LMFDB - Embedded newform 546.2.s.b.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.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{10} +(4.50000 - 2.59808i) q^{11} -1.00000 q^{12} +(0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(0.633975 - 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.13397 + 1.96410i) q^{17} +1.00000i q^{18} +(-0.401924 - 0.232051i) q^{19} +(0.633975 + 0.366025i) q^{20} -1.00000i q^{21} +(2.59808 - 4.50000i) q^{22} +(-3.73205 - 6.46410i) q^{23} +(-0.866025 + 0.500000i) q^{24} +4.46410 q^{25} +(-1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(1.76795 + 3.06218i) q^{29} +(0.366025 - 0.633975i) q^{30} -3.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.50000 - 2.59808i) q^{33} +2.26795i q^{34} +(-0.366025 + 0.633975i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.83013 - 3.36603i) q^{37} -0.464102 q^{38} +(-3.46410 + 1.00000i) q^{39} +0.732051 q^{40} +(-7.33013 + 4.23205i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.36603 + 7.56218i) q^{43} -5.19615i q^{44} +(-0.633975 - 0.366025i) q^{45} +(-6.46410 - 3.73205i) q^{46} +3.92820i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +2.26795 q^{51} +(-2.59808 - 2.50000i) q^{52} -9.92820 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.90192 + 3.29423i) q^{55} +(0.500000 - 0.866025i) q^{56} +0.464102i q^{57} +(3.06218 + 1.76795i) q^{58} +(7.73205 + 4.46410i) q^{59} -0.732051i q^{60} +(-1.86603 + 3.23205i) q^{61} +(-1.63397 - 2.83013i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(2.56218 + 0.633975i) q^{65} -5.19615 q^{66} +(8.66025 - 5.00000i) q^{67} +(1.13397 + 1.96410i) q^{68} +(-3.73205 + 6.46410i) q^{69} +0.732051i q^{70} +(6.29423 + 3.63397i) q^{71} +(0.866025 + 0.500000i) q^{72} -1.46410i q^{73} +(3.36603 - 5.83013i) q^{74} +(-2.23205 - 3.86603i) q^{75} +(-0.401924 + 0.232051i) q^{76} +5.19615 q^{77} +(-2.50000 + 2.59808i) q^{78} +9.00000 q^{79} +(0.633975 - 0.366025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.23205 + 7.33013i) q^{82} +9.26795i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-1.43782 - 0.830127i) q^{85} +8.73205i q^{86} +(1.76795 - 3.06218i) q^{87} +(-2.59808 - 4.50000i) q^{88} +(-14.5981 + 8.42820i) q^{89} -0.732051 q^{90} +(2.50000 - 2.59808i) q^{91} -7.46410 q^{92} +(-2.83013 + 1.63397i) q^{93} +(1.96410 + 3.40192i) q^{94} +(0.169873 - 0.294229i) q^{95} +1.00000i q^{96} +(-12.2942 - 7.09808i) q^{97} +(0.866025 + 0.500000i) q^{98} +5.19615i 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} - 2 q^{10} + 18 q^{11} - 4 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{20} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 14 q^{29} - 2 q^{30} - 18 q^{33} + 2 q^{35} + 2 q^{36} + 6 q^{37} + 12 q^{38} - 4 q^{40} - 12 q^{41} - 2 q^{42} - 14 q^{43} - 6 q^{45} - 12 q^{46} - 2 q^{48} + 2 q^{49} + 12 q^{50} + 16 q^{51} - 12 q^{53} + 18 q^{55} + 2 q^{56} - 12 q^{58} + 24 q^{59} - 4 q^{61} - 10 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{68} - 8 q^{69} - 6 q^{71} + 10 q^{74} - 2 q^{75} - 12 q^{76} - 10 q^{78} + 36 q^{79} + 6 q^{80} - 2 q^{81} - 10 q^{82} - 30 q^{85} + 14 q^{87} - 48 q^{89} + 4 q^{90} + 10 q^{91} - 16 q^{92} + 6 q^{93} - 6 q^{94} + 18 q^{95} - 18 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 18 * q^11 - 4 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^20 - 8 * q^23 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 14 * q^29 - 2 * q^30 - 18 * q^33 + 2 * q^35 + 2 * q^36 + 6 * q^37 + 12 * q^38 - 4 * q^40 - 12 * q^41 - 2 * q^42 - 14 * q^43 - 6 * q^45 - 12 * q^46 - 2 * q^48 + 2 * q^49 + 12 * q^50 + 16 * q^51 - 12 * q^53 + 18 * q^55 + 2 * q^56 - 12 * q^58 + 24 * q^59 - 4 * q^61 - 10 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^68 - 8 * q^69 - 6 * q^71 + 10 * q^74 - 2 * q^75 - 12 * q^76 - 10 * q^78 + 36 * q^79 + 6 * q^80 - 2 * q^81 - 10 * q^82 - 30 * q^85 + 14 * q^87 - 48 * q^89 + 4 * q^90 + 10 * q^91 - 16 * q^92 + 6 * q^93 - 6 * q^94 + 18 * q^95 - 18 * 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
$5$			0.732051i			0.327383i	0.986512	+	0.163692i	$0.0523402\pi$
$5$			0.732051i			0.327383i	−0.986512	+	0.163692i	$0.947660\pi$
$6$	−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
$10$	0.366025	+	0.633975i	0.115747	+	0.200480i
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.367610	−	0.929980i	$-0.380176\pi$
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.989191	+	0.146631i	$0.0468429\pi$
$12$	−1.00000			−0.288675
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$	1.00000			0.267261
$15$	0.633975	−	0.366025i	0.163692	−	0.0945074i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.13397	+	1.96410i	−0.275029	+	0.476365i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$	−1.13397	+	1.96410i	−0.275029	+	0.476365i	0.695113	+	0.718900i	$0.255354\pi$
$18$			1.00000i			0.235702i
$19$	−0.401924	−	0.232051i	−0.0922076	−	0.0532361i	0.453187	−	0.891415i	$-0.350287\pi$
$19$	−0.401924	−	0.232051i	−0.0922076	−	0.0532361i	−0.545395	+	0.838179i	$0.683620\pi$
$20$	0.633975	+	0.366025i	0.141761	+	0.0818458i
$21$		−	1.00000i		−	0.218218i
$22$	2.59808	−	4.50000i	0.553912	−	0.959403i
$23$	−3.73205	−	6.46410i	−0.778186	−	1.34786i	−0.932986	−	0.359912i	$-0.882807\pi$
$23$	−3.73205	−	6.46410i	−0.778186	−	1.34786i	0.154800	−	0.987946i	$-0.450527\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	4.46410			0.892820
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$	1.00000			0.192450
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	1.76795	+	3.06218i	0.328300	+	0.568632i	0.982175	−	0.187971i	$-0.0601910\pi$
$29$	1.76795	+	3.06218i	0.328300	+	0.568632i	−0.653875	+	0.756603i	$0.726858\pi$
$30$	0.366025	−	0.633975i	0.0668268	−	0.115747i
$31$		−	3.26795i		−	0.586941i	−0.955968	−	0.293471i	$-0.905190\pi$
$31$		−	3.26795i		−	0.586941i	0.955968	−	0.293471i	$-0.0948102\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−4.50000	−	2.59808i	−0.783349	−	0.452267i
$34$			2.26795i			0.388950i
$35$	−0.366025	+	0.633975i	−0.0618696	+	0.107161i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	5.83013	−	3.36603i	0.958467	−	0.553371i	0.0627661	−	0.998028i	$-0.480008\pi$
$37$	5.83013	−	3.36603i	0.958467	−	0.553371i	0.895701	+	0.444657i	$0.146674\pi$
$38$	−0.464102			−0.0752872
$39$	−3.46410	+	1.00000i	−0.554700	+	0.160128i
$40$	0.732051			0.115747
$41$	−7.33013	+	4.23205i	−1.14477	+	0.660935i	−0.947608	−	0.319435i	$-0.896507\pi$
$41$	−7.33013	+	4.23205i	−1.14477	+	0.660935i	−0.197165	+	0.980370i	$0.563174\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−4.36603	+	7.56218i	−0.665813	+	1.15322i	0.313252	+	0.949670i	$0.398582\pi$
$43$	−4.36603	+	7.56218i	−0.665813	+	1.15322i	−0.979064	+	0.203551i	$0.934752\pi$
$44$		−	5.19615i		−	0.783349i
$45$	−0.633975	−	0.366025i	−0.0945074	−	0.0545638i
$46$	−6.46410	−	3.73205i	−0.953080	−	0.550261i
$47$			3.92820i			0.572987i	0.958082	+	0.286494i	$0.0924897\pi$
$47$			3.92820i			0.572987i	−0.958082	+	0.286494i	$0.907510\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.86603	−	2.23205i	0.546739	−	0.315660i
$51$	2.26795			0.317576
$52$	−2.59808	−	2.50000i	−0.360288	−	0.346688i
$53$	−9.92820			−1.36374			−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820			−1.36374			−0.681872	+	0.731472i	$0.738834\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	1.90192	+	3.29423i	0.256455	+	0.444194i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$			0.464102i			0.0614718i
$58$	3.06218	+	1.76795i	0.402084	+	0.232143i
$59$	7.73205	+	4.46410i	1.00663	+	0.581177i	0.910202	−	0.414164i	$-0.135926\pi$
$59$	7.73205	+	4.46410i	1.00663	+	0.581177i	0.0964249	+	0.995340i	$0.469259\pi$
$60$		−	0.732051i		−	0.0945074i
$61$	−1.86603	+	3.23205i	−0.238920	+	0.413822i	−0.960405	−	0.278609i	$-0.910127\pi$
$61$	−1.86603	+	3.23205i	−0.238920	+	0.413822i	0.721485	+	0.692430i	$0.243460\pi$
$62$	−1.63397	−	2.83013i	−0.207515	−	0.359426i
$63$	−0.866025	+	0.500000i	−0.109109	+	0.0629941i
$64$	−1.00000			−0.125000
$65$	2.56218	+	0.633975i	0.317799	+	0.0786349i
$66$	−5.19615			−0.639602
$67$	8.66025	−	5.00000i	1.05802	−	0.610847i	0.133135	−	0.991098i	$-0.457496\pi$
$67$	8.66025	−	5.00000i	1.05802	−	0.610847i	0.924883	+	0.380251i	$0.124162\pi$
$68$	1.13397	+	1.96410i	0.137515	+	0.238182i
$69$	−3.73205	+	6.46410i	−0.449286	+	0.778186i
$70$			0.732051i			0.0874968i
$71$	6.29423	+	3.63397i	0.746988	+	0.431273i	0.824604	−	0.565710i	$-0.191398\pi$
$71$	6.29423	+	3.63397i	0.746988	+	0.431273i	−0.0776169	+	0.996983i	$0.524731\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	1.46410i		−	0.171360i	−0.996323	−	0.0856801i	$-0.972694\pi$
$73$		−	1.46410i		−	0.171360i	0.996323	−	0.0856801i	$-0.0273063\pi$
$74$	3.36603	−	5.83013i	0.391293	−	0.677738i
$75$	−2.23205	−	3.86603i	−0.257735	−	0.446410i
$76$	−0.401924	+	0.232051i	−0.0461038	+	0.0266181i
$77$	5.19615			0.592157
$78$	−2.50000	+	2.59808i	−0.283069	+	0.294174i
$79$	9.00000			1.01258			0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000			1.01258			0.506290	+	0.862364i	$0.331017\pi$
$80$	0.633975	−	0.366025i	0.0708805	−	0.0409229i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.23205	+	7.33013i	−0.467352	+	0.809477i
$83$			9.26795i			1.01729i	0.860976	+	0.508645i	$0.169853\pi$
$83$			9.26795i			1.01729i	−0.860976	+	0.508645i	$0.830147\pi$
$84$	−0.866025	−	0.500000i	−0.0944911	−	0.0545545i
$85$	−1.43782	−	0.830127i	−0.155954	−	0.0900399i
$86$			8.73205i			0.941601i
$87$	1.76795	−	3.06218i	0.189544	−	0.328300i
$88$	−2.59808	−	4.50000i	−0.276956	−	0.479702i
$89$	−14.5981	+	8.42820i	−1.54739	+	0.893388i	−0.549053	+	0.835787i	$0.685012\pi$
$89$	−14.5981	+	8.42820i	−1.54739	+	0.893388i	−0.998340	+	0.0576004i	$0.981655\pi$
$90$	−0.732051			−0.0771649
$91$	2.50000	−	2.59808i	0.262071	−	0.272352i
$92$	−7.46410			−0.778186
$93$	−2.83013	+	1.63397i	−0.293471	+	0.169435i
$94$	1.96410	+	3.40192i	0.202582	+	0.350882i
$95$	0.169873	−	0.294229i	0.0174286	−	0.0301872i
$96$			1.00000i			0.102062i
$97$	−12.2942	−	7.09808i	−1.24829	−	0.720700i	−0.277522	−	0.960719i	$-0.589513\pi$
$97$	−12.2942	−	7.09808i	−1.24829	−	0.720700i	−0.970768	+	0.240019i	$0.922846\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$			5.19615i			0.522233i
$100$	2.23205	−	3.86603i	0.223205	−	0.386603i
$101$	2.46410	+	4.26795i	0.245187	+	0.424677i	0.962184	−	0.272399i	$-0.0878172\pi$
$101$	2.46410	+	4.26795i	0.245187	+	0.424677i	−0.716997	+	0.697076i	$0.754484\pi$
$102$	1.96410	−	1.13397i	0.194475	−	0.112280i
$103$	16.1962			1.59585			0.797927	−	0.602754i	$-0.205930\pi$
$103$	16.1962			1.59585			0.797927	+	0.602754i	$0.205930\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$	0.732051			0.0714408
$106$	−8.59808	+	4.96410i	−0.835119	+	0.482156i
$107$	3.03590	+	5.25833i	0.293491	+	0.508342i	0.974633	−	0.223810i	$-0.0718495\pi$
$107$	3.03590	+	5.25833i	0.293491	+	0.508342i	−0.681141	+	0.732152i	$0.738516\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			11.2679i			1.07927i	0.841898	+	0.539637i	$0.181438\pi$
$109$			11.2679i			1.07927i	−0.841898	+	0.539637i	$0.818562\pi$
$110$	3.29423	+	1.90192i	0.314092	+	0.181341i
$111$	−5.83013	−	3.36603i	−0.553371	−	0.319489i
$112$		−	1.00000i		−	0.0944911i
$113$	−3.83013	+	6.63397i	−0.360308	+	0.624072i	−0.988011	−	0.154381i	$-0.950662\pi$
$113$	−3.83013	+	6.63397i	−0.360308	+	0.624072i	0.627703	+	0.778453i	$0.283995\pi$
$114$	0.232051	+	0.401924i	0.0217335	+	0.0376436i
$115$	4.73205	−	2.73205i	0.441266	−	0.254765i
$116$	3.53590			0.328300
$117$	2.59808	+	2.50000i	0.240192	+	0.231125i
$118$	8.92820			0.821908
$119$	−1.96410	+	1.13397i	−0.180049	+	0.103951i
$120$	−0.366025	−	0.633975i	−0.0334134	−	0.0578737i
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$			3.73205i			0.337884i
$123$	7.33013	+	4.23205i	0.660935	+	0.381591i
$124$	−2.83013	−	1.63397i	−0.254153	−	0.146735i
$125$			6.92820i			0.619677i
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	7.19615	+	12.4641i	0.638555	+	1.10601i	0.985750	+	0.168217i	$0.0538010\pi$
$127$	7.19615	+	12.4641i	0.638555	+	1.10601i	−0.347195	+	0.937793i	$0.612866\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	8.73205			0.768814
$130$	2.53590	−	0.732051i	0.222413	−	0.0642051i
$131$	−14.9282			−1.30428			−0.652142	−	0.758097i	$-0.726129\pi$
$131$	−14.9282			−1.30428			−0.652142	+	0.758097i	$0.726129\pi$
$132$	−4.50000	+	2.59808i	−0.391675	+	0.226134i
$133$	−0.232051	−	0.401924i	−0.0201214	−	0.0348512i
$134$	5.00000	−	8.66025i	0.431934	−	0.748132i
$135$			0.732051i			0.0630049i
$136$	1.96410	+	1.13397i	0.168420	+	0.0972375i
$137$	−16.8564	−	9.73205i	−1.44014	−	0.831465i	−0.442282	−	0.896876i	$-0.645831\pi$
$137$	−16.8564	−	9.73205i	−1.44014	−	0.831465i	−0.997858	+	0.0654110i	$0.979164\pi$
$138$			7.46410i			0.635387i
$139$	−8.52628	+	14.7679i	−0.723190	+	1.25260i	0.236525	+	0.971625i	$0.423991\pi$
$139$	−8.52628	+	14.7679i	−0.723190	+	1.25260i	−0.959715	+	0.280976i	$0.909342\pi$
$140$	0.366025	+	0.633975i	0.0309348	+	0.0535806i
$141$	3.40192	−	1.96410i	0.286494	−	0.165407i
$142$	7.26795			0.609913
$143$	−5.19615	−	18.0000i	−0.434524	−	1.50524i
$144$	1.00000			0.0833333
$145$	−2.24167	+	1.29423i	−0.186161	+	0.107480i
$146$	−0.732051	−	1.26795i	−0.0605850	−	0.104936i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$		−	6.73205i		−	0.553371i
$149$	−6.92820	−	4.00000i	−0.567581	−	0.327693i	0.188602	−	0.982054i	$-0.439604\pi$
$149$	−6.92820	−	4.00000i	−0.567581	−	0.327693i	−0.756182	+	0.654361i	$0.772938\pi$
$150$	−3.86603	−	2.23205i	−0.315660	−	0.182246i
$151$		−	1.19615i		−	0.0973415i	−0.998815	−	0.0486708i	$-0.984501\pi$
$151$		−	1.19615i		−	0.0973415i	0.998815	−	0.0486708i	$-0.0154985\pi$
$152$	−0.232051	+	0.401924i	−0.0188218	+	0.0326003i
$153$	−1.13397	−	1.96410i	−0.0916764	−	0.158788i
$154$	4.50000	−	2.59808i	0.362620	−	0.209359i
$155$	2.39230			0.192155
$156$	−0.866025	+	3.50000i	−0.0693375	+	0.280224i
$157$	−11.4641			−0.914935			−0.457467	−	0.889226i	$-0.651243\pi$
$157$	−11.4641			−0.914935			−0.457467	+	0.889226i	$0.651243\pi$
$158$	7.79423	−	4.50000i	0.620076	−	0.358001i
$159$	4.96410	+	8.59808i	0.393679	+	0.681872i
$160$	0.366025	−	0.633975i	0.0289368	−	0.0501201i
$161$		−	7.46410i		−	0.588254i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−6.16987	−	3.56218i	−0.483262	−	0.279011i	0.238513	−	0.971139i	$-0.423340\pi$
$163$	−6.16987	−	3.56218i	−0.483262	−	0.279011i	−0.721775	+	0.692128i	$0.756673\pi$
$164$			8.46410i			0.660935i
$165$	1.90192	−	3.29423i	0.148065	−	0.256455i
$166$	4.63397	+	8.02628i	0.359666	+	0.622960i
$167$	−4.39230	+	2.53590i	−0.339887	+	0.196234i	−0.660222	−	0.751071i	$-0.729538\pi$
$167$	−4.39230	+	2.53590i	−0.339887	+	0.196234i	0.320335	+	0.947304i	$0.396204\pi$
$168$	−1.00000			−0.0771517
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	−1.66025			−0.127336
$171$	0.401924	−	0.232051i	0.0307359	−	0.0177454i
$172$	4.36603	+	7.56218i	0.332906	+	0.576611i
$173$	1.09808	−	1.90192i	0.0834852	−	0.144601i	−0.821260	−	0.570555i	$-0.806728\pi$
$173$	1.09808	−	1.90192i	0.0834852	−	0.144601i	0.904745	+	0.425954i	$0.140062\pi$
$174$		−	3.53590i		−	0.268056i
$175$	3.86603	+	2.23205i	0.292244	+	0.168727i
$176$	−4.50000	−	2.59808i	−0.339200	−	0.195837i
$177$		−	8.92820i		−	0.671085i
$178$	−8.42820	+	14.5981i	−0.631721	+	1.09417i
$179$	−1.73205	−	3.00000i	−0.129460	−	0.224231i	0.794008	−	0.607908i	$-0.207991\pi$
$179$	−1.73205	−	3.00000i	−0.129460	−	0.224231i	−0.923467	+	0.383677i	$0.874658\pi$
$180$	−0.633975	+	0.366025i	−0.0472537	+	0.0272819i
$181$	14.2679			1.06053			0.530264	−	0.847832i	$-0.322093\pi$
$181$	14.2679			1.06053			0.530264	+	0.847832i	$0.322093\pi$
$182$	0.866025	−	3.50000i	0.0641941	−	0.259437i
$183$	3.73205			0.275881
$184$	−6.46410	+	3.73205i	−0.476540	+	0.275130i
$185$	2.46410	+	4.26795i	0.181164	+	0.313786i
$186$	−1.63397	+	2.83013i	−0.119809	+	0.207515i
$187$			11.7846i			0.861776i
$188$	3.40192	+	1.96410i	0.248111	+	0.143247i
$189$	0.866025	+	0.500000i	0.0629941	+	0.0363696i
$190$		−	0.339746i		−	0.0246478i
$191$	4.09808	−	7.09808i	0.296526	−	0.513599i	−0.678812	−	0.734312i	$-0.737505\pi$
$191$	4.09808	−	7.09808i	0.296526	−	0.513599i	0.975339	+	0.220713i	$0.0708384\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	6.57180	−	3.79423i	0.473048	−	0.273115i	−0.244467	−	0.969658i	$-0.578613\pi$
$193$	6.57180	−	3.79423i	0.473048	−	0.273115i	0.717515	+	0.696543i	$0.245280\pi$
$194$	−14.1962			−1.01922
$195$	−0.732051	−	2.53590i	−0.0524232	−	0.181599i
$196$	1.00000			0.0714286
$197$	0.232051	−	0.133975i	0.0165329	−	0.00954529i	−0.491711	−	0.870759i	$-0.663628\pi$
$197$	0.232051	−	0.133975i	0.0165329	−	0.00954529i	0.508244	+	0.861213i	$0.330295\pi$
$198$	2.59808	+	4.50000i	0.184637	+	0.319801i
$199$	12.2942	−	21.2942i	0.871515	−	1.50951i	0.0110851	−	0.999939i	$-0.496471\pi$
$199$	12.2942	−	21.2942i	0.871515	−	1.50951i	0.860430	−	0.509569i	$-0.170195\pi$
$200$		−	4.46410i		−	0.315660i
$201$	−8.66025	−	5.00000i	−0.610847	−	0.352673i
$202$	4.26795	+	2.46410i	0.300292	+	0.173374i
$203$			3.53590i			0.248171i
$204$	1.13397	−	1.96410i	0.0793941	−	0.137515i
$205$	−3.09808	−	5.36603i	−0.216379	−	0.374779i
$206$	14.0263	−	8.09808i	0.977257	−	0.564220i
$207$	7.46410			0.518791
$208$	−3.46410	+	1.00000i	−0.240192	+	0.0693375i
$209$	−2.41154			−0.166810
$210$	0.633975	−	0.366025i	0.0437484	−	0.0252582i
$211$	−12.4641	−	21.5885i	−0.858064	−	1.48621i	−0.873773	−	0.486334i	$-0.838334\pi$
$211$	−12.4641	−	21.5885i	−0.858064	−	1.48621i	0.0157088	−	0.999877i	$-0.495000\pi$
$212$	−4.96410	+	8.59808i	−0.340936	+	0.590518i
$213$		−	7.26795i		−	0.497992i
$214$	5.25833	+	3.03590i	0.359452	+	0.207530i
$215$	−5.53590	−	3.19615i	−0.377545	−	0.217976i
$216$		−	1.00000i		−	0.0680414i
$217$	1.63397	−	2.83013i	0.110921	−	0.192122i
$218$	5.63397	+	9.75833i	0.381581	+	0.660918i
$219$	−1.26795	+	0.732051i	−0.0856801	+	0.0494674i
$220$	3.80385			0.256455
$221$	5.89230	+	5.66987i	0.396359	+	0.381397i
$222$	−6.73205			−0.451826
$223$	−4.73205	+	2.73205i	−0.316882	+	0.182952i	−0.650002	−	0.759933i	$-0.725232\pi$
$223$	−4.73205	+	2.73205i	−0.316882	+	0.182952i	0.333120	+	0.942884i	$0.391899\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−2.23205	+	3.86603i	−0.148803	+	0.257735i
$226$			7.66025i			0.509553i
$227$	−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	$0.812418\pi$
$228$	0.401924	+	0.232051i	0.0266181	+	0.0153679i
$229$			17.3923i			1.14932i	0.818394	+	0.574658i	$0.194865\pi$
$229$			17.3923i			1.14932i	−0.818394	+	0.574658i	$0.805135\pi$
$230$	2.73205	−	4.73205i	0.180146	−	0.312022i
$231$	−2.59808	−	4.50000i	−0.170941	−	0.296078i
$232$	3.06218	−	1.76795i	0.201042	−	0.116072i
$233$	18.5885			1.21777			0.608885	−	0.793258i	$-0.291617\pi$
$233$	18.5885			1.21777			0.608885	+	0.793258i	$0.291617\pi$
$234$	3.50000	+	0.866025i	0.228802	+	0.0566139i
$235$	−2.87564			−0.187586
$236$	7.73205	−	4.46410i	0.503314	−	0.290588i
$237$	−4.50000	−	7.79423i	−0.292306	−	0.506290i
$238$	−1.13397	+	1.96410i	−0.0735047	+	0.127314i
$239$			26.5885i			1.71986i	0.510408	+	0.859932i	$0.329494\pi$
$239$			26.5885i			1.71986i	−0.510408	+	0.859932i	$0.670506\pi$
$240$	−0.633975	−	0.366025i	−0.0409229	−	0.0236268i
$241$	9.46410	+	5.46410i	0.609636	+	0.351974i	0.772823	−	0.634621i	$-0.218844\pi$
$241$	9.46410	+	5.46410i	0.609636	+	0.351974i	−0.163187	+	0.986595i	$0.552177\pi$
$242$		−	16.0000i		−	1.02852i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.86603	+	3.23205i	0.119460	+	0.206911i
$245$	−0.633975	+	0.366025i	−0.0405032	+	0.0233845i
$246$	8.46410			0.539651
$247$	−1.16025	+	1.20577i	−0.0738252	+	0.0767214i
$248$	−3.26795			−0.207515
$249$	8.02628	−	4.63397i	0.508645	−	0.293666i
$250$	3.46410	+	6.00000i	0.219089	+	0.379473i
$251$	8.75833	−	15.1699i	0.552821	−	0.957514i	−0.445249	−	0.895407i	$-0.646885\pi$
$251$	8.75833	−	15.1699i	0.552821	−	0.957514i	0.998070	−	0.0621069i	$-0.0197820\pi$
$252$			1.00000i			0.0629941i
$253$	−33.5885	−	19.3923i	−2.11169	−	1.21918i
$254$	12.4641	+	7.19615i	0.782067	+	0.451527i
$255$			1.66025i			0.103969i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.5263	−	21.6962i	−0.781368	−	1.35337i	−0.931145	−	0.364649i	$-0.881189\pi$
$257$	−12.5263	−	21.6962i	−0.781368	−	1.35337i	0.149777	−	0.988720i	$-0.452144\pi$
$258$	7.56218	−	4.36603i	0.470801	−	0.271817i
$259$	6.73205			0.418309
$260$	1.83013	−	1.90192i	0.113500	−	0.117952i
$261$	−3.53590			−0.218867
$262$	−12.9282	+	7.46410i	−0.798707	+	0.461134i
$263$	−1.56218	−	2.70577i	−0.0963280	−	0.166845i	0.813834	−	0.581097i	$-0.197376\pi$
$263$	−1.56218	−	2.70577i	−0.0963280	−	0.166845i	−0.910162	+	0.414252i	$0.864043\pi$
$264$	−2.59808	+	4.50000i	−0.159901	+	0.276956i
$265$		−	7.26795i		−	0.446467i
$266$	−0.401924	−	0.232051i	−0.0246435	−	0.0142279i
$267$	14.5981	+	8.42820i	0.893388	+	0.515798i
$268$		−	10.0000i		−	0.610847i
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	−0.798591	−	0.601874i	$-0.794421\pi$
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	0.920534	+	0.390664i	$0.127754\pi$
$270$	0.366025	+	0.633975i	0.0222756	+	0.0385825i
$271$	6.63397	−	3.83013i	0.402985	−	0.232664i	−0.284786	−	0.958591i	$-0.591923\pi$
$271$	6.63397	−	3.83013i	0.402985	−	0.232664i	0.687771	+	0.725927i	$0.258589\pi$
$272$	2.26795			0.137515
$273$	−3.50000	−	0.866025i	−0.211830	−	0.0524142i
$274$	−19.4641			−1.17587
$275$	20.0885	−	11.5981i	1.21138	−	0.699390i
$276$	3.73205	+	6.46410i	0.224643	+	0.389093i
$277$	−7.19615	+	12.4641i	−0.432375	+	0.748895i	−0.997077	−	0.0763993i	$-0.975658\pi$
$277$	−7.19615	+	12.4641i	−0.432375	+	0.748895i	0.564702	+	0.825295i	$0.308991\pi$
$278$			17.0526i			1.02274i
$279$	2.83013	+	1.63397i	0.169435	+	0.0978235i
$280$	0.633975	+	0.366025i	0.0378872	+	0.0218742i
$281$			12.7321i			0.759530i	0.925083	+	0.379765i	$0.123995\pi$
$281$			12.7321i			0.759530i	−0.925083	+	0.379765i	$0.876005\pi$
$282$	1.96410	−	3.40192i	0.116961	−	0.202582i
$283$	−8.92820	−	15.4641i	−0.530727	−	0.919245i	−0.999357	−	0.0358512i	$-0.988586\pi$
$283$	−8.92820	−	15.4641i	−0.530727	−	0.919245i	0.468631	−	0.883394i	$-0.344748\pi$
$284$	6.29423	−	3.63397i	0.373494	−	0.215637i
$285$	−0.339746			−0.0201248
$286$	−13.5000	−	12.9904i	−0.798272	−	0.768137i
$287$	−8.46410			−0.499620
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	5.92820	+	10.2679i	0.348718	+	0.603997i
$290$	−1.29423	+	2.24167i	−0.0759997	+	0.131635i
$291$			14.1962i			0.832193i
$292$	−1.26795	−	0.732051i	−0.0742011	−	0.0428400i
$293$	0.928203	+	0.535898i	0.0542262	+	0.0313075i	0.526868	−	0.849947i	$-0.323366\pi$
$293$	0.928203	+	0.535898i	0.0542262	+	0.0313075i	−0.472642	+	0.881255i	$0.656700\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	−3.26795	+	5.66025i	−0.190267	+	0.329553i
$296$	−3.36603	−	5.83013i	−0.195646	−	0.338869i
$297$	4.50000	−	2.59808i	0.261116	−	0.150756i
$298$	−8.00000			−0.463428
$299$	−25.8564	+	7.46410i	−1.49531	+	0.431660i
$300$	−4.46410			−0.257735
$301$	−7.56218	+	4.36603i	−0.435877	+	0.251654i
$302$	−0.598076	−	1.03590i	−0.0344154	−	0.0596093i
$303$	2.46410	−	4.26795i	0.141559	−	0.245187i
$304$			0.464102i			0.0266181i
$305$	−2.36603	−	1.36603i	−0.135478	−	0.0782184i
$306$	−1.96410	−	1.13397i	−0.112280	−	0.0648250i
$307$		−	5.00000i		−	0.285365i	−0.989769	−	0.142683i	$-0.954427\pi$
$307$		−	5.00000i		−	0.285365i	0.989769	−	0.142683i	$-0.0455728\pi$
$308$	2.59808	−	4.50000i	0.148039	−	0.256411i
$309$	−8.09808	−	14.0263i	−0.460683	−	0.797927i
$310$	2.07180	−	1.19615i	0.117670	−	0.0679369i
$311$	14.8038			0.839449			0.419725	−	0.907652i	$-0.362127\pi$
$311$	14.8038			0.839449			0.419725	+	0.907652i	$0.362127\pi$
$312$	1.00000	+	3.46410i	0.0566139	+	0.196116i
$313$	6.87564			0.388634			0.194317	−	0.980939i	$-0.437751\pi$
$313$	6.87564			0.388634			0.194317	+	0.980939i	$0.437751\pi$
$314$	−9.92820	+	5.73205i	−0.560281	+	0.323478i
$315$	−0.366025	−	0.633975i	−0.0206232	−	0.0357204i
$316$	4.50000	−	7.79423i	0.253145	−	0.438460i
$317$			14.7846i			0.830386i	0.909733	+	0.415193i	$0.136286\pi$
$317$			14.7846i			0.830386i	−0.909733	+	0.415193i	$0.863714\pi$
$318$	8.59808	+	4.96410i	0.482156	+	0.278373i
$319$	15.9115	+	9.18653i	0.890875	+	0.514347i
$320$		−	0.732051i		−	0.0409229i
$321$	3.03590	−	5.25833i	0.169447	−	0.293491i
$322$	−3.73205	−	6.46410i	−0.207979	−	0.360230i
$323$	0.911543	−	0.526279i	0.0507196	−	0.0292830i
$324$	−1.00000			−0.0555556
$325$	3.86603	−	15.6244i	0.214449	−	0.866683i
$326$	−7.12436			−0.394582
$327$	9.75833	−	5.63397i	0.539637	−	0.311560i
$328$	4.23205	+	7.33013i	0.233676	+	0.404739i
$329$	−1.96410	+	3.40192i	−0.108284	+	0.187554i
$330$		−	3.80385i		−	0.209395i
$331$	5.87564	+	3.39230i	0.322955	+	0.186458i	0.652709	−	0.757609i	$-0.273633\pi$
$331$	5.87564	+	3.39230i	0.322955	+	0.186458i	−0.329754	+	0.944067i	$0.606966\pi$
$332$	8.02628	+	4.63397i	0.440499	+	0.254322i
$333$			6.73205i			0.368914i
$334$	−2.53590	+	4.39230i	−0.138758	+	0.240336i
$335$	3.66025	+	6.33975i	0.199981	+	0.346377i
$336$	−0.866025	+	0.500000i	−0.0472456	+	0.0272772i
$337$	−11.0000			−0.599208			−0.299604	−	0.954064i	$-0.596855\pi$
$337$	−11.0000			−0.599208			−0.299604	+	0.954064i	$0.596855\pi$
$338$	−12.9904	+	0.500000i	−0.706584	+	0.0271964i
$339$	7.66025			0.416048
$340$	−1.43782	+	0.830127i	−0.0779769	+	0.0450200i
$341$	−8.49038	−	14.7058i	−0.459780	−	0.796362i
$342$	0.232051	−	0.401924i	0.0125479	−	0.0217335i
$343$			1.00000i			0.0539949i
$344$	7.56218	+	4.36603i	0.407725	+	0.235400i
$345$	−4.73205	−	2.73205i	−0.254765	−	0.147089i
$346$		−	2.19615i		−	0.118066i
$347$	3.23205	−	5.59808i	0.173506	−	0.300520i	−0.766138	−	0.642677i	$-0.777824\pi$
$347$	3.23205	−	5.59808i	0.173506	−	0.300520i	0.939643	+	0.342156i	$0.111157\pi$
$348$	−1.76795	−	3.06218i	−0.0947720	−	0.164150i
$349$	5.32051	−	3.07180i	0.284800	−	0.164430i	−0.350794	−	0.936453i	$-0.614088\pi$
$349$	5.32051	−	3.07180i	0.284800	−	0.164430i	0.635595	+	0.772023i	$0.280755\pi$
$350$	4.46410			0.238616
$351$	0.866025	−	3.50000i	0.0462250	−	0.186816i
$352$	−5.19615			−0.276956
$353$	27.1244	−	15.6603i	1.44368	−	0.833511i	0.445591	−	0.895237i	$-0.352994\pi$
$353$	27.1244	−	15.6603i	1.44368	−	0.833511i	0.998093	+	0.0617256i	$0.0196604\pi$
$354$	−4.46410	−	7.73205i	−0.237264	−	0.410954i
$355$	−2.66025	+	4.60770i	−0.141192	+	0.244551i
$356$			16.8564i			0.893388i
$357$	1.96410	+	1.13397i	0.103951	+	0.0600163i
$358$	−3.00000	−	1.73205i	−0.158555	−	0.0915417i
$359$		−	34.4449i		−	1.81793i	−0.416872	−	0.908965i	$-0.636874\pi$
$359$		−	34.4449i		−	1.81793i	0.416872	−	0.908965i	$-0.363126\pi$
$360$	−0.366025	+	0.633975i	−0.0192912	+	0.0334134i
$361$	−9.39230	−	16.2679i	−0.494332	−	0.856208i
$362$	12.3564	−	7.13397i	0.649438	−	0.374953i
$363$	−16.0000			−0.839782
$364$	−1.00000	−	3.46410i	−0.0524142	−	0.181568i
$365$	1.07180			0.0561004
$366$	3.23205	−	1.86603i	0.168942	−	0.0975387i
$367$	−6.66025	−	11.5359i	−0.347662	−	0.602169i	0.638171	−	0.769894i	$-0.279691\pi$
$367$	−6.66025	−	11.5359i	−0.347662	−	0.602169i	−0.985834	+	0.167725i	$0.946358\pi$
$368$	−3.73205	+	6.46410i	−0.194547	+	0.336965i
$369$		−	8.46410i		−	0.440624i
$370$	4.26795	+	2.46410i	0.221880	+	0.128103i
$371$	−8.59808	−	4.96410i	−0.446390	−	0.257723i
$372$			3.26795i			0.169435i
$373$	7.56218	−	13.0981i	0.391555	−	0.678193i	−0.601100	−	0.799174i	$-0.705271\pi$
$373$	7.56218	−	13.0981i	0.391555	−	0.678193i	0.992655	+	0.120981i	$0.0386040\pi$
$374$	5.89230	+	10.2058i	0.304684	+	0.527728i
$375$	6.00000	−	3.46410i	0.309839	−	0.178885i
$376$	3.92820			0.202582
$377$	12.2487	−	3.53590i	0.630841	−	0.182108i
$378$	1.00000			0.0514344
$379$	−31.2224	+	18.0263i	−1.60379	+	0.925948i	−0.613069	+	0.790030i	$0.710065\pi$
$379$	−31.2224	+	18.0263i	−1.60379	+	0.925948i	−0.990720	+	0.135918i	$0.956602\pi$
$380$	−0.169873	−	0.294229i	−0.00871430	−	0.0150936i
$381$	7.19615	−	12.4641i	0.368670	−	0.638555i
$382$		−	8.19615i		−	0.419352i
$383$	26.8468	+	15.5000i	1.37181	+	0.792013i	0.991155	−	0.132706i	$-0.0423665\pi$
$383$	26.8468	+	15.5000i	1.37181	+	0.792013i	0.380651	+	0.924719i	$0.375700\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			3.80385i			0.193862i
$386$	3.79423	−	6.57180i	0.193121	−	0.334496i
$387$	−4.36603	−	7.56218i	−0.221938	−	0.384407i
$388$	−12.2942	+	7.09808i	−0.624145	+	0.360350i
$389$	21.4641			1.08827			0.544137	−	0.838997i	$-0.316857\pi$
$389$	21.4641			1.08827			0.544137	+	0.838997i	$0.316857\pi$
$390$	−1.90192	−	1.83013i	−0.0963077	−	0.0926721i
$391$	16.9282			0.856096
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$	7.46410	+	12.9282i	0.376514	+	0.652142i
$394$	0.133975	−	0.232051i	0.00674954	−	0.0116906i
$395$			6.58846i			0.331501i
$396$	4.50000	+	2.59808i	0.226134	+	0.130558i
$397$	−18.5263	−	10.6962i	−0.929807	−	0.536825i	−0.0430567	−	0.999073i	$-0.513710\pi$
$397$	−18.5263	−	10.6962i	−0.929807	−	0.536825i	−0.886751	+	0.462248i	$0.847043\pi$
$398$		−	24.5885i		−	1.23251i
$399$	−0.232051	+	0.401924i	−0.0116171	+	0.0201214i
$400$	−2.23205	−	3.86603i	−0.111603	−	0.193301i
$401$	−9.58846	+	5.53590i	−0.478825	+	0.276450i	−0.719927	−	0.694050i	$-0.755825\pi$
$401$	−9.58846	+	5.53590i	−0.478825	+	0.276450i	0.241102	+	0.970500i	$0.422491\pi$
$402$	−10.0000			−0.498755
$403$	−11.4378	−	2.83013i	−0.569759	−	0.140979i
$404$	4.92820			0.245187
$405$	0.633975	−	0.366025i	0.0315025	−	0.0181879i
$406$	1.76795	+	3.06218i	0.0877418	+	0.151973i
$407$	17.4904	−	30.2942i	0.866966	−	1.50163i
$408$		−	2.26795i		−	0.112280i
$409$	−14.3660	−	8.29423i	−0.710354	−	0.410123i	0.100838	−	0.994903i	$-0.467848\pi$
$409$	−14.3660	−	8.29423i	−0.710354	−	0.410123i	−0.811192	+	0.584780i	$0.801181\pi$
$410$	−5.36603	−	3.09808i	−0.265009	−	0.153003i
$411$			19.4641i			0.960093i
$412$	8.09808	−	14.0263i	0.398964	−	0.691025i
$413$	4.46410	+	7.73205i	0.219664	+	0.380469i
$414$	6.46410	−	3.73205i	0.317693	−	0.183420i
$415$	−6.78461			−0.333043
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$	17.0526			0.835067
$418$	−2.08846	+	1.20577i	−0.102150	+	0.0589762i
$419$	7.29423	+	12.6340i	0.356346	+	0.617210i	0.987347	−	0.158572i	$-0.0506890\pi$
$419$	7.29423	+	12.6340i	0.356346	+	0.617210i	−0.631001	+	0.775782i	$0.717356\pi$
$420$	0.366025	−	0.633975i	0.0178602	−	0.0309348i
$421$			25.3205i			1.23405i	0.786945	+	0.617023i	$0.211661\pi$
$421$			25.3205i			1.23405i	−0.786945	+	0.617023i	$0.788339\pi$
$422$	−21.5885	−	12.4641i	−1.05091	−	0.606743i
$423$	−3.40192	−	1.96410i	−0.165407	−	0.0954979i
$424$			9.92820i			0.482156i
$425$	−5.06218	+	8.76795i	−0.245552	+	0.425308i
$426$	−3.63397	−	6.29423i	−0.176067	−	0.304956i
$427$	−3.23205	+	1.86603i	−0.156410	+	0.0903033i
$428$	6.07180			0.293491
$429$	−12.9904	+	13.5000i	−0.627182	+	0.651786i
$430$	−6.39230			−0.308264
$431$	11.3660	−	6.56218i	0.547482	−	0.316089i	−0.200624	−	0.979668i	$-0.564297\pi$
$431$	11.3660	−	6.56218i	0.547482	−	0.316089i	0.748106	+	0.663579i	$0.230964\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	6.07180	−	10.5167i	0.291792	−	0.505398i	−0.682442	−	0.730940i	$-0.739082\pi$
$433$	6.07180	−	10.5167i	0.291792	−	0.505398i	0.974234	+	0.225542i	$0.0724152\pi$
$434$		−	3.26795i		−	0.156867i
$435$	2.24167	+	1.29423i	0.107480	+	0.0620535i
$436$	9.75833	+	5.63397i	0.467339	+	0.269818i
$437$			3.46410i			0.165710i
$438$	−0.732051	+	1.26795i	−0.0349787	+	0.0605850i
$439$	11.6603	+	20.1962i	0.556514	+	0.963910i	0.997784	+	0.0665356i	$0.0211946\pi$
$439$	11.6603	+	20.1962i	0.556514	+	0.963910i	−0.441270	+	0.897374i	$0.645472\pi$
$440$	3.29423	−	1.90192i	0.157046	−	0.0906707i
$441$	−1.00000			−0.0476190
$442$	7.93782	+	1.96410i	0.377564	+	0.0934228i
$443$	−25.0000			−1.18779			−0.593893	−	0.804544i	$-0.702410\pi$
$443$	−25.0000			−1.18779			−0.593893	+	0.804544i	$0.702410\pi$
$444$	−5.83013	+	3.36603i	−0.276686	+	0.159744i
$445$	−6.16987	−	10.6865i	−0.292480	−	0.506590i
$446$	−2.73205	+	4.73205i	−0.129366	+	0.224069i
$447$			8.00000i			0.378387i
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	25.0981	+	14.4904i	1.18445	+	0.683843i	0.957040	−	0.289955i	$-0.0936405\pi$
$449$	25.0981	+	14.4904i	1.18445	+	0.683843i	0.227411	+	0.973799i	$0.426974\pi$
$450$			4.46410i			0.210440i
$451$	−21.9904	+	38.0885i	−1.03549	+	1.79352i
$452$	3.83013	+	6.63397i	0.180154	+	0.312036i
$453$	−1.03590	+	0.598076i	−0.0486708	+	0.0281001i
$454$	−13.3205			−0.625162
$455$	1.90192	+	1.83013i	0.0891636	+	0.0857977i
$456$	0.464102			0.0217335
$457$	−25.7321	+	14.8564i	−1.20369	+	0.694953i	−0.961375	−	0.275243i	$-0.911242\pi$
$457$	−25.7321	+	14.8564i	−1.20369	+	0.694953i	−0.242320	+	0.970196i	$0.577908\pi$
$458$	8.69615	+	15.0622i	0.406345	+	0.703809i
$459$	−1.13397	+	1.96410i	−0.0529294	+	0.0916764i
$460$		−	5.46410i		−	0.254765i
$461$	6.00000	+	3.46410i	0.279448	+	0.161339i	0.633173	−	0.774010i	$-0.281752\pi$
$461$	6.00000	+	3.46410i	0.279448	+	0.161339i	−0.353726	+	0.935349i	$0.615085\pi$
$462$	−4.50000	−	2.59808i	−0.209359	−	0.120873i
$463$			15.3397i			0.712898i	0.934315	+	0.356449i	$0.116013\pi$
$463$			15.3397i			0.712898i	−0.934315	+	0.356449i	$0.883987\pi$
$464$	1.76795	−	3.06218i	0.0820750	−	0.142158i
$465$	−1.19615	−	2.07180i	−0.0554702	−	0.0960773i
$466$	16.0981	−	9.29423i	0.745729	−	0.430547i
$467$	18.9282			0.875893			0.437946	−	0.899001i	$-0.355706\pi$
$467$	18.9282			0.875893			0.437946	+	0.899001i	$0.355706\pi$
$468$	3.46410	−	1.00000i	0.160128	−	0.0462250i
$469$	10.0000			0.461757
$470$	−2.49038	+	1.43782i	−0.114873	+	0.0663218i
$471$	5.73205	+	9.92820i	0.264119	+	0.457467i
$472$	4.46410	−	7.73205i	0.205477	−	0.355896i
$473$			45.3731i			2.08626i
$474$	−7.79423	−	4.50000i	−0.358001	−	0.206692i
$475$	−1.79423	−	1.03590i	−0.0823249	−	0.0475303i
$476$			2.26795i			0.103951i
$477$	4.96410	−	8.59808i	0.227291	−	0.393679i
$478$	13.2942	+	23.0263i	0.608064	+	1.05320i
$479$	4.20577	−	2.42820i	0.192167	−	0.110947i	−0.400830	−	0.916153i	$-0.631278\pi$
$479$	4.20577	−	2.42820i	0.192167	−	0.110947i	0.592996	+	0.805205i	$0.297945\pi$
$480$	−0.732051			−0.0334134
$481$	−6.73205	−	23.3205i	−0.306955	−	1.06332i
$482$	10.9282			0.497766
$483$	−6.46410	+	3.73205i	−0.294127	+	0.169814i
$484$	−8.00000	−	13.8564i	−0.363636	−	0.629837i
$485$	5.19615	−	9.00000i	0.235945	−	0.408669i
$486$			1.00000i			0.0453609i
$487$	−25.5000	−	14.7224i	−1.15552	−	0.667137i	−0.205290	−	0.978701i	$-0.565814\pi$
$487$	−25.5000	−	14.7224i	−1.15552	−	0.667137i	−0.950225	+	0.311564i	$0.899147\pi$
$488$	3.23205	+	1.86603i	0.146308	+	0.0844710i
$489$			7.12436i			0.322174i
$490$	−0.366025	+	0.633975i	−0.0165353	+	0.0286401i
$491$	−3.19615	−	5.53590i	−0.144240	−	0.249832i	0.784849	−	0.619687i	$-0.212741\pi$
$491$	−3.19615	−	5.53590i	−0.144240	−	0.249832i	−0.929089	+	0.369856i	$0.879407\pi$
$492$	7.33013	−	4.23205i	0.330468	−	0.190796i
$493$	−8.01924			−0.361168
$494$	−0.401924	+	1.62436i	−0.0180834	+	0.0730832i
$495$	−3.80385			−0.170970
$496$	−2.83013	+	1.63397i	−0.127076	+	0.0733676i
$497$	3.63397	+	6.29423i	0.163006	+	0.282335i
$498$	4.63397	−	8.02628i	0.207653	−	0.359666i
$499$			20.5885i			0.921666i	0.887487	+	0.460833i	$0.152449\pi$
$499$			20.5885i			0.921666i	−0.887487	+	0.460833i	$0.847551\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$	4.39230	+	2.53590i	0.196234	+	0.113296i
$502$		−	17.5167i		−	0.781807i
$503$	15.4641	−	26.7846i	0.689510	−	1.19427i	−0.282486	−	0.959271i	$-0.591159\pi$
$503$	15.4641	−	26.7846i	0.689510	−	1.19427i	0.971996	−	0.234995i	$-0.0755075\pi$
$504$	0.500000	+	0.866025i	0.0222718	+	0.0385758i
$505$	−3.12436	+	1.80385i	−0.139032	+	0.0802702i
$506$	−38.7846			−1.72419
$507$	0.500000	+	12.9904i	0.0222058	+	0.576923i
$508$	14.3923			0.638555
$509$	−25.6865	+	14.8301i	−1.13854	+	0.657334i	−0.946068	−	0.323969i	$-0.894983\pi$
$509$	−25.6865	+	14.8301i	−1.13854	+	0.657334i	−0.192468	+	0.981303i	$0.561649\pi$
$510$	0.830127	+	1.43782i	0.0367586	+	0.0636678i
$511$	0.732051	−	1.26795i	0.0323840	−	0.0560908i
$512$			1.00000i			0.0441942i
$513$	−0.401924	−	0.232051i	−0.0177454	−	0.0102453i
$514$	−21.6962	−	12.5263i	−0.956976	−	0.552511i
$515$			11.8564i			0.522456i
$516$	4.36603	−	7.56218i	0.192204	−	0.332906i
$517$	10.2058	+	17.6769i	0.448849	+	0.777430i
$518$	5.83013	−	3.36603i	0.256161	−	0.147895i
$519$	−2.19615			−0.0964004
$520$	0.633975	−	2.56218i	0.0278016	−	0.112359i
$521$	−21.5885			−0.945807			−0.472904	−	0.881114i	$-0.656794\pi$
$521$	−21.5885			−0.945807			−0.472904	+	0.881114i	$0.656794\pi$
$522$	−3.06218	+	1.76795i	−0.134028	+	0.0773810i
$523$	12.5981	+	21.8205i	0.550875	+	0.954144i	0.998212	+	0.0597784i	$0.0190394\pi$
$523$	12.5981	+	21.8205i	0.550875	+	0.954144i	−0.447336	+	0.894366i	$0.647627\pi$
$524$	−7.46410	+	12.9282i	−0.326071	+	0.564771i
$525$		−	4.46410i		−	0.194829i
$526$	−2.70577	−	1.56218i	−0.117977	−	0.0681142i
$527$	6.41858	+	3.70577i	0.279598	+	0.161426i
$528$			5.19615i			0.226134i
$529$	−16.3564	+	28.3301i	−0.711148	+	1.23174i
$530$	−3.63397	−	6.29423i	−0.157850	−	0.273404i
$531$	−7.73205	+	4.46410i	−0.335542	+	0.193726i
$532$	−0.464102			−0.0201214
$533$	8.46410	+	29.3205i	0.366621	+	1.27001i
$534$	16.8564			0.729448
$535$	−3.84936	+	2.22243i	−0.166423	+	0.0960841i
$536$	−5.00000	−	8.66025i	−0.215967	−	0.374066i
$537$	−1.73205	+	3.00000i	−0.0747435	+	0.129460i
$538$		−	4.00000i		−	0.172452i
$539$	4.50000	+	2.59808i	0.193829	+	0.111907i
$540$	0.633975	+	0.366025i	0.0272819	+	0.0157512i
$541$			8.05256i			0.346207i	0.984904	+	0.173103i	$0.0553794\pi$
$541$			8.05256i			0.346207i	−0.984904	+	0.173103i	$0.944621\pi$
$542$	3.83013	−	6.63397i	0.164518	−	0.284954i
$543$	−7.13397	−	12.3564i	−0.306148	−	0.530264i
$544$	1.96410	−	1.13397i	0.0842102	−	0.0486188i
$545$	−8.24871			−0.353336
$546$	−3.46410	+	1.00000i	−0.148250	+	0.0427960i
$547$	−4.19615			−0.179415			−0.0897073	−	0.995968i	$-0.528593\pi$
$547$	−4.19615			−0.179415			−0.0897073	+	0.995968i	$0.528593\pi$
$548$	−16.8564	+	9.73205i	−0.720070	+	0.415733i
$549$	−1.86603	−	3.23205i	−0.0796400	−	0.137941i
$550$	11.5981	−	20.0885i	0.494544	−	0.856575i
$551$		−	1.64102i		−	0.0699096i
$552$	6.46410	+	3.73205i	0.275130	+	0.158847i
$553$	7.79423	+	4.50000i	0.331444	+	0.191359i
$554$			14.3923i			0.611470i
$555$	2.46410	−	4.26795i	0.104595	−	0.181164i
$556$	8.52628	+	14.7679i	0.361595	+	0.626301i
$557$	17.0885	−	9.86603i	0.724061	−	0.418037i	−0.0921844	−	0.995742i	$-0.529385\pi$
$557$	17.0885	−	9.86603i	0.724061	−	0.418037i	0.816246	+	0.577705i	$0.196052\pi$
$558$	3.26795			0.138343
$559$	22.6865	+	21.8301i	0.959538	+	0.923316i
$560$	0.732051			0.0309348
$561$	10.2058	−	5.89230i	0.430888	−	0.248773i
$562$	6.36603	+	11.0263i	0.268535	+	0.465116i
$563$	−6.83013	+	11.8301i	−0.287856	+	0.498580i	−0.973298	−	0.229547i	$-0.926276\pi$
$563$	−6.83013	+	11.8301i	−0.287856	+	0.498580i	0.685442	+	0.728127i	$0.259609\pi$
$564$		−	3.92820i		−	0.165407i
$565$	−4.85641	−	2.80385i	−0.204311	−	0.117959i
$566$	−15.4641	−	8.92820i	−0.650005	−	0.375280i
$567$		−	1.00000i		−	0.0419961i
$568$	3.63397	−	6.29423i	0.152478	−	0.264100i
$569$	0.830127	+	1.43782i	0.0348007	+	0.0602766i	0.882901	−	0.469559i	$-0.155587\pi$
$569$	0.830127	+	1.43782i	0.0348007	+	0.0602766i	−0.848100	+	0.529835i	$0.822254\pi$
$570$	−0.294229	+	0.169873i	−0.0123239	+	0.00711520i
$571$	39.5167			1.65372			0.826860	−	0.562407i	$-0.190125\pi$
$571$	39.5167			1.65372			0.826860	+	0.562407i	$0.190125\pi$
$572$	−18.1865	−	4.50000i	−0.760417	−	0.188154i
$573$	−8.19615			−0.342399
$574$	−7.33013	+	4.23205i	−0.305954	+	0.176642i
$575$	−16.6603	−	28.8564i	−0.694781	−	1.20340i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	28.5885i		−	1.19015i	−0.803669	−	0.595077i	$-0.797122\pi$
$577$		−	28.5885i		−	1.19015i	0.803669	−	0.595077i	$-0.202878\pi$
$578$	10.2679	+	5.92820i	0.427090	+	0.246581i
$579$	−6.57180	−	3.79423i	−0.273115	−	0.157683i
$580$			2.58846i			0.107480i
$581$	−4.63397	+	8.02628i	−0.192250	+	0.332986i
$582$	7.09808	+	12.2942i	0.294225	+	0.509612i
$583$	−44.6769	+	25.7942i	−1.85033	+	1.06829i
$584$	−1.46410			−0.0605850
$585$	−1.83013	+	1.90192i	−0.0756664	+	0.0786349i
$586$	1.07180			0.0442755
$587$	−4.43782	+	2.56218i	−0.183169	+	0.105752i	−0.588781	−	0.808293i	$-0.700392\pi$
$587$	−4.43782	+	2.56218i	−0.183169	+	0.105752i	0.405612	+	0.914045i	$0.367058\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	−0.758330	+	1.31347i	−0.0312465	+	0.0541204i
$590$			6.53590i			0.269079i
$591$	−0.232051	−	0.133975i	−0.00954529	−	0.00551098i
$592$	−5.83013	−	3.36603i	−0.239617	−	0.138343i
$593$		−	37.0000i		−	1.51941i	−0.650269	−	0.759704i	$-0.725344\pi$
$593$		−	37.0000i		−	1.51941i	0.650269	−	0.759704i	$-0.274656\pi$
$594$	2.59808	−	4.50000i	0.106600	−	0.184637i
$595$	−0.830127	−	1.43782i	−0.0340319	−	0.0589450i
$596$	−6.92820	+	4.00000i	−0.283790	+	0.163846i
$597$	−24.5885			−1.00634
$598$	−18.6603	+	19.3923i	−0.763075	+	0.793010i
$599$	−47.5692			−1.94363			−0.971813	−	0.235754i	$-0.924244\pi$
$599$	−47.5692			−1.94363			−0.971813	+	0.235754i	$0.924244\pi$
$600$	−3.86603	+	2.23205i	−0.157830	+	0.0911231i
$601$	24.1506	+	41.8301i	0.985125	+	1.70629i	0.641380	+	0.767223i	$0.278362\pi$
$601$	24.1506	+	41.8301i	0.985125	+	1.70629i	0.343745	+	0.939063i	$0.388304\pi$
$602$	−4.36603	+	7.56218i	−0.177946	+	0.308211i
$603$			10.0000i			0.407231i
$604$	−1.03590	−	0.598076i	−0.0421501	−	0.0243354i
$605$	10.1436	+	5.85641i	0.412396	+	0.238097i
$606$		−	4.92820i		−	0.200195i
$607$	12.8301	−	22.2224i	0.520759	−	0.901981i	−0.478950	−	0.877842i	$-0.658982\pi$
$607$	12.8301	−	22.2224i	0.520759	−	0.901981i	0.999709	−	0.0241384i	$-0.00768424\pi$
$608$	0.232051	+	0.401924i	0.00941090	+	0.0163002i
$609$	3.06218	−	1.76795i	0.124086	−	0.0716409i
$610$	−2.73205			−0.110618
$611$	13.7487	+	3.40192i	0.556213	+	0.137627i
$612$	−2.26795			−0.0916764
$613$	−41.3205	+	23.8564i	−1.66892	+	0.963551i	−0.700698	+	0.713458i	$0.747128\pi$
$613$	−41.3205	+	23.8564i	−1.66892	+	0.963551i	−0.968222	+	0.250093i	$0.919539\pi$
$614$	−2.50000	−	4.33013i	−0.100892	−	0.174750i
$615$	−3.09808	+	5.36603i	−0.124926	+	0.216379i
$616$		−	5.19615i		−	0.209359i
$617$	11.9545	+	6.90192i	0.481269	+	0.277861i	0.720945	−	0.692992i	$-0.243708\pi$
$617$	11.9545	+	6.90192i	0.481269	+	0.277861i	−0.239676	+	0.970853i	$0.577041\pi$
$618$	−14.0263	−	8.09808i	−0.564220	−	0.325752i
$619$			11.3923i			0.457895i	0.973439	+	0.228948i	$0.0735285\pi$
$619$			11.3923i			0.457895i	−0.973439	+	0.228948i	$0.926472\pi$
$620$	1.19615	−	2.07180i	0.0480386	−	0.0832054i
$621$	−3.73205	−	6.46410i	−0.149762	−	0.259395i
$622$	12.8205	−	7.40192i	0.514056	−	0.296790i
$623$	−16.8564			−0.675338
$624$	2.59808	+	2.50000i	0.104006	+	0.100080i
$625$	17.2487			0.689948
$626$	5.95448	−	3.43782i	0.237989	−	0.137403i
$627$	1.20577	+	2.08846i	0.0481539	+	0.0834049i
$628$	−5.73205	+	9.92820i	−0.228734	+	0.396178i
$629$			15.2679i			0.608773i
$630$	−0.633975	−	0.366025i	−0.0252582	−	0.0145828i
$631$	1.62436	+	0.937822i	0.0646646	+	0.0373341i	0.531984	−	0.846755i	$-0.321447\pi$
$631$	1.62436	+	0.937822i	0.0646646	+	0.0373341i	−0.467319	+	0.884089i	$0.654780\pi$
$632$		−	9.00000i		−	0.358001i
$633$	−12.4641	+	21.5885i	−0.495404	+	0.858064i
$634$	7.39230	+	12.8038i	0.293586	+	0.508506i
$635$	−9.12436	+	5.26795i	−0.362089	+	0.209052i
$636$	9.92820			0.393679
$637$	3.46410	−	1.00000i	0.137253	−	0.0396214i
$638$	18.3731			0.727397
$639$	−6.29423	+	3.63397i	−0.248996	+	0.143758i
$640$	−0.366025	−	0.633975i	−0.0144684	−	0.0250600i
$641$	−8.66025	+	15.0000i	−0.342059	+	0.592464i	−0.984815	−	0.173607i	$-0.944458\pi$
$641$	−8.66025	+	15.0000i	−0.342059	+	0.592464i	0.642756	+	0.766071i	$0.277791\pi$
$642$		−	6.07180i		−	0.239635i
$643$	2.00962	+	1.16025i	0.0792516	+	0.0457560i	0.539102	−	0.842240i	$-0.318764\pi$
$643$	2.00962	+	1.16025i	0.0792516	+	0.0457560i	−0.459851	+	0.887996i	$0.652097\pi$
$644$	−6.46410	−	3.73205i	−0.254721	−	0.147063i
$645$			6.39230i			0.251697i
$646$	0.526279	−	0.911543i	0.0207062	−	0.0358642i
$647$	−11.8660	−	20.5526i	−0.466502	−	0.808004i	0.532766	−	0.846262i	$-0.321152\pi$
$647$	−11.8660	−	20.5526i	−0.466502	−	0.808004i	−0.999268	+	0.0382579i	$0.987819\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	46.3923			1.82106
$650$	−4.46410	−	15.4641i	−0.175096	−	0.606552i
$651$	−3.26795			−0.128081
$652$	−6.16987	+	3.56218i	−0.241631	+	0.139506i
$653$	7.35641	+	12.7417i	0.287878	+	0.498620i	0.973303	−	0.229523i	$-0.0737168\pi$
$653$	7.35641	+	12.7417i	0.287878	+	0.498620i	−0.685425	+	0.728144i	$0.740383\pi$
$654$	5.63397	−	9.75833i	0.220306	−	0.381581i
$655$		−	10.9282i		−	0.427000i
$656$	7.33013	+	4.23205i	0.286193	+	0.165234i
$657$	1.26795	+	0.732051i	0.0494674	+	0.0285600i
$658$			3.92820i			0.153137i
$659$	6.62436	−	11.4737i	0.258048	−	0.446953i	−0.707671	−	0.706542i	$-0.750254\pi$
$659$	6.62436	−	11.4737i	0.258048	−	0.446953i	0.965719	+	0.259590i	$0.0835873\pi$
$660$	−1.90192	−	3.29423i	−0.0740323	−	0.128228i
$661$	19.5167	−	11.2679i	0.759110	−	0.438272i	−0.0698660	−	0.997556i	$-0.522257\pi$
$661$	19.5167	−	11.2679i	0.759110	−	0.438272i	0.828976	+	0.559284i	$0.188924\pi$
$662$	6.78461			0.263691
$663$	1.96410	−	7.93782i	0.0762794	−	0.308279i
$664$	9.26795			0.359666
$665$	0.294229	−	0.169873i	0.0114097	−	0.00658739i
$666$	3.36603	+	5.83013i	0.130431	+	0.225913i
$667$	13.1962	−	22.8564i	0.510957	−	0.885004i
$668$			5.07180i			0.196234i
$669$	4.73205	+	2.73205i	0.182952	+	0.105627i
$670$	6.33975	+	3.66025i	0.244926	+	0.141408i
$671$			19.3923i			0.748632i
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	−21.8205	−	37.7942i	−0.841119	−	1.45686i	−0.888950	−	0.458005i	$-0.848564\pi$
$673$	−21.8205	−	37.7942i	−0.841119	−	1.45686i	0.0478308	−	0.998855i	$-0.484769\pi$
$674$	−9.52628	+	5.50000i	−0.366939	+	0.211852i
$675$	4.46410			0.171823
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	43.2679			1.66292			0.831461	−	0.555583i	$-0.187505\pi$
$677$	43.2679			1.66292			0.831461	+	0.555583i	$0.187505\pi$
$678$	6.63397	−	3.83013i	0.254776	−	0.147095i
$679$	−7.09808	−	12.2942i	−0.272399	−	0.471809i
$680$	−0.830127	+	1.43782i	−0.0318339	+	0.0551380i
$681$			13.3205i			0.510443i
$682$	−14.7058	−	8.49038i	−0.563113	−	0.325113i
$683$	−15.0000	−	8.66025i	−0.573959	−	0.331375i	0.184770	−	0.982782i	$-0.440846\pi$
$683$	−15.0000	−	8.66025i	−0.573959	−	0.331375i	−0.758729	+	0.651406i	$0.774179\pi$
$684$		−	0.464102i		−	0.0177454i
$685$	7.12436	−	12.3397i	0.272208	−	0.471477i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	15.0622	−	8.69615i	0.574658	−	0.331779i
$688$	8.73205			0.332906
$689$	−8.59808	+	34.7487i	−0.327561	+	1.32382i
$690$	−5.46410			−0.208015
$691$	32.1051	−	18.5359i	1.22134	−	0.705139i	0.256133	−	0.966641i	$-0.417551\pi$
$691$	32.1051	−	18.5359i	1.22134	−	0.705139i	0.965203	+	0.261503i	$0.0842180\pi$
$692$	−1.09808	−	1.90192i	−0.0417426	−	0.0723003i
$693$	−2.59808	+	4.50000i	−0.0986928	+	0.170941i
$694$		−	6.46410i		−	0.245374i
$695$	−10.8109	−	6.24167i	−0.410080	−	0.236760i
$696$	−3.06218	−	1.76795i	−0.116072	−	0.0670139i
$697$		−	19.1962i		−	0.727106i
$698$	3.07180	−	5.32051i	0.116269	−	0.201384i
$699$	−9.29423	−	16.0981i	−0.351540	−	0.608885i
$700$	3.86603	−	2.23205i	0.146122	−	0.0843636i
$701$	−25.7846			−0.973871			−0.486936	−	0.873438i	$-0.661885\pi$
$701$	−25.7846			−0.973871			−0.486936	+	0.873438i	$0.661885\pi$
$702$	−1.00000	−	3.46410i	−0.0377426	−	0.130744i
$703$	−3.12436			−0.117837
$704$	−4.50000	+	2.59808i	−0.169600	+	0.0979187i
$705$	1.43782	+	2.49038i	0.0541515	+	0.0937932i
$706$	15.6603	−	27.1244i	0.589381	−	1.02084i
$707$			4.92820i			0.185344i
$708$	−7.73205	−	4.46410i	−0.290588	−	0.167771i
$709$	44.4904	+	25.6865i	1.67087	+	0.964678i	0.967152	+	0.254200i	$0.0818123\pi$
$709$	44.4904	+	25.6865i	1.67087	+	0.964678i	0.703720	+	0.710478i	$0.251521\pi$
$710$			5.32051i			0.199675i
$711$	−4.50000	+	7.79423i	−0.168763	+	0.292306i
$712$	8.42820	+	14.5981i	0.315860	+	0.547086i
$713$	−21.1244	+	12.1962i	−0.791113	+	0.456749i
$714$	2.26795			0.0848759
$715$	13.1769	−	3.80385i	0.492789	−	0.142256i
$716$	−3.46410			−0.129460
$717$	23.0263	−	13.2942i	0.859932	−	0.496482i
$718$	−17.2224	−	29.8301i	−0.642735	−	1.11325i
$719$	19.7224	−	34.1603i	0.735523	−	1.27396i	−0.218971	−	0.975731i	$-0.570270\pi$
$719$	19.7224	−	34.1603i	0.735523	−	1.27396i	0.954494	−	0.298231i	$-0.0963966\pi$
$720$			0.732051i			0.0272819i
$721$	14.0263	+	8.09808i	0.522366	+	0.301588i
$722$	−16.2679	−	9.39230i	−0.605430	−	0.349545i
$723$		−	10.9282i		−	0.406424i
$724$	7.13397	−	12.3564i	0.265132	−	0.459222i
$725$	7.89230	+	13.6699i	0.293113	+	0.507686i
$726$	−13.8564	+	8.00000i	−0.514259	+	0.296908i
$727$	3.60770			0.133802			0.0669010	−	0.997760i	$-0.478689\pi$
$727$	3.60770			0.133802			0.0669010	+	0.997760i	$0.478689\pi$
$728$	−2.59808	−	2.50000i	−0.0962911	−	0.0926562i
$729$	1.00000			0.0370370
$730$	0.928203	−	0.535898i	0.0343543	−	0.0198345i
$731$	−9.90192	−	17.1506i	−0.366236	−	0.634339i
$732$	1.86603	−	3.23205i	0.0689703	−	0.119460i
$733$		−	25.7846i		−	0.952376i	−0.879343	−	0.476188i	$-0.842018\pi$
$733$		−	25.7846i		−	0.952376i	0.879343	−	0.476188i	$-0.157982\pi$
$734$	−11.5359	−	6.66025i	−0.425798	−	0.245834i
$735$	0.633975	+	0.366025i	0.0233845	+	0.0135011i
$736$			7.46410i			0.275130i
$737$	25.9808	−	45.0000i	0.957014	−	1.65760i
$738$	−4.23205	−	7.33013i	−0.155784	−	0.269826i
$739$	−33.9282	+	19.5885i	−1.24807	+	0.720573i	−0.970724	−	0.240197i	$-0.922788\pi$
$739$	−33.9282	+	19.5885i	−1.24807	+	0.720573i	−0.277345	+	0.960770i	$0.589455\pi$
$740$	4.92820			0.181164
$741$	1.62436	+	0.401924i	0.0596722	+	0.0147650i
$742$	−9.92820			−0.364476
$743$	12.1699	−	7.02628i	0.446469	−	0.257769i	−0.259869	−	0.965644i	$-0.583679\pi$
$743$	12.1699	−	7.02628i	0.446469	−	0.257769i	0.706338	+	0.707875i	$0.250346\pi$
$744$	1.63397	+	2.83013i	0.0599044	+	0.103757i
$745$	2.92820	−	5.07180i	0.107281	−	0.185816i
$746$		−	15.1244i		−	0.553742i
$747$	−8.02628	−	4.63397i	−0.293666	−	0.169548i
$748$	10.2058	+	5.89230i	0.373160	+	0.215444i
$749$			6.07180i			0.221859i
$750$	3.46410	−	6.00000i	0.126491	−	0.219089i
$751$	2.57180	+	4.45448i	0.0938462	+	0.162546i	0.909126	−	0.416520i	$-0.136750\pi$
$751$	2.57180	+	4.45448i	0.0938462	+	0.162546i	−0.815280	+	0.579067i	$0.803417\pi$
$752$	3.40192	−	1.96410i	0.124055	−	0.0716234i
$753$	−17.5167			−0.638343
$754$	8.83975	−	9.18653i	0.321925	−	0.334554i
$755$	0.875644			0.0318680
$756$	0.866025	−	0.500000i	0.0314970	−	0.0181848i
$757$	−8.09808	−	14.0263i	−0.294330	−	0.509794i	0.680499	−	0.732749i	$-0.261763\pi$
$757$	−8.09808	−	14.0263i	−0.294330	−	0.509794i	−0.974829	+	0.222955i	$0.928430\pi$
$758$	−18.0263	+	31.2224i	−0.654744	+	1.13405i
$759$			38.7846i			1.40779i
$760$	−0.294229	−	0.169873i	−0.0106728	−	0.00616194i
$761$	−15.8038	−	9.12436i	−0.572889	−	0.330758i	0.185413	−	0.982661i	$-0.440638\pi$
$761$	−15.8038	−	9.12436i	−0.572889	−	0.330758i	−0.758302	+	0.651903i	$0.773971\pi$
$762$		−	14.3923i		−	0.521378i
$763$	−5.63397	+	9.75833i	−0.203964	+	0.353275i
$764$	−4.09808	−	7.09808i	−0.148263	−	0.256799i
$765$	1.43782	−	0.830127i	0.0519846	−	0.0300133i
$766$	31.0000			1.12008
$767$	22.3205	−	23.1962i	0.805947	−	0.837565i
$768$	1.00000			0.0360844
$769$	−37.4711	+	21.6340i	−1.35124	+	0.780141i	−0.988424	−	0.151718i	$-0.951519\pi$
$769$	−37.4711	+	21.6340i	−1.35124	+	0.780141i	−0.362820	+	0.931859i	$0.618186\pi$

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{10} +(4.50000 - 2.59808i) q^{11} -1.00000 q^{12} +(0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(0.633975 - 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.13397 + 1.96410i) q^{17} +1.00000i q^{18} +(-0.401924 - 0.232051i) q^{19} +(0.633975 + 0.366025i) q^{20} -1.00000i q^{21} +(2.59808 - 4.50000i) q^{22} +(-3.73205 - 6.46410i) q^{23} +(-0.866025 + 0.500000i) q^{24} +4.46410 q^{25} +(-1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(1.76795 + 3.06218i) q^{29} +(0.366025 - 0.633975i) q^{30} -3.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.50000 - 2.59808i) q^{33} +2.26795i q^{34} +(-0.366025 + 0.633975i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.83013 - 3.36603i) q^{37} -0.464102 q^{38} +(-3.46410 + 1.00000i) q^{39} +0.732051 q^{40} +(-7.33013 + 4.23205i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.36603 + 7.56218i) q^{43} -5.19615i q^{44} +(-0.633975 - 0.366025i) q^{45} +(-6.46410 - 3.73205i) q^{46} +3.92820i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +2.26795 q^{51} +(-2.59808 - 2.50000i) q^{52} -9.92820 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.90192 + 3.29423i) q^{55} +(0.500000 - 0.866025i) q^{56} +0.464102i q^{57} +(3.06218 + 1.76795i) q^{58} +(7.73205 + 4.46410i) q^{59} -0.732051i q^{60} +(-1.86603 + 3.23205i) q^{61} +(-1.63397 - 2.83013i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(2.56218 + 0.633975i) q^{65} -5.19615 q^{66} +(8.66025 - 5.00000i) q^{67} +(1.13397 + 1.96410i) q^{68} +(-3.73205 + 6.46410i) q^{69} +0.732051i q^{70} +(6.29423 + 3.63397i) q^{71} +(0.866025 + 0.500000i) q^{72} -1.46410i q^{73} +(3.36603 - 5.83013i) q^{74} +(-2.23205 - 3.86603i) q^{75} +(-0.401924 + 0.232051i) q^{76} +5.19615 q^{77} +(-2.50000 + 2.59808i) q^{78} +9.00000 q^{79} +(0.633975 - 0.366025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.23205 + 7.33013i) q^{82} +9.26795i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-1.43782 - 0.830127i) q^{85} +8.73205i q^{86} +(1.76795 - 3.06218i) q^{87} +(-2.59808 - 4.50000i) q^{88} +(-14.5981 + 8.42820i) q^{89} -0.732051 q^{90} +(2.50000 - 2.59808i) q^{91} -7.46410 q^{92} +(-2.83013 + 1.63397i) q^{93} +(1.96410 + 3.40192i) q^{94} +(0.169873 - 0.294229i) q^{95} +1.00000i q^{96} +(-12.2942 - 7.09808i) q^{97} +(0.866025 + 0.500000i) q^{98} +5.19615i 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	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 18 q^{11} - 4 q^{12} + 4 q^{14} + 6 q^{15} - 2 q^{16} - 8 q^{17} - 12 q^{19} + 6 q^{20} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 14 q^{29} - 2 q^{30} - 18 q^{33} + 2 q^{35} + 2 q^{36} + 6 q^{37} + 12 q^{38} - 4 q^{40} - 12 q^{41} - 2 q^{42} - 14 q^{43} - 6 q^{45} - 12 q^{46} - 2 q^{48} + 2 q^{49} + 12 q^{50} + 16 q^{51} - 12 q^{53} + 18 q^{55} + 2 q^{56} - 12 q^{58} + 24 q^{59} - 4 q^{61} - 10 q^{62} - 4 q^{64} - 14 q^{65} + 8 q^{68} - 8 q^{69} - 6 q^{71} + 10 q^{74} - 2 q^{75} - 12 q^{76} - 10 q^{78} + 36 q^{79} + 6 q^{80} - 2 q^{81} - 10 q^{82} - 30 q^{85} + 14 q^{87} - 48 q^{89} + 4 q^{90} + 10 q^{91} - 16 q^{92} + 6 q^{93} - 6 q^{94} + 18 q^{95} - 18 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 18 * q^11 - 4 * q^12 + 4 * q^14 + 6 * q^15 - 2 * q^16 - 8 * q^17 - 12 * q^19 + 6 * q^20 - 8 * q^23 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 14 * q^29 - 2 * q^30 - 18 * q^33 + 2 * q^35 + 2 * q^36 + 6 * q^37 + 12 * q^38 - 4 * q^40 - 12 * q^41 - 2 * q^42 - 14 * q^43 - 6 * q^45 - 12 * q^46 - 2 * q^48 + 2 * q^49 + 12 * q^50 + 16 * q^51 - 12 * q^53 + 18 * q^55 + 2 * q^56 - 12 * q^58 + 24 * q^59 - 4 * q^61 - 10 * q^62 - 4 * q^64 - 14 * q^65 + 8 * q^68 - 8 * q^69 - 6 * q^71 + 10 * q^74 - 2 * q^75 - 12 * q^76 - 10 * q^78 + 36 * q^79 + 6 * q^80 - 2 * q^81 - 10 * q^82 - 30 * q^85 + 14 * q^87 - 48 * q^89 + 4 * q^90 + 10 * q^91 - 16 * q^92 + 6 * q^93 - 6 * q^94 + 18 * q^95 - 18 * q^97

Introduction

L-functions

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