LMFDB - Embedded newform 570.2.i.d.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.i.d.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +6.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +1.00000 q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +11.0000 q^{37} +(0.500000 + 4.33013i) q^{38} +5.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-6.00000 + 10.3923i) q^{47} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{55} +1.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -6.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.50000 + 4.33013i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -5.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(0.500000 - 0.866025i) q^{67} +6.00000 q^{69} +(0.500000 - 0.866025i) q^{70} +(0.500000 - 0.866025i) q^{72} +(0.500000 + 0.866025i) q^{73} +(5.50000 + 9.52628i) q^{74} +1.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -6.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(3.50000 + 6.06218i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} -1.00000 q^{84} +(-0.500000 + 0.866025i) q^{86} +6.00000 q^{87} -6.00000 q^{88} +(6.00000 - 10.3923i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(2.50000 - 4.33013i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-2.50000 - 4.33013i) q^{93} -12.0000 q^{94} +(0.500000 + 4.33013i) q^{95} -1.00000 q^{96} +(-7.00000 - 12.1244i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - q^{10} + 12 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} + q^{15} - q^{16} - 2 q^{18} + 8 q^{19} - 2 q^{20} + q^{21} + 6 q^{22} - 6 q^{23} + q^{24} - q^{25} - 10 q^{26} + 2 q^{27} + q^{28} - 6 q^{29} + 2 q^{30} + 10 q^{31} + q^{32} - 6 q^{33} - q^{35} - q^{36} + 22 q^{37} + q^{38} + 10 q^{39} - q^{40} - 6 q^{41} - q^{42} + q^{43} - 6 q^{44} - 2 q^{45} - 12 q^{46} - 12 q^{47} - q^{48} - 12 q^{49} - 2 q^{50} - 5 q^{52} + 12 q^{53} + q^{54} + 6 q^{55} + 2 q^{56} - q^{57} - 12 q^{58} - 6 q^{59} + q^{60} + 7 q^{61} + 5 q^{62} + q^{63} + 2 q^{64} - 10 q^{65} + 6 q^{66} + q^{67} + 12 q^{69} + q^{70} + q^{72} + q^{73} + 11 q^{74} + 2 q^{75} - 7 q^{76} - 12 q^{77} + 5 q^{78} + 7 q^{79} + q^{80} - q^{81} + 6 q^{82} - 12 q^{83} - 2 q^{84} - q^{86} + 12 q^{87} - 12 q^{88} + 12 q^{89} - q^{90} + 5 q^{91} - 6 q^{92} - 5 q^{93} - 24 q^{94} + q^{95} - 2 q^{96} - 14 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9 - q^10 + 12 * q^11 + 2 * q^12 - 5 * q^13 - q^14 + q^15 - q^16 - 2 * q^18 + 8 * q^19 - 2 * q^20 + q^21 + 6 * q^22 - 6 * q^23 + q^24 - q^25 - 10 * q^26 + 2 * q^27 + q^28 - 6 * q^29 + 2 * q^30 + 10 * q^31 + q^32 - 6 * q^33 - q^35 - q^36 + 22 * q^37 + q^38 + 10 * q^39 - q^40 - 6 * q^41 - q^42 + q^43 - 6 * q^44 - 2 * q^45 - 12 * q^46 - 12 * q^47 - q^48 - 12 * q^49 - 2 * q^50 - 5 * q^52 + 12 * q^53 + q^54 + 6 * q^55 + 2 * q^56 - q^57 - 12 * q^58 - 6 * q^59 + q^60 + 7 * q^61 + 5 * q^62 + q^63 + 2 * q^64 - 10 * q^65 + 6 * q^66 + q^67 + 12 * q^69 + q^70 + q^72 + q^73 + 11 * q^74 + 2 * q^75 - 7 * q^76 - 12 * q^77 + 5 * q^78 + 7 * q^79 + q^80 - q^81 + 6 * q^82 - 12 * q^83 - 2 * q^84 - q^86 + 12 * q^87 - 12 * q^88 + 12 * q^89 - q^90 + 5 * q^91 - 6 * q^92 - 5 * q^93 - 24 * q^94 + q^95 - 2 * q^96 - 14 * q^97 - 6 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$	1.00000			0.288675
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−1.00000			−0.235702
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$	−1.00000			−0.223607
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−5.00000			−0.980581
$27$	1.00000			0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	1.00000			0.182574
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$		0			0
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	11.0000			1.80839			0.904194	−	0.427121i	$-0.140472\pi$
$37$	11.0000			1.80839			0.904194	+	0.427121i	$0.140472\pi$
$38$	0.500000	+	4.33013i	0.0811107	+	0.702439i
$39$	5.00000			0.800641
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	−1.00000			−0.149071
$46$	−6.00000			−0.884652
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.0186297	+	0.999826i	$0.505930\pi$
$47$	−6.00000	+	10.3923i	−0.875190	+	1.51587i	−0.856560	+	0.516047i	$0.827403\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.00000			−0.857143
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	1.00000			0.133631
$57$	−0.500000	−	4.33013i	−0.0662266	−	0.573539i
$58$	−6.00000			−0.787839
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	2.50000	+	4.33013i	0.317500	+	0.549927i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	−5.00000			−0.620174
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	−0.833866	−	0.551967i	$-0.813877\pi$
$67$	0.500000	−	0.866025i	0.0610847	−	0.105802i	0.894951	+	0.446165i	$0.147211\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$	5.50000	+	9.52628i	0.639362	+	1.10741i
$75$	1.00000			0.115470
$76$	−3.50000	+	2.59808i	−0.401478	+	0.298020i
$77$	−6.00000			−0.683763
$78$	2.50000	+	4.33013i	0.283069	+	0.490290i
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	0.992945	−	0.118578i	$-0.0378336\pi$
$79$	3.50000	+	6.06218i	0.393781	+	0.682048i	−0.599164	+	0.800626i	$0.704500\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−1.00000			−0.109109
$85$		0			0
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	6.00000			0.643268
$88$	−6.00000			−0.639602
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	2.50000	−	4.33013i	0.262071	−	0.453921i
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$	−12.0000			−1.23771
$95$	0.500000	+	4.33013i	0.0512989	+	0.444262i
$96$	−1.00000			−0.102062
$97$	−7.00000	−	12.1244i	−0.710742	−	1.23104i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−7.00000	−	12.1244i	−0.710742	−	1.23104i	0.253837	−	0.967247i	$-0.418307\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	11.0000			1.08386			0.541931	−	0.840423i	$-0.317693\pi$
$103$	11.0000			1.08386			0.541931	+	0.840423i	$0.317693\pi$
$104$	2.50000	−	4.33013i	0.245145	−	0.424604i
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$	12.0000			1.16554
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	−5.50000	−	9.52628i	−0.522037	−	0.904194i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−18.0000			−1.69330			−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000			−1.69330			−0.846649	+	0.532152i	$0.821383\pi$
$114$	3.50000	−	2.59808i	0.327805	−	0.243332i
$115$	−6.00000			−0.559503
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	−2.50000	−	4.33013i	−0.231125	−	0.400320i
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$		0			0
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	25.0000			2.27273
$122$	7.00000			0.633750
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$	−1.00000			−0.0894427
$126$	1.00000			0.0890871
$127$	8.00000	−	13.8564i	0.709885	−	1.22956i	−0.255014	−	0.966937i	$-0.582080\pi$
$127$	8.00000	−	13.8564i	0.709885	−	1.22956i	0.964899	−	0.262620i	$-0.0845865\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	0.500000	−	0.866025i	0.0440225	−	0.0762493i
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$	6.00000			0.522233
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$	1.00000			0.0863868
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$	3.00000	+	5.19615i	0.255377	+	0.442326i
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	−0.844042	−	0.536278i	$-0.819830\pi$
$139$	0.500000	−	0.866025i	0.0424094	−	0.0734553i	0.886451	+	0.462822i	$0.153163\pi$
$140$	1.00000			0.0845154
$141$	12.0000			1.01058
$142$		0			0
$143$	−15.0000	+	25.9808i	−1.25436	+	2.17262i
$144$	1.00000			0.0833333
$145$	−6.00000			−0.498273
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	−5.50000	+	9.52628i	−0.452097	+	0.783055i
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−4.00000	−	1.73205i	−0.324443	−	0.140488i
$153$		0			0
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	2.50000	+	4.33013i	0.200805	+	0.347804i
$156$	−2.50000	+	4.33013i	−0.200160	+	0.346688i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	−3.50000	+	6.06218i	−0.278445	+	0.482281i
$159$	−12.0000			−0.951662
$160$	1.00000			0.0790569
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	6.00000			0.468521
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	−0.273252	−	0.961943i	$-0.588099\pi$
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	0.969693	−	0.244328i	$-0.0785675\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	−3.50000	+	2.59808i	−0.267652	+	0.198680i
$172$	−1.00000			−0.0762493
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	3.00000	+	5.19615i	0.227429	+	0.393919i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	12.0000			0.899438
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−13.0000	+	22.5167i	−0.966282	+	1.67365i	−0.260153	+	0.965567i	$0.583773\pi$
$181$	−13.0000	+	22.5167i	−0.966282	+	1.67365i	−0.706129	+	0.708083i	$0.749560\pi$
$182$	5.00000			0.370625
$183$	−7.00000			−0.517455
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	5.50000	+	9.52628i	0.404368	+	0.700386i
$186$	2.50000	−	4.33013i	0.183309	−	0.317500i
$187$		0			0
$188$	−6.00000	−	10.3923i	−0.437595	−	0.757937i
$189$	−1.00000			−0.0727393
$190$	−3.50000	+	2.59808i	−0.253917	+	0.188484i
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$	2.50000	+	4.33013i	0.179029	+	0.310087i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−6.00000			−0.426401
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−1.00000			−0.0705346
$202$	6.00000			0.422159
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	5.50000	+	9.52628i	0.383203	+	0.663727i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	5.00000			0.346688
$209$	24.0000	+	10.3923i	1.66011	+	0.718851i
$210$	−1.00000			−0.0690066
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	−0.500000	+	0.866025i	−0.0340997	+	0.0590624i
$216$	−1.00000			−0.0680414
$217$	−5.00000			−0.339422
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$	0.500000	−	0.866025i	0.0337869	−	0.0585206i
$220$	−6.00000			−0.404520
$221$		0			0
$222$	5.50000	−	9.52628i	0.369136	−	0.639362i
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	4.00000	+	1.73205i	0.264906	+	0.114708i
$229$	−25.0000			−1.65205			−0.826023	−	0.563636i	$-0.809402\pi$
$229$	−25.0000			−1.65205			−0.826023	+	0.563636i	$0.809402\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	0.992853	−	0.119342i	$-0.0380786\pi$
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	−0.599780	+	0.800165i	$0.704745\pi$
$234$	2.50000	−	4.33013i	0.163430	−	0.283069i
$235$	−12.0000			−0.782794
$236$	6.00000			0.390567
$237$	3.50000	−	6.06218i	0.227349	−	0.393781i
$238$		0			0
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$	−1.00000			−0.0645497
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$	−3.00000	−	5.19615i	−0.191663	−	0.331970i
$246$	−6.00000			−0.382546
$247$	−17.5000	+	12.9904i	−1.11350	+	0.826558i
$248$	−5.00000			−0.317500
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	−0.945036	−	0.326965i	$-0.893974\pi$
$251$	−3.00000	+	5.19615i	−0.189358	+	0.327978i	0.755678	+	0.654943i	$0.227307\pi$
$252$	0.500000	+	0.866025i	0.0314970	+	0.0545545i
$253$	−18.0000	+	31.1769i	−1.13165	+	1.96008i
$254$	16.0000			1.00393
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	1.00000			0.0622573
$259$	−11.0000			−0.683507
$260$	2.50000	−	4.33013i	0.155043	−	0.268543i
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$	3.00000	−	5.19615i	0.185341	−	0.321019i
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$	12.0000			0.737154
$266$	−0.500000	−	4.33013i	−0.0306570	−	0.265497i
$267$	−12.0000			−0.734388
$268$	0.500000	+	0.866025i	0.0305424	+	0.0529009i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$	−5.00000			−0.302614
$274$	6.00000			0.362473
$275$	−3.00000	+	5.19615i	−0.180907	+	0.313340i
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	14.0000			0.841178			0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000			0.841178			0.420589	+	0.907251i	$0.361823\pi$
$278$	1.00000			0.0599760
$279$	−2.50000	+	4.33013i	−0.149671	+	0.259238i
$280$	0.500000	+	0.866025i	0.0298807	+	0.0517549i
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	0.462174	+	0.886789i	$0.347070\pi$
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	−0.999069	+	0.0431402i	$0.986264\pi$
$282$	6.00000	+	10.3923i	0.357295	+	0.618853i
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	0.999608	−	0.0280052i	$-0.00891551\pi$
$283$	8.00000	+	13.8564i	0.475551	+	0.823678i	−0.524057	+	0.851683i	$0.675582\pi$
$284$		0			0
$285$	3.50000	−	2.59808i	0.207322	−	0.153897i
$286$	−30.0000			−1.77394
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$	−1.00000			−0.0585206
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	−3.00000	+	5.19615i	−0.174964	+	0.303046i
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$	−11.0000			−0.639362
$297$	6.00000			0.348155
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$	−15.0000	−	25.9808i	−0.867472	−	1.50251i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−0.500000	−	0.866025i	−0.0288195	−	0.0499169i
$302$	4.00000	+	6.92820i	0.230174	+	0.398673i
$303$	−6.00000			−0.344691
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$	7.00000			0.400819
$306$		0			0
$307$	−10.0000	−	17.3205i	−0.570730	−	0.988534i	−0.996491	−	0.0836980i	$-0.973327\pi$
$307$	−10.0000	−	17.3205i	−0.570730	−	0.988534i	0.425761	−	0.904836i	$-0.360006\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$	−5.50000	−	9.52628i	−0.312884	−	0.541931i
$310$	−2.50000	+	4.33013i	−0.141990	+	0.245935i
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$	−5.00000			−0.283069
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	−6.50000	+	11.2583i	−0.366816	+	0.635344i
$315$	1.00000			0.0563436
$316$	−7.00000			−0.393781
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$	−18.0000	+	31.1769i	−1.00781	+	1.74557i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$	6.00000			0.334367
$323$		0			0
$324$	1.00000			0.0555556
$325$	−2.50000	−	4.33013i	−0.138675	−	0.240192i
$326$	5.50000	+	9.52628i	0.304617	+	0.527612i
$327$	−7.00000	+	12.1244i	−0.387101	+	0.670478i
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	6.00000			0.330289
$331$	29.0000			1.59398			0.796992	−	0.603990i	$-0.206423\pi$
$331$	29.0000			1.59398			0.796992	+	0.603990i	$0.206423\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−5.50000	+	9.52628i	−0.301398	+	0.522037i
$334$	18.0000			0.984916
$335$	1.00000			0.0546358
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	0.676441	−	0.736497i	$-0.263521\pi$
$337$	−5.50000	−	9.52628i	−0.299604	−	0.518930i	−0.976045	+	0.217567i	$0.930188\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$		0			0
$341$	30.0000			1.62459
$342$	−4.00000	−	1.73205i	−0.216295	−	0.0936586i
$343$	13.0000			0.701934
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$	3.00000	+	5.19615i	0.161515	+	0.279751i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	−19.0000			−1.01705			−0.508523	−	0.861048i	$-0.669808\pi$
$349$	−19.0000			−1.01705			−0.508523	+	0.861048i	$0.669808\pi$
$350$	1.00000			0.0534522
$351$	−2.50000	+	4.33013i	−0.133440	+	0.231125i
$352$	3.00000	−	5.19615i	0.159901	−	0.276956i
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	−6.00000			−0.318896
$355$		0			0
$356$	6.00000	+	10.3923i	0.317999	+	0.550791i
$357$		0			0
$358$	9.00000	+	15.5885i	0.475665	+	0.823876i
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$	1.00000			0.0527046
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	−26.0000			−1.36653
$363$	−12.5000	−	21.6506i	−0.656080	−	1.13636i
$364$	2.50000	+	4.33013i	0.131036	+	0.226960i
$365$	−0.500000	+	0.866025i	−0.0261712	+	0.0453298i
$366$	−3.50000	−	6.06218i	−0.182948	−	0.316875i
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	6.00000			0.312772
$369$	6.00000			0.312348
$370$	−5.50000	+	9.52628i	−0.285931	+	0.495248i
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$	5.00000			0.259238
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	6.00000	−	10.3923i	0.309426	−	0.535942i
$377$	−15.0000	−	25.9808i	−0.772539	−	1.33808i
$378$	−0.500000	−	0.866025i	−0.0257172	−	0.0445435i
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	−4.00000	−	1.73205i	−0.205196	−	0.0888523i
$381$	−16.0000			−0.819705
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−3.00000	−	5.19615i	−0.152894	−	0.264820i
$386$	2.50000	−	4.33013i	0.127247	−	0.220398i
$387$	−1.00000			−0.0508329
$388$	14.0000			0.710742
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$	−2.50000	+	4.33013i	−0.126592	+	0.219265i
$391$		0			0
$392$	6.00000			0.303046
$393$	−3.00000	+	5.19615i	−0.151330	+	0.262111i
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	−3.50000	+	6.06218i	−0.176104	+	0.305021i
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	0.988080	+	0.153941i	$0.0491966\pi$
$397$	12.5000	+	21.6506i	0.627357	+	1.08661i	−0.360723	+	0.932673i	$0.617470\pi$
$398$	7.00000			0.350878
$399$	0.500000	+	4.33013i	0.0250313	+	0.216777i
$400$	1.00000			0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	−0.500000	−	0.866025i	−0.0249377	−	0.0431934i
$403$	−12.5000	+	21.6506i	−0.622669	+	1.07849i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	6.00000			0.297775
$407$	66.0000			3.27150
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	6.00000			0.296319
$411$	−6.00000			−0.295958
$412$	−5.50000	+	9.52628i	−0.270966	+	0.469326i
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	−1.00000			−0.0489702
$418$	3.00000	+	25.9808i	0.146735	+	1.27076i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	−0.500000	−	0.866025i	−0.0243975	−	0.0422577i
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	0.353233	−	0.935536i	$-0.385082\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$		0			0
$426$		0			0
$427$	−3.50000	+	6.06218i	−0.169377	+	0.293369i
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$	30.0000			1.44841
$430$	−1.00000			−0.0482243
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	−0.769588	−	0.638541i	$-0.779538\pi$
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	0.937787	+	0.347212i	$0.112871\pi$
$434$	−2.50000	−	4.33013i	−0.120004	−	0.207853i
$435$	3.00000	+	5.19615i	0.143839	+	0.249136i
$436$	14.0000			0.670478
$437$	−21.0000	+	15.5885i	−1.00457	+	0.745697i
$438$	1.00000			0.0477818
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	0.704405	−	0.709798i	$-0.251214\pi$
$439$	−5.50000	−	9.52628i	−0.262501	−	0.454665i	−0.966906	+	0.255134i	$0.917881\pi$
$440$	−3.00000	−	5.19615i	−0.143019	−	0.247717i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$		0			0
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	−0.426414	−	0.904528i	$-0.640223\pi$
$443$	12.0000	−	20.7846i	0.570137	−	0.987507i	0.996551	−	0.0829786i	$-0.0264433\pi$
$444$	11.0000			0.522037
$445$	12.0000			0.568855
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$	9.00000	−	15.5885i	0.425685	−	0.737309i
$448$	−1.00000			−0.0472456
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	−18.0000	−	31.1769i	−0.847587	−	1.46806i
$452$	9.00000	−	15.5885i	0.423324	−	0.733219i
$453$	−4.00000	−	6.92820i	−0.187936	−	0.325515i
$454$	−9.00000	−	15.5885i	−0.422391	−	0.731603i
$455$	5.00000			0.234404
$456$	0.500000	+	4.33013i	0.0234146	+	0.202777i
$457$	11.0000			0.514558			0.257279	−	0.966337i	$-0.417174\pi$
$457$	11.0000			0.514558			0.257279	+	0.966337i	$0.417174\pi$
$458$	−12.5000	−	21.6506i	−0.584087	−	1.01167i
$459$		0			0
$460$	3.00000	−	5.19615i	0.139876	−	0.242272i
$461$	−18.0000	−	31.1769i	−0.838344	−	1.45205i	−0.891279	−	0.453456i	$-0.850191\pi$
$461$	−18.0000	−	31.1769i	−0.838344	−	1.45205i	0.0529352	−	0.998598i	$-0.483142\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	17.0000			0.790057			0.395029	−	0.918669i	$-0.370735\pi$
$463$	17.0000			0.790057			0.395029	+	0.918669i	$0.370735\pi$
$464$	6.00000			0.278543
$465$	2.50000	−	4.33013i	0.115935	−	0.200805i
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$	5.00000			0.231125
$469$	−0.500000	+	0.866025i	−0.0230879	+	0.0399893i
$470$	−6.00000	−	10.3923i	−0.276759	−	0.479361i
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	7.00000			0.321521
$475$	−3.50000	+	2.59808i	−0.160591	+	0.119208i
$476$		0			0
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−27.5000	+	47.6314i	−1.25389	+	2.17180i
$482$	−5.00000			−0.227744
$483$	−6.00000			−0.273009
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$	−1.00000			−0.0453609
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$	−3.50000	+	6.06218i	−0.158438	+	0.274422i
$489$	−5.50000	−	9.52628i	−0.248719	−	0.430793i
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$	−3.00000	−	5.19615i	−0.135250	−	0.234261i
$493$		0			0
$494$	−20.0000	−	8.66025i	−0.899843	−	0.389643i
$495$	−6.00000			−0.269680
$496$	−2.50000	−	4.33013i	−0.112253	−	0.194428i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	0.500000	+	0.866025i	0.0223831	+	0.0387686i	0.877000	−	0.480490i	$-0.159541\pi$
$499$	0.500000	+	0.866025i	0.0223831	+	0.0387686i	−0.854617	+	0.519259i	$0.826208\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−18.0000			−0.804181
$502$	−6.00000			−0.267793
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	−0.464107	−	0.885779i	$-0.653625\pi$
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	0.999161	−	0.0409609i	$-0.0130419\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	6.00000			0.266996
$506$	−36.0000			−1.60040
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	18.0000	−	31.1769i	0.797836	−	1.38189i	−0.123187	−	0.992384i	$-0.539311\pi$
$509$	18.0000	−	31.1769i	0.797836	−	1.38189i	0.921023	−	0.389509i	$-0.127355\pi$
$510$		0			0
$511$	−0.500000	−	0.866025i	−0.0221187	−	0.0383107i
$512$	−1.00000			−0.0441942
$513$	4.00000	+	1.73205i	0.176604	+	0.0764719i
$514$	−6.00000			−0.264649
$515$	5.50000	+	9.52628i	0.242359	+	0.419778i
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	−36.0000	+	62.3538i	−1.58328	+	2.74232i
$518$	−5.50000	−	9.52628i	−0.241656	−	0.418561i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$	5.00000			0.219265
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	−0.297884	−	0.954602i	$-0.596281\pi$
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	0.975652	−	0.219326i	$-0.0703858\pi$
$524$	6.00000			0.262111
$525$	−1.00000			−0.0436436
$526$	−3.00000	+	5.19615i	−0.130806	+	0.226563i
$527$		0			0
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	6.00000	+	10.3923i	0.260623	+	0.451413i
$531$	6.00000			0.260378
$532$	3.50000	−	2.59808i	0.151744	−	0.112641i
$533$	30.0000			1.29944
$534$	−6.00000	−	10.3923i	−0.259645	−	0.449719i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	−0.500000	+	0.866025i	−0.0215967	+	0.0374066i
$537$	−9.00000	−	15.5885i	−0.388379	−	0.672692i
$538$	9.00000	−	15.5885i	0.388018	−	0.672066i
$539$	−36.0000			−1.55063
$540$	−1.00000			−0.0430331
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$	26.0000			1.11577
$544$		0			0
$545$	7.00000	−	12.1244i	0.299847	−	0.519350i
$546$	−2.50000	−	4.33013i	−0.106990	−	0.185312i
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	−0.692948	−	0.720988i	$-0.743688\pi$
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	0.970868	+	0.239616i	$0.0770217\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$	−6.00000			−0.255841
$551$	−21.0000	+	15.5885i	−0.894630	+	0.664091i
$552$	−6.00000			−0.255377
$553$	−3.50000	−	6.06218i	−0.148835	−	0.257790i
$554$	7.00000	+	12.1244i	0.297402	+	0.515115i
$555$	5.50000	−	9.52628i	0.233462	−	0.404368i
$556$	0.500000	+	0.866025i	0.0212047	+	0.0367277i
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	−0.710457	−	0.703740i	$-0.751512\pi$
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	0.964686	+	0.263404i	$0.0848453\pi$
$558$	−5.00000			−0.211667
$559$	−5.00000			−0.211477
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−6.00000			−0.252870			−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000			−0.252870			−0.126435	+	0.991975i	$0.540353\pi$
$564$	−6.00000	+	10.3923i	−0.252646	+	0.437595i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	−8.00000	+	13.8564i	−0.336265	+	0.582428i
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$		0			0
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$	4.00000	+	1.73205i	0.167542	+	0.0725476i
$571$	23.0000			0.962520			0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000			0.962520			0.481260	+	0.876578i	$0.340179\pi$
$572$	−15.0000	−	25.9808i	−0.627182	−	1.08631i
$573$	−6.00000	−	10.3923i	−0.250654	−	0.434145i
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$	−3.00000	−	5.19615i	−0.125109	−	0.216695i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−34.0000			−1.41544			−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000			−1.41544			−0.707719	+	0.706494i	$0.750276\pi$
$578$	17.0000			0.707107
$579$	−2.50000	+	4.33013i	−0.103896	+	0.179954i
$580$	3.00000	−	5.19615i	0.124568	−	0.215758i
$581$	6.00000			0.248922
$582$	−14.0000			−0.580319
$583$	36.0000	−	62.3538i	1.49097	−	2.58243i
$584$	−0.500000	−	0.866025i	−0.0206901	−	0.0358364i
$585$	2.50000	−	4.33013i	0.103362	−	0.179029i
$586$	−9.00000	−	15.5885i	−0.371787	−	0.643953i
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$	−6.00000			−0.247436
$589$	20.0000	+	8.66025i	0.824086	+	0.356840i
$590$	6.00000			0.247016
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	−5.50000	−	9.52628i	−0.226049	−	0.391528i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$	3.00000	+	5.19615i	0.123091	+	0.213201i
$595$		0			0
$596$	−18.0000			−0.737309
$597$	−7.00000			−0.286491
$598$	15.0000	−	25.9808i	0.613396	−	1.06243i
$599$	−24.0000	+	41.5692i	−0.980613	+	1.69847i	−0.320607	+	0.947212i	$0.603887\pi$
$599$	−24.0000	+	41.5692i	−0.980613	+	1.69847i	−0.660006	+	0.751260i	$0.729446\pi$
$600$	−1.00000			−0.0408248
$601$	−1.00000			−0.0407909			−0.0203954	−	0.999792i	$-0.506493\pi$
$601$	−1.00000			−0.0407909			−0.0203954	+	0.999792i	$0.506493\pi$
$602$	0.500000	−	0.866025i	0.0203785	−	0.0352966i
$603$	0.500000	+	0.866025i	0.0203616	+	0.0352673i
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	12.5000	+	21.6506i	0.508197	+	0.880223i
$606$	−3.00000	−	5.19615i	−0.121867	−	0.211079i
$607$	−1.00000			−0.0405887			−0.0202944	−	0.999794i	$-0.506460\pi$
$607$	−1.00000			−0.0405887			−0.0202944	+	0.999794i	$0.506460\pi$
$608$	3.50000	−	2.59808i	0.141944	−	0.105366i
$609$	−6.00000			−0.243132
$610$	3.50000	+	6.06218i	0.141711	+	0.245450i
$611$	−30.0000	−	51.9615i	−1.21367	−	2.10214i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$	−6.00000			−0.241943
$616$	6.00000			0.241747
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	−0.516710	−	0.856161i	$-0.672843\pi$
$617$	12.0000	−	20.7846i	0.483102	−	0.836757i	0.999812	+	0.0194037i	$0.00617676\pi$
$618$	5.50000	−	9.52628i	0.221242	−	0.383203i
$619$	11.0000			0.442127			0.221064	−	0.975259i	$-0.429047\pi$
$619$	11.0000			0.442127			0.221064	+	0.975259i	$0.429047\pi$
$620$	−5.00000			−0.200805
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	3.00000	+	5.19615i	0.120289	+	0.208347i
$623$	−6.00000	+	10.3923i	−0.240385	+	0.416359i
$624$	−2.50000	−	4.33013i	−0.100080	−	0.173344i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	22.0000			0.879297
$627$	−3.00000	−	25.9808i	−0.119808	−	1.03757i
$628$	−13.0000			−0.518756
$629$		0			0
$630$	0.500000	+	0.866025i	0.0199205	+	0.0345033i
$631$	3.50000	−	6.06218i	0.139333	−	0.241331i	−0.787911	−	0.615789i	$-0.788838\pi$
$631$	3.50000	−	6.06218i	0.139333	−	0.241331i	0.927244	+	0.374457i	$0.122171\pi$
$632$	−3.50000	−	6.06218i	−0.139223	−	0.241140i
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$	18.0000			0.714871
$635$	16.0000			0.634941
$636$	6.00000	−	10.3923i	0.237915	−	0.412082i
$637$	15.0000	−	25.9808i	0.594322	−	1.02940i
$638$	−36.0000			−1.42525
$639$		0			0
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	18.0000	+	31.1769i	0.710957	+	1.23141i	0.964498	+	0.264089i	$0.0850714\pi$
$641$	18.0000	+	31.1769i	0.710957	+	1.23141i	−0.253541	+	0.967325i	$0.581595\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	−0.996379	−	0.0850262i	$-0.972903\pi$
$643$	−14.5000	−	25.1147i	−0.571824	−	0.990429i	0.424555	−	0.905402i	$-0.360431\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$	1.00000			0.0393750
$646$		0			0
$647$	−42.0000			−1.65119			−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000			−1.65119			−0.825595	+	0.564263i	$0.809160\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−18.0000	−	31.1769i	−0.706562	−	1.22380i
$650$	2.50000	−	4.33013i	0.0980581	−	0.169842i
$651$	2.50000	+	4.33013i	0.0979827	+	0.169711i
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$	−14.0000			−0.547443
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	−1.00000			−0.0390137
$658$	12.0000			0.467809
$659$	−15.0000	+	25.9808i	−0.584317	+	1.01207i	0.410643	+	0.911796i	$0.365304\pi$
$659$	−15.0000	+	25.9808i	−0.584317	+	1.01207i	−0.994960	+	0.100271i	$0.968029\pi$
$660$	3.00000	+	5.19615i	0.116775	+	0.202260i
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	14.5000	+	25.1147i	0.563559	+	0.976112i
$663$		0			0
$664$	6.00000			0.232845
$665$	−0.500000	−	4.33013i	−0.0193892	−	0.167915i
$666$	−11.0000			−0.426241
$667$	−18.0000	−	31.1769i	−0.696963	−	1.20717i
$668$	9.00000	+	15.5885i	0.348220	+	0.603136i
$669$	0.500000	−	0.866025i	0.0193311	−	0.0334825i
$670$	0.500000	+	0.866025i	0.0193167	+	0.0334575i
$671$	21.0000	−	36.3731i	0.810696	−	1.40417i
$672$	1.00000			0.0385758
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	5.50000	−	9.52628i	0.211852	−	0.366939i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	12.0000			0.461538
$677$	−12.0000			−0.461197			−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000			−0.461197			−0.230599	+	0.973049i	$0.574068\pi$
$678$	−9.00000	+	15.5885i	−0.345643	+	0.598671i
$679$	7.00000	+	12.1244i	0.268635	+	0.465290i
$680$		0			0
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$	15.0000	+	25.9808i	0.574380	+	0.994855i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−0.500000	−	4.33013i	−0.0191180	−	0.165567i
$685$	6.00000			0.229248
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	12.5000	+	21.6506i	0.476905	+	0.826023i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	30.0000	+	51.9615i	1.14291	+	1.97958i
$690$	−3.00000	+	5.19615i	−0.114208	+	0.197814i
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$	6.00000			0.228086
$693$	3.00000	−	5.19615i	0.113961	−	0.197386i
$694$	−6.00000	+	10.3923i	−0.227757	+	0.394486i
$695$	1.00000			0.0379322
$696$	−6.00000			−0.227429
$697$		0			0
$698$	−9.50000	−	16.4545i	−0.359580	−	0.622811i
$699$	6.00000	−	10.3923i	0.226941	−	0.393073i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$701$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$702$	−5.00000			−0.188713
$703$	44.0000	+	19.0526i	1.65949	+	0.718581i
$704$	6.00000			0.226134
$705$	6.00000	+	10.3923i	0.225973	+	0.391397i
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	−0.856484	−	0.516174i	$-0.827356\pi$
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	0.875262	+	0.483650i	$0.160689\pi$
$710$		0			0
$711$	−7.00000			−0.262521
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$	−15.0000	+	25.9808i	−0.561754	+	0.972987i
$714$		0			0
$715$	−30.0000			−1.12194
$716$	−9.00000	+	15.5885i	−0.336346	+	0.582568i
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	−3.00000	+	5.19615i	−0.111959	+	0.193919i
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	0.930087	+	0.367338i	$0.119731\pi$
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	−0.146920	+	0.989148i	$0.546936\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−11.0000			−0.409661
$722$	−5.50000	+	18.1865i	−0.204689	+	0.676833i
$723$	5.00000			0.185952
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	12.5000	−	21.6506i	0.463919	−	0.803530i
$727$	−17.5000	−	30.3109i	−0.649039	−	1.12417i	−0.983353	−	0.181707i	$-0.941838\pi$
$727$	−17.5000	−	30.3109i	−0.649039	−	1.12417i	0.334314	−	0.942462i	$-0.391496\pi$
$728$	−2.50000	+	4.33013i	−0.0926562	+	0.160485i
$729$	1.00000			0.0370370
$730$	−1.00000			−0.0370117
$731$		0			0
$732$	3.50000	−	6.06218i	0.129364	−	0.224065i
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$	−17.0000			−0.627481
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$	−11.0000			−0.404368
$741$	20.0000	+	8.66025i	0.734718	+	0.318142i
$742$	−12.0000			−0.440534
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	0.652369	−	0.757902i	$-0.273775\pi$
$743$	−9.00000	−	15.5885i	−0.330178	−	0.571885i	−0.982547	+	0.186017i	$0.940442\pi$
$744$	2.50000	+	4.33013i	0.0916544	+	0.158750i
$745$	−9.00000	+	15.5885i	−0.329734	+	0.571117i
$746$	1.00000	+	1.73205i	0.0366126	+	0.0634149i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$		0			0
$749$	12.0000			0.438470
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−2.50000	+	4.33013i	−0.0912263	+	0.158009i	−0.908027	−	0.418911i	$-0.862412\pi$
$751$	−2.50000	+	4.33013i	−0.0912263	+	0.158009i	0.816801	+	0.576919i	$0.195745\pi$
$752$	12.0000			0.437595
$753$	6.00000			0.218652
$754$	15.0000	−	25.9808i	0.546268	−	0.946164i
$755$	4.00000	+	6.92820i	0.145575	+	0.252143i
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	15.5000	+	26.8468i	0.563357	+	0.975763i	0.997200	+	0.0747748i	$0.0238238\pi$
$757$	15.5000	+	26.8468i	0.563357	+	0.975763i	−0.433843	+	0.900988i	$0.642843\pi$
$758$	−9.50000	−	16.4545i	−0.345056	−	0.597654i
$759$	36.0000			1.30672
$760$	−0.500000	−	4.33013i	−0.0181369	−	0.157070i
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$	−8.00000	−	13.8564i	−0.289809	−	0.501965i
$763$	7.00000	+	12.1244i	0.253417	+	0.438931i
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$		0			0
$766$	−6.00000	+	10.3923i	−0.216789	+	0.375489i
$767$	30.0000			1.08324
$768$	1.00000			0.0360844
$769$	−11.5000	+	19.9186i	−0.414701	+	0.718283i	−0.995397	−	0.0958377i	$-0.969447\pi$
$769$	−11.5000	+	19.9186i	−0.414701	+	0.718283i	0.580696	+	0.814120i	$0.302780\pi$
$770$	3.00000	−	5.19615i	0.108112	−	0.187256i
$771$	6.00000			0.216085
$772$	5.00000			0.179954
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	−0.459418	−	0.888220i	$-0.651942\pi$
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	0.998930	−	0.0462427i	$-0.0147248\pi$
$774$	−0.500000	−	0.866025i	−0.0179721	−	0.0311286i
$775$	−2.50000	+	4.33013i	−0.0898027	+	0.155543i
$776$	7.00000	+	12.1244i	0.251285	+	0.435239i
$777$	5.50000	+	9.52628i	0.197311	+	0.341753i
$778$	6.00000			0.215110
$779$	−3.00000	−	25.9808i	−0.107486	−	0.930857i
$780$	−5.00000			−0.179029
$781$		0			0
$782$		0			0
$783$	−3.00000	+	5.19615i	−0.107211	+	0.185695i
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	−6.50000	+	11.2583i	−0.231995	+	0.401827i
$786$	−6.00000			−0.214013
$787$	53.0000			1.88925			0.944623	−	0.328158i	$-0.106428\pi$
$787$	53.0000			1.88925			0.944623	+	0.328158i	$0.106428\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$	−7.00000			−0.249049
$791$	18.0000			0.640006
$792$	3.00000	−	5.19615i	0.106600	−	0.184637i
$793$	17.5000	+	30.3109i	0.621443	+	1.07637i
$794$	−12.5000	+	21.6506i	−0.443608	+	0.768352i
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$	−3.50000	+	2.59808i	−0.123899	+	0.0919709i
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	0.500000	−	0.866025i	0.0176336	−	0.0305424i
$805$	6.00000			0.211472
$806$	−25.0000			−0.880587
$807$	−9.00000	+	15.5885i	−0.316815	+	0.548740i
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$	1.00000			0.0351364
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	8.00000	−	13.8564i	0.280572	−	0.485965i
$814$	33.0000	+	57.1577i	1.15665	+	2.00338i
$815$	5.50000	+	9.52628i	0.192657	+	0.333691i
$816$		0			0
$817$	0.500000	+	4.33013i	0.0174928	+	0.151492i
$818$	−2.00000			−0.0699284
$819$	2.50000	+	4.33013i	0.0873571	+	0.151307i
$820$	3.00000	+	5.19615i	0.104765	+	0.181458i
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	0.476122	+	0.879379i	$0.342042\pi$
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	−0.999626	+	0.0273557i	$0.991291\pi$
$822$	−3.00000	−	5.19615i	−0.104637	−	0.181237i
$823$	14.0000	−	24.2487i	0.488009	−	0.845257i	−0.511896	−	0.859048i	$-0.671057\pi$
$823$	14.0000	−	24.2487i	0.488009	−	0.845257i	0.999905	+	0.0137907i	$0.00438987\pi$
$824$	−11.0000			−0.383203
$825$	6.00000			0.208893
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	−9.00000	+	15.5885i	−0.312961	+	0.542064i	−0.979002	−	0.203851i	$-0.934654\pi$
$827$	−9.00000	+	15.5885i	−0.312961	+	0.542064i	0.666041	+	0.745915i	$0.267987\pi$
$828$	6.00000			0.208514
$829$	11.0000			0.382046			0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000			0.382046			0.191023	+	0.981586i	$0.438820\pi$
$830$	3.00000	−	5.19615i	0.104132	−	0.180361i
$831$	−7.00000	−	12.1244i	−0.242827	−	0.420589i
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$		0			0
$834$	−0.500000	−	0.866025i	−0.0173136	−	0.0299880i
$835$	18.0000			0.622916
$836$	−21.0000	+	15.5885i	−0.726300	+	0.539138i
$837$	5.00000			0.172825
$838$		0			0
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	0.950813	−	0.309764i	$-0.100250\pi$
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	−0.743670	+	0.668546i	$0.766917\pi$
$840$	0.500000	−	0.866025i	0.0172516	−	0.0298807i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	13.0000	−	22.5167i	0.448010	−	0.775975i
$843$	18.0000			0.619953
$844$	−13.0000			−0.447478
$845$	6.00000	−	10.3923i	0.206406	−	0.357506i
$846$	6.00000	−	10.3923i	0.206284	−	0.357295i
$847$	−25.0000			−0.859010
$848$	−12.0000			−0.412082
$849$	8.00000	−	13.8564i	0.274559	−	0.475551i
$850$		0			0
$851$	−33.0000	+	57.1577i	−1.13123	+	1.95934i
$852$		0			0
$853$	−23.5000	−	40.7032i	−0.804625	−	1.39365i	−0.916544	−	0.399934i	$-0.869033\pi$
$853$	−23.5000	−	40.7032i	−0.804625	−	1.39365i	0.111919	−	0.993717i	$-0.464300\pi$
$854$	−7.00000			−0.239535
$855$	−4.00000	−	1.73205i	−0.136797	−	0.0592349i
$856$	12.0000			0.410152
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$	15.0000	+	25.9808i	0.512092	+	0.886969i
$859$	−2.50000	+	4.33013i	−0.0852989	+	0.147742i	−0.905519	−	0.424307i	$-0.860518\pi$
$859$	−2.50000	+	4.33013i	−0.0852989	+	0.147742i	0.820220	+	0.572049i	$0.193851\pi$
$860$	−0.500000	−	0.866025i	−0.0170499	−	0.0295312i
$861$	3.00000	−	5.19615i	0.102240	−	0.177084i
$862$	24.0000			0.817443
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	7.00000			0.237870
$867$	−17.0000			−0.577350
$868$	2.50000	−	4.33013i	0.0848555	−	0.146974i
$869$	21.0000	+	36.3731i	0.712376	+	1.23387i
$870$	−3.00000	+	5.19615i	−0.101710	+	0.176166i
$871$	2.50000	+	4.33013i	0.0847093	+	0.146721i
$872$	7.00000	+	12.1244i	0.237050	+	0.410582i
$873$	14.0000			0.473828
$874$	−24.0000	−	10.3923i	−0.811812	−	0.351525i
$875$	1.00000			0.0338062
$876$	0.500000	+	0.866025i	0.0168934	+	0.0292603i
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	0.603897	−	0.797062i	$-0.293614\pi$
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	−0.992225	+	0.124459i	$0.960280\pi$
$878$	5.50000	−	9.52628i	0.185616	−	0.321496i
$879$	9.00000	+	15.5885i	0.303562	+	0.525786i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$	6.00000			0.202031
$883$	−17.5000	+	30.3109i	−0.588922	+	1.02004i	0.405452	+	0.914116i	$0.367114\pi$
$883$	−17.5000	+	30.3109i	−0.588922	+	1.02004i	−0.994374	+	0.105926i	$0.966219\pi$
$884$		0			0
$885$	−6.00000			−0.201688
$886$	24.0000			0.806296
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$	5.50000	+	9.52628i	0.184568	+	0.319681i
$889$	−8.00000	+	13.8564i	−0.268311	+	0.464729i
$890$	6.00000	+	10.3923i	0.201120	+	0.348351i
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$	−1.00000			−0.0334825
$893$	−42.0000	+	31.1769i	−1.40548	+	1.04330i
$894$	18.0000			0.602010
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	−15.0000	+	25.9808i	−0.500835	+	0.867472i
$898$	12.0000	+	20.7846i	0.400445	+	0.693591i
$899$	−15.0000	+	25.9808i	−0.500278	+	0.866507i
$900$	1.00000			0.0333333
$901$		0			0
$902$	18.0000	−	31.1769i	0.599334	−	1.03808i
$903$	−0.500000	+	0.866025i	−0.0166390	+	0.0288195i
$904$	18.0000			0.598671
$905$	−26.0000			−0.864269
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	0.791944	−	0.610594i	$-0.209069\pi$
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	−0.924762	+	0.380547i	$0.875736\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$	3.00000	+	5.19615i	0.0995037	+	0.172345i
$910$	2.50000	+	4.33013i	0.0828742	+	0.143542i
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	−3.50000	+	2.59808i	−0.115897	+	0.0860309i
$913$	−36.0000			−1.19143
$914$	5.50000	+	9.52628i	0.181924	+	0.315101i
$915$	−3.50000	−	6.06218i	−0.115706	−	0.200409i
$916$	12.5000	−	21.6506i	0.413012	−	0.715357i
$917$	3.00000	+	5.19615i	0.0990687	+	0.171592i
$918$		0			0
$919$	−25.0000			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$920$	6.00000			0.197814
$921$	−10.0000	+	17.3205i	−0.329511	+	0.570730i
$922$	18.0000	−	31.1769i	0.592798	−	1.02676i
$923$		0			0
$924$	−6.00000			−0.197386
$925$	−5.50000	+	9.52628i	−0.180839	+	0.313222i
$926$	8.50000	+	14.7224i	0.279327	+	0.483809i
$927$	−5.50000	+	9.52628i	−0.180644	+	0.312884i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−30.0000	−	51.9615i	−0.984268	−	1.70480i	−0.645145	−	0.764060i	$-0.723203\pi$
$929$	−30.0000	−	51.9615i	−0.984268	−	1.70480i	−0.339123	−	0.940742i	$-0.610130\pi$
$930$	5.00000			0.163956
$931$	−24.0000	−	10.3923i	−0.786568	−	0.340594i
$932$	−12.0000			−0.393073
$933$	−3.00000	−	5.19615i	−0.0982156	−	0.170114i
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$		0			0
$936$	2.50000	+	4.33013i	0.0817151	+	0.141535i
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	−0.803176	−	0.595742i	$-0.796858\pi$
$937$	3.50000	−	6.06218i	0.114340	−	0.198043i	0.917516	+	0.397699i	$0.130191\pi$
$938$	−1.00000			−0.0326512
$939$	−22.0000			−0.717943
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	0.288988	+	0.957333i	$0.406681\pi$
$941$	−21.0000	+	36.3731i	−0.684580	+	1.18573i	−0.973568	+	0.228395i	$0.926652\pi$
$942$	13.0000			0.423563
$943$	36.0000			1.17232
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$	−0.500000	−	0.866025i	−0.0162650	−	0.0281718i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	0.974244	+	0.225497i	$0.0724007\pi$
$947$	21.0000	+	36.3731i	0.682408	+	1.18197i	−0.291835	+	0.956469i	$0.594266\pi$
$948$	3.50000	+	6.06218i	0.113675	+	0.196890i
$949$	−5.00000			−0.162307
$950$	−4.00000	−	1.73205i	−0.129777	−	0.0561951i
$951$	−18.0000			−0.583690
$952$		0			0
$953$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$953$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$954$	−6.00000	+	10.3923i	−0.194257	+	0.336463i
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	9.00000	−	15.5885i	0.291081	−	0.504167i
$957$	36.0000			1.16371
$958$	−6.00000			−0.193851
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−6.00000			−0.193548
$962$	−55.0000			−1.77327
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	−2.50000	−	4.33013i	−0.0805196	−	0.139464i
$965$	2.50000	−	4.33013i	0.0804778	−	0.139392i
$966$	−3.00000	−	5.19615i	−0.0965234	−	0.167183i
$967$	21.5000	+	37.2391i	0.691393	+	1.19753i	0.971381	+	0.237525i	$0.0763362\pi$
$967$	21.5000	+	37.2391i	0.691393	+	1.19753i	−0.279988	+	0.960003i	$0.590331\pi$
$968$	−25.0000			−0.803530
$969$		0			0
$970$	14.0000			0.449513
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−0.500000	+	0.866025i	−0.0160293	+	0.0277635i
$974$	16.0000	+	27.7128i	0.512673	+	0.887976i
$975$	−2.50000	+	4.33013i	−0.0800641	+	0.138675i
$976$	−7.00000			−0.224065
$977$	6.00000			0.191957			0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000			0.191957			0.0959785	+	0.995383i	$0.469402\pi$
$978$	5.50000	−	9.52628i	0.175871	−	0.304617i
$979$	36.0000	−	62.3538i	1.15056	−	1.99284i
$980$	6.00000			0.191663
$981$	14.0000			0.446986
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$	−12.0000			−0.381964
$988$	−2.50000	−	21.6506i	−0.0795356	−	0.688798i
$989$	−6.00000			−0.190789
$990$	−3.00000	−	5.19615i	−0.0953463	−	0.165145i
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	0.950603	−	0.310409i	$-0.100466\pi$
$991$	6.50000	+	11.2583i	0.206479	+	0.357633i	−0.744124	+	0.668042i	$0.767133\pi$
$992$	2.50000	−	4.33013i	0.0793751	−	0.137482i
$993$	−14.5000	−	25.1147i	−0.460144	−	0.796992i
$994$		0			0
$995$	7.00000			0.221915
$996$	−6.00000			−0.190117
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	−0.744548	−	0.667568i	$-0.767335\pi$
$997$	6.50000	−	11.2583i	0.205857	−	0.356555i	0.950405	+	0.311014i	$0.100668\pi$
$998$	−0.500000	+	0.866025i	−0.0158272	+	0.0274136i
$999$	11.0000			0.348025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.d.121.1	✓	2
3.2	odd	2		1710.2.l.a.1261.1		2
19.11	even	3	inner	570.2.i.d.391.1	yes	2
57.11	odd	6		1710.2.l.a.1531.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.d.121.1	✓	2	1.1	even	1	trivial
570.2.i.d.391.1	yes	2	19.11	even	3	inner
1710.2.l.a.1261.1		2	3.2	odd	2
1710.2.l.a.1531.1		2	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +6.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +1.00000 q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +11.0000 q^{37} +(0.500000 + 4.33013i) q^{38} +5.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-6.00000 + 10.3923i) q^{47} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{55} +1.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -6.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.50000 + 4.33013i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -5.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(0.500000 - 0.866025i) q^{67} +6.00000 q^{69} +(0.500000 - 0.866025i) q^{70} +(0.500000 - 0.866025i) q^{72} +(0.500000 + 0.866025i) q^{73} +(5.50000 + 9.52628i) q^{74} +1.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -6.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(3.50000 + 6.06218i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} -1.00000 q^{84} +(-0.500000 + 0.866025i) q^{86} +6.00000 q^{87} -6.00000 q^{88} +(6.00000 - 10.3923i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(2.50000 - 4.33013i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-2.50000 - 4.33013i) q^{93} -12.0000 q^{94} +(0.500000 + 4.33013i) q^{95} -1.00000 q^{96} +(-7.00000 - 12.1244i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9} - q^{10} + 12 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} + q^{15} - q^{16} - 2 q^{18} + 8 q^{19} - 2 q^{20} + q^{21} + 6 q^{22} - 6 q^{23} + q^{24} - q^{25} - 10 q^{26} + 2 q^{27} + q^{28} - 6 q^{29} + 2 q^{30} + 10 q^{31} + q^{32} - 6 q^{33} - q^{35} - q^{36} + 22 q^{37} + q^{38} + 10 q^{39} - q^{40} - 6 q^{41} - q^{42} + q^{43} - 6 q^{44} - 2 q^{45} - 12 q^{46} - 12 q^{47} - q^{48} - 12 q^{49} - 2 q^{50} - 5 q^{52} + 12 q^{53} + q^{54} + 6 q^{55} + 2 q^{56} - q^{57} - 12 q^{58} - 6 q^{59} + q^{60} + 7 q^{61} + 5 q^{62} + q^{63} + 2 q^{64} - 10 q^{65} + 6 q^{66} + q^{67} + 12 q^{69} + q^{70} + q^{72} + q^{73} + 11 q^{74} + 2 q^{75} - 7 q^{76} - 12 q^{77} + 5 q^{78} + 7 q^{79} + q^{80} - q^{81} + 6 q^{82} - 12 q^{83} - 2 q^{84} - q^{86} + 12 q^{87} - 12 q^{88} + 12 q^{89} - q^{90} + 5 q^{91} - 6 q^{92} - 5 q^{93} - 24 q^{94} + q^{95} - 2 q^{96} - 14 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^5 + q^6 - 2 * q^7 - 2 * q^8 - q^9 - q^10 + 12 * q^11 + 2 * q^12 - 5 * q^13 - q^14 + q^15 - q^16 - 2 * q^18 + 8 * q^19 - 2 * q^20 + q^21 + 6 * q^22 - 6 * q^23 + q^24 - q^25 - 10 * q^26 + 2 * q^27 + q^28 - 6 * q^29 + 2 * q^30 + 10 * q^31 + q^32 - 6 * q^33 - q^35 - q^36 + 22 * q^37 + q^38 + 10 * q^39 - q^40 - 6 * q^41 - q^42 + q^43 - 6 * q^44 - 2 * q^45 - 12 * q^46 - 12 * q^47 - q^48 - 12 * q^49 - 2 * q^50 - 5 * q^52 + 12 * q^53 + q^54 + 6 * q^55 + 2 * q^56 - q^57 - 12 * q^58 - 6 * q^59 + q^60 + 7 * q^61 + 5 * q^62 + q^63 + 2 * q^64 - 10 * q^65 + 6 * q^66 + q^67 + 12 * q^69 + q^70 + q^72 + q^73 + 11 * q^74 + 2 * q^75 - 7 * q^76 - 12 * q^77 + 5 * q^78 + 7 * q^79 + q^80 - q^81 + 6 * q^82 - 12 * q^83 - 2 * q^84 - q^86 + 12 * q^87 - 12 * q^88 + 12 * q^89 - q^90 + 5 * q^91 - 6 * q^92 - 5 * q^93 - 24 * q^94 + q^95 - 2 * q^96 - 14 * q^97 - 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more