LMFDB - Embedded newform 315.2.i.a.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.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:	$2.51528766367$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	315.211
Dual form			315.2.i.a.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} -2.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} -3.46410i q^{12} +(-3.00000 + 5.19615i) q^{13} +(-1.00000 + 1.73205i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -2.00000 q^{17} -6.00000 q^{18} -2.00000 q^{19} +(1.00000 + 1.73205i) q^{20} +(1.50000 + 0.866025i) q^{21} +(-3.00000 + 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +12.0000 q^{26} +5.19615i q^{27} +2.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(3.00000 - 1.73205i) q^{30} +(-5.00000 + 8.66025i) q^{31} +(4.00000 - 6.92820i) q^{32} +(4.50000 + 2.59808i) q^{33} +(2.00000 + 3.46410i) q^{34} -1.00000 q^{35} +(3.00000 + 5.19615i) q^{36} -2.00000 q^{37} +(2.00000 + 3.46410i) q^{38} -10.3923i q^{39} +(3.00000 - 5.19615i) q^{41} -3.46410i q^{42} +(-2.00000 - 3.46410i) q^{43} +6.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +8.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.00000 + 1.73205i) q^{50} +(3.00000 - 1.73205i) q^{51} +(-6.00000 - 10.3923i) q^{52} -4.00000 q^{53} +(9.00000 - 5.19615i) q^{54} -3.00000 q^{55} +(3.00000 - 1.73205i) q^{57} +(1.00000 - 1.73205i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-3.00000 - 1.73205i) q^{60} +(-2.00000 - 3.46410i) q^{61} +20.0000 q^{62} -3.00000 q^{63} -8.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -10.3923i q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} -6.92820i q^{69} +(1.00000 + 1.73205i) q^{70} -9.00000 q^{71} +13.0000 q^{73} +(2.00000 + 3.46410i) q^{74} +(1.50000 + 0.866025i) q^{75} +(2.00000 - 3.46410i) q^{76} +(-1.50000 + 2.59808i) q^{77} +(-18.0000 + 10.3923i) q^{78} +(-8.50000 - 14.7224i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{82} +(-6.50000 - 11.2583i) q^{83} +(-3.00000 + 1.73205i) q^{84} +(-1.00000 + 1.73205i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-1.50000 - 0.866025i) q^{87} +6.00000 q^{89} +(-3.00000 + 5.19615i) q^{90} +6.00000 q^{91} +(-4.00000 - 6.92820i) q^{92} -17.3205i q^{93} +(-7.00000 + 12.1244i) q^{94} +(-1.00000 + 1.73205i) q^{95} +13.8564i q^{96} +(4.50000 + 7.79423i) q^{97} +2.00000 q^{98} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 6 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 6 * q^6 - q^7 + 3 * q^9	$ 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 6 q^{6} - q^{7} + 3 q^{9} - 4 q^{10} - 3 q^{11} - 6 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} - 12 q^{18} - 4 q^{19} + 2 q^{20} + 3 q^{21} - 6 q^{22} - 4 q^{23} - q^{25} + 24 q^{26} + 4 q^{28} + q^{29} + 6 q^{30} - 10 q^{31} + 8 q^{32} + 9 q^{33} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} + 12 q^{44} - 3 q^{45} + 16 q^{46} - 7 q^{47} - 12 q^{48} - q^{49} - 2 q^{50} + 6 q^{51} - 12 q^{52} - 8 q^{53} + 18 q^{54} - 6 q^{55} + 6 q^{57} + 2 q^{58} - 14 q^{59} - 6 q^{60} - 4 q^{61} + 40 q^{62} - 6 q^{63} - 16 q^{64} + 6 q^{65} + 2 q^{67} + 4 q^{68} + 2 q^{70} - 18 q^{71} + 26 q^{73} + 4 q^{74} + 3 q^{75} + 4 q^{76} - 3 q^{77} - 36 q^{78} - 17 q^{79} + 8 q^{80} - 9 q^{81} - 24 q^{82} - 13 q^{83} - 6 q^{84} - 2 q^{85} - 8 q^{86} - 3 q^{87} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 8 q^{92} - 14 q^{94} - 2 q^{95} + 9 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 6 * q^6 - q^7 + 3 * q^9 - 4 * q^10 - 3 * q^11 - 6 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 - 12 * q^18 - 4 * q^19 + 2 * q^20 + 3 * q^21 - 6 * q^22 - 4 * q^23 - q^25 + 24 * q^26 + 4 * q^28 + q^29 + 6 * q^30 - 10 * q^31 + 8 * q^32 + 9 * q^33 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 + 12 * q^44 - 3 * q^45 + 16 * q^46 - 7 * q^47 - 12 * q^48 - q^49 - 2 * q^50 + 6 * q^51 - 12 * q^52 - 8 * q^53 + 18 * q^54 - 6 * q^55 + 6 * q^57 + 2 * q^58 - 14 * q^59 - 6 * q^60 - 4 * q^61 + 40 * q^62 - 6 * q^63 - 16 * q^64 + 6 * q^65 + 2 * q^67 + 4 * q^68 + 2 * q^70 - 18 * q^71 + 26 * q^73 + 4 * q^74 + 3 * q^75 + 4 * q^76 - 3 * q^77 - 36 * q^78 - 17 * q^79 + 8 * q^80 - 9 * q^81 - 24 * q^82 - 13 * q^83 - 6 * q^84 - 2 * q^85 - 8 * q^86 - 3 * q^87 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 8 * q^92 - 14 * q^94 - 2 * q^95 + 9 * q^97 + 4 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.00000	+	1.73205i	1.22474	+	0.707107i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−2.00000			−0.632456
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		−	3.46410i		−	1.00000i
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$			1.73205i			0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	−6.00000			−1.41421
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$	1.50000	+	0.866025i	0.327327	+	0.188982i
$22$	−3.00000	+	5.19615i	−0.639602	+	1.10782i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	12.0000			2.35339
$27$			5.19615i			1.00000i
$28$	2.00000			0.377964
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	3.00000	−	1.73205i	0.547723	−	0.316228i
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	−1.00000			−0.169031
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$		−	10.3923i		−	1.66410i
$40$		0			0
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		−	3.46410i		−	0.534522i
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	0.672264	−	0.740312i	$-0.265322\pi$
$43$	−2.00000	−	3.46410i	−0.304997	−	0.528271i	−0.977261	+	0.212041i	$0.931989\pi$
$44$	6.00000			0.904534
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	8.00000			1.17954
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$	−6.00000	−	3.46410i	−0.866025	−	0.500000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−1.00000	+	1.73205i	−0.141421	+	0.244949i
$51$	3.00000	−	1.73205i	0.420084	−	0.242536i
$52$	−6.00000	−	10.3923i	−0.832050	−	1.44115i
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$	9.00000	−	5.19615i	1.22474	−	0.707107i
$55$	−3.00000			−0.404520
$56$		0			0
$57$	3.00000	−	1.73205i	0.397360	−	0.229416i
$58$	1.00000	−	1.73205i	0.131306	−	0.227429i
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.0991242	+	0.995075i	$0.531604\pi$
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.812198	+	0.583382i	$0.801729\pi$
$60$	−3.00000	−	1.73205i	−0.387298	−	0.223607i
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$	20.0000			2.54000
$63$	−3.00000			−0.377964
$64$	−8.00000			−1.00000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		−	10.3923i		−	1.27920i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$		−	6.92820i		−	0.834058i
$70$	1.00000	+	1.73205i	0.119523	+	0.207020i
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$		0			0
$73$	13.0000			1.52153			0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000			1.52153			0.760767	+	0.649025i	$0.224823\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	1.50000	+	0.866025i	0.173205	+	0.100000i
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−1.50000	+	2.59808i	−0.170941	+	0.296078i
$78$	−18.0000	+	10.3923i	−2.03810	+	1.17670i
$79$	−8.50000	−	14.7224i	−0.956325	−	1.65640i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	−8.50000	−	14.7224i	−0.956325	−	1.65640i	−0.225018	−	0.974355i	$-0.572244\pi$
$80$	4.00000			0.447214
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−12.0000			−1.32518
$83$	−6.50000	−	11.2583i	−0.713468	−	1.23576i	−0.963548	−	0.267537i	$-0.913790\pi$
$83$	−6.50000	−	11.2583i	−0.713468	−	1.23576i	0.250080	−	0.968225i	$-0.419543\pi$
$84$	−3.00000	+	1.73205i	−0.327327	+	0.188982i
$85$	−1.00000	+	1.73205i	−0.108465	+	0.187867i
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	−1.50000	−	0.866025i	−0.160817	−	0.0928477i
$88$		0			0
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−3.00000	+	5.19615i	−0.316228	+	0.547723i
$91$	6.00000			0.628971
$92$	−4.00000	−	6.92820i	−0.417029	−	0.722315i
$93$		−	17.3205i		−	1.79605i
$94$	−7.00000	+	12.1244i	−0.721995	+	1.25053i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$			13.8564i			1.41421i
$97$	4.50000	+	7.79423i	0.456906	+	0.791384i	0.998796	−	0.0490655i	$-0.0156243\pi$
$97$	4.50000	+	7.79423i	0.456906	+	0.791384i	−0.541890	+	0.840450i	$0.682291\pi$
$98$	2.00000			0.202031
$99$	−9.00000			−0.904534
$100$	2.00000			0.200000
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	−6.00000	−	3.46410i	−0.594089	−	0.342997i
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.163335	−	0.986571i	$-0.447775\pi$
$103$	9.50000	−	16.4545i	0.936063	−	1.62131i	0.772728	−	0.634738i	$-0.218892\pi$
$104$		0			0
$105$	1.50000	−	0.866025i	0.146385	−	0.0845154i
$106$	4.00000	+	6.92820i	0.388514	+	0.672927i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	9.00000			0.862044			0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000			0.862044			0.431022	+	0.902342i	$0.358153\pi$
$110$	3.00000	+	5.19615i	0.286039	+	0.495434i
$111$	3.00000	−	1.73205i	0.284747	−	0.164399i
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	−6.00000	−	3.46410i	−0.561951	−	0.324443i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	−2.00000			−0.185695
$117$	9.00000	+	15.5885i	0.832050	+	1.44115i
$118$	28.0000			2.57761
$119$	1.00000	+	1.73205i	0.0916698	+	0.158777i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$			10.3923i			0.937043i
$124$	−10.0000	−	17.3205i	−0.898027	−	1.55543i
$125$	−1.00000			−0.0894427
$126$	3.00000	+	5.19615i	0.267261	+	0.462910i
$127$	−10.0000			−0.887357			−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000			−0.887357			−0.443678	+	0.896186i	$0.646327\pi$
$128$		0			0
$129$	6.00000	+	3.46410i	0.528271	+	0.304997i
$130$	6.00000	−	10.3923i	0.526235	−	0.911465i
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	−0.636676	−	0.771132i	$-0.719691\pi$
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	0.986157	+	0.165812i	$0.0530244\pi$
$132$	−9.00000	+	5.19615i	−0.783349	+	0.452267i
$133$	1.00000	+	1.73205i	0.0867110	+	0.150188i
$134$	−4.00000			−0.345547
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$		0			0
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	0.767853	−	0.640626i	$-0.221325\pi$
$137$	−2.00000	−	3.46410i	−0.170872	−	0.295958i	−0.938725	+	0.344668i	$0.887992\pi$
$138$	−12.0000	+	6.92820i	−1.02151	+	0.589768i
$139$	−3.00000	+	5.19615i	−0.254457	+	0.440732i	−0.964748	−	0.263176i	$-0.915230\pi$
$139$	−3.00000	+	5.19615i	−0.254457	+	0.440732i	0.710291	+	0.703908i	$0.248563\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$	10.5000	+	6.06218i	0.884260	+	0.510527i
$142$	9.00000	+	15.5885i	0.755263	+	1.30815i
$143$	18.0000			1.50524
$144$	12.0000			1.00000
$145$	1.00000			0.0830455
$146$	−13.0000	−	22.5167i	−1.07589	−	1.86349i
$147$		−	1.73205i		−	0.142857i
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	−0.973028	−	0.230689i	$-0.925902\pi$
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	0.686296	+	0.727322i	$0.259235\pi$
$150$		−	3.46410i		−	0.282843i
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$		0			0
$153$	−3.00000	+	5.19615i	−0.242536	+	0.420084i
$154$	6.00000			0.483494
$155$	5.00000	+	8.66025i	0.401610	+	0.695608i
$156$	18.0000	+	10.3923i	1.44115	+	0.832050i
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	−0.885288	−	0.465044i	$-0.846039\pi$
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	0.845383	+	0.534160i	$0.179372\pi$
$158$	−17.0000	+	29.4449i	−1.35245	+	2.34251i
$159$	6.00000	−	3.46410i	0.475831	−	0.274721i
$160$	−4.00000	−	6.92820i	−0.316228	−	0.547723i
$161$	4.00000			0.315244
$162$	−9.00000	+	15.5885i	−0.707107	+	1.22474i
$163$	18.0000			1.40987			0.704934	−	0.709273i	$-0.250976\pi$
$163$	18.0000			1.40987			0.704934	+	0.709273i	$0.250976\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	4.50000	−	2.59808i	0.350325	−	0.202260i
$166$	−13.0000	+	22.5167i	−1.00900	+	1.74763i
$167$	−8.00000	+	13.8564i	−0.619059	+	1.07224i	0.370599	+	0.928793i	$0.379152\pi$
$167$	−8.00000	+	13.8564i	−0.619059	+	1.07224i	−0.989658	+	0.143448i	$0.954181\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$	4.00000			0.306786
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	8.00000			0.609994
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$			3.46410i			0.262613i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	6.00000	−	10.3923i	0.452267	−	0.783349i
$177$		−	24.2487i		−	1.82264i
$178$	−6.00000	−	10.3923i	−0.449719	−	0.778936i
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$	6.00000			0.447214
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$	−6.00000	−	10.3923i	−0.444750	−	0.770329i
$183$	6.00000	+	3.46410i	0.443533	+	0.256074i
$184$		0			0
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$	−30.0000	+	17.3205i	−2.19971	+	1.27000i
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	14.0000			1.02105
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$	4.00000			0.290191
$191$	3.50000	+	6.06218i	0.253251	+	0.438644i	0.964419	−	0.264378i	$-0.0851668\pi$
$191$	3.50000	+	6.06218i	0.253251	+	0.438644i	−0.711168	+	0.703022i	$0.751833\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	−0.737620	−	0.675216i	$-0.764050\pi$
$193$	3.00000	−	5.19615i	0.215945	−	0.374027i	0.953564	+	0.301189i	$0.0973836\pi$
$194$	9.00000	−	15.5885i	0.646162	−	1.11919i
$195$	−9.00000	−	5.19615i	−0.644503	−	0.372104i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	9.00000	+	15.5885i	0.639602	+	1.10782i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$			3.46410i			0.244339i
$202$	8.00000	−	13.8564i	0.562878	−	0.974933i
$203$	0.500000	−	0.866025i	0.0350931	−	0.0607831i
$204$			6.92820i			0.485071i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	−38.0000			−2.64759
$207$	6.00000	+	10.3923i	0.417029	+	0.722315i
$208$	−24.0000			−1.66410
$209$	3.00000	+	5.19615i	0.207514	+	0.359425i
$210$	−3.00000	−	1.73205i	−0.207020	−	0.119523i
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	−0.882723	−	0.469894i	$-0.844292\pi$
$211$	−0.500000	+	0.866025i	−0.0344214	+	0.0596196i	0.848301	+	0.529514i	$0.177626\pi$
$212$	4.00000	−	6.92820i	0.274721	−	0.475831i
$213$	13.5000	−	7.79423i	0.925005	−	0.534052i
$214$	12.0000	+	20.7846i	0.820303	+	1.42081i
$215$	−4.00000			−0.272798
$216$		0			0
$217$	10.0000			0.678844
$218$	−9.00000	−	15.5885i	−0.609557	−	1.05578i
$219$	−19.5000	+	11.2583i	−1.31769	+	0.760767i
$220$	3.00000	−	5.19615i	0.202260	−	0.350325i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$	−6.00000	−	3.46410i	−0.402694	−	0.232495i
$223$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$223$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$224$	−8.00000			−0.534522
$225$	−3.00000			−0.200000
$226$	−12.0000			−0.798228
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	0.967692	−	0.252136i	$-0.0811332\pi$
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	−0.702202	+	0.711977i	$0.747800\pi$
$228$			6.92820i			0.458831i
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$		−	5.19615i		−	0.341882i
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	18.0000	−	31.1769i	1.17670	−	2.03810i
$235$	−7.00000			−0.456630
$236$	−14.0000	−	24.2487i	−0.911322	−	1.57846i
$237$	25.5000	+	14.7224i	1.65640	+	0.956325i
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	14.5000	−	25.1147i	0.937927	−	1.62454i	0.168598	−	0.985685i	$-0.446076\pi$
$239$	14.5000	−	25.1147i	0.937927	−	1.62454i	0.769329	−	0.638852i	$-0.220591\pi$
$240$	−6.00000	+	3.46410i	−0.387298	+	0.223607i
$241$	−15.0000	−	25.9808i	−0.966235	−	1.67357i	−0.706260	−	0.707953i	$-0.749619\pi$
$241$	−15.0000	−	25.9808i	−0.966235	−	1.67357i	−0.259975	−	0.965615i	$-0.583714\pi$
$242$	−4.00000			−0.257130
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	8.00000			0.512148
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	18.0000	−	10.3923i	1.14764	−	0.662589i
$247$	6.00000	−	10.3923i	0.381771	−	0.661247i
$248$		0			0
$249$	19.5000	+	11.2583i	1.23576	+	0.713468i
$250$	1.00000	+	1.73205i	0.0632456	+	0.109545i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$	3.00000	−	5.19615i	0.188982	−	0.327327i
$253$	12.0000			0.754434
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$		−	3.46410i		−	0.216930i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		−	13.8564i		−	0.862662i
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$	−12.0000			−0.744208
$261$	3.00000			0.185695
$262$	−16.0000			−0.988483
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	0.977993	−	0.208635i	$-0.0669022\pi$
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	−0.669680	+	0.742650i	$0.733569\pi$
$264$		0			0
$265$	−2.00000	+	3.46410i	−0.122859	+	0.212798i
$266$	2.00000	−	3.46410i	0.122628	−	0.212398i
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−20.0000			−1.21942			−0.609711	−	0.792624i	$-0.708714\pi$
$269$	−20.0000			−1.21942			−0.609711	+	0.792624i	$0.708714\pi$
$270$		−	10.3923i		−	0.632456i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−4.00000	−	6.92820i	−0.242536	−	0.420084i
$273$	−9.00000	+	5.19615i	−0.544705	+	0.314485i
$274$	−4.00000	+	6.92820i	−0.241649	+	0.418548i
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$	12.0000	+	6.92820i	0.722315	+	0.417029i
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$	12.0000			0.719712
$279$	15.0000	+	25.9808i	0.898027	+	1.55543i
$280$		0			0
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	0.988273	+	0.152699i	$0.0487965\pi$
$281$	10.5000	+	18.1865i	0.626377	+	1.08492i	−0.361895	+	0.932219i	$0.617870\pi$
$282$		−	24.2487i		−	1.44399i
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	−0.930714	−	0.365748i	$-0.880813\pi$
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	0.782104	+	0.623148i	$0.214146\pi$
$284$	9.00000	−	15.5885i	0.534052	−	0.925005i
$285$		−	3.46410i		−	0.205196i
$286$	−18.0000	−	31.1769i	−1.06436	−	1.84353i
$287$	−6.00000			−0.354169
$288$	−12.0000	−	20.7846i	−0.707107	−	1.22474i
$289$	−13.0000			−0.764706
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$	−13.5000	−	7.79423i	−0.791384	−	0.456906i
$292$	−13.0000	+	22.5167i	−0.760767	+	1.31769i
$293$	8.50000	−	14.7224i	0.496575	−	0.860094i	−0.503417	−	0.864044i	$-0.667924\pi$
$293$	8.50000	−	14.7224i	0.496575	−	0.860094i	0.999992	+	0.00395000i	$0.00125733\pi$
$294$	−3.00000	+	1.73205i	−0.174964	+	0.101015i
$295$	7.00000	+	12.1244i	0.407556	+	0.705907i
$296$		0			0
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	14.0000			0.810998
$299$	−12.0000	−	20.7846i	−0.693978	−	1.20201i
$300$	−3.00000	+	1.73205i	−0.173205	+	0.100000i
$301$	−2.00000	+	3.46410i	−0.115278	+	0.199667i
$302$	16.0000	−	27.7128i	0.920697	−	1.59469i
$303$	−12.0000	−	6.92820i	−0.689382	−	0.398015i
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$	−4.00000			−0.229039
$306$	12.0000			0.685994
$307$	12.0000			0.684876			0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000			0.684876			0.342438	+	0.939540i	$0.388747\pi$
$308$	−3.00000	−	5.19615i	−0.170941	−	0.296078i
$309$			32.9090i			1.87213i
$310$	10.0000	−	17.3205i	0.567962	−	0.983739i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−14.5000	−	25.1147i	−0.819588	−	1.41957i	−0.905986	−	0.423308i	$-0.860869\pi$
$313$	−14.5000	−	25.1147i	−0.819588	−	1.41957i	0.0863973	−	0.996261i	$-0.472465\pi$
$314$	2.00000			0.112867
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$	34.0000			1.91265
$317$	−2.00000	−	3.46410i	−0.112331	−	0.194563i	0.804379	−	0.594117i	$-0.202498\pi$
$317$	−2.00000	−	3.46410i	−0.112331	−	0.194563i	−0.916710	+	0.399554i	$0.869165\pi$
$318$	−12.0000	−	6.92820i	−0.672927	−	0.388514i
$319$	1.50000	−	2.59808i	0.0839839	−	0.145464i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	18.0000	−	10.3923i	1.00466	−	0.580042i
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$	4.00000			0.222566
$324$	18.0000			1.00000
$325$	6.00000			0.332820
$326$	−18.0000	−	31.1769i	−0.996928	−	1.72673i
$327$	−13.5000	+	7.79423i	−0.746552	+	0.431022i
$328$		0			0
$329$	−3.50000	+	6.06218i	−0.192961	+	0.334219i
$330$	−9.00000	−	5.19615i	−0.495434	−	0.286039i
$331$	16.5000	+	28.5788i	0.906922	+	1.57084i	0.818316	+	0.574768i	$0.194908\pi$
$331$	16.5000	+	28.5788i	0.906922	+	1.57084i	0.0886058	+	0.996067i	$0.471759\pi$
$332$	26.0000			1.42694
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	32.0000			1.75096
$335$	−1.00000	−	1.73205i	−0.0546358	−	0.0946320i
$336$			6.92820i			0.377964i
$337$	10.0000	−	17.3205i	0.544735	−	0.943508i	−0.453889	−	0.891058i	$-0.649964\pi$
$337$	10.0000	−	17.3205i	0.544735	−	0.943508i	0.998624	−	0.0524499i	$-0.0167030\pi$
$338$	−23.0000	+	39.8372i	−1.25104	+	2.16686i
$339$			10.3923i			0.564433i
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$	30.0000			1.62459
$342$	12.0000			0.648886
$343$	1.00000			0.0539949
$344$		0			0
$345$	−6.00000	−	3.46410i	−0.323029	−	0.186501i
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$	3.00000	−	1.73205i	0.160817	−	0.0928477i
$349$	−10.0000	−	17.3205i	−0.535288	−	0.927146i	−0.999149	−	0.0412379i	$-0.986870\pi$
$349$	−10.0000	−	17.3205i	−0.535288	−	0.927146i	0.463862	−	0.885908i	$-0.346463\pi$
$350$	2.00000			0.106904
$351$	−27.0000	−	15.5885i	−1.44115	−	0.832050i
$352$	−24.0000			−1.27920
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$	−42.0000	+	24.2487i	−2.23227	+	1.28880i
$355$	−4.50000	+	7.79423i	−0.238835	+	0.413675i
$356$	−6.00000	+	10.3923i	−0.317999	+	0.550791i
$357$	−3.00000	−	1.73205i	−0.158777	−	0.0916698i
$358$	15.0000	+	25.9808i	0.792775	+	1.37313i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$	20.0000	+	34.6410i	1.05118	+	1.82069i
$363$			3.46410i			0.181818i
$364$	−6.00000	+	10.3923i	−0.314485	+	0.544705i
$365$	6.50000	−	11.2583i	0.340226	−	0.589288i
$366$		−	13.8564i		−	0.724286i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	−16.0000			−0.834058
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$	4.00000			0.207950
$371$	2.00000	+	3.46410i	0.103835	+	0.179847i
$372$	30.0000	+	17.3205i	1.55543	+	0.898027i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	6.00000	−	10.3923i	0.310253	−	0.537373i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$		0			0
$377$	−6.00000			−0.309016
$378$	−9.00000	−	5.19615i	−0.462910	−	0.267261i
$379$	35.0000			1.79783			0.898915	−	0.438124i	$-0.144357\pi$
$379$	35.0000			1.79783			0.898915	+	0.438124i	$0.144357\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	15.0000	−	8.66025i	0.768473	−	0.443678i
$382$	7.00000	−	12.1244i	0.358151	−	0.620336i
$383$	−11.5000	+	19.9186i	−0.587623	+	1.01779i	0.406920	+	0.913464i	$0.366603\pi$
$383$	−11.5000	+	19.9186i	−0.587623	+	1.01779i	−0.994543	+	0.104328i	$0.966731\pi$
$384$		0			0
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	−12.0000			−0.610784
$387$	−12.0000			−0.609994
$388$	−18.0000			−0.913812
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$			20.7846i			1.05247i
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$		0			0
$393$			13.8564i			0.698963i
$394$	18.0000	+	31.1769i	0.906827	+	1.57067i
$395$	−17.0000			−0.855363
$396$	9.00000	−	15.5885i	0.452267	−	0.783349i
$397$	11.0000			0.552074			0.276037	−	0.961147i	$-0.410979\pi$
$397$	11.0000			0.552074			0.276037	+	0.961147i	$0.410979\pi$
$398$	10.0000	+	17.3205i	0.501255	+	0.868199i
$399$	−3.00000	−	1.73205i	−0.150188	−	0.0867110i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	6.00000	−	3.46410i	0.299253	−	0.172774i
$403$	−30.0000	−	51.9615i	−1.49441	−	2.58839i
$404$	−16.0000			−0.796030
$405$	−9.00000			−0.447214
$406$	−2.00000			−0.0992583
$407$	3.00000	+	5.19615i	0.148704	+	0.257564i
$408$		0			0
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	0.341994	+	0.939702i	$0.388898\pi$
$409$	−13.0000	+	22.5167i	−0.642809	+	1.11338i	−0.984803	+	0.173675i	$0.944436\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$	6.00000	+	3.46410i	0.295958	+	0.170872i
$412$	19.0000	+	32.9090i	0.936063	+	1.62131i
$413$	14.0000			0.688895
$414$	12.0000	−	20.7846i	0.589768	−	1.02151i
$415$	−13.0000			−0.638145
$416$	24.0000	+	41.5692i	1.17670	+	2.03810i
$417$		−	10.3923i		−	0.508913i
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	−0.783394	−	0.621525i	$-0.786513\pi$
$419$	3.00000	−	5.19615i	0.146560	−	0.253849i	0.929954	+	0.367677i	$0.119847\pi$
$420$			3.46410i			0.169031i
$421$	−0.500000	−	0.866025i	−0.0243685	−	0.0422075i	0.853584	−	0.520955i	$-0.174424\pi$
$421$	−0.500000	−	0.866025i	−0.0243685	−	0.0422075i	−0.877952	+	0.478748i	$0.841091\pi$
$422$	2.00000			0.0973585
$423$	−21.0000			−1.02105
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$	−27.0000	−	15.5885i	−1.30815	−	0.755263i
$427$	−2.00000	+	3.46410i	−0.0967868	+	0.167640i
$428$	12.0000	−	20.7846i	0.580042	−	1.00466i
$429$	−27.0000	+	15.5885i	−1.30357	+	0.752618i
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	32.0000			1.54139			0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000			1.54139			0.770693	+	0.637207i	$0.219910\pi$
$432$	−18.0000	+	10.3923i	−0.866025	+	0.500000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−10.0000	−	17.3205i	−0.480015	−	0.831411i
$435$	−1.50000	+	0.866025i	−0.0719195	+	0.0415227i
$436$	−9.00000	+	15.5885i	−0.431022	+	0.746552i
$437$	4.00000	−	6.92820i	0.191346	−	0.331421i
$438$	39.0000	+	22.5167i	1.86349	+	1.07589i
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$	−24.0000			−1.14156
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$			6.92820i			0.328798i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$		0			0
$447$		−	12.1244i		−	0.573462i
$448$	4.00000	+	6.92820i	0.188982	+	0.327327i
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$	3.00000	+	5.19615i	0.141421	+	0.244949i
$451$	−18.0000			−0.847587
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−24.0000	−	13.8564i	−1.12762	−	0.651031i
$454$	8.00000	−	13.8564i	0.375459	−	0.650313i
$455$	3.00000	−	5.19615i	0.140642	−	0.243599i
$456$		0			0
$457$	−18.0000	−	31.1769i	−0.842004	−	1.45839i	−0.888197	−	0.459462i	$-0.848042\pi$
$457$	−18.0000	−	31.1769i	−0.842004	−	1.45839i	0.0461929	−	0.998933i	$-0.485291\pi$
$458$	20.0000			0.934539
$459$		−	10.3923i		−	0.485071i
$460$	−8.00000			−0.373002
$461$	2.00000	+	3.46410i	0.0931493	+	0.161339i	0.908835	−	0.417156i	$-0.136973\pi$
$461$	2.00000	+	3.46410i	0.0931493	+	0.161339i	−0.815685	+	0.578496i	$0.803640\pi$
$462$	−9.00000	+	5.19615i	−0.418718	+	0.241747i
$463$	−3.00000	+	5.19615i	−0.139422	+	0.241486i	−0.927278	−	0.374374i	$-0.877858\pi$
$463$	−3.00000	+	5.19615i	−0.139422	+	0.241486i	0.787856	+	0.615859i	$0.211191\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$	−15.0000	−	8.66025i	−0.695608	−	0.401610i
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	−7.00000			−0.323921			−0.161961	−	0.986797i	$-0.551782\pi$
$467$	−7.00000			−0.323921			−0.161961	+	0.986797i	$0.551782\pi$
$468$	−36.0000			−1.66410
$469$	−2.00000			−0.0923514
$470$	7.00000	+	12.1244i	0.322886	+	0.559255i
$471$		−	1.73205i		−	0.0798087i
$472$		0			0
$473$	−6.00000	+	10.3923i	−0.275880	+	0.477839i
$474$		−	58.8897i		−	2.70489i
$475$	1.00000	+	1.73205i	0.0458831	+	0.0794719i
$476$	−4.00000			−0.183340
$477$	−6.00000	+	10.3923i	−0.274721	+	0.475831i
$478$	−58.0000			−2.65286
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$	12.0000	+	6.92820i	0.547723	+	0.316228i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	−30.0000	+	51.9615i	−1.36646	+	2.36678i
$483$	−6.00000	+	3.46410i	−0.273009	+	0.157622i
$484$	2.00000	+	3.46410i	0.0909091	+	0.157459i
$485$	9.00000			0.408669
$486$		−	31.1769i		−	1.41421i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$		0			0
$489$	−27.0000	+	15.5885i	−1.22098	+	0.704934i
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	−18.0000	+	31.1769i	−0.812329	+	1.40699i	0.0989017	+	0.995097i	$0.468467\pi$
$491$	−18.0000	+	31.1769i	−0.812329	+	1.40699i	−0.911230	+	0.411897i	$0.864866\pi$
$492$	−18.0000	−	10.3923i	−0.811503	−	0.468521i
$493$	−1.00000	−	1.73205i	−0.0450377	−	0.0780076i
$494$	−24.0000			−1.07981
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$	−40.0000			−1.79605
$497$	4.50000	+	7.79423i	0.201853	+	0.349619i
$498$		−	45.0333i		−	2.01799i
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$		−	27.7128i		−	1.23812i
$502$	24.0000	+	41.5692i	1.07117	+	1.85533i
$503$	−13.0000			−0.579641			−0.289821	−	0.957081i	$-0.593596\pi$
$503$	−13.0000			−0.579641			−0.289821	+	0.957081i	$0.593596\pi$
$504$		0			0
$505$	8.00000			0.355995
$506$	−12.0000	−	20.7846i	−0.533465	−	0.923989i
$507$	34.5000	+	19.9186i	1.53220	+	0.884615i
$508$	10.0000	−	17.3205i	0.443678	−	0.768473i
$509$	−10.0000	+	17.3205i	−0.443242	+	0.767718i	−0.997928	−	0.0643419i	$-0.979505\pi$
$509$	−10.0000	+	17.3205i	−0.443242	+	0.767718i	0.554686	+	0.832060i	$0.312839\pi$
$510$	−6.00000	+	3.46410i	−0.265684	+	0.153393i
$511$	−6.50000	−	11.2583i	−0.287543	−	0.498039i
$512$	32.0000			1.41421
$513$		−	10.3923i		−	0.458831i
$514$	30.0000			1.32324
$515$	−9.50000	−	16.4545i	−0.418620	−	0.725071i
$516$	−12.0000	+	6.92820i	−0.528271	+	0.304997i
$517$	−10.5000	+	18.1865i	−0.461789	+	0.799843i
$518$	2.00000	−	3.46410i	0.0878750	−	0.152204i
$519$	−13.5000	−	7.79423i	−0.592584	−	0.342129i
$520$		0			0
$521$	20.0000			0.876216			0.438108	−	0.898922i	$-0.355649\pi$
$521$	20.0000			0.876216			0.438108	+	0.898922i	$0.355649\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	11.0000			0.480996			0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000			0.480996			0.240498	+	0.970650i	$0.422689\pi$
$524$	8.00000	+	13.8564i	0.349482	+	0.605320i
$525$		−	1.73205i		−	0.0755929i
$526$	10.0000	−	17.3205i	0.436021	−	0.755210i
$527$	10.0000	−	17.3205i	0.435607	−	0.754493i
$528$			20.7846i			0.904534i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	8.00000			0.347498
$531$	21.0000	+	36.3731i	0.911322	+	1.57846i
$532$	−4.00000			−0.173422
$533$	18.0000	+	31.1769i	0.779667	+	1.35042i
$534$	18.0000	+	10.3923i	0.778936	+	0.449719i
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$	22.5000	−	12.9904i	0.970947	−	0.560576i
$538$	20.0000	+	34.6410i	0.862261	+	1.49348i
$539$	3.00000			0.129219
$540$	−9.00000	+	5.19615i	−0.387298	+	0.223607i
$541$	−6.00000			−0.257960			−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000			−0.257960			−0.128980	+	0.991647i	$0.541170\pi$
$542$		0			0
$543$	30.0000	−	17.3205i	1.28742	−	0.743294i
$544$	−8.00000	+	13.8564i	−0.342997	+	0.594089i
$545$	4.50000	−	7.79423i	0.192759	−	0.333868i
$546$	18.0000	+	10.3923i	0.770329	+	0.444750i
$547$	6.00000	+	10.3923i	0.256541	+	0.444343i	0.965313	−	0.261095i	$-0.0840836\pi$
$547$	6.00000	+	10.3923i	0.256541	+	0.444343i	−0.708772	+	0.705438i	$0.750750\pi$
$548$	8.00000			0.341743
$549$	−12.0000			−0.512148
$550$	6.00000			0.255841
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$		0			0
$553$	−8.50000	+	14.7224i	−0.361457	+	0.626061i
$554$	22.0000	−	38.1051i	0.934690	−	1.61893i
$555$		−	3.46410i		−	0.147043i
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	40.0000			1.69485			0.847427	−	0.530912i	$-0.178150\pi$
$557$	40.0000			1.69485			0.847427	+	0.530912i	$0.178150\pi$
$558$	30.0000	−	51.9615i	1.27000	−	2.19971i
$559$	24.0000			1.01509
$560$	−2.00000	−	3.46410i	−0.0845154	−	0.146385i
$561$	−9.00000	−	5.19615i	−0.379980	−	0.219382i
$562$	21.0000	−	36.3731i	0.885832	−	1.53431i
$563$	3.50000	−	6.06218i	0.147507	−	0.255490i	−0.782798	−	0.622276i	$-0.786208\pi$
$563$	3.50000	−	6.06218i	0.147507	−	0.255490i	0.930306	+	0.366785i	$0.119542\pi$
$564$	−21.0000	+	12.1244i	−0.884260	+	0.510527i
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	10.0000			0.420331
$567$	−4.50000	+	7.79423i	−0.188982	+	0.327327i
$568$		0			0
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	0.756151	−	0.654398i	$-0.227078\pi$
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	−0.944800	+	0.327647i	$0.893744\pi$
$570$	−6.00000	+	3.46410i	−0.251312	+	0.145095i
$571$	−7.50000	+	12.9904i	−0.313865	+	0.543631i	−0.979196	−	0.202919i	$-0.934957\pi$
$571$	−7.50000	+	12.9904i	−0.313865	+	0.543631i	0.665330	+	0.746549i	$0.268291\pi$
$572$	−18.0000	+	31.1769i	−0.752618	+	1.30357i
$573$	−10.5000	−	6.06218i	−0.438644	−	0.253251i
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$	4.00000			0.166812
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	13.0000	+	22.5167i	0.540729	+	0.936570i
$579$			10.3923i			0.431889i
$580$	−1.00000	+	1.73205i	−0.0415227	+	0.0719195i
$581$	−6.50000	+	11.2583i	−0.269665	+	0.467074i
$582$			31.1769i			1.29232i
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		0			0
$585$	18.0000			0.744208
$586$	−34.0000			−1.40453
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	−0.951151	−	0.308725i	$-0.900098\pi$
$587$	−18.0000	−	31.1769i	−0.742940	−	1.28681i	0.208212	−	0.978084i	$-0.433236\pi$
$588$	3.00000	+	1.73205i	0.123718	+	0.0714286i
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$	14.0000	−	24.2487i	0.576371	−	0.998304i
$591$	27.0000	−	15.5885i	1.11063	−	0.641223i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	−3.00000			−0.123195			−0.0615976	−	0.998101i	$-0.519620\pi$
$593$	−3.00000			−0.123195			−0.0615976	+	0.998101i	$0.519620\pi$
$594$	−27.0000	−	15.5885i	−1.10782	−	0.639602i
$595$	2.00000			0.0819920
$596$	−7.00000	−	12.1244i	−0.286731	−	0.496633i
$597$	15.0000	−	8.66025i	0.613909	−	0.354441i
$598$	−24.0000	+	41.5692i	−0.981433	+	1.69989i
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.0699877	−	0.997548i	$-0.477704\pi$
$599$	22.0000	−	38.1051i	0.898896	−	1.55693i	0.828908	−	0.559385i	$-0.188963\pi$
$600$		0			0
$601$	15.0000	+	25.9808i	0.611863	+	1.05978i	0.990926	+	0.134407i	$0.0429129\pi$
$601$	15.0000	+	25.9808i	0.611863	+	1.05978i	−0.379063	+	0.925371i	$0.623754\pi$
$602$	8.00000			0.326056
$603$	−3.00000	−	5.19615i	−0.122169	−	0.211604i
$604$	−32.0000			−1.30206
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$			27.7128i			1.12576i
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	−8.00000	+	13.8564i	−0.324443	+	0.561951i
$609$			1.73205i			0.0701862i
$610$	4.00000	+	6.92820i	0.161955	+	0.280515i
$611$	42.0000			1.69914
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−12.0000			−0.484675			−0.242338	−	0.970192i	$-0.577914\pi$
$613$	−12.0000			−0.484675			−0.242338	+	0.970192i	$0.577914\pi$
$614$	−12.0000	−	20.7846i	−0.484281	−	0.838799i
$615$	9.00000	+	5.19615i	0.362915	+	0.209529i
$616$		0			0
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$	57.0000	−	32.9090i	2.29288	−	1.32379i
$619$	6.00000	+	10.3923i	0.241160	+	0.417702i	0.961045	−	0.276392i	$-0.0891387\pi$
$619$	6.00000	+	10.3923i	0.241160	+	0.417702i	−0.719885	+	0.694094i	$0.755805\pi$
$620$	−20.0000			−0.803219
$621$	−18.0000	−	10.3923i	−0.722315	−	0.417029i
$622$	−24.0000			−0.962312
$623$	−3.00000	−	5.19615i	−0.120192	−	0.208179i
$624$	36.0000	−	20.7846i	1.44115	−	0.832050i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−29.0000	+	50.2295i	−1.15907	+	2.00757i
$627$	−9.00000	−	5.19615i	−0.359425	−	0.207514i
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	4.00000			0.159490
$630$	6.00000			0.239046
$631$	15.0000			0.597141			0.298570	−	0.954388i	$-0.403490\pi$
$631$	15.0000			0.597141			0.298570	+	0.954388i	$0.403490\pi$
$632$		0			0
$633$		−	1.73205i		−	0.0688428i
$634$	−4.00000	+	6.92820i	−0.158860	+	0.275154i
$635$	−5.00000	+	8.66025i	−0.198419	+	0.343672i
$636$			13.8564i			0.549442i
$637$	−3.00000	−	5.19615i	−0.118864	−	0.205879i
$638$	−6.00000			−0.237542
$639$	−13.5000	+	23.3827i	−0.534052	+	0.925005i
$640$		0			0
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$	−36.0000	−	20.7846i	−1.42081	−	0.820303i
$643$	−15.5000	+	26.8468i	−0.611260	+	1.05873i	0.379768	+	0.925082i	$0.376004\pi$
$643$	−15.5000	+	26.8468i	−0.611260	+	1.05873i	−0.991028	+	0.133652i	$0.957330\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$	6.00000	−	3.46410i	0.236250	−	0.136399i
$646$	−4.00000	−	6.92820i	−0.157378	−	0.272587i
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$		0			0
$649$	42.0000			1.64864
$650$	−6.00000	−	10.3923i	−0.235339	−	0.407620i
$651$	−15.0000	+	8.66025i	−0.587896	+	0.339422i
$652$	−18.0000	+	31.1769i	−0.704934	+	1.22098i
$653$	−14.0000	+	24.2487i	−0.547862	+	0.948925i	0.450558	+	0.892747i	$0.351225\pi$
$653$	−14.0000	+	24.2487i	−0.547862	+	0.948925i	−0.998421	+	0.0561784i	$0.982108\pi$
$654$	27.0000	+	15.5885i	1.05578	+	0.609557i
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$	24.0000			0.937043
$657$	19.5000	−	33.7750i	0.760767	−	1.31769i
$658$	14.0000			0.545777
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$			10.3923i			0.404520i
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	33.0000	−	57.1577i	1.28258	−	2.22150i
$663$			20.7846i			0.807207i
$664$		0			0
$665$	2.00000			0.0775567
$666$	12.0000			0.464991
$667$	−4.00000			−0.154881
$668$	−16.0000	−	27.7128i	−0.619059	−	1.07224i
$669$		0			0
$670$	−2.00000	+	3.46410i	−0.0772667	+	0.133830i
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$	12.0000	−	6.92820i	0.462910	−	0.267261i
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	−40.0000			−1.54074
$675$	4.50000	−	2.59808i	0.173205	−	0.100000i
$676$	46.0000			1.76923
$677$	−13.0000	−	22.5167i	−0.499631	−	0.865386i	0.500369	−	0.865812i	$-0.333198\pi$
$677$	−13.0000	−	22.5167i	−0.499631	−	0.865386i	−1.00000		0.000426509i	$0.999864\pi$
$678$	18.0000	−	10.3923i	0.691286	−	0.399114i
$679$	4.50000	−	7.79423i	0.172694	−	0.299115i
$680$		0			0
$681$	−12.0000	−	6.92820i	−0.459841	−	0.265489i
$682$	−30.0000	−	51.9615i	−1.14876	−	1.98971i
$683$	6.00000			0.229584			0.114792	−	0.993390i	$-0.463380\pi$
$683$	6.00000			0.229584			0.114792	+	0.993390i	$0.463380\pi$
$684$	−6.00000	−	10.3923i	−0.229416	−	0.397360i
$685$	−4.00000			−0.152832
$686$	−1.00000	−	1.73205i	−0.0381802	−	0.0661300i
$687$		−	17.3205i		−	0.660819i
$688$	8.00000	−	13.8564i	0.304997	−	0.528271i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$			13.8564i			0.527504i
$691$	3.00000	+	5.19615i	0.114125	+	0.197671i	0.917430	−	0.397898i	$-0.130260\pi$
$691$	3.00000	+	5.19615i	0.114125	+	0.197671i	−0.803304	+	0.595569i	$0.796927\pi$
$692$	−18.0000			−0.684257
$693$	4.50000	+	7.79423i	0.170941	+	0.296078i
$694$	−32.0000			−1.21470
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$		0			0
$697$	−6.00000	+	10.3923i	−0.227266	+	0.393637i
$698$	−20.0000	+	34.6410i	−0.757011	+	1.31118i
$699$	9.00000	−	5.19615i	0.340411	−	0.196537i
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$			62.3538i			2.35339i
$703$	4.00000			0.150863
$704$	12.0000	+	20.7846i	0.452267	+	0.783349i
$705$	10.5000	−	6.06218i	0.395453	−	0.228315i
$706$	21.0000	−	36.3731i	0.790345	−	1.36892i
$707$	4.00000	−	6.92820i	0.150435	−	0.260562i
$708$	42.0000	+	24.2487i	1.57846	+	0.911322i
$709$	8.50000	+	14.7224i	0.319224	+	0.552913i	0.980326	−	0.197383i	$-0.0632444\pi$
$709$	8.50000	+	14.7224i	0.319224	+	0.552913i	−0.661102	+	0.750296i	$0.729911\pi$
$710$	18.0000			0.675528
$711$	−51.0000			−1.91265
$712$		0			0
$713$	−20.0000	−	34.6410i	−0.749006	−	1.29732i
$714$			6.92820i			0.259281i
$715$	9.00000	−	15.5885i	0.336581	−	0.582975i
$716$	15.0000	−	25.9808i	0.560576	−	0.970947i
$717$			50.2295i			1.87585i
$718$	−24.0000	−	41.5692i	−0.895672	−	1.55135i
$719$	−38.0000			−1.41716			−0.708580	−	0.705630i	$-0.750664\pi$
$719$	−38.0000			−1.41716			−0.708580	+	0.705630i	$0.750664\pi$
$720$	6.00000	−	10.3923i	0.223607	−	0.387298i
$721$	−19.0000			−0.707597
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$	45.0000	+	25.9808i	1.67357	+	0.966235i
$724$	20.0000	−	34.6410i	0.743294	−	1.28742i
$725$	0.500000	−	0.866025i	0.0185695	−	0.0321634i
$726$	6.00000	−	3.46410i	0.222681	−	0.128565i
$727$	2.50000	+	4.33013i	0.0927199	+	0.160596i	0.908655	−	0.417548i	$-0.137111\pi$
$727$	2.50000	+	4.33013i	0.0927199	+	0.160596i	−0.815935	+	0.578144i	$0.803777\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−26.0000			−0.962303
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	−12.0000	+	6.92820i	−0.443533	+	0.256074i
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	−0.423802	−	0.905755i	$-0.639305\pi$
$733$	15.5000	−	26.8468i	0.572506	−	0.991609i	0.996308	−	0.0858539i	$-0.0273618\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$	−1.50000	−	0.866025i	−0.0553283	−	0.0319438i
$736$	16.0000	+	27.7128i	0.589768	+	1.02151i
$737$	−6.00000			−0.221013
$738$	−18.0000	+	31.1769i	−0.662589	+	1.14764i
$739$	−19.0000			−0.698926			−0.349463	−	0.936950i	$-0.613636\pi$
$739$	−19.0000			−0.698926			−0.349463	+	0.936950i	$0.613636\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$			20.7846i			0.763542i
$742$	4.00000	−	6.92820i	0.146845	−	0.254342i
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$		0			0
$745$	3.50000	+	6.06218i	0.128230	+	0.222101i
$746$	28.0000			1.02515
$747$	−39.0000			−1.42694
$748$	−12.0000			−0.438763
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$	−3.00000	−	1.73205i	−0.109545	−	0.0632456i
$751$	−23.5000	+	40.7032i	−0.857527	+	1.48528i	0.0167534	+	0.999860i	$0.494667\pi$
$751$	−23.5000	+	40.7032i	−0.857527	+	1.48528i	−0.874281	+	0.485421i	$0.838666\pi$
$752$	14.0000	−	24.2487i	0.510527	−	0.884260i
$753$	36.0000	−	20.7846i	1.31191	−	0.757433i
$754$	6.00000	+	10.3923i	0.218507	+	0.378465i
$755$	16.0000			0.582300
$756$			10.3923i			0.377964i
$757$	−34.0000			−1.23575			−0.617876	−	0.786276i	$-0.712006\pi$
$757$	−34.0000			−1.23575			−0.617876	+	0.786276i	$0.712006\pi$
$758$	−35.0000	−	60.6218i	−1.27126	−	2.20188i
$759$	−18.0000	+	10.3923i	−0.653359	+	0.377217i
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	−30.0000	−	17.3205i	−1.08679	−	0.627456i
$763$	−4.50000	−	7.79423i	−0.162911	−	0.282170i
$764$	−14.0000			−0.506502
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$	46.0000			1.66205
$767$	−42.0000	−	72.7461i	−1.51653	−	2.62671i
$768$		−	27.7128i		−	1.00000i
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$	3.00000	−	5.19615i	0.108112	−	0.187256i
$771$		−	25.9808i		−	0.935674i
$772$	6.00000	+	10.3923i	0.215945	+	0.374027i
$773$	21.0000			0.755318			0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000			0.755318			0.377659	+	0.925945i	$0.376729\pi$
$774$	12.0000	+	20.7846i	0.431331	+	0.747087i
$775$	10.0000			0.359211
$776$		0			0
$777$	−3.00000	−	1.73205i	−0.107624	−	0.0621370i
$778$	15.0000	−	25.9808i	0.537776	−	0.931455i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	18.0000	−	10.3923i	0.644503	−	0.372104i
$781$	13.5000	+	23.3827i	0.483068	+	0.836698i
$782$	−16.0000			−0.572159
$783$	−4.50000	+	2.59808i	−0.160817	+	0.0928477i
$784$	−4.00000			−0.142857
$785$	0.500000	+	0.866025i	0.0178458	+	0.0309098i
$786$	24.0000	−	13.8564i	0.856052	−	0.494242i
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	−0.630905	−	0.775860i	$-0.717316\pi$
$787$	10.0000	−	17.3205i	0.356462	−	0.617409i	0.987367	+	0.158450i	$0.0506498\pi$
$788$	18.0000	−	31.1769i	0.641223	−	1.11063i
$789$	−15.0000	−	8.66025i	−0.534014	−	0.308313i
$790$	17.0000	+	29.4449i	0.604833	+	1.04760i
$791$	−6.00000			−0.213335
$792$		0			0
$793$	24.0000			0.852265
$794$	−11.0000	−	19.0526i	−0.390375	−	0.676150i
$795$		−	6.92820i		−	0.245718i
$796$	10.0000	−	17.3205i	0.354441	−	0.613909i
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$			6.92820i			0.245256i
$799$	7.00000	+	12.1244i	0.247642	+	0.428929i
$800$	−8.00000			−0.282843
$801$	9.00000	−	15.5885i	0.317999	−	0.550791i
$802$	−30.0000			−1.05934
$803$	−19.5000	−	33.7750i	−0.688140	−	1.19189i
$804$	−6.00000	−	3.46410i	−0.211604	−	0.122169i
$805$	2.00000	−	3.46410i	0.0704907	−	0.122094i
$806$	−60.0000	+	103.923i	−2.11341	+	3.66053i
$807$	30.0000	−	17.3205i	1.05605	−	0.609711i
$808$		0			0
$809$	18.0000			0.632846			0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000			0.632846			0.316423	+	0.948618i	$0.397518\pi$
$810$	9.00000	+	15.5885i	0.316228	+	0.547723i
$811$	12.0000			0.421377			0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000			0.421377			0.210688	+	0.977553i	$0.432429\pi$
$812$	1.00000	+	1.73205i	0.0350931	+	0.0607831i
$813$		0			0
$814$	6.00000	−	10.3923i	0.210300	−	0.364250i
$815$	9.00000	−	15.5885i	0.315256	−	0.546040i
$816$	12.0000	+	6.92820i	0.420084	+	0.242536i
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$	52.0000			1.81814
$819$	9.00000	−	15.5885i	0.314485	−	0.544705i
$820$	12.0000			0.419058
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		−	13.8564i		−	0.483298i
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	−0.985997	−	0.166762i	$-0.946669\pi$
$823$	−10.0000	+	17.3205i	−0.348578	+	0.603755i	0.637419	+	0.770517i	$0.280002\pi$
$824$		0			0
$825$		−	5.19615i		−	0.180907i
$826$	−14.0000	−	24.2487i	−0.487122	−	0.843721i
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$	−24.0000			−0.834058
$829$	−54.0000			−1.87550			−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−54.0000			−1.87550			−0.937749	+	0.347314i	$0.887094\pi$
$830$	13.0000	+	22.5167i	0.451237	+	0.781565i
$831$	−33.0000	−	19.0526i	−1.14476	−	0.660926i
$832$	24.0000	−	41.5692i	0.832050	−	1.44115i
$833$	1.00000	−	1.73205i	0.0346479	−	0.0600120i
$834$	−18.0000	+	10.3923i	−0.623289	+	0.359856i
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$	−12.0000			−0.415029
$837$	−45.0000	−	25.9808i	−1.55543	−	0.898027i
$838$	−12.0000			−0.414533
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	−1.00000	+	1.73205i	−0.0344623	+	0.0596904i
$843$	−31.5000	−	18.1865i	−1.08492	−	0.626377i
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$	−23.0000			−0.791224
$846$	21.0000	+	36.3731i	0.721995	+	1.25053i
$847$	−2.00000			−0.0687208
$848$	−8.00000	−	13.8564i	−0.274721	−	0.475831i
$849$		−	8.66025i		−	0.297219i
$850$	2.00000	−	3.46410i	0.0685994	−	0.118818i
$851$	4.00000	−	6.92820i	0.137118	−	0.237496i
$852$			31.1769i			1.06810i
$853$	21.0000	+	36.3731i	0.719026	+	1.24539i	0.961386	+	0.275204i	$0.0887453\pi$
$853$	21.0000	+	36.3731i	0.719026	+	1.24539i	−0.242360	+	0.970186i	$0.577921\pi$
$854$	8.00000			0.273754
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$	54.0000	+	31.1769i	1.84353	+	1.06436i
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	−0.768031	−	0.640412i	$-0.778763\pi$
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	0.938629	+	0.344928i	$0.112097\pi$
$860$	4.00000	−	6.92820i	0.136399	−	0.236250i
$861$	9.00000	−	5.19615i	0.306719	−	0.177084i
$862$	−32.0000	−	55.4256i	−1.08992	−	1.88780i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	36.0000	+	20.7846i	1.22474	+	0.707107i
$865$	9.00000			0.306009
$866$	14.0000	+	24.2487i	0.475739	+	0.824005i
$867$	19.5000	−	11.2583i	0.662255	−	0.382353i
$868$	−10.0000	+	17.3205i	−0.339422	+	0.587896i
$869$	−25.5000	+	44.1673i	−0.865028	+	1.49827i
$870$	3.00000	+	1.73205i	0.101710	+	0.0587220i
$871$	6.00000	+	10.3923i	0.203302	+	0.352130i
$872$		0			0
$873$	27.0000			0.913812
$874$	−16.0000			−0.541208
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$		−	45.0333i		−	1.52153i
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	−0.983995	−	0.178195i	$-0.942974\pi$
$877$	−10.0000	+	17.3205i	−0.337676	+	0.584872i	0.646319	+	0.763067i	$0.276307\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$			29.4449i			0.993151i
$880$	−6.00000	−	10.3923i	−0.202260	−	0.350325i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	3.00000	−	5.19615i	0.101015	−	0.174964i
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$	12.0000	+	20.7846i	0.403604	+	0.699062i
$885$	−21.0000	−	12.1244i	−0.705907	−	0.407556i
$886$		0			0
$887$	−10.0000	+	17.3205i	−0.335767	+	0.581566i	−0.983632	−	0.180190i	$-0.942329\pi$
$887$	−10.0000	+	17.3205i	−0.335767	+	0.581566i	0.647865	+	0.761755i	$0.275662\pi$
$888$		0			0
$889$	5.00000	+	8.66025i	0.167695	+	0.290456i
$890$	−12.0000			−0.402241
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		0			0
$893$	7.00000	+	12.1244i	0.234246	+	0.405726i
$894$	−21.0000	+	12.1244i	−0.702345	+	0.405499i
$895$	−7.50000	+	12.9904i	−0.250697	+	0.434221i
$896$		0			0
$897$	36.0000	+	20.7846i	1.20201	+	0.693978i
$898$	9.00000	+	15.5885i	0.300334	+	0.520194i
$899$	−10.0000			−0.333519
$900$	3.00000	−	5.19615i	0.100000	−	0.173205i
$901$	8.00000			0.266519
$902$	18.0000	+	31.1769i	0.599334	+	1.03808i
$903$		−	6.92820i		−	0.230556i
$904$		0			0
$905$	−10.0000	+	17.3205i	−0.332411	+	0.575753i
$906$			55.4256i			1.84139i
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	0.882150	−	0.470968i	$-0.156095\pi$
$907$	1.00000	+	1.73205i	0.0332045	+	0.0575118i	−0.848946	+	0.528480i	$0.822762\pi$
$908$	−16.0000			−0.530979
$909$	24.0000			0.796030
$910$	−12.0000			−0.397796
$911$	1.50000	+	2.59808i	0.0496972	+	0.0860781i	0.889804	−	0.456343i	$-0.150841\pi$
$911$	1.50000	+	2.59808i	0.0496972	+	0.0860781i	−0.840107	+	0.542421i	$0.817508\pi$
$912$	12.0000	+	6.92820i	0.397360	+	0.229416i
$913$	−19.5000	+	33.7750i	−0.645356	+	1.11779i
$914$	−36.0000	+	62.3538i	−1.19077	+	2.06248i
$915$	6.00000	−	3.46410i	0.198354	−	0.114520i
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$	−8.00000			−0.264183
$918$	−18.0000	+	10.3923i	−0.594089	+	0.342997i
$919$	−21.0000			−0.692726			−0.346363	−	0.938101i	$-0.612583\pi$
$919$	−21.0000			−0.692726			−0.346363	+	0.938101i	$0.612583\pi$
$920$		0			0
$921$	−18.0000	+	10.3923i	−0.593120	+	0.342438i
$922$	4.00000	−	6.92820i	0.131733	−	0.228168i
$923$	27.0000	−	46.7654i	0.888716	−	1.53930i
$924$	9.00000	+	5.19615i	0.296078	+	0.170941i
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	12.0000			0.394344
$927$	−28.5000	−	49.3634i	−0.936063	−	1.62131i
$928$	8.00000			0.262613
$929$	29.0000	+	50.2295i	0.951459	+	1.64798i	0.742271	+	0.670100i	$0.233749\pi$
$929$	29.0000	+	50.2295i	0.951459	+	1.64798i	0.209189	+	0.977875i	$0.432918\pi$
$930$			34.6410i			1.13592i
$931$	1.00000	−	1.73205i	0.0327737	−	0.0567657i
$932$	6.00000	−	10.3923i	0.196537	−	0.340411i
$933$			20.7846i			0.680458i
$934$	7.00000	+	12.1244i	0.229047	+	0.396721i
$935$	6.00000			0.196221
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	2.00000	+	3.46410i	0.0653023	+	0.113107i
$939$	43.5000	+	25.1147i	1.41957	+	0.819588i
$940$	7.00000	−	12.1244i	0.228315	−	0.395453i
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	−0.910773	−	0.412908i	$-0.864513\pi$
$941$	−3.00000	+	5.19615i	−0.0977972	+	0.169390i	0.812975	+	0.582298i	$0.197846\pi$
$942$	−3.00000	+	1.73205i	−0.0977453	+	0.0564333i
$943$	12.0000	+	20.7846i	0.390774	+	0.676840i
$944$	−56.0000			−1.82264
$945$		−	5.19615i		−	0.169031i
$946$	24.0000			0.780307
$947$	28.0000	+	48.4974i	0.909878	+	1.57595i	0.814232	+	0.580539i	$0.197158\pi$
$947$	28.0000	+	48.4974i	0.909878	+	1.57595i	0.0956453	+	0.995415i	$0.469509\pi$
$948$	−51.0000	+	29.4449i	−1.65640	+	0.956325i
$949$	−39.0000	+	67.5500i	−1.26599	+	2.19277i
$950$	2.00000	−	3.46410i	0.0648886	−	0.112390i
$951$	6.00000	+	3.46410i	0.194563	+	0.112331i
$952$		0			0
$953$	−16.0000			−0.518291			−0.259145	−	0.965838i	$-0.583441\pi$
$953$	−16.0000			−0.518291			−0.259145	+	0.965838i	$0.583441\pi$
$954$	24.0000			0.777029
$955$	7.00000			0.226515
$956$	29.0000	+	50.2295i	0.937927	+	1.62454i
$957$			5.19615i			0.167968i
$958$	20.0000	−	34.6410i	0.646171	−	1.11920i
$959$	−2.00000	+	3.46410i	−0.0645834	+	0.111862i
$960$		−	13.8564i		−	0.447214i
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	−24.0000			−0.773791
$963$	−18.0000	+	31.1769i	−0.580042	+	1.00466i
$964$	60.0000			1.93247
$965$	−3.00000	−	5.19615i	−0.0965734	−	0.167270i
$966$	12.0000	+	6.92820i	0.386094	+	0.222911i
$967$	16.0000	−	27.7128i	0.514525	−	0.891184i	−0.485333	−	0.874330i	$-0.661301\pi$
$967$	16.0000	−	27.7128i	0.514525	−	0.891184i	0.999858	−	0.0168544i	$-0.00536518\pi$
$968$		0			0
$969$	−6.00000	+	3.46410i	−0.192748	+	0.111283i
$970$	−9.00000	−	15.5885i	−0.288973	−	0.500515i
$971$	−32.0000			−1.02693			−0.513464	−	0.858111i	$-0.671638\pi$
$971$	−32.0000			−1.02693			−0.513464	+	0.858111i	$0.671638\pi$
$972$	−27.0000	+	15.5885i	−0.866025	+	0.500000i
$973$	6.00000			0.192351
$974$	−2.00000	−	3.46410i	−0.0640841	−	0.110997i
$975$	−9.00000	+	5.19615i	−0.288231	+	0.166410i
$976$	8.00000	−	13.8564i	0.256074	−	0.443533i
$977$	−17.0000	+	29.4449i	−0.543878	+	0.942025i	0.454798	+	0.890594i	$0.349711\pi$
$977$	−17.0000	+	29.4449i	−0.543878	+	0.942025i	−0.998677	+	0.0514302i	$0.983622\pi$
$978$	54.0000	+	31.1769i	1.72673	+	0.996928i
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	−2.00000			−0.0638877
$981$	13.5000	−	23.3827i	0.431022	−	0.746552i
$982$	72.0000			2.29761
$983$	−24.5000	−	42.4352i	−0.781429	−	1.35347i	−0.931110	−	0.364740i	$-0.881158\pi$
$983$	−24.5000	−	42.4352i	−0.781429	−	1.35347i	0.149681	−	0.988734i	$-0.452175\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$		−	12.1244i		−	0.385922i
$988$	12.0000	+	20.7846i	0.381771	+	0.661247i
$989$	16.0000			0.508770
$990$	18.0000			0.572078
$991$	21.0000			0.667087			0.333543	−	0.942735i	$-0.391756\pi$
$991$	21.0000			0.667087			0.333543	+	0.942735i	$0.391756\pi$
$992$	40.0000	+	69.2820i	1.27000	+	2.19971i
$993$	−49.5000	−	28.5788i	−1.57084	−	0.906922i
$994$	9.00000	−	15.5885i	0.285463	−	0.494436i
$995$	−5.00000	+	8.66025i	−0.158511	+	0.274549i
$996$	−39.0000	+	22.5167i	−1.23576	+	0.713468i
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	0.993213	−	0.116310i	$-0.0371066\pi$
$997$	12.5000	+	21.6506i	0.395879	+	0.685682i	−0.597334	+	0.801993i	$0.703773\pi$
$998$	−56.0000			−1.77265
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.a.211.1	yes	2
3.2	odd	2		945.2.i.b.631.1		2
9.2	odd	6		945.2.i.b.316.1		2
9.4	even	3		2835.2.a.h.1.1		1
9.5	odd	6		2835.2.a.b.1.1		1
9.7	even	3	inner	315.2.i.a.106.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.a.106.1	✓	2	9.7	even	3	inner
315.2.i.a.211.1	yes	2	1.1	even	1	trivial
945.2.i.b.316.1		2	9.2	odd	6
945.2.i.b.631.1		2	3.2	odd	2
2835.2.a.b.1.1		1	9.5	odd	6
2835.2.a.h.1.1		1	9.4	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} -2.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} -3.46410i q^{12} +(-3.00000 + 5.19615i) q^{13} +(-1.00000 + 1.73205i) q^{14} +1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} -2.00000 q^{17} -6.00000 q^{18} -2.00000 q^{19} +(1.00000 + 1.73205i) q^{20} +(1.50000 + 0.866025i) q^{21} +(-3.00000 + 5.19615i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +12.0000 q^{26} +5.19615i q^{27} +2.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(3.00000 - 1.73205i) q^{30} +(-5.00000 + 8.66025i) q^{31} +(4.00000 - 6.92820i) q^{32} +(4.50000 + 2.59808i) q^{33} +(2.00000 + 3.46410i) q^{34} -1.00000 q^{35} +(3.00000 + 5.19615i) q^{36} -2.00000 q^{37} +(2.00000 + 3.46410i) q^{38} -10.3923i q^{39} +(3.00000 - 5.19615i) q^{41} -3.46410i q^{42} +(-2.00000 - 3.46410i) q^{43} +6.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +8.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(-6.00000 - 3.46410i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.00000 + 1.73205i) q^{50} +(3.00000 - 1.73205i) q^{51} +(-6.00000 - 10.3923i) q^{52} -4.00000 q^{53} +(9.00000 - 5.19615i) q^{54} -3.00000 q^{55} +(3.00000 - 1.73205i) q^{57} +(1.00000 - 1.73205i) q^{58} +(-7.00000 + 12.1244i) q^{59} +(-3.00000 - 1.73205i) q^{60} +(-2.00000 - 3.46410i) q^{61} +20.0000 q^{62} -3.00000 q^{63} -8.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -10.3923i q^{66} +(1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} -6.92820i q^{69} +(1.00000 + 1.73205i) q^{70} -9.00000 q^{71} +13.0000 q^{73} +(2.00000 + 3.46410i) q^{74} +(1.50000 + 0.866025i) q^{75} +(2.00000 - 3.46410i) q^{76} +(-1.50000 + 2.59808i) q^{77} +(-18.0000 + 10.3923i) q^{78} +(-8.50000 - 14.7224i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -12.0000 q^{82} +(-6.50000 - 11.2583i) q^{83} +(-3.00000 + 1.73205i) q^{84} +(-1.00000 + 1.73205i) q^{85} +(-4.00000 + 6.92820i) q^{86} +(-1.50000 - 0.866025i) q^{87} +6.00000 q^{89} +(-3.00000 + 5.19615i) q^{90} +6.00000 q^{91} +(-4.00000 - 6.92820i) q^{92} -17.3205i q^{93} +(-7.00000 + 12.1244i) q^{94} +(-1.00000 + 1.73205i) q^{95} +13.8564i q^{96} +(4.50000 + 7.79423i) q^{97} +2.00000 q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 6 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 6 * q^6 - q^7 + 3 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 6 q^{6} - q^{7} + 3 q^{9} - 4 q^{10} - 3 q^{11} - 6 q^{13} - 2 q^{14} + 4 q^{16} - 4 q^{17} - 12 q^{18} - 4 q^{19} + 2 q^{20} + 3 q^{21} - 6 q^{22} - 4 q^{23} - q^{25} + 24 q^{26} + 4 q^{28} + q^{29} + 6 q^{30} - 10 q^{31} + 8 q^{32} + 9 q^{33} + 4 q^{34} - 2 q^{35} + 6 q^{36} - 4 q^{37} + 4 q^{38} + 6 q^{41} - 4 q^{43} + 12 q^{44} - 3 q^{45} + 16 q^{46} - 7 q^{47} - 12 q^{48} - q^{49} - 2 q^{50} + 6 q^{51} - 12 q^{52} - 8 q^{53} + 18 q^{54} - 6 q^{55} + 6 q^{57} + 2 q^{58} - 14 q^{59} - 6 q^{60} - 4 q^{61} + 40 q^{62} - 6 q^{63} - 16 q^{64} + 6 q^{65} + 2 q^{67} + 4 q^{68} + 2 q^{70} - 18 q^{71} + 26 q^{73} + 4 q^{74} + 3 q^{75} + 4 q^{76} - 3 q^{77} - 36 q^{78} - 17 q^{79} + 8 q^{80} - 9 q^{81} - 24 q^{82} - 13 q^{83} - 6 q^{84} - 2 q^{85} - 8 q^{86} - 3 q^{87} + 12 q^{89} - 6 q^{90} + 12 q^{91} - 8 q^{92} - 14 q^{94} - 2 q^{95} + 9 q^{97} + 4 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 6 * q^6 - q^7 + 3 * q^9 - 4 * q^10 - 3 * q^11 - 6 * q^13 - 2 * q^14 + 4 * q^16 - 4 * q^17 - 12 * q^18 - 4 * q^19 + 2 * q^20 + 3 * q^21 - 6 * q^22 - 4 * q^23 - q^25 + 24 * q^26 + 4 * q^28 + q^29 + 6 * q^30 - 10 * q^31 + 8 * q^32 + 9 * q^33 + 4 * q^34 - 2 * q^35 + 6 * q^36 - 4 * q^37 + 4 * q^38 + 6 * q^41 - 4 * q^43 + 12 * q^44 - 3 * q^45 + 16 * q^46 - 7 * q^47 - 12 * q^48 - q^49 - 2 * q^50 + 6 * q^51 - 12 * q^52 - 8 * q^53 + 18 * q^54 - 6 * q^55 + 6 * q^57 + 2 * q^58 - 14 * q^59 - 6 * q^60 - 4 * q^61 + 40 * q^62 - 6 * q^63 - 16 * q^64 + 6 * q^65 + 2 * q^67 + 4 * q^68 + 2 * q^70 - 18 * q^71 + 26 * q^73 + 4 * q^74 + 3 * q^75 + 4 * q^76 - 3 * q^77 - 36 * q^78 - 17 * q^79 + 8 * q^80 - 9 * q^81 - 24 * q^82 - 13 * q^83 - 6 * q^84 - 2 * q^85 - 8 * q^86 - 3 * q^87 + 12 * q^89 - 6 * q^90 + 12 * q^91 - 8 * q^92 - 14 * q^94 - 2 * q^95 + 9 * q^97 + 4 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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