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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.73205i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.73205i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.36603 - 2.36603i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.00000 q^{12} +(-3.59808 + 0.232051i) q^{13} -1.00000 q^{14} +(-2.36603 + 1.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.133975 - 0.232051i) q^{17} +1.00000i q^{18} +(-0.866025 - 0.500000i) q^{19} +(-2.36603 - 1.36603i) q^{20} +1.00000i q^{21} +(0.866025 - 1.50000i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-3.00000 + 2.00000i) q^{26} +1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.232051 + 0.401924i) q^{29} +(-1.36603 + 2.36603i) q^{30} -8.19615i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} -0.267949i q^{34} +(-1.36603 + 2.36603i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.83013 + 1.63397i) q^{37} -1.00000 q^{38} +(2.00000 + 3.00000i) q^{39} -2.73205 q^{40} +(-2.59808 + 1.50000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(3.36603 - 5.83013i) q^{43} -1.73205i q^{44} +(2.36603 + 1.36603i) q^{45} +(3.00000 + 1.73205i) q^{46} -4.46410i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.13397 + 1.23205i) q^{50} -0.267949 q^{51} +(-1.59808 + 3.23205i) q^{52} +7.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.36603 - 4.09808i) q^{55} +(-0.500000 + 0.866025i) q^{56} +1.00000i q^{57} +(0.401924 + 0.232051i) q^{58} +(11.1962 + 6.46410i) q^{59} +2.73205i q^{60} +(2.59808 - 4.50000i) q^{61} +(-4.09808 - 7.09808i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(0.633975 + 9.83013i) q^{65} -1.73205 q^{66} +(4.26795 - 2.46410i) q^{67} +(-0.133975 - 0.232051i) q^{68} +(1.73205 - 3.00000i) q^{69} +2.73205i q^{70} +(-7.09808 - 4.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.46410i q^{73} +(-1.63397 + 2.83013i) q^{74} +(1.23205 + 2.13397i) q^{75} +(-0.866025 + 0.500000i) q^{76} -1.73205 q^{77} +(3.23205 + 1.59808i) q^{78} +15.9282 q^{79} +(-2.36603 + 1.36603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -10.1962i q^{83} +(0.866025 + 0.500000i) q^{84} +(-0.633975 - 0.366025i) q^{85} -6.73205i q^{86} +(0.232051 - 0.401924i) q^{87} +(-0.866025 - 1.50000i) q^{88} +(3.06218 - 1.76795i) q^{89} +2.73205 q^{90} +(3.23205 + 1.59808i) q^{91} +3.46410 q^{92} +(-7.09808 + 4.09808i) q^{93} +(-2.23205 - 3.86603i) q^{94} +(-1.36603 + 2.36603i) q^{95} +1.00000i q^{96} +(1.43782 + 0.830127i) q^{97} +(0.866025 + 0.500000i) q^{98} +1.73205i 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} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{20} + 4 q^{25} - 12 q^{26} + 4 q^{27} - 6 q^{29} - 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 8 q^{39} - 4 q^{40} + 2 q^{42} + 10 q^{43} + 6 q^{45} + 12 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{50} - 8 q^{51} + 4 q^{52} + 28 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 24 q^{59} - 6 q^{62} - 4 q^{64} + 6 q^{65} + 24 q^{67} - 4 q^{68} - 18 q^{71} - 10 q^{74} - 2 q^{75} + 6 q^{78} + 36 q^{79} - 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{85} - 6 q^{87} - 12 q^{89} + 4 q^{90} + 6 q^{91} - 18 q^{93} - 2 q^{94} - 2 q^{95} + 30 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^20 + 4 * q^25 - 12 * q^26 + 4 * q^27 - 6 * q^29 - 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 4 * q^38 + 8 * q^39 - 4 * q^40 + 2 * q^42 + 10 * q^43 + 6 * q^45 + 12 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^50 - 8 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 24 * q^59 - 6 * q^62 - 4 * q^64 + 6 * q^65 + 24 * q^67 - 4 * q^68 - 18 * q^71 - 10 * q^74 - 2 * q^75 + 6 * q^78 + 36 * q^79 - 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^85 - 6 * q^87 - 12 * q^89 + 4 * q^90 + 6 * q^91 - 18 * q^93 - 2 * q^94 - 2 * q^95 + 30 * 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
$5$		−	2.73205i		−	1.22181i	−0.791704	−	0.610905i	$-0.790806\pi$
$5$		−	2.73205i		−	1.22181i	0.791704	−	0.610905i	$-0.209194\pi$
$6$	−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
$10$	−1.36603	−	2.36603i	−0.431975	−	0.748203i
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	−0.256520	−	0.966539i	$-0.582576\pi$
$11$	1.50000	−	0.866025i	0.452267	−	0.261116i	0.708787	+	0.705422i	$0.249243\pi$
$12$	−1.00000			−0.288675
$13$	−3.59808	+	0.232051i	−0.997927	+	0.0643593i
$13$	−3.59808	+	0.232051i	−0.997927	+	0.0643593i
$14$	−1.00000			−0.267261
$15$	−2.36603	+	1.36603i	−0.610905	+	0.352706i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.133975	−	0.232051i	0.0324936	−	0.0562806i	−0.849321	−	0.527876i	$-0.822988\pi$
$17$	0.133975	−	0.232051i	0.0324936	−	0.0562806i	0.881815	+	0.471596i	$0.156322\pi$
$18$			1.00000i			0.235702i
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	0.397360	−	0.917663i	$-0.369927\pi$
$19$	−0.866025	−	0.500000i	−0.198680	−	0.114708i	−0.596040	+	0.802955i	$0.703260\pi$
$20$	−2.36603	−	1.36603i	−0.529059	−	0.305453i
$21$			1.00000i			0.218218i
$22$	0.866025	−	1.50000i	0.184637	−	0.319801i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−2.46410			−0.492820
$26$	−3.00000	+	2.00000i	−0.588348	+	0.392232i
$27$	1.00000			0.192450
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	0.232051	+	0.401924i	0.0430908	+	0.0746354i	0.886766	−	0.462218i	$-0.152946\pi$
$29$	0.232051	+	0.401924i	0.0430908	+	0.0746354i	−0.843676	+	0.536853i	$0.819613\pi$
$30$	−1.36603	+	2.36603i	−0.249401	+	0.431975i
$31$		−	8.19615i		−	1.47207i	−0.676942	−	0.736036i	$-0.736695\pi$
$31$		−	8.19615i		−	1.47207i	0.676942	−	0.736036i	$-0.263305\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.50000	−	0.866025i	−0.261116	−	0.150756i
$34$		−	0.267949i		−	0.0459529i
$35$	−1.36603	+	2.36603i	−0.230900	+	0.399931i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−2.83013	+	1.63397i	−0.465270	+	0.268624i	−0.714258	−	0.699883i	$-0.753235\pi$
$37$	−2.83013	+	1.63397i	−0.465270	+	0.268624i	0.248988	+	0.968507i	$0.419902\pi$
$38$	−1.00000			−0.162221
$39$	2.00000	+	3.00000i	0.320256	+	0.480384i
$40$	−2.73205			−0.431975
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	3.36603	−	5.83013i	0.513314	−	0.889086i	−0.486567	−	0.873643i	$-0.661751\pi$
$43$	3.36603	−	5.83013i	0.513314	−	0.889086i	0.999881	−	0.0154426i	$-0.00491573\pi$
$44$		−	1.73205i		−	0.261116i
$45$	2.36603	+	1.36603i	0.352706	+	0.203635i
$46$	3.00000	+	1.73205i	0.442326	+	0.255377i
$47$		−	4.46410i		−	0.651156i	−0.945515	−	0.325578i	$-0.894441\pi$
$47$		−	4.46410i		−	0.651156i	0.945515	−	0.325578i	$-0.105559\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−2.13397	+	1.23205i	−0.301790	+	0.174238i
$51$	−0.267949			−0.0375204
$52$	−1.59808	+	3.23205i	−0.221613	+	0.448205i
$53$	7.00000			0.961524			0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000			0.961524			0.480762	+	0.876851i	$0.340360\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−2.36603	−	4.09808i	−0.319035	−	0.552584i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$			1.00000i			0.132453i
$58$	0.401924	+	0.232051i	0.0527752	+	0.0304698i
$59$	11.1962	+	6.46410i	1.45761	+	0.841554i	0.998894	−	0.0470259i	$-0.0149743\pi$
$59$	11.1962	+	6.46410i	1.45761	+	0.841554i	0.458721	+	0.888580i	$0.348308\pi$
$60$			2.73205i			0.352706i
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	−0.650381	−	0.759608i	$-0.725391\pi$
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	0.983030	+	0.183442i	$0.0587240\pi$
$62$	−4.09808	−	7.09808i	−0.520456	−	0.901457i
$63$	0.866025	−	0.500000i	0.109109	−	0.0629941i
$64$	−1.00000			−0.125000
$65$	0.633975	+	9.83013i	0.0786349	+	1.21928i
$66$	−1.73205			−0.213201
$67$	4.26795	−	2.46410i	0.521413	−	0.301038i	−0.216100	−	0.976371i	$-0.569334\pi$
$67$	4.26795	−	2.46410i	0.521413	−	0.301038i	0.737513	+	0.675333i	$0.236000\pi$
$68$	−0.133975	−	0.232051i	−0.0162468	−	0.0281403i
$69$	1.73205	−	3.00000i	0.208514	−	0.361158i
$70$			2.73205i			0.326543i
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	0.0156881	−	0.999877i	$-0.495006\pi$
$71$	−7.09808	−	4.09808i	−0.842387	−	0.486352i	−0.858075	+	0.513525i	$0.828339\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			1.46410i			0.171360i	0.996323	+	0.0856801i	$0.0273063\pi$
$73$			1.46410i			0.171360i	−0.996323	+	0.0856801i	$0.972694\pi$
$74$	−1.63397	+	2.83013i	−0.189946	+	0.328996i
$75$	1.23205	+	2.13397i	0.142265	+	0.246410i
$76$	−0.866025	+	0.500000i	−0.0993399	+	0.0573539i
$77$	−1.73205			−0.197386
$78$	3.23205	+	1.59808i	0.365958	+	0.180946i
$79$	15.9282			1.79206			0.896031	−	0.443991i	$-0.146438\pi$
$79$	15.9282			1.79206			0.896031	+	0.443991i	$0.146438\pi$
$80$	−2.36603	+	1.36603i	−0.264530	+	0.152726i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$		−	10.1962i		−	1.11917i	−0.828772	−	0.559587i	$-0.810960\pi$
$83$		−	10.1962i		−	1.11917i	0.828772	−	0.559587i	$-0.189040\pi$
$84$	0.866025	+	0.500000i	0.0944911	+	0.0545545i
$85$	−0.633975	−	0.366025i	−0.0687642	−	0.0397010i
$86$		−	6.73205i		−	0.725936i
$87$	0.232051	−	0.401924i	0.0248785	−	0.0430908i
$88$	−0.866025	−	1.50000i	−0.0923186	−	0.159901i
$89$	3.06218	−	1.76795i	0.324590	−	0.187402i	−0.328847	−	0.944383i	$-0.606660\pi$
$89$	3.06218	−	1.76795i	0.324590	−	0.187402i	0.653437	+	0.756981i	$0.273327\pi$
$90$	2.73205			0.287983
$91$	3.23205	+	1.59808i	0.338811	+	0.167524i
$92$	3.46410			0.361158
$93$	−7.09808	+	4.09808i	−0.736036	+	0.424951i
$94$	−2.23205	−	3.86603i	−0.230218	−	0.398750i
$95$	−1.36603	+	2.36603i	−0.140151	+	0.242749i
$96$			1.00000i			0.102062i
$97$	1.43782	+	0.830127i	0.145989	+	0.0842866i	0.571215	−	0.820800i	$-0.306472\pi$
$97$	1.43782	+	0.830127i	0.145989	+	0.0842866i	−0.425226	+	0.905087i	$0.639806\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$			1.73205i			0.174078i
$100$	−1.23205	+	2.13397i	−0.123205	+	0.213397i
$101$	8.46410	+	14.6603i	0.842210	+	1.45875i	0.888023	+	0.459800i	$0.152079\pi$
$101$	8.46410	+	14.6603i	0.842210	+	1.45875i	−0.0458130	+	0.998950i	$0.514588\pi$
$102$	−0.232051	+	0.133975i	−0.0229765	+	0.0132655i
$103$	−11.2679			−1.11026			−0.555132	−	0.831762i	$-0.687332\pi$
$103$	−11.2679			−1.11026			−0.555132	+	0.831762i	$0.687332\pi$
$104$	0.232051	+	3.59808i	0.0227545	+	0.352820i
$105$	2.73205			0.266621
$106$	6.06218	−	3.50000i	0.588811	−	0.339950i
$107$	8.42820	+	14.5981i	0.814785	+	1.41125i	0.909482	+	0.415743i	$0.136478\pi$
$107$	8.42820	+	14.5981i	0.814785	+	1.41125i	−0.0946969	+	0.995506i	$0.530188\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			1.26795i			0.121448i	0.998155	+	0.0607238i	$0.0193409\pi$
$109$			1.26795i			0.121448i	−0.998155	+	0.0607238i	$0.980659\pi$
$110$	−4.09808	−	2.36603i	−0.390736	−	0.225592i
$111$	2.83013	+	1.63397i	0.268624	+	0.155090i
$112$			1.00000i			0.0944911i
$113$	−9.36603	+	16.2224i	−0.881082	+	1.52608i	−0.0309416	+	0.999521i	$0.509851\pi$
$113$	−9.36603	+	16.2224i	−0.881082	+	1.52608i	−0.850140	+	0.526557i	$0.823483\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$	8.19615	−	4.73205i	0.764295	−	0.441266i
$116$	0.464102			0.0430908
$117$	1.59808	−	3.23205i	0.147742	−	0.298803i
$118$	12.9282			1.19014
$119$	−0.232051	+	0.133975i	−0.0212721	+	0.0122814i
$120$	1.36603	+	2.36603i	0.124700	+	0.215988i
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$		−	5.19615i		−	0.470438i
$123$	2.59808	+	1.50000i	0.234261	+	0.135250i
$124$	−7.09808	−	4.09808i	−0.637426	−	0.368018i
$125$		−	6.92820i		−	0.619677i
$126$	0.500000	−	0.866025i	0.0445435	−	0.0771517i
$127$	−4.26795	−	7.39230i	−0.378719	−	0.655961i	0.612157	−	0.790736i	$-0.290302\pi$
$127$	−4.26795	−	7.39230i	−0.378719	−	0.655961i	−0.990876	+	0.134775i	$0.956969\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−6.73205			−0.592724
$130$	5.46410	+	8.19615i	0.479233	+	0.718850i
$131$	13.8564			1.21064			0.605320	−	0.795982i	$-0.293045\pi$
$131$	13.8564			1.21064			0.605320	+	0.795982i	$0.293045\pi$
$132$	−1.50000	+	0.866025i	−0.130558	+	0.0753778i
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	2.46410	−	4.26795i	0.212866	−	0.368695i
$135$		−	2.73205i		−	0.235137i
$136$	−0.232051	−	0.133975i	−0.0198982	−	0.0114882i
$137$	5.53590	+	3.19615i	0.472964	+	0.273066i	0.717480	−	0.696580i	$-0.245296\pi$
$137$	5.53590	+	3.19615i	0.472964	+	0.273066i	−0.244516	+	0.969645i	$0.578629\pi$
$138$		−	3.46410i		−	0.294884i
$139$	9.79423	−	16.9641i	0.830736	−	1.43888i	−0.0667201	−	0.997772i	$-0.521253\pi$
$139$	9.79423	−	16.9641i	0.830736	−	1.43888i	0.897456	−	0.441105i	$-0.145413\pi$
$140$	1.36603	+	2.36603i	0.115450	+	0.199966i
$141$	−3.86603	+	2.23205i	−0.325578	+	0.187973i
$142$	−8.19615			−0.687806
$143$	−5.19615	+	3.46410i	−0.434524	+	0.289683i
$144$	1.00000			0.0833333
$145$	1.09808	−	0.633975i	0.0911903	−	0.0526487i
$146$	0.732051	+	1.26795i	0.0605850	+	0.104936i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$			3.26795i			0.268624i
$149$	12.0000	+	6.92820i	0.983078	+	0.567581i	0.903198	−	0.429224i	$-0.141213\pi$
$149$	12.0000	+	6.92820i	0.983078	+	0.567581i	0.0798802	+	0.996804i	$0.474546\pi$
$150$	2.13397	+	1.23205i	0.174238	+	0.100597i
$151$		−	5.19615i		−	0.422857i	−0.977393	−	0.211428i	$-0.932188\pi$
$151$		−	5.19615i		−	0.422857i	0.977393	−	0.211428i	$-0.0678115\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	0.133975	+	0.232051i	0.0108312	+	0.0187602i
$154$	−1.50000	+	0.866025i	−0.120873	+	0.0697863i
$155$	−22.3923			−1.79859
$156$	3.59808	−	0.232051i	0.288077	−	0.0185789i
$157$	−7.46410			−0.595700			−0.297850	−	0.954613i	$-0.596270\pi$
$157$	−7.46410			−0.595700			−0.297850	+	0.954613i	$0.596270\pi$
$158$	13.7942	−	7.96410i	1.09741	−	0.633590i
$159$	−3.50000	−	6.06218i	−0.277568	−	0.480762i
$160$	−1.36603	+	2.36603i	−0.107994	+	0.187051i
$161$		−	3.46410i		−	0.273009i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	0.633975	+	0.366025i	0.0496567	+	0.0286693i	0.524623	−	0.851335i	$-0.324206\pi$
$163$	0.633975	+	0.366025i	0.0496567	+	0.0286693i	−0.474966	+	0.880004i	$0.657540\pi$
$164$			3.00000i			0.234261i
$165$	−2.36603	+	4.09808i	−0.184195	+	0.319035i
$166$	−5.09808	−	8.83013i	−0.395687	−	0.685351i
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.886365	−	0.462988i	$-0.846777\pi$
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.0422232	+	0.999108i	$0.513444\pi$
$168$	1.00000			0.0771517
$169$	12.8923	−	1.66987i	0.991716	−	0.128452i
$170$	−0.732051			−0.0561457
$171$	0.866025	−	0.500000i	0.0662266	−	0.0382360i
$172$	−3.36603	−	5.83013i	−0.256657	−	0.444543i
$173$	7.56218	−	13.0981i	0.574942	−	0.995828i	−0.421106	−	0.907011i	$-0.638358\pi$
$173$	7.56218	−	13.0981i	0.574942	−	0.995828i	0.996048	−	0.0888170i	$-0.0283086\pi$
$174$		−	0.464102i		−	0.0351835i
$175$	2.13397	+	1.23205i	0.161313	+	0.0931343i
$176$	−1.50000	−	0.866025i	−0.113067	−	0.0652791i
$177$		−	12.9282i		−	0.971743i
$178$	1.76795	−	3.06218i	0.132513	−	0.229520i
$179$	2.26795	+	3.92820i	0.169514	+	0.293608i	0.938249	−	0.345960i	$-0.112447\pi$
$179$	2.26795	+	3.92820i	0.169514	+	0.293608i	−0.768735	+	0.639568i	$0.779113\pi$
$180$	2.36603	−	1.36603i	0.176353	−	0.101818i
$181$	−14.6603			−1.08969			−0.544844	−	0.838537i	$-0.683411\pi$
$181$	−14.6603			−1.08969			−0.544844	+	0.838537i	$0.683411\pi$
$182$	3.59808	−	0.232051i	0.266707	−	0.0172008i
$183$	−5.19615			−0.384111
$184$	3.00000	−	1.73205i	0.221163	−	0.127688i
$185$	4.46410	+	7.73205i	0.328207	+	0.568472i
$186$	−4.09808	+	7.09808i	−0.300486	+	0.520456i
$187$		−	0.464102i		−	0.0339385i
$188$	−3.86603	−	2.23205i	−0.281959	−	0.162789i
$189$	−0.866025	−	0.500000i	−0.0629941	−	0.0363696i
$190$			2.73205i			0.198204i
$191$	0.562178	−	0.973721i	0.0406778	−	0.0704559i	−0.844970	−	0.534814i	$-0.820382\pi$
$191$	0.562178	−	0.973721i	0.0406778	−	0.0704559i	0.885647	+	0.464358i	$0.153715\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−7.96410	+	4.59808i	−0.573269	+	0.330977i	−0.758454	−	0.651727i	$-0.774045\pi$
$193$	−7.96410	+	4.59808i	−0.573269	+	0.330977i	0.185185	+	0.982704i	$0.440712\pi$
$194$	1.66025			0.119199
$195$	8.19615	−	5.46410i	0.586939	−	0.391292i
$196$	1.00000			0.0714286
$197$	−8.08846	+	4.66987i	−0.576279	+	0.332715i	−0.759653	−	0.650328i	$-0.774631\pi$
$197$	−8.08846	+	4.66987i	−0.576279	+	0.332715i	0.183374	+	0.983043i	$0.441298\pi$
$198$	0.866025	+	1.50000i	0.0615457	+	0.106600i
$199$	−2.90192	+	5.02628i	−0.205712	+	0.356304i	−0.950359	−	0.311155i	$-0.899284\pi$
$199$	−2.90192	+	5.02628i	−0.205712	+	0.356304i	0.744647	+	0.667458i	$0.232618\pi$
$200$			2.46410i			0.174238i
$201$	−4.26795	−	2.46410i	−0.301038	−	0.173804i
$202$	14.6603	+	8.46410i	1.03149	+	0.595532i
$203$		−	0.464102i		−	0.0325735i
$204$	−0.133975	+	0.232051i	−0.00938010	+	0.0162468i
$205$	4.09808	+	7.09808i	0.286222	+	0.495751i
$206$	−9.75833	+	5.63397i	−0.679895	+	0.392538i
$207$	−3.46410			−0.240772
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$	−1.73205			−0.119808
$210$	2.36603	−	1.36603i	0.163271	−	0.0942647i
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.833858	−	0.551979i	$-0.813873\pi$
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.0610990	−	0.998132i	$-0.519461\pi$
$212$	3.50000	−	6.06218i	0.240381	−	0.416352i
$213$			8.19615i			0.561591i
$214$	14.5981	+	8.42820i	0.997904	+	0.576140i
$215$	−15.9282	−	9.19615i	−1.08629	−	0.627172i
$216$		−	1.00000i		−	0.0680414i
$217$	−4.09808	+	7.09808i	−0.278196	+	0.481849i
$218$	0.633975	+	1.09808i	0.0429382	+	0.0743711i
$219$	1.26795	−	0.732051i	0.0856801	−	0.0494674i
$220$	−4.73205			−0.319035
$221$	−0.428203	+	0.866025i	−0.0288041	+	0.0582552i
$222$	3.26795			0.219330
$223$	−3.12436	+	1.80385i	−0.209222	+	0.120795i	−0.600950	−	0.799287i	$-0.705211\pi$
$223$	−3.12436	+	1.80385i	−0.209222	+	0.120795i	0.391728	+	0.920081i	$0.371878\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	1.23205	−	2.13397i	0.0821367	−	0.142265i
$226$			18.7321i			1.24604i
$227$	2.07180	+	1.19615i	0.137510	+	0.0793914i	0.567177	−	0.823596i	$-0.308036\pi$
$227$	2.07180	+	1.19615i	0.137510	+	0.0793914i	−0.429667	+	0.902988i	$0.641369\pi$
$228$	0.866025	+	0.500000i	0.0573539	+	0.0331133i
$229$		−	6.07180i		−	0.401236i	−0.979670	−	0.200618i	$-0.935705\pi$
$229$		−	6.07180i		−	0.401236i	0.979670	−	0.200618i	$-0.0642949\pi$
$230$	4.73205	−	8.19615i	0.312022	−	0.540438i
$231$	0.866025	+	1.50000i	0.0569803	+	0.0986928i
$232$	0.401924	−	0.232051i	0.0263876	−	0.0152349i
$233$	−15.1244			−0.990829			−0.495415	−	0.868657i	$-0.664984\pi$
$233$	−15.1244			−0.990829			−0.495415	+	0.868657i	$0.664984\pi$
$234$	−0.232051	−	3.59808i	−0.0151696	−	0.235214i
$235$	−12.1962			−0.795589
$236$	11.1962	−	6.46410i	0.728807	−	0.420777i
$237$	−7.96410	−	13.7942i	−0.517324	−	0.896031i
$238$	−0.133975	+	0.232051i	−0.00868428	+	0.0150416i
$239$		−	2.73205i		−	0.176722i	−0.996089	−	0.0883608i	$-0.971837\pi$
$239$		−	2.73205i		−	0.176722i	0.996089	−	0.0883608i	$-0.0281629\pi$
$240$	2.36603	+	1.36603i	0.152726	+	0.0881766i
$241$	6.92820	+	4.00000i	0.446285	+	0.257663i	0.706260	−	0.707953i	$-0.250381\pi$
$241$	6.92820	+	4.00000i	0.446285	+	0.257663i	−0.259975	+	0.965615i	$0.583714\pi$
$242$			8.00000i			0.514259i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.59808	−	4.50000i	−0.166325	−	0.288083i
$245$	2.36603	−	1.36603i	0.151160	−	0.0872722i
$246$	3.00000			0.191273
$247$	3.23205	+	1.59808i	0.205650	+	0.101683i
$248$	−8.19615			−0.520456
$249$	−8.83013	+	5.09808i	−0.559587	+	0.323077i
$250$	−3.46410	−	6.00000i	−0.219089	−	0.379473i
$251$	−5.56218	+	9.63397i	−0.351082	+	0.608091i	−0.986439	−	0.164127i	$-0.947519\pi$
$251$	−5.56218	+	9.63397i	−0.351082	+	0.608091i	0.635358	+	0.772218i	$0.280853\pi$
$252$		−	1.00000i		−	0.0629941i
$253$	5.19615	+	3.00000i	0.326679	+	0.188608i
$254$	−7.39230	−	4.26795i	−0.463834	−	0.267795i
$255$			0.732051i			0.0458428i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.66987	+	2.89230i	0.104164	+	0.180417i	0.913396	−	0.407072i	$-0.133450\pi$
$257$	1.66987	+	2.89230i	0.104164	+	0.180417i	−0.809232	+	0.587489i	$0.800117\pi$
$258$	−5.83013	+	3.36603i	−0.362968	+	0.209560i
$259$	3.26795			0.203060
$260$	8.83013	+	4.36603i	0.547621	+	0.270769i
$261$	−0.464102			−0.0287272
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	−4.56218	−	7.90192i	−0.281316	−	0.487253i	0.690393	−	0.723434i	$-0.257438\pi$
$263$	−4.56218	−	7.90192i	−0.281316	−	0.487253i	−0.971709	+	0.236181i	$0.924104\pi$
$264$	−0.866025	+	1.50000i	−0.0533002	+	0.0923186i
$265$		−	19.1244i		−	1.17480i
$266$	0.866025	+	0.500000i	0.0530994	+	0.0306570i
$267$	−3.06218	−	1.76795i	−0.187402	−	0.108197i
$268$		−	4.92820i		−	0.301038i
$269$	−8.92820	+	15.4641i	−0.544362	+	0.942863i	0.454285	+	0.890857i	$0.349895\pi$
$269$	−8.92820	+	15.4641i	−0.544362	+	0.942863i	−0.998647	+	0.0520063i	$0.983438\pi$
$270$	−1.36603	−	2.36603i	−0.0831337	−	0.143992i
$271$	−8.70577	+	5.02628i	−0.528838	+	0.305325i	−0.740543	−	0.672009i	$-0.765432\pi$
$271$	−8.70577	+	5.02628i	−0.528838	+	0.305325i	0.211705	+	0.977334i	$0.432098\pi$
$272$	−0.267949			−0.0162468
$273$	−0.232051	−	3.59808i	−0.0140444	−	0.217765i
$274$	6.39230			0.386173
$275$	−3.69615	+	2.13397i	−0.222886	+	0.128684i
$276$	−1.73205	−	3.00000i	−0.104257	−	0.180579i
$277$	−12.6603	+	21.9282i	−0.760681	+	1.31754i	0.181819	+	0.983332i	$0.441801\pi$
$277$	−12.6603	+	21.9282i	−0.760681	+	1.31754i	−0.942500	+	0.334206i	$0.891532\pi$
$278$		−	19.5885i		−	1.17484i
$279$	7.09808	+	4.09808i	0.424951	+	0.245345i
$280$	2.36603	+	1.36603i	0.141397	+	0.0816356i
$281$		−	17.6603i		−	1.05352i	−0.850013	−	0.526761i	$-0.823406\pi$
$281$		−	17.6603i		−	1.05352i	0.850013	−	0.526761i	$-0.176594\pi$
$282$	−2.23205	+	3.86603i	−0.132917	+	0.230218i
$283$	8.92820	+	15.4641i	0.530727	+	0.919245i	0.999357	+	0.0358512i	$0.0114142\pi$
$283$	8.92820	+	15.4641i	0.530727	+	0.919245i	−0.468631	+	0.883394i	$0.655252\pi$
$284$	−7.09808	+	4.09808i	−0.421193	+	0.243176i
$285$	2.73205			0.161833
$286$	−2.76795	+	5.59808i	−0.163672	+	0.331021i
$287$	3.00000			0.177084
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	8.46410	+	14.6603i	0.497888	+	0.862368i
$290$	0.633975	−	1.09808i	0.0372283	−	0.0644813i
$291$		−	1.66025i		−	0.0973258i
$292$	1.26795	+	0.732051i	0.0742011	+	0.0428400i
$293$	26.7846	+	15.4641i	1.56477	+	0.903422i	0.996763	+	0.0804015i	$0.0256203\pi$
$293$	26.7846	+	15.4641i	1.56477	+	0.903422i	0.568011	+	0.823021i	$0.307713\pi$
$294$		−	1.00000i		−	0.0583212i
$295$	17.6603	−	30.5885i	1.02822	−	1.78093i
$296$	1.63397	+	2.83013i	0.0949728	+	0.164498i
$297$	1.50000	−	0.866025i	0.0870388	−	0.0502519i
$298$	13.8564			0.802680
$299$	−6.92820	−	10.3923i	−0.400668	−	0.601003i
$300$	2.46410			0.142265
$301$	−5.83013	+	3.36603i	−0.336043	+	0.194014i
$302$	−2.59808	−	4.50000i	−0.149502	−	0.258946i
$303$	8.46410	−	14.6603i	0.486250	−	0.842210i
$304$			1.00000i			0.0573539i
$305$	−12.2942	−	7.09808i	−0.703965	−	0.406435i
$306$	0.232051	+	0.133975i	0.0132655	+	0.00765882i
$307$			29.3923i			1.67751i	0.544511	+	0.838754i	$0.316715\pi$
$307$			29.3923i			1.67751i	−0.544511	+	0.838754i	$0.683285\pi$
$308$	−0.866025	+	1.50000i	−0.0493464	+	0.0854704i
$309$	5.63397	+	9.75833i	0.320506	+	0.555132i
$310$	−19.3923	+	11.1962i	−1.10141	+	0.635899i
$311$	−7.73205			−0.438444			−0.219222	−	0.975675i	$-0.570352\pi$
$311$	−7.73205			−0.438444			−0.219222	+	0.975675i	$0.570352\pi$
$312$	3.00000	−	2.00000i	0.169842	−	0.113228i
$313$	−31.5167			−1.78143			−0.890713	−	0.454565i	$-0.849795\pi$
$313$	−31.5167			−1.78143			−0.890713	+	0.454565i	$0.849795\pi$
$314$	−6.46410	+	3.73205i	−0.364790	+	0.210612i
$315$	−1.36603	−	2.36603i	−0.0769668	−	0.133310i
$316$	7.96410	−	13.7942i	0.448016	−	0.775986i
$317$		−	15.8564i		−	0.890585i	−0.895385	−	0.445292i	$-0.853100\pi$
$317$		−	15.8564i		−	0.890585i	0.895385	−	0.445292i	$-0.146900\pi$
$318$	−6.06218	−	3.50000i	−0.339950	−	0.196270i
$319$	0.696152	+	0.401924i	0.0389771	+	0.0225034i
$320$			2.73205i			0.152726i
$321$	8.42820	−	14.5981i	0.470416	−	0.814785i
$322$	−1.73205	−	3.00000i	−0.0965234	−	0.167183i
$323$	−0.232051	+	0.133975i	−0.0129117	+	0.00745455i
$324$	−1.00000			−0.0555556
$325$	8.86603	−	0.571797i	0.491799	−	0.0317176i
$326$	0.732051			0.0405445
$327$	1.09808	−	0.633975i	0.0607238	−	0.0350589i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−2.23205	+	3.86603i	−0.123057	+	0.213141i
$330$			4.73205i			0.260491i
$331$	−0.124356	−	0.0717968i	−0.00683520	−	0.00394631i	0.496579	−	0.867992i	$-0.334589\pi$
$331$	−0.124356	−	0.0717968i	−0.00683520	−	0.00394631i	−0.503414	+	0.864046i	$0.667923\pi$
$332$	−8.83013	−	5.09808i	−0.484616	−	0.279793i
$333$		−	3.26795i		−	0.179083i
$334$	−6.92820	+	12.0000i	−0.379094	+	0.656611i
$335$	−6.73205	−	11.6603i	−0.367811	−	0.637068i
$336$	0.866025	−	0.500000i	0.0472456	−	0.0272772i
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	10.3301	−	7.89230i	0.561885	−	0.429285i
$339$	18.7321			1.01739
$340$	−0.633975	+	0.366025i	−0.0343821	+	0.0198505i
$341$	−7.09808	−	12.2942i	−0.384382	−	0.665770i
$342$	0.500000	−	0.866025i	0.0270369	−	0.0468293i
$343$		−	1.00000i		−	0.0539949i
$344$	−5.83013	−	3.36603i	−0.314339	−	0.181484i
$345$	−8.19615	−	4.73205i	−0.441266	−	0.254765i
$346$		−	15.1244i		−	0.813090i
$347$	7.69615	−	13.3301i	0.413151	−	0.715599i	−0.582081	−	0.813131i	$-0.697761\pi$
$347$	7.69615	−	13.3301i	0.413151	−	0.715599i	0.995232	+	0.0975319i	$0.0310948\pi$
$348$	−0.232051	−	0.401924i	−0.0124392	−	0.0215454i
$349$	−27.4641	+	15.8564i	−1.47012	+	0.848774i	−0.999438	−	0.0335290i	$-0.989325\pi$
$349$	−27.4641	+	15.8564i	−1.47012	+	0.848774i	−0.470682	+	0.882303i	$0.655992\pi$
$350$	2.46410			0.131712
$351$	−3.59808	+	0.232051i	−0.192051	+	0.0123860i
$352$	−1.73205			−0.0923186
$353$	2.19615	−	1.26795i	0.116889	−	0.0674861i	−0.440415	−	0.897794i	$-0.645169\pi$
$353$	2.19615	−	1.26795i	0.116889	−	0.0674861i	0.557305	+	0.830308i	$0.311835\pi$
$354$	−6.46410	−	11.1962i	−0.343563	−	0.595069i
$355$	−11.1962	+	19.3923i	−0.594230	+	1.02924i
$356$		−	3.53590i		−	0.187402i
$357$	0.232051	+	0.133975i	0.0122814	+	0.00709069i
$358$	3.92820	+	2.26795i	0.207612	+	0.119865i
$359$		−	14.1962i		−	0.749244i	−0.927178	−	0.374622i	$-0.877772\pi$
$359$		−	14.1962i		−	0.749244i	0.927178	−	0.374622i	$-0.122228\pi$
$360$	1.36603	−	2.36603i	0.0719959	−	0.124700i
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	−12.6962	+	7.33013i	−0.667295	+	0.385263i
$363$	8.00000			0.419891
$364$	3.00000	−	2.00000i	0.157243	−	0.104828i
$365$	4.00000			0.209370
$366$	−4.50000	+	2.59808i	−0.235219	+	0.135804i
$367$	4.66025	+	8.07180i	0.243263	+	0.421344i	0.961642	−	0.274308i	$-0.0884488\pi$
$367$	4.66025	+	8.07180i	0.243263	+	0.421344i	−0.718379	+	0.695652i	$0.755115\pi$
$368$	1.73205	−	3.00000i	0.0902894	−	0.156386i
$369$		−	3.00000i		−	0.156174i
$370$	7.73205	+	4.46410i	0.401970	+	0.232078i
$371$	−6.06218	−	3.50000i	−0.314733	−	0.181711i
$372$			8.19615i			0.424951i
$373$	3.83013	−	6.63397i	0.198316	−	0.343494i	−0.749666	−	0.661816i	$-0.769786\pi$
$373$	3.83013	−	6.63397i	0.198316	−	0.343494i	0.947983	+	0.318322i	$0.103119\pi$
$374$	−0.232051	−	0.401924i	−0.0119991	−	0.0207830i
$375$	−6.00000	+	3.46410i	−0.309839	+	0.178885i
$376$	−4.46410			−0.230218
$377$	−0.928203	−	1.39230i	−0.0478049	−	0.0717073i
$378$	−1.00000			−0.0514344
$379$	26.3660	−	15.2224i	1.35433	−	0.781924i	0.365479	−	0.930820i	$-0.380905\pi$
$379$	26.3660	−	15.2224i	1.35433	−	0.781924i	0.988853	+	0.148896i	$0.0475719\pi$
$380$	1.36603	+	2.36603i	0.0700756	+	0.121375i
$381$	−4.26795	+	7.39230i	−0.218654	+	0.378719i
$382$		−	1.12436i		−	0.0575270i
$383$	10.7942	+	6.23205i	0.551559	+	0.318443i	0.749751	−	0.661720i	$-0.230173\pi$
$383$	10.7942	+	6.23205i	0.551559	+	0.318443i	−0.198191	+	0.980163i	$0.563507\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			4.73205i			0.241168i
$386$	−4.59808	+	7.96410i	−0.234036	+	0.405362i
$387$	3.36603	+	5.83013i	0.171105	+	0.296362i
$388$	1.43782	−	0.830127i	0.0729944	−	0.0421433i
$389$	12.3923			0.628315			0.314157	−	0.949371i	$-0.398278\pi$
$389$	12.3923			0.628315			0.314157	+	0.949371i	$0.398278\pi$
$390$	4.36603	−	8.83013i	0.221082	−	0.447131i
$391$	0.928203			0.0469413
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$	−6.92820	−	12.0000i	−0.349482	−	0.605320i
$394$	−4.66987	+	8.08846i	−0.235265	+	0.407491i
$395$		−	43.5167i		−	2.18956i
$396$	1.50000	+	0.866025i	0.0753778	+	0.0435194i
$397$	−18.9904	−	10.9641i	−0.953100	−	0.550272i	−0.0590574	−	0.998255i	$-0.518809\pi$
$397$	−18.9904	−	10.9641i	−0.953100	−	0.550272i	−0.894043	+	0.447982i	$0.852143\pi$
$398$			5.80385i			0.290921i
$399$	0.500000	−	0.866025i	0.0250313	−	0.0433555i
$400$	1.23205	+	2.13397i	0.0616025	+	0.106699i
$401$	−2.41154	+	1.39230i	−0.120427	+	0.0695284i	−0.559003	−	0.829165i	$-0.688816\pi$
$401$	−2.41154	+	1.39230i	−0.120427	+	0.0695284i	0.438577	+	0.898694i	$0.355483\pi$
$402$	−4.92820			−0.245796
$403$	1.90192	+	29.4904i	0.0947416	+	1.46902i
$404$	16.9282			0.842210
$405$	−2.36603	+	1.36603i	−0.117569	+	0.0678783i
$406$	−0.232051	−	0.401924i	−0.0115165	−	0.0199471i
$407$	−2.83013	+	4.90192i	−0.140284	+	0.242979i
$408$			0.267949i			0.0132655i
$409$	30.5429	+	17.6340i	1.51025	+	0.871944i	0.999928	+	0.0119609i	$0.00380738\pi$
$409$	30.5429	+	17.6340i	1.51025	+	0.871944i	0.510323	+	0.859983i	$0.329526\pi$
$410$	7.09808	+	4.09808i	0.350549	+	0.202390i
$411$		−	6.39230i		−	0.315309i
$412$	−5.63397	+	9.75833i	−0.277566	+	0.480758i
$413$	−6.46410	−	11.1962i	−0.318078	−	0.550927i
$414$	−3.00000	+	1.73205i	−0.147442	+	0.0851257i
$415$	−27.8564			−1.36742
$416$	3.23205	+	1.59808i	0.158464	+	0.0783521i
$417$	−19.5885			−0.959251
$418$	−1.50000	+	0.866025i	−0.0733674	+	0.0423587i
$419$	1.36603	+	2.36603i	0.0667347	+	0.115588i	0.897462	−	0.441091i	$-0.145409\pi$
$419$	1.36603	+	2.36603i	0.0667347	+	0.115588i	−0.830727	+	0.556679i	$0.812075\pi$
$420$	1.36603	−	2.36603i	0.0666552	−	0.115450i
$421$			1.60770i			0.0783543i	0.999232	+	0.0391771i	$0.0124737\pi$
$421$			1.60770i			0.0783543i	−0.999232	+	0.0391771i	$0.987526\pi$
$422$	−22.5167	−	13.0000i	−1.09609	−	0.632830i
$423$	3.86603	+	2.23205i	0.187973	+	0.108526i
$424$		−	7.00000i		−	0.339950i
$425$	−0.330127	+	0.571797i	−0.0160135	+	0.0277362i
$426$	4.09808	+	7.09808i	0.198552	+	0.343903i
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	16.8564			0.814785
$429$	5.59808	+	2.76795i	0.270278	+	0.133638i
$430$	−18.3923			−0.886956
$431$	3.29423	−	1.90192i	0.158677	−	0.0916124i	−0.418559	−	0.908190i	$-0.637465\pi$
$431$	3.29423	−	1.90192i	0.158677	−	0.0916124i	0.577236	+	0.816577i	$0.304131\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−20.4641	+	35.4449i	−0.983442	+	1.70337i	−0.334777	+	0.942297i	$0.608661\pi$
$433$	−20.4641	+	35.4449i	−0.983442	+	1.70337i	−0.648665	+	0.761074i	$0.724672\pi$
$434$			8.19615i			0.393428i
$435$	−1.09808	−	0.633975i	−0.0526487	−	0.0303968i
$436$	1.09808	+	0.633975i	0.0525883	+	0.0303619i
$437$		−	3.46410i		−	0.165710i
$438$	0.732051	−	1.26795i	0.0349787	−	0.0605850i
$439$	18.5885	+	32.1962i	0.887179	+	1.53664i	0.843196	+	0.537606i	$0.180671\pi$
$439$	18.5885	+	32.1962i	0.887179	+	1.53664i	0.0439826	+	0.999032i	$0.485995\pi$
$440$	−4.09808	+	2.36603i	−0.195368	+	0.112796i
$441$	−1.00000			−0.0476190
$442$	0.0621778	+	0.964102i	0.00295750	+	0.0458576i
$443$	35.6410			1.69336			0.846678	−	0.532106i	$-0.178599\pi$
$443$	35.6410			1.69336			0.846678	+	0.532106i	$0.178599\pi$
$444$	2.83013	−	1.63397i	0.134312	−	0.0775450i
$445$	−4.83013	−	8.36603i	−0.228970	−	0.396588i
$446$	−1.80385	+	3.12436i	−0.0854147	+	0.147943i
$447$		−	13.8564i		−	0.655386i
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	9.16987	+	5.29423i	0.432753	+	0.249850i	0.700519	−	0.713634i	$-0.252952\pi$
$449$	9.16987	+	5.29423i	0.432753	+	0.249850i	−0.267766	+	0.963484i	$0.586285\pi$
$450$		−	2.46410i		−	0.116159i
$451$	−2.59808	+	4.50000i	−0.122339	+	0.211897i
$452$	9.36603	+	16.2224i	0.440541	+	0.763039i
$453$	−4.50000	+	2.59808i	−0.211428	+	0.122068i
$454$	2.39230			0.112276
$455$	4.36603	−	8.83013i	0.204682	−	0.413963i
$456$	1.00000			0.0468293
$457$	13.7321	−	7.92820i	0.642358	−	0.370866i	−0.143164	−	0.989699i	$-0.545728\pi$
$457$	13.7321	−	7.92820i	0.642358	−	0.370866i	0.785522	+	0.618833i	$0.212394\pi$
$458$	−3.03590	−	5.25833i	−0.141858	−	0.245706i
$459$	0.133975	−	0.232051i	0.00625340	−	0.0108312i
$460$		−	9.46410i		−	0.441266i
$461$	11.3205	+	6.53590i	0.527249	+	0.304407i	0.739895	−	0.672722i	$-0.234875\pi$
$461$	11.3205	+	6.53590i	0.527249	+	0.304407i	−0.212647	+	0.977129i	$0.568208\pi$
$462$	1.50000	+	0.866025i	0.0697863	+	0.0402911i
$463$		−	9.73205i		−	0.452287i	−0.974094	−	0.226143i	$-0.927388\pi$
$463$		−	9.73205i		−	0.452287i	0.974094	−	0.226143i	$-0.0726118\pi$
$464$	0.232051	−	0.401924i	0.0107727	−	0.0186588i
$465$	11.1962	+	19.3923i	0.519209	+	0.899297i
$466$	−13.0981	+	7.56218i	−0.606757	+	0.350311i
$467$	−13.8564			−0.641198			−0.320599	−	0.947215i	$-0.603884\pi$
$467$	−13.8564			−0.641198			−0.320599	+	0.947215i	$0.603884\pi$
$468$	−2.00000	−	3.00000i	−0.0924500	−	0.138675i
$469$	−4.92820			−0.227563
$470$	−10.5622	+	6.09808i	−0.487197	+	0.281283i
$471$	3.73205	+	6.46410i	0.171964	+	0.297850i
$472$	6.46410	−	11.1962i	0.297534	−	0.515345i
$473$		−	11.6603i		−	0.536139i
$474$	−13.7942	−	7.96410i	−0.633590	−	0.365803i
$475$	2.13397	+	1.23205i	0.0979135	+	0.0565304i
$476$			0.267949i			0.0122814i
$477$	−3.50000	+	6.06218i	−0.160254	+	0.277568i
$478$	−1.36603	−	2.36603i	−0.0624805	−	0.108219i
$479$	22.1147	−	12.7679i	1.01045	−	0.583382i	0.0991253	−	0.995075i	$-0.468396\pi$
$479$	22.1147	−	12.7679i	1.01045	−	0.583382i	0.911323	+	0.411692i	$0.135062\pi$
$480$	2.73205			0.124700
$481$	9.80385	−	6.53590i	0.447017	−	0.298011i
$482$	8.00000			0.364390
$483$	−3.00000	+	1.73205i	−0.136505	+	0.0788110i
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	2.26795	−	3.92820i	0.102982	−	0.178371i
$486$			1.00000i			0.0453609i
$487$	−0.571797	−	0.330127i	−0.0259106	−	0.0149595i	0.486989	−	0.873408i	$-0.338095\pi$
$487$	−0.571797	−	0.330127i	−0.0259106	−	0.0149595i	−0.512899	+	0.858449i	$0.671429\pi$
$488$	−4.50000	−	2.59808i	−0.203705	−	0.117609i
$489$		−	0.732051i		−	0.0331045i
$490$	1.36603	−	2.36603i	0.0617107	−	0.106886i
$491$	14.2679	+	24.7128i	0.643904	+	1.11527i	0.984554	+	0.175083i	$0.0560195\pi$
$491$	14.2679	+	24.7128i	0.643904	+	1.11527i	−0.340650	+	0.940190i	$0.610647\pi$
$492$	2.59808	−	1.50000i	0.117130	−	0.0676252i
$493$	0.124356			0.00560070
$494$	3.59808	−	0.232051i	0.161885	−	0.0104405i
$495$	4.73205			0.212690
$496$	−7.09808	+	4.09808i	−0.318713	+	0.184009i
$497$	4.09808	+	7.09808i	0.183824	+	0.318392i
$498$	−5.09808	+	8.83013i	−0.228450	+	0.395687i
$499$			33.5167i			1.50041i	0.661204	+	0.750206i	$0.270046\pi$
$499$			33.5167i			1.50041i	−0.661204	+	0.750206i	$0.729954\pi$
$500$	−6.00000	−	3.46410i	−0.268328	−	0.154919i
$501$	12.0000	+	6.92820i	0.536120	+	0.309529i
$502$			11.1244i			0.496504i
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	−0.778404	−	0.627763i	$-0.783971\pi$
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	0.932861	+	0.360236i	$0.117304\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	40.0526	−	23.1244i	1.78232	−	1.02902i
$506$	6.00000			0.266733
$507$	−7.89230	−	10.3301i	−0.350510	−	0.458777i
$508$	−8.53590			−0.378719
$509$	34.3468	−	19.8301i	1.52239	−	0.878955i	0.522745	−	0.852489i	$-0.324908\pi$
$509$	34.3468	−	19.8301i	1.52239	−	0.878955i	0.999650	−	0.0264657i	$-0.00842529\pi$
$510$	0.366025	+	0.633975i	0.0162079	+	0.0280729i
$511$	0.732051	−	1.26795i	0.0323840	−	0.0560908i
$512$			1.00000i			0.0441942i
$513$	−0.866025	−	0.500000i	−0.0382360	−	0.0220755i
$514$	2.89230	+	1.66987i	0.127574	+	0.0736549i
$515$			30.7846i			1.35653i
$516$	−3.36603	+	5.83013i	−0.148181	+	0.256657i
$517$	−3.86603	−	6.69615i	−0.170028	−	0.294496i
$518$	2.83013	−	1.63397i	0.124349	−	0.0717927i
$519$	−15.1244			−0.663886
$520$	9.83013	−	0.633975i	0.431080	−	0.0278016i
$521$	−31.0526			−1.36044			−0.680219	−	0.733009i	$-0.738115\pi$
$521$	−31.0526			−1.36044			−0.680219	+	0.733009i	$0.738115\pi$
$522$	−0.401924	+	0.232051i	−0.0175917	+	0.0101566i
$523$	19.0622	+	33.0167i	0.833531	+	1.44372i	0.895221	+	0.445622i	$0.147018\pi$
$523$	19.0622	+	33.0167i	0.833531	+	1.44372i	−0.0616902	+	0.998095i	$0.519649\pi$
$524$	6.92820	−	12.0000i	0.302660	−	0.524222i
$525$		−	2.46410i		−	0.107542i
$526$	−7.90192	−	4.56218i	−0.344540	−	0.198920i
$527$	−1.90192	−	1.09808i	−0.0828491	−	0.0478330i
$528$			1.73205i			0.0753778i
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	−9.56218	−	16.5622i	−0.415354	−	0.719415i
$531$	−11.1962	+	6.46410i	−0.485872	+	0.280518i
$532$	1.00000			0.0433555
$533$	9.00000	−	6.00000i	0.389833	−	0.259889i
$534$	−3.53590			−0.153013
$535$	39.8827	−	23.0263i	1.72428	−	0.995513i
$536$	−2.46410	−	4.26795i	−0.106433	−	0.184347i
$537$	2.26795	−	3.92820i	0.0978692	−	0.169514i
$538$			17.8564i			0.769844i
$539$	1.50000	+	0.866025i	0.0646096	+	0.0373024i
$540$	−2.36603	−	1.36603i	−0.101818	−	0.0587844i
$541$		−	41.6603i		−	1.79111i	−0.444947	−	0.895557i	$-0.646777\pi$
$541$		−	41.6603i		−	1.79111i	0.444947	−	0.895557i	$-0.353223\pi$
$542$	−5.02628	+	8.70577i	−0.215897	+	0.373945i
$543$	7.33013	+	12.6962i	0.314566	+	0.544844i
$544$	−0.232051	+	0.133975i	−0.00994910	+	0.00574411i
$545$	3.46410			0.148386
$546$	−2.00000	−	3.00000i	−0.0855921	−	0.128388i
$547$	−4.73205			−0.202328			−0.101164	−	0.994870i	$-0.532257\pi$
$547$	−4.73205			−0.202328			−0.101164	+	0.994870i	$0.532257\pi$
$548$	5.53590	−	3.19615i	0.236482	−	0.136533i
$549$	2.59808	+	4.50000i	0.110883	+	0.192055i
$550$	−2.13397	+	3.69615i	−0.0909930	+	0.157604i
$551$		−	0.464102i		−	0.0197714i
$552$	−3.00000	−	1.73205i	−0.127688	−	0.0737210i
$553$	−13.7942	−	7.96410i	−0.586590	−	0.338668i
$554$			25.3205i			1.07577i
$555$	4.46410	−	7.73205i	0.189491	−	0.328207i
$556$	−9.79423	−	16.9641i	−0.415368	−	0.719438i
$557$	21.6962	−	12.5263i	0.919295	−	0.530755i	0.0358852	−	0.999356i	$-0.488575\pi$
$557$	21.6962	−	12.5263i	0.919295	−	0.530755i	0.883410	+	0.468600i	$0.155242\pi$
$558$	8.19615			0.346971
$559$	−10.7583	+	21.7583i	−0.455029	+	0.920279i
$560$	2.73205			0.115450
$561$	−0.401924	+	0.232051i	−0.0169692	+	0.00979719i
$562$	−8.83013	−	15.2942i	−0.372476	−	0.645148i
$563$	−12.9019	+	22.3468i	−0.543751	+	0.941805i	0.454933	+	0.890526i	$0.349663\pi$
$563$	−12.9019	+	22.3468i	−0.543751	+	0.941805i	−0.998684	+	0.0512792i	$0.983670\pi$
$564$			4.46410i			0.187973i
$565$	44.3205	+	25.5885i	1.86458	+	1.07651i
$566$	15.4641	+	8.92820i	0.650005	+	0.375280i
$567$			1.00000i			0.0419961i
$568$	−4.09808	+	7.09808i	−0.171951	+	0.297829i
$569$	10.2224	+	17.7058i	0.428547	+	0.742265i	0.996744	−	0.0806276i	$-0.0256924\pi$
$569$	10.2224	+	17.7058i	0.428547	+	0.742265i	−0.568198	+	0.822892i	$0.692359\pi$
$570$	2.36603	−	1.36603i	0.0991019	−	0.0572165i
$571$	34.9808			1.46390			0.731950	−	0.681359i	$-0.238611\pi$
$571$	34.9808			1.46390			0.731950	+	0.681359i	$0.238611\pi$
$572$	0.401924	+	6.23205i	0.0168053	+	0.260575i
$573$	−1.12436			−0.0469706
$574$	2.59808	−	1.50000i	0.108442	−	0.0626088i
$575$	−4.26795	−	7.39230i	−0.177986	−	0.308280i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	27.6603i		−	1.15151i	−0.817622	−	0.575756i	$-0.804708\pi$
$577$		−	27.6603i		−	1.15151i	0.817622	−	0.575756i	$-0.195292\pi$
$578$	14.6603	+	8.46410i	0.609786	+	0.352060i
$579$	7.96410	+	4.59808i	0.330977	+	0.191090i
$580$		−	1.26795i		−	0.0526487i
$581$	−5.09808	+	8.83013i	−0.211504	+	0.366335i
$582$	−0.830127	−	1.43782i	−0.0344099	−	0.0595996i
$583$	10.5000	−	6.06218i	0.434866	−	0.251070i
$584$	1.46410			0.0605850
$585$	−8.83013	−	4.36603i	−0.365081	−	0.180513i
$586$	30.9282			1.27763
$587$	−25.6865	+	14.8301i	−1.06020	+	0.612105i	−0.925487	−	0.378780i	$-0.876344\pi$
$587$	−25.6865	+	14.8301i	−1.06020	+	0.612105i	−0.134710	+	0.990885i	$0.543010\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	−4.09808	+	7.09808i	−0.168858	+	0.292471i
$590$		−	35.3205i		−	1.45412i
$591$	8.08846	+	4.66987i	0.332715	+	0.192093i
$592$	2.83013	+	1.63397i	0.116318	+	0.0671559i
$593$		−	6.46410i		−	0.265449i	−0.991153	−	0.132724i	$-0.957627\pi$
$593$		−	6.46410i		−	0.265449i	0.991153	−	0.132724i	$-0.0423725\pi$
$594$	0.866025	−	1.50000i	0.0355335	−	0.0615457i
$595$	0.366025	+	0.633975i	0.0150056	+	0.0259904i
$596$	12.0000	−	6.92820i	0.491539	−	0.283790i
$597$	5.80385			0.237536
$598$	−11.1962	−	5.53590i	−0.457845	−	0.226380i
$599$	40.6410			1.66055			0.830273	−	0.557356i	$-0.188184\pi$
$599$	40.6410			1.66055			0.830273	+	0.557356i	$0.188184\pi$
$600$	2.13397	−	1.23205i	0.0871191	−	0.0502983i
$601$	9.63397	+	16.6865i	0.392978	+	0.680658i	0.992841	−	0.119445i	$-0.0381115\pi$
$601$	9.63397	+	16.6865i	0.392978	+	0.680658i	−0.599863	+	0.800103i	$0.704778\pi$
$602$	−3.36603	+	5.83013i	−0.137189	+	0.237618i
$603$			4.92820i			0.200692i
$604$	−4.50000	−	2.59808i	−0.183102	−	0.105714i
$605$	18.9282	+	10.9282i	0.769541	+	0.444295i
$606$		−	16.9282i		−	0.687661i
$607$	−6.75833	+	11.7058i	−0.274312	+	0.475123i	−0.969961	−	0.243259i	$-0.921783\pi$
$607$	−6.75833	+	11.7058i	−0.274312	+	0.475123i	0.695649	+	0.718382i	$0.255117\pi$
$608$	0.500000	+	0.866025i	0.0202777	+	0.0351220i
$609$	−0.401924	+	0.232051i	−0.0162868	+	0.00940317i
$610$	−14.1962			−0.574785
$611$	1.03590	+	16.0622i	0.0419080	+	0.649806i
$612$	0.267949			0.0108312
$613$	−3.46410	+	2.00000i	−0.139914	+	0.0807792i	−0.568323	−	0.822806i	$-0.692408\pi$
$613$	−3.46410	+	2.00000i	−0.139914	+	0.0807792i	0.428409	+	0.903585i	$0.359074\pi$
$614$	14.6962	+	25.4545i	0.593088	+	1.02726i
$615$	4.09808	−	7.09808i	0.165250	−	0.286222i
$616$			1.73205i			0.0697863i
$617$	7.09808	+	4.09808i	0.285758	+	0.164982i	0.636027	−	0.771667i	$-0.280577\pi$
$617$	7.09808	+	4.09808i	0.285758	+	0.164982i	−0.350269	+	0.936649i	$0.613910\pi$
$618$	9.75833	+	5.63397i	0.392538	+	0.226632i
$619$			35.9282i			1.44408i	0.691853	+	0.722038i	$0.256795\pi$
$619$			35.9282i			1.44408i	−0.691853	+	0.722038i	$0.743205\pi$
$620$	−11.1962	+	19.3923i	−0.449648	+	0.778814i
$621$	1.73205	+	3.00000i	0.0695048	+	0.120386i
$622$	−6.69615	+	3.86603i	−0.268491	+	0.155013i
$623$	−3.53590			−0.141663
$624$	1.59808	−	3.23205i	0.0639742	−	0.129386i
$625$	−31.2487			−1.24995
$626$	−27.2942	+	15.7583i	−1.09090	+	0.629830i
$627$	0.866025	+	1.50000i	0.0345857	+	0.0599042i
$628$	−3.73205	+	6.46410i	−0.148925	+	0.257946i
$629$			0.875644i			0.0349142i
$630$	−2.36603	−	1.36603i	−0.0942647	−	0.0544238i
$631$	−23.5526	−	13.5981i	−0.937613	−	0.541331i	−0.0484014	−	0.998828i	$-0.515413\pi$
$631$	−23.5526	−	13.5981i	−0.937613	−	0.541331i	−0.889211	+	0.457497i	$0.848746\pi$
$632$		−	15.9282i		−	0.633590i
$633$	−13.0000	+	22.5167i	−0.516704	+	0.894957i
$634$	−7.92820	−	13.7321i	−0.314869	−	0.545369i
$635$	−20.1962	+	11.6603i	−0.801460	+	0.462723i
$636$	−7.00000			−0.277568
$637$	−2.00000	−	3.00000i	−0.0792429	−	0.118864i
$638$	0.803848			0.0318246
$639$	7.09808	−	4.09808i	0.280796	−	0.162117i
$640$	1.36603	+	2.36603i	0.0539969	+	0.0935254i
$641$	−15.5885	+	27.0000i	−0.615707	+	1.06644i	0.374553	+	0.927206i	$0.377796\pi$
$641$	−15.5885	+	27.0000i	−0.615707	+	1.06644i	−0.990260	+	0.139230i	$0.955537\pi$
$642$		−	16.8564i		−	0.665269i
$643$	−4.45448	−	2.57180i	−0.175668	−	0.101422i	0.409588	−	0.912271i	$-0.365672\pi$
$643$	−4.45448	−	2.57180i	−0.175668	−	0.101422i	−0.585256	+	0.810849i	$0.699006\pi$
$644$	−3.00000	−	1.73205i	−0.118217	−	0.0682524i
$645$			18.3923i			0.724196i
$646$	−0.133975	+	0.232051i	−0.00527116	+	0.00912992i
$647$	−21.9186	−	37.9641i	−0.861708	−	1.49252i	−0.870279	−	0.492560i	$-0.836061\pi$
$647$	−21.9186	−	37.9641i	−0.861708	−	1.49252i	0.00857027	−	0.999963i	$-0.497272\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	22.3923			0.878975
$650$	7.39230	−	4.92820i	0.289950	−	0.193300i
$651$	8.19615			0.321233
$652$	0.633975	−	0.366025i	0.0248284	−	0.0143347i
$653$	4.35641	+	7.54552i	0.170479	+	0.295279i	0.938588	−	0.345041i	$-0.112135\pi$
$653$	4.35641	+	7.54552i	0.170479	+	0.295279i	−0.768108	+	0.640320i	$0.778802\pi$
$654$	0.633975	−	1.09808i	0.0247904	−	0.0429382i
$655$		−	37.8564i		−	1.47917i
$656$	2.59808	+	1.50000i	0.101438	+	0.0585652i
$657$	−1.26795	−	0.732051i	−0.0494674	−	0.0285600i
$658$			4.46410i			0.174029i
$659$	−19.6962	+	34.1147i	−0.767253	+	1.32892i	0.171794	+	0.985133i	$0.445044\pi$
$659$	−19.6962	+	34.1147i	−0.767253	+	1.32892i	−0.939047	+	0.343789i	$0.888290\pi$
$660$	2.36603	+	4.09808i	0.0920974	+	0.159517i
$661$	7.26795	−	4.19615i	0.282690	−	0.163211i	−0.351950	−	0.936019i	$-0.614481\pi$
$661$	7.26795	−	4.19615i	0.282690	−	0.163211i	0.634641	+	0.772807i	$0.281148\pi$
$662$	−0.143594			−0.00558092
$663$	0.964102	−	0.0621778i	0.0374426	−	0.00241479i
$664$	−10.1962			−0.395687
$665$	2.36603	−	1.36603i	0.0917505	−	0.0529722i
$666$	−1.63397	−	2.83013i	−0.0633152	−	0.109665i
$667$	−0.803848	+	1.39230i	−0.0311251	+	0.0539103i
$668$			13.8564i			0.536120i
$669$	3.12436	+	1.80385i	0.120795	+	0.0697408i
$670$	−11.6603	−	6.73205i	−0.450475	−	0.260082i
$671$		−	9.00000i		−	0.347441i
$672$	0.500000	−	0.866025i	0.0192879	−	0.0334077i
$673$	11.3564	+	19.6699i	0.437757	+	0.758218i	0.997516	−	0.0704376i	$-0.0224396\pi$
$673$	11.3564	+	19.6699i	0.437757	+	0.758218i	−0.559759	+	0.828656i	$0.689106\pi$
$674$	−16.4545	+	9.50000i	−0.633803	+	0.365926i
$675$	−2.46410			−0.0948433
$676$	5.00000	−	12.0000i	0.192308	−	0.461538i
$677$	33.2679			1.27859			0.639296	−	0.768961i	$-0.279226\pi$
$677$	33.2679			1.27859			0.639296	+	0.768961i	$0.279226\pi$
$678$	16.2224	−	9.36603i	0.623019	−	0.359700i
$679$	−0.830127	−	1.43782i	−0.0318574	−	0.0551786i
$680$	−0.366025	+	0.633975i	−0.0140364	+	0.0243118i
$681$		−	2.39230i		−	0.0916733i
$682$	−12.2942	−	7.09808i	−0.470770	−	0.271799i
$683$	−43.6410	−	25.1962i	−1.66988	−	0.964104i	−0.967701	−	0.252101i	$-0.918879\pi$
$683$	−43.6410	−	25.1962i	−1.66988	−	0.964104i	−0.702176	−	0.712003i	$-0.747788\pi$
$684$		−	1.00000i		−	0.0382360i
$685$	8.73205	−	15.1244i	0.333635	−	0.577872i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−5.25833	+	3.03590i	−0.200618	+	0.115827i
$688$	−6.73205			−0.256657
$689$	−25.1865	+	1.62436i	−0.959531	+	0.0618830i
$690$	−9.46410			−0.360292
$691$	10.1436	−	5.85641i	0.385880	−	0.222788i	−0.294493	−	0.955654i	$-0.595151\pi$
$691$	10.1436	−	5.85641i	0.385880	−	0.222788i	0.680374	+	0.732865i	$0.261817\pi$
$692$	−7.56218	−	13.0981i	−0.287471	−	0.497914i
$693$	0.866025	−	1.50000i	0.0328976	−	0.0569803i
$694$		−	15.3923i		−	0.584284i
$695$	−46.3468	−	26.7583i	−1.75803	−	1.01500i
$696$	−0.401924	−	0.232051i	−0.0152349	−	0.00879586i
$697$			0.803848i			0.0304479i
$698$	−15.8564	+	27.4641i	−0.600174	+	1.03953i
$699$	7.56218	+	13.0981i	0.286028	+	0.495415i
$700$	2.13397	−	1.23205i	0.0806567	−	0.0465671i
$701$	−28.8564			−1.08989			−0.544946	−	0.838471i	$-0.683450\pi$
$701$	−28.8564			−1.08989			−0.544946	+	0.838471i	$0.683450\pi$
$702$	−3.00000	+	2.00000i	−0.113228	+	0.0754851i
$703$	3.26795			0.123253
$704$	−1.50000	+	0.866025i	−0.0565334	+	0.0326396i
$705$	6.09808	+	10.5622i	0.229667	+	0.397795i
$706$	1.26795	−	2.19615i	0.0477199	−	0.0826533i
$707$		−	16.9282i		−	0.636651i
$708$	−11.1962	−	6.46410i	−0.420777	−	0.242936i
$709$	−5.24167	−	3.02628i	−0.196855	−	0.113654i	0.398333	−	0.917241i	$-0.369589\pi$
$709$	−5.24167	−	3.02628i	−0.196855	−	0.113654i	−0.595188	+	0.803587i	$0.702922\pi$
$710$			22.3923i			0.840368i
$711$	−7.96410	+	13.7942i	−0.298677	+	0.517324i
$712$	−1.76795	−	3.06218i	−0.0662567	−	0.114760i
$713$	24.5885	−	14.1962i	0.920845	−	0.531650i
$714$	0.267949			0.0100277
$715$	9.46410	+	14.1962i	0.353937	+	0.530906i
$716$	4.53590			0.169514
$717$	−2.36603	+	1.36603i	−0.0883608	+	0.0510152i
$718$	−7.09808	−	12.2942i	−0.264898	−	0.458817i
$719$	−9.25833	+	16.0359i	−0.345277	+	0.598038i	−0.985404	−	0.170231i	$-0.945549\pi$
$719$	−9.25833	+	16.0359i	−0.345277	+	0.598038i	0.640127	+	0.768269i	$0.278882\pi$
$720$		−	2.73205i		−	0.101818i
$721$	9.75833	+	5.63397i	0.363419	+	0.209820i
$722$	−15.5885	−	9.00000i	−0.580142	−	0.334945i
$723$		−	8.00000i		−	0.297523i
$724$	−7.33013	+	12.6962i	−0.272422	+	0.471849i
$725$	−0.571797	−	0.990381i	−0.0212360	−	0.0367818i
$726$	6.92820	−	4.00000i	0.257130	−	0.148454i
$727$	−15.3205			−0.568206			−0.284103	−	0.958794i	$-0.591696\pi$
$727$	−15.3205			−0.568206			−0.284103	+	0.958794i	$0.591696\pi$
$728$	1.59808	−	3.23205i	0.0592286	−	0.119788i
$729$	1.00000			0.0370370
$730$	3.46410	−	2.00000i	0.128212	−	0.0740233i
$731$	−0.901924	−	1.56218i	−0.0333589	−	0.0577792i
$732$	−2.59808	+	4.50000i	−0.0960277	+	0.166325i
$733$			14.1769i			0.523636i	0.965117	+	0.261818i	$0.0843221\pi$
$733$			14.1769i			0.523636i	−0.965117	+	0.261818i	$0.915678\pi$
$734$	8.07180	+	4.66025i	0.297935	+	0.172013i
$735$	−2.36603	−	1.36603i	−0.0872722	−	0.0503866i
$736$		−	3.46410i		−	0.127688i
$737$	4.26795	−	7.39230i	0.157212	−	0.272299i
$738$	−1.50000	−	2.59808i	−0.0552158	−	0.0956365i
$739$	40.8564	−	23.5885i	1.50293	−	0.867715i	0.502933	−	0.864325i	$-0.332254\pi$
$739$	40.8564	−	23.5885i	1.50293	−	0.867715i	0.999994	−	0.00339000i	$-0.00107907\pi$
$740$	8.92820			0.328207
$741$	−0.232051	−	3.59808i	−0.00852460	−	0.132179i
$742$	−7.00000			−0.256978
$743$	−20.8301	+	12.0263i	−0.764183	+	0.441201i	−0.830796	−	0.556578i	$-0.812114\pi$
$743$	−20.8301	+	12.0263i	−0.764183	+	0.441201i	0.0666124	+	0.997779i	$0.478781\pi$
$744$	4.09808	+	7.09808i	0.150243	+	0.260228i
$745$	18.9282	−	32.7846i	0.693476	−	1.20114i
$746$		−	7.66025i		−	0.280462i
$747$	8.83013	+	5.09808i	0.323077	+	0.186529i
$748$	−0.401924	−	0.232051i	−0.0146958	−	0.00848462i
$749$		−	16.8564i		−	0.615920i
$750$	−3.46410	+	6.00000i	−0.126491	+	0.219089i
$751$	−23.4282	−	40.5788i	−0.854907	−	1.48074i	−0.876731	−	0.480981i	$-0.840281\pi$
$751$	−23.4282	−	40.5788i	−0.854907	−	1.48074i	0.0218237	−	0.999762i	$-0.493053\pi$
$752$	−3.86603	+	2.23205i	−0.140979	+	0.0813945i
$753$	11.1244			0.405394
$754$	−1.50000	−	0.741670i	−0.0546268	−	0.0270100i
$755$	−14.1962			−0.516651
$756$	−0.866025	+	0.500000i	−0.0314970	+	0.0181848i
$757$	−15.2942	−	26.4904i	−0.555878	−	0.962809i	−0.997835	−	0.0657728i	$-0.979049\pi$
$757$	−15.2942	−	26.4904i	−0.555878	−	0.962809i	0.441956	−	0.897037i	$-0.354285\pi$
$758$	15.2224	−	26.3660i	0.552904	−	0.957657i
$759$		−	6.00000i		−	0.217786i
$760$	2.36603	+	1.36603i	0.0858248	+	0.0495509i
$761$	16.7321	+	9.66025i	0.606536	+	0.350184i	0.771609	−	0.636098i	$-0.219452\pi$
$761$	16.7321	+	9.66025i	0.606536	+	0.350184i	−0.165072	+	0.986281i	$0.552786\pi$
$762$			8.53590i			0.309223i
$763$	0.633975	−	1.09808i	0.0229514	−	0.0397530i
$764$	−0.562178	−	0.973721i	−0.0203389	−	0.0352280i
$765$	0.633975	−	0.366025i	0.0229214	−	0.0132337i
$766$	12.4641			0.450346
$767$	−41.7846	−	20.6603i	−1.50875	−	0.745999i
$768$	1.00000			0.0360844
$769$	38.3660	−	22.1506i	1.38351	−	0.798772i	0.390940	−	0.920416i	$-0.372150\pi$
$769$	38.3660	−	22.1506i	1.38351	−	0.798772i	0.992574	+	0.121644i	$0.0388165\pi$
$770$	2.36603	+	4.09808i	0.0852656	+	0.147684i
$771$	1.66987	−	2.89230i	0.0601390	−	0.104164i
$772$			9.19615i			0.330977i
$773$	−13.1436	−	7.58846i	−0.472742	−	0.272938i	0.244645	−	0.969613i	$-0.421329\pi$
$773$	−13.1436	−	7.58846i	−0.472742	−	0.272938i	−0.717387	+	0.696675i	$0.754662\pi$
$774$	5.83013	+	3.36603i	0.209560	+	0.120989i
$775$			20.1962i			0.725467i
$776$	0.830127	−	1.43782i	0.0297998	−	0.0516148i
$777$	−1.63397	−	2.83013i	−0.0586185	−	0.101530i
$778$	10.7321	−	6.19615i	0.384763	−	0.222143i
$779$	3.00000			0.107486
$780$	−0.633975	−	9.83013i	−0.0226999	−	0.351975i
$781$	−14.1962			−0.507978
$782$	0.803848	−	0.464102i	0.0287455	−	0.0165962i
$783$	0.232051	+	0.401924i	0.00829282	+	0.0143636i
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$			20.3923i			0.727833i
$786$	−12.0000	−	6.92820i	−0.428026	−	0.247121i
$787$	−33.1865	−	19.1603i	−1.18297	−	0.682989i	−0.226272	−	0.974064i	$-0.572654\pi$
$787$	−33.1865	−	19.1603i	−1.18297	−	0.682989i	−0.956700	+	0.291075i	$0.905987\pi$
$788$			9.33975i			0.332715i
$789$	−4.56218	+	7.90192i	−0.162418	+	0.281316i
$790$	−21.7583	−	37.6865i	−0.774127	−	1.34083i
$791$	16.2224	−	9.36603i	0.576803	−	0.333018i
$792$	1.73205			0.0615457
$793$	−8.30385	+	16.7942i	−0.294878	+	0.596381i
$794$	−21.9282			−0.778203
$795$	−16.5622	+	9.56218i	−0.587400	+	0.339135i
$796$	2.90192	+	5.02628i	0.102856	+	0.178152i
$797$	−13.5622	+	23.4904i	−0.480397	+	0.832072i	−0.999747	−	0.0224896i	$-0.992841\pi$
$797$	−13.5622	+	23.4904i	−0.480397	+	0.832072i	0.519350	+	0.854562i	$0.326174\pi$
$798$		−	1.00000i		−	0.0353996i
$799$	−1.03590	−	0.598076i	−0.0366475	−	0.0211584i
$800$	2.13397	+	1.23205i	0.0754474	+	0.0435596i
$801$			3.53590i			0.124935i
$802$	−1.39230	+	2.41154i	−0.0491640	+	0.0851545i
$803$	1.26795	+	2.19615i	0.0447450	+	0.0775005i
$804$	−4.26795	+	2.46410i	−0.150519	+	0.0869022i
$805$	−9.46410			−0.333566
$806$	16.3923	+	24.5885i	0.577394	+	0.866091i
$807$	17.8564			0.628575
$808$	14.6603	−	8.46410i	0.515746	−	0.297766i
$809$	−26.2224	−	45.4186i	−0.921932	−	1.59683i	−0.796423	−	0.604740i	$-0.793277\pi$
$809$	−26.2224	−	45.4186i	−0.921932	−	1.59683i	−0.125509	−	0.992093i	$-0.540056\pi$
$810$	−1.36603	+	2.36603i	−0.0479972	+	0.0831337i
$811$		−	31.4641i		−	1.10485i	−0.833561	−	0.552427i	$-0.813702\pi$
$811$		−	31.4641i		−	1.10485i	0.833561	−	0.552427i	$-0.186298\pi$
$812$	−0.401924	−	0.232051i	−0.0141048	−	0.00814339i
$813$	8.70577	+	5.02628i	0.305325	+	0.176279i
$814$			5.66025i			0.198392i
$815$	1.00000	−	1.73205i	0.0350285	−	0.0606711i
$816$	0.133975	+	0.232051i	0.00469005	+	0.00812340i
$817$	−5.83013	+	3.36603i	−0.203970	+	0.117762i
$818$	35.2679			1.23311
$819$	−3.00000	+	2.00000i	−0.104828	+	0.0698857i
$820$	8.19615			0.286222
$821$	−24.1077	+	13.9186i	−0.841364	+	0.485762i	−0.857728	−	0.514104i	$-0.828124\pi$
$821$	−24.1077	+	13.9186i	−0.841364	+	0.485762i	0.0163634	+	0.999866i	$0.494791\pi$
$822$	−3.19615	−	5.53590i	−0.111479	−	0.193087i
$823$	17.3923	−	30.1244i	0.606258	−	1.05007i	−0.385594	−	0.922669i	$-0.626003\pi$
$823$	17.3923	−	30.1244i	0.606258	−	1.05007i	0.991851	−	0.127400i	$-0.0406633\pi$
$824$			11.2679i			0.392538i
$825$	3.69615	+	2.13397i	0.128684	+	0.0742955i
$826$	−11.1962	−	6.46410i	−0.389564	−	0.224915i
$827$			27.3205i			0.950027i	0.879978	+	0.475014i	$0.157557\pi$
$827$			27.3205i			0.950027i	−0.879978	+	0.475014i	$0.842443\pi$
$828$	−1.73205	+	3.00000i	−0.0601929	+	0.104257i
$829$	−17.3301	−	30.0167i	−0.601900	−	1.04252i	−0.992533	−	0.121975i	$-0.961077\pi$
$829$	−17.3301	−	30.0167i	−0.601900	−	1.04252i	0.390633	−	0.920547i	$-0.372256\pi$
$830$	−24.1244	+	13.9282i	−0.837369	+	0.483455i
$831$	25.3205			0.878359
$832$	3.59808	−	0.232051i	0.124741	−	0.00804491i
$833$	0.267949			0.00928389
$834$	−16.9641	+	9.79423i	−0.587419	+	0.339146i
$835$	18.9282	+	32.7846i	0.655037	+	1.13456i
$836$	−0.866025	+	1.50000i	−0.0299521	+	0.0518786i
$837$		−	8.19615i		−	0.283300i
$838$	2.36603	+	1.36603i	0.0817330	+	0.0471886i
$839$	−36.4641	−	21.0526i	−1.25888	−	0.726815i	−0.286024	−	0.958223i	$-0.592334\pi$
$839$	−36.4641	−	21.0526i	−1.25888	−	0.726815i	−0.972857	+	0.231408i	$0.925667\pi$
$840$		−	2.73205i		−	0.0942647i
$841$	14.3923	−	24.9282i	0.496286	−	0.859593i
$842$	0.803848	+	1.39230i	0.0277024	+	0.0479820i
$843$	−15.2942	+	8.83013i	−0.526761	+	0.304126i
$844$	−26.0000			−0.894957
$845$	−4.56218	−	35.2224i	−0.156944	−	1.21169i
$846$	4.46410			0.153479
$847$	6.92820	−	4.00000i	0.238056	−	0.137442i
$848$	−3.50000	−	6.06218i	−0.120190	−	0.208176i
$849$	8.92820	−	15.4641i	0.306415	−	0.530727i
$850$			0.660254i			0.0226465i
$851$	−9.80385	−	5.66025i	−0.336072	−	0.194031i
$852$	7.09808	+	4.09808i	0.243176	+	0.140398i
$853$			5.92820i			0.202978i	0.994837	+	0.101489i	$0.0323606\pi$
$853$			5.92820i			0.202978i	−0.994837	+	0.101489i	$0.967639\pi$
$854$	−2.59808	+	4.50000i	−0.0889043	+	0.153987i
$855$	−1.36603	−	2.36603i	−0.0467171	−	0.0809164i
$856$	14.5981	−	8.42820i	0.498952	−	0.288070i
$857$	39.4641			1.34807			0.674034	−	0.738700i	$-0.264560\pi$
$857$	39.4641			1.34807			0.674034	+	0.738700i	$0.264560\pi$
$858$	6.23205	−	0.401924i	0.212759	−	0.0137215i
$859$	−50.7654			−1.73209			−0.866046	−	0.499964i	$-0.833346\pi$
$859$	−50.7654			−1.73209			−0.866046	+	0.499964i	$0.833346\pi$
$860$	−15.9282	+	9.19615i	−0.543147	+	0.313586i
$861$	−1.50000	−	2.59808i	−0.0511199	−	0.0885422i
$862$	1.90192	−	3.29423i	0.0647798	−	0.112202i
$863$			16.9282i			0.576243i	0.957594	+	0.288121i	$0.0930307\pi$
$863$			16.9282i			0.576243i	−0.957594	+	0.288121i	$0.906969\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−35.7846	−	20.6603i	−1.21671	−	0.702470i
$866$			40.9282i			1.39080i
$867$	8.46410	−	14.6603i	0.287456	−	0.497888i
$868$	4.09808	+	7.09808i	0.139098	+	0.240924i
$869$	23.8923	−	13.7942i	0.810491	−	0.467937i
$870$	−1.26795			−0.0429875
$871$	−14.7846	+	9.85641i	−0.500957	+	0.333972i
$872$	1.26795			0.0429382
$873$	−1.43782	+	0.830127i	−0.0486629	+	0.0280955i
$874$	−1.73205	−	3.00000i	−0.0585875	−	0.101477i
$875$	−3.46410	+	6.00000i	−0.117108	+	0.202837i
$876$		−	1.46410i		−	0.0494674i
$877$	−23.1506	−	13.3660i	−0.781741	−	0.451339i	0.0553057	−	0.998469i	$-0.482387\pi$
$877$	−23.1506	−	13.3660i	−0.781741	−	0.451339i	−0.837047	+	0.547131i	$0.815720\pi$
$878$	32.1962	+	18.5885i	1.08657	+	0.627330i
$879$		−	30.9282i		−	1.04318i
$880$	−2.36603	+	4.09808i	−0.0797587	+	0.138146i
$881$	4.53590	+	7.85641i	0.152818	+	0.264689i	0.932262	−	0.361783i	$-0.117832\pi$
$881$	4.53590	+	7.85641i	0.152818	+	0.264689i	−0.779444	+	0.626472i	$0.784498\pi$
$882$	−0.866025	+	0.500000i	−0.0291606	+	0.0168359i
$883$	−30.0526			−1.01135			−0.505675	−	0.862724i	$-0.668756\pi$
$883$	−30.0526			−1.01135			−0.505675	+	0.862724i	$0.668756\pi$
$884$	0.535898	+	0.803848i	0.0180242	+	0.0270363i
$885$	−35.3205			−1.18729
$886$	30.8660	−	17.8205i	1.03696	−	0.598692i
$887$	−21.7224	−	37.6244i	−0.729368	−	1.26330i	−0.957151	−	0.289590i	$-0.906481\pi$
$887$	−21.7224	−	37.6244i	−0.729368	−	1.26330i	0.227783	−	0.973712i	$-0.426852\pi$
$888$	1.63397	−	2.83013i	0.0548326	−	0.0949728i
$889$			8.53590i			0.286285i
$890$	−8.36603	−	4.83013i	−0.280430	−	0.161906i
$891$	−1.50000	−	0.866025i	−0.0502519	−	0.0290129i
$892$			3.60770i			0.120795i
$893$	−2.23205	+	3.86603i	−0.0746927	+	0.129372i
$894$	−6.92820	−	12.0000i	−0.231714	−	0.401340i
$895$	10.7321	−	6.19615i	0.358733	−	0.207115i
$896$	1.00000			0.0334077
$897$	−5.53590	+	11.1962i	−0.184838	+	0.373829i
$898$	10.5885			0.353341
$899$	3.29423	−	1.90192i	0.109869	−	0.0634327i
$900$	−1.23205	−	2.13397i	−0.0410684	−	0.0711325i
$901$	0.937822	−	1.62436i	0.0312434	−	0.0541151i
$902$			5.19615i			0.173013i
$903$	5.83013	+	3.36603i	0.194014	+	0.112014i
$904$	16.2224	+	9.36603i	0.539550	+	0.311509i
$905$			40.0526i			1.33139i
$906$	−2.59808	+	4.50000i	−0.0863153	+	0.149502i
$907$	−11.1962	−	19.3923i	−0.371762	−	0.643911i	0.618075	−	0.786119i	$-0.287913\pi$
$907$	−11.1962	−	19.3923i	−0.371762	−	0.643911i	−0.989837	+	0.142209i	$0.954580\pi$
$908$	2.07180	−	1.19615i	0.0687550	−	0.0396957i
$909$	−16.9282			−0.561473
$910$	−0.633975	−	9.83013i	−0.0210161	−	0.325866i
$911$	28.8372			0.955418			0.477709	−	0.878518i	$-0.341467\pi$
$911$	28.8372			0.955418			0.477709	+	0.878518i	$0.341467\pi$
$912$	0.866025	−	0.500000i	0.0286770	−	0.0165567i
$913$	−8.83013	−	15.2942i	−0.292235	−	0.506165i
$914$	7.92820	−	13.7321i	0.262242	−	0.454216i
$915$			14.1962i			0.469310i
$916$	−5.25833	−	3.03590i	−0.173740	−	0.100309i
$917$	−12.0000	−	6.92820i	−0.396275	−	0.228789i
$918$		−	0.267949i		−	0.00884364i
$919$	−2.57180	+	4.45448i	−0.0848357	+	0.146940i	−0.905321	−	0.424728i	$-0.860370\pi$
$919$	−2.57180	+	4.45448i	−0.0848357	+	0.146940i	0.820485	+	0.571667i	$0.193703\pi$
$920$	−4.73205	−	8.19615i	−0.156011	−	0.270219i
$921$	25.4545	−	14.6962i	0.838754	−	0.484255i
$922$	13.0718			0.430497
$923$	26.4904	+	13.0981i	0.871942	+	0.431128i
$924$	1.73205			0.0569803
$925$	6.97372	−	4.02628i	0.229295	−	0.132383i
$926$	−4.86603	−	8.42820i	−0.159908	−	0.276968i
$927$	5.63397	−	9.75833i	0.185044	−	0.320506i
$928$		−	0.464102i		−	0.0152349i
$929$	27.9904	+	16.1603i	0.918335	+	0.530201i	0.883103	−	0.469178i	$-0.155450\pi$
$929$	27.9904	+	16.1603i	0.918335	+	0.530201i	0.0352312	+	0.999379i	$0.488783\pi$
$930$	19.3923	+	11.1962i	0.635899	+	0.367136i
$931$		−	1.00000i		−	0.0327737i
$932$	−7.56218	+	13.0981i	−0.247707	+	0.429042i
$933$	3.86603	+	6.69615i	0.126568	+	0.219222i
$934$	−12.0000	+	6.92820i	−0.392652	+	0.226698i
$935$	−1.26795			−0.0414664
$936$	−3.23205	−	1.59808i	−0.105643	−	0.0522348i
$937$	14.9282			0.487683			0.243842	−	0.969815i	$-0.421592\pi$
$937$	14.9282			0.487683			0.243842	+	0.969815i	$0.421592\pi$
$938$	−4.26795	+	2.46410i	−0.139353	+	0.0804558i
$939$	15.7583	+	27.2942i	0.514254	+	0.890713i
$940$	−6.09808	+	10.5622i	−0.198897	+	0.344500i
$941$		−	32.3923i		−	1.05596i	−0.849257	−	0.527979i	$-0.822950\pi$
$941$		−	32.3923i		−	1.05596i	0.849257	−	0.527979i	$-0.177050\pi$
$942$	6.46410	+	3.73205i	0.210612	+	0.121597i
$943$	−9.00000	−	5.19615i	−0.293080	−	0.169210i
$944$		−	12.9282i		−	0.420777i
$945$	−1.36603	+	2.36603i	−0.0444368	+	0.0769668i
$946$	−5.83013	−	10.0981i	−0.189554	−	0.328317i
$947$	−10.8397	+	6.25833i	−0.352244	+	0.203368i	−0.665673	−	0.746243i	$-0.731856\pi$
$947$	−10.8397	+	6.25833i	−0.352244	+	0.203368i	0.313429	+	0.949612i	$0.398522\pi$
$948$	−15.9282			−0.517324
$949$	−0.339746	−	5.26795i	−0.0110286	−	0.171005i
$950$	2.46410			0.0799460
$951$	−13.7321	+	7.92820i	−0.445292	+	0.257090i
$952$	0.133975	+	0.232051i	0.00434214	+	0.00752081i
$953$	11.9019	−	20.6147i	0.385541	−	0.667777i	−0.606303	−	0.795234i	$-0.707348\pi$
$953$	11.9019	−	20.6147i	0.385541	−	0.667777i	0.991844	+	0.127457i	$0.0406815\pi$
$954$			7.00000i			0.226633i
$955$	−2.66025	−	1.53590i	−0.0860838	−	0.0497005i
$956$	−2.36603	−	1.36603i	−0.0765227	−	0.0441804i
$957$		−	0.803848i		−	0.0259847i
$958$	12.7679	−	22.1147i	0.412514	−	0.714495i
$959$	−3.19615	−	5.53590i	−0.103209	−	0.178763i
$960$	2.36603	−	1.36603i	0.0763631	−	0.0440883i
$961$	−36.1769			−1.16700
$962$	5.22243	−	10.5622i	0.168378	−	0.340538i
$963$	−16.8564			−0.543190
$964$	6.92820	−	4.00000i	0.223142	−	0.128831i
$965$	12.5622	+	21.7583i	0.404391	+	0.700425i
$966$	−1.73205	+	3.00000i	−0.0557278	+	0.0965234i
$967$			55.7128i			1.79160i	0.444454	+	0.895802i	$0.353398\pi$
$967$			55.7128i			1.79160i	−0.444454	+	0.895802i	$0.646602\pi$
$968$	6.92820	+	4.00000i	0.222681	+	0.128565i
$969$	0.232051	+	0.133975i	0.00745455	+	0.00430388i
$970$		−	4.53590i		−	0.145639i
$971$	−11.0526	+	19.1436i	−0.354693	+	0.614347i	−0.987065	−	0.160318i	$-0.948748\pi$
$971$	−11.0526	+	19.1436i	−0.354693	+	0.614347i	0.632372	+	0.774665i	$0.282081\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−16.9641	+	9.79423i	−0.543844	+	0.313989i
$974$	−0.660254			−0.0211559
$975$	−4.92820	−	7.39230i	−0.157829	−	0.236743i
$976$	−5.19615			−0.166325
$977$	−3.80385	+	2.19615i	−0.121696	+	0.0702611i	−0.559612	−	0.828755i	$-0.689050\pi$
$977$	−3.80385	+	2.19615i	−0.121696	+	0.0702611i	0.437916	+	0.899016i	$0.355717\pi$
$978$	−0.366025	−	0.633975i	−0.0117042	−	0.0202723i
$979$	3.06218	−	5.30385i	0.0978676	−	0.169512i
$980$		−	2.73205i		−	0.0872722i
$981$	−1.09808	−	0.633975i	−0.0350589	−	0.0202413i
$982$	24.7128	+	14.2679i	0.788618	+	0.455309i
$983$		−	8.14359i		−	0.259740i	−0.991531	−	0.129870i	$-0.958544\pi$
$983$		−	8.14359i		−	0.259740i	0.991531	−	0.129870i	$-0.0414560\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$	12.7583	+	22.0981i	0.406514	+	0.704103i
$986$	0.107695	−	0.0621778i	0.00342971	−	0.00198015i
$987$	4.46410			0.142094
$988$	3.00000	−	2.00000i	0.0954427	−	0.0636285i
$989$	23.3205			0.741549
$990$	4.09808	−	2.36603i	0.130245	−	0.0751972i
$991$	5.37564	+	9.31089i	0.170763	+	0.295770i	0.938687	−	0.344771i	$-0.112043\pi$
$991$	5.37564	+	9.31089i	0.170763	+	0.295770i	−0.767924	+	0.640541i	$0.778710\pi$
$992$	−4.09808	+	7.09808i	−0.130114	+	0.225364i
$993$			0.143594i			0.00455680i
$994$	7.09808	+	4.09808i	0.225137	+	0.129983i
$995$	13.7321	+	7.92820i	0.435335	+	0.251341i
$996$			10.1962i			0.323077i
$997$	−8.52628	+	14.7679i	−0.270030	+	0.467706i	−0.968869	−	0.247573i	$-0.920367\pi$
$997$	−8.52628	+	14.7679i	−0.270030	+	0.467706i	0.698839	+	0.715279i	$0.253700\pi$
$998$	16.7583	+	29.0263i	0.530476	+	0.918811i
$999$	−2.83013	+	1.63397i	−0.0895413	+	0.0516967i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.73205i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.73205i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.36603 - 2.36603i) q^{10} +(1.50000 - 0.866025i) q^{11} -1.00000 q^{12} +(-3.59808 + 0.232051i) q^{13} -1.00000 q^{14} +(-2.36603 + 1.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.133975 - 0.232051i) q^{17} +1.00000i q^{18} +(-0.866025 - 0.500000i) q^{19} +(-2.36603 - 1.36603i) q^{20} +1.00000i q^{21} +(0.866025 - 1.50000i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-3.00000 + 2.00000i) q^{26} +1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.232051 + 0.401924i) q^{29} +(-1.36603 + 2.36603i) q^{30} -8.19615i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} -0.267949i q^{34} +(-1.36603 + 2.36603i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.83013 + 1.63397i) q^{37} -1.00000 q^{38} +(2.00000 + 3.00000i) q^{39} -2.73205 q^{40} +(-2.59808 + 1.50000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(3.36603 - 5.83013i) q^{43} -1.73205i q^{44} +(2.36603 + 1.36603i) q^{45} +(3.00000 + 1.73205i) q^{46} -4.46410i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.13397 + 1.23205i) q^{50} -0.267949 q^{51} +(-1.59808 + 3.23205i) q^{52} +7.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.36603 - 4.09808i) q^{55} +(-0.500000 + 0.866025i) q^{56} +1.00000i q^{57} +(0.401924 + 0.232051i) q^{58} +(11.1962 + 6.46410i) q^{59} +2.73205i q^{60} +(2.59808 - 4.50000i) q^{61} +(-4.09808 - 7.09808i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(0.633975 + 9.83013i) q^{65} -1.73205 q^{66} +(4.26795 - 2.46410i) q^{67} +(-0.133975 - 0.232051i) q^{68} +(1.73205 - 3.00000i) q^{69} +2.73205i q^{70} +(-7.09808 - 4.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.46410i q^{73} +(-1.63397 + 2.83013i) q^{74} +(1.23205 + 2.13397i) q^{75} +(-0.866025 + 0.500000i) q^{76} -1.73205 q^{77} +(3.23205 + 1.59808i) q^{78} +15.9282 q^{79} +(-2.36603 + 1.36603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -10.1962i q^{83} +(0.866025 + 0.500000i) q^{84} +(-0.633975 - 0.366025i) q^{85} -6.73205i q^{86} +(0.232051 - 0.401924i) q^{87} +(-0.866025 - 1.50000i) q^{88} +(3.06218 - 1.76795i) q^{89} +2.73205 q^{90} +(3.23205 + 1.59808i) q^{91} +3.46410 q^{92} +(-7.09808 + 4.09808i) q^{93} +(-2.23205 - 3.86603i) q^{94} +(-1.36603 + 2.36603i) q^{95} +1.00000i q^{96} +(1.43782 + 0.830127i) q^{97} +(0.866025 + 0.500000i) q^{98} +1.73205i 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	\( 4 q - 2 q^{3} + 2 q^{4} - 2 q^{9} - 2 q^{10} + 6 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 4 q^{17} - 6 q^{20} + 4 q^{25} - 12 q^{26} + 4 q^{27} - 6 q^{29} - 2 q^{30} - 6 q^{33} - 2 q^{35} + 2 q^{36} + 6 q^{37} - 4 q^{38} + 8 q^{39} - 4 q^{40} + 2 q^{42} + 10 q^{43} + 6 q^{45} + 12 q^{46} - 2 q^{48} + 2 q^{49} - 12 q^{50} - 8 q^{51} + 4 q^{52} + 28 q^{53} - 6 q^{55} - 2 q^{56} + 12 q^{58} + 24 q^{59} - 6 q^{62} - 4 q^{64} + 6 q^{65} + 24 q^{67} - 4 q^{68} - 18 q^{71} - 10 q^{74} - 2 q^{75} + 6 q^{78} + 36 q^{79} - 6 q^{80} - 2 q^{81} - 6 q^{82} - 6 q^{85} - 6 q^{87} - 12 q^{89} + 4 q^{90} + 6 q^{91} - 18 q^{93} - 2 q^{94} - 2 q^{95} + 30 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^4 - 2 * q^9 - 2 * q^10 + 6 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 4 * q^17 - 6 * q^20 + 4 * q^25 - 12 * q^26 + 4 * q^27 - 6 * q^29 - 2 * q^30 - 6 * q^33 - 2 * q^35 + 2 * q^36 + 6 * q^37 - 4 * q^38 + 8 * q^39 - 4 * q^40 + 2 * q^42 + 10 * q^43 + 6 * q^45 + 12 * q^46 - 2 * q^48 + 2 * q^49 - 12 * q^50 - 8 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^55 - 2 * q^56 + 12 * q^58 + 24 * q^59 - 6 * q^62 - 4 * q^64 + 6 * q^65 + 24 * q^67 - 4 * q^68 - 18 * q^71 - 10 * q^74 - 2 * q^75 + 6 * q^78 + 36 * q^79 - 6 * q^80 - 2 * q^81 - 6 * q^82 - 6 * q^85 - 6 * q^87 - 12 * q^89 + 4 * q^90 + 6 * q^91 - 18 * q^93 - 2 * q^94 - 2 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more