.20898			0.604488	−	0.796615i	$-0.293378\pi$
$311$	21.3205			1.20898			0.604488	+	0.796615i	$0.293378\pi$
$312$	−3.50000	+	0.866025i	−0.198148	+	0.0490290i
$313$	35.3205			1.99643			0.998217	−	0.0596964i	$-0.0190133\pi$
$313$	35.3205			1.99643			0.998217	+	0.0596964i	$0.0190133\pi$
$314$	−9.46410	−	5.46410i	−0.534090	−	0.308357i
$315$	−1.73205	+	3.00000i	−0.0975900	+	0.169031i
$316$	−1.26795	−	2.19615i	−0.0713277	−	0.123543i
$317$		−	9.53590i		−	0.535589i	−0.963476	−	0.267795i	$-0.913705\pi$
$317$		−	9.53590i		−	0.535589i	0.963476	−	0.267795i	$-0.0862949\pi$
$318$	−10.1603	+	5.86603i	−0.569759	+	0.328950i
$319$	27.7128	−	16.0000i	1.55162	−	0.895828i
$320$			3.46410i			0.193649i
$321$	−7.73205	−	13.3923i	−0.431561	−	0.747486i
$322$	−1.13397	+	1.96410i	−0.0631939	+	0.109455i
$323$	0.215390	+	0.124356i	0.0119846	+	0.00691933i
$324$	−1.00000			−0.0555556
$325$	18.1865	−	17.5000i	1.00881	−	0.970725i
$326$	18.6603			1.03350
$327$	−10.3923	−	6.00000i	−0.574696	−	0.331801i
$328$	−3.46410	+	6.00000i	−0.191273	+	0.331295i
$329$	−3.73205	−	6.46410i	−0.205755	−	0.356377i
$330$			13.8564i			0.762770i
$331$	11.5359	−	6.66025i	0.634070	−	0.366081i	−0.148256	−	0.988949i	$-0.547366\pi$
$331$	11.5359	−	6.66025i	0.634070	−	0.366081i	0.782327	+	0.622868i	$0.214033\pi$
$332$	−1.50000	+	0.866025i	−0.0823232	+	0.0475293i
$333$			8.92820i			0.489263i
$334$	10.0000	+	17.3205i	0.547176	+	0.947736i
$335$	5.53590	−	9.58846i	0.302458	−	0.523873i
$336$	−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
$339$	16.3923			0.890308
$340$	−1.39230	−	0.803848i	−0.0755083	−	0.0435948i
$341$	−0.928203	+	1.60770i	−0.0502650	+	0.0870616i
$342$	−0.267949	−	0.464102i	−0.0144890	−	0.0250957i
$343$		−	1.00000i		−	0.0539949i
$344$	−2.13397	+	1.23205i	−0.115056	+	0.0664277i
$345$	6.80385	−	3.92820i	0.366307	−	0.211487i
$346$		−	14.9282i		−	0.802545i
$347$	14.8564	+	25.7321i	0.797534	+	1.38137i	0.921218	+	0.389047i	$0.127196\pi$
$347$	14.8564	+	25.7321i	0.797534	+	1.38137i	−0.123684	+	0.992322i	$0.539471\pi$
$348$	4.00000	−	6.92820i	0.214423	−	0.371391i
$349$	−29.1340	−	16.8205i	−1.55951	−	0.900381i	−0.997304	−	0.0733812i	$-0.976621\pi$
$349$	−29.1340	−	16.8205i	−1.55951	−	0.900381i	−0.562202	−	0.827000i	$-0.690046\pi$
$350$	7.00000			0.374166
$351$	−2.59808	+	2.50000i	−0.138675	+	0.133440i
$352$	−4.00000			−0.213201
$353$	−23.0885	−	13.3301i	−1.22887	−	0.709491i	−0.262080	−	0.965046i	$-0.584408\pi$
$353$	−23.0885	−	13.3301i	−1.22887	−	0.709491i	−0.966795	+	0.255555i	$0.917742\pi$
$354$	4.86603	−	8.42820i	0.258626	−	0.447954i
$355$	−20.6603	−	35.7846i	−1.09653	−	1.89925i
$356$			8.26795i			0.438200i
$357$	0.401924	−	0.232051i	0.0212721	−	0.0122814i
$358$	2.66025	−	1.53590i	0.140599	−	0.0811748i
$359$		−	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
$361$	−9.35641	+	16.2058i	−0.492442	+	0.852935i
$362$	−14.5359	−	8.39230i	−0.763990	−	0.441090i
$363$	−5.00000			−0.262432
$364$	−3.50000	+	0.866025i	−0.183450	+	0.0453921i
$365$	10.1436			0.530940
$366$	−4.50000	−	2.59808i	−0.235219	−	0.135804i
$367$	−2.52628	+	4.37564i	−0.131871	+	0.228407i	−0.924398	−	0.381430i	$-0.875432\pi$
$367$	−2.52628	+	4.37564i	−0.131871	+	0.228407i	0.792527	+	0.609837i	$0.208765\pi$
$368$	1.13397	+	1.96410i	0.0591125	+	0.102386i
$369$			6.92820i			0.360668i
$370$	26.7846	−	15.4641i	1.39247	−	0.803940i
$371$	−10.1603	+	5.86603i	−0.527494	+	0.304549i
$372$			0.464102i			0.0240625i
$373$	−11.1244	−	19.2679i	−0.575997	−	0.997657i	−0.995932	−	0.0901025i	$-0.971281\pi$
$373$	−11.1244	−	19.2679i	−0.575997	−	0.997657i	0.419935	−	0.907554i	$-0.362053\pi$
$374$	0.928203	−	1.60770i	0.0479962	−	0.0831319i
$375$	−6.00000	−	3.46410i	−0.309839	−	0.178885i
$376$	−7.46410			−0.384932
$377$	−6.92820	−	28.0000i	−0.356821	−	1.44207i
$378$	−1.00000			−0.0514344
$379$	26.3205	+	15.1962i	1.35199	+	0.780574i	0.988529	−	0.151034i	$-0.0482603\pi$
$379$	26.3205	+	15.1962i	1.35199	+	0.780574i	0.363465	+	0.931608i	$0.381594\pi$
$380$	−0.928203	+	1.60770i	−0.0476158	+	0.0824730i
$381$	9.46410	+	16.3923i	0.484861	+	0.839803i
$382$			18.5167i			0.947395i
$383$	23.6603	−	13.6603i	1.20898	−	0.698006i	0.246445	−	0.969157i	$-0.420737\pi$
$383$	23.6603	−	13.6603i	1.20898	−	0.698006i	0.962537	+	0.271150i	$0.0874040\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$			13.8564i			0.706188i
$386$	−4.92820	−	8.53590i	−0.250839	−	0.434466i
$387$	−1.23205	+	2.13397i	−0.0626287	+	0.108476i
$388$	7.26795	+	4.19615i	0.368974	+	0.213027i
$389$	−2.66025			−0.134880			−0.0674401	−	0.997723i	$-0.521483\pi$
$389$	−2.66025			−0.134880			−0.0674401	+	0.997723i	$0.521483\pi$
$390$	12.0000	+	3.46410i	0.607644	+	0.175412i
$391$	−1.05256			−0.0532302
$392$	−0.866025	−	0.500000i	−0.0437409	−	0.0252538i
$393$	−9.50000	+	16.4545i	−0.479212	+	0.830019i
$394$	11.6962	+	20.2583i	0.589244	+	1.02060i
$395$			8.78461i			0.442002i
$396$	−3.46410	+	2.00000i	−0.174078	+	0.100504i
$397$	−10.2058	+	5.89230i	−0.512213	+	0.295726i	−0.733743	−	0.679427i	$-0.762228\pi$
$397$	−10.2058	+	5.89230i	−0.512213	+	0.295726i	0.221530	+	0.975154i	$0.428895\pi$
$398$		−	2.12436i		−	0.106484i
$399$	−0.267949	−	0.464102i	−0.0134142	−	0.0232341i
$400$	3.50000	−	6.06218i	0.175000	−	0.303109i
$401$	−3.80385	−	2.19615i	−0.189955	−	0.109671i	0.402006	−	0.915637i	$-0.368313\pi$
$401$	−3.80385	−	2.19615i	−0.189955	−	0.109671i	−0.591962	+	0.805966i	$0.701646\pi$
$402$	3.19615			0.159410
$403$	1.16025	+	1.20577i	0.0577964	+	0.0600637i
$404$		0			0
$405$	3.00000	+	1.73205i	0.149071	+	0.0860663i
$406$	4.00000	−	6.92820i	0.198517	−	0.343841i
$407$	17.8564	+	30.9282i	0.885109	+	1.53305i
$408$		−	0.464102i		−	0.0229765i
$409$	12.4641	−	7.19615i	0.616310	−	0.355827i	−0.159121	−	0.987259i	$-0.550866\pi$
$409$	12.4641	−	7.19615i	0.616310	−	0.355827i	0.775431	+	0.631432i	$0.217533\pi$
$410$	20.7846	−	12.0000i	1.02648	−	0.592638i
$411$		−	13.8564i		−	0.683486i
$412$	3.33013	+	5.76795i	0.164064	+	0.284166i
$413$	4.86603	−	8.42820i	0.239441	−	0.414725i
$414$	1.96410	+	1.13397i	0.0965303	+	0.0557318i
$415$	6.00000			0.294528
$416$	−1.00000	+	3.46410i	−0.0490290	+	0.169842i
$417$	−10.9282			−0.535156
$418$	−1.85641	−	1.07180i	−0.0907998	−	0.0524233i
$419$	2.50000	−	4.33013i	0.122133	−	0.211541i	−0.798476	−	0.602027i	$-0.794360\pi$
$419$	2.50000	−	4.33013i	0.122133	−	0.211541i	0.920609	+	0.390487i	$0.127693\pi$
$420$	1.73205	+	3.00000i	0.0845154	+	0.146385i
$421$			22.3923i			1.09133i	0.838002	+	0.545667i	$0.183724\pi$
$421$			22.3923i			1.09133i	−0.838002	+	0.545667i	$0.816276\pi$
$422$	−19.8564	+	11.4641i	−0.966595	+	0.558064i
$423$	−6.46410	+	3.73205i	−0.314295	+	0.181459i
$424$			11.7321i			0.569759i
$425$	1.62436	+	2.81347i	0.0787928	+	0.136473i
$426$	5.96410	−	10.3301i	0.288962	−	0.500496i
$427$	−4.50000	−	2.59808i	−0.217770	−	0.125730i
$428$	−15.4641			−0.747486
$429$	−4.00000	+	13.8564i	−0.193122	+	0.668994i
$430$	8.53590			0.411638
$431$	19.7942	+	11.4282i	0.953454	+	0.550477i	0.894152	−	0.447763i	$-0.147779\pi$
$431$	19.7942	+	11.4282i	0.953454	+	0.550477i	0.0593021	+	0.998240i	$0.481112\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−8.92820	−	15.4641i	−0.429062	−	0.743157i	0.567728	−	0.823216i	$-0.307823\pi$
$433$	−8.92820	−	15.4641i	−0.429062	−	0.743157i	−0.996790	+	0.0800589i	$0.974489\pi$
$434$			0.464102i			0.0222776i
$435$	−24.0000	+	13.8564i	−1.15071	+	0.664364i
$436$	−10.3923	+	6.00000i	−0.497701	+	0.287348i
$437$			1.21539i			0.0581400i
$438$	1.46410	+	2.53590i	0.0699575	+	0.121170i
$439$	−17.1962	+	29.7846i	−0.820728	+	1.42154i	0.0844136	+	0.996431i	$0.473098\pi$
$439$	−17.1962	+	29.7846i	−0.820728	+	1.42154i	−0.905141	+	0.425111i	$0.860235\pi$
$440$	12.0000	+	6.92820i	0.572078	+	0.330289i
$441$	−1.00000			−0.0476190
$442$	−1.16025	−	1.20577i	−0.0551877	−	0.0573527i
$443$	−1.60770			−0.0763839			−0.0381920	−	0.999270i	$-0.512160\pi$
$443$	−1.60770			−0.0763839			−0.0381920	+	0.999270i	$0.512160\pi$
$444$	7.73205	+	4.46410i	0.366947	+	0.211857i
$445$	14.3205	−	24.8038i	0.678857	−	1.17582i
$446$	−7.23205	−	12.5263i	−0.342448	−	0.593137i
$447$			18.4641i			0.873322i
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	−15.5885	+	9.00000i	−0.735665	+	0.424736i	−0.820491	−	0.571660i	$-0.806300\pi$
$449$	−15.5885	+	9.00000i	−0.735665	+	0.424736i	0.0848262	+	0.996396i	$0.472967\pi$
$450$		−	7.00000i		−	0.329983i
$451$	13.8564	+	24.0000i	0.652473	+	1.13012i
$452$	8.19615	−	14.1962i	0.385515	−	0.667731i
$453$	10.3923	+	6.00000i	0.488273	+	0.281905i
$454$	21.3205			1.00062
$455$	12.0000	+	3.46410i	0.562569	+	0.162400i
$456$	−0.535898			−0.0250957
$457$	7.96410	+	4.59808i	0.372545	+	0.215089i	0.674570	−	0.738211i	$-0.264329\pi$
$457$	7.96410	+	4.59808i	0.372545	+	0.215089i	−0.302025	+	0.953300i	$0.597663\pi$
$458$	3.03590	−	5.25833i	0.141858	−	0.245706i
$459$	−0.232051	−	0.401924i	−0.0108312	−	0.0187602i
$460$		−	7.85641i		−	0.366307i
$461$	16.3923	−	9.46410i	0.763466	−	0.440787i	−0.0670730	−	0.997748i	$-0.521366\pi$
$461$	16.3923	−	9.46410i	0.763466	−	0.440787i	0.830539	+	0.556961i	$0.188033\pi$
$462$	−3.46410	+	2.00000i	−0.161165	+	0.0930484i
$463$		−	40.2487i		−	1.87052i	−0.353966	−	0.935258i	$-0.615167\pi$
$463$		−	40.2487i		−	1.87052i	0.353966	−	0.935258i	$-0.384833\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$	0.803848	−	1.39230i	0.0372775	−	0.0645666i
$466$	5.66025	+	3.26795i	0.262206	+	0.151385i
$467$	−29.6410			−1.37162			−0.685811	−	0.727779i	$-0.740552\pi$
$467$	−29.6410			−1.37162			−0.685811	+	0.727779i	$0.740552\pi$
$468$	0.866025	+	3.50000i	0.0400320	+	0.161788i
$469$	3.19615			0.147585
$470$	22.3923	+	12.9282i	1.03288	+	0.596334i
$471$	−5.46410	+	9.46410i	−0.251773	+	0.436083i
$472$	−4.86603	−	8.42820i	−0.223977	−	0.387939i
$473$			9.85641i			0.453198i
$474$	−2.19615	+	1.26795i	−0.100873	+	0.0582388i
$475$	3.24871	−	1.87564i	0.149061	−	0.0860605i
$476$		−	0.464102i		−	0.0212721i
$477$	5.86603	+	10.1603i	0.268587	+	0.465206i
$478$	7.42820	−	12.8660i	0.339758	−	0.588478i
$479$	−14.1962	−	8.19615i	−0.648639	−	0.374492i	0.139296	−	0.990251i	$-0.455516\pi$
$479$	−14.1962	−	8.19615i	−0.648639	−	0.374492i	−0.787935	+	0.615759i	$0.788849\pi$
$480$	3.46410			0.158114
$481$	31.2487	−	7.73205i	1.42482	−	0.352551i
$482$	−11.8564			−0.540045
$483$	1.96410	+	1.13397i	0.0893697	+	0.0515976i
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	−14.5359	−	25.1769i	−0.660041	−	1.14322i
$486$			1.00000i			0.0453609i
$487$	17.6603	−	10.1962i	0.800262	−	0.462032i	−0.0433004	−	0.999062i	$-0.513787\pi$
$487$	17.6603	−	10.1962i	0.800262	−	0.462032i	0.843563	+	0.537030i	$0.180454\pi$
$488$	−4.50000	+	2.59808i	−0.203705	+	0.117609i
$489$		−	18.6603i		−	0.843846i
$490$	1.73205	+	3.00000i	0.0782461	+	0.135526i
$491$	8.92820	−	15.4641i	0.402924	−	0.697885i	−0.591153	−	0.806559i	$-0.701327\pi$
$491$	8.92820	−	15.4641i	0.402924	−	0.697885i	0.994077	+	0.108674i	$0.0346605\pi$
$492$	6.00000	+	3.46410i	0.270501	+	0.156174i
$493$	3.71281			0.167217
$494$	−1.39230	+	1.33975i	−0.0626428	+	0.0602780i
$495$	13.8564			0.622799
$496$	0.401924	+	0.232051i	0.0180469	+	0.0104194i
$497$	5.96410	−	10.3301i	0.267527	−	0.463370i
$498$	0.866025	+	1.50000i	0.0388075	+	0.0672166i
$499$			3.73205i			0.167070i	0.996505	+	0.0835348i	$0.0266210\pi$
$499$			3.73205i			0.167070i	−0.996505	+	0.0835348i	$0.973379\pi$
$500$	−6.00000	+	3.46410i	−0.268328	+	0.154919i
$501$	17.3205	−	10.0000i	0.773823	−	0.446767i
$502$			23.9282i			1.06797i
$503$	−3.46410	−	6.00000i	−0.154457	−	0.267527i	0.778404	−	0.627763i	$-0.216029\pi$
$503$	−3.46410	−	6.00000i	−0.154457	−	0.267527i	−0.932861	+	0.360236i	$0.882696\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$		0			0
$506$	9.07180			0.403291
$507$	11.0000	+	6.92820i	0.488527	+	0.307692i
$508$	18.9282			0.839803
$509$	−12.3397	−	7.12436i	−0.546950	−	0.315782i	0.200941	−	0.979603i	$-0.435600\pi$
$509$	−12.3397	−	7.12436i	−0.546950	−	0.315782i	−0.747891	+	0.663822i	$0.768933\pi$
$510$	−0.803848	+	1.39230i	−0.0355950	+	0.0616523i
$511$	1.46410	+	2.53590i	0.0647680	+	0.112182i
$512$			1.00000i			0.0441942i
$513$	−0.464102	+	0.267949i	−0.0204906	+	0.0118302i
$514$	5.59808	−	3.23205i	0.246921	−	0.142560i
$515$		−	23.0718i		−	1.01666i
$516$	1.23205	+	2.13397i	0.0542380	+	0.0939430i
$517$	−14.9282	+	25.8564i	−0.656542	+	1.13716i
$518$	7.73205	+	4.46410i	0.339727	+	0.196141i
$519$	−14.9282			−0.655275
$520$	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
$523$	−0.535898	+	0.928203i	−0.0234332	+	0.0405875i	−0.877504	−	0.479569i	$-0.840793\pi$
$523$	−0.535898	+	0.928203i	−0.0234332	+	0.0405875i	0.854071	+	0.520156i	$0.174126\pi$
$524$	9.50000	+	16.4545i	0.415009	+	0.718817i
$525$		−	7.00000i		−	0.305505i
$526$	15.0000	−	8.66025i	0.654031	−	0.377605i
$527$	−0.186533	+	0.107695i	−0.00812553	+	0.00469127i
$528$			4.00000i			0.174078i
$529$	8.92820	+	15.4641i	0.388183	+	0.672352i
$530$	20.3205	−	35.1962i	0.882666	−	1.52882i
$531$	−8.42820	−	4.86603i	−0.365753	−	0.211168i
$532$	−0.535898			−0.0232341
$533$	24.2487	−	6.00000i	1.05033	−	0.259889i
$534$	8.26795			0.357789
$535$	46.3923	+	26.7846i	2.00571	+	1.15800i
$536$	1.59808	−	2.76795i	0.0690264	−	0.119557i
$537$	−1.53590	−	2.66025i	−0.0662789	−	0.114798i
$538$			1.60770i			0.0693127i
$539$	−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	$0.121442\pi$
$541$			17.3205i			0.744667i	−0.928099	+	0.372333i	$0.878558\pi$
$542$	2.76795	+	4.79423i	0.118894	+	0.205930i
$543$	−8.39230	+	14.5359i	−0.360148	+	0.623795i
$544$	−0.401924	−	0.232051i	−0.0172323	−	0.00994910i
$545$	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
$551$		−	4.28719i		−	0.182640i
$552$	1.96410	−	1.13397i	0.0835977	−	0.0482652i
$553$	−2.19615	+	1.26795i	−0.0933899	+	0.0539187i
$554$			27.3205i			1.16074i
$555$	−15.4641	−	26.7846i	−0.656415	−	1.13694i
$556$	−5.46410	+	9.46410i	−0.231730	+	0.401367i
$557$	−39.3109	−	22.6962i	−1.66566	−	0.961667i	−0.969938	−	0.243351i	$-0.921753\pi$
$557$	−39.3109	−	22.6962i	−1.66566	−	0.961667i	−0.695718	−	0.718315i	$-0.744914\pi$
$558$	0.464102			0.0196470
$559$	8.53590	+	2.46410i	0.361030	+	0.104220i
$560$	3.46410			0.146385
$561$	−1.60770	−	0.928203i	−0.0678769	−	0.0391888i
$562$	9.19615	−	15.9282i	0.387916	−	0.671891i
$563$	6.92820	+	12.0000i	0.291989	+	0.505740i	0.974280	−	0.225341i	$-0.0723496\pi$
$563$	6.92820	+	12.0000i	0.291989	+	0.505740i	−0.682291	+	0.731081i	$0.739016\pi$
$564$			7.46410i			0.314295i
$565$	−49.1769	+	28.3923i	−2.06889	+	1.19447i
$566$	3.92820	−	2.26795i	0.165115	−	0.0953290i
$567$			1.00000i			0.0419961i
$568$	−5.96410	−	10.3301i	−0.250248	−	0.433443i
$569$	4.26795	−	7.39230i	0.178922	−	0.309902i	−0.762590	−	0.646882i	$-0.776072\pi$
$569$	4.26795	−	7.39230i	0.178922	−	0.309902i	0.941511	+	0.336981i	$0.109406\pi$
$570$	1.60770	+	0.928203i	0.0673389	+	0.0388782i
$571$	−17.3923			−0.727845			−0.363923	−	0.931429i	$-0.618563\pi$
$571$	−17.3923			−0.727845			−0.363923	+	0.931429i	$0.618563\pi$
$572$	10.0000	+	10.3923i	0.418121	+	0.434524i
$573$	18.5167			0.773545
$574$	6.00000	+	3.46410i	0.250435	+	0.144589i
$575$	−7.93782	+	13.7487i	−0.331030	+	0.573361i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	42.7846i		−	1.78115i	−0.454840	−	0.890573i	$-0.650303\pi$
$577$		−	42.7846i		−	1.78115i	0.454840	−	0.890573i	$-0.349697\pi$
$578$	−14.5359	+	8.39230i	−0.604614	+	0.349074i
$579$	−8.53590	+	4.92820i	−0.354740	+	0.204809i
$580$			27.7128i			1.15071i
$581$	0.866025	+	1.50000i	0.0359288	+	0.0622305i
$582$	4.19615	−	7.26795i	0.173936	−	0.301266i
$583$	40.6410	+	23.4641i	1.68318	+	0.971784i
$584$	2.92820			0.121170
$585$	3.46410	−	12.0000i	0.143223	−	0.496139i
$586$	−26.5359			−1.09619
$587$	13.9641	+	8.06218i	0.576360	+	0.332762i	0.759686	−	0.650291i	$-0.225353\pi$
$587$	13.9641	+	8.06218i	0.576360	+	0.332762i	−0.183325	+	0.983052i	$0.558686\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	0.124356	+	0.215390i	0.00512399	+	0.00887500i
$590$			33.7128i			1.38793i
$591$	20.2583	−	11.6962i	0.833316	−	0.481115i
$592$	7.73205	−	4.46410i	0.317785	−	0.183473i
$593$			7.73205i			0.317517i	0.987317	+	0.158759i	$0.0507492\pi$
$593$			7.73205i			0.317517i	−0.987317	+	0.158759i	$0.949251\pi$
$594$	2.00000	+	3.46410i	0.0820610	+	0.142134i
$595$	−0.803848	+	1.39230i	−0.0329545	+	0.0570789i
$596$	15.9904	+	9.23205i	0.654992	+	0.378160i
$597$	−2.12436			−0.0869441
$598$	2.26795	−	7.85641i	0.0927433	−	0.321272i
$599$	19.0526			0.778466			0.389233	−	0.921139i	$-0.372740\pi$
$599$	19.0526			0.778466			0.389233	+	0.921139i	$0.372740\pi$
$600$	−6.06218	−	3.50000i	−0.247487	−	0.142887i
$601$	−12.1244	+	21.0000i	−0.494563	+	0.856608i	−0.999980	−	0.00626702i	$-0.998005\pi$
$601$	−12.1244	+	21.0000i	−0.494563	+	0.856608i	0.505418	+	0.862875i	$0.331338\pi$
$602$	1.23205	+	2.13397i	0.0502146	+	0.0869743i
$603$		−	3.19615i		−	0.130157i
$604$	10.3923	−	6.00000i	0.422857	−	0.244137i
$605$	15.0000	−	8.66025i	0.609837	−	0.352089i
$606$		0			0
$607$	2.40192	+	4.16025i	0.0974911	+	0.168860i	0.910646	−	0.413188i	$-0.135585\pi$
$607$	2.40192	+	4.16025i	0.0974911	+	0.168860i	−0.813154	+	0.582048i	$0.802252\pi$
$608$	−0.267949	+	0.464102i	−0.0108668	+	0.0188218i
$609$	−6.92820	−	4.00000i	−0.280745	−	0.162088i
$610$	18.0000			0.728799
$611$	18.6603	+	19.3923i	0.754913	+	0.784529i
$612$	−0.464102			−0.0187602
$613$	−11.7846	−	6.80385i	−0.475976	−	0.274805i	0.242762	−	0.970086i	$-0.421947\pi$
$613$	−11.7846	−	6.80385i	−0.475976	−	0.274805i	−0.718738	+	0.695281i	$0.755280\pi$
$614$	−11.0000	+	19.0526i	−0.443924	+	0.768899i
$615$	−12.0000	−	20.7846i	−0.483887	−	0.838116i
$616$			4.00000i			0.161165i
$617$	−18.9282	+	10.9282i	−0.762021	+	0.439953i	−0.830021	−	0.557732i	$-0.811672\pi$
$617$	−18.9282	+	10.9282i	−0.762021	+	0.439953i	0.0680000	+	0.997685i	$0.478338\pi$
$618$	5.76795	−	3.33013i	0.232021	−	0.133957i
$619$		−	10.7846i		−	0.433470i	−0.976230	−	0.216735i	$-0.930459\pi$
$619$		−	10.7846i		−	0.433470i	0.976230	−	0.216735i	$-0.0695408\pi$
$620$	−0.803848	−	1.39230i	−0.0322833	−	0.0559163i
$621$	1.13397	−	1.96410i	0.0455048	−	0.0788167i
$622$	−18.4641	−	10.6603i	−0.740343	−	0.427437i
$623$	8.26795			0.331248
$624$	3.46410	+	1.00000i	0.138675	+	0.0400320i
$625$	−11.0000			−0.440000
$626$	−30.5885	−	17.6603i	−1.22256	−	0.705846i
$627$	−1.07180	+	1.85641i	−0.0428034	+	0.0741377i
$628$	5.46410	+	9.46410i	0.218041	+	0.377659i
$629$			4.14359i			0.165216i
$630$	3.00000	−	1.73205i	0.119523	−	0.0690066i
$631$	−18.2487	+	10.5359i	−0.726470	+	0.419427i	−0.817129	−	0.576454i	$-0.804436\pi$
$631$	−18.2487	+	10.5359i	−0.726470	+	0.419427i	0.0906596	+	0.995882i	$0.471102\pi$
$632$			2.53590i			0.100873i
$633$	11.4641	+	19.8564i	0.455657	+	0.789221i
$634$	−4.76795	+	8.25833i	−0.189359	+	0.327980i
$635$	−56.7846	−	32.7846i	−2.25343	−	1.30102i
$636$	11.7321			0.465206
$637$	0.866025	+	3.50000i	0.0343132	+	0.138675i
$638$	−32.0000			−1.26689
$639$	−10.3301	−	5.96410i	−0.408654	−	0.235936i
$640$	1.73205	−	3.00000i	0.0684653	−	0.118585i
$641$	21.3205	+	36.9282i	0.842109	+	1.45858i	0.888108	+	0.459635i	$0.152020\pi$
$641$	21.3205	+	36.9282i	0.842109	+	1.45858i	−0.0459986	+	0.998942i	$0.514647\pi$
$642$			15.4641i			0.610319i
$643$	−24.4641	+	14.1244i	−0.964770	+	0.557010i	−0.897638	−	0.440734i	$-0.854718\pi$
$643$	−24.4641	+	14.1244i	−0.964770	+	0.557010i	−0.0671322	+	0.997744i	$0.521385\pi$
$644$	1.96410	−	1.13397i	0.0773964	−	0.0446849i
$645$		−	8.53590i		−	0.336101i
$646$	−0.124356	−	0.215390i	−0.00489271	−	0.00847442i
$647$	1.33975	−	2.32051i	0.0526708	−	0.0912286i	−0.838488	−	0.544920i	$-0.816560\pi$
$647$	1.33975	−	2.32051i	0.0526708	−	0.0912286i	0.891159	+	0.453692i	$0.149893\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	−38.9282			−1.52807
$650$	−24.5000	+	6.06218i	−0.960969	+	0.237778i
$651$	0.464102			0.0181896
$652$	−16.1603	−	9.33013i	−0.632884	−	0.365396i
$653$	3.20577	−	5.55256i	0.125452	−	0.217288i	−0.796458	−	0.604694i	$-0.793295\pi$
$653$	3.20577	−	5.55256i	0.125452	−	0.217288i	0.921909	+	0.387406i	$0.126629\pi$
$654$	6.00000	+	10.3923i	0.234619	+	0.406371i
$655$		−	65.8179i		−	2.57172i
$656$	6.00000	−	3.46410i	0.234261	−	0.135250i
$657$	2.53590	−	1.46410i	0.0989348	−	0.0571200i
$658$			7.46410i			0.290981i
$659$	−11.1962	−	19.3923i	−0.436140	−	0.755417i	0.561248	−	0.827648i	$-0.310321\pi$
$659$	−11.1962	−	19.3923i	−0.436140	−	0.755417i	−0.997388	+	0.0722309i	$0.976988\pi$
$660$	6.92820	−	12.0000i	0.269680	−	0.467099i
$661$	4.08142	+	2.35641i	0.158749	+	0.0916536i	0.577270	−	0.816553i	$-0.304118\pi$
$661$	4.08142	+	2.35641i	0.158749	+	0.0916536i	−0.418521	+	0.908207i	$0.637451\pi$
$662$	−13.3205			−0.517716
$663$	−1.20577	+	1.16025i	−0.0468283	+	0.0450605i
$664$	1.73205			0.0672166
$665$	1.60770	+	0.928203i	0.0623437	+	0.0359942i
$666$	4.46410	−	7.73205i	0.172980	−	0.299611i
$667$	9.07180	+	15.7128i	0.351261	+	0.608403i
$668$		−	20.0000i		−	0.773823i
$669$	−12.5263	+	7.23205i	−0.484294	+	0.279607i
$670$	−9.58846	+	5.53590i	−0.370434	+	0.213870i
$671$			20.7846i			0.802381i
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	−14.8205	+	25.6699i	−0.571289	+	0.989501i	0.425145	+	0.905125i	$0.360223\pi$
$673$	−14.8205	+	25.6699i	−0.571289	+	0.989501i	−0.996434	+	0.0843758i	$0.973110\pi$
$674$	5.19615	+	3.00000i	0.200148	+	0.115556i
$675$	−7.00000			−0.269430
$676$	11.5000	−	6.06218i	0.442308	−	0.233161i
$677$	14.9282			0.573737			0.286869	−	0.957970i	$-0.407386\pi$
$677$	14.9282			0.573737			0.286869	+	0.957970i	$0.407386\pi$
$678$	−14.1962	−	8.19615i	−0.545200	−	0.314771i
$679$	4.19615	−	7.26795i	0.161034	−	0.278918i
$680$	0.803848	+	1.39230i	0.0308261	+	0.0533925i
$681$		−	21.3205i		−	0.817004i
$682$	1.60770	−	0.928203i	0.0615618	−	0.0355427i
$683$	9.67949	−	5.58846i	0.370375	−	0.213836i	−0.303247	−	0.952912i	$-0.598071\pi$
$683$	9.67949	−	5.58846i	0.370375	−	0.213836i	0.673622	+	0.739076i	$0.264737\pi$
$684$			0.535898i			0.0204906i
$685$	24.0000	+	41.5692i	0.916993	+	1.58828i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−5.25833	−	3.03590i	−0.200618	−	0.115827i
$688$	2.46410			0.0939430
$689$	30.4808	−	29.3301i	1.16122	−	1.11739i
$690$	−7.85641			−0.299088
$691$	−18.3397	−	10.5885i	−0.697677	−	0.402804i	0.108805	−	0.994063i	$-0.465298\pi$
$691$	−18.3397	−	10.5885i	−0.697677	−	0.402804i	−0.806482	+	0.591259i	$0.798631\pi$
$692$	−7.46410	+	12.9282i	−0.283743	+	0.491457i
$693$	2.00000	+	3.46410i	0.0759737	+	0.131590i
$694$		−	29.7128i		−	1.12788i
$695$	32.7846	−	18.9282i	1.24359	−	0.717988i
$696$	−6.92820	+	4.00000i	−0.262613	+	0.151620i
$697$			3.21539i			0.121792i
$698$	16.8205	+	29.1340i	0.636666	+	1.10274i
$699$	3.26795	−	5.66025i	0.123605	−	0.214090i
$700$	−6.06218	−	3.50000i	−0.229129	−	0.132288i
$701$	−22.1244			−0.835625			−0.417813	−	0.908533i	$-0.637203\pi$
$701$	−22.1244			−0.835625			−0.417813	+	0.908533i	$0.637203\pi$
$702$	3.50000	−	0.866025i	0.132099	−	0.0326860i
$703$	4.78461			0.180455
$704$	3.46410	+	2.00000i	0.130558	+	0.0753778i
$705$	12.9282	−	22.3923i	0.486904	−	0.843343i
$706$	13.3301	+	23.0885i	0.501686	+	0.868946i
$707$		0			0
$708$	−8.42820	+	4.86603i	−0.316751	+	0.182876i
$709$	−41.3205	+	23.8564i	−1.55182	+	0.895946i	−0.553831	+	0.832629i	$0.686835\pi$
$709$	−41.3205	+	23.8564i	−1.55182	+	0.895946i	−0.997993	+	0.0633169i	$0.979832\pi$
$710$			41.3205i			1.55073i
$711$	1.26795	+	2.19615i	0.0475518	+	0.0823622i
$712$	4.13397	−	7.16025i	0.154927	−	0.268342i
$713$	−0.911543	−	0.526279i	−0.0341375	−	0.0197093i
$714$	−0.464102			−0.0173686
$715$	−12.0000	−	48.4974i	−0.448775	−	1.81370i
$716$	−3.07180			−0.114798
$717$	−12.8660	−	7.42820i	−0.480491	−	0.277411i
$718$	−4.00000	+	6.92820i	−0.149279	+	0.258558i
$719$	20.7321	+	35.9090i	0.773175	+	1.33918i	0.935814	+	0.352493i	$0.114666\pi$
$719$	20.7321	+	35.9090i	0.773175	+	1.33918i	−0.162639	+	0.986686i	$0.552001\pi$
$720$		−	3.46410i		−	0.129099i
$721$	5.76795	−	3.33013i	0.214810	−	0.124020i
$722$	16.2058	−	9.35641i	0.603116	−	0.348209i
$723$			11.8564i			0.440945i
$724$	8.39230	+	14.5359i	0.311898	+	0.540222i
$725$	28.0000	−	48.4974i	1.03989	−	1.80115i
$726$	4.33013	+	2.50000i	0.160706	+	0.0927837i
$727$	−42.9090			−1.59141			−0.795703	−	0.605687i	$-0.792898\pi$
$727$	−42.9090			−1.59141			−0.795703	+	0.605687i	$0.792898\pi$
$728$	3.46410	+	1.00000i	0.128388	+	0.0370625i
$729$	1.00000			0.0370370
$730$	−8.78461	−	5.07180i	−0.325133	−	0.187716i
$731$	−0.571797	+	0.990381i	−0.0211487	+	0.0366306i
$732$	2.59808	+	4.50000i	0.0960277	+	0.166325i
$733$			22.8564i			0.844221i	0.906544	+	0.422110i	$0.138711\pi$
$733$			22.8564i			0.844221i	−0.906544	+	0.422110i	$0.861289\pi$
$734$	4.37564	−	2.52628i	0.161508	−	0.0932467i
$735$	3.00000	−	1.73205i	0.110657	−	0.0638877i
$736$		−	2.26795i		−	0.0835977i
$737$	−6.39230	−	11.0718i	−0.235464	−	0.407835i
$738$	3.46410	−	6.00000i	0.127515	−	0.220863i
$739$	−3.69615	−	2.13397i	−0.135965	−	0.0784995i	0.430474	−	0.902603i	$-0.358346\pi$
$739$	−3.69615	−	2.13397i	−0.135965	−	0.0784995i	−0.566440	+	0.824103i	$0.691680\pi$
$740$	−30.9282			−1.13694
$741$	1.33975	+	1.39230i	0.0492168	+	0.0511476i
$742$	11.7321			0.430697
$743$	34.4545	+	19.8923i	1.26401	+	0.729778i	0.973848	−	0.227199i	$-0.0729568\pi$
$743$	34.4545	+	19.8923i	1.26401	+	0.729778i	0.290164	+	0.956977i	$0.406290\pi$
$744$	0.232051	−	0.401924i	0.00850740	−	0.0147352i
$745$	−31.9808	−	55.3923i	−1.17168	−	2.02942i
$746$			22.2487i			0.814583i
$747$	1.50000	−	0.866025i	0.0548821	−	0.0316862i
$748$	−1.60770	+	0.928203i	−0.0587832	+	0.0339385i
$749$			15.4641i			0.565046i
$750$	3.46410	+	6.00000i	0.126491	+	0.219089i
$751$	−2.66025	+	4.60770i	−0.0970740	+	0.168137i	−0.910472	−	0.413570i	$-0.864282\pi$
$751$	−2.66025	+	4.60770i	−0.0970740	+	0.168137i	0.813398	+	0.581707i	$0.197615\pi$
$752$	6.46410	+	3.73205i	0.235722	+	0.136094i
$753$	23.9282			0.871992
$754$	−8.00000	+	27.7128i	−0.291343	+	1.00924i
$755$	−41.5692			−1.51286
$756$	0.866025	+	0.500000i	0.0314970	+	0.0181848i
$757$	3.92820	−	6.80385i	0.142773	−	0.247290i	−0.785767	−	0.618523i	$-0.787731\pi$
$757$	3.92820	−	6.80385i	0.142773	−	0.247290i	0.928540	+	0.371233i	$0.121065\pi$
$758$	−15.1962	−	26.3205i	−0.551949	−	0.956004i
$759$		−	9.07180i		−	0.329285i
$760$	1.60770	−	0.928203i	0.0583172	−	0.0336695i
$761$	6.00000	−	3.46410i	0.217500	−	0.125574i	−0.387292	−	0.921957i	$-0.626590\pi$
$761$	6.00000	−	3.46410i	0.217500	−	0.125574i	0.604792	+	0.796383i	$0.293256\pi$
$762$		−	18.9282i		−	0.685696i
$763$	6.00000	+	10.3923i	0.217215	+	0.376227i
$764$	9.25833	−	16.0359i	0.334955	−	0.580158i
$765$	1.39230	+	0.803848i	0.0503389	+	0.0290632i
$766$	−27.3205			−0.987130
$767$	−9.73205	+	33.7128i	−0.351404	+	1.21730i
$768$	1.00000			0.0360844
$769$	23.0718	+	13.3205i	0.831990	+	0.480350i	0.854534	−	0.519396i	$-0.173843\pi$
$769$	23.0718	+	13.3205i	0.831990	+	0.480350i	−0.0225434	+	0.999746i	$0.507176\pi$
$770$	6.92820	−	12.0000i	0.249675	−	0.432450i

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} +(-0.232051 - 0.401924i) q^{17} +1.00000i q^{18} +(-0.464102 + 0.267949i) q^{19} +(3.00000 - 1.73205i) q^{20} +1.00000i q^{21} +(2.00000 + 3.46410i) q^{22} +(1.13397 - 1.96410i) 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} -0.464102i q^{31} +(0.866025 - 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} +0.464102i q^{34} +(-1.73205 - 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-7.73205 - 4.46410i) q^{37} +0.535898 q^{38} +(-0.866025 - 3.50000i) q^{39} -3.46410 q^{40} +(-6.00000 - 3.46410i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-1.23205 - 2.13397i) q^{43} -4.00000i q^{44} +(-3.00000 + 1.73205i) q^{45} +(-1.96410 + 1.13397i) q^{46} -7.46410i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(6.06218 + 3.50000i) q^{50} +0.464102 q^{51} +(-3.46410 - 1.00000i) q^{52} -11.7321 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-6.92820 + 12.0000i) q^{55} +(-0.500000 - 0.866025i) q^{56} -0.535898i q^{57} +(6.92820 - 4.00000i) q^{58} +(8.42820 - 4.86603i) q^{59} +3.46410i q^{60} +(-2.59808 - 4.50000i) q^{61} +(-0.232051 + 0.401924i) q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(8.66025 + 9.00000i) q^{65} -4.00000 q^{66} +(2.76795 + 1.59808i) q^{67} +(0.232051 - 0.401924i) q^{68} +(1.13397 + 1.96410i) q^{69} +3.46410i q^{70} +(10.3301 - 5.96410i) q^{71} +(-0.866025 + 0.500000i) q^{72} +2.92820i q^{73} +(4.46410 + 7.73205i) q^{74} +(3.50000 - 6.06218i) q^{75} +(-0.464102 - 0.267949i) q^{76} -4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -2.53590 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} +(-1.39230 + 0.803848i) q^{85} +2.46410i q^{86} +(-4.00000 - 6.92820i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(7.16025 + 4.13397i) q^{89} +3.46410 q^{90} +(-1.00000 + 3.46410i) q^{91} +2.26795 q^{92} +(0.401924 + 0.232051i) q^{93} +(-3.73205 + 6.46410i) q^{94} +(0.928203 + 1.60770i) q^{95} +1.00000i q^{96} +(7.26795 - 4.19615i) 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

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